A cylindrical shell with a stress-free end which contains an axial part-through or through crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Yahsi, O. S.

1985-01-01

The interaction problem of a through or a part through crack with a stress free boundary in a semi-infinite cylindrical shell is considered. It is assumed that the crack lies in a meridional plane which is a plane of symmetry with respect to the external loads as well as the geometry. The circular boundary of the semi-infinite cylinder is assumed to be stress free. By using a transverse shear theory the problem is formulated in terms of a system of singular integral equations. The line spring model is used to treat the part through crack problem. In the case of a through crack the interaction between the perturbed stress fields due to the crack and the free boundary is quite strong and there is a considerable increase in the stress intensity factors caused by the interaction. On the other hand in the problem of a surface crack the interaction appears to be much weaker and consequently the magnification in the stress intensity factors is much less significant.

A cylindrical shell with a stress-free end which contains an axial part-through or through crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Yahsi, O. S.

1983-01-01

The interaction problem of a through or a part through crack with a stress free boundary in a semi-infinite cylindrical shell is considered. It is assumed that the crack lies in a meridional plane which is a plane of symmetry with respect to the external loads as well as the geometry. The circular boundary of the semi-infinite cylinder is assumed to be stress free. By using a transverse shear theory the problem is formulated in terms of a system of singular integral equations. The line spring model is used to treat the part through crack problem. In the case of a through crack the interaction between the perturbed stress fields due to the crack and the free boundary is quite strong and there is a considerable increase in the stress intensity factors caused by the interaction. On the other hand in the problem of a surface crack the interaction appears to be much weaker and consequently the magnification in the stress intensity factors is much less significant.

The Fundamental Solutions for the Stress Intensity Factors of Modes I, II And III. The Axially Symmetric Problem

NASA Astrophysics Data System (ADS)

Rogowski, B.

2015-05-01

The subject of the paper are Green's functions for the stress intensity factors of modes I, II and III. Green's functions are defined as a solution to the problem of an elastic, transversely isotropic solid with a penny-shaped or an external crack under general axisymmetric loadings acting along a circumference on the plane parallel to the crack plane. Exact solutions are presented in a closed form for the stress intensity factors under each type of axisymmetric ring forces as fundamental solutions. Numerical examples are employed and conclusions which can be utilized in engineering practice are formulated.

Bonded half planes containing an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Aksogan, O.

1973-01-01

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin transforms, the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given include the stress intensity factors, tHe strain energy release rates, and tHe probable cleavage angles giving the direction of crack propagation.

The crack problem in a specially orthotropic shell with double curvature

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1983-01-01

The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip. Previously announced in STAR as N83-16782

The crack problem in a specially orthotropic shell with double curvature

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip.

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface. Part 1: Analysis

NASA Technical Reports Server (NTRS)

Lu, M. C.; Erdogan, F.

1980-01-01

The basic crack problem which is essential for the study of subcritical crack propagation and fracture of layered structural materials is considered. Because of the apparent analytical difficulties, the problem is idealized as one of plane strain or plane stress. An additional simplifying assumption is made by restricting the formulation of the problem to crack geometries and loading conditions which have a plane of symmetry perpendicular to the interface. The general problem is formulated in terms of a coupled system of four integral equations. For each relevant crack configuration of practical interest, the singular behavior of the solution near and at the ends and points of intersection of the cracks is investigated and the related characteristic equations are obtained. The edge crack terminating at and crossing the interface, the T-shaped crack consisting of a broken layer and a delamination crack, the cross-shaped crack which consists of a delamination crack intersecting a crack which is perpendicular to the interface, and a delamination crack initiating from a stress-free boundary of the bonded layers are some of the practical crack geometries considered.

Stress-intensity factors of r-cracks in fiber-reinforced composites under thermal and mechanical loading

NASA Astrophysics Data System (ADS)

Mueller, W. H.; Schmauder, S.

1993-02-01

The plane stress/plane strain problem of radial matrix cracking in fiber-reinforced composites, due to thermal mismatch and externally applied stress is solved numerically in the framework of linear elasticity, using Erdogan's integral equation technique. It is shown that, in order to obtain the results of the combined loading case, the solutions of purely thermal and purely mechanical loading can simply be superimposed. Stress-intensity factors are calculated for various lengths and distances of the crack from the interface for each of these loading conditions.

Discretization and Numerical Solution of a Plane Problem in the Mechanics of Interfacial Cracks

NASA Astrophysics Data System (ADS)

Khoroshun, L. P.

2017-01-01

The Fourier transform is used to reduce the linear plane problem of the tension of a body with an interfacial crack to a system of dual equations for the transformed stresses and, then, to a system of integro-differential equations for the difference of displacements of the crack faces. After discretization, this latter system transforms into a system of algebraic equations for displacements of the crack faces. The effect of the bielastic constant and the number of discretization points on the half-length of the crack faces and the distribution of stresses at the interface is studied

User's guide for analysis of finite elastoplastic deformation: The FIPDEF and FIPAX programs for the CDC 6600

NASA Technical Reports Server (NTRS)

Osias, J. R.

1974-01-01

Computer programs are presented which provide incremental finite-element analysis capability for problems of quasi-static, finite, elastoplastic deformation in two spatial dimensions (plane strain, plane stress, axisymmetric). Monotonic or cyclic loading of isotropic hardening materials is considered. The only restriction on the form of the stress-strain curve is that the rate of work hardening exceed some small positive value. The user's guide assumes familiarity with both finite-element analysis and FORTRAN IV programming for the CDC 6600. Sufficient information is provided to support problem solving ultization of the programs.

Measurement of non-uniform residual stresses by combined Moiré interferometry and hole-drilling method: Theory, experimental method and applications

NASA Astrophysics Data System (ADS)

Ya, Min; Dai, Fulong; Xie, Huimin; Lü, Jian

2003-12-01

Hole-drilling method is one of the most convenient methods for engineering residual stress measurement. Combined with moiré interferometry to obtain the relaxed whole-field displacement data, hole-drilling technique can be used to solve non-uniform residual stress problems, both in-depth and in-plane. In this paper, the theory of moiré interferometry and incremental hole-drilling (MIIHD) for non-uniform residual stress measurement is introduced. Three dimensional finite element model is constructed by ABAQUS to obtain the coefficients for the residual stress calculation. An experimental system including real-time measurement, automatic data processing and residual stresses calculation is established. Two applications for non-uniform in-depth residual stress of surface nanocrystalline material and non-uniform in-plane residual stress of friction stir welding are presented. Experimental results show that MIIHD is effective for both non-uniform in-depth and in-plane residual stress measurements.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

A pressurized cylindrical shell with a fixed end which contains an axial part-through or through crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1983-01-01

A cylindrical shell having a very stiff and plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flaw which may be modeled as a part through surface crack or a through crack. The effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter is studied. The applied loads acting on the cylinder are assumed to be axisymmetric. Thus the crack problem under consideration is symmetric with respect to the plane of the crack and consequently only the Mode 1 stress intensity factors are nonzero. With this limitation, the general perturbation problem for a cylinder with a built in end containing an axial crack is considered. Reissner's shell theory is used to formulate the problem. The part through crack problem is treated by using a line spring model. In the case of a crack tip terminating at the fixed end it is shown that the integral equations of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem.

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface. I Analysis. II - Solution and results

NASA Technical Reports Server (NTRS)

Lu, M.-C.; Erdogan, F.

1983-01-01

The basic crack problem which is essential for the study of subcritical crack propagation and fracture of layered structural materials is considered. Because of the apparent analytical difficulties, the problem is idealized as one of plane strain or plane stress. An additional simplifying assumption is made by restricting the formulation of the problem to crack geometries and loading conditions which have a plane of symmetry perpendicular to the interface. The general problem is formulated in terms of a coupled systems of four integral equations. For each relevant crack configuration of practical interest, the singular behavior of the solution near and at the ends and points of intersection of the cracks is investigated and the related characteristic equations are obtained. The edge crack terminating at and crossing the interface, the T-shaped crack consisting of a broken layer and a delamination crack, the cross-shaped crack which consists of a delamination crack intersecting a crack which is perpendicular to the interface, and a delamination crack initiating from a stress-free boundary of the bonded layers are some of the practical crack geometries considered. Previously announced in STAR as N80-18428 and N80-18429

Derivation of the out-of-plane behaviour of an English bond masonry wall through homogenization strategies

NASA Astrophysics Data System (ADS)

Silva, Luís Carlos; Milani, Gabriele; Lourenço, Paulo B.

2017-11-01

Two finite element homogenized-based strategies are presented for the out-of-plane behaviour characterization of an English bond masonry wall. A finite element micro-modelling approach using Cauchy stresses and first order movements are assumed for both strategies. The material nonlinearity is lumped on joints interfaces and bricks are considered elastic. Nevertheless, the first model is based on a Plane-stress assumption, in which the out-of-plane quantities are derived through on-thickness wall integration considering a Kirchhoff-plate theory. The second model is a tridimensional one, in which the homogenized out-of-plane quantities can be directly derived after solving the boundary value problem. The comparison is conducted by assessing the obtained out-of-plane bending- and torsion-curvature diagrams. A good agreement is found for the present study case.

Crack growth in bonded elastic half planes

NASA Technical Reports Server (NTRS)

Goree, J. G.

1975-01-01

Two solutions were developed for the two dimensional problem of bonded linearly elastic half-planes. For each solution, numerical results are presented for the stress intensity factors, strain energy release rate, stresses, and displacements. The behavior predicted by the studies was investigated experimentally using polymers for the material pairs. Close agreement was found for the critical stress intensity factor at fracture for the perpendicular crack near the interface. Fracture along the interface proved to be inconclusive due to difficulties in obtaining a brittle bond. Some interesting and predictable behavior regarding the potential for the crack to cross the interface was observed and is discussed.

The crack-contact and the free-end problem for a strip under residual stress

NASA Technical Reports Server (NTRS)

Bakioglu, M.; Erdogan, F.

1977-01-01

The plane problem for an infinite strip with two edge cracks under a given state of residual stress is considered. The residual stress is compressive near and at the surfaces and tensile in the interior of the strip. If the crack is deep enough to penetrate into the tensile zone, then the problem is one of crack-contact where the depth of the contact area is an unknown which depends on the crack depth and the residual stress profile. The problem has applications to the static fatigue of glass plates and is solved for three typical residual-stress profiles. In the limiting case of the crack's crossing the entire plate thickness, the problem becomes a stressfree end problem for a semiinfinite strip under a given residual-stress state away from the end. This is a typical stress diffusion problem in which decay behavior of the residual stress near and the nature of the normal displacement at the end of the semiinfinite strip are of special interest. For two typical residual-stress states the solution is obtained, and some numerical results are given.

The Crack-contact and the Free End Problem for a Strip Under Residual Stress

NASA Technical Reports Server (NTRS)

Bakioglu, M.; Erdogan, F.

1976-01-01

The plane problem for an infinite strip with two edge cracks under a given state of residual stress is considered. The residual stress is compressive near and at the surfaces and tensile in the interior of the strip. If the crack is deep enough to penetrate into the tensile zone, then the problem is one of crack-contact problem in which the depth of the contact area is an unknown which depends on the crack depth and the residual stress profile. The problem has applications to the static fatigue of glass plates and is solved for three typical residual stress profiles. In the limiting case of the crack crossing the entire plate thickness, the problem becomes a stress-free end problem for a semi-infinite strip under a given residual stress state away from the end. This is a typical stress diffusion problem in which decay behavior of the residual stress near and the nature of the normal displacement at the end of the semi-infinite strip are of special interest. For two typical residual stress states the solution is obtained, and some numerical results are given.

Elasticity Theory Solution of the Problem on Plane Bending of a Narrow Layered Cantilever Beam by Loads at Its Free End

NASA Astrophysics Data System (ADS)

Goryk, A. V.; Koval'chuk, S. B.

2018-05-01

An exact elasticity theory solution for the problem on plane bending of a narrow layered composite cantilever beam by tangential and normal loads distributed on its free end is presented. Components of the stress-strain state are found for the whole layers package by directly integrating differential equations of the plane elasticity theory problem by using an analytic representation of piecewise constant functions of the mechanical characteristics of layer materials. The continuous solution obtained is realized for a four-layer beam with account of kinematic boundary conditions simulating the rigid fixation of its one end. The solution obtained allows one to predict the strength and stiffness of composite cantilever beams and to construct applied analytical solutions for various problems on the elastic bending of layered beams.

Stresses in adhesively bonded joints: A closed form solution. [plate theory

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Aydinoglu, M. N.

1980-01-01

The plane strain of adhesively bonded structures which consist of two different orthotropic adherents is considered. Assuming that the thicknesses of the adherends are constant and are small in relation to the lateral dimensions of the bonded region, the adherends are treated as plates. The transverse shear effects in the adherends and the in-plane normal strain in the adhesive are taken into account. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form. A single lap joint and a stiffened plate under various loading conditions are considered as examples. To verify the basic trend of the solutions obtained from the plate theory a sample problem is solved by using the finite element method and by treating the adherends and the adhesive as elastic continua. The plate theory not only predicts the correct trend for the adhesive stresses but also gives rather surprisingly accurate results.

Crack Tip Dislocation Nucleation in FCC Solids

NASA Astrophysics Data System (ADS)

Knap, J.; Sieradzki, K.

1999-02-01

We present results of molecular dynamic simulations aimed at examining crack tip dislocation emission in fcc solids. The results are analyzed in terms of recent continuum formulations of this problem. In mode II, Au, Pd, and Pt displayed a new unanticipated mechanism of crack tip dislocation emission involving the creation of a pair of Shockley partials on a slip plane one plane below the crack plane. In mode I, for all the materials examined, Rice's continuum formulation [J. Mech. Phys. Solids 40, 239 (1992)] underestimated the stress intensity for dislocation emission by almost a factor of 2. Surface stress corrections to the emission criterion brought the agreement between continuum predictions and simulations to within 20%.

Stress waves in transversely isotropic media: The homogeneous problem

NASA Technical Reports Server (NTRS)

Marques, E. R. C.; Williams, J. H., Jr.

1986-01-01

The homogeneous problem of stress wave propagation in unbounded transversely isotropic media is analyzed. By adopting plane wave solutions, the conditions for the existence of the solution are established in terms of phase velocities and directions of particle displacements. Dispersion relations and group velocities are derived from the phase velocity expressions. The deviation angles (e.g., angles between the normals to the adopted plane waves and the actual directions of their propagation) are numerically determined for a specific fiber-glass epoxy composite. A graphical method is introduced for the construction of the wave surfaces using magnitudes of phase velocities and deviation angles. The results for the case of isotropic media are shown to be contained in the solutions for the transversely isotropic media.

The surface and through crack problems in layered orthotropic plates

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Wu, Binghua

1991-01-01

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

Simple quasi-analytical holonomic homogenization model for the non-linear analysis of in-plane loaded masonry panels: Part 1, meso-scale

NASA Astrophysics Data System (ADS)

Milani, G.; Bertolesi, E.

2017-07-01

A simple quasi analytical holonomic homogenization approach for the non-linear analysis of masonry walls in-plane loaded is presented. The elementary cell (REV) is discretized with 24 triangular elastic constant stress elements (bricks) and non-linear interfaces (mortar). A holonomic behavior with softening is assumed for mortar. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how homogenized stress-strain behavior can be evaluated semi-analytically.

Stress state of a piecewise uniform layered space with doubly periodic internal cracks

NASA Astrophysics Data System (ADS)

Hakobyan, V. N.; Dashtoyan, L. L.

2018-04-01

The present paper deals with the stress state of a piecewise homogeneous plane formed by alternation junction of two distinct strips of equal height manufactured of different materials. There is a doubly periodic system of cracks on the plane. The governing system of singular integral equations of the first kind for the density of the crack dislocation is derived. The solution of the problem in the case where only one of the repeated strips contains one doubly-periodic crack is obtained by the method of mechanical quadratures.

Interlaminar stresses in composite laminates: A perturbation analysis

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1976-01-01

A general method of solution for an elastic balanced symmetric composite laminate subject to a uniaxial extension was developed based upon a perturbation analysis of a limiting free body containing an interfacial plane. The solution satisfies more physical requirements and boundary conditions than previous investigations, and predicts smooth continuous interlaminar stresses with no instabilities. It determines the finite maximum intensity for the interlaminar normal stress in all laminates, provides mathematical evidences for the singular stresses in angle-ply laminates, suggests the need for the experimental determination of an important problem parameter, and introduces a viable means for solving related problems of practical interest.

A pressurized cylindrical shell with a fixed end which contains an axial part-through or through crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1985-01-01

In this paper a cylindrical shell having a very stiff end plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flow which may be modeled as a part-through surface crack or through crack. The primary objective is to study the effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter. The applied loads acting on the cylinder are assumed to be axisymmetric. Thus the crack problem under consideration is symmetric with respect to the plane of the crack and consequently only the mode I stress intensity factors are nonzero. With this limitation, the general perturbation problem for a cylinder with a built-in end containing an axial crack is considered. Reissner's shell theory is used to formulate the problem. The part-through crack problem is treated by using a line-spring model. In the case of a crack tip terminating at the fixed end it is shown that the integral equation of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem. Even though the problem is formulated for a general surface crack profile and arbitrary crack surface tractions, the numerical results are obtained only for a semielliptic part-through axial crack located at the inside or outside surface of the cylinder and for internal pressure acting on the cylinder. The stress intensity factors are calculated and presented for a relatively wide range of dimensionless length parameters of the problem.

Stress singularities at the vertex of a cylindrically anisotropic wedge

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Boduroglu, H.

1980-01-01

The plane elasticity problem for a cylindrically anisotropic solid is formulated. The form of the solution for an infinite wedge shaped domain with various homogeneous boundary conditions is derived and the nature of the stress singularity at the vertex of the wedge is studied. The characteristic equations giving the stress singularity and the angular distribution of the stresses around the vertex of the wedge are obtained for three standard homogeneous boundary conditions. The numerical examples show that the singular behavior of the stresses around the vertex of an anisotropic wedge may be significantly different from that of the isotropic material. Some of the results which may be of practical importance are that for a half plane the stress state at r = 0 may be singular and for a crack the power of stress singularity may be greater or less than 1/2.

Bonded orthotropic strips with cracks

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1979-01-01

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. It is assumed that the plane contains a series of collinear cracks perpendicular to the interfaces and is loaded in tension away from and perpendicular to the cracks. The problem of cracks fully imbedded into the homogeneous strips is considered. The singular behavior of the stresses for two special crack geometries is studied. The first is the case of a broken laminate in which the crack tips touch the interfaces. The second is the case of cracks crossing the interfaces. An interesting result found from the analysis of the latter is that for certain orthotropic material combinations the stress state at the point of intersection of a crack and an interface may be bounded whereas in isotropic materials at this point stresses are always singular. A number of numerical examples are worked out to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters. Some numerical results are given for the stress intensity factors in certain basic crack geometries and for typical material combinations.

Green's functions for dislocations in bonded strips and related crack problems

NASA Technical Reports Server (NTRS)

Ballarini, R.; Luo, H. A.

1990-01-01

Green's functions are derived for the plane elastostatics problem of a dislocation in a bimaterial strip. Using these fundamental solutions as kernels, various problems involving cracks in a bimaterial strip are analyzed using singular integral equations. For each problem considered, stress intensity factors are calculated for several combinations of the parameters which describe loading, geometry and material mismatch.

Interlaminar stress analysis of dropped-ply laminated plates and shells by a mixed method. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Harrison, Peter N.; Johnson, Eric R.; Starnes, James H., Jr.

1994-01-01

A mixed method of approximation based on Reissner's variational principle is developed for the linear analysis of interlaminar stresses in laminated composites, with special interest in laminates that contain terminated internal plies (dropped-ply laminates). Two models are derived, one for problems of generalized plane deformation and the other for the axisymmetric response of shells of revolution. A layerwise approach is taken in which the stress field is assumed with an explicit dependence on the thickness coordinate in each layer. The dependence of the stress field on the thickness coordinate is determined such that the three-dimensional equilibrium equations are satisfied by the approximation. The solution domain is reduced to one dimension by integration through the thickness. Continuity of tractions and displacements between layers is imposed. The governing two-point boundary value problem is composed of a system of both differential and algebraic equations (DAE's) and their associated boundary conditions. Careful evaluation of the system of DAE's was required to arrive at a form that allowed application of a one-step finite difference approximation. A two-stage Gauss implicit Runge-Kutta finite difference scheme was used for the solution because of its relatively high degree of accuracy. Patch tests of the two models revealed problems with solution accuracy for the axisymmetric model of a cylindrical shell loaded by internal pressure. Parametric studies of dropped-ply laminate characteristics and their influence on the interlaminar stresses were performed using the generalized plane deformation model. Eccentricity of the middle surface of the laminate through the ply drop-off was found to have a minimal effect on the interlaminar stresses under longitudinal compression, transverse tension, and in-plane shear. A second study found the stiffness change across the ply termination to have a much greater influence on the interlaminar stresses.

Plane elasto-plastic analysis of v-notched plate under bending by boundary integral equation method. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Rzasnicki, W.

1973-01-01

A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.

Stress intensity factors for bonded orthotropic strips with cracks

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1978-01-01

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. It is assumed that the plane contains a series of collinear cracks perpendicular to the interfaces and is loaded in tension away from and perpendicular to the cracks. Cracks fully imbedded into the homogenous strips were analyzed as well as the singular behavior of the stresses for two special crack geometries. The analysis of cracks crossing interfaces indicates that, for certain orthotropic material combinations, the stress state at the point of intersection of a crack and an interface may be bounded. A number of numerical examples are worked out in order to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters.

Comparative analysis of methods for modeling the penetration and plane-parallel motion of conical projectiles in soil

NASA Astrophysics Data System (ADS)

Bazhenov, V. G.; Bragov, A. M.; Konstantinov, A. Yu.; Kotov, V. L.

2015-05-01

This paper presents an analysis of the accuracy of known and new modeling methods using the hypothesis of local and plane sections for solution of problems of the impact and plane-parallel motion of conical bodies at an angle to the free surface of the half-space occupied by elastoplastic soil. The parameters of the local interaction model that is quadratic in velocity are determined by solving the one-dimensional problem of the expansion of a spherical cavity. Axisymmetric problems for each of the meridional section are solved simultaneously neglecting mass and momentum transfer in the circumferential direction and using an approach based on the hypothesis of plane sections. The dynamic and kinematic parameters of oblique penetration obtained using modified models are compared with the results of computer simulation in a three-dimensional formulation. The results obtained with regard to the contact stress distribution along the generator of the pointed cone are in satisfactory agreement.

A study for high accuracy measurement of residual stress by deep hole drilling technique

NASA Astrophysics Data System (ADS)

Kitano, Houichi; Okano, Shigetaka; Mochizuki, Masahito

2012-08-01

The deep hole drilling technique (DHD) received much attention in recent years as a method for measuring through-thickness residual stresses. However, some accuracy problems occur when residual stress evaluation is performed by the DHD technique. One of the reasons is that the traditional DHD evaluation formula applies to the plane stress condition. The second is that the effects of the plastic deformation produced in the drilling process and the deformation produced in the trepanning process are ignored. In this study, a modified evaluation formula, which is applied to the plane strain condition, is proposed. In addition, a new procedure is proposed which can consider the effects of the deformation produced in the DHD process by investigating the effects in detail by finite element (FE) analysis. Then, the evaluation results obtained by the new procedure are compared with that obtained by traditional DHD procedure by FE analysis. As a result, the new procedure evaluates the residual stress fields better than the traditional DHD procedure when the measuring object is thick enough that the stress condition can be assumed as the plane strain condition as in the model used in this study.

Boundary-integral methods in elasticity and plasticity. [solutions of boundary value problems

NASA Technical Reports Server (NTRS)

Mendelson, A.

1973-01-01

Recently developed methods that use boundary-integral equations applied to elastic and elastoplastic boundary value problems are reviewed. Direct, indirect, and semidirect methods using potential functions, stress functions, and displacement functions are described. Examples of the use of these methods for torsion problems, plane problems, and three-dimensional problems are given. It is concluded that the boundary-integral methods represent a powerful tool for the solution of elastic and elastoplastic problems.

Effects of Prosthesis Stem Tapers on Stress Distribution of Cemented Hip Arthroplasty

NASA Astrophysics Data System (ADS)

Abdullah, Abdul Halim; Nor, Mohd Asri Mohd; Saman, Alias Mohd; Tamin, Mohd Nasir; Kadir, Mohammed Rafiq Abdul

2010-10-01

Aseptic loosening effects are critical issues in encouraging long term stability of cemented hip arthroplasty. Stress shielding is believed to be an important factor that contributes to the aseptic loosening problems. The numerous changes in the prosthesis stem design are intended to minimize the stress shielding and aseptic loosening problems and to improve the long term performance of the implants. In this study, the stress distribution in cemented hip arthroplasty is established using finite element method. The taper of the prosthesis is designed to be 3° at anterior/posterior, 3° at medial/lateral and 10° from wide lateral to narrow medial. Major muscle loads and contact forces are simulated for walking (toe-off phase) and stair climbing load cases. Effects of prosthesis stem tapers on the resulting stress distribution are investigated. Results show that compressive stress dominates in the medial plane while tensile stress in the lateral plane of the femur. The corresponding stress levels of intact femur for walking and stair-climbing load cases are 22 and 29 MPa, respectively. The magnitude of Tresca stress for the THA femur in stair-climbing load case remains higher in the region of 85 MPa while the walking load case induces around 40 MPa. The stress range in the straight and single taper stem prosthesis is lower than 260 MPa, while localized Tresca stress is in the order of the yield strength of Ti-6Al-4V alloy for double and triple taper stem design.

On stress analysis of a crack-layer

NASA Technical Reports Server (NTRS)

Chudnovsky, A.; Dolgopolsky, A.; Kachanov, M.

1984-01-01

This work considers the problem of elastic interaction of a macrocrack with an array of microcracks in the vicinity of the macrocrack tip. Using the double layer potential techniques, the solution to the problem within the framework of the plane problem of elastostatics has been obtained. Three particular problems of interest to fracture mechanics have been analyzed. It follows from analysis that microcrack array can either amplify or reduce the resulting stress field of the macrocrack-microcrack array system depending on the array's configuration. Using the obtained elastic solution the energy release rate associated with the translational motion of the macrocrack-microcrack array system has been evaluated.

A Curved, Elastostatic Boundary Element for Plane Anisotropic Structures

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S.; Klang, Eric C.

2001-01-01

The plane-stress equations of linear elasticity are used in conjunction with those of the boundary element method to develop a novel curved, quadratic boundary element applicable to structures composed of anisotropic materials in a state of plane stress or plane strain. The curved boundary element is developed to solve two-dimensional, elastostatic problems of arbitrary shape, connectivity, and material type. As a result of the anisotropy, complex variables are employed in the fundamental solution derivations for a concentrated unit-magnitude force in an infinite elastic anisotropic medium. Once known, the fundamental solutions are evaluated numerically by using the known displacement and traction boundary values in an integral formulation with Gaussian quadrature. All the integral equations of the boundary element method are evaluated using one of two methods: either regular Gaussian quadrature or a combination of regular and logarithmic Gaussian quadrature. The regular Gaussian quadrature is used to evaluate most of the integrals along the boundary, and the combined scheme is employed for integrals that are singular. Individual element contributions are assembled into the global matrices of the standard boundary element method, manipulated to form a system of linear equations, and the resulting system is solved. The interior displacements and stresses are found through a separate set of auxiliary equations that are derived using an Airy-type stress function in terms of complex variables. The capabilities and accuracy of this method are demonstrated for a laminated-composite plate with a central, elliptical cutout that is subjected to uniform tension along one of the straight edges of the plate. Comparison of the boundary element results for this problem with corresponding results from an analytical model show a difference of less than 1%.

A solution to the problem of elastic half-plane with a cohesive edge crack

NASA Astrophysics Data System (ADS)

Thanh, Le Thi; Belaya, L. A.; Lavit, I. M.

2018-03-01

This paper considers the problem of extension of an elastic half-plane slackened by a rectilinear edge crack. The opposite edges of the crack are attracted to each other. The intensity of attracting forces – the forces of cohesion – depends on displacements of the edges; this dependence is nonlinear in the general case. External load and cohesive forces are related to each other by the condition of finite stresses at the crack tip. The authors apply Picard’s method of successive approximation. In each iteration, Irwin’s method is used to solve the problem of a half-plane with a crack, the edges of which are subjected to irregularly distributed load. The solution of the resulting integral equation is found by Galerkin’s method. The paper includes examples of calculations and their results. Some of them are compared with the data of previous studies.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1974-01-01

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1976-01-01

The paper deals with the plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abdullah, Abdul Halim; Nor, Mohd Asri Mohd; Saman, Alias Mohd

Aseptic loosening effects are critical issues in encouraging long term stability of cemented hip arthroplasty. Stress shielding is believed to be an important factor that contributes to the aseptic loosening problems. The numerous changes in the prosthesis stem design are intended to minimize the stress shielding and aseptic loosening problems and to improve the long term performance of the implants. In this study, the stress distribution in cemented hip arthroplasty is established using finite element method. The taper of the prosthesis is designed to be 3 deg. at anterior/posterior, 3 deg. at medial/lateral and 10 deg. from wide lateral tomore » narrow medial. Major muscle loads and contact forces are simulated for walking (toe-off phase) and stair climbing load cases. Effects of prosthesis stem tapers on the resulting stress distribution are investigated. Results show that compressive stress dominates in the medial plane while tensile stress in the lateral plane of the femur. The corresponding stress levels of intact femur for walking and stair-climbing load cases are 22 and 29 MPa, respectively. The magnitude of Tresca stress for the THA femur in stair-climbing load case remains higher in the region of 85 MPa while the walking load case induces around 40 MPa. The stress range in the straight and single taper stem prosthesis is lower than 260 MPa, while localized Tresca stress is in the order of the yield strength of Ti-6Al-4V alloy for double and triple taper stem design.« less

Analysis of edge impact stresses in composite plates

NASA Technical Reports Server (NTRS)

Moon, F. C.; Kang, C. K.

1974-01-01

The in-plane edge impact of composite plates, with or without a protection strip, is investigated. A computational analysis based on the Fast Fourier Transform technique is presented. The particular application of the present method is in the understanding of the foreign object damage problem of composite fan blades. The method is completely general and may be applied to the study of other stress wave propagation problems in a half space. Results indicate that for the protective strip to be effective in reducing impact stresses in the composite the thickness must be equal or greater than the impact contact dimension. Large interface shear stresses at the strip - composite boundary can be induced under impact.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoynov, Y.; Dineva, P.

The stress, magnetic and electric field analysis of multifunctional composites, weakened by impermeable cracks, is of fundamental importance for their structural integrity and reliable service performance. The aim is to study dynamic behavior of a plane of functionally graded magnetoelectroelastic composite with more than one crack. The coupled material properties vary exponentially in an arbitrary direction. The plane is subjected to anti-plane mechanical and in-plane electric and magnetic load. The boundary value problem described by the partial differential equations with variable coefficients is reduced to a non-hypersingular traction boundary integral equation based on the appropriate functional transform and frequency-dependent fundamentalmore » solution derived in a closed form by Radon transform. Software code based on the boundary integral equation method (BIEM) is developed, validated and inserted in numerical simulations. The obtained results show the sensitivity of the dynamic stress, magnetic and electric field concentration in the cracked plane to the type and characteristics of the dynamic load, to the location and cracks disposition, to the wave-crack-crack interactions and to the magnitude and direction of the material gradient.« less

The crack-inclusion interaction problem

NASA Technical Reports Server (NTRS)

Liu, X.-H.; Erdogan, F.

1986-01-01

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

The crack-inclusion interaction problem

NASA Technical Reports Server (NTRS)

Xue-Hui, L.; Erdogan, F.

1984-01-01

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

The crack problem in a reinforced cylindrical shell

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1986-01-01

In this paper a partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z=0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.

The crack problem in a reinforced cylindrical shell

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1986-01-01

A partially reinforced cylinder containing an axial through crack is considered. The reinforcement is assumed to be fully bonded to the main cylinder. The composite cylinder is thus modelled by a nonhomogeneous shell having a step change in the elastic properties at the z = 0 plane, z being the axial coordinate. Using a Reissner type transverse shear theory the problem is reduced to a pair of singular integral equations. In the special case of a crack tip touching the bimaterial interface it is shown that the dominant parts of the kernels of the integral equations associated with both membrane loading and bending of the shell reduce to the generalized Cauchy kernel obtained for the corresponding plane stress case. The integral equations are solved and the stress intensity factors are given for various crack and shell dimensions. A bonded fiberglass reinforcement which may serve as a crack arrestor is used as an example.

Nonstationary Deformation of an Elastic Layer with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-11-01

The analytic solution to the plane problem for an elastic layer under a nonstationary surface load is found for mixed boundary conditions: normal stress and tangential displacement are specified on one side of the layer (fourth boundary-value problem of elasticity) and tangential stress and normal displacement are specified on the other side of the layer (second boundary-value problem of elasticity). The Laplace and Fourier integral transforms are applied. The inverse Laplace and Fourier transforms are found exactly using tabulated formulas and convolution theorems for various nonstationary loads. Explicit analytical expressions for stresses and displacements are derived. Loads applied to a constant surface area and to a surface area varying in a prescribed manner are considered. Computations demonstrate the dependence of the normal stress on time and spatial coordinates. Features of wave processes are analyzed

Inclined edge crack in two bonded elastic quarter planes under out-of-plane loading

NASA Astrophysics Data System (ADS)

Hwang, E. H.; Choi, S. R.; Earmme, Y. Y.

1992-08-01

The problem of the interfacial edge crack in which the crack-inclination angle = zero is solved analytically by means of the Wiener-Hopf technique with the Mellin transform. The results are found to confirm the result by Bassani and Erdogan (1979) showing that there is no stress singularity for the interface perpendicular to the free boundary at the junction with a straight inclined interface with no crack.

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Nakagaki, M.; Kathiresan, K.

1980-01-01

In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

Stresses in adhesively bonded joints - A closed-form solution

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Aydinoglu, M. N.

1981-01-01

The general plane strain problem of adhesively bonded structures consisting of two different, orthotropic adherends is considered, under the assumption that adherend thicknesses are constant and small in relation to the lateral dimensions of the bonded region, so that they may be treated as plates. The problem is reduced to a system of differential equations for the adhesive stresses which is solved in closed form, with a single lap joint and a stiffened plate under various loading conditions being considered as examples. It is found that the plate theory used in the analysis not only predicts the correct trend for adhesive stresses but gives surprisingly accurate results, the solution being obtained by assuming linear stress-strain relations for the adhesive.

Method for selectively orienting induced fractures in subterranean earth formations

DOEpatents

Shuck, Lowell Z.

1977-02-01

The orientation of hydraulically-induced fractures in relatively deep subterranean earth formations is normally confined to vertical projections along a plane parallel to the maximum naturally occurring (tectonic) compressive stress field. It was found that this plane of maximum compressive stress may be negated and, in effect, re-oriented in a plane projecting generally orthogonal to the original tectonic stress plane by injecting liquid at a sufficiently high pressure into a wellbore fracture oriented in a plane parallel to the plane of tectonic stress for the purpose of stressing the surrounding earth formation in a plane generally orthogonal to the plane of tectonic stress. With the plane of maximum compressive stress re-oriented due to the presence of the induced compressive stress, liquid under pressure is injected into a second wellbore disposed within the zone influenced by the induced compressive stress but at a location in the earth formation laterally spaced from the fracture in the first wellbore for effecting a fracture in the second wellbore along a plane generally orthogonal to the fracture in the first wellbore.

Interaction of a conductive crack and of an electrode at a piezoelectric bimaterial interface

NASA Astrophysics Data System (ADS)

Onopriienko, Oleg; Loboda, Volodymyr; Sheveleva, Alla; Lapusta, Yuri

2018-06-01

The interaction of a conductive crack and an electrode at a piezoelectric bi-material interface is studied. The bimaterial is subjected to an in-plane electrical field parallel to the interface and an anti-plane mechanical loading. The problem is formulated and reduced, via the application of sectionally analytic vector functions, to a combined Dirichlet-Riemann boundary value problem. Simple analytical expressions for the stress, the electric field, and their intensity factors as well as for the crack faces' displacement jump are derived. Our numerical results illustrate the proposed approach and permit to draw some conclusions on the crack-electrode interaction.

Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface. Part 2: Solution and results

NASA Technical Reports Server (NTRS)

Lu, M. C.; Erdogan, F.

1980-01-01

The numerical method is given for solving the plane problem for two bonded infinite dissimilar elastic strips which contain cracks of various configurations. The problem is intended to approximate a composite beam or a plate having cracks perpendicular to and on the interface of the two layers.

Interaction between a circular inclusion and an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.; Ratwani, M.

1975-01-01

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Stress distribution in and equivalent width of flanges of wide, thin-wall steel beams

NASA Technical Reports Server (NTRS)

Winter, George

1940-01-01

The use of different forms of wide-flange, thin-wall steel beams is becoming increasingly widespread. Part of the information necessary for a national design of such members is the knowledge of the stress distribution in and the equivalent width of the flanges of such beams. This problem is analyzed in this paper on the basis of the theory of plane stress. As a result, tables and curves are given from which the equivalent width of any given beam can be read directly for use in practical design. An investigation is given of the limitations of this analysis due to the fact that extremely wide and thin flanges tend to curve out of their plane toward the neutral axis. A summary of test data confirms very satisfactorily the analytical results.

An internal crack parallel to the boundary of a nonhomogeneous half plane under thermal loading

NASA Astrophysics Data System (ADS)

Jin, Zhi-He; Noda, Naotake

1993-05-01

This paper considers the crack problem for a semi-infinite nonhomogeneous thermoelastic solid subjected to steady heat flux over the boundary. The crack faces are assumed to be insulated. The research is aimed at understanding the effect of nonhomogeneities of materials on stress intensity factors. By using the Fourier transform, the problem is reduced to a system of singular integral equations which are solved numerically. Results are presented illustrating the influence of the nonhomogeneity of the material on the stress intensity factors. Zero Mode I stress intensity factors are found for some groups of the material constants, which may be interesting for the understanding of compositions of advanced Functionally Gradient Materials.

Finite element solutions for crack-tip behavior in small-scale yielding

NASA Technical Reports Server (NTRS)

Tracey, D. M.

1976-01-01

The subject considered is the stress and deformation fields in a cracked elastic-plastic power law hardening material under plane strain tensile loading. An incremental plasticity finite element formulation is developed for accurate analysis of the complete field problem including the extensively deformed near tip region, the elastic-plastic region, and the remote elastic region. The formulation has general applicability and was used to solve the small scale yielding problem for a set of material hardening exponents. Distributions of stress, strain, and crack opening displacement at the crack tip and through the elastic-plastic zone are presented as a function of the elastic stress intensity factor and material properties.

The crack and wedging problem for an orthotropic strip

NASA Technical Reports Server (NTRS)

Cinar, A.; Erdogan, F.

1982-01-01

The plane elasticity problem for an orthotropic strip containing a crack parallel to its boundaries is considered. The problem is formulated under general mixed mode loading conditions. The stress intensity factors depend on two dimensionless orthotropic constants only. For the crack problem the results are given for a single crack and two collinear cracks. The calculated results show that of the two orthotropic constants the influence of the stiffness ratio on the stress intensity factors is much more significant than that of the shear parameter. The problem of loading the strip by a rigid rectangular lengths continuous contact is maintained along the wedge strip interface; at a certain critical wedge length the separation starts at the midsection of the wedge, and the length of the separation zone increases rapidly with increasing wedge length.

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

NASA Astrophysics Data System (ADS)

Yi, Dake; Wang, TzuChiang

2018-06-01

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J( z), the stress intensity factor K( z) and the tri-axial stress constraint level T z ( z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J( z) and T z ( z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

Bonded orthotropic strips with cracks

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1978-01-01

The elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. First, the problem of cracks fully imbedded into the homogeneous strips is considered. Then, the singular behavior of the stresses for two special crack geometries is studied in some detail. The first is the case of a broken laminate in which the crack tips touch the interfaces. The second is the case of cracks crossing the interfaces. A number of numerical examples are worked out in order to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters. Finally, some numerical results are given for the stress intensity factors in certain basic crack geometries and for typical material combinations.

Bending of a Bonded Beam as a Test Method for Adhesive Properties

DTIC Science & Technology

1987-08-01

Beam U 3.2.1 Stress Function Analysis (13) In an elasticity problem, in this case a two-dimensional plane stresu problem, three families of equations...TYPE OF REPORT 1b. TIME COVERED 11 4. DATE OF REPORT I[Year, ?v0ontri, Llay) fI ý. YP~’-J WWII! 1 1_ POM Se~ 86 TO June-871 August 1987 I 82 16 SUP...reverse if nccessary and irlr’rsljiy by block number) A strength-ot--materials type solution is obtained for the shear stress state in the4 ~adhesive

The effect of transverse shear in a cracked plate under skew-symmetric loading

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1979-01-01

The problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered. By using a bending theory which allows the satisfaction of the boundary conditions on the crack surface regarding the normal and the twisting moments and the transverse shear load separately, it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems. The problem is solved for uniformly distributed or concentrated twisting moment or transverse shear load and the normalized Mode II and Mode III stress-intensity factors are tabulated. The results also include the effect of the Poisson's ratio and material orthotropy for specially orthotropic materials on the stress-intensity factors.

Comparison of 2D Finite Element Modeling Assumptions with Results From 3D Analysis for Composite Skin-Stiffener Debonding

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Paris, Isbelle L.; OBrien, T. Kevin; Minguet, Pierre J.

2004-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized plane strain type approaches were performed. The computed skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Influence of 2D Finite Element Modeling Assumptions on Debonding Prediction for Composite Skin-stiffener Specimens Subjected to Tension and Bending

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Minguet, Pierre J.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane strain elements as well as three different generalized plane strain type approaches were performed. The computed deflections, skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with lamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Transverse shear effect in a circumferentially cracked cylindrical shell

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1979-01-01

The objectives of the paper are to solve the problem of a circumferentially-cracked cylindrical shell by taking into account the effect of transverse shear, and to obtain the stress intensity factors for the bending moment as well as the membrane force as the external load. The formulation of the problem is given for a specially orthotropic material within the framework of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions as to moment and stress resultants on the crack surface. The effect of Poisson's ratio on the stress intensity factors and the nature of the out-of-plane displacement along the edges of the crack, i.e., bulging, are also studied.

The crack and wedging problem for an orthotropic strip

NASA Technical Reports Server (NTRS)

Cinar, A.; Erdogan, F.

1983-01-01

The plane elasticity problem for an orthotropic strip containing a crack parallel to its boundaries is considered. The problem is formulated under general mixed mode loading conditions. The stress intensity factors depend on two dimensionless orthotropic constants only. For the crack problem the results are given for a single crack and two collinear cracks. The calculated results show that of the two orthotropic constants the influence of the stiffness ratio on the stress intensity factors is much more significant than that of the shear parameter. The problem of loading the strip by a rigid rectangular lengths continuous contact is maintained along the wedge strip interface; at a certain critical wedge length the separation starts at the midsection of the wedge, and the length of the separation zone increases rapidly with increasing wedge length. Previously announced in STAR as N82-26707

NOLIN: A nonlinear laminate analysis program

NASA Technical Reports Server (NTRS)

Kibler, J. J.

1975-01-01

A nonlinear, plane-stress, laminate analysis program, NOLIN, was developed which accounts for laminae nonlinearity under inplane shear and transverse extensional stress. The program determines the nonlinear stress-strain behavior of symmetric laminates subjected to any combination of inplane shear and biaxial extensional loadings. The program has the ability to treat different stress-strain behavior in tension and compression, and predicts laminate failure using any or all of maximum stress, maximum strain, and quadratic interaction failure criteria. A brief description of the program is presented including discussion of the flow of information and details of the input required. Sample problems and a complete listing of the program is also provided.

Visualising Three Dimensional Damage and Failure Envelopes: Implications for True Triaxial Deformation

NASA Astrophysics Data System (ADS)

Harland, S. R.; Browning, J.; Healy, D.; Meredith, P. G.; Mitchell, T. M.

2017-12-01

Ultimate failure in brittle rocks is commonly accepted to occur as a coalescence of micro-crack damage into a single failure plane. The geometry and evolution with stress of the cracks (damage) within the medium will play a role in dictating the geometry of the ultimate failure plane. Currently, the majority of experimental studies investigating damage evolution and rock failure use conventional triaxial stress states (σ1 > σ2 = σ3). Results from these tests can easily be represented on a Mohr-Coulomb plot (σn - τ), conveniently allowing the user to determine the geometry of the resultant failure plane. In reality however, stress in the subsurface is generally truly triaxial (σ1 > σ2 > σ3) and in this case, the Mohr-Coulomb failure criterion is inadequate as it incorporates no dependence on the intermediate stress (σ2), which has been shown to play an important role in controlling failure. It has recently been shown that differential stress is the key driver in initiating crack growth, regardless of the mean stress. Polyaxial failure criteria that incorporate the effect of the intermediate stress do exist and include the Modified Lade, Modified Wiebols and Cook, and the Drucker-Prager criteria. However, unlike the Mohr-Coulomb failure criterion, these polyaxial criteria do not offer any prediction of, or insight into, the geometry of the resultant failure plane. An additional downfall of all of the common conventional and polyaxial failure criteria is that they fail to describe the geometry of the damage (i.e. pre-failure microcracking) envelope with progressive stress; it is commonly assumed that the damage envelope is parallel to the ultimate brittle failure envelope. Here we use previously published polyaxial failure data for the Shirahama sandstone and Westerley granite to illustrate that the commonly used Mohr-Coulomb and polyaxial failure criteria do not sufficiently describe or capture failure or damage envelopes under true triaxial stress states. We investigate if and how Mohr-Coulomb type constructions can provide geometrical solutions to truly-triaxial problems. We look to incorporate both the intermediate stress and the differential stress as the controlling parameters in failure and examine the geometry of damage envelopes using damage onset data.

A Direct Approach to In-Plane Stress Separation using Photoelastic Ptychography

NASA Astrophysics Data System (ADS)

Anthony, Nicholas; Cadenazzi, Guido; Kirkwood, Henry; Huwald, Eric; Nugent, Keith; Abbey, Brian

2016-08-01

The elastic properties of materials, either under external load or in a relaxed state, influence their mechanical behaviour. Conventional optical approaches based on techniques such as photoelasticity or thermoelasticity can be used for full-field analysis of the stress distribution within a specimen. The circular polariscope in combination with holographic photoelasticity allows the sum and difference of principal stress components to be determined by exploiting the temporary birefringent properties of materials under load. Phase stepping and interferometric techniques have been proposed as a method for separating the in-plane stress components in two-dimensional photoelasticity experiments. In this paper we describe and demonstrate an alternative approach based on photoelastic ptychography which is able to obtain quantitative stress information from far fewer measurements than is required for interferometric based approaches. The complex light intensity equations based on Jones calculus for this setup are derived. We then apply this approach to the problem of a disc under diametrical compression. The experimental results are validated against the analytical solution derived by Hertz for the theoretical displacement fields for an elastic disc subject to point loading.

A Direct Approach to In-Plane Stress Separation using Photoelastic Ptychography

PubMed Central

Anthony, Nicholas; Cadenazzi, Guido; Kirkwood, Henry; Huwald, Eric; Nugent, Keith; Abbey, Brian

2016-01-01

The elastic properties of materials, either under external load or in a relaxed state, influence their mechanical behaviour. Conventional optical approaches based on techniques such as photoelasticity or thermoelasticity can be used for full-field analysis of the stress distribution within a specimen. The circular polariscope in combination with holographic photoelasticity allows the sum and difference of principal stress components to be determined by exploiting the temporary birefringent properties of materials under load. Phase stepping and interferometric techniques have been proposed as a method for separating the in-plane stress components in two-dimensional photoelasticity experiments. In this paper we describe and demonstrate an alternative approach based on photoelastic ptychography which is able to obtain quantitative stress information from far fewer measurements than is required for interferometric based approaches. The complex light intensity equations based on Jones calculus for this setup are derived. We then apply this approach to the problem of a disc under diametrical compression. The experimental results are validated against the analytical solution derived by Hertz for the theoretical displacement fields for an elastic disc subject to point loading. PMID:27488605

Opening of an interface flaw in a layered elastic half-plane under compressive loading

NASA Technical Reports Server (NTRS)

Kennedy, J. M.; Fichter, W. B.; Goree, J. G.

1984-01-01

A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.

An algorithm for full parametric solution of problems on the statics of orthotropic plates by the method of boundary states with perturbations

NASA Astrophysics Data System (ADS)

Penkov, V. B.; Ivanychev, D. A.; Novikova, O. S.; Levina, L. V.

2018-03-01

The article substantiates the possibility of building full parametric analytical solutions of mathematical physics problems in arbitrary regions by means of computer systems. The suggested effective means for such solutions is the method of boundary states with perturbations, which aptly incorporates all parameters of an orthotropic medium in a general solution. We performed check calculations of elastic fields of an anisotropic rectangular region (test and calculation problems) for a generalized plane stress state.

The inhibiting effect of dislocation helices on the stress-induced orientation of S' precipitates in Al–Cu–Mg alloy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Xiaobin; Deng, Yunlai, E-mail: luckdeng@csu.edu.cn; State Key Laboratory of High Performance and Complex Manufacturing, Central South University, Changsha

The phenomenon of restrained stress-induced preferential orientation of S′ precipitates is investigated using a single-crystal of Al–1.23Cu–0.43 Mg alloy. Al–1.23Cu–0.43 Mg single-crystal specimens are subjected to stress aging, and the microstructure is analyzed by transmission electron microscopy (TEM). It is found that the stress-induced preferential orientation of S′ precipitates is restrained owing to the dislocations produced by a higher stress. The effect of dislocations on the oriented precipitates depends on the total length of the intersection lines for precipitate habit planes and dislocation glide planes. This investigation not only provides important insight into solving the anisotropy problem attributed to precipitationmore » strengthening, but also offers a benchmark for choosing the appropriate stress range in manufacturing of Al–Cu–Mg alloys. - Highlights: • Single crystals of an Al–Cu–Mg alloy were prepared for the investigations. • A phenomenon of restrained stress-induced preferential orientation of S′ precipitates was found. • The influence of dislocation helices on precipitation during stress-aging was studied. • Difference of orientation degree of S′ precipitates and θ′ precipitates was explained. • A basis for choosing the appropriate stress range in manufacturing of Al–Cu–Mg alloys is provided.« less

The mode 3 crack problem in bonded materials with a nonhomogeneous interfacial zone

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Kaya, A. C.; Joseph, P. F.

1988-01-01

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.

The mode III crack problem in bonded materials with a nonhomogeneous interfacial zone

NASA Technical Reports Server (NTRS)

Erdogan, F.; Joseph, P. F.; Kaya, A. C.

1991-01-01

The mode 3 crack problem for two bonded homogeneous half planes was considered. The interfacial zone was modelled by a nonhomogeneous strip in such a way that the shear modulus is a continuous function throughout the composite medium and has discontinuous derivatives along the boundaries of the interfacial zone. The problem was formulated for cracks perpendicular to the nominal interface and was solved for various crack locations in and around the interfacial region. The asymptotic stress field near the tip of a crack terminating at an interface was examined and it was shown that, unlike the corresponding stress field in piecewise homogeneous materials, in this case the stresses have the standard square root singularity and their angular variation was identical to that of a crack in a homogeneous medium. With application to the subcritical crack growth process in mind, the results given include mostly the stress intensity factors for some typical crack geometries and various material combinations.

Line-spring model for surface cracks in a Reissner plate

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

In this paper the line-spring model developed by Rice and Levy for a surface crack in elastic plates is reconsidered. The problem is formulated by using Reissner's plate bending theory. For the plane strain problem of a strip containing an edge crack and subjected to tension and bending new expressions for stress intensity factors are used which are valid up to a depth-to-thickness ratio of 0.8. The stress intensity factors for a semi-elliptic and a rectangular crack are calculated. Considering the simplicity of the technique and the severity of the underlying assumptions, the results compare rather well with the existing finite element solutions.

The effect of contact stresses in four-point bend testing of graphite/epoxy and graphite/PMR-15 composite beams

NASA Technical Reports Server (NTRS)

Binienda, Wieslaw K.; Roberts, Gary D.; Papadopoulos, Demetrios S.

1992-01-01

The results of in-plane four-point bend experiments on unidirectionally reinforced composite beams are presented for graphite/epoxy (T300/934) and graphite/polyimide (G30-500/PMR-15) composites. The maximum load and the location of cracks formed during failure were measured for testpieces with fibers oriented at various angles to the beam axis. Since most of the beams failed near one or more of the load points, the strength of the beams was evaluated in terms of a proposed model, for the local stress distribution. In this model, an exact solution to the problem of a localized contact force acting on a unidirectionally reinforced half plane is used to describe the local stress field. The stress singularity at the load points is treated in a manner similar to the stress singularity at a crack tip in fracture mechanisms problems. Using this approach, the effect of fiber angle and elastic material properties on the strength of the beam is described in terms of a load intensity factor. For fiber angles less than 45 deg from the beam axis, a single crack is initiated near one of the load points at a critical value of the load intensity factor. The critical load intensity factor decreases with the increasing fiber angle. For larger fiber angles, multiple cracks occur at locations both near and away from the load points, and the load intensity factor at failure increases sharply with increasing fiber angle.

Effect of contact stresses in four-point bend testing of graphite/epoxy and graphite/PMR-15 composite beams

NASA Technical Reports Server (NTRS)

Binienda, W. K.; Roberts, G. D.; Papadopoulos, D. S.

1992-01-01

The results of in-plane four-point bend experiments on unidirectionally reinforced composite beams are presented for graphite/epoxy (T300/934) and graphite/polyimide (G30-500/PMR-15) composites. The maximum load and the location of cracks formed during failure were measured for testpieces with fibers oriented at various angles to the beam axis. Since most of the beams failed near one or more of the load points, the strength of the beams was evaluated in terms of a proposed model for the local stress distribution. In this model, an exact solution to the problem of a localized contact force acting on a unidirectionally reinforced half plane is used to describe the local stress field. The stress singularity at the load points is treated in a manner similar to the stress singularity at a crack tip in fracture mechanisms problems. Using this approach, the effect of fiber angle and elastic material properties on the strength of the beam is described in terms of a load intensity factor. For fiber angles less than 45 deg from the beam axis, a single crack is initiated near one of the load points at a critical value of the load intensity factor. The critical load intensity factor decreases with increasing fiber angle. For larger fiber angles, multiple cracks occur at locations both near and away from the load points, and the load intensity factor at failure increases sharply with increasing fiber angle.

Collateral Damage to Satellites from an EMP Attack

DTIC Science & Technology

2010-08-01

peak dose is computed in an infinite half plane of silicon. The resulting in- plane stresses in silicon are shown in Figure VI.23. In- plane refers to...achieved by the SLAR coating 81 Figure VIII.6. Ratio of the peak in- plane compressive stress to the maximum compressive stress for the SLAR coating...82 Figure VIII.7. Maximum in- plane compressive stress in a SLAR coating on DMSP/NOAA subjected to the threat events 83 Figure VIII.8. Maximum in

Some remarks on elastic crack-tip stress fields.

NASA Technical Reports Server (NTRS)

Rice, J. R.

1972-01-01

It is shown that if the displacement field and stress intensity factor are known as functions of crack length for any symmetrical load system acting on a linear elastic body in plane strain, then the stress intensity factor for any other symmetrical load system whatsoever on the same body may be directly determined. The result is closely related to Bueckner's (1970) weight function, through which the stress intensity factor is expressed as a sum of work-like products between applied forces and values of the weight function at their points of application. An example of the method is given wherein the solution for a crack in a remotely uniform stress field is used to generate the expression for the stress intensity factor due to an arbitrary traction distribution on the faces of a crack. A corresponding theory is developed in an appendix for three-dimensional crack problems, although this appears to be directly useful chiefly for problems in which there is axial symmetry.

Applications of FEM and BEM in two-dimensional fracture mechanics problems

NASA Technical Reports Server (NTRS)

Min, J. B.; Steeve, B. E.; Swanson, G. R.

1992-01-01

A comparison of the finite element method (FEM) and boundary element method (BEM) for the solution of two-dimensional plane strain problems in fracture mechanics is presented in this paper. Stress intensity factors (SIF's) were calculated using both methods for elastic plates with either a single-edge crack or an inclined-edge crack. In particular, two currently available programs, ANSYS for finite element analysis and BEASY for boundary element analysis, were used.

Role of fiber-stitching in eliminating transverse fracture in cross-ply ceramic composites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, T.J.; Hutchinson, J.W.

1995-12-31

A theoretical study of the feasibility of using fiber stitching to prevent transverse matrix cracking in cross-ply ceramic composites is first reported. The prototype problem solved is a curved composite beam subject to pure bending (the C-specimen), which develops a transverse tensile stress Go acting across its circumferential mid-plane. This transverse stress is cause for concern if the beam is unstitched since there is no mechanism to arrest a matrix crack once one becomes critical. Fiber stitches normal to this plane are introduced to bridge a circumferential matrix crack lying along the mid-plane of the specimen. Results are presented formore » the energy release rate of this matrix crack as a function of a nondimensional parameter characterizing the density and fiber sliding stress of the fiber stitches. A parameter is identified which assures the applicability of the classical ACK (Aveston, Cooper and Kelly) limit for a steady-state matrix crack subject to {sigma}{sub 0}. The results obtained can be used to choose the level of stitching such that transverse matrix cracking will be excluded. The second problem we address is thermal delamination in a cross-ply ceramic composite plate due to high temperature gradients applied in the thickness direction. It is shown that a preexistent crack with a size of the order of the plate thickness will propagate unstably when a moderately large through-thickness temperature gradient is enforced. The possibility of using cross-fiber stitches to suppress thermal delamination cracking is discussed.« less

Constitutive Behavior of Reinforced Concrete Membrane Elements under Tri-directional Shear

NASA Astrophysics Data System (ADS)

Labib, Moheb

The two-dimensional behavior of typical reinforced concrete (RC) structures has been extensively studied in the past several decades by investigating the constitutive behavior of full-scale reinforced concrete elements subjected to a bi-axial state of stress. In order to understand the true behavior of many large complex structures, the goal of this investigation is to develop new constitutive relationships for RC elements subjected to tri-directional shear stresses. Recently, additional out-of-plane jacks were installed on the panel tester at University of Houston so that concrete elements could be subjected to tri-directional shear stresses. This upgrade makes the panel tester the only one of its kind in the US that is capable of applying such combinations of stresses on full-scale reinforced concrete elements. This dissertation presents the details of the mounting and installation of the additional hydraulic jacks on the universal panel tester. The experimental program includes a series of seven reinforced concrete elements subjected to different combinations of in-plane and out-of-plane shear stresses. Increasing the applied out-of-plane shear stresses reduced the membrane shear strength of the elements. The effect of applying out-of-plane shear stresses on the in-plane shear strength was represented by modifying the softening coefficient in the compression stress strain curve of concrete struts. The modified model was able to capture the behavior and the ultimate capacity of the tested elements. The effect of the in-plane shear reinforcement ratio on the interaction between in-plane and out-of-plane shear stresses was evaluated. The model was implemented in the Finite Element package FEAP and was used to predict the ultimate capacity of many structures subjected to a combination of in-plane and out-of-plane shear stresses. The results of the analytical model were used to develop simplified design equations for members subjected to bi-directional shear loads. The applied out-of-plane shear load was resolved in two equal out-of-plane shear components to construct tri-directional shear interaction diagrams.

Effect of the out-of-plane stress on the properties of epitaxial SrTiO3 films with nano-pillar array on Si-substrate

NASA Astrophysics Data System (ADS)

Bai, Gang; Xie, Qiyun; Liu, Zhiguo; Wu, Dongmei

2015-08-01

A nonlinear thermodynamic formalism has been proposed to calculate the physical properties of the epitaxial SrTiO3 films containing vertical nano-pillar array on Si-substrate. The out-of-plane stress induced by the mismatch between film and nano-pillars provides an effective way to tune the physical properties of ferroelectric SrTiO3 films. Tensile out-of-plane stress raises the phase transition temperature and increases the out-of-plane polarization, but decreases the out-of-plane dielectric constant below Curie temperature, pyroelectric coefficient, and piezoelectric coefficient. These results showed that by properly controlling the out-of-plane stress, the out-of-plane stress induced paraelectric-ferroelectric phase transformation will appear near room temperature. Excellent dielectric, pyroelectric, piezoelectric properties of these SrTiO3 films similar to PZT and other lead-based ferroelectrics can be expected.

Plates and shells containing a surface crack under general loading conditions

NASA Technical Reports Server (NTRS)

Joseph, Paul F.; Erdogan, Fazil

1987-01-01

Various through and part-through crack problems in plates and shells are considered. The line-spring model of Rice and Levy is generalized to the skew-symmetric case to solve surface crack problems involving mixed-mode, coplanar crack growth. Compliance functions are introduced which are valid for crack depth to thickness ratios at least up to .95. This includes expressions for tension and bending as well as expressions for in-plane shear, out-of-plane shear, and twisting. Transverse shear deformation is taken into account in the plate and shell theories and this effect is shown to be important in comparing stress intensity factors obtained from the plate theory with three-dimensional solutions. Stress intensity factors for cylinders obtained by the line-spring model also compare well with three-dimensional solution. By using the line-spring approach, stress intensity factors can be obtained for the through crack and for part-through crack of any crack front shape, without recalculation integrals that take up the bulk of the computer time. Therefore, parameter studies involving crack length, crack depth, shell type, and shell curvature are made in some detail. The results will be useful in brittle fracture and in fatigue crack propagation studies. All problems considered are of the mixed boundary value type and are reducted to strongly singular integral equations which make use of the finite-part integrals of Hadamard. The equations are solved numerically in a manner that is very efficient.

Quasi-static earthquake cycle simulation based on nonlinear viscoelastic finite element analyses

NASA Astrophysics Data System (ADS)

Agata, R.; Ichimura, T.; Hyodo, M.; Barbot, S.; Hori, T.

2017-12-01

To explain earthquake generation processes, simulation methods of earthquake cycles have been studied. For such simulations, the combination of the rate- and state-dependent friction law at the fault plane and the boundary integral method based on Green's function in an elastic half space is widely used (e.g. Hori 2009; Barbot et al. 2012). In this approach, stress change around the fault plane due to crustal deformation can be computed analytically, while the effects of complex physics such as mantle rheology and gravity are generally not taken into account. To consider such effects, we seek to develop an earthquake cycle simulation combining crustal deformation computation based on the finite element (FE) method with the rate- and state-dependent friction law. Since the drawback of this approach is the computational cost associated with obtaining numerical solutions, we adopt a recently developed fast and scalable FE solver (Ichimura et al. 2016), which assumes use of supercomputers, to solve the problem in a realistic time. As in the previous approach, we solve the governing equations consisting of the rate- and state-dependent friction law. In solving the equations, we compute stress changes along the fault plane due to crustal deformation using FE simulation, instead of computing them by superimposing slip response function as in the previous approach. In stress change computation, we take into account nonlinear viscoelastic deformation in the asthenosphere. In the presentation, we will show simulation results in a normative three-dimensional problem, where a circular-shaped velocity-weakening area is set in a square-shaped fault plane. The results with and without nonlinear viscosity in the asthenosphere will be compared. We also plan to apply the developed code to simulate the post-earthquake deformation of a megathrust earthquake, such as the 2011 Tohoku earthquake. Acknowledgment: The results were obtained using the K computer at the RIKEN (Proposal number hp160221).

Stress–strain state in an elastoplastic pipe taking into account the temperature and compressibility of the material

NASA Astrophysics Data System (ADS)

Gornostaev, K. K.; Kovalev, A. V.; Malygina, Y. V.

2018-03-01

In the article the authors have considered the problem of determining the stress-strain state of the elastoplastic pipe with the Mises’ condition in case of plane strain for the compressible material taking into account the temperature. The task was solved using the method of the small parameter. The expressions for the fields of stresses and displacements were received as well as the ratio of the radius of the elastoplastic boundary in the zero and first approximations.

Analytical and numerical analysis of the slope of von Mises planar trusses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalina, M.; Frantík, P.

2016-06-08

In the present paper, there are presented post-critical stress states which will occur at loading by vertical shift of the top joint in the direction downwards. The formation of certain stress states depends on the size of the angle formed by a straight beam of the von Mises planar truss with horizontal plane. Numerical and analytical methods and their problems with finding the angle were described. The numerical solution applies the method of searching for a minimum of potential energy.

Cell division plane orientation based on tensile stress in Arabidopsis thaliana

PubMed Central

Louveaux, Marion; Julien, Jean-Daniel; Mirabet, Vincent; Boudaoud, Arezki; Hamant, Olivier

2016-01-01

Cell geometry has long been proposed to play a key role in the orientation of symmetric cell division planes. In particular, the recently proposed Besson–Dumais rule generalizes Errera’s rule and predicts that cells divide along one of the local minima of plane area. However, this rule has been tested only on tissues with rather local spherical shape and homogeneous growth. Here, we tested the application of the Besson–Dumais rule to the divisions occurring in the Arabidopsis shoot apex, which contains domains with anisotropic curvature and differential growth. We found that the Besson–Dumais rule works well in the central part of the apex, but fails to account for cell division planes in the saddle-shaped boundary region. Because curvature anisotropy and differential growth prescribe directional tensile stress in that region, we tested the putative contribution of anisotropic stress fields to cell division plane orientation at the shoot apex. To do so, we compared two division rules: geometrical (new plane along the shortest path) and mechanical (new plane along maximal tension). The mechanical division rule reproduced the enrichment of long planes observed in the boundary region. Experimental perturbation of mechanical stress pattern further supported a contribution of anisotropic tensile stress in division plane orientation. Importantly, simulations of tissues growing in an isotropic stress field, and dividing along maximal tension, provided division plane distributions comparable to those obtained with the geometrical rule. We thus propose that division plane orientation by tensile stress offers a general rule for symmetric cell division in plants. PMID:27436908

A penny-shaped crack in a filament reinforced matrix. 1: The filament model

NASA Technical Reports Server (NTRS)

Erdogan, F.; Pacella, A. H.

1973-01-01

The electrostatic problem of a penny-shaped crack in an elastic matrix which reinforced by filaments or fibers perpendicular to the plane of the crack was studied. The elastic filament model was developed for application to evaluation studies of the stress intensity factor along the periphery of the crack, the stresses in the filaments or fibers, and the interface shear between the matrix and the filaments or fibers. The requirements expected of the model are a sufficiently accurate representation of the filament and applicability to the interaction problems involving a cracked elastic continuum with multi-filament reinforcements. The technique for developing the model and numerical examples of it are shown.

Penny-shaped crack in a fiber-reinforced matrix. [elastostatics

NASA Technical Reports Server (NTRS)

Narayanan, T. V.; Erdogan, F.

1974-01-01

Using a slender inclusion model developed earlier, the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles, the problem was reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given, and distribution of the stress intensity factor along the crack border was obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.

Penny-shaped crack in a fiber-reinforced matrix

NASA Technical Reports Server (NTRS)

Narayanan, T. V.; Erdogan, F.

1975-01-01

Using the slender inclusion model developed earlier the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles the problem is reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given and distribution of the stress intensity factor along the crack border is obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.

Disruption of the Globular Cluster Pal 5

NASA Technical Reports Server (NTRS)

Miller, R. H.; Smith, B. F.; Cuzzi, Jeffrey N. (Technical Monitor)

1995-01-01

Orbit calculations suggest that the sparse globular cluster, Pal 5, will pass within 7 kpc of the Galactic center the next time it crosses the plane, where it might be destroyed by tidal stresses. We study this problem, treating Pal 5 as a self-consistent dynamical system orbiting through an external potential that represents the Galaxy. The first part of the problem is to find suitable analytic approximations to the Galactic potential. They must be valid in all regions the cluster is likely to explore. Observed velocity and positional data for Pal 5 are used as initial conditions to determine the orbit. Methods we used for a different problem some 12 years ago have been adapted to this problem. Three experiments have been run, with M/L= 1, 3, and 10, for the cluster model. The cluster blew up shortly after passing through the Galactic plane (about 130 Myrs after the beginning of the run) with M/L=1. At M/L = 3 and 10 the cluster survived, although it got quite a kick in the fundamental mode on passing through the plane. But the fundamental mode oscillation died out in a couple of oscillation cycles at M/L=10. Pal 5 will probably be destroyed on its next crossing of the Galactic plane if M/L=1, but it can survive (albeit with fairly heavy damage) if NI/L=3. We haven't tried to trap the mass limits more closely than that. Pal 5 comes through pretty well unscathed at M/L=10. An interesting follow-up experiment would be to back the cluster up along its orbit to look at its previous passage through the Galactic plane, to see what kind of object it might have been at earlier times.

Interface stresses in fiber-reinforced materials with regular fiber arrangements

NASA Astrophysics Data System (ADS)

Mueller, W. H.; Schmauder, S.

The theory of linear elasticity is used here to analyze the stresses inside and at the surface of fiber-reinforced composites. Plane strain, plane stress, and generalized plane strain are analyzed using the shell model and the BHE model and are numerically studied using finite element analysis. Interface stresses are shown to depend weakly on Poisson's ratio. For equal values of the ratio, generalized plane strain and plane strain results are identical. For small volume fractions up to 40 vol pct of fibers, the shell and the BHE models predict the interface stresses very well over a wide range of elastic mismatches and for different fiber arrangements. At higher volume fractions the stresses are influenced by interactions with neighboring fibers. Introducing an external pressure into the shell model allows the prediction of interface stresses in real composite with isolated or regularly arranged fibers.

Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2006-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

Modeling and stress analysis of large format InSb focal plane arrays detector under thermal shock

NASA Astrophysics Data System (ADS)

Zhang, Li-Wen; Meng, Qing-Duan; Zhang, Xiao-Ling; Yu, Qian; Lv, Yan-Qiu; Si, Jun-Jie

2013-09-01

Higher fracture probability, appearing in large format InSb infrared focal plane arrays detector under thermal shock loadings, limits its applicability and suitability for large format equipment, and has been an urgent problem to be solved. In order to understand the fracture mechanism and improve the reliability, three dimensional modeling and stress analysis of large format InSb detector is necessary. However, there are few reports on three dimensional modeling and simulation of large format InSb detector, due to huge meshing numbers and time-consuming operation to solve. To solve the problems, basing on the thermal mismatch displacement formula, an equivalent modeling method is proposed in this paper. With the proposed equivalent modeling method, employing the ANSYS software, three dimensional large format InSb detector is modeled, and the maximum Von Mises stress appearing in InSb chip dependent on array format is researched. According to the maximum Von Mises stress location shift and stress increasing tendency, the adaptability range of the proposed equivalent method is also derived, that is, for 16 × 16, 32 × 32 and 64 × 64 format, its adaptability ranges are not larger than 64 × 64, 256 × 256 and 1024 × 1024 format, respectively. Taking 1024 × 1024 InSb detector as an example, the Von Mises stress distribution appearing in InSb chip, Si readout integrated circuits and indium bump arrays are described, and the causes are discussed in detail. All these will provide a feasible research plan to identify the fracture origins of InSb chip and reduce fracture probability for large format InSb detector.

Stress wave calculations in composite plates using the fast Fourier transform.

NASA Technical Reports Server (NTRS)

Moon, F. C.

1973-01-01

The protection of composite turbine fan blades against impact forces has prompted the study of dynamic stresses in composites due to transient loads. The mathematical model treats the laminated plate as an equivalent anisotropic material. The use of Mindlin's approximate theory of crystal plates results in five two-dimensional stress waves. Three of the waves are flexural and two involve in-plane extensional strains. The initial value problem due to a transient distributed transverse force on the plate is solved using Laplace and Fourier transforms. A fast computer program for inverting the two-dimensional Fourier transform is used. Stress contours for various stresses and times after application of load are obtained for a graphite fiber-epoxy matrix composite plate. Results indicate that the points of maximum stress travel along the fiber directions.

Steady sliding frictional contact problem for a 2d elastic half-space with a discontinuous friction coefficient and related stress singularities

NASA Astrophysics Data System (ADS)

Ballard, Patrick

2016-12-01

The steady sliding frictional contact problem between a moving rigid indentor of arbitrary shape and an isotropic homogeneous elastic half-space in plane strain is extensively analysed. The case where the friction coefficient is a step function (with respect to the space variable), that is, where there are jumps in the friction coefficient, is considered. The problem is put under the form of a variational inequality which is proved to always have a solution which, in addition, is unique in some cases. The solutions exhibit different kinds of universal singularities that are explicitly given. In particular, it is shown that the nature of the universal stress singularity at a jump of the friction coefficient is different depending on the sign of the jump.

Limit analysis of multi-layered plates. Part I: The homogenized Love-Kirchhoff model

NASA Astrophysics Data System (ADS)

Dallot, Julien; Sab, Karam

The purpose of this paper is to determine Gphom, the overall homogenized Love-Kirchhoff strength domain of a rigid perfectly plastic multi-layered plate, and to study the relationship between the 3D and the homogenized Love-Kirchhoff plate limit analysis problems. In the Love-Kirchhoff model, the generalized stresses are the in-plane (membrane) and the out-of-plane (flexural) stress field resultants. The homogenization method proposed by Bourgeois [1997. Modélisation numérique des panneaux structuraux légers. Ph.D. Thesis, University Aix-Marseille] and Sab [2003. Yield design of thin periodic plates by a homogenization technique and an application to masonry wall. C. R. Méc. 331, 641-646] for in-plane periodic rigid perfectly plastic plates is justified using the asymptotic expansion method. For laminated plates, an explicit parametric representation of the yield surface ∂Gphom is given thanks to the π-function (the plastic dissipation power density function) that describes the local strength domain at each point of the plate. This representation also provides a localization method for the determination of the 3D stress components corresponding to every generalized stress belonging to ∂Gphom. For a laminated plate described with a yield function of the form F(x3,σ)=σu(x3)F^(σ), where σu is a positive even function of the out-of-plane coordinate x3 and F^ is a convex function of the local stress σ, two effective constants and a normalization procedure are introduced. A symmetric sandwich plate consisting of two Von-Mises materials ( σu=σ1u in the skins and σu=σ2u in the core) is studied. It is found that, for small enough contrast ratios ( r=σ1u/σ2u≤5), the normalized strength domain G^phom is close to the one corresponding to a homogeneous Von-Mises plate [Ilyushin, A.-A., 1956. Plasticité. Eyrolles, Paris].

Off-axis impact of unidirectional composites with cracks: Dynamic stress intensification

NASA Technical Reports Server (NTRS)

Sih, G. C.; Chen, E. P.

1979-01-01

The dynamic response of unidirectional composites under off axis (angle loading) impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. The analytical method utilizes Fourier transform for the space variable and Laplace transform for the time variable. The off axis impact is separated into two parts, one being symmetric and the other skew-symmetric with reference to the crack plane. Transient boundary conditions of normal and shear tractions are applied to a crack embedded in the matrix of the unidirectional composite. The two boundary conditions are solved independently and the results superimposed. Mathematically, these conditions reduce the problem to a system of dual integral equations which are solved in the Laplace transform plane for the transformation of the dynamic stress intensity factor. The time inversion is carried out numerically for various combinations of the material properties of the composite and the results are displayed graphically.

Development of basic theories and techniques for determining stresses in rotating turbine or compressor blades

NASA Technical Reports Server (NTRS)

Chien, C. H.; Swinson, W. F.; Turner, J. L.; Moslehy, F. A.; Ranson, W. F.

1980-01-01

A method for measuring in-plane displacement of a rotating structure by using two laser speckle photographs is described. From the displacement measurements one can calculate strains and stresses due to a centrifugal load. This technique involves making separate speckle photographs of a test model. One photograph is made with the model loaded (model is rotating); the second photograph is made with no load on the model (model is stationary). A sandwich is constructed from the two speckle photographs and data are recovered in a manner similar to that used with conventional speckle photography. The basic theory, experimental procedures of this method, and data analysis of a simple rotating specimen are described. In addition the measurement of in-plane surface displacement components of a deformed solid, and the application of the coupled laser speckle interferometry and boundary-integral solution technique to two dimensional elasticity problems are addressed.

Mode I analysis of a cracked circular disk subject to a couple and a force

NASA Technical Reports Server (NTRS)

Gross, B.

1978-01-01

Mode I stress intensity coefficients were obtained for an edge-cracked disk (round compact specimen). Results for this plane elastostatic problem, obtained by a boundary collocation analysis are presented for A/D ratios of 0.35 to 1, where A is the crack length and D is the disk diameter. The results presented are for two complementary types of loading. By superposition of these results the stress intensity factor for any practical load line location of a pin-loaded round compact specimen can be obtained.

Stiffener-skin interactions in pressure-loaded composite panels

NASA Technical Reports Server (NTRS)

Loup, D. C.; Hyer, M. W.; Starnes, J. H., Jr.

1986-01-01

The effects of flange thickness, web height, and skin stiffness on the strain distributions in the skin-stiffener interface region of pressure-loaded graphite-epoxy panels, stiffened by the type-T stiffener, were examined at pressure levels up to one atmosphere. The results indicate that at these pressures geometric nonlinearities are important, and that the overall stiffener stiffness has a significant effect on panel response, particularly on the out-of-plane deformation or pillowing of the skin. The strain gradients indicated that the interface between the skin and the stiffener experiences two components of shear stress, in addition to a normal (peel) stress. Thus, the skin-stiffener interface problem is a three-dimensional problem rather than a two-dimensional one, as is often assumed.

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

NASA Technical Reports Server (NTRS)

Chen, QI; Liu, Hao-Wen

1988-01-01

Fatigue crack growth in large grain Al alloy was studied. Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The crack paths in the large crystals are very irregular and zigzag. The crack planes are often inclined to the loading axis both in the inplane direction and the thickness direction. The stress intensity factors of such inclined cracks are approximated from the two dimensional finite element calculations. The plastic deformation in a large crystal is highly anisotropic, and dislocation motion in such crystals are driven by the resolved shear stress. The resolved shear stress intensity coefficient in a crack solid, RSSIC, is defined, and the coefficients for the slip systems at a crack tip are evaluated from the calculated stress intensity factors. The orientations of the crack planes are closely related to the slip planes with the high RSSIC values. If a single slip system has a much higher RSSIC than all the others, the crack will follow the slip plane, and the slip plane becomes the crack plane. If two or more slip systems have a high RSSIC, the crack plane is the result of the decohesion processes on these active slip planes.

Stress distribution in composite flatwise tension test specimens

NASA Technical Reports Server (NTRS)

Scott, Curtis A.; Pereira, J. Michael

1993-01-01

A finite element analysis was conducted to determine the stress distribution in typical graphite/epoxy composite flat wise tension (FWT) specimens under normal loading conditions. The purpose of the analysis was to determine the relationship between the applied load and the stress in the sample to evaluate the validity of the test as a means of measuring the out-of-plane strength of a composite laminate. Three different test geometries and three different material lay ups were modeled. In all cases, the out-of-plane component of stress in the test section was found to be uniform, with no stress concentrations, and very close to the nominal applied stress. The stress in the sample was found to be three-dimensional, and the magnitude of in-plane normal and shear stresses varied with the anisotropy of the test specimen. However, in the cases considered here, these components of stress were much smaller than the out-of-plane normal stress. The geometry of the test specimen had little influence on the results. It was concluded that the flat wise tension test provides a good measure of the out-of-plane strength for the representative materials that were studied.

Stresses and strains in thick perforated orthotropic plates

Treesearch

A. Alshaya; John Hunt; R. Rowlands

2016-01-01

Stress and strain concentrations and in-plane and out-of-plane stress constraint factors associated with a circular hole in thick, loaded orthotropic composite plates are determined by three-dimensional finite element method. The plate has essentially infinite in-plane geometry but finite thickness. Results for Sitka Spruce wood are emphasized, although some for carbon...

Three Dimensional Parametric Analyses of Stress Concentration Factor and Its Mitigation in Isotropic and Orthotropic Plate with Central Circular Hole Under Axial In-Plane Loading

NASA Astrophysics Data System (ADS)

Nagpal, Shubhrata; Jain, Nitin Kumar; Sanyal, Shubhashis

2016-01-01

The problem of finding the stress concentration factor of a loaded rectangular plate has offered considerably analytical difficulty. The present work focused on understanding of behavior of isotropic and orthotropic plate subjected to static in-plane loading using finite element method. The complete plate model configuration has been analyzed using finite element method based software ANSYS. In the present work two parameters: thickness to width of plate (T/A) and diameter of hole to width of plate (D/A) have been varied for analysis of stress concentration factor (SCF) and its mitigation. Plates of five different materials have been considered for complete analysis to find out the sensitivity of stress concentration factor. The D/A ratio varied from 0.1 to 0.7 for analysis of SCF and varied from 0.1 to 0.5 for analyzing the mitigation of SCF. 0.01, 0.05 and 0.1 are considered as T/A ratio for all the cases. The results are presented in graphical form and discussed. The mitigation in SCF reported is very encouraging. The SCF is more sensitive to D/A ratio as compared to T/A.

Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method

NASA Astrophysics Data System (ADS)

Zhang, Z.; Zhu, G.; Chen, X.

2011-12-01

We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.

Deformation of a geo-medium with considering for internal self-balancing stresses

NASA Astrophysics Data System (ADS)

Lavrikov, S. V.; Revuzhenko, A. F.

2016-11-01

Based on the general concept of rock as a medium with inner sources and sinks of energy, the authors consider an approach to mathematical modeling of a geo-medium with account for internal self-balancing stresses. The description of stresses and strains at the level of microstructural elements and macrovolume of the medium uses methods of non-Archimedean analysis. The model allows describing the accumulation of elastic energy in the form of internal self-balancing stresses. A finite element algorithm and a software program for solving plane boundary-value problems have been developed. The calculated data on rock specimen compression are given. It is shown that the behavior of plastic deformation zones depends on the pre-assigned initial microstresses.

Impact of composite plates: Analysis of stresses and forces

NASA Technical Reports Server (NTRS)

Moon, F. C.; Kim, B. S.; Fang-Landau, S. R.

1976-01-01

The foreign object damage resistance of composite fan blades was studied. Edge impact stresses in an anisotropic plate were first calculated incorporating a constrained layer damping model. It is shown that a very thin damping layer can dramatically decrease the maximum normal impact stresses. A multilayer model of a composite plate is then presented which allows computation of the interlaminar normal and shear stresses. Results are presented for the stresses due to a line impact load normal to the plane of a composite plate. It is shown that significant interlaminar tensile stresses can develop during impact. A computer code was developed for this problem using the fast Fourier transform. A marker and cell computer code were also used to investigate the hydrodynamic impact of a fluid slug against a wall or turbine blade. Application of fluid modeling of bird impact is reviewed.

Buckling of graded coatings: A continuum model

NASA Astrophysics Data System (ADS)

Chiu, Tz-Cheng

2000-12-01

Requirements for the protection of hot section components in many high temperature applications such as earth-to-orbit winged planes and advanced turbine systems have led to the application of thermal barrier coatings (TBCs) that utilize ceramic coatings on metal substrates. An alternative concept to homogeneous ceramic coatings is the functionally graded materials (FGM) in which the composition of the coating is intentionally graded to improve the bonding strength and to reduce the magnitude of the residual and thermal stresses. A widely observed failure mode in such layered systems is known to be interface cracking that leads to spallation fracture. In most cases, the final stage of the failure process for a thin coating appears to be due to buckling instability under thermally or mechanically induced compressive stress. The objective of this study is to develop a solution to the buckling instability problem by using continuum elasticity rather than a structural mechanics approach. The emphasis in the solution will be on the investigation of the effect of material inhomogeneity in graded coatings on the instability load, the postbuckling behavior, and fracture mechanics parameters such as the stress intensity factors and strain energy release rate. In this analysis, a nonlinear continuum theory is employed to examine the interface crack problem. The analytical solution of the instability problem permits the study of the effect of material inhomogeneity upon the inception of buckling and establishes benchmark results for the numerical solutions of related problems. To study the postbuckling behavior and to calculate the stress intensity factors and strain energy release rate a geometrically nonlinear finite element procedure with enriched crack-tip element is developed. Both plane strain and axisymmetric interface crack problems in TBCs with either homogeneous or graded coating are then considered by using the finite element procedure. It is assumed that the applied load is a uniform temperature drop. Comparison of the results with that obtained from the plate approximation shows that because of the higher constraints the plate theory predicts greater instability strains and lower strain energy release rates. It is also observed that compared with a homogeneous coating the graded coating gives lower strain energy release rate because of the lower thermal residual stress and higher bending stiffness. (Abstract shortened by UMI.)

Surface cracks in a plate of finite width under extension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Stress concentration investigations using NASTRAN

NASA Technical Reports Server (NTRS)

Gillcrist, M. C.; Parnell, L. A.

1986-01-01

Parametic investigations are performed using several two dimensional finite element formulations to determine their suitability for use in predicting extremum stresses in marine propellers. Comparisons are made of two NASTRAN elements (CTRIM6 and CTRAIA2) wherein elasticity properties have been modified to yield plane strain results. The accuracy of the elements is investigated by comparing finite element stress predictions with experimentally determined stresses in two classical cases: (1) tension in a flat plate with a circular hole; and (2) a filleted flat bar subjected to in-plane bending. The CTRIA2 element is found to provide good results. The displacement field from a three dimensional finite element model of a representative marine propeller is used as the boundary condition for the two dimensional plane strain investigations of stresses in the propeller blade and fillet. Stress predictions from the three dimensional analysis are compared with those from the two dimensional models. The validity of the plane strain modifications to the NASTRAN element is checked by comparing the modified CTRIA2 element stress predictions with those of the ABAQUS plane strain element, CPE4.

Toward Effective Shell Modeling of Wrinkled Thin-Film Membranes Exhibiting Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2004-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns. An element-level, strain-energy density criterion is suggested for facilitating automated, adaptive mesh refinements specifically aimed at the modeling of thin-film membranes undergoing wrinkling deformations.

Evaluation of an improved finite-element thermal stress calculation technique

NASA Technical Reports Server (NTRS)

Camarda, C. J.

1982-01-01

A procedure for generating accurate thermal stresses with coarse finite element grids (Ojalvo's method) is described. The procedure is based on the observation that for linear thermoelastic problems, the thermal stresses may be envisioned as being composed of two contributions; the first due to the strains in the structure which depend on the integral of the temperature distribution over the finite element and the second due to the local variation of the temperature in the element. The first contribution can be accurately predicted with a coarse finite-element mesh. The resulting strain distribution can then be combined via the constitutive relations with detailed temperatures from a separate thermal analysis. The result is accurate thermal stresses from coarse finite element structural models even where the temperature distributions have sharp variations. The range of applicability of the method for various classes of thermostructural problems such as in-plane or bending type problems and the effect of the nature of the temperature distribution and edge constraints are addressed. Ojalvo's method is used in conjunction with the SPAR finite element program. Results are obtained for rods, membranes, a box beam and a stiffened panel.

A thermoelastic transversely isotropic thick walled cylinder/disk application: An analytical solution and study

NASA Technical Reports Server (NTRS)

Arnold, S. M.

1989-01-01

A continuum theory is utilized to represent the thermoelastic behavior of a thick walled composite cylinder that can be idealized as transversely isotropic. A multiaxial statement of the constitutive theory employed is presented, as well as the out of the plane of isotropy, plane stress, and plane strain reductions. The derived analytical solution presented is valid for a cylindrical tube or thin disk with a concentric hole, subjected to internal and/or external pressure and a general radial temperature distribution. A specific problem examined is that of a thick walled cylinder subjected to an internal and external pressure loading and a linear radial temperature distribution. The results are expressed in nondimensional form and the effects on the response behavior are examined for various material properties, fiber orientation and types of loadings.

A penny-shaped crack in a filament-reinforced matrix. I - The filament model. II - The crack problem

NASA Technical Reports Server (NTRS)

Erdogan, F.; Pacella, A. H.

1974-01-01

The study deals with the elastostatic problem of a penny-shaped crack in an elastic matrix which is reinforced by filaments or fibers perpendicular to the plane of the crack. An elastic filament model is first developed, followed by consideration of the application of the model to the penny-shaped crack problem in which the filaments of finite length are asymmetrically distributed around the crack. Since the primary interest is in the application of the results to studies relating to the fracture of fiber or filament-reinforced composites and reinforced concrete, the main emphasis of the study is on the evaluation of the stress intensity factor along the periphery of the crack, the stresses in the filaments or fibers, and the interface shear between the matrix and the filaments or fibers. Using the filament model developed, the elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix is formulated.

Stress intensity factors and COD in an orthotropic strip

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1980-01-01

The elasticity problem for an orthotropic strip or a beam with an internal or an edge crack under general loading conditions is considered. The numerical results are given for four basic loading conditions, namely, uniform tension, pure bending, three point bending, and concentrated surface shear loading. For the strip with an edge crack additional results regarding the crack opening displacements are obtained by using the plastic strip model. A critical quantity which is tabulated is the maximum compressive stress in the plane of the crack. It is shown that this stress may easily exceed the yield limit in compression and hence may severely limit the range of application of the plasticity results.

Refraction of the principal stress trajectories and the stress jumps on faults and contact surfaces: Part 1. Non-constrained regular trajectories

NASA Astrophysics Data System (ADS)

Mukhamediev, Sh. A.

2014-09-01

Rock masses contain ubiquitous multiscale heterogeneities, which (or whose boundaries) serve as the surfaces of discontinuity for some characteristics of the stress state, e.g., for the orientation of principal stress axes. Revealing the regularities that control these discontinuities is a key to understanding the processes taking place at the boundaries of the heterogeneities and for designing the correct procedures for reconstructing and theoretical modeling of tectonic stresses. In the present study, the local laws describing the refraction of the axes of extreme principal stresses T 1 (maximal tension in the deviatoric sense) and T 3 (maximal compression) of the Cauchy stress tensor at the transition over the elementary area n of discontinuity whose orientation is specified by the unit normal n are derived. It is assumed that on the area n of discontinuity, frictional contact takes place. No hypotheses are made on the constitutive equations, and a priori constraints are not posed on the orientation on the stress axes. Two domains, which adjoin area n on the opposite sides and are conventionally marked + and -, are distinguished. In the case of the two-dimensional (2D) stress state, any principal stress axis on passing from domain - to domain + remains in the same quadrant of the plane as the continuation of this axis in domain +. The sign and size of the refraction angle depend on the sign and amplitude of the jump of the normal stress, which is tangential to the surface of discontinuity. In the three-dimensional (3D) case, the refraction of axes T 1 and T 3 should be analyzed simultaneously. For each side, + and -, the projections of the T 1 and T 3 axes on the generally oriented plane n form the shear sectors S + and S -, which are determined unambiguously and to whose angular domains the possible directions p + and p - of the shear stress vectors belong. In order for the extreme stress axes T {1/+}, T {3/+} and T {1/-}, T {3/-} to be statically compatible on the generally oriented plane n, it is required that sectors S + and S - had a nonempty intersection. The direction vectors p + and p - are determined uniquely if, besides axes T {1/-}, T {3/-} and T {1/+}, T {3/+}, also the ratios of differential stresses R + and R - (0 ≤ R ± ≤ 1) are known. This is equivalent to specifying the reduced stress tensors T {/R +} and T {/R -} The necessary condition for tensors T {/R +} and T {/R -} being statically compatible on plane n is the equality p + = p -. In this paper, simple methods are suggested for solving the inverse problem of constructing the set of the orientations of the extreme stress axes from the known direction p of the shear stress vector on plane n and from the data on the shear sector. Based on these methods and using the necessary conditions of local equilibrium on plane n formulated above, all the possible orientations of axes T {1/+}, T {3/+} are determined if the projections of axes T {1/-}, T {3/-} axes on side — are given. The angle between the projections of axes T {1/+}, T {1/-} and/or T {3/+}, T {3/-} on the plane can attain 90°. Besides the general case, also the particular cases of the contact between the degenerate stress states and the special position of plane n relative to the principal stress axes are thoroughly examined. Generalization of the obtained results makes it possible to plot the local diagram of the orientations of axes T {1/+}, T {3/+} for a given sector S -. This diagram is a so-called stress orientation sphere, which is subdivided into three pairs of areas (compression, tension, and compression-extension). The tension and compression zones cannot contain the poles of T {3/+} and T {1/+} axes, respectively. The compression-extension zones can contain the poles of either T {1/+} or T {3/+} axis but not both poles simultaneously. In the particular case when the shear stress vector has a unique direction p - on side -, the areas of compression-extension disappear and the diagram is reduced to a beach-ball plot, which visualizes the focal mechanism solution of an earthquake. If area n is a generally oriented plane and if the orientation of the pairs of the statically compatible axes T {1/-}, T {3/-} and T {1/+}, T {3/+} is specified, then, the stress values on side + are uniquely determined from the known stress values on side -. From the value of differential stress ratio R -, one can calculate the value of R +, and using the values of the principal stresses on side -, determine the total stress tensor T + on side +. The obtained results are supported by the laboratory experiments and drilling data. In particular, these results disclose the drawbacks of some established notions and methods in which the possible refraction of the stress axes is unreasonably ignored or taken into account improperly. For example, it is generally misleading to associate the slip on the preexisting fault with the orientation of any particular trihedron of the principal stress axes. The reconstruction should address the potentially statically compatible principal stress axes, which are differently oriented on opposite sides of the fault plane. The fact that, based on the orientation of the intraplate principal stresses at the base of the lithosphere, one cannot make a conclusion on the active or passive influence of the mantle flows on the lithospheric plate motion is another example. The present relationships linking the stress values on the opposite sides of the fault plane on which the orientations of the principal stress axes are known demonstrate the incorrectness of the existing methods, in which the reduced stress tensors within the material domains are reconstructed without allowance for the dynamic interaction of these domains with their neighbors. In addition, using the obtained results, one can generalize the notion of the zone of dynamical control of a fault onto the case of the existence of discontinuities in this region and analyze the stress transfer across the system of the faults.

Transverse shear effects on the stress-intensity factor for a circumferentially cracked, specially orthotropic cylindrical shell

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1977-01-01

The problem of a cylindrical shell containing a circumferential through crack is considered by taking into account the effect of transverse shear deformations. The formulation is given for a specially orthotropic material within the confines of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions regarding moment and stress resultants on the crack surface. Consequently, aside from multiplicative constants representing the stress intensity factors, the membrane and bending components of the asymptotic stress fields near the crack tip are found to be identical. The stress intensity factors are calculated separately for a cylinder under a uniform membrane load, and that under a uniform bending moment. Sample results showing the nature of the out-of-plane crack surface displacement and the effect of the Poisson's ratio are presented.

Mode I analysis of a cracked circular disk subject to a couple and a force

NASA Technical Reports Server (NTRS)

Gross, B.

1977-01-01

Mode 1 stress intensity coefficients were obtained for an edge-cracked disk (round compact specimen). Results for this plane elastostatic problem, obtained by a boundary collocation analysis are presented for ratios 0.35 less than A/D less than 1, where A is the crack length and D is the disk diameter. The results presented are for two complementary types of loading. By superposition of these results the stress intensity factor K sub I for any practical load line location of a pin-loaded round compact specimen can be obtained.

Contact problem for a composite material with nacre inspired microstructure

NASA Astrophysics Data System (ADS)

Berinskii, Igor; Ryvkin, Michael; Aboudi, Jacob

2017-12-01

Bi-material composites with nacre inspired brick and mortar microstructures, characterized by stiff elements of one phase with high aspect ratio separated by thin layers of the second one, are considered. Such microstructure is proved to provide an efficient solution for the problem of a crack arrest. However, contrary to the case of a homogeneous material, an external pressure, applied to a part of the composite boundary, can cause significant tensile stresses which increase the danger of crack nucleation. Investigation of the influence of microstructure parameters on the magnitude of tensile stresses is performed by means of the classical Flamant-like problem of an orthotropic half-plane subjected to a normal external distributed loading. Adequate analysis of this problem represents a serious computational task due to the geometry of the considered layout and the high contrast between the composite constituents. This difficulty is presently circumvented by deriving a micro-to-macro analysis in the framework of which an analytical solution of the auxiliary elasticity problem, followed by the discrete Fourier transform and the higher-order theory are employed. As a result, full scale continuum modeling of both composite constituents without employing any simplifying assumptions is presented. In the framework of the present proposed modeling, the influence of stiff elements aspect ratio on the overall stress distribution is demonstrated.

Effective one-dimensional approach to the source reconstruction problem of three-dimensional inverse optoacoustics

NASA Astrophysics Data System (ADS)

Stritzel, J.; Melchert, O.; Wollweber, M.; Roth, B.

2017-09-01

The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.

Study of the mechanical behavior of a 2-D carbon-carbon composite

NASA Technical Reports Server (NTRS)

Avery, W. B.; Herakovich, C. T.

1987-01-01

The out-of-plane fracture of a 2-D carbon-carbon composite was observed and characterized to gain an understanding of the factors influencing the stress distribution in such a laminate. Finite element analyses of a two-ply carbon-carbon composite under in-plane, out-of-plane, and thermal loading were performed. Under in-plane loading all components of stress were strong functions of geometry. Additionally, large thermal stresses were predicted. Out-of-plane tensile tests revealed that failure was interlaminar, and that cracks propagated along the fiber-matrix interface. An elasticity solution was utilized to analyze an orthotropic fiber in an isotropic matrix under uniform thermal load. The analysis reveals that the stress distributions in a transversely orthotropic fiber are radically different than those predicted assuming the fiber to be transversely isotropic.

Subsurface Stress Fields in FCC Single Crystal Anisotropic Contacts

NASA Technical Reports Server (NTRS)

Arakere, Nagaraj K.; Knudsen, Erik; Swanson, Gregory R.; Duke, Gregory; Ham-Battista, Gilda

2004-01-01

Single crystal superalloy turbine blades used in high pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes, and non-crystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two and three dimensional subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii. Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis (FEA). Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single crystal contact problems require extremely refined three-dimensional (3-D) finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses (RSS) on the principal slip planes also involves considerable post-processing work. For these reasons it is very advantageous to develop analytical solution schemes for subsurface stresses, whenever possible.

A constitutive framework for modelling thin incompressible viscoelastic materials under plane stress in the finite strain regime

NASA Astrophysics Data System (ADS)

Kroon, M.

2011-11-01

Rubbers and soft biological tissues may undergo large deformations and are also viscoelastic. The formulation of constitutive models for these materials poses special challenges. In several applications, especially in biomechanics, these materials are also relatively thin, implying that in-plane stresses dominate and that plane stress may therefore be assumed. In the present paper, a constitutive model for viscoelastic materials in the finite strain regime and under the assumption of plane stress is proposed. It is assumed that the relaxation behaviour in the direction of plane stress can be treated separately, which makes it possible to formulate evolution laws for the plastic strains on explicit form at the same time as incompressibility is fulfilled. Experimental results from biomechanics (dynamic inflation of dog aorta) and rubber mechanics (biaxial stretching of rubber sheets) were used to assess the proposed model. The assessment clearly indicates that the model is fully able to predict the experimental outcome for these types of material.

On the origin of diverse aftershock mechanisms following the 1989 Loma Prieta earthquake

USGS Publications Warehouse

Kilb, Debi; Ellis, M.; Gomberg, J.; Davis, S.

1997-01-01

We test the hypothesis that the origin of the diverse suite of aftershock mechanisms following the 1989 M 7.1 Loma Prieta, California, earthquake is related to the post-main-shock static stress field. We use a 3-D boundary-element algorithm to calculate static stresses, combined with a Coulomb failure criterion to calculate conjugate failure planes at aftershock locations. The post-main-shock static stress field is taken as the sum of a pre-existing stress field and changes in stress due to the heterogeneous slip across the Loma Prieta rupture plane. The background stress field is assumed to be either a simple shear parallel to the regional trend of the San Andreas fault or approximately fault-normal compression. A suite of synthetic aftershock mechanisms from the conjugate failure planes is generated and quantitatively compared (allowing for uncertainties in both mechanism parameters and earthquake locations) to well-constrained mechanisms reported in the US Geological Survey Northern California Seismic Network catalogue. We also compare calculated rakes with those observed by resolving the calculated stress tensor onto observed focal mechanism nodal planes, assuming either plane to be a likely rupture plane. Various permutations of the assumed background stress field, frictional coefficients of aftershock fault planes, methods of comparisons, etc. explain between 52 and 92 per cent of the aftershock mechanisms. We can explain a similar proportion of mechanisms however by comparing a randomly reordered catalogue with the various suites of synthetic aftershocks. The inability to duplicate aftershock mechanisms reliably on a one-to-one basis is probably a function of the combined uncertainties in models of main-shock slip distribution, the background stress field, and aftershock locations. In particular we show theoretically that any specific main-shock slip distribution and a reasonable background stress field are able to generate a highly variable suite of failure planes such that quite different aftershock mechanisms may be expected to occur within a kilometre or less of each other. This scale of variability is less than the probable location error of aftershock earthquakes in the Loma Prieta region. We successfully duplicate a measure of the variability in the mechanisms of the entire suite of aftershocks. If static stress changes are responsible for the generation of aftershock mechanisms, we are able to place quantitative constraints on the level of stress that must have existed in the upper crust prior to the Loma Prieta rupture. This stress level appears to be too low to generate the average slip across the main-shock rupture plane. Possible reasons for this result range from incorrect initial assumptions of homogeneity in the background stress field, friction and fault geometry to driving stresses that arise from deeper in the crust or upper mantle. Alternatively, aftershock focal mechanisms may be determined by processes other than, or in addition to, static stress changes, such as pore-pressure changes or dynamic stresses.

Zipping, entanglement, and the elastic modulus of aligned single-walled carbon nanotube films

PubMed Central

Won, Yoonjin; Gao, Yuan; Panzer, Matthew A.; Xiang, Rong; Maruyama, Shigeo; Kenny, Thomas W.; Cai, Wei; Goodson, Kenneth E.

2013-01-01

Reliably routing heat to and from conversion materials is a daunting challenge for a variety of innovative energy technologies––from thermal solar to automotive waste heat recovery systems––whose efficiencies degrade due to massive thermomechanical stresses at interfaces. This problem may soon be addressed by adhesives based on vertically aligned carbon nanotubes, which promise the revolutionary combination of high through-plane thermal conductivity and vanishing in-plane mechanical stiffness. Here, we report the data for the in-plane modulus of aligned single-walled carbon nanotube films using a microfabricated resonator method. Molecular simulations and electron microscopy identify the nanoscale mechanisms responsible for this property. The zipping and unzipping of adjacent nanotubes and the degree of alignment and entanglement are shown to govern the spatially varying local modulus, thereby providing the route to engineered materials with outstanding combinations of mechanical and thermal properties. PMID:24309375

On the determination of stress fields and displacements in a thin elastoplastic plate containing elastic inclusion - a shim

NASA Astrophysics Data System (ADS)

Kovalev, A. V.; Rusina, E. Y.; Yakovlev, A. Y.

2018-03-01

The paper is devoted to the determination of the stress-strain state of a mechanical structure, which consists of a thin infinite elastoplastic plate with a hole and a continuous fine elastic inclusion. The complexity of this problem lies in the fact that the shape of the boundary between the elastic and plastic zones in the plate is not known in advance. The small parameter method is used as the solution method, while the small parameter characterizes the deviation of the shape of the contour from the circle and the perturbation of external static boundary conditions. As the zero solution, the axisymmetric elastoplastic state of the plate with inclusion is chosen. Two variants of inclusion fixation in a plate are considered: inclusion is enclosed with tension or soldered. As a result of solving the problem within the framework of ideal plasticity, the distribution of the stress and displacement fields and the shape of the elastoplastic boundary are obtained. To illustrate the case of a plane-stressed state, the results of a numerical experiment on the mathematical model obtained are presented.

Low-stress doped ultrananocrystalline diamond

DOEpatents

Sumant, Anirudha V.; Buja, Federico; van Spengen, Willem Merlijn

2016-10-25

Nanocrystalline diamond coatings exhibit stress in nano/micro-electro mechanical systems (MEMS). Doped nanocrstalline diamond coatings exhibit increased stress. A carbide forming metal coating reduces the in-plane stress. In addition, without any metal coating, simply growing UNCD or NCD with thickness in the range of 3-4 micron also reduces in-plane stress significantly. Such coatings can be used in MEMS applications.

ZIP2DL: An Elastic-Plastic, Large-Rotation Finite-Element Stress Analysis and Crack-Growth Simulation Program

NASA Technical Reports Server (NTRS)

Deng, Xiaomin; Newman, James C., Jr.

1997-01-01

ZIP2DL is a two-dimensional, elastic-plastic finte element program for stress analysis and crack growth simulations, developed for the NASA Langley Research Center. It has many of the salient features of the ZIP2D program. For example, ZIP2DL contains five material models (linearly elastic, elastic-perfectly plastic, power-law hardening, linear hardening, and multi-linear hardening models), and it can simulate mixed-mode crack growth for prescribed crack growth paths under plane stress, plane strain and mixed state of stress conditions. Further, as an extension of ZIP2D, it also includes a number of new capabilities. The large-deformation kinematics in ZIP2DL will allow it to handle elastic problems with large strains and large rotations, and elastic-plastic problems with small strains and large rotations. Loading conditions in terms of surface traction, concentrated load, and nodal displacement can be applied with a default linear time dependence or they can be programmed according to a user-defined time dependence through a user subroutine. The restart capability of ZIP2DL will make it possible to stop the execution of the program at any time, analyze the results and/or modify execution options and resume and continue the execution of the program. This report includes three sectons: a theoretical manual section, a user manual section, and an example manual secton. In the theoretical secton, the mathematics behind the various aspects of the program are concisely outlined. In the user manual section, a line-by-line explanation of the input data is given. In the example manual secton, three types of examples are presented to demonstrate the accuracy and illustrate the use of this program.

SASS-1--SUBASSEMBLY STRESS SURVEY CODE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Friedrich, C.M.

1960-01-01

SASS-1, an IBM-704 FORTRAN code, calculates pressure, thermal, and combined stresses in a nuclear reactor core subassembly. In addition to cross- section stresses, the code calculates axial shear stresses needed to keep plane cross sections plane under axial variations of temperature. The input and output nomenclature, arrangement, and formats are described. (B.O.G.)

Thermo-viscoelastic analysis of composite materials, volume 1

NASA Technical Reports Server (NTRS)

Lin, K. Y.; Hwang, I. H.

1988-01-01

Advanced composite materials, especially graphite/epoxy, are being applied to aircraft structures in order to improve performance and save weight. An important consideration in composite design is the residual strength of a structure containing holes, delaminations, or interlaminar damage when subjected to compressive loads. Recent studies have revealed the importance of viscoelastic effects in polymer-based composites. The viscoelastic effect is particularly significant at elevated temperature/moisture conditions since the matrix material is strongly affected by the environment. The solution of viscoelastic problems in composites was limited to special cases which can be solved by classical lamination theory. A finite element procedure is presented for calculating time-dependent stresses and strains in composite structures with general configurations and complicated boundary conditions. Using this procedure the in-plane and interlaminar stress distributions and histories in notched and unnotched composites were obtained for mechanical and thermal loads. Both two-dimensional and three-dimensional viscoelastic problems are analyzed. The effects of layup orientation and load spectrum on creep response and stress relaxation were also studied.

Lithospheric flexure under the Hawaiian volcanic load: Internal stresses and a broken plate revealed by earthquakes

NASA Astrophysics Data System (ADS)

Klein, Fred W.

2016-04-01

Several lines of earthquake evidence indicate that the lithospheric plate is broken under the load of the island of Hawai`i, where the geometry of the lithosphere is circular with a central depression. The plate bends concave downward surrounding a stress-free hole, rather than bending concave upward as with past assumptions. Earthquake focal mechanisms show that the center of load stress and the weak hole is between the summits of Mauna Loa and Mauna Kea where the load is greatest. The earthquake gap at 21 km depth coincides with the predicted neutral plane of flexure where horizontal stress changes sign. Focal mechanism P axes below the neutral plane display a striking radial pattern pointing to the stress center. Earthquakes above the neutral plane in the north part of the island have opposite stress patterns; T axes tend to be radial. The M6.2 Honomu and M6.7 Kiholo main shocks (both at 39 km depth) are below the neutral plane and show radial compression, and the M6.0 Kiholo aftershock above the neutral plane has tangential compression. Earthquakes deeper than 20 km define a donut of seismicity around the stress center where flexural bending is a maximum. The hole is interpreted as the soft center where the lithospheric plate is broken. Kilauea's deep conduit is seismically active because it is in the ring of maximum bending. A simplified two-dimensional stress model for a bending slab with a load at one end yields stress orientations that agree with earthquake stress axes and radial P axes below the neutral plane. A previous inversion of deep Hawaiian focal mechanisms found a circular solution around the stress center that agrees with the model. For horizontal faults, the shear stress within the bending slab matches the slip in the deep Kilauea seismic zone and enhances outward slip of active flanks.

Lithospheric flexure under the Hawaiian volcanic load: Internal stresses and a broken plate revealed by earthquakes

USGS Publications Warehouse

Klein, Fred W.

2016-01-01

Several lines of earthquake evidence indicate that the lithospheric plate is broken under the load of the island of Hawai`i, where the geometry of the lithosphere is circular with a central depression. The plate bends concave downward surrounding a stress-free hole, rather than bending concave upward as with past assumptions. Earthquake focal mechanisms show that the center of load stress and the weak hole is between the summits of Mauna Loa and Mauna Kea where the load is greatest. The earthquake gap at 21 km depth coincides with the predicted neutral plane of flexure where horizontal stress changes sign. Focal mechanism P axes below the neutral plane display a striking radial pattern pointing to the stress center. Earthquakes above the neutral plane in the north part of the island have opposite stress patterns; T axes tend to be radial. The M6.2 Honomu and M6.7 Kiholo main shocks (both at 39 km depth) are below the neutral plane and show radial compression, and the M6.0 Kiholo aftershock above the neutral plane has tangential compression. Earthquakes deeper than 20 km define a donut of seismicity around the stress center where flexural bending is a maximum. The hole is interpreted as the soft center where the lithospheric plate is broken. Kilauea's deep conduit is seismically active because it is in the ring of maximum bending. A simplified two-dimensional stress model for a bending slab with a load at one end yields stress orientations that agree with earthquake stress axes and radial P axes below the neutral plane. A previous inversion of deep Hawaiian focal mechanisms found a circular solution around the stress center that agrees with the model. For horizontal faults, the shear stress within the bending slab matches the slip in the deep Kilauea seismic zone and enhances outward slip of active flanks.

Simulating and Synthesizing Substructures Using Neural Network and Genetic Algorithms

NASA Technical Reports Server (NTRS)

Liu, Youhua; Kapania, Rakesh K.; VanLandingham, Hugh F.

1997-01-01

The feasibility of simulating and synthesizing substructures by computational neural network models is illustrated by investigating a statically indeterminate beam, using both a 1-D and a 2-D plane stress modelling. The beam can be decomposed into two cantilevers with free-end loads. By training neural networks to simulate the cantilever responses to different loads, the original beam problem can be solved as a match-up between two subsystems under compatible interface conditions. The genetic algorithms are successfully used to solve the match-up problem. Simulated results are found in good agreement with the analytical or FEM solutions.

Elasticity Solution of an Adhesively Bonded Cover Plate of Various Geometries

NASA Technical Reports Server (NTRS)

Aksel, G. N.; Erdogan, F.

1985-01-01

The plane strain of adhesively bonded structures consisting of two different isotropic adherends is considered. By expressing the x-y components of the displacements in terms of Fourier integrals and using the corresponding boundary and continuity conditions, the integral equations for the general problem are obtained and solved numerically by applying Gauss-Chebyshev integration scheme. The shear and the normal stresses in the adhesive are calculated for various geometries and material properties for a stiffened plate under uniaxial tension. Numerical results involving the stress intensity factors and the strain energy release rate are presented. The closed-form expressions for the Fredholm kernels are provided to obtain the solution for an arbitrary geometry and material properties. For the general geometry, the contribution of the normal stress is quite significant, while for symmetric geometries, the shear stress is dominant, the normal stress vanishes if the adherends are of the same material and the same thickness.

Discrete shear-transformation-zone plasticity modeling of notched bars

NASA Astrophysics Data System (ADS)

Kondori, Babak; Amine Benzerga, A.; Needleman, Alan

2018-02-01

Plane strain tension analyses of un-notched and notched bars are carried out using discrete shear transformation zone plasticity. In this framework, the carriers of plastic deformation are shear transformation zones (STZs) which are modeled as Eshelby inclusions. Superposition is used to represent a boundary value problem solution in terms of discretely modeled Eshelby inclusions, given analytically for an infinite elastic medium, and an image solution that enforces the prescribed boundary conditions. The image problem is a standard linear elastic boundary value problem that is solved by the finite element method. Potential STZ activation sites are randomly distributed in the bars and constitutive relations are specified for their evolution. Results are presented for un-notched bars, for bars with blunt notches and for bars with sharp notches. The computed stress-strain curves are serrated with the magnitude of the associated stress-drops depending on bar size, notch acuity and STZ evolution. Cooperative deformation bands (shear bands) emerge upon straining and, in some cases, high stress levels occur within the bands. Effects of specimen geometry and size on the stress-strain curves are explored. Depending on STZ kinetics, notch strengthening, notch insensitivity or notch weakening are obtained. The analyses provide a rationale for some conflicting findings regarding notch effects on the mechanical response of metallic glasses.

Aseismic Slip of a Thin Slab Due to a Fluid Source

NASA Astrophysics Data System (ADS)

Aubin, P. W.; Viesca, R. C.

2017-12-01

We explore the effects of an increase of pore pressure on the frictional interface along the base of a thin slab. The thin slab approximation corresponds to a layer overriding a substrate in which variations along the layer's length occur over distances much greater than the layer thickness. We consider deformation that may be in-plane or anti-plane, but approximately uniform in depth, such that spatial variations of displacement (and hence, slip) occur only along one direction parallel to the interface. Such a thin-sheet model may well represent the deformation of landslides and glacial ice streams, and also serves as a first-pass for fault systems, which, while better represented by elastic half-spaces in frictional contact, nonetheless show qualitatively similar behavior. We consider that the friction coefficient at the layer's interface remains (approximately) constant, and that aseismic slip is initiated by a (line) source of fluid at constant pressure, with one-dimensional diffusion parallel to the interface. As posed, the problem yields a self-similar expansion of slip, whose extent grows proportionally to (α * t)^(1/2) (where α is the hydraulic diffusivity) and can either lag behind or outpace the fluid diffusion front. The problem is controlled by a single parameter, accounting for the friction coefficient and the initial (pre-injection) states of stress and pore pressure. The problem solution consists of the self-similar slip profile and the coefficient of proportionality for the crack-front motion. Within the problem parameter range, two end-member scenarios result: one in which the initial level of shear stress on the interface is close to the value of the pre-injection strength (critically stressed) or another in which fluid pressure is just enough to induce slip (marginally pressurized). For the critically stressed and marginally pressurized cases, the aseismic slip front lies far ahead or far behind, respectively, the fluid diffusion front. We find closed-form solutions for both end-members, and in the former case, via matched asymptotics. These solutions provide a basis to solve the general problem, which we also solve numerically for comparison. The solutions also provide a starting point for examining the progression of slip and locking following the shutoff of the fluid source.

Determination of Stress Coefficient Terms in Cracked Solids for Monoclinic Materials with Plane Symmetry at x3 = 0

NASA Technical Reports Server (NTRS)

Yuan, F. G.

1998-01-01

Determination of all the coefficients in the crack tip field expansion for monoclinic materials under two-dimensional deformation is presented in this report. For monoclinic materials with a plane of material symmetry at x(sub 3) = 0, the in-plane deformation is decoupled from the anti-plane deformation. In the case of in-plane deformation, utilizing conservation laws of elasticity and Betti's reciprocal theorem, together with selected auxiliary fields, T-stress and third-order stress coefficients near the crack tip are evaluated first from path-independent line integrals. To determine the T-stress terms using the J-integral and Betti's reciprocal work theorem, auxiliary fields under a concentrated force and moment acting at the crack tip are used respectively. Through the use of Stroh formalism in anisotropic elasticity, analytical expressions for all the coefficients including the stress intensity factors are derived in a compact form that has surprisingly simple structure in terms of the Barnett-Lothe tensors, L. The solution forms for degenerated materials, orthotropic, and isotropic materials are presented.

Scattering of SH wave by a semi-cylindrical salient near vertical interface in the bi-material half space

NASA Astrophysics Data System (ADS)

Qi, Hui; Zhang, Xi-meng

2017-10-01

With the aid of the Green function method and image method, the problem of scattering of SH-wave by a semi-cylindrical salient near vertical interface in bi-material half-space is considered to obtain its steady state response. Firstly, by the means of the image method, Green function which is the essential solution of displacement field is constructed to satisfy the stress-free condition on the horizontal boundary in a right-angle space including a semi-cylindrical salient and bearing a harmonic out-of-plane line source force at any point on the vertical boundary. Secondly, the bi-material is separated into two parts along the vertical interface, then unknown anti-plane forces are applied on the vertical interface, and according to the continuity condition, the first kind of Fredholm integral equations is established to determine unknown anti-plane forces by "the conjunction method", then the integral equations are reduced to the linear algebraic equations by effective truncation. Finally, the dynamic stress concentration factor (DSCF) around the edge of semi-cylindrical salient is calculated, and the influences of incident wave number, incident angle, effect of interface and different combination of material parameters, etc. on DSCF are discussed.

Torque Limits for Fasteners in Composites

NASA Technical Reports Server (NTRS)

Zhao, Yi

2002-01-01

The two major classes of laminate joints are bonded and bolted. Often the two classes are combined as bonded-bolted joints. Several characteristics of fiber reinforced composite materials render them more susceptible to joint problems than conventional metals. These characteristics include weakness in in-plane shear, transverse tension/compression, interlaminar shear, and bearing strength relative to the strength and stiffness in the fiber direction. Studies on bolted joints of composite materials have been focused on joining assembly subject to in-plane loads. Modes of failure under these loading conditions are net-tension failure, cleavage tension failure, shear-out failure, bearing failure, etc. Although the studies of torque load can be found in literature, they mainly discussed the effect of the torque load on in-plane strength. Existing methods for calculating torque limit for a mechanical fastener do not consider connecting members. The concern that a composite member could be crushed by a preload inspired the initiation of this study. The purpose is to develop a fundamental knowledge base on how to determine a torque limit when a composite member is taken into account. Two simplified analytical models were used: a stress failure analysis model based on maximum stress criterion, and a strain failure analysis model based on maximum strain criterion.

Stress-intensity factors for cracks emanating from the loaded fastener hole

NASA Technical Reports Server (NTRS)

Shivakumar, V.; Hsu, Y. C.

1977-01-01

Using a series approach and the Muskhelishvili formulation in the two-dimensional theory of elasticity, stress-intensity factors K are derived for problems in which cracks emanate radially from the boundary of an arbitrarily loaded internal circular hole in an infinite plate. Numerical values are obtained for K(I) and K(II) for radial cracks from a hole containing a loose-fitted pin or rivet that is pulled perpendicular to the crack direction in the plane of the plate. The method is a general one for determining K for a set of symmetrically emanating radial cracks for a variety of concentrated or distributed tractions on the circular hole.

COLLABORATIVE RESEARCH AND DEVELOPMENT (CR&D) Delivery Order 0060: Gradient Materials Morphology Modeling Support

DTIC Science & Technology

2007-08-01

antiplane eigenstrain . ASME Journal of Applied Mechanics (In press, to appear in the September issue). [4] Wang, X., Pan, E., Roy, A. K, 2007. Three...problem of a functionally graded plane with a circular inclusion under a uniform antiplane eigenstrain is investigated, where the shear modulus varies...strain and stress fields inside the circular inclusion under uniform antiplane eigenstrains are intrinsically nOliuniform. This phenomenon differs

Integrating Experimentation, Modeling, and Visualization Through Full-Field Methods (Preprint)

DTIC Science & Technology

2009-04-01

including fatigue, fatigue-crack growth, tribology , fracture toughness, Figure 1. Full-field, in-plane, maximum principal stress in a fully lamellar...studied, and 3) the correlation between 1) and 2). The emphases in this paper will be on the first and second areas, but the need for work in the third ...problems, concentrating on displacements rather than strains is appropriate for this work. The top figure shows the overall displacements, after rigid- body

Temperature effects on the deformation and fracture of Al-Li-Cu-In alloys

NASA Technical Reports Server (NTRS)

Wagner, John A.; Gangloff, Richard P.

1991-01-01

The crack initiation and growth fracture resistance of Al-Cu-Li and Al-Cu-Li-In alloys were characterized and optimized for cryogenic tank applications. Presently, the effects of stress state and temperature is being determined on the fracture toughness and fracture mechanisms of commercially available Vintage 3 2090-T81 and experimental 2090+In-T6. Precracked J-integral specimens of both alloys were tested at ambient and cryogenic temperatures in the plane stress and plane strain conditions. Considering ambient temperature, results showed that 2090-T81 exhibited the highest toughness in both plane strain and plane stress conditions. For the plane strain condition, reasonable crack initiation and growth toughness of 1090-T81 are associated with a significant amount of delamination and transgranular fracture. Plane stress toughnesses were higher and fracture was characterized by shear cracking with minimal delaminations. In comparisons, the fracture behavior of 2090+In-T6 is significantly degraded by subgrain boundary precipitation. Toughness is low and characterized by intersubgranular fracture with no delamination in the plane stress or plane strain conditions. Intersubgranular cracking is a low energy event which presumably occurs prior to the onset of slip band cracking. Copious grain boundary precipitation is atypical of commercially available 2090. At cryogenic temperatures, both alloys exhibit increased yield strength, toughness, and amount of delamination and shear cracking. The change in fracture mode of 2090+In-T6 from intersubgranular cracking at ambient temperature to a combination of intersubgranular cracking, shear cracking, and delamination at cryogenic temperature is the subject of further investigation.

Influence of basal-plane dislocation structures on expansion of single Shockley-type stacking faults in forward-current degradation of 4H-SiC p-i-n diodes

NASA Astrophysics Data System (ADS)

Hayashi, Shohei; Yamashita, Tamotsu; Senzaki, Junji; Miyazato, Masaki; Ryo, Mina; Miyajima, Masaaki; Kato, Tomohisa; Yonezawa, Yoshiyuki; Kojima, Kazutoshi; Okumura, Hajime

2018-04-01

The origin of expanded single Shockley-type stacking faults in forward-current degradation of 4H-SiC p-i-n diodes was investigated by the stress-current test. At a stress-current density lower than 25 A cm-2, triangular stacking faults were formed from basal-plane dislocations in the epitaxial layer. At a stress-current density higher than 350 A cm-2, both triangular and long-zone-shaped stacking faults were formed from basal-plane dislocations that converted into threading edge dislocations near the interface between the epitaxial layer and the substrate. In addition, the conversion depth of basal-plane dislocations that expanded into the stacking fault was inside the substrate deeper than the interface. These results indicate that the conversion depth of basal-plane dislocations strongly affects the threshold stress-current density at which the expansion of stacking faults occurs.

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

NASA Technical Reports Server (NTRS)

Chen, Q.; Liu, H. W.

1988-01-01

Fatigue crack growth tests were carried out on large-grain Al 7029 aluminum alloy and the finite element method was used to calculate the stress field near the tip of a zigzag crack. The resolved shear stresses on all 12 slip systems were computed, and the resolved shear stress intensity coefficient (RSSIC) was defined. The RSSIC was used to analyze the irregular crack path and was correlated with the rate of single-slip-plane shear crack growth. Fatigue crack growth was found to be caused primarily by shear decohesion at a crack tip. When the RSSIC on a single-slip system was much larger than all the others, the crack followed a single-slip plane. When the RSSICs on two conjugate slip systems were comparable, a crack grew in a zigzag manner on these planes and the macrocrack-plane bisected the two active slip planes. The maximum RSSIC on the most active slip system is proposed as a parameter to correlate with the shear fatigue crack growth rate in large crystals.

Some methodological aspects of tectonic stress reconstruction based on geological indicators

NASA Astrophysics Data System (ADS)

Sim, Lidiya A.

2012-03-01

The impact of the initial heterogeneity in rocks on the distribution of slickensides (slip planes), which are used to reconstruct local stress-state, is discussed. The stress-state was reconstructed by a graphic variant of the cinematic method. A new type of stress-state - Variation of Stress-State Type (VSST) - is introduced. The VSST is characterized by dislocation vectors originated both by uniaxial compression and uniaxial tension in the same rock volume, i.e. coefficient μσ = 1-2R varies from +1 to -1. The reasons for differences between slip planes from those predicted by the model are discussed. The distribution of slip planes depends on the stress-state type (μσ coefficient) and on the initial heterogeneity of the rocks. A criterion for the identification of tectonic stress rank is suggested. It is based on the models of tectonic stress distribution in the fracture vicinities. Examples of results of tectonic stress studies are given. Studies of tectonic stresses based on geological indicators are of methodological and practical importance.

FEM Modeling of In-Plane Stress Distribution in Thick Brittle Coatings/Films on Ductile Substrates Subjected to Tensile Stress to Determine Interfacial Strength.

PubMed

Wang, Kaishi; Zhang, Fangzhou; Bordia, Rajendra K

2018-03-27

The ceramic-metal interface is present in various material structures and devices that are vulnerable to failures, like cracking, which are typically due to their incompatible properties, e.g., thermal expansion mismatch. In failure of these multilayer systems, interfacial shear strength is a good measure of the robustness of interfaces, especially for planar films. There is a widely-used shear lag model and method by Agrawal and Raj to analyse and measure the interfacial shear strength of thin brittle film on ductile substrates. The use of this classical model for a type of polymer derived ceramic coatings (thickness ~18 μm) on steel substrate leads to high values of interfacial shear strength. Here, we present finite element simulations for such a coating system when it is subjected to in-plane tension. Results show that the in-plane stresses in the coating are non-uniform, i.e., varying across the thickness of the film. Therefore, they do not meet one of the basic assumptions of the classical model: uniform in-plane stress. Furthermore, effects of three significant parameters, film thickness, crack spacing, and Young's modulus, on the in-plane stress distribution have also been investigated. 'Thickness-averaged In-plane Stress' (TIS), a new failure criterion, is proposed for estimating the interfacial shear strength, which leads to a more realistic estimation of the tensile strength and interfacial shear strength of thick brittle films/coatings on ductile substrates.

Damage states in laminated composite three-point bend specimens: An experimental-analytical correlation study

NASA Technical Reports Server (NTRS)

Starbuck, J. Michael; Guerdal, Zafer; Pindera, Marek-Jerzy; Poe, Clarence C.

1990-01-01

Damage states in laminated composites were studied by considering the model problem of a laminated beam subjected to three-point bending. A combination of experimental and theoretical research techniques was used to correlate the experimental results with the analytical stress distributions. The analytical solution procedure was based on the stress formulation approach of the mathematical theory of elasticity. The solution procedure is capable of calculating the ply-level stresses and beam displacements for any laminated beam of finite length using the generalized plane deformation or plane stress state assumption. Prior to conducting the experimental phase, the results from preliminary analyses were examined. Significant effects in the ply-level stress distributions were seen depending on the fiber orientation, aspect ratio, and whether or not a grouped or interspersed stacking sequence was used. The experimental investigation was conducted to determine the different damage modes in laminated three-point bend specimens. The test matrix consisted of three-point bend specimens of 0 deg unidirectional, cross-ply, and quasi-isotropic stacking sequences. The dependence of the damage initiation loads and ultimate failure loads were studied, and their relation to damage susceptibility and damage tolerance of the mean configuration was discussed. Damage modes were identified by visual inspection of the damaged specimens using an optical microscope. The four fundamental damage mechanisms identified were delaminations, matrix cracking, fiber breakage, and crushing. The correlation study between the experimental results and the analytical results were performed for the midspan deflection, indentation, damage modes, and damage susceptibility.

Analysis of shear test method for composite laminates

NASA Technical Reports Server (NTRS)

Bergner, H. W., Jr.; Davis, J. G., Jr.; Herakovich, C. T.

1977-01-01

An elastic plane stress finite element analysis of the stress distributions in four flat test specimens for in-plane shear response of composite materials subjected to mechanical or thermal loads is presented. The shear test specimens investigated include: slotted coupon, cross beam, losipescu, and rail shear. Results are presented in the form of normalized shear contour plots for all three in-plane stess components. It is shown that the cross beam, losipescu, and rail shear specimens have stress distributions which are more than adequate for determining linear shear behavior of composite materials. Laminate properties, core effects, and fixture configurations are among the factors which were found to influence the stress distributions.

Crystallographic Orientation Identification in Multicrystalline Silicon Wafers Using NIR Transmission Intensity

NASA Astrophysics Data System (ADS)

Skenes, Kevin; Kumar, Arkadeep; Prasath, R. G. R.; Danyluk, Steven

2018-02-01

Near-infrared (NIR) polariscopy is a technique used for the non-destructive evaluation of the in-plane stresses in photovoltaic silicon wafers. Accurate evaluation of these stresses requires correct identification of the stress-optic coefficient, a material property which relates photoelastic parameters to physical stresses. The material stress-optic coefficient of silicon varies with crystallographic orientation. This variation poses a unique problem when measuring stresses in multicrystalline silicon (mc-Si) wafers. This paper concludes that the crystallographic orientation of silicon can be estimated by measuring the transmission of NIR light through the material. The transmission of NIR light through monocrystalline wafers of known orientation were compared with the transmission of NIR light through various grains in mc-Si wafers. X-ray diffraction was then used to verify the relationship by obtaining the crystallographic orientations of these assorted mc-Si grains. Variation of transmission intensity for different crystallographic orientations is further explained by using planar atomic density. The relationship between transmission intensity and planar atomic density appears to be linear.

Fiber-reinforced materials: finite elements for the treatment of the inextensibility constraint

NASA Astrophysics Data System (ADS)

Auricchio, Ferdinando; Scalet, Giulia; Wriggers, Peter

2017-12-01

The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.

Surface cracks in a plate of finite width under tension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

The problem of a finite plate containing collinear surface cracks is considered and solved by using the line spring model with plane elasticity and Reissner's plate theory. The main focus is on the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors in an effort to provide extensive numerical results which may be useful in applications. Some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks, and two corner cracks for wide range of relative dimensions. Particularly in corner cracks, the agreement with the finite element solution is surprisingly very good. The results are obtained for semi-elliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Synchrotron Radial X-ray Diffraction Studies of Deformation of Polycrystalline MgO

NASA Astrophysics Data System (ADS)

Girard, J.; Tsujino, N.; Mohiuddin, A.; Karato, S. I.

2016-12-01

X-ray diffraction analyses have been used for decades to study mechanical properties of polycrystalline samples during in-situ high-pressure deformation. When polycrystalline materials are deformed, stresses develop in grains and lead to lattice distortion. Using X-ray diffraction we can estimate the lattice strain for each (hkl) diffraction plans and calculate the applied stress for each (hkl), using [Singh, 1993] relation. However, this method doesn't take into account plastic anisotropy. As a results of plastic anisotropy present in the material, stress estimated from this method can be largely differ depending on (hkl) diffraction planes [Karato, 2009]. Studying the stress estimate for each (hkl) plane, might help us distinguish dominant deformation mechanisms activated during deformation such as diffusion (we will observe small stress variation as a function of (hkl) diffraction planes) or dislocation creep (we will observe a stress variation as a function of (hkl) diffraction planes that could also give us clues on potential slip system activity). In this study we observed stress evolution in MgO polycrystalline samples deformed under mantle pressure and temperature for (200) and (220) diffraction planes. Using a range MgO grain sizes we were able to control the active deformation mechanism (for e.g. diffusion creep or dislocation creep). For coarse-grained specimens, we observed strong (hkl) dependence of radial strain indicating the operation of dislocation creep. The observed (hkl) dependence changes with pressure suggesting a change in the slip system: at pressures higher than 27 GPa, (200) shows larger stress estimate than (220). In contrast, at lower pressures, (220) shows larger stress estimate than (200). This might indicate a slip system transition in MgO occurring under lower mantle conditions. From {110} plane to {100} plane. This is in good agreement with theoretical predictions and numerical calculation [Amodeo et al., 2012] and has an important implication for the interpretation of seismic anisotropy in the D" layer [Karato, 1998]. Amodeo, J., Carrey P., and P. Cordier (2012), Philosophical Magazine, 92(12). Karato, S-I. (1998), Earth and planets Space, 50, 1019-1028 Karato, S.-I. (2009), Physical Review. B, 79(21). Singh, A. K., (1993), Journal of Applied Physic, 73, 4278.

Determination of plane stress state using terahertz time-domain spectroscopy

PubMed Central

Wang, Zhiyong; Kang, Kai; Wang, Shibin; Li, Lin'an; Xu, Ningning; Han, Jiaguang; He, Mingxia; Wu, Liang; Zhang, Weili

2016-01-01

THz wave has been increasingly applied in engineering practice. One of its outstanding advantages is the penetrability through certain optically opaque materials, whose interior properties could be therefore obtained. In this report, we develop an experimental method to determine the plane stress state of optically opaque materials based on the stress-optical law using terahertz time-domain spectroscopy (THz-TDS). In this method, two polarizers are combined into the conventional THz-TDS system to sense and adjust the polarization state of THz waves and a theoretical model is established to describe the relationship between phase delay of the received THz wave and the plane stress applied on the specimen. Three stress parameters that represent the plane stress state are finally determined through an error function of THz wave phase-delay. Experiments were conducted on polytetrafluoroethylene (PTFE) specimen and a reasonably good agreement was found with measurement using traditional strain gauges. The presented results validate the effectiveness of the proposed method. The proposed method could be further used in nondestructive tests for a wide range of optically opaque materials. PMID:27824112

Determination of plane stress state using terahertz time-domain spectroscopy

NASA Astrophysics Data System (ADS)

Wang, Zhiyong; Kang, Kai; Wang, Shibin; Li, Lin'an; Xu, Ningning; Han, Jiaguang; He, Mingxia; Wu, Liang; Zhang, Weili

2016-11-01

THz wave has been increasingly applied in engineering practice. One of its outstanding advantages is the penetrability through certain optically opaque materials, whose interior properties could be therefore obtained. In this report, we develop an experimental method to determine the plane stress state of optically opaque materials based on the stress-optical law using terahertz time-domain spectroscopy (THz-TDS). In this method, two polarizers are combined into the conventional THz-TDS system to sense and adjust the polarization state of THz waves and a theoretical model is established to describe the relationship between phase delay of the received THz wave and the plane stress applied on the specimen. Three stress parameters that represent the plane stress state are finally determined through an error function of THz wave phase-delay. Experiments were conducted on polytetrafluoroethylene (PTFE) specimen and a reasonably good agreement was found with measurement using traditional strain gauges. The presented results validate the effectiveness of the proposed method. The proposed method could be further used in nondestructive tests for a wide range of optically opaque materials.

Improvement of the 2D/1D Method in MPACT Using the Sub-Plane Scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Graham, Aaron M; Collins, Benjamin S; Downar, Thomas

Oak Ridge National Laboratory and the University of Michigan are jointly developing the MPACTcode to be the primary neutron transport code for the Virtual Environment for Reactor Applications (VERA). To solve the transport equation, MPACT uses the 2D/1D method, which decomposes the problem into a stack of 2D planes that are then coupled with a 1D axial calculation. MPACT uses the Method of Characteristics for the 2D transport calculations and P3 for the 1D axial calculations, then accelerates the solution using the 3D Coarse mesh Finite Dierence (CMFD) method. Increasing the number of 2D MOC planes will increase the accuracymore » of the alculation, but will increase the computational burden of the calculations and can cause slow convergence or instability. To prevent these problems while maintaining accuracy, the sub-plane scheme has been implemented in MPACT. This method sub-divides the MOC planes into sub-planes, refining the 1D P3 and 3D CMFD calculations without increasing the number of 2D MOC planes. To test the sub-plane scheme, three of the VERA Progression Problems were selected: Problem 3, a single assembly problem; Problem 4, a 3x3 assembly problem with control rods and pyrex burnable poisons; and Problem 5, a quarter core problem. These three problems demonstrated that the sub-plane scheme can accurately produce intra-plane axial flux profiles that preserve the accuracy of the fine mesh solution. The eigenvalue dierences are negligibly small, and dierences in 3D power distributions are less than 0.1% for realistic axial meshes. Furthermore, the convergence behavior with the sub-plane scheme compares favorably with the conventional 2D/1D method, and the computational expense is decreased for all calculations due to the reduction in expensive MOC calculations.« less

Creep crack-growth: A new path-independent integral (T sub c), and computational studies. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Stonesifer, R. B.; Atluri, S. N.

1982-01-01

The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

A fourth order accurate finite difference scheme for the computation of elastic waves

NASA Technical Reports Server (NTRS)

Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.

1986-01-01

A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.

Design Guidelines for In-Plane Mechanical Properties of SiC Fiber-Reinforced Melt-Infiltrated SiC Composites

NASA Technical Reports Server (NTRS)

Morscher, Gregory N.; Pujar, Vijay V.

2008-01-01

In-plane tensile stress-strain, tensile creep, and after-creep retained tensile properties of melt-infiltrated SiC-SiC composites reinforced with different fiber types were evaluated with an emphasis on obtaining simple or first-order microstructural design guidelines for these in-plane mechanical properties. Using the mini-matrix approach to model stress-strain behavior and the results of this study, three basic general design criteria for stress and strain limits are formulated, namely a design stress limit, a design total strain limit, and an after-creep design retained strength limit. It is shown that these criteria can be useful for designing components for high temperature applications.

Wrinkling instability of an inhomogeneously stretched viscous sheet

NASA Astrophysics Data System (ADS)

Srinivasan, Siddarth; Wei, Zhiyan; Mahadevan, L.

2017-07-01

Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed nonuniform temperature field. We first determine the associated base flow by solving the long-time-scale stretching flow of a flat sheet as a function of two dimensionless parameters: the normalized stretching velocity α and a dimensionless width of the heating zone β . This allows us to determine the conditions for the onset of an out-of-plane wrinkling instability stated in terms of an eigenvalue problem for a linear partial differential equation governing the displacement of the midsurface of the sheet. We show that the sheet can become unstable in two regions that are upstream and downstream of the heating zone where the minimum in-plane stress is negative. This yields the shape and growth rates of the most unstable buckling mode in both regions for various values of the stretching velocity and heating zone width. A transition from stationary to oscillatory unstable modes is found in the upstream region with increasing β , while the downstream region is always stationary. We show that the wrinkling instability can be entirely suppressed when the surface tension is large enough relative to the magnitude of the in-plane stress. Finally, we present an operating diagram that indicates regions of the parameter space that result in a required outlet sheet thickness upon stretching while simultaneously minimizing or suppressing the out-of-plane buckling, a result that is relevant for the glass redraw method used to create ultrathin glass sheets.

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle

PubMed Central

Brzezicki, Samuel J.

2017-01-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function. PMID:28690412

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle.

PubMed

Crowdy, Darren G; Brzezicki, Samuel J

2017-06-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.

Highly accurate symplectic element based on two variational principles

NASA Astrophysics Data System (ADS)

Qing, Guanghui; Tian, Jia

2018-02-01

For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element (NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses.

Development of a numerical procedure for mixed mode K-solutions and fatigue crack growth in FCC single crystal superalloys

NASA Astrophysics Data System (ADS)

Ranjan, Srikant

2005-11-01

Fatigue-induced failures in aircraft gas turbine and rocket engine turbopump blades and vanes are a pervasive problem. Turbine blades and vanes represent perhaps the most demanding structural applications due to the combination of high operating temperature, corrosive environment, high monotonic and cyclic stresses, long expected component lifetimes and the enormous consequence of structural failure. Single crystal nickel-base superalloy turbine blades are being utilized in rocket engine turbopumps and jet engines because of their superior creep, stress rupture, melt resistance, and thermomechanical fatigue capabilities over polycrystalline alloys. These materials have orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. Computation of stress intensity factors (SIFs) and the ability to model fatigue crack growth rate at single crystal cracks subject to mixed-mode loading conditions are important parts of developing a mechanistically based life prediction for these complex alloys. A general numerical procedure has been developed to calculate SIFs for a crack in a general anisotropic linear elastic material subject to mixed-mode loading conditions, using three-dimensional finite element analysis (FEA). The procedure does not require an a priori assumption of plane stress or plane strain conditions. The SIFs KI, KII, and KIII are shown to be a complex function of the coupled 3D crack tip displacement field. A comprehensive study of variation of SIFs as a function of crystallographic orientation, crack length, and mode-mixity ratios is presented, based on the 3D elastic orthotropic finite element modeling of tensile and Brazilian Disc (BD) specimens in specific crystal orientations. Variation of SIF through the thickness of the specimens is also analyzed. The resolved shear stress intensity coefficient or effective SIF, Krss, can be computed as a function of crack tip SIFs and the resolved shear stress on primary slip planes. The maximum value of Krss and DeltaKrss was found to determine the crack growth direction and the fatigue crack growth rate respectively. The fatigue crack driving force parameter, DeltaK rss, forms an important multiaxial fatigue damage parameter that can be used to predict life in superalloy components.

Stress state of rocks with a system of workings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nikiforovskii, V.S.; Seryakov, V.M.

1979-09-01

An investigation of the state of rocks in undisturbed form, and during disturbance by drivage of development workings and the working of seams or ore beds, is both important and also extremely complex in practice. The complete physical and mathematical formulation of the problem must take into account the complex geological structure (allowing for tectonics) of the region, the mutual influence of the systems of workings, the change in the mechanical characteristics in the vicinity of the workings, etc. All these factors make it necessary to solve spatial problems with inclusions and workings of arbitrary form. The literature gives datamore » on the stress in the rock in the vicinity of a working remote from the free surface and in its vicinity. However, the possibilities of an analytical investigation of the problem are limited to the simplest cases under conditions of plane deformation. Considerable success in the solution of problems of geomechanics has been attained using numerical methods, particularly the finite-element method, which enables us, without altering the algorithm, to change fairly rapidly and simply the outer and inner boundaries of the region and the properties of the medium, or to assign various boundary conditions. In this article we calculate the stress in the rocks around mining-out and development workings during mining of the Talnakh and Oktyabr' deposits by the longwall slicing system with stowing of the worked-out area.« less

Stress decay in an orthotropic half-plane under self-equilibrating sinusoidal loading

NASA Technical Reports Server (NTRS)

Fichter, W. B.

1984-01-01

An elastic orthotropic half-plane subjected to sinusoidal normal loading along an entire straight edge is analyzed. Stresses are calculated for material property combinations which are representative of some unidirectional fiber reinforced composites and of (+ or - 45) (subs) laminates made from the same unidirectional materials. Plots of the stresses as functions of the distance from the loaded boundary show that they can differ greatly from their counterparts in the isotropic half-plane under the same loading. How the results impact the question of the applicability of St. Venant's principle to orthotropic materials is briefly discussed.

FEM Modeling of In-Plane Stress Distribution in Thick Brittle Coatings/Films on Ductile Substrates Subjected to Tensile Stress to Determine Interfacial Strength

PubMed Central

Zhang, Fangzhou; Bordia, Rajendra K.

2018-01-01

The ceramic-metal interface is present in various material structures and devices that are vulnerable to failures, like cracking, which are typically due to their incompatible properties, e.g., thermal expansion mismatch. In failure of these multilayer systems, interfacial shear strength is a good measure of the robustness of interfaces, especially for planar films. There is a widely-used shear lag model and method by Agrawal and Raj to analyse and measure the interfacial shear strength of thin brittle film on ductile substrates. The use of this classical model for a type of polymer derived ceramic coatings (thickness ~18 μm) on steel substrate leads to high values of interfacial shear strength. Here, we present finite element simulations for such a coating system when it is subjected to in-plane tension. Results show that the in-plane stresses in the coating are non-uniform, i.e., varying across the thickness of the film. Therefore, they do not meet one of the basic assumptions of the classical model: uniform in-plane stress. Furthermore, effects of three significant parameters, film thickness, crack spacing, and Young’s modulus, on the in-plane stress distribution have also been investigated. ‘Thickness-averaged In-plane Stress’ (TIS), a new failure criterion, is proposed for estimating the interfacial shear strength, which leads to a more realistic estimation of the tensile strength and interfacial shear strength of thick brittle films/coatings on ductile substrates. PMID:29584647

A Comprehensive Study on Damage Tolerance Properties of Notched Composite Laminates.

DTIC Science & Technology

1988-02-01

of Applied Mechanics, Vol. 46, pp. 90-96, the strain energy release rate. 1979. [14] F. Delae and F. Erdogan , "Bosid,;d Orlhotropic REFERENCES Strips...with Cracks", Int. J. of Fracture, Vol. 15, [1] F. Erdogan and G.C. Sih, "On the Crack Extension in pp.33-364,1979. Plates Under Plane Loading and...1987. Vol. 34, pp. 967-974, 1967. (17] F. Erdogan , "Mixed Boundary-VL..t; Problems in [4] B. Cotterell, "The Influence of the Stress Distribution

Crack Turning and Arrest Mechanisms for Integral Structure

NASA Technical Reports Server (NTRS)

Pettit, Richard; Ingraffea, Anthony

1999-01-01

In the course of several years of research efforts to predict crack turning and flapping in aircraft fuselage structures and other problems related to crack turning, the 2nd order maximum tangential stress theory has been identified as the theory most capable of predicting the observed test results. This theory requires knowledge of a material specific characteristic length, and also a computation of the stress intensity factors and the T-stress, or second order term in the asymptotic stress field in the vicinity of the crack tip. A characteristic length, r(sub c), is proposed for ductile materials pertaining to the onset of plastic instability, as opposed to the void spacing theories espoused by previous investigators. For the plane stress case, an approximate estimate of r(sub c), is obtained from the asymptotic field for strain hardening materials given by Hutchinson, Rice and Rosengren (HRR). A previous study using of high order finite element methods to calculate T-stresses by contour integrals resulted in extremely high accuracy values obtained for selected test specimen geometries, and a theoretical error estimation parameter was defined. In the present study, it is shown that a large portion of the error in finite element computations of both K and T are systematic, and can be corrected after the initial solution if the finite element implementation utilizes a similar crack tip discretization scheme for all problems. This scheme is applied for two-dimensional problems to a both a p-version finite element code, showing that sufficiently accurate values of both K(sub I) and T can be obtained with fairly low order elements if correction is used. T-stress correction coefficients are also developed for the singular crack tip rosette utilized in the adaptive mesh finite element code FRANC2D, and shown to reduce the error in the computed T-stress significantly. Stress intensity factor correction was not attempted for FRANC2D because it employs a highly accurate quarter-point scheme to obtain stress intensity factors.

Three dimensional finite-element analysis of finite-thickness fracture specimens

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1977-01-01

The stress-intensity factors for most of the commonly used fracture specimens (center-crack tension, single and double edge-crack tension, and compact), those that have a through-the-thickness crack, were calculated using a three dimensional finite-element elastic stress analysis. Three-dimensional singularity elements were used around the crack front. The stress intensity factors along the crack front were evaluated by using a force method, developed herein, that requires no prior assumption of either plane stress or plane strain. The calculated stress-intensity factors from the present analysis were compared with those from the literature whenever possible and were generally found to be in good agreement. The stress-intensity factors at the midplane for all specimens analyzed were within 3 percent of the two dimensional plane strain values. The stress intensity factors at the specimen surfaces were considerably lower than at the midplanes. For the center-crack tension specimens with large thickness to crack-length ratios, the stress-intensity factor reached a maximum near the surface of the specimen. In all other specimens considered the maximum stress intensity occurred at the midplane.

Analysis of crack propagation in roller bearings using the boundary integral equation method - A mixed-mode loading problem

NASA Technical Reports Server (NTRS)

Ghosn, L. J.

1988-01-01

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions, making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.

AC-DCFS: a toolchain implementation to Automatically Compute Coulomb Failure Stress changes after relevant earthquakes.

NASA Astrophysics Data System (ADS)

Alvarez-Gómez, José A.; García-Mayordomo, Julián

2017-04-01

We present an automated free software-based toolchain to obtain Coulomb Failure Stress change maps on fault planes of interest following the occurrence of a relevant earthquake. The system uses as input the focal mechanism data of the event occurred and an active fault database for the region. From the focal mechanism the orientations of the possible rupture planes, the location of the event and the size of the earthquake are obtained. From the size of the earthquake, the dimensions of the rupture plane are obtained by means of an algorithm based on empirical relations. Using the active fault database in the area, the stress-receiving planes are obtained and a verisimilitude index is assigned to the source plane from the two nodal planes of the focal mechanism. The obtained product is a series of layers in a format compatible with any type of GIS (or map completely edited in PDF format) showing the possible stress change maps on the different families of fault planes present in the epicentral zone. These type of products are presented generally in technical reports developed in the weeks following the occurrence of the event, or in scientific publications; however they have been proven useful for emergency management in the hours and days after a major event being these stress changes responsible of aftershocks, in addition to the mid-term earthquake forecasting. The automation of the calculation allows its incorporation within the products generated by the alert and surveillance agencies shortly after the earthquake occurred. It is now being implemented in the Spanish Geological Survey as one of the products that this agency would provides after the occurrence of relevant seismic series in Spain.

Design and Analysis of Orthotrophic Ring-Stiffened Cylindrical Shells Subjected to External Hydrostatic Pressure

DTIC Science & Technology

2008-03-28

in plane bending stiffness. Figure 4. Non-Symmetric General Buckling In accordance with equations (4) through (11), the...the DAPS3 version of the code documented in reference 1, the DAPS4 code computes the stresses and deflections, interbay buckling pressure, general ... plane and out- of- plane bending , eliminating the simple support assumption at the bay ends. b. Stresses and deflections at all points between the

Influence of load interactions on crack growth as related to state of stress and crack closure

NASA Technical Reports Server (NTRS)

Telesman, J.

1985-01-01

Fatigue crack propagation (FCP) after an application of a low-high loading sequence was investigated as a function of specimen thickness and crack closure. No load interaction effects were detected for specimens in a predominant plane strain state. However, for the plane stress specimens, initially high FCP rates after transition to a higher stress intensity range were observed. The difference in observed behavior was explained by examining the effect of the resulting closure stress intensity values on the effective stress intensity range.

Transverse Stress Decay in a Specially Orthotropic Strip Under Localizing Normal Edge Loading

NASA Technical Reports Server (NTRS)

Fichter, W. B.

2000-01-01

Solutions are presented for the stresses in a specially orthotropic infinite strip which is subjected to localized uniform normal loading on one edge while the other edge is either restrained against normal displacement only, or completely fixed. The solutions are used to investigate the diffusion of load into the strip and in particular the decay of normal stress across the width of the strip. For orthotropic strips representative of a broad range of balanced and symmetric angle-ply composite laminates, minimum strip widths are found that ensure at least 90% decay of the normal stress across the strip. In addition, in a few cases where, on the fixed edge the peak shear stress exceeds the normal stress in magnitude, minimum strip widths that ensure 90% decay of both stresses are found. To help in putting these results into perspective, and to illustrate the influence of material properties on load 9 orthotropic materials, closed-form solutions for the stresses in similarly loaded orthotropic half-planes are obtained. These solutions are used to generate illustrative stress contour plots for several representative laminates. Among the laminates, those composed of intermediate-angle plies, i.e., from about 30 degrees to 60 degrees, exhibit marked changes in normal stress contour shape with stress level. The stress contours are also used to find 90% decay distances in the half-planes. In all cases, the minimum strip widths for 90% decay of the normal stress exceed the 90% decay distances in the corresponding half-planes, in amounts ranging from only a few percent to about 50% of the half-plane decay distances. The 90% decay distances depend on both material properties and the boundary conditions on the supported edge.

PROPAGATION AND LINKAGE OF OCEANIC RIDGE SEGMENTS.

USGS Publications Warehouse

Pollard, David D.; Aydin, Atilla

1984-01-01

An investigation was made of spreading ridges and the development of structures that link ridge segments using an analogy between ridges and cracks in elastic plates. The ridge-propagation force and a path factor that controls propagation direction were calculated for echelon ridge segments propagating toward each other. The ridge-propagation force increases as ridge ends approach but then declines sharply as the ends pass, so ridge segments may overlap somewhat. The sign of the path factor changes as ridge ends approach and pass, so the overlapping ridge ends may diverge and then converge following a hook-shaped path. The magnitudes of shear stresses in the plane of the plate and orientations of maximum shear planes between adjacent ridge segments were calculated to study transform faulting. For different loading conditions simulating ridge push, plate pull, and ridge suction, a zone of intense mechanical interaction between adjacent ridge ends in which stresses are concentrated was identified. The magnitudes of mean stresses in the plane of the plate and orientations of principal stress planes were also calculated.

Fatigue Crack Growth Rate and Stress-Intensity Factor Corrections for Out-of-Plane Crack Growth

NASA Technical Reports Server (NTRS)

Forth, Scott C.; Herman, Dave J.; James, Mark A.

2003-01-01

Fatigue crack growth rate testing is performed by automated data collection systems that assume straight crack growth in the plane of symmetry and use standard polynomial solutions to compute crack length and stress-intensity factors from compliance or potential drop measurements. Visual measurements used to correct the collected data typically include only the horizontal crack length, which for cracks that propagate out-of-plane, under-estimates the crack growth rates and over-estimates the stress-intensity factors. The authors have devised an approach for correcting both the crack growth rates and stress-intensity factors based on two-dimensional mixed mode-I/II finite element analysis (FEA). The approach is used to correct out-of-plane data for 7050-T7451 and 2025-T6 aluminum alloys. Results indicate the correction process works well for high DeltaK levels but fails to capture the mixed-mode effects at DeltaK levels approaching threshold (da/dN approximately 10(exp -10) meter/cycle).

Application of the Finite Element Method to Reveal the Causes of Loss of Planeness of Hot-Rolled Steel Sheets during Laser Cutting

NASA Astrophysics Data System (ADS)

Garber, E. A.; Bolobanova, N. L.; Trusov, K. A.

2018-01-01

A finite element technique is developed to simulate the stresses and the strains during strip flattening to reveal the causes of the cutting-assisted loss of planeness of hot-rolled steel sheets processed in roller levelers. The loss of planeness is found to be caused by a nonuniform distribution of the flattening-induced longitudinal tensile stresses over the strip thickness and width. The application of tensile forces to a strip in a roller leveler decreases this nonuniformity and prevents loss of planeness in cutting.

Aging of XLPE cable insulation under combined electrical and mechanical stresses

DOE Office of Scientific and Technical Information (OSTI.GOV)

David, E.; Parpal, J.L.; Crine, J.P.

1996-12-31

Extruded crosslinked polyethylene (XLPE) insulation is widely used in high-voltage cables since it presents such attractive features as excellent dielectric properties and good thermomechanical behavior. However, its performance is affected by long-term degradation when it is subjected to the various thermal, mechanical and environmental stresses occurring in service in combination with electrical stress. The synergetic effect of superposed electrical and other stresses remains to be fully clarified. In particular, a fairly high level of mechanical stresses can be present in the insulation volume, originating from residual internal stresses created during the cooling process in the fabrication, external forces when cablesmore » are bent sharply, or thermomechanical stresses caused by differential thermal expansion between the conductor and the insulating material. In order to investigate the influence of the superposition of mechanical and electrical stresses, various measurements were conducted on XLPE and LDPE specimens in tip-plane and plane-plane geometries. Experimental data of time-to-breakdown, breakdown field and tree length are presented as a function of the magnitude of the stresses. In all cases, superposition of the mechanical stress was found to reduce the dielectric strength of the material.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

St.John, C.M.

The SHAFT code incorporates equations to compute stresses in a shaft liner when the rock through which a shaft passes is subject to known three-dimensional states of stress or strain. The deformation modes considered are hoop deformation, axial deformation, and shear on a plane normal to the shaft axis. Interaction between the liner and the soil and rock is considered, and it is assumed that the liner is in place before loading is applied. This code is intended to be used interactively but creates a permanent record complete with necessary quality assurance information. The code has been carefully verified formore » the case of generalized plane strain, in which an arbitrary axial strain can be defined. It may also be used for plane stress analysis. Output is given in the form of stresses at selected sample points in the linear and the rock and a simple graphical representation of the distribution of stress through the liner. 12 figs., 13 tabs.« less

Error estimation and adaptive mesh refinement for parallel analysis of shell structures

NASA Technical Reports Server (NTRS)

Keating, Scott C.; Felippa, Carlos A.; Park, K. C.

1994-01-01

The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.

A uniform GTD analysis of the EM diffraction by a thin dielectric/ferrite half-plane and related configurations

NASA Technical Reports Server (NTRS)

Rojas, Roberto G.

1985-01-01

A uniform geometrical theory of diffraction (UTD) solution is developed for the problem of the diffraction by a thin dielectric/ferrite half plane when it is excited by a plane, cylindrical, or surface wave field. Both transverse electric and transverse magnetic cases are considered. The solution of this problem is synthesized from the solutions to the related problems of EM diffraction by configurations involving perfectly conducting electric and magnetic walls covered by a dielectric/ferrite half-plane of one half the thickness of the original half-plane.

Scattering of three-dimensional plane waves in a self-reinforced half-space lying over a triclinic half-space

NASA Astrophysics Data System (ADS)

Gupta, Shishir; Pramanik, Abhijit; Smita; Pramanik, Snehamoy

2018-06-01

The phenomenon of plane waves at the intersecting plane of a triclinic half-space and a self-reinforced half-space is discussed with possible applications during wave propagation. Analytical expressions of the phase velocities of reflection and refraction for quasi-compressional and quasi-shear waves under initial stress are discussed carefully. The closest form of amplitude proportions on reflection and refraction factors of three quasi-plane waves are developed mathematically by applying appropriate boundary conditions. Graphics are sketched to exhibit the consequences of initial stress in the three-dimensional plane wave on reflection and refraction coefficients. Some special cases that coincide with the fundamental properties of several layers are designed to express the reflection and refraction coefficients.

Effect of Local Crystallographic Texture on the Fissure Formation During Charpy Impact Testing of Low-Carbon Steel

NASA Astrophysics Data System (ADS)

Ghosh, Abhijit; Patra, Sudipta; Chatterjee, Arya; Chakrabarti, Debalay

2016-06-01

The severity of the formation of fissures (also known as splitting or delamination) on the fracture surface of Charpy impact-tested samples of a low-carbon steel has been found to increase with the decrease in finish rolling temperature [1093 K to 923 K (820 °C to 650 °C)]. Combined scanning electron microscopy and electron back-scattered diffraction study revealed that crystallographic texture was the prime factor responsible for the fissure formation. Through-thickness texture band composed of cube [Normal Direction (ND)║<001>] and gamma [ND║<111>] orientations developed during the inter-critical rolling treatment. Strain incompatibility between these two texture bands causes fissure cracking on the main fracture plane. A new approach based on the angle between {001} planes of neighboring crystals has been employed in order to estimate the `effective grain size,' which is used to determine the cleavage fracture stress on different planes of a sample. The severity of fissure formation was found to be directly related to the difference in cleavage fracture stress between the `main fracture plane' and `fissure plane.' Clustering of ferrite grains having cube texture promoted the fissure crack propagation along the transverse `fissure plane,' by increasing the `effective grain size' and decreasing the cleavage fracture stress on that plane.

Stress Recovery and Error Estimation for 3-D Shell Structures

NASA Technical Reports Server (NTRS)

Riggs, H. R.

2000-01-01

The C1-continuous stress fields obtained from finite element analyses are in general lower- order accurate than are the corresponding displacement fields. Much effort has focussed on increasing their accuracy and/or their continuity, both for improved stress prediction and especially error estimation. A previous project developed a penalized, discrete least squares variational procedure that increases the accuracy and continuity of the stress field. The variational problem is solved by a post-processing, 'finite-element-type' analysis to recover a smooth, more accurate, C1-continuous stress field given the 'raw' finite element stresses. This analysis has been named the SEA/PDLS. The recovered stress field can be used in a posteriori error estimators, such as the Zienkiewicz-Zhu error estimator or equilibrium error estimators. The procedure was well-developed for the two-dimensional (plane) case involving low-order finite elements. It has been demonstrated that, if optimal finite element stresses are used for the post-processing, the recovered stress field is globally superconvergent. Extension of this work to three dimensional solids is straightforward. Attachment: Stress recovery and error estimation for shell structure (abstract only). A 4-node, shear-deformable flat shell element developed via explicit Kirchhoff constraints (abstract only). A novel four-node quadrilateral smoothing element for stress enhancement and error estimation (abstract only).

Investigating Plane Geometry Problem-Solving Strategies of Prospective Mathematics Teachers in Technology and Paper-and-Pencil Environments

ERIC Educational Resources Information Center

Koyuncu, Ilhan; Akyuz, Didem; Cakiroglu, Erdinc

2015-01-01

This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies…

Stress fields around two pores in an elastic body: exact quadrature domain solutions.

PubMed

Crowdy, Darren

2015-08-08

Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky-Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores.

Spreading of a surfactant-laden droplet down an inclined and pre-wetted plane - Numerics, Asymptotics and Linear Stability Analysis

NASA Astrophysics Data System (ADS)

Goddard, Joseph

2012-11-01

Non-uniformities in surfactant concentration result in a surface shear stress, known as the Marangoni stress. This stress, if sufficiently large, can influence the flow at the interface. Naturally occurring surfactants in the mammalian lung reduce the surface tension within the liquid lining the airways and help to prevent collapse of smaller airways. Premature infants produce insufficient surfactant because the lungs are under developed. Resulting Respiratory Distress Syndrome is treated by Surfactant Replacement Therapy. Motivated by this medical application we theoretically investigate a model problem involving the spreading of a drop laden with an insoluble surfactant down an inclined and pre-wetted plane. Our focus is on understanding the mechanisms behind a ``fingering'' instability observed experimentally by high-resolution numerics revealing a multi-region asymptotic structure of the spreading droplet. Approximate solutions for each region are then derived using asymptotic analysis. In particular, a quasi-steady similarity solution is obtained for the leading edge of the droplet and a linear stability analysis shows that the base state is linearly unstable to long-wavelength perturbations for all inclination angles. The Marangoni effect is shown to be behind this instability at small inclination angles. A stability criterion is derived at small wave number and it's implication in the onset of the instability will be discussed.

Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

NASA Astrophysics Data System (ADS)

Fukuda, J.; Johnson, K. M.

2009-12-01

Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress drop.

Effects of Rock Joints on Failure of Tunnels Subject to Blast Loading

DTIC Science & Technology

2013-11-01

The out of plane component of stress , if present, is denoted by σ33, associated with an orthonormal basis vector e3. The principal directions of stress ...lies within the plane of stress or strain, and forms an angle, θ, with respect to the first principal direction p1. Define the normal vector to the...surface of material failure by the critical angle, θc. For the regime (a), (b), (c)-(d), n is equal to p1, the direction of maximum principal stress

In situ synchrotron X-ray diffraction study of hydrides in Zircaloy-4 during thermomechanical cycling

DOE PAGES

Cinbiz, Mahmut N.; Koss, Donald A.; Motta, Arthur T.; ...

2017-02-20

The d-spacing evolution of both in-plane and out-of-plane hydrides has been studied using in situ synchrotron radiation X-ray diffraction during thermo-mechanical cycling of cold-worked stress-relieved Zircaloy-4. The structure of the hydride precipitates is such that the δ{111} d-spacing of the planes aligned with the hydride platelet face is greater than the d-spacing of the 111 planes aligned with the platelet edges. Upon heating from room temperature, the δ{111} planes aligned with hydride plate edges exhibit bi-linear thermally-induced expansion. In contrast, the d-spacing of the (111) plane aligned with the hydride plate face initially contracts upon heating. Furthermore, these experimental resultsmore » can be understood in terms of a reversal of stress state associated with precipitating or dissolving hydride platelets within the α-zirconium matrix.« less

The effect of an overload on the rate of fatigue crack propagation under plane stress conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bao, H.; McEvily, A.J.

1995-07-01

It has been shown that the retardation in the rate of fatigue crack growth following an overload is largely the result of surface-related, plane-stress deformation. In the present article, in order to isolate the plane-stress behavior, the effect of an overload on the subsequent rate of fatigue crack growth of 0.3-mm-thick specimens of 9Cr-1Mo steel has been investigated and compared to results obtained using 6.35-mm-thick specimens. It was found that for the 0.3-mm thickness, as with thicker specimens, two opening load levels were associated with the overload process. The upper opening load is associated with plane-stress deformation in the overloadmore » plastic zone, and this opening process is more clearly observed with thin as compared to thicker specimens. Based upon the determined level of the upper opening load, a semiempirical analysis is developed for calculating the number of delay cycles due to an overload as a function of thickness.« less

Numerical Simulation of Hydraulic Fracturing in Low-/High-Permeability, Quasi-Brittle and Heterogeneous Rocks

NASA Astrophysics Data System (ADS)

Pakzad, R.; Wang, S. Y.; Sloan, S. W.

2018-04-01

In this study, an elastic-brittle-damage constitutive model was incorporated into the coupled fluid/solid analysis of ABAQUS to iteratively calculate the equilibrium effective stress of Biot's theory of consolidation. The Young's modulus, strength and permeability parameter of the material were randomly assigned to the representative volume elements of finite element models following the Weibull distribution function. The hydraulic conductivity of elements was associated with their hydrostatic effective stress and damage level. The steady-state permeability test results for sandstone specimens under different triaxial loading conditions were reproduced by employing the same set of material parameters in coupled transient flow/stress analyses of plane-strain models, thereby indicating the reliability of the numerical model. The influence of heterogeneity on the failure response and the absolute permeability was investigated, and the post-peak permeability was found to decrease with the heterogeneity level in the coupled analysis with transient flow. The proposed model was applied to the plane-strain simulation of the fluid pressurization of a cavity within a large-scale block under different conditions. Regardless of the heterogeneity level, the hydraulically driven fractures propagated perpendicular to the minimum principal far-field stress direction for high-permeability models under anisotropic far-field stress conditions. Scattered damage elements appeared in the models with higher degrees of heterogeneity. The partially saturated areas around propagating fractures were simulated by relating the saturation degree to the negative pore pressure in low-permeability blocks under high pressure. By replicating previously reported trends in the fracture initiation and breakdown pressure for different pressurization rates and hydraulic conductivities, the results showed that the proposed model for hydraulic fracture problems is reliable for a wide range of pressurization rates and permeability conditions.

Determination of Residual Stress in Composite Materials Using Ultrasonic Waves

NASA Technical Reports Server (NTRS)

Rokhlin, S. I.

1997-01-01

The performance of high temperature composites can be significantly affected by the presence of residual stresses. These stresses arise during cooling processes from fabrication to room temperature due to mismatch of thermal expansion coefficients between matrix and fiber materials. This effect is especially pronounced in metal matrix and intermetallic composites. It can lead to plastic deformations, matrix cracking and fiber/matrix interface debonding. In this work the feasibility of ultrasonic techniques for residual stress assessment in composites is addressed. A novel technique for absolute stress determination in orthotropic materials from angular dependencies of ultrasonic velocities is described. The technique is applicable for determination of both applied and residual stresses and does not require calibration measurements on a reference sample. The important advantage of this method is that stress is determined simultaneously with stress-dependent elastic constants and is thus decoupled from the material texture. It is demonstrated that when the principal plane stress directions coincide with acoustical axes, the angular velocity data in the plane perpendicular to the stress plane may be used to determine both stress components. When the stress is off the acoustical axes, the shear and the difference of the normal stress components may be determined from the angular dependence of group velocities in the plane of stresses. Synthetic sets of experimental data corresponding to materials with different anisotropy and stress levels are used to check the applicability of the technique. The method is also verified experimentally. A high precision ultrasonic wave transmission technique is developed to measure angular dependence of ultrasonic velocities. Examples of stress determination from experimental velocity data are given. A method is presented for determination of velocities of ultrasonic waves propagating through the composite material with residual stresses. It is based on the generalized self-consistent multiple scattering model. Calculation results for longitudinal and shear ultrasonic wave velocities propagating perpendicular to the fibers direction in SCS-6/Ti composite with and without residual stresses are presented. They show that velocity changes due to presence of stresses are of order 1%.

Speckle techniques for determining stresses in moving objects

NASA Technical Reports Server (NTRS)

Murphree, E. A.; Wilson, T. F.; Ranson, W. F.; Swinson, W. F.

1978-01-01

Laser speckle interferometry is a relatively new experimental technique which shows promise of alleviating many difficult problems in experimental mechanics. The method utilizes simple high-resolution photographs of the surface which is illuminated by coherent light. The result is a real-time or permanently stored whole-field record of interference fringes which yields a map of displacements in the object. In this thesis, the time-average theory using the Fourier transform is developed to present the application of this technique to measurement of in-plane displacement induced by the vibration of an object.

Direct restoration modalities of fractured central maxillary incisors: A multi-levels validated finite elements analysis with in vivo strain measurements.

PubMed

Davide, Apicella; Raffaella, Aversa; Marco, Tatullo; Michele, Simeone; Syed, Jamaluddin; Massimo, Marrelli; Marco, Ferrari; Antonio, Apicella

2015-12-01

To quantify the influence of fracture geometry and restorative materials rigidity on the stress intensity and distribution of restored fractured central maxillary incisors (CMI) with particular investigation of the adhesive interfaces. Ancillary objectives are to present an innovative technology to measure the in vivo strain state of sound maxillary incisors and to present the collected data. A validation experimental biomechanics approach has been associated to finite element analysis. FEA models consisted of CMI, periodontal ligament and the corresponding alveolar bone process. Three models were created representing different orientation of the fracture planes. Three different angulations of the fracture plane in buccal-palatal direction were modeled: the fracture plane perpendicular to the long axis in the buccal-palatal direction (0°); the fracture plane inclined bucco-palatally in apical-coronal direction (-30°); the fracture plane inclined palatal-buccally in apical-coronal direction (+30°). First set of computing runs was performed for in vivo FE-model validation purposes. In the second part, a 50N force was applied on the buccal aspect of the CMI models. Ten patients were selected and subjected to the strain measurement of CMI under controlled loading conditions. The main differences were noticed in the middle and incisal thirds of incisors crowns, due to the presence of the incisal portion restoration. The stress intensity in -30° models is increased in the enamel structure close to the restoration, due to a thinning of the remaining natural tissues. The rigidity of the restoring material slightly reduces such phenomenon. -30° model exhibits the higher interfacial stress in the adhesive layer with respect to +30° and 0° models. The lower stress intensity was noticed in the 0° models, restoration material rigidity did not influenced the interfacial stress state in 0° models. On the contrary, material rigidity influenced the interfacial stress state in +30° and -30° models, higher rigidity restoring materials exhibits lower interfacial stress with respect to low rigidity materials. Fracture planes inclined palatal-buccally in apical-coronal direction (+30°) reduce the interfacial stress intensity and natural tissues stress intensity with respect to the other tested configurations. Copyright © 2015 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Spatially varying stress state in the central U.S. from joint inversion of focal mechanism and maximum horizontal stress data

NASA Astrophysics Data System (ADS)

Carlson, G.; Johnson, K. M.; Rupp, J. A.

2017-12-01

The Midcontinental United States continues to experience anomalously high rates of seismicity and generate large earthquakes despite its location in the cratonic interior, far from any plate boundary. There is renewed interest in Midcontinent seismicity with the concern that fluid injection within the Illinois basin could induce seismicity. In order to better understand the seismic hazard and inform studies of risk mitigation, we present an assessment of the contemporary crustal stress state in the Illinois basin and surrounding region, looking specifically at how the orientation of maximum horizontal compressive stress varies throughout the region. This information will help identify which faults are critically stressed and therefore most likely to fail under increased pore pressures. We conduct a Bayesian stress inversion of focal mechanism solutions and maximum horizontal stress orientations from borehole breakout, core fracture, overcoring, hydraulic fracture, and strain gauge measurements for maximum horizontal compressive stress orientations across the Midcontinent region and produce a map of expected faulting styles. Because distinguishing the slipping fault plane from the auxiliary nodal plane is ambiguous for focal mechanisms, the choice of the fault plane and associated slip vector to use in the inversion is important in the estimation of the stress tensor. The stress inversion provides an objective means to estimate nonlinear parameters including the spatial smoothing parameter, unknown data uncertainties, as well as the selection of focal mechanism nodal planes. We find a systematic rotation of the maximum horizontal stress orientation (SHmax) across a 1000 km width of the Midcontinent. We find that SHmax rotates from N60E to E/W orientation across the southern Illinois basin and returns to N60E in the western Appalachian basin. The stress regime is largely consistent with strike-slip faulting with pockets of a reverse-faulting stress regime near the New Madrid and Wabash Valley seismic zones.

Inversion of calcite twin data for paleostress (1) : improved Etchecopar technique tested on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

Parlangeau, Camille; Lacombe, Olivier; Daniel, Jean-Marc; Schueller, Sylvie

2015-04-01

Inversion of calcite twin data are known to be a powerful tool to reconstruct the past-state of stress in carbonate rocks of the crust, especially in fold-and-thrust belts and sedimentary basins. This is of key importance to constrain results of geomechanical modelling. Without proposing a new inversion scheme, this contribution reports some recent improvements of the most efficient stress inversion technique to date (Etchecopar, 1984) that allows to reconstruct the 5 parameters of the deviatoric paleostress tensors (principal stress orientations and differential stress magnitudes) from monophase and polyphase twin data sets. The improvements consist in the search of the possible tensors that account for the twin data (twinned and untwinned planes) and the aid to the user to define the best stress tensor solution, among others. We perform a systematic exploration of an hypersphere in 4 dimensions by varying different parameters, Euler's angles and the stress ratio. We first record all tensors with a minimum penalization function accounting for 20% of the twinned planes. We then define clusters of tensors following a dissimilarity criterion based on the stress distance between the 4 parameters of the reduced stress tensors and a degree of disjunction of the related sets of twinned planes. The percentage of twinned data to be explained by each tensor is then progressively increased and tested using the standard Etchecopar procedure until the best solution that explains the maximum number of twinned planes and the whole set of untwinned planes is reached. This new inversion procedure is tested on monophase and polyphase numerically-generated as well as natural calcite twin data in order to more accurately define the ability of the technique to separate more or less similar deviatoric stress tensors applied in sequence on the samples, to test the impact of strain hardening through the change of the critical resolved shear stress for twinning as well as to evaluate the possible bias due to measurement uncertainties or clustering of grain optical axes in the samples.

[Characteristics of Raman spectra of minerals in the veins of Wenchuan earthquake fault zone].

PubMed

Xie, Chao; Zhou, Ben-gang; Liu, Lei; Zhou, Xiao-cheng; Yi, Li; Chen, Zhi; Cui, Yue-ju; Li, Jing; Chen, Zheng-wei; Du, Jian-guo

2015-01-01

Quartz in the veins at the Shenxigou section of Wenchuan earthquake fault zone was investigated by micro-Raman spectroscopic measurement, and the distribution of compressive stress in the fault zone was estimated by the frequency shifts of the 464 cm-1 vibrational mode of quartz grains in the veins. It was showed that the 464 cm-1 peak arising from the quartz grains in the veins near the fault plane shifts by 3. 29 cm-1 , and the corresponding compressive stress is 368. 63 MPa, which is significantly lower than the stress accumulation on both sides due to multi-stage events. Stress accumulation increased with moving away from the fault plane in the footwall with the offset of the 464 cm-1 peak arising from the quartz grains in the veins increasing, which can reach 494. 77 MPa at a distance of 21 m with a high offset of 4. 40 cm-1 of the 464 cm-1 peak. The compressive stress gets the maximum value of 519.87 MPa at a distance of 10 m from the fault plane in the hanging wall with the offset of the 464 cm-1 peak arising from the quartz grains in the veins being 4. 62 cm-1, followed by a sudden drop in stress accumulation, and it drops to 359. 59 MPa at a distance of 17 m. Because of moving away from the foult plane at the edge of the foult zone, the stress drops to 359. 59 MPa with a small value of 464 cm-1 peak offset 3. 21 cm-1 at a distance of 27 m from the fault plane in the hanging wall due to the little effect by the fault activity. Therefore, the stress of Wenchuan earthquake fault zone is partially released, but the rest of the stress distribution is uneven, and there is also a high stress accumulation in somewhere in the fault zone, which reflects that the mechanical properties of the rocks in the fault zone have a characteristic of unevenness in space.

The Inclusion of In-Plane Stresses in Delamination Criteria

NASA Technical Reports Server (NTRS)

Vizzini, Anthony J.; Fenske, Matthew T.

1998-01-01

A study of delamination is performed including strength of materials and fracture mechanics approaches with emphasis placed on methods of delamination prediction. Evidence is presented which supports the inclusion of the in-plane stresses in addition to the inter-laminar stress terms in delamination criteria. The delamination can be modeled as a resin rich region in between ply sets. The entire six component stress state in this resin layer is calculated through a finite element analysis and inputted into a new Modified Von Mises Delamination Criterion. This criterion builds onto previous criteria by including all six stress components. The MVMDC shows improved correlation to experimental data.

On a Minimum Problem in Smectic Elastomers

NASA Astrophysics Data System (ADS)

Buonsanti, Michele; Giovine, Pasquale

2008-07-01

Smectic elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. Balance equations for smectic elastomers are derived from the general theory of continua with constrained microstructure. In this work we investigate a very simple minimum problem based on multi-well potentials where the microstructure is taken into account. The set of polymeric strains minimizing the elastic energy contains a one-parameter family of simple strain associated with a micro-variation of the degree of freedom. We develop the energy functional through two terms, the first one nematic and the second one considering the tilting phenomenon; after, by developing in the rubber elasticity framework, we minimize over the tilt rotation angle and extract the engineering stress.

Finite element analysis and optimization of composite structures

NASA Technical Reports Server (NTRS)

Thomsen, Jan

1990-01-01

Linearly elastic fiber reinforced composite discs and laminates in plane stress with variable local orientation and concentration of one or two fiber fields embedded in the matrix material, are considered. The thicknesses and the domain of the discs or laminates are assumed to be given, together with prescribed boundary conditions and in-plane loading along the edge. The problem under study consists in determining throughout the structural domain the optimum orientations and concentrations of the fiber fields in such a way as to maximize the integral stiffness of the composite disc or laminate under the seven loading. Minimization of the integral stiffness can also be performed. The optimization is performed subject to a prescribed bound on the total cost or weight of the composite that for given unit cost factors or specific weights determines the amounts of fiber and matrix materials in the structure. Examples are presented.

Evaluation of stress distribution of implant-retained mandibular overdenture with different vertical restorative spaces: A finite element analysis

PubMed Central

Ebadian, Behnaz; Farzin, Mahmoud; Talebi, Saeid; Khodaeian, Niloufar

2012-01-01

Background: Available restorative space and bar height is an important factor in stress distribution of implant-supported overdentures. The purpose of this study was to evaluate the effect of different vertical restorative spaces and different bar heights on the stress distribution around implants by 3D finite element analysis. Materials and Methods: 3D finite element models were developed from mandibular overdentures with two implants in the interforaminal region. In these models, four different bar heights from gingival crest (0.5, 1, 1.5, 2 mm) with 15 mm occlusal plane height and three different occlusal plane heights from gingival crest (9, 12, 15 mm) with 2 mm bar height were analyzed. A vertical unilateral and a bilateral load of 150 N were applied to the central occlusal fossa of the first molar and the stress of bone around implant was analyzed by finite element analysis. Results: By increasing vertical restorative space, the maximum stress values around implants were found to be decreased in unilateral loading models but slightly increased in bilateral loading cases. By increasing bar height from gingival crest, the maximum stress values around implants were found to be increased in unilateral loading models but slightly decreased in bilateral loading cases. In unilateral loading models, maximum stress was found in a model with 9 mm occlusal plane height and 1.5 mm bar height (6.254 MPa), but in bilateral loading cases, maximum stress was found in a model with 15 mm occlusal plane height and 0.5 mm bar height (3.482 MPa). Conclusion: The reduction of bar height and increase in the thickness of acrylic resin base in implant-supported overdentures are biomechanically favorable and may result in less stress in periimplant bone. PMID:23559952

Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1981-01-01

An approximate solution was obtained for a cylindrical shell containing a part-through surface crack. It was assumed that the shell contains a circumferential or axial semi-elliptic internal or external surface crack and was subjected to a uniform membrane loading or a uniform bending moment away from the crack region. A Reissner type theory was used to account for the effects of the transverse shear deformations. The stress intensity factor at the deepest penetration point of the crack was tabulated for bending and membrane loading by varying three dimensionless length parameters of the problem formed from the shell radius, the shell thickness, the crack length, and the crack depth. The upper bounds of the stress intensity factors are provided by the results of the elasticity solution obtained from the axisymmetric crack problem for the circumferential crack, and that found from the plane strain problem for a circular ring having a radial crack for the axial crack. The line-spring model gives the expected results in comparison with the elasticity solutions. Results also compare well with the existing finite element solution of the pressurized cylinder containing an internal semi-elliptic surface crack.

Plane stress analysis of wood members using isoparametric finite elements, a computer program

Treesearch

Gary D. Gerhardt

1983-01-01

A finite element program is presented which computes displacements, strains, and stresses in wood members of arbitrary shape which are subjected to plane strain/stressloading conditions. This report extends a program developed by R. L. Taylor in 1977, by adding both the cubic isoparametric finite element and the capability to analyze nonisotropic materials. The...

Physically elastic analysis of a cylindrical ring as a unit cell of a complete composite under applied stress in the complex plane using cubic polynomials

NASA Astrophysics Data System (ADS)

Monfared, Vahid

2018-03-01

Elastic analysis is analytically presented to predict the behaviors of the stress and displacement components in the cylindrical ring as a unit cell of a complete composite under applied stress in the complex plane using cubic polynomials. This analysis is based on the complex computation of the stress functions in the complex plane and polar coordinates. Also, suitable boundary conditions are considered and assumed to analyze along with the equilibrium equations and bi-harmonic equation. This method has some important applications in many fields of engineering such as mechanical, civil and material engineering generally. One of the applications of this research work is in composite design and designing the cylindrical devices under various loadings. Finally, it is founded that the convergence and accuracy of the results are suitable and acceptable through comparing the results.

Crashworthiness: Planes, trains, and automobiles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Logan, R.W.; Tokarz, F.J.; Whirley, R.G.

A powerful DYNA3D computer code simulates the dynamic effects of stress traveling through structures. It is the most advanced modeling tool available to study crashworthiness problems and to analyze impacts. Now used by some 1000 companies, government research laboratories, and universities in the U.S. and abroad, DYNA3D is also a preeminent example of successful technology transfer. The initial interest in such a code was to simulate the structural response of weapons systems. The need was to model not the explosive or nuclear events themselves but rather the impacts of weapons systems with the ground, tracking the stress waves as theymore » move through the object. This type of computer simulation augmented or, in certain cases, reduced the need for expensive and time-consuming crash testing.« less

Stress Transfer and Structural Failure of Bilayered Material Systems

NASA Astrophysics Data System (ADS)

Prieto-Munoz, Pablo Arthur

Bilayered material systems are common in naturally formed or artificially engineered structures. Understanding how loads transfer within these structural systems is necessary to predict failure and develop effective designs. Existing methods for evaluating the stress transfer in bilayered materials are limited to overly simplified models or require experimental calibration. As a result, these methods have failed to accurately account for such structural failures as the creep induced roofing panel collapse of Boston's I-90 connector tunnel, which was supported by adhesive anchors. The one-dimensional stress analyses currently used for adhesive anchor design cannot account for viscoelastic creep failure, and consequently results in dangerously under-designed structural systems. In this dissertation, a method for determining the two-dimensional stress and displacement fields for a generalized bilayered material system is developed, and proposes a closed-form analytical solution. A general linear-elastic solution is first proposed by decoupling the elastic governing equations from one another through the so-called plane assumption. Based on this general solution, an axisymmetric problem and a plane strain problem are formulated. These are applied to common bilayered material systems such as: (1) concrete adhesive anchors, (2) material coatings, (3) asphalt pavements, and (4) layered sedimentary rocks. The stress and displacement fields determined by this analytical analysis are validated through the use of finite element models. Through the correspondence principle, the linear-elastic solution is extended to consider time-dependent viscoelastic material properties, thus facilitating the analysis of adhesive anchors and asphalt pavements while incorporating their viscoelastic material behavior. Furthermore, the elastic stress analysis can explain the fracturing phenomenon of material coatings, pavements, and layered rocks, successfully predicting their fracture saturation ratio---which is the ratio of fracture spacing to the thickness of the weak layer where an increase in load will not cause any new fractures to form. Moreover, these specific material systems are looked at in the context of existing and novel experimental results, further demonstrating the advantage of the stress transfer analysis proposed. This research provides a closed-form stress solution for various structural systems that is applied to different failure analyses. The versatility of this method is in the flexibility and the ease upon which the stress and displacement field results can be applied to existing stress- or displacement-based structural failure criteria. As presented, this analysis can be directly used to: (1) design adhesive anchoring systems for long-term creep loading, (2) evaluate the fracture mechanics behind bilayered material coatings and pavement overlay systems, and (3) determine the fracture spacing to layer thickness ratio of layered sedimentary rocks. As is shown in the four material systems presented, this general solution has far reaching applications in facilitating design and analysis of typical bilayered structural systems.

3-D Dynamic Rupture Simulations of the 2016 Kumamoto, Japan, Earthquake

NASA Astrophysics Data System (ADS)

Fukuyama, E.; Urata, Y.; Yoshida, K.

2016-12-01

On April 16, 2016 at 01:25 (JST), an M7.3 main shock of the 2016 Kumamoto, Japan, earthquake sequence occurred along the Futagawa and Hinagu faults. A few days before, three M6-class foreshocks occurred: M6.5 on April 14 at 21:26, M5.8 on April 14 at 22:27, and M6.4 on April 15 at 00:03 (JST). The focal mechanisms of the first and third foreshocks were similar to those of the main shock; therefore, the extensive stress shadow should have been generated on the fault plane of the main shock. The purpose of this study is to illuminate why the rupture of the main shock propagated successfully under such stress conditions by 3-D dynamic rupture simulations, assuming the fault planes estimated by the distributions of aftershocks.First, we investigated time evolution of aftershock hypocenters relocated by the Double Difference method (Waldhauser & Ellsworth, 2000). The result showed that planar distribution of the hypocenters was formed after each M6 event. It allows us to estimate fault planes of the three foreshocks and the main shock.Then, we evaluated stress changes on the fault planes of the main shock due to the three foreshocks. We obtained the slip distributions of the foreshocks by using Eshelby (1957)'s solution, assuming elliptical cracks with constant stress drops on the estimated fault planes. The stress changes on the fault planes of the main shock were calculated by using Okada (1992)'s solution. The obtained stress change distribution showed that the hypocenter of the main shock existed on the region with positive ΔCFF while ΔCFF in the shallower regions than the hypocenter was negative. Therefore, the foreshocks could encourage the initiation of the main shock rupture and could hinder the rupture propagating toward the shallow region.Finally, we conducted 3-D dynamic rupture simulations (Hok and Fukuyama, 2011) of the main shock under the initial stresses, which were the sum of the stress changes by these foreshocks and the regional stress field estimated by Yoshida et al. (2016, submitted). We used slip-weakening law with uniform friction parameters. We conducted many simulations varying unknown parameters (the friction parameters and the values of the principal stresses), and we will discuss the conditions for the rupture propagation of the main shock and the effects of the foreshocks on the main shock.

Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felício B.

2017-12-01

Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

Detoxification strategies and regulation of oxygen production and flowering of Platanus acerifolia under lead (Pb) stress by transcriptome analysis.

PubMed

Wang, Limin; Yang, Haijiao; Liu, Rongning; Fan, Guoqiang

2015-08-01

Toxic metal pollution is a major environmental problem that has received wide attention. Platanus acerifolia (London plane tree) is an important greening tree species that can adapt to environmental pollution. The genetic basis and molecular mechanisms associated with the ability of P. acerifolia to respond lead (Pb) stress have not been reported so far. In this study, 16,246 unigenes differentially expressed unigenes that were obtained from P. acerifolia under Pb stress using next-generation sequencing. Essential pathways such as photosynthesis, and gibberellins and glutathione metabolism were enriched among the differentially expressed unigenes. Furthermore, many important unigenes, including antioxidant enzymes, plants chelate compounds, and metal transporters involved in defense and detoxification mechanisms, were differentially expressed in response to Pb stress. The unigenes encoding the oxygen-evolving enhancer Psb and OEE protein families were downregulated in Pb-stressed plants, implying that oxygen production might decrease in plants under Pb stress. The relationship between gibberellin and P. acerifolia flowering is also discussed. The information and new insights obtained in this study will contribute to further investigations into the molecular regulation mechanisms of Pb accumulation and tolerance in greening tree species.

Effects induced by an earthquake on its fault plane:a boundary element study

NASA Astrophysics Data System (ADS)

Bonafede, Maurizio; Neri, Andrea

2000-04-01

Mechanical effects left by a model earthquake on its fault plane, in the post-seismic phase, are investigated employing the `displacement discontinuity method'. Simple crack models, characterized by the release of a constant, unidirectional shear traction are investigated first. Both slip components-parallel and normal to the traction direction-are found to be non-vanishing and to depend on fault depth, dip, aspect ratio and fault plane geometry. The rake of the slip vector is similarly found to depend on depth and dip. The fault plane is found to suffer some small rotation and bending, which may be responsible for the indentation of a transform tectonic margin, particularly if cumulative effects are considered. Very significant normal stress components are left over the shallow portion of the fault surface after an earthquake: these are tensile for thrust faults, compressive for normal faults and are typically comparable in size to the stress drop. These normal stresses can easily be computed for more realistic seismic source models, in which a variable slip is assigned; normal stresses are induced in these cases too, and positive shear stresses may even be induced on the fault plane in regions of high slip gradient. Several observations can be explained from the present model: low-dip thrust faults and high-dip normal faults are found to be facilitated, according to the Coulomb failure criterion, in repetitive earthquake cycles; the shape of dip-slip faults near the surface is predicted to be upward-concave; and the shallower aftershock activity generally found in the hanging block of a thrust event can be explained by `unclamping' mechanisms.

Skyrmion motion induced by plane stress waves

NASA Astrophysics Data System (ADS)

Gungordu, Utkan; Kovalev, Alexey A.

Skyrmions are typically driven by currents and magnetic fields. We propose an alternative method of driving skyrmions using plane stress waves in a chiral ferromagnetic nanotrack. We find that the effective force due to surface acoustic waves couples both to the helicity and the topological charge of the skyrmion. This coupling can be used to probe the helicity of the skyrmion as well as the nature of the Dzyaloshinskii-Moriya interaction. This is particularly important when a ferromagnet lacks both surface- and bulk-inversion symmetry. Plane stress waves can be generated using a pair of interdigital transducers (IDTs). As the nanowire is subject to half-open space boundary conditions, the skyrmion is driven by normal stress in this setup. We find that skyrmions get pinned at the antinodes of the stress wave, much similar to domain walls, which enables skyrmion motion by detuned IDTs. We also consider a nanotrack sandwiched between a piezoelectric layer and a substrate, with electrical contacts placed on top, which results in shear stress in addition to normal stress in nanotrack. We find that unlike domain walls, skyrmions can be driven using shear component of a standing stress wave. This work was supported primarily by the DOE Early Career Award DE-SC0014189, and in part by the NSF under Grants Nos. Phy-1415600, and DMR-1420645 (UG).

Some boundary-value problems for anisotropic quarter plane

NASA Astrophysics Data System (ADS)

Arkhypenko, K. M.; Kryvyi, O. F.

2018-04-01

To solve the mixed boundary-value problems of the anisotropic elasticity for the anisotropic quarter plane, a method based on the use of the space of generalized functions {\\Im }{\\prime }({\\text{R}}+2) with slow growth properties was developed. The two-dimensional integral Fourier transform was used to construct the system of fundamental solutions for the anisotropic quarter plane in this space and a system of eight boundary integral relations was obtained, which allows one to reduce the mixed boundary-value problems for the anisotropic quarter plane directly to systems of singular integral equations with fixed singularities. The exact solutions of these systems were found by using the integral Mellin transform. The asymptotic behavior of solutions was investigated at the vertex of the quarter plane.

Thermal residual stress evaluation based on phase-shift lateral shearing interferometry

NASA Astrophysics Data System (ADS)

Dai, Xiangjun; Yun, Hai; Shao, Xinxing; Wang, Yanxia; Zhang, Donghuan; Yang, Fujun; He, Xiaoyuan

2018-06-01

An interesting phase-shift lateral shearing interferometry system was proposed to evaluate the thermal residual stress distribution in transparent specimen. The phase-shift interferograms was generated by moving a parallel plane plate. Based on analyzing the fringes deflected by deformation and refractive index change, the stress distribution can be obtained. To verify the validity of the proposed method, a typical experiment was elaborately designed to determine thermal residual stresses of a transparent PMMA plate subjected to the flame of a lighter. The sum of in-plane stress distribution was demonstrated. The experimental data were compared with values measured by digital gradient sensing method. Comparison of the results reveals the effectiveness and feasibility of the proposed method.

Fatigue crack closure: a review of the physical phenomena

PubMed Central

Pippan, R.

2017-01-01

Abstract Plasticity‐induced, roughness‐induced and oxide‐induced crack closures are reviewed. Special attention is devoted to the physical origin, the consequences for the experimental determination and the prediction of the effective crack driving force for fatigue crack propagation. Plasticity‐induced crack closure under plane stress and plane strain conditions require, in principle, a different explanation; however, both types are predictable. This is even the case in the transition region from the plane strain to the plane stress state and all types of loading conditions including constant and variable amplitude loading, the short crack case or the transition from small‐scale to large‐scale yielding. In contrast, the prediction of roughness‐induced and oxide‐induced closures is not as straightforward. PMID:28616624

Low-Velocity Impact Response of Sandwich Beams with Functionally Graded Core

NASA Technical Reports Server (NTRS)

Apetre, N. A.; Sankar, B. V.; Ambur, D. R.

2006-01-01

The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young's modulus is represented by a polynomial in the thickness coordinate, but the Poisson's ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel - the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of thc beam with graded core Increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load arc reduced considerably due to grading of thc core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites.

Intertwined Hamiltonians in two-dimensional curved spaces

NASA Astrophysics Data System (ADS)

Aghababaei Samani, Keivan; Zarei, Mina

2005-04-01

The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincaré half plane (AdS2), de Sitter plane (dS2), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle.

A platform-based foot pressure/shear sensor

NASA Astrophysics Data System (ADS)

Chang, Chun-Te; Liu, Chao Shih; Soetanto, William; Wang, Wei-Chih

2012-04-01

The proposed research is aimed at developing, fabricating and implementing a flexible fiber optic bend loss sensor for the measurement of plantar pressure and shear stress for diabetic patients. The successful development of the sensor will greatly impact the study of diabetic foot ulcers by allowing clinicians to measure a parameter (namely, shear stress) that has been implicated in ulceration, but heretofore, has not been routinely quantified on high risk patients. A full-scale foot pressure/shear sensor involves a tactile sensor array using intersecting optical waveguides is presented. The basic configuration of the optical sensor systems incorporates a mesh that is comprised of two sets of parallel optical waveguide planes; the planes are configured so the parallel rows of waveguides of the top and bottom planes are perpendicular to each other. The planes are sandwiched together creating one sensing sheet. Two-dimensional information is determined by measuring the loss of light from each of the waveguide to map the overall pressure distribution. The shifting of the layers relative to each other allows determination of the shear stress in the plane of the sensor. This paper presents latest development and improvement in the sensors design. Fabrication and results from the latest tests will be described.

Tensile behavior and flow stress anisotropy of accumulative roll bonded Cu-Nb nanolaminates

DOE PAGES

Nizolek, Thomas; Beyerlein, Irene J.; Mara, Nathan A.; ...

2016-02-01

The flow stress, ductility, and in-plane anisotropy are evaluated for bulk accumulative roll bonded copper-niobium nanolaminates with layer thicknesses ranging from 1.8 μm to 15 nm. Uniaxial tensile tests conducted parallel to the rolling direction and transverse direction demonstrate that ductility generally decreases with decreasing layer thickness; however, at 30 nm, both high strengths (1200 MPa) and significant ductility (8%) are achieved. The yield strength increases monotonically with decreasing layer thickness, consistent with the Hall-Petch relationship, and significant in-plane flow stress anisotropy is observed. As a result, Taylor polycrystal modeling is used to demonstrate that crystallographic texture is responsible formore » the in-plane anisotropy and that the effects of texture dominate even at nanoscale layer thicknesses.« less

A cylindrical shell with an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1982-01-01

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system of five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented.

Analysis of a thin-walled pressurized torus in contact with a plane. [aircraft tires study

NASA Technical Reports Server (NTRS)

Mack, M. J., Jr.; Gassman, P. M.; Baumgarten, J. R.

1983-01-01

Finite element analysis is applied to study the large deflection of a standing torus loaded by a plane. The internally pressurized thin-walled structure is found to have an elliptical footprint area. Considerable bulge occurs in the sidewall in the region of the load plane. Stress distributions throughout the torus are shown for various load levels and for various modeling strategies at a given load level. In large load ranges finite element calculations show compressive circumferential stress and negative curvature in the footprint region. Results are compared with inelastic wall analysis.

Stresses in Circular Plates with Rigid Elements

NASA Astrophysics Data System (ADS)

Velikanov, N. L.; Koryagin, S. I.; Sharkov, O. V.

2018-05-01

Calculations of residual stress fields are carried out by numerical and static methods, using the flat cross-section hypothesis. The failure of metal when exposed to residual stresses is, in most cases, brittle. The presence in the engineering structures of rigid elements often leads to the crack initiation and structure failure. This is due to the fact that rigid elements under the influence of external stresses are stress concentrators. In addition, if these elements are fixed by welding, the residual welding stresses can lead to an increase in stress concentration and, ultimately, to failure. The development of design schemes for such structures is a very urgent task for complex technical systems. To determine the stresses in a circular plate with a welded circular rigid insert under the influence of an external load, one can use the solution of the plane stress problem for annular plates in polar coordinates. The polar coordinates of the points are the polar radius and the polar angle, and the stress state is determined by normal radial stresses, tangential and shearing stresses. The use of the above mentioned design schemes, formulas, will allow more accurate determination of residual stresses in annular welded structures. This will help to establish the most likely directions of failure and take measures at the stages of designing, manufacturing and repairing engineering structures to prevent these failures. However, it must be taken into account that the external load, the presence of insulation can lead to a change in the residual stress field.

Direct formulation of a 4-node hybrid shell element with rotational degrees of freedom

NASA Technical Reports Server (NTRS)

Aminpour, Mohammad A.

1990-01-01

A simple 4-node assumed-stress hybrid quadrilateral shell element with rotational or drilling degrees of freedom is formulated. The element formulation is based directly on a 4-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 8-node isoparametric element in which the midside degrees of freedom are eliminated in favor of rotational degree of freedom at the corner nodes. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom including rotational degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields are assumed along the edges of the element. The element Cartesian-coordinate system is chosen such as to make the stress field invariant with respect to node numbering. The membrane part of the stress field is based on a 9-parameter equilibrating stress field, while the bending part is based on a 13-parameter equilibrating stress field. The element passes the patch test, is nearly insensitive to mesh distortion, does not lock, possesses the desirable invariance properties, has no spurious modes, and produces accurate and reliable results.

Hybrid near-optimal aeroassisted orbit transfer plane change trajectories

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Duckeman, Gregory A.

1994-01-01

In this paper, a hybrid methodology is used to determine optimal open loop controls for the atmospheric portion of the aeroassisted plane change problem. The method is hybrid in the sense that it combines the features of numerical collocation with the analytically tractable portions of the problem which result when the two-point boundary value problem is cast in the form of a regular perturbation problem. Various levels of approximation are introduced by eliminating particular collocation parameters and their effect upon problem complexity and required number of nodes is discussed. The results include plane changes of 10, 20, and 30 degrees for a given vehicle.

Application of boundary integral equations to elastoplastic problems

NASA Technical Reports Server (NTRS)

Mendelson, A.; Albers, L. U.

1975-01-01

The application of boundary integral equations to elastoplastic problems is reviewed. Details of the analysis as applied to torsion problems and to plane problems is discussed. Results are presented for the elastoplastic torsion of a square cross section bar and for the plane problem of notched beams. A comparison of different formulations as well as comparisons with experimental results are presented.

The Solar Dynamo

NASA Technical Reports Server (NTRS)

Hathaway, David H.

1998-01-01

The solar dynamo is the process by which the Sun's magnetic field is generated through the interaction of the field with convection and rotation. In this, it is kin to planetary dynamos and other stellar dynamos. Although the precise mechanism by which the Sun generates its field remains poorly understood despite decades of theoretical and observational work, recent advances suggest that solutions to this solar dynamo problem may be forthcoming. Two basic processes are involved in dynamo activity. When the fluid stresses dominate the magnetic stresses (high plasma beta = 8(pi)rho/B(sup 2)), shear flows can stretch magnetic field lines in the direction of the shear (the "alpha effect") and helical flows can lift and twist field lines into orthogonal planes (the "alpha effect"). These two processes can be active anywhere in the solar convection zone but with different results depending upon their relative strengths and signs. Little is known about how and where these processes occur. Other processes, such as magnetic diffusion and the effects of the fine scale structure of the solar magnetic field, pose additional problems.

Stress intensity factors in a hollow cylinder containing a radial crack

NASA Technical Reports Server (NTRS)

Delale, F.

1980-01-01

An exact formulation of the plane elasticity problem for a hollow cylinder or a disk containing a radial crack is given. The crack may be an external edge crack, an internal edge crack, or an embedded crack. It is assumed that on the crack surfaces the shear traction is zero and the normal traction is an arbitrary function of r. For various crack geometries and radius ratios, the numerical results are obtained for a uniform crack surface pressure, for a uniform pressure acting on the inside wall of the cylinder, and for a rotating disk.

Stress intensity factors in a hollow cylinder containing a radial crack

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1982-01-01

In this paper, an exact formulation of the plane elasticity problem for a hollow cylinder or a disk containing a radial crack is given. The crack may be an external edge crack, an internal edge crack, or an embedded crack. It is assumed that on the crack surfaces the shear traction is zero, and the normal traction is an arbitrary function of radius. For various crack geometries and radius ratios, the numerical results are obtained for a uniform crack surface pressure, for a uniform pressure acting on the inside wall of the cylinder, and for a rotating disk.

Viscoelastic study of an adhesively bonded joint

NASA Technical Reports Server (NTRS)

Joseph, P. F.

1983-01-01

The plane strain problem of two dissimilar orthotropic plates bonded with an isotropic, linearly viscoelastic adhesive is considered. Both the shear and the normal stresses in the adhesive are calculated for various geometries and loading conditions. Transverse shear deformations of the adherends are taken into account, and their effect on the solution is shown in the results. All three inplane strains of the adhesive are included. Attention is given to the effect of temperature, both in the adhesive joint problem and to the heat generation in a viscoelastic material under cyclic loading. This separate study is included because heat generation and or spatially varying temperature are at present too difficult to account for in the analytical solution of the bonded joint, but whose effect can not be ignored in design.

Dynamic stability of unidirectional fiber-reinforced viscoelastic composite plates

NASA Technical Reports Server (NTRS)

Chandiramani, N. K.; Librescu, L.

1989-01-01

This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a three-dimensional viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi's micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.

Fretting Stresses in Single Crystal Superalloy Turbine Blade Attachments

NASA Technical Reports Server (NTRS)

Arakere, Nagaraj K.; Swanson, Gregory

2000-01-01

Single crystal nickel base superalloy turbine blades are being utilized in rocket engine turbopumps and turbine engines because of their superior creep, stress rupture, melt resistance and thermomechanical fatigue capabilities over polycrystalline alloys. Currently the most widely used single crystal nickel base turbine blade superalloys are PWA 1480/1493 and PWA 1484. These alloys play an important role in commercial, military and space propulsion systems. High Cycle Fatigue (HCF) induced failures in aircraft gas turbine and rocket engine turbopump blades is a pervasive problem. Blade attachment regions are prone to fretting fatigue failures. Single crystal nickel base superalloy turbine blades are especially prone to fretting damage because the subsurface shear stresses induced by fretting action at the attachment regions can result in crystallographic initiation and crack growth along octahedral planes. Furthermore, crystallographic crack growth on octahedral planes under fretting induced mixed mode loading can be an order of magnitude faster than under pure mode I loading. This paper presents contact stress evaluation in the attachment region for single crystal turbine blades used in the NASA alternate Advanced High Pressure Fuel Turbo Pump (HPFTP/AT) for the Space Shuttle Main Engine (SSME). Single crystal materials have highly orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. Blades and the attachment region are modeled using a large-scale 3D finite element (FE) model capable of accounting for contact friction, material orthotrophy, and variation in primary and secondary crystal orientation. Contact stress analysis in the blade attachment regions is presented as a function of coefficient of friction and primary and secondary crystal orientation, Stress results are used to discuss fretting fatigue failure analysis of SSME blades. Attachment stresses are seen to reach peak values at locations where fretting cracks have been observed. Fretting stresses at the attachment region are seen to vary significantly as a function of crystal orientation. Attempts to adapt techniques used for estimating fatigue life in the airfoil region, for life calculations in the attachment region, are presented. An effective model for predicting crystallographic crack initiation under mixed mode loading is required for life prediction under fretting action.

Defects in crystalline packings of twisted filament bundles. I. Continuum theory of disclinations.

PubMed

Grason, Gregory M

2012-03-01

We develop the theory of the coupling between in-plane order and out-of-plane geometry in twisted, two-dimensionally ordered filament bundles based on the nonlinear continuum elasticity theory of columnar materials. We show that twisted textures of filament backbones necessarily introduce stresses into the cross-sectional packing of bundles and that these stresses are formally equivalent to the geometrically induced stresses generated in thin elastic sheets that are forced to adopt spherical curvature. As in the case of crystalline order on curved membranes, geometrically induced stresses couple elastically to the presence of topological defects in the in-plane order. We derive the effective theory of multiple disclination defects in the cross section of bundle with a fixed twist and show that above a critical degree of twist, one or more fivefold disclinations is favored in the elastic energy ground state. We study the structure and energetics of multidisclination packings based on models of equilibrium and nonequilibrium cross-sectional order.

Spatial variations in shear stress in a 3-D bifurcation model at low Reynolds numbers.

PubMed

Rouhanizadeh, Mahsa; Lin, Tiantian C; Arcas, Diego; Hwang, Juliana; Hsiai, Tzung K

2005-10-01

Real-time wall shear stress is difficult to monitor precisely because it varies in space and time. Microelectromechanical systems sensor provides high spatial resolution to resolve variations in shear stress in a 3-D bifurcation model for small-scaled hemodynamics. At low Reynolds numbers from 1.34 to 6.7 skin friction coefficients (C(f)) varied circumferentially by a factor of two or more within the bifurcation. At a Reynolds number of 6.7, the C(f) value at the lateral wall of the bifurcation along the 270 degree plane was 7.1, corresponding to a shear stress value of 0.0061 dyn/cm(2). Along the 180 degree plane, C(f) was 13 or 0.0079 dyn/cm(2), and at the medial wall along the 90 degree plane, C(f) was 10.3 or 0.0091 dyn/cm(2). The experimental skin friction coefficients correlated with values derived from the Navier-Stokes solutions.

Comparative study of tool machinery sliding systems; comparison between plane and cylindrical basic shapes

NASA Astrophysics Data System (ADS)

Glăvan, D. O.; Babanatsas, T.; Babanatis Merce, R. M.; Glăvan, A.

2018-01-01

The paper brings in attention the importance that the sliding system of a tool machinery is having in the final precision of the manufacturing. We are basically comparing two type of slides, one constructed with plane surfaces and the other one with circular cross-sections (as known as cylindrical slides), analysing each solution from the point of view of its technology of manufacturing, of the precision that the particular slides are transferring to the tool machinery, cost of production, etc. Special attention is given to demonstrate theoretical and to confirm by experimental works what is happening with the stress distribution in the case of plane slides and cylindrical slides, both in longitudinal and in cross-over sections. Considering the results obtained for the stress distribution in the transversal and longitudinal cross sections, by composing them, we can obtain the stress distribution on the semicircular slide. Based on the results, special solutions for establishing the stress distribution between two surfaces without interact in the contact zone have been developed.

Earthquake-induced static stress change on magma pathway in promoting the 2012 Copahue eruption

NASA Astrophysics Data System (ADS)

Bonali, F. L.

2013-11-01

It was studied how tectonic earthquake-induced static stress changes could have contributed to favouring the 22 December 2012 major eruption at Copahue volcano, Chile. Numerical modelling indicates that the vertical N60°E-striking magma pathway below Copahue was affected by a normal stress reduction induced by the Mw 8.8 Chile earthquake of 27 February 2010. A sensitivity analysis suggests that N-, NE- and E-striking vertical planes are affected by normal stress decrease (maximum at the NE-striking plane), and that also a possible inclined N60°E plane is affected by this reduction. Copahue did not have any magmatic event since 2000. Seismic signals of awakening started in April 2012 and the first volcanic event occurred on July 2012. Thus, it is here suggested a possible earthquake-induced feedback effect on the crust below the volcanic arc up to at least 3 years after a large subduction earthquake, favouring new eruptions.

Reynolds Stress Balance in Plane Wakes Subjected to Irrotational Strains

NASA Technical Reports Server (NTRS)

Rogers, Miichael M.; Merriam, Marshal (Technical Monitor)

1997-01-01

Direct numerical simulations of time-evolving turbulent plane wakes developing in the presence of various irrotational plane strains have been generated. A pseudospectral numerical method with up to 25 million modes is used to solve the equations in a reference frame moving with the irrotational strain. The initial condition for each simulation is taken from a previous turbulent self-similar plane wake direct numerical simulation at a velocity deficit Reynolds number, R(sub e), of about 2,000. All the terms in the equations governing the evolution of the Reynolds stresses have been calculated. The relative importance of the various terms is examined for the different strain geometries and the behavior of the individual terms is used to better assess whether the strained wakes are evolving self-similarly.

In-plane and Interlaminar Shear Strength of a Unidirectional Hi-nicalon Fiber-reinforced Celsian Matrix Composite

NASA Technical Reports Server (NTRS)

Uenal, O.; Bansal, N. P.

2000-01-01

In-plane and interlaminar shear strength of a unidirectional SiC fiber-reinforced (BaSr)Al2Si2O8 celsian composite were measured by the double-notch shear test method between room temperature and 1200 C. The interlaminar shear strength was lower than the in-plane shear strength at all temperatures. Stress analysis, using finite element modeling, indicated that shear stress concentration was not responsible for the observed difference in strength. Instead, the difference in layer architecture and thus, the favorable alignment of fiber-rich layers with the shear plane in the interlaminar specimens appears to be the reason for the low strength of this composite. A rapid decrease in strength was observed with temperature due to softening of the glassy phase in the material.

Mode 1 crack surface displacements for a round compact specimen subject to a couple and force

NASA Technical Reports Server (NTRS)

Gross, B.

1979-01-01

Mode I displacement coefficients along the crack surface are presented for a radially cracked round compact specimen, treated as a plane elastostatic problem, subjected to two types of loading; a uniform tensile stress and a nominal bending stress distribution across the net section. By superposition the resultant displacement coefficient or the corresponding influence coefficient can be obtained for any practical load location. Load line displacements are presented for A/D ratios ranging from 0.40 to 0.95, where A is the crack length measured from the crack mouth to the crack tip and D is the specimen diameter. Through a linear extrapolation procedure crack mouth displacements are also obtained. Experimental evidence shows that the results are valid over the range of A/D ratios analyzed for a practical pin loaded round compact specimen.

Steinhaus’ Geometric Location Problem for Random Samples in the Plane.

DTIC Science & Technology

1982-05-11

NAL 411R A1, ’I 7 - I STEINHAUS ’ GEOMETRIC LOCATION PROBLEM FOR RANDOM SAMPLES IN THE PLANE By Dorit Hochbaum and J. Michael Steele TECHNICAL REPORT...DEPARTMENT OF STATISTICS -Dltrib’ytion/ STANFORD UNIVERSITY A-I.abilty Codes STANFORD, CALIFORNIA Dist Spciat ecial Steinhaus ’ Geometric Location Problem for...Random Samples in the Plane By Dorit Hochbaum and J. Michael Steele I. Introduction. The work of H. Steinhaus U wf94 as apparently the first explicit

The relative stress-corrosion-cracking susceptibility of candidate aluminum-lithium alloys for aerospace structural applications

NASA Technical Reports Server (NTRS)

Pizzo, P. P.

1980-01-01

The microstructure and tensile properties of two powder metallurgy processed aluminum-lithium alloys were determined. Strength properties of 480 MPa yield and 550 MPa ultimate tensile strength with 5% strain to fracture were attained. Very little reduction in area was observed and fracture characteristics were brittle. The magnesium bearing alloy exhibited the highest strength and ductility, but fracture was intergranular. Recrystallization and grain growth, as well as coarse grain boundary precipitation, occurred in Alloy 2. The fracture morphology of the two alloys differed. Alloy 1 fractured along a plane of maximum shear stress, while Alloy 2 fractured along a plane of maximum tensile stress. It is found that a fixed orientation relationship exists between the shear fracture plane and the rolling direction which suggests that the PM alloys are strongly textured.

3-D Spontaneous Rupture Simulations of the 2016 Kumamoto, Japan, Earthquake

NASA Astrophysics Data System (ADS)

Urata, Yumi; Yoshida, Keisuke; Fukuyama, Eiichi

2017-04-01

We investigated the M7.3 Kumamoto, Japan, earthquake to illuminate why and how the rupture of the main shock propagated successfully by 3-D dynamic rupture simulations, assuming a complicated fault geometry estimated based on the distributions of aftershocks. The M7.3 main shock occurred along the Futagawa and Hinagu faults. A few days before, three M6-class foreshocks occurred. Their hypocenters were located along by the Hinagu and Futagawa faults and their focal mechanisms were similar to those of the main shock; therefore, an extensive stress shadow can have been generated on the fault plane of the main shock. First, we estimated the geometry of the fault planes of the three foreshocks as well as that of the main shock based on the temporal evolution of relocated aftershock hypocenters. Then, we evaluated static stress changes on the main shock fault plane due to the occurrence of the three foreshocks assuming elliptical cracks with constant stress drops on the estimated fault planes. The obtained static stress change distribution indicated that the hypocenter of the main shock is located on the region with positive Coulomb failure stress change (ΔCFS) while ΔCFS in the shallow region above the hypocenter was negative. Therefore, these foreshocks could encourage the initiation of the main shock rupture and could hinder the rupture propagating toward the shallow region. Finally, we conducted 3-D dynamic rupture simulations of the main shock using the initial stress distribution, which was the sum of the static stress changes by these foreshocks and the regional stress field. Assuming a slip-weakening law with uniform friction parameters, we conducted 3-D dynamic rupture simulations by varying the friction parameters and the values of the principal stresses. We obtained feasible parameter ranges to reproduce the rupture propagation of the main shock consistent with those revealed by seismic waveform analyses. We also demonstrated that the free surface encouraged the slip evolution of the main shock.

A 4-node assumed-stress hybrid shell element with rotational degrees of freedom

NASA Technical Reports Server (NTRS)

Aminpour, Mohammad A.

1990-01-01

An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or drilling degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8-node isoparametric element. This process is accomplished by assuming quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields along the edges of the element. In addition, the degrees of freedom at midside nodes are approximated in terms of the degrees of freedom at corner nodes. During this process the rotational degrees of freedom at the corner nodes enter into the formulation of the element. The stress field are expressed in the element natural-coordinate system such that the element remains invariant with respect to node numbering.

Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies

NASA Technical Reports Server (NTRS)

Llorente, Ignacio M.; Melson, N. Duane

1998-01-01

We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems.

Comparative study on hydrostatic strain, stress and dislocation density of Al{sub 0.3}Ga{sub 0.7}N/GaN heterostructure before and after a-Si{sub 3}N{sub 4} passivation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dinara, Syed Mukulika, E-mail: smdinara.iit@gmail.com; Jana, Sanjay Kr.; Mukhopadhyay, Partha

2015-08-28

The hydrostatic strain, stress and dislocation densities were comparatively analyzed before and after passivation of amorphous silicon nitride (a-Si{sub 3}N{sub 4}) layer on Al{sub 0.3}Ga{sub 0.7}N/GaN heterostructure by nondestructive high resolution x-ray diffraction (HRXRD) technique. The crystalline quality, in-plane and out-of plane strain were evaluated from triple-axis (TA) (ω-2θ) diffraction profile across the (002) reflection plane and double-axis (DA) (ω-2θ) glancing incidence (GI) diffraction profile across (105) reflection plane. The hydrostatic strain and stress of Al{sub 0.3}Ga{sub 0.7}N barrier layer were increased significantly after passivation and both are tensile in nature. The dislocation density of GaN was also analyzed andmore » no significant change was observed after passivation of the heterostructure. The crystalline quality was not degraded after passivation on the heterostructure confirmed by the full-width-half-maximum (FWHM) analysis.« less

Gravitational stresses in long symmetric ridges and valleys in anisotropic rock

USGS Publications Warehouse

Pan, E.; Amadei, B.; Savage, W.Z.

1994-01-01

The effect of topography and rock mass anisotropy on gravitational stresses in long isolated symmetric ridges and valleys is modeled using an analytical method proposed earlier by the first two authors. The rock mass deforms under a condition of plane strain. A parametric study is presented on the effect of (1) topography, (2) orientation of anisotropy and (3) degree of anisotropy on the magnitude and distribution of gravitational stresses in transversely isotropic rock masses with planes of anisotropy striking parallel to the ridge or valley axis. It is found that compressive stresses develop near ridge crests and that tensile stresses develop in valley bottoms and valley walls. The magnitude of the gravitational stresses is of the order of the characteristics stress ??{variant}g??b?? where ??{variant} is the rock density, g is the gravitational acceleration and ??b?? is the height of the ridge or depth of the valley. ?? 1994.

Photoelastic Analysis of Cracked Thick Walled Cylinders

NASA Astrophysics Data System (ADS)

Pastramă, Ştefan Dan

2017-12-01

In this paper, the experimental determination of the stress intensity factor in thick walled cylinders subject to uniform internal pressure and having longitudinal non-penetrating cracks is presented. Photoelastic measurements were used together with the expressions of the stress field near the crack tip for Mode I crack extension and a specific methodology for stress intensity factor determination. Two types of longitudinal cracks - internal and external - were considered. Four plane models were manufactured and analyzed in a plane polariscope at different values of the applied internal pressure. The values of the normalized stress intensity factor were calculated and the results were compared to those reported by other authors. A good accuracy was noticed, showing the reliability of the experimental procedure.

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

NASA Astrophysics Data System (ADS)

Zheng, R.-F.; Wu, T.-H.; Li, X.-Y.; Chen, W.-Q.

2018-06-01

The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

NASTRAN cyclic symmetry capability. [application to solid rocket propellant grains and space antennas

NASA Technical Reports Server (NTRS)

Macneal, R. H.; Harder, R. L.; Mason, J. B.

1973-01-01

A development for NASTRAN which facilitates the analysis of structures made up of identical segments symmetrically arranged with respect to an axis is described. The key operation in the method is the transformation of the degrees of freedom for the structure into uncoupled symmetrical components, thereby greatly reducing the number of equations which are solved simultaneously. A further reduction occurs if each segment has a plane of reflective symmetry. The only required assumption is that the problem be linear. The capability, as developed, will be available in level 16 of NASTRAN for static stress analysis, steady state heat transfer analysis, and vibration analysis. The paper includes a discussion of the theory, a brief description of the data supplied by the user, and the results obtained for two example problems. The first problem concerns the acoustic modes of a long prismatic cavity imbedded in the propellant grain of a solid rocket motor. The second problem involves the deformations of a large space antenna. The latter example is the first application of the NASTRAN Cyclic Symmetry capability to a really large problem.

46 CFR Appendix B to Part 154 - Stress Analyses Definitions

Code of Federal Regulations, 2010 CFR

2010-10-01

... 46 Shipping 5 2010-10-01 2010-10-01 false Stress Analyses Definitions B Appendix B to Part 154...—Stress Analyses Definitions The following are the standard definitions of stresses for the analysis of an independent tank type B: Normal stress means the component of stress normal to the plane of reference...

46 CFR Appendix B to Part 154 - Stress Analyses Definitions

Code of Federal Regulations, 2012 CFR

2012-10-01

... 46 Shipping 5 2012-10-01 2012-10-01 false Stress Analyses Definitions B Appendix B to Part 154...—Stress Analyses Definitions The following are the standard definitions of stresses for the analysis of an independent tank type B: Normal stress means the component of stress normal to the plane of reference...

46 CFR Appendix B to Part 154 - Stress Analyses Definitions

Code of Federal Regulations, 2013 CFR

2013-10-01

... 46 Shipping 5 2013-10-01 2013-10-01 false Stress Analyses Definitions B Appendix B to Part 154...—Stress Analyses Definitions The following are the standard definitions of stresses for the analysis of an independent tank type B: Normal stress means the component of stress normal to the plane of reference...

46 CFR Appendix B to Part 154 - Stress Analyses Definitions

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 5 2014-10-01 2014-10-01 false Stress Analyses Definitions B Appendix B to Part 154...—Stress Analyses Definitions The following are the standard definitions of stresses for the analysis of an independent tank type B: Normal stress means the component of stress normal to the plane of reference...

46 CFR Appendix B to Part 154 - Stress Analyses Definitions

Code of Federal Regulations, 2011 CFR

2011-10-01

... 46 Shipping 5 2011-10-01 2011-10-01 false Stress Analyses Definitions B Appendix B to Part 154...—Stress Analyses Definitions The following are the standard definitions of stresses for the analysis of an independent tank type B: Normal stress means the component of stress normal to the plane of reference...

A Transversely Isotropic Thermoelastic Theory

NASA Technical Reports Server (NTRS)

Arnold, S. M.

1989-01-01

A continuum theory is presented for representing the thermoelastic behavior of composites that can be idealized as transversely isotropic. This theory is consistent with anisotropic viscoplastic theories being developed presently at NASA Lewis Research Center. A multiaxial statement of the theory is presented, as well as plane stress and plane strain reductions. Experimental determination of the required material parameters and their theoretical constraints are discussed. Simple homogeneously stressed elements are examined to illustrate the effect of fiber orientation on the resulting strain distribution. Finally, the multiaxial stress-strain relations are expressed in matrix form to simplify and accelerate implementation of the theory into structural analysis codes.

Crack growth measured on flat and curved surfaces at cryogenic temperatures

NASA Technical Reports Server (NTRS)

Orange, T. W.; Sullivan, T. L.

1967-01-01

Multiple element continuity gage measures plane stress crack growth plus surface crack growth under plane strain conditions. The gage measures flat and curved surfaces and operates at cryogenic temperatures.

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

Stress interactions among arrays of tensile cracks in 3D: Implications for the nucleation of shear failure and the orientations of faults.

NASA Astrophysics Data System (ADS)

Healy, D.; Davis, T.

2017-12-01

In low porosity rocks it is widely believed that planes of shear failure nucleate through the interaction of arrays of smaller tensile microcracks. This model has been confirmed through laboratory rock deformation experiments and detailed microstructural analyses. In this contribution we use the Boundary Element Method (BEM) to model the interactions of arrays of tensile cracks, discretised as ellipsoidal voids in three dimensions (3D). We calculate the elastic stresses in the solid matrix surrounding the cracks resulting from an applied load and include the interaction effects of each crack upon all the others. We explore the role of variations in crack shape, size, position and orientation upon the total and locally perturbed stress fields. We calculate the average crack normal stress (CNS) acting over the area of each tensile crack, and then find the locus of the maximum value of this stress throughout the modelled volume. Following Reches & Lockner (1994) and Healy et al. (2006a, 2006b), we assert that planes of shear failure will most likely nucleate on surfaces parallel to the locus of maximum average CNS. These shear planes are oblique to all three principal stresses in the far field.

In plane stress analysis

NASA Technical Reports Server (NTRS)

Dillon, O. W., Jr.

1985-01-01

An investigation of the blowing up of UK numerical results for the inplane stress calculations for silicon ribbon is presented. The inplane stress that exists in a thin plate is governed by two general equations of equilibrium and compatibility.

Nano-indentation used to study pyramidal slip in GaN single crystals

NASA Astrophysics Data System (ADS)

Krimsky, E.; Jones, K. A.; Tompkins, R. P.; Rotella, P.; Ligda, J.; Schuster, B. E.

2018-02-01

The nucleation and structure of dislocations created by the nano-indentation of GaN samples with dislocation densities ≈103, 106 or 109 ⊥/cm2 were studied in the interest of learning how dislocations can be created to relieve the mismatch strain in ternary nitride films grown on (0001) oriented binary nitride substrates. Using transmission electron microscopy and stress analyses to assist in interpreting the nano-indentation data, we determined that the pop-ins in the indenter load vs. penetration depth curves are created by an avalanche process at stresses well above the typical yield stress. The process begins by the homogeneous formation of a basal plane screw dislocation that triggers the formation of pyramidal and other basal plane dislocations that relieve the excess stored elastic energy. It appears that pyramidal slip can occur on either the {1122} or {0111} planes, as there is little resistance to the cross slip of screw dislocations.

The generation and morphology of single-crystal silicon carbide wear particles under adhesive conditions

NASA Technical Reports Server (NTRS)

Miyoshi, K.; Buckley, D. H.

1981-01-01

Sliding friction experiments were performed in vacuum at room temperature on a plane-type SiC surface in contact with iron-based binary alloys. Multiangular and spherical wear particles were found to form as a result of multipass sliding. The multiangular particles were produced by primary and secondary cracking of the 0001, 10(-)10, and 11(-)20 plane-type cleavage planes under the Hertzian stress field or local inelastic deformation zone. When alloy surfaces are in contact with silicon carbide under a load of 0.2 N, the alloy around the contact area is subjected to stresses that are close to the elastic limit in the elastic deformation region and/or exceed it. It was also found that spherical wear particles may be produced by two mechanisms: a penny-shaped fracture along the circular stress trajectories under the local inelastic deformation zone, and the attrition and fatigue of wear particles.

Centre-based restricted nearest feature plane with angle classifier for face recognition

NASA Astrophysics Data System (ADS)

Tang, Linlin; Lu, Huifen; Zhao, Liang; Li, Zuohua

2017-10-01

An improved classifier based on the nearest feature plane (NFP), called the centre-based restricted nearest feature plane with the angle (RNFPA) classifier, is proposed for the face recognition problems here. The famous NFP uses the geometrical information of samples to increase the number of training samples, but it increases the computation complexity and it also has an inaccuracy problem coursed by the extended feature plane. To solve the above problems, RNFPA exploits a centre-based feature plane and utilizes a threshold of angle to restrict extended feature space. By choosing the appropriate angle threshold, RNFPA can improve the performance and decrease computation complexity. Experiments in the AT&T face database, AR face database and FERET face database are used to evaluate the proposed classifier. Compared with the original NFP classifier, the nearest feature line (NFL) classifier, the nearest neighbour (NN) classifier and some other improved NFP classifiers, the proposed one achieves competitive performance.

Understanding of the development of in-plane residual stress in sol-gel-derived metal oxide thin films

NASA Astrophysics Data System (ADS)

Ohno, Kentaro; Uchiyama, Hiroaki; Kozuka, Hiromitsu

2012-01-01

The in-plane residual stress in thin films greatly affects their properties and functionality as well as the substrate bending, and hence is an important factor to be controlled. In order to obtain general knowledge on the development of residual stress in sol-gel-derived oxide thin films, the in-plane residual stress was measured for yttria stabilized zirconia gel films on Si(100) wafers as a function of firing temperature by measuring the substrate curvature. The films showed a rather complex variation in residual stress, and the mechanism of the residual stress evolution was discussed, referencing the intrinsic stress and the x-ray diffraction data. At low annealing temperatures of 100-200 °C, the residual tensile stress decreased and became compressive partially due to the structural relaxation occurring during cooling. When the firing temperature was increased over 200 °C, the residual stress turned tensile, and increased with increasing annealing temperature, which was attributed to the increase in intrinsic stress due to film densification as well as to the reduced structural relaxation due to the progress of densification. The residual tensile stress slightly decreased at firing temperatures of 500-600 °C, which was attributed to the reduction in intrinsic stress due to thermally activated atomic diffusion as well as to emergence of thermal stress. At firing temperature over 600 °C, the residual tensile stress increased again, which was attributed to the increase in thermal stress generated during cooling due to the increased Young's modulus of the film. Although appearing to be complicated, the whole variation of residual stress with firing temperature could be understood in terms of film densification, structural relaxation, atomic diffusion, progress of crystallization and thermal strain. The illustration presented in the work may provide a clear insight on how the residual stress could be developed in a variety of functional sol-gel-derived, crystalline oxide thin films.

Fracture Mechanics of Thin, Cracked Plates Under Tension, Bending and Out-of-Plane Shear Loading

NASA Technical Reports Server (NTRS)

Zehnder, Alan T.; Hui, C. Y.; Potdar, Yogesh; Zucchini, Alberto

1999-01-01

Cracks in the skin of aircraft fuselages or other shell structures can be subjected to very complex stress states, resulting in mixed-mode fracture conditions. For example, a crack running along a stringer in a pressurized fuselage will be subject to the usual in-plane tension stresses (Mode-I) along with out-of-plane tearing stresses (Mode-III like). Crack growth and initiation in this case is correlated not only with the tensile or Mode-I stress intensity factor, K(sub I), but depends on a combination of parameters and on the history of crack growth. The stresses at the tip of a crack in a plate or shell are typically described in terms of either the small deflection Kirchhoff plate theory. However, real applications involve large deflections. We show, using the von-Karman theory, that the crack tip stress field derived on the basis of the small deflection theory is still valid for large deflections. We then give examples demonstrating the exact calculation of energy release rates and stress intensity factors for cracked plates loaded to large deflections. The crack tip fields calculated using the plate theories are an approximation to the actual three dimensional fields. Using three dimensional finite element analyses we have explored the relationship between the three dimensional elasticity theory and two dimensional plate theory results. The results show that for out-of-plane shear loading the three dimensional and Kirchhoff theory results coincide at distance greater than h/2 from the crack tip, where h/2 is the plate thickness. Inside this region, the distribution of stresses through the thickness can be very different from the plate theory predictions. We have also explored how the energy release rate varies as a function of crack length to plate thickness using the different theories. This is important in the implementation of fracture prediction methods using finite element analysis. Our experiments show that under certain conditions, during fatigue crack growth, the presence of out-of-plane shear loads induces a great deal of contact and friction on the crack surfaces, dramatically reducing crack growth rate. A series of experiments and a proposed computational approach for accounting for the friction is discussed.

The Inclusion of In-Plane Stresses in Delamination Criteria

NASA Technical Reports Server (NTRS)

Fenske, Matthew T.

1999-01-01

A study of delamination failure was conducted with emphasis on delamination criteria. Evidence is presented which supports the inclusion of the in-plane stresses in addition to the interlaminar stress terms in delamination criteria. The delamination is characterized as the failure of a resin rich region in between ply sets. The entire six component stress state in this resin layer is calculated through a finite element analysis, averaged over a dimension of 1.75 ply thicknesses, and used in a Modified von Mises Delamination Criterion. This criterion builds onto previous criteria by including all six stress components in the interply resin layer. The MVMDC shows good correlation to experimental data. The results show that the treatment of delamination as the failure of a finite interply resin layer is a valid method and that the MVMDC, considering the full stress state, accurately indicates delamination for different laminate families.

Failure analysis of composite laminates including biaxial compression

NASA Technical Reports Server (NTRS)

Tennyson, R. C.; Elliott, W. G.

1983-01-01

This report describes a continued effort on the development and application of the tensor polynomial failure criterion for composite laminate analysis. In particular, emphasis is given to the design, construction and testing of a cross-beam laminate configuration to obtain "pure' biaxial compression failure. The purpose of this test case was to provide to permit "closure' of the cubic form of the failure surface in the 1-2 compression-compression quadrant. This resulted in a revised set of interaction strength parameters and the construction of a failure surface which can be used with confidence for strength predictions, assuming a plane stress state exists. Furthermore, the problem of complex conjugate roots which can occur in some failure regions is addressed and an "engineering' interpretation is provided. Results are presented illustrating this behavior and the methodology for overcoming this problem is discussed.

Absence of earthquake correlation with Earth tides: An indication of high preseismic fault stress rate

USGS Publications Warehouse

Vidale, J.E.; Agnew, D.C.; Johnston, M.J.S.; Oppenheimer, D.H.

1998-01-01

Because the rate of stress change from the Earth tides exceeds that from tectonic stress accumulation, tidal triggering of earthquakes would be expected if the final hours of loading of the fault were at the tectonic rate and if rupture began soon after the achievement of a critical stress level. We analyze the tidal stresses and stress rates on the fault planes and at the times of 13,042 earthquakes which are so close to the San Andreas and Calaveras faults in California that we may take the fault plane to be known. We find that the stresses and stress rates from Earth tides at the times of earthquakes are distributed in the same way as tidal stresses and stress rates at random times. While the rate of earthquakes when the tidal stress promotes failure is 2% higher than when the stress does not, this difference in rate is not statistically significant. This lack of tidal triggering implies that preseismic stress rates in the nucleation zones of earthquakes are at least 0.15 bar/h just preceding seismic failure, much above the long-term tectonic stress rate of 10-4 bar/h.

Mode I crack surface displacements for a round compact specimen subject to a couple and force

NASA Technical Reports Server (NTRS)

Gross, B.

1979-01-01

Mode I displacement coefficients along the crack surface are presented for a radially cracked round compact specimen, treated as a plane elastostatic problem, subjected to two types of loading; a uniform tensile stress and a nominal bending stress distribution across the net section. By superposition the resultant displacement coefficient or the corresponding influence coefficient can be obtained for any practical load location. Load line displacements are presented for A/D ratios ranging from 0.40 to 0.95, where A is the crack length measured from the crack mouth to the crack tip and D is the specimen diameter. Through a linear extrapolation procedure crack mouth displacements are also obtained. Experimental evidence shows that the results of this study are valid over the range of A/D ratios analyzed for a practical pin loaded round compact specimen.

On investigating wall shear stress in two-dimensional plane turbulent wall jets

NASA Astrophysics Data System (ADS)

Mehdi, Faraz; Johansson, Gunnar; White, Christopher; Naughton, Jonathan

2012-11-01

Mehdi & White [Exp Fluids 50:43-51(2011)] presented a full momentum integral based method for determining wall shear stress in zero pressure gradient turbulent boundary layers. They utilized the boundary conditions at the wall and at the outer edge of the boundary layer. A more generalized expression is presented here that uses just one boundary condition at the wall. The method is mathematically exact and has an advantage of having no explicit streamwise gradient terms. It is successfully applied to two different experimental plane turbulent wall jet datasets for which independent estimates of wall shear stress were known. Complications owing to experimental inaccuracies in determining wall shear stress from the proposed method are also discussed.

Texture formation in FePt thin films via thermal stress management

NASA Astrophysics Data System (ADS)

Rasmussen, P.; Rui, X.; Shield, J. E.

2005-05-01

The transformation variant of the fcc to fct transformation in FePt thin films was tailored by controlling the stresses in the thin films, thereby allowing selection of in- or out-of-plane c-axis orientation. FePt thin films were deposited at ambient temperature on several substrates with differing coefficients of thermal expansion relative to the FePt, which generated thermal stresses during the ordering heat treatment. X-ray diffraction analysis revealed preferential out-of-plane c-axis orientation for FePt films deposited on substrates with a similar coefficients of thermal expansion, and random orientation for FePt films deposited on substrates with a very low coefficient of thermal expansion, which is consistent with theoretical analysis when considering residual stresses.

A Finite Element Study on Crack Tip Deformation.

DTIC Science & Technology

1976-08-01

REPOPINUMDER • TNOR(.) CONTRACT OR GRANT NUMSER(.) ______ ~~~ ~~~ /I. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMEN T. PROJECT . TASKJ AREA ...that the bulk of the strain measurements agree well with the results of the plane stress calculations except in the small area close to the crack tip...that the bulk of the strain measurements agree veil with the results of the plane stress calcula- tions except in the small area cloae to the crack

A mixed formulation for interlaminar stresses in dropped-ply laminates

NASA Technical Reports Server (NTRS)

Harrison, Peter N.; Johnson, Eric R.

1993-01-01

A structural model is developed for the linear elastic response of structures consisting of multiple layers of varying thickness such as laminated composites containing internal ply drop-offs. The assumption of generalized plane deformation is used to reduce the solution domain to two dimensions while still allowing some out-of-plane deformation. The Hellinger-Reissner variational principle is applied to a layerwise assumed stress distribution with the resulting governing equations solved using finite differences.

Iterative joint inversion of in-situ stress state along Simeulue-Nias Island

NASA Astrophysics Data System (ADS)

Agustina, Anisa; Sahara, David P.; Nugraha, Andri Dian

2017-07-01

In-situ stress inversion from focal mechanisms requires knowledge of which of the two nodal planes is the fault. This is challenging, in particular, because of the inherent ambiguity of focal mechanisms the fault and the auxiliary nodal plane could not be distinguished. A relatively new inversion technique for estimating both stress and fault plane is developed by Vavryĉuk in 2014. The fault orientations are determined by applying the fault instability constraint, and the stress is calculated in iterations. In this study, this method is applied to a high-density earthquake regions, Simeulue-Batu Island. This area is interesting to be investigated because of the occurrence of the two large earthquakes, i.e. Aceh 2004 and Nias 2005 earthquake. The inversion was done based on 343 focal mechanisms data with Magnitude ≥5.5 Mw between 25th Mei 1977- 25th August 2015 from Harvard and Global Centroid Moment Tensor (GCMT) catalog. The area is divided into some grids, in which the analysis of stress orientation variation and its shape ratio is done for each grid. Stress inversion results show that there are three segments along Simeulue-Batu Island based on the variation of orientation stress σ1. The stress characteristics of each segments are discussed, i.e. shape ratio, principal stress orientation and subduction angle. Interestingly, the highest value of shape ratio is 0.93 and its association with the large earthquake Aceh 2004. This suggest that the zonation obtained in this study could also be used as a proxy for the hazard map.

Stress Distribution Around a Circular Hole in Square Plates, Loaded Uniformly in the Plane, on Two Opposite Sides of the Square. Optimum Shapes of Central Holes in Square Plates Subjected to Uniaxial Uniform Load. Optimization of Hole Shapes in Circular Cylindrical Shells Under Axial Tension,

DTIC Science & Technology

1981-09-01

brittle and photoelastic coatings, gages, grids, holography and speckle to solve two- and three-dimensional problems in elasticity, plasticity...weight by 10%. The efficiency coefficient is increased from 0.59 to 0.95. Tests with 4 brittle material show an increase in strength of 20%. An ideal...particularly useful for components made with brittle materials, or components made with ductile materials subjected to fatigue. Ple I Fa 441 ( .t

DD3MAT - a code for yield criteria anisotropy parameters identification.

NASA Astrophysics Data System (ADS)

Barros, P. D.; Carvalho, P. D.; Alves, J. L.; Oliveira, M. C.; Menezes, L. F.

2016-08-01

This work presents the main strategies and algorithms adopted in the DD3MAT inhouse code, specifically developed for identifying the anisotropy parameters. The algorithm adopted is based on the minimization of an error function, using a downhill simplex method. The set of experimental values can consider yield stresses and r -values obtained from in-plane tension, for different angles with the rolling direction (RD), yield stress and r -value obtained for biaxial stress state, and yield stresses from shear tests performed also for different angles to RD. All these values can be defined for a specific value of plastic work. Moreover, it can also include the yield stresses obtained from in-plane compression tests. The anisotropy parameters are identified for an AA2090-T3 aluminium alloy, highlighting the importance of the user intervention to improve the numerical fit.

Simultaneous determination of the residual stress, elastic modulus, density and thickness of ultrathin film utilizing vibrating doubly clamped micro-/nanobeams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stachiv, Ivo, E-mail: stachiv@fzu.cz; Institute of Physics, Czech Academy of Sciences, Prague; Kuo, Chih-Yun

2016-04-15

Measurement of ultrathin film thickness and its basic properties can be highly challenging and time consuming due to necessity of using several very sophisticated devices. Here, we report an easy accessible resonant based method capable to simultaneously determinate the residual stress, elastic modulus, density and thickness of ultrathin film coated on doubly clamped micro-/nanobeam. We show that a general dependency of the resonant frequencies on the axial load is also valid for in-plane vibrations, and the one depends only on the considered vibrational mode. As a result, we found that the film elastic modulus, density and thickness can be evaluatedmore » from two measured in-plane and out-plane fundamental resonant frequencies of micro-/nanobeam with and without film under different prestress forces. Whereas, the residual stress can be determined from two out-plane (in-plane) measured consecutive resonant frequencies of beam with film under different prestress forces without necessity of knowing film and substrate properties and dimensions. Moreover, we also reveal that the common uncertainties in force (and thickness) determination have a negligible (and minor) impact on the determined film properties. The application potential of the present method is illustrated on the beam made of silicon and SiO{sub 2} with deposited 20 nm thick AlN and 40 nm thick Au thin films, respectively.« less

Crack Turning Mechanics of Composite Wing Skin Panels

NASA Technical Reports Server (NTRS)

Yuan, F. G.; Reeder, James R. (Technical Monitor)

2001-01-01

The safety of future composite wing skin integral stiffener panels requires a full understanding of failure mechanisms of these damage tolerance critical structures under both in-plane and bending loads. Of primary interest is to derive mathematical models using fracture mechanics in anisotropic cracked plate structures, to assess the crack turning mechanisms, and thereby to enhance the residual strength in the integral stiffener composite structures. The use of fracture mechanics to assess the failure behavior in a cracked structure requires the identification of critical fracture parameters which govern the severity of stress and deformation field ahead of the flaw, and which can be evaluated using information obtained from the flaw tip. In the three-year grant, the crack-tip fields under plane deformation, crack-tip fields for anisotropic plates and anisotropic shells have been obtained. In addition, methods for determining the stress intensity factors, energy release rate, and the T-stresses have been proposed and verified. The research accomplishments can be summarized as follows: (1) Under plane deformation in anisotropic solids, the asymptotic crack-tip fields have been obtained using Stroh formalism; (2) The T-stress and the coefficient of the second term for sigma(sub y), g(sub 32), have been obtained using path-independent integral, the J-integral and Betti's reciprocal theorem together with auxiliary fields; (3) With experimental data performed by NASA, analyses indicated that the mode-I critical stress intensity factor K(sub Q) provides a satisfactory characterization of fracture initiation for a given laminate thickness, provided the failure is fiber-dominated and crack extends in a self-similar manner; (4) The high constraint specimens, especially for CT specimens, due to large T-stress and large magnitude of negative g(sub 32) term may be expected to inhibit the crack extension in the same plane and promote crack turning; (5) Crack turning out of crack plane in generally anisotropic solids under plane deformation has been studied; (6) The role of T-stress and the higher-order term of sigma(sub y) on the crack turning and stability of the kinked crack has been quantified; (7) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner plate theory) in an anisotropic plate under bending, twisting moments, and transverse shear loads has been presented; (8) The expression of the path-independent J-integral in terms of the generalized stress and strain has been derived; (9) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner shallow shell theory) in a general anisotropic shell has been developed; (10) The Stroh formalism was used to characterize the crack tip fields in shells up to the second term and the energy release rate was expressed in a very compact form.

Lattice strain of osmium diboride under high pressure and nonhydrostatic stress

NASA Astrophysics Data System (ADS)

Kavner, Abby; Weinberger, Michelle B.; Shahar, Anat; Cumberland, Robert W.; Levine, Jonathan B.; Kaner, Richard B.; Tolbert, Sarah H.

2012-07-01

The lattice strain behavior of osmium diboride—a member of a group of third-row transition metal borides associated with hard/superhard behavior—has been studied using radial diffraction in a diamond anvil cell under high pressure and non-hydrostatic stress. We interpret the average values of the measured lattice strains as a lower-bound to the lattice-plane dependent yield strengths using existing estimates for the elastic constants of OsB2, with a yield strength of 11 GPa at 27.5 GPa of hydrostatic pressure. The measured differential lattice strains show significant plane-dependent anisotropy, with the (101) lattice plane showing the largest differential strain and the (001) lattice plane showing the least strain. At the highest pressure, the a-axis develops a larger compressive strain and supports a larger differential strain than either the b or c axes. This causes an increase in the c/a ratio and a decrease in the a/b ratio especially in the maximum stress direction. The large strength anisotropy of this material points to possible ways to modulate directional mechanical properties by taking advantage of the interplay between aggregate polycrystalline texture with directional mechanical properties.

Observations of static Coulomb stress triggering of the November 2011 M5.7 Oklahoma earthquake sequence

USGS Publications Warehouse

Sumy, Danielle F.; Cochran, Elizabeth S.; Keranen, Katie M.; Wei, Maya; Abers, Geoffrey A.

2014-01-01

In November 2011, a M5.0 earthquake occurred less than a day before a M5.7 earthquake near Prague, Oklahoma, which may have promoted failure of the mainshock and thousands of aftershocks along the Wilzetta fault, including a M5.0 aftershock. The M5.0 foreshock occurred in close proximity to active fluid injection wells; fluid injection can cause a buildup of pore fluid pressure, decrease the fault strength, and may induce earthquakes. Keranen et al. [2013] links the M5.0 foreshock with fluid injection, but the relationship between the foreshock and successive events has not been investigated. Here we examine the role of coseismic Coulomb stress transfer on earthquakes that follow the M5.0 foreshock, including the M5.7 mainshock. We resolve the static Coulomb stress change onto the focal mechanism nodal plane that is most consistent with the rupture geometry of the three M ≥ 5.0 earthquakes, as well as specified receiver fault planes that reflect the regional stress orientation. We find that Coulomb stress is increased, e.g., fault failure is promoted, on the nodal planes of ~60% of the events that have focal mechanism solutions, and more specifically, that the M5.0 foreshock promoted failure on the rupture plane of the M5.7 mainshock. We test our results over a range of effective coefficient of friction values. Hence, we argue that the M5.0 foreshock, induced by fluid injection, potentially triggered a cascading failure of earthquakes along the complex Wilzetta fault system.

Effect of screw position on load transfer in lumbar pedicle screws: A non-idealized finite element analysis

PubMed Central

Newcomb, Anna G. U. S.; Baek, Seungwon; Kelly, Brian P.; Crawford, Neil R.

2016-01-01

Angled screw insertion has been advocated to enhance fixation strength during posterior spine fixation. Stresses on a pedicle screw and surrounding vertebral bone with different screw angles were studied by finite element analysis during simulated multidirectional loading. Correlations between screw-specific vertebral geometric parameters and stresses were studied. Angulations in both the sagittal and axial planes affected stresses on the cortical and cancellous bones and the screw. Pedicle screws pointing laterally (vs. straight or medially) in the axial plane during superior screw angulation may be advantageous in terms of reducing the risk of both screw loosening and screw breakage. PMID:27454197

Manual for Program PSTRESS: Peel stress computation

NASA Technical Reports Server (NTRS)

Barkey, Derek A.; Madan, Ram C.

1987-01-01

Described is the use of the interactive FORTRAN computer program PSTRESS, which computes a closed form solution for two bonded plates subjected to applied moments, vertical shears, and in-plane forces. The program calculates in-plane stresses in the plates, deflections of the plates, and peel and shear stresses in the adhesive. The document briefly outlines the analytical method used by PSTRESS, describes the input and output of the program, and presents a sample analysis. The results of the latter are shown to be within a few percent of results obtained using a NASTRAN finite element analysis. An appendix containing a listing of PSTRESS is included.

Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory. I - Stress and displacement

NASA Technical Reports Server (NTRS)

Librescu, L.; Khdeir, A. A.

1988-01-01

A simple theory for bending of composite anisotropic plates that are laminated symmetrically about their mid-plane is presented. This theory incorporates transverse shear deformation and transverse normal stress as well as the higher-order effects and fulfills the static conditions on the external boundary planes. Further on, by using Levy-type solutions considered in conjunction with the state space concept, the state of stress and displacement of rectangular plates for a variety of edge conditions is determined and the results are compared to their first-order shear deformation and classical counterparts, obtained by using the same state-space technique.

Sendai-Okura earthquake swarm induced by the 2011 Tohoku-Oki earthquake in the stress shadow of NE Japan: Detailed fault structure and hypocenter migration

NASA Astrophysics Data System (ADS)

Yoshida, Keisuke; Hasegawa, Akira

2018-05-01

We investigated the distribution and migration of hypocenters of an earthquake swarm that occurred in Sendai-Okura (NE Japan) 15 days after the 2011 M9.0 Tohoku-Oki earthquake, despite the decrease in shear stress due to the static stress change. Hypocenters of 2476 events listed in the JMA catalogue were relocated based on the JMA unified catalogue data in conjunction with data obtained by waveform cross correlation. Hypocenter relocation was successful in delineating several thin planar structures, although the original hypocenters presented a cloud-like distribution. The hypocenters of this swarm event migrated along several planes from deeper to shallower levels rather than diffusing three-dimensionally. One of the nodal planes of the focal mechanisms was nearly parallel to the planar structure of the hypocenters, supporting the idea that each earthquake occurred by causing slip on parts of the same plane. The overall migration velocity of the hypocenters could be explained by the fluid diffusion model with a typical value of hydraulic diffusivity (0.15 m2/s); however, the occurrence of some burst-like activity with much higher migration velocity suggests the possibility that aseismic slip also contributed to triggering the earthquakes. We suggest that the 2011 Sendai-Okura earthquake swarm was generated as follows. (1) The 2011 Tohoku-Oki earthquake caused WNW-ESE extension in the focal region of the swarm, which accordingly reduced shear stress on the fault planes. However, the WNW-ESE extension allowed fluids to move upward from the S-wave reflectors in the mid-crust immediately beneath the focal region. (2) The fluids rising from the mid-crust intruded into several existing planes, which reduced their frictional strengths and caused the observed earthquake swarm. (3) The fluids, and accordingly, the hypocenters of the triggered earthquakes, migrated upward along the fault planes. It is possible that the fluids also triggered aseismic slip, which caused intermittent burst-like activity.

Measurement of multiaxial ply strength by an off-axis flexure test

NASA Technical Reports Server (NTRS)

Crews, John H., Jr.; Naik, Rajiv A.

1992-01-01

An off-axis flexure (OAF) test was performed to measure ply strength under multiaxial stress states. This test involves unidirectional off-axis specimens loaded in bending, using an apparatus that allows these anisotropic specimens to twist as well as flex without the complications of a resisting torque. A 3D finite element stress analysis verified that simple beam theory could be used to compute the specimen bending stresses at failure. Unidirectional graphite/epoxy specimens with fiber angles ranging from 90 deg to 15 deg have combined normal and shear stresses on their failure planes that are typical of 45 deg plies in structural laminates. Tests for a range of stress states with AS4/3501-6 specimens showed that both normal and shear stresses on the failure plane influenced cracking resistance. This OAF test may prove to be useful for generating data needed to predict ply cracking in composite structures and may also provide an approach for studying fiber-matrix interface failures under stress states typical of structures.

A cylindrical shell with an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1983-01-01

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system to five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented. Previously annunced in STAR as N83-16783

3-D dynamic rupture simulations of the 2016 Kumamoto, Japan, earthquake

NASA Astrophysics Data System (ADS)

Urata, Yumi; Yoshida, Keisuke; Fukuyama, Eiichi; Kubo, Hisahiko

2017-11-01

Using 3-D dynamic rupture simulations, we investigated the 2016 Mw7.1 Kumamoto, Japan, earthquake to elucidate why and how the rupture of the main shock propagated successfully, assuming a complicated fault geometry estimated on the basis of the distributions of the aftershocks. The Mw7.1 main shock occurred along the Futagawa and Hinagu faults. Within 28 h before the main shock, three M6-class foreshocks occurred. Their hypocenters were located along the Hinagu and Futagawa faults, and their focal mechanisms were similar to that of the main shock. Therefore, an extensive stress shadow should have been generated on the fault plane of the main shock. First, we estimated the geometry of the fault planes of the three foreshocks as well as that of the main shock based on the temporal evolution of the relocated aftershock hypocenters. We then evaluated the static stress changes on the main shock fault plane that were due to the occurrence of the three foreshocks, assuming elliptical cracks with constant stress drops on the estimated fault planes. The obtained static stress change distribution indicated that Coulomb failure stress change (ΔCFS) was positive just below the hypocenter of the main shock, while the ΔCFS in the shallow region above the hypocenter was negative. Therefore, these foreshocks could encourage the initiation of the main shock rupture and could hinder the propagation of the rupture toward the shallow region. Finally, we conducted 3-D dynamic rupture simulations of the main shock using the initial stress distribution, which was the sum of the static stress changes caused by these foreshocks and the regional stress field. Assuming a slip-weakening law with uniform friction parameters, we computed 3-D dynamic rupture by varying the friction parameters and the values of the principal stresses. We obtained feasible parameter ranges that could reproduce the characteristic features of the main shock rupture revealed by seismic waveform analyses. We also observed that the free surface encouraged the slip evolution of the main shock.[Figure not available: see fulltext.

Three-dimensional finite element analyses of the local mechanical behavior of riveted lap joints

NASA Astrophysics Data System (ADS)

Iyer, Kaushik Arjunan

Three-dimensional elastic-plastic finite element models of single and double rivet-row lap joints have been developed to evaluate local distortions and the mechanics of airframe-type 7075-T6 aluminum alloy riveted assemblies. Loading induced distortion features such as the excess assembly compliance, rivet tilt, local in- and out-of-plane slips and stress concentration factors are evaluated as functions of rivet countersinking, rivet material and friction coefficient. Computed features are examined to identify alterations in the proportions of in-plane and out-of-plane load transmission across rivet-panel interfaces and isolate global and lower-order effects present in the complex response of these multi-body assemblies. Analytical procedures are validated by comparing calculated and measured values of excess assembly compliance and local panel bending. Direct out-of-plane load transmission between the rivet heads and panels affects global deformation features such as remote panel bending and local features such as the panel stress concentration factor. The increase in stress concentration due to panel bending is self-limiting owing to decreasing in-plane load bearing with increasing rivet tilt, which is a composite reflection of the basic rivet deformation modes of shear and rotation. Calculations have also been performed to define approximate steady-state fretting fatigue conditions that lead to crack initiation at a panel hole surface in single and double rivet-row assemblies for countersunk and non-countersunk rivets. These account for and isolate effects of interference and clamping forces on fatigue performance by comparing computed circumferential variations of bulk residual stresses, cyclic stress range and mean stress. With interference, a non-countersunk assembly is shown to be as prone to crack initiation as a countersunk assembly. Frictional work due to fretting is evaluated and the physical location of fretting fatigue crack initiation is predicted by interpreting combined effects of primary fretting fatigue parameters such as contact pressure and slip amplitude. Angular shifts in the peaks of conventional fatigue and fretting fatigue parameters caused by interference may be exploited to optimize the residual life of aging airframes.

The effects of eccentricities on the fracture of off-axis fiber composites. [carbon fiber reinforced plastics

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Sinclair, J. H.

1978-01-01

Finite element analyses were performed to investigate theoretically the effects of in-plane and out-of-plane eccentricities, bending or twisting, and thickness nonuniformity on the axial stress and strain variations across the width of off-axis specimens. The results are compared with measured data and are also used to assess the effects of these eccentricities on the fracture stress of off-axis fiber composites. Guidelines for detecting and minimizing the presence of eccentricities are described.

The effects of eccentricities on the fracture of off-axis fiber composites

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Sinclair, J. H.

1978-01-01

Finite element analyses were performed to investigate theoretically the effects of in-plane and out-of plane eccentricities, bending or twisting, and thickness nonuniformity on the axial stress and strain variations across the width of off-axis specimens. The results are compared with measured data and are also used to access the effects of these eccentricities on the fracture stress of off-axis fiber composites. Guidelines for detecting and minimizing the presence of eccentricities are described.

Tracking Local Spatiotemporal Microfracturing Processes and Stress Field Evolution Before and After Laboratory Fault Slip

NASA Astrophysics Data System (ADS)

Kwiatek, G.; Orlecka-Sikora, B.; Goebel, T.; Martínez-Garzón, P.; Dresen, G.; Bohnhoff, M.

2017-12-01

In this study we investigate details of spatial and temporal evolution of the stress field and damage at a pre-existing fault plane in laboratory stick-slip friction experiments performed on Westerly Granite sample. Specimen of 10 cm height and 4 cm diameter was deformed at a constant strain rate of 3×10-6 s-1 and confining pressure of 150 MPa. Here we analyze a series of 6 macroscopic slip events occurring on a rough fault during the course of experiment. Each macroscopic slip was associated with an intense femtoseismic acoustic emission (AE) activity recorded using a 16-channel transient recording system. To monitor the the spatiotemporal damage evolution, and unravel the micromechanical processes governing nucleation and propagation of slip events, we analyzed AE source characteristics (magnitude, seismic moment tensors, focal mechanisms), as well as the statistical properties (b-, c-, d- value) of femtoseismicity. In addition, the calculated AE focal mechanisms were used to reveal the spatiotemporal evolution of local stress field orientations and stress shape ratio coefficients over the fault plane, as well as additional parameters quantifying proximity to failure of individual fault patches. The calculated characteristics are used to comprehensively describe the complexity of the spatial and temporal evolution of the stress over the fault plane, and properties of the corresponding seismicity before and after the macroscopic slips. The observed faulting processes and characteristics are discussed in the context of global strain and stress changes, fault maturation, and earthquake stress drop.

Towards a unified solution of localization failure with mixed finite elements

NASA Astrophysics Data System (ADS)

Benedetti, Lorenzo; Cervera, Miguel; Chiumenti, Michele; Zeidler, Antonia; Fischer, Jan-Thomas

2015-04-01

Notwithstanding computational scientists made significant steps in the numerical simulation of failure in last three decades, the strain localization problem is still an open question. Especially in a geotechnical setting, when dealing with stability analysis of slopes, it is necessary to provide correct distribution of displacements, to evaluate the stresses in the ground and, therefore, to be able to identify the slip lines that brings to progressive collapse of the slope. Finite elements are an attractive method of solution thanks to profound mathematical foundations and the possibility of describing generic geometries. In order to account for the onset of localization band, the smeared crack approach [1] is introduced, that is the strain localization is assumed to occur in a band of finite width where the displacements are continuous and the strains are discontinuous but bounded. It is well known that this kind of approach poses some challenges. The standard irreducible formulation of FEM is known to be heavily affected by spurious mesh dependence when softening behavior occurs and, consequently, slip lines evolution is biased by the orientation of the mesh. Moreover, in the case of isochoric behavior, unbounded pressure oscillations arise and the consequent locking of the stresses pollutes the numerical solution. Both problems can be shown not to be related to the mathematical statement of the continuous problem but instead to its discrete (FEM) counterpart. Mixed finite element formulations represent a suitable alternative to mitigate these drawbacks. As it has been shown in previous works by Cervera [2], a mixed formulation in terms of displacements and pressure not only provides a propitious solution to the problem of incompressibility, but also it was found to possess the needed robustness in case of strain concentration. This presentation introduces a (stabilized) mixed finite element formulation with continuous linear strain and displacement interpolations. As a fundamental enhancement of the displacement-pressure formulation above mentioned, this kind of formulation benefits of the following advantages: it provides enhanced rate of convergence for the strain (and stress) and it is able to deal with incompressible situations. The method is completed with constitutive laws from Von Mises and Drucker-Prager local plasticity models with nonlinear strain softening. Moreover, global and local error norms are discussed to support the advantages of the proposed method. Then, numerical examples of stability analysis of slopes are presented to demonstrate the capability of the method. It will be shown that not only soil slopes can be modeled but also snow avalanche release and their weak layer fracture can be similarly treated. Consequently, this formulation appears to be a general and accurate tool for the solution of mechanical problem involving failure with localization bands [3,4]. References [1] Y.R. Rashid, 'Ultimate strength analysis of prestressed concrete pressure vessels', Nuclear Engineering and Design, Volume 7, Issue 4, April, Pages 334-344, 1968. [2] M. Cervera, M. Chiumenti, D. Di Capua. 'Benchmarking on bifurcation and localization in J 2 plasticity for plane stress and plane strain conditions.' Computer Methods in Applied Mechanics and Engineering, Vol. 241-244, Pages 206-224, 2012. [3] L. Benedetti, M. Cervera, M. Chiumenti. 'Stress-accurate mixed FEM for soil failure under shallow foundations involving strain localization in plasticity' Computers and Geotechnics, Vol. 64, pp. 32-47, 2015. [4] Cervera, M., Chiumenti, M., Benedetti, L., Codina, R. 'Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity' Computer Methods in Applied Mechanics and Engineering, to appear, 2015.

The Mohr-Coulomb criterion for intact rock strength and friction - a re-evaluation and consideration of failure under polyaxial stresses

NASA Astrophysics Data System (ADS)

Hackston, Abigail; Rutter, Ernest

2016-04-01

Darley Dale and Pennant sandstones were tested under conditions of both axisymmetric shortening and extension normal to bedding. These are the two extremes of loading under polyaxial stress conditions. Failure under generalized stress conditions can be predicted from the Mohr-Coulomb failure criterion under axisymmetric shortening conditions, provided the best form of polyaxial failure criterion is known. The sandstone data are best reconciled using the Mogi (1967) empirical criterion. Fault plane orientations produced vary greatly with respect to the maximum compressive stress direction in the two loading configurations. The normals to the Mohr-Coulomb failure envelopes do not predict the orientations of the fault planes eventually produced. Frictional sliding on variously inclined saw cuts and failure surfaces produced in intact rock samples was also investigated. Friction coefficient is not affected by fault plane orientation in a given loading configuration, but friction coefficients in extension were systematically lower than in compression for both rock types. Friction data for these and other porous sandstones accord well with the Byerlee (1978) generalization about rock friction being largely independent of rock type. For engineering and geodynamic modelling purposes, the stress-state-dependent friction coefficient should be used for sandstones, but it is not known to what extent this might apply to other rock types.

Assessment of Creep Deformation, Damage, and Rupture Life of 304HCu Austenitic Stainless Steel Under Multiaxial State of Stress

NASA Astrophysics Data System (ADS)

Sahoo, K. C.; Goyal, Sunil; Parameswaran, P.; Ravi, S.; Laha, K.

2018-03-01

The role of the multiaxial state of stress on creep deformation and rupture behavior of 304HCu austenitic stainless steel was assessed by performing creep rupture tests on both smooth and notched specimens of the steel. The multiaxial state of stress was introduced by incorporating circumferential U-notches of different root radii ranging from 0.25 to 5.00 mm on the smooth specimens of the steel. Creep tests were carried out at 973 K over the stress range of 140 to 220 MPa. In the presence of notch, the creep rupture strength of the steel was found to increase with the associated decrease in rupture ductility. Over the investigated stress range and notch sharpness, the strengthening was found to increase drastically with notch sharpness and tended toward saturation. The fractographic studies revealed the mixed mode of failure consisting of transgranular dimples and intergranular creep cavitation for shallow notches, whereas the failure was predominantly intergranular for relatively sharper notches. Detailed finite element analysis of stress distribution across the notch throat plane on creep exposure was carried out to assess the creep failure of the material in the presence of notch. The reduction in von-Mises stress across the notch throat plane, which was greater for sharper notches, increased the creep rupture strength of the material. The variation in fracture behavior of the material in the presence of notch was elucidated based on the von-Mises, maximum principal, and hydrostatic stresses. Electron backscatter diffraction analysis of creep strain distribution across the notch revealed localized creep straining at the notch root for sharper notches. A master curve for predicting creep rupture life under the multiaxial state of stress was generated considering the representative stress having contributions from both the von-Mises and principal stress components of the stress field in the notch throat plane. Rupture ductility was also predicted based on the multiaxial state of stress.

Crack problems for a rectangular plate and an infinite strip

NASA Technical Reports Server (NTRS)

Civelek, M. B.; Erdogan, F.

1980-01-01

The general plane problem for an infinite strip containing multiple cracks perpendicular to its boundaries is considered. The problem is reduced to a system of singular integral equations. Two specific problems of practical interest are then studied in detail. The first problem explores the interaction effect of multiple edge cracks in a plate or beam under tension or bending. The second problem is that of a rectangular plate containing an arbitrarily oriented crack in the plane of symmetry. Particular emphasis is placed on the problem of a plate containing an edge crack and subjected to concentrated forces.

Monolithic ceramic analysis using the SCARE program

NASA Technical Reports Server (NTRS)

Manderscheid, Jane M.

1988-01-01

The Structural Ceramics Analysis and Reliability Evaluation (SCARE) computer program calculates the fast fracture reliability of monolithic ceramic components. The code is a post-processor to the MSC/NASTRAN general purpose finite element program. The SCARE program automatically accepts the MSC/NASTRAN output necessary to compute reliability. This includes element stresses, temperatures, volumes, and areas. The SCARE program computes two-parameter Weibull strength distributions from input fracture data for both volume and surface flaws. The distributions can then be used to calculate the reliability of geometrically complex components subjected to multiaxial stress states. Several fracture criteria and flaw types are available for selection by the user, including out-of-plane crack extension theories. The theoretical basis for the reliability calculations was proposed by Batdorf. These models combine linear elastic fracture mechanics (LEFM) with Weibull statistics to provide a mechanistic failure criterion. Other fracture theories included in SCARE are the normal stress averaging technique and the principle of independent action. The objective of this presentation is to summarize these theories, including their limitations and advantages, and to provide a general description of the SCARE program, along with example problems.

Transient thermal stresses of work roll by coupled thermoelasticity

NASA Astrophysics Data System (ADS)

Lai, W. B.; Chen, T. C.; Weng, C. I.

1991-01-01

A numerical method, based on a two-dimensional plane strain model, is developed to predict the transient responses (that include distributions of temperature, thermal deformation, and thermal stress) of work roll during strip rolling by coupled thermoelasticity. The method consists of discretizing the space domain of the problem by finite element method first, and then treating the time domain by implicit time integration techniques. In order to avoid the difficulty in analysis due to relative movement between work roll and its thermal boundary, the energy equation is formulated with respect to a fixed Eulerian reference frame. The effect of thermoelastic coupling term, that is generally disregarded in strip rolling, can be considered and assessed. The influences of some important process parameters, such as rotational speed of the roll and intensity of heat flux, on transient solutions are also included and discussed. Furthermore, since the stress history at any point of the roll in both transient and steady state could be accurately evaluated, it is available to perform the analysis of thermal fatigue for the roll by means of previous data.

Finite element stress analysis of the human left ventricle whose irregular shape is developed from single plane cineangiocardiogram

NASA Technical Reports Server (NTRS)

Ghista, D. N.; Hamid, M. S.

1977-01-01

The three-dimensional left ventricular chamber geometrical model is developed from single plane cineangiocardiogram. This left ventricular model is loaded by an internal pressure monitored by cardiac catheterization. The resulting stresses in the left ventricular model chamber's wall are determined by computerized finite element procedure. For the discretization of this left ventricular model structure, a 20-node, isoparametric finite element is employed. The analysis and formulation of the computerised procedure is presented in the paper, along with the detailed algorithms and computer programs. The procedure is applied to determine the stresses in a left ventricle at an instant, during systole. Next, a portion (represented by a finite element) of this left ventricular chamber is simulated as being infarcted by making its active-state modulus value equal to its passive-state value; the neighbouring elements are shown to relieve the 'infarcted' element of stress by themselves taking on more stress.

Thermal stresses in the laser disc from a tetragonal c-cut crystal

NASA Astrophysics Data System (ADS)

Yumashev, K. V.; Loiko, P. A.

2014-12-01

Analytical expressions for thermal stresses and strains, as well as displacements, are obtained for the laser disc from a tetragonal crystal cut along the [0 0 1] axis under plane stress approximation, for the first time, to our knowledge. This study illustrates that, in polar coordinates, the normal stresses, σr and σθ, are angular independent, while the shear one τrθ is zero. The thermal strains, εr and εθ, and displacements, u and υ, depend on both radial and tangential coordinates; this dependence has the shape of a four-leaf rose. For considered crystal cutting with isotropic in-plane thermal expansion, the displacements are not pure radial (υ≠0). The values of stresses, strains and displacements are calculated for the disc from a c-cut yttrium vanadate laser crystal, Nd:YVO4. The thermal fracture issues are analyzed for this crystal.

[The psychological profile of pilots of passenger planes: Analysis of temperamental traits, aggression and risk].

PubMed

Makarowski, Ryszard; Piotrowski, Andrzej

2017-07-26

Over the years it has been assumed, that the greater the number of pilot flight hours, the better the development of problem-solving skills among pilots. Research suggests, however, that the problem is more complex than that. Not only one's experience is of importance - temperament, aggression and risk may also affect the decision-making process under stressful conditions. We examined 97 male pilots of passenger planes, who had flew ATRs, Boeings, Airbuses, Embraers, and Saabs. The comparative group was made up of 127 graduates of technical studies (not connected with aviation). In our study, we used the following methods: the PTS (Pavlovian Temperament Survey) Temperament Questionnaire by Strelau, the Aggression Questionnaire by Buss and Perry, and the Stimulating-Instrumental Risk Inventory (SIRI) by Zaleśkiewicz. Following the analyses we could categorize the pilots into 3 distinct groups: group 1 - strong type of nervous system with a tendency to avoid risk; group 2 - strong type of nervous system with a tendency to take risks; group 3 - the relatively weakest type of nervous system with a tendency toward aggressive behavior. Members of each group were analyzed to assess how they function in a task situation, i.e., whilst piloting a passenger plane. The study showed that individuals with high need for stimulation may - consciously or not - seek situations of excessive or unnecessary risks, and this is done in order to reach the right level of stimulation. A constellation of the following variables: temperament, risk, and aggression could be - we argue - useful in psychological examinations, and should be taken into account in training procedures for pilots. Med Pr 2017;68(5):639-651. This work is available in Open Access model and licensed under a CC BY-NC 3.0 PL license.

Stress fluctuations in fracture networks from theoretical and numerical models

NASA Astrophysics Data System (ADS)

Davy, P.; Darcel, C.; Mas Ivars, D.; Le Goc, R.

2017-12-01

We analyze the spatial fluctuations of stress in a simple tridimensional model constituted by a population of disc-shaped fractures embedded in an elastic matrix with uniform and isotropic properties. The fluctuations arise from the classical stress enhancement at fracture tips and stress shadowing around fracture centers that are amplified or decreased by the interactions between close-by fractures. The distribution of local stresses is calculated at the elementary mesh scale with the 3DEC numerical program based on the distinct element method. As expected, the stress distributions vary with fracture density, the larger is the density, the wider is the distribution. For freely slipping fractures, it is mainly controlled by the percolation parameter p (i.e., the total volume of spheres surrounding fractures). For stresses smaller than the remote deviatoric stress, the distribution depends only on for the range of density that has been studied. For large stresses, the distribution decreases exponentially when increasing stress, with a characteristic stress that increases with entailing a widening of the stress distribution. We extend the analysis to fractures with plane resistance defined by an elastic shear stiffness ks and a slip Coulomb threshold. A consequence of the fracture plane resistance is to lower the stress perturbation in the surrounding matrix by a factor that depends on the ratio between ks and a fracture-matrix stiffness km mainly dependent on the ratio between Young modulus and fracture size. km is also the ratio between the remote shear stress and the displacement across the fracture plane in the case of freely slipping fractures. A complete analytical derivation of the expressions of the stress perturbations and of the fracture displacements is obtained and checked with numerical simulations. In the limit ks >> km, the stress perturbation tends to 0 and the stress state is spatially uniform. The analysis allows us to quantify the intensity of the stress fluctuations in fractured rocks as a function of both the fracture network characteristics (density and size distribution), and the mechanical properties (fracture shear stiffness vs matrix elastic properties).

Non-linear analysis and the design of Pumpkin Balloons: stress, stability and viscoelasticity

NASA Astrophysics Data System (ADS)

Rand, J. L.; Wakefield, D. S.

Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures Founded upon their inTENS finite element analysis suite these activities have broadened to encompass lighter than air structures such as aerostats hybrid air-vehicles and stratospheric balloons Winzen Engineering couple many years of practical balloon design and fabrication experience with both academic and practical knowledge of the characterisation of the non-linear viscoelastic response of the polymeric films typically used for high-altitude scientific balloons Both companies have provided consulting services to the NASA Ultra Long Duration Balloon ULDB Program Early implementations of pumpkin balloons have shown problems of geometric instability characterised by improper deployment and these difficulties have been reproduced numerically using inTENS The solution lies in both the shapes of the membrane lobes and also the need to generate a biaxial stress field in order to mobilise in-plane shear stiffness Balloons undergo significant temperature and pressure variations in flight The different thermal characteristics between tendons and film can lead to significant meridional stress Fabrication tolerances can lead to significant local hoop stress concentrations particularly adjacent to the base and apex end fittings The non-linear viscoelastic response of the envelope film acts positively to help dissipate stress concentrations However creep over time may produce lobe geometry variations that may

Dynamic growth of mixed-mode shear cracks

USGS Publications Warehouse

Andrews, D.J.

1994-01-01

A pure mode II (in-plane) shear crack cannot propagate spontaneously at a speed between the Rayleigh and S-wave speeds, but a three-dimensional (3D) or two-dimensional (2D) mixed-mode shear crack can propagate in this range, being driven by the mode III (antiplane) component. Two different analytic solutions have been proposed for the mode II component in this case. The first is the solution valid for crack speed less than the Rayleigh speed. When applied above the Rayleigh speed, it predicts a negative stress intensity factor, which implies that energy is generated at the crack tip. Burridge proposed a second solution, which is continuous at the crack tip, but has a singularity in slip velocity at the Rayleigh wave. Spontaneous propagation of a mixed-mode rupture has been calculated with a slip-weakening friction law, in which the slip velocity vector is colinear with the total traction vector. Spontaneous trans-Rayleigh rupture speed has been found. The solution depends on the absolute stress level. The solution for the in-plane component appears to be a superposition of smeared-out versions of the two analytic solutions. The proportion of the first solution increases with increasing absolute stress. The amplitude of the negative in-plane traction pulse is less than the absolute final sliding traction, so that total in-plane traction does not reverse. The azimuth of the slip velocity vector varies rapidly between the onset of slip and the arrival of the Rayleigh wave. The variation is larger at smaller absolute stress.

Mechanical properties of β-HMX.

PubMed

Gallagher, Hugh G; Miller, John C; Sheen, David B; Sherwood, John N; Vrcelj, Ranko M

2015-01-01

For a full understanding of the mechanical properties of a material, it is essential to understand the defect structures and associated properties and microhardness indentation is a technique that can aid this understanding. The Vickers hardness on (010), {011} and {110} faces lay in the range of 304-363 MPa. The Knoop Hardnesses on the same faces lay in the range 314-482 MPa. From etching of three indented surfaces, the preferred slip planes have been identified as (001) and (101). For a dislocation glide, the most likely configuration for dislocation movement on the (001) planes is (001) [100] (|b| = 0.65 nm) and for the (101) plane as (101) [Formula: see text] (|b| = 1.084 nm) although (101) [010] (|b| = 1.105 nm) is possible. Tensile testing showed that at a stress value of 2.3 MPa primary twinning occurred and grew with increasing stress. When the stress was relaxed, the twins decreased in size, but did not disappear. The twinning shear strain was calculated to be 0.353 for the (101) twin plane. HMX is considered to be brittle, compared to other secondary explosives. Comparing HMX with a range of organic solids, the values for hardness numbers are similar to those of other brittle systems. Under the conditions developed beneath a pyramidal indenter, dislocation slip plays a major part in accommodating the local deformation stresses. Graphical abstractHMX undergoing tensile testing.

Regularized finite element modeling of progressive failure in soils within nonlocal softening plasticity

NASA Astrophysics Data System (ADS)

Huang, Maosong; Qu, Xie; Lü, Xilin

2017-11-01

By solving a nonlinear complementarity problem for the consistency condition, an improved implicit stress return iterative algorithm for a generalized over-nonlocal strain softening plasticity was proposed, and the consistent tangent matrix was obtained. The proposed algorithm was embodied into existing finite element codes, and it enables the nonlocal regularization of ill-posed boundary value problem caused by the pressure independent and dependent strain softening plasticity. The algorithm was verified by the numerical modeling of strain localization in a plane strain compression test. The results showed that a fast convergence can be achieved and the mesh-dependency caused by strain softening can be effectively eliminated. The influences of hardening modulus and material characteristic length on the simulation were obtained. The proposed algorithm was further used in the simulations of the bearing capacity of a strip footing; the results are mesh-independent, and the progressive failure process of the soil was well captured.

The planes of satellite galaxies problem, suggested solutions, and open questions

NASA Astrophysics Data System (ADS)

Pawlowski, Marcel S.

2018-02-01

Satellite galaxies of the Milky Way and of the Andromeda galaxy have been found to preferentially align in significantly flattened planes of satellite galaxies, and available velocity measurements are indicative of a preference of satellites in those structures to co-orbit. There is an increasing evidence that such kinematically correlated satellite planes are also present around more distant hosts. Detailed comparisons show that similarly anisotropic phase-space distributions of sub-halos are exceedingly rare in cosmological simulations based on the ΛCDM paradigm. Analogs to the observed systems have frequencies of ≤ 0.5% in such simulations. In contrast to other small-scale problems, the satellite planes issue is not strongly affected by baryonic processes because the distribution of sub-halos on scales of hundreds of kpc is dominated by gravitational effects. This makes the satellite planes one of the most serious small-scale problems for ΛCDM. This review summarizes the observational evidence for planes of satellite galaxies in the Local Group and beyond, and provides an overview of how they compare to cosmological simulations. It also discusses scenarios which aim at explaining the coherence of satellite positions and orbits, and why they all are currently unable to satisfactorily resolve the issue.

Crack Growth Prediction Methodology for Multi-Site Damage: Layered Analysis and Growth During Plasticity

NASA Technical Reports Server (NTRS)

James, Mark Anthony

1999-01-01

A finite element program has been developed to perform quasi-static, elastic-plastic crack growth simulations. The model provides a general framework for mixed-mode I/II elastic-plastic fracture analysis using small strain assumptions and plane stress, plane strain, and axisymmetric finite elements. Cracks are modeled explicitly in the mesh. As the cracks propagate, automatic remeshing algorithms delete the mesh local to the crack tip, extend the crack, and build a new mesh around the new tip. State variable mapping algorithms transfer stresses and displacements from the old mesh to the new mesh. The von Mises material model is implemented in the context of a non-linear Newton solution scheme. The fracture criterion is the critical crack tip opening displacement, and crack direction is predicted by the maximum tensile stress criterion at the crack tip. The implementation can accommodate multiple curving and interacting cracks. An additional fracture algorithm based on nodal release can be used to simulate fracture along a horizontal plane of symmetry. A core of plane strain elements can be used with the nodal release algorithm to simulate the triaxial state of stress near the crack tip. Verification and validation studies compare analysis results with experimental data and published three-dimensional analysis results. Fracture predictions using nodal release for compact tension, middle-crack tension, and multi-site damage test specimens produced accurate results for residual strength and link-up loads. Curving crack predictions using remeshing/mapping were compared with experimental data for an Arcan mixed-mode specimen. Loading angles from 0 degrees to 90 degrees were analyzed. The maximum tensile stress criterion was able to predict the crack direction and path for all loading angles in which the material failed in tension. Residual strength was also accurately predicted for these cases.

Dwell fatigue in two Ti alloys: An integrated crystal plasticity and discrete dislocation study

NASA Astrophysics Data System (ADS)

Zheng, Zebang; Balint, Daniel S.; Dunne, Fionn P. E.

2016-11-01

It is a well known and important problem in the aircraft engine industry that alloy Ti-6242 shows a significant reduction in fatigue life, termed dwell debit, if a stress dwell is included in the fatigue cycle, whereas Ti-6246 does not; the mechanistic explanation for the differing dwell debit of these alloys has remained elusive for decades. In this work, crystal plasticity modelling has been utilised to extract the thermal activation energies for pinned dislocation escape for both Ti alloys based on independent experimental data. This then allows the markedly different cold creep responses of the two alloys to be captured accurately and demonstrates why the observed near-identical rate sensitivity under non-dwell loading is entirely consistent with the dwell behaviour. The activation energies determined are then utilised within a recently developed thermally-activated discrete dislocation plasticity model to predict the strain rate sensitivities of the two alloys associated with nano-indentation into basal and prism planes. It is shown that Ti-6242 experiences a strong crystallographic orientation-dependent rate sensitivity while Ti-6246 does not which is shown to agree with recently published independent measurements; the dependence of rate sensitivity on indentation slip plane is also well captured. The thermally-activated discrete dislocation plasticity model shows that the incorporation of a stress dwell in fatigue loading leads to remarkable stress redistribution from soft to hard grains in the classical cold dwell fatigue rogue grain combination in alloy Ti-6242, but that no such load shedding occurs in alloy Ti-6246. The key property controlling the behaviour is the time constant of the thermal activation process relative to that of the loading. This work provides the first mechanistic basis to explain why alloy Ti-6242 shows a dwell debit but Ti-6246 does not.

Nonlinear Phase Field Theory for Fracture and Twinning with Analysis of Simple Shear

DTIC Science & Technology

2015-09-01

elasticity; crystal; shear deformation 1. Introduction Cleavage fracture and deformation twinning are two fundamental inelastic deformation mechanisms that...stress [2,3]. Both of these anisotropic mechanisms involve deformation on specific planes (the cleavage plane for fracture or the habit plane for...be the first phase field theory accounting for both fracture and deformation twinning wherein each mechanism is repre- sented by a distinct-order

Preliminary Design and Analysis of an In-plane PRSEUS Joint

NASA Technical Reports Server (NTRS)

Lovejoy, Andrew E.; Poplawski, Steven

2013-01-01

As part of the National Aeronautics and Space Administration's (NASA's) Environmentally Responsible Aviation (ERA) program, the Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) has been designed, developed and tested. However, PRSEUS development efforts to date have only addressed joints required to transfer bending moments between PRSEUS panels. Development of in-plane joints for the PRSEUS concept is necessary to facilitate in-plane transfer of load from PRSEUS panels to an adjacent structure, such as from a wing panel into a fuselage. This paper presents preliminary design and analysis of an in-plane PRSEUS joint for connecting PRSEUS panels at the termination of the rod-stiffened stringers. Design requirements are provided, the PRSEUS blade joint concept is presented, and preliminary design changes and analyses are carried out to examine the feasibility of the proposed in-plane PRSEUS blade joint. The study conducted herein focuses mainly on the PRSEUS structure on one side of the joint. In particular, the design requirements for the rod shear stress and bolt bearing stress are examined. A PRSEUS blade joint design was developed that demonstrates the feasibility of this in-plane PRSEUS joint concept to terminate the rod-stiffened stringers. The presented design only demonstrates feasibility, therefore, some areas of refinement are presented that would lead to a more optimum and realistic design.

Thermal stresses in layered barium titanate-based semiconductor ceramics

NASA Astrophysics Data System (ADS)

Shut, V. N.; Gavrilov, A. V.

2008-11-01

Thermal stresses emerging in a barium titanate-based semiconducting ceramic during heating by electric current are studied using numerical methods. It is shown that the highest tensile stresses are formed in the plane equidistant from the electrodes. The values of these stresses can be as high as 70 MPa, which is commensurate with the critical stresses. A method is proposed for reducing stresses by developing thermistors with a layered structure.

The Effect of Crystallite Size and Texture on the Strength of MgGeO3 Post-Perovskite

NASA Astrophysics Data System (ADS)

Miyagi, Lowell

2011-06-01

In-situ radial synchrotron x-ray diffraction is used to measure lattice strain and lattice preferred orientation (texture) in MgGeO3 post-perovskite synthesized and deformed in the diamond anvil cell up to 135 GPa. Lattice strains are used to calculate differential stress supported by the sample and can provide a lower bounds estimate on yield strength. MgGeO3 post-perovskite synthesized from the enstatite phase exhibits a weak transformation texture of (100) planes at high angles to the direction of compression. In a sample with larger crystallites, pressure increase and deformation results in (001) lattice planes orienting nearly perpendicular to compression, consistent with dominant (001) slip. In another sample with smaller crystallites it is difficult to induce texture change, and differential stress is higher than in the sample with larger crystallites. When MgGeO3 post-perovskite is synthesized from the perovskite phase a different transformation texture of (001) planes at high angles to compression is observed. This sample is able to support large differential stress as the direction perpendicular to the (001) plane is a plastically hard orientation for MgGeO3 post-perovskite. This work was supported by the Carnegie DOE Alliance Center and a Bateman fellowship at Yale University.

A New Multiaxial High-Cycle Fatigue Criterion Based on the Critical Plane for Ductile and Brittle Materials

NASA Astrophysics Data System (ADS)

Wang, Cong; Shang, De-Guang; Wang, Xiao-Wei

2015-02-01

An improved high-cycle multiaxial fatigue criterion based on the critical plane was proposed in this paper. The critical plane was defined as the plane of maximum shear stress (MSS) in the proposed multiaxial fatigue criterion, which is different from the traditional critical plane based on the MSS amplitude. The proposed criterion was extended as a fatigue life prediction model that can be applicable for ductile and brittle materials. The fatigue life prediction model based on the proposed high-cycle multiaxial fatigue criterion was validated with experimental results obtained from the test of 7075-T651 aluminum alloy and some references.

The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential

NASA Astrophysics Data System (ADS)

Grosche, Christian

1988-10-01

Rigorous path integral treatments on the Poincaré upper half-plane with a magnetic field and for the Morse potential are presented. The calculation starts with the path integral on the Poincaré upper half-plane with a magnetic field. By a Fourier expansion and a non-linear transformation this problem is reformulated in terms of the path integral for the Morse potential. This latter problem can be reduced by an appropriate space-time transformation to the path integral for the harmonic oscillator with generalised angular momentum, a technique which has been developed in recent years. The well-known solution for the last problem enables one to give explicit expressions for the Feynman kernels for the Morse potential and for the Poincaré upper half-plane with magnetic field, respectively. The wavefunctions and the energy spectrum for the bound and scattering states are given, respectively.

Thermal stress effects on the flexural wave bandgap of a two-dimensional locally resonant acoustic metamaterial

NASA Astrophysics Data System (ADS)

Li, Zhen; Zhu, Yun; Li, Yueming

2018-05-01

The elastic wave bandgap is obviously affected by heat while considering thermal stress. Nevertheless, the flat band, occurring in the lowest flexural branch, has not yet been explained clearly. This study investigates the influence of thermal stress on a flexural wave bandgap in a two-dimensional three-component acoustic metamaterial. Simulation results demonstrate that the band structure shifts to a lower frequency range, and the vibration response appears at a larger amplitude due to the bending stiffness being softened by the compressive membrane force. In addition, the first flexural band reduces to zero frequency in the central Brillouin zone. By viewing the vibration modes of the proposed unit cell, it is found that the out-of-plane mode shape attenuates with increasing temperature, while the in-plane vibration modes are unaffected by thermal stress.

An Experimental Investigation into Additive Manufacturing-Induced Residual Stresses in 316L Stainless Steel

NASA Astrophysics Data System (ADS)

Wu, Amanda S.; Brown, Donald W.; Kumar, Mukul; Gallegos, Gilbert F.; King, Wayne E.

2014-12-01

Additive manufacturing (AM) technology provides unique opportunities for producing net-shape geometries at the macroscale through microscale processing. This level of control presents inherent trade-offs necessitating the establishment of quality controls aimed at minimizing undesirable properties, such as porosity and residual stresses. Here, we perform a parametric study into the effects of laser scanning pattern, power, speed, and build direction in powder bed fusion AM on residual stress. In an effort to better understand the factors influencing macroscale residual stresses, a destructive surface residual stress measurement technique (digital image correlation in conjunction with build plate removal and sectioning) has been coupled with a nondestructive volumetric evaluation method ( i.e., neutron diffraction). Good agreement between the two measurement techniques is observed. Furthermore, a reduction in residual stress is obtained by decreasing scan island size, increasing island to wall rotation to 45 deg, and increasing applied energy per unit length (laser power/speed). Neutron diffraction measurements reveal that, while in-plane residual stresses are affected by scan island rotation, axial residual stresses are unchanged. We attribute this in-plane behavior to misalignment between the greatest thermal stresses (scan direction) and largest part dimension.

In-plane dynamic Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic half-space

NASA Astrophysics Data System (ADS)

Ba, Zhenning; Kang, Zeqing; Liang, Jianwen

2018-04-01

The dynamic stiffness method combined with the Fourier transform is utilized to derive the in-plane Green's functions for inclined and uniformly distributed loads in a multi-layered transversely isotropic (TI) half-space. The loaded layer is fixed to obtain solutions restricted in it and the corresponding reactions forces, which are then applied to the total system with the opposite sign. By adding solutions restricted in the loaded layer to solutions from the reaction forces, the global solutions in the wavenumber domain are obtained, and the dynamic Green's functions in the space domain are recovered by the inverse Fourier transform. The presented formulations can be reduced to the isotropic case developed by Wolf (1985), and are further verified by comparisons with existing solutions in a uniform isotropic as well as a layered TI half-space subjected to horizontally distributed loads which are special cases of the more general problem addressed. The deduced Green's functions, in conjunction with boundary element methods, will lead to significant advances in the investigation of a variety of wave scattering, wave radiation and soil-structure interaction problems in a layered TI site. Selected numerical results are given to investigate the influence of material anisotropy, frequency of excitation, inclination angle and layered on the responses of displacement and stress, and some conclusions are drawn.

Mechanical signals in plant development: a new method for single cell studies

NASA Technical Reports Server (NTRS)

Lynch, T. M.; Lintilhac, P. M.

1997-01-01

Cell division, which is critical to plant development and morphology, requires the orchestration of hundreds of intracellular processes. In the end, however, cells must make critical decisions, based on a discrete set of mechanical signals such as stress, strain, and shear, to divide in such a way that they will survive the mechanical loads generated by turgor pressure and cell enlargement within the growing tissues. Here we report on a method whereby tobacco protoplasts swirled into a 1.5% agarose entrapment medium will survive and divide. The application of a controlled mechanical load to agarose blocks containing protoplasts orients the primary division plane of the embedded cells. Photoelastic analysis of the agarose entrapment medium can identify the lines of principal stress within the agarose, confirming the hypothesis that cells divide either parallel or perpendicular to the principal stress tensors. The coincidence between the orientation of the new division wall and the orientation of the principal stress tensors suggests that the perception of mechanical stress is a characteristic of individual plant cells. The ability of a cell to determine a shear-free orientation for a new partition wall may be related to the applied load through the deformation of the matrix material. In an isotropic matrix a uniaxial load will produce a rotationally symmetric strain field, which will define a shear-free plane. Where high stress intensities combine with the loading geometry to produce multiaxial loads there will be no axis of rotational symmetry and hence no shear free plane. This suggests that two mechanisms may be orienting the division plane, one a mechanism that works in rotationally symmetrical fields, yielding divisions perpendicular to the compressive tensor, parallel to the long axis of the cell, and one in asymmetric fields, yielding divisions parallel to the short axis of the cell and the compressive tensor.

Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod

NASA Astrophysics Data System (ADS)

Gula, I. A.; Samsonov, A. M.

2017-12-01

The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.

Slicken 1.0: Program for calculating the orientation of shear on reactivated faults

NASA Astrophysics Data System (ADS)

Xu, Hong; Xu, Shunshan; Nieto-Samaniego, Ángel F.; Alaniz-Álvarez, Susana A.

2017-07-01

The slip vector on a fault is an important parameter in the study of the movement history of a fault and its faulting mechanism. Although there exist many graphical programs to represent the shear stress (or slickenline) orientations on faults, programs to quantitatively calculate the orientation of fault slip based on a given stress field are scarce. In consequence, we develop Slicken 1.0, a software to rapidly calculate the orientation of maximum shear stress on any fault plane. For this direct method of calculating the resolved shear stress on a planar surface, the input data are the unit vector normal to the involved plane, the unit vectors of the three principal stress axes, and the stress ratio. The advantage of this program is that the vertical or horizontal principal stresses are not necessarily required. Due to its nimble design using Java SE 8.0, it runs on most operating systems with the corresponding Java VM. The software program will be practical for geoscience students, geologists and engineers and will help resolve a deficiency in field geology, and structural and engineering geology.

Relationships among in-situ stress, fractures and faults, and fluid flow: Monterey formation, Santa Maria Basin, California

USGS Publications Warehouse

Finkbeiner, T.; Barton, C.A.; Zoback, M.D.

1997-01-01

We used borehole televiewer (BHTV) data from four wells within the onshore and offshore Santa Maria basin, California, to investigate the relationships among fracture distribution, orientation, and variation with depth and in-situ stress. Our analysis of stress-induced well-bore breakouts shows a uniform northeast maximum horizontal stress (SH max) orientation in each well. This direction is consistent with the SH max direction determined from well-bore breakouts in other wells in this region, the northwest trend of active fold axes, and kinematic inversion of nearby earthquake focal plane mechanisms. In contrast to the uniformity of the stress field, fracture orientation, dip, and frequency vary considerably from well to well and within each well. With depth, fractures can be divided into distinct subsets on the basis of fracture frequency and orientation, which correlate with changes of lithology and physical properties. Although factors such as tectonic history, diagenesis, and structural variations obviously have influenced fracture distribution, integration of the in-situ stress and fracture data sets indicates that many of the fractures, faults, and bedding planes are active, small-scale strike-slip and reverse faults in the current northeast-trending transpressive stress field. In fact, we observed local breakout rotations in the wells, providing kinematic evidence for recent shear motion along fracture and bedding-parallel planes. Only in the onshore well do steeply dipping fractures strike parallel to SHmax. Drill-stem tests from two of the offshore wells indicate that formation permeability is greatly enhanced in sections of the wells where fractures are favorably oriented for shear failure in the modern stress field. Thus, relatively small-scale active faults provide important conduits along which fluids migrate.

Determination of the Fracture Parameters in a Stiffened Composite Panel

NASA Technical Reports Server (NTRS)

Lin, Chung-Yi

2000-01-01

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

Spectral Collocation Time-Domain Modeling of Diffractive Optical Elements

NASA Astrophysics Data System (ADS)

Hesthaven, J. S.; Dinesen, P. G.; Lynov, J. P.

1999-11-01

A spectral collocation multi-domain scheme is developed for the accurate and efficient time-domain solution of Maxwell's equations within multi-layered diffractive optical elements. Special attention is being paid to the modeling of out-of-plane waveguide couplers. Emphasis is given to the proper construction of high-order schemes with the ability to handle very general problems of considerable geometric and material complexity. Central questions regarding efficient absorbing boundary conditions and time-stepping issues are also addressed. The efficacy of the overall scheme for the time-domain modeling of electrically large, and computationally challenging, problems is illustrated by solving a number of plane as well as non-plane waveguide problems.

Three-dimensional finite element analysis of the application of attachment for obturator framework in unilateral maxillary defect.

PubMed

Sun, J; Jiao, T; Tie, Y; Wang, D-M

2008-09-01

The aim of this study was to evaluate the stress on the abutment teeth and framework ina unilateral maxillary defect which was restored by an obturator retained by resin-bonded extra coronal attachment. A three-dimensional finite element model of the human unilateral maxillary defect was constructed. Traditional obturator framework with four casting circumferential clasp was established (model 1). A continuous lingual guide plane of 0.5 mm thickness on all of the remaining teeth, with Mini-SG/F attachment on the mesial surface of the central incisor was also established (model 2). The modelling and analytical processes were performed using the ANSYS technologies. Stress was transmitted to the anterior part of the palate, with stress values being lower on the anterior teeth compared with the posteriors. The highest stress value of model 1 and model 2 was 13.1 Mpa, 19.9 Mpa respectively. Stress concentrations were found at the junction of the attachment to the lingual guide plane and the anterior part of the lingual plane. The results of this study suggest that the application of a resin-bonded extra coronal attachment for obturator retention is in accordance with the design principles for the restorative treatment of maxillary defects.The design of the attachment framework needs to be further investigated. Benefit can be gained by splinting the abutment teeth.

[Hodge and his planes].

PubMed

van Gijn, Jan; Gijselhart, Joost P

2010-01-01

Hugh Lenox Hodge (1796-1873) was professor of obstetrics at the University of Pennsylvania for more than 25 years. He divided the birth canal into four virtual and parallel planes through pelvic protuberances, a method still widely used. He also developed a pessary that is now mainly used in stress incontinence.

Soil Models and Vehicle System Dynamics

DTIC Science & Technology

2013-05-07

of the deviatoric stress , ’p is the effective mean stress , the pre-consolidation stress ’cp acts as a internal...and matric suction as stress state variables allows modeling independently the effects of a change in the skeleton stress and of a change in suction...in the plane of effective mean- stress p’ and deviatoric stress q with  1 2 3’ 3p        and using

Influence of meniscus shape in the cross sectional plane on the knee contact mechanics.

PubMed

Łuczkiewicz, Piotr; Daszkiewicz, Karol; Witkowski, Wojciech; Chróścielewski, Jacek; Zarzycki, Witold

2015-06-01

We present a three dimensional finite element analysis of stress distribution and menisci deformation in the human knee joint. The study is based on the Open Knee model with the geometry of the lateral meniscus which shows some degenerative disorders. The nonlinear analysis of the knee joint under compressive axial load is performed. We present results for intact knee, knee with complete radial posterior meniscus root tear and knee with total meniscectomy of medial or lateral meniscus. We investigate how the meniscus shape in the cross sectional plane influences knee-joint mechanics by comparing the results for flat (degenerated) lateral and normal medial meniscus. Specifically, the deformation of the menisci in the coronal plane and the corresponding stress values in cartilages are studied. By analysing contact resultant force acting on the menisci in axial plane we have shown that restricted extrusion of the torn lateral meniscus can be attributed to small slope of its cross section in the coronal plane. Additionally, the change of the contact area and the resultant force acting on the menisci as the function of compressive load are investigated. Copyright © 2015 Elsevier Ltd. All rights reserved.

Turbulent boundary layers with secondary flow

NASA Technical Reports Server (NTRS)

Grushwitz, E.

1984-01-01

An experimental analysis of the boundary layer on a plane wall, along which the flow occurs, whose potential flow lines are curved in plane parallel to the wall is discussed. According to the equation frequently applied to boundary layers in a plane flow, which is usually obtained by using the pulse law, a generalization is derived which is valid for boundary layers with spatial flow. The wall shear stresses were calculated with this equation.

From Number Lines to Graphs in the Coordinate Plane: Investigating Problem Solving across Mathematical Representations

ERIC Educational Resources Information Center

Earnest, Darrell

2015-01-01

This article reports on students' problem-solving approaches across three representations--number lines, coordinate planes, and function graphs--the axes of which conventional mathematics treats in terms of consistent geometric and numeric coordinations. I consider these representations to be a part of a "hierarchical representational…

Extended linear detection range for optical tweezers using image-plane detection scheme

NASA Astrophysics Data System (ADS)

Hajizadeh, Faegheh; Masoumeh Mousavi, S.; Khaksar, Zeinab S.; Reihani, S. Nader S.

2014-10-01

Ability to measure pico- and femto-Newton range forces using optical tweezers (OT) strongly relies on the sensitivity of its detection system. We show that the commonly used back-focal-plane detection method provides a linear response range which is shorter than that of the restoring force of OT for large beads. This limits measurable force range of OT. We show, both theoretically and experimentally, that utilizing a second laser beam for tracking could solve the problem. We also propose a new detection scheme in which the quadrant photodiode is positioned at the plane optically conjugate to the object plane (image plane). This method solves the problem without need for a second laser beam for the bead sizes that are commonly used in force spectroscopy applications of OT, such as biopolymer stretching.

The effect of stress state on zirconium hydride reorientation

NASA Astrophysics Data System (ADS)

Cinbiz, Mahmut Nedim

Prior to storage in a dry-cask facility, spent nuclear fuel must undergo a vacuum drying cycle during which the spent fuel rods are heated up to elevated temperatures of ≤ 400°C to remove moisture the canisters within the cask. As temperature increases during heating, some of the hydride particles within the cladding dissolve while the internal gas pressure in fuel rods increases generating multi-axial hoop and axial stresses in the closed-end thin-walled cladding tubes. As cool-down starts, the hydrogen in solid solution precipitates as hydride platelets, and if the multiaxial stresses are sufficiently large, the precipitating hydrides reorient from their initial circumferential orientation to radial orientation. Radial hydrides can severely embrittle the spent nuclear fuel cladding at low temperature in response to hoop stress loading. Because the cladding can experience a range of stress states during the thermo-mechanical treatment induced during vacuum drying, this study has investigated the effect of stress state on the process of hydride reorientation during controlled thermo-mechanical treatments utilizing the combination of in situ X-ray diffraction and novel mechanical testing analyzed by the combination of metallography and finite element analysis. The study used cold worked and stress relieved Zircaloy-4 sheet containing approx. 180 wt. ppm hydrogen as its material basis. The failure behavior of this material containing radial hydrides was also studied over a range of temperatures. Finally, samples from reactor-irradiated cladding tubes were examined by X-ray diffraction using synchrotron radiation. To reveal the stress state effect on hydride reorientation, the critical threshold stress to reorient hydrides was determined by designing novel mechanical test samples which produce a range of stress states from uniaxial to "near-equibiaxial" tension when a load is applied. The threshold stress was determined after thermo-mechanical treatments by correlating the finite element stress-state results with the spatial distribution of hydride microstructures observed within the optical micrographs for each sample. Experiments showed that the hydride reorientation was enhanced as the stress biaxiality increased. The threshold stress decreased from 150 MPa to 80 MPa when stress biaxiality ratio increased from uniaxial tension to near-equibiaxial tension. This behavior was also predicted by classical nucleation theory based on the Gibbs free energy of transformation being assisted by the far-field stress. An analysis of in situ X-ray diffraction data obtained during a thermo-mechanical cycle typical of vacuum drying showed a complex lattice-spacing behavior of the hydride phase during the dissolution and precipitation. The in-plane hydrides showed bilinear lattice expansion during heating with the intrinsic thermal expansion rate of the hydrides being observed only at elevated temperatures as they dissolve. For radial hydrides that precipitate during cooling under stress, the spacing of the close-packed {111} planes oriented normal to the maximum applied stress was permanently higher than the corresponding {111} plane spacing in the other directions. This behavior is believed to be a result of a complex stress state within the precipitating plate-like hydrides that induces a strain component within the hydrides normal to its "plate" face (i.e., the applied stress direction) that exceeds the lattice spacing strains in the other directions. During heat-up, the lattice spacing of these same "plate" planes actually contract due to the reversion of the stress state within the plate-like hydrides as they dissolve. The presence of radial hydrides and their connectivity with in-plane hydrides was shown to increase the ductile-to-brittle transition temperature during tensile testing. This behavior can be understood in terms of the role of radial hydrides in promoting the initiation of a long crack that subsequently propagates under fracture mechanics conditions. Finally, the d-spacing of irradiated Zircaloy-4 and M5 cladding tubes was measured at room temperature and compared to that of unirradiated samples.

Effect of temperature, microstructure, and stress state on the low cycle fatigue behavior of Waspaloy

NASA Technical Reports Server (NTRS)

Stahl, D. R.; Antolovich, S. D.; Mirdamadi, M.; Zamrik, S. Y.

1988-01-01

Specimens of Waspaloy of two different microstructures were tested in uniaxial and torsional low-cycle fatigue at 24 and 649 C. For all specimens, deformation and failure mechanisms are found to be independent of stress state at 24 C; in both microstructures, failure is associated with the formation of shear cracks. At 649 C, deformation and failure mechanisms for the fine-grain large gamma-prime specimens are independent of stress state, and the mechanisms are similar to those observed at 24 C. For the coarse-grain small gamma-prime specimens, however, failure occurs on principal planes in torsion and on shear plane in uniaxial tension. The results are interpreted in terms of deformation mode and microstructural instability.

Highly mobile type II twin boundary in Ni-Mn-Ga five-layered martensite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sozinov, A.; Lanska, N.; Soroka, A.

2011-09-19

Twin relationships and stress-induced reorientation were studied in Ni{sub 2}Mn{sub 1.14}Ga{sub 0.86} single crystal with five-layered modulated martensite crystal structure. Very low twinning stress of about 0.1 MPa was found for twin boundaries which deviated a few degrees from the (011) crystallographic plane. However, twin boundaries oriented exactly parallel to the (011) plane exhibited considerably higher level of twinning stress, above 1 MPa. X-ray diffraction experiments and calculations based on approximation of the martensite crystal lattice as a tetragonal lattice with a slight monoclinic distortion identified the two different kinds of twin interfaces as type II and type I twinmore » boundaries.« less

Topological analysis of the motion of an ellipsoid on a smooth plane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ivochkin, M Yu

2008-06-30

The problem of the motion of a dynamically and geometrically symmetric heavy ellipsoid on a smooth horizontal plane is investigated. The problem is integrable and can be considered a generalization of the problem of motion of a heavy rigid body with fixed point in the Lagrangian case. The Smale bifurcation diagrams are constructed. Surgeries of tori are investigated using methods developed by Fomenko and his students. Bibliography: 9 titles.

Look down from the Sky: Is It a Bird? Is It Superman? No, It's a Plane

ERIC Educational Resources Information Center

Chick, Helen

2016-01-01

The plane problem is a real-world problem, presented without any suggestion as to how it might be solved. It arose unexpectedly as the author was messing around on the internet, not thinking about maths at all. She did not encounter the problem in a maths lesson, nor as homework in the middle of a unit on a particular topic, and so she had no…

Stress Drop and Directivity Patterns Observed in Small-Magnitude (

NASA Astrophysics Data System (ADS)

Ruhl, C. J.; Hatch, R. L.; Abercrombie, R. E.; Smith, K.

2017-12-01

Recent improvements in seismic instrumentation and network coverage in the Reno, NV area have provided high-quality records of abundant microseismicity, including several swarms and clusters. Here, we discuss stress drop and directivity patterns of small-magnitude seismicity in the 2008 Mw4.9 Mogul earthquake swarm in Reno, NV and in the nearby region of an ML3.2 sequence near Virginia City, NV. In both sequences, double-difference relocated earthquakes cluster on multiple distinct structures consistent with focal mechanism and moment tensor fault plane solutions. Both sequences also show migration potentially related to fluid flow. We estimate corner frequency and stress drop using EGF-derived spectral ratios, convolving earthquake pairs (target*EGF) such that we preserve phase and recover source-time functions (STF) on a station-by-station basis. We then stack individual STFs per station for all EGF-target pairs per target earthquake, increasing the signal-to-noise of our results. By applying an azimuthal- and incidence-angle-dependent stretching factor to STFs in the time domain, we are able to invert for rupture directivity and velocity assuming both unilateral and bilateral rupture. Earthquakes in both sequences, some as low as ML2.1, show strong unilateral directivity consistent with independent fault plane solutions. We investigate and compare the relationship between rupture and migration directions on subfaults within each sequence. Average stress drops for both sequences are 4 MPa, but there is large variation in individual estimates for both sequences. Although this variation is not explained simply by any one parameter (e.g., depth), spatiotemporal variation in the Mogul swarm is distinct: coherent clusters of high and low stress drop earthquakes along the mainshock fault plane are seen, and high-stress-drop foreshocks correlate with an area of reduced aftershock productivity. These observations are best explained by a difference in rheology along the fault plane. The unprecedented detail achieved for these small magnitude earthquakes confirms that stress drop, when measured precisely, is a valuable observation of physically-meaningful fault zone properties and earthquake behavior.

Comment on "Out-of-plane equilibrium points in the restricted three-body problem with oblateness (Research Note)"

NASA Astrophysics Data System (ADS)

Wu, Nan; Wang, Xuefeng; Zhou, Li-Yong

2018-06-01

Douskos & Markellos (2006, A&A, 446, 357) first reported the existence of the out-of-plane equilibrium points in restricted three-body problem with oblateness. This result deviates significantly from the intuitive physical point of view that there is no other force that can balance the combined gravitation in Z direction. In fact, the out-of-plane equilibrium in that model is illusory and we prove here that such equilibrium points arise from the improper application of the potential function.

Effects of local film properties on the nucleation and growth of tin whiskers and hillocks

NASA Astrophysics Data System (ADS)

Sarobol, Pylin

Whiskers and hillocks grow spontaneously on Pb-free Sn electrodeposited films as a response to thin film stresses. Stress relaxation occurs by atom deposition to specific grain boundaries in the plane of the film, with hillocks being formed when grain boundary migration accompanies growth out of the plane of the film. The implication for whisker formation in electronics is serious: whiskers can grow to be millimeters long, sometimes causing short circuiting between adjacent components and, thereby, posing serious electrical reliability risks. In order to develop more effective whisker mitigation strategies, a predictive physics-based model has been needed. A growth model is developed, based on grain boundary faceting, localized Coble creep, as well as grain boundary sliding for whiskers, and grain boundary sliding with shear induced grain boundary migration for hillocks. In this model of whisker formation, two mechanisms are important: accretion of atoms by Coble creep on grain boundary planes normal to the growth direction inducing a grain boundary shear and grain boundary sliding in the direction of whisker growth. The model accurately captures the importance of the geometry of "surface grains"---shallow grains on film surfaces whose depths are significantly less than their in-plane grain sizes. A critical factor in the analysis is the ratio of the grain boundary sliding coefficient to the in-plane film compressive stress. If the accretion-induced shear stresses are not coupled to grain boundary motion and sliding occurs, a whisker forms. If the shear stress is coupled to grain boundary migration, a hillock forms. Based on this model, long whiskers grow from shallow surface grains with easy grain boundary sliding in the direction of growth. Other observed growth morphologies will be discussed in light of our model. Additional insights into the preferred sites for whisker and hillock growth were developed based on elastic anisotropy, local film microstructure, grain misorientation, and elastic strain energy density (ESED) as the driving force for growth. Local grain orientations and strains measured by synchrotron micro-diffraction in regions containing whiskers or hillocks were compared with elastic finite element analysis simulations, including Sn elastic anisotropy. Whisker and hillock grains were observed to have higher crystallographic misorientations with neighboring grains than generally observed in the microstructure. While elastic simulations predicted higher local out-of-plane elastic strains and ESEDs for whisker and hillock grains, synchrotron measurements of out-of-plane strains of whisker and hillock grains after growth showed relaxation, with correspondingly low ESEDs calculated from measured strains. This suggests that, before whisker or hillock formation, highly misoriented grains with high out-of-plane elastic strains and ESEDs relative to their neighbors determined, at least in part, which grains became whiskers or hillocks. Based on the models and experiments in this thesis, a clearer picture emerges of the necessary and sufficient conditions for tin whisker and hillock formation in thin films.

Growth characteristics of a plane crack subjected to three-dimensional loading. [based on stress intensity factors

NASA Technical Reports Server (NTRS)

Hartranft, R. J.; Sih, G. C.

1973-01-01

The closed form expressions for the stress intensity factors due to concentrated forces applied to the surfaces of a half plane crack in an infinite body are used to generate solutions for distributed loads in this geometry. The stress intensity factors for uniformly distributed loads applied over a rectangular portion of the crack surface are given in closed form. An example of non-uniformly distributed loads which can be treated numerically is also included. In particular, combinations of normal and shear stresses on the crack which simulate the case of loading at an angle to the crack front are considered. The resulting stress intensity factors are combined with the strain energy density fracture criterion for the purpose of predicting the most likely direction of crack propagation. The critical value of the energy density factor can then be used for determining the allowable load on a specimen with a crack front not perpendicular to the tensile axis.

Evaluation of support loss in micro-beam resonators: A revisit

NASA Astrophysics Data System (ADS)

Chen, S. Y.; Liu, J. Z.; Guo, F. L.

2017-12-01

This paper presents an analytical study on evaluation of support loss in micromechanical resonators undergoing in-plane flexural vibrations. Two-dimensional elastic wave theory is used to determine the energy transmission from the vibrating resonator to the support. Fourier transform and Green's function technique are adopted to solve the problem of wave motions on the surface of the support excited by the forces transmitted by the resonator onto the support. Analytical expressions of support loss in terms of quality factor, taking into account distributed normal stress and shear stress in the attachment region, and coupling between the normal stress and shear stress as well as material disparity between the support and the resonator, have been derived. Effects of geometry of micro-beam resonators, and material dissimilarity between support and resonator on support loss are examined. Numerical results show that 'harder resonator' and 'softer support' combination leads to larger support loss. In addition, the Perfectly Matched Layer (PML) numerical simulation technique is employed for validation of the proposed analytical model. Comparing with results of quality factor obtained by PML technique, we find that the present model agrees well with the results of PML technique and the pure-shear model overestimates support loss noticeably, especially for resonators with small aspect ratio and large material dissimilarity between the support and resonator.

A stable numerical solution method in-plane loading of nonlinear viscoelastic laminated orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1989-01-01

In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.

Birefringence control of solution-cast film of cellulose triacetate

NASA Astrophysics Data System (ADS)

Kiyama, Ayumi; Nobukawa, Shogo; Yamaguchi, Masayuki

2017-10-01

We controlled the optical anisotropy of a solution-cast film composed of cellulose triacetate (CTA) by adding ferrocene. Owing to the molecular orientation in the film plane of solution-cast films, which results from the normal stress applied during the solvent evaporation process, the average refractive index is usually higher in the plane of the film than in the thickness direction. We found that the addition of ferrocene, which is miscible with CTA, reduced the optical anisotropy by nematic interaction; i.e., ferrocene molecules are forcibly embedded into the film plane accompanying the CTA chains. Because the direction of anisotropic polarizability of ferrocene is perpendicular to the long axis of the molecule, the refractive index in the thickness direction is reduced. Furthermore, the stress-optical coefficient in the glassy state is reduced by the addition of ferrocene.

Precision improving of double beam shadow moiré interferometer by phase shifting interferometry for the stress of flexible substrate

NASA Astrophysics Data System (ADS)

Huang, Kuo-Ting; Chen, Hsi-Chao; Lin, Ssu-Fan; Lin, Ke-Ming; Syue, Hong-Ye

2012-09-01

While tin-doped indium oxide (ITO) has been extensively applied in flexible electronics, the problem of the residual stress has many obstacles to overcome. This study investigated the residual stress of flexible electronics by the double beam shadow moiré interferometer, and focused on the precision improvement with phase shifting interferometry (PSI). According to the out-of-plane displacement equation, the theoretical error depends on the grating pitch and the angle between incident light and CCD. The angle error could be reduced to 0.03% by the angle shift of 10° as a result of the double beam interferometer was a symmetrical system. But the experimental error of the double beam moiré interferometer still reached to 2.2% by the noise of the vibration and interferograms. In order to improve the measurement precision, PSI was introduced to the double shadow moiré interferometer. Wavefront phase was reconstructed by the five interferograms with the Hariharan algorithm. The measurement results of standard cylinder indicating the error could be reduced from 2.2% to less than 1% with PSI. The deformation of flexible electronic could be reconstructed fast and calculated the residual stress with the Stoney correction formula. This shadow moiré interferometer with PSI could improve the precision of residual stress for flexible electronics.

Dynamic Curvature and Stress Studies for MBE CdTe on Si and GaAs Substrates

NASA Astrophysics Data System (ADS)

Jacobs, R. N.; Jaime Vasquez, M.; Lennon, C. M.; Nozaki, C.; Almeida, L. A.; Pellegrino, J.; Arias, J.; Taylor, C.; Wissman, B.

2015-09-01

Infrared focal plane arrays (IRFPA) based on HgCdTe semiconductor alloys have been shown to be ideal for tactical and strategic applications. High density (>1 M pixel), high operability HgCdTe detectors on large area, low-cost composite substrates, such as CdTe-buffered Si or GaAs, are envisioned for next-generation IRFPAs. Thermal expansion mismatch is among various material parameters that govern the structural properties of the final detector layer. It has previously been shown that thermal expansion mismatch plays the dominant role in the residual stress characteristics of these heteroepitaxial structures (Jacobs et al. in J Electron Mater 37:1480, 2008). The wafer curvature (bowing) resulting from residual stress, is a likely source of problems that may occur during subsequent processing. This includes cracking of the film and substrate during post-growth annealing processes or even certain characterization techniques. In this work, we examine dynamic curvature and stress during molecular beam epitaxy (MBE), of CdTe on Si and GaAs substrates. The effect of temperature changes on wafer curvature throughout the growth sequence is documented using a multi-beam optical sensor developed by K-Space Associates. This monitoring technique makes possible the study of growth sequences which employ annealing schemes and/or interlayers to influence the final residual stress state of the heteroepitaxial structures.

Structural Constraints On The Spatial Distribution of Aftershocks

NASA Astrophysics Data System (ADS)

McCloskey, J.; Nalbant, S. S.; Steacy, S.; Nostro, C.; Scotti, O.; Baumont, D.

Real-time, forward modelling of spatial distributions of potentially damaging after- shocks by calculating stress perturbations due to large earthquakes may produce so- cially useful, time- dependent hazard estimates in the foreseeable future. Such calcula- tions, however, rely on the resolution of a stress perturbation tensor (SPT) onto planes whose geometry is unknown and decisions as to the orientations of these planes have a first order effect on the geometry of the resulting hazard distributions. Commonly, these decisions are based on the assumption that structures optimally oriented for fail- ure in the regional stress field, exist everywhere and stress maps are produced by resolving onto these orientations. Here we investigate this proposition using a 3D cal- culation for the optimally oriented planes (OOPs) for the 1992 Landers earthquake (M = 7.3). We examine the encouraged mechanisms as a function of location and show that enhancement for failure exists over a much wider area than in the equivalent, and more usual, 2.5D calculations. Mechanisms predicted in these areas are not consistent with the local structural geology, however, and corresponding aftershocks are gener- ally not observed. We argue that best hazard estimates will result from geometrically restricted versions of the OOP concept in which observed structure constrains possible orientations for failure.

Laboratory investigation of shale rock to identify fracture propagation in vertical direction to bedding

NASA Astrophysics Data System (ADS)

Peng, Tan; Yan, Jin; Bing, Hou; Yingcao, Zhou; Ruxin, Zhang; Zhi, Chang; Meng, Fan

2018-06-01

Affected by beddings and natural fractures, fracture geometry in the vertical plane is complex in shale formation, which differs from a simple fracture in homogeneous sandstone reservoirs. However, the propagation mechanism of a hydraulic fracture in the vertical plane has not been well understood. In this paper, a true tri-axial pressure machine was deployed for shale horizontal well fracturing simulation experiments of shale outcrops. The effects of multiple factors on hydraulic fracture vertical propagation were studied. The results revealed that hydraulic fracture initiation and propagation displayed four basic patterns in the vertical plane of laminated shale formation. A hydraulic fracture would cross the beddings under the high vertical stress difference between a vertical stress and horizontal minimum stress of 12 MPa, while a hydraulic fracture propagates along the beddings under a low vertical stress difference of 3 MPa. Four kinds of fracture geometry, including a single main fracture, a nonplanar fracture, a complex fracture, and a complex fracture network, were observed due to the combined effects of flow rate and viscosity. Due to the influence of binding strength (or cementing strength) on the fracture communication effects between a hydraulic fracture and the beddings, the opening region of the beddings takes the shape of an ellipse.

Variation of yield loci in finite element analysis by considering texture evolution for AA5042 aluminum sheets

NASA Astrophysics Data System (ADS)

Yoon, Jonghun; Kim, Kyungjin; Yoon, Jeong Whan

2013-12-01

Yield function has various material parameters that describe how materials respond plastically in given conditions. However, a significant number of mechanical tests are required to identify the many material parameters for yield function. In this study, an effective method using crystal plasticity through a virtual experiment is introduced to develop the anisotropic yield function for AA5042. The crystal plasticity approach was used to predict the anisotropic response of the material in order to consider a number of stress or strain modes that would not otherwise be evident through mechanical testing. A rate-independent crystal plasticity model based on a smooth single crystal yield surface, which removes the innate ambiguity problem within the rate-independent model and Taylor model for polycrystalline deformation behavior were employed to predict the material's response in the balanced biaxial stress, pure shear, and plane strain states to identify the parameters for the anisotropic yield function of AA5042.

Shock-induced thermal wave propagation and response analysis of a viscoelastic thin plate under transient heating loads

NASA Astrophysics Data System (ADS)

Li, Chenlin; Guo, Huili; Tian, Xiaogeng

2018-04-01

This paper is devoted to the thermal shock analysis for viscoelastic materials under transient heating loads. The governing coupled equations with time-delay parameter and nonlocal scale parameter are derived based on the generalized thermo-viscoelasticity theory. The problem of a thin plate composed of viscoelastic material, subjected to a sudden temperature rise at the boundary plane, is solved by employing Laplace transformation techniques. The transient responses, i.e. temperature, displacement, stresses, heat flux as well as strain, are obtained and discussed. The effects of time-delay and nonlocal scale parameter on the transient responses are analyzed and discussed. It can be observed that: the propagation of thermal wave is dynamically smoothed and changed with the variation of time-delay; while the displacement, strain, and stress can be rapidly reduced by nonlocal scale parameter, which can be viewed as an important indicator for predicting the stiffness softening behavior for viscoelastic materials.

On Compression of a Heavy Compressible Layer of an Elastoplastic or Elastoviscoplastic Medium

NASA Astrophysics Data System (ADS)

Kovtanyuk, L. V.; Panchenko, G. L.

2017-11-01

The problem of deformation of a horizontal plane layer of a compressible material is solved in the framework of the theory of small strains. The upper boundary of the layer is under the action of shear and compressing loads, and the no-slip condition is satisfied on the lower boundary of the layer. The loads increase in absolute value with time, then become constant, and then decrease to zero.Various plasticity conditions are consideredwith regard to the material compressibility, namely, the Coulomb-Mohr plasticity condition, the von Mises-Schleicher plasticity condition, and the same conditions with the viscous properties of the material taken into account. To solve the system of partial differential equations for the components of irreversible strains, a finite-difference scheme is developed for a spatial domain increasing with time. The laws of motion of elastoplastic boundaries are presented, the stresses, strains, rates of strain, and displacements are calculated, and the residual stresses and strains are found.

A Bridge between Two Important Problems in Optics and Electrostatics

ERIC Educational Resources Information Center

Capelli, R.; Pozzi, G.

2008-01-01

It is shown how the same physically appealing method can be applied to find analytic solutions for two difficult and apparently unrelated problems in optics and electrostatics. They are: (i) the diffraction of a plane wave at a perfectly conducting thin half-plane and (ii) the electrostatic field associated with a parallel array of stripes held at…

Wiimote Experiments: 3-D Inclined Plane Problem for Reinforcing the Vector Concept

ERIC Educational Resources Information Center

Kawam, Alae; Kouh, Minjoon

2011-01-01

In an introductory physics course where students first learn about vectors, they oftentimes struggle with the concept of vector addition and decomposition. For example, the classic physics problem involving a mass on an inclined plane requires the decomposition of the force of gravity into two directions that are parallel and perpendicular to the…

The impact of static stress change, dynamic stress change, and the background stress on aftershock focal mechanisms

USGS Publications Warehouse

Hardebeck, Jeanne L.

2014-01-01

The focal mechanisms of earthquakes in Southern California before and after four M ≥ 6.7 main shocks provide insight into how fault systems respond to stress and changes in stress. The main shock static stress changes have two observed impacts on the seismicity: changing the focal mechanisms in a given location to favor those aligned with the static stress change and changing the spatial distribution of seismicity to favor locations where the static stress change aligns with the background stress. The aftershock focal mechanisms are significantly aligned with the static stress changes for absolute stress changes of ≥ 0.02 MPa, for up to ~20 years following the main shock. The dynamic stress changes have similar, although smaller, effects on the local focal mechanisms and the spatial seismicity distribution. Dynamic stress effects are best observed at long periods (30–60 s) and for metrics based on repeated stress cycling in the same direction. This implies that dynamic triggering operates, at least in part, through cyclic shear stress loading in the direction of fault slip. The background stress also strongly controls both the preshock and aftershock mechanisms. While most aftershock mechanisms are well oriented in the background stress field, 10% of aftershocks are identified as poorly oriented outliers, which may indicate limited heterogeneity in the postmain shock stress field. The fault plane orientations of the outliers are well oriented in the background stress, while their slip directions are not, implying that the background stress restricts the distribution of available fault planes.

High-order integral equation methods for problems of scattering by bumps and cavities on half-planes.

PubMed

Pérez-Arancibia, Carlos; Bruno, Oscar P

2014-08-01

This paper presents high-order integral equation methods for the evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely, scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled, or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined-even at and around points where singular fields and infinite currents exist.

Numerical and experimental analyses of out-of-plane deformation of triaxial woven fabric

NASA Astrophysics Data System (ADS)

Zhou, Hongtao; Xiao, Xueliang; Qian, Kun; Zhang, Kun; Zhang, Diantang

2018-05-01

With three sets of yarns interwoven in plane for angle-interlock structure, triaxial woven fabric (TWF) is a unique and perfect construction material for products subjected to multi-directional loads, as compared to classic fabrics of orthogonal structure. Finite-element analysis (FEA) and experimental methods are applied to study the out-of-plane deformation (OPD) behaviors of TWF and plain woven fabric (PWF). Among this, the yarn cross section, path and woven structure are obtained using optical microscopy, the related parameters are input to finite element model (FEM) for simulating the OPD behavior. This paper presents a detailed analysis on out-of-plane deformation behavior of TWF and PWF by the finite element method and experiment. In consideration of the comparability, TWF and PWF are designed and prepared with the same yarns and areal density (g/m2). The deformation profile, maximum stress and maximum deflection of TWF and PWF are obtained by FEA and experiment. It has been found that the maximum deflection and maximum stress of TWF is smaller than that of PWF under the same uniform negative pressure, both FEA and experiment. Furthermore, the stress distribution of TWF is more evenly than that of PWF, indicating that TWF exhibited superior isotropy in comparison with PWF for one more directional set of yarns in undertaking the OPD.

Cross-layer shared protection strategy towards data plane in software defined optical networks

NASA Astrophysics Data System (ADS)

Xiong, Yu; Li, Zhiqiang; Zhou, Bin; Dong, Xiancun

2018-04-01

In order to ensure reliable data transmission on the data plane and minimize resource consumption, a novel protection strategy towards data plane is proposed in software defined optical networks (SDON). Firstly, we establish a SDON architecture with hierarchical structure of data plane, which divides the data plane into four layers for getting fine-grained bandwidth resource. Then, we design the cross-layer routing and resource allocation based on this network architecture. Through jointly considering the bandwidth resource on all the layers, the SDN controller could allocate bandwidth resource to working path and backup path in an economical manner. Next, we construct auxiliary graphs and transform the shared protection problem into the graph vertex coloring problem. Therefore, the resource consumption on backup paths can be reduced further. The simulation results demonstrate that the proposed protection strategy can achieve lower protection overhead and higher resource utilization ratio.

Microscopic Study of the Influence of Impurities on Interface Bonding.

DTIC Science & Technology

1985-01-25

with different impurities (P,S) levels were specially made by Armco, Inc. In addition to these four alloys, commercial alloys including Armco’s Nitronic ...25 30 40 50 60 70 Percent Intergranular, % IG Figu re A. 10 Variation of K and plane stress Keff with IGA for the Fe-P-W specimens. 20 AIO 40 Fe-P-Mo...iIS- Ke f f q !m=- 0.218 35 E 30 - 30- ~m=-0. 145 25 20 25 30 40 50 60 70 Percent Intergranular, % IG Figurej A.9 Vriation of K and plane stress Keff

Analysis of a Generally Oriented Crack in a Functionally Graded Strip Sandwiched Between Two Homogeneous Half Planes

NASA Technical Reports Server (NTRS)

Shbeeb, N.; Binienda, W. K.; Kreider, K.

1999-01-01

The driving forces for a generally oriented crack embedded in a Functionally Graded strip sandwiched between two half planes are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various nonhomogeneity ratios, crack lengths. crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.

On double shearing in frictional materials

NASA Astrophysics Data System (ADS)

Teunissen, J. A. M.

2007-01-01

This paper evaluates the mechanical behaviour of yielding frictional geomaterials. The general Double Shearing model describes this behaviour. Non-coaxiality of stress and plastic strain increments for plane strain conditions forms an important part of this model. The model is based on a micro-mechanical and macro-mechanical formulation. The stress-dilatancy theory in the model combines the mechanical behaviour on both scales.It is shown that the general Double Shearing formulation comprises other Double Shearing models. These models differ in the relation between the mobilized friction and dilatancy and in non-coaxiality. In order to describe reversible and irreversible deformations the general Double Shearing model is extended with elasticity.The failure of soil masses is controlled by shear mechanisms. These shear mechanisms are determined by the conditions along the shear band. The shear stress ratio of a shear band depends on the orientation of the stress in the shear band. There is a difference between the peak strength and the residual strength in the shear band. While peak stress depends on strength properties only, the residual strength depends upon the yield conditions and the plastic deformation mechanisms and is generally considerably lower than the maximum strength. It is shown that non-coaxial models give non-unique solutions for the shear stress ratio on the shear band. The Double Shearing model is applied to various failure problems of soils such as the direct simple shear test, the biaxial test, infinite slopes, interfaces and for the calculation of the undrained shear strength. Copyright

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

NASA Technical Reports Server (NTRS)

Rose, Cheryl A.; Herakovich, Carl T.

1992-01-01

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Static and kinetic friction of granite at high normal stress

USGS Publications Warehouse

Byerlee, J.D.

1970-01-01

Frictional sliding on ground surfaces of granite, angle of sliding planes 30?? and 45??, was investigated as a function of confining pressure. Over the normal stress range of 2-12 kb, the static frictional shear stress ??s follows the relationship ??s = 0??5 + 0?? ??n and the kinetic frictional shear stress ??k was calculated to be ??k = 0??25 + 0??47 ??n. ?? 1970.

Electronic and optical properties of GaN/AlN quantum dots on Si(111) subject to in-plane uniaxial stresses and variable excitation

NASA Astrophysics Data System (ADS)

Moshe, O.; Rich, D. H.; Birner, S.; Povolotskyi, M.; Damilano, B.; Massies, J.

2010-10-01

We have studied the excitation- and polarization-dependent optical properties of GaN/AlN self-assembled quantum dots (QDs) grown on Si(111) substrates. Ensembles of QDs were subject to various external stress configurations that resulted from the thermal expansion coefficient mismatch between the GaN/AlN layers and the Si(111) substrate and ranged from in-plane uniaxial stress, primarily along the ⟨112¯0⟩ directions, to in-plane biaxial stress, having magnitudes ranging from 20-30 kbar. Limited regions of uniaxial stress were obtained by exploiting naturally occurring microcracks that form during the postgrowth cooling. These microcracks act as stressors in order to create the highly localized regions of uniaxial stress. The local strain tensors for such QDs, which are subject to an interfacial stress perturbation, have been determined by modeling the dependence of the QD excitonic transition energy on the interfacial stress. Cathodoluminescence (CL) measurements of the excitonic transitions exhibit an in-plane linear polarization anisotropy in close proximity to microcracks. The polarization anisotropy is strongly dependent on the sample temperature and the electron beam excitation conditions used to excite the QD ensemble. Localized CL spectroscopy of the QDs exhibits emissions from both the ground and excited states, whose relative contributions depend on the level of excitation and temperature. Experimental results indicate that the polarization anisotropy vanishes at high temperatures (˜300 K) with an increasing excitation of the QDs, while the anisotropy decreases more slowly with excitation at low temperatures (˜60 K). A theoretical modeling of the effect of carrier filling on the polarization anisotropy and the excitonic transition energy was performed, as based on three-dimensional self-consistent solutions of the Schrödinger and Poisson equations using the 6×6 kṡp and effective mass methods for calculations of the e-h wave functions and electron and hole quasi-Fermi levels for varying levels of state filling. We attribute carrier filling and a thermal excitation of holes into higher energy QD hole states during excitation to account for the observed gradual decrease in the polarization anisotropy with an increasing electron-hole pair excitation density at T =300 K.

Plane Poiseuille Flow of a Rarefied Gas in the Presence of a Strong Gravitation

NASA Astrophysics Data System (ADS)

Doi, Toshiyuki

2010-11-01

Poiseuille flow of a rarefied gas between two horizontal planes in the presence of a strong gravitation is considered, where the gravity is so strong that the path of a molecule is curved considerably as it ascends or descends the distance of the planes. The gas behavior is studied based on the Boltzmann equation. An asymptotic analysis for a slow variation in the longitudinal direction is carried out and the problem is reduced to a spatially one dimensional problem, as was in the Poiseuille flow problem in the absence of the gravitation. The mass flow rate as well as the macroscopic variables is obtained for a wide range of the mean free path of the gas and the gravity. A numerical analysis of a two dimensional problem is also carried out and the result of the asymptotic analysis is verified.

Novel Approach on the Optimisation of Mid-Course Corrections Along Interplanetary Trajectories

NASA Astrophysics Data System (ADS)

Iorfida, Elisabetta; Palmer, Phil; Roberts, Mark

The primer vector theory, firstly proposed by Lawden, defines a set of necessary conditions to characterise whether an impulsive thrust trajectory is optimal with respect to propellant usage, within a two-body problem context. If the conditions are not satisfied, one or more potential intermediate impulses are performed along the transfer arc, in order to lower the overall cost. The method is based on the propagation of the state transition matrix and on the solution of a boundary value problem, which leads to a mathematical and computational complexity.In this paper, a different approach is introduced. It is based on a polar coordinates transformation of the primer vector which allows the decoupling between its in-plane and out-of-plane components. The out-of-plane component is solved analytically while for the in-plane ones a Hamiltonian approximation is made.The novel procedure reduces the mathematical complexity and the computational cost of Lawden's problem and gives also a different perspective about the optimisation of a transfer trajectory.

Numerical analysis of stress effects on Frank loop evolution during irradiation in austenitic Fe&z.sbnd;Cr&z.sbnd;Ni alloy

NASA Astrophysics Data System (ADS)

Tanigawa, Hiroyasu; Katoh, Yutai; Kohyama, Akira

1995-08-01

Effects of applied stress on early stages of interstitial type Frank loop evolution were investigated by both numerical calculation and irradiation experiments. The final objective of this research is to propose a comprehensive model of complex stress effects on microstructural evolution under various conditions. In the experimental part of this work, the microstructural analysis revealed that the differences in resolved normal stress caused those in the nucleation rates of Frank loops on {111} crystallographic family planes, and that with increasing external applied stress the total nucleation rate of Frank loops was increased. A numerical calculation was carried out primarily to evaluate the validity of models of stress effects on nucleation processes of Frank loop evolution. The calculation stands on rate equuations which describe evolution of point defects, small points defect clusters and Frank loops. The rate equations of Frank loop evolution were formulated for {111} planes, considering effects of resolved normal stress to clustering processes of small point defects and growth processes of Frank loops, separately. The experimental results and the predictions from the numerical calculation qualitatively coincided well with each other.

Exact solution for an optimal impermeable parachute problem

NASA Astrophysics Data System (ADS)

Lupu, Mircea; Scheiber, Ernest

2002-10-01

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.

Purdue Plane Structures Analyzer II : a computerized wood engineering system

Treesearch

S. K. Suddarth; R. W. Wolfe

1984-01-01

The Purdue Plane Structures Analyzer (PPSA) is a computer program developed specifically for the analysis of wood structures. It uses recognized analysis procedures, in conjunction with recommendations of the 1982 National Design Specification for Wood Construction, to determine stresses and deflections of wood trusses and frames. The program offers several options for...

A Review of Australian Investigations on Aeronautical Fatigue during the Period April 1981 to March 1983.

DTIC Science & Technology

1983-03-01

13. Jeffery, G.B. Plane stress and plane strain in bipolar co-ordinates. Royal Society of London, Phil . Trans. Series A, Vol. 221, 1921, pp 265-293...Commerce Central Library .../cont. DISTRIBUTfION (CONTD.) Statutory &State Authorities and Industry Ccuimonwealth Aircraft Corporation, Mr R.C. Beckett

Investigation of Strain-Relaxation Characteristics of Nitrides Grown on Si(110) by Metalorganic Chemical Vapor Deposition Using X-ray Diffraction

NASA Astrophysics Data System (ADS)

Jiang, Quanzhong; Lewins, Christopher J.; Allsopp, Duncan W. E.; Bowen, Chris R.; Wang, Wang N.

2013-08-01

This paper describes the effect of an interfacial biaxial stress field on the dislocation formation dynamics during epitaxial growth of nitrides on Si(110). The anisotropic mismatch stress between a 2-fold symmetry Si(110) atomic plane and the AlN basal plane of 6-fold symmetry may be relaxed through the creation of additional characteristic dislocations, as proposed by Ruiz-Zepeda et al. with Burgers vectors: b= 1/2[bar 2110] and b= [1bar 210], +/-60° from [11bar 20]. The dislocations generated under such a biaxial stress field appear annihilating more efficiently with increasing thickness, leading to high-quality nitride epilayers on Si(110) for improved quantum efficiency of InGaN/GaN quantum wells.

Plume-Surface Interaction Modeling for a Human-Scale Mars Lander

NASA Technical Reports Server (NTRS)

Hart, Kenneth

2017-01-01

Landing vehicles impart thermal and strain energy onto the landing site from the retrorocket exhaust. Depending on the design of the vehicle, the energy may be great enough to cause spallation at the landing site. This damage may be minor and repairable in the case of landing on a terrestrial landing pad. For missions to other planetary bodies, the spallation may cause the landing site to become uneven and unstable, as well as damage. Simulating this phenomenon in a laboratory or computationally would require a significant amount of time and other resources. These resources typically are not available during the design phase of a mission. This paper presents a computationally-efficient model for the temperature and stress distributions that arise during landing. These quantities can be used along with existing failure criteria, such as the Hoek-Brown criterion for geological materials, to quickly determine whether spallation will occur. The stress and temperature distributions at the landing site are inherently 3D; however, there is a plane of symmetry and in that plane the distributions are 2D. Both quantities are modeled using series solutions to their governing partial differential equations (PDEs). The stress is modeled using the Airy stress potential function and its governing PDE is the biharmonic equation. The temperature is governed by Fourier's law. The models assume that stress due to gravity can be neglected, the points in the plane do not accelerate, and that the material properties are constant.

A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum

NASA Technical Reports Server (NTRS)

Kim, S.-W.; Chen, C.-P.

1987-01-01

A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

A multiple-time-scale turbulence model based on variable partitioning of the turbulent kinetic energy spectrum

NASA Technical Reports Server (NTRS)

Kim, S.-W.; Chen, C.-P.

1989-01-01

A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

Galois groups of Schubert problems via homotopy computation

NASA Astrophysics Data System (ADS)

Leykin, Anton; Sottile, Frank

2009-09-01

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of the Schubert problem of 3-planes in mathbb{C}^8 meeting 15 fixed 5-planes non-trivially is the full symmetric group S_{6006} .

Analysis of gob gas venthole production performances for strata gas control in longwall mining.

PubMed

Karacan, C Özgen

2015-10-01

Longwall mining of coal seams affects a large area of overburden by deforming it and creating stress-relief fractures, as well as bedding plane separations, as the mining face progresses. Stress-relief fractures and bedding plane separations are recognized as major pathways for gas migration from gas-bearing strata into sealed and active areas of the mines. In order for strata gas not to enter and inundate the ventilation system of a mine, gob gas ventholes (GGVs) can be used as a methane control measure. The aim of this paper is to analyze production performances of GGVs drilled over a longwall panel. These boreholes were drilled to control methane emissions from the Pratt group of coals due to stress-relief fracturing and bedding plane separations into a longwall mine operating in the Mary Lee/Blue Creek coal seam of the Upper Pottsville Formation in the Black Warrior Basin, Alabama. During the course of the study, Pratt coal's reservoir properties were integrated with production data of the GGVs. These data were analyzed by using material balance techniques to estimate radius of influence of GGVs, gas-in-place and coal pressures, as well as their variations during mining. The results show that the GGVs drilled to extract gas from the stress-relief zone of the Pratt coal interval is highly effective in removing gas from the Upper Pottsville Formation. The radii of influence of the GGVs were in the order of 330-380 m, exceeding the widths of the panels, due to bedding plane separations and stress relieved by fracturing. Material balance analyses indicated that the initial pressure of the Pratt coals, which was around 648 KPa when longwall mining started, decreased to approximately 150 KPa as the result of strata fracturing and production of released gas. Approximately 70% of the initial gas-in-place within the area of influence of the GGVs was captured during a period of one year.

Reconstruction of structural damage based on reflection intensity spectra of fiber Bragg gratings

NASA Astrophysics Data System (ADS)

Huang, Guojun; Wei, Changben; Chen, Shiyuan; Yang, Guowei

2014-12-01

We present an approach for structural damage reconstruction based on the reflection intensity spectra of fiber Bragg gratings (FBGs). Our approach incorporates the finite element method, transfer matrix (T-matrix), and genetic algorithm to solve the inverse photo-elastic problem of damage reconstruction, i.e. to identify the location, size, and shape of a defect. By introducing a parameterized characterization of the damage information, the inverse photo-elastic problem is reduced to an optimization problem, and a relevant computational scheme was developed. The scheme iteratively searches for the solution to the corresponding direct photo-elastic problem until the simulated and measured (or target) reflection intensity spectra of the FBGs near the defect coincide within a prescribed error. Proof-of-concept validations of our approach were performed numerically and experimentally using both holed and cracked plate samples as typical cases of plane-stress problems. The damage identifiability was simulated by changing the deployment of the FBG sensors, including the total number of sensors and their distance to the defect. Both the numerical and experimental results demonstrate that our approach is effective and promising. It provides us with a photo-elastic method for developing a remote, automatic damage-imaging technique that substantially improves damage identification for structural health monitoring.

A Critical Plane-energy Model for Multiaxial Fatigue Life Prediction of Homogeneous and Heterogeneous Materials

NASA Astrophysics Data System (ADS)

Wei, Haoyang

A new critical plane-energy model is proposed in this thesis for multiaxial fatigue life prediction of homogeneous and heterogeneous materials. Brief review of existing methods, especially on the critical plane-based and energy-based methods, are given first. Special focus is on one critical plane approach which has been shown to work for both brittle and ductile metals. The key idea is to automatically change the critical plane orientation with respect to different materials and stress states. One potential drawback of the developed model is that it needs an empirical calibration parameter for non-proportional multiaxial loadings since only the strain terms are used and the out-of-phase hardening cannot be considered. The energy-based model using the critical plane concept is proposed with help of the Mroz-Garud hardening rule to explicitly include the effect of non-proportional hardening under fatigue cyclic loadings. Thus, the empirical calibration for non-proportional loading is not needed since the out-of-phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature and it is shown the proposed model can work for both proportional and non-proportional loadings without the empirical calibration. Next, the model is extended for the fatigue analysis of heterogeneous materials integrating with finite element method. Fatigue crack initiation of representative volume of heterogeneous materials is analyzed using the developed critical plane-energy model and special focus is on the microstructure effect on the multiaxial fatigue life predictions. Several conclusions and future work is drawn based on the proposed study.

Enhancement of piezoelectric constants induced by cation-substitution and two-dimensional strain effects on ZnO predicted by density functional perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakamura, Kaoru, E-mail: n-kaoru@criepi.denken.or.jp; Higuchi, Sadao; Ohnuma, Toshiharu

2016-03-21

Using density functional perturbation theory, we investigated the effect of various substitutional dopant elements and in-plane strain on the piezoelectric properties of ZnO. The piezoelectric stress constant e{sub 33} of doped ZnO was found to depend on the formal charge of the substitutional dopant. By decomposing the piezoelectric stress constant e{sub 33} into the individual atomic contributions, the change in the piezoelectric properties was found to originate from a change in the coupling between the atomic displacement and the strain. Furthermore, we found that in-plane tensile strain along the a axis, which is specific to the thin film, can enhancemore » the piezoelectric constant of ZnO. A phase transition from wurtzite to h-BN-type structure was found to occur with increasing in-plane tensile. The piezoelectric strain constant d{sub 33} was predicted to reach ∼200 pC/N for 2.78 at. % V-substituted ZnO at 5.5% in-plane strain, just before the phase transition. These theoretical results suggest that the piezoelectric constant of ZnO can be enhanced by controlling the in-plane strain via selection of the substrate material and dopant element.« less

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

PubMed

Guo, Xiao; Wei, Peijun

2016-03-01

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.

Ductile fracture theories for pressurised pipes and containers

NASA Technical Reports Server (NTRS)

Erdogan, F.

1976-01-01

Two mechanisms of fracture are distinguished. Plane strain fractures occur in materials which do not undergo large-scale plastic deformations prior to and during a possible fracture deformation. Plane stress or high energy fractures are generally accompanied by large inelastic deformations. Theories for analyzing plane stress are based on the concepts of critical crack opening stretch, K(R) characterization, J-integral, and plastic instability. This last is considered in some detail. The ductile fracture process involves fracture initiation followed by a stable crack growth and the onset of unstable fracture propagation. The ductile fracture propagation process may be characterized by either a multiparameter (discrete) model, or some type of a resistance curve which may be considered as a continuous model expressed graphically. These models are studied and an alternative model is also proposed for ductile fractures which cannot be modeled as progressive crack growth phenomena.

A gradient based algorithm to solve inverse plane bimodular problems of identification

NASA Astrophysics Data System (ADS)

Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing

2018-02-01

This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.

Focus information is used to interpret binocular images

PubMed Central

Hoffman, David M.; Banks, Martin S.

2011-01-01

Focus information—blur and accommodation—is highly correlated with depth in natural viewing. We examined the use of focus information in solving the binocular correspondence problem and in interpreting monocular occlusions. We presented transparent scenes consisting of two planes. Observers judged the slant of the farther plane, which was seen through the nearer plane. To do this, they had to solve the correspondence problem. In one condition, the two planes were presented with sharp rendering on one image plane, as is done in conventional stereo displays. In another condition, the planes were presented on two image planes at different focal distances, simulating focus information in natural viewing. Depth discrimination performance improved significantly when focus information was correct, which shows that the visual system utilizes the information contained in depth-of-field blur in solving binocular correspondence. In a second experiment, we presented images in which one eye could see texture behind an occluder that the other eye could not see. When the occluder's texture was sharp along with the occluded texture, binocular rivalry was prominent. When the occluded and occluding textures were presented with different blurs, rivalry was significantly reduced. This shows that blur aids the interpretation of scene layout near monocular occlusions. PMID:20616139

Controlled multiple neutral planes by low elastic modulus adhesive for flexible organic photovoltaics.

PubMed

Kim, Wansun; Lee, Inhwa; Yoon Kim, Dong; Yu, Youn-Yeol; Jung, Hae-Yoon; Kwon, Seyeoul; Seo Park, Weon; Kim, Taek-Soo

2017-05-12

To protect brittle layers in organic photovoltaic devices, the mechanical neutral plane strategy can be adopted through placing the brittle functional materials close to the neutral plane where stress and strain are zero during bending. However, previous research has been significantly limited in the location and number of materials to protect through using a single neutral plane. In this study, multiple neutral planes are generated using low elastic modulus adhesives and are controlled through quantitative analyses in order to protect the multiple brittle materials at various locations. Moreover, the protection of multiple brittle layers at various locations under both concave and convex bending directions is demonstrated. Multilayer structures that have soft adhesives are further analyzed using the finite element method analysis in order to propose guidelines for structural design when employing multiple neutral planes.

Torsional bridge setup for the characterization of integrated circuits and microsensors under mechanical shear stress.

PubMed

Herrmann, M; Gieschke, P; Ruther, P; Paul, O

2011-12-01

We present a torsional bridge setup for the electro-mechanical characterization of devices integrated in the surface of silicon beams under mechanical in-plane shear stress. It is based on the application of a torsional moment to the longitudinal axis of the silicon beams, which results in a homogeneous in-plane shear stress in the beam surface. The safely applicable shear stresses span the range of ±50 MPa. Thanks to a specially designed clamping mechanism, the unintended normal stress typically stays below 2.5% of the applied shear stress. An analytical model is presented to compute the induced shear stress. Numerical computations verify the analytical results and show that the homogeneity of the shear stress is very high on the beam surface in the region of interest. Measurements with piezoresistive microsensors fabricated using a complementary metal-oxide-semiconductor process show an excellent agreement with both the computational results and comparative measurements performed on a four-point bending bridge. The electrical connection to the silicon beam is performed with standard bond wires. This ensures that minimal forces are applied to the beam by the electrical interconnection to the external instrumentation and that devices with arbitrary bond pad layout can be inserted into the setup.

Effect of mesh distortion on the accuracy of transverse shear stresses and their sensitivity coefficients in multilayered composites

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Kim, Yong H.

1995-01-01

A study is made of the effect of mesh distortion on the accuracy of transverse shear stresses and their first-order and second-order sensitivity coefficients in multilayered composite panels subjected to mechanical and thermal loads. The panels are discretized by using a two-field degenerate solid element, with the fundamental unknowns consisting of both displacement and strain components, and the displacement components having a linear variation throughout the thickness of the laminate. A two-step computational procedure is used for evaluating the transverse shear stresses. In the first step, the in-plane stresses in the different layers are calculated at the numerical quadrature points for each element. In the second step, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of transverse shear stresses. Numerical results are presented showing no noticeable degradation in the accuracy of the in-plane stresses and their sensitivity coefficients with mesh distortion. However, such degradation is observed for the transverse shear stresses and their sensitivity coefficients. The standard of comparison is taken to be the exact solution of the three-dimensional thermoelasticity equations of the panel.

A numerical method for determination of source time functions for general three-dimensional rupture propagation

NASA Technical Reports Server (NTRS)

Das, S.

1979-01-01

A method to determine the displacement and the stress on the crack plane for a three-dimensional shear crack of arbitrary shape propagating in an infinite, homogeneous medium which is linearly elastic everywhere off the crack plane is presented. The main idea of the method is to use a representation theorem in which the displacement at any given point on the crack plane is written as an integral of the traction over the whole crack plane. As a test of the accuracy of the numerical technique, the results are compared with known solutions for two simple cases.

Study on Initiation Mechanisms of Hydraulic Fracture Guided by Vertical Multi-radial Boreholes

NASA Astrophysics Data System (ADS)

Guo, Tiankui; Liu, Binyan; Qu, Zhanqing; Gong, Diguang; Xin, Lei

2017-07-01

The conventional hydraulic fracturing fails in the target oil development zone (remaining oil or gas, closed reservoir, etc.) which is not located in the azimuth of maximum horizontal in situ stress of available wellbores. The technology of directional propagation of hydraulic fracture guided by vertical multi-radial boreholes is innovatively developed. The effects of in situ stress, wellbore internal pressure and fracturing fluid percolation effect on geostress field distribution are taken into account, a mechanical model of two radial boreholes (basic research unit) is established, and the distribution and change rule of the maximum principal stress on the various parameters have been studied. The results show that as the radial borehole azimuth increases, the preferential rock tensile fracturing in the axial plane of radial boreholes becomes increasingly difficult. When the radial borehole azimuth increases to a certain extent, the maximum principal stress no longer appears in the azimuth of the radial boreholes, but will go to other orientations outside the axial plane of radial boreholes and the maximum horizontal stress orientation. Therefore, by reducing the ratio between the distance of the radial boreholes and increasing the diameter of the radial boreholes can enhance the guiding strength. In the axial plane of the radical boreholes, particularly in the radial hole wall, position closer to the radial boreholes is more prone to rock tensile destruction. Even in the case of large radial borehole azimuth, rock still preferentially ruptures in this position. The more the position is perpendicularly far from the axis of the wellbore, the lesser it will be affected by wellbore, and the lesser the tensile stress of each point. Meanwhile, at a certain depth, due to the decrease in the impact of the wellbore and the impact of the two radial boreholes increases accordingly, at the further position from the wellbore axis, the tensile fracture is the most prone to occur and it will be closer to the axial plane of the two radial boreholes. The study provides theoretical support for the technology of directional propagation of hydraulic fracture promoted by radial borehole, which is helpful for planning well-completion parameters in technology of hydraulic fracturing promoted by radial borehole.

Stress-dependent permeability evolution in sandstones with anisotropic physical properties

NASA Astrophysics Data System (ADS)

Metz, V.; David, C.; Louis, L.; Rodriguez Rey, A.; Ruiz de Argandona, V. G.

2003-04-01

Fluid flow in reservoir rocks is strongly dependent on stress path and rock microstructure which may present a significant anisotropy. We present recent experimental data on the evolution of permeability with applied stress for three sandstones tested under triaxial conditions in the low confining pressure range (<10 MPa). Samples with diameter 40 mm and length 80 mm were cored in three orthogonal directions in blocks retrieved from quarries. One coring direction was perpendicular to the bedding plane whereas the other directions were arbitrarily chosen within the bedding plane. The selected rocks are the Bentheim sandstone (BNT), a quartz-rich cretaceous sandstone from Germany with 24% porosity, and two different varieties of a same jurassic formation in Northern Spain, the La Marina sandstone. The Yellow La Marina sandstone (YLM) with porosity 28% has a low cohesion and is the weathered form of the well-consolidated Grey La Marina sandstone (GLM) with porosity 17%. When loaded up to the failure stress, the more porous sandstones (BNT, YLM) exhibited a monotonic decrease of permeability even when the rock was dilating at deviatoric stresses close to the failure stress. On the other hand the permeability of the less porous sandstone (GLM) increased during the dilating phase. These results are in agreement with previous studies. In addition we observed that all three sandstones are anisotropic with respect to several physical properties including permeability. We systematically found a lower permeability in the direction perpendicular to the bedding plane, but the ratio of "vertical" to "horizontal" permeability varies from one sandstone to the other. The permeability anisotropy is compared to the anisotropy of electrical conductivity, acoustic velocity, capillary imbibition and elastic moduli: in general good correlations are found for all the properties. For the Bentheim sandstone, a microstructural study on thin sections revealed that the rock anisotropy is due to the anisotropy of intergranular pores which statistically are found to be elongated within the bedding plane. This result is in agreement with the prediction of Kachanov's model for the anisotropy of acoustic velocity in Bentheim sandstone.

Influence of Stress State, Stress Orientation, and Rock Properties on the Development of Deformation-Band 'Ladder' Arrays in Porous Sandstone

NASA Astrophysics Data System (ADS)

Schultz, R. A.; Soliva, R.; Fossen, H.

2013-12-01

Deformation bands in porous rocks tend to develop into spatially organized arrays that display a variety of lengths and thicknesses, and their geometries and arrangements are of interest with respect to fluid flow in reservoirs. Field examples of deformation band arrays in layered clastic sequences suggest that the development of classic deformation band arrays, such as ladders and conjugate sets, and the secondary formation of through-going faults appear to be related to the physical properties of the host rock, the orientation of stratigraphic layers relative to the far-field stress state, and the evolution of the local stress state within the developing array. We have identified several field examples that demonstrate changes in band properties, such as type and orientation, as a function of one or more of these three main factors. Normal-sense deformation-band arrays such as those near the San Rafael Swell (Utah) develop three-dimensional ladder-style arrays at a high angle to the maximum compression direction; these cataclastic shear bands form at acute angles to the maximum compression not very different from that of the optimum frictional sliding plane, thus facilitating the eventual nucleation of a through-going fault. At Orange quarry (France), geometrically conjugate sets of reverse-sense compactional shear bands form with angles to the maximum compression direction that inhibit fault nucleation within them; the bands in this case also form at steep enough angles to bedding that stratigraphic heterogeneities within the deforming formation were apparently not important. Two exposures of thrust-sense ladders at Buckskin Gulch (Utah) demonstrate the importance of host-rock properties, bedding-plane involvement, and local stress perturbations on band-array growth. In one ladder, thrust-sense shear deformation bands nucleated along suitably oriented bedding planes, creating overprinting sets of compaction bands that can be attributed to layer properties and local stress changes near the shear-band tips. Two other ladder exposures preserve compaction bands having nearly perpendicular orientations relative the bounding shear bands that define contractional stepovers that also nucleated on bedding planes. These cases suggest that local stress changes within a deformation-band stepover may lead to either rotation of bands or changes in band type relative to bands formed outside the stepover. The development of the common geometries of deformation band arrays, such as ladders, and the deformation paths to faulting thus depend on a combination of stress state, stress orientation, and rock properties.

1r2dinv: A finite-difference model for inverse analysis of two dimensional linear or radial groundwater flow

USGS Publications Warehouse

Bohling, Geoffrey C.; Butler, J.J.

2001-01-01

We have developed a program for inverse analysis of two-dimensional linear or radial groundwater flow problems. The program, 1r2dinv, uses standard finite difference techniques to solve the groundwater flow equation for a horizontal or vertical plane with heterogeneous properties. In radial mode, the program simulates flow to a well in a vertical plane, transforming the radial flow equation into an equivalent problem in Cartesian coordinates. The physical parameters in the model are horizontal or x-direction hydraulic conductivity, anisotropy ratio (vertical to horizontal conductivity in a vertical model, y-direction to x-direction in a horizontal model), and specific storage. The program allows the user to specify arbitrary and independent zonations of these three parameters and also to specify which zonal parameter values are known and which are unknown. The Levenberg-Marquardt algorithm is used to estimate parameters from observed head values. Particularly powerful features of the program are the ability to perform simultaneous analysis of heads from different tests and the inclusion of the wellbore in the radial mode. These capabilities allow the program to be used for analysis of suites of well tests, such as multilevel slug tests or pumping tests in a tomographic format. The combination of information from tests stressing different vertical levels in an aquifer provides the means for accurately estimating vertical variations in conductivity, a factor profoundly influencing contaminant transport in the subsurface. ?? 2001 Elsevier Science Ltd. All rights reserved.

Development, characterization, and modeling of ballistic impact on composite laminates under compressive pre-stress

NASA Astrophysics Data System (ADS)

Kerr-Anderson, Eric

Structural composite laminates were ballistically impacted while under in-plane compressive pre-stress. Residual properties, damage characterization, and energy absorption were compared to determine synergistic effects of in-plane compressive pre-stress and impact velocity. A fixture was developed to apply in-plane compressive loads up to 30 tons to structural composites during an impact event using a single-stage light-gas gun. Observed failure modes included typical conical delamination, the development of an impact initiated shear crack (IISC), and the shear failure of a pre-stressed composite due to impact. It was observed that the compressive failure threshold quadratically decreased in relation to the impact velocity up to velocities that caused partial penetration. For all laminates impacted at velocities causing partial or full penetration up to 350 ms-1, the failure threshold was consistent and used as an experimental normalization. Samples impacted below 65% of the failure threshold witnessed no significant change in damage morphology or residual properties when compared to typical conical delamination. Samples impacted above 65% of the failure threshold witnessed additional damage in the form of a shear crack extending perpendicular to the applied load from the point of impact. The presence of an IISC reduced the residual properties and even caused failure upon impact at extreme combinations. Four failure envelopes have been established as: transient failure, steady state failure, impact initiated shear crack, and conical damage. Boundaries and empirically based equations for residual compressive strength have been developed for each envelope with relation to two E-glass/vinyl ester laminate systems. Many aspects of pre-stressed impact have been individually examined, but there have been no comprehensive examinations of pre-stressed impact. This research has resulted in the exploration and characterization of compressively pre-stressed damage for impact velocities resulting in reflection, partial penetration, and penetration at pre-stress levels resulting in conical damage, shear cracking, and failure.

Bone stress in runners with tibial stress fracture.

PubMed

Meardon, Stacey A; Willson, John D; Gries, Samantha R; Kernozek, Thomas W; Derrick, Timothy R

2015-11-01

Combinations of smaller bone geometry and greater applied loads may contribute to tibial stress fracture. We examined tibial bone stress, accounting for geometry and applied loads, in runners with stress fracture. 23 runners with a history of tibial stress fracture & 23 matched controls ran over a force platform while 3-D kinematic and kinetic data were collected. An elliptical model of the distal 1/3 tibia cross section was used to estimate stress at 4 locations (anterior, posterior, medial and lateral). Inner and outer radii for the model were obtained from 2 planar x-ray images. Bone stress differences were assessed using two-factor ANOVA (α=0.05). Key contributors to observed stress differences between groups were examined using stepwise regression. Runners with tibial stress fracture experienced greater anterior tension and posterior compression at the distal tibia. Location, but not group, differences in shear stress were observed. Stepwise regression revealed that anterior-posterior outer diameter of the tibia and the sagittal plane bending moment explained >80% of the variance in anterior and posterior bone stress. Runners with tibial stress fracture displayed greater stress anteriorly and posteriorly at the distal tibia. Elevated tibial stress was associated with smaller bone geometry and greater bending moments about the medial-lateral axis of the tibia. Future research needs to identify key running mechanics associated with the sagittal plane bending moment at the distal tibia as well as to identify ways to improve bone geometry in runners in order to better guide preventative and rehabilitative efforts. Copyright © 2015 Elsevier Ltd. All rights reserved.

Constraints on upper plate deformation in the Nicaraguan subduction zone from earthquake relocation and directivity analysis

NASA Astrophysics Data System (ADS)

French, S. W.; Warren, L. M.; Fischer, K. M.; Abers, G. A.; Strauch, W.; Protti, J. M.; Gonzalez, V.

2010-03-01

In the Nicaraguan segment of the Central American subduction zone, bookshelf faulting has been proposed as the dominant style of Caribbean plate deformation in response to oblique subduction of the Cocos plate. A key element of this model is left-lateral motion on arc-normal strike-slip faults. On 3 August 2005, a Mw 6.3 earthquake and its extensive foreshock and aftershock sequence occurred near Ometepe Island in Lake Nicaragua. To determine the fault plane that ruptured in the main shock, we relocated main shock, foreshock, and aftershock hypocenters and analyzed main shock source directivity using waveforms from the TUCAN Broadband Seismic Experiment. The relocation analysis was carried out by applying the hypoDD double-difference method to P and S onset times and differential traveltimes for event pairs determined by waveform cross correlation. The relocated hypocenters define a roughly vertical plane of seismicity with an N60°E strike. This plane aligns with one of the two nodal planes of the main shock source mechanism. The directivity analysis was based on waveforms from 16 TUCAN stations and indicates that rupture on the N60°E striking main shock nodal plane provides the best fit to the data. The relocation and directivity analyses identify the N60°E vertical nodal plane as the main shock fault plane, consistent with the style of faulting required by the bookshelf model. Relocated hypocenters also define a second fault plane that lies to the south of the main shock fault plane with a strike of N350°E-N355°E. This fault plane became seismically active 5 h after the main shock, suggesting the influence of stresses transferred from the main shock fault plane. The August 2005 earthquake sequence was preceded by a small eruption of a nearby volcano, Concepción, on 28 July 2005. However, the local seismicity does not provide evidence for earthquake triggering of the eruption or eruption triggering of the main shock through crustal stress transfer.

Crack problem in superconducting cylinder with exponential distribution of critical-current density

NASA Astrophysics Data System (ADS)

Zhao, Yufeng; Xu, Chi; Shi, Liang

2018-04-01

The general problem of a center crack in a long cylindrical superconductor with inhomogeneous critical-current distribution is studied based on the extended Bean model for zero-field cooling (ZFC) and field cooling (FC) magnetization processes, in which the inhomogeneous parameter η is introduced for characterizing the critical-current density distribution in inhomogeneous superconductor. The effect of the inhomogeneous parameter η on both the magnetic field distribution and the variations of the normalized stress intensity factors is also obtained based on the plane strain approach and J-integral theory. The numerical results indicate that the exponential distribution of critical-current density will lead a larger trapped field inside the inhomogeneous superconductor and cause the center of the cylinder to fracture more easily. In addition, it is worth pointing out that the nonlinear field distribution is unique to the Bean model by comparing the curve shapes of the magnetization loop with homogeneous and inhomogeneous critical-current distribution.

Calculation of flow about posts and powerhead model. [space shuttle main engine

NASA Technical Reports Server (NTRS)

Anderson, P. G.; Farmer, R. C.

1985-01-01

A three dimensional analysis of the non-uniform flow around the liquid oxygen (LOX) posts in the Space Shuttle Main Engine (SSME) powerhead was performed to determine possible factors contributing to the failure of the posts. Also performed was three dimensional numerical fluid flow analysis of the high pressure fuel turbopump (HPFTP) exhaust system, consisting of the turnaround duct (TAD), two-duct hot gas manifold (HGM), and the Version B transfer ducts. The analysis was conducted in the following manner: (1) modeling the flow around a single and small clusters (2 to 10) of posts; (2) modeling the velocity field in the cross plane; and (3) modeling the entire flow region with a three dimensional network type model. Shear stress functions which will permit viscous analysis without requiring excessive numbers of computational grid points were developed. These wall functions, laminar and turbulent, have been compared to standard Blasius solutions and are directly applicable to the cylinder in cross flow class of problems to which the LOX post problem belongs.

Lubrication of dislocation glide in MgO by hydrous defects

NASA Astrophysics Data System (ADS)

Skelton, Richard; Walker, Andrew M.

2018-02-01

Water-related defects, principally in the form of protonated cation vacancies, are potentially able to weaken minerals under high-stress or low-temperature conditions by reducing the Peierls stress required to initiate dislocation glide. In this study, we use the Peierls-Nabarro (PN) model to determine the effect of protonated Mg vacancies on the 1/2<110>{110} and 1/2<110>{100} slip systems in MgO. This PN model is parameterized using generalized stacking fault energies calculated using plane-wave density functional theory, with and without protonated Mg vacancies present at the glide plane. It found that these defects increase dislocation core widths and reduce the Peierls stress over the entire pressure range 0-125 GPa. Furthermore, 1/2<110>{110} slip is found to be more sensitive to the presence of protonated vacancies which increases in the pressure at which {100} becomes the easy glide plane for 1/2<110> screw dislocations. These results demonstrate, for a simple mineral system, that water-related defects can alter the deformation behavior of minerals in the glide-creep regime by reducing the stress required to move dislocations by glide. (Mg, Fe)O is the most anisotropic mineral in the Earth's lower mantle, so the differential sensitivity of the major slip systems in MgO to hydrous defects has potential implications for the interpretation of the seismic anisotropy in this region.

The Mohr-Coulomb criterion for intact rock strength and friction - a re-evaluation and consideration of failure under polyaxial stresses

NASA Astrophysics Data System (ADS)

Hackston, A.; Rutter, E.

2015-12-01

Abstract Darley Dale and Pennant sandstones were tested under conditions of both axisymmetric shortening and extension normal to bedding. These are the two extremes of loading under polyaxial stress conditions. Failure under generalized stress conditions can be predicted from the Mohr-Coulomb failure criterion under axisymmetric compression conditions provided the best form of polyaxial failure criterion is known. The sandstone data are best reconciled using the Mogi (1967) empirical criterion. Fault plane orientations produced vary greatly with respect to the maximum compression direction in the two loading configurations. The normals to the Mohr-Coulomb failure envelopes do not predict the orientations of the fault planes eventually produced. Frictional sliding on variously inclined sawcuts and failure surfaces produced in intact rock samples was also investigated. Friction coefficient is not affected by fault plane orientation in a given loading configuration, but friction coefficients in extension were systematically lower than in compression for both rock types and could be reconciled by a variant on the Mogi (1967) failure criterion. Friction data for these and other porous sandstones accord well with the Byerlee (1977) generalization about rock friction being largely independent of rock type. For engineering and geodynamic modelling purposes, the stress-state dependent friction coefficient should be used for sandstones, but it is not known to what extent this might apply to other rock types.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Merkle, J.G.

In order to study effects of constraint on fracture toughness, it is important to select the right location within the crack-tip field for investigation. In 1950 Hill postulated that close to a circular notch tip the principal stress directions would be radial and circumferential, so that the plastic slip lines (maximum shear stress trajectories) would be logarithmic spirals. The resulting equation for stress normal to the notch symmetry plane, neglecting strain hardening, was identical to that for the circumferential stress near the bore of an ideally plastic thick-walled hollow cylinder under external radial tension, because the relevant geometries are identical.more » In 1969, Rice and Johnson developed a near crack-tip, plane strain, large-strain rigid-plastic analysis considering strain hardening and assuming an infinitely sharp initial crack tip. Shortly afterwards, Merkle, following Hill's suggestion, proposed an approximate analysis of the stresses and strains ahead of a blunted crack tip on the plane of symmetry, based on a circular blunted crack tip. The analysis amounted to a hollow cylinder analogy, including the effects of strain hardening. The original hollow cylinder analogy was based on small strain theory, and the calculated strain distributions did not agree well with the Rice and Johnson results very near the blunted crack tip. Therefore, the hollow cylinder analogy equations have been rederived, based on large strain theory, and the agreement with the Rice and Johnson results and other more recent numerical results is good. Calculations illustrate the effects of transverse strain on the principal stresses very close to a blunting crack tip and show that, theoretically, a singularity still exists at the tip of a blunting crack. 10 refs., 9 figs.« less

A Study of the Magnetoelastic Effect of Metal Textured Ni-5 at % W Tapes

NASA Astrophysics Data System (ADS)

Nikonov, A. A.

2018-01-01

In the temperature range of 50-360 K, the effect of the plane mechanical deformations on the magnetic susceptibility χac( T) of metal biaxially textured Ni-5.0 at % W tapes has been investigated. To create the state of plane stress, the temperature cycling of thin tapes cemented to thick substrates of Si, Mo, Ti, and D16T aluminum alloy has been performed. It has been shown that the main features of the magnetic susceptibility behavior can be explained by magnetoorientation transitions and the appearance of internal stresses σ( T) exceeding the yield strength of the tape material.

Tensile stress effect on epitaxial BiFeO 3 thin film grown on KTaO 3

DOE PAGES

Bae, In-Tae; Ichinose, Tomohiro; Han, Myung-Geun; ...

2018-01-17

Comprehensive crystal structural study is performed for BiFeO 3 (BFO) film grown on KTaO 3 (KTO) substrate using transmission electron microscopy (TEM) and x-ray diffraction (XRD). Nano beam electron diffraction (NBED) combined with structure factor calculation and high resolution TEM images clearly reveal that the crystal structure within BFO thin film is rhombohedral BFO, i.e., bulk BFO phase. Epitaxial relationship found by NBED indicates the BFO film grows in a manner that minimizes lattice mismatch with KTO. It further suggests BFO film is under slight biaxial tensile stress (~0.35%) along in-plane direction. XRD reveals BFO lattice is under compressive stressmore » (~1.6%), along out-of-plane direction as a result of the biaxial tensile stress applied along in-plane direction. This leads to Poisson’s ratio of ~0.68. In addition, we demonstrate (1) why hexagonal notation rather than pseudocubic one is required for accurate BFO phase evaluation and (2) a new XRD method that shows how rhombohedral BFO can readily be identified among other phases by measuring a rhombohedral specific Bragg’s peak.« less

Characterization of a defective PbWO4 crystal cut along the a-c crystallographic plane: structural assessment and a novel photoelastic stress analysis

NASA Astrophysics Data System (ADS)

Montalto, L.; Natali, P. P.; Daví, F.; Mengucci., P.; Paone, N.; Rinaldi, D.

2017-12-01

Among scintillators, the PWO is one of the most widely used, for instance in CMS calorimeter at CERN and PANDA project. Crystallographic structure and chemical composition as well as residual stress condition, are indicators of homogeneity and good quality of the crystal. In this paper, structural characterization of a defective PbWO4 (PWO) crystal has been performed by X-ray Diffraction (XRD), Energy Dispersive Spectroscopy (EDS) and Photoelasticity in the unusual (a, c) crystallographic plane. XRD and EDS analysis have been used to investigate crystallographic orientation and chemical composition, while stress distribution, which indicates macroscopic inhomogeneities and defects, has been obtained by photoelastic approaches, in Conoscopic and Sphenoscopic configuration. Since the sample is cut along the (a, c) crystallographic plane, a new method is proposed for the interpretation of the fringe pattern. The structural analysis has detected odds from the nominal lattice dimension, which can be attributed to the strong presence of Pb and W. A strong inhomogeneity over the crystal sample has been revealed by the photoelastic inspection. The results give reliability to the proposed procedure which is exploitable in crystals with other structures.

Tensile stress effect on epitaxial BiFeO 3 thin film grown on KTaO 3

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bae, In-Tae; Ichinose, Tomohiro; Han, Myung-Geun

Comprehensive crystal structural study is performed for BiFeO 3 (BFO) film grown on KTaO 3 (KTO) substrate using transmission electron microscopy (TEM) and x-ray diffraction (XRD). Nano beam electron diffraction (NBED) combined with structure factor calculation and high resolution TEM images clearly reveal that the crystal structure within BFO thin film is rhombohedral BFO, i.e., bulk BFO phase. Epitaxial relationship found by NBED indicates the BFO film grows in a manner that minimizes lattice mismatch with KTO. It further suggests BFO film is under slight biaxial tensile stress (~0.35%) along in-plane direction. XRD reveals BFO lattice is under compressive stressmore » (~1.6%), along out-of-plane direction as a result of the biaxial tensile stress applied along in-plane direction. This leads to Poisson’s ratio of ~0.68. In addition, we demonstrate (1) why hexagonal notation rather than pseudocubic one is required for accurate BFO phase evaluation and (2) a new XRD method that shows how rhombohedral BFO can readily be identified among other phases by measuring a rhombohedral specific Bragg’s peak.« less

The effect of thickness on fatigue crack propagation in 7475-T731 aluminum alloy sheet

NASA Technical Reports Server (NTRS)

Daiuto, R. A.; Hillberry, B. M.

1984-01-01

Tests were conducted on three thicknesses of 7475-T731 aluminum alloy sheet to investigate the effect of thickness on fatigue crack propagation under constant amplitude loading conditions and on retardation following a single peak overload. Constant amplitude loading tests were performed at stress ratios of 0.05 and 0.75 to obtain data for conditions with crack closure and without crack closure, respectively. At both stress ratios a thickness effect was clearly evident, with thicker specimens exhibiting higher growth rates in the transition from plane strain to plane stress region. The effect of thickness for a stress ratio of 0.05 corresponded well with the fracturing mode transitions observed on the specimens. A model based on the strain energy release rate which accounted for the fracture mode transition was found to correlate the thickness effects well. The specimens tested at the stress ratio of 0.75 did not make the transition from tensile mode to shear mode, indicating that another mechanism besides crack closure or fracture mode transition was active.

Comparison of mechanical and microstructural properties of conventional and severe plastic deformation processes

NASA Astrophysics Data System (ADS)

Szombathelyi, V.; Krallics, Gy

2014-08-01

The effect of the deformation processes on yield stress, Vickers microhardness and dislocation density were investigated using commercial purity (A1050) and alloyed aluminum (Al 6082). For the evolution of the dislocation density X-ray line profile analysis was used. In the large plastic strain range the variation of mechanical and microstructure evolution of A1050 and of Al 6082 processed by equal channel angular pressing are investigated using route BC and route C. In the plastic strain range up to 3 plane strain compression test was used to evaluate mechanical properties. The hardness and the yield stress showed a sharp increase after the first pass. In the case of A1050 it was found that the two examined routes has not resulted difference in the flow stress. In the case of Al 6082 the effect of the routes on the yield stress is significant. The present results showed that in the comparable plastic strain range higher yield stress values can be achieved by plane strain compression test than by ECAP.

Neutron Bragg-edge-imaging for strain mapping under in situ tensile loading

NASA Astrophysics Data System (ADS)

Woracek, R.; Penumadu, D.; Kardjilov, N.; Hilger, A.; Strobl, M.; Wimpory, R. C.; Manke, I.; Banhart, J.

2011-05-01

Wavelength selective neutron radiography at a cold neutron reactor source was used to measure strain and determine (residual) stresses in a steel sample under plane stress conditions. We present a new technique that uses an energy-resolved neutron imaging system based on a double crystal monochromator and is equipped with a specially developed (in situ) biaxial load frame to perform Bragg edge based transmission imaging. The neutron imaging technique provides a viewing area of 7 cm by 7 cm with a spatial resolution on the order of ˜ 100 μm. The stress-induced shifts of the Bragg edge corresponding to the (110) lattice plane were resolved spatially for a ferritic steel alloy A36 (ASTM international) sample. Furthermore it is demonstrated that results agree with comparative data obtained using neutron diffraction and resistance based strain-gauge rosettes.

Perspective - Systematic study of Reynolds stress closure models in the computations of plane channel flows

NASA Technical Reports Server (NTRS)

Demuren, A. O.; Sarkar, S.

1993-01-01

The roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models are investigated. Three turbulent diffusion and five pressure-strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the directional numerical simulation are used to further clarify this behavior of the models.

Systematic study of Reynolds stress closure models in the computations of plane channel flows

NASA Technical Reports Server (NTRS)

Demuren, A. O.; Sarkar, S.

1992-01-01

The roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models are investigated. Three turbulent diffusion and five pressure-strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the directional numerical simulation are used to further clarify this behavior of the models.

Synchronized oscillations and acoustic fluidization in confined granular materials

NASA Astrophysics Data System (ADS)

Giacco, F.; de Arcangelis, L.; Ciamarra, M. Pica; Lippiello, E.

2018-01-01

According to the acoustic fluidization hypothesis, elastic waves at a characteristic frequency form inside seismic faults even in the absence of an external perturbation. These waves are able to generate a normal stress which contrasts the confining pressure and promotes failure. Here, we study the mechanisms responsible for this wave activation via numerical simulations of a granular fault model. We observe the particles belonging to the percolating backbone, which sustains the stress, to perform synchronized oscillations over ellipticlike trajectories in the fault plane. These oscillations occur at the characteristic frequency of acoustic fluidization. As the applied shear stress increases, these oscillations become perpendicular to the fault plane just before the system fails, opposing the confining pressure, consistently with the acoustic fluidization scenario. The same change of orientation can be induced by external perturbations at the acoustic fluidization frequency.

Approximate Analysis for Interlaminar Stresses in Composite Structures with Thickness Discontinuities

NASA Technical Reports Server (NTRS)

Rose, Cheryl A.; Starnes, James H., Jr.

1996-01-01

An efficient, approximate analysis for calculating complete three-dimensional stress fields near regions of geometric discontinuities in laminated composite structures is presented. An approximate three-dimensional local analysis is used to determine the detailed local response due to far-field stresses obtained from a global two-dimensional analysis. The stress results from the global analysis are used as traction boundary conditions for the local analysis. A generalized plane deformation assumption is made in the local analysis to reduce the solution domain to two dimensions. This assumption allows out-of-plane deformation to occur. The local analysis is based on the principle of minimum complementary energy and uses statically admissible stress functions that have an assumed through-the-thickness distribution. Examples are presented to illustrate the accuracy and computational efficiency of the local analysis. Comparisons of the results of the present local analysis with the corresponding results obtained from a finite element analysis and from an elasticity solution are presented. These results indicate that the present local analysis predicts the stress field accurately. Computer execution-times are also presented. The demonstrated accuracy and computational efficiency of the analysis make it well suited for parametric and design studies.

A method for mapping apparent stress and energy radiation applied to the 1994 Northridge earthquake fault zone

USGS Publications Warehouse

McGarr, A.; Fletcher, Joe B.

2000-01-01

Using the Northridge earthquake as an example, we demonstrate a new technique able to resolve apparent stress within subfaults of a larger fault plane. From the model of Wald et al. (1996), we estimated apparent stress for each subfault using τa = (G/β)/2 where G is the modulus of rigidity, β is the shear wave speed, and is the average slip rate. The image of apparent stress mapped over the Northridge fault plane supports the idea that the stresses causing fault slip are inhomogeneous, but limited by the strength of the crust. Indeed, over the depth range 5 to 17 km, maximum values of apparent stress for a given depth interval agree with τa(max)=0.06S(z), where S is the laboratory estimate of crustal strength as a function of depth z. The seismic energy from each subfault was estimated from the product τaDA, where A is subfault area and D its slip. Over the fault zone, we found that the radiated energy is quite variable spatially, with more than 50% of the total coming from just 15% of the subfaults.

Three dimensional stress vector sensor array and method therefor

DOEpatents

Pfeifer, Kent Bryant; Rudnick, Thomas Jeffery

2005-07-05

A sensor array is configured based upon capacitive sensor techniques to measure stresses at various positions in a sheet simultaneously and allow a stress map to be obtained in near real-time. The device consists of single capacitive elements applied in a one or two dimensional array to measure the distribution of stresses across a mat surface in real-time as a function of position for manufacturing and test applications. In-plane and normal stresses in rolling bodies such as tires may thus be monitored.

Ferroelectric and structural properties of stress-constrained and stress-relaxed polycrystalline BiFeO3 thin films

NASA Astrophysics Data System (ADS)

Nakashima, Seiji; Ricinschi, Dan; Park, Jung Min; Kanashima, Takeshi; Fujisawa, Hironori; Shimizu, Masaru; Okuyama, Masanori

2009-03-01

The stress influence of the structural and ferroelectric properties of polycrystalline BiFeO3 (BFO) thin films has been investigated using a membrane substrate for relaxing stress. Reciprocal space mapping (RSM) measurement has been performed to confirm the stress dependence of the crystal structure of polycrystalline BFO thin films on the Pt (200 nm)/TiO2 (50 nm)/SiO2 (600 nm)/Si (625 μm) substrate (stress-constrained BFO film) and the Pt (200 nm)/TiO2 (50 nm)/SiO2 (600 nm)/Si (15 μm) membrane substrate (stress-relaxed BFO film). The BFO thin films prepared by pulsed laser deposition were polycrystalline and mainly exhibit a texture with (001) and (110) plane orientations. From the RSM results, the crystal structure of the (001)-oriented domain changes from Pm monoclinic to Cm monoclinic or to R3c rhombohedral due to stress relaxation. Moreover, at room temperature as well as at 150 K, remanent polarization (Pr) increases and double coercive field (2Ec) decreases (in the latter case from 88 to 94 μC/cm2 and from 532 to 457 kV/cm, respectively) due to relaxing stress. The enhancement of ferroelectricity is attributed to the crystal structural deformation and/or transition and angle change between the polarization direction and film plane.

Investigation of flaw geometry and loading effects on plane strain fracture in metallic structures

NASA Technical Reports Server (NTRS)

Hall, L. R.; Finger, R. W.

1971-01-01

The effects on fracture and flaw growth of weld-induced residual stresses, combined bending and tension stresses, and stress fields adjacent to circular holes in 2219-T87 aluminum and 5AI-2.5Sn(ELI) titanium alloys were evaluated. Static fracture tests were conducted in liquid nitrogen; fatigue tests were performed in room air, liquid nitrogen, and liquid hydrogen. Evaluation of results was based on linear elastic fracture mechanics concepts and was directed to improving existing methods of estimating minimum fracture strength and fatigue lives for pressurized structure in spacecraft and booster systems. Effects of specimen design in plane-strain fracture toughness testing were investigated. Four different specimen types were tested in room air, liquid nitrogen and liquid hydrogen environments using the aluminum and titanium alloys. Interferometry and holograph were used to measure crack-opening displacements in surface-flawed plexiglass test specimens. Comparisons were made between stress intensities calculated using displacement measurements, and approximate analytical solutions.

Wetting of a partially immersed compliant rod

NASA Astrophysics Data System (ADS)

Hui, Chung-Yuen; Jagota, Anand

2016-11-01

The force on a solid rod partially immersed in a liquid is commonly used to determine the liquid-vapor surface tension by equating the measured force required to remove the rod from the liquid to the vertical component of the liquid-vapor surface tension. Here, we study how this process is affected when the rod is compliant. For equilibrium, we enforce force and configurational energy balance, including contributions from elastic energy. We show that, in general, the contact angle does not equal that given by Young's equation. If surface stresses are tensile, the strain in the immersed part of the rod is found to be compressive and to depend only on the solid-liquid surface stress. The strain in the dry part of the rod can be either tensile or compressive, depending on a combination of parameters that we identify. We also provide results for compliant plates partially immersed in a liquid under plane strain and plane stress. Our results can be used to extract solid surface stresses from such experiments.

Shape optimization of shear fracture specimen considering plastic anisotropy

NASA Astrophysics Data System (ADS)

Zhang, S.; Yoon, J. W.; Lee, S.; Lou, Y.

2017-10-01

It is important to fabricate fracture specimens with minimum variation of triaxiality in order to characterize the failure behaviors experimentally. Fracture in ductile materials is usually calibrated by uniaxial tensile, shear and plane strain tests. However, it is often observed that triaxiality for shear specimen changes severely during shear fracture test. The nonlinearity of triaxiality is most critical for shear test. In this study, a simple in-plane shear specimen is optimized by minimizing the variation of stress triaxiality in the shear zone. In the optimization, the Hill48 and Yld2000-2d criteria are employed to model the anisotropic plastic deformation of an aluminum alloy of 6k21. The evolution of the stress triaxiality of the optimized shear specimen is compared with that of the initial design of the shear specimen. The comparison reveals that the stress triaxiality changes much less for the optimized shear specimen than the evolution of the stress triaxiality with the original design of the shear specimen.

Study on observation planning of LAMOST focal plane positioning system and its simulation

NASA Astrophysics Data System (ADS)

Zhai, Chao; Jin, Yi; Peng, Xiaobo; Xing, Xiaozheng

2006-06-01

Fiber Positioning System of LAMOST focal plane based on subarea thinking, adopts a parallel controllable positioning plan, the structure is designed as a round area and overlapped each other in order to eliminate the un-observation region. But it also makes the observation efficiency of the system become an important problem. In this paper According to the system, the model of LAMOST focal plane Observation Planning including 4000 fiber positioning units is built, Stars are allocated using netflow algorithm and mechanical collisions are diminished through the retreat algorithm, then the simulation of the system's observation efficiency is carried out. The problem of observation efficiency of LAMOST focal plane is analysed systemic and all-sided from the aspect of overlapped region, fiber positioning units, observation radius, collisions and so on. The observation efficiency of the system in theory is describes and the simulation indicates that the system's observation efficiency is acceptable. The analyses play an indicative role on the design of the LAMOST focal plane structure.

On the solution of two-point linear differential eigenvalue problems. [numerical technique with application to Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Antar, B. N.

1976-01-01

A numerical technique is presented for locating the eigenvalues of two point linear differential eigenvalue problems. The technique is designed to search for complex eigenvalues belonging to complex operators. With this method, any domain of the complex eigenvalue plane could be scanned and the eigenvalues within it, if any, located. For an application of the method, the eigenvalues of the Orr-Sommerfeld equation of the plane Poiseuille flow are determined within a specified portion of the c-plane. The eigenvalues for alpha = 1 and R = 10,000 are tabulated and compared for accuracy with existing solutions.

Distribution of stress on TMJ disc induced by use of chincup therapy: assessment by the finite element method.

PubMed

Calçada, Flávio Siqueira; Guimarães, Antônio Sérgio; Teixeira, Marcelo Lucchesi; Takamatsu, Flávio Atsushi

2017-01-01

To assess the distribution of stress produced on TMJ disc by chincup therapy, by means of the finite element method. a simplified three-dimensional TMJ disc model was developed by using Rhinoceros 3D software, and exported to ANSYS software. A 4.9N load was applied on the inferior surface of the model at inclinations of 30, 40, and 50 degrees to the mandibular plane (GoMe). ANSYS was used to analyze stress distribution on the TMJ disc for the different angulations, by means of finite element method. The results showed that the tensile and compressive stresses concentrations were higher on the inferior surface of the model. More presence of tensile stress was found in the middle-anterior region of the model and its location was not altered in the three directions of load application. There was more presence of compressive stress in the middle and mid-posterior regions, but when a 50o inclined load was applied, concentration in the middle region was prevalent. Tensile and compressive stresses intensities progressively diminished as the load was more vertically applied. stress induced by the chincup therapy is mainly located on the inferior surface of the model. Loads at greater angles to the mandibular plane produced distribution of stresses with lower intensity and a concentration of compressive stresses in the middle region. The simplified three-dimensional model proved useful for assessing the distribution of stresses on the TMJ disc induced by the chincup therapy.

Plastic deformation of silicon dendritic web ribbons during the growth

NASA Technical Reports Server (NTRS)

Cheng, L. J.; Dumas, K. A.; Su, B. M.; Leipold, M. H.

1984-01-01

The distribution of slip dislocations in silicon dendritic web ribbons due to plastic deformation during the cooling phase of the growth was studied. The results show the existence of two distinguishable stress regions across the ribbon formed during the plastic deformation stage, namely, shear stress at the ribbon edges and tensile stress at the middle. In addition, slip dislocations caused by shear stress near the edges appear to originate at the twin plane.

Lattice strain effects on the optical properties of MoS2 nanosheets

PubMed Central

Yang, Lei; Cui, Xudong; Zhang, Jingyu; Wang, Kan; Shen, Meng; Zeng, Shuangshuang; Dayeh, Shadi A.; Feng, Liang; Xiang, Bin

2014-01-01

“Strain engineering” in functional materials has been widely explored to tailor the physical properties of electronic materials and improve their electrical and/or optical properties. Here, we exploit both in plane and out of plane uniaxial tensile strains in MoS2 to modulate its band gap and engineer its optical properties. We utilize X-ray diffraction and cross-sectional transmission electron microscopy to quantify the strains in the as-synthesized MoS2 nanosheets and apply measured shifts of Raman-active modes to confirm lattice strain modification of both the out-of-plane and in-plane phonon vibrations of the MoS2 nanosheets. The induced band gap evolution due to in-plane and out-of-plane tensile stresses is validated by photoluminescence (PL) measurements, promising a potential route for unprecedented manipulation of the physical, electrical and optical properties of MoS2. PMID:25008782

Role of stresses in annealing of ion-implantation damage in Si

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seshan, K.; EerNisse, E.P.

Recent results showing a crystallographic orientation dependence of growth kinetics, secondary defects, and stress relief in annealing of ion-implanted Si are shown to be self-consistent if interpreted in terms of the influence of stresses upon annealing processes. The stress influence proposed is microplastic shear which is induced in (112) directions on (111) planes inclined to the implant surface by the biaxial stress created in the implant region by ion-implantation damage. The shear stresses are shown to be dependent on crystallographic orientation in a manner consistent with the model.

Fault growth and acoustic emissions in confined granite

USGS Publications Warehouse

Lockner, David A.; Byerlee, James D.

1992-01-01

The failure process in a brittle granite was studied by using acoustic emission techniques to obtain three dimensional locations of the microfracturing events. During a creep experiment the nucleation of faulting coincided with the onset of tertiary creep, but the development of the fault could not be followed because the failure occurred catastrophically. A technique has been developed that enables the failure process to be stabilized by controlling the axial stress to maintain a constant acoustic emission rate. As a result the post-failure stress-strain curve has been followed quasi-statically, extending to hours the fault growth process that normally would occur violently in a fraction of a second. The results from the rate-controlled experiments show that the fault plane nucleated at a point on the sample surface after the stress-strain curve reached its peak. Before nucleation, the microcrack growth was distributed throughout the sample. The fault plane then grew outward from the nucleation site and was accompanied by a gradual drop in stress. Acoustic emission locations showed that the fault propagated as a fracture front (process zone) with dimensions of 1 to 3 cm. As the fracture front passed by a given fixed point on the fault plane, the subsequent acoustic emission would drop. When growth was allowed to progress until the fault bisected the sample, the stress dropped to the frictional strength. These observations are in accord with the behavior predicted by Rudnicki and Rice's bifurcation analysis but conflict with experiments used to infer that shear localization would occur in brittle rock while the material is still hardening.

Transient reaction of an elastic half-plane on a source of a concentrated boundary disturbance

NASA Astrophysics Data System (ADS)

Okonechnikov, A. S.; Tarlakovski, D. V.; Ul'yashina, A. N.; Fedotenkov, G. V.

2016-11-01

One of the key problems in studying the non-stationary processes of solid mechanics is obtaining of influence functions. These functions serve as solutions for the problems of effect of sudden concentrated loads on a body with linear elastic properties. Knowledge of the influence functions allows us to obtain the solutions for the problems with non-mixed boundary and initial conditions in the form of quadrature formulae with the help of superposition principle, as well as get the integral governing equations for the problems with mixed boundary and initial conditions. This paper offers explicit derivations for all nonstationary surface influence functions of an elastic half-plane in a plane strain condition. It is achieved with the help of combined inverse transform of a Fourier-Laplace integral transformation. The external disturbance is both dynamic and kinematic. The derived functions in xτ-domain are studied to find and describe singularities and are supplemented with graphs.

An extended 3D discrete-continuous model and its application on single- and bi-crystal micropillars

NASA Astrophysics Data System (ADS)

Huang, Minsheng; Liang, Shuang; Li, Zhenhuan

2017-04-01

A 3D discrete-continuous model (3D DCM), which couples the 3D discrete dislocation dynamics (3D DDD) and finite element method (FEM), is extended in this study. New schemes for two key information transfers between DDD and FEM, i.e. plastic-strain distribution from DDD to FEM and stress transfer from FEM to DDD, are suggested. The plastic strain induced by moving dislocation segments is distributed to an elementary spheroid (ellipsoid or sphere) via a specific new distribution function. The influence of various interfaces (such as free surfaces and grain boundaries (GBs)) on the plastic-strain distribution is specially considered. By these treatments, the deformation fields can be solved accurately even for dislocations on slip planes severely inclined to the FE mesh, with no spurious stress concentration points produced. In addition, a stress correction by singular and non-singular theoretical solutions within a cut-off sphere is introduced to calculate the stress on the dislocations accurately. By these schemes, the present DCM becomes less sensitive to the FE mesh and more numerically efficient, which can also consider the interaction between neighboring dislocations appropriately even though they reside in the same FE mesh. Furthermore, the present DCM has been employed to model the compression of single-crystal and bi-crystal micropillars with rigid and dislocation-absorbed GBs. The influence of internal GB on the jerky stress-strain response and deformation mode is studied in detail to shed more light on these important micro-plastic problems.

Technology for pressure-instrumented thin airfoil models, phase 1

NASA Technical Reports Server (NTRS)

Wigley, D. A.

1985-01-01

A network of channels was chemically milled into one surface of a pair of matched plates having bond planes which were neither planar or profiled to match the contour of the trailing edge of a supercritical airfoil for testing in cryogenic wind tunnels. Vacuum brazing bonded the plates together to create a network of pressure passages without blockages or cross leaks. The greatest success was achieved with the smaller samples and planar bonding surfaces. In larger samples, problems were encountered due to warpage created by the relief of residual stresses. Successful bonds were formed by brazing A286, Nitronic 40 and 300 series stainless steels at 1065 C using AMS 4777B brazing alloy, but excessive grain growth occurred in samples of 200 grade 18 nickel maraging steels. Good bonds were obtained with maraging steel using a 47 percent Nickel-47 percent Palladium-6 percent Silicon alloy and brazing at 927 C. Electro-Discharge-Machining was an effective method of cutting profiled bond planes and airfoil contours. Orifices of good definition were obtained when the EDM wire cut passed through predrilled holes. Possible configurations for joints between small segments and the larger main wing were also studied.

A proposed standard round compact specimen for plane strain fracture toughness testing

NASA Technical Reports Server (NTRS)

Underwood, J. H.; Newman, J. C., Jr.; Seeley, R. R.

1980-01-01

A round, disk-shaped specimen is proposed as a standard test specimen for addition to ASTM Test for Plane-Strain Fracture Toughness of Metallic Materials (E 399-78A). The specimen is diametrically cracked, and loaded in the same way as the existing standard compact specimen. Tests and analyses were performed to verify that the proposed round compact specimen and associated stress intensity factor K solution are appropriate for a standard plane strain fracture toughness test. The use of the round compact specimen for other fracture tests is described.

Sets that Contain Their Circle Centers

ERIC Educational Resources Information Center

Martin, Greg

2008-01-01

Say that a subset S of the plane is a "circle-center set" if S is not a subset of a line, and whenever we choose three non-collinear points from S, the center of the circle through those three points is also an element of S. A problem appearing on the Macalester College Problem of the Week website stated that a finite set of points in the plane,…

Analysis of borehole expansion and gallery tests in anisotropic rock masses

USGS Publications Warehouse

Amadei, B.; Savage, W.Z.

1991-01-01

Closed-form solutions are used to show how rock anisotropy affects the variation of the modulus of deformation around the walls of a hole in which expansion tests are conducted. These tests include dilatometer and NX-jack tests in boreholes and gallery tests in tunnels. The effects of rock anisotropy on the modulus of deformation are shown for transversely isotropic and regularly jointed rock masses with planes of transverse isotropy or joint planes parallel or normal to the hole longitudinal axis for plane strain or plane stress condition. The closed-form solutions can also be used when determining the elastic properties of anisotropic rock masses (intact or regularly jointed) in situ. ?? 1991.

Role of basal stress hormones and amygdala dimensions in stress coping strategies of male rhesus monkeys in response to a hazard-reward conflict.

PubMed

Tekieh, Elaheh; Riahi, Esmail; Kazemi, Masoomeh; Sahraei, Hedayat; Tavakoli, Hassan; Aliyary, Hamed; Hajinasrollah, Mostafa; Salehi, Maryam; Meftahi, Gholamhossein; Saberi, Mehdi

2017-08-01

In the present study the effect of stress on monkeys that had learned to retrieve food from a five-chamber receptacle, as well as the relationship between their behavior and the serum cortisol and epinephrine levels and relative size of the amygdala was evaluated. Six male rhesus monkeys were individually given access to the food reward orderly. They could easily retrieve the rewards from all chambers except for the chamber 4, which a brief, mild electric shock (3 V) was delivered to them upon touching the chamber's interior. The coping behaviors were video-recorded and analyzed offline. Baseline serum cortisol and epinephrine levels were measured before the experiments using monkey enzyme-linked immunosorbent assay kit. One week after the behavioral experiment, the monkeys' brains were scanned using magnetic resonance imaging under general anesthesia. The cross-sectional area of the left amygdala in sagittal plane relative to the area of the whole brain in the same slice was evaluated by the planimetric method using ImageJ software. Exposure to the distressing condition caused different behavioral responses. Monkeys with higher baseline levels of serum cortisol and epinephrine and larger amygdala behaved more violently in the face of stress, indicating adopting emotion-focused stress-coping strategies. Conversely, those with low plasma epinephrine, moderate cortisol, and smaller amygdala showed perseverative behavior, indicating a problem-focused coping style. In dealing with the same stress, different responses might be observed from nonhuman primates according to their cortisol and epinephrine levels as well as their amygdala dimensions.

Failure in lithium-ion batteries under transverse indentation loading

NASA Astrophysics Data System (ADS)

Chung, Seung Hyun; Tancogne-Dejean, Thomas; Zhu, Juner; Luo, Hailing; Wierzbicki, Tomasz

2018-06-01

Deformation and failure of constrained cells and modules in the battery pack under transverse loading is one of the most common conditions in batteries subjected to mechanical impacts. A combined experimental, numerical and analytical approach was undertaken to reveal the underlying mechanism and develop a new cell failure model. When large format pouch cells were subjected to local indentation all the way to failure, the post-mortem examination of the failure zones beneath the punches indicates a consistent slant fracture surface angle to the battery plane. This type of behavior can be described by the critical fracture plane theory in which fracture is caused by the shear stress modified by the normal stress. The Mohr-Coulomb fracture criterion is then postulated and it is shown how the two material constants can be determined from just one indentation test. The orientation of the fracture plane is invariant with respect to the type of loading and can be considered as a property of the cell stack. In addition, closed-form solutions are derived for the load-displacement relation for both plane-strain and axisymmetric cases. The results are in good agreement with the numerical simulation of the homogenized model and experimentally measured responses.

Discrimination between induced, triggered, and natural earthquakes close to hydrocarbon reservoirs: A probabilistic approach based on the modeling of depletion-induced stress changes and seismological source parameters

NASA Astrophysics Data System (ADS)

Dahm, Torsten; Cesca, Simone; Hainzl, Sebastian; Braun, Thomas; Krüger, Frank

2015-04-01

Earthquakes occurring close to hydrocarbon fields under production are often under critical view of being induced or triggered. However, clear and testable rules to discriminate the different events have rarely been developed and tested. The unresolved scientific problem may lead to lengthy public disputes with unpredictable impact on the local acceptance of the exploitation and field operations. We propose a quantitative approach to discriminate induced, triggered, and natural earthquakes, which is based on testable input parameters. Maxima of occurrence probabilities are compared for the cases under question, and a single probability of being triggered or induced is reported. The uncertainties of earthquake location and other input parameters are considered in terms of the integration over probability density functions. The probability that events have been human triggered/induced is derived from the modeling of Coulomb stress changes and a rate and state-dependent seismicity model. In our case a 3-D boundary element method has been adapted for the nuclei of strain approach to estimate the stress changes outside the reservoir, which are related to pore pressure changes in the field formation. The predicted rate of natural earthquakes is either derived from the background seismicity or, in case of rare events, from an estimate of the tectonic stress rate. Instrumentally derived seismological information on the event location, source mechanism, and the size of the rupture plane is of advantage for the method. If the rupture plane has been estimated, the discrimination between induced or only triggered events is theoretically possible if probability functions are convolved with a rupture fault filter. We apply the approach to three recent main shock events: (1) the Mw 4.3 Ekofisk 2001, North Sea, earthquake close to the Ekofisk oil field; (2) the Mw 4.4 Rotenburg 2004, Northern Germany, earthquake in the vicinity of the Söhlingen gas field; and (3) the Mw 6.1 Emilia 2012, Northern Italy, earthquake in the vicinity of a hydrocarbon reservoir. The three test cases cover the complete range of possible causes: clearly "human induced," "not even human triggered," and a third case in between both extremes.

Slab Geometry and Stress State of the Southwestern Colombia Subduction Zone

NASA Astrophysics Data System (ADS)

Chang, Ying

A high rate of intermediate-depth earthquakes is concentrates in the Cauca cluster (3.5°N-5.5°N) and isolated from nearby seismicity in the southwestern Colombia subduction zone. Previously-studied nests of intermediate-depth earthquakes show that a high seismicity rate is often associated with a slab tear, detachment, or contortion. The cause of the less-studied Cauca cluster is unknown. To investigate the cause, we image the slab geometry using precise relative locations of intermediate-depth earthquakes. We use the earthquake catalog produced and seismic waveforms recorded by the Colombian National Seismic Network from January 2010 to March 2014. We calculate the focal mechanisms to examine whether the earthquakes reactivate pre-existing faults or form new fractures. The focal mechanisms are inverted for the intraslab stress field to check the stress guide hypothesis and to evaluate the stress orientations with regard to the change in the slab geometry. The earthquake relocations indicate that the Cauca segment has a continuous 20 km thick seismic zone and increases in dip angle from north to south. Two 40-km-tall fingers of earthquakes extend out of the slab and into the mantle wedge. Different from the previously-studied nests, the Cauca cluster does not correspond to slab contortions or tearing. The cluster may be associated with a high amount of dehydrated fluid. The determined focal mechanisms of 69 earthquakes have various types and variably-oriented nodal planes, corresponding to the reactivation of pre-existing faults and the formation of new fractures. The results of stress inversion show that the extensional axis in the northern Cauca segment is in the plane of the slab and 25° from the downdip direction, and the southern part has along-strike extension. The compression is subnormal to the plane of the slab. The stress field supports the stress guide hypothesis and shows a consistent rotation with increase in slab dip angle.

Stress wave velocity patterns in the longitudinal-radial plane of trees for defect diagnosis

Treesearch

Guanghui Li; Xiang Weng; Xiaocheng Du; Xiping Wang; Hailin Feng

2016-01-01

Acoustic tomography for urban tree inspection typically uses stress wave data to reconstruct tomographic images for the trunk cross section using interpolation algorithm. This traditional technique does not take into account the stress wave velocity patterns along tree height. In this study, we proposed an analytical model for the wave velocity in the longitudinal–...

Serial Back-Plane Technologies in Advanced Avionics Architectures

NASA Technical Reports Server (NTRS)

Varnavas, Kosta

2005-01-01

Current back plane technologies such as VME, and current personal computer back planes such as PCI, are shared bus systems that can exhibit nondeterministic latencies. This means a card can take control of the bus and use resources indefinitely affecting the ability of other cards in the back plane to acquire the bus. This provides a real hit on the reliability of the system. Additionally, these parallel busses only have bandwidths in the 100s of megahertz range and EMI and noise effects get worse the higher the bandwidth goes. To provide scalable, fault-tolerant, advanced computing systems, more applicable to today s connected computing environment and to better meet the needs of future requirements for advanced space instruments and vehicles, serial back-plane technologies should be implemented in advanced avionics architectures. Serial backplane technologies eliminate the problem of one card getting the bus and never relinquishing it, or one minor problem on the backplane bringing the whole system down. Being serial instead of parallel improves the reliability by reducing many of the signal integrity issues associated with parallel back planes and thus significantly improves reliability. The increased speeds associated with a serial backplane are an added bonus.

Correlation of 0.67um scatter with local stress in Ge impacted with the modified Cambridge liquid jet device

NASA Astrophysics Data System (ADS)

Wilson, Michael; Price, D.; Strohecker, Steve

1994-09-01

Germanium witness samples were impacted with the NAWCADWAR modified Cambridge liquid jet device introducing varying levels of damage about the center of each sample. Surface damage statistics were collected, scatter measurements were made at 0.67 micrometers and the samples were failed in tension using a bi-axial flexure test setup. The level and character of the damage was correlated with the reflected scatter measurements as a function of local stress and flaw size distribution. Bi-axial flexure data was analyzed to predict fracture stress and the probability of failure of the germanium samples. The mechanical data were then correlated with the scatter data in order to correlate the BRDF with the material failure. The BRDF measurements were taken in several different orientations in order to study the differences in scatter character for the in-plane and out-of-plane conditions.

Internal stresses at the crystalline scale in textured ZrO2 films before lateral cracking

NASA Astrophysics Data System (ADS)

Berdin, Clotilde; Pascal, Serge; Tang, Yan

2015-05-01

Zirconium oxide layers are submitted to internal stresses that play a role in damage of the layer. Lateral cracking is often observed during Zr alloys oxidation. In this paper, we investigated the influence of the microstresses at the crystalline scale on the lateral cracking within a growing oxide on a plane substrate. A parametric study was carried out taking into account the crystallographic texture of the oxide and the presence of a tetragonal zirconia at the metal-oxide interface. Macroscopic computations and polycrystalline aggregate computations were performed. The result indicating the (1 0 6 bar) fiber texture as the most favorable was recovered. It was found that under macroscopic compressive stresses parallel to the plane metal-oxide interface, positive microstresses perpendicular to the interface develops. They can trigger the lateral cracking and the phenomenon is promoted by the presence of tetragonal zirconia at the metal-oxide interface.

Effect of Ply Orientation and Crack Location on SIFs in Finite Multilayers with Aligned Cracks

NASA Astrophysics Data System (ADS)

Chen, Linfeng; Pindera, Marek-Jerzy

2008-02-01

An exact elasticity solution is presented for arbitrarily laminated finite multilayers in a state of generalized plane deformation under horizontally pinned end constraints that are weakened by aligned cracks. Based on half-range Fourier series and the local/global stiffness matrix approach, the mixed boundary-value problem is reduced to Cauchy-type singular integral equations in the unknown displacement discontinuities. Solution to these equations is obtained using the approach developed by Erdogan and co-workers. Numerical results quantify the thus-far undocumented geometric and material effects on Mode I, II and III stress intensity factors in composite multilayers with interacting cracks under uniform vertical displacement. These effects include finite dimensions, crack location, material anisotropy due to a unidirectional fiber-reinforced layer/s orientation, and orientational grading.

Estimate of the dispersivity of rock crushing in the zone of demolition of mine workings by the action of an explosion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sushkov, Y.V.; Borulev, A.D.; Yakovlev, N.A.

1986-05-01

The authors consider the problems of modeling the process of collapse of extended mine workings on plane models. Their derivation has been effected on the basis of the model of the ground and criteria of its demolition. It is assumed that in order to ensure similarity of crushing, equality of the amount of fissures developed in the natural state and the model is necessary. An analysis of the dependence of the average size of a ''lump'' in the demolition zone on the magnitude of the maximum stress in the wave, carried out by the method of least squares, showed thatmore » it can be represented quite well in the form of two intersecting straight lines.« less

Propagation of elastic wave in nanoporous material with distributed cylindrical nanoholes

NASA Astrophysics Data System (ADS)

Qiang, FangWei; Wei, PeiJun; Liu, XiQiang

2013-08-01

The effective propagation constants of plane longitudinal and shear waves in nanoporous material with random distributed parallel cylindrical nanoholes are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is used to obtain the scattering waves from the single nanohole. The multiple scattering effects are taken into consideration by summing the scattered waves from all scatterers and performing the configuration averaging of random distributed scatterers. The effective propagation constants of coherent waves along with the associated dynamic effective elastic modulus are numerically evaluated. The influences of surface stress are discussed based on the numerical results.

New views of granular mass flows

USGS Publications Warehouse

Iverson, R.M.; Vallance, J.W.

2001-01-01

Concentrated grain-fluid mixtures in rock avalanches, debris flows, and pyroclastic flows do not behave as simple materials with fixed rheologies. Instead, rheology evolves as mixture agitation, grain concentration, and fluid-pressure change during flow initiation, transit, and deposition. Throughout a flow, however, normal forces on planes parallel to the free upper surface approximately balance the weight of the superincumbent mixture, and the Coulomb friction rule describes bulk intergranular shear stresses on such planes. Pore-fluid pressure can temporarily or locally enhance mixture mobility by reducing Coulomb friction and transferring shear stress to the fluid phase. Initial conditions, boundary conditions, and grain comminution and sorting can influence pore-fluid pressures and cause variations in flow dynamics and deposits.

An Interactive Artificial Cutting Plane Method for Bicriterion Integer Programming Problems

DTIC Science & Technology

1992-08-01

AUTHOR(S) Diane Breivik Allen, 1st Lt 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER AFIT Student Attending...INTERACTIVE ARTIFICIAL CUTTING PLANE METHOD FOR BICRITERION INTEGER PROGRAMMING PROBLEMS By Diane Breivik Allen A Thesis Submitted to the Faculty of...ITfiSRA&1 DTIC TAB 0 Unannounced 0 Justirication By BY Diane Breivik Allen Distributlon/ Availability CQdes Avail and/or Dist Special Approved: DTI

C1,1 regularity for degenerate elliptic obstacle problems

NASA Astrophysics Data System (ADS)

Daskalopoulos, Panagiota; Feehan, Paul M. N.

2016-03-01

The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.

Time-resolved spectroscopic measurements of shock-wave induced decomposition in cyclotrimethylene trinitramine (RDX) crystals: anisotropic response.

PubMed

Dang, Nhan C; Dreger, Zbigniew A; Gupta, Yogendra M; Hooks, Daniel E

2010-11-04

Plate impact experiments on the (210), (100), and (111) planes were performed to examine the role of crystalline anisotropy on the shock-induced decomposition of cyclotrimethylenetrinitramine (RDX) crystals. Time-resolved emission spectroscopy was used to probe the decomposition of single crystals shocked to peak stresses ranging between 7 and 20 GPa. Emission produced by decomposition intermediates was analyzed in terms of induction time to emission, emission intensity, and the emission spectra shapes as a function of stress and time. Utilizing these features, we found that the shock-induced decomposition of RDX crystals exhibits considerable anisotropy. Crystals shocked on the (210) and (100) planes were more sensitive to decomposition than crystals shocked on the (111) plane. The possible sources of the observed anisotropy are discussed with regard to the inelastic deformation mechanisms of shocked RDX. Our results suggest that, despite the anisotropy observed for shock initiation, decomposition pathways for all three orientations are similar.

Failure Criteria for FRP Laminates in Plane Stress

NASA Technical Reports Server (NTRS)

Davila, Carlos G.; Camanho, Pedro P.

2003-01-01

A new set of six failure criteria for fiber reinforced polymer laminates is described. Derived from Dvorak's fracture mechanics analyses of cracked plies and from Puck's action plane concept, the physically-based criteria, denoted LaRC03, predict matrix and fiber failure accurately without requiring curve-fitting parameters. For matrix failure under transverse compression, the fracture plane is calculated by maximizing the Mohr-Coulomb effective stresses. A criterion for fiber kinking is obtained by calculating the fiber misalignment under load, and applying the matrix failure criterion in the coordinate frame of the misalignment. Fracture mechanics models of matrix cracks are used to develop a criterion for matrix in tension and to calculate the associated in-situ strengths. The LaRC03 criteria are applied to a few examples to predict failure load envelopes and to predict the failure mode for each region of the envelope. The analysis results are compared to the predictions using other available failure criteria and with experimental results. Predictions obtained with LaRC03 correlate well with the experimental results.

Experiments on shells under base excitation

NASA Astrophysics Data System (ADS)

Pellicano, Francesco; Barbieri, Marco; Zippo, Antonio; Strozzi, Matteo

2016-05-01

The aim of the present paper is a deep experimental investigation of the nonlinear dynamics of circular cylindrical shells. The specific problem regards the response of circular cylindrical shells subjected to base excitation. The shells are mounted on a shaking table that furnishes a vertical vibration parallel to the cylinder axis; a heavy rigid disk is mounted on the top of the shells. The base vibration induces a rigid body motion, which mainly causes huge inertia forces exerted by the top disk to the shell. In-plane stresses due to the aforementioned inertias give rise to impressively large vibration on the shell. An extremely violent dynamic phenomenon suddenly appears as the excitation frequency varies up and down close to the linear resonant frequency of the first axisymmetric mode. The dynamics are deeply investigated by varying excitation level and frequency. Moreover, in order to generalise the investigation, two different geometries are analysed. The paper furnishes a complete dynamic scenario by means of: (i) amplitude frequency diagrams, (ii) bifurcation diagrams, (iii) time histories and spectra, (iv) phase portraits and Poincaré maps. It is to be stressed that all the results presented here are experimental.

Acromioclavicular joint dislocation: a Dog Bone button fixation alone versus Dog Bone button fixation augmented with acromioclavicular repair-a finite element analysis study.

PubMed

Sumanont, Sermsak; Nopamassiri, Supachoke; Boonrod, Artit; Apiwatanakul, Punyawat; Boonrod, Arunnit; Phornphutkul, Chanakarn

2018-03-20

Suspension suture button fixation was frequently used to treat acromioclavicular joint (ACJ) dislocation. However, there were many studies reporting about complications and residual horizontal instability after fixation. Our study compared the stability of ACJ after fixation between coracoclavicular (CC) fixation alone and CC fixation combined with ACJ repair by using finite element analysis (FEA). A finite element model was created by using CT images from the normal shoulder. The model 1 was CC fixation with suture button alone, and the model 2 was CC fixation with suture button combined with ACJ repair. Three different forces (50, 100, 200 N) applied to the model in three planes; inferior, anterior and posterior direction load to the acromion. The von Mises stress of the implants and deformation at ACJs was recorded. The ACJ repair in the model 2 could reduce the peak stress on the implant after applying the loading forces to the acromion which the ACJ repair could reduce the peak stress of the FiberWire at suture button about 90% when compared to model 1. And, the ACJ repair could reduce the deformation of the ACJ after applying the loading forces to the acromion in both vertical and horizontal planes. This FEA supports that the high-grade injuries of the ACJ should be treated with CC fixation combined with ACJ repair because this technique provides excellent stability in both vertical and horizontal planes and reduces stress to the suture button.

Comparison of erythrocyte dynamics in shear flow under different stress-free configurations

NASA Astrophysics Data System (ADS)

Cordasco, Daniel; Yazdani, Alireza; Bagchi, Prosenjit

2014-04-01

An open question that has persisted for decades is whether the cytoskeleton of a red blood cell is stress-free or under a stress. This question is important in the context of theoretical modeling of cellular motion under a flowing condition where it is necessary to make an assumption about the stress-free state. Here, we present a 3D numerical study to compare the cell dynamics in a simple shear flow under two different stress-free states, a biconcave discocyte representing the resting shape of the cell, and a nearly spherical oblate shape. We find that whether the stress-free states make a significant difference or not depends on the viscosity of the suspending medium. If the viscosity is close to that of blood plasma, the two stress-free states do not show any significant difference in cell dynamics. However, when the suspending medium viscosity is well above that of the physiological range, as in many in vitro studies, the shear rate separating the tank-treading and tumbling dynamics is observed to be higher for the biconcave stress-free state than the spheroidal state. The former shows a strong shape oscillation with repeated departures from the biconcave shape, while the latter shows a nearly stable biconcave shape. It is found that the cell membrane in the biconcave stress-free state is under a compressive stress and a weaker bending force density, leading to a periodic compression of the cell. The shape oscillation then leads to a higher energy barrier against membrane tank-tread leading to an early transition to tumbling. However, if the cells are released with a large off-shear plane angle, the oscillations can be suppressed due to an azimuthal motion of the membrane along the vorticity direction leading to a redistribution of the membrane points and lowering of the energy barrier, which again results in a nearly similar behavior of the cells under the two different stress-free states. A variety of off-shear plane dynamics is observed, namely, rolling, kayaking, precession, and a new dynamics termed "hovering." For the physiological viscosity range, the shear-plane tumbling appears to be relatively less common, while the rolling is observed to be more stable.

The generalized fracture criteria based on the multi-parameter representation of the crack tip stress field

NASA Astrophysics Data System (ADS)

Stepanova, L. V.

2017-12-01

The paper is devoted to the multi-parameter asymptotic description of the stress field near the crack tip of a finite crack in an infinite isotropic elastic plane medium subject to 1) tensile stress; 2) in-plane shear; 3) mixed mode loading for a wide range of mode-mixity situations (Mode I and Mode II). The multi-parameter series expansion of stress tensor components containing higher-order terms is obtained. All the coefficients of the multiparameter series expansion of the stress field are given. The main focus is on the discussion of the influence of considering the higher-order terms of the Williams expansion. The analysis of the higher-order terms in the stress field is performed. It is shown that the larger the distance from the crack tip, the more terms it is necessary to keep in the asymptotic series expansion. Therefore, it can be concluded that several more higher-order terms of the Williams expansion should be used for the stress field description when the distance from the crack tip is not small enough. The crack propagation direction angle is calculated. Two fracture criteria, the maximum tangential stress criterion and the strain energy density criterion, are used. The multi-parameter form of the two commonly used fracture criteria is introduced and tested. Thirty and more terms of the Williams series expansion for the near-crack-tip stress field enable the angle to be calculated more precisely.

Trajectory optimization for the National Aerospace Plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1993-01-01

The objective of this second phase research is to investigate the optimal ascent trajectory for the National Aerospace Plane (NASP) from runway take-off to orbital insertion and address the unique problems associated with the hypersonic flight trajectory optimization. The trajectory optimization problem for an aerospace plane is a highly challenging problem because of the complexity involved. Previous work has been successful in obtaining sub-optimal trajectories by using energy-state approximation and time-scale decomposition techniques. But it is known that the energy-state approximation is not valid in certain portions of the trajectory. This research aims at employing full dynamics of the aerospace plane and emphasizing direct trajectory optimization methods. The major accomplishments of this research include the first-time development of an inverse dynamics approach in trajectory optimization which enables us to generate optimal trajectories for the aerospace plane efficiently and reliably, and general analytical solutions to constrained hypersonic trajectories that has wide application in trajectory optimization as well as in guidance and flight dynamics. Optimal trajectories in abort landing and ascent augmented with rocket propulsion and thrust vectoring control were also investigated. Motivated by this study, a new global trajectory optimization tool using continuous simulated annealing and a nonlinear predictive feedback guidance law have been under investigation and some promising results have been obtained, which may well lead to more significant development and application in the near future.

Use of the Contour Method to Determine Autofrettage Residual Stresses: A Proposed Experimental Procedure

DTIC Science & Technology

2013-05-01

autofrettage of a long tube: Residual hoop, radial and axial stresses, 70% overstrain, numerical, open-end Autofrettage of A723 steel including non- linear...concentrate axial stresses which are expected to range between 18% of yield in compression at the bore to 15% in tension at the OD. So the zone of the...experiments is that they were conducted on axially thin (quasi plane stress) ring specimens cut from much longer gun tubes. A recent paper [2

Flaw Growth of 6Al-4V Titanium in a Freon TF Environment

NASA Technical Reports Server (NTRS)

Tiffany, C. F.; Masters, J. N.; Bixler, W. D.

1969-01-01

The plane strain threshold stress intensity and sustained stress flaw growth rates were experimentally determined for 6AI-4V S.T.A. titanium forging and weldments in environments of Freon TF at room temperature. Sustained load tests of surface flawed specimens were conducted with the experimental approach based on linear elastic fracture mechanics. It was concluded that sustained stress flaw growth rates, in conjunction with threshold stress intensities, can be used in assessing the service life of pressure vessels.

Elastic and dielectric anisotropy in barium strontium titanate thin films on orthorhombic neodymium gallate substrates

NASA Astrophysics Data System (ADS)

Simon, William Kurt

Functional oxide thin films often focus on standard cubic substrates that impose an equal biaxial plane stress condition (sigma11 = sigma22) to the film. These internal stresses in thin films reach magnitudes not easily achieved in bulk materials and represent an important influence on the properties of thin films. Equal biaxial plane stress is a small sub-set of stress conditions. Anisotropic stress (sigma11 ≠ sigma 22) represents a wide range of influences that can be utilized to manipulate the properties of thin films. To investigate these conditions, heteroepitaxial thin films of paraelectric Ba0.6Sr0.4TiO3 (BST) were deposited on [100] and [110] oriented single crystal NdGaO 3 (NGO) substrates. Films were grown in the thickness range of 25 to 1200 nm by Pulsed Laser Deposition. The films grown on [100]NGO substrates were [110] oriented, while [110]NGO substrates resulted in [100] oriented BST films. The [100]BST films exhibit a small variation of the epitaxial misfit with direction: -2.6% and -2.8% along the [010]BST and [001 ]BST directions respectively. The epitaxial misfit for the [110]BST films show a greater variation with direction; -1.9% and -2.8% along the [1¯10]BST, and [001]BST directions respectively. The interfacial dislocations that form to relieve stress are found to be dependant on the growth orientation of the film and to contribute to the degree of elastic and dielectric anisotropy. The variation of the residual strains, with thickness and direction are correlated to the non-linear dielectric permittivity at 10 GHz. The relative permittivity is seen to vary from 150 to 500 with in-plane direction of a single [110]BST film. Tunabilities in the same film vary from 30 to 54%, with the greater tunability occurring along the directions with greater permittivity. Analysis of the non-linear polarization curves illustrate that the higher order permittivity terms, which are responsible for tunability, are all adversely affected by strain and reach an elastically saturated limit regardless of growth orientation or in-plane direction. Through the use of unequal epitaxial strains, anisotropy is imparted to the otherwise spherically symmetric permittivity tensor. This asymmetry allows a single film to have a variable response and fill a variety of performance requirements in microwave passive devices.

An information-theoretic approach to designing the plane spacing for multifocal plane microscopy

PubMed Central

Tahmasbi, Amir; Ram, Sripad; Chao, Jerry; Abraham, Anish V.; Ward, E. Sally; Ober, Raimund J.

2015-01-01

Multifocal plane microscopy (MUM) is a 3D imaging modality which enables the localization and tracking of single molecules at high spatial and temporal resolution by simultaneously imaging distinct focal planes within the sample. MUM overcomes the depth discrimination problem of conventional microscopy and allows high accuracy localization of a single molecule in 3D along the z-axis. An important question in the design of MUM experiments concerns the appropriate number of focal planes and their spacings to achieve the best possible 3D localization accuracy along the z-axis. Ideally, it is desired to obtain a 3D localization accuracy that is uniform over a large depth and has small numerical values, which guarantee that the single molecule is continuously detectable. Here, we address this concern by developing a plane spacing design strategy based on the Fisher information. In particular, we analyze the Fisher information matrix for the 3D localization problem along the z-axis and propose spacing scenarios termed the strong coupling and the weak coupling spacings, which provide appropriate 3D localization accuracies. Using these spacing scenarios, we investigate the detectability of the single molecule along the z-axis and study the effect of changing the number of focal planes on the 3D localization accuracy. We further review a software module we recently introduced, the MUMDesignTool, that helps to design the plane spacings for a MUM setup. PMID:26113764

Numerical Simulation of Shock Wave Propagation in Fractured Cortical Bone

NASA Astrophysics Data System (ADS)

Padilla, Frédéric; Cleveland, Robin

2009-04-01

Shock waves (SW) are considered a promising method to treat bone non unions, but the associated mechanisms of action are not well understood. In this study, numerical simulations are used to quantify the stresses induced by SWs in cortical bone tissue. We use a 3D FDTD code to solve the linear lossless equations that describe wave propagation in solids and fluids. A 3D model of a fractured rat femur was obtained from micro-CT data with a resolution of 32 μm. The bone was subject to a plane SW pulse with a peak positive pressure of 40 MPa and peak negative pressure of -8 MPa. During the simulations the principal tensile stress and maximum shear stress were tracked throughout the bone. It was found that the simulated stresses in a transverse plane relative to the bone axis may reach values higher than the tensile and shear strength of the bone tissue (around 50 MPa). These results suggest that the stresses induced by the SW may be large enough to initiate local micro-fractures, which may in turn trigger the start of bone healing for the case of a non union.

Precession of a Spinning Ball Rolling down an Inclined Plane

ERIC Educational Resources Information Center

Cross, Rod

2015-01-01

A routine problem in an introductory physics course considers a rectangular block at rest on a plane inclined at angle a to the horizontal. In order for the block not to slide down the incline, the coefficient of sliding friction, µ, must be at least tan a. The situation is similar for the case of a ball rolling down an inclined plane. In order…

Model test study on propagation law of plane stress wave in jointed rock mass under different in-situ stresses

NASA Astrophysics Data System (ADS)

Dong, Qian

2017-12-01

The study of propagation law of plane stress wave in jointed rock mass under in-situ stress has important significance for safety excavation of underground rock mass engineering. A model test of the blasting stress waves propagating in the intact rock and jointed rock mass under different in-situ stresses was carried out, and the influencing factors on the propagation law, such as the scale of static loads and the number of joints were studied respectively. The results show that the transmission coefficient of intact rock is larger than that of jointed rock mass under the same loading condition. With the increase of confining pressure, the transmission coefficients of intact rock and jointed rock mass both show an trend of increasing first and then decreasing, and the variation of transmission coefficients in intact rock is smaller than that of jointed rock mass. Transmission coefficient of jointed rock mass decreases with the increase of the number of joints under the same loading condition, when the confining pressure is relatively small, the reduction of transmission coefficients decreases with the increasing of the number of joints, and the variation law of the reduction of transmission coefficients is contrary when the confining pressure is large.

Stress tensor and focal mechanisms in the Dead Sea basin

NASA Astrophysics Data System (ADS)

Hofstetter, A.; Dorbath, C.; Dorbath, L.; Braeuer, B.; Weber, M. H.

2015-12-01

We use the recorded seismicity, confined to the Dead Sea basin and its boundaries, by the Dead Sea Integrated Research (DESIRE) portable seismic network and the Israel and Jordan permanent seismic networks for studying the mechanisms of earthquakes that occurred in the Dead Sea basin. The observed seismicity in the Dead Sea basin was divided into 9 regions according to the spatial distribution of the earthquakes and the known tectonic features. The large number of recording stations and the good station distribution allowed the reliable determinations of 494 earthquake focal mechanisms. For each region, based on the inversion of the observed polarities of the earthquakes, we determine the focal mechanisms and the associated stress tensor. For 159 earthquakes out of the 494 mechanisms we could determine compatible fault planes. On the eastern side, the focal mechanisms are mainly strike-slip mechanism with nodal planes in the N-S and E-W directions. The azimuths of the stress axes are well constrained presenting minimal variability in the inversion of the data, which is in good agreement with the Arava fault on the eastern side of the Dead Sea basin and what we had expected from the regional geodynamics. However, larger variabilities of the azimuthal and dip angles are observed on the western side of the basin. Due to the wider range of azimuths of the fault planes, we observe the switching of sigma1 and sigma2 or the switching of sigma2 and sigma3as major horizontal stress directions. This observed switching of stress axes allows having dip-slip and normal mechanisms in a region that is dominated by strike-slip motion.

Lunar Flight Study Series: Volume 8. Earth-Moon Transit Studies Based on Ephemeris Data and Using Best Available Computer Program. Part 3: Analysis of Some Lunar Landing Site Problems Utilizing Two Fundamental Principles

NASA Technical Reports Server (NTRS)

Tucker, W. B.; Hooper, H. L.

1963-01-01

This report presents two fundamental properties of lunar trajectories and makes use of these properties to solve various lunar landing site problems. Not only are various problems treated and solved but the properties and methods are established for use in the solution of other problems. This report presents an analysis of lunar landing site problems utilizing the direct mission mode as well as the orbital mission mode. A particular landing site is then specified and different flight profiles are analyzed for getting an exploration vehicle to that landing site. Rendezvous compatible lunar orbits for various stay-times at the landing site are treated. Launch opportunities are discussed for establishing rendezvous compatible lunar orbits without powered plane changes. Then, the minimum required plane changes for rendezvous in the lunar orbit are discussed for launching from earth on any day. On days that afford rendezvous compatible opportunities, there are no powered plane change requirements in the operations from launch at AMR through the rendezvous in lunar orbit, after the stay at the lunar site.

Plane waves and structures in turbulent channel flow

NASA Technical Reports Server (NTRS)

Sirovich, L.; Ball, K. S.; Keefe, L. R.

1990-01-01

A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.

A simple 2-D model for the evolution of an island-arc system

NASA Astrophysics Data System (ADS)

Zharinov, S. E.; Demin, S. S.

1990-07-01

Slow seismotectonic movements along inclined deep fault planes under compressive horizontal stresses are supposed to be the principal mechanism controlling the structure and processes in island-arc systems. In order to treat the stress variations caused by this mechanism, a simple geomechanical model is investigated. We consider a shearing surface crack embedded in a homogeneous elastic half-space. The key element of the model is viscous interaction between the sides of the crack, the viscosity varying with depth. The model differs from the classical steady-state mode of subduction by nonstationary creep processes on deep faults and possibly by cyclical evolution of island-arc systems. The results of our numerical analysis are in good agreement with geological, geophysical and seismological data. (i) Vertical displacements of the free surface in the model fit well with the typical topography of a trench—arc-basement rise—back-arc basin system. (ii) The Benioff seismic zone is supposed to be formed due to the concentration of shear stresses near the fault plane. The characteristic patterns of seismicity, the fine geometry of Benioff zones, and their double-planed structure can be explained in terms of our model. (iii) A zone of considerable heat generation caused by viscous dissipation along the fault plane is found within a narrow area in the depth range 100-200 km. Moreover, the island-arc basement rise is characterized in the model by a relative tension of a few tens or even hundreds of bars, while at depths of 100-150 km below the surface, additional compression of the same order of magnitude acts. The magmatic plumbing system may be visualised as a "toothpaste tube" or a sponge filled with magma which is squeezed from the depths to the surface due to the redistribution of the tectonic stresses only. This can explain the physical origin of island-arc magmatism and the typical position of volcanic belts.

Investigation of Three-Dimensional Stress Fields and Slip Systems for FCC Single Crystal Superalloy Notched Specimens

NASA Technical Reports Server (NTRS)

Arakere, Nagaraj K.; Magnan, Shannon; Ebrahimi, Fereshteh; Ferroro, Luis

2004-01-01

Metals and their alloys, except for a few intermetallics, are inherently ductile, i.e. plastic deformation precedes fracture in these materials. Therefore, resistance to fracture is directly related to the development of the plastic zone at the crack tip. Recent studies indicate that the fracture toughness of single crystals depends on the crystallographic orientation of the notch as well as the loading direction. In general, the dependence of crack propagation resistance on crystallographic orientation arises from the anisotropy of (i) elastic constants, (ii) plastic deformation (or slip), and (iii) the weakest fracture planes (e.g. cleavage planes). Because of the triaxial stress state at the notch tips, many slip systems that otherwise would not be activated during uniaxial testing, become operational. The plastic zone formation in single crystals has been tackled theoretically by Rice and his co-workers and only limited experimental work has been conducted in this area. The study of the stresses and strains in the vicinity of a FCC single crystal notch tip is of relatively recent origin. We present experimental and numerical investigation of 3D stress fields and evolution of slip sector boundaries near notches in FCC single crystal tension test specimens, and demonstrate that a 3D linear elastic finite element model that includes the effect of material anisotropy is shown to predict active slip planes and sectors accurately. The slip sector boundaries are shown to have complex curved shapes with several slip systems active simultaneously near the notch. Results are presented for surface and mid-plane of the specimens. The results demonstrate that accounting for 3D elastic anisotropy is very important for accurate prediction of slip activation near FCC single crystal notches loaded in tension. Results from the study will help establish guidelines for fatigue damage near single crystal notches.

A Multiphysics Finite Element and Peridynamics Model of Dielectric Breakdown

DTIC Science & Technology

2017-09-01

A method for simulating dielectric breakdown in solid materials is presented that couples electro-quasi-statics, the adiabatic heat equation, and...temperatures or high strains. The Kelvin force computation used in the method is verified against a 1-D solution and the linearization scheme used to treat the...plane problems, a 2-D composite capacitor with a conductive flaw, and a 3-D point–plane problem. The results show that the method is capable of

Image classification independent of orientation and scale

NASA Astrophysics Data System (ADS)

Arsenault, Henri H.; Parent, Sebastien; Moisan, Sylvain

1998-04-01

The recognition of targets independently of orientation has become fairly well developed in recent years for in-plane rotation. The out-of-plane rotation problem is much less advanced. When both out-of-plane rotations and changes of scale are present, the problem becomes very difficult. In this paper we describe our research on the combined out-of- plane rotation problem and the scale invariance problem. The rotations were limited to rotations about an axis perpendicular to the line of sight. The objects to be classified were three kinds of military vehicles. The inputs used were infrared imagery and photographs. We used a variation of a method proposed by Neiberg and Casasent, where a neural network is trained with a subset of the database and a minimum distances from lines in feature space are used for classification instead of nearest neighbors. Each line in the feature space corresponds to one class of objects, and points on one line correspond to different orientations of the same target. We found that the training samples needed to be closer for some orientations than for others, and that the most difficult orientations are where the target is head-on to the observer. By means of some additional training of the neural network, we were able to achieve 100% correct classification for 360 degree rotation and a range of scales over a factor of five.

Focal mechanism determination of induced micro-earthquakes in reservoir by non linear inversion of amplitudes

NASA Astrophysics Data System (ADS)

Godano, M.; Regnier, M.; Deschamps, A.; Bardainne, T.

2009-04-01

Since these last years, the feasibility of CO2 storage in geological reservoir is carefully investigated. The monitoring of the seismicity (natural or induced by the gas injection) in the reservoir area is crucial for safety concerns. The location of the seismic events provide an imaging of the active structures which can be a potential leakage paths. Besides, the focal mechanism is an other important seismic attribute providing direct informations about the rock fracturing, and indirect information about the state of stress in the reservoir. We address the problem of focal mechanism determination for the micro-earthquakes induced in reservoirs with a potential application to the sites of CO2 storage. We developed a non linear inversion method of P, SV and SH direct waves amplitudes. To solve the inverse problem, we perfected our own simulated annealing algorithm. Our method allows simply determining the fault plane solution (strike, dip and rake of the fault plane) in the case of a double-couple source assumption. More generally, our method allows also determining the full moment tensor in case of non-purely shear source assumption. We searched to quantify the uncertainty associated to the obtained focal mechanisms. We defined three uncertainty causes. The first is related to the convergence process of the inversion, the second is related the amplitude picking error caused by the noise level and the third is related to the event location uncertainty. We performed a series of tests on synthetic data generated in reservoir configuration in order to validate our inversion method.

Elevated Temperature Effects on the Plastic Anisotropy of an Extruded Mg-4 Wt Pct Li Alloy: Experiments and Polycrystal Modeling

NASA Astrophysics Data System (ADS)

Risse, Marcel; Lentz, Martin; Fahrenson, Christoph; Reimers, Walter; Knezevic, Marko; Beyerlein, Irene J.

2017-01-01

In this work, we study the deformation behavior of Mg-4 wt pct Li in uniaxial tension as a function of temperature and loading direction. Standard tensile tests were performed at temperatures in the range of 293 K (20 °C) ≤ T ≤ 473 K (200 °C) and in two in-plane directions: the extrusion and the transverse. We find that while the in-plane plastic anisotropy (PA) decreases with temperature, the anisotropy in failure strain and texture development increases. To uncover the temperature dependence in the critical stresses for slip and in the amounts of slip and twinning systems mediating deformation, we employ the elastic-plastic self-consistent polycrystal plasticity model with a thermally activated dislocation density based hardening law for activating slip with individual crystals. We demonstrate that the model, with a single set of intrinsic material parameters, achieves good agreement with the stress-strain curves, deformation textures, and intragranular misorientation axis analysis for all test directions and temperatures. With the model, we show that at all temperatures the in-plane tensile behavior is driven primarily by < a rangle slip and both < {c + a} rangle slip and twinning play a minor role. The analysis explains that the in-plane PA decreases and failure strains increase with temperature as a result of a significant reduction in the activation stress for pyramidal < {c + a} rangle slip, which effectively promotes strain accommodation from multiple types of < a rangle and < {c + a} rangle slip. The results also show that because of the strong initial texture, in-plane texture development is anisotropic since prismatic slip dominates the deformation in one test, although it is not the easiest slip mode, and basal slip in the other. These findings reveal the relationship between the temperature-sensitive thresholds needed to activate crystallographic slip and the development of texture and macroscopic PA.

Elastic behavior of a red blood cell with the membrane's nonuniform natural state: equilibrium shape, motion transition under shear flow, and elongation during tank-treading motion.

PubMed

Tsubota, Ken-Ichi; Wada, Shigeo; Liu, Hao

2014-08-01

Direct numerical simulations of the mechanics of a single red blood cell (RBC) were performed by considering the nonuniform natural state of the elastic membrane. A RBC was modeled as an incompressible viscous fluid encapsulated by an elastic membrane. The in-plane shear and area dilatation deformations of the membrane were modeled by Skalak constitutive equation, while out-of-plane bending deformation was formulated by the spring model. The natural state of the membrane with respect to in-plane shear deformation was modeled as a sphere ([Formula: see text]), biconcave disk shape ([Formula: see text]) and their intermediate shapes ([Formula: see text]) with the nonuniformity parameter [Formula: see text], while the natural state with respect to out-of-plane bending deformation was modeled as a flat plane. According to the numerical simulations, at an experimentally measured in-plane shear modulus of [Formula: see text] and an out-of-plane bending rigidity of [Formula: see text] of the cell membrane, the following results were obtained. (i) The RBC shape at equilibrium was biconcave discoid for [Formula: see text] and cupped otherwise; (ii) the experimentally measured fluid shear stress at the transition between tumbling and tank-treading motions under shear flow was reproduced for [Formula: see text]; (iii) the elongation deformation of the RBC during tank-treading motion from the simulation was consistent with that from in vitro experiments, irrespective of the [Formula: see text] value. Based on our RBC modeling, the three phenomena (i), (ii), and (iii) were mechanically consistent for [Formula: see text]. The condition [Formula: see text] precludes a biconcave discoid shape at equilibrium (i); however, it gives appropriate fluid shear stress at the motion transition under shear flow (ii), suggesting that a combined effect of [Formula: see text] and the natural state with respect to out-of-plane bending deformation is necessary for understanding details of the RBC mechanics at equilibrium. Our numerical results demonstrate that moderate nonuniformity in a membrane's natural state with respect to in-plane shear deformation plays a key role in RBC mechanics.

Stress orientations of Taiwan Chelungpu-Fault Drilling Project (TCDP) hole-A as observed from geophysical logs

USGS Publications Warehouse

Wu, H.-Y.; Ma, K.-F.; Zoback, M.; Boness, N.; Ito, H.; Hung, J.-H.; Hickman, S.

2007-01-01

The Taiwan Chelungpu-fault Drilling Project (TCDP) drilled a 2-km-deep research borehole to investigate the structure and mechanics of the Chelungpu Fault that ruptured in the 1999 Mw 7.6 Chi-Chi earthquake. Geophysical logs of the TCDP were carried out over depths of 500-1900 in, including Dipole Sonic Imager (DSI) logs and Formation Micro Imager (FMI) logs in order to identify bedding planes, fractures and shear zones. From the continuous core obtained from the borehole, a shear zone at a depth of 1110 meters is interpreted to be the Chelungpu fault, located within the Chinshui Shale, which extends from 1013 to 1300 meters depth. Stress-induced borehole breakouts were observed over nearly the entire length of the wellbore. These data show an overall stress direction (???N115??E) that is essentially parallel to the regional stress field and parallel to the convergence direction of the Philippine Sea plate with respect to the Eurasian plate. Variability in the average stress direction is seen at various depths. In particular there is a major stress orientation anomaly in the vicinity of the Chelungpu fault. Abrupt stress rotations at depths of 1000 in and 1310 in are close to the Chinshui Shale's upper and lower boundaries, suggesting the possibility that bedding plane slip occurred during the Chi-Chi earthquake. Copyright 2007 by the American Geophysical Union.

Theory and application of equivalent transformation relationships between plane wave and spherical wave

NASA Astrophysics Data System (ADS)

Wang, Yao; Yang, Zailin; Zhang, Jianwei; Yang, Yong

2017-10-01

Based on the governing equations and the equivalent models, we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radially inhomogeneous properties. These equivalent relationships can help us to obtain the analytical solutions of the elastodynamic issues in an inhomogeneous medium. The physical essence of the presented equivalent transformations is the equivalent relationships between the geometry and the material properties. It indicates that the spherical wave problem in globular geometry can be transformed into the plane wave problem in the bar with variable property fields, and its inverse transformation is valid as well. Four different examples of wave motion problems in the inhomogeneous media are solved based on the presented equivalent relationships. We obtain two basic analytical solution forms in Examples I and II, investigate the reflection behavior of inhomogeneous half-space in Example III, and exhibit a special inhomogeneity in Example IV, which can keep the traveling spherical wave in constant amplitude. This study implies that our idea makes solving the associated problem easier.

Computer program for stresses and buckling of heated composite-stiffened panels and other structures (BUCLASP 3)

NASA Technical Reports Server (NTRS)

Viswanathan, A. V.; Tamekuni, M.; Tripp, L. L.

1974-01-01

General-purpose program is intended for thermal stress and instability analyses of structures such as axially-stiffened curved panels. Two types of instability analyses can be effected by program: (1) thermal buckling with temperature variation as specified and (2) buckling due to in-plane biaxial loading.

Theoretical Analysis on Mechanical Deformation of Membrane-Based Photomask Blanks

NASA Astrophysics Data System (ADS)

Marumoto, Kenji; Aya, Sunao; Yabe, Hedeki; Okada, Tatsunori; Sumitani, Hiroaki

2012-04-01

Membrane-based photomask is used in proximity X-ray lithography including that in LIGA (Lithographie, Galvanoformung und Abformung) process, and near-field photolithography. In this article, out-of-plane deformation (OPD) and in-plane displacement (IPD) of membrane-based photomask blanks are theoretically analyzed to obtain the mask blanks with flat front surface and low stress absorber film. First, we derived the equations of OPD and IPD for the processing steps of membrane-based photomask such as film deposition, back-etching and bonding, using a theory of symmetrical bending of circular plates with a coaxial circular hole and that of deformation of cylinder under hydrostatic pressure. The validity of the equations was proved by comparing the calculation results with experimental ones. Using these equations, we investigated the relation between the geometry of the mask blanks and the distortions generally, and gave the criterion to attain the flat front surface. Moreover, the absorber stress-bias required to obtain zero-stress on finished mask blanks was also calculated and it has been found that only little stress-bias was required for adequate hole size of support plate.

Inference of stress and texture from angular dependence of ultrasonic plate mode velocities

NASA Technical Reports Server (NTRS)

Thompson, R. B.; Smith, J. F.; Lee, S. S.

1986-01-01

The theory for the angular dependence of the ultrasonic wave velocity in a symmetry plane of an orthorhombic, stressed material is presented. The two waves having polarizations in this plane are shown to have velocities which can be estimated from measurements of the SH sub 0 and S sub 0 guided modes of a thin plate: the relationship being exact for the SH sub 0 mode and requiring a 10% correction for the S sub 0 mode at long wavelength. It is then shown how stress and texture can be independently inferred from various features of the angular dependence of these two velocities. From the SH sub 0 data, the ability to determine the directions and differences in magnitudes of principal stresses is described and supported by experimental data on several materials. From a combination of the SH sub 0 and S sub 0 data, a procedure is proposed for determining the coefficients W sub 400, W sub 420 and W sub 440 of an expansion of the crystallite orientation distribution function in terms of generalized Legendre functions. Possible applications in process control are indicated.

Residual-stress-induced grain growth of twinned grains and its effect on formability of magnesium alloy sheet at room temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Se-Jong; Kim, Daeyong, E-mail: daeyong@kims.re.kr; Lee, Keunho

2015-11-15

A magnesium alloy sheet was subjected to in-plane compression along with a vertical load to avoid buckling during compression. Pre-compressed specimens machined from the sheet were annealed at different temperatures and the changes in microstructure and texture were observed using electron back scattered diffraction (EBSD). Twinned grains preferentially grew during annealing at 300 °C, so that a strong texture with the < 0001 > direction parallel to the transverse direction developed. EBSD analysis confirmed that the friction caused by the vertical load induced inhomogeneous distribution of residual stress, which acted as an additional driving force for preferential grain growth ofmore » twinned grain during annealing. The annealed specimen showed excellent formability. - Highlights: • A magnesium alloy sheet subjected to in-plane compression under a vertical load • The vertical load induced inhomogeneous distribution of the residual stress. • The residual stress acted as an additional driving force for grain growth. • The annealed specimen with strong non-basal texture showed excellent formability.« less

Substrate temperature effect on the structural anisotropy in amorphous Tb-Fe films

NASA Astrophysics Data System (ADS)

Harris, V. G.; Hellman, F.; Elam, W. T.; Koon, N. C.

1993-05-01

Using extended x-ray absorption fine structures (EXAFS) measurements we have investigated the atomic environment around the Fe atom in a series of amorphous Tb0.26Fe0.74 films having different magnetic anisotropy energies owing to different deposition temperatures. The polarization properties of synchrotron radiation allowed the separate study of structure parallel and perpendicular to the sample plane. An anisotropy between these two structures was observed. Modeling results indicate this anisotropy is due to anisotropic pair correlations where the Fe-Fe pairs are statistically preferred in-plane and the Fe-Tb pairs out-of-plane. The amplitude of this anisotropy scales with both the substrate temperature and the magnetic anisotropy energy. A ≊1% in-plane compression of the Fe-Fe distance was measured between the in-plane and out-of-plane structure of the sample grown at 77 K. This sample had no detectable local chemical anisotropy suggesting that intrinsic stress plays an important role in determining its magnetic anisotropy.

An Experimental Study of the Influence of in-Plane Fiber Waviness on Unidirectional Laminates Tensile Properties

NASA Astrophysics Data System (ADS)

Zhao, Cong; Xiao, Jun; Li, Yong; Chu, Qiyi; Xu, Ting; Wang, Bendong

2017-12-01

As one of the most common process induced defects of automated fiber placement, in-plane fiber waviness and its influences on mechanical properties of fiber reinforced composite lack experimental studies. In this paper, a new approach to prepare the test specimen with in-plane fiber waviness is proposed in consideration of the mismatch between the current test standard and actual fiber trajectory. Based on the generation mechanism of in-plane fiber waviness during automated fiber placement, the magnitude of in-plane fiber waviness is characterized by axial compressive strain of prepreg tow. The elastic constants and tensile strength of unidirectional laminates with in-plane fiber waviness are calculated by off-axis and maximum stress theory. Experimental results show that the tensile properties infade dramatically with increasing magnitude of the waviness, in good agreement with theoretical analyses. When prepreg tow compressive strain reaches 1.2%, the longitudinal tensile modulus and strength of unidirectional laminate decreased by 25.5% and 57.7%, respectively.

Colored Flag by Double Refraction.

ERIC Educational Resources Information Center

Reid, Bill

1994-01-01

Describes various demonstrations that illustrate double refraction and rotation of the plane of polarization in stressed, transparent plastics, with the consequent production of colored designs. (ZWH)

Microstructure and Optical Properties of Nonpolar m-Plane GaN Films Grown on m-Plane Sapphire by Hydride Vapor Phase Epitaxy

NASA Astrophysics Data System (ADS)

Wei, Tongbo; Duan, Ruifei; Wang, Junxi; Li, Jinmin; Huo, Ziqiang; Yang, Jiankun; Zeng, Yiping

2008-05-01

Thick nonpolar (1010) GaN layers were grown on m-plane sapphire substrates by hydride vapor phase epitaxy (HVPE) using magnetron sputtered ZnO buffers, while semipolar (1013) GaN layers were obtained by the conventional two-step growth method using the same substrate. The in-plane anisotropic structural characteristics and stress distribution of the epilayers were revealed by high resolution X-ray diffraction and polarized Raman scattering measurements. Atomic force microscopy (AFM) images revealed that the striated surface morphologies correlated with the basal plane stacking faults for both (1010) and (1013) GaN films. The m-plane GaN surface showed many triangular-shaped pits aligning uniformly with the tips pointing to the c-axis after etching in boiled KOH, whereas the oblique hillocks appeared on the semipolar epilayers. In addition, the dominant emission at 3.42 eV in m-plane GaN films displayed a red shift with respect to that in semipolar epilayers, maybe owing to the different strain states present in the two epitaxial layers.