Crack initiation under generalized plane strain conditions
Shum, D.K.M.; Merkle, J.G.
1991-01-01
A method for estimating the decrease in crack-initiation toughness, from a reference plane strain value, due to positive straining along the crack front of a circumferential flaw in a reactor pressure vessel is presented in this study. This method relates crack initiation under generalized plane strain conditions with material failure at points within a distance of a few crack-tip-opening displacements ahead of a crack front, and involves the formulation of a micromechanical crack-initiation model. While this study is intended to address concerns regarding the effects of positive out-of- plane straining on ductile crack initiation, the approach adopted in this work can be extended in a straightforward fashion to examine conditions of macroscopic cleavage crack initiation. Provided single- parameter dominance of near-tip fields exists in the flawed structure, results from this study could be used to examine the appropriateness of applying plane strain fracture toughness to the evaluation of circumferential flaws, in particular to those in ring-forged vessels which have no longitudinal welds. In addition, results from this study could also be applied toward the analysis of the effects of thermal streaming on the fracture resistance of circumferentially oriented flaws in a pressure vessel. 37 refs., 8 figs., 1 tab.
Analysis of crack closure under plane strain conditions
NASA Technical Reports Server (NTRS)
Fleck, Norman A.; Newman, James C., Jr.
1988-01-01
The phenomenon of plasticity-induced crack closure is associated with the development of residual material on the flanks of an advancing fatigue crack. While it is easy to see that this residual material can come from the side faces of a specimen under plane stress conditions, it is difficult to discover the origin of this extra volume of material on the crack flanks when it is assumed that plane deformations occur and plastic flow is incompressible. The purpose of this paper is to determine whether plasticity-induced fatigue crack closure occurs in an elastic-perfectly plastic body under plane strain conditions.
Analysis of crack closure under plane strain conditions
NASA Technical Reports Server (NTRS)
Fleck, N. A.; Newman, J. C.
1986-01-01
The phenomenon of plasticity-induced crack closure is associated with the development of residual material on the flanks of an advancing fatigue crack. While it is easy to see that this residual material can come from the side faces of a specimen under plane stress conditions, it is difficult to discover the origin of this extra volume of material on the crack flanks when it is assumed that plane deformations occur and plastic flow is incompressible. The purpose of this paper is to determine whether plasticity-induced fatigue crack closure occurs in an elastic-perfectly plastic body under plane strain conditions.
Comparison of experiment and theory for elastic-plastic plane strain crack growth
Hermann, L; Rice, J R
1980-02-01
Recent theoretical results on elastic-plastic plane strain crack growth, and experimental results for crack growth in a 4140 steel in terms of the theoretical concepts are reviewed. The theory is based on a recent asymptotic analysis of crack surface opening and strain distributions at a quasi-statically advancing crack tip in an ideally-plastic solid. The analysis is incomplete in that some of the parameters which appear in it are known only approximately, especially at large scale yielding. Nevertheless, it suffices to derive a relation between the imposed loading and amount of crack growth, prior to general yielding, based on the assumption that a geometrically similar near-tip crack profile is maintained during growth. The resulting predictions for the variation of J with crack growth are found to fit well to the experimental results obtained on deeply cracked compact specimens.
Tests and analyses for fully plastic fracture mechanics of plane strain mode I crack growth
McClintock, F.A.; Parks, D.M.; Kim, Y.J.
1995-12-31
Under monotonic loading, structures should ideally be ductile enough to provide continued resistance during crack growth. For fully plastic crack growth in low strength alloys, existing asymptotic solutions for elastic-plastic growing cracks are not applicable because they reach the fracture strain only in regions small compared to the inhomogeneities of the actual fracture process. For the limiting case of non-hardening fully-plastic plane strain crack growth, in a number of geometries and loadings the near-tip fields are characterized in terms of three parameters: an effective angle 2{theta}{sub s} between a pair of slip planes, and the normal stress {sigma}{sub s} and the increment of displacement {delta}u{sub s} across the planes. This three-parameter characterization is in contrast to the one- or two-parameter (K or J and T or Q) characterization in linear or non-linear elastic fracture mechanics. These {theta}{sub s}, {sigma}{sub s}, and {delta}u{sub s} parameters are found form the far-field geometries and loadings through slip line fields or least upper bound analyses based on circular arcs. The resulting crack growth, in terms of the crack tip opening angle (CTOA), is a function of {theta}{sub s}, {sigma}{sub s}, and the material. The geometry of the crack growing between two moving slip planes emanating from its tip reduces this function to the critical fracture shear strain left behind the slip planes, {gamma}f, as a function of {sigma}{sub s}. {gamma}f({sigma}{sub s}) is found theoretically from a hole initiation and growth model. It is also found from preliminary fully plastic crack growth experiments on unequally grooved specimens with fixed-grip extension or 4-point bending of a 1018 CF steel.
NASA Astrophysics Data System (ADS)
Begley, Matthew R.; Creton, Costantino; McMeeking, Robert M.
2015-11-01
A general asymptotic plane strain crack tip stress field is constructed for linear versions of neo-Hookean materials, which spans a wide variety of special cases including incompressible Mooney elastomers, the compressible Blatz-Ko elastomer, several cases of the Ogden constitutive law and a new result for a compressible linear neo-Hookean material. The nominal stress field has dominant terms that have a square root singularity with respect to the distance of material points from the crack tip in the undeformed reference configuration. At second order, there is a uniform tension parallel to the crack. The associated displacement field in plane strain at leading order has dependence proportional to the square root of the same coordinate. The relationship between the amplitude of the crack tip singularity (a stress intensity factor) and the plane strain energy release rate is outlined for the general linear material, with simplified relationships presented for notable special cases.
Nobrega, B.N.
1984-01-01
The segmented expanding mandrel test (SEMT) method is generally regarded as a good laboratory simulator of pellet-cladding interactions (PCI) in LWR fuel rods. Yet it does not reproduce the low strain failures in Zircaloy cladding typical of PCI-failed fuel elements and commonly observed in other types of laboratory specimens. This investigation addressed this apparent inconsistency. Iodine-stress corrosion cracking (I-SCC) of cold worked, unirradiated Zircaloy-2 cladding was induced in three different types of tubing specimens (known as regular, thin-wall, and chamfered) in a modified SEMT apparatus designed to test mechanical conditions that could lead to slow strain failures. Only the chamfered sample, which has been shown to be subjected to more nearly plane strain conditions than either of the other two specimen types, failed consistently at low (0.8%) total diametral strains in good agreement with in-reactor failure data. Such conditions were numerically and experimentally quantified by means of finite element calculational models and local strain measurements. The numerical analyses and strain measurements provide valuable insight into the PCI simulating power of the segmented expanding mandrel test and its experimental limitations. Failure-strain results for chamfered barrier claddings were obtained and compared with available literature data. The improved I-SCC resistance of this type of cladding was confirmed but the failure strains were significantly lower than reported for regular barrier tubes.
Supersonic crack growth in a solid of upturn stress?strain relation under anti-plane shear
NASA Astrophysics Data System (ADS)
Guo, Gaofeng; Yang, Wei; Huang, Y.
2003-11-01
This paper examines, from the prospect of continuum analysis, the possibility for a supersonic crack growth in a solid with an upturn stress-strain relation. The stress has a linear-upturn power-law relation with the strain, resulting in an elastic modulus, and consequently a wave speed, that increase with the strain. Though appearing to be "supersonic", the local wave speed in the crack tip vicinity of the solid with a sufficient upturn stress-strain relation exceeds the crack extension speed. A pre-request for such a supersonic crack growth is the storage of sufficient deformation energy within the solid to nurse the energy flux drawn to the crack tip that extends at an "apparent supersonic" speed. The idea is demonstrated for the simplest case, the anti-plane shear. We examine the steady-state supersonic crack growth in a hyperelastic material. The governing equation is elliptical in the crack tip vicinity but hyperbolic elsewhere. The boundary between two regions is determined with a certain extent. An asymptotic solution is constructed within the super-hardening zone. The solution connects to the hyperbolic radiation strips by weak discontinuity boundaries and to the pre-stressed frontal field by a strong discontinuity boundary.
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 for a nonhomogeneous plane
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1983-01-01
The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.
Crack problem for a nonhomogeneous plane
Delale, F.; Erdogan, F.
1983-09-01
This study considers the plane elasticity problem for a nonhomogeneous medium containing a crack. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then, the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy-type kernel. Hence, its solution and the stresses around the crack tips have the conventional square-root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible. 14 references.
The crack problem for a nonhomogeneous plane
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1982-01-01
The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.
A plane stress finite element model for elastic-plastic mode I/II crack growth
NASA Astrophysics Data System (ADS)
James, Mark Anthony
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.
Closure of fatigue cracks at high strains
NASA Technical Reports Server (NTRS)
Iyyer, N. S.; Dowling, N. E.
1985-01-01
Experiments were conducted on smooth specimens to study the closure behavior of short cracks at high cyclic strains under completely reversed cycling. Testing procedures and methodology, and closure measurement techniques, are described in detail. The strain levels chosen for the study cover from predominantly elastic to grossly plastic strains. Crack closure measurements are made at different crack lengths. The study reveals that, at high strains, cracks close only as the lowest stress level in the cycle is approached. The crack opening is observed to occur in the compressive part of the loading cycle. The applied stress needed to open a short crack under high strain is found to be less than for cracks under small scale yielding. For increased plastic deformations, the value of sigma sub op/sigma sub max is observed to decrease and approaches the value of R. Comparison of the experimental results with existing analysis is made and indicates the limitations of the small scale yielding approach where gross plastic deformation behavior occurs.
Turbulent Plane Wakes Subjected to Successive Strains
NASA Technical Reports Server (NTRS)
Rogers, Michael M.
2003-01-01
Six direct numerical simulations of turbulent time-evolving strained plane wakes have been examined to investigate the response of a wake to successive irrotational plane strains of opposite sign. The orientation of the applied strain field has been selected so that the flow is the time-developing analogue of a spatially developing wake evolving in the presence of either a favourable or an adverse streamwise pressure gradient. The magnitude of the applied strain rate a is constant in time t until the total strain e(sup at) reaches about four. At this point, a new simulation is begun with the sign of the applied strain being reversed (the original simulation is continued as well). When the total strain is reduced back to its original value of one, yet another simulation is begun with the sign of the strain being reversed again back to its original sign. This process is done for both initially "favourable" and initially "adverse" strains, providing simulations for each of these strain types from three different initial conditions. The evolution of the wake mean velocity deficit and width is found to be very similar for all the adversely strained cases, with both measures rapidly achieving exponential growth at the rate associated with the cross-stream expansive strain e(sup at). In the "favourably" strained cases, the wake widths approach a constant and the velocity deficits ultimately decay rapidly as e(sup -2at). Although all three of these cases do exhibit the same asymptotic exponential behaviour, the time required to achieve this is longer for the cases that have been previously adversely strained (by at approx. equals 1). These simulations confirm the generality of the conclusions drawn in Rogers (2002) regarding the response of plane wakes to strain. The evolution of strained wakes is not consistent with the predictions of classical self-similar analysis; a more general equilibrium similarity solution is required to describe the results. At least for the cases
On the modified Westergaard equations for certain plane crack problems
NASA Technical Reports Server (NTRS)
Eftis, J.; Liebowitz, H.
1972-01-01
An error in Westergaard's equation for a certain class of plane crack problems, originally pointed out by Sih, is briefly discussed. The source of the difficulty is traced to an oversight in an earlier work by MacGregor, upon whose work Westergaard based his equations. Several examples of interest illustrating the consequences of the necessary correction to these equations are given.
Biaxial load effects on the crack border elastic strain energy and strain energy rate
NASA Technical Reports Server (NTRS)
Eftis, J.; Subramonian, N.; Liebowitz, H.
1977-01-01
The validity of the singular solution (first term of a series representation) is investigated for the crack tip stress and displacement field in an infinite sheet with a flat line crack with biaxial loads applied to the outer boundaries. It is shown that if one retains the second contribution to the series approximations for stress and displacement in the calculation of the local elastic strain energy density and elastic strain energy rate in the crack border region, both these quantities have significant biaxial load dependency. The value of the J-integral does not depend on the presence of the second term of the series expansion for stress and displacement. Thus J(I) is insensitive to the presence of loads applied parallel to the plane of the crack.
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.
Opening and closing of cracks at high cyclic strains
NASA Technical Reports Server (NTRS)
Iyyer, N. S.; Dowling, N. E.
1986-01-01
The closure behavior of cracks of different length and at different cyclic strain levels (ranging from predominantly elastic to grossly plastic strains) was studied to observe the effect of residual crack-tip plasticity on crack closure. Cracks were initiated either naturally or artificially (from electric discharge machining pits) in uniaxial test specimens of strengthened alloy steel AISI 4340 with a grain size of 0.016 mm. It was found that, at high strains, cracks closed only when the lowest stress level in the cycle was approached. The stress or the strain opening level depended upon the exact point along the crack length where the observations were made. As the plastic deformation increased, the relative crack opening level was found to decrease and approach the value of stress ratio R. The experimental results were compared with those of three analytical models of crack closure and opening, demonstrating the limitations of the currently available elastic-plastic crack growth analysis.
Axial strain redistribution resulting from off-axis ply cracking in polymer composites
NASA Astrophysics Data System (ADS)
Katerelos, Dionisis G.; Galiotis, Costas
2004-10-01
The initial mode of damage in multidirectional composites is the accumulation of matrix cracks in the off-axis plies. Remote laser Raman spectroscopy, using aramid (Kevlar 49®) fibers as Raman strain sensors, has been employed to monitor the local strains in cracked crossply composites. The strain magnification in the 0° ply caused by 90° matrix cracking are measured at different levels of loading. A relationship between the values of strain magnification and the distance between the position of the fibers sensors vis-à-vis the crack front has been established. The effect of damage progression within the 0° plies on the remaining/surviving glass fibers is modeled satisfactorily and verified against predictions on the basis of a generalized plane strain model by assuming that the 90° ply "expands" in relative size against the 0° ply thickness.
NASA Technical Reports Server (NTRS)
Bassani, J. L.; Erdogan, F.
1979-01-01
The antiplane shear problem for two bonded dissimilar half planes containing a semi-infinite crack or two arbitrarily located collinear cracks is considered. For the semi-infinite crack the problem is solved for a concentrated wedge load and the stress intensity factor and the angular distribution of stresses are calculated. For finite cracks the problem is reduced to a pair of integral equations. Numerical results are obtained for cracks fully imbedded in a homogeneous medium, one crack tip touching the interface, and a crack crossing the interface for various crack angles.
NASA Technical Reports Server (NTRS)
Bassani, J. L.; Erdogan, F.
1978-01-01
The antiplane shear problem for two bonded dissimilar half planes containing a semi-infinite crack or two arbitrarily located collinear cracks was considered. For the semi-infinite crack the problem was solved for a concentrated wedge load and the stress intensity factor and the angular distribution of stresses were calculated. For finite cracks the problem was reduced to a pair of integral equations. Numerical results were obtained for cracks fully imbedded in a homogeneous medium, one crack tip touching the interface, and a crack crossing the interface for various crack angles.
Dynamic crack propagation in elastic-perfectly plastic solids under plane stress conditions
NASA Astrophysics Data System (ADS)
Deng, Xiaomin; Rosakis, Ares J.
THE phenomenon of steady-state dynamic crack propagation in elastic-perfectly plastic solids under mode I plane stress, small-scale yielding conditions is investigated numerically. An Eulerian finite element scheme is employed. The materials are assumed to obey the von Mises yield criterion and the associated flow rule. The ratio of the crack tip plastic zone size to that of the element nearest to the crack tip is of the order of 1.6 × 10 4. Two subjects of general interest are discussed. These are the asymptotic structure of the crack tip stress and deformation fields, and the appropriateness of a crack growth fracture criterion based on the far-field dynamic stress intensity factor. The crack-line solution by ACHENBACH and LI (Report NU-SML-TR-No. 84-1, Dept. of Civil Engineering, Northwestern University, Evanston, IL 60201, 1984a; in Fundamentals of Deformation and Fracture (edited by B.A. Brilby et al.). Cambridge University Press, 1984b) is discussed and compared to the numerical solution. The results of this study strongly indicate that the crack tip strain and velocity fields possess logarithmic singularities, which is consistent with the assumptions in the asymptotic analysis by Gao ( Int. J. Fracture34, 111, 1987). However, it is revealed that the crack tip field variations in Gao's solution present features often contrary to the numerical findings. To this end, a preliminary asymptotic analysis is performed in an effort to resolve certain issues. Finally, the critical plastic strain criterion ( MCCLINTOCK and IRWIN, in Fracture Toughness Testing and Its Applications, ASTM STP 381, p. 84, 1964) is adopted to obtain theoretical relations between the critical dynamic stress intensity factor and the crack propagation speed. These relations are found to agree well with experimental measurements by Rosakis et al. ( J. Mech. Phys. Solids32, 443, 1984) and by ZEHNDER and ROSAKIS ( Int. J. Fracture, to appear 1990), performed on thin 4340 steel plates whose
Strain oxidation cracking of austenitic stainless steels at 610 C
Calvar, M. Le; Scott, P.M.; Magnin, T.; Rieux, P.
1998-02-01
Strain oxidation cracking of both forged and welded austenitic stainless steels (SS) was studied. Creep and slow strain rate tests (SSRT) were performed in vacuum, air, and a gas furnace environment (air + carbon dioxide [CO{sub 2}] + water [H{sub 2}O]). Results showed cracking was environmentally dependent. Almost no cracking was observed in vacuum, whereas intergranular cracking was observed with increasing severity in passing from an air to a gas furnace environment. The most severe cracking was associated with formation of a less protective film formed in the gas furnace environment (air: haematite-like M{sub 2}O{sub 3} oxide; gas furnace environment: spinel M{sub 3}O{sub 4} oxide). Cracking depended strongly on the carbon content and the sensitization susceptibility of the material: the higher the carbon content, the more susceptible the alloy. This cracking was believed to be similar to other oxidation-induced cracking phenomena.
Finite strain crack tip fields in soft incompressible elastic solids.
Krishnan, Venkat R; Hui, Chung Yuen; Long, Rong
2008-12-16
A finite element model (FEM) is used to study the behavior of the large deformation field near the tip of a crack in a soft incompressible plane stress fracture specimen loaded in mode I. Results are obtained for the case of a neo-Hookean solid (ideal rubber) and a hyperelastic solid with exponentially hardening behavior. In contrast to the predictions of linear elastic fracture mechanics (LEFM), the near tip stress fields are dominated by the opening stress which shows a 1/R singularity for the neo-Hookean material and a -1/(R ln R) singularity for the exponential hardening solid. We found very similar qualitative behavior in the near tip stress fields despite the very large difference in strain hardening behavior of the two material models. Our result shows that the near tip opening stress is controlled by the far field energy release rate for large applied loads. PMID:19053624
Intergranular Strain Evolution near Fatigue Crack Tips in Polycrystalline Metals
Zheng, Lili; Gao, Yanfei; Lee, Sooyeol; Barabash, Rozaliya; Lee, Jinhaeng; Liaw, Peter K
2011-01-01
The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.
The crack problem for a half plane stiffened by elastic cover plates
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1981-01-01
An elastic half plane containing a crack and stiffened by a cover plate is discussed. The asymptotic nature of the stress state in the half plane around an end point of the stiffener to determine the likely orientation of a possible fracture initiation and growth was studied. The problem is formulated for an arbitrary oriented radial crack in a system of singular integral equations. For an internal crack and for an edge crack, the problem is solved and the stress intensity factors at the crack tips and the interface stress are calculated. A cracked half plane with two symmetrically located cover plates is also considered. It is concluded that the case of two stiffeners appears to be more severe than that of a single stiffener.
A half plane and a strip with an arbitrarily located crack
NASA Technical Reports Server (NTRS)
Erdogan, F.; Arin, K.
1973-01-01
A technique is presented for dealing with the problem of an elastic domain containing an arbitrarily oriented internal crack. The problem is formulated as a system of integral equations for a fictitious layer of body forces imbedded in the plane along a closed smooth curve encircling the original domain. The problems of a half plane with a crack in the neighborhood of its free boundary and of an infinite strip containing a symmetrically located internal crack with an arbitrary orientation are considered as examples. In each case the stress intensity factors are computed and are given as functions of the crack angle.
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).
Panontin, T.L.; Sheppard, S.D.
1997-12-01
Large-strain, 3-D finite element analyses with incremental plasticity were performed for a variety of crack geometries to study local crack-tip stress-strain fields and associated global fracture parameters under conditions of large-scale yielding. The geometries analyzed include thin, single-edge crack tension, single-edge crack bending, and center-crack tension fracture specimens with varying crack depth (a/W) ratios. Two materials were investigated: a high-hardening, low-strength steel and a moderate-hardening, high-strength steel. Mesh refinement studies were performed to ensure convergence of the finite element predictions. The studies examine the effects of in-plane crack-tip element size, initial crack-tip radius size, and number of through-thickness layers on predicted distributions of crack-tip stress and plastic strain and predicted values of the J-integral and CTOD. In addition, the finite element predictions of specimen behavior were verified experimentally by direct measurements, namely load displacement, load longitudinal strain, and load CTOS, made during and following testing of the fracture specimens. Representative results of the finite element analyses are presented and compared to previously published data where pertinent. Results from the mesh refinement studies and the verification testing are shown. Predicted trends among the specimens and materials in local distributions of crack-tip plastic strain, triaxiality, and opening stress as well as in global parameters, J-integral and m-factor, are discussed.
Strain-age cracking in Rene 41 alloy
NASA Technical Reports Server (NTRS)
Prager, M.; Thompson, E. G.
1969-01-01
Weldability test determines the effects of material and process variables on the occurrence of strain-age cracking, and demonstrates effective and practical means for its reduction. Studies consist of tensile, impact, and stress-rupture tests.
Characterization of oriented cracks with differential strain analysis
NASA Technical Reports Server (NTRS)
Siegfried, R.; Simmons, G.
1978-01-01
Linear strain of a rock sample as a function of hydrostatic pressure can be measured with a precision of 2 millionths. Such high-precision data for three orthogonal directions allow calculation of the distribution function for the porosity due to cracks' closing completely at a given pressure. Such data for at least six independent directions yield the zero-pressure strain tensor due to cracks' closing completely at a given pressure. The principal values and axes of this tensor distribution function provide information about the orientation of cracks as a function of closure pressure. The mathematical basis for the technique is developed, and the technique is illustrated with differential strain data for two samples, the Westerly (Rhode Island) granite and the Twin Sisters (Washington) dunite. Strain-tensor calculations reveal that each of these samples has a different type of anisotropic crack distribution.
Out-of-plane deviation of a mode I+III crack encountering a tougher obstacle
NASA Astrophysics Data System (ADS)
Leblond, Jean-Baptiste; Ponson, Laurent
2016-07-01
One possible explanation of out-of-plane deviations of cracks loaded in mode I+III was suggested by Gao and Rice in 1986. These authors noted that small in-plane undulations of the crack front, arising from fluctuations of the fracture toughness, should generate a small local mode-II component, causing the crack to depart from planarity. Their analysis is completed here by explicitly calculating the evolution in time of the out-of-plane deviation of a mode-I+III crack encountering a tougher obstacle. The calculation is based on (i) first-order formulae for the stress intensity factors of a crack slightly perturbed within and out of its plane; and (ii) a "double" propagation criterion combining a Griffith condition on the local energy-release rate and a Goldstein-Salganik condition on the local stress intensity factor of mode II. It is predicted that the crack must evolve toward a stationary state, wherein the orthogonal distance from the average fracture plane to the perturbed crack front is constant outside the obstacle and varies linearly across it. We hope that this theoretical prediction will encourage comparison with experiments, and propose a fracture test involving propagation of a mode-I+III crack through a 3D-printed specimen containing some designed obstacle. xml:lang="fr"
Mechanics of fatigue crack closure
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr. (Editor); Elber, Wolf (Editor)
1988-01-01
Papers are presented on plasticity induced crack closure, crack closure in fatigue crack growth, the dependence of crack closure on fatigue loading variables, and a procedure for standardizing crack closure levels. Also considered are a statistical approach to crack closure determination, the crack closure behavior of surface cracks under pure bending, closure measurements on short fatigue cracks, and crack closure under plane strain conditions. Other topics include fatigue crack closure behavior at high stress ratios, the use of acoustic waves for the characterization of closed fatigue cracks, and the influence of fatigue crack wake length and state of stress on crack closure.
The Stress-Strain Condition Estimation of Detail in Crack Tip by Integral Strain Gauges
NASA Astrophysics Data System (ADS)
Syzrantsev, V.; Syzrantseva, K.
2016-04-01
The paper considers the task of stress-strain condition calculation of experimental sample in fatigue crack tip on weld boundary at its cyclic deforming. For this task decision authors use the information obtained by original means of cyclic strains measurement: Integral Strain Gauges. The results of carried experimental researches are compared with data of stress-strain condition estimation of detail in crack tip calculated by Finish Element Method.
Numerical simulation of out-of-plane distortion fatigue crack growth in bridge girders
NASA Astrophysics Data System (ADS)
MIller, Paula A.
Aging of the United States infrastructure systems has resulted in the degradation of many operational bridge structures throughout the country. Structural deficiencies can result from material fatigue caused by cyclical loadings leading to localized structural damage. While fatigue crack growth is viewed as a serviceability problem, unstable crack growth can compromise the integrity of the structure. Multi-girder bridges designed with transverse cross bracing systems can be prone to distortion fatigue at unstiffened web gaps. Cracking is exhibited within this fatigue prone region from the application of cyclical multi-mode loadings. Focus of fatigue analysis has largely been directed at pure Mode I loading through the development of AASHTO fatigue classifications for crack initiation and the Paris Law for crack propagation. Numerical modeling approaches through the ABAQUS Extended Finite Element Method offers a unique avenue in which this detail can be assessed. Finite element simulations were developed to first evaluate the applicability of the Paris Law crack propagation under multi-mode loading against experimental data. Following the validation, fatigue crack growth in plate girders with various web gap sizes was assessed due to mixed-mode loadings. Modeling results showed enlargement of horizontal initial crack lengths within stiffer web gap regions arrested crack development. Crack directionality was also seen to change as initial crack lengths were increased. From this research it is hypothesized that deterioration of the transverse stiffener connection can be minimized by increasing the horizontal length of initial fatigue cracks. Enlargement of the crack plane away from regions of localized stress concentrations within the web gap may result in arrestment of the out-of-plane distortion induced cracking.
Near tip stress and strain fields for short elastic cracks
NASA Technical Reports Server (NTRS)
Soediono, A. H.; Kardomateas, G. A.; Carlson, R. L.
1994-01-01
Recent experimental fatigue crack growth studies have concluded an apparent anomalous behavior of short cracks. To investigate the reasons for this unexpected behavior, the present paper focuses on identifying the crack length circumstances under which the requirements for a single parameter (K(sub I) or delta K(sub I) if cyclic loading is considered) characterization are violated. Furthermore, an additional quantity, the T stress, as introduced by Rice, and the related biaxiality ratio, B, are calculated for several crack lengths and two configurations, the single-edge-cracked and the centrally-cracked specimen. It is postulated that a two-parameter characterization by K and T (or B) is needed for the adequate description of the stress and strain field around a short crack. To further verify the validity of this postulate, the influence of the third term of the Williams series on the stress, strain and displacement fields around the crack tip and in particular on the B parameter is also examined. It is found that the biaxiality ratio would be more negative if the third term effects are included in both geometries. The study is conducted using the finite element method with linearly elastic material and isoparametric elements and axial (mode I) loading. Moreover, it is clearly shown that it is not proper to postulate the crack size limits for 'short crack' behavior as a normalized ratio with the specimen width, a/w; it should instead be stated as an absolute, or normalized with respect to a small characteristic dimension such as the grain size. Finally, implications regarding the prediction of cyclic (fatigue) growth of short cracks are discussed.
Growth behavior of surface cracks in the circumferential plane of solid and hollow cylinders
NASA Technical Reports Server (NTRS)
Forman, R. G.; Shivakumar, V.
1986-01-01
Experiments were conducted to study the growth behavior of surface fatigue cracks in the circumferential plane of solid and hollow cylinders. In the solid cylinders, the fatigue cracks were found to have a circular arc crack front with specific upper and lower limits to the arc radius. In the hollow cylinders, the fatigue cracks were found to agree accurately with the shape of a transformed semiellipse. A modification to the usual nondimensionalization expression used for surface flaws in flat plates was found to give correct trends for the hollow cylinder problem.
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.
Lee, S.Y.; Huang, E.-W.; Wu, W.; Liaw, P.K.; Paradowska, A.M.
2013-05-15
In-situ neutron diffraction was employed to directly measure the crystallographic-orientation-dependent (i.e. hkl) internal strains as a function of distance from the crack tip on the pre-cracked Hastelloy C-2000 compact-tension specimen. Both in-plane (IP) and through-thickness (TT) strain evolutions for various grain orientations were examined during tensile overloading and compressive underloading cycles. After overloading, underloading and their combination loadings were applied and unloaded, the significantly different (hkl) residual strain profiles were obtained in the vicinity of the crack tip. The load responses of the (200) grain orientation in both the IP and TT directions were more significant than those of any other orientations. It is suggested that the different orientation-dependent strain distributions around the crack tip are caused by the combined effects of elastic and plastic anisotropy of each (hkl) reflection upon loading and the subsequent development of residual stresses generated near the crack tip during unloading as a result of the plastic deformation. - Highlights: ► (hkl) strains are examined in situ using neutron diffraction. ► Distinct strain responses are developed around the crack tip under loading. ► The strain response of the (200) grain orientation is more significant. ► Possible mechanisms for the orientation-dependent strain responses are provided.
Dynamic crack propagation in a 2D elastic body: The out-of-plane case
NASA Astrophysics Data System (ADS)
Nicaise, Serge; Sandig, Anna-Margarete
2007-05-01
Already in 1920 Griffith has formulated an energy balance criterion for quasistatic crack propagation in brittle elastic materials. Nowadays, a generalized energy balance law is used in mechanics [F. Erdogan, Crack propagation theories, in: H. Liebowitz (Ed.), Fracture, vol. 2, Academic Press, New York, 1968, pp. 498-586; L.B. Freund, Dynamic Fracture Mechanics, Cambridge Univ. Press, Cambridge, 1990; D. Gross, Bruchmechanik, Springer-Verlag, Berlin, 1996] in order to predict how a running crack will grow. We discuss this situation in a rigorous mathematical way for the out-of-plane state. This model is described by two coupled equations in the reference configuration: a two-dimensional scalar wave equation for the displacement fields in a cracked bounded domain and an ordinary differential equation for the crack position derived from the energy balance law. We handle both equations separately, assuming at first that the crack position is known. Then the weak and strong solvability of the wave equation will be studied and the crack tip singularities will be derived under the assumption that the crack is straight and moves tangentially. Using the energy balance law and the crack tip behavior of the displacement fields we finally arrive at an ordinary differential equation for the motion of the crack tip.
The Evolution of Plane Wakes Subjected to Irrotational Strains
NASA Technical Reports Server (NTRS)
Rogers, M. R.; Rai, Man Mohan (Technical Monitor)
1995-01-01
Three 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 26 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, Re, of about 2000. Three different plane strains (of the same magnitude) are imposed. In the first two simulations the strain is in a plane normal to the streamwise wake direction (the two cases having strain of opposite sign); in the third the wake is compressed in the streamwise direction and stretched in the inhomogeneous cross-stream direction. The two flows that are stretched in the cross-stream direction experience an exponential increase of Re; flow visualization indicates many small-scale vortices with little or no organized large-scale structure. In the flow that is compressed in the cross-stream direction Re decays exponentially and the layer appears to be relaminarizing. The evolution of several turbulence statistics in each of these flows is examined.
Barker, D.B.; Chona, R.; Fourney, W.L.; Irwin, G.R.
1988-01-01
This report summarizes the results from a Round Robin Program that was conducted during 1983-1985 to evaluate a proposed ASTM Test Method for Crack Arrest Fracture Toughness of Ferritic Materials. The Round Robin attracted a total of twenty-seven participants from the United States, Canada, Europe and Japan, each of whom agreed to test three specimens of A514 bridge steel, three specimens of A588 bridge steel, and six specimens of A533 Grade B Class 1 reactor pressure vessel steel. Twenty-one participants completed their testing and forwarded test results for inclusion and discussion in this report. Modifications to the proposed test method that are called for in the light of the experience gained from the Round Robin are also discussed. The test method has been revised and is currently in the process of being considered by ASTM Committee E-24 on Fracture Testing as a Proposed Standard Test Method. 20 refs., 44 figs., 6 tabs.
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
Real-time measurement system for in-plane displacement and strain based on vision
NASA Astrophysics Data System (ADS)
Luo, Tao; Jin, Yi; Zhu, Ye; Zhai, Chao
2013-08-01
In this paper, combining optical measurement with conventional material testing machine, a real-time in-plane displacement and strain measurement system is built, which is applied to the material testing machine. This system can realize displacement and strain measurement of a large deformation sample moreover it can observe the sample crack on line. The change of displacement field is obtained through the change of center coordinate of each point of a grid lattice in the surface of the testing sample, according to two-dimensional sort coding for the grid in the traditional automated grid method, in this paper, an improved one-dimensional code method is adopted which make calculating speed much faster and the algorithm more adaptable. The measurement of the stability and precision of this system are made using the calibration board whose position precision is about 1.5 micron. The results show that the short-time stability of this system is about 0.5micron. At last, this system is used for strain measurement in a sample tension test, and the result shows that the system can acquire in-plane displacement and strain measurement results accurately and real-time, the velocity of image processing can reach 10 frame per second; or it can observe sample crack on line and storage the test process, the max velocity of observation and storage is 100 frame per second.
Ultrafast vascular strain compounding using plane wave transmission.
Hansen, H H G; Saris, A E C M; Vaka, N R; Nillesen, M M; de Korte, C L
2014-03-01
Deformations of the atherosclerotic vascular wall induced by the pulsating blood can be estimated using ultrasound strain imaging. Because these deformations indirectly provide information on mechanical plaque composition, strain imaging is a promising technique for differentiating between stable and vulnerable atherosclerotic plaques. This paper first explains 1-D radial strain estimation as applied intravascularly in coronary arteries. Next, recent methods for noninvasive vascular strain estimation in a transverse imaging plane are discussed. Finally, a compounding technique that our group recently developed is explained. This technique combines motion estimates of subsequently acquired focused ultrasound images obtained at various insonification angles. However, because the artery moves and deforms during the multi-angle acquisition, errors are introduced when compounding. Recent advances in computational power have enabled plane wave ultrasound acquisition, which allows 100 times faster image acquisition and thus might resolve the motion artifacts. In this paper the performance of strain imaging using plane wave compounding is investigated using simulations of an artery with a vulnerable plaque and experimental data of a two-layered vessel phantom. The results show that plane wave compounding outperforms 0° focused strain imaging. For the simulations, the root mean squared error reduced by 66% and 50% for radial and circumferential strain, respectively. For the experiments, the elastographic signal-to-noise and contrast-to-noise ratio (SNR(e) and CNR(e)) increased with 2.1 dB and 3.7 dB radially, and 5.6 dB and 16.2dB circumferentially. Because of the high frame rate, the plane wave compounding technique can even be further optimized and extended to 3D in future. PMID:24484646
The plane strain tests in the PROMETRA program
NASA Astrophysics Data System (ADS)
Cazalis, B.; Desquines, J.; Carassou, S.; Le Jolu, T.; Bernaudat, C.
2016-04-01
A fuel cladding mechanical test, performed under conditions of plane strain deformation in the transverse direction of tube axis, was originally developed at Pennsylvania State University. It was decided to implement this original test within the PROMETRA program using the same experimental procedure and its optimization for a ring mechanical testing on plane strain conditions (PST tests) in hot cells laboratory. This paper presents a detailed description and an interpretation of the Plane Strain Tensile (PST) tests performed in the framework of the PROMETRA program on fresh and irradiated claddings. At first, the context of the PST tests is situated and the specificities of these tests implemented at CEA are justified. Indeed, a significant adjustment of the original experimental procedure is carried out in order to test the irradiated fuel cladding in the best possible conditions. Then, the tests results on fresh Zircaloy-4 and on irradiated Zircaloy-4, M5™ and ZIRLO® specimens are gathered. The main analyses in support of these tests, such as metallographies, fractographic examinations and finite element simulations are detailed. Finally, a synthesis of the interpretation of the tests is proposed. The PST test seems only representative of plane strain fracture conditions when the test material is very ductile (fresh or high temperature or low hydride material like M5TM). However, it provides a relevant representation of the RIA rupture initiation which is observed in irradiated cladding resulting from hydride rim damage due to the strong irradiation of a fuel rod.
Crack-free AlGaN for solar-blind focal plane arrays through reduced area epitaxy
NASA Astrophysics Data System (ADS)
Cicek, E.; McClintock, R.; Vashaei, Z.; Zhang, Y.; Gautier, S.; Cho, C. Y.; Razeghi, M.
2013-02-01
We report on crack reduction for solar-blind ultraviolet detectors via the use of a reduced area epitaxy (RAE) method to regrow on patterned AlN templates. With the RAE method, a pre-deposited AlN template is patterned into isolated mesas in order to reduce the formation of cracks in the subsequently grown high Al-content AlxGa1-xN structure. By restricting the lateral dimensions of the epitaxial growth area, the biaxial strain is relaxed by the edges of the patterned squares, which resulted in ˜97% of the pixels being crack-free. After successful implementation of RAE method, we studied the optical characteristics, the external quantum efficiency, and responsivity of average pixel-sized detectors of the patterned sample increased from 38% and 86.2 mA/W to 57% and 129.4 mA/W, respectively, as the reverse bias is increased from 0 V to 5 V. Finally, we discussed the possibility of extending this approach for focal plane array, where crack-free large area material is necessary for high quality imaging.
NASA Astrophysics Data System (ADS)
Nibur, Kevin A.; Somerday, Brian P.; Marchi, Chris San; Foulk, James W.; Dadfarnia, Mohsen; Sofronis, Petros
2013-01-01
Threshold stress intensity factors were measured in high-pressure hydrogen gas for a variety of low alloy ferritic steels using both constant crack opening displacement and rising crack opening displacement procedures. Thresholds for crack extension under rising displacement, K THi, for crack extension under constant displacement, K_{{THi}}^{*} , and for crack arrest under constant displacement K THa, were identified. These values were not found to be equivalent, i.e. K THi < K THa < K_{{THi}}^{*} . The hydrogen assisted fracture mechanism was determined to be strain controlled for all of the alloys in this study, and the micromechanics of strain controlled fracture are used to explain the observed disparities between the different threshold measurements. K THa and K THi differ because the strain singularity of a stationary crack is stronger than that of a propagating crack; K THa must be larger than K THi to achieve equivalent crack tip strain at the same distance from the crack tip. Hydrogen interacts with deformation mechanisms, enhancing strain localization and consequently altering both the nucleation and growth stages of strain controlled fracture mechanisms. The timing of load application and hydrogen exposure, i.e., sequential for constant displacement tests and concurrent for rising displacement tests, leads to differences in the strain history relative to the environmental exposure history and promotes the disparity between K_{{THi}}^{*} and K THi. K THi is the only conservative measurement of fracture threshold among the methods presented here.
The inspection of crack initiation in mid-plane by ultrasonic method
NASA Astrophysics Data System (ADS)
Liu, Quanliang; Jiang, Yuejin; Ge, Sen; Guo, Wanlin
2010-03-01
Ultra-sonic is one of the major methods to inspect and locate the damage or flaws of materials in the components or structures in engineering1. The technique to inspect the crack initiation in mid-plane by ultrasonic in real time is presented and developed upon the requirement of detecting the initiation of cracks for thick compact tension specimen (CTS) to set up the I-II mixed mode fracture criterion. The paper is concerned with the application of an ultra-sonic scheme to detect initiation or growth of through-thickness crack at mid-plane from the surface during the loading. The technique in relation to the inspection of crack initiation in mid-plane by ultra-sonic is described in detail. The principles of the technique, and the equipment required to facilitate it are reviewed. The verification of the technique which is supported by a specific example of a CTS inspection performed on an I-II mixed mode fracture test shows that the method is valid and the technique can be capable of detecting delaminations, disbonds and lack-of-adhesion in a wide diversity of coated and uncoated materials. It is also capable of assessing the quality of composites.
The inspection of crack initiation in mid-plane by ultrasonic method
NASA Astrophysics Data System (ADS)
Liu, Quanliang; Jiang, Yuejin; Ge, Sen; Guo, Wanlin
2009-12-01
Ultra-sonic is one of the major methods to inspect and locate the damage or flaws of materials in the components or structures in engineering1. The technique to inspect the crack initiation in mid-plane by ultrasonic in real time is presented and developed upon the requirement of detecting the initiation of cracks for thick compact tension specimen (CTS) to set up the I-II mixed mode fracture criterion. The paper is concerned with the application of an ultra-sonic scheme to detect initiation or growth of through-thickness crack at mid-plane from the surface during the loading. The technique in relation to the inspection of crack initiation in mid-plane by ultra-sonic is described in detail. The principles of the technique, and the equipment required to facilitate it are reviewed. The verification of the technique which is supported by a specific example of a CTS inspection performed on an I-II mixed mode fracture test shows that the method is valid and the technique can be capable of detecting delaminations, disbonds and lack-of-adhesion in a wide diversity of coated and uncoated materials. It is also capable of assessing the quality of composites.
NASA Astrophysics Data System (ADS)
Jacques, Patrick; Lefebvre, Florence; Lemaignan, Clément
1999-01-01
For a better understanding of the initiation step of iodine induced stress corrosion cracking (SCC) in Zr alloys, responsible for pellet-cladding interaction (PCI) fuel rod failures, an analytical study has been undertaken, the aim of which being focused on the respective roles of local chemistry and stress/strain state on the crack nucleation. This second part is mostly related to the local stress induced by strain incompatibilities between grains. Using EBSP (electron back-scattering pattern) to analyze the crystallographic orientation of all the grains of the samples tested in SCC, it was possible to conclude that the major parameter controlling the nucleation of the intergranular cracks is not related to grain to grain strain incompatibilities, but to the orientation of the grain boundary planes with respect to the tensile stress.
Luo, P.F.; Wang, J.S.; Chao, Y.J.; Sutton, M.A.
1996-12-31
The stereo vision is used to study the fracture behavior in the compact tension (CT) specimen made from 304L stainless steel. During crack tip blunting, initiation, and growth in the CT specimen, both in-plane and out-of-plane displacement fields near the crack tip are measured by the stereo vision. Based on the plane stress assumption and the deformation theory of plasticity, the J integral is evaluated along several rectangular paths surrounding the crack tip by using the measured in-plane displacement field. Prior to crack growth, the J integral is path independent. For crack extension up to {Delta}a {approx} 3 mm, the near field J integral values are 6% to 10% lower than far field J integral values. For the crack extension of {Delta}a {approx} 4 mm, the J integral lost path independence. The far field J integral values are in good agreement with results obtained from Merkle-Corten`s formula. Both J-{Delta}a and CTOA-{Delta}a are obtained by computing the J integral value and crack tip opening angle (CTOA) at each {Delta}a. Results indicate that CTOA reached a nearly constant value at a crack extension of {Delta}a = 3 mm with a leveled resistance curve thereafter. Also, the J integral value is determined by the maximum transverse diameter of the shadow spots, which are generated by using the out-of-plane displacement field. Results indicate that for crack extension up to 0.25 mm, the J integral values evaluated by using the out-of- plane displacement are close to those obtained by using in-plane displacements and Merkle-Corten`s formula.
The influence of strain rate and hydrogen on the plane-strain ductility of Zircaloy cladding
Link, T.M.; Motta, A.T.; Koss, D.A.
1998-03-01
The authors studied the ductility of unirradiated Zircaloy-4 cladding under loading conditions prototypical of those found in reactivity-initiated accidents (RIA), i.e.: near plane-strain deformation in the hoop direction (transverse to the cladding axis) at room temperature and 300 C and high strain rates. To conduct these studies, they developed a specimen configuration in which near plane-strain deformation is achieved in the gage section, and a testing methodology that allows one to determine both the limit strain at the onset of localized necking and the fracture strain. The experiments indicate that there is little effect of strain rate (10{sup {minus}3} to 10{sup 2} s{sup {minus}1}) on the ductility of unhydrided Zircaloy tubing deformed under near plane-strain conditions at either room temperature or 300 C. Preliminary experiments on cladding containing 190 ppm hydrogen show only a small loss of fracture strain but no clear effect on limit strain. The experiments also indicate that there is a significant loss of Zircaloy ductility when surface flaws are present in the form of thickness imperfections.
Transient response of a single-edge crack in an elastic half-plane
Chen, E.P.
1980-01-01
The elasto-dynamic response of a single-edge crack in a semi-infinite elastic medium is considered in this study. The crack is assumed to appear suddenly in an elastic half-plane that is being stretched by a remote stress field. Near the crack, the interactions between the wave emanating from the tip and those reflected from the free edge take place. This investigation focuses its attention on the determination of the effect of this interaction on the stress intensity factor. Laplace and Fourier transforms are used to reduce the solution to a pair of dual integral equations. A numerical Laplace inversion procedure is used to obtain the time dependence of the solution. Numerical results on the dynamic stress intensity factor are obtained and are presented in a graphical form.
Crack Growth Mechanisms under Anti-Plane Shear in Composite Laminates
NASA Astrophysics Data System (ADS)
Horner, Allison Lynne
The research conducted for this dissertation focuses on determining the mechanisms associated with crack growth in polymer matrix composite laminates subjected to anti-plane shear (mode III) loading. For mode III split-beam test methods were proposed, and initial evaluations were conducted. A single test method was selected for further evaluation. Using this test method, it was determined that the apparent mode III delamination toughness, GIIIc , depended on geometry, which indicated a true material property was not being measured. Transverse sectioning and optical microscopy revealed an array of transverse matrix cracks, or echelon cracks, oriented at approximately 45° and intersecting the plane of the delamination. Subsequent investigations found the echelon array formed prior to the onset of planar delamination advance and that growth of the planar delamination is always coupled to echelon array formation in these specimens. The evolution of the fracture surfaces formed by the echelon array and planar delamination were studied, and it was found that the development was similar to crack growth in homogenous materials subjected to mode III or mixed mode I-III loading, although the composite laminate architecture constrained the fracture surface development differently than homogenous materials. It was also found that, for split-beam specimens such as those used herein, applying an anti-plane shear load results in twisting of the specimen's uncracked region which gives rise to a mixed-mode I-III load condition. This twisting has been related to the apparent mode III toughness as well as the orientation of the transverse matrix cracks. A finite element model was then developed to study the mechanisms of initial echelon array formation. From this, it is shown that an echelon array will develop, but will become self-limiting prior to the onset of planar delamination growth.
Shear Band Formation in Plane Strain Experiments of Sand
NASA Technical Reports Server (NTRS)
Alshibli, Khalid A.; Sture, Stein
2000-01-01
A series of biaxial (plane strain) experiments were conducted on three sands under low (15 kPa) and high (100 kPa) confining pressure conditions to investigate the effects of specimen density, confining pressure, and sand grain size and shape on the constitutive and stability behavior of granular materials. The three sands used in the experiments were fine-, medium-, and coarse-grained uniform silica sands with rounded, subangular, and angular grains, respectively. Specimen deformation was readily monitored and analyzed with the help of a grid pattern imprinted on the latex membrane. The overall stress-strain behavior is strongly dependent on the specimen density, confining pressure, sand grain texture, and the resulting failure mode(s). That became evident in different degrees of softening responses at various axial strains. The relationship between the constitutive behavior and the specimens' modes of instability is presented. The failure in all specimens was characterized by two distinct and opposite shear bands. It was found that the measured dilatancy angles increase as the sand grains' angularities and sizes increase. The measured shear band inclination angles are also presented and compared with classical Coulomb and Roscoe solutions.
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.
Strained layer superlattice focal plane array having a planar structure
Kim, Jin K; Carroll, Malcolm S; Gin, Aaron; Marsh, Phillip F; Young, Erik W; Cich, Michael J
2012-10-23
An infrared focal plane array (FPA) is disclosed which utilizes a strained-layer superlattice (SLS) formed of alternating layers of InAs and In.sub.xGa.sub.1-xSb with 0.ltoreq.x.ltoreq.0.5 epitaxially grown on a GaSb substrate. The FPA avoids the use of a mesa structure to isolate each photodetector element and instead uses impurity-doped regions formed in or about each photodetector for electrical isolation. This results in a substantially-planar structure in which the SLS is unbroken across the entire width of a 2-D array of the photodetector elements which are capped with an epitaxially-grown passivation layer to reduce or eliminate surface recombination. The FPA has applications for use in the wavelength range of 3-25 .mu.m.
To Crack or Not to Crack: Strain in High TemperatureSuperconductors
Godeke, Arno
2007-08-22
Round wire Bi 2212 is emerging as a viable successor ofNb3Sn in High Energy Physics and Nuclear Magnetic Resonance, to generatemagnetic fields that surpass the intrinsic limitations of Nb3Sn. Ratherbold claims are made on achievable magnetic fields in applications usingBi 2212, due to the materials' estimated critical magnetic field of 100 Tor higher. High transport currents in high magnetic fields, however, leadto large stress on, and resulting large strain in the superconductor. Theeffect of strain on the critical properties of Bi-2212 is far fromunderstood, and strain is, as with Nb3Sn, often treated as a secondaryparameter in the design of superconducting magnets. Reversibility of thestrain induced change of the critical surface of Nb3Sn, points to anelectronic origin of the observed strain dependence. Record breaking highfield magnets are enabled by virtue of such reversible behavior. Straineffects on the critical surface of Bi-2212, in contrast, are mainlyirreversible and suggest a non-electronic origin of the observed straindependence, which appears to be dominated by the formation of cracks inthe superconductor volumes. A review is presented of available results onthe effects of strain on the critical surface of Bi-2212, Bi-2223 andYBCO. It is shown how a generic behavior emerges for the (axial) straindependence of the critical current density, and how the irreversiblereduction of the critical current density is dominated by strain inducedcrack formation in the superconductor. From this generic model it becomesclear that magnets using high temperature superconductors will be strainlimited far before the intrinsic magnetic field limitations will beapproached, or possibly even before the magnetic field limitation ofNb3Sn can be surpassed. On a positive note, in a very promising recentresult from NIST on the axial strain dependence of the critical currentdensity in extremely well aligned YBCO, reversible behavior was observed.This result emphasizes the need
Stress-Strain Behaviour of a Micacious Sand in Plane Strain Condition
NASA Astrophysics Data System (ADS)
Yasin, S. J. M.; Tatsuoka, F.
Unusual failures of river banks and river training structures have been reported during construction and shortly after commissioning of several structures along Jamuna river in Bangladesh that raised widespread questions regarding the design principles and parameters used. The natural sand deposit along the Jamuna river contain relatively larger amount of mica than most other natural soils. Jamuna sand needs to be studied under wide range of loading conditions (such as triaxial, plane strain, simple shear etc.), drainage and density conditions (i.e. drained / undrained, dry / saturated, dense/loose state etc.) to reveal the extent of variation of its strength and deformation characteristics in order to facilitate understanding of the mechanism of past failures of structures and suggest rational design parameters. A series of plane strain compression tests were performed on Jamuna sand. It is observed that Jamuna sand is highly contractive under shear and more anisotropic than other non-mica sands.
Characterization of a soft elastomeric capacitive strain sensor for fatigue crack monitoring
NASA Astrophysics Data System (ADS)
Kong, Xiangxiong; Li, Jian; Laflamme, Simon; Bennett, Caroline; Matamoros, Adolfo
2015-04-01
Fatigue cracks have been one of the major factors for the deterioration of steel bridges. In order to maintain structural integrity, monitoring fatigue crack activities such as crack initiation and propagation is critical to prevent catastrophic failure of steel bridges due to the accumulation of fatigue damage. Measuring the strain change under cracking is an effective way of monitoring fatigue cracks. However, traditional strain sensors such as metal foil gauges are not able to capture crack development due to their small size, limited measurement range, and high failure rate under harsh environmental conditions. Recently, a newly developed soft elastomeric capacitive sensor has great promise to overcome these limitations. In this paper, crack detection capability of the capacitive sensor is demonstrated through Finite Element (FE) analysis. A nonlinear FE model of a standard ASTM compact tension specimen is created which is calibrated to experimental data to simulate its response under fatigue loading, with the goal to 1) depict the strain distribution of the specimen under the large area covered by the capacitive sensor due to cracking; 2) characterize the relationship between capacitance change and crack width; 3) quantify the minimum required resolution of data acquisition system for detecting the fatigue cracks. The minimum resolution serves as a basis for the development of a dedicated wireless data acquisition system for the capacitive strain sensor.
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.
NASA Astrophysics Data System (ADS)
Hu, Keqiang; Chen, Zengtao
2012-12-01
An opening crack in a magnetoelectroelastic strip under in-plane mechanical, electric, and magnetic impact loadings is considered for magneto-electrically impermeable and permeable crack surface boundary conditions. Laplace and Fourier transforms are applied to reduce the mixed boundary value problem of the crack to dual integral equations, which are expressed in terms of Fredholm integral equations of the second kind. The asymptotic fields near the crack tip are obtained in explicit form and the corresponding field intensity factors are defined. The crack curving phenomena are investigated by applying the criterion of maximum hoop stress intensity factors. Numerical results show that the hoop stress intensity factors are influenced by the electric and magnetic loadings and the geometric size ratios.
Seven-year-long crack detection monitoring by Brillouin-based fiber optic strain sensor
NASA Astrophysics Data System (ADS)
Imai, Michio
2015-03-01
As an optical fiber is able to act as a sensing medium, a Brillouin-based sensor provides continuous strain information along an optical fiber. The sensor has been used in a wide range of civil engineering applications because no other tool can satisfactorily detect discontinuity such as a crack. Cracking generates a local strain change on the embedded optical fiber, thus Brillouin optical correlation domain analysis (BOCDA), which offers a high spatial resolution by stimulated Brillouin scattering, is expected to detect a fine crack on concrete structures. The author installed the surface-mounted optical fiber on a concrete deck and periodically monitored strain distribution for seven years. This paper demonstrates how a BOCDA-based strain sensor can be employed to monitor cracks in a concrete surface. Additionally, focusing on another advantage of the sensor, the natural frequency of the deck is successfully measured by dynamic strain history.
NASA Astrophysics Data System (ADS)
Zhao, Yanlin; Zhang, Lianyang; Wang, Weijun; Pu, Chengzhi; Wan, Wen; Tang, Jingzhou
2016-07-01
This paper investigates the cracking and stress-strain behavior, especially the local strain concentration near the flaw tips, of rock-like material containing two flaws. A series of uniaxial compression tests were carried out on rock-like specimens containing two flaws, with strain gauges mounted near the flaw tips to measure the local strain concentration under the uniaxial compressive loading. Four different types of cracks (wing cracks, anti-wing cracks, coplanar shear cracks and oblique shear cracks) and seven patterns of crack coalescences (T1 and T2; S1 and S2; and TS1, TS2 and TS3) are observed in the experiments. The type of crack coalescence is related to the geometry of the flaws. In general, the crack coalescence varies from the S-mode to the TS-mode and then to the T-mode with the increase of the rock bridge ligament angle. The stress-strain curves of the specimens containing two flaws are closely related to the crack development and coalescence process. The strain measurements indicate that the local tensile strain concentration below or above the pre-existing flaw tip causes wing or anti-wing cracks, while the local compressive strain concentration near the flaw tip is related to the shear crack. The measured local tensile strain shows a jump at the initiation of wing- and anti-wing cracks, reflecting the instant opening of the wing- and anti-wing crack propagating through the strain gauge. During the propagation of wing- and anti-wing cracks, the measured local tensile strain gradually increases with few jumps, implying that the opening deformation of wing- and anti-wing cracks occurs in a stable manner. The shear cracks initiate followed by a large and abrupt compressive strain jump and then quickly propagate in an unstable manner resulting in the failure of specimens.
Ulaganathan, Jaganathan Newman, Roger C.
2014-06-01
The dynamic strain rate ahead of a crack tip formed during stress corrosion cracking (SCC) under a static load is assumed to arise from the crack propagation. The strain surrounding the crack tip would be redistributed as the crack grows, thereby having the effect of dynamic strain. Recently, several studies have shown cold work to cause accelerated crack growth rates during SCC, and the slip-dissolution mechanism has been widely applied to account for this via a supposedly increased crack-tip strain rate in cold worked material. While these interpretations consider cold work as a homogeneous effect, dislocations are generated inhomogeneously within the microstructure during cold work. The presence of grain boundaries results in dislocation pile-ups that cause local strain concentrations. The local strains generated from cold working α-brass by tensile elongation were characterized using electron backscatter diffraction (EBSD). The role of these local strains in SCC was studied by measuring the strain distributions from the same regions of the sample before cold work, after cold work, and after SCC. Though, the cracks did not always initiate or propagate along boundaries with pre-existing local strains from the applied cold work, the local strains surrounding the cracked boundaries had contributions from both the crack propagation and the prior cold work. - Highlights: • Plastic strain localization has a complex relationship with SCC susceptibility. • Surface relief created by cold work creates its own granular strain localization. • Cold work promotes crack growth but several other factors are involved.
NASA Astrophysics Data System (ADS)
Bhadauria, S. S.; Pathak, K. K.; Hora, M. S.
2012-09-01
It is widely accepted that failure due to plastic deformation in metals greatly depends on the stress triaxiality factor (TF). This article investigates the variation of stress triaxiality along the yield locus of ductile materials. Von Mises yield criteria and triaxiality factor have been used to determine the critical limits of stress triaxiality for the materials under plane strain condition. A generalized mathematical model for triaxiality factor has been formulated and a constrained optimization has been carried out using genetic algorithm. Finite element analysis of a two dimensional square plate has been carried out to verify the results obtained by the mathematical model. It is found that the set of values of the first and the second principal stresses on the yield locus, which results in maximum stress triaxiality, can be used to determine the location at which crack initiation may occur. Thus, the results indicate that while designing a certain component, such combination of stresses which leads the stress triaxiality to its critical value, should be avoided.
Back-Face Strain for Monitoring Stable Crack Extension in Precracked Flexure Specimens
NASA Technical Reports Server (NTRS)
Salem, Jonathan A.; Ghosn, Louis J.
2010-01-01
Calibrations relating back-face strain to crack length in precracked flexure specimens were developed for different strain gage sizes. The functions were verified via experimental compliance measurements of notched and precracked ceramic beams. Good agreement between the functions and experiments occurred, and fracture toughness was calculated via several operational methods: maximum test load and optically measured precrack length; load at 2 percent crack extension and optical precrack length; maximum load and back-face strain crack length. All the methods gave vary comparable results. The initiation toughness, K(sub Ii) , was also estimated from the initial compliance and load.The results demonstrate that stability of precracked ceramics specimens tested in four-point flexure is a common occurrence, and that methods such as remotely-monitored load-point displacement are only adequate for detecting stable extension of relatively deep cracks.
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.
Castelluccio, Gustavo M.; McDowell, David L.
2015-09-16
Fatigue crack initiation in the high cycle fatigue regime is strongly influenced by microstructural features. Research efforts have usually focused on predicting fatigue resistance against crack incubation without considering the early fatigue crack growth after encountering the first grain boundary. However, a significant fraction of the variability of the total fatigue life can be attributed to growth of small cracks as they encounter the first few grain boundaries, rather than crack formation within the first grain. Our paper builds on the framework previously developed by the authors to assess microstructure-sensitive small fatigue crack formation and early growth under complex loading conditions. Moreover, the scheme employs finite element simulations that explicitly render grains and crystallographic directions along with simulation of microstructurally small fatigue crack growth from grain to grain. The methodology employs a crystal plasticity algorithm in ABAQUS that was previously calibrated to study fatigue crack initiation in RR1000 Ni-base superalloy. Our work present simulations with non-zero applied mean strains and geometric discontinuities that were not previously considered for calibration. Results exhibit trends similar to those found in experiments for multiple metallic materials, conveying a consistent physical description of fatigue damage phenomena.
Castelluccio, Gustavo M.; McDowell, David L.
2015-09-16
Fatigue crack initiation in the high cycle fatigue regime is strongly influenced by microstructural features. Research efforts have usually focused on predicting fatigue resistance against crack incubation without considering the early fatigue crack growth after encountering the first grain boundary. However, a significant fraction of the variability of the total fatigue life can be attributed to growth of small cracks as they encounter the first few grain boundaries, rather than crack formation within the first grain. Our paper builds on the framework previously developed by the authors to assess microstructure-sensitive small fatigue crack formation and early growth under complex loadingmore » conditions. Moreover, the scheme employs finite element simulations that explicitly render grains and crystallographic directions along with simulation of microstructurally small fatigue crack growth from grain to grain. The methodology employs a crystal plasticity algorithm in ABAQUS that was previously calibrated to study fatigue crack initiation in RR1000 Ni-base superalloy. Our work present simulations with non-zero applied mean strains and geometric discontinuities that were not previously considered for calibration. Results exhibit trends similar to those found in experiments for multiple metallic materials, conveying a consistent physical description of fatigue damage phenomena.« less
In situ SEM observation of microscale strain fields around a crack tip in polycrystalline molybdenum
NASA Astrophysics Data System (ADS)
Li, J. J.; Li, W. C.; Jin, Y. J.; Wang, L. F.; Zhao, C. W.; Xing, Y. M.; Lang, F. C.; Yan, L.; Yang, S. T.
2016-06-01
In situ scanning electron microscopy was employed to investigate the crack initiation and propagation in polycrystalline molybdenum under uniaxial tensile load at room temperature. The microscale grid pattern was fabricated using the sputtering deposition technology on the specimen surface covered with a fine square mesh copper grid. The microscale strain fields around the crack tip were measured by geometric phase analysis technique and compared with the theoretical solutions based on the linear elastic fracture mechanics theory. The results showed that as the displacement increases, the crack propagated mainly perpendicular to the tensile direction during the fracture process of molybdenum. The normal strain ɛ xx and shear strain ɛ xy are relatively small, and the normal strain ɛ yy holds a dominant position in the deformation fields and plays a key role in the whole fracture process of molybdenum. With the increase in displacement, the ɛ yy increases rapidly and the two lobes grow significantly but maintain the same shape and orientation. The experimental ɛ yy is in agreement with the theoretical solution. Along the x-axis in front of the crack tip, there is minor discrepancy between the experimental ɛ yy and theoretical ɛ yy within 25 μm from the crack tip, but the agreement between them is very good far from the crack tip (>25 μm).
NASA Astrophysics Data System (ADS)
Thongnum, Anusit; Pinsook, Udomsilp
2015-03-01
Anisotropic transport properties of a two-dimensional electron gas in nonpolar m-plane AlN/GaN heterostructures with the interface roughness coupled anisotropic in-plane strain scattering were investigated theoretically using a path-integral framework. The scattering potential was composed of the interface roughness and the effective field from the electron charge and the net piezoelectric polarization. We showed that the anisotropic biaxial strains generate only the net piezoelectric polarization along the [0 0 0 1]-direction and cause anisotropy in electron mobility with a magnitude lower than the ≤ft[11\\bar{2}0\\right] -direction. We also showed that the anisotropy in electron mobility reduced with increasing electron density. Moreover, the anisotropic electron mobility disappeared when the anisotropic in-plane strain scattering was removed, and the relation for pure interface roughness scattering was reestablished. This formulation with existing roughness parameters gave a good description for the experimental results of polar c-plane AlN/GaN heterostructures.
Detection of Steel Fatigue Cracks with Strain Sensing Sheets Based on Large Area Electronics
Yao, Yao; Glisic, Branko
2015-01-01
Reliable early-stage damage detection requires continuous monitoring over large areas of structure, and with sensors of high spatial resolution. Technologies based on Large Area Electronics (LAE) can enable direct sensing and can be scaled to the level required for Structural Health Monitoring (SHM) of civil structures and infrastructure. Sensing sheets based on LAE contain dense arrangements of thin-film strain sensors, associated electronics and various control circuits deposited and integrated on a flexible polyimide substrate that can cover large areas of structures. This paper presents the development stage of a prototype strain sensing sheet based on LAE for crack detection and localization. Two types of sensing-sheet arrangements with size 6 × 6 inch (152 × 152 mm) were designed and manufactured, one with a very dense arrangement of sensors and the other with a less dense arrangement of sensors. The sensing sheets were bonded to steel plates, which had a notch on the boundary, so the fatigue cracks could be generated under cyclic loading. The sensors within the sensing sheet that were close to the notch tip successfully detected the initialization of fatigue crack and localized the damage on the plate. The sensors that were away from the crack successfully detected the propagation of fatigue cracks based on the time history of the measured strain. The results of the tests have validated the general principles of the proposed sensing sheets for crack detection and identified advantages and challenges of the two tested designs. PMID:25853407
Lee, S. Y.; Sun, Yinan; An, Ke; Choo, Hahn; Hubbard, Camden R; Liaw, Peter K
2010-01-01
Neutron diffraction was employed to investigate the crack-growth retardation phenomenon after a single tensile overload by mapping both one-dimensional and two-dimensional residual-strain distributions around the crack tip in a series of compact-tension specimens representing various crack-growth stages through an overload-induced retardation period. The results clearly show a large compressive residual-strain field near the crack tip immediately after the overload. As the fatigue crack propagates through the overload-induced plastic zone, the compressive residual strains are gradually relaxed, and a new compressive residual-strain field is developed around the propagating crack tip, illustrating that the subsequent fatigue-induced plastic zone grows out of the large plastic zone caused by the overloading. The relationship between the overload-induced plastic zone and subsequent fatigue-induced plastic zone, and its influence on the residual-strain distributions in the perturbed plastic zone are discussed.
T{sub {epsilon}}{sup *} integral under plane stress crack growth
Omori, Yoshika; Ma, Leong; Kobayashi, A.S.; Okada, Hiroshi; Atluri, S.N.
1997-12-01
The T{sub {epsilon}}{sup *} integral values associated with stable crack growth in A606 HSLA steel single-edge-notched (SEN) specimens were determined experimentally and numerically. The displacement fields obtained through Moire interferometry and elastic-plastic finite element analysis were used to evaluate T{sub {epsilon}}{sup *} associated with the moving crack tip. T{sub {epsilon}}{sup *} decreased with the reduction in the size of the integration contour, {Gamma}{sub {epsilon}}, and continually increased with stable crack growth in this specimen. The measured and computed crack-tip opening angle (CTOA), on the other hand, was a constant 15{degree} during stable crack growth after dropping from the measured and computed initial high values of 35 and 57{degree}, respectively.
Influence of pre-strain on fracture toughness and stable crack growth in low carbon steels
Miyata, Takashi; Tagawa, Tetsuya; Aihara, Syuji
1997-12-31
Experimental investigations demonstrate a significant effect of pre-strain on fracture toughness and stable crack growth resistance of a low carbon structural steel. Fracture toughness, Ji for the onset of stable ductile crack growth is decreased to one half with a 9% pre-strain due to cold rolling. The characteristic distance model for ductile crack initiation was applied to analyze parameters affecting the degradation of fracture resistance. The model predicts that value of Ji is given as a linear function of yield strength and ductility of the material. In order to confirm the theoretical prediction, notched round bar tensile tests were performed and ductility under a high triaxial stress state was measured. Critical plastic strain for micro-void coalescence is significantly decreased with increasing pre-strain. Degradation in Ji due to pre-strain can be well explained by the characteristic distance model. To clarify micro-mechanisms of degradation in ductility due to pre-strain, fracture process in notched round bar specimens was investigated emphasizing the role of micro-void nucleation and growth. Experimental observation indicates that the significant decrease of the critical strain due to pre-strain is attributed to the increase of void nucleation sites under a high triaxial stress state.
A semi-implicit finite strain shell algorithm using in-plane strains based on least-squares
NASA Astrophysics Data System (ADS)
Areias, P.; Rabczuk, T.; de Sá, J. César; Natal Jorge, R.
2015-04-01
The use of a semi-implicit algorithm at the constitutive level allows a robust and concise implementation of low-order effective shell elements. We perform a semi-implicit integration in the stress update algorithm for finite strain plasticity: rotation terms (highly nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the (in this case evolving) reference configuration and relative Green-Lagrange strains (quadratic) are used to account for change in the equilibrium configuration implicitly. We parametrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use a common configuration. A finite strain quadrilateral element with least-squares assumed in-plane shear strains (in curvilinear coordinates) and classical transverse shear assumed strains is introduced. It is an alternative to enhanced-assumed-strain (EAS) formulations and, contrary to this, produces an element satisfying ab-initio the Patch test. No additional degrees-of-freedom are present, contrasting with EAS. Least-squares fit allows the derivation of invariant finite strain elements which are both in-plane and out-of-plane shear-locking free and amenable to standardization in commercial codes. Two thickness parameters per node are adopted to reproduce the Poisson effect in bending. Metric components are fully deduced and exact linearization of the shell element is performed. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.
Texture development and hardening characteristics of steel sheets under plane-strain compression
Friedman, P.A.; Liao, K.C.; Pan, J.; Barlat, F.
1999-04-01
Crystallographic texture development and hardening characteristics of a hot-rolled, low-carbon steel sheet due to cold rolling were investigated by idealizing the cold rolling process as plane-strain compression. The starting anisotropy of the test material was characterized by examination of the grain structure by optical microscopy and the preferred crystal orientation distribution by x-ray diffraction. Various heat treatments were used in an effort to remove the initial deformation texture resulting from hot rolling. The plastic anisotropy of the starting material was investigated with tensile tests on samples with the tensile axis parallel, 45{degree}, and perpendicular to the rolling direction. The grain structure after plane-strain compression was studied by optical microscopy, and the new deformation texture was characterized by x-ray diffraction pole figures. These figures are compared with the theoretical pole figures produced from a Taylor-like polycrystal model based on a pencil-glide slip system. The uniaxial tensile stress-strain curve and the plane-strain, compressive stress-strain curve of the sheet were used to calibrate the material parameters in the model. The experimental pole figures were consistent with the findings in the theoretical study. The experimental and theoretical results suggest that the initial texture due to hot rolling was insignificant as compared with the texture induced by large strains under plane-strain compression.
Crack-tip strain field mapping and the toughness of metallic glasses.
Hufnagel, Todd C; Vempati, Uday K; Almer, Jonathan D
2013-01-01
We have used high-energy x-ray scattering to map the strain fields around crack tips in fracture specimens of a bulk metallic glass under load at room temperature and below. From the measured strain fields we can calculate the components of the stress tensor as a function of position and determine the size and shape of the plastic process zone around the crack tip. Specimens tested at room temperature develop substantial plastic zones and achieve high stress intensities ((K(If) = 76 MPa m(1/2)) prior to fracture. Specimens tested at cryogenic temperatures fail at reduced but still substantial stress intensities (K(If) = 39 MPa m(1/2)) and show only limited evidence of crack-tip plasticity. We propose that the difference in behavior is associated with changes in the flow stress and elastic constants, which influence the number density of shear bands in the plastic zone and thus the strain required to initiate fracture on an individual band. A secondary effect is a change in the triaxial state of stress around the crack tip due to the temperature dependence of Poisson's ratio. It is likely that this ability to map elastic strains on the microscale will be useful in other contexts, although interpreting shifts in the position of the scattering peaks in amorphous materials in terms of elastic strains must be done with caution. PMID:24386172
Crack-Tip Strain Field Mapping and the Toughness of Metallic Glasses
Hufnagel, Todd C.; Vempati, Uday K.; Almer, Jonathan D.
2013-01-01
We have used high-energy x-ray scattering to map the strain fields around crack tips in fracture specimens of a bulk metallic glass under load at room temperature and below. From the measured strain fields we can calculate the components of the stress tensor as a function of position and determine the size and shape of the plastic process zone around the crack tip. Specimens tested at room temperature develop substantial plastic zones and achieve high stress intensities () prior to fracture. Specimens tested at cryogenic temperatures fail at reduced but still substantial stress intensities () and show only limited evidence of crack-tip plasticity. We propose that the difference in behavior is associated with changes in the flow stress and elastic constants, which influence the number density of shear bands in the plastic zone and thus the strain required to initiate fracture on an individual band. A secondary effect is a change in the triaxial state of stress around the crack tip due to the temperature dependence of Poisson's ratio. It is likely that this ability to map elastic strains on the microscale will be useful in other contexts, although interpreting shifts in the position of the scattering peaks in amorphous materials in terms of elastic strains must be done with caution. PMID:24386172
Strain-mediated control of orbital ordering planes in heteroepitaxial lanthanum manganite thin films
NASA Astrophysics Data System (ADS)
Kim, Yong-Jin; Lee, Jin Hong; Koo, Tae Yeong; Yang, Chan-Ho
Strain engineering which controls the misfit strain of heteroepitaxial thin films leads to distinctive physical properties in contrast to the intrinsic properties of unstrained bulk materials Perovskite LaMnO3 (LMO) has attracted considerable attention due to strong coupling among the lattice, charge, spin and orbital degrees of freedom. Bulk LMO is known to be an A-type antiferromagnetic (TN~140 K) Mott insulator, and its orbital ordering plane is established due to cooperative Jahn-Teller distortion below ~750 K. Previous studies have focused on the orbital ordering planes of the bulk LMO but not researched on correlation between orbital planes and misfit stain. To figure out the strain dependence of orbital ordering planes, we have grown LMO thin films on four different substrates, i . e . , DyScO3(110), GaScO3(110), SrTiO3(001), and LSAT(001), using the pulsed laser deposition technique. The films have been characterized by atomic force microscopy and x-ray diffraction. We have performed resonant x-ray scattering to identify orbital ordering plane on each film. We have found that orbital ordering planes can be modulated depending on the misfit strain.
NASA Astrophysics Data System (ADS)
Adumitroaie, Adi
applications in the range of cryogenic temperatures. The process of matrix cracking under
Paul, S.C.; Pirskawetz, S.; Zijl, G.P.A.G. van; Schmidt, W.
2015-03-15
This paper presents the analysis of crack propagation in strain-hardening cement-based composite (SHCC) under tensile and flexural load by using acoustic emission (AE). AE is a non-destructive technique to monitor the development of structural damage due to external forces. The main objective of this research was to characterise the cracking behaviour in SHCC in direct tensile and flexural tests by using AE. A better understanding of the development of microcracks in SHCC will lead to a better understanding of pseudo strain-hardening behaviour of SHCC and its general performance. ARAMIS optical deformation analysis was also used in direct tensile tests to observe crack propagation in SHCC materials. For the direct tensile tests, SHCC specimens were prepared with polyvinyl alcohol (PVA) fibre with three different volume percentages (1%, 1.85% and 2.5%). For the flexural test beam specimens, only a fibre dosage of 1.85% was applied. It was found that the application of AE in SHCC can be a good option to analyse the crack growth in the specimens under increasing load, the location of the cracks and most importantly the identification of matrix cracking and fibre rupture or slippage.
NASA Astrophysics Data System (ADS)
Zhang, Siyuan; Cui, Ying; Griffiths, James T.; Fu, Wai Y.; Freysoldt, Christoph; Neugebauer, Jörg; Humphreys, Colin J.; Oliver, Rachel A.
2015-12-01
I nxG a1 -xN structures epitaxially grown on a -plane or m -plane GaN exhibit in-plane optical polarization. Linear elasticity theory treats the two planes equivalently and is hence unable to explain the experimentally observed higher degree of linear polarization for m -plane than a -plane I nxG a1 -xN . Using density functional theory, we study the response of I nxG a1 -xN random alloys to finite biaxial strains on both nonpolar planes. The calculated m -plane I nxG a1 -xN valence band splitting is larger than that of the a plane, due to a greater degree of structural relaxation in a -plane I nxG a1 -xN . We provide a parametrization of the valence band splitting of I nxG a1 -xN strained to a -plane and m -plane GaN for In compositions between 0 and 0.5, which agrees with experimental measurements and qualitatively explains the experimentally observed difference between a -plane and m -plane polarization.
Stress Corrosion Cracking Behavior of Interstitial Free Steel Via Slow Strain Rate Technique
NASA Astrophysics Data System (ADS)
Murkute, Pratik; Ramkumar, J.; Mondal, K.
2016-07-01
An interstitial free steel is subjected to slow strain rate tests to investigate the stress corrosion cracking (SCC) behavior at strain rates ranging from 10-4 to 10-6s-1 in air and 3.5 wt.% NaCl solution. The ratios of time to failure, failure strain, and ultimate tensile stress at different strain rates in air to that in corrosive were considered as SCC susceptibility. Serrated stress-strain curve observed at lowest strain rate is explained by the Portevin-Le Chatelier effect. Maximum susceptibility to SCC at lowest strain rate is attributed to the soluble γ-FeOOH in the rust analyzed by Fourier Transformed Infrared spectroscopy. Mechanism for SCC relates to the anodic dissolution forming the groove, where hydrogen embrittlement can set in and finally fracture happens due to triaxiality.
Tunable biaxial in-plane compressive strain in a Si nanomembrane transferred on a polyimide film
NASA Astrophysics Data System (ADS)
Kim, Munho; Mi, Hongyi; Cho, Minkyu; Seo, Jung-Hun; Zhou, Weidong; Gong, Shaoqin; Ma, Zhenqiang
2015-05-01
A method of creating tunable and programmable biaxial compressive strain in silicon nanomembranes (Si NMs) transferred onto a Kapton® HN polyimide film has been demonstrated. The programmable biaxial compressive strain (up to 0.54%) was generated utilizing a unique thermal property exhibited by the Kapton HN film, namely, it shrinks from its original size when exposed to elevated temperatures. The correlation between the strain and the annealing temperature was carefully investigated using Raman spectroscopy and high resolution X-ray diffraction. It was found that various amounts of compressive strains can be obtained by controlling the thermal annealing temperatures. In addition, a numerical model was used to evaluate the strain distribution in the Si NM. This technique provides a viable approach to forming in-plane compressive strain in NMs and offers a practical platform for further studies in strain engineering.
Tunable biaxial in-plane compressive strain in a Si nanomembrane transferred on a polyimide film
Kim, Munho; Mi, Hongyi; Cho, Minkyu; Seo, Jung-Hun; Ma, Zhenqiang; Zhou, Weidong; Gong, Shaoqin
2015-05-25
A method of creating tunable and programmable biaxial compressive strain in silicon nanomembranes (Si NMs) transferred onto a Kapton{sup ®} HN polyimide film has been demonstrated. The programmable biaxial compressive strain (up to 0.54%) was generated utilizing a unique thermal property exhibited by the Kapton HN film, namely, it shrinks from its original size when exposed to elevated temperatures. The correlation between the strain and the annealing temperature was carefully investigated using Raman spectroscopy and high resolution X-ray diffraction. It was found that various amounts of compressive strains can be obtained by controlling the thermal annealing temperatures. In addition, a numerical model was used to evaluate the strain distribution in the Si NM. This technique provides a viable approach to forming in-plane compressive strain in NMs and offers a practical platform for further studies in strain engineering.
NASA Astrophysics Data System (ADS)
Avitzur, Boaz
1993-04-01
There is a long-standing interest in developing a capability to predict the distribution of retained stresses in thick-walled pressure vessels after the removal of an internal pressure--post autofrettage. The key to such a prediction is in the capacity to compute the stress distribution in a vessel while under externally imposed stress sufficient enough to cause at least partial plastic deformation. A good approximation of the stress distribution was developed by Mises in his 1913 plane-stress solution. The fact that such vessels are not representative of the plane-stress condition not withstanding, Mises recognized that his solution was mathematically restricted to a limited range of vessels' wall ratios. More recently, Avitzur offered a solution similar to that of Mises, but for a plane-strain condition. Depending on the material's Poisson's factor, Avitzur's solution is also mathematically applicable for a limited range of vessels' wall ratios only. The wall ratio, beyond which Avitzur's solution in plane-strain is not applicable, is a few times larger than that which limits Mises' solution in plane-stress. This work introduces a modification to Avitzur's solution in plane-strain, which makes its applicability unlimited.
Cracking monitoring by FBG strain sensor in the small scale dam model
NASA Astrophysics Data System (ADS)
Ren, Liang; Li, Hongnan; Li, Dongsheng
2009-03-01
Accurate measurement of strain variation and effective prediction of failure within models has been a major objective for strain sensors in dam model tests. In this paper, a FBG strain sensor with enhanced strain sensitivity and packaged by two gripper tubes is presented and applied in the seismic tests of a small scale dam model. This paper discusses the principle of enhanced sensitivity of the FBG strain sensor. Calibration experiments were conducted to evaluate the sensor's strain transferring characteristics on plates of different material. This paper also investigates the applicability of the FBG strain sensors in seismic tests of a dam model by conducting a comparison between the test measurements of FBG sensors and analytical predictions, monitoring the failure progress and predicting the cracking inside the dam model. Results of the dam model tests prove that this FBG strain sensor has the advantages of small size, high precision and embedability, demonstrate promising potential in cracking and failure monitoring and in identification of the dam model.
... sound the drug makes as it heats up. Short-Term Effects Crack is a stimulant that is absorbed through ... quickly, after about 5 or 10 minutes. Other short-term effects include: higher heart rate, breathing rate, blood pressure , ...
Strain and hysteresis by stochastic matrix cracking in ceramic matrix composites
NASA Astrophysics Data System (ADS)
Ahn, B. K.; Curtin, W. A.
1997-02-01
A theory is presented to predict the stress/strain relations and unload/reload hysteresis behavior during the evolution of multiple matrix cracking in unidirectional fiber reinforced ceramic matrix composites (CMCs). The theory is based on the similarity between multiple matrix cracking and fiber fragmentation in a single fiber composite, and determines the crack and strain evolution as a function of the statistical distribution of initial flaws in the material, the interfacial sliding resistance τ, and the thermal residual stresses in the composite. The model properly includes matrix fragments of all lengths, from lengths smaller than the current slip length δ(σ) to larger than 2δ(σ), at applied stress σ, and accounts for their respective and differing contributions to the overall strain and hysteresis behavior of the composite. The procedure by which experimental stress/strain and hysteresis data can be interpreted to derive values for the interfacial shear stress, thermal stresses, and intrinsic matrix flaw distribution is discussed. The actual physical crack spacing needs only to be determined at one load level, such as post-fracture, which greatly simplifies the data acquisition and analysis. Several detailed examples are presented, and the results compared with a widely-used approach in which the crack spacing is assumed constant and equal to the average spacing obtained directly from experiment. The discrepancy between the previous and present theories is manifest in an incorrect estimate for the interfacial sliding, but only by approximately 10%. The effect of changing temperature, and hence residual stresses, without changing either matrix flaws or interfacial sliding resistance, is studied.
NASA Astrophysics Data System (ADS)
Ontiveros, Victor Luis
A critical challenge to the continued use of engineering structures as they are asked to perform longer than their design life is the prediction of an initiating crack and the prevention of damage, estimation of remaining useful life, schedule maintenance and to reduce costly downtimes and inspections. The research presented in this dissertation explores the cumulative plastic strain energy density and thermodynamic entropy generation up to crack initiation. Plastic strain energy density and thermodynamic entropy generation are evaluated to investigate whether they would be capable of providing a physical basis for fatigue life and structural risk and reliability assessments. Navy aircraft, specifically, the Orion P-3C, which represent an engineered structure currently being asked to perform past is design life, which are difficult and time consuming to inspect from carrier based operations and are currently evaluated using an empirically based damage index the, fatigue life expended, is used as an example in this investigation. A set of experimental results for aluminum alloy 7075-T651, used in airframe structures, are presented to determine the correlation between plastic strain energy dissipation and the thermodynamic entropy generation versus fatigue crack initiation over a wide range of fatigue loadings. Cumulative plastic strain energy and thermodynamic entropy generation measured from hysteresis energy and temperature rise proved to be valid physical indices for estimation of the probability of crack initiation. Crack initiation is considered as a major evidence of fatigue damage and structural integrity risk. A Bayesian estimation and validation approach is used to determine systematic errors in the developed models as well as other model uncertainties. Comparisons of the energy-based and entropy-based models are presented and benefits of using one over the other are discussed.
A numerical method for determining the strain rate intensity factor under plane strain conditions
NASA Astrophysics Data System (ADS)
Alexandrov, S.; Kuo, C.-Y.; Jeng, Y.-R.
2016-07-01
Using the classical model of rigid perfectly plastic solids, the strain rate intensity factor has been previously introduced as the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since then, many strain rate intensity factors have been determined by means of analytical and semi-analytical solutions. However, no attempt has been made to develop a numerical method for calculating the strain rate intensity factor. This paper presents such a method for planar flow. The method is based on the theory of characteristics. First, the strain rate intensity factor is derived in characteristic coordinates. Then, a standard numerical slip-line technique is supplemented with a procedure to calculate the strain rate intensity factor. The distribution of the strain rate intensity factor along the friction surface in compression of a layer between two parallel plates is determined. A high accuracy of this numerical solution for the strain rate intensity factor is confirmed by comparison with an analytic solution. It is shown that the distribution of the strain rate intensity factor is in general discontinuous.
Matsui, Hiroaki Tabata, Hitoshi; Hasuike, Noriyuki; Harima, Hiroshi
2014-09-21
In-plane anisotropic strains in A-plane layers on the electronic band structure of ZnO were investigated from the viewpoint of optical polarization anisotropy. Investigations utilizing k·p perturbation theory revealed that energy transitions and associated oscillation strengths were dependent on in-plane strains. The theoretical correlation between optical polarizations and in-plane strains was experimentally demonstrated using A-plane ZnO layers with different in-plane strains. Finally, optical polarization anisotropy and its implications for in-plane optical properties are discussed in relation to the energy shift between two orthogonal directions. Higher polarization rotations were obtained in an A-plane ZnO layer with in-plane biaxially compressive strains as compared to strain-free ZnO. This study provides detailed information concerning the role played by in-plane strains in optically polarized applications based on nonpolar ZnO in the ultra-violet region.
Hall, M.M. Jr.; Symons, D.M.
1996-05-01
A strain energy density-distance criterion was previously developed and used to correlate rising-load K{sub c} initiation data for notched and fatigue precracked specimens of hydrogen precharged Alloy X-750. This criterion, which was developed for hydrogen embrittlement (HE) cracking, is used here to correlate static-load stress corrosion cracking (SCC) initiation times obtained for smooth geometry, notched and fatigue precracked specimens. The onset of SCC crack growth is hypothesized to occur when a critical strain, which is due to environment-enhanced creep, is attained within the specimen interior. For notched and precracked specimens, initiation is shown by analysis to occur at a variable distance from notch and crack tips. The initiation site varies from very near the crack tip, for highly loaded sharp cracks, to a site that is one grain diameter from the notch, for lower loaded, blunt notches. The existence of hydrogen gradients, which are due to strain-induced hydrogen trapping in the strain fields of notch and crack tips, is argued to be controlling the site for initiation of cracking. By considering the sources of the hydrogen, these observations are shown to be consistent with those from the previous HE study, in which the characteristic distance for crack initiation was found to be one grain diameter from the notch tip, independent of notch radius, applied stress intensity factor and hydrogen level.
Jin, Y.J.; Lu, H. Yu, C.; Xu, J.J.
2013-10-15
Intergranular reheat cracking in the coarse-grained heat-affected zone of T23 steel was produced by strain to fracture tests on a Gleeble 3500 thermal–mechanical simulator. Then the grain boundary character, as well as the strain distribution after reheat crack propagation, was studied by electron backscatter diffraction technique. The results showed that incoherent Σ3 boundaries were seldom found on the prior austenite grain boundaries. Therefore, only the type of random high-angle boundaries played a crucial role in the intergranular cracking. Microstructurally cavities and small cracks were preferentially initiated from high-angle grain boundaries. Low-angle grain boundaries and high-angle ones with misorientation angles less than 15° were more resistant to the cracking. More importantly, the fraction of high-angle grain boundaries increased with the plastic strain induced by both temperature gradient and stress in the coarse-grained heat-affected zone, which contributed to the crack initiation and propagation. Furthermore, the strain distributions in the vicinity of cavities and cracks revealed the accommodation processes of plastic deformation during stress relaxation. It also reflected the strength differences between grain interior and grain boundary at different heat-treated temperatures, which had a large influence on the cracking mechanism. - Highlights: • The coincidence site lattice boundaries play little role in the reheat cracking. • Cavity and crack occur at high-angle grain boundaries rather than low-angle ones. • The strain leads low-angle grain boundaries to transform to high-angle ones. • Strain distribution differs for cavity and crack zones at different temperatures.
NASA Astrophysics Data System (ADS)
Wong, Meng Fei; Zeng, Kaiyang
2010-06-01
This paper presents recent studies on surface and cross-sectional domain structures of Pb(Zn1/3Nb2/3)O3-(6-7)%PbTiO3 (PZN-PT) single crystals using piezoresponse force microscopy and three-point bending technique. The surface domain structures for the rhombohedral-based single crystals in (001) orientation are found to be influenced by polishing process, whereas the surface domains on the (011)-oriented single crystals are aligned along [011¯] direction, unaffected by the polishing process. On the other hand, the domain structures on the cross-sectional fracture surface show preferential alignment which agrees reasonably with the rhombohedral dipoles on the {100} and {110} planes. The differences between the surface and cross-sectional domain structures could be attributed to stress compensation between the surface strain effect and the minimization of elastic energy. In addition, both surface and cross-sectional surface demonstrate nanoscale domains, about 100-200 nm in size. Further fractography observation suggests that the preferred cracking planes for the PZN-PT single crystals are {110} and {100} planes. The {110} planes may be the slip planes along which material pile up is observed upon indentation loading. The pile up results in tensile hoop stress, producing radial cracks along the {100} cleavage planes. To accommodate the localized stress change, new ferroelastic domains by mechanical stress are then formed without interrupting the out-of-plane piezoelectric response. Since the material pile up is thought to cause enhanced toughness along {110} planes, the PZN-PT single crystal in [011]-poled orientation exhibits more superior piezoelectric properties compared to that of the [001]-poled counterpart.
Strain Profiling of Fatigue Crack Overload Effects Using Energy Dispersive X-Ray Diffraction
Croft,M.; Zhong, Z.; Jisrawi, N.; Zakharchenko, I.; Holtz, R.; Gulak, Y.; Skaritka, J.; Fast, T.; Sadananda, K.; Tsakalakos, T.
2005-01-01
In this paper, an assessment of commonly used assumptions associated with {Delta}K{sub eff} and their implications on FCG predictions in light of existing experimental and numerical data is presented. In particular, the following assumptions are examined: (1). {Delta}K{sub eff} fully describes cyclic stresses and strains at the crack-tip vicinity. (2). K{sub op} can be determined experimentally or numerically with certain accuracy. (3). Overload alters K{sub op} but not K{sub max} and associated s{sub max} at the crack-tip 'process zone'. (4). Contact of crack faces curtails the crack driving force in terms of {Delta}K{sub eff}. The analysis indicates that there is insufficient support to justify the above assumptions. In contrary, the analysis demonstrates that a two-parameter fatigue crack driving force in terms of {Delta}K and K{sub max}, which accounts for both applied and the internal stresses should be used in FCG analyses and predictions.
NASA Astrophysics Data System (ADS)
Connolly, Matthew; Slifka, Andrew; Drexler, Elizabeth; Hydrogen Pipeline Safety Team
Hydrogen (H2) is desirable for energy storage as it is cleaner burning and can store a larger amount of energy than an equal mass of gasoline. One problem in the development of a hydrogen economy is to find or develop materials that ensure the safe, reliable, and cost-effective flow of energy from the source to the user. It is expected steels will be needed to serve this function. However, the existing network of natural gas pipeline, for example, is constructed of ferrous materials which are susceptible to embrittlement and subsequent increased fatigue crack growth rates after exposure to hydrogen. In order to improve current modeling efforts, experimental determination of hydrogen concentration, hydrogen diffusion rates, and strain fields are required to inform and validate the model. Here we report neutron imaging measurements of the hydrogen concentration near a fatigue crack and the corresponding strain field, measured via neutron transmission Bragg edge spectroscopy. Nist Materials Measurement Laboratory, Applied Chemicals and Materials Division.
The plane strain shear fracture of the advanced high strength steels
Sun, Li
2013-12-16
The “shear fracture” which occurs at the high-curvature die radii in the sheet metal forming has been reported to remarkably limit the application of the advanced high strength steels (AHSS) in the automobile industry. However, this unusual fracture behavior generally cannot be predicted by the traditional forming limit diagram (FLD). In this research, a new experimental system was developed in order to simulate the shear fracture, especially at the plane strain state which is the most common state in the auto-industry and difficult to achieve in the lab due to sample size. Furthermore, the system has the capability to operate in a strain rate range from quasi-static state to the industrial forming state. One kinds of AHSS, Quenching-Partitioning (QP) steels have been performed in this test and the results show that the limiting fracture strain is related to the bending ratio and strain rate. The experimental data support that deformation-induced heating is an important cause of “shear fracture” phenomena for AHSS: a deformation-induced quasi-heating caused by smaller bending ratio and high strain rate produce a smaller limiting plane strain and lead a “shear fracture” in the component.
NASA Astrophysics Data System (ADS)
Shatskii, I. P.; Makoviichuk, N. V.
2011-05-01
The problem of closure of collinear cracks during bending of a shallow shell is considered within the framework of the Kirchhoff theory. Crack closure is described using the model of contact along a line on one of the shell faces. Strain and moment intensity factors and fracture load are studied as functions of shell curvature and defect location, and the distribution of contact forces along the cracks is investigated.
Imaging in-plane and normal stresses near an interface crack using traction force microscopy
Xu, Ye; Engl, Wilfried C.; Jerison, Elizabeth R.; Wallenstein, Kevin J.; Hyland, Callen; Wilen, Larry A.; Dufresne, Eric R.
2010-01-01
Colloidal coatings, such as paint, are all around us. However, we know little about the mechanics of the film-forming process because the composition and properties of drying coatings vary dramatically in space and time. To surmount this challenge, we extend traction force microscopy to quantify the spatial distribution of all three components of the stress at the interface of two materials. We apply this approach to image stress near the tip of a propagating interface crack in a drying colloidal coating and extract the stress intensity factor. PMID:20696929
Mathematical model of the strain-softening curve for crack extension
NASA Astrophysics Data System (ADS)
Fujii, K.; Nakagawa, K.; Duan, S. J.
1994-07-01
We show in this paper a method of simulating the load-displacement diagrams of notched four-point bending beams with crack extension and the corresponding relation between stress distribution and crack opening displacement (also called the tensile strain-softening curve). As is well-known, the whole fracture behavior of concrete structures as expressed by a complete load-displacement diagram is generally influenced by fracture energy G(sub f) and the shape of the strain-softening curve, which has to be simulated by the FEM or other numerical methods. The present simulation is based on the superposition of the complex stress functions with the finite stress concentration at the crack tips derived from the authors' proposed weight integral method. The character of this model is such that it is possible to approach the material's strain-softening behavior and the fracture process by simply changing the fracture process zone length and the ligament length, although only the elastic solutions are used.
Super switching and control of in-plane ferroelectric nanodomains in strained thin films
NASA Astrophysics Data System (ADS)
Matzen, S.; Nesterov, O.; Rispens, G.; Heuver, J. A.; Biegalski, M.; Christen, H. M.; Noheda, B.
2014-07-01
With shrinking device sizes, controlling domain formation in nanoferroelectrics becomes crucial. Periodic nanodomains that self-organize into so-called ‘superdomains’ have been recently observed, mainly at crystal edges or in laterally confined nanoobjects. Here we show that in extended, strain-engineered thin films, superdomains with purely in-plane polarization form to mimic the single-domain ground state, a new insight that allows a priori design of these hierarchical domain architectures. Importantly, superdomains behave like strain-neutral entities whose resultant polarization can be reversibly switched by 90°, offering promising perspectives for novel device geometries.
NASA Astrophysics Data System (ADS)
Miao, Yu; Chen, L.; Sammynaiken, R.; Lin, Y.; Zhang, W. J.
2011-12-01
The use of carbon nanotubes (CNT) for the application in in-plane strain detection is promising. In recent years, in-plane strain sensors constructed from CNT networks have been developed; however, few studied optimization of these sensors. In this paper, a study of the optimization of pure CNT networks in terms of piezoresistive response is reported. The so-called pure CNT networks are CNT networks free of surfactants. The performances of piezoresistive response are gauge factor (GF) and linearity. The variables are the number of layers of networks, concentration of CNT solution, and length of sonication time. As a result, the study concluded an optimal pure CNT networks sensor (GF: 2.59, linearity 0.98) with ten layers of networks, 0.8 mg/ml concentration, and 2 h of sonication time.
The unique effect of in-plane anisotropic strain in the magnetization control by electric field
NASA Astrophysics Data System (ADS)
Zhao, Y. Y.; Wang, J.; Hu, F. X.; Liu, Y.; Kuang, H.; Wu, R. R.; Sun, J. R.; Shen, B. G.
2016-05-01
The electric field control of magnetization in both (100)- and (011)-Pr0.7Sr0.3MnO3/Pb(Mg1/3Nb2/3)0.7Ti0.3O3(PSMO/PMN-PT) heterostructures were investigated. It was found that the in-plane isotropic strain induced by electric field only slightly reduces the magnetization at low temperature in (100)-PSMO/PMN-PT film. On the other hand, for (011)-PSMO/PMN-PT film, the in-plane anisotropic strain results in in-plane anisotropic, nonvolatile change of magnetization at low-temperature. The magnetization, remanence and coercivity along in-plane [100] direction are suppressed by the electric field while the ones along [01-1] direction are enhanced, which is ascribed to the extra effective magnetic anisotropy induced by the electric field via anisotropic piezostrains. More interestingly, such anisotropic modulation behaviors are nonvolatile, demonstrating a memory effect.
Optical Strain and Crack-Detection Measurements on a Rotating Disk
NASA Technical Reports Server (NTRS)
Woike, Mark; Abdul-Aziz, Ali; Clem, Michelle; Fralick, Gustave
2013-01-01
The development of techniques for the in-situ measurement and structural health monitoring of the rotating components in gas turbine engines is of major interest to NASA. As part of this on-going effort, several experiments have been undertaken to develop methods for detecting cracks and measuring strain on rotating turbine engine like disks. Previous methods investigated have included the use of blade tip clearance sensors to detect the presence of cracks by monitoring the change in measured blade tip clearance and analyzing the combined disk-rotor system's vibration response. More recently, an experiment utilizing a novel optical Moiré based concept has been conducted on a subscale turbine engine disk to demonstrate a potential strain measurement and crack detection technique. Moiré patterns result from the overlap of two repetitive patterns with slightly different spacing. When this technique is applied to a rotating disk, it has the potential to allow for the detection of very small changes in spacing and radial growth in a rotating disk due to a flaw such as a crack. This investigation was a continuation of previous efforts undertaken in 2011-2012 to validate this optical concept. The initial demonstration attempted on a subscale turbine engine disk was inconclusive due to the minimal radial growth experienced by the disk during operation. For the present experiment a new subscale Aluminum disk was fabricated and improvements were made to the experimental setup to better demonstrate the technique. A circular reference pattern was laser etched onto a subscale engine disk and the disk was operated at speeds up to 12 000 rpm as a means of optically monitoring the Moiré created by the shift in patterns created by the radial growth due the presence of the simulated crack. Testing was first accomplished on a clean defect free disk as a means of acquiring baseline reference data. A notch was then machined in to the disk to simulate a crack and testing was repeated
Optical Strain and Crack-Detection Measurements on a Rotating Disk
NASA Technical Reports Server (NTRS)
Woike, Mark; Abdul-Aziz, Ali; Clem, Michelle M.; Fralick, Gustave
2013-01-01
The development of techniques for the in-situ measurement and structural health monitoring of the rotating components in gas turbine engines is of major interest to NASA. As part of this on-going effort, several experiments have been undertaken to develop methods for detecting cracks and measuring strain on rotating turbine engine like disks. Previous methods investigated have included the use of blade tip clearance sensors to detect the presence of cracks by monitoring the change in measured blade tip clearance and analyzing the combined disk-rotor system's vibration response. More recently, an experiment utilizing a novel optical Moiré based concept has been conducted on a subscale turbine engine disk to demonstrate a potential strain measurement and crack detection technique. Moiré patterns result from the overlap of two repetitive patterns with slightly different spacing. When this technique is applied to a rotating disk, it has the potential to allow for the detection of very small changes in spacing and radial growth in a rotating disk due to a flaw such as a crack. This investigation was a continuation of previous efforts undertaken in 2011 to 2012 to validate this optical concept. The initial demonstration attempted on a subscale turbine engine disk was inconclusive due to the minimal radial growth experienced by the disk during operation. For the present experiment a new subscale Aluminum disk was fabricated and improvements were made to the experimental setup to better demonstrate the technique. A circular reference pattern was laser etched onto a subscale engine disk and the disk was operated at speeds up to 12 000 rpm as a means of optically monitoring the Moiré created by the shift in patterns created by the radial growth due the presence of the simulated crack. Testing was first accomplished on a clean defect free disk as a means of acquiring baseline reference data. A notch was then machined in to the disk to simulate a crack and testing was
NASA Astrophysics Data System (ADS)
Cherukuri, Harish P.; Ulysse, Patrick; Smelser, Ronald E.; Subramanian, Kannan; Kotaru, Deepti
2010-06-01
Rapid quenching of aluminum extrusions often results in residual stresses and distortion. The out-of-plane normal component of the residual stress is typically very large and results in undesirable bending (bowing) of the extruded shape. Three-dimensional models to predict the residual stresses and bending of extruded thin-walled shapes are difficult to implement since the wall-thicknesses are often very small compared with the axial dimensions. In this paper, a generalized plane-strain model is presented to predict the residual stresses and distortion. For illusrative purposes of the model, a Z-shaped extrusion is chosen. The model predicts the bowing of the extruded shape along with the in-plane and out-of-plane stress components. An internal state-variable model is used for the constitutive description. The residual stresses and distortion are studied for cold and warm water quenching and three different cases of spray quenching. The numerical results indicate that cold water quenching and the two spray quenching cases with the higher discharge rates lead to significantly larger residual stresses compared to the remaining two cases. For each case, the out-of-plane bows of the extruded shapes are also shown to be significant.
Bio-inspired sensitive and reversible mechanochromisms via strain-dependent cracks and folds.
Zeng, Songshan; Zhang, Dianyun; Huang, Wenhan; Wang, Zhaofeng; Freire, Stephan G; Yu, Xiaoyuan; Smith, Andrew T; Huang, Emily Y; Nguon, Helen; Sun, Luyi
2016-01-01
A number of marine organisms use muscle-controlled surface structures to achieve rapid changes in colour and transparency with outstanding reversibility. Inspired by these display tactics, we develop analogous deformation-controlled surface-engineering approaches via strain-dependent cracks and folds to realize the following four mechanochromic devices: (1) transparency change mechanochromism (TCM), (2) luminescent mechanochromism (LM), (3) colour alteration mechanochromism (CAM) and (4) encryption mechanochromism (EM). These devices are based on a simple bilayer system that exhibits a broad range of mechanochromic behaviours with high sensitivity and reversibility. The TCM device can reversibly switch between transparent and opaque states. The LM can emit intensive fluorescence as stretched with very high strain sensitivity. The CAM can turn fluorescence from green to yellow to orange as stretched within 20% strain. The EM device can reversibly reveal and conceal any desirable patterns. PMID:27389480
Bio-inspired sensitive and reversible mechanochromisms via strain-dependent cracks and folds
NASA Astrophysics Data System (ADS)
Zeng, Songshan; Zhang, Dianyun; Huang, Wenhan; Wang, Zhaofeng; Freire, Stephan G.; Yu, Xiaoyuan; Smith, Andrew T.; Huang, Emily Y.; Nguon, Helen; Sun, Luyi
2016-07-01
A number of marine organisms use muscle-controlled surface structures to achieve rapid changes in colour and transparency with outstanding reversibility. Inspired by these display tactics, we develop analogous deformation-controlled surface-engineering approaches via strain-dependent cracks and folds to realize the following four mechanochromic devices: (1) transparency change mechanochromism (TCM), (2) luminescent mechanochromism (LM), (3) colour alteration mechanochromism (CAM) and (4) encryption mechanochromism (EM). These devices are based on a simple bilayer system that exhibits a broad range of mechanochromic behaviours with high sensitivity and reversibility. The TCM device can reversibly switch between transparent and opaque states. The LM can emit intensive fluorescence as stretched with very high strain sensitivity. The CAM can turn fluorescence from green to yellow to orange as stretched within 20% strain. The EM device can reversibly reveal and conceal any desirable patterns.
Bio-inspired sensitive and reversible mechanochromisms via strain-dependent cracks and folds
Zeng, Songshan; Zhang, Dianyun; Huang, Wenhan; Wang, Zhaofeng; Freire, Stephan G.; Yu, Xiaoyuan; Smith, Andrew T.; Huang, Emily Y.; Nguon, Helen; Sun, Luyi
2016-01-01
A number of marine organisms use muscle-controlled surface structures to achieve rapid changes in colour and transparency with outstanding reversibility. Inspired by these display tactics, we develop analogous deformation-controlled surface-engineering approaches via strain-dependent cracks and folds to realize the following four mechanochromic devices: (1) transparency change mechanochromism (TCM), (2) luminescent mechanochromism (LM), (3) colour alteration mechanochromism (CAM) and (4) encryption mechanochromism (EM). These devices are based on a simple bilayer system that exhibits a broad range of mechanochromic behaviours with high sensitivity and reversibility. The TCM device can reversibly switch between transparent and opaque states. The LM can emit intensive fluorescence as stretched with very high strain sensitivity. The CAM can turn fluorescence from green to yellow to orange as stretched within 20% strain. The EM device can reversibly reveal and conceal any desirable patterns. PMID:27389480
Dislocation microstructures and strain-gradient plasticity with one active slip plane
NASA Astrophysics Data System (ADS)
Conti, Sergio; Garroni, Adriana; Müller, Stefan
2016-08-01
We study dislocation networks in the plane using the vectorial phase-field model introduced by Ortiz and coworkers, in the limit of small lattice spacing. We show that, in a scaling regime where the total length of the dislocations is large, the phase field model reduces to a simpler model of the strain-gradient type. The limiting model contains a term describing the three-dimensional elastic energy and a strain-gradient term describing the energy of the geometrically necessary dislocations, characterized by the tangential gradient of the slip. The energy density appearing in the strain-gradient term is determined by the solution of a cell problem, which depends on the line tension energy of dislocations. In the case of cubic crystals with isotropic elasticity our model shows that complex microstructures may form in which dislocations with different Burgers vector and orientation react with each other to reduce the total self-energy.
NASA Astrophysics Data System (ADS)
Sakaguchi, Junichi; Nakajima, Akinori; Suzuki, Yasuo
The sophisticated numerical analysis method is required to simulate the strain behavior of the reinforcement and the crack width of the RC slab, although many researches are conducted on the cracking behavior of the RC slab in the composite girder under the negative bending. In this paper, the numerical analysis method is constructed to evaluate the strain behavior of the reinforcement and the crack width of the RC slab in the steel-concrete composite girder subjected to the negative bending. The analysis method using the rigid body spring model takes into account the imperfect composite action between the steel girder and the RC slab, the bond between the reinforcement and the concrete, and the shrinkage of the concrete. As a result, it is confirmed that the analysis method can simulate the crack and the strain behavior of RC slab quantitatively in the steel-concrete composite girder under the negative bending.
NASA Astrophysics Data System (ADS)
Tung, S.-T.; Yao, Y.; Glisic, B.
2014-07-01
Increasing concerns regarding the conditions of civil structures and infrastructure give rise to the need for efficient strategies to identify and repair structural anomalies. ‘Sensing sheets’ based on large-area electronics consist of a dense array of unit strain sensors. These are an effective and affordable structural health monitoring tool that can identify and continuously monitor the growth of cracks in structures. This paper presents a study on the quantitative relationship between crack width and strain, the latter measured by an individual sensor that would be part of a sensing sheet. We investigate the sensitivity of thin-film full-bridge strain sensors to concrete cracks by conducting laboratory experiments in temperature-controlled settings. The results show a distribution of near-linear relationships with an average sensitivity of 31 µɛ µm-1. Experiments were also conducted to investigate the effect of crack position and orientation with respect to the sensor, and it appears that both variables affect the sensitivity of strain sensors to cracks. Overall, this study confirms that full-bridge resistive strain sensors can successfully detect and quantify cracks in structural materials and are therefore appropriate as part of a dense array of sensors on a sensing sheet.
Analysis of plane-plastic stress problems with axial symmetry in strain-hardening range
NASA Technical Reports Server (NTRS)
Wu, M H Lee
1951-01-01
A simple method is developed for solving plane-plastic-stress problems with axial symmetry in the strain-hardening range which is based on the deformation theory of plasticity employing the finite-strain concept. The equations defining the problems are first reduced to two simultaneous nonlinear differential equations involving two dependent variables: (a) the octahedral shear strain, and (b) a parameter indicating the ratio of principal stresses. By multiplying the load and dividing the radius by an arbitrary constant, it is possible to solve these problems without iteration for any value of the modified load. The constant is determined by the boundary condition. This method is applied to a circular membrane under pressure, a rotating disk without and with a central hole, and an infinite plate with a circular hole. Two materials, inconel x and 16-25-6, the octahedral shear stress-strain relations of which do not follow the power law, are used. Distributions of octahedral shear strain, as well as of principal stresses and strains, are obtained. These results are compared with the results of the same problems in the elastic range.
Xiao, Xia; Zhang, Yaoyuan; Jiang, Guiyuan; Liu, Jia; Han, Shanlei; Zhao, Zhen; Wang, Ruipu; Li, Cong; Xu, Chunming; Duan, Aijun; Wang, Yajun; Liu, Jian; Wei, Yuechang
2016-08-01
Nanosheet ZSM-5 zeolite with highly exposed (010) crystal planes demonstrates high reactivity and good anti-coking stability for the catalytic cracking of n-heptane, which is attributed to the synergy of high external surface area and acid sites, fully accessible channel intersection acid sites, and hierarchical porosity caused by the unique morphology. PMID:27458616
In-plane displacement and strain measurements using a camera phone and digital image correlation
NASA Astrophysics Data System (ADS)
Yu, Liping; Pan, Bing
2014-05-01
In-plane displacement and strain measurements of planar objects by processing the digital images captured by a camera phone using digital image correlation (DIC) are performed in this paper. As a convenient communication tool for everyday use, the principal advantages of a camera phone are its low cost, easy accessibility, and compactness. However, when used as a two-dimensional DIC system for mechanical metrology, the assumed imaging model of a camera phone may be slightly altered during the measurement process due to camera misalignment, imperfect loading, sample deformation, and temperature variations of the camera phone, which can produce appreciable errors in the measured displacements. In order to obtain accurate DIC measurements using a camera phone, the virtual displacements caused by these issues are first identified using an unstrained compensating specimen and then corrected by means of a parametric model. The proposed technique is first verified using in-plane translation and out-of-plane translation tests. Then, it is validated through a determination of the tensile strains and elastic properties of an aluminum specimen. Results of the present study show that accurate DIC measurements can be conducted using a common camera phone provided that an adequate correction is employed.
Dependence of electronic properties of germanium on the in-plane biaxial tensile strains
NASA Astrophysics Data System (ADS)
Yang, C. H.; Yu, Z. Y.; Liu, Y. M.; Lu, P. F.; Gao, T.; Li, M.; Manzoor, S.
2013-10-01
The hybrid HSE06 functional with the spin-orbit coupling effects is used to calculate the habituation of the electronic properties of Ge on the (0 0 1), (1 1 1), (1 0 1) in-plane biaxial tensile strains (IPBTSs). Our motivation is to explore the nature of electronic properties of tensile-strained Ge on different substrate orientations. The calculated results demonstrate that one of the most effective and practical approaches for transforming Ge into a direct transition semiconductor is to introduce (0 0 1) IPBTS to Ge. At 2.3% (0 0 1) IPBTS, Ge becomes a direct bandgap semiconductor with 0.53 eV band gap, in good agreement with the previous theoretical and experimental results. We find that the (1 1 1) and (1 0 1) IPBTSs are not efficient since the shear strain and inner displacement of atoms introduced by them quickly decrease the indirect gap of Ge. By investigating the dependence of valence band spin-orbit splitting on strain, we prove that the dependency relationship and the coupled ways between the valence-band states of tensile-strained Ge are closely related to the symmetry of strain tensor, i.e., the symmetry of the substrate orientation. The first- and second-order coefficients describing the dependence of indirect gap, direct gap, the valence band spin-orbit coupling splitting, and heavy-hole-light-hole splitting of Ge on IPBTSs have been obtained by the least squares polynomial fitting. These coefficients are significant to quantitatively modulate the electronic properties of Ge by tensile strain and design tensile-strained Ge devices by semiconductor epitaxial technique.
NASA Technical Reports Server (NTRS)
Gabb, Timothy P.; Telesman, Jack; Banik, Anthony; McDevitt, Erin
2014-01-01
Intergranular fatigue crack initiation and growth due to environmental degradation, especially at notched features, can often limit the fatigue life of disk superalloys at high temperatures. For clear comparisons, the effects of alloy composition on cracking in air needs to be understood and compared separately from variables associated with notches and cracks such as effective stress concentration, plastic flow, stress relaxation, and stress redistribution. The objective of this study was to attempt using simple tensile tests of specimens with uniform gage sections to compare the effects of varied alloy composition on environment-assisted cracking of several powder metal and cast and wrought superalloys including ME3, LSHR, Udimet 720, ATI 718Plus alloy, Haynes 282, and Inconel 740. Slow and fast strain-rate tensile tests were found to be a useful tool to compare propensities for intergranular surface crack initiation and growth. The effects of composition and heat treatment on tensile fracture strain and associated failure modes were compared. Environment interactions were determined to often limit ductility, by promoting intergranular surface cracking. The response of various superalloys and heat treatments to slow strain rate tensile testing varied substantially, showing that composition and microstructure can significantly influence environmental resistance to cracking.
Analysis of crack propagation as an energy absorption mechanism in metal matrix composites
NASA Technical Reports Server (NTRS)
Adams, D. F.; Murphy, D. P.
1981-01-01
The crack initiation and crack propagation capability was extended to the previously developed generalized plane strain, finite element micromechanics analysis. Also, an axisymmetric analysis was developed, which contains all of the general features of the plane analysis, including elastoplastic material behavior, temperature-dependent material properties, and crack propagation. These analyses were used to generate various example problems demonstrating the inelastic response of, and crack initiation and propagation in, a boron/aluminum composite.
An Accurate Upper Bound Solution for Plane Strain Extrusion through a Wedge-Shaped Die
Mustafa, Yusof; Lyamina, Elena
2014-01-01
An upper bound method for the process of plane strain extrusion through a wedge-shaped die is derived. A technique for constructing a kinematically admissible velocity field satisfying the exact asymptotic singular behavior of real velocity fields in the vicinity of maximum friction surfaces (the friction stress at sliding is equal to the shear yield stress on such surfaces) is described. Two specific upper bound solutions are found using the method derived. The solutions are compared to an accurate slip-line solution and it is shown that the accuracy of the new method is very high. PMID:25101311
Biologically inspired crack delocalization in a high strain-rate environment.
Knipprath, Christian; Bond, Ian P; Trask, Richard S
2012-04-01
Biological materials possess unique and desirable energy-absorbing mechanisms and structural characteristics worthy of consideration by engineers. For example, high levels of energy dissipation at low strain rates via triggering of crack delocalization combined with interfacial hardening by platelet interlocking are observed in brittle materials such as nacre, the iridescent material in seashells. Such behaviours find no analogy in current engineering materials. The potential to mimic such toughening mechanisms on different length scales now exists, but the question concerning their suitability under dynamic loading conditions and whether these mechanisms retain their energy-absorbing potential is unclear. This paper investigates the kinematic behaviour of an 'engineered' nacre-like structure within a high strain-rate environment. A finite-element (FE) model was developed which incorporates the pertinent biological design features. A parametric study was carried out focusing on (i) the use of an overlapping discontinuous tile arrangement for crack delocalization and (ii) application of tile waviness (interfacial hardening) for improved post-damage behaviour. With respect to the material properties, the model allows the permutation and combination of a variety of different material datasets. The advantage of such a discontinuous material shows notable improvements in sustaining high strain-rate deformation relative to an equivalent continuous morphology. In the case of the continuous material, the shockwaves propagating through the material lead to localized failure while complex shockwave patterns are observed in the discontinuous flat tile arrangement, arising from platelet interlocking. The influence of the matrix properties on impact performance is investigated by varying the dominant material parameters. The results indicate a deceleration of the impactor velocity, thus delaying back face nodal displacement. A final series of FE models considered the
Biologically inspired crack delocalization in a high strain-rate environment
Knipprath, Christian; Bond, Ian P.; Trask, Richard S.
2012-01-01
Biological materials possess unique and desirable energy-absorbing mechanisms and structural characteristics worthy of consideration by engineers. For example, high levels of energy dissipation at low strain rates via triggering of crack delocalization combined with interfacial hardening by platelet interlocking are observed in brittle materials such as nacre, the iridescent material in seashells. Such behaviours find no analogy in current engineering materials. The potential to mimic such toughening mechanisms on different length scales now exists, but the question concerning their suitability under dynamic loading conditions and whether these mechanisms retain their energy-absorbing potential is unclear. This paper investigates the kinematic behaviour of an ‘engineered’ nacre-like structure within a high strain-rate environment. A finite-element (FE) model was developed which incorporates the pertinent biological design features. A parametric study was carried out focusing on (i) the use of an overlapping discontinuous tile arrangement for crack delocalization and (ii) application of tile waviness (interfacial hardening) for improved post-damage behaviour. With respect to the material properties, the model allows the permutation and combination of a variety of different material datasets. The advantage of such a discontinuous material shows notable improvements in sustaining high strain-rate deformation relative to an equivalent continuous morphology. In the case of the continuous material, the shockwaves propagating through the material lead to localized failure while complex shockwave patterns are observed in the discontinuous flat tile arrangement, arising from platelet interlocking. The influence of the matrix properties on impact performance is investigated by varying the dominant material parameters. The results indicate a deceleration of the impactor velocity, thus delaying back face nodal displacement. A final series of FE models considered the
NASA Astrophysics Data System (ADS)
Zaitsev, V. Yu.; Matveev, L. A.
2012-05-01
Presently, experimental evidence for extremely high strain-sensitivity of dissipation in rocks and similar microstructured materials is obtained both in laboratory and field conditions, in particular observations of pronounced amplitude modulation of the radiation of high-stability seismo-acoustic sources by tidal deformations of rocks with typical strains ~ 10-8. Such data indicate the presence of some thresholdless in amplitude and very efficient mechanism of strain-dependent dissipation. Conventionally, its origin is discussed in the context of frictional or adhesion-hysteretic loss at cracks in rocks. However, such dissipation mechanisms are not relevant to weak perturbations with displacements smaller than atomic size. Here, we revise thresholdless thermoelastic loss in dry cracks and viscous loss in saturated cracks taking into account wavy asperities typical of real cracks, which can create elongated (strip-like) contacts or almost closed "waists" in cracks. Thermoelastic loss at these contacts can be very efficient. Besides, the state of such contacts can already be strongly perturbed by the average strain which yet practically does not change the mean opening of the entire crack. Thus the dissipation localized at such contacts can be significantly affected by quite small average strain (e.g., 10-8), which is usually believed to be unable to produce any appreciable effect on the dissipation. Next, for liquid-saturated cracks, the presence of inner elongated asperities also drastically changes the character of squirt-type viscous dissipation. Velocity gradients and consequently the dissipation are localized in the vicinity of the nearly-closed waists which almost harness the liquid flow in the crack. This dissipation can be comparable in magnitude with viscous dissipation at the entire crack with smooth interface, but the decrement maximum is strongly shifted downwards on the frequency axis. Since near the waist the gap is much smaller than the average crack
NASA Astrophysics Data System (ADS)
Sun, Y. W.; Holec, D.; Dunstan, D. J.
2015-09-01
Stacking graphene sheets forms graphite. Two in-plane vibrational modes of graphite, E1 u and E2g (2 ), are derived from the graphene E2 g mode, the shifts of which under compression are considered as results of the in-plane bond shortening. Values of the Grüneisen parameter have been reported to quantify such a relation. However, the reason why the shift rates of these three modes with pressure differ is unclear. In this work, we introduce new parameters γE2g'=-0.0131 and γE1u'=0.0585 to quantify the contribution of out-of-plane strain to the shift of the in-plane vibrational frequencies, suggesting that the compression of the π - electrons plays a non-negligible part in both graphite and graphene under high pressure.
NASA Astrophysics Data System (ADS)
Kim, Young Suk; Kim, Sung Soo
2016-07-01
We show that enhanced stress corrosion cracking (SCC) initiation in cold-rolled Alloy 690 with decreasing strain rate is related to the rate of short-range ordering (SRO) but not to the time-dependent corrosion process. Evidence for SRO is provided by aging tests on cold-rolled Alloy 690 at 623 K and 693 K (350 °C and 420 °C), respectively, which demonstrate its enhanced lattice contraction and hardness increase with aging temperature and time, respectively. Secondary intergranular cracks formed only in thermally treated and cold-rolled Alloy 690 during SCC tests, which are not SCC cracks, are caused by its lattice contraction by SRO before SCC tests but not by the orientation effect.
NASA Astrophysics Data System (ADS)
Kim, Young Suk; Kim, Sung Soo
2016-09-01
We show that enhanced stress corrosion cracking (SCC) initiation in cold-rolled Alloy 690 with decreasing strain rate is related to the rate of short-range ordering (SRO) but not to the time-dependent corrosion process. Evidence for SRO is provided by aging tests on cold-rolled Alloy 690 at 623 K and 693 K (350 °C and 420 °C), respectively, which demonstrate its enhanced lattice contraction and hardness increase with aging temperature and time, respectively. Secondary intergranular cracks formed only in thermally treated and cold-rolled Alloy 690 during SCC tests, which are not SCC cracks, are caused by its lattice contraction by SRO before SCC tests but not by the orientation effect.
The impact of strain, bedding plane friction and overburden pressure on joint spacing
NASA Astrophysics Data System (ADS)
Arslan, Arzu; Schöpfer, Martin P. J.; Walsh, John J.; Childs, Conrad
2010-05-01
In layered sequences, rock joints usually best develop within the more brittle layers and commonly display a regular spacing that scales with layer thickness. A variety of conceptual and mechanical models have been advanced to explain this relationship. A limitation of previous approaches, however, is that fracture initiation and associated bedding-parallel slip are not explicitly simulated; instead, fractures were predefined and interfaces were welded. To surmount this problem, we have modelled the formation and growth of joints in layered sequences by using the two-dimensional Distinct Element Method (DEM) as implemented in the Particle Flow Code (PFC-2D). In PFC-2D, rock is represented by an assemblage of circular particles that are bonded at particle-particle contacts, with failure occurring when either the tensile or shear strength of a bond is exceeded. Model materials with different rheological properties can be generated by calibrating the results of synthetic mechanical test procedures with those of real rocks. Our simple models of jointing comprise a central brittle layer with high Young's modulus, which is embedded in a low Young's modulus matrix. The interfaces between the layers (i.e. bedding planes) are defined by ‘smooth joint' contacts, a modelling feature that eliminates interparticle bumpiness and associated interlocking friction. Consequently, this feature allows the user to assign macroscopic properties such as friction along layer interfaces in a controlled manner. Layer parallel extension is applied by assigning a velocity to particles at the lateral boundaries of the model while maintaining a constant vertical confining pressure. Models were extended until joint saturation was reached in the central layer. We thereby explored the impact of strain, bedding plane friction and overburden pressure on joint spacing. The modelling revealed that joint spacing decreases as strain, bedding plane friction and overburden pressure are increased
Effect of material damage on the stress-strain state near a crack tip in creep
NASA Astrophysics Data System (ADS)
Astaf'ev, V. I.; Grigorova, T. V.; Pastukhov, V. A.
1992-02-01
The asymptotic stress and damage fields near the tip of a growing crack are determined for a creep-damaged material described by Rabotnov-Hayhurst-Leckie constitutive equations. It is found that the singular stress field, characteristic of the crack theory, is absent near the crack tip, which is consistent with the results of finite element solutions for tearing cracks. A crack growth law is obtained which provides a qualitative description of the crack growth process in stainless steels under constant loading.
NASA Astrophysics Data System (ADS)
Kim, K.; Okayasu, K.; Fukutomi, H.
2015-04-01
The formation behavior of basal texture during high temperature deformation of AZ80 magnesium alloys in single phase was investigated by plane strain compression deformation. Three kinds of specimens with different initial textures were machined out from an extruded bar having a <101¯0> texture. Plane strain compression tests were conducted at temperatures of 623K and 723K and a strain rate of 5.0×10-2s-1, with a strain range of between - 0.4 and -1.0. After deformation, the specimens were immediately quenched in oil. Texture measurement was carried out on the compression planes by the Schulz reflection method using nickel filtered Cu Kα radiation. Electron backscatter diffraction (EBSD) measurements were also conducted in order to examine the spatial distribution of orientations. Three kinds of specimens named A, B and C were prepared from the same extruded bar. In the specimens A, B and C, {0001} was distributed preferentially parallel to ND, TD, and RD, respectively. After deformation, texture evaluation was conducted on the mid-plane section. At the plane strain compression deformation, peaks appeared in the true stress-true strain curves irrespective of the kinds of specimen used. It was found that the main components and the pole densities of the textures vary depending on deformation condition and initial texture. Six kinds of texture components were observed after deformation. The (0001)<101¯0> has formed regardless of the initial texture. There are two types of texture components; one exists before the deformation, and the other does not. Either types are considered to have stable orientations for plane strain compression. Also, the basal texture is composed of two crystal orientation components - (0001)<101¯0> and (0001)<112¯0>. When (0001) existed before deformation, an extremely sharp (0001) (compression plane) texture is formed.
Assessment of Constitutive and Stability Behavior of Sands Under Plane Strain Condition
NASA Technical Reports Server (NTRS)
Alshibli, Khalid A.; Sture, Stein
2000-01-01
A series of biaxial (plane strain) experiments were conducted on three sands under low (15 kPa) and high (100 kPa) confining pressure conditions to investigate the effects of specimen density, confining pressure, and sand grains size and shape on the constitutive and stability behavior of granular materials. The three sands used in the experiments were fine, medium, and coarse-grained uniform silica sands with rounded, sub-angular, and angular grains, respectively. Specimen deformation was readily monitored and analyzed with the help of a grid pattern imprinted on the latex membrane. The overall stress-strain behavior is strongly dependent on the specimen density, confining pressure, sand grain texture, and the resulting failure mode(s). That became evident in different degrees of softening responses at various axial strains. The relationship between the constitutive behavior and the specimens' modes of instability is presented. The failure in all specimens was characterized by two distinct and opposite shear bands. It was found that the measured dilatancy angles increase as the sand grains' angularity and size increase. The measured shear band inclination angles are also presented and compared with classical Coulomb and Roscoe solutions.
Development of a new model for plane strain bending and springback analysis
Zhang, Z.T.; Lee, D.
1995-06-01
A new mathematical model is presented for plane strain bending and springback analysis in sheet metal forming. This model combines effects associated with bending and stretching, considers stress and strain distributions and different thickness variations in the thickness direction, and takes force equilibrium into account. An elastic-plastic material model and Hill`s nonquadratic yield function are incorporated in the model. The model is used to obtain force, bending moment, and springback curvature. A typical two-dimensional draw bending part is divided into five regions along the strip, and the forces and moments acting on each region and the deformation history of each region are examined. Three different methods are applied to the two-dimensional draw bending problems: the first using the new model, the second using the new model but also including a kinematic directional hardening material model to consider the bending and unbending deformation in the wall, and the third using membrane theory plus bending strain. Results from these methods, including those from the recent benchmark program, are compared.
Uniqueness of the interior plane strain time-harmonic viscoelastic inverse problem
NASA Astrophysics Data System (ADS)
Zhang, Yixiao; Barbone, Paul E.; Harari, Isaac; Oberai, Assad A.
2016-07-01
Elasticity imaging has emerged as a promising medical imaging technique with applications in the detection, diagnosis and treatment monitoring of several types of disease. In elasticity imaging measured displacement fields are used to generate images of elastic parameters of tissue by solving an inverse problem. When the tissue excitation, and the resulting tissue motion is time-harmonic, elasticity imaging can be extended to image the viscoelastic properties of the tissue. This leads to an inverse problem for the complex-valued shear modulus at a given frequency. In this manuscript we have considered the uniqueness of this inverse problem for an incompressible, isotropic linear viscoelastic solid in a state of plane strain. For a single measured displacement field we conclude that the solution is infinite dimensional, and the data required to render it unique is determined by the measured strain field. In contrast, for two independent displacement fields such that the principal directions of the resulting strain fields are different, the space of possible solutions is eight dimensional, and given additional data, like the value of the shear modulus at four locations, or over a calibration region, we may determine the shear modulus everywhere. We have also considered simple analytical examples that verify these results and offer additional insights. The results derived in this paper may be used as guidelines by the practitioners of elasticity imaging in designing more robust and accurate imaging protocols.
NASA Astrophysics Data System (ADS)
Ridzuan, M. J. M.; Hafis, S. M.; Saifullah, K. N.; Syahrullail, S.
2012-06-01
Large quantities of lubricant are being widely used in the metal forming industry and this high consumption is negatively affecting the environment. Finding an alternative to this current situation is getting more serious and urgent in response to environmental and operational cost pressures. This paper deals with an experimental investigation to obtain the minimum quantity of lubricant (MQL) of RBD palm stearin, which is used as lubricant between the contact sliding surfaces of the taper die and billet via plane-strain-extrusion apparatus. The symmetrical workpieces are designed as combined billets made from pure aluminium A1100. The dies of the apparatus are made of SKD 11 steel. The extrusion ratio of the processes is 3 and the workpieces are extruded by hydraulic press machine. Four conditions of the quantity selected are 0.1 mg, 1 mg, 5 mg, and 20 mg. The analysis of the result shows that the conditions of the quantity are in the load reducing order from 0.1 mg, 1mg and 5 mg. The highest distribution of surface roughness is at 0.1 mg, whereby for others, the conditions are quite similar. However, the distribution of velocity and effective strain are lowest at 5 mg. The minimum quantity of lubricant (MQL) of the RBD palm stearin as lubricant on the contact sliding surfaces in planestrain-extrusion is determined based on the results of load, surface roughness, velocity and effective strain.
Plane strain finite element analysis of sheet forming operations including bending effects
NASA Astrophysics Data System (ADS)
Cho, Uk Youn
1993-01-01
An improved finite element method suitable for the plane-strain analysis of sheet metal forming operations is presented. The method incorporates a computationally efficient shell model and a consistent frictional contact algorithm through an implicit updated Lagrangian formulation. The workpiece material model is rigid-viscoplastic with a choice of power law hardening and plastic normal anisotropy and is capable of modeling a wide variety of sheet metals. A simplified nonlinear incremental shell theory is employed along with an optional reduced integration through the thickness for computational efficiency, while retaining the advantages of the kinematic model containing the bending effects. Complex tool geometry can be handled by discrete data points, by primitives (lines and arcs), or by analytical functions. The capabilities of the method are demonstrated through verification problems and comparisons with experimental data, benchmark results, and published data for several practical problems of the sheet metal forming industry. The problems include stretching and/or deep drawing operations, simulation of automobile panel section, and brake bending operation. As an independent investigation from the first portion of the dissertation, measured data from a set of simple bending experiments of two types of aluminum are presented and analyzed. Generated data from the experiments include strain histories (loading and unloading), spring back information (spring back angle and strains), and friction coefficients. As a by-product, a simple way of estimating the friction coefficient (Coulomb's law) during a bending operation is proposed and demonstrated.
NASA Astrophysics Data System (ADS)
Kvasha, Oleg V.; Boström, Anders; Glushkova, Natalia V.; Glushkov, Evgeny V.
2011-08-01
The propagation of in-plane (P-SV) waves in a symmetrically three-layered thick plate with a periodic array of interface cracks is investigated. The exact dispersion relation is derived based on an integral equation approach and Floquet's theorem. The interface cracks can be a model for interface damage, but a much simpler model is a recently developed spring boundary condition. This boundary condition is used for the thick plate and also in the derivation of plate equations with the help of power series expansions in the thickness coordinate. For low frequencies (cracks small compared to the wavelength) the three approaches give more or less coinciding dispersion curves, and this is a confirmation that the spring boundary condition is a reasonable approximation at low frequencies.
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.
NASA Astrophysics Data System (ADS)
EL-Bealy, Mostafa Omar
2012-06-01
In a study of the early stages of dendritic solidification in the direct-chill cast sheet ingots, the coupled effect of interdendritic strain and macrosegregation on the interdendritic cracks formation in dendritic equiaxed structure has been investigated by the metallographic study of ingot samples and by performing a set of mathematical analyses for AA-6061 and AA-1050 aluminum alloys. The metallographic investigation contains microstructure examinations and macrosegregation measurements of collected samples from plant trials. The mathematical analysis consists of a two-dimensional (2-D) fluid flow, heat flow, interdendritic strain, and macrosegregation-coupled model. Also, a simple approach to measure interdendritic crack has been developed based on the accumulative interdendritic strain criterion, local dendritic phases, and the crystal distortion correlation factor resulting from steep positive local segregation. The model predications have clarified the effect of high positive macrosegregation on the surface and subsurface interdendritic crack formation. It has been revealed that interdendritic strain starts to generate just below the liquidus temperature, resulting from shrinkage of liquid→solid phase transformation and contraction of dendritic solid in the incoherent mushy region. In this region, the coupled effect of the shrinkage/contraction mechanism increases the interdendritic distances between equiaxed crystals and the interdendritic crack begins to nucleate. Subsequently, in the coherent mushy region, the different interdendritic strain sources start to affect significantly the distances between equiaxed crystals in a diverse way, and therefore, the final morphology of interdendritic crack begins to form. The mechanism of interdendritic crack formation during dendritic equiaxed structure solidification and the possible solutions to this problem are discussed.
NASA Technical Reports Server (NTRS)
Obrien, T. K.
1991-01-01
An analysis utilizing laminated plate theory is developed to calculate the strain energy release rate associated with local delaminations originating at off-axis, single ply, matrix cracks in laminates subjected to uniaxial loads. The analysis includes the contribution of residual thermal and moisture stresses to the strain energy released. Examples are calculated for the strain energy release rate associated with local delaminations originating at 90 degrees and angle-ply (non-90 degrees) matrix ply cracks in glass epoxy and graphite epoxy laminates. The solution developed may be used to assess the relative contribution of mechanical, residual thermal, and moisture stresses on the strain energy release rate for local delamination for a variety of layups and materials.
Strained-layer superlattice focal plane array having a planar structure
Kim, Jin K.; Carroll, Malcolm S.; Gin, Aaron; Marsh, Phillip F.; Young, Erik W.; Cich, Michael J.
2010-07-13
An infrared focal plane array (FPA) is disclosed which utilizes a strained-layer superlattice (SLS) formed of alternating layers of InAs and In.sub.xGa.sub.1-xSb with 0.ltoreq.x.ltoreq.0.5 epitaxially grown on a GaSb substrate. The FPA avoids the use of a mesa structure to isolate each photodetector element and instead uses impurity-doped regions formed in or about each photodetector for electrical isolation. This results in a substantially-planar structure in which the SLS is unbroken across the entire width of a 2-D array of the photodetector elements which are capped with an epitaxially-grown passivation layer to reduce or eliminate surface recombination. The FPA has applications for use in the wavelength range of 3-25 .mu.m.
Infrared focal plane arrays based on dots in a well and strained layer superlattices
NASA Astrophysics Data System (ADS)
Krishna, Sanjay
2009-01-01
In this paper, we will review some of the recent progress that we have made on developing single pixel detectors and focal plane arrays based on dots-in-a-well (DWELL) heterostructure and Type II strained layer superlattice (SLS). The DWELL detector consists of an active region composed of InAs quantum dots embedded in InGaAs/GaAs quantum wells. By varying the thickness of the InGaAs well, the DWELL heterostructure allows for the manipulation of the operating wavelength and the nature of the transitions (bound-to-bound, bound-to-quasibound and bound-to-continuum) of the detector. Based on these principles, DWELL samples were grown using molecular beam epitaxy and fabricated into 320 x 256 focal plane arrays (FPAs) with Indium bumps using standard lithography at the University of New Mexico. The FPA evaluated was hybridized to an Indigo 9705 readout integrated circuit (ROIC). From this evaluation, we have reported the first two-color, co-located quantum dot based imaging system that can be used to take multicolor images using a single FPA. We have also been investigating the use of miniband transitions in Type II SLS to develop infrared detectors using PIN and nBn based designs.
NASA Astrophysics Data System (ADS)
Salvo, Maxime; Sercombe, Jérôme; Helfer, Thomas; Sornay, Philippe; Désoyer, Thierry
2015-05-01
In this paper, the behavior of a dense UO2 (porosity less than 2%) was studied experimentally on a range of temperatures (1100-1700 °C) and strain rates (10-4-10-1 /s) representative of RIA loading conditions. The yield stress was found to increase with strain rate and to decrease with temperature. Macroscopic cracking of the samples was apparent after the tests at 1100 °C. Scanning Electron Microscopy (SEM) image analyses revealed a pronounced grain boundary cracking in the core of the samples tested at 10-1 /s and at 1550-1700 °C. A hyperbolic sine model for the viscoplastic strain rate with a clear dependency on porosity was first developed. It was completed by a Drucker-Prager yield criterion with associated plastic flow to account for the porosity increase induced by grain boundary cracking. Finite Elements simulations of the compression tests on the dense UO2 were then successfully compared to the stress-strain curves, post-test diameter profiles and porosities at the pellets' center, periphery and top extremity. The response of the grain boundary cracking model was then studied in biaxial compression, this condition being closer to that of the pellet during a RIA power transient.
NASA Astrophysics Data System (ADS)
Bao, Yi; Chen, Genda
2016-01-01
This study aims at evaluating the feasibility of strain measurement and crack detection in thin unbonded concrete pavement overlays with pulse prepump Brillouin optical time domain analysis. Single-mode optical fibers with two-layer and three-layer coatings, respectively, were applied as fully distributed sensors, their performances were compared with analytical predictions. They were successfully protected from damage during concrete casting of three full-scale concrete panels when 5 to 10-cm-thick protective mortar covers had been set for 2 h. Experimental results from three-point loading tests of the panels indicated that the strain distributions measured from the two types of sensors were in good agreement, and cracks can be detected at sharp peaks of the measured strain distributions. The two-layer and three-layer coated fibers can be used to measure strains up to 2.33% and 2.42% with a corresponding sensitivity of 5.43×10-5 and 4.66×10-5 GHz/μɛ, respectively. Two cracks as close as 7 to 9 cm can be clearly detected. The measured strains in optical fiber were lower than the analytical prediction by 10% to 25%. Their difference likely resulted from strain transfer through various coatings, idealized point loading, varying optical fiber embedment, and concrete heterogeneity.
Andrews, D.J.
1985-01-01
A numerical boundary integral method, relating slip and traction on a plane in an elastic medium by convolution with a discretized Green function, can be linked to a slip-dependent friction law on the fault plane. Such a method is developed here in two-dimensional plane-strain geometry. Spontaneous plane-strain shear ruptures can make a transition from sub-Rayleigh to near-P propagation velocity. Results from the boundary integral method agree with earlier results from a finite difference method on the location of this transition in parameter space. The methods differ in their prediction of rupture velocity following the transition. The trailing edge of the cohesive zone propagates at the P-wave velocity after the transition in the boundary integral calculations. Refs.
Wireless Open-Circuit In-Plane Strain and Displacement Sensor Requiring No Electrical Connections
NASA Technical Reports Server (NTRS)
Woodard, Stanley E. (Inventor)
2014-01-01
A wireless in-plane strain and displacement sensor includes an electrical conductor fixedly coupled to a substrate subject to strain conditions. The electrical conductor is shaped between its ends for storage of an electric field and a magnetic field, and remains electrically unconnected to define an unconnected open-circuit having inductance and capacitance. In the presence of a time-varying magnetic field, the electrical conductor so-shaped resonates to generate harmonic electric and magnetic field responses. The sensor also includes at least one electrically unconnected electrode having an end and a free portion extending from the end thereof. The end of each electrode is fixedly coupled to the substrate and the free portion thereof remains unencumbered and spaced apart from a portion of the electrical conductor so-shaped. More specifically, at least some of the free portion is disposed at a location lying within the magnetic field response generated by the electrical conductor. A motion guidance structure is slidingly engaged with each electrode's free portion in order to maintain each free portion parallel to the electrical conductor so-shaped.
A New Look at Self-Similarity in Strained Plane Wakes. 1.3
NASA Technical Reports Server (NTRS)
Rogers, Michael M.; Mansour, Nagi N. (Technical Monitor)
2001-01-01
In early experiments, A. J. Reynolds and J. F. Keffer sought to determine whether plane wakes of circular cylinders, when strained by a wind tunnel of varying cross-section, evolved in accordance with an analytically derived self-similar solution. As pointed out by Reynolds, for the strain geometry considered this self-similar solution indicated exponential growth of the viscous term in the mean momentum equation, a result which he interpreted as suggesting that such wakes would eventually relaminarize. The experimental results were found not to agree with the similarity theory and recent direct numerical simulations confirm this. However, a more general self-similar analysis of the kind suggested by W. K. George is found to lead to families of possible similarity solutions, some of which do indeed describe the observed flaw behavior. These equilibrium similarity solutions result from creating a balance in the governing equations by grouping certain terms. For these solutions the viscous terms can be retained in the analysis.
Strain-induced crack formations in PDMS/DXA drug collars.
Warner, J A; Polkinghorne, J C; Gonerka, J; Meyer, S; Luo, B; Frethem, C; Haugstad, G
2013-07-01
Drug-eluting systems are currently used in cardiac leads in order to reduce inflammation and fibrosis at the lead-tissue interface. Drug release from these drug delivery systems can be modulated by the manufacturing processes used to create the drug systems and assemble them onto the cardiac lead. In this study, scanning electron microscopy, atomic force microscopy and Raman microscopy are employed to explore the material characteristics of a polydimethylsiloxane-dexamethasone acetate drug collar used on cardiac leads when varying the strain during collar assembly on the lead. A novel test fixture was created in order to investigate these drug collars under simulated stresses. Measurements of the collar while fitted to a rod revealed microcracks that are hypothesized to affect the drug release performance, resulting in increased drug elution. It was found that the strain that occurs during assembly of the collar onto the lead is a key factor in the formation of these microcracks. Results also suggest that cracks tend to form in areas of high drug particle density, and propagate between drug particles. PMID:23541599
Wang, Cheng-Cai; Mao, Yun-Wei; Shan, Zhi-Wei; Dao, Ming; Li, Ju; Sun, Jun; Ma, Evan; Suresh, Subra
2013-12-01
Metallic glasses (MGs) exhibit greater elastic limit and stronger resistance to plastic deformation than their crystalline metal counterparts. Their capacity to withstand plastic straining is further enhanced at submicrometer length scales. For a range of microelectromechanical applications, the resistance of MGs to damage and cracking from thermal and mechanical stress or strain cycling under partial or complete constraint is of considerable scientific and technological interest. However, to our knowledge, no real-time, high-resolution transmission electron microscopy observations are available of crystallization, damage, and failure from the controlled imposition of cyclic strains or displacements in any metallic glass. Here we present the results of a unique in situ study, inside a high-resolution transmission electron microscope, of glass-to-crystal formation and fatigue of an Al-based MG. We demonstrate that cyclic straining progressively leads to nanoscale surface roughening in the highly deformed region of the starter notch, causing crack nucleation and formation of nanocrystals. The growth of these nanograins during cyclic straining impedes subsequent crack growth by bridging the crack. In distinct contrast to this fatigue behavior, only distributed nucleation of smaller nanocrystals is observed with no surface roughening under monotonic deformation. We further show through molecular dynamics simulation that these findings can be rationalized by the accumulation of strain-induced nonaffine atomic rearrangements that effectively enhances diffusion through random walk during repeated strain cycling. The present results thus provide unique insights into fundamental mechanisms of fatigue of MGs that would help shape strategies for material design and engineering applications. PMID:24255113
Wang, Cheng-Cai; Mao, Yun-Wei; Shan, Zhi-Wei; Dao, Ming; Li, Ju; Sun, Jun; Ma, Evan; Suresh, Subra
2013-01-01
Metallic glasses (MGs) exhibit greater elastic limit and stronger resistance to plastic deformation than their crystalline metal counterparts. Their capacity to withstand plastic straining is further enhanced at submicrometer length scales. For a range of microelectromechanical applications, the resistance of MGs to damage and cracking from thermal and mechanical stress or strain cycling under partial or complete constraint is of considerable scientific and technological interest. However, to our knowledge, no real-time, high-resolution transmission electron microscopy observations are available of crystallization, damage, and failure from the controlled imposition of cyclic strains or displacements in any metallic glass. Here we present the results of a unique in situ study, inside a high-resolution transmission electron microscope, of glass-to-crystal formation and fatigue of an Al-based MG. We demonstrate that cyclic straining progressively leads to nanoscale surface roughening in the highly deformed region of the starter notch, causing crack nucleation and formation of nanocrystals. The growth of these nanograins during cyclic straining impedes subsequent crack growth by bridging the crack. In distinct contrast to this fatigue behavior, only distributed nucleation of smaller nanocrystals is observed with no surface roughening under monotonic deformation. We further show through molecular dynamics simulation that these findings can be rationalized by the accumulation of strain-induced nonaffine atomic rearrangements that effectively enhances diffusion through random walk during repeated strain cycling. The present results thus provide unique insights into fundamental mechanisms of fatigue of MGs that would help shape strategies for material design and engineering applications. PMID:24255113
Wentzell, Scott; Nesbitt, Robert Sterling; Macione, James; Kotha, Shiva
2016-07-01
The maintenance of healthy bone tissue depends upon the ability of osteocytes to respond to mechanical cues on the cellular level. The combination of digital volume correlation and second harmonic generation microscopy offers the opportunity to investigate the mechanical microenvironment of intact bone on the scale of individual osteocytes. Adult human femurs were imaged under tensile loads of 5 and 15MPa and volumes of approximately 492×429×31μm(3) were analyzed, along with an image of a bone microcrack under the same loading conditions. Principal strains were significantly higher in three-dimensional digital volume correlation when compared to two-dimensional digital image correlation. The average maximum principal strain magnitude was 5.06-fold greater than the applied global strain, with peak strains of up to 23.14-fold over global strains measured at the borders of osteocyte lacunae. Finally, a microcrack that initiated at an osteocyte lacunae had its greatest tensile strain magnitudes at the crack expansion front in the direction of a second lacunae, but strain at the crack border was reduced to background strain magnitudes upon breaching the second lacunae. This serveed to demonstrate the role of lacunae in initiating, mediating and terminating microcrack growth. PMID:26807766
NASA Astrophysics Data System (ADS)
Benito, L.; Ballesteros, C.; Ward, R. C. C.
2014-04-01
We report on the magnetic and structural characterization of high lattice-mismatched [Dy2nm/SctSc] superlattices, with variable Sc thickness tSc= 2-6 nm. We find that the characteristic in-plane effective hexagonal magnetic anisotropy K66,ef reverses sign and undergoes a dramatic reduction, attaining values of ≈13-24 kJm-3, when compared to K66=-0.76 MJm-3 in bulk Dy. As a result, the basal plane magnetic anisotropy is dominated by a uniaxial magnetic anisotropy (UMA) unfound in bulk Dy, which amounts to ≈175-142 kJm-3. We attribute the large downsizing in K66,ef to the compression epitaxial strain, which generates a competing sixfold magnetoelastic (MEL) contribution to the magnetocrystalline (strain-free) magnetic anisotropy. Our study proves that the in-plane UMA is caused by the coupling between a giant symmetry-breaking MEL constant Mγ ,22≈1 GPa and a morphic orthorhombiclike strain ɛγ ,1≈10-4, whose origin resides on the arising of an in-plane anisotropic strain relaxation process of the pseudoepitaxial registry between the nonmagnetic bottom layers in the superstructure. This investigation shows a broader perspective on the crucial role played by epitaxial strains at engineering the magnetic anisotropy in multilayers.
NASA Technical Reports Server (NTRS)
Buczek, M. B.; Gregory, M. A.; Herakovich, C. T.
1983-01-01
CLFE2D is a two dimensional generalized plane strain finite element code, using a linear, four node, general quadrilateral, isoparametric element. The program is developed to calculate the displacements, strains, stresses, and strain energy densities in a finite width composite laminate. CLFE2D offers any combination of the following load types: nodal displacements, nodal forces, uniform normal strain, or hygrothermal. The program allows the user to input one set of three dimensional orthotropic material properties. The user can then specify the angle of material principal orientation for each element in the mesh. Output includes displacements, stresses, strains and strain densities at points selected by the user. An option is also available to plot the underformed and deformed finite element meshes.
Line Spring Model and Its Applications to Part-Through Crack Problems in Plates and Shells
NASA Technical Reports Server (NTRS)
Erdogan, F.; Aksel, B.
1986-01-01
The line spring model is described and extended to cover the problem of interaction of multiple internal and surface cracks in plates and shells. The shape functions for various related crack geometries obtained from the plane strain solution and the results of some multiple crack problems are presented. The problems considered include coplanar surface cracks on the same or opposite sides of a plate, nonsymmetrically located coplanar internal elliptic cracks, and in a very limited way the surface and corner cracks in a plate of finite width and a surface crack in a cylindrical shell with fixed end.
Line spring model and its applications to part-through crack problems in plates and shells
NASA Technical Reports Server (NTRS)
Erdogan, Fazil; Aksel, Bulent
1988-01-01
The line spring model is described and extended to cover the problem of interaction of multiple internal and surface cracks in plates and shells. The shape functions for various related crack geometries obtained from the plane strain solution and the results of some multiple crack problems are presented. The problems considered include coplanar surface cracks on the same or opposite sides of a plate, nonsymmetrically located coplanar internal elliptic cracks, and in a very limited way the surface and corner cracks in a plate of finite width and a surface crack in a cylindrical shell with fixed end.
NASA Astrophysics Data System (ADS)
Terasaki, Hidenori; Shintome, Yutaro; Komizo, Yu-ichi; Ohata, Mitsuru; Moriguchi, Koji; Tomio, Yusaku
2015-05-01
Global effect of Bain-zone boundaries and the local effect of close-packed plane (CP) boundaries on the path of secondary cleavage cracks (observed on a fractured V-notch Charpy specimen) were visualized and discussed in simulated coarse-grained HAZ of bainitic steel. Microstructural unit map (Bain-zone map and CP map) was obtained by electron backscatter diffraction method for a prior austenite grain of a few hundred micrometers. Furthermore, a correlation between CP boundaries and sites that favored formation of the blocky martensite-austenite (M-A) constituent was confirmed. It was clarified that two crack deviation/local changing factors (CP boundaries and blocky M-A) are paired.
Zaitsev, V Yu; Matveev, L A
2012-01-01
Mechanisms of acoustic energy dissipation in heterogeneous solids attract much attention in view of their importance for material characterization, nondestructive testing, and geophysics. Due to the progress in measurement techniques in recent years, it has been revealed that rocks can demonstrate extremely high strain sensitivity of seismoacoustic loss. In particular, it has been found that strains of order 10(-8) produced by lunar and solar tides are capable of causing variations in the seismoacoustic decrement on the order of several percent. Some laboratory data (although obtained for higher frequencies) also indicate the presence of very high dissipative nonlinearity. Conventionally discussed dissipation mechanisms (thermoelastic loss in dry solids, Biot and squirt-type loss in fluid-saturated ones) do not suffice to interpret such data. Here the dissipation at individual cracks is revised taking into account the influence of wavy asperities of their surfaces quite typical of real cracks, which can drastically change the values of the relaxation frequencies and can result in giant strain sensitivity of the dissipation without the necessity of assuming the presence of unrealistically thin (and, therefore, unrealistically soft) cracks. In particular, these mechanisms suggest interpretation for observations of pronounced amplitude modulation of seismo-acoustic waves by tidal strains. PMID:22280566
NASA Astrophysics Data System (ADS)
Komaragiri, Uday; Agnew, Sean R.; Gangloff, Richard P.; Begley, Matthew R.
This paper quantifies the effect of strain gradient plasticity (SGP) on crack tip stress elevation for a broad range of applied loading conditions and constitutive model parameters, including both macroscopic hardening parameters and individual material length-scales controlling gradient effects. Finite element simulations incorporating the Fleck-Hutchinson SGP theory are presented for an asymptotically sharp stationary crack. Results identify fundamental scaling relationships describing (i) the physical length-scales over which strain gradients are prominent, and (ii) the degree of stress elevation over conventional Hutchinson-Rice-Rosengren (HRR) fields. Results illustrate that the three length-scale theory predicts much larger SGP effects than the single length-scale theory. Critically, the first length-scale parameter dominates SGP stress elevation: this suggests that SGP effects in fracture can be predicted using the length-scales extracted from nanoindentation, which exhibits similar behavior. Transitional loading/material parameters are identified that establish regimes of SGP relevance: this provides the foundation for the rational application of SGP when developing new micromechanical models of crack tip damage mechanisms and associated subcritical crack propagation behavior in structural alloys.
NASA Technical Reports Server (NTRS)
Oldrieve, R. E.
1978-01-01
Analysis of high temperature low cycle fatigue of AISI 304LC and 316 stainless steels by the method of strainrange partitioning results in four separate strainrange versus life relationships, depending upon the way in which creep-strain and plastic strain are combined within a cycle. Fractography is used in this investigation of the creep-fatigue interaction associated with these cycles. The PP and PC-cycle fractures were transgranular. The PC-cycle resulted in fewer cycles of initiation and shorter total cyclic life for the same applied inelastic strainrange. The CC-cycle had mixed transgranular and intergranular fracture, fewer cycles of initiation and shorter cycle life than PP or PC. The CP-cycle had fully integranular cracking, and failed in fewer cycles than were required for cracks to initate for PP,PC, and CC.
Cracked shells under skew-symmetric loading
NASA Technical Reports Server (NTRS)
Lelale, F.
1982-01-01
A shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and antiplane elasticity solutions. Extensive results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform inplane shearing, out of plane shearing, and torsion. The effect of orthotropy on the results is also studied.
Stress corrosion cracking of Alloy 600 using the constant strain rate test
Bulischeck, T.S.; Van Rooyen, D.
1981-10-01
Nuclear grade production tubing of Alloy 600 was evaluated for stress corrosion cracking (SCC) susceptibility in high purity water at 365, 345, 325, and 290 C. Reverse tube U-bend specimens provided crack initiation data and constant extension rate tests were employed to determine the crack velocities experienced in th crack propagation stage. Initial results indicate that a linear extrapolation of data received from high temperature tests can be used to predict the service life of steam generator tubing that has been plastically deformed or is continually deforming by ''denting.''
NASA Astrophysics Data System (ADS)
Li, Hong; Tsai, Charlie; Koh, Ai Leen; Cai, Lili; Contryman, Alex W.; Fragapane, Alex H.; Zhao, Jiheng; Han, Hyun Soon; Manoharan, Hari C.; Abild-Pedersen, Frank; Nørskov, Jens K.; Zheng, Xiaolin
2016-01-01
As a promising non-precious catalyst for the hydrogen evolution reaction (HER; refs ,,,,), molybdenum disulphide (MoS2) is known to contain active edge sites and an inert basal plane. Activating the MoS2 basal plane could further enhance its HER activity but is not often a strategy for doing so. Herein, we report the first activation and optimization of the basal plane of monolayer 2H-MoS2 for HER by introducing sulphur (S) vacancies and strain. Our theoretical and experimental results show that the S-vacancies are new catalytic sites in the basal plane, where gap states around the Fermi level allow hydrogen to bind directly to exposed Mo atoms. The hydrogen adsorption free energy (ΔGH) can be further manipulated by straining the surface with S-vacancies, which fine-tunes the catalytic activity. Proper combinations of S-vacancy and strain yield the optimal ΔGH = 0 eV, which allows us to achieve the highest intrinsic HER activity among molybdenum-sulphide-based catalysts.
Cracked shells under skew-symmetric loading. [Reissner theory
NASA Technical Reports Server (NTRS)
Delale, F.
1981-01-01
The general problem of a shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and anti-plane elasticity solutions. Results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform in-plane shearing, out of plane shearing, and torsion. The problem is formulated for specially orthostropic materials, therefore, the effect of orthotropy on the results is also studied.
Fracture Analysis of Semi-Elliptical Surface Cracks in Ductile Materials
NASA Technical Reports Server (NTRS)
Daniewicz, S. R.; Newman, J. C., Jr.; Leach, A. M.
2004-01-01
Accurate life assessment of structural components may require advanced life prediction criteria and methodologies. Structural components often exhibit several different types of defects, among the most prevalent being surface cracks. A semi-elliptical surface crack subjected to monotonic loading will exhibit stable crack growth until the crack has reached a critical size, at which the crack loses stability and fracture ensues (Newman, 2000). The shape and geometry of the flaw are among the most influential factors. When considering simpler crack configurations, such as a through-the-thickness crack, a three-dimensional (3D) geometry may be modeled under the approximation of two-dimensional (2D) plane stress or plane strain. The more complex surface crack is typically modeled numerically with the Finite Element Method (FEM). A semi-elliptical surface crack is illustrated in Figure 1-1.
NASA Astrophysics Data System (ADS)
Wu, Huaping; Ma, Xuefu; Zhang, Zheng; Zhu, Jun; Wang, Jie; Chai, Guozhong
2016-04-01
A nonlinear thermodynamic model based on the vertically aligned nanocomposite (VAN) thin films of ferroelectric-metal oxide system has been developed to investigate the physical properties of the epitaxial Ba0.6Sr0.4TiO3 (BST) films containing vertical Sm2O3 (SmO) nanopillar arrays on the SrTiO3 substrate. The phase diagrams of out-of-plane lattice mismatch vs. volume fraction of SmO are calculated by minimizing the total free energy. It is found that the phase transformation and dielectric response of BST-SmO VAN systems are extremely dependent on the in-plane misfit strain, the out-of-plane lattice mismatch, the volume fraction of SmO phase, and the external electric field applied to the nanocomposite films at room temperature. In particular, the BST-SmO VAN systems exhibit higher dielectric properties than pure BST films. Giant dielectric response and maximum tunability are obtained near the lattice mismatch where the phase transition occurs. Under the in-plane misfit strain of umf=0.3 % and the out-of-plane lattice mismatch of u3=0.002 , the dielectric tunability can be dramatically enhanced to 90% with the increase of SmO volume fraction, which is well consistent with previous experimental results. This work represents an approach to further understand the dependence of physical properties on the lattice mismatch (in-plane and out-of-plane) and volume fraction, and to manipulate or optimize functionalities in the nanocomposite oxide thin films.
Comparison of fatigue crack propagation in Modes I and III
Ritchie, R.O.
1985-06-01
The propagation behavior of fatigue cracks in Mode III (anti-plane shear), measured under cyclic torsion, is described and compared with more commonly encountered behavior under Mode I (tensile opening) loads. It is shown that a unique, global characterization of Mode III growth rates, akin to the Paris ''law'' in Mode I, is only possible if characterizating parameters appropriate to large-scale yielding are employed and allowance is made for crack tip shielding from sliding crack surface interference (i.e., friction and abrasion) between mating fracture surfaces. Based on the crack tip stress and deformation fields for Mode III stationary cracks, the cyclic crack tip displacement, (..delta..CTD/sub III/, and plastic strain intensity range ..delta..GAMMA/sub III/, have been proposed and are found to provide an adequate description of behavior in a range of steels, provided crack surface interference is minimized. The magnitude of this interference, which is somewhat analogous to crack closure in Mode I, is further examined in the light of the complex fractography of torsional fatigue failures and the question of a ''fatigue threshold'' for Mode III crack growth. Finally, micro-mechanical models for cyclic crack extension in anti-plane shear are briefly described, and the contrasting behavior between Mode III and Mode I cracks subjected to simple variable amplitude spectra is examined in terms of the differing role of crack tip blunting and closure in influencing shear, as opposed to tensile opening, modes of crack growth.
NASA Astrophysics Data System (ADS)
Garcia, V.; Sidis, Y.; Marangolo, M.; Vidal, F.; Eddrief, M.; Bourges, P.; Maccherozzi, F.; Ott, F.; Panaccione, G.; Etgens, V. H.
2007-09-01
The α-β magnetostructural phase transition in MnAs/GaAs(111) epilayers is investigated by elastic neutron scattering. The in-plane parameter of MnAs remains almost constant with temperature from 100 to 420 K, following the thermal evolution of the GaAs substrate. This induces a temperature dependent biaxial strain that is responsible for an α-β phase coexistence and, more importantly, for the stabilization of the ferromagnetic α phase at a higher temperature than in the bulk. We explain the premature appearance of the β phase at 275 K and the persistence of the ferromagnetic α phase up to 350 K with thermodynamical arguments based on the MnAs phase diagram. It results that the biaxial strain in the hexagonal plane is the key parameter to extend the ferromagnetic phase well over room temperature.
Garcia, V; Sidis, Y; Marangolo, M; Vidal, F; Eddrief, M; Bourges, P; Maccherozzi, F; Ott, F; Panaccione, G; Etgens, V H
2007-09-14
The alpha-beta magnetostructural phase transition in MnAs/GaAs(111) epilayers is investigated by elastic neutron scattering. The in-plane parameter of MnAs remains almost constant with temperature from 100 to 420 K, following the thermal evolution of the GaAs substrate. This induces a temperature dependent biaxial strain that is responsible for an alpha-beta phase coexistence and, more importantly, for the stabilization of the ferromagnetic alpha phase at a higher temperature than in the bulk. We explain the premature appearance of the beta phase at 275 K and the persistence of the ferromagnetic alpha phase up to 350 K with thermodynamical arguments based on the MnAs phase diagram. It results that the biaxial strain in the hexagonal plane is the key parameter to extend the ferromagnetic phase well over room temperature. PMID:17930469
NASA Astrophysics Data System (ADS)
Peeters, Michael; Panajotov, Krassimir P.; Verschaffelt, Guy; Nagler, Bob; Albert, Jan; Thienpont, Hugo; Veretennicoff, Irina P.; Danckaert, Jan
2002-06-01
It is well known that vertical-cavity surface-emitting lasers (VCSELs) can abruptly switch between two orthogonal linear polarization states if the current is changed. The impact of externally induced in-plane anisotropic strain on this switching was experimentally demonstrated in proton-implanted devices. In this contribution we present a further and thorough experimental investigation of the polarization behavior of different types of VCSELs (proton-implanted, air-post and oxide-confined), under varying strain conditions. We first measure the influence of the strain on the orientation of the axes of the linear polarization states. These axes can be rotated from the crystallographic direction [110] over [100] to [110]. At the same time, we monitor the exact birefringence. From the combination of these two measurements the amount of residual strain in these devices is deduced. Applying strain not only changes the frequency splitting between the two modes (due to birefringence) and their orientation, but also lifts the degeneracy in the gain of the polarization modes. We therefore also measure the gain difference (dichroism) as a function of the applied strain, via the mode suppression ratio and the optical spectrum. Due to the effect on both the birefringence and the dichroism, strain also changes the position of the polarization switching point as a function of current and can lead to the observation of double (consecutive) polarization switching. All this experimental evidence will help to build up a better understanding of the physics of polarization switching in VCSELs.
Shimada, T; Okuno, J; Ishii, Y; Kitamura, T
2012-03-01
We investigated a nanometer-sharp magnetic domain wall (DW) structure in a free-standing Fe(110) monolayer and studied the crucial role of in-plane strain using fully unconstrained noncollinear ab initio spin-density-functional theory calculations within the generalized gradient approximation. The DW width is calculated to be 0.86 nm. A precise vector-field description of the magnetization density revealed that a noncollinear character in the DW was spatially confined between atoms, whereas a collinear and high magnetization density was localized around each atom. In the rapid rotation of magnetic moments in the DW, we found an electron rearrangement from the d(zx) and d(x(2)-y(2)) states to the d(xy), d(yz) and d(z(2)) states due to a shift of band structures. Applied tensile and compressive in-plane strains both bring about narrower DWs in the monolayer except when the strain is small. The strain dependence of the DW width is discussed in terms of both exchange interaction and magnetocrystalline anisotropy. PMID:22322862
Kirkwood, Jonah; Ghetler, Andrew; Sedman, Jacqueline; Leclair, Daniel; Pagotto, Franco; Austin, John W; Ismail, Ashraf A
2006-10-01
A method was developed for whole-organism fingerprinting of Clostridium botulinum isolates by focal plane array Fourier transform infrared (FPA-FTIR) spectroscopy. A database of 150,000 infrared spectra of 44 strains of C. botulinum was acquired using a FPA-FTIR imaging spectrometer equipped with a 16 x 16 array detector to evaluate the ability of FTIR spectroscopy to differentiate the 44 strains. The database contained strains from C. botulinum groups I and II producing botulinum neurotoxin of serotypes A, B, E, and F. All strains were grown on each of three agar media (brain heart infusion, McClung Toabe agar base, and universal) prior to spectral acquisition. Given the dependence of the infrared spectra of microorganisms on the composition of the growth medium, the spectra were initially separated into three subsets corresponding to the three growth media employed. However, the replicate spectra of all strains, regardless of growth medium, were properly clustered by hierarchical cluster analysis based on differences in their infrared spectral profiles in three narrow spectral regions (1,428 to 1,412, 1,296 to 1,284, and 1,112 to 1,100 cm(-1)). The dendrogram generated from the FTIR data revealed complete separation between group I and group II strains. The spectral differences between group I and group II strains allowed accurate classification of C. botulinum strains at the group level in two blind validation studies (n = 40). These results demonstrate that FPA-FTIR spectroscopy has the potential for rapid discrimination of group I and group II C. botulinum strains in less than 3 min per sample. PMID:17066916
NASA Technical Reports Server (NTRS)
Morscher, Gregory N.; Yun, Hee Mann; DiCarlo, James A.
2007-01-01
The tensile mechanical properties of ceramic matrix composites (CMC) in directions off the primary axes of the reinforcing fibers are important for architectural design of CMC components that are subjected to multi-axial stress states. In this study, 2D-woven melt-infiltrated (MI) SiC/SiC composite panels with balanced fiber content in the 0 degree and 90 degree directions were tensile loaded in-plane in the 0 degree direction and at 45 degree to this direction. In addition, a 2D triaxially-braided MI composite panel with balanced fiber content in the plus or minus 67 degree bias directions and reduced fiber content in the axial direction was tensile loaded perpendicular to the axial direction tows (i.e., 23 degrees from the bias fibers). Stress-strain behavior, acoustic emission, and optical microscopy were used to quantify stress-dependent matrix cracking and ultimate strength in the panels. It was observed that both off-axis loaded panels displayed higher composite onset stresses for through-thickness matrix cracking than the 2D-woven 0/90 panels loaded in the primary 0 degree direction. These improvements for off-axis cracking strength can in part be attributed to higher effective fiber fractions in the loading direction, which in turn reduces internal stresses on critical matrix flaws for a given composite stress. Also for the 0/90 panel loaded in the 45 degree direction, an improved distribution of matrix flaws existed due to the absence of fiber tows perpendicular to the loading direction. In addition, for the +67/0/-67 braided panel, the axial tows perpendicular to the loading direction were not only low in volume fraction, but were also were well separated from one another. Both off-axis oriented panels also showed relatively good ultimate tensile strength when compared to other off-axis oriented composites in the literature, both on an absolute strength basis as well as when normalized by the average fiber strength within the composites. Initial
C-shaped specimen plane strain fracture toughness tests. [metallic materials
NASA Technical Reports Server (NTRS)
Buzzard, R. T.; Fisher, D. M.
1977-01-01
Test equipment, procedures, and data obtained in the evaluation of C-shaped specimens are presented. Observations reported on include: specimen preparation and dimensional measurement; modifications to the standard ASTM E 399 displacement gage, which permit punch mark gage point engagement; and a measurement device for determining the interior and exterior radii of ring segments. Load displacement ratios were determined experimentally which agreed with analytically determined coefficients for three different gage lengths on the inner surfaces of radially-cracked ring segments.
Full in-plane strain tensor analysis using the microscale ring-core FIB milling and DIC approach
NASA Astrophysics Data System (ADS)
Lunt, Alexander J. G.; Salvati, Enrico; Ma, Lifeng; Dolbyna, Igor P.; Neo, Tee K.; Korsunsky, Alexander M.
2016-09-01
Microscale Full In-plane Strain Tensor (FIST) analysis is crucial for improving understanding of residual stress and mechanical failure in many applications. This study outlines the first Focused Ion Beam (FIB) milling and Digital Image Correlation (DIC) based technique capable of performing precise, reliable and rapid quantification of this behaviour. The nature of semi-destructive FIB milling overcomes the main limitations of X-Ray Diffraction (XRD) strain tensor quantification: unstrained lattice parameter estimates are not required, analysis is performed in within a precisely defined 3D microscale volume, both amorphous and crystalline materials can be studied and access to X-ray/neutron facilities is not required. The FIST FIB milling and DIC experimental technique is based on extending the ring-core milling geometry to quantify the strain variation with angle and therefore benefits from the excellent precision and simple analytical approach associated with this method. In this study in-plane strain analysis was performed on sample of commercial interest: a porcelain veneered Yttria Partially Stabilised Zirconia (YPSZ) dental prosthesis, and was compared with the results of XRD. The two methods sample different gauge volumes and mechanical states: approximately plane stress for ring-core milling, and a through-thickness average for XRD. We demonstrate using complex analysis methods and Finite Element (FE) modelling that valid comparisons can be drawn between these two stress states. Excellent agreement was obtained between principal stress orientation and magnitudes, leading to realistic residual stress estimates that agree well with the literature (σAv ≈ 460 MPa) . As a measure of validity of the matching approach we report the upper and lower bounds on the (101) interplanar spacing of YPSZ that are found to correspond to the range 2.9586 - 2.9596 Å , closely matching published values.
NASA Technical Reports Server (NTRS)
Gabb, Timothy P.; Telesman, Jack; Banik, Anthony; McDevitt, Erin
2014-01-01
Intergranular fatigue crack initiation and growth due to environmental degradation, especially at notched features, can often limit the fatigue life of disk superalloys at high temperatures. For clear comparisons, the effects of alloy composition on cracking in air needs to be understood and compared separately from variables associated with notches and cracks such as effective stress concentration, plastic flow, stress relaxation, and stress redistribution. The objective of this study was to attempt using simple tensile tests of specimens with uniform gage sections to compare the effects of varied alloy composition on environment-assisted cracking of several powder metal and cast and wrought superalloys including ME3, LSHR, Udimet 720(TradeMark) ATI 718Plus(Registered TradeMark) alloy, Haynes 282(Trademark), and Inconel 740(TradeMark) Slow and fast strain-rate tensile tests were found to be a useful tool to compare propensities for intergranular surface crack initiation and growth. The effects of composition and heat treatment on tensile fracture strain and associated failure modes were compared. Environment interactions were determined to often limit ductility, by promoting intergranular surface cracking. The response of various superalloys and heat treatments to slow strain rate tensile testing varied substantially, showing that composition and microstructure can significantly influence environmental resistance to cracking.
NASA Astrophysics Data System (ADS)
Shin, J. K.; Ochiai, S.; Okuda, H.; Sugano, M.; Oh, S. S.
2008-11-01
The critical current at 77 K of multifilamentary Bi2223 composite tape was studied under applied tensile strain experimentally and analytically. Beyond the irreversible strain, the critical currents (IC) decreased significantly with increasing applied tensile strain (ɛc), due to the enhanced cracking of the Bi2223 filaments. The voltage generation in the voltage-current relation was calculated by the current share model in which the transport current is shared by the Bi2223 filament and Ag near the cracked portion. Then the critical current was estimated with a 1 µV cm-1 criterion. By the application of the current share model to the experimental result, the effective crack length responsible for the reduction in critical current was estimated, with which the change of critical current could be described satisfactorily as a function of applied strain.
Cracking phenomena in In{sub 0.25}Ga{sub 0.75}As films on InP substrates
Wu, X.; Weatherly, G.C.
1999-09-29
The strain relaxation of a series of In{sup 0.25}Ga{sub 0.75}As films grown on (100) InP substrates (lattice mismatch = 2%) has been studied by electron microscopy. The mechanisms of strain relief (in the first stages of growth) occurred by cracking on (0{bar 1}1), and by twinning on (111) and ({bar 1}11) planes. Cracking was a transitory process with the density of cracks being highest in a 20 nm thick film, while a 500 nm thick film was crack-free. These results are discussed in the context of different cracking and crack-healing models.
Stress corrosion cracking of zirconium in nitric acid
Beavers, J A; Griess, J C; Boyd, W K
1980-01-01
The susceptibility of zirconium and its common alloys to stress corrosion cracking (SCC) in nitric acid was investigated by slow strain-rate and constant deflection techniques. Cracking occurred at 25/sup 0/C over a wide range of acid concentrations and electrochemical potentials. The crack velocity increased slightly with increasing temperature. The failure mode was transgranular and the morphology was similar to SCC failures of zirconium alloys in other environments. The fracture was very orientation-dependent suggesting that it occurs on a single crystallographic plane in the material. The results of the study are not consistent with a hydrogen mechanism for cracking.
NASA Astrophysics Data System (ADS)
Zhang, P.; Wittmann, F. H.; Zhao, T. J.; Lehmann, E. H.; Tian, L.; Vontobel, P.
2010-08-01
Durability of reinforced concrete structures has become a crucial issue with respect to economy, ecology and sustainability. One major reason for durability problems of concrete structures is the limited strain capacity of cement-based materials under imposed tensile stress. By adding PVA fibers, a new material named Strain Hardening Cement-based Composites (SHCC) with high strain capacity can be produced. Due to the formation of multiple micro-cracks, wide cracks can be avoided in SHCC under an imposed strain. The high strain capacity, however, is beneficial with respect to durability only if the multi-crack formation in SHCC does not lead to significantly increased water penetration. If water and aggressive chemical compounds such as chlorides and sulfates dissolved in water penetrate into the cement-based matrix and reach the steel reinforcement service-life of reinforced concrete structures will be reduced significantly. In this project, neutron radiography was applied to observe and quantify the process of water penetration into uncracked SHCC and after the multi-crack formation. In addition, water penetration into integral water repellent cracked and uncracked SHCC, which has been produced by adding a silane-based water repellent agent to the fresh SHCC mortar has been investigated. Results will be discussed with respect to durability.
Albocher, U.; Barbone, P.E.; Richards, M.S.; Oberai, A.A.; Harari, I.
2014-01-01
We apply the adjoint weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing the displacements and appending a regularization term to the AWE formulation, a dramatic improvement in the reconstruction can be achieved. With these improvements, the advantages of the AWE method as a direct solution approach can be extended to a wider range of problems. PMID:25383085
NASA Technical Reports Server (NTRS)
Fisher, D. M.; Buzzard, R. J.
1979-01-01
Standard round specimen fracture test results compared satisfactorily with results from standard rectangular compact specimens machined from the same material. The location of the loading pin holes was found to provide adequate strength in the load bearing region for plane strain fracture toughness testing. Excellent agreement was found between the stress intensity coefficient values obtained from compliance measurements and the analytic solution proposed for inclusion in the standard test method. Load displacement measurements were made using long armed displacement gages and hollow loading cylinders. Gage points registered on the loading hole surfaces through small holes in the walls of the loading cylinders.
An orthotropic laminate composite containing a layer with a crack
NASA Technical Reports Server (NTRS)
Arin, K.
1974-01-01
A laminate composite containing an orthotropic layer with a crack situated normal to the interfaces, and bonded to two orthotropic half-planes of dissimilar materials was considered. The solutions for two different classes of orthotropic materials are presented. In each case, the problem was first reduced to a system of dual integral equations, then to a singular integral equation which was subsequently solved numerically for the stress intensity factors at the tip of the crack. The effect of the material properties on the stress intensity factor was investigated. The generalized plane stress and the plane strain were treated simultaneously.
Development of plane strain fracture toughness test for ceramics using Chevron notched specimens
NASA Technical Reports Server (NTRS)
Bubsey, R. T.; Shannon, J. L., Jr.; Munz, D.
1983-01-01
Chevron-notched four-point-bend and short-bar specimens have been used to determine the fracture toughness of sintered aluminum oxide and hot-pressed silicon nitride ceramics. The fracture toughness for Si3N4 is found to be essentially independent of the specimen size and chevron notch configuration, with values ranging from 4.6 to 4.9 MNm exp -3/2. In contrast, significant specimen size and notch geometry effects have been observed for Al2O3, with the fracture toughness ranging from 3.1 to 4.7 MNm exp -3/2. These effects are attributed to a rising crack growth resistance curve for the Al2O3 tested.
NASA Astrophysics Data System (ADS)
Fournier, L.; Serres, A.; Auzoux, Q.; Leboulch, D.; Was, G. S.
2009-01-01
The radiation-induced microstructure, strain localization, and iodine-induced stress corrosion cracking (I-SCC) behaviour of recrystallized Zircaloy-4 proton-irradiated to 2 dpa at 305 °C was examined. type dislocation loops having 1/3<1 1 2¯ 0> Burgers vector and a mean diameter and density of, respectively, 10 nm and 17 × 10 21 m -3 were observed while no Zr(Fe,Cr) 2 precipitates amorphization or Fe redistribution were detected after irradiation. After transverse tensile testing to 0.5% macroscopic plastic strain at room temperature, almost exclusively basal channels were imaged. Statistical Schmid factor analysis shows that irradiation leads to a change in slip system activation from prismatic to basal due to a higher increase of critical resolved shear stresses for prismatic slip systems than for basal slip system. Finite element calculations suggest that dislocation channeling occurs in the irradiated proton layer at an equivalent stress close to 70% of the yield stress of the irradiated material, i.e. while the irradiated layer is still in the elastic regime for a 0.5% applied macroscopic plastic strain. Comparative constant elongation rate tensile tests performed at a strain rate of 10 -5 s -1 in iodized methanol solutions at room temperature on specimens both unirradiated and proton-irradiated to 2 dpa demonstrated a detrimental effect of irradiation on I-SCC.
Uniform strain field inside a non-circular inhomogeneity with homogeneously imperfect interface in anisotropic anti-plane shear
NASA Astrophysics Data System (ADS)
Dai, Ming; Schiavone, Peter; Gao, Cun-Fa
2016-06-01
We re-examine the conclusion established earlier in the literature that in the presence of a homogeneously imperfect interface, the circular inhomogeneity is the only shape of inhomogeneity which can achieve a uniform internal strain field in an isotropic or anisotropic material subjected to anti-plane shear. We show that under certain conditions, it is indeed possible to design such non-circular inhomogeneities despite the limitation of a homogeneously imperfect interface. Our method proceeds by prescribing a uniform strain field inside a non-circular inhomogeneity via perturbations of the uniform strain field inside the analogous circular inhomogeneity and then subsequently identifying the corresponding (non-circular) shape via the use of a conformal mapping whose unknown coefficients are determined from a system of nonlinear equations. We illustrate our results with several examples. We note also that, for a given size of inhomogeneity, the minimum value of the interface parameter required to guarantee the desired uniform internal strain increases as the elastic constants of the inclusion approach those of the matrix. Finally, we discuss in detail the relationship between the curvature of the interface and the displacement jump across the interface in the design of such inhomogeneities.
Crack propagation and arrest in CFRP materials with strain softening regions
NASA Astrophysics Data System (ADS)
Dilligan, Matthew Anthony
Understanding the growth and arrest of cracks in composite materials is critical for their effective utilization in fatigue-sensitive and damage susceptible applications such as primary aircraft structures. Local tailoring of the laminate stack to provide crack arrest capacity intermediate to major structural components has been investigated and demonstrated since some of the earliest efforts in composite aerostructural design, but to date no rigorous model of the crack arrest mechanism has been developed to allow effective sizing of these features. To address this shortcoming, the previous work in the field is reviewed, with particular attention to the analysis methodologies proposed for similar arrest features. The damage and arrest processes active in such features are investigated, and various models of these processes are discussed and evaluated. Governing equations are derived based on a proposed mechanistic model of the crack arrest process. The derived governing equations are implemented in a numerical model, and a series of simulations are performed to ascertain the general characteristics of the proposed model and allow qualitative comparison to existing experimental results. The sensitivity of the model and the arrest process to various parameters is investigated, and preliminary conclusions regarding the optimal feature configuration are developed. To address deficiencies in the available material and experimental data, a series of coupon tests are developed and conducted covering a range of arrest zone configurations. Test results are discussed and analyzed, with a particular focus on identification of the proposed failure and arrest mechanisms. Utilizing the experimentally derived material properties, the tests are reproduced with both the developed numerical tool as well as a FEA-based implementation of the arrest model. Correlation between the simulated and experimental results is analyzed, and future avenues of investigation are identified
Effects of surface cracks and strain rate on the tensile behavior of Balmoral Red granite
NASA Astrophysics Data System (ADS)
Mardoukhi, Ahmad; Hokka, Mikko; Kuokkala, Veli-Tapani
2015-09-01
This paper presents an experimental procedure for studying the effects of surface cracks on the mechanical behavior of Balmoral Red granite under dynamic and quasi-static loading. Three different thermal shocks were applied on the surface of the Brazilian Disc test samples by keeping a flame torch at a fixed distance from the sample surface for 10, 30, and 60 seconds. Microscopy clearly shows that the number of the surface cracks increases with the duration of the thermal shock. After the thermal shock, the Brazilian Disc tests were performed using a servohydraulic materials testing machine and a compression Split Hopkinson Pressure Bar (SHPB) device. The results show that the tensile strength of the rock decreases and the rate sensitivity of the rock increases as more cracks are introduced to the structure. The DIC analysis of the Brazilian disc tests shows that the fracture of the sample initiates at the center of the samples or slightly closer to the incident bar contact point. This is followed by crushing of the samples at both contact points with the stress bars.
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.
NASA Astrophysics Data System (ADS)
Teomete, Egemen
2016-07-01
Earthquakes, material degradations and other environmental factors necessitate structural health monitoring (SHM). Metal foil strain gages used for SHM have low durability and low sensitivity. These factors motivated researchers to work on cement based strain sensors. In this study, the effects of temperature and moisture on electrical resistance, compressive and tensile strain gage factors (strain sensitivity) and crack sensitivity were determined for steel fiber reinforced cement based composite. A rapid increase of electrical resistance at 200 °C was observed due to damage occurring between cement paste, aggregates and steel fibers. The moisture—electrical resistance relationship was investigated. The specimens taken out of the cure were saturated with water and had a moisture content of 9.49%. The minimum electrical resistance was obtained at 9% moisture at which fiber–fiber and fiber–matrix contact was maximum and the water in micro voids was acting as an electrolyte, conducting electrons. The variation of compressive and tensile strain gage factors (strain sensitivities) and crack sensitivity were investigated by conducting compression, split tensile and notched bending tests with different moisture contents. The highest gage factor for the compression test was obtained at optimal moisture content, at which electrical resistance was minimum. The tensile strain gage factor for split tensile test and crack sensitivity increased by decreasing moisture content. The mechanisms between moisture content, electrical resistance, gage factors and crack sensitivity were elucidated. The relations of moisture content with electrical resistance, gage factors and crack sensitivities have been presented for the first time in this study for steel fiber reinforced cement based composites. The results are important for the development of self sensing cement based smart materials.
Insight into the band structure engineering of single-layer SnS2 with in-plane biaxial strain.
Zhou, Wei; Umezawa, Naoto
2016-03-21
The effects of in-plane biaxial strain on the electronic structure of a photofunctional material, single-layer SnS2, were systematically investigated using hybrid density functional calculations. The bonding diagram for the band gap was firstly proposed based on the crystal orbital overlap population analysis. The conduction band-edge of single-layer SnS2 is determined by the anti-bonding interaction between Sn-5s and S-3p orbitals, while the valence band-edge comes from the anti-bonding between the neighboring S atoms. It is found that the compressive strain not only decreases the indirect band gap of single-layer SnS2, but also effectively promotes the band-edges of the conduction band to realize the overall water splitting. Besides, the dispersion of the valence band of single-layer SnS2 becomes weaker with increasing tensile strain which is beneficial for the photo-excitation through direct transitions. PMID:26912413
Analysis of fatigue crack propagation
NASA Technical Reports Server (NTRS)
Liu, H. W.
1972-01-01
The correlation between fatigue crack propagation and stress intensity factor is analyzed. When determining fatigue crack propagation rate, a crack increment, delta a, and its corresponding increment in load cycles, delta N, are measured. Fatigue crack propagation must be caused by a shear and/or a normal separation mode. Both of these two processes are discrete if one looks at the atomic level. If the average deformation and fracture properties over the crack increments, delta a, can be considered as homogeneous, if the characteristic discrete lengths of sigma a, if the plastic zone size is small, and if a plate is thick enough to insure a plane strain case, da/dN is proportional to delta K squared. Any deviation of empirical data from this relation must be caused by the fact that one or more of these conditions are not satisfied. The effects of plate thickness and material inhomogeneity are discussed in detail. A shear separation mode of fatigue crack propagation is described and is used to illustrate the effects of material inhomogeneity.
NASA Astrophysics Data System (ADS)
Harikumar, M.; Sankar, N.; Chandrakaran, S.
2015-09-01
Since 1969, when the concept of earth reinforcing was brought about by Henry Vidal, a large variety of materials such as steel bars, tire shreds, polypropylene, polyester, glass fibres, coir and jute fibres etc. have been widely added to soil mass randomly or in a regular, oriented manner. The conventional reinforcements in use were two dimensional or planar, in the form of strips with negligible widths or in the form of sheets. In this investigation, a novel concept of multi oriented plastic reinforcement (hexa-pods) is discussed. Direct shear tests were conducted on unreinforced and reinforced dry fine, medium and coarse sands. Detailed parametric studies with respect to the effective grain size of soil (d10), normal stress (σ) and the volume ratio of hexa-pods (Vr) were performed. It was noticed that addition of hexa-pods resulted in increase in the shear strength parameters viz. peak deviatoric stresses and increased angle of internal friction. The hexa-pods also changed the brittle behaviour of unreinforced sand samples to ductile ones. Although the peak shear stress did not show a considerable improvement, the angle of internal friction improved noticeably. Addition of a single layer of reinforcement along the shear plane also reduced the post peak loss of strength and changed the soil behavior from brittle to a ductile one.
Development of a Plane Strain Tensile Geometry to Assess Shear Fracture in Dual Phase Steels
NASA Astrophysics Data System (ADS)
Taylor, M. D.; Matlock, D. K.; De Moor, E.; Speer, J. G.
2014-10-01
A geometrically modified sample capable of generating a triaxial stress state when tested on a standard uniaxial tensile frame was developed to replicate shear fractures observed during stretch bend tests and industrial sheet stamping operations. Seven commercially produced dual phase (DP) steels were tested using the geometrically modified sample, and the modified sample successfully produced shear fractures on a unique shear plane for all steels. For each steel, void densities were determined, based on metallographic analyses, as a function of imposed displacement. Microstructural properties of ferrite and martensite grain size, martensite volume fraction (MVF), retained austenite content, Vickers hardness, average nanoindentation hardness, average ferrite and martensite constituent hardness, and tensile properties were obtained in order to evaluate potential correlations with void data. A linear correlation was observed between Vickers hardness and the average nanoindentation hardness, verifying the ability of nanoindentation to produce data consistent with more traditional hardness measurement techniques. A linear relationship was observed between the number of voids present at 90% failure displacement and the martensite/ferrite hardness ratio, indicating that a decrease in relative hardness difference in a microstructure can suppress void formation, and potentially extend formability limits. The void population appeared independent of MVF, grain size, and tensile properties suggesting that constituent hardness may be a dominant parameter when considering suppression of void nucleation in DP steels.
Comparison of acoustic and strain gauge techniques for crack closure measurements
NASA Technical Reports Server (NTRS)
Buck, O.; Inman, R. V.; Frandsen, J. D.
1976-01-01
A quantitative study on the systems performances of the COD gauge and the acoustic transmission techniques to elastic deformation of part-through crack and compact tension specimens has been conducted. It is shown that the two instruments measure two completely different quantities: The COD gauge yields information on the length change of the specimen whereas the acoustic technique is sensitive directly to the amount of contract area between two surfaces, interfering with the acoustic signal. In another series of experiments, compression tests on parts with specifically prepared surfaces were performed so that the surface contact area could be correlated with the transmitted acoustic signal, as well as the acoustic with the COD gauge signal. A linear relation between contact area and COD gauge signal was obtained until full contact had been established.
NASA Astrophysics Data System (ADS)
Dustin, Joshua S.
A state-of-the-art multi-scale analysis was performed to predict failure initiation at the free-edge of an angle-ply laminate using the Strain Invariant Failure Theory (SIFT), and multiple improvements to this analysis methodology were proposed and implemented. Application of this analysis and theory led to the conclusion that point-wise failure criteria which ignore the singular stress and strain fields from a homogenized analysis and the presence of free-edge damage in the form of micro-cracking, may do so at the expense of failure prediction capability. The main contributions of this work then are made in the study of the laminate free-edge singularity and in the effects of micro-cracking at the composite laminate free-edge. Study of both classical elasticity and finite element solutions of the laminate free-edge stress field based upon the assumption of homogenized lamina properties reveal that the order of the free-edge singularity is sufficiently small such that the domain of dominance of this term away from the laminate free-edge is much smaller than the relevant dimensions of the microstructure. In comparison to a crack-tip field, these free-edge singularities generate stress and strain fields which are half as intense as those at the crack-tip, leading to the conclusion that existing flaws at the free-edge in the form of micro-cracks would be more prone to the initiation of free-edge failure than the existence of a singularity in the free-edge elasticity solutions. A methodical experiment was performed on a family of [±25°/90°] s laminates made of IM7/8552 carbon/epoxy composite, to both characterize micro-cracks present at the laminate free-edge and to study their behavior under the application of a uniform extensional load. The majority of these micro-cracks were of length on the order of a few fiber diameters, though larger micro-cracks as long as 100 fiber diameters were observed in thicker laminates. A strong correlation between the application of
NASA Astrophysics Data System (ADS)
Qiu, J. H.; Jiang, Q.
2007-10-01
A phenomenological Landau Devonshire thermodynamic theory is used to describe the effects of anisotropic in-plane misfit strains on equilibrium polarization states and dielectric properties of single domain epitaxial Pb(Zr1-xTix)O3 thin films grown on dissimilar orthorhombic substrates. Compared with the “isotropic in-plane misfit strains-temperature” phase diagrams, the characteristic features of “misfit strain-misfit strain” and “misfit strain-temperature” phase diagrams under the circumstance of strain anisotropy are the presence of four different phases (a, a, ac, and ac) and the direct 90° polarization switching between c phase and a phase (or a phase), between a phase and a phase. The misfit strain dependence of polarization components, the small-signal dielectric responses and the tunabilities at room temperature are also calculated. We find that the phase diagrams and dielectric properties largely depend on anisotropic in-plane misfit strains as well. Moreover, the strain anisotropy will lead to the polarization and dielectric anisotropy.
NASA Technical Reports Server (NTRS)
Finger, R. W.
1978-01-01
Static fracture tests were performed on surface flawed specimens of aluminum and titanium alloys. A simulated proof overload cycle was applied prior to all of the cyclic tests. Variables included in each test series were flaw shapes and thickness. Additionally, test temperature was a variable for the aluminum test series. The crack opening displacement and stress-strain data obtained are presented.
Crack curving in a ductile pressurized fuselage
NASA Astrophysics Data System (ADS)
Lam, Paul W.
magnitude of CTOA and CTOD depends on the structural geometry, and including plasticity increases the crack tip displacements. An estimate of the strain in the skin flaps at the crack tip may indicate the tendency for flapping. Out-of-plane effects become significant as the crack propagates and curves.
Deformation fields near a steady fatigue crack with anisotropic plasticity
Gao, Yanfei
2015-11-30
In this work, from finite element simulations based on an irreversible, hysteretic cohesive interface model, a steady fatigue crack can be realized if the crack extension exceeds about twice the plastic zone size, and both the crack increment per loading cycle and the crack bridging zone size are smaller than the plastic zone size. The corresponding deformation fields develop a plastic wake behind the crack tip and a compressive residual stress field ahead of the crack tip. In addition, the Hill’s plasticity model is used to study the role of plastic anisotropy on the retardation of fatigue crack growth andmore » the elastic strain fields. It is found that for Mode-I cyclic loading, an enhanced yield stress in directions that are inclined from the crack plane will lead to slower crack growth rate, but this retardation is insignificant for typical degrees of plastic anisotropy. Furthermore, these results provide key inputs for future comparisons to neutron and synchrotron diffraction measurements that provide full-field lattice strain mapping near fracture and fatigue crack tips, especially in textured materials such as wrought or rolled Mg alloys.« less
Deformation fields near a steady fatigue crack with anisotropic plasticity
Gao, Yanfei
2015-11-30
In this work, from finite element simulations based on an irreversible, hysteretic cohesive interface model, a steady fatigue crack can be realized if the crack extension exceeds about twice the plastic zone size, and both the crack increment per loading cycle and the crack bridging zone size are smaller than the plastic zone size. The corresponding deformation fields develop a plastic wake behind the crack tip and a compressive residual stress field ahead of the crack tip. In addition, the Hill’s plasticity model is used to study the role of plastic anisotropy on the retardation of fatigue crack growth and the elastic strain fields. It is found that for Mode-I cyclic loading, an enhanced yield stress in directions that are inclined from the crack plane will lead to slower crack growth rate, but this retardation is insignificant for typical degrees of plastic anisotropy. Furthermore, these results provide key inputs for future comparisons to neutron and synchrotron diffraction measurements that provide full-field lattice strain mapping near fracture and fatigue crack tips, especially in textured materials such as wrought or rolled Mg alloys.
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.
Constraint effects observed in crack initiation stretch
Lambert, D.M.; Ernst, H.A.
1995-12-31
The current paper characterizes constraint in fracture: J-modified resistance (Jr) curves were developed for two tough structural materials, 6061-T651 (aluminum) and IN718-STA1 (nickel-base superalloy). A wide variety of configurations was tested to consider load configurations from bending to tension including three specimen types (compact tension, center-crack tension, and single-edge notched tension), and a range of ligament lengths and thicknesses, as well as side-grooved and smooth-sided ligaments. The Jr curves exhibited an inflection point after some crack extension, and the data were excluded beyond the inflection. Qualified Jr curves for the two materials showed similar behavior, but R-curves were identical for equal ligament length-to-thickness ratio (RL), for the aluminum alloy, with increasing slope for increasing RL, while for the nickel, the resistance curves aligned for equal ligament thickness, B, and the slope increased for decreasing B. Displacements at the original crack tip (CToD) were recorded throughout the test for several specimens. CToD-versus-crack extension curves were developed, and data were excluded beyond the inflection point (as with the Jr curves). The data collapsed into two distinct curves, thought to represent the surface, plane stress effect and the central, plane strain effect. This was observed for both materials. A technique called profiling is presented for the aluminum alloy only, where the crack face displacements are recorded at the final point of the test as a function of the position throughout the crack cavity, along with an effort to extract the observations in a usable form. Displacements were consistent throughout the cross-section at and behind the original crack tip. In the region where the crack grew, this displacement was developed by a combination of stretch and crack growth. The stretch required to initiate crack extension was a function of the depth beneath the surface into the cross-section.
The application of a logic framework for fatigue crack growth analyses to microstructural effects
Xu, J.G.; Liu, H.W.
1995-12-31
{Delta}K has been widely used to correlate da/dN data. The relation between da/dN and {Delta}K is usually found empirically. However, fatigue crack growth relations can also be derived theoretically. Three fatigue crack growth theories are derived for the state of small scale yielding and plane strain. These three theories constitute a logic framework useful for fatigue crack growth analyses. The application of the logic framework to the analyses of microstructural effects on fatigue crack growth is illustrated. The fatigue crack growth curve of 7075-T651 aluminum alloy has five distinct regions. A fatigue crack grows by crack-tip shear decohesion forming striations and by brittle fractures of particles followed by localized shear decohesion at these microcracks forming dimples. The logic framework helps to relate the fatigue crack growth behaviors in these five regions to the fractures of inclusions and to the resistance of grain boundaries and dispersoids to shear decohesion.
NASA Astrophysics Data System (ADS)
Oliveira, M. C.; Baptista, A. J.; Alves, J. L.; Menezes, L. F.; Green, D. E.; Ghaei, A.
2007-05-01
The main purpose of the "Numisheet'05 Benchmark♯3: Channel Draw/Cylindrical Cup" was to evaluate the forming characteristics of materials in multi-stage processes. The concept was to verify the strain fields achieved during the two stage forming process and also to test the ability of numerical models to predict both strain and stress fields. The first stage consisted of forming channel sections in an industrial-scale channel draw die. The material that flows through the drawbead and over the die radii into the channel sidewalls is prestrained by cyclic bending and unbending. The prestrained channel sidewalls are subsequently cut and subjected to near plane-strain Marciniak-style cup test. This study emphasizes the analysis of the first stage process, the Channel Draw, since accurate numerical results for the first stage forming and springback are essential to guarantee proper initial state variables for the subsequent stage simulation. Four different sheet materials were selected: mild steel AKDQ-HDG, high strength steel HSLA-HDG, dual phase steel DP600-HDG and an aluminium alloy AA6022-T43. The four sheet materials were formed in the same channel draw die, but with drawbead penetrations of 25%, 50% and 100%. This paper describes the testing and measurement procedures for the numerical simulation of these conditions with DD3IMP FE code. A comparison between experimental and numerical simulation results for the first stage is presented. The experimental results indicate that an increase in drawbead penetration is accompanied by a general decrease in springback, with both sidewall radius of curvature and the sidewall angle increasing with increasing drawbead penetration. An exception to this trend occurs at the shallowest bead penetration: the radius of curvature in the sidewall is larger than expected. The sequence of cyclic tension and compression is numerically studied for each drawbead penetration in order to investigate this phenomenon.
Oliveira, M. C.; Baptista, A. J.; Menezes, L. F.; Alves, J. L.; Green, D. E.; Ghaei, A.
2007-05-17
The main purpose of the 'Numisheet'05 Benchmark no. 3: Channel Draw/Cylindrical Cup' was to evaluate the forming characteristics of materials in multi-stage processes. The concept was to verify the strain fields achieved during the two stage forming process and also to test the ability of numerical models to predict both strain and stress fields. The first stage consisted of forming channel sections in an industrial-scale channel draw die. The material that flows through the drawbead and over the die radii into the channel sidewalls is prestrained by cyclic bending and unbending. The prestrained channel sidewalls are subsequently cut and subjected to near plane-strain Marciniak-style cup test. This study emphasizes the analysis of the first stage process, the Channel Draw, since accurate numerical results for the first stage forming and springback are essential to guarantee proper initial state variables for the subsequent stage simulation. Four different sheet materials were selected: mild steel AKDQ-HDG, high strength steel HSLA-HDG, dual phase steel DP600-HDG and an aluminium alloy AA6022-T43. The four sheet materials were formed in the same channel draw die, but with drawbead penetrations of 25%, 50% and 100%. This paper describes the testing and measurement procedures for the numerical simulation of these conditions with DD3IMP FE code. A comparison between experimental and numerical simulation results for the first stage is presented. The experimental results indicate that an increase in drawbead penetration is accompanied by a general decrease in springback, with both sidewall radius of curvature and the sidewall angle increasing with increasing drawbead penetration. An exception to this trend occurs at the shallowest bead penetration: the radius of curvature in the sidewall is larger than expected. The sequence of cyclic tension and compression is numerically studied for each drawbead penetration in order to investigate this phenomenon.
Crack propagation and fracture in silicon wafers under thermal stress
Danilewsky, Andreas; Wittge, Jochen; Kiefl, Konstantin; Allen, David; McNally, Patrick; Garagorri, Jorge; Elizalde, M. Reyes; Baumbach, Tilo; Tanner, Brian K.
2013-01-01
The behaviour of microcracks in silicon during thermal annealing has been studied using in situ X-ray diffraction imaging. Initial cracks are produced with an indenter at the edge of a conventional Si wafer, which was heated under temperature gradients to produce thermal stress. At temperatures where Si is still in the brittle regime, the strain may accumulate if a microcrack is pinned. If a critical value is exceeded either a new or a longer crack will be formed, which results with high probability in wafer breakage. The strain reduces most efficiently by forming (hhl) or (hkl) crack planes of high energy instead of the expected low-energy cleavage planes like {111}. Dangerous cracks, which become active during heat treatment and may shatter the whole wafer, can be identified from diffraction images simply by measuring the geometrical dimensions of the strain-related contrast around the crack tip. Once the plastic regime at higher temperature is reached, strain is reduced by generating dislocation loops and slip bands and no wafer breakage occurs. There is only a small temperature window within which crack propagation is possible during rapid annealing. PMID:24046487
Lai, Chih-Ming; Huang, Yu-En; Feng, Shih-Wei; Kou, Kuang-Yang; Chen, Chien-Hsun; Tu, Li-Wei
2015-07-13
Anisotropic strain relaxation and the resulting degree of polarization of photoluminescence (PL) in nonpolar a-plane textured ZnO are experimentally and theoretically studied. A thicker nonpolar a-plane textured ZnO film enhances the anisotropic in-plane strain relaxation, resulting in a larger degree of polarization of PL and better sample quality. Anisotropic in-plane strains, sample quality, and degree of polarization of PL in nonpolar a-plane ZnO are consequences of the degree of anisotropic in-plane strain relaxation. By the k·p perturbation approach, simulation results of the variation of the degree of polarization for the electronic transition upon anisotropic in-plane strain relaxation agree with experimental results.
Mode I and mixed I/III crack initiation and propagation behavior of V-4Cr-4Ti alloy at 25{degrees}C
Li, H.X.; Kurtz, R.J.; Jones, R.H.
1997-04-01
The mode I and mixed-mode I/III fracture behavior of the production-scale heat (No. 832665) of V-4Cr-4Ti has been investigated at 25{degrees}C using compact tension (CT) specimens for a mode I crack and modified CT specimens for a mixed-mode I/III crack. The mode III to mode I load ratio was 0.47. Test specimens were vacuum annealed at 1000{degrees}C for 1 h after final machining. Both mode I and mixed-mode I/III specimens were fatigue cracked prior to J-integral testing. It was noticed that the mixed-mode I/III crack angle decreased from an initial 25 degrees to approximately 23 degrees due to crack plane rotation during fatigue cracking. No crack plane rotation occurred in the mode I specimen. The crack initiation and propagation behavior was evaluated by generating J-R curves. Due to the high ductility of this alloy and the limited specimen thickness (6.35 mm), plane strain requirements were not met so valid critical J-integral values were not obtained. However, it was found that the crack initiation and propagation behavior was significantly different between the mode I and the mixed-mode I/III specimens. In the mode I specimen crack initiation did not occur, only extensive crack tip blunting due to plastic deformation. During J-integral testing the mixed-mode crack rotated to an increased crack angle (in contrast to fatigue precracking) by crack blunting. When the crack initiated, the crack angle was about 30 degrees. After crack initiation the crack plane remained at 30 degrees until the test was completed. Mixed-mode crack initiation was difficult, but propagation was easy. The fracture surface of the mixed-mode specimen was characterized by microvoid coalescence.
Wu, Huaping; Chai, Guozhong; Zhou, Ting; Zhang, Zheng; Kitamura, Takayuki; Zhou, Haomiao
2014-03-21
The strain-mediated magnetoelectric (ME) property of self-assembled vertical multiferroic nanocomposite films epitaxially grown on cubic substrates was calculated by a nonlinear thermodynamic theory combined with the elastic theory. The dependent relations of phase state of ferroelectric films with the in-plane misfit strain, out-of-plane misfit strain, temperature, and volume fraction of ferromagnetic phase were confirmed. The effects of in-plane misfit strain and ferromagnetic volume fraction on the polarization and dielectric constant of ferroelectric films at room temperature were elaborately analyzed for the vertical BaTiO{sub 3}-CoFe{sub 2}O{sub 4} and PbTiO{sub 3}-CoFe{sub 2}O{sub 4} nanocomposite films. Our calculated results confirmed the relationship among ME effect and in-plane misfit strain and ferromagnetic volume fraction in the nanocomposite films. The ME voltage coefficients of vertical BaTiO{sub 3}-CoFe{sub 2}O{sub 4} and PbTiO{sub 3}-CoFe{sub 2}O{sub 4} nanocomposite films displayed various maximums and abrupt points at special phases and phase transition boundaries. The ME voltage coefficients of lead-free BaTiO{sub 3}-CoFe{sub 2}O{sub 4} nanocomposite films epitaxially grown on different substrates could reach a comparative value of ∼2 V·cm{sup −1}·Oe{sup −1} under the controllable in-plane misfit strain induced by substrate clamping. Our results provided an available method for the optimal design of vertical multiferroic nanocomposites with adjustable ME effect by optimizing the ferromagnetic volume fraction and substrate type.
Fracture of Hydrided Zircaloy-4 Sheet under Through-Thickness Crack Growth Conditions
Raynaud, P.A.; Koss, D.A.; Motta, A.T.; Chan, K.S.
2007-07-01
The failure of thin-wall components such as fuel cladding may be caused by crack initiation on the component surface and subsequent crack growth through its thickness. This study has determined the fracture toughness of hydrided cold-worked stress relieved Zircaloy-4 sheet subject to through-thickness crack growth at 25 deg. C. The experimental approach utilizes a novel procedure in which a narrow linear strip of brittle hydride blister across the specimen width creates a well-defined pre-crack upon initial loading. The subsequent crack growth resistance is then characterized by four-point bending of the specimen and an elastic-plastic fracture mechanics analysis. At room temperature, the through-thickness fracture toughness (K{sub Q}) is sensitive to the orientation of the hydride platelets, and K{sub Q} {approx_equal} 25 MPavm for crack growth through a mixed in-plane/out-of-plane hydride field. In contrast, K{sub Q} is much higher ({approx_equal} 75 MPavm) when the hydride platelets are oriented predominantly in the plane of the sheet (and therefore normal to both the crack plane and the crack growth direction). The implication of these fracture toughness values to the fracture strain behavior of hydrided Zircaloy-4 under through-thickness crack growth conditions is illustrated. (authors)
Mapping and load response of overload strain fields: Synchrotron X-ray measurements
Shukla, V; Jisrawi, N M; Sadangi, R K; Pao, P S; Horvath, K; Sadananda, K; Ignatov, A; Skaritka, J; Tsakalakos, T
2009-02-05
High energy synchrotron X-ray diffraction measurements have been performed to provide quantitative microscopic guidance for modeling of fatigue crack growth. Specifically we report local strain mapping, along with in situ loading strain response, results on 4140 steel fatigue specimens exhibiting the crack growth retardation 'overload effect'. Detailed, 2D, {epsilon}{gamma}{gamma}-strain field mapping shows that a single overload (OL) cycle creates a compressive strain field extending millimeters above and below the crack plane. The OL strain field structures are shown to persist after the crack tip has grown well beyond the OL position. The specimen exhibiting the maximal crack growth rate retardation following overload exhibits a tensile residual strain region at the crack tip. Strain field results, on in situ tensile loaded specimens, show a striking critical threshold load, F{sub c}, phenomenon in their strain response. At loads below F{sub c} the strain response is dominated by a rapid suppression of the compressive OL feature with modest response at the crack tip. At loads above F{sub c} the strain response at the OL position terminates and the response at the crack tip becomes large. This threshold load response behavior is shown to exhibit lower F{sub c} values, and dramatically enhanced rates of strain change with load as the crack tip propagates farther beyond the OL position. The OL strain feature behind the crack tip also is shown to be suppressed by removing the opposing crack faces via an electron discharge cut passing through the crack tip. Finally unique 2D strain field mapping (imaging) results, through the depth of the specimen, of the fatigue crack front and the OL feature in the wake are also presented.
Støylen, Asbjørn; Ingul, Charlotte B; Torp, Hans
2003-01-01
Background We describe a method for 3-/4D reconstruction of tissue Doppler data from three standard apical planes, post processing to derived data of strain rate / strain and parametric colour imaging of the data. The data can be displayed as M-mode arrays from all six walls, Bull's eye projection and a 3D surface figure that can be scrolled and rotated. Numerical data and waveforms can be re-extracted. Methods Feasibility was tested by Strain Rate Imaging in 6 normal subjects and 6 patients with acute myocardial infarction. Reverberation artefacts and dyssynergy was identified by colour images. End systolic strain, peak systolic and mid systolic strain rate were measured. Results Infarcts were visualised in all patients by colour imaging of mid systolic strain rate, end systolic strain and post systolic shortening by strain rate. Reverberation artefacts were visible in 3 of 6 normals, and 2 of 6 patients, and were identified both on bull's eye and M-mode display, but influenced quantitative measurement. Peak systolic strain rate was in controls minimum -1.11, maximum -0.89 and in patients minimum -1.66, maximum 0.02 (p = 0.04). Mid systolic strain rate and end systolic strain did not separate the groups significantly. Conclusion 3-/4D reconstruction and colour display is feasible, allowing quick visual identification of infarcts and artefacts, as well as extension of area of post systolic shortening. Strain rate is better suited to colour parametric display than strain. PMID:12956886
NASA Astrophysics Data System (ADS)
Edsinger, K.; Odette, G. R.; Lucas, G. E.; Sheckherd, J. W.
1996-10-01
Fracture toughness K( T) curves for F82H were determined as a function of specimen size, crack size and strain rate. It was found that F82H shows a relatively abrupt transition from lower-shelf, quasi-cleavage fracture to upper-shelf ductile fracture. However, decreasing specimen size, crack size and strain rate resulted in a shift of the K( T) curve to lower temperatures. The differences in the lower shelf/knee regime were reconciled by combining a critical stressed area criteria for quasi-cleavage fracture with stress fields determined by finite element methods for the different specimen geometries. The results demonstrated that the large effective toughness for small specimens or specimens with shallow cracks are a consequence of having to deform the specimens to much higher Js before the stressed-area criteria are met ahead of the crack. Such large toughnesses and low transition temperatures support the contention that thin-walled ferritic structures should remain a viable option for advanced fusion reactors.
NASA Astrophysics Data System (ADS)
Hu, Lun-Hui; Xu, Dong-Hui; Zhang, Fu-Chun; Zhou, Yi
2016-08-01
Motivated by the recent discovery of quantized spin Hall effect in InAs/GaSb quantum wells [Du, Knez, Sullivan, and Du, Phys. Rev. Lett. 114, 096802 (2015), 10.1103/PhysRevLett.114.096802], we theoretically study the effects of in-plane magnetic field and strain effect to the quantization of charge conductance by using Landauer-B ütikker formalism. Our theory predicts a robustness of the conductance quantization against the in-plane magnetic field up to a very high field of 20 T. We use a disordered hopping term to model the strain and show that the strain may help the quantization of the conductance. Relevance to the experiments will be discussed.
NASA Astrophysics Data System (ADS)
Ning, Xiaoguang; Murayama, Hideaki; Kageyama, Kazuro; Wada, Daichi; Kanai, Makoto; Ohsawa, Isamu; Igawa, Hirotaka
2014-10-01
In this study, the dynamic strain distribution measurement of an adhesive-bonded single-lap joint was carried out in a cyclic load test using a fiber Bragg grating (FBG) sensor embedded into the adhesive/adherend interface along the overlap length direction. Unidirectional carbon fiber reinforced plastic (CFRP) substrates were bonded by epoxy resin to form the joint, and the FBG sensor was embedded into the surface of one substrate during its curing. The measurement was carried out with a sampling rate of 5 Hz by the sensing system, based on the optical frequency domain reflectometry (OFDR) throughout the test. A finite element analysis (FEA) was performed for the measurement evaluation using a three-dimensional model, which included the embedded FBG sensor. The crack detection method, based on the longitudinal strain distribution measurement, was introduced and performed to estimate the cracks that occurred at the adhesive/adherend interface in the test.
THERMAL-MECHANICAL RESPONSE OF CRACKED SATIN WEAVE CFRP COMPOSITES AT CRYOGENIC TEMPERATURES
Watanabe, S.; Shindo, Y.; Narita, F.; Takeda, T.
2008-03-03
This paper examines the thermal-mechanical response of satin weave carbon fiber reinforced polymer (CFRP) laminates with internal and/or edge cracks subjected to uniaxial tension load at cryogenic temperatures. Cracks are considered to occur in the transverse fiber bundles and extend through the entire thickness of the fiber bundles. Two-dimentional generalized plane strain finite element models are developed to study the effects of residual thermal stresses and cracks on the mechanical behavior of CFRP woven laminates. A detailed examination of the Young's modulus and stress distributions near the crack tip is carried out which provides insight into material behavior at cryogenic temperatures.
Thermal-Mechanical Response of Cracked Satin Weave CFRP Composites at Cryogenic Temperatures
NASA Astrophysics Data System (ADS)
Watanabe, S.; Shindo, Y.; Narita, F.; Takeda, T.
2008-03-01
This paper examines the thermal-mechanical response of satin weave carbon fiber reinforced polymer (CFRP) laminates with internal and/or edge cracks subjected to uniaxial tension load at cryogenic temperatures. Cracks are considered to occur in the transverse fiber bundles and extend through the entire thickness of the fiber bundles. Two-dimentional generalized plane strain finite element models are developed to study the effects of residual thermal stresses and cracks on the mechanical behavior of CFRP woven laminates. A detailed examination of the Young's modulus and stress distributions near the crack tip is carried out which provides insight into material behavior at cryogenic temperatures.
NASA Astrophysics Data System (ADS)
Kelestemur, Mehmet Halidun
1998-12-01
acceleration right after the overload application was observed. However, the acceleration was not detected on the interior of the material along the crack tip. Only the surface in which the plane stress was effective showed crack propagation in acceleration zone. This result were explained by strain hardening and plastic deformation of grains at the overload zone. Discontinuous crack closure occurred following the overload. In other words, at the overload position, fracture surfaces on which stretching occurred came into contact at high stress intensity factor values and far away from the overload position. As a result of discontinuous crack closure, crack opening or closing data were very high although the fatigue crack growth rate reached its original value.
Diffraction-based study of fatigue crack initiation and propagation in aerospace aluminum alloys
NASA Astrophysics Data System (ADS)
Gupta, Vipul K.
crystallographic {111} slip-plane cracking typical of the Stage I crack growth mode observed in single crystals and high purity polycrystals of face centered cubic metals, and which has presently been assumed for the present materials within fatigue crack initiation models. Rather, the facets tend to have near-Mode I spatial orientation, which is another indicator of the importance of environmentally affected fatigue damage. The results provide a physical basis to develop microstructurally-based next generation multi-stage fatigue (MSF) models that should include a new crack decohesion criteria based upon environmental fatigue cracking mechanisms. EBSD study of small-cracks in alloy 7050-T7451, stressed in warm-humid environment, showed that crack-path orientation changes and crack-branching occurred at both low/high-angle grain and subgrain boundaries. Single surface trace analysis suggests that the crack-path differs substantially from crystallographic slip-planes. EBSD-based observations of small-crack propagation through subgrain structure, either formed by cyclic plastic strain accumulation or pre-existing (typical of unrecrystallized grain structure in the present materials), suggest that subgrain structure plays a crucial role in small fatigue crack propagation. As mentioned earlier, local fluctuations in small-crack growth rates appear to be caused by frequent interaction with subgrain boundaries, and multiple occurrences of crack-branching and crack-path orientation changes at low/high-angle grain and subgrain boundaries. The aforementioned deviation from low-index {001}/{101}-planes and the occurrence of high-index cracking planes observed by EBSD/Stereology, in this study and others, are interpreted as trans-subgranular decohesion or inter-subgranular cracking, due to trapped hydrogen. In summary, the results provide a firmer experimental foundation for, and clearer understanding of, the mechanisms of environmental fatigue cracking of aluminum alloys, especially the
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
Subcritical crack growth in two titanium alloys.
NASA Technical Reports Server (NTRS)
Williams, D. N.
1973-01-01
Measurement of subcritical crack growth during static loading of precracked titanium alloys in salt water using samples too thin for plane strain loading to predominate was examined as a method for determining the critical stress intensity for crack propagation in salt water. Significant internal crack growth followed by arrest was found at quite low stress intensities, but crack growth rates were relatively low. Assuming these techniques provided a reliable measurement of the critical stress intensity, the value for annealed Ti-4Al-1.5Mo-0.5V alloy was apparently about 35 ksi-in. to the 1/2 power, while that for annealed Ti-4Al-3Mo-1V was below 45 ksi-in. to the 1/2 power. Crack growth was also observed in tests conducted in both alloys in an air environment. At 65 ksi-in. to the 1/2 power, the extent of crack growth was greater in air than in salt water. Ti-4Al-3Mo-1V showed arrested crack growth in air at a stress intensity of 45 ksi-in. to the 1/2 power.
Frefer, Abdulbaset Ali; Raddad, Bashir S.
2013-12-16
In the present study, stress corrosion cracking (SCC) behavior of naturally aged advanced silver-bearing Al-Li alloy in NaCl solution was investigated using slow strain rate test (SSRT) method. The SSRT’s were conducted at different strain rates and applied potentials at room temperature. The results were discussed based on percent reductions in tensile elongation in a SCC-causing environment over those in air tended to express the SCC susceptbility of the alloy under study at T3. The SCC behavior of the alloy was also discussed based on the microstructural and fractographic examinations.
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.
Fatigue crack closure behavior at high stress ratios
NASA Technical Reports Server (NTRS)
Turner, C. Christopher; Carman, C. Davis; Hillberry, Ben M.
1988-01-01
Fatigue crack delay behavior at high stress ratio caused by single peak overloads was investigated in two thicknesses of 7475-T731 aluminum alloy. Closure measurements indicated no closure occurred before or throughout the overload plastic zones following the overload. This was further substantiated by comparing the specimen compliance following the overload with the compliance of a low R ratio test when the crack was fully open. Scanning electron microscope studies revealed that crack tunneling and possibly reinitiation of the crack occurred, most likely a result of crack-tip blunting. The number of delay cycles was greater for the thinner mixed mode stress state specimen than for the thicker plane strain stress state specimen, which is similar to low R ratio test results and may be due to a larger plastic zone for the mixed mode cased.
Stable crack growth during actuation in shape memory alloys
NASA Astrophysics Data System (ADS)
Jape, Sameer; Baxevanis, Theocharis; Lagoudas, Dimitris C.
2014-03-01
A finite element analysis of crack growth is carried out in an in nite center-cracked shape memory alloy plate subjected to thermal variations under plane strain mode I constant applied loading. Crack is assumed to propagate when the energy release rate reaches a material specific critical value. The virtual crack growth technique is employed to calculate the energy release rate, which was shown to increase an order of magnitude at constant applied loading as a result of phase transformation induced by thermal variations.1 A fracture toughening is observed associated with the energy dissipated by the transformed material in the wake of the growing crack and its sensitivity over key thermomechanical parameters is presented.
Residual strength of thin panels with cracks
NASA Technical Reports Server (NTRS)
Madenci, Erdogan
1994-01-01
The previous design philosophies involving safe life, fail-safe and damage tolerance concepts become inadequate for assuring the safety of aging aircraft structures. For example, the failure mechanism for the Aloha Airline accident involved the coalescence of undetected small cracks at the rivet holes causing a section of the fuselage to peel open during flight. Therefore, the fuselage structure should be designed to have sufficient residual strength under worst case crack configurations and in-flight load conditions. Residual strength is interpreted as the maximum load carrying capacity prior to unstable crack growth. Internal pressure and bending moment constitute the two major components of the external loads on the fuselage section during flight. Although the stiffeners in the form of stringers, frames and tear straps sustain part of the external loads, the significant portion of the load is taken up by the skin. In the presence of a large crack in the skin, the crack lips bulge out with considerable yielding; thus, the geometric and material nonlinearities must be included in the analysis for predicting residual strength. Also, these nonlinearities do not permit the decoupling of in-plane and out-of-plane bending deformations. The failure criterion combining the concepts of absorbed specific energy and strain energy density addresses the aforementioned concerns. The critical absorbed specific energy (local toughness) for the material is determined from the global specimen response and deformation geometry based on the uniaxial tensile test data and detailed finite element modeling of the specimen response. The use of the local toughness and stress-strain response at the continuum level eliminates the size effect. With this critical parameter and stress-strain response, the finite element analysis of the component by using STAGS along with the application of this failure criterion provides the stable crack growth calculations for residual strength predictions.
The structure of the near-tip field during transient elastodynamic crack growth
NASA Astrophysics Data System (ADS)
Freund, L. B.; Rosakis, A. J.
T HE PROCESS of dynamic crack growth in a nominally elastic malerial under conditions of plane strain or plane stress is considered. Of particular concern is the influence of the transient nature of the process on the stress field in the immediate vicinity of the crack tip during nonsteady growth. Asymptotically, the crack tip stress field is square root singular at the crack tip, with the angular variation of the singular field depending weakly on the instantaneous crack tip speed and with the instantaneous stress intensity factor being a scalar multiplier of the singular field. However, for a material particle at a small distance from the moving crack, the local stress field depends not only on instantaneous values of crack speed and stress intensity factor, but also on the past history of these lime-dependent quantities. A representation of the crack tip field is obtained in the form of an expansion about the crack up in powers of radial coordinate, with the coefficients depending on the time rates of change of crack tip speed and stress intensity factor. This representation is used to interpret some experimental observations, with the conclusion that the higher-order expansion provides an accurate description of crack tip fields under fairly severe transient conditions. In addition, some estimates are made of the practical limits of using a stress intensity factor field alone to characterize the local fields.
The application of Newman crack-closure model to predicting fatigue crack growth
NASA Technical Reports Server (NTRS)
Si, Erjian
1994-01-01
Newman crack-closure model and the relevant crack growth program were applied to the analysis of crack growth under constant amplitude and aircraft spectrum loading on a number of aluminum alloy materials. The analysis was performed for available test data of 2219-T851, 2024-T3, 2024-T351, 7075-T651, 2324-T39, and 7150-T651 aluminum materials. The results showed that the constraint factor is a significant factor in the method. The determination of the constraint factor is discussed. For constant amplitude loading, satisfactory crack growth lives could be predicted. For the above aluminum specimens, the ratio of predicted to experimental lives, Np/Nt, ranged from 0.74 to 1.36. The mean value of Np/Nt was 0.97. For a specified complex spectrum loading, predicted crack growth lives are not in very good agreement with the test data. Further effort is needed to correctly simulate the transition between plane strain and plane stress conditions, existing near the crack tip.
The application of Newman crack-closure model to predicting fatigue crack growth
NASA Astrophysics Data System (ADS)
Si, Erjian
1994-09-01
Newman crack-closure model and the relevant crack growth program were applied to the analysis of crack growth under constant amplitude and aircraft spectrum loading on a number of aluminum alloy materials. The analysis was performed for available test data of 2219-T851, 2024-T3, 2024-T351, 7075-T651, 2324-T39, and 7150-T651 aluminum materials. The results showed that the constraint factor is a significant factor in the method. The determination of the constraint factor is discussed. For constant amplitude loading, satisfactory crack growth lives could be predicted. For the above aluminum specimens, the ratio of predicted to experimental lives, Np/Nt, ranged from 0.74 to 1.36. The mean value of Np/Nt was 0.97. For a specified complex spectrum loading, predicted crack growth lives are not in very good agreement with the test data. Further effort is needed to correctly simulate the transition between plane strain and plane stress conditions, existing near the crack tip.
NASA Astrophysics Data System (ADS)
Larsen, James M.; Allison, John E.
This book contains chapters on fracture mechanics parameters for small fatigue cracks, monitoring small-crack growth by the replication method, measurement of small cracks by photomicroscopy (experiments and analysis), and experimental mechanics of microcracks. Other topics discussed are the real-time measurement of small-crack-opening behavior using an interferometric strain/displacement gage; direct current electrical potential measurement of the growth of small cracks; an ultrasonic method for the measurement of the size and opening behavior of small fatigue cracks; and the simulation of short crack and other low closure loading conditions, utilizing constant K(max) Delta-K-decreasing fatigue crack growth procedures.
A Continuum-Atomistic Analysis of Transgranular Crack Propagation in Aluminum
NASA Technical Reports Server (NTRS)
Yamakov, V.; Saether, E.; Glaessgen, E.
2009-01-01
A concurrent multiscale modeling methodology that embeds a molecular dynamics (MD) region within a finite element (FEM) domain is used to study plastic processes at a crack tip in a single crystal of aluminum. The case of mode I loading is studied. A transition from deformation twinning to full dislocation emission from the crack tip is found when the crack plane is rotated around the [111] crystallographic axis. When the crack plane normal coincides with the [112] twinning direction, the crack propagates through a twinning mechanism. When the crack plane normal coincides with the [011] slip direction, the crack propagates through the emission of full dislocations. In intermediate orientations, a transition from full dislocation emission to twinning is found to occur with an increase in the stress intensity at the crack tip. This finding confirms the suggestion that the very high strain rates, inherently present in MD simulations, which produce higher stress intensities at the crack tip, over-predict the tendency for deformation twinning compared to experiments. The present study, therefore, aims to develop a more realistic and accurate predictive modeling of fracture processes.
NASA Astrophysics Data System (ADS)
Kim, Ji Hoon; Park, Jung Ho; Hwang, Sung-Min; Baik, Kwang Hyeon
2012-05-01
We studied the growth and the characteristics of nonpolar Si-doped a-plane GaN grown on r-plane sapphire substrates with different off-cut angles which were changed in the range of -0.2° ˜ +0.4°. Samples grown by using -0.2° and +0.2° off-cut angles showed triangular pit-free and smooth surfaces, which resulted from enhanced lateral growth owing to the epitaxial films having a Ga face. On the other hand, the sample grown by using +0.4° off-cut angles revealed a high density of pits and low crystalline quality due to a high density of dislocations. The strain determined by using calculations with the lattice parameters also showed a dependence on the off-cut angles. We expect r-plane sapphire with off-cut angles in the range of -0.2° ˜ +0.2° to be very effective for improving the crystalline quality and the surface morphology of a-plane GaN.
A Study of Failure in Small Pressurized Cylindrical Shells Containing a Crack
NASA Technical Reports Server (NTRS)
Barwell, Craig A.; Eber, Lorenz; Fyfe, Ian M.
1998-01-01
The deformation in the vicinity of axial cracks in thin pressurized cylinders is examined using small experimental The deformation in the vicinity of axial cracks in thin pressurized cylinders is examined using small experimental models. The loading applied was either symmetric or unsymmetric about the crack plane, the latter being caused by structural constraints such as stringers. The objective was two fold - one, to provide the experimental results which will allow computer modeling techniques to be evaluated for deformations that are significantly different from that experienced by flat plates, and the other to examine the deformations and conditions associated with the onset of crack kinking which often precedes crack curving. The stresses which control crack growth in a cylindrical geometry depend on conditions introduced by the axial bulging, which is an integral part of this type of failure. For the symmetric geometry, both the hoop and radial strain just ahead off the crack, r = a, were measured and these results compared with those obtained from a variety of structural analysis codes, in particular STAGS [1], ABAQUS and ANSYS. In addition to these measurements, the pressures at the onset of stable and unstable crack growth were obtained and the corresponding crack deformations measured as the pressures were increased to failure. For the unsymmetric cases, measurements were taken of the crack kinking angle, and the displacements in the vicinity of the crack. In general, the strains ahead of the crack showed good agreement between the three computer codes and between the codes and the experiments. In the case of crack behavior, it was determined that modeling stable tearing with a crack-tip opening displacement fracture criterion could be successfully combined with the finite-element analysis techniques as used in structural analysis codes. The analytic results obtained in this study were very compatible with the experimental observations of crack growth
NASA Astrophysics Data System (ADS)
Liu, Z. Y.; Li, X. G.; Cheng, Y. F.
2011-10-01
The effect of strain rate on cathodic reactions of X70 pipeline steel during stress corrosion cracking in a near-neutral pH solution was investigated by electrochemical impedance spectroscope and potentiodynamic polarization curve measurements as well as slow strain rate tests. A local additional potential model was used to understand mechanistically the role of strain rate in electrochemical cathodic reaction. It was found that an application of elastic stress would not affect the electrochemical stable state of the steel specimen at a macroscopic scale. Under a weak cathodic polarization, the interfacial charge-transfer process occurring on steel contains both cathodic and anodic reactions. Since the anodic reaction process is still significant, localized dissolution could occur even at such a cathodic potential, resulting in generation of corrosion pits. These pits could be the start sites to initiate stress corrosion cracks. Strain rate affects the corrosion reaction, which is associated with the generation of dislocation emergence points and slip steps on the specimen surface, resulting in a negative local additional potential to enhance the cathodic reaction locally.
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.
NASA Technical Reports Server (NTRS)
Smith, Robert W.; Smith, Gordon T.
1960-01-01
Thermal-fatigue crack-growth characteristics of notched- and unnotched-disk specimens of A-286, Discaloy, hot-cold worked 16-25-6, and overaged 16-25-6 were experimentally studied. Separately controlled variables were total strain range (0.0043 to 0.0079 in./in.), maximum cycle temperature (1300 and 1100 F), and hold time at maximum temperature (O and 5 min). A limited number of mechanical, push-pull, constant-strain cycle tests at room temperature were made using notched and un-notched bars of the same materials. In these tests the number of cycles to failure as well as the variation of load change with accumulated cycles was measured, and the effects of mean stress were observed. Constant-strain-range mechanical-fatigue tests at room temperature revealed notched-bar fatigue life to be strongly influenced by mean stress. For a specific strain range, the longest fatigue life was always found to be associated with the least-tensile (or most compressive) mean stress. By defining thermal-fatigue life as the number of cycles required to produce a crack area of 6000 square mils, the relative thermal-fatigue resistances of the test materials were established. Notched-disk specimens of A-286 and Discaloy steels exhibited longer fatigue lives than either hot-cold worked or overaged 16-25-6. On the other hand, unnotched-disk specimens of Discaloy and hot-cold worked 16-25-6 had longer lives than A-286 and overaged 16-25-6. Separation of the crack-growth data into microstage and macrostage periods revealed that the macrostage period accounted for the greatest part of the difference among materials when tested in the notched configuration, while the microstage was largely responsible for the differences encountered in unnotched disks.
Characteristics of thermally-induced transverse cracks in graphite epoxy composite laminates
NASA Technical Reports Server (NTRS)
Adams, D. S.; Bowles, D. E.; Herakovich, C. T.
1983-01-01
The characteristics of thermally induced transverse cracks in T300/5208 graphite-epoxy cross-ply and quasi-isotropic laminates were investigated both experimentally and analytically. The formation of transverse cracks and the subsequent crack spacing present during cool down to -250 F (116K) and thermal cycling between 250 and -250 F (116 and 394K) was investigated. The state of stress in the vicinity of a transverse crack and the influence of transverse cracking on the laminate coefficient of thermal expansion (CTE) was predicted using a generalized plane strain finite element analysis and a modified shear lag analysis. A majority of the cross-ply laminates experienced transverse cracking during the initial cool down to -250 F whereas the quasi-isotropic laminates remained uncracked. The in situ transverse strength of the 90 degree layers was more than 1.9 times greater than the transverse strength of the unidirectional 90 degree material for all laminates investigated.
Matrix cracking in laminated composites under monotonic and cyclic loadings
NASA Technical Reports Server (NTRS)
Allen, David H.; Lee, Jong-Won
1991-01-01
An analytical model based on the internal state variable (ISV) concept and the strain energy method is proposed for characterizing the monotonic and cyclic response of laminated composites containing matrix cracks. A modified constitution is formulated for angle-ply laminates under general in-plane mechanical loading and constant temperature change. A monotonic matrix cracking criterion is developed for predicting the crack density in cross-ply laminates as a function of the applied laminate axial stress. An initial formulation for a cyclic matrix cracking criterion for cross-ply laminates is also discussed. For the monotonic loading case, a number of experimental data and well-known models are compared with the present study for validating the practical applicability of the ISV approach.
NASA Astrophysics Data System (ADS)
Feng, Shih-Wei; Chen, Yu-Yu; Lai, Chih-Ming; Tu, Li-Wei; Han, Jung
2013-12-01
Anisotropic strain relaxation and the resulting degree of polarization of the electronic transition in nonpolar a-plane GaN using one- and two-step growth are studied. By using two-step growth, a slower coalescence and a longer roughening-recovery process lead to larger anisotropic strain relaxation, a less striated surface, and lower densities of basal stacking fault (BSF) and prismatic stacking fault (PSF). It is suggested that anisotropic in-plane strains, surface striation, and BSF and PSF densities in nonpolar a-GaN are consequences of the rate of coalescence, the period of roughening-recovery process, and the degree of anisotropic strain relaxation. In addition, the two-step growth mode can enhance the degree of polarization of the electronic transition. The simulation results of the kṡp perturbation approach show that the oscillator strength and degree of polarization of the electronic transition strongly depend on the in-plane strains upon anisotropic in-plane strain relaxation. The research results provide important information for optimized growth of nonpolar III-nitrides. By using two-step growth and by fabricating the devices on the high-quality nonpolar free-standing GaN substrates, high-efficiency nonpolar a-plane InGaN LEDs can be realized. Nonpolar a-plane InGaN/GaN LEDs can exhibit a strongly polarized light to improve the contrast, glare, eye discomfort and eye strain, and efficiency in display application.
Feng, Shih-Wei Chen, Yu-Yu; Lai, Chih-Ming; Tu, Li-Wei; Han, Jung
2013-12-21
Anisotropic strain relaxation and the resulting degree of polarization of the electronic transition in nonpolar a-plane GaN using one- and two-step growth are studied. By using two-step growth, a slower coalescence and a longer roughening-recovery process lead to larger anisotropic strain relaxation, a less striated surface, and lower densities of basal stacking fault (BSF) and prismatic stacking fault (PSF). It is suggested that anisotropic in-plane strains, surface striation, and BSF and PSF densities in nonpolar a-GaN are consequences of the rate of coalescence, the period of roughening-recovery process, and the degree of anisotropic strain relaxation. In addition, the two-step growth mode can enhance the degree of polarization of the electronic transition. The simulation results of the k⋅p perturbation approach show that the oscillator strength and degree of polarization of the electronic transition strongly depend on the in-plane strains upon anisotropic in-plane strain relaxation. The research results provide important information for optimized growth of nonpolar III-nitrides. By using two-step growth and by fabricating the devices on the high-quality nonpolar free-standing GaN substrates, high-efficiency nonpolar a-plane InGaN LEDs can be realized. Nonpolar a-plane InGaN/GaN LEDs can exhibit a strongly polarized light to improve the contrast, glare, eye discomfort and eye strain, and efficiency in display application.
Stable Crack Growth During Thermal Actuation of Shape Memory Alloys
NASA Astrophysics Data System (ADS)
Jape, S.; Baxevanis, T.; Lagoudas, D. C.
2016-03-01
A finite element analysis of crack growth is carried out in shape memory alloys subjected to thermal variations under plane strain, mode I, constant applied loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate which is modeled using the virtual crack closure technique. The load level, applied at a high temperature at which the austenite phase is stable, is assumed sufficiently low so that the resulting crack-tip energy release rate is smaller than the critical value but sufficiently high so that the critical value is reached during cooling, initiating crack growth (Baxevanis and Lagoudas in Int J Fract 191:191-213, 2015). Stable crack growth is observed, mainly associated with the shielding effect of the transformed material left in the wake of the advancing crack. Results pertaining to the near-tip mechanical fields and fracture toughness are presented and their sensitivity to phase transformation metrics and bias load levels is investigated.
Elasto-plastic bending of cracked plates, including the effects of crack closure. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Jones, D. P.
1972-01-01
A capability for solving elasto-plastic plate bending problems is developed using assumptions consistent with Kirchhoff plate theory. Both bending and extensional modes of deformation are admitted with the two modes becoming coupled as yielding proceeds. Equilibrium solutions are obtained numerically by determination of the stationary point of a functional which is analogous to the potential strain energy. The stationary value of the functional for each load increment is efficiently obtained through use of the conjugate gradient. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.
Energy absorption mechanisms during crack propagation in metal matrix composites
NASA Technical Reports Server (NTRS)
Murphy, D. P.; Adams, D. F.
1979-01-01
The stress distributions around individual fibers in a unidirectional boron/aluminum composite material subjected to axial and transverse loadings are being studied utilizing a generalized plane strain finite element analysis. This micromechanics analysis was modified to permit the analysis of longitudinal sections, and also to incorporate crack initiation and propagation. The analysis fully models the elastoplastic response of the aluminum matrix, as well as temperature dependent material properties and thermal stress effects. The micromechanics analysis modifications are described, and numerical results are given for both longitudinal and transverse models loaded into the inelastic range, to first failure. Included are initially cracked fiber models.
Structure and switching of in-plane ferroelectric nano-domains in strained PbxSr1-xTiO3 thin films
Matzen, Sylivia; Nesterov, Okeksiy; Rispens, Gregory; Heuver, J. A.; Bark, C; Biegalski, Michael D; Christen, Hans M; Noheda, Beatriz
2014-01-01
Nanoscale ferroelectrics, the active elements of a variety of nanoelectronic devices, develop denser and richer domain structures than the bulk counterparts. With shrinking device sizes understanding and controlling domain formation in nanoferroelectrics is being intensely studied. Here we show that a precise control of the epitaxy and the strain allows stabilizing a hierarchical domain architecture in PbxSr1-xTiO3 thin films, showing periodic, purely in-plane polarized, ferroelectric nano-domains that can be switched by a scanning probe.
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.
Automatic crack propagation tracking
NASA Technical Reports Server (NTRS)
Shephard, M. S.; Weidner, T. J.; Yehia, N. A. B.; Burd, G. S.
1985-01-01
A finite element based approach to fully automatic crack propagation tracking is presented. The procedure presented combines fully automatic mesh generation with linear fracture mechanics techniques in a geometrically based finite element code capable of automatically tracking cracks in two-dimensional domains. The automatic mesh generator employs the modified-quadtree technique. Crack propagation increment and direction are predicted using a modified maximum dilatational strain energy density criterion employing the numerical results obtained by meshes of quadratic displacement and singular crack tip finite elements. Example problems are included to demonstrate the procedure.
Mode II fatigue crack propagation.
NASA Technical Reports Server (NTRS)
Roberts, R.; Kibler, J. J.
1971-01-01
Fatigue crack propagation rates were obtained for 2024-T3 bare aluminum plates subjected to in-plane, mode I, extensional loads and transverse, mode II, bending loads. These results were compared to the results of Iida and Kobayashi for in-plane mode I-mode II extensional loads. The engineering significance of mode I-mode II fatigue crack growth is considered in view of the present results. A fatigue crack growth equation for handling mode I-mode II fatigue crack growth rates from existing mode I data is also discussed.
NASA Astrophysics Data System (ADS)
Ren, Zhenhua; Zeng, Xiantao; Liu, Hanlong; Zhou, Fengjun
2013-03-01
The application of fiber reinforced plastic (FRP), including carbon FRP and glass FRP, for structural repair and strengthening has grown due to their numerous advantages over conventional materials such as externally bonded reinforcement (EBR) and near-surface mounted (NSM) strengthening techniques. This paper summarizes the results from 21 reinforced concrete beams strengthened with different methods, including externally-bonded and near-surface mounted FRP, to study the strain coordination of the FRP and steel rebar of the RC beam. Since there is relative slipping between the RC beam and the FRP, the strain of the FRP and steel rebar of the RC beam satisfy the quasi-plane-hypothesis; that is, the strain of the longitudinal fiber that parallels the neutral axis of the plated beam within the scope of the effective height ( h 0) of the cross section is in direct proportion to the distance from the fiber to the neutral axis. The strain of the FRP and steel rebar satisfies the equation: ɛ FRP= βɛ steel, and the value of β is equal to 1.1-1.3 according to the test results.
Numerical investigation on the geometry dependence of the crack growth resistance in CT specimens
NASA Astrophysics Data System (ADS)
Shan, G. X.; Kolednik, O.; Fischer, F. D.
1994-03-01
The influence of the specimen thickness B and the ligament length b on the J(sub R)-curves is numerically investigated for CT specimens. The thickness effect is taken into account with 2-D analyses by dividing a plain sided specimen into a plane stress part and a plane strain part. The fracture process is controlled by experimentally determined critical values of the crack tip opening displacement for crack growth initiation (CTOD(sub i)) and the crack tip opening angle for stable crack growth (CTOA(sub C)). It is shown that for the global behavior of a plain sided specimen, the B/b ratio is essential. The difference between the geometry dependence of the initiation value of the J-integral and the geometry dependence of the slope of the J(sub R)-curves is also shown.
Marquez, J. Pablo; Genin, Guy M.; Zahalak, George I.; Elson, Elliot L.
2005-01-01
Constitutive models are needed to relate the active and passive mechanical properties of cells to the overall mechanical response of bio-artificial tissues. The Zahalak model attempts to explicitly describe this link for a class of bio-artificial tissues. A fundamental assumption made by Zahalak is that cells stretch in perfect registry with a tissue. We show this assumption to be valid only for special cases, and we correct the Zahalak model accordingly. We focus on short-term and very long-term behavior, and therefore consider tissue constituents that are linear in their loading response (although not necessarily linear in unloading). In such cases, the average strain in a cell is related to the macroscopic tissue strain by a scalar we call the “strain factor”. We incorporate a model predicting the strain factor into the Zahalak model, and then reinterpret experiments reported by Zahalak and co-workers to determine the in situ stiffness of cells in a tissue construct. We find that, without the modification in this article, the Zahalak model can underpredict cell stiffness by an order of magnitude. PMID:15596492
Creep crack-growth: A new path-independent T sub o and computational studies
NASA Technical Reports Server (NTRS)
Stonesifer, R. B.; Atluri, S. N.
1981-01-01
Two path independent integral parameters which show some degree of promise as fracture criteria are the C* and delta T sub c integrals. The mathematical aspects of these parameters are reviewed. This is accomplished 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 is a valid crack tip parameter during nonsteady as well as steady state creep and that delta T sub c has an energy rate interpretation whereas C* does not. An efficient, small displacement, infinitestimal strain, displacement based finite element model is developed for general elastic/plastic material behavior. For the numerical studies, this model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations.
NASA Astrophysics Data System (ADS)
Cakmak, M.; Hassan, M.; Unsal, E.; Martins, C.
2012-12-01
An instrumented and highly integrated biaxial stretching system was designed and constructed to obtain true stress, true strain, and optical behavior of polymeric films during biaxial stretching. With programmable drive motors, any form of temporally varying biaxial deformation profiles, including linear, exponential, logarithmic as well as cyclic, can be applied to a square-shaped films. This machine allows the investigation of mechano-optical behavior of films under profiles captured in industrial processes. To overcome the edge effects, the samples are painted with a dot pattern that is imaged using a high speed video capture system. This system accurately determines the locations of the each dot matrix in subsequent images acquired and calculates the true strains in both directions. The in-plane optical retardation is determined using spectral birefringence method that uses polarized white light and optical spectrometer in the optical train. This is carried out automatically at less than 10 nm in retardation resolution with the light beam passing through the symmetry center of the sample. Out of plane retardation is measured with an identical optical train tilted 45° to the plane of the film with its light beam going through the same spot on the sample as 0° beam. The true stress and birefringences are calculated with the determined instantaneous thickness of the film. With this system, the stress optical behavior of PET's is determined up to very large deformation levels at moderate to high deformation rates. Beyond the initial linear stress optical behavior, these films exhibit sudden positive deviation from linearity and this start of nonlinearity was directly associated with the stress induced crystallization.
Elevated temperature crack growth
NASA Technical Reports Server (NTRS)
Kim, K. S.; Vanstone, R. H.; Malik, S. N.; Laflen, J. H.
1988-01-01
A study was performed to examine the applicability of path-independent (P-I) integrals to crack growth problems in hot section components of gas turbine aircraft engines. Alloy 718 was used and the experimental parameters included combined temperature and strain cycling, thermal gradients, elastic-plastic strain levels, and mean strains. A literature review was conducted of proposed P-I integrals, and those capable of analyzing hot section component problems were selected and programmed into the postprocessor of a finite element code. Detailed elastic-plastic finite element analyses were conducted to simulate crack growth and crack closure of the test specimen, and to evaluate the P-I integrals. It was shown that the selected P-I integrals are very effective for predicting crack growth for isothermal conditions.
Crack Turning Mechanics of Composite Wing Skin Panels
NASA Technical Reports Server (NTRS)
Yuan, F. G.; Reeder, James R. (Technical Monitor)
2001-01-01
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.
3D crack tip fields for FCC single crystals
Cuitino, A.M.; Ortiz, M.
1995-12-31
Cracks in single crystals are of concern in a number of structural and non-structural applications, ranging form single-crystal turbine blades and rotors to metal interconnect lines in microcircuits. In this paper we present 3D numerical simulations of the crack-tip fields of a Cu single crystal, including stress, strain and slip activity patterns. The orientation of the crack tip is along the crystallographic orientation (101), while the crack plane is (010). A material model based on dislocation mechanics is used in these simulations. This model correctly predicts the observed behavior of Cu, including the basic hardening characteristics of single crystals, orientation dependence and stage I-II-III structure of the stress-strain curves, the observed levels of latent hardening and their variation with orientation and deformation in the primary system and slip activities and dislocation densities. We use the FEM within the context of finite deformation plasticity. In the figure below, we show the finite element mesh composed by 12-noded tetrahedrons with 6-noded triangular faces. The model simulates half of a beam, which is subjected to a concentrated load at 1/8 of total length from the support. Detailed results of the stress, deformation and slip activity are presented at different radii from crack tip and at different depths from the surface. In general, the results show a strong difference in the slip activity pattern form the interior to the exterior, while smaller differences are encountered in the stress and strain fields.
Transient solution for a plane-strain fracture driven by a shear-thinning, power-law fluid
NASA Astrophysics Data System (ADS)
Garagash, D. I.
2006-12-01
This paper analyses the problem of a fluid-driven fracture propagating in an impermeable, linear elastic rock with finite toughness. The fracture is driven by injection of an incompressible viscous fluid with power-law rheology. The relation between the fracture opening and the internal fluid pressure and the fracture propagation in mobile equilibrium are described by equations of linear elastic fracture mechanics (LEFM), and the flow of fluid inside the fracture is governed by the lubrication theory. It is shown that for shear-thinning fracturing fluids, the fracture propagation regime evolves in time from the toughness- to the viscosity-dominated regime. In the former, dissipation in the viscous fluid flow is negligible compared to the dissipation in extending the fracture in the rock, and in the later, the opposite holds. Corresponding self-similar asymptotic solutions are given by the zero-viscosity and zero-toughness (J. Numer. Anal. Meth. Geomech. 2002; 26:579-604) solutions, respectively. A transient solution in terms of the crack length, the fracture opening, and the net fluid pressure, which describes the fracture evolution from the early-time (toughness-dominated) to the large-time (viscosity-dominated) asymptote is presented and some of the implications for the practical range of parameters are discussed. Copyright
Zheng, X.J.; Metzger, D.R.; Glinka, G.; Dubey, R.N.
1996-12-01
Zirconium alloys may be susceptible to hydride formation under certain service conditions, due to hydrogen diffusion and precipitation in the presence of stress concentrations and temperature gradients. The inhomogeneous brittle hydride platelets that form are modeled as plane defects of zero thickness, with fracture toughness less than that of the matrix. A fracture criterion based on sufficient energy and stress is proposed for either delayed hydride cracking (DHC) under constant loading conditions, or hydride cracking at rising loads, such as in a fracture toughness test. The fracture criterion is validated against available experimental data concerning initiation of hydride fracture in smooth specimens, and DHC in cracked specimens under various loading and temperature conditions.
A study of creep crack growth in 2219-T851
NASA Astrophysics Data System (ADS)
Bensussan, Philippe L.; Jablonski, David A.; Pelloux, Regis M.
1984-01-01
Creep crack growth rates were measured in high strength 2219-T851 aluminum alloy with a computerized fully automated test procedure. Crack growth tests were performed on CT specimens with side grooves. The experimental set-up is described. During a test, the specimen is cyclically loaded on a servohydraulic testing machine under computer control, maintained at maximum load for a given hold time at each cycle, unloaded, and then reloaded. Crack lengths are obtained from compliance measurements recorded during each unloading. It is shown that the measured crack growth rates per cycle do represent creep crack growth rates per unit time for hold times longer than 10 seconds. The validity of LEFM concepts for side-grooved specimens is reviewed, and compliance and stress intensity factor calibrations for such specimens are reported. For the range of testing conditions of this study, 2219-T851 is shown to be creep brittle in terms of concepts of fracture mechanics of creeping solids. It is found that, under these testing conditions, a correlation exists between the creep crack growth rates under plane strain conditions and the stress intensity factor ( da/dt = A K 3.8 at 175 °C) for simple K histories in a regime of steady or quasi-steady state crack growth. The micromechanisms of fracture are determined to be of complex nature. The fracture mode is observed to be mixed inter- and transgranular, the relative amount of intergranular fracture decreasing as K and da/dt increase.
NASA Astrophysics Data System (ADS)
Kroon, Martin
2012-01-01
In the present study, a computational framework for studying high-speed crack growth in rubber-like solids under conditions of plane stress and steady-state is proposed. Effects of inertia, viscoelasticity and finite strains are included. The main purpose of the study is to examine the contribution of viscoelastic dissipation to the total work of fracture required to propagate a crack in a rubber-like solid. The computational framework builds upon a previous work by the present author (Kroon in Int J Fract 169:49-60, 2011). The model was fully able to predict experimental results in terms of the local surface energy at the crack tip and the total energy release rate at different crack speeds. The predicted distributions of stress and dissipation around the propagating crack tip are presented. The predicted crack tip profiles also agree qualitatively with experimental findings.
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.
Zhang, T.Y.; Hack, J.E.
1999-01-01
Calculations of the equilibrium hydrogen concentration profiles about a mixed ode I-mode III crack in single crystal iron were performed. Both material anisotropy and the tetragonal nature of the distortion induced in the iron crystal structure by interstitial hydrogen were incorporated. Results show that, unlike the case of a spherical distortion, a strong coupling exists between the strain field of the interstitial hydrogen and the stress field of the crack for orientations of the crack plane that are not coincident with the cube axes of the lattice. As a result, the predicated enhancement of hydrogen in the crack tip region increases with increasing levels of mode III loading for those orientations. The results may help reconcile conflicting observations concerning the potential role of shear stresses in hydrogen embrittlement and preferential cracking of grains ahead of loaded crack tips in sustained load cracking experiments.
NASA Astrophysics Data System (ADS)
Strine, Matthew; Wojtal, Steven F.
2004-10-01
We report quartz c-axis patterns, grain-shape fabrics, and microstructures for 11 mylonitic quartzites and quartz-phyllosilicate schists from a transect across the Moine thrust at Loch Srath nan Aisinnin, North-West Scotland. In the footwall samples collected more than 42 m normal distance from the thrust surface, quartz c-axis textures indicate a general flattening strain (i.e. 0< k<1). Samples within 19 m normal distance of the thrust are completely recrystallized and exhibit asymmetric c-axis patterns. Recrystallized hanging wall fault rocks exhibit random c-axis patterns on the scale of a standard thin section. Relict footwall grains provide the closest approximation of finite strain; they have octahedral shear strains ( ɛs) between 1.10 and 1.47 and exhibit general flattening k-values (0.0524-0.659). The long axis of the mean relict grain shape trends parallel to the regional transport direction and plunges gently to the ESE. In contrast, recrystallized footwall grains have a mean grain shape with the longest axis oriented nearly perpendicular to the transport direction. Furthermore, these samples have grain shape k-value ranges from 0.157 to 0.295. Recrystallized hanging wall grain shapes exhibit the lowest octahedral shear 'strains' ( ɛs=0.532-0.733) and largest mean k-values (0.351-0.961) of this sample set. The long axes of the mean recrystallized hanging wall grain shapes are parallel to transport, similar to that of relict footwall grains. Unrecrystallized quartz overgrowths about opaque mineral grains suggest concurrent elongation in all directions within the mylonitic foliation and support the inference of general flattening deformation. The mylonitic foliation and penetrative lineation are consistent with a WNW shearing direction; however, both were folded during later deformation increments. Recrystallized grains in footwall quartzites suggest a 305-320° azimuth for the shearing direction. The best-fit π-axis of the poles to the foliation is 18
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.
Reciprocity principle and crack identification
NASA Astrophysics Data System (ADS)
Andrieux, Stéphane; Ben Abda, Amel; Duong Bui, Huy
1999-02-01
In this paper we are concerned with the planar crack identification problem defined by a unique complete elastostatic overdetermined boundary datum. Based on the reciprocity gap principle, we give a direct process for locating the host plane and we establish a new constuctive identifiability result for 3D planar cracks.
Goel, V.S.
1986-01-01
Various papers on corrosion cracking are presented. The topics addressed include: unique case studies on hydrogen embrittlement failures in components used in aeronautical industry; analysis of subcritical cracking in a Ti-5Al-2.5Sn liquid hydrogen control valve; corrosion fatigue and stress corrosion cracking of 7475-T7351 aluminum alloy; effects of salt water environment and loading frequency on crack initiation in 7075-T7651 aluminum alloy and Ti-6Al-4V; stress corrosion cracking of 4340 steel in aircraft ignition starter residues. Also discussed are: stress corrosion cracking of a titanium alloy in a hydrogen-free environment; automation in corrosion fatigue crack growth rate measurements; the breaking load method, a new approach for assessing resistance to growth of early stage stress corrosion cracks; stress corrosion cracking properties of 2090 Al-Li alloy; repair welding of cracked free machining Invar 36; radial bore cracks in rotating disks.
Polycrystal orientation effects on microslip and mixed-mode behavior of microstructural small cracks
Bennett, V.; McDowell, D.L.
1999-07-01
There are two sources of mode mixity--on a macro level (combined loading situation), and on the micro level--that affect the propagation of small crystallographic cracks. This work explores mode mixity on the micro level by utilizing a computational model to simulate microstructural influences on driving forces for the formation and growth of small cracks. Two-dimensional computational cyclic crystal plasticity calculations are conducted to study the distribution of cyclic slip and critical plane-type fatigue parameters in a material with nominal stress-strain characteristics of 4340 steel. Cases of applied cyclic tension-compression and cyclic shear are analyzed at strain amplitudes below macroscopic yielding. Emphasis is placed on stress state and amplitude dependence of the distribution of these parameters among grains. The role of anisotropic plasticity is isolated by assuming the elastic behavior of grains to obey homogeneous, isotropic linear elasticity. All grains are of equal dimension and are assigned a random orientation distribution. It is found that the distribution of the Fatemi-Socie critical plane fatigue parameter among grains is Weibull-distributed, and it is argued that it forms an improved linkage to cyclic crack tip displacement for microstructurally small cracks. The authors also present computed crack tip opening and sliding displacements as a function of maximum applied tensile strain (from well below to just above nominal yielding) for small cracks within surface grains surrounded by a nearly random orientation distribution of grains. Multiple realizations of the local microstructure are examined for each crack length for sub-grain size cracks, with results normalized to the ratio of crack length to grain size. Key results include a very strong role of the free surface on crack tip displacement, with opening displacement being much greater than the sliding for suitably small crystallographic cracks in the surface grains. There is also a
NASA Astrophysics Data System (ADS)
Takeda, T.; Shindo, Y.; Narita, F.
2004-06-01
This paper presents the thermo-mechanical response of multi-layered G-11 woven glass/epoxy laminates with internal and/or edge cracks under tensile loading at cryogenic temperatures obtained from a two-dimensional finite element analysis. A condition of generalized plane strain is assumed to exist in the composite. Cracks are considered to occur in the transverse fiber bundles and extend through the entire thickness of the fiber bundles. The finite element model accounts for the temperature-dependent constituent properties. A detailed examination of the Young's modulus and stress distributions near the crack tip is carried out which provides insight into material behavior at cryogenic temperatures.
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.
Batra, R.C.; Peng, Z.
1995-12-31
The authors study the initiation and growth of shear bands in prismatic bodies of rectangular cross-section made of either depleted uranium or tungsten and deformed in plane strain compression at a nominal strain-rate of 5000/s. It is found that, in the deformed configuration, shear bands in depleted uranium blocks are inclined at approximately 42.5 deg counterclockwise from the horizontal axis, those in tungsten are inclined at nearly l35 deg. When shear bands initiate, the total compressive force required to deform the body drops sharply for the uranium blocks but gradually for the tungsten blocks. After a shear band has developed, dead zones form in both uranium and tungsten blocks; the size of the dead zone in the tungsten block is more than that in the uranium block. When the shear modulus for the tungsten is artificially changed so as to equal that for the uranium, the angle of inclination for the shear bands in tungsten blocks changes to that found for the uranium blocks. This suggests that the value of the shear modulus plays a noticeable role in the development of shear bands.
Elastic-plastic analysis of growing cracks
Rice, J.R.; Drugan, W.J.; Sham, T.L.
1980-01-01
The elastic-plastic stress and deformation fields at the tip of a crack which grow in an ideally plastic solid under plane strain, small-scale yielding conditions is discussed. Asymptotic analysis suggests a crack-tip stress state similar to that of the classical Prandtl field, but containing elastic unloading between the centered fan region and the trailing constant stress plastic region. The near tip expression for the rate of opening displacement delta at distance r from the growing tip is found to have the same form suggested by Rice and Sorensen, delta = ..cap alpha..J/sigma/sub 0/ + ..beta..(sigma/sub 0//E)a ln (R/r), but now the presence of the elastic wedge causes ..beta.. to have the revised value of 5.08 (for Poisson ratio ..nu.. = 0.3). Here, a = crack length, sigma/sub 0/ = yield strength, E = elastic modulus, and J denotes the far-field value (1 - ..nu../sup 2/) K/sup 2//E for the small scale yielding conditions considered. The parameters ..cap alpha.. and R cannot be determined from the asymptotic analysis, but ..cap alpha.. is approximately the same for stationary and growing cracks, and R scales approximately with the size of the plastic zone, being about 15 to 30% larger. For large scale yielding, a similar form applies with possible variations in ..cap alpha.. and ..beta.., at least in cases which maintain triaxial constraint at the crack tip, but in the fully yielded case R is expected to be proportional to the dimension of the uncracked ligament. The model crack growth criterion of Rice and Sorensen, requiring a critical delta at some fixed r from the tip, is reexamined. Results suggest that the J versus ..delta..a relation describing growth will be dependent on the extent of yielding, although it is suggested that this dependency might be small for highly ductile materials, provided that a similar triaxial constraint is maintained in all cases.
Formation and interpretation of dilatant echelon cracks.
Pollard, D.D.; Segall, P.; Delaney, P.T.
1982-01-01
The relative displacements of the walls of many veins, joints, and dikes demonstrate that these structures are dilatant cracks. We infer that dilatant cracks propagate in a principal stress plane, normal to the maximum tensile or least compressive stress. Arrays of echelon crack segments appear to emerge from the peripheries of some dilatant cracks. Breakdown of a parent crack into an echelon array may be initiated by a spatial or temporal rotation of the remote principal stresses about an axis parallel to the crack propagation direction. Near the parent-crack tip, a rotation of the local principal stresses is induced in the same sense, but not necessarily through the same angle. Incipient echelon cracks form at the parent-crack tip normal to the local maximum tensile stress. Further longitudinal growth along surfaces that twist about axes parallel to the propagation direction realigns each echelon crack into a remote principal stress plane. The walls of these twisted cracks may be idealized as helicoidal surfaces. An array of helicoidal cracks sweeps out less surface area than one parent crack twisting through the same angle. Thus, many echelon cracks grow from a single parent because the work done in creating the array, as measured by its surface area decreases as the number of cracks increases. -from Authors
Warren, N.
1980-09-01
Compressional and shear velocities, static strain, and permeabilities were measured for a suite of 7 rocks from LASL. The sample included two gneisses (cored parallel and perpendicular to the plane of foliation), a diorite, a granite, two quartzites and a marble. This interim report is a partial compilation of data, presented simply as a useable inventory and as a reference source of data for other studies in the future. The import of this data set is that for each sample it consists of measurements of four physical properties all of which are controlled by the sample's microstructure. Therefore, the sets of data for any one rock are expected to show strong cross-correlations, and to provide insight into the inverse problem of predicting physical properties from petrostructural models.
Dial, B.W.; Maxwell, D.E.
1986-12-01
Numerical studies of the far-field repository and near-field shaft response for a nuclear waste repository in bedded salt have been performed with the STEALTH computer code using the CAVS model for jointed rock. CAVS is a constitutive model that can simulate the slip and dilatancy of fracture planes in a jointed rock mass. The initiation and/or propagation of fractures can also be modeled when stress intensity criteria are met. The CAVS models are based on the joint models proposed with appropriate modifications for numerical simulations. The STEALTH/CAVS model has been previously used to model (1) explosive fracturing of a wellbore, (2) earthquake effects on tunnels in a generic nuclear waste repository, (3) horizontal emplacement for a nuclear waste repository in jointed granite, and (4) tunnel response in jointed rock. The use of CAVS to model far-field repository and near-field shaft response was different from previous approaches because it represented a spatially oriented approach to rock response and failure, rather than the traditional stress invariant formulation for yielding. In addition, CAVS tracked the response of the joint apertures to the time-dependent stress changes in the far-field repository and near-field shaft regions. 28 refs., 21 figs., 11 tabs.
Automatic crack growth tracking of bimaterial interface cracks
NASA Technical Reports Server (NTRS)
Yehia, Nabil A. B.; Shephard, Mark S.
1988-01-01
The propagation process of an interfacial crack in composite material is studied using the modified maximum dilatational strain energy density criterion, NT-criterion. Some necessary assumptions have been adopted to facilitate the use of the NT-criterion in this case. The stress intensity factors at the crack tip are extracted from the complex displacement field and finite element results. A simple algorithm for automatic crack propagation is presented with an illustrative example.
Procedures for evaluating filament cracking during fatigue testing of Nb3Sn strand
NASA Astrophysics Data System (ADS)
Sheth, M. K.; Lee, Peter; McRae, D. M.; Walsh, Robert; Starch, W. L.; Jewell, M. C.; Devred, A.; Larbalestier, D. C.
2012-06-01
In Tokamak fusion reactors, such as ITER, superconducting strands are subjected to repeated Lorentz force loading and unloading which may degrade performance over time. The Cu matrix which surrounds the brittle Nb3Sn filaments allows the possibility of some elastic-plastic deformation that can initiate filament cracking. We seek to understand if there are strand design variables that might ameliorate such degradation but before being able to do such experiments, we need to establish procedures that can unambiguously detect the cracking caused by loading, rather than by subsequent metallographic examination. Here we make a first report of our procedures after fatigue testing at 77K. Filament crack densities were quantified from large montages covering ≈20 mm length of strand. Three types of cracks were present. The most common were cracks transverse to the filament axis adjacent to voids. Cracks away from voids were of low density until close to the fracture strain. A third kind of crack which generally initiates at unreacted Nb cores of filaments extends radially and in the plane parallel to the wire axis. Example results on one bronze strand fatigued for 1000 loading cycles at axial strains from 0.4% to 1.14% are shown.
Measuring Crack Length in Coarse Grain Ceramics
NASA Technical Reports Server (NTRS)
Salem, Jonathan A.; Ghosn, Louis J.
2010-01-01
Due to a coarse grain structure, crack lengths in precracked spinel specimens could not be measured optically, so the crack lengths and fracture toughness were estimated by strain gage measurements. An expression was developed via finite element analysis to correlate the measured strain with crack length in four-point flexure. The fracture toughness estimated by the strain gaged samples and another standardized method were in agreement.
van Kessel, Marco; Seaton, David; Chan, Jonathan; Yamada, Akira; Kermeen, Fiona; Butler, Thomas; Sabapathy, Surendran; Morris, Norman
2016-06-01
Pulmonary hypertension (PH) is a progressively fatal disease having a significant impact on right ventricular (RV) function, a major determinant of long-term outcome in PH patients. In our clinic we frequently noticed the combination of PH and reduced RV function, but with discordant Tricuspid Annular Plane Systolic Excursion (TAPSE) values. The present study focuses on whether RV free wall strain measured using 2-dimensional speckle-tracking echocardiography is able to predict mortality in this subgroup of PH patients. 57 patients with PH and RV dysfunction (visual echocardiographic assessment of ≥2) and pseudo-normalized TAPSE values (defined as ≥16 mm) were retrospectively evaluated. Patients were divided by RV free -20 % as cut-off value. Follow-up data on all-cause mortality were registered after a median follow-up time of 27.9 ± 1.7 months. RV free of ≥-20 % was predictive of all-cause mortality after a median follow-up time of 27.9 ± 1.7 months (HR 3.76, 95 % CI 1.02-13.92, p = 0.05). RV free ≥-20 % remained a significant predictor of all-cause mortality (HR 4.30, 95 % CI 1.11-16.61, p = 0.04) after adjusting for PH-specific treatment. On the contrary, TAPSE was not a significant predictor of all-cause mortality. RV free wall strain provides prognostic information in patients with PH and RV dysfunction, but with normal TAPSE values. Future studies with larger cohorts, longer follow-up periods and inclusion of more echocardiographic parameters measuring LV and RV function could confirm the strength of RV free ≥-20 % as a predictor of mortality for this subgroup of patients with PH. PMID:26931558
Cryogenic Behavior of Cracks in Satin Woven CFRP Laminates under Tensile Loading
NASA Astrophysics Data System (ADS)
Watanabe, Shinya; Shindo, Yasuhide; Takeda, Tomo; Narita, Fumio; Sanada, Kazuaki
The objective of this research is to investigate the crack behavior in five harness satin woven carbon fiber reinforced polymer (CFRP) composite laminates with temperature-dependent material properties under tension at cryogenic temperatures. A situation of generalized plane strain is considered, and cracks are assumed to have occurred in the transverse fiber bundles. Also, both cases where the tips of the cracks are located in the fiber bundles or at the interfaces between two fiber bundles are treated, and a finite element technique utilizing special singular elements is used to obtain the stress intensity factors at the tips of the transverse cracks in two-layer woven CFRP laminates. The numerical results are then discussed in detail.
The Evolution of Stress Intensity Factors and the Propagation of Cracks in Elastic Media
NASA Astrophysics Data System (ADS)
Friedman, Avner; Hu, Bei; Velazquez, Juan J. L.
When a crack Γs propagates in an elastic medium the stress intensity factors evolve with the tip x(s) of Γs. In this paper we derive formulae which describe the evolution of these stress intensity factors for a homogeneous isotropic elastic medium under plane strain conditions. Denoting by ψ=ψ(x,s) the stress potential (ψ is biharmonic and has zero traction along the crack Γs) and by κ(s) the curvature of the crack at the tip x(s), we prove that the stress intensity factors A1(s), A2(s), as functions of s, satisfy:
Influence of the slip conditions on the stress corrosion cracking microprocesses in fcc materials
Chambreuil-Paret, A.; Chateau, J.P.; Magnin, T.
1997-11-01
The aim of the present paper is to carefully analyze the stress corrosion cracking (SCC) microprocesses of f.c.c. single crystals, not only for the influence of the tensile axis orientation but also for the influence of the cracking direction (imposed or not). 316L (in MgCl{sub 2}) and copper (in nitrites) single crystals of well defined tensile axis will be strained using the slow strain rate technique. The authors focus on the influence of the relative orientations of the cracking direction and the slip planes on the crystallography of fracture. The effect of slip conditions on the corrosion-deformation interactions leading to fracture are then emphasized, which gives major information relevant to the micromodelling of SCC.
The effect of non-singular stresses on crack-tip constraint
NASA Astrophysics Data System (ADS)
Du, Z.-Z.; Hancock, J. W.
T HE EFFECT of the T-stress on the small-scale yielding field of a crack in plane strain conditions has been examined using modified boundary layer formulations. The numerically calculated stresses at the crack tip are represented by slip line fields for small-strain theory. Positive T-stresses cause plasticity to envelop the crack tip and exhibit a Prandtl field, corresponding to the limiting solution of the HRR field for a nonhardening material. Moderate compressive T-stresses reduce the direct stresses within the plastic zone by decreasing the hydrostatic stress by T. This causes a loss of J-dominance, and a stress distribution represented by an incomplete Prandtl field.
Subcritical crack growth under mode I, II, and III loading for Coconino sandstone
NASA Astrophysics Data System (ADS)
Ko, Tae Young
In systems subjected to long-term loading, subcritical crack growth is the principal mechanism causing the time-dependent deformation and failure of rocks. Subcritical crack growth is environmentally-assisted crack growth, which can allow cracks to grow over a long period of time at stresses far smaller than their failure strength and at tectonic strain rates. The characteristics of subcritical crack growth can be described by a relationship between the stress intensity factor and the crack velocity. This study presents the results of studies conducted to validate the constant stress-rate test for determining subcritical crack growth parameters in Coconino sandstone, compared with the conventional testing method, the double torsion test. The results of the constant stress-rate test are in good agreement with the results of double torsion test. More importantly, the stress-rate tests can determine the parameter A with a much smaller standard deviation than the double torsion test. Thus the constant stress-rate test seems to be both a valid and preferred test method for determining the subcritical crack growth parameters in rocks. We investigated statistical aspects of the constant stress-rate test. The effects of the number of tests conducted on the subcritical crack growth parameters were examined and minimum specimen numbers were determined. The mean and standard deviation of the subcritical crack growth parameters were obtained by randomly selecting subsets from the original strength data. In addition, the distribution form of the subcritical crack growth parameters and the relation between the parameter n and A were determined. We extended the constant stress-rate test technique to modes II and III subcritical crack growth in rocks. The experimental results of the modes I, II and III tests show that the values of the subcritical crack growth parameters are similar to each other. The subcritical crack growth parameter n value for Coconino sandstone has the range
Bending effects of unsymmetric adhesively bonded composite repairs on cracked aluminum panels
NASA Technical Reports Server (NTRS)
Arendt, Cory; Sun, C. T.
1994-01-01
The bending effects of unsymmetrically bonded composite repairs on cracked aluminum panels were quantified using a plate linear finite element model. Stress intensity factors and strain energy release rates were obtained from the model twice, once with out-of-plane displacement suppressed and another time without these restrictions. Several configurations were examined, crack growth stability was identified, and the effect of a debond was considered. The maximum stress intensity factor was also analyzed. Previous work by other authors was found to underpredict the bending effect.
NASA Astrophysics Data System (ADS)
Padmanabhan, R.; Oliveira, M. C.; Baptista, A. J.; Alves, J. L.; Menezes, L. F.
2007-05-01
Springback phenomenon associated with the elastic properties of sheet metals makes the design of forming dies a complex task. Thus, to develop consistent algorithms for springback compensation an accurate prediction of the amount of springback is mandatory. The numerical simulation using the finite element method is consensually the only feasible method to predict springback. However, springback prediction is a very complicated task and highly sensitive to various numerical parameters of finite elements (FE), such as: type, order, integration scheme, shape and size, as well the time integration formulae and the unloading strategy. All these numerical parameters make numerical simulation of springback more sensitive to numerical tolerances than the forming operation. In case of an unconstrained cylindrical bending, the in-plane to thickness FE size ratio is more relevant than the number of FE layers through-thickness, for the numerical prediction of final stress and strain states, variables of paramount importance for an accurate springback prediction. The aim of the present work is to evaluate the influence of the refinement of a 3-D FE mesh, namely the in-plane mesh refinement and the number of through-thickness FE layers, in springback prediction. The selected example corresponds to the first stage of the "Numisheet'05 Benchmark♯3", which consists basically in the sheet forming of a channel section in an industrial-scale channel draw die. The physical drawbeads are accurately taken into account in the numerical model in order to accurately reproduce its influence during the forming process simulation. FEM simulations were carried out with the in-house code DD3IMP. Solid finite elements were used. They are recommended for accuracy in FE springback simulation when the ratio between the tool radius and blank thickness is lower than 5-6. In the selected example the drawbead radius is 4.0 mm. The influence of the FE mesh refinement in springback prediction is
An analytically enriched finite element method for cohesive crack modeling.
Cox, James V.
2010-04-01
Meaningful computational investigations of many solid mechanics problems require accurate characterization of material behavior through failure. A recent approach to fracture modeling has combined the partition of unity finite element method (PUFEM) with cohesive zone models. Extension of the PUFEM to address crack propagation is often referred to as the extended finite element method (XFEM). In the PUFEM, the displacement field is enriched to improve the local approximation. Most XFEM studies have used simplified enrichment functions (e.g., generalized Heaviside functions) to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. As such, the mesh had to be sufficiently fine for the FEM basis functions to capture these gradients.In this study enrichment functions based upon two analytical investigations of the cohesive crack problem are examined. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack with a relatively coarse mesh and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation are summarized. Analysis results for simple model problems are presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. A standard finite element solution with interface elements is used to provide the accurate reference solution, so the model problems are limited to a straight, mode I crack in plane stress. Except for the cohesive zone, the material model for the problems is homogenous, isotropic linear elasticity. The effects of mesh refinement, mesh orientation, and enrichment schemes that enrich a larger region around the cohesive crack are considered in the study. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are presented. The analysis
Fracture behavior of shallow cracks in full-thickness clad beams from an RPV wall section
Keeney, J.A.; Bass, B.R.; McAfee, W.J.
1995-04-01
A testing program is described that utilizes full-thickness clad beam specimens to quantify fracture toughness for shallow cracks in weld material for which metallurgical conditions are prototypic of those found in reactor pressure vessels (RPVs). The beam specimens are fabricated from an RPV shell segment that includes weld, plate and clad material. Metallurgical factors potentially influencing fracture toughness for shallow cracks in the beam specimens include material gradients and material inhomogeneities in welded regions. The shallow-crack clad beam specimens showed a significant loss of constraint similar to that of other shallow-crack single-edge notch bend (SENB) specimens. The stress-based Dodds-Anderson scaling model appears to be effective in adjusting the test data to account for in-plane loss of constraint for uniaxially tested beams, but cannot predict the observed effects of out-of-plane biaxial loading on shallow-crack fracture toughness. A strain-based dual-parameter fracture toughness correlation (based on plastic zone width) performed acceptably when applied to the uniaxial and biaxial shallow-crack fracture toughness data.
Interface cracks in piezoelectric materials
NASA Astrophysics Data System (ADS)
Govorukha, V.; Kamlah, M.; Loboda, V.; Lapusta, Y.
2016-02-01
Due to their intrinsic electromechanical coupling behavior, piezoelectric materials are widely used in sensors, actuators and other modern technologies. It is well known that piezoelectric ceramics are very brittle and susceptible to fracture. In many cases, fracture occurs at interfaces as debonding and cracks. This leads to an undesired degradation of electrical and mechanical performance. Because of the practical and fundamental importance of the problem, interface cracks in piezoelectric materials have been actively studied in the last few decades. This review provides a comprehensive survey of recent works on cracks situated at the interface of two materials, at least one of which has piezoelectric or piezoelectromagnetic properties. Different electric boundary conditions along the crack faces are discussed. The oscillating and contact zone models for in-plane straight interface cracks between two dissimilar piezoelectric materials or between piezoelectric and non-piezoelectric ones are reviewed. Different peculiarities related to the investigation of interface cracks in piezoelectric materials for the anti-plane case, for functionally graded and thermopiezoelectric materials are presented. Papers related to magnetoelectroelastic bimaterials, to steady state motion of interface cracks in piezoelectric bimaterials and to circular arc-cracks at the interface of piezoelectric materials are reviewed, and various methods used to address these problems are discussed. The review concludes with an outlook on future research directions.
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.
NASA Technical Reports Server (NTRS)
Salpekar, S. A.; O'Brien, T. K.
1991-01-01
Several 3D finite element analyses of (O/theta/-theta)sub s graphite epoxy laminates, where theta = 15, 20, 25, 30, and 45 deg, subjected to axial tension load were performed. The interlaminar stresses in the theta/-theta interface were calculated with and without a matrix crack in the central -theta plies. The interlaminar normal stress changes from a small compressive stress when no matrix crack is present to a high tensile stress at the intersection of the matrix crack and free edge. The analysis of local delamination from the -theta matrix crack indicates a high strain energy release rate and a localized mode I component near the free edge, within one ply distance from the matrix crack. In order to examine the stress state causing the matrix cracking the maximum principal normal stress in a plane perpendicular to the fiber direction in the -theta ply was calculated in an uncracked laminate. The corresponding shear stress parallel to the fiber was also calculated. The principal normal stress at the laminate edge increases through the ply thickness and reached a very high tensile value at the theta/-theta interface indicating that the crack in the -theta ply may initiate at the theta/-theta interface. Crack profiles on the laminate edge in the -theta ply were constructed from the principal stress directions. The cracks were found to be more curved for layups with smaller theta angles, which is consistent with experimental observations in the literature.
NASA Technical Reports Server (NTRS)
Salpekar, S. A.; Obrien, T. K.
1991-01-01
Several 3D finite element analyses of (0/theta/-theta)sub s graphite epoxy laminates, where theta=15, 20, 25, 30, and 45 deg, subjected to axial tension load were performed. The interlaminar stresses in the theta/-theta interface were calculated with and without a matrix crack in the central -theta plies. The interlaminar normal stress changes from a small compressive stress when no matrix crack is present to a high tensile stress at the intersection of the matrix crack and free edge. The analysis of local delamination from the -theta matrix crack indicates a high strain energy release rate and a localized mode I component near the free edge, within one ply distance from the matrix crack. In order to examine the stress state causing the matrix cracking the maximum principal normal stress in a plane perpendicular to the fiber direction in the -theta ply was calculated in an uncracked laminate. The corresponding shear stress parallel to the fiber was also calculated. The principal normal stress at the laminate edge increases through the ply thickness and reached a very high tensile value at the theta/-theta interface indicating that the crack in the -theta ply may initiate at the theta/-theta interface. Crack profiles on the laminate edge in the -theta ply were constructed from the principal stress directions. The cracks were found to be more curved for layups with smaller theta angles, which is consistent with experimental observations in the literature.
Shapes Formed By Interacting Cracks
NASA Astrophysics Data System (ADS)
Daniels, K.
2014-12-01
Brittle failure through multiple cracks occurs in a wide variety of contexts, from microscopic failures in rocks to geological faults and planetary ice crusts. In each of these situations, with complicated stress geometries and different microscopic mechanisms, pairwise interactions between approaching cracks nonetheless produce characteristically curved fracture paths. We investigate the origins of this widely observed "en passant" crack pattern by fracturing a rectangular slab which is notched on two sides and then subjected to quasistatic uniaxial, biaxial, or shear strain. The two cracks propagate along approximately straight paths until they pass each other, after which they curve and release a lens-shaped fragment. Under uniaxial strain, we find that each crack path has a universal shape and aspect ratio which is independent of the material. By changing the geometry of the applied strain, we are able to achieve different aspect ratios for the crack paths. With birefringent materials, it is possible to interpret these patterns in light of the stress geometry, and we are able to explain the origins of these universal shapes with a simple geometrical model. Since a variety of aspect ratios have similarly been observed in geological contexts, this raises the possibility of using observed crack shapes as a diagnostic for the stress conditions under which cracks were formed in nature. In particular, the shape may serve as a means to infer the boundary loading in situations where history and dynamics are inaccessible.
Crack arrest toughness of a heat-affected zone containing local brittle zones
Malik, L.; Pussegoda, L.N.; Graville, B.A.; Tyson, W.R.
1996-11-01
The awareness of the presence of local brittle zones (LBZs) in the heat-affected zone (HAZ) of welds has led to the requirements for minimum initiation toughness for the HAZ for critical applications. A fracture control philosophy that is proposed to be an attractive alternative for heat-affected zones containing LBZs is the prevention of crack propagation rather than of crack initiation. Such an approach would be viable if it could be demonstrated that cracks initiated in the LBZs will be arrested without causing catastrophic failure, notwithstanding the low initiation (CTOD) toughness resulting from the presence of LBZs. Unstable propagation of a crack initiating from an LBZ requires the rupture of tougher microstructural regions surrounding the LBZ in HAZ, and therefore the CTOD value reflecting the presence of LBZ is unlikely to provide a true indication of the potential for fast fracture along the heat-affected zone. Base metal specifications usually ensure that small unstable cracks propagating from the weld zone into the base metal would be arrested. To investigate the likelihood of fast fracture within the HAZ, a test program has been carried out that involved performing compact plane strain and plane stress crack arrest tests on a heat-affected zone that contained LBZs, and thus exhibited unacceptable low CTOD toughness for resistance to brittle fracture initiation. The results indicated that the crack arrest toughness was little influenced by the presence of local brittle zones. Instead, the superior toughness of the larger proportion of finer-grain HAZ surrounding the LBZ present along the crack path has a greater influence on the crack arrest toughness.
Finite element modeling for strain rate dependency of fracture resistance in compact bone.
Charoenphan, S; Polchai, A
2007-02-01
Crack growths in compact bones driven by various strain rate levels were studied using finite element modeling. The energy resistance curves in bovine femur cortical bones were characterized, whereas the orthotropic viscoelasticity in bone materials was accounted for to assess the effect of strain rate on the energy resistance curve. The models were also used to justify the anticipated plane strain response as a result of rather thick specimens used in experiments. Similarities were found between the experimental and model results when crack resistance ability exhibited in bones with slow loading rates, while unstable crack growth existed in bones with rapid loading rates. The critical energy release rates slightly decreased with the increase in strain rates. The hybrid experimental and computational method introduced in this study could be beneficial for application in fracture study in which standard experiments cannot be validly performed. PMID:17227094
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.
Crack problems in cylindrical and spherical shells
NASA Technical Reports Server (NTRS)
Erdogan, F.
1976-01-01
Standard plate or shell theories were used as a starting point to study the fracture problems in thin-walled cylindrical and spherical shells, assuming that the plane of the crack is perpendicular to the surface of the sheet. Since recent studies have shown that local shell curvatures may have a rather considerable effect on the stress intensity factor, the crack problem was considered in conjunction with a shell rather than a plate theory. The material was assumed to be isotropic and homogeneous, so that approximate solutions may be obtained by approximating the local shell crack geometry with an ideal shell which has a solution, namely a spherical shell with a meridional crack, a cylindrical shell with a circumferential crack, or a cylindrical shell with an axial crack. A method of solution for the specially orthotropic shells containing a crack was described; symmetric and skew-symmetric problems are considered in cylindrical shells with an axial crack.
Damage analysis of a crack layer
NASA Technical Reports Server (NTRS)
Botsis, J.
1989-01-01
Damage analysis of a crack layer in polystyrene is carried out by employing optical microscopy and principles of quantitative stereology. The results show that, within the quasistatic phase of crack layer propagation, the average crazing density, along the trailing edge of the active zone, is constant. This is consistent with a self-similarity hypothesis of damage evolution employed by the crack layer theory. The average crazing densities within the active zone and along its trailing edge are found to be practically equal. A layer of constant crazing density, adjacent to the crack planes, accompanies the crack during its quasi-static growth. This suggests that: (1) a certain level of crazing density should be reached, around the crack tip, prior to crack advance; (2) the specific energy, associated with this 'core' of damage, could be considered as a Griffith's type energy. The results are in favor of certain hypothesis adopted by the crack layer theory.
FASTRAN II - FATIGUE CRACK GROWTH STRUCTURAL ANALYSIS (UNIX VERSION)
NASA Technical Reports Server (NTRS)
Newman, J. C.
1994-01-01
Predictions of fatigue crack growth behavior can be made with the Fatigue Crack Growth Structural Analysis (FASTRAN II) computer program. As cyclic loads are applied to a selected crack configuration with an initial crack size, FASTRAN II predicts crack growth as a function of cyclic load history until either a desired crack size is reached or failure occurs. FASTRAN II is based on plasticity-induced crack-closure behavior of cracks in metallic materials and accounts for load-interaction effects, such as retardation and acceleration, under variable-amplitude loading. The closure model is based on the Dugdale model with modifications to allow plastically deformed material to be left along the crack surfaces as the crack grows. Plane stress and plane strain conditions, as well as conditions between these two, can be simulated in FASTRAN II by using a constraint factor on tensile yielding at the crack front to approximately account for three-dimensional stress states. FASTRAN II contains seventeen predefined crack configurations (standard laboratory fatigue crack growth rate specimens and many common crack configurations found in structures); and the user can define one additional crack configuration. The baseline crack growth rate properties (effective stress-intensity factor against crack growth rate) may be given in either equation or tabular form. For three-dimensional crack configurations, such as surface cracks or corner cracks at holes or notches, the fatigue crack growth rate properties may be different in the crack depth and crack length directions. Final failure of the cracked structure can be modelled with fracture toughness properties using either linear-elastic fracture mechanics (brittle materials), a two-parameter fracture criterion (brittle to ductile materials), or plastic collapse (extremely ductile materials). The crack configurations in FASTRAN II can be subjected to either constant-amplitude, variable-amplitude or spectrum loading. The applied
FASTRAN II - FATIGUE CRACK GROWTH STRUCTURAL ANALYSIS (IBM PC VERSION)
NASA Technical Reports Server (NTRS)
Newman, J. C.
1994-01-01
Predictions of fatigue crack growth behavior can be made with the Fatigue Crack Growth Structural Analysis (FASTRAN II) computer program. As cyclic loads are applied to a selected crack configuration with an initial crack size, FASTRAN II predicts crack growth as a function of cyclic load history until either a desired crack size is reached or failure occurs. FASTRAN II is based on plasticity-induced crack-closure behavior of cracks in metallic materials and accounts for load-interaction effects, such as retardation and acceleration, under variable-amplitude loading. The closure model is based on the Dugdale model with modifications to allow plastically deformed material to be left along the crack surfaces as the crack grows. Plane stress and plane strain conditions, as well as conditions between these two, can be simulated in FASTRAN II by using a constraint factor on tensile yielding at the crack front to approximately account for three-dimensional stress states. FASTRAN II contains seventeen predefined crack configurations (standard laboratory fatigue crack growth rate specimens and many common crack configurations found in structures); and the user can define one additional crack configuration. The baseline crack growth rate properties (effective stress-intensity factor against crack growth rate) may be given in either equation or tabular form. For three-dimensional crack configurations, such as surface cracks or corner cracks at holes or notches, the fatigue crack growth rate properties may be different in the crack depth and crack length directions. Final failure of the cracked structure can be modelled with fracture toughness properties using either linear-elastic fracture mechanics (brittle materials), a two-parameter fracture criterion (brittle to ductile materials), or plastic collapse (extremely ductile materials). The crack configurations in FASTRAN II can be subjected to either constant-amplitude, variable-amplitude or spectrum loading. The applied
Fatigue-crack propagation behavior in the shape-memory and superelastic alloy nitinol
NASA Astrophysics Data System (ADS)
McKelvey, Aindrea Leigh
This dissertation presents a detailed study on the fatigue-crack propagation behavior in 50Ni-50Ti (at. %), and the effect of a stress-induced martensitic transformation on the material's crack-growth resistance. Furthermore, the effect of environment on crack-growth rates was also investigated. Specifically, fatigue-crack growth was characterized in stable austenite (120°C), superelastic austenite (37°C), and martensite (-65°C and -196°C). In general, as the temperature decreased the fatigue-crack growth resistance increased, where the fatigue threshold was greater and crack-growth rates slower in martensite compared to stable austenite and superelastic austenite. It was found that plane-strain superelastic austenite fatigue specimens did not transform to martensite near the crack tip. The stress-induced transformation was prevented by the existence of the tensile hydrostatic stress-state near the crack tip in fatigue specimens. Plane stress samples, however, did undergo the stress-induced martensitic transformation, as the tensile hydrostatic stress-state was reduced in thinner samples. Fatigue-crack growth rates in Nitinol at a frequency of 10 Hz were found to be essentially identical in air, aerated deionized water, and aerated Hank's solution (a simulated physiological environment), suggesting that at this frequency, any environmentally-assisted contributions to crack growth are minimal. Specifically, the threshold for the onset of fatigue-crack growth was equal to ˜2 MPa√m for all three environments. Furthermore, the slopes of the mid-growth regime were also similar and equal to ˜3; the maximum applied stress-intensity range at instability prior to failure was 30 MPa√m for all three environments. However, when compared to other biomedical implant alloys, the fatigue-crack growth resistance of Nitinol was the lowest. Specifically, the fatigue threshold, at a fixed load ratio value of ˜0.1, was significantly less (by a factor between 2 and 5) than
The crack problem in bonded nonhomogeneous materials
NASA Technical Reports Server (NTRS)
Erdogan, F.; Joseph, P. F.; Kaya, A. C.
1991-01-01
The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip termination at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.
The crack problem in bonded nonhomogeneous materials
NASA Technical Reports Server (NTRS)
Erdogan, Fazil; Kaya, A. C.; Joseph, P. F.
1988-01-01
The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.
Morphological study of near threshold fatigue crack growth in a coarse grain aluminum alloy
NASA Technical Reports Server (NTRS)
Maurer, Gerhard; Liu, H. W.
1984-01-01
Fatigue crack propagation in the near-threshold region has been studied in coarse grain Al 7029 alloy. Over eighty percent of the crack surfaces are planar areas parallel to either 100-oriented or 111-oriented planes. The 100-plane crack surfaces show 'pine tree' morphological features formed by slip on two sets of intersecting planes. The 111-plane crack surfaces were planar and shiny. They were formed primarily by slip on a single dominant 111-oriented slip plane with sparse and very light secondary slip markings. Crack growth rates were measured and correlated with Delta-K.
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.
Molecular dynamics simulation of propagating cracks
NASA Technical Reports Server (NTRS)
Mullins, M.
1982-01-01
Steady state crack propagation is investigated numerically using a model consisting of 236 free atoms in two (010) planes of bcc alpha iron. The continuum region is modeled using the finite element method with 175 nodes and 288 elements. The model shows clear (010) plane fracture to the edge of the discrete region at moderate loads. Analysis of the results obtained indicates that models of this type can provide realistic simulation of steady state crack propagation.
NASA Astrophysics Data System (ADS)
Nandal, J. S.; Saini, T. N.
2013-04-01
Porous solid is in contact with a cracked elastic solid at a plane interface between them. For the presence of vertically aligned microcracks, the elastic solid behaves transversely isotropic to wave propagation. The coefficients of elastic anisotropy depend on the crack density and crack porosity in the medium. A loose bonding is considered between the two solids so that a limiting case could be the welded contact. At the plane interface, the imperfection in welded bonding is represented by tangential slipping and, hence, results in the dissipation of a part of strain energy. Three types of waves propagate in an isotropic fluid-saturated porous medium, which are considered for incidence at the interface. Incidence of a wave results in three reflected waves and two refracted waves. Partition of incident energy among the reflected and refracted waves is studied for each incidence, varying from normal to grazing directions. Numerical example calculates the energy shares of reflected and refracted waves at the plane interface between water-saturated sandstone and basalt. These energy shares are computed and analyzed for different values of crack parameters as well as loose bonding parameter.
Effects of friction and high torque on fatigue crack propagation in Mode III
NASA Astrophysics Data System (ADS)
Nayeb-Hashemi, H.; McClintock, F. A.; Ritchie, R. O.
1982-12-01
Turbo-generator and automotive shafts are often subjected to complex histories of high torques. To provide a basis for fatigue life estimation in such components, a study of fatigue crack propagation in Mode III (anti-plane shear) for a mill-annealed AISI 4140 steel (RB88, 590 MN/m2 tensile strength) has been undertaken, using torsionally-loaded, circumferentially-notched cylindrical specimens. As demonstrated previously for higher strength AISI 4340 steel, Mode III cyclic crack growth rates (dc/dN) IIIcan be related to the alternating stress intensity factor ΔKIII for conditions of small-scale yielding. However, to describe crack propagation behavior over an extended range of crack growth rates (˜10-6 to 10-2 mm per cycle), where crack growth proceeds under elastic-plastic and full plastic conditions, no correlation between (dc/dN) III and ΔKIII is possible. Accordingly, a new parameter for torsional crack growth, termed the plastic strain intensity Γ III, is introduced and is shown to provide a unique description of Mode III crack growth behavior for a wide range of testing conditions, provided a mean load reduces friction, abrasion, and interlocking between mating fracture surfaces. The latter effect is found to be dependent upon the mode of applied loading (i.e., the presence of superimposed axial loads) and the crack length and torque level. Mechanistically, high-torque surfaces were transverse, macroscopically flat, and smeared. Lower torques showed additional axial cracks (longitudinal shear cracking) perpendicular to the main transverse surface. A micro-mechanical model for the main radi l Mode III growth, based on the premise that crack advance results from Mode II coalescence of microcracks initiated at inclusions ahead of the main crack front, is extended to high nominal stress levels, and predicts that Mode III fatigue crack propagation rates should be proportional to the range of plastic strain intensity (ΔΓIII if local Mode II growth rates are
NASA Astrophysics Data System (ADS)
Li, Yanrong; Huang, Da; Li, Xi'an
2014-07-01
Strain rate during testing, uniaxial or triaxial, has important influence on the measured mechanical properties of rocks. Uniaxial compression tests were performed at nine pre-specified static-to-quasistatic strain rates (ranging from 1 × 10-5 to 1 × 10-1 s-1) on coarse crystal marble. The aim is to gain deep insight into the influence of strain rate on characteristic stresses, deformation properties and conversion of strain energy of such rock. It is found that the strain rate of 5 × 10-3 s-1 is the threshold to delineate the failure modes the tested coarse marble behaves in. At a strain rate less than this threshold, single-plane shear and conjugate X-shaped shear are the main failure modes, while beyond this threshold, extensile and splitting failures are dominant. The stress for crack initiation, the critical stress for dilation, the peak stress, and Young's modulus are all found to increase with strain rate, with an exception that the above stresses and modulus appear relatively low compared to the strain rate in the range of between 1 × 10-4 and 5 × 10-3 s-1. The pre-peak absorbed strain energy, damage strain energy and elastic strain energy are found to increase with strain rate. In addition, the elastic strain energy stored before peak point favors brittle failure of the specimen, as the more stored elastic energy in the specimen, the stronger the fragmenting.
Strain energy release rate determination of stress intensity factors by finite element methods
NASA Technical Reports Server (NTRS)
Walsh, R. M., Jr.; Pipes, R. B.
1985-01-01
The stiffness derivative finite element technique is used to determine the Mode I stress intensity factors for three-crack configurations. The geometries examined include the double edge notch, single edge notch, and the center crack. The results indicate that when the specified guidelines of the Stiffness Derivative Method are used, a high degree of accuracy can be achieved with an optimized, relatively coarse finite element mesh composed of standard, four-node, plane strain, quadrilateral elements. The numerically generated solutions, when compared with analytical ones, yield results within 0.001 percent of each other for the double edge crack, 0.858 percent for the single edge crack, and 2.021 percent for the center crack.
Elevated temperature crack growth
NASA Technical Reports Server (NTRS)
Yau, J. F.; Malik, S. N.; Kim, K. S.; Vanstone, R. H.; Laflen, J. H.
1985-01-01
The objective of the Elevated Temperature Crack Growth Project is to evaluate proposed nonlinear fracture mechanics methods for application to combustor liners of aircraft gas turbine engines. During the first year of this program, proposed path-independent (P-I) integrals were reviewed for such applications. Several P-I integrals were implemented into a finite-element postprocessor which was developed and verified as part of the work. Alloy 718 was selected as the analog material for use in the forthcoming experimental work. A buttonhead, single-edge notch specimen was designed and verified for use in elevated-temperature strain control testing with significant inelastic strains. A crack mouth opening displacement measurement device was developed for further use.
... older obese people. Question: Can cracking knuckles / joints lead to arthritis? Answer: There is no evidence of ... or damaged joints due to arthritis could potentially lead more easily to ligament injury or acute trauma ...
Subcritical crack growth of selected aerospace pressure vessel materials
NASA Technical Reports Server (NTRS)
Hall, L. R.; Bixler, W. D.
1972-01-01
This experimental program was undertaken to determine the effects of combined cyclic/sustained loads, stress level, and crack shape on the fatigue crack growth rate behavior of cracks subjected to plane strain conditions. Material/environment combinations tested included: 2219-T87 aluminum plate in gaseous helium, room air, and 3.5% NaCl solution at room temperature, liquid nitrogen, and liquid hydrogen; 5Al-2.5 Sn (ELI) titanium plate in liquid nitrogen and liquid hydrogen and 6AL-4V (ELI) STA titanium plate in gaseous helium and methanol at room temperature. Most testing was accomplished using surface flawed specimens instrumented with a clip gage to continuously monitor crack opening displacements at the specimen surface. Tapered double cantilever beam specimens were also tested. Static fracture and ten hour sustained load tests were conducted to determine fracture toughness and apparent threshold stress intensity values. Cyclic tests were performed using sinusoidal loading profiles at 333 MHz (20 cpm) and trapezoidal loading profiles at both 8.3 MHz (0.5 cpm) and 3.3 MHz (0.2 cpm). Data were evaluated using modified linear elastic fracture mechanics parameters.
Numerical demonstration of MEMS strain sensor
NASA Astrophysics Data System (ADS)
Saboonchi, Hossain; Ozevin, Didem
2012-04-01
Silicon has piezoresistive property that allows designing strain sensor with higher gauge factor compared to conventional metal foil gauges. The sensing element can be micro-scale using MEMS, which minimizes the effect of strain gradient on measurement at stress concentration regions such as crack tips. The challenge of MEMS based strain sensor design is to decouple the sensing element from substrate for true strain measurement and to compensate the temperature effect on the piezoresistive coefficients of silicon. In this paper, a family of MEMS strain sensors with different geometric designs is introduced. Each strain sensor is made of single crystal silicon and manufactured using deposition/ etching/oxidation steps on a n- doped silicon wafer in (100) plane. The geometries include sensing element connected to the free heads of U shape substrate, a set of two or more sensing elements in an array in order to capture strain gradients and two directional sensors. The response function and the gauge factor of the strain sensors are identified using multi-physics models that combine structural and electrical behaviors of sensors mounted on a strained structure. The relationship between surface strain and strain at microstructure is identified numerically in order to include the relationship in the response function calculation.
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.
Crack tip plasticity in single crystal UO2: Atomistic simulations
Yongfeng Zhang; Paul C. Millett; Michael Tonks; Bulent Biner; Xiang-Yang Liu; David A. Andersson
2012-11-01
The fracture behavior of single crystal uranium dioxide is studied using molecular dynamics simulations at room temperature. Initially, an elliptical notch is created on either {111} or {110} planes, and tensile loading is applied normal to the crack planes. For cracks on both planes, shielding of crack tips by plastic deformation is observed, and crack extension occurs for crack on {111} planes only. Two plastic processes, dislocation emission and phase transformation are identified at crack tips. The dislocations have a Burgers vector of ?110?/2, and glide on {100} planes. Two metastable phases, the so-called Rutile and Scrutinyite phases, are identified during the phase transformation, and their relative stability is confirmed by separate density- functional-theory calculations. Examination of stress concentration near crack tips reveals that dislocation emission is not an effective shielding mechanism. The formation of new phases may effectively shield the crack provided all phase interfaces formed near the crack tips are coherent, as in the case of cracks residing on {110} planes.
Crack tip field and fatigue crack growth in general yielding and low cycle fatigue
NASA Technical Reports Server (NTRS)
Minzhong, Z.; Liu, H. W.
1984-01-01
Fatigue life consists of crack nucleation and crack propagation periods. Fatigue crack nucleation period is shorter relative to the propagation period at higher stresses. Crack nucleation period of low cycle fatigue might even be shortened by material and fabrication defects and by environmental attack. In these cases, fatigue life is largely crack propagation period. The characteristic crack tip field was studied by the finite element method, and the crack tip field is related to the far field parameters: the deformation work density, and the product of applied stress and applied strain. The cyclic carck growth rates in specimens in general yielding as measured by Solomon are analyzed in terms of J-integral. A generalized crack behavior in terms of delta is developed. The relations between J and the far field parameters and the relation for the general cyclic crack growth behavior are used to analyze fatigue lives of specimens under general-yielding cyclic-load. Fatigue life is related to the applied stress and strain ranges, the deformation work density, crack nucleus size, fracture toughness, fatigue crack growth threshold, Young's modulus, and the cyclic yield stress and strain. The fatigue lives of two aluminum alloys correlate well with the deformation work density as depicted by the derived theory. The general relation is reduced to Coffin-Manson low cycle fatigue law in the high strain region.
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.
NASA Technical Reports Server (NTRS)
Krempl, Erhard; Hong, Bor Zen
1989-01-01
A macromechanics analysis is presented for the in-plane, anisotropic time-dependent behavior of metal matrix laminates. The small deformation, orthotropic viscoplasticity theory based on overstress represents lamina behavior in a modified simple laminate theory. Material functions and constants can be identified in principle from experiments with laminae. Orthotropic invariants can be repositories for tension-compression asymmetry and for linear elasticity in one direction while the other directions behave in a viscoplastic manner. Computer programs are generated and tested for either unidirectional or symmetric laminates under in-plane loading. Correlations with the experimental results on metal matrix composites are presented.
The transition from subsonic to supersonic cracks
Behn, Chris; Marder, M.
2015-01-01
We present the full analytical solution for steady-state in-plane crack motion in a brittle triangular lattice. This allows quick numerical evaluation of solutions for very large systems, facilitating comparisons with continuum fracture theory. Cracks that propagate faster than the Rayleigh wave speed have been thought to be forbidden in the continuum theory, but clearly exist in lattice systems. Using our analytical methods, we examine in detail the motion of atoms around a crack tip as crack speed changes from subsonic to supersonic. Subsonic cracks feature displacement fields consistent with a stress intensity factor. For supersonic cracks, the stress intensity factor disappears. Subsonic cracks are characterized by small-amplitude, high-frequency oscillations in the vertical displacement of an atom along the crack line, while supersonic cracks have large-amplitude, low-frequency oscillations. Thus, while supersonic cracks are no less physical than subsonic cracks, the connection between microscopic and macroscopic behaviour must be made in a different way. This is one reason supersonic cracks in tension had been thought not to exist. PMID:25713443
Crack modeling of rotating blades with cracked hexahedral finite element method
NASA Astrophysics Data System (ADS)
Liu, Chao; Jiang, Dongxiang
2014-06-01
Dynamic analysis is the basis in investigating vibration features of cracked blades, where the features can be applied to monitor health state of blades, detect cracks in an early stage and prevent failures. This work presents a cracked hexahedral finite element method for dynamic analysis of cracked blades, with the purpose of addressing the contradiction between accuracy and efficiency in crack modeling of blades in rotor system. The cracked hexahedral element is first derived with strain energy release rate method, where correction of stress intensity factors of crack front and formulation of load distribution of crack surface are carried out to improve the modeling accuracy. To consider nonlinear characteristics of time-varying opening and closure effects caused by alternating loads, breathing function is proposed for the cracked hexahedral element. Second, finite element method with contact element is analyzed and used for comparison. Finally, validation of the cracked hexahedral element is carried out in terms of breathing effects of cracked blades and natural frequency in different crack depths. Good consistency is acquired between the results with developed cracked hexahedral element and contact element, while the computation time is significantly reduced in the previous one. Therefore, the developed cracked hexahedral element achieves good accuracy and high efficiency in crack modeling of rotating blades.
Kinetic studies of the stress corrosion cracking of D6AC steel
NASA Technical Reports Server (NTRS)
Noronha, P. J.
1975-01-01
The effect of load interactions on the crack growth velocity of D6AC steel under stress corrosion cracking conditions was determined. The environment was a 3.5 percent salt solution. The modified-wedge opening load specimens were fatigue precracked and subjected to a deadweight loading in creep machines. The effects of load shedding on incubation times and crack growth rates were measured using high-sensitivity compliance measurement techniques. Load shedding results in an incubation time, the length of which depends on the amount of load shed and the baseline stress intensity. The sequence of unloading the specimen also controls the subsequent incubation period. The incubation period is shorter when load shedding passes through zero load than when it does not if the specimen initially had the same baseline stress intensity. The crack growth rates following the incubation period are also different from the steady-state crack growth rate at the operating stress intensity. These data show that the susceptibility of this alloy system to stress corrosion cracking depends on the plane-strain fracture toughness and on the yield strength of the material.
How fatigue cracks grow, interact with microstructure, and lose similitude
Davidson, D.L.
1997-12-01
This paper reviews the processes by which fatigue cracks grow and interact with applied load and microstructure. Fatigue crack growth processes are remarkably similar irrespective of microstructure, crack size, or nature of the loading. Large strains at fatigue crack tips applied over repeated cycles severely alter, or homogenize, microstructures, followed by crack advance. Microstructure affects fatigue crack growth kinetics more than growth processes. But, under marginal conditions, fatigue crack growth rates are also affected by microstructural features. Examples are small cracks growing under low stresses or large cracks growing near threshold. The prediction of safe lifetimes for machine parts, such as gas turbine components, requires that laboratory-generated fatigue crack growth rate data be transferred to field-operating conditions. This transfer depends on the maintenance of similitude: microstructurely, mechanically, and environmentally. However, for many industrially important conditions, similitude with large fatigue crack growth is lost, partially because of changes in fatigue crack closure. The effect of closure on similitude is discussed. New data are presented to illustrate the loss of similitude between applied loading and crack tip strain response. The resulting strain rates of material within the process zone are unexpected. Environmentally influenced fatigue crack growth rates are likely to be influenced by these strain rates.
Interface crack in a nonhomogeneous elastic medium
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1988-01-01
The linear elasticity problem for an interface crack between two bonded half planes is reconsidered. It is assumed that one of the half planes is homogeneous and the second is nonhomogeneous in such a way that the elastic properties are continuous throughout the plane and have discontinuous derivatives along the interface. The problem is formulated in terms of a system of integral equations and the asymptotic behavior of the stress state near the crack tip is determined. The results lead to the conclusion that the singular behavior of stresses in the nonhomogeneous medium is identical to that in a homogeneous material provided the spacial distribution of material properties is continuous near and at the crack tip. The problem is solved for various values of the nonhomogeneity parameter and for four different sets of crack surface tractions, and the corresponding stress intensity factors are tabulated.
NASA Technical Reports Server (NTRS)
Jones, M. H.; Bubsey, R. T.; Brown, W. F., Jr.; Bucci, R. J.; Collis, S. F.; Kohm, R. F.; Kaufman, J. G.
1977-01-01
A description is presented of studies which have been conducted to establish an improved technology base for a use of the sharply notched cylindrical specimen in quality assurance tests of aluminum alloy products. The results are presented of an investigation of fundamental variables associated with specimen preparation and testing, taking into account the influence of the notch root radius, the eccentricity of loading, the specimen diameter, and the notch depth on the sharp notch strength. Attention is given to the statistical procedures which are necessary to establish correlations between the sharp notch strength and the plane-strain fracture toughness for high-strength aluminum alloys.
Characterization of M-plane GaN thin films grown on misoriented γ-LiAlO2 (100) substrates
NASA Astrophysics Data System (ADS)
Lin, Yu-Chiao; Lo, Ikai; Wang, Ying-Chieh; Yang, Chen-Chi; Hu, Chia-Hsuan; Chou, Mitch M. C.; Schaadt, D. M.
2016-09-01
M-plane GaN thin films were grown on 11° misoriented γ-LiAlO2 substrates without peeling off or cracking by plasma-assisted molecular beam epitaxy. Because of anisotropic growth kinetics, which leads to an anisotropic compressive in-plane strain in the M-plane GaN films, the surface presents a rough morphology with worse crystal quality. The crystal quality of sample was optimally improved, XRD rocking curve FWHM of which is about 900 arcsec, by raising growth temperature to 800 °C with proper Ga/N flux ratio. As the crystal quality was improved, the polarization ratio decreased from the unity (less than 0.8) which could be attributed to the effect of exciton localization due to the partial increased in-plane strain.
NASA Technical Reports Server (NTRS)
Hudson, C. M.; Lewis, P. E.
1979-01-01
A round-robin study was conducted which evaluated and compared different methods currently in practice for predicting crack growth in surface-cracked specimens. This report describes the prediction methods used by the Fracture Mechanics Engineering Section, at NASA-Langley Research Center, and presents a comparison between predicted crack growth and crack growth observed in laboratory experiments. For tests at higher stress levels, the correlation between predicted and experimentally determined crack growth was generally quite good. For tests at lower stress levels, the predicted number of cycles to reach a given crack length was consistently higher than the experimentally determined number of cycles. This consistent overestimation of the number of cycles could have resulted from a lack of definition of crack-growth data at low values of the stress intensity range. Generally, the predicted critical flaw sizes were smaller than the experimentally determined critical flaw sizes. This underestimation probably resulted from using plane-strain fracture toughness values to predict failure rather than the more appropriate values based on maximum load.
NASA Technical Reports Server (NTRS)
Salpekar, S. A.; O'Brien, T. K.
1993-01-01
Three-dimensional element analyses of (0/theta/-theta)s graphite epoxy laminates, where theta = 15, 20, 25, 30, and 45 deg, subjected to axial tensile load, were performed. The interlaminar stresses in the theta/-theta interface were calculated with and without a matrix crack in the central -theta plies. The interlaminar normal stress changes from a small compressive stress when no matrix crack is present to a high tensile stress at the intersection of the matrix crack and the free edge. The analysis of local delamination from the -theta matrix crack indicates a high strain energy release rate and a localized Mode I component near the free edge, within one-ply distance from the matrix crack. To examine the stress state causing the matrix cracking, the maximum principal normal stress in a plane perpendicular to the fiber direction in the -theta ply was calculated in an uncracked laminate. The corresponding shear stress parallel to the fiber was also calculated. The principal normal stress at the laminate edge increased through the ply thickness and reached a very high tensile value at the theta/-theta interface indicating that the crack in the -theta ply may initiate at the theta/-theta interface.
Crack growth direction in unidirectional off-axis graphite epoxy
NASA Technical Reports Server (NTRS)
Herakovich, C. T.; Gregory, M. A.; Beuth, J. L., Jr.
1984-01-01
An anisotropic elasticity crack tip stress analysis is implemented using three crack extension direction criteria (the normal stress ratio, the tensor polynominal and the strain energy density) to predict the direction of crack extension in unidirectional off axis graphite-epoxy. The theoretical predictions of crack extension direction are then compared with experimental results for 15 deg off axis tensile coupons with center cracks. Specimens of various aspect ratios and crack orientations are analyzed. It is shown that only the normal stress ratio criterion predicts the correct direction of crack growth.
Measurement and analysis of critical crack tip processes during fatigue crack growth
NASA Technical Reports Server (NTRS)
Davidson, D. L.; Hudak, S. J.; Dexter, R. J.
1985-01-01
The mechanics of fatigue crack growth under constant-amplitudes and variable-amplitude loading were examined. Critical loading histories involving relatively simple overload and overload/underload cycles were studied to provide a basic understanding of the underlying physical processes controlling crack growth. The material used for this study was 7091-T7E69, a powder metallurgy aluminum alloy. Local crack-tip parameters were measured at various times before, during, and after the overloads, these include crack-tip opening loads and displacements, and crack-tip strain fields. The latter were useed, in combination with the materials cyclic and monotonic stress-strain properties, to compute crack-tip residual stresses. The experimental results are also compared with analytical predictions obtained using the FAST-2 computer code. The sensitivity of the analytical model to constant-amplitude fatigue crack growth rate properties and to through-thickness constrain are studied.
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.
NASA Astrophysics Data System (ADS)
Saka, M.; Abé, H.; Tanaka, S.
1986-03-01
The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.
NASA Astrophysics Data System (ADS)
Badica, P.; Awaji, S.; Oguro, H.; Nishijima, G.; Watanabe, K.
2006-04-01
Six Nb3Sn composite wires with different architectures ('central and near-the-edge reinforcement') were repeatedly in-plane bent at room temperature (in-plane 'pre-bending'). Breakage behaviour was revealed from scanning electron microscopy observations by semi-quantitative analysis of the filament crack formation and evolution. Cracks are formed in the transversal and longitudinal directions. Transversal cracks show some tolerance to the applied bending strain due to the fact that filaments are composite materials; residual Nb core can arrest development of a partial transversal crack initiated in the Nb3Sn outer part of the filament. Together with the density of cracks C and the evolution of this parameter with pre-bending strain, ɛpb, in different regions of the wire, R-ɛpb curves are important to understand breakage behaviour of the wires. R is the ratio (number of full transversal cracks)/(number of full transversal cracks + number of partial transversal cracks). Parameters C and R allow us to reveal and satisfactorily understand the wire architecture—breakage—critical current decay relationship when pre-bending treatment is applied. As a consequence, breakage criteria necessary to minimize Ic decay were defined and the positive influence of the reinforcement in preventing breakage was observed. It was also found that, in this regard, more Nb in the CuNb reinforcement, for the investigated wires, is better, if the heat treatment for the wire synthesis is performed at 670 °C for 96 h. A different heat treatment, 650 °C for 240 h, is less efficient in preventing filament breakage. Our results suggest the possibility of control and improvement of the breakage susceptibility of the filaments in the wires and, hence, of the bending Ic decay, through the wise design of the wire architecture (i.e. by correlating design with the choice of composing materials and heat treatments).
Visual simulation of fatigue crack growth
Wang, S.; Margolin, H.; Lin, F.B.
1998-07-01
An attempt has been made to visually simulate fatigue crack propagation from a precrack. An integrated program was developed for this purpose. The crack-tip shape was determined at four load positions in the first load cycle. The final shape was a blunt front with an ear profile at the precrack tip. A more general model, schematically illustrating the mechanism of fatigue crack growth and striation formation in a ductile material, was proposed based on this simulation. According to the present model, fatigue crack growth is an intermittent process; cyclic plastic shear strain is the driving force applied to both state 1 and 2 crack growth. No fracture mode transition occurs between the two stages in the present study. The crack growth direction alternates, moving up and down successively, producing fatigue striations. A brief examination has been made of the crack growth path in a ductile two-phase material.
Thermoelastic analysis of matrix crack growth in particulate composites
Sridhar, N.; Rickman, J.M.; Srolovitz, D.J.
1995-04-01
The authors examine the conditions under which differences in thermal expansion between a particle and the matrix lead to crack growth within the matrix. Using linear elasticity fracture mechanics, they obtain closed-form, analytical results for the case of a penny shaped crack present in the matrix interacting with a spherical inclusion which is misfitting with respect to the matrix. A simple and direct relationship is established between the strain energy release rate, the crack size, the crack orientation with respect to the inclusion, the crack/inclusion separation, the degree of thermal expansion mismatch and the elastic properties of the medium. The authors also analyze the size to which these cracks can grow and find that for a given misfit strain and material properties, crack growth is inhibited beyond a certain critical crack size. They find that beyond this critical size, the elastic strain energy released upon crack growth is no longer sufficient to compensate for the energy expended in extending the crack, since the crack is growing into the rapidly decreasing stress field. The modification of the above conditions for crack growth due to the superposition of an external stress field has also been analyzed. The preferred orientation of these cracks as a function of misfit strain is predicted. The implication of these results for thermal cycling are analyzed.
Dienes, J.K.
1983-01-01
An alternative to the use of plasticity theory to characterize the inelastic behavior of solids is to represent the flaws by statistical methods. We have taken such an approach to study fragmentation because it offers a number of advantages. Foremost among these is that, by considering the effects of flaws, it becomes possible to address the underlying physics directly. For example, we have been able to explain why rocks exhibit large strain-rate effects (a consequence of the finite growth rate of cracks), why a spherical explosive imbedded in oil shale produces a cavity with a nearly square section (opening of bedding cracks) and why propellants may detonate following low-speed impact (a consequence of frictional hot spots).
Slow Crack Growth of Germanium
NASA Technical Reports Server (NTRS)
Salem, Jon
2016-01-01
The fracture toughness and slow crack growth parameters of germanium supplied as single crystal beams and coarse grain disks were measured. Although germanium is anisotropic (A=1.7), it is not as anisotropic as SiC, NiAl, or Cu, as evidence by consistent fracture toughness on the 100, 110, and 111 planes. Germanium does not exhibit significant slow crack growth in distilled water. (n=100). Practical values for engineering design are a fracture toughness of 0.7 MPam and a Weibull modulus of m=6+/-2. For well ground and reasonable handled coupons, fracture strength should be greater than 30 MPa.
Effect of size on cracking of materials
NASA Technical Reports Server (NTRS)
Glucklick, J.
1971-01-01
Brittle behavior of large mild steel elements, glass plasticity, and fatigue specimen size sensitivity are manifestations of strain-energy size effect. Specimens physical size effect on material cracking initiation occurs according to flaw distribution statistics. Fracture size effect depends on stability or instability of crack propagation.
Peridynamic model for fatigue cracking.
Silling, Stewart Andrew; Abe Askari
2014-10-01
The peridynamic theory is an extension of traditional solid mechanics in which the field equations can be applied on discontinuities, such as growing cracks. This paper proposes a bond damage model within peridynamics to treat the nucleation and growth of cracks due to cyclic loading. Bond damage occurs according to the evolution of a variable called the "remaining life" of each bond that changes over time according to the cyclic strain in the bond. It is shown that the model reproduces the main features of S-N data for typical materials and also reproduces the Paris law for fatigue crack growth. Extensions of the model account for the effects of loading spectrum, fatigue limit, and variable load ratio. A three-dimensional example illustrates the nucleation and growth of a helical fatigue crack in the torsion of an aluminum alloy rod.
The crystallography of fatigue crack initiation in Incoloy-908 and A-286 steel
Krenn, C.R. |
1996-12-01
Fatigue crack initiation in the austenitic Fe-Ni superalloys Incoloy-908 and A-286 is examined using local crystallographic orientation measurements. Results are consistent with sharp transgranular initiation and propagation occurring almost exclusively on {l_brace}111{r_brace} planes in Incoloy-908 but on a variety of low index planes in A-286. This difference is attributed to the influence of the semicoherent grain boundary {eta} phase in A-286. Initiation in each alloy occurred both intergranularly and transgranularly and was often associated with blocky surface oxide and carbide inclusions. Taylor factor and resolved shear stress and strain crack initiation hypotheses were tested, but despite an inconclusive suggestion of a minimum required {l_brace}111{r_brace} shear stress, none of the hypotheses were found to convincingly describe preferred initiation sites, even within the subsets of transgranular cracks apparently free from the influence of surface inclusions. Subsurface inclusions are thought to play a significant role in crack initiation. These materials have applications for use in structural conduit for high field superconducting magnets designed for fusion energy use.
Prediction of fatique crack growth under flight-simulation loading with the modified CORPUS model
NASA Technical Reports Server (NTRS)
Padmadinata, U. H.; Schijve, J.
1994-01-01
The CORPUS (Computation Of Retarded Propagation Under Spectrum loading) crack growth prediction model for variable-amplitude loading, as introduced by De Koning, was based on crack closure. It includes a multiple-overload effect and a transition from plane strain to plane stress. In the modified CORPUS model an underload affected zone (ULZ) is introduced, which is significant for flight-simulation loading in view of the once per flight compressive ground load. The ULZ is associated with reversed plastic deformation induced by the underloads after crack closure has already occurred. Predictions of the crack growth fatigue life are presented for a large variety of flight-simulation test series on 2024-T3 sheet specimens in order to reveal the effects of a number of variables: the design stress level, the gust spectrum severity, the truncation level (clipping), omission of small cycles, and the ground stress level. Tests with different load sequences are also included. The trends of the effects induced by the variables are correctly predicted. The quantitative agreement between the predictions and the test results is also satisfactory.
Environmental fatigue of an Al-Li-Cu alloy; Part II: Microscopic hydrogen cracking processes
Piascik, R.S.; Gangloff, R.P.
1993-12-01
Microscopic fatigue crack propagation (FCP) paths in peak-aged unrecrystallized alloy 2090 are identified as functions of intrinsic da/dN-{Delta}K kinetics and environment. The FCP rates in longitudinal-transverse (LT)-oriented 2090 are accelerated by hydrogen-producing environments (pure water vapor, moist air, and aqueous NaCl), as defined in Part 1. Subgrain boundary cracking (SGC) dominates for {Delta}K values where the cyclic plastic zone is sufficient to envelop subgrains. At low {Delta}K, when this crack tip process zone is smaller than the subgrain size, environmental FCP progresses on or near [100] or [110] planes, based on etch-pit shape. For inert environments (vacuum and He) and pure O{sub 2} with crack surface oxidation, FCP produces large facets along [111] oriented slip bands. This mode does not change with {Delta}K, and T{sub 1} decorated subgrain boundaries do not effect an expected da/dN-{Delta}K transition for the inert environments. Rather, the complex dependence of da/dN on {Delta}K is controlled by the environmental contribution to process zone microstructure-plastic strain interactions. A hydrogen embrittlement mechanism for FCP in 2090 is supported by similar brittle crack paths for low pressure water vapor and the electrolyte, the SGC and [100]/[110] crystallographic cracking modes, the influence of cyclic plastic zone volume ({Delta}K), and the benignancy of O{sub 2}. The SGC may be due to hydrogen production and trapping at T{sub 1} bearing sub-boundaries after process zone dislocation transport, while crystallographic cracking may be due to lattice decohesion or hydride cracking.
Modeling the Interactions Between Multiple Crack Closure Mechanisms at Threshold
NASA Technical Reports Server (NTRS)
Newman, John A.; Riddell, William T.; Piascik, Robert S.
2003-01-01
A fatigue crack closure model is developed that includes interactions between the three closure mechanisms most likely to occur at threshold; plasticity, roughness, and oxide. This model, herein referred to as the CROP model (for Closure, Roughness, Oxide, and Plasticity), also includes the effects of out-of plane cracking and multi-axial loading. These features make the CROP closure model uniquely suited for, but not limited to, threshold applications. Rough cracks are idealized here as two-dimensional sawtooths, whose geometry induces mixed-mode crack- tip stresses. Continuum mechanics and crack-tip dislocation concepts are combined to relate crack face displacements to crack-tip loads. Geometric criteria are used to determine closure loads from crack-face displacements. Finite element results, used to verify model predictions, provide critical information about the locations where crack closure occurs.
Environmentally assisted cracking of LWR materials
Chopra, O.K.; Chung, H.M.; Kassner, T.F.; Shack, W.J.
1995-12-01
Research on environmentally assisted cracking (EAC) of light water reactor materials has focused on (a) fatigue initiation in pressure vessel and piping steels, (b) crack growth in cast duplex and austenitic stainless steels (SSs), (c) irradiation-assisted stress corrosion cracking (IASCC) of austenitic SSs, and (d) EAC in high- nickel alloys. The effect of strain rate during different portions of the loading cycle on fatigue life of carbon and low-alloy steels in 289{degree}C water was determined. Crack growth studies on wrought and cast SSs have been completed. The effect of dissolved-oxygen concentration in high-purity water on IASCC of irradiated Type 304 SS was investigated and trace elements in the steel that increase susceptibility to intergranular cracking were identified. Preliminary results were obtained on crack growth rates of high-nickel alloys in water that contains a wide range of dissolved oxygen and hydrogen concentrations at 289 and 320{degree}C. The program on Environmentally Assisted Cracking of Light Water Reactor Materials is currently focused on four tasks: fatigue initiation in pressure vessel and piping steels, fatigue and environmentally assisted crack growth in cast duplex and austenitic SS, irradiation-assisted stress corrosion cracking of austenitic SSs, and environmentally assisted crack growth in high-nickel alloys. Measurements of corrosion-fatigue crack growth rates (CGRs) of wrought and cast stainless steels has been essentially completed. Recent progress in these areas is outlined in the following sections.
Controlled crack growth specimen for brittle systems
NASA Technical Reports Server (NTRS)
Calomino, Anthony M.; Brewer, David N.
1990-01-01
A pure Mode 1 fracture specimen and test procedure has been developed which provides extended, stable, through-thickness crack growth in ceramics and other brittle, nonmetallic materials. Fixed displacement loading, applied at the crack mouth, promotes stable crack extension by reducing the stored elastic strain energy. Extremely fine control of applied displacements is achieved by utilizing the Poisson's expansion of a compressively loaded cylindrical pin. Stable cracks were successfully grown in soda-lime glass and monolithic Al2O3 for lengths in excess of 20 mm without uncontrollable catastrophic failure.
Controlled crack growth specimen for brittle systems
NASA Technical Reports Server (NTRS)
Calomino, Anthony M.; Brewer, David N.
1992-01-01
A pure Mode 1 fracture specimen and test procedure has been developed which provides extended, stable, through-thickness crack growth in ceramics and other brittle, nonmetallic materials. Fixed displacement loading, applied at the crack mouth, promotes stable crack extension by reducing the stored elastic strain energy. Extremely fine control of applied displacements is achieved by utilizing the Poisson's expansion of a compressively loaded cylindrical pin. Stable cracks were successfully grown in soda-lime glass and monolithic Al2O3 for lengths in excess of 2O mm without uncontrollable catastrophic failure.
Transient thermoelastic fracture of interface cracks
Kokini, K.; Reynolds, R.R. )
1992-09-01
The transient behavior of an interface crack at the center and edge of two finite dissimilar materials free to bend and subjected to a transient thermal load was studied. It was first assumed that the crack was insulated. The effect of allowing heat to conduct through the crack upon closing was also investigated. The effects of the mechanical and thermal material property ratios as well as the thickness ratio on the crack deformations and the transient strain energy release rate were calculated. 13 refs.
Effects of crack geometry and material behavior on scattering by cracks for QNDE applications
Achenbach, J.D.
1989-09-15
In work carried out on this project, the usual mathematical modeling of ultrasonic wave scattering by flaws is being extended to account for several typical characteristics of fatigue and stress-corrosion cracks, and the environment of such cracks. Work has been completed on scattering by macrocrack-microcrack configurations. We have also investigated reflection and transmission by a flaw plane consisting of an infinite array of randomly oriented cracks. In another investigation the propagation of mechanical disturbances in solids with periodically distributed cracks has been studied.
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.
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.
Reuter, W.G.; Elfer, N.C.; Hull, D.A.; Newman, J.C. Jr.; Munz, D.; Panontin, T.L.
1997-12-31
Specimens containing surface cracks were tested in either tension or bending to compare the stress intensity factor at failure with plane strain fracture toughness (K{sub Ic}) in an International Cooperative Test Program. The material was heat treated to {sigma}{sub ys} = 1 587 MPa and K{sub Ic} = 54 MPa m{sub 1/2}. Because substantial stable crack growth occurred for some specimens, the test plan was modified to include detecting the onset of crack growth. It is shown that P{sub max} and the original fatigue precrack size cannot be employed to calculate K{sub max} for comparison with K{sub Ic} when significant stable crack growth occurs. However, using P{sub init} (load at which stable crack growth is initiated) and the original fatigue precrack size to calculate K{sub max} or K{sub {phi}=30{degree}} provides a very useful comparison with K{sub Ic}. The influence of variations in fatigue precrack configuration on test results are also discussed.
Fatigue crack growth with single overload - Measurement and modeling
NASA Technical Reports Server (NTRS)
Davidson, D. L.; Hudak, S. J., Jr.; Dexter, R. J.
1987-01-01
This paper compares experiments with an analytical model of fatigue crack growth under variable amplitude. The stereoimaging technique was used to measure displacements near the tips of fatigue cracks undergoing simple variations in load amplitude-single overloads and overload/underload combinations. Measured displacements were used to compute strains, and stresses were determined from the strains. Local values of crack driving force (Delta-K effective) were determined using both locally measured opening loads and crack tip opening displacements. Experimental results were compared with simulations made for the same load variation conditions using Newman's FAST-2 model. Residual stresses caused by overloads, crack opening loads, and growth retardation periods were compared.
Crack tip deformation and fatigue crack growth
NASA Technical Reports Server (NTRS)
Liu, H.-W.
1981-01-01
Recent research on fatigue crack growth is summarized. Topics discussed include the use of the differential stress intensity factor to characterize crack tip deformation, the use of the unzipping model to study the growth of microcracks and the fatigue crack growth in a ferritic-martensitic steel, and the development of a model of fatige crack growth threshold. It is shown that in the case of small yielding, the differential stress intensity factor provides an adequate description of cyclic plastic deformation at the crack tip and correlates well with the crack growth rate. The unzipping model based on crack tip shear decohesion process is found to be in good agreement with the measured crack growth and striation spacing measurements. The proposed model of crack growth threshold gives correct predictions of the crack growth behavior in the near-threshold region.
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.
Expansive soil crack depth under cumulative damage.
Shi, Bei-xiao; Chen, Sheng-shui; Han, Hua-qiang; Zheng, Cheng-feng
2014-01-01
The crack developing depth is a key problem to slope stability of the expansive soil and its project governance and the crack appears under the roles of dry-wet cycle and gradually develops. It is believed from the analysis that, because of its own cohesion, the expansive soil will have a certain amount of deformation under pulling stress but without cracks. The soil body will crack only when the deformation exceeds the ultimate tensile strain that causes cracks. And it is also believed that, due to the combined effect of various environmental factors, particularly changes of the internal water content, the inherent basic physical properties of expansive soil are weakened, and irreversible cumulative damages are eventually formed, resulting in the development of expansive soil cracks in depth. Starting from the perspective of volumetric strain that is caused by water loss, considering the influences of water loss rate and dry-wet cycle on crack developing depth, the crack developing depth calculation model which considers the water loss rate and the cumulative damages is established. Both the proposal of water loss rate and the application of cumulative damage theory to the expansive soil crack development problems try to avoid difficulties in matrix suction measurement, which will surely play a good role in promoting and improving the research of unsaturated expansive soil. PMID:24737974
Expansive Soil Crack Depth under Cumulative Damage
Shi, Bei-xiao; Chen, Sheng-shui; Han, Hua-qiang; Zheng, Cheng-feng
2014-01-01
The crack developing depth is a key problem to slope stability of the expansive soil and its project governance and the crack appears under the roles of dry-wet cycle and gradually develops. It is believed from the analysis that, because of its own cohesion, the expansive soil will have a certain amount of deformation under pulling stress but without cracks. The soil body will crack only when the deformation exceeds the ultimate tensile strain that causes cracks. And it is also believed that, due to the combined effect of various environmental factors, particularly changes of the internal water content, the inherent basic physical properties of expansive soil are weakened, and irreversible cumulative damages are eventually formed, resulting in the development of expansive soil cracks in depth. Starting from the perspective of volumetric strain that is caused by water loss, considering the influences of water loss rate and dry-wet cycle on crack developing depth, the crack developing depth calculation model which considers the water loss rate and the cumulative damages is established. Both the proposal of water loss rate and the application of cumulative damage theory to the expansive soil crack development problems try to avoid difficulties in matrix suction measurement, which will surely play a good role in promoting and improving the research of unsaturated expansive soil. PMID:24737974
Crack Healing in Quartz: Influence of Crack Morphology and pOH-
NASA Astrophysics Data System (ADS)
Fallon, J. A.; Kronenberg, A. K.; Popp, R. K.; Lamb, W. M.
2004-12-01
Crack healing in quartz has been investigated by optical microscopy and interferometry of rhombohedral r-cleavage cracks in polished Brazilian quartz prisms that were hydrothermally annealed. Quartz prisms were pre-cracked at room temperature and then annealed at temperatures T of 250° and 400° C for 2.4 to 240 hours, fluid pressure Pf = 41 MPa (equal to confining pressure Pc), and varying pOH- (from 5.4 to 1.2 at 250° C for fluids consisting of distilled water and NaOH solutions). Crack morphologies before and after annealing were recorded for each sample in plane light digital images and apertures were determined from interference fringes recorded using transmitted monochromatic light (λ = 598 nm). As documented in previous studies (Smith and Evans, 1984; Brantley et al., 1990; Beeler and Hickman, 1996), crack healing of quartz is driven by reductions in surface energy and healing rates appear to be limited by diffusional solute transport; sharply defined crack tips become blunted and break up into fluid-filled tubes and inclusions. However, fluid inclusion geometries are also observed with nonequilibrium shapes that depend on initial surface roughness. Crack healing is significant at 400° C after short run durations (24 hr) with healing rates reaching 10-5 mm/s. Crack healing is also observed at T=250° C, but only for smooth cracks with apertures < 0.6 μ m or for cracks subject to low pOH-. The extent of crack healing is sensitive to crack aperture and to hackles formed by fine-scale crack branching during crack growth. Initial crack apertures appear to be governed by the presence of fine particles, often found in the vicinity of hackles, which maintain the separation of crack surfaces. Where rough cracks exhibit healing, hackles are sites of either enhanced or reduced loss of fluid-solid interface depending on slight mismatches and sense of twist of opposing crack surfaces. Hackles of open r-cleavage cracks are replaced either by (1) healed curvilinear
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%.
Scaling of crack propagation in rubber sheets
NASA Astrophysics Data System (ADS)
Chen, C. H.; Zhang, H. P.; Niemczura, J.; Ravi-Chandar, K.; Marder, M.
2011-11-01
We have conducted experiments and numerical simulations to investigate supersonic cracks. The experiments are performed at 85 °C to suppress strain-induced crystallites that complicate experiments at lower temperature. Calibration experiments were performed to obtain the parameters needed to compare with a theory including viscous dissipation. We find that both experiments and numerical simulations support supersonic cracks, and we discover a transition from subsonic to supersonic as we plot experimental crack speed curves vs. extension ratio for different sized samples. Both experiments and simulations show two different scaling regimes: the speed of subsonic cracks scales with the elastic energy density while the speed of supersonic cracks scales with the extension ratio. Crack openings have qualitatively different shapes in the two scaling regimes.
Online Bridge Crack Monitoring with Smart Film
Wang, Shuliang; Li, Xingxing; Zhou, Zhixiang; Zhang, Xu; Yang, Guang; Qiu, Minfeng
2013-01-01
Smart film crack monitoring method, which can be used for detecting initiation, length, width, shape, location, and propagation of cracks on real bridges, is proposed. Firstly, the fabrication of the smart film is developed. Then the feasibility of the method is analyzed and verified by the mechanical sensing character of the smart film under the two conditions of normal strain and crack initiation. Meanwhile, the coupling interference between parallel enameled wires of the smart film is discussed, and then low-frequency detecting signal and the custom communication protocol are used to decrease interference. On this basis, crack monitoring system with smart film is designed, where the collected crack data is sent to the remote monitoring center and the cracks are simulated and recurred. Finally, the monitoring system is applied to six bridges, and the effects are discussed. PMID:24489496
Online bridge crack monitoring with smart film.
Zhang, Benniu; Wang, Shuliang; Li, Xingxing; Zhou, Zhixiang; Zhang, Xu; Yang, Guang; Qiu, Minfeng
2013-01-01
Smart film crack monitoring method, which can be used for detecting initiation, length, width, shape, location, and propagation of cracks on real bridges, is proposed. Firstly, the fabrication of the smart film is developed. Then the feasibility of the method is analyzed and verified by the mechanical sensing character of the smart film under the two conditions of normal strain and crack initiation. Meanwhile, the coupling interference between parallel enameled wires of the smart film is discussed, and then low-frequency detecting signal and the custom communication protocol are used to decrease interference. On this basis, crack monitoring system with smart film is designed, where the collected crack data is sent to the remote monitoring center and the cracks are simulated and recurred. Finally, the monitoring system is applied to six bridges, and the effects are discussed. PMID:24489496
Crack Growth in Single-Crystal Silicon
NASA Technical Reports Server (NTRS)
Chen, C. P.; Leipold, M. H.
1986-01-01
Report describes experiments on crack growth in single-crystal silicon at room temperature in air. Crack growth in (111) cleavage plane of wafers, 50 by 100 by 0.76 mm in dimension, cut from Czochralski singlecrystal silicon studied by double-torsion load-relaxation method and by acoustic-emission measurements. Scanning electron microscopy and X-ray topography also employed. Results aid in design and fabrication of silicon photovoltaic and microelectronic devices.
The NT-criterion for predicting crack growth increments
NASA Technical Reports Server (NTRS)
Yehia, Nabil A. B.; Shephard, Mark S.
1987-01-01
A new approach is presented to determine the crack propagation increment after the direction of crack propagation has been predicted. The maximum dilatational strain energy density (NT-criterion) is employed in the derivation for predicting both direction and increment of the propagating crack. The crack propagation path predicted by the NT-criterion is compared to the one predicted by the S-criterion and to some available experimental data.
Analysis of Multiple Cracks in an Infinite Functionally Graded Plate
NASA Technical Reports Server (NTRS)
Shbeeb, N. I.; Binienda, W. K.; Kreider, K. L.
1999-01-01
A general methodology was constructed to develop the fundamental solution for a crack embedded in an infinite non-homogeneous material in which the shear modulus varies exponentially with the y coordinate. The fundamental solution was used to generate a solution to fully interactive multiple crack problems for stress intensity factors and strain energy release rates. Parametric studies were conducted for two crack configurations. The model displayed sensitivity to crack distance, relative angular orientation, and to the coefficient of nonhomogeneity.
Steady crack growth through ductile metals: Computational studies
NASA Astrophysics Data System (ADS)
Sobotka, James C.
This thesis examines the crack-front response during sustained ductile tearing in structural metals at quasistatic rates using high resolution finite element computations. At load levels approaching the steady-growth regime, well-established computational methods that model material damage break down numerically as vanishingly small load increments produce increasingly large amounts of crack extension. The computational model adopted here determines the deformation history of a steadily advancing crack directly without the need for a priori (transient) analysis that considers blunting of the pre-existing stationary crack and subsequent growth through the associated initial plastic zone. Crack extension occurs at the remotely applied, fixed loading without the need for a local growth criteria. This numerical scheme utilizes a streamline integration technique to determine the elastic-plastic fields, generalized from a two-dimensional to a fully three-dimensional setting and implemented within mixed Matlab/C++/F-90 based software. Modifications of the conventional finite element formulation lead to an efficient procedure -- readily parallelized -- and determine the invariant near-front fields, representative of steady-state growth, on a fixed mesh in a boundary-layer framework. In the small-scale yielding regime, the crack front does not sense the existence of remote boundaries, and computational results retain a strong transferability among various geometric configurations where near-front, plastic deformation remains entirely enclosed by the surrounding linear-elastic material. The global stress intensity factor (KI ) and imposed T-stress fully specify displacement constraints along the far-field boundary, and in a three-dimensional setting, the panel thickness reflects the only natural length scale. The initial studies in this work consider steady crack advance within the small-scale yielding context under plane-strain conditions and mode I loading. These analyses
A study of near tip phenomena for cracks in a particulate composite
Rezvani, M.A.
1989-01-01
An experimental investigation using grids with a frequency of 125 lines/in. (5 lines/mm) was performed on inert propellant and pure binder at two different global head rates of 0.1 in./min (2.5 mm/min) and 1.0 in./min (25.4 mm/min). From the extracted data, displacements, strains, and dominant eigenvalue for displacement were calculated. An idealized model was used to explain the high strain zone ahead of inert propellant that caused severe blunting at the crack tip. Using the available algorithms and three dimensional photoelasticity, the dominant stress singularity order values were calculated in a four point single edged cracked bend specimen with both straight front and thumbnailed cracks. The free surface values are the same as for the inert propellant and in good agreement with analytical values. A boundary layer is observed in the singularity order which extends towards the mid-plane of the specimen. This region is about twenty percent of the distance from the free surface to mid-depth of the fractured body. The slow and fast head rates alter the global behavior of the specimen as well as the density of the displacement and strain contours. However, the near tip mechanisms are not altered.
Crack interaction with 3-D dislocation loops
NASA Astrophysics Data System (ADS)
Gao, Huajian
CRACKS in a solid often interact with other crystal defects such as dislocation loops. The interaction effects are of 3-D character yet their analytical treatment has been mostly limited to the 2-D regime due to mathematical complications. This paper shows that distribution of the stress intensity factors along a crack front due to arbitrary dislocation loops may be expressed as simple line integrals along the loop contours. The method of analysis is based on the 3-D Bueckner-Rice weight function theory for elastic crack analysis. Our results have significantly simplified the calculations for 3-D dislocation loops produced in the plastic processes at the crack front due to highly concentrated crack tip stress fields. Examples for crack-tip 3-D loops and 2-D straight dislocations emerging from the crack tip are given to demonstrate applications of the derived formulae. The results are consistent with some previous analytical solutions existing in the literature. As further applications we also analyse straight dislocations that are parallel or perpendicular to the crack plane but are not parallel to the crack front.
Croft,M.; Jisrawi, N.; Zhong, Z.; Holtz, R.; Sadananda, K.; Skaritka, J.; Tsakalakos, T.
2007-01-01
High-energy synchrotron X-ray diffraction experiments are used to perform local crack plane strain profiling of 4140 steel compact tension specimens fatigued at constant amplitude, subjected to a single overload cycle, then fatigued some more at constant amplitude. X-ray strain profiling results on a series of samples employing in-situ load cycling are correlated with the crack growth rate (da/dN) providing insight into the da/dN retardation known as the 'overload effect'. Immediately after the overload, the strain under maximum load is greatly reduced but the range of strain, between zero and maximum load, remains unchanged compared to the pre-overload values. At the point of maximum retardation, it is the strain range that is greatly reduced while the maximum-load strain has begun to recover to the pre-overload value. For a sample that has recovered to approximately half of the original da/dN value following the overload, the strain at maximum load is fully recovered while the strain range, though partially recovered, is still substantially reduced. The dominance of the strain range in the overload effect is clearly indicated. Subject to some assumptions, strong quantitative support for a crack growth rate driving force of the suggested form [(K{sub max}){sup -p}({Delta}K){sup p}]{sup {gamma}} is found. A dramatic nonlinear load dependence in the spatial distribution of the strain at maximum retardation is also demonstrated: at low load the response is dominantly at the overload position; whereas at high loads it is dominantly at the crack tip position. This transfer of load response away from the crack tip to the overload position appears fundamental to the overload effect for high R-ratio fatigue as studied here.
NASA Astrophysics Data System (ADS)
Ro, Yunjo
The effect of environmental exposure [given by the ratio of water vapor pressure to the loading frequency (PH2O/f)] on fatigue crack growth rates (FCGR) and damage mechanisms has been investigated for Al-Cu-Li/Mg alloys tested at constant stress intensity range (DeltaK = KMAX - KMIN). Different exposure dependences of the FCGR are explained by H-embrittlement and 3 rate-limiting processes that are similar for each alloy and aging condition. It is shown that the dislocation slip character (heterogeneous planar vs. wavy) controls FCGR at low to moderate exposures, rather than alloy composition and strengthening precipitate reactivity. However, the benefit of planar slip is significantly reduced at higher exposures. An SEM-based electron backscattered diffraction (EBSD)/stereology method was used to successfully quantify changes in fatigue fracture surface crystallography as a function of exposure for a peak aged Al-Cu-Li alloy and an under-aged Al-Cu-Mg alloy. Near-{111} slip band cracking (SBC) observed under high vacuum conditions is gradually replaced by near-{001}/{011} and high index, {hkl}, cracking planes as PH2O/f is increased. The complete absence of near-{111} SBC at higher exposures suggests H enhanced decohesion rather than slip based damage process enhanced by H. This conclusion was substantiated by direct TEM observation. Focused Ion Beam (FIB) milling was used to produce thin foils for TEM, which successfully revealed the underlying dislocation structure at the crack surface and within surrounding materials in under-aged Al-Cu-Mg tested at exposure conditions of ˜10 -8 and 50 Pa·sec. Both conditions exhibit a similar layer of dislocation cells just below the fracture surface which abruptly changes to localized slip bands away from the fracture surface, confirming the presence of a strain gradient at the crack tip. However, the thickness of the substructure layer and slip band width observed at ˜10-8 Pa·sec was larger than those observed at 50 Pa
Finite-element analysis of crack growth under monotonic and cyclic loading
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr.
1977-01-01
An elastic-plastic (incremental) finite-element analysis, in conjunction with a crack-growth criterion, was used to study crack-growth behavior under monotonic and cyclic loading. The crack-growth criterion was based on crack-tip strain. Whenever the crack-tip strain equals or exceeds a critical strain value, the crack grows. The effects of element-mesh size, critical strain, strain hardening, and specimen type (tension or bending) on crack growth under monotonic loading were investigated. Crack growth under cyclic loading (constant amplitude and simple variable amplitude) were also studied. A combined hardening theory, which incorporates features of both isotropic and kinematic hardening under cyclic loading, was also developed for smooth yield surfaces and was used in the analysis.
Ply-Cracking Damage Theory for Cross-Ply Laminate and Its Application to Finite Element Method
NASA Astrophysics Data System (ADS)
Tohgo, Keiichiro; Sugiyama, Yuji; Akizuki, Kenji
This paper deals with a theory of ply-cracking damage on 90° and 0° plies in cross-ply laminate and its application to finite element method. An energy approach is extended to predict the initiation and evolution of ply-crcaking damage on 90° and 0° plies and the corresponding nonlinear stress-strain behavior of the cross-ply laminate under multiaxial in-plane loading. In this appraoch, the stress and strain condition for the progressive damage are determined by equating the decrease in potential energy to the released energy, where the former and latter are estimated from the stiffness reduction due to ply-cracking damage and from the mixed-mode critical energy release rate for cracking of unidirectional ply, respectively. This approach provides us with the constitutive relation of cross-ply laminates including the progressive ply-cracking damage. This theory is applied to the finite element method in order to analyze the ply-cracking damage and stress/strain distributions of the structures made of cross-ply laminates. As an example, finite element analysis is carried out on the seven kinds of CFRP cross-ply laminates with a circular hole. The numerical results show that the transverse cracking damage in 90° plies is widely spread out on the ligament of the plate, and the splitting damage in 0° plies extends in the longitudinal direction from the edge of the hole. The details of the damage evolution around a circular hole in CFRP cross-ply laminate depend on the stacking lay-up.
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.
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
Crack tip shielding observed with high-resolution transmission electron microscopy
Adhika, Damar Rastri; Tanaka, Masaki; Daio, Takeshi; Higashida, Kenji
2015-01-01
The dislocation shielding field at a crack tip was experimentally proven at the atomic scale by measuring the local strain in front of the crack tip using high-resolution transmission electron microscopy (HRTEM) and geometric phase analysis (GPA). Single crystalline (110) silicon wafers were employed. Cracks were introduced using a Vickers indenter at room temperature. The crack tip region was observed using HRTEM followed by strain measurements using GPA. The measured strain field at the crack tip was compressive owing to dislocation shielding, which is in good agreement with the strain field calculated from elastic theory. PMID:26115957
Thomas, Larry E.; Bruemmer, Stephen M.
2000-06-01
Intergranular (IG) attack regions and stress-corrosion cracks in alloy 600 U-bend samples tested in 330C, pressurized-water-reactor water have been characterized by analytical transmission electron microscopy (ATEM). Observations of cross-sectional samples revealed short oxidized zones preceding crack tips and narrow (10-nm wide), deeply penetrated, oxidized zones along grain boundaries exposed along open cracks. High-resolution TEM imaging and fine-probe analysis were used to determine the local chemistries and structures in these corrosion-affected zones. Matrix areas surrounding the crack tips appeared highly strained, whereas the IG penetrations generally did not. The predominant oxide structure found along crack walls and just ahead of crack tips was NiO with metal-atom ratios similar to the alloy. The attacked grain boundaries off open cracks contained similar fine-grained NiO-structure oxide together with local areas of Cr-rich oxide and Ni-rich metal. In contrast, Cr-rich oxide identified as Cr2O3 predominated at the leading edges of the IG attack. Stereoscopic imaging of these tip structures revealed nm-scale porosity and tunnels within the oxide and pores along the grain-boundary plane ahead of the oxide. The general interpretation of these results is that IG attack and cracking follows local dissolution or oxidation and the formation of pores at grain boundaries. This degradation occurs at the nanometer scale and therefore requires high-resolution ATEM methods to reveal detailed characteristics. Experimental support for several possible IG degradation mechanisms is considered.
Fatigue crack nucleation in metallic materials
Peralta, P.; Laird, C.; Ramamurty, U.; Suresh, S.; Campbell, G.H.; King, W.E.; Mitchell, T.E.
1999-04-01
The process of fatigue crack nucleation in metallic materials is reviewed placing emphasis in results derived for pure FCC metals with wavy slip behavior. The relationship between Persistent Slip Bands (PSB`s) and crack initiation will be examined for both single crystals and polycrystals, including the conditions for inter- and transgranular crack nucleation and their connection to type of loading, crystallography and slip geometry. The latter has been found to be an important parameter in the nucleation of intergranular cracks in polycrystals subjected to high strain fatigue, whereby primary slip bands with long slip lengths impinging on a grain boundary produce intergranular crack nucleation under the right conditions. Recent results related to intergranular crack nucleation in copper bicrystals and crack nucleation in Cu/Sapphire interfaces indicate that this mechanism controls crack nucleation in those simpler systems as well. Furthermore, it is found that under multiple slip conditions the crack nucleation location is controlled by the presence of local single slip conditions and long slip lengths for a particular Burgers vector that does not have to be in the primary slip system.
Dynamics of cracking in drying colloidal sheets.
Sengupta, Rajarshi; Tirumkudulu, Mahesh S
2016-04-01
Colloidal dispersions are known to display a fascinating network of cracks on drying. We probe the fracture mechanics of free-standing films of aqueous polymer-particle dispersions. Thin films of the dispersion are cast between a pair of plain steel wires and allowed to dry under ambient conditions. The strain induced on the particle network during drying is relieved by cracking. The stress which causes the films to crack has been calculated by measuring the deflection of the wires. The critical cracking stress varied inversely to the two-thirds' power of the film thickness. We also measure the velocity of the tip of a moving crack. The motion of a crack has been modeled as a competition between the release of the elastic energy stored in the particle network, the increase in surface energy as a result of the growth of a crack, the rate of viscous dissipation of the interstitial fluid and the kinetic energy associated with a moving crack. There is fair agreement between the measured crack velocities and predictions. PMID:26924546
BWR pipe crack remedies evaluation
Shack, W.J.; Kassner, T.F.; Maiya, P.S.; Park, J.Y.; Ruther, W.E.
1986-10-01
This paper presents results on: (a) the influence of simulated BWR environments on the stress-corrosion-craking (SCC) susceptibility of Types 304, 316NG, and 347 stainless (SS); (b) fracture-mechanics crack-growth-rate measurements on these materials and weld overlay specimens in different environments; and (c) residual stress measurements and metallographic evaluations of conventional pipe weldments treated by a mechanical-stress-improvement process (MSIP) as well as those produced by a narrow-gap welding procedure. Crack initiation studies on Types 304 and 316NG SS under crevice and non-crevice conditions in 289/sup 0/C water containing 0.25 ppM dissolved oxygen with low sulfate concentrations indicate that SCC initiates at very low strains (<3%) in the nuclear grade material. Crack growth measurements on fracture-mechanics-type specimens, under low-frequency cyclic loading, show that the Type 316NG steel cracks at a somewhat lower rate (approx.40%) than sensitized Type 304 SS in an impurity environment with 0.25 ppM dissolved-oxygen; however, the latter material stops cracking when sulfate is removed from the water. Crack growth in both materials ceases under simulated hydrogen-water chemistry conditions (<5 ppB oxygen) even with 100 ppB sulfate present in the water. An unexpected result was obtained in the test on a weld overlay specimen in the impurity environment, viz., the crack grew to the overlay interface at a nominal rate, branched at 90/sup 0/ in both directions, and then grew at high rate (parallel to the nominal applied load). Residual stress measurements on MSIP-treated weldments and those produced by a narrow-gap welding procedure indicate that these techniques produce compressive stresses over most of the inner surface near the weld and heat-affected zones.
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.
NASA Astrophysics Data System (ADS)
Moradian, Zabihallah; Einstein, Herbert H.; Ballivy, Gerard
2016-03-01
Determination of the cracking levels during the crack propagation is one of the key challenges in the field of fracture mechanics of rocks. Acoustic emission (AE) is a technique that has been used to detect cracks as they occur across the specimen. Parametric analysis of AE signals and correlating these parameters (e.g., hits and energy) to stress-strain plots of rocks let us detect cracking levels properly. The number of AE hits is related to the number of cracks, and the AE energy is related to magnitude of the cracking event. For a full understanding of the fracture process in brittle rocks, prismatic specimens of granite containing pre-existing flaws have been tested in uniaxial compression tests, and their cracking process was monitored with both AE and high-speed video imaging. In this paper, the characteristics of the AE parameters and the evolution of cracking sequences are analyzed for every cracking level. Based on micro- and macro-crack damage, a classification of cracking levels is introduced. This classification contains eight stages (1) crack closure, (2) linear elastic deformation, (3) micro-crack initiation (white patch initiation), (4) micro-crack growth (stable crack growth), (5) micro-crack coalescence (macro-crack initiation), (6) macro-crack growth (unstable crack growth), (7) macro-crack coalescence and (8) failure.
Short fatigue crack characterization and detection using confocal scanning laser microscopy (CSLM)
Varvani-Farahani, A.; Topper, T.H.
1997-12-31
This paper presents a new technique for studying the growth and morphology of fatigue cracks. The technique allows short fatigue crack growth, crack depth, aspect ratio (crack depth/half crack length), and crack front configuration to be measured using a Confocal Scanning Laser Microscope (CSLM). CSLM measurements of the initial stage of crack growth in Al 2024-T351 revealed that microstructurally short fatigue cracks grew initially along a plane inclined to the applied stress. The angle of the inclined plane (Stage I crack growth) was found to be about 45 degrees to the axis of the applied tensile load. Aspect ratio and the angle of maximum shear plane (Mode II), obtained using the CSLM technique, showed a good agreement with those obtained using a Surface Removal (SR) technique. The aspect ratios obtained using the CSLM technique were found to remain constant with increasing crack length in Al 2024-T351 and SAE 1045 Steel at 0.83 and 0.80, respectively. Optical sectioning along the length of a crack revealed that the crack front in the interior of the materials has a semi-elliptical shape. These results are in good agreement with results obtained using the SR technique. The CSLM technique was employed to characterize the fracture surface of fatigue cracks in an SAE 1045 Steel. CSLM image processing of the fracture surface near the crack tip constructed a three dimensional profile of fracture surface asperities. The heights of asperities were obtained from this profile. Optical sectioning from a post-image-processed crack provided crack depth and crack mouth width at every point along the crack length for each load level. The crack opening stress was taken as the stress level at which the crack depth stopped increasing with increases in a lied stress. 6 refs., 9 figs., 1 tab.
Crack, crack house sex, and HIV risk.
Inciardi, J A
1995-06-01
Limited attention has been focused on HIV risk behaviors of crack smokers and their sex partners, yet there is evidence that the crack house and the crack-using life-style may be playing significant roles in the transmission of HIV and other sexually transmitted diseases. The purposes of this research were to study the attributes and patterns of "sex for crack" exchanges, particularly those that occurred in crack houses, and to assess their potential impact on the spread of HIV. Structured interviews were conducted with 17 men and 35 women in Miami, Florida, who were regular users of crack and who had exchanged sex for crack (or for money to buy crack) during the past 30 days. In addition, participant observation was conducted in 8 Miami crack houses. Interview and observational data suggest that individuals who exchange sex for crack do so with considerable frequency, and through a variety of sexual activities. Systematic data indicated that almost a third of the men and 89% of the women had had 100 or more sex partners during the 30-day period prior to study recruitment. Not only were sexual activities anonymous, extremely frequent, varied, uninhibited (often undertaken in public areas of crack houses), and with multiple partners but, in addition, condoms were not used during the majority of contacts. Of the 37 subjects who were tested for HIV and received their test results 31% of the men and 21% of the women were HIV seropositive. PMID:7611845
Dynamic delamination crack propagation in a graphite/epoxy laminate
NASA Technical Reports Server (NTRS)
Sun, C. T.; Grady, J. E.
1986-01-01
The dynamic delamination crack propagation behavior during ballistic tests of (90/0)5s T-300/934 graphite/epoxy laminates with embedded interfacial cracks was investigated using high speed photography. The impact on the beam-like specimen was produced with a silicon rubber ball, and the crack propagation speeds and the threshold impact velocities required to initiate dynamic crack propagation were determined for several crack positions. The results suggest that the mode of crack propagation depends on the specimen geometry as well as the loading condition. A simplified finite element analysis of the experimental data obtained from one of the midplane-cracked specimens was used to estimate the critical strain energy release rate, which may determine the onset of unstable crack propagation.
The analysis of crack tip fields in ferroelastic materials
NASA Astrophysics Data System (ADS)
Carka, Dorinamaria; Landis, Chad M.
2011-09-01
The stress and strain fields near a stationary crack in a ferroelastic material are analyzed. The constitutive response of the material is taken to be characteristic of a polycrystalline sample assembled from randomly oriented tetragonal single crystal grains. The constitutive law accounts for the strain saturation, asymmetry in tension versus compression, Bauschinger effects, reverse switching, and strain reorientation that can occur in these materials due to the non-proportional loading that can arise near a crack tip. Detailed finite element calculations are carried out to determine the stress and strain fields in the vicinity of the crack tip, and to compute values for the J-integral on various integration paths around the tip. The results of the calculations are discussed in relation to results for growing cracks and for stationary cracks in standard elastic-plastic materials.
Physical and Mechanical Properties of a Thermally Cracked Fine-Grained Granite
NASA Astrophysics Data System (ADS)
Wang, X.; Schubnel, A.; Fortin, J.; Gueguen, Y.; Ge, H.
2013-12-01
Effects of thermal-crack damage on the rupture processes of a fine-grained granite were investigated under triaxial stress, under water (wet) and argon gas (dry) saturated conditions, and room temperature. Thermal cracking was introduced by slowly heating and cooling two samples of La Peyratte granite up to 700oC, which were compared to two intact specimens. For each rock sample, a hydrostatic test was first carried up to 90 MPa effective pressure (5 MPa constant pore pressure). The samples were then deformed to failure at a constant strain rate of 2.10-6 s-1, at 30 MPa effective pressure. Our results show that: (1) permeability of heat-treated specimens was 4-5 orders of magnitude larger than that of intact specimens at low effective mean pressure; (2) nevertheless, at our experimental conditions (2.10-6s-1), thermal cracking had no significant influence on the brittle strength: (3) similarly, no obvious water weakening effect was observed; (4) however, with increasing stress, elastic anisotropy appeared at lower differential stress in heat-treated specimens than in intact ones, but close to failure, the magnitude of P wave anisotropy was approximately the same for both types of specimens; (5) acoustic emission hypocenter locations and P wave velocity anisotropy in the basal plane demonstrate that strain localization started right at the onset of dilatancy for heat-treated specimens, later in the intact specimens; (6) inverting wave velocities for crack density, we show that failure was reached for vertical crack densities of 0.35 for dry specimens, and possibly 0.5 for water-saturated specimens.
NASA Astrophysics Data System (ADS)
Wang, Xu; Xu, Yang
2015-12-01
We analytically investigate the contribution of surface piezoelectricity to the interaction between a piezoelectric screw dislocation and a finite crack in a hexagonal piezoelectric solid. The piezoelectric screw dislocation suffers jumps in the displacement and in the electric potential across the slip plane, and meanwhile it is subjected to a line force and a line charge at its core. The original boundary value problem is reduced to two sets of coupled first-order Cauchy singular integro-differential equations by considering a distribution of line dislocations, electric-potential-dislocations, line forces and line charges on the crack. By using a diagonalization method, the two sets of equations are decoupled into four independent singular integro-differential equations, each of which can be numerically solved by means of the collocation method. Our analysis reveals that in general the stresses, strains, electric displacements and electric fields exhibit both the weak logarithmic and the strong square root singularities at the two crack tips. The image force acting on the piezoelectric screw dislocation due to its interaction with the finite crack is calculated.
Pirgazi, Hadi; Ghodrat, Sepideh; Kestens, Leo A.I.
2014-04-01
In cylinder heads made of compacted graphitic iron (CGI), heating and cooling cycles can lead to localized cracking due to thermo-mechanical fatigue (TMF). To meticulously characterize the complex crack path morphology of CGI under TMF condition, in relation to microstructural features and to find out how and by which mechanisms the cracks predominantly develop, three-dimensional electron back scattering diffraction (EBSD) was employed. Based on the precise quantitative microstructural analysis, it is found that graphite particles not only play a crucial role in the crack initiation, but also are of primary significance for crack propagation, i.e. crack growth is enhanced by the presence of graphite particles. Furthermore, the density of graphite particles on the fracture plane is more than double as high as in any other arbitrary plane of the structure. The obtained results did not indicate a particular crystallographic preference of fracture plane, i.e. the crystal plane parallel to the fracture plane was nearly of random orientation. - Highlights: • Crystallographic features of a thermo-mechanical fatigue (TMF) crack were studied. • Wide-field 3D EBSD is used to characterize the TMF crack morphology. • Data processing was applied on a large length scale of the order of millimeters. • Graphite density in the fracture plane is much higher than any other random plane. • It is revealed that crack growth is enhanced by the presence of graphite particles.
Environmental stress cracking of polymers
NASA Technical Reports Server (NTRS)
Mahan, K. I.
1980-01-01
A two point bending method for use in studying the environmental stress cracking and crazing phenomena is described and demonstrated for a variety of polymer/solvent systems. Critical strain values obtained from these curves are reported for various polymer/solvent systems including a considerable number of systems for which critical strain values have not been previously reported. Polymers studied using this technique include polycarbonate (PC), ABS, high impact styrene (HIS), polyphenylene oxide (PPO), and polymethyl methacrylate (PMMA). Critical strain values obtained using this method compared favorably with available existing data. The major advantage of the technique is the ability to obtain time vs. strain curves over a short period of time. The data obtained suggests that over a short period of time the transition in most of the polymer solvent systems is more gradual than previously believed.
NASA Astrophysics Data System (ADS)
Khanikar, Prasenjit
Different aluminum alloys can be combined, as composites, for tailored dynamic applications. Most investigations pertaining to metallic alloy layered composites, however, have been based on quasi-static approaches. The dynamic failure of layered metallic composites, therefore, needs to be characterized in terms of strength, toughness, and fracture response. A dislocation-density based crystalline plasticity formulation, finite-element techniques, rational crystallographic orientation relations and a new fracture methodology were used to predict the failure modes associated with the high strain rate behavior of aluminum layered composites. Two alloy layers, a high strength alloy, aluminum 2195, and an aluminum alloy 2139, with high toughness, were modeled with representative microstructures that included precipitates, dispersed particles, and different grain boundary (GB) distributions. The new fracture methodology, based on an overlap method and phantom nodes, is used with a fracture criteria specialized for fracture on different cleavage planes. One of the objectives of this investigation, therefore, was to determine the optimal arrangements of the 2139 and 2195 aluminum alloys for a metallic layered composite that would combine strength, toughness and fracture resistance for high strain-rate applications. Different layer arrangements were investigated for high strain-rate applications, and the optimal arrangement was with the high toughness 2139 layer on the bottom, which provided extensive shear strain localization, and the high strength 2195 layer on the top for high strength resistance. The layer thickness of the bottom high toughness layer also affected the bending behavior of the roll-boned interface and the potential delamination of the layers. Shear strain localization, dynamic cracking and delamination were the mutually competing failure mechanisms for the layered metallic composite, and control of these failure modes can be optimized for high strain
Modeling and deformation analyzing of InSb focal plane arrays detector under thermal shock
NASA Astrophysics Data System (ADS)
Zhang, Xiaoling; Meng, Qingduan; Zhang, Liwen; Lv, Yanqiu
2014-03-01
A higher fracture probability appearing in indium antimonide (InSb) infrared focal plane arrays (IRFPAs) subjected to the thermal shock test, restricts its final yield. In light of the proposed equivalent method, where a 32 × 32 array is employed to replace the real 128 × 128 array, a three-dimensional modeling of InSb IRFPAs is developed to explore its deformation rules. To research the damage degree to the mechanical properties of InSb chip from the back surface thinning process, the elastic modulus of InSb chip along the normal direction is lessened. Simulation results show when the out-of-plane elastic modulus of InSb chip is set with 30% of its Young's modulus, the simulated Z-components of strain distribution agrees well with the top surface deformation features in 128 × 128 InSb IRFPAs fracture photographs, especially with the crack origination sites, the crack distribution and the global square checkerboard buckling pattern. Thus the Z-components of strain are selected to explore the deformation rules in the layered structure of InSb IRFPAs. Analyzing results show the top surface deformation of InSb IRFPAs originates from the thermal mismatch between the silicon readout integrated circuits (ROIC) and the intermediate layer above, made up of the alternating indium bump array and the reticular underfill. After passing through both the intermediate layer and the InSb chip, the deformation amplitude is reduced firstly from 2.23 μm to 0.24 μm, finally to 0.09 μm. Finally, von Mises stress criterion is employed to explain the causes that cracks always appear in the InSb chip.
Discrete dislocation plasticity and crack tip fields in single crystals
NASA Astrophysics Data System (ADS)
Van der Giessen, E.; Deshpande, V. S.; Cleveringa, H. H. M.; Needleman, A.
2001-09-01
Small-scale yielding around a stationary plane strain mode I crack is analyzed using discrete dislocation plasticity. The dislocations are all of edge character, and are modeled as line singularities in a linear elastic material. Superposition is used to represent the solution in terms of analytical fields for edge dislocations in a half-space and a numerical image solution that enforces the boundary conditions. The description of the dislocation dynamics includes the lattice resistance to dislocation motion, dislocation nucleation, interaction with obstacles and annihilation. A model planar crystal with three slip systems is considered. Two slip system orientations are analyzed that differ by a 90° rotation. The non-hardening, single crystal plasticity continuum slip solution of Rice (Mech. Mater. 6 (1987) 317) for this model crystal predicts that slip and kink bands emerge for both crystal geometries, while Drugan (J. Mech. Phys. Solids 49 (2001) 2155) has obtained kink band free solutions. For a reference set of parameter values, kink band free solutions are found in one orientation while the emergence of kink bands is seen in the other orientation. However, lowering the dislocation source density suppresses the formation of kink bands in this orientation as well. In all calculations, the opening stress in the immediate vicinity of the crack tip is much larger than predicted by continuum slip theory.
Gear Crack Propagation Investigation
NASA Technical Reports Server (NTRS)
1995-01-01
Reduced weight is a major design goal in aircraft power transmissions. Some gear designs incorporate thin rims to help meet this goal. Thin rims, however, may lead to bending fatigue cracks. These cracks may propagate through a gear tooth or into the gear rim. A crack that propagates through a tooth would probably not be catastrophic, and ample warning of a failure could be possible. On the other hand, a crack that propagates through the rim would be catastrophic. Such cracks could lead to disengagement of a rotor or propeller from an engine, loss of an aircraft, and fatalities. To help create and validate tools for the gear designer, the NASA Lewis Research Center performed in-house analytical and experimental studies to investigate the effect of rim thickness on gear-tooth crack propagation. Our goal was to determine whether cracks grew through gear teeth (benign failure mode) or through gear rims (catastrophic failure mode) for various rim thicknesses. In addition, we investigated the effect of rim thickness on crack propagation life. A finite-element-based computer program simulated gear-tooth crack propagation. The analysis used principles of linear elastic fracture mechanics, and quarter-point, triangular elements were used at the crack tip to represent the stress singularity. The program had an automated crack propagation option in which cracks were grown numerically via an automated remeshing scheme. Crack-tip stress-intensity factors were estimated to determine crack-propagation direction. Also, various fatigue crack growth models were used to estimate crack-propagation life. Experiments were performed in Lewis' Spur Gear Fatigue Rig to validate predicted crack propagation results. Gears with various backup ratios were tested to validate crack-path predictions. Also, test gears were installed with special crack-propagation gages in the tooth fillet region to measure bending-fatigue crack growth. From both predictions and tests, gears with backup ratios
Role of Grain Boundaries and Microstructure on the Environment Assisted Cracking of Pipeline Steels
NASA Astrophysics Data System (ADS)
Arafin, Muhammad
2011-12-01
reconstruction model has been developed that can reproduce the experimentally determined grain boundary character distribution (GBCD) from the simple texture and overall GBCD descriptions. This model has been coupled with the intergranular crack propagation model that can take into account the crystallographic orientations of the grains and the resulting grain boundary character, individual grain boundary fracture strength, and projected local stress onto the grain boundary plane based on applied stress magnitude and in-situ crack propagation length. The predicted threshold fracture stress has been compared with the experimental fracture stress data of various textured and random Mo polycrystals obtained from the literature, and good agreement was observed. Besides, hydrogen induced cracking (HIC) behaviour of two relatively new high strength pipeline steels, API X80 and API X100, in high pH carbonate-bicarbonate environment has been studied using slow strain rate test (SSRT) technique. While both the steels are found to be highly susceptible to HIC at cathodic potentials, the bainitic lath type microstructure (API X100) is more susceptible to HIC compared to the ferritic/granular bainitic steel (API X80) at high cathodic potential. This can be primarily attributed to the bainitic lath boundary separation phenomenon in the API X100 steel. This study also shows that applying cathodic protection can lead to significant hydrogen embrittlement in these steels.
Physically Based Failure Criteria for Transverse Matrix Cracking
NASA Technical Reports Server (NTRS)
Davila, Carlos G.; Camanho, Pedro P.
2003-01-01
A criterion for matrix failure of laminated composite plies in transverse tension and in-plane shear is developed by examining the mechanics of transverse matrix crack growth. Matrix cracks are assumed to initiate from manufacturing defects and can propagate within planes parallel to the fiber direction and normal to the ply mid-plane. Fracture mechanics models of cracks in unidirectional laminates, embedded plies and outer plies are developed to determine the onset and direction of propagation for unstable crack growth. The models for each ply configuration relate ply thickness and ply toughness to the corresponding in-situ ply strength. Calculated results for several materials are shown to correlate well with experimental results.
Eshelby tensor for a crack in an orthotropic elastic medium
NASA Astrophysics Data System (ADS)
Gruescu, Cosmin; Monchiet, Vincent; Kondo, Djimedo
2005-06-01
In the present Note, we provide new analytical expressions of the components of Hill tensor P (or equivalently the Eshelby tensor S) associated to an arbitrarily oriented crack in orthotropic elastic medium. The crack is modelled as an infinite cylinder along a symmetry axis of the matrix, with low aspect ratio. The three dimensional results obtained show explicitly the interaction between the primary (structural) anisotropy and the crack-induced anisotropy. They are validated by comparison with existing results in the case where the crack is in a symmetry plane. To cite this article: C. Gruescu et al., C. R. Mecanique 333 (2005).
Finite-element analysis of corner cracks in rectangular bars
NASA Technical Reports Server (NTRS)
Raju, L. S.; Newman, J. C., Jr.
1987-01-01
Stress intensity factors for a wide range of quarter-elliptical corner cracks in rectangular bars are presented. Cracked configurations were subjected to remote tension, in-plane bending, or out-of-plane bending. Results were compared with other numerical results for a quarter-circular corner crack configuration. The present results along the interior of the crack generally agreed within 3 percent with those from the literature. Some larger differences (3 to 13 percent) were observed near the intersection of the crack front and the free surfaces in the boundary layer region. Analyses were performed to study the effect of mesh refinement in the boundary layer region and the influence of Poisson's ratio on the distribution of stress-intensity factors.
Interface crack problems in layered orthotropic materials
NASA Astrophysics Data System (ADS)
Erdogan, F.; Wu, Binghua
1993-05-01
T HE PRIMARY objective of this paper is to study the influence of the structure and thickness of the interfacial regions on the strain energy release rate in bonded isotropic or orthotropic materials containing collinear interface cracks. The problem is formulated in terms of a system of singular integral equations of the second kind which is solved by using a relatively simple and efficient technique. A number of examples are given for various crack geometries and material combinations. The results show that the effect of the properties and the relative thickness of the interfacial region on the stress intensity factors and the strain energy release rate can be highly significant.
Variation of crack-opening stresses in three-dimensions - Finite thickness plate
NASA Technical Reports Server (NTRS)
Chermahini, R. G.; Blom, A. F.
1991-01-01
A 3D elastic-plastic finite-element analysis is conducted to study crack-growth behavior of thin and thick center-cracked specimens under constant-amplitude loading conditions. The numerical analysis and the specimen configuration and loading are described for both the thin and thick conditions. Stabilized crack-opening stresses of interior and exterior regions are given as are the closure and opening profiles of the crack-surface plane after the tenth cycle. The effect of thickness is discussed with respect to the crack-opening stress levels and the plastic zones of the interior and exterior regions. A load-reduced-displacement technique allows the calculation of the crack-opening stresses at three locations on the crack surface plane. The constraint effect related to thickness gives a lower stabilized crack-opening stress level for the thick specimens.
Tiernan, M.
1980-09-01
Crack spectra derived from velocity data have been shown to exhibit systematics which reflect microstructural and textural differences between samples (Warren and Tiernan, 1980). Further research into both properties and information content of crack spectra have yielded the following: Spectral features are reproducible even at low pressures; certain observed spectral features may correspond to non-in-situ crack populations created during sample retrieval; the functional form of a crack spectra may be diagnostic of the sample's grain texture; hysteresis is observed in crack spectra between up and down pressure runs - it may be due to friction between the faces of closed crack populations.
NASA Technical Reports Server (NTRS)
Lee, Jong-Won; Allen, D. H.; Harris, C. E.
1989-01-01
A mathematical model utilizing the internal state variable concept is proposed for predicting the upper bound of the reduced axial stiffnesses in cross-ply laminates with matrix cracks. The axial crack opening displacement is explicitly expressed in terms of the observable axial strain and the undamaged material properties. A crack parameter representing the effect of matrix cracks on the observable axial Young's modulus is calculated for glass/epoxy and graphite/epoxy material systems. The results show that the matrix crack opening displacement and the effective Young's modulus depend not on the crack length, but on its ratio to the crack spacing.
NASA Technical Reports Server (NTRS)
Salpekar, S. A.; Raju, I. S.; Obrien, T. K.
1987-01-01
Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtural crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finite-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.
Gear crack propagation investigations
NASA Technical Reports Server (NTRS)
Lewicki, David G.; Ballarini, Roberto
1996-01-01
Analytical and experimental studies were performed to investigate the effect of gear rim thickness on crack propagation life. The FRANC (FRacture ANalysis Code) computer program was used to simulate crack propagation. The FRANC program used principles of linear elastic fracture mechanics, finite element modeling, and a unique re-meshing scheme to determine crack tip stress distributions, estimate stress intensity factors, and model crack propagation. Various fatigue crack growth models were used to estimate crack propagation life based on the calculated stress intensity factors. Experimental tests were performed in a gear fatigue rig to validate predicted crack propagation results. Test gears were installed with special crack propagation gages in the tooth fillet region to measure bending fatigue crack growth. Good correlation between predicted and measured crack growth was achieved when the fatigue crack closure concept was introduced into the analysis. As the gear rim thickness decreased, the compressive cyclic stress in the gear tooth fillet region increased. This retarded crack growth and increased the number of crack propagation cycles to failure.
Interaction between Interfacial Collinear Griffith Cracks in Composite Media under Thermal Loading
NASA Astrophysics Data System (ADS)
Mishra, P. K.; Das, S.
2016-05-01
This article deals with the interactions between a central crack and a pair of outer cracks situated at the interface of orthotropic elastic half planes under thermo-mechanical loading. The mixed boundary value problem has been reduced to a pair of singular integral equations which has been solved numerically using Jacobi polynomial method. The interaction effects have been obtained in terms of stress magnification factors depending on the crack spacing and crack length. The phenomena of crack shielding and crack amplification have been depicted through graphs for different particular cases.
NASA Astrophysics Data System (ADS)
Frühwirt, Thomas; Plößer, Arne; Konietzky, Heinz
2015-04-01
The main focus of this work was to investigate temporary and spatial features of crack development in concrete blocks due to the action of a swelling agent. A commercial available cement-based mortar which shows heavily swelling behaviour when hydrating is used to provide inside pressure in boreholes in conrete blocks and hence serves as cracking agent. As no data for the swelling behaviour of the cracking agent were available the maximum axial swelling stress and axial free swelling strain were determined experimentally. In a first series of tests on concrete blocks the influence of an external mechanical, unidirectional stress on the development-time and orientation of cracks has been investigated for a range of loading levels. The stress state in the blocks prepared with a single borehole was determined by a superposition of internal stresses caused by swelling pressure and external mechanical loading. For a second series of tests prismatic blocks with two boreholes where prepared. This test setup allowed to realize different orientation of boreholes with respect to the uniaxial loading direction. Complementary tests were done using the cracking agent in both, only one or none of the boreholes. Different modes of crack interaction and influence of filled or unfilled boreholes have been observed. Features of crack development showed significant sensitivity to external loading. Starting even at very low load levels crack orientation was primarely determined by the direction of the external load. Temporal change in crack development due to the different load levels was insignificant and no consistent conclusion could be drawn. Crack interaction phenomena only were observed with two boreholes orientated primarely in direction of the external loading. Even in these cases crack orientation was mainly determined by the external stress field and only locally influenced by other cracks or the unfilled borehole. The work provides us with an extensive catalogue of
NASA Astrophysics Data System (ADS)
Betka, P. M.; Seeber, L.; Steckler, M. S.
2015-12-01
, contractional structures that formed internally within the FTB are indicative of east-west horizontal shortening and plane strain. This result suggests that the dextral component of shear measured by geodetic data is primarily partitioned onto discrete right-lateral strike-slip faults such as the Churachandpur-Mao and Kabaw faults.
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NASA Astrophysics Data System (ADS)
Budarapu, P. R.; Javvaji, B.; Sutrakar, V. K.; Roy Mahapatra, D.; Zi, G.; Rabczuk, T.
2015-08-01
The crack initiation and growth mechanisms in an 2D graphene lattice structure are studied based on molecular dynamics simulations. Crack growth in an initial edge crack model in the arm-chair and the zig-zag lattice configurations of graphene are considered. Influence of the time steps on the post yielding behaviour of graphene is studied. Based on the results, a time step of 0.1 fs is recommended for consistent and accurate simulation of crack propagation. Effect of temperature on the crack propagation in graphene is also studied, considering adiabatic and isothermal conditions. Total energy and stress fields are analyzed. A systematic study of the bond stretching and bond reorientation phenomena is performed, which shows that the crack propagates after significant bond elongation and rotation in graphene. Variation of the crack speed with the change in crack length is estimated.
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
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr.
1982-01-01
An elastic-plastic (incremental and small strain) finite element analysis was used with a crack growth criterion to study crack initiation, stable crack growth, and instability under monotonic loading to failure of metallic materials. The crack growth criterion was a critical crack-tip-opening displacement (CTOD) at a specified distance from the crack tip, or equivalently, a critical crack-tip-opening angle (CTOA). Whenever the CTOD (or CTOA) equaled or exceeded a critical value, the crack was assumed to grow. Single values of critical CTOD were used in the analysis to model crack initiation, stable crack growth, and instability for 7075-T651 and 2024-T351 aluminum alloy compact specimens. Calculated and experimentally measured CTOD values at initiation agreed well for both aluminum alloys. These critical CTOD values were also used to predict failure loads on center-crack tension specimens and a specially-designed three-hole-crack tension specimen made of the two aluminum alloys and of 304 stainless steel. All specimens were 12.7 mm thick. Predicted failure loads for 7075-T651 aluminum alloy and 304 stainless steel specimens were generally within + or - 15 percent of experimental failure loads, whereas the predicted failure loads for 2024-T351 aluminum alloy specimens were generally within + or - 5 percent of the experimental loads.
Crack nucleation in Fe-3% Si in a hydrogen environment
NASA Technical Reports Server (NTRS)
Kamdar, M. H.
1974-01-01
An investigation has been made of the grain-size and strain-rate dependence of the crack nucleation process in iron-3% silicon polycrystals tested in a low-pressure hydrogen environment. The results are compared with similar observations made in an air environment and are discussed in terms of the role of hydrogen on the process of crack nucleation in iron.
Crack opening stretch in a plate of finite width
NASA Technical Reports Server (NTRS)
Erdogan, F.; Bakioglu, M.
1974-01-01
The problem of a uniaxially stressed plate of finite width containing a centrally located damage zone is considered. It is assumed that the flaw may be represented by a part-through crack perpendicular to the plate surface, the net ligaments in the plane of the crack and through-the-thickness narrow strips ahead of the crack ends are fully yielded, and in the yielded sections the material may carry only a constant normal traction with magnitude equal to the yield strength. The problem is solved by neglecting the bending effects and the crack opening stretches at the center and the ends of the crack are obtained. Some applications of the results are indicated by using the concepts of critical crack opening stretch and constant slope plastic instability.
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.
Crack healing in silicon nitride due to oxidation
NASA Technical Reports Server (NTRS)
Choi, Sung R.; Tikare, Veena; Pawlik, Ralph
1991-01-01
The crack healing behavior of a commercial, MgO-containing, hot pressed Si3N4 was studied as a function of temperature in oxidizing and inert annealing environments. Crack healing occurred at a temperature 800 C or higher due to oxidation regardless of crack size, which ranged from 100 microns (indentation crack) to 1.7 mm (SEPB precrack). The resulting strength and apparent fracture toughness increased at crack healing temperature by 100 percent and 300 percent, respectively. The oxide layer present in the crack plane was found to be highly fatigue resistant, indicating that the oxide is not solely silicate glass, but a mixture of glass, enstatite, and/or cristobalite that was insensitive to fatigue in a room temperature water environment.
Crack opening stretch in a plate of finite width
NASA Technical Reports Server (NTRS)
Erdogan, F.; Bakioglu, M.
1975-01-01
The problem of a uniaxially stressed plate of finite width containing a centrally located damage zone is considered. It is assumed that the flaw may be represented by a part-through crack perpendicular to the plate surface, the net ligaments in the plane of the crack and through-the-thickness narrow strips ahead of the crack ends are fully yielded, and in the yielded sections the material may carry only a constant normal traction with magnitude equal to the yield strength. The problem is solved by neglecting the bending effects and the crack opening stretches at the center and the ends of the crack are obtained. Some applications of the results are indicated by using the concepts of critical crack opening stretch and constant slope plastic instability.
Sadananda, K.; Vasudevan, A.K.
1997-12-01
The authors have re-evaluated short crack growth behavior using concepts developed recently, and they show that these concepts provide a unified framework that can explain both short and long crack growth behavior without resorting to the crack closure effect. They consider that the behavior of long cracks, including the effects of load ratio, R, is fundamental. they had shown previously that, since fatigue is at least a two-parameter problem in that at least two load parameters are required for an unambiguous description, there are two critical driving forces required simultaneously for fatigue cracks to grow. In extending this analysis to the growth of short cracks, they reject the current notion of the lack of similitude for short cracks and express the similitude as a fundamental postulate that, for a given crack growth mechanism, equal crack tip driving forces result in equal crack growth rates. Short crack growth behavior confirms the concept that two parameters are required to define fatigue; consequently, for fatigue cracks to grow, two thresholds need to be satisfied simultaneously. The authors present examples from the literature to illustrate the concepts discussed.
Modelling microstructurally sensitive fatigue short crack growth
NASA Astrophysics Data System (ADS)
de Los Rios, E. R.; Xin, X. J.; Navarro, A.
1994-10-01
Microstructurally sensitive fatigue short crack growth can occur in many engineering components devoid of large defects. Continuum mechanics principles, including linear elastic fracture mechanics, used in damage tolerance design and life prediction methods are not applicable in these situations and therefore new concepts need to be developed to characterize this type of growth. A microstructurally sensitive model of fatigue crack growth is presented in which the effect of microstructure is dominant in the early stage of growth but plays a negligible role after the crack has gone through the transition from structure-sensitive to structure-insensitive growth. The effect of both microstructure and structure sensitive variables on the transition from short cracks to continuum mechanics and the conditions for crack instability leading to final failure are examined. The microstructural variables incorporated in the equations that describe the model are those controlling the extent and intensity of crack tip plasticity such as grain size, precipitation and dispersion hardening, strain hardening and mis-orientation between grains. It is expected that the concepts developed within the model will form the basis for the design of new crack-resistant materials.
Fracture Analysis in a Functionally Graded Magnetoelectroelastic Plane by BIEM
NASA Astrophysics Data System (ADS)
Stoynov, Y. D.
2011-11-01
A functionally graded magnetoelectroelastic (MEE) plane with a finite crack is considered. The crack is impermeable and subjected to anti-plane mechanical and in-plane electric and magnetic load. The fundamental solutions of the coupled system of the governing equations are derived in a closed form by the Radon transform. They are implemented in a non-hypersingular traction boundary integral equation method (BIEM). A program code in Fortran, based on the BIEM, is created. Comparison with the results obtained by a different method is presented. The numerical examples show the dependence of the stress intensity factor (SIF) on the normalized frequency for different magnitude of the material inhomogeneity. Results for a non-straight crack are also given.
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.
NASA Technical Reports Server (NTRS)
Smith, C. W.
1997-01-01
The present study was undertaken in order to develop test methods and procedures for measuring the variation of the stress intensity factor through the thickness in bimaterial specimens containing cracks within and parallel to the bond line using the frozen stress photoelastic method. Since stress freezing materials are incompressible above critical temperature, and since thick plates are to be employed which tend to produce a state of plane strain near the crack tip, the interface near tip fracture equations reduce to the classic form for homogeneous materials. Moreover, zero thickness interfaces do not exist when materials are bonded together. It was decided early on that it would be important to insure a uniform straight and accurate crack tip region through the thickness of the body to reduce scatter in the SIF distribution through the thickness. It was also observed that rubberlike materials which were desired to be modeled exhibited significant tip blunting prior to crack extension and that some blunting of the tip would provide a more realistic model. It should be noted that, in normal stress freezing photoelastic work, it is considered good practice to avoid utilizing data near bond lines in photoelastic models due to the bond line stresses which inevitably develop when two parts are bonded together. Thus, the present study involves certain exploratory aspects in deviating from standard practice in stress freezing work. With the above ideas in mind, several different test methods were investigated and are described in the following sections and appendices. The geometry selected for the program was a thick, edge cracked specimen containing a bond line.
Microstructural Influences on Very-High-Cycle Fatigue-Crack Initiation in Ti-6246
NASA Astrophysics Data System (ADS)
Szczepanski, C. J.; Jha, S. K.; Larsen, J. M.; Jones, J. W.
2008-12-01
The fatigue behavior of an alpha + beta titanium alloy, Ti-6Al-2Sn-4Zr-6Mo, has been characterized in the very-high-cycle fatigue (VHCF) regime using ultrasonic-fatigue (20 kHz) techniques. Stress levels ( σ max) of 40 to 60 pct of the yield strength of this alloy have been examined. Fatigue lifetimes in the range of 106 to 109 cycles are observed, and fatigue cracks initiate from both surface and subsurface sites. This study examines the mechanisms of fatigue-crack formation by quantifying critical microstructural features observed in the fatigue-crack initiation region. The fracture surface near the fatigue-crack-initiation site was crystallographic in nature. Facets, which result from the fracture of primary alpha ( α p ) grains, are associated with the crack-initiation process. The α p grains that form facets are typically larger in size than average. The spatial distribution of α p grains relative to each other observed near the initiation site did not correlate with fatigue life. Furthermore, the spatial distribution of α p grains did not provide a suitable means for discerning crack-initiation sites from randomly selected nominal areas. Stereofractography measurements have shown that the facets observed at or near the initiation sites are oriented for high shear stress; i.e., they are oriented close to 45 deg with respect to the loading axis. Furthermore, a large majority of the grains and laths near the site of crack initiation are preferentially oriented for either basal or prism slip, suggesting that regions where α p grains and α laths have similar crystallographic orientations favor crack initiation. Microtextured regions with favorable and similar orientations of α p grains and the lath α are believed to promote cyclic-strain accumulation by basal and prism slip. Orientation imaging microscopy (OIM) indicates that these facets form on the basal plane of α p grains. The absence of a significant role of spatial clustering of α p grains
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.
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.
Cracked tooth diagnosis and treatment: An alternative paradigm
Mamoun, John S.; Napoletano, Donato
2015-01-01
This article reviews the diagnosis and treatment of cracked teeth, and explores common clinical examples of cracked teeth, such as cusp fractures, fractures into tooth furcations, and root fractures. This article provides alternative definitions of terms such as cracked teeth, complete and incomplete fractures and crack lines, and explores the scientific rationale for dental terminology commonly used to describe cracked teeth, such as cracked tooth syndrome, structural versus nonstructural cracks, and vertical, horizontal, and oblique fractures. The article explains the advantages of high magnification loupes (×6–8 or greater), or the surgical operating microscope, combined with co-axial or head-mounted illumination, when observing teeth for microscopic crack lines or enamel craze lines. The article explores what biomechanical factors help to facilitate the development of cracks in teeth, and under what circumstances a full coverage crown may be indicated for preventing further propagation of a fracture plane. Articles on cracked tooth phenomena were located via a PubMed search using a variety of keywords, and via selective hand-searching of citations contained within located articles. PMID:26038667
Corrosion pitting and environmentally assisted small crack growth
Turnbull, Alan
2014-01-01
In many applications, corrosion pits act as precursors to cracking, but qualitative and quantitative prediction of damage evolution has been hampered by lack of insights into the process by which a crack develops from a pit. An overview is given of recent breakthroughs in characterization and understanding of the pit-to-crack transition using advanced three-dimensional imaging techniques such as X-ray computed tomography and focused ion beam machining with scanning electron microscopy. These techniques provided novel insights with respect to the location of crack development from a pit, supported by finite-element analysis. This inspired a new concept for the role of pitting in stress corrosion cracking based on the growing pit inducing local dynamic plastic strain, a critical factor in the development of stress corrosion cracks. Challenges in quantifying the subsequent growth rate of the emerging small cracks are then outlined with the potential drop technique being the most viable. A comparison is made with the growth rate for short cracks (through-thickness crack in fracture mechanics specimen) and long cracks and an electrochemical crack size effect invoked to rationalize the data. PMID:25197249
Corrosion pitting and environmentally assisted small crack growth.
Turnbull, Alan
2014-09-01
In many applications, corrosion pits act as precursors to cracking, but qualitative and quantitative prediction of damage evolution has been hampered by lack of insights into the process by which a crack develops from a pit. An overview is given of recent breakthroughs in characterization and understanding of the pit-to-crack transition using advanced three-dimensional imaging techniques such as X-ray computed tomography and focused ion beam machining with scanning electron microscopy. These techniques provided novel insights with respect to the location of crack development from a pit, supported by finite-element analysis. This inspired a new concept for the role of pitting in stress corrosion cracking based on the growing pit inducing local dynamic plastic strain, a critical factor in the development of stress corrosion cracks. Challenges in quantifying the subsequent growth rate of the emerging small cracks are then outlined with the potential drop technique being the most viable. A comparison is made with the growth rate for short cracks (through-thickness crack in fracture mechanics specimen) and long cracks and an electrochemical crack size effect invoked to rationalize the data. PMID:25197249
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.
Cohesive models of fatigue crack growth and stress-corrosion cracking
NASA Astrophysics Data System (ADS)
Nguyen, Olivier T.
The aim of this dissertation was to develop models of fatigue crack growth and stress-corrosion cracking by investigating cohesive theories of fracture. These models were integrated in a finite-element framework embedding a contact algorithm and techniques of remeshing and adaptive meshing.For the fatigue model, we developed a phenomenological cohesive law which exhibits unloading-reloading hysteresis. This model qualitatively predicts fatigue crack growth rates in metals under constant amplitude regime for short and long cracks, as well as growth retardation due to overload. Quantitative predictions were obtained in the case of long cracks.We developed a chemistry-dependent cohesive law which serves as a basis for the stress-corrosion cracking model. In order to determine this cohesive law, two approaches, based on energy relaxation and the renormalization group, were used for coarse-graining interplanar potentials. We analyzed the cohesive behavior of a large--but finite--number of interatomic planes and found that the macroscopic cohesive law adopts a universal asymptotic form. The resulting stress-corrosion crack growth rates agreed well with those observed experimentally in 'static' fatigue tests given in the literature.
Fatigue crack growth behavior in equine cortical bone
NASA Astrophysics Data System (ADS)
Shelton, Debbie Renee
2001-07-01
Objectives for this research were to experimentally determine crack growth rates, da/dN, as a function of alternating stress intensity factor, DeltaK, for specimens from lateral and dorsal regions of equine third metacarpal cortical bone tissue, and to determine if the results were described by the Paris law. In one set of experiments, specimens were oriented for crack propagation in the circumferential direction with the crack plane transverse to the long axis of the bone. In the second set of experiments, specimens were oriented for radial crack growth with the crack plane parallel to the long axis of the bone. Results of fatigue tests from the latter specimens were used to evaluate the hypothesis that crack growth rates differ regionally. The final experiments were designed to determine if crack resistance was dependent on region, proportion of hooped osteons (those with circumferentially oriented collagen fibers in the outer lamellae) or number of osteons penetrated by the crack, and to address the hypothesis that hooped osteons resist invasion by cracks better than other osteonal types. The transverse crack growth data for dorsal specimens were described by the Paris law with an exponent of 10.4 and suggested a threshold stress intensity factor, DeltaKth, of 2.0 MPa·m1/2 and fracture toughness of 4.38 MPa·m 1/2. Similar results were not obtained for lateral specimens because the crack always deviated from the intended path and ran parallel to the loading direction. Crack growth for the dorsal and lateral specimens in the radial orientation was described by the Paris law with exponents of 8.7 and 10.2, respectively, and there were no regional differences in the apparent DeltaK th (0.5 MPa·m1/2) or fracture toughness (1.2 MPa·m 1/2). Crack resistance was not associated with cortical region, proportion of hooped osteons or the number of osteons penetrated by the crack. The extent to which cracks penetrate osteons was influenced by whether the collagen fiber
J-integral estimates for cracks in infinite bodies
NASA Technical Reports Server (NTRS)
Dowling, N. E.
1986-01-01
An analysis and discussion is presented of existing estimates of the J-integral for cracks in infinite bodies. Equations are presented which provide convenient estimates for Ramberg-Osgood type elastoplastic materials containing cracks and subjected to multiaxial loading. The relationship between J and the strain normal to the crack is noted to be only weakly dependent on state of stress. But the relationship between J and the stress normal to the crack is strongly dependent on state of stress. A plastic zone correction term often employed is found to be arbitrary, and its magnitude is seldom significant.
Lattice strain development in Inconel-690 under bi-axial compression and tension
NASA Astrophysics Data System (ADS)
Toda, Rebecca Midori
Nuclear reactor steam generator tubes, manufactured from Nickel alloys such as Inconel 690 (INC690), are potentially susceptible to failure by Stress Corrosion Cracking where crack initiation may be exacerbated by internal stress fields. A more comprehensive understanding of this potential failure mechanism was gained via an exploration of a model of INC690.s behaviour under Constrained loading conditions in compression and tension. An Elasto-Plastic Self-Consistent (EPSC) model was used to predict the lattice stresses and strains resulting from Constrained loading in INC690 for four crystallographic planes. The internal strain fields generated under such conditions were shown to be markedly different from those developed under Uniaxial loading. Finite Element Modeling was used to design tensile and compression samples as well as a testing rig that would allow the application of a compressive load along one axis of the specimen with simultaneous constraint along another and free-deformation along the third. Lattice strain measurements were done for both compressive and tensile loading using Time-Of-Flight neutron diffraction. The predicted and experimental values showed reasonable agreement; mainly in terms of crystallographic plane interaction and behaviour. Iterative computer modeling was used to achieve a more realistic depiction of the lattice strains developed. This research allowed for an extension on the Uniaxial findings by examining the material's behaviour under more complex loading that better approximates steam generator tube operating conditions.
Cohesive zone finite element analysis of crack initiation from a butt joint’s interface corner
Reedy, E. D.
2014-09-06
The Cohesive zone (CZ) fracture analysis techniques are used to predict the initiation of crack growth from the interface corner of an adhesively bonded butt joint. In this plane strain analysis, a thin linear elastic adhesive layer is sandwiched between rigid adherends. There is no preexisting crack in the problem analyzed, and the focus is on how the shape of the traction–separation (T–U) relationship affects the predicted joint strength. Unlike the case of a preexisting interfacial crack, the calculated results clearly indicate that the predicted joint strength depends on the shape of the T–U relationship. Most of the calculations usedmore » a rectangular T–U relationship whose shape (aspect ratio) is defined by two parameters: the interfacial strength σ* and the work of separation/unit area Γ. The principal finding of this study is that for a specified adhesive layer thickness, there is any number of σ*, Γ combinations that generate the same predicted joint strength. For each combination there is a corresponding CZ length. We developed an approximate CZ-like elasticity solution to show how such combinations arise and their connection with the CZ length.« less
Cohesive zone finite element analysis of crack initiation from a butt joint’s interface corner
Reedy, E. D.
2014-09-06
The Cohesive zone (CZ) fracture analysis techniques are used to predict the initiation of crack growth from the interface corner of an adhesively bonded butt joint. In this plane strain analysis, a thin linear elastic adhesive layer is sandwiched between rigid adherends. There is no preexisting crack in the problem analyzed, and the focus is on how the shape of the traction–separation (T–U) relationship affects the predicted joint strength. Unlike the case of a preexisting interfacial crack, the calculated results clearly indicate that the predicted joint strength depends on the shape of the T–U relationship. Most of the calculations used a rectangular T–U relationship whose shape (aspect ratio) is defined by two parameters: the interfacial strength σ* and the work of separation/unit area Γ. The principal finding of this study is that for a specified adhesive layer thickness, there is any number of σ*, Γ combinations that generate the same predicted joint strength. For each combination there is a corresponding CZ length. We developed an approximate CZ-like elasticity solution to show how such combinations arise and their connection with the CZ length.
The role of cyclic plastic zone size on fatigue crack growth behavior in high strength steels
NASA Astrophysics Data System (ADS)
Korda, Akhmad A.; Miyashita, Y.; Mutoh, Y.
2015-09-01
The role of cyclic plastic zone in front of the crack tip was studied in high strength steels. Estimated plastic zone size would be compared with actual observation. Strain controlled fatigue tests of the steels were carried out to obtain cyclic stress-strain curves for plastic zone estimation. Observations of plastic zone were carried out using in situ SEM fatigue crack growth tests under a constant-ΔK. Hard microstructures in structural steels showed to inhibit the extent of plastic deformation around the crack tip. The rate of crack growth can be correlated with the size of plastic zone. The smaller the plastic zone size, the slower the fatigue crack growth.
Through-the-thickness fatigue crack closure behavior in an aluminum alloy
NASA Technical Reports Server (NTRS)
Dawicke, D. S.; Newman, J. C., Jr.; Grandt, A. F., Jr.
1990-01-01
The variation in fatigue crack closure behavior across the thickness of aluminum alloy specimens was investigated. The specimen geometries examined were the middle crack tension M(T) and compact tension C(T). The fatigue crack closure behavior was determined using remote displacement and strain gages, near tip strain gages, and fatigue striations. A hybrid experimental/numerical method was also used to infer the crack opening loads. The results indicate a variation in crack opening load, of 0.2 in the specimen interior to 0.4 to 0.5 at the surface.
Investigation of Helicopter Longeron Cracks
NASA Technical Reports Server (NTRS)
Newman, John A.; Baughman, James; Wallace, Terryl A.
2009-01-01
Four cracked longerons, containing a total of eight cracks, were provided for study. Cracked regions were cut from the longerons. Load was applied to open the cracks, enabling crack surface examination. Examination revealed that crack propagation was driven by fatigue loading in all eight cases. Fatigue crack initiation appears to have occurred on the top edge of the longerons near geometric changes that affect component bending stiffness. Additionally, metallurgical analysis has revealed a local depletion in alloying elements in the crack initiation regions that may be a contributing factor. Fatigue crack propagation appeared to be initially driven by opening-mode loading, but at a crack length of approximately 0.5 inches (12.7 mm), there is evidence of mixed-mode crack loading. For the longest cracks studied, shear-mode displacements destroyed crack-surface features of interest over significant portions of the crack surfaces.
NASA Technical Reports Server (NTRS)
Jackson, Wade C.; Portanova, Marc A.
1995-01-01
This paper summarizes three areas of research which were performed to characterize out-of-plane properties of composite materials. In the first investigation, a series of tests was run to characterize the through-the-thickness tensile strength for a variety of composites that included 2D braids, 2D and 3D weaves, and prepreg tapes. A new test method based on a curved beam was evaluated. Failures were significantly different between the 2D materials and the 3D weaves. The 2D materials delaminated between layers due to out-of-plane tensile stresses while the 3D weaves failed due to the formation of radial cracks between the surface plies caused by high circumferential stresses along the inner radius. The strength of the 2D textile composites did not increase relative to the tapes. Final failure in the 3D weaves was caused by a circumferential crack similar to the 2D materials and occurred at a lower bending moment than in other materials. The early failures in the 3D weaves were caused by radial crack formation rather than a low through-the-thickness strength. The second investigation focused on the development of a standard impact test method to measure impact damage resistance. The only impact tests that currently exist are compression after impact (CAI) tests which incorporate elements of both damage resistance and damage tolerance. A new impact test method is under development which uses a quasi-static indentation (QSI) test to directly measure damage resistance. Damage resistance is quantified in terms of the contact force to produce a unit of damage where a metric for damage may be area in C-scan, depth of residual dent , penetration, damage growth, etc. A final draft of an impact standard that uses a QSI test method will be presented to the ASTM Impact Task Group on impact. In the third investigation, the impact damage resistance behavior of a variety of textile materials was studied using the QSI test method. In this study, the force where large damage
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.
Crack width monitoring of concrete structures based on smart film
NASA Astrophysics Data System (ADS)
Zhang, Benniu; Wang, Shuliang; Li, Xingxing; Zhang, Xu; Yang, Guang; Qiu, Minfeng
2014-04-01
Due to its direct link to structural security, crack width is thought to be one of the most important parameters reflecting damage conditions of concrete structures. However, the width problem is difficult to solve with the existing structural health monitoring methods. In this paper, crack width monitoring by means of adhering enameled copper wires with different ultimate strains on the surface of structures is proposed, based on smart film crack monitoring put forward by the present authors. The basic idea of the proposed method is related to a proportional relationship between the crack width and ultimate strain of the broken wire. Namely, when a certain width of crack passes through the wire, some low ultimate strain wires will be broken and higher ultimate strain wires may stay non-broken until the crack extends to a larger scale. Detection of the copper wire condition as broken or non-broken may indicate the width of the structural crack. Thereafter, a multi-layered stress transfer model and specimen experiment are performed to quantify the relationship. A practical smart film is then redesigned with this idea and applied to Chongqing Jiangjin Yangtze River Bridge.
Effect of Measured Welding Residual Stresses on Crack Growth
NASA Technical Reports Server (NTRS)
Hampton, Roy W.; Nelson, Drew; Doty, Laura W. (Technical Monitor)
1998-01-01
Welding residual stresses in thin plate A516-70 steel and 2219-T87 aluminum butt weldments were measured by the strain-gage hole drilling and X-ray diffraction methods. The residual stress data were used to construct 3D strain fields which were modeled as thermally induced strains. These 3D strain fields were then analyzed with the WARP31) FEM fracture analysis code in order to predict their effect on fatigue and on fracture. For analyses of fatigue crack advance and subsequent verification testing, fatigue crack growth increments were simulated by successive saw-cuts and incremental loading to generate, as a function of crack length, effects on crack growth of the interaction between residual stresses and load induced stresses. The specimen experimental response was characterized and compared to the WARM linear elastic and elastic-plastic fracture mechanics analysis predictions. To perform the fracture analysis, the plate material's crack tearing resistance was determined by tests of thin plate M(T) specimens. Fracture analyses of these specimen were performed using WARP31D to determine the critical Crack Tip Opening Angle [CTOA] of each material. These critical CTOA values were used to predict crack tearing and fracture in the weldments. To verify the fracture predictions, weldment M(T) specimen were tested in monotonic loading to fracture while characterizing the fracture process.
Experimental characterization of crack tip deformation fields in Alloy 718 at high temperatures
Liu, J.; Lyons, J.; Sutton, M.; Reynolds, A.
1998-01-01
A series of fracture mechanics tests were conducted at temperatures of 650 C and 704 C in air, using Inconel 719. A noncontacting measurement technique, based on computer vision and digital image correlation, was applied to directly measure surface displacements and strains prior to and during creep crack growth. For the first time, quantitative comparisons at elevated temperatures are presented between experimentally measured near-crack-tip deformation fields and theoretical linear elastic and viscoelastic fracture mechanics solutions. The results establish that linear elastic conditions dominate the near-crack-tip displacements and strains at 650 C during crack growth, and confirm that K{sub 1} is a viable continuum-based fracture parameter for creep crack growth characterization. Postmortem fractographic analyses indicate that grain boundary embrittlement leads to crack extension before a significant amount of creep occurs at this temperature. At higher temperatures, however, no crack growth was observed due to crack tip blunting and concurrent stress reduction after load application.
NASA Astrophysics Data System (ADS)
Cervera, M.; Lafontaine, N.; Rossi, R.; Chiumenti, M.
2016-06-01
This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P1P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.
NASA Astrophysics Data System (ADS)
Cervera, M.; Lafontaine, N.; Rossi, R.; Chiumenti, M.
2016-09-01
This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields ( P1 P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.
NASA Astrophysics Data System (ADS)
Miyoshi, Y.; van Lanen, E. P. A.; Dhallé, M. M. J.; Nijhuis, A.
2009-08-01
Two ITER-type Nb3Sn superconductor strands, one prepared with the bronze route and the other with the internal-tin route, were used to investigate the impact of filament cracking on the strand's transport properties. Careful mechanical polishing allowed unambiguous identification of the microscopic fractures of filaments caused by axial straining of the strands. After application of high axial tensile strain, densely and uniformly spaced cracks were observed in the bronze strand, while fewer but more correlated cracks occurred in the internal-tin strand. Crack initiation was observed in the bronze strand after an applied tensile strain of more than 0.8%, while for the internal-tin strand cracks were found already in the unloaded specimen, with further crack growth beyond 0.3% applied strain. With the Pacman strain device, the voltage-current characteristics at zero applied strain were measured after several successive applications of incrementally increasing tensile strain. Distinct dissimilarities in the voltage-current characteristics were observed between the dispersed and the collective crack distributions. We also modelled the influence of cracks on the voltage-current characteristics of the two strands by considering two limiting cases of the crack behaviour.
Multiple Cracks Propagate Simultaneously in Polymer Liquids in Tension.
Huang, Qian; Alvarez, Nicolas J; Shabbir, Aamir; Hassager, Ole
2016-08-19
Understanding the mechanism of fracture is essential for material and process design. While the initiation of fracture in brittle solids is generally associated with the preexistence of material imperfections, the mechanism for initiation of fracture in viscoelastic fluids, e.g., polymer melts and solutions, remains an open question. We use high speed imaging to visualize crack propagation in entangled polymer liquid filaments under tension. The images reveal the simultaneous propagation of multiple cracks. The critical stress and strain for the onset of crack propagation are found to be highly reproducible functions of the stretch rate, while the position of initiation is completely random. The reproducibility of conditions for fracture points to a mechanism for crack initiation that depends on the dynamic state of the material alone, while the crack profiles reveal the mechanism of energy dissipation during crack propagation. PMID:27588883
Treatment of singularities in a middle-crack tension specimen
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Raju, I. S.
1990-01-01
A three-dimensional finite-element analysis of a middle-crack tension specimen subjected to mode I loading was performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements with collapsed nonsingular elements at the crack front. The displacements and stresses from the analysis were used to estimate the power of singularities, by a log-log regression analysis, along the crack front. Analyses showed that finite-sized cracked bodies have two singular stress fields. Because of two singular stress fields near the free surface and the classical square root singularity elsewhere, the strain energy release rate appears to be an appropriate parameter all along the crack front.
Haddad, R.E.; Dorado, A.O.
1994-12-31
This paper describes the tests conducted to determine the conditions leading to cracking of a specified grain of metal, during the iodine stress corrosion cracking (SCC) of zirconium alloys, focusing on the crystallographic orientation of crack paths, the critical stress conditions, and the significance of the fractographic features encountered. In order to perform crystalline orientation of fracture surfaces, a specially heat-treated Zircaloy-4 having very large grains, grown up to the wall thickness, was used. Careful orientation work has proved that intracrystalline pseudo-cleavage occurs only along basal planes. the effects of anisotropy, plasticity, triaxiality, and residual stresses originated in thermal contraction have to be considered to account for the influence of the stress state. A grain-by-grain calculation led to the conclusion that transgranular cracking always takes place on those bearing the maximum resolved tensile stress perpendicular to basal planes. Propagation along twin boundaries has been identified among the different fracture modes encountered.
Elevated temperature crack growth
NASA Technical Reports Server (NTRS)
Kim, K. S.; Vanstone, R. H.
1992-01-01
The purpose of this program was to extend the work performed in the base program (CR 182247) into the regime of time-dependent crack growth under isothermal and thermal mechanical fatigue (TMF) loading, where creep deformation also influences the crack growth behavior. The investigation was performed in a two-year, six-task, combined experimental and analytical program. The path-independent integrals for application to time-dependent crack growth were critically reviewed. The crack growth was simulated using a finite element method. The path-independent integrals were computed from the results of finite-element analyses. The ability of these integrals to correlate experimental crack growth data were evaluated under various loading and temperature conditions. The results indicate that some of these integrals are viable parameters for crack growth prediction at elevated temperatures.
Slow crack propagation in glass and creep prediction
NASA Astrophysics Data System (ADS)
Mallet, Celine; Fortin, Jerome; Gueguen, Yves
2013-04-01
The context of our study is the observation of the time-dependent deformation of cracked glass. The aim of our study is to observe the slow crack propagation, to quantify it and to predict finally the creep behavior. We performed creep experiments in compaction conditions in a triaxial cell, on cracked boro-silicate glass samples. The chemical composition of the investigated glass is very close to the composition of waste vitrified packages. The matrix of the original glass (OG) is perfectly amorphous, without porosity. A few isolated air bubbles are trapped during the glass flow. Cracks are introduced in the OG through thermal shocks. Strain and acoustic emission (AE) are recorded. Several experiments are performed at different confining pressures (15 or 25 MPa), different pore fluid conditions (with argon gas, considered as the dry case, with tap water saturated porosity, or with distilled water) and different temperatures (ambiant temperature, 50oC or 80oC). Linear increase of the volumetric strain is first observed. A dilatancy increase is recorded. Note that dilatancy does not appear in constant strain rate tests. Constant stress tests show that dilatancy develops during a time interval that depends on the stress level. In addition AE rate are recorded. A non zero AE rate is an evidence of crack propagation. We use a micro-mechanical model that gives the stress intensity factor at the crack tips. This factor depends on stress and geometrical parameters (all known). An exponential law describe the rate of crack propagation, as a function of temperature, environment and applied stresses. This model allows us to predict the creep rate in glass. Assuming a constant crack aspect ratio, crack length and volumetric strain are related. The volumetric strain rate is calculated from model and compared to the data.
CRACK MODELLING FOR RADIOGRAPHY
Chady, T.; Napierala, L.
2010-02-22
In this paper, possibility of creation of three-dimensional crack models, both random type and based on real-life radiographic images is discussed. Method for storing cracks in a number of two-dimensional matrices, as well algorithm for their reconstruction into three-dimensional objects is presented. Also the possibility of using iterative algorithm for matching simulated images of cracks to real-life radiographic images is discussed.
Crack Modelling for Radiography
NASA Astrophysics Data System (ADS)
Chady, T.; Napierała, L.
2010-02-01
In this paper, possibility of creation of three-dimensional crack models, both random type and based on real-life radiographic images is discussed. Method for storing cracks in a number of two-dimensional matrices, as well algorithm for their reconstruction into three-dimensional objects is presented. Also the possibility of using iterative algorithm for matching simulated images of cracks to real-life radiographic images is discussed.
Duisters, H.A.M. )
1994-01-01
This paper presents experimental data on the thermal cracking of butadiene in a pilot plant, under conditions representative of industrial operation. The product distribution of pure-butadiene cracking is shown. Results from cocracking experiments in naphtha and C[sub 4]-raffinate are also presented. It is shown that butadiene cracking can be an interesting outlet for the increasing butadiene overcapacity in steam crackers. Some aspects of coke formation during butadiene pyrolysis are addressed as well.
NASA Technical Reports Server (NTRS)
Bass, B. R.; Pugh, C. E.; Swindeman, R. W.
1988-01-01
Applications of nonlinear techniques to the first series of six HSST wide-plate crack-arrest tests that were performed are described. The experiments include crack initiations at low temperatures and relatively long (20 cm) cleavage propagation phases which are terminated by arrest in high temperature regions. Crack arrest are then followed by ductile tearing events. Consequently, the crack front regions are exposed to wide ranges of strain rates and temperatures.
Thermoelastic finite element analysis of subsurface cracking due to sliding surface traction
Cho, S.S.; Komvopoulos, K.
1997-01-01
A linear elastic fracture mechanics analysis of subsurface crack propagation in a half-space subjected to moving thermomechanical surface traction was performed using the finite element method. The effect of frictional heating at the sliding surface on the crack growth behavior is analyzed in terms of the coefficient of friction, crack length-to-depth ratio, and Peclet number. The crack propagation characteristics are interpreted in light of results for the directions and magnitudes of the maximum shear and tensile stress intensity factor ranges, respectively. It is shown that, while frictional heating exhibits a negligible effect on the crack propagation direction, it increases the in-plane crack growth rate and reduces the critical crack length at the onset of out-of-plane crack growth at the right tip due to the tensile mechanism (kink formation). The effect of frictional heating becomes more pronounced with increasing contact friction, crack length-to-depth ratio, and Peclet number. Crack mechanism maps showing the occurrence of opening, slip, and stick regions between the crack surfaces are presented for different values of crack length-to-depth ratio, coefficient of friction, and position of thermomechanical surface traction.
The Effect of Water on Crack Interaction
NASA Astrophysics Data System (ADS)
Gaede, O.; Regenauer-Lieb, K.
2009-04-01
parallel crack configurations and assume that the solute transport in the solid phase is diffusion limited. First, the stress field around the crack-tip is modeled. In a second step, the stress field is used to determine the chemical potential gradient and subsequently the diffusion process is modeled. In order to obtain the effective elastoplastic stress-strain relations for a cracked solid with hydrolytic weakening, the numerical results for the individual cracks are upscaled with an effective medium approximation. We follow the approach of Chernyakov et al. (2003) and incorporate the size of the process zone via the Dugdale crack model. We show that a chemical reaction, such as hydrolytic weakening, changes the overall effective mechanical properties of a cracked solid. The time scale of this change is a function of the diffusion and reaction rates. These rates themselves are dependent on other environment variables such as temperature and pressure. References: D. T. Griggs and J. D. Blacic, 1965. Quartz: Anomalous Weakness of Synthetic Crystals. Science 147, 292-295. Y.A. Chernyakov, V. Grychanyuk and I. Tsukrov, 2003. Stress-strain relations in elastoplastic solids with Dugdale-type cracks. Engineering Fracture Mechanics 70, 2163-2174.
Micromechanisms of fatigue crack propagation in particulate-reinforced metal-matrix composites
Shang, Jianku.
1989-01-01
Consequences of the interaction of cracks with SiC particles are examined with emphasis on micromechanisms influencing fatigue crack propagation in high strength aluminum alloy matrix composites. Fatigue crack propagation is found to show three distinct regimes; each accompanied by growth mechanisms reflecting different roles of SiC particles. At near-threshold levels, SiC particles impeded fatigue crack growth by deflecting the crack to promote roughness-induced crack closure and by acting as crack traps along the crack front. A two-dimensional crack trapping analysis based on the interaction of a finite crack with a SiC particle indicates that a limiting criterion for fatigue crack growth in SiC{sub p}/Al composites can be established, which requires that the maximum plastic-zone size exceed the effective mean particle size or that the tensile stress in the matrix beyond the particle on the crack front exceed the yield strength of the material. Implications of crack closure and crack trapping to near-threshold crack growth, including load-ration and particle-size dependence of fatigue thresholds, are discussed in terms of contributions from each mechanism. At higher stress intensities, limited fracture of SiC particles ahead of the crack tip leads to the development of uncracked ligaments along the crack length, resulting in a reduced crack-tip stress intensity from ligament bridging. Micromechanical models are developed for such bridges induced by both overlapping cracks and co-planar ligaments, based on the notion of a limiting crack opening displacement or limiting strain in the ligament. The predicted reduction in crack tip stress intensity is shown to be consistent with experimental observations.
Deformations and strains in adhesive joints by moire interferometry
NASA Technical Reports Server (NTRS)
Post, D.; Czarnek, R.; Wood, J.; John, D.; Lubowinski, S.
1984-01-01
Displacement fields in a thick adherend lap joint and a cracked lap shear specimen were measured by high sensitivity moire interferometry. Contour maps of in-plane U and V displacements were obtained across adhesive and adherent surfaces. Loading sequences ranged from modest loads to near-failure loads. Quantitative results are given for displacements and certain strains in the adhesive and along the adhesive/adherend boundary lines. The results show nonlinear displacements and strains as a function of loads or stresses and they show viscoelastic or time-dependent response. Moire interferometry is an excellent method for experimental studies of adhesive joint performance. Subwavelength displacement resolution of a few micro-inches, and spatial resolution corresponding to 1600 fringes/inch (64 fringes/mm), were obtained in these studies. The whole-field contour maps offer insights not available from local measurements made by high sensitivity gages.
NASA Astrophysics Data System (ADS)
Shang, Jian Ku; Ritchie, R. O.
1989-05-01
Micro-mechanisms of crack-tip shielding associated with the growth of fatigue cracks in metalmatrix composites are examined with specific emphasis on the role of crack bridging by uncracked ligaments. Simple analytical models are developed for such bridging induced by both overlapping cracks and by coplanar ligaments in the wake of the crack tip; the models are based on respective notions of a critical tensile strain or critical crack-opening displacement in the ligament. The predicted degree of shielding derived from these mechanisms is not large, but is found to be consistent with experimental observations in high-strength P/M aluminum alloys reinforced with 15 to 20 vol pct of SiC particulate.
Quantifying weld solidification cracking susceptibility using the varestraint test
Lin, W.; Lippold, J.C.; Nelson, T.W.
1994-12-31
Since the introduction of the original Varestraint concept in the 1960`s, the longitudinal- and transverse-type Varestraint tests have become the most widely utilized techniques for quantifying weld solidification cracking susceptibility. Conventionally, cracking susceptibility is assessed by threshold strain to cause cracking and the degree of cracking as quantified by total crack strain to cause cracking and the degree of cracking as quantified by total crack length or maximum crack length. Although material-specific quantifications such as the brittle temperature range (BTR) have been proposed for the transverse-type test, similar quantifications have not been developed for the longitudinal type test. Various alloys including 304, 310, 316L, A-286, AL6XN, 20Cb-3, RA253, and RA333 stainless steels, 625, 690, and 718 nickel-base alloys, 2090, 2219, 5083, and 6061 aluminum alloys were investigated using both longitudinal- and transverse-type Varestraint tests. Tests were performed using a newly developed, computer-controlled Varestraint unit equipped with a 3-axis movable torch, spring-loaded fixture and a servo-hydraulic loading system. It was found that extensive cracking was observed in the fusion zone emanating radially from the solid-liquid inteface toward the fusion boundary in the longitudinal-type test, while weld centerline cracking was prevalent in the transverse-type test. The theoretical basis for the formation of the CSR is that liquation-related cracking only occurs in a certain temperature range known as the BTR. The detailed procedure in the development of the CSR in the fusion zone is described and discussed. This approach allows a weldability data base to be created and the comparison of results from different laboratories using different test techniques.
Transient Elastodynamic Crack Growth in Functionally Graded Materials
Chalivendra, Vijaya B.
2008-02-15
A generalized elastic solution for an arbitrarily propagating transient crack in Functionally Graded Materials (FGMs) is obtained through an asymptotic analysis. The shear modulus and mass density of the FGM are assumed to vary exponentially along the gradation direction. The mode-mixity due to the inclination of property gradient with respect to the propagating crack tip is accommodated in the analysis through superposition of the opening and shear modes. First three terms of out of plane displacement field and its gradients about the crack tip are obtained in powers of radial coordinates, with the coefficients depending on the time rate of change of crack tip speed and stress intensity factors. Using these displacement fields, the effect of transient stress intensity factors and acceleration on synthetic contours of constant out of plane displacement under both opening and mixed mode loading conditions has been studied. These contours show that the transient terms cause significant spatial variation on out of plane displacements around the crack tip. Therefore, in studying dynamic fracture of FGMs, it is appropriate to include the transient terms in the field equations for the situations of sudden variation of stress intensity factor or crack tip velocity.
Castelluccio, Gustavo M.; McDowell, David L.
2015-05-22
The number of cycles required to form and grow microstructurally small fatigue cracks in metals exhibits substantial variability, particularly for low applied strain amplitudes. This variability is commonly attributed to the heterogeneity of cyclic plastic deformation within the microstructure, and presents a challenge to minimum life design of fatigue resistant components. Our paper analyzes sources of variability that contribute to the driving force of transgranular fatigue cracks within nucleant grains. We also employ crystal plasticity finite element simulations that explicitly render the polycrystalline microstructure and Fatigue Indicator Parameters (FIPs) averaged over different volume sizes and shapes relative to the anticipated fatigue damage process zone. Volume averaging is necessary to both achieve description of a finite fatigue damage process zone and to regularize mesh dependence in simulations. Furthermore, results from constant amplitude remote applied straining are characterized in terms of the extreme value distributions of volume averaged FIPs. Grain averaged FIP values effectively mitigate mesh sensitivity, but they smear out variability within grains. Furthermore, volume averaging over bands that encompass critical transgranular slip planes appear to present the most attractive approach to mitigate mesh sensitivity while preserving variability within grains.
Castelluccio, Gustavo M.; McDowell, David L.
2015-05-22
The number of cycles required to form and grow microstructurally small fatigue cracks in metals exhibits substantial variability, particularly for low applied strain amplitudes. This variability is commonly attributed to the heterogeneity of cyclic plastic deformation within the microstructure, and presents a challenge to minimum life design of fatigue resistant components. Our paper analyzes sources of variability that contribute to the driving force of transgranular fatigue cracks within nucleant grains. We also employ crystal plasticity finite element simulations that explicitly render the polycrystalline microstructure and Fatigue Indicator Parameters (FIPs) averaged over different volume sizes and shapes relative to the anticipatedmore » fatigue damage process zone. Volume averaging is necessary to both achieve description of a finite fatigue damage process zone and to regularize mesh dependence in simulations. Furthermore, results from constant amplitude remote applied straining are characterized in terms of the extreme value distributions of volume averaged FIPs. Grain averaged FIP values effectively mitigate mesh sensitivity, but they smear out variability within grains. Furthermore, volume averaging over bands that encompass critical transgranular slip planes appear to present the most attractive approach to mitigate mesh sensitivity while preserving variability within grains.« less
Crack Detection with Lamb Wave Wavenumber Analysis
NASA Technical Reports Server (NTRS)
Tian, Zhenhua; Leckey, Cara; Rogge, Matt; Yu, Lingyu
2013-01-01
In this work, we present our study of Lamb wave crack detection using wavenumber analysis. The aim is to demonstrate the application of wavenumber analysis to 3D Lamb wave data to enable damage detection. The 3D wavefields (including vx, vy and vz components) in time-space domain contain a wealth of information regarding the propagating waves in a damaged plate. For crack detection, three wavenumber analysis techniques are used: (i) two dimensional Fourier transform (2D-FT) which can transform the time-space wavefield into frequency-wavenumber representation while losing the spatial information; (ii) short space 2D-FT which can obtain the frequency-wavenumber spectra at various spatial locations, resulting in a space-frequency-wavenumber representation; (iii) local wavenumber analysis which can provide the distribution of the effective wavenumbers at different locations. All of these concepts are demonstrated through a numerical simulation example of an aluminum plate with a crack. The 3D elastodynamic finite integration technique (EFIT) was used to obtain the 3D wavefields, of which the vz (out-of-plane) wave component is compared with the experimental measurement obtained from a scanning laser Doppler vibrometer (SLDV) for verification purposes. The experimental and simulated results are found to be in close agreement. The application of wavenumber analysis on 3D EFIT simulation data shows the effectiveness of the analysis for crack detection. Keywords: : Lamb wave, crack detection, wavenumber analysis, EFIT modeling
Thermal cracking and amplitude dependent attenuation
Johnston, D.H.; Toksoez, M.N.
1980-02-10
The role of crack and grain boundary contacts in determining seismic wave attenuation in rock is investigated by examining Q as a function of thermal cycling (cracking) and wave strain amplitude. Q values are obtained using a longitudinal resonant bar technique in the 10- to 20-kHz range for maximum strain amplitudes varying from roughly 10/sup -8/ to 10/sup -5/. The samples studied include the Berea and Navajo sandstones, Plexiglas, Westerly granite, Solenhofen limestone, and Frederick diabase, the latter two relatively crack free in their virgin state. Measurements were made at room temperature and pressure in air. Q values for both sandstones are constant at low strains (<10/sup -6/) but decrease rapidly with amplitude at higher strains. There is no hysteresis of Q with amplitude. Q values for Plexiglas show no indication of amplitude dependent behavior. The granite, limestone, and diabase are thermally cycled at both fast and slow heating rates in order to induce cracking. Samples slowly cycled at 400/sup 0/C show a marked increase in Q that cannot be entirely explained by outgassing of volatiles. Cycling may also widen thin cracks and grain boundaries, reducing contact areas. Samples heated beyond 400/sup 0/C, or rapidly heated, result in generally decreasing Q values. The amplitude dependence of Q is found to be coupled to the effects of thermal cycling. For rock slowly cycled 400)C or less, the transition from low-amplitude contant Q to high-amplitude variable Q behavior decreases to lower amplitudes as a function of maximum temperature. Above 400/sup 0/C, and possibly in th rapidly heated samples also, the transition moves to higher amplitudes.
Results of crack-arrest tests on irradiated a 508 class 3 steel
Iskander, S.K.; Milella, P.P.; Pini, M.A.
1998-02-01
Ten crack-arrest toughness values for irradiated specimens of A 508 class 3 forging steel have been obtained. The tests were performed according to the American Society for Testing and Materials (ASTM) Standard Test Method for Determining Plane-Strain Crack-Arrest Fracture Toughness, K{sub la} of Ferritic Steels, E 1221-88. None of these values are strictly valid in all five ASTM E 1221-88 validity criteria. However, they are useful when compared to unirradiated crack-arrest specimen toughness values since they show the small (averaging approximately 10{degrees}C) shifts in the mean and lower-bound crack-arrest toughness curves. This confirms that a low copper content in ASTM A 508 class 3 forging material can be expected to result in small shifts of the transition toughness curve. The shifts due to neutron irradiation of the lower bound and mean toughness curves are approximately the same as the Charpy V-notch (CVN) 41-J temperature shift. The nine crack-arrest specimens were irradiated at temperatures varying from 243 to 280{degrees}C, and to a fluence varying from 1.7 to 2.7 x 10{sup 19} neutrons/cm{sup 2} (> 1 MeV). The test results were normalized to reference values that correspond to those of CVN specimens irradiated at 284{degrees}C to a fluence of 3.2 x 10{sup 19} neutrons/cm{sup 2} (> 1 MeV) in the same capsule as the crack-arrest specimens. This adjustment resulted in a shift to lower temperatures of all the data, and in particular moved two data points that appeared to lie close to or lower than the American Society of Mechanical Engineers K{sub la} curve to positions that seemed more reasonable with respect to the remaining data. A special fixture was designed, fabricated, and successfully used in the testing. For reasons explained in the text, special blocks to receive the Oak Ridge National Laboratory clip gage were designed, and greater-than-standard crack-mouth opening displacements measured were accounted for. 24 refs., 13 figs., 12 tabs.
Separation of crack extension modes in orthotropic delamination models
NASA Technical Reports Server (NTRS)
Beuth, Jack L.
1995-01-01
In the analysis of an interface crack between dissimilar elastic materials, the mode of crack extension is typically not unique, due to oscillatory behavior of near-tip stresses and displacements. This behavior currently limits the applicability of interfacial fracture mechanics as a means to predict composite delamination. The Virtual Crack Closure Technique (VCCT) is a method used to extract mode 1 and mode 2 energy release rates from numerical fracture solutions. The mode of crack extension extracted from an oscillatory solution using the VCCT is not unique due to the dependence of mode on the virtual crack extension length, Delta. In this work, a method is presented for using the VCCT to extract Delta-independent crack extension modes for the case of an interface crack between two in-plane orthotropic materials. The method does not involve altering the analysis to eliminate its oscillatory behavior. Instead, it is argued that physically reasonable, Delta-independent modes of crack extension can be extracted from oscillatory solutions. Knowledge of near-tip fields is used to determine the explicit Delta dependence of energy release rate parameters. Energy release rates are then defined that are separated from the oscillatory dependence on Delta. A modified VCCT using these energy release rate definitions is applied to results from finite element analyses, showing that Delta-independent modes of crack extension result. The modified technique has potential as a consistent method for extracting crack extension modes from numerical solutions. The Delta-independent modes extracted using this technique can also serve as guides for testing the convergence of finite element models. Direct applications of this work include the analysis of planar composite delamination problems, where plies or debonded laminates are modeled as in-plane orthotropic materials.
Super-stretchable metallic interconnects on polymer with a linear strain of up to 100%
NASA Astrophysics Data System (ADS)
Arafat, Yeasir; Dutta, Indranath; Panat, Rahul
2015-08-01
Metal interconnects in flexible and wearable devices are heterogeneous metal-polymer systems that are expected to sustain large deformation without failure. The principal strategy to make strain tolerant interconnect lines on flexible substrates has comprised of creating serpentine structures of metal films with either in-plane or out-of-plane waves, using porous substrates, or using highly ductile materials such as gold. The wavy and helical serpentine patterns preclude high-density packing of interconnect lines on devices, while ductile materials such as Au are cost prohibitive for real world applications. Ductile copper films can be stretched if bonded to the substrate, but show high level of cracking beyond few tens of % strain. In this paper, we demonstrate a material system consisting of Indium metal film over an elastomer (PDMS) with a discontinuous Cr layer such that the metal interconnect can be stretched to extremely high linear strain (up to 100%) without any visible cracks. Such linear strain in metal interconnects exceeds that reported in literature and is obtained without the use of any geometrical manipulations or porous substrates. Systematic experimentation is carried out to explain the mechanisms that allow the Indium film to sustain the high strain level without failure. The islands forming the discontinuous Cr layer are shown to move apart from each other during stretching without delamination, providing strong adhesion to the Indium film while accommodating the large strain in the system. The Indium film is shown to form surface wrinkles upon release from the large strain, confirming its strong adhesion to PDMS. A model is proposed based upon the observations that can explain the high level of stretch-ability of the Indium metal film over the PDMS substrate.
Super-stretchable metallic interconnects on polymer with a linear strain of up to 100%
Arafat, Yeasir; Dutta, Indranath; Panat, Rahul
2015-08-24
Metal interconnects in flexible and wearable devices are heterogeneous metal-polymer systems that are expected to sustain large deformation without failure. The principal strategy to make strain tolerant interconnect lines on flexible substrates has comprised of creating serpentine structures of metal films with either in-plane or out-of-plane waves, using porous substrates, or using highly ductile materials such as gold. The wavy and helical serpentine patterns preclude high-density packing of interconnect lines on devices, while ductile materials such as Au are cost prohibitive for real world applications. Ductile copper films can be stretched if bonded to the substrate, but show high level of cracking beyond few tens of % strain. In this paper, we demonstrate a material system consisting of Indium metal film over an elastomer (PDMS) with a discontinuous Cr layer such that the metal interconnect can be stretched to extremely high linear strain (up to 100%) without any visible cracks. Such linear strain in metal interconnects exceeds that reported in literature and is obtained without the use of any geometrical manipulations or porous substrates. Systematic experimentation is carried out to explain the mechanisms that allow the Indium film to sustain the high strain level without failure. The islands forming the discontinuous Cr layer are shown to move apart from each other during stretching without delamination, providing strong adhesion to the Indium film while accommodating the large strain in the system. The Indium film is shown to form surface wrinkles upon release from the large strain, confirming its strong adhesion to PDMS. A model is proposed based upon the observations that can explain the high level of stretch-ability of the Indium metal film over the PDMS substrate.
Stress intensity factors in a cracked infinite elastic wedge loaded by a rigid punch
NASA Technical Reports Server (NTRS)
Erdogan, F.; Civelek, M. B.
1978-01-01
A plane elastic wedge-shaped solid was split through the application of a rigid punch. It was assumed that the coefficient of friction on the the contact area was constant, and the problem had a plane of symmetry with respect to loading and geometry, with the crack in the plane of symmetry. The problem was formulated in terms of a system of integral equations with the contact stress and the derivative of the crack surface displacement as the unknown functions. The solution was obtained for an internal crack and for an edge crack. The results include primarily the stress intensity factors at the crack tips, and the measure of the stress singularity at the wedge apex, and at the end points of the contact area.
Periodic cracking of films supported on compliant substrates
Thouless, M. D.; Li, Z.; Douville, N. J.; Takayama, S.
2011-01-01
When a tensile strain is applied to a film supported on a compliant substrate, a pattern of parallel cracks can channel through both the film and substrate. A linear-elastic fracture-mechanics model for the phenomenon is presented to extend earlier analyses in which cracking was limited to the film. It is shown how failure of the substrate reduces the critical strain required to initiate fracture of the film. This effect is more pronounced for relatively tough films. However, there is a critical ratio of the film to substrate toughness above which stable cracks do not form in response to an applied load. Instead, catastrophic failure of the substrate occurs simultaneously with the propagation of a single channel crack. This critical toughness ratio increases with the modulus mismatch between the film and substrate, so that periodic crack patterns are more likely to be observed with relatively stiff films. With relatively low values of modulus mismatch, even a film that is more brittle than the substrate can cause catastrophic failure of the substrate. Below the critical toughness ratio, there is a regime in which stable crack arrays can be formed in the film and substrate. The depth of these arrays increases, while the spacing decreases, as the strain is increased. Eventually, the crack array can become deep enough to cause substrate failure. PMID:21927507
NASA Technical Reports Server (NTRS)
Chudnovsky, A.
1987-01-01
A damage parameter is introduced in addition to conventional parameters of continuum mechanics and consider a crack surrounded by an array of microdefects within the continuum mechanics framework. A system consisting of the main crack and surrounding damage is called crack layer (CL). Crack layer propagation is an irreversible process. The general framework of the thermodynamics of irreversible processes are employed to identify the driving forces (causes) and to derive the constitutive equation of CL propagation, that is, the relationship between the rates of the crack growth and damage dissemination from one side and the conjugated thermodynamic forces from another. The proposed law of CL propagation is in good agreement with the experimental data on fatigue CL propagation in various materials. The theory also elaborates material toughness characterization.
NASA Technical Reports Server (NTRS)
Chudnovsky, A.
1984-01-01
A damage parameter is introduced in addition to conventional parameters of continuum mechanics and consider a crack surrounded by an array of microdefects within the continuum mechanics framework. A system consisting of the main crack and surrounding damage is called crack layer (CL). Crack layer propagation is an irreversible process. The general framework of the thermodynamics of irreversible processes are employed to identify the driving forces (causes) and to derive the constitutive equation of CL propagation, that is, the relationship between the rates of the crack growth and damage dissemination from one side and the conjugated thermodynamic forces from another. The proposed law of CL propagation is in good agreement with the experimental data on fatigue CL propagation in various materials. The theory also elaborates material toughness characterization.
Fracture of surface cracks loaded in bending
Chao, Y.J.; Reuter, W.G.
1997-12-31
Theoretical background of the constraint effect in brittle fracture of solids is reviewed. Fracture test data from D6-aC, a high strength steel, using three-point-bend (SE(B)) specimens and surface cracked plate (SC(B)) specimens under bending are presented. It is shown that the SE(B) data has an elevated fracture toughness for increasing a/W, i.e., a crack geometry with a larger T/K corresponds to a higher K{sub c} which is consistent with the theoretical prediction. The fundamental fracture properties, i.e., the critical strain and the critical distance, determined from the SE(B) test data are then applied to the interpretation and prediction of the SC(B) test data. Reasonable agreement is achieved for the crack growth initiation site and the load.
Comparative Analysis of Uniaxial Strain Shock Tests and Taylor Tests for Armor and Maraging Steels
NASA Astrophysics Data System (ADS)
Mescheryakov, Yu. I.; Zhigacheva, N. I.; Petrov, Yu. A.; Divakov, A. K.; Cline, C. F.
2004-07-01
High-strength constructional 38KhN3MFA steel and 02H18К9M5-BИ maraging steel were tested to determine the yield stress under dynamic loading. The 38KhN3MFA steel was used as central test material to work out the experimental technique. For both kinds of steel the results obtained in the plane shock tests under uniaxial strain condition show approximately the identical yield stress values as those obtained in Taylor tests. Cracking of maraging steel occurs along the shock-induced austenite bands where microhardness is much smaller than that for the rest of the matrix.
Further Study of near Solidus Intergranular Cracking in Inconel 718
NASA Technical Reports Server (NTRS)
Thompson, R. G.
1981-01-01
A series of tests, performed to determine the strain necessary to initiate intergranular cracking in Inconel 718 as a function of temperature, contained enough scatter near the melting temperature that questions remained as to the best curve of curves to fit to the data. Fracture surface analysis showed that the scatter was due to incipient melting in the grain boundary region. The melting contributed to low fracture strain but had only a small on the incipient cracking strain. Gleeble tests, which could be interrupted by water quenching, were used to study the incipient intergranular melting of Inconel 718. This modified weld simulation test provided a sufficiently rapid quench to preserve the intergranular microstructure created during incipient melting. This structure was studied both microscopically and with energy dispensive X-ray analysis. The implications of incipient melting and low-strain incipient cracking on the development of microfissuring envelopes are discussed.
An analysis of ductile rupture modes at a crack tip
NASA Astrophysics Data System (ADS)
Needleman, A.; Tvergaard, V.
A N ELASTIC-VISCOPLASTIC model of a ductile, porous solid is used to study the influence of the nucleation and growth of micro-voids in the material near the tip of a crack. Conditions of small scale yielding are assumed, and the numerical analyses of the stress and strain fields are based on finite strain theory, so that crack tip blunting is fully accounted for. An array of large inclusions or inclusion colonies, with a relatively low strength, results in large voids near the crack tip at a rather early stage, whereas small second phase particles in the matrix material between the inclusions require large strains before cavities nucleate. Various distributions of the large inclusions, and various critical strains for nucleation of the small scale voids between the inclusions, are considered. Localization of plastic flow plays an important role in determining the failure path between the crack tip and the nearest larger void, and the path is strongly sensitive to the distribution of the large inclusions. Values of the J-integral and the crack opening displacement at fracture initiation are estimated, together with values of the tearing modulus during crack growth, and these values are related to experimental results.
Contributions of aging to the fatigue crack growth resistance of human dentin.
Ivancik, Juliana; Majd, Hessam; Bajaj, Devendra; Romberg, Elaine; Arola, Dwayne
2012-07-01
An evaluation of the fatigue crack resistance of human dentin was conducted to identify the degree of degradation that arises with aging and the dependency on tubule orientation. Fatigue crack growth was achieved in specimens of coronal dentin through application of Mode I cyclic loading and over clinically relevant lengths (0 ≤ a ≤ 2 mm). The study considered two directions of cyclic crack growth in which the crack was either in-plane (0°) or perpendicular (90°) to the dentin tubules. Results showed that regardless of tubule orientation, aging of dentin is accompanied by a significant reduction in the resistance to the initiation of fatigue crack growth, as well as a significant increase in the rate of incremental extension. Perpendicular to the tubules, the fatigue crack exponent increased significantly (from m=14.2 ± 1.5 to 24.1 ± 5.0), suggesting an increase in brittleness of the tissue with age. For cracks extending in-plane with the tubules, the fatigue crack growth exponent does not change significantly with patient age (from m=25.4 ± 3.03 to 22.9 ± 5.3), but there is a significant increase in the incremental crack growth rate. Regardless of age, coronal dentin exhibits the lowest resistance to fatigue crack growth perpendicular to the tubules. While there are changes in the cyclic crack growth rate and mechanisms of cyclic extension with aging, this tissue maintains its anisotropy. PMID:22484693
Contributions of Aging to the Fatigue Crack Growth Resistance of Human Dentin
Ivancik, Juliana; Majd, Hessam; Bajaj, Devendra; Romberg, Elaine; Arola, Dwayne
2012-01-01
An evaluation of the fatigue crack resistance of human dentin was conducted to identify the degree of degradation that arises with aging and the dependency on tubule orientation. Fatigue crack growth was achieved in specimens of coronal dentin through application of Mode I cyclic loading and over clinically relevant lengths (0 ≤ a ≤ 2 mm). The study considered two directions of cyclic crack growth in which the crack was either in-plane (0°) or perpendicular (90°) to the dentin tubules. Results showed that regardless of tubule orientation, aging of dentin is accompanied by a significant reduction in the resistance to the initiation of fatigue crack growth, as well as a significant increase in the rate of incremental extension. Perpendicular to the tubules, the fatigue crack exponent increased significantly (from m=14.2±1.5 to 24.1±5.0), suggesting an increase in brittleness of the tissue with age. For cracks extending in plane with the tubules, the fatigue crack growth exponent does not change significantly with patient age (from m=25.4±3.03 to 22.9±5.3), but there is a significant increase in the incremental crack growth rate. Regardless of age, coronal dentin exhibits the lowest resistance to fatigue crack growth perpendicular to the tubules. While there are changes in the cyclic crack growth rate and mechanisms of cyclic extension with aging, this tissue maintains its anisotropy. PMID:22484693
Effect of crack surface geometry on fatigue crack closure
Drury, W.J.; Gokhale, A.M.; Antolovich, S.D.
1995-10-01
The geometry of crack faces often plays a critical role in reducing crack extension forces when crack closure occurs during fatigue crack growth. Most previous studies of fatigue crack closure are concerned with mechanical measure of closure as related to the crack growth rate; very little attention has been given to the geometry of the crack surfaces. The objective is to identify those aspects of crack surface geometry that are important in the closure process, to develop quantitative fractographic techniques to estimate such attributes in a statistically significant and robust manner, and to correlate them to the physical process of crack closure. For this purpose, fatigue crack propagation experiments were performed on a Ni-base superalloy and crack growth rates and crack closure loads were measured. Digital image profilometry and software-based analysis techniques were used for statistically reliable and detailed quantitative characterization of fatigue crack profiles. It is shown that the dimensionless, scale-independent attributes, such a height-to-width ratio of asperities, fractal dimensions, dimensionless roughness parameters, etc., do not represent the aspects of crack geometry that are of primary importance in the crack closure phenomena. Furthermore, it is shown that the scale-dependent characteristics, such as average asperity height, do represent the aspects of crack geometry that play an interactive role in the closure process. These observations have implications concerning the validity of geometry-dependent, closure-based models for fatigue crack growth.
Effect of crack surface geometry on fatigue crack closure
NASA Astrophysics Data System (ADS)
Drury, W. J.; Gokhale, Arun M.; Antolovich, S. D.
1995-10-01
The geometry of crack faces often plays a critical role in reducing crack extension forces when crack closure occurs during fatigue crack growth. Most previous studies of fatigue crack closure are concerned with mechanical measures of closure as related to the crack growth rate; very little attention has been given to the geometry of the crack surfaces. Our objective is to identify those aspects of crack surface geometry that are important in the closure process, to develop quantitative fractographic techniques to estimate such attributes in a statistically significant and robust manner, and to correlate them to the physical process of crack closure. For this purpose, fatigue crack propagation experiments were performed on a Ni-base superalloy and crack growth rates and crack closure loads were measured. Digital image profilometry and software-based analysis techniques were used for statistically reliable and detailed quantitative characterization of fatigue crack profiles. It is shown that the dimensionless, scale-independent attributes, such as height-to-width ratio of asperities, fractal dimensions, dimensionless roughness parameters, etc., do not represent the aspects of crack geometry that are of primary importance in the crack closure phenomena. Furthermore, it is shown that the scaledependent characteristics, such as average asperity height, do represent the aspects of crack geometry that play an interactive role in the closure process. These observations have implications concerning the validity of geometry-dependent, closure-based models for fatigue crack growth.
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.
NASA Technical Reports Server (NTRS)
Bray, G. H.; Reynolds, A. P.; Starke, E. A., Jr.
1992-01-01
In ingot metallurgy (IM) alloys, the number of delay cycles following a single tensile overload typically increases from a minimum at an intermediate baseline stress intensity range, Delta-K(B), with decreasing Delta-K(B) approaching threshold and increasing Delta-K(B) approaching unstable fracture to produce a characteristic 'U' shaped curve. Two models have been proposed to explain this behavior. One model is based on the interaction between roughness and plasticity-induced closure, while the other model only utilizes plasticity-induced closure. This article examines these models, using experimental results from constant amplitude and single overload fatigue tests performed on two powder metallurgy (PM) aluminum alloys, AL-905XL and AA 8009. The results indicate that the 'U'-shaped curve is primarily due to plasticity-induced closure, and that the plasticity-induced retardation effect is through-thickness in nature, occurring in both the surface and interior regions. However, the retardation effect is greater at the surface, because the increase in plastic strain at the crack tip and overload plastic zone size are larger in the plane-stress surface regions than in the plane-strain interior regions. These results are not entirely consistent with either of the proposed models.
Experiments with Planing Surfaces
NASA Technical Reports Server (NTRS)
Sottorf, W
1934-01-01
A previous report discusses the experimental program of a systematic exploration of all questions connected with the planing problem as well as the first fundamental results of the investigation of a flat planing surface. The present report is limited to the conversion of the model test data to full scale.
Gladrow, E.M.; Winter, W.E.
1980-04-29
The octane number of a cracked naphtha can be significantly improved in a catalytic cracking unit, without significant decrease in naphtha yield, by maintaining certain critical concentrations of metals on the catalyst, suitably by blending or adding a heavy metals-containing component to the gas oil feed. Suitably, in a catalytic cracking process unit wherein a gas oil feed is cracked in a cracking reactor (Zone) at an elevated temperature in the presence of a cracking catalyst, the cracking catalyst is regenerated in a regenerator (Regeneration zone) by burning coke off the catalyst, and catalyst is circulated between the reactor and regenerator, sufficient of a metals-containing heavy feedstock is admixed, intermittantly or continuously, with the gas oil feed to deposit metals on said catalyst and raise the metals-content of said catalyst to a level of from about 1500 to about 6000 parts per million, preferably from about 2500 to about 4000 parts per million expressed as equivalent nickel, base the weight of the catalyst, and said metals level is maintained on the catalyst throughout the operation by withdrawing high metals-containing catalyst and adding low metals-containing catalyst to the regenerator.
Treatment of singularities in cracked bodies
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Raju, I. S.
1989-01-01
Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.
Treatment of singularities in cracked bodies
NASA Technical Reports Server (NTRS)
Shivakumar, K. N.; Raju, I. S.
1990-01-01
Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.
Analysis of reinforced concrete structures with occurrence of discrete cracks at arbitrary positions
NASA Technical Reports Server (NTRS)
Blaauwendraad, J.; Grootenboer, H. J.; Bouma, A. L.; Reinhardt, H. W.
1980-01-01
A nonlinear analysis of in-plane loaded plates is presented, which eliminates the disadvantages of the smeared crack approach. The elements used and the computational method are discussed. An example is shown in which one or more discrete cracks are dominant.
An interferometric strain-displacement measurement system
NASA Technical Reports Server (NTRS)
Sharpe, William N., Jr.
1989-01-01
A system for measuring the relative in-plane displacement over a gage length as short as 100 micrometers is described. Two closely spaced indentations are placed in a reflective specimen surface with a Vickers microhardness tester. Interference fringes are generated when they are illuminated with a He-Ne laser. As the distance between the indentations expands or contracts with applied load, the fringes move. This motion is monitored with a minicomputer-controlled system using linear diode arrays as sensors. Characteristics of the system are: (1) gage length ranging from 50 to 500 micrometers, but 100 micrometers is typical; (2) least-count resolution of approximately 0.0025 micrometer; and (3) sampling rate of 13 points per second. In addition, the measurement technique is non-contacting and non-reinforcing. It is useful for strain measurements over small gage lengths and for crack opening displacement measurements near crack tips. This report is a detailed description of a new system recently installed in the Mechanisms of Materials Branch at the NASA Langley Research Center. The intent is to enable a prospective user to evaluate the applicability of the system to a particular problem and assemble one if needed.
Size effects and strain localization in atomic-scale cleavage modeling.
Elsner, B A M; Müller, S
2015-09-01
In this work, we study the adhesion and decohesion of Cu(1 0 0) surfaces using density functional theory (DFT) calculations. An upper stress to surface decohesion is obtained via the universal binding energy relation (UBER), but the model is limited to rigid separation of bulk-terminated surfaces. When structural relaxations are included, an unphysical size effect arises if decohesion is considered to occur as soon as the strain energy equals the energy of the newly formed surfaces. We employ the nudged elastic band (NEB) method to show that this size effect is opposed by a size-dependency of the energy barriers involved in the transition. Further, we find that the transition occurs via a localization of bond strain in the vicinity of the cleavage plane, which resembles the strain localization at the tip of a sharp crack that is predicted by linear elastic fracture mechanics. PMID:26219654
Environmentally assisted cracking in light water reactors
Shack, W.J.; Kassner, T.F.; Maiya, P.S.; Park, J.Y.; Ruther, W.E.
1988-10-01
Research during the past year focused on (1) stress corrosion cracking (SCC) of austentitic stainless steels (SS), (2) fatigue of Type 316NG SS, and (3) SCC of ferritic steels used in reactor piping, pressure vessels, and steam generators. Stress corrosion cracking studies on austentitic SS explored the critical strains required for crack initiation, the effects of crevice conditions on SCC susceptibility, heat-to-heat variations in SCC susceptibility of Type 316NG and modified Type 347 SS, the effect of heat treatment on the susceptibility of Type 347 SS, threshold stress intensity values for crack growth in Type 316NG SS, and the effects of cuprous ion and several organic salts on the SCC of sensitized Type 304 SS. Crevice conditions were observed to strongly promote SCC. Significant heat-to-heat variations were observed in SCC susceptibility of Types 316NG and 347 SS. No correlation was found between SCC behavior and minor variations in chemical composition. A significant effect of heat treatment was observed in Type 347 SS. A heat that was extremely resistant to SCC after heat treatment at 650/degree/C for 24 h was susceptible to transgranular stress corrosion cracking (TGSCC) in the solution-annealed condition. Although there was no sensitization in either condition, the presence or absence of precipitates and differences in precipitate morphology appear to influence the SCC behavior. 20 refs., 20 figs., 11 tabs.
Enhanced Strength via crack friction and Pressure
NASA Astrophysics Data System (ADS)
Wiegand, Donald; Ellis, Kevin; Leppard, Claire
2011-03-01
The effect of pressure on the mechanical response of particulate polymer composites is being studied. Between about 0.1 and 7 MPa for one composite the results indicate that slow crack growth is the dominant failure mode. With continuously creasing strain at low pressures the stress initially increases to a maximum, the compressive strength, then decreases indicating work softening and them becomes approximately constant at a plateau value. Both the compressive strength and the plateau stress increases linearly with pressure but the plateau stress increases with a steeper slope such that at higher pressures work softening is not observed. The results are analyzed in terms of shear cracks with friction between the crack surfaces. The model predicts a threshold stress for crack growth which increases linearly with pressure and further predicts that the compressive strength increases linearly with pressure as observed and with the same slope as the threshold stress. These results clearly indicate that the pressure dependence of the compressive strength is due to the pressure dependence of the threshold stress for crack growth. The changes in the plateau region can also be attributed to frictional effects. Supported by AWE Aldermaston.
Short fatigue crack behavior in notched 2024-T3 aluminum specimens
NASA Technical Reports Server (NTRS)
Lee, J. J.; Sharpe, W. N., Jr.
1986-01-01
Single-edge, semi-circular notched specimens of Al 2024-T3, 2.3 mm thick, were cyclicly loaded at R-ratios of 0.5, 0.0, -1.0, and -2.0. The notch roots were periodically inspected using a replica technique which duplicates the bore surface. The replicas were examined under an optical microscope to determine the initiation of very short cracks and to monitor the growth of short cracks ranging in length from a few tens of microns to the specimen thickness. In addition to short crack growth measurements, the crack opening displacement (COD) was measured for surface cracks as short as 0.035 mm and for through-thickness cracks using the Interferometric Strain/Displacement Gage (ISDG), a laser-based optical technique. The growth rates of short cracks were faster than the long crack growth rates for R-ratios of -1.0 and -2.0. No significant difference between short and long crack growth rates was observed for R = 0.0. Short cracks had slower growth rates than long cracks for R = 0.5. The crack opening stresses measured for short cracks were smaller than those predicted for large cracks, with little difference appearing for positive R-ratios and large differences noted for negative R-ratios.
Creep crack growth behavior of aluminum alloy 2519. Part 2: Numerical analysis
Hall, D.E.; Hamilton, B.C.; McDowell, D.L.; Saxena, A.
1997-12-31
The experimental analysis of high temperature fracture in Aluminum Alloy 2519-T87 presented in Part 1 of this paper highlighted the creep-brittle fracture characteristics of the material and showed reasonable correlation of crack growth rates with the stress intensity factor K. Part 2 continues this investigation numerically using growing crack finite element analyses. Experimentally observed crack growth histories of four aluminum 2519-T87 compact specimens are enforced by controlling the rate of release of finite element nodes along the crack growth path to gain insight into the relation of the crack tip fields to far field fracture parameters and to crack growth rates. A variable time-step, nodal-release algorithm is presented to model the high strain rates that occur during the initial stages of crack growth. The numerical results indicate an initial transient period of crack growth followed by a quasi-steady-state crack growth regime in which the crack tip fields change slowly with increasing crack length. Transition of crack growth to the quasi-steady-state regime, where similitude and small-scale creep conditions roughly exist, is given by a transition time t{sub g} that depends on the crack growth history and material properties. Excellent correlation of the stress intensity factor K with the crack growth rates is observed after time t{sub g}. Experimental difficulties in measuring the creep component of the load-line deflection rate are also discussed.
Environmentally assisted cracking in light water reactors.
Chopra, O. K.; Chung, H. M.; Clark, R. W.; Gruber, E. E.; Shack, W. J.; Soppet, W. K.; Strain, R. V.
2007-11-06
This report summarizes work performed by Argonne National Laboratory on fatigue and environmentally assisted cracking (EAC) in light water reactors (LWRs) from January to December 2002. Topics that have been investigated include: (a) environmental effects on fatigue crack initiation in carbon and low-alloy steels and austenitic stainless steels (SSs), (b) irradiation-assisted stress corrosion cracking (IASCC) of austenitic SSs in BWRs, (c) evaluation of causes and mechanisms of irradiation-assisted cracking of austenitic SS in PWRs, and (d) cracking in Ni-alloys and welds. A critical review of the ASME Code fatigue design margins and an assessment of the conservation in the current choice of design margins are presented. The existing fatigue {var_epsilon}-N data have been evaluated to define the effects of key material, loading, and environmental parameters on the fatigue lives of carbon and low-alloy steels and austenitic SSs. Experimental data are presented on the effects of surface roughness on fatigue crack initiation in these materials in air and LWR environments. Crack growth tests were performed in BWR environments on SSs irradiated to 0.9 and 2.0 x 10{sup 21} n x cm{sup -2}. The crack growth rates (CGRs) of the irradiated steels are a factor of {approx}5 higher than the disposition curve proposed in NUREG-0313 for thermally sensitized materials. The CGRs decreased by an order of magnitude in low-dissolved oxygen (DO) environments. Slow-strain-rate tensile (SSRT) tests were conducted in high-purity 289 C water on steels irradiated to {approx}3 dpa. The bulk S content correlated well with the susceptibility to intergranular SCC in 289 C water. The IASCC susceptibility of SSs that contain >0.003 wt. % S increased drastically. bend tests in inert environments at 23 C were conducted on broken pieces of SSRT specimens and on unirradiated specimens of the same materials after hydrogen charging. The results of the tests and a review of other data in the literature
Crack Instability Predictions Using a Multi-Term Approach
NASA Technical Reports Server (NTRS)
Zanganeh, Mohammad; Forman, Royce G.
2015-01-01
Present crack instability analysis for fracture critical flight hardware is normally performed using a single parameter, K(sub C), fracture toughness value obtained from standard ASTM 2D geometry test specimens made from the appropriate material. These specimens do not sufficiently match the boundary conditions and the elastic-plastic constraint characteristics of the hardware component, and also, the crack instability of most commonly used aircraft and aerospace structural materials have some amount of stable crack growth before fracture which makes the normal use of a K(sub C) single parameter toughness value highly approximate. In the past, extensive studies have been conducted to improve the single parameter (K or J controlled) approaches by introducing parameters accounting for the geometry or in-plane constraint effects. Using 'J-integral' and 'A' parameter as a measure of constraint is one of the most accurate elastic-plastic crack solutions currently available. In this work the feasibility of the J-A approach for prediction of the crack instability was investigated first by ignoring the effects of stable crack growth i.e. using a critical J and A and second by considering the effects of stable crack growth using the corrected J-delta a using the 'A' parameter. A broad range of initial crack lengths and a wide range of specimen geometries including C(T), M(T), ESE(T), SE(T), Double Edge Crack (DEC), Three-Hole-Tension (THT) and NC (crack from a notch) manufactured from Al7075 were studied. Improvements in crack instability predictions were observed compared to the other methods available in the literature.
Achenbach, J.D.
1989-09-15
In work carried out on this project, the usual mathematical modeling of ultrasonic wave scattering by flaws is being extended to account for several typical characteristics of fatigue and stress-corrosion cracks, and the environment of such cracks. Work has been completed on scattering by macrocrack-microcrack configurations. We have also investigated reflection and transmission by a flaw plane consisting of an infinite array of randomly oriented cracks. In another investigation the propagation of mechanical disturbances in solids with periodically distributed cracks has been studied.
Stress corrosion cracking of zirconium used in the reprocessing plant
Kato, Chiaki; Motooka, Takafumi; Yamamoto, Masahiro
2007-07-01
We investigated stress corrosion cracking (SCC) of zirconium by constant load test and the small-scale mock-up test simulated the fuel dissolve. These tests operated in the simulated solution, which substituted non-radioactive elements, i.e. V with radioactive elements such as Pu and Np. From the results of constant load test, the cracks were not observed on 150 MPa after 908 hours in approximately 3 % strain. However a lot of cracks caused by SCC were observed over 20 % strain under high tensile stress in the simulated solution and the heat-transfer condition having more corrosive circumstance and noble potential accelerated the susceptibility of SCC. The cracking behavior would be caused by the creep phenomena. The small-scale mock-up test had been operated for about 50000 hours during 7 year. From the results, zirconium showed excellent corrosion resistance and no SCC was observed during these long-term operations. (authors)
Spiral and croissant crack in drying thin films
NASA Astrophysics Data System (ADS)
Marthelot, Joel; Roman, Benoit; Bico, Jose; Barthel, Etienne; Teisseire, Jeremie; Dalmas, Davy; Melo, Francisco
2012-02-01
Drying mud or crazing in ceramics glaze leads to familiar hierarchical cracks network where a new crack connects perpendicularly to older ones. We report unusual spirals and croissants crack patterns in methylsiloxane drying thin films moderately adhering on a substrate. Such cracks are also observed in a very different situation when magnetron sputtering multilayers are under external tension. The amplitude and wavelength of the pattern are robusts and are orders of magnitude larger than the thickness of the layer. The propagation of the spiral and croissant cracks occurs in a narrow range of adhesion energy between the film and the substrate and strain in the film. We will show how the propagation is driven by a cooperation between fracture and adhesion.
Quantity Effect of Radial Cracks on the Cracking Propagation Behavior and the Crack Morphology
Chen, Jingjing; Xu, Jun; Liu, Bohan; Yao, Xuefeng; Li, Yibing
2014-01-01
In this letter, the quantity effect of radial cracks on the cracking propagation behavior as well as the circular crack generation on the impacted glass plate within the sandwiched glass sheets are experimentally investigated via high-speed photography system. Results show that the radial crack velocity on the backing glass layer decreases with the crack number under the same impact conditions during large quantities of repeated experiments. Thus, the “energy conversion factor” is suggested to elucidate the physical relation between the cracking number and the crack propagation speed. Besides, the number of radial crack also takes the determinative effect in the crack morphology of the impacted glass plate. This study may shed lights on understanding the cracking and propagation mechanism in laminated glass structures and provide useful tool to explore the impact information on the cracking debris. PMID:25048684