stress corrosion cracking susceptibility were conducted on materials after plastic strain levels of 1, 3, and 5% were achieved in tensile blanks...impact toughness, fracture toughness, fatigue, stress corrosion cracking and weldability of ASTM A710 Grade A Class 3 steel plate in thicknesses...Caustics Measurements 6. Crack Velocity as a Function of the Instantaneous Stress Intensity Factor for HOMALITE-100 7. Crack Arrest Toughness Plotted as
Needleman, A.; Shi, Z.; Ben-Zion, Y.
We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gradually overstressing a localized nucleation zone. Our simulations with model parameters representative of Homalite-100 indicate that different values of parameters controlling the velocity dependence of friction, the strength excess parameter and the length of the nucleation zone, can lead to the following four rupture modes: supershear crack-like rupture, subshear crack-like rupture, subshear single pulse and supershear train of pulses. High initial shear stress and weak velocity dependence of friction favor crack-like ruptures, while the opposite conditions favor the pulse mode. The rupture mode can switch from a subshear single pulse to a supershear train of pulses when the width of the nucleation zone increases. The elastic strain energy released over the same propagation distance by the different rupture modes has the following order: supershear crack, subshear crack, supershear train of pulses and subshear single pulse. The same order applies also to the ratio of kinetic energy (radiation) to total change of elastic energy for the different rupture modes. Decreasing the dynamic coefficient of friction increases the fraction of stored energy that is converted to kinetic energy. In the current study we use model parameters representative of rocks instead of Homalite-100, by modeling recent results of Kilgore et al. (2007) who measured and estimated various energy components in laboratory friction experiments with granite. We are also incorporating into the code ingredients that will allow us to study rupture properties and energy partition for cases with a bimaterial interface and dynamic generation of plastic strain
Ghosh, S.; Raju, J.; Dwivedi, K. K.
Studies of particle tracks in solids have wide ranging applications in many diverse fields of science and technology. Most of these studies require a precise knowledge of heavy ion track lengths or ranges in various knowledge of heavy ion track lengths or ranges in various commonly used solid dielectrics. We have measured the maximum etchable track lengths of 132Xe at 12 different energies ranging from 5.8 MeV/u to 17.0 MeV/u in CR-39 (Homalite). The ion beam with an initial energy of 17.0 MeV/u was degraded by aluminium foils of different thickness. The detectors were irradiated at an angle of 45° to the beam direction and were etched for a period of 2?6 hrs in 6N NaOH at 55°C to reveal the tracks. The track lengths were measured using an optical microscope and the maximum etchable track lengths were determined. The standard deviations have been evaluated and the experimental results are compared with theoretical values obtained from computer codes ?RANGE? and ?TRIM? and the program of Henke and Benton.
Mello, M.; Bhat, H. S.; Rosakis, A. J.; Kanamori, H.
The near field ground motion signatures associated with sub-Rayleigh and supershear ruptures are investigated using the laboratory earthquake experiment originally developed by Rosakis and coworkers (Xia et al., 2004, 2005a; Lu et al., 2007; Rosakis et al., 2007). Heterodyne laser interferometers enable continuous, high bandwidth measurements of fault-normal (FN) and fault-parallel (FP) particle velocity "ground motion" records at discrete locations on the surface of a Homalite test specimen as a sub-Rayleigh or a supershear rupture sweeps along the frictional fault. Photoelastic interference fringes, acquired using high-speed digital photography, provide a synchronized, spatially resolved, whole field view of the advancing rupture tip and surrounding maximum shear stress field. Experimental results confirm that near field ground motion records associated with the passage of a sub-Rayleigh rupture are characterized by a FN velocity swing which dominates over the FP velocity swing. The situation is shown to reverse in the supershear rupture speed regime whereby the motion along the shear Mach front is characterized by a FP particle velocity swing which dominates over the FN velocity swing. Additional distinguishing particle velocity signatures, consistent with theoretical and numerical predictions, and repeatedly observed in experimental records are (1) a pronounced peak in the FP velocity record, induced by the leading dilatational field, which sweeps the measurement station just prior to the arrival of the shear Mach front, and (2) a pronounced velocity swing in the FN record associated with the arrival of a "trailing Rayleigh disturbance", which sweeps the measurement station following passage of the shear Mach front. Each of these features are addressed in detail. We conclude by reexamining the 2002, Mw7.9 Denali fault earthquake and the remarkable set of ground motion records obtained at Pump Station 10 (PS10), located approximately 85 km east of the epicenter
Templeton, Elizabeth L.; Baudet, AuréLie; Bhat, Harsha S.; Dmowska, Renata; Rice, James R.; Rosakis, Ares J.; Rousseau, Carl-Ernst
We analyze the nucleation and propagation of shear cracks along nonplanar, kinked, and branched fault paths corresponding to the configurations used in recent laboratory fracture studies by Rousseau and Rosakis (2003, 2009). The aim is to reproduce numerically those shear rupture experiments and from that provide an insight into processes which are active when a crack, initially propagating in mode II along a straight path, interacts with a bend in the fault or a branching junction. The experiments involved impact loading of thin Homalite-100 (a photoelastic polymer) plates, which had been cut along bent or branched paths and weakly glued back together everywhere except along a starter notch near the impact site. Strain gage recordings and high-speed photography of isochromatic lines provided characterization of the transient deformation fields associated with the impact and fracture propagation. We found that dynamic explicit 2-D plane-stress finite element analyses with a simple linear slip-weakening description of cohesive and frictional strength of the bonded interfaces can reproduce the qualitative rupture behavior past the bend and branch junctions in most cases and reproduce the principal features revealed by the photographs of dynamic isochromatic line patterns. The presence of a kink or branch can cause an abrupt change in rupture propagation velocity. Additionally, the finite element results allow comparison between total slip accumulated along the main and inclined fault segments. We found that slip along inclined faults can be substantially less than slip along the main fault, and the amount depends on the branch angle and kink or branch configuration.
Rubino, V.; Rosakis, A.; Lapusta, N.
Dynamic imaging of strain and stress during rupture enables unprecedented observations of key rupture features as well as decoding the nature of friction. We present the dynamic evolution of strains and stresses in our dynamic rupture experiments. We employ a laboratory earthquake setup to study dynamic ruptures in a highly instrumented setting, where we produce both supershear and sub-Rayleigh events. Earthquakes are mimicked in the laboratory by dynamic rupture propagating along the inclined frictional interface of two quadrilateral Homalite plates prestressed in compression and shear. The diagnostics previously employed in this setup include temporally accurate but spatially sparse laser velocimetry measurements as well as a sequence of full-field photoelastic images. These measurements have been successfully employed to capture important rupture features but they do not give enough information to characterize the full-field strains and stresses. In this study, we obtain the experimental sequences of full-field displacements, velocities, strains and stresses produced under a wide range of slip rates by our newly developed technique of ultra high-speed digital image correlation (DIC). This is the first technique capable of imaging spatial and temporal variations in strains and stresses during spontaneously developing experimental dynamic rupture. This technique combines pattern-matching algorithms with ultra-high-speed photography and highly tailored analysis to obtain full-field time histories. We have verified the accuracy of the measurements by comparing the velocity time-histories at selected locations with the measurements using the well-developed technique of laser velocimetry. The newly developed ultra-high-speed full-field imaging technique can also be used to obtain unprecedented measurements of evolving dynamic friction during dynamic rupture, and we will report on our initial results on the dynamic friction evolution.
Templeton, E. L.; Baudet, A.; Bhat, H. S.; Rice, J. R.
The study of dynamically propagating shear cracks along weak paths like faults is of great interest for the study of earthquakes. We adapted the ABAQUS/Explicit dynamic finite element program to analyze the nucleation and propagation of shear cracks along a non-planar, kinked, weak path corresponding to the one that was used in recent laboratory fracture studies by Rousseau and Rosakis [JGR, 2003]. Their experiments involved impact loading of thin plates of Homalite-100, a photoelastically sensitive brittle polymer, which had been cut along a kinked path and then weakly glued back together everywhere except along a starter notch near the impact site. Under different conditions, propagation speeds were observed in both the sub-Rayleigh and intersonic (supershear) regimes. Strain gage recordings and high speed photography of isochromatic lines (lines of constant difference between the in-plane principal strains) provided characterization of the transient deformation fields associated with the impact and fracture propagation. For the finite element analyses, we implemented a slip-weakening failure model through an option in the ABAQUS program allowing user defined constitutive relations. The analyses of impact loading and of rupture nucleation and propagation were then carried out in the 2D framework of plane stress. In a first set of studies of nucleation and propagation of rupture along a straight fault, we determined after some trial and error an appropriate CFL number, and examined different element types and layouts, finding that the most acceptable results were obtained for low order elements. We used constant strain triangles, arrayed in groups of four to effectively form four-sided elements with corner nodes and one internal node. The studies also showed that to obtain representations of slip rate and shear stress near the propagating rupture tip that were relatively free from numerical oscillations, it was necessary to have element side lengths of order Ro/50
Dynamic crack growth along weak planes is a significant mode of failure in composites and other layered/sandwiched structures and is also the principal mechanism of shallow crustal earthquakes. In order to shed light on this phenomenon dynamic crack initiation and propagation characteristics of a model fiber-reinforced unidirectional graphite/epoxy composite plate was investigated experimentally. Dynamic fracture experiments were conducted by subjecting the composite plates to in-plane, symmetric and asymmetric, impact loading. The lateral shearing interferometric technique of coherent gradient sensing (CGS) in conjunction with high-speed photography was used to visualize the failure process in real time. It was found that mode-I cracks propagated subsonically with crack speeds increasing to the neighborhood of the Rayleigh wave speed of the composite. Also in mode-I, the dependence of the dynamic initiation fracture toughness on the loading rate was determined and was found to be constant for low loading rates and to increase rapidly above K˙dI>10 5 . The dynamic crack propagation toughness, KID, was observed to decrease with crack tip speed up to the Rayleigh wave speed of the composite. For asymmetric, mode-II, types of loading the results revealed highly unstable and intersonic shear-dominated crack growth along the fibers. These cracks propagated with unprecedented speeds reaching 7400 m/s which is the dilatational wave speed of the composite along the fibers. For intersonic crack growth, the interferograms, featured a shock wave structure typical of disturbances traveling with speeds higher than one of the characteristic wave speeds in the solid. In addition high speed thermographic measurements are conducted that show concentrated hot spots behind the crack tip indicating non-uniform crack face frictional contact. In addition, shear dominated dynamic crack growth is investigated along composite/Homalite interfaces subjected to impact loading. The crack
Rubino, V.; Lapusta, N.; Rosakis, A.
Mapping full-field displacements and strains on the Earth's surface during an earthquake is of paramount importance to enhance our understanding of earthquake mechanics. In this study, the feasibility of such measurements using image correlation methods is investigated in a laboratory earthquake setup. Earthquakes are mimicked in the laboratory by dynamic rupture propagating along an inclined frictional interface formed by two Homalite plates under compression, using the configuration developed by Rosakis and coworkers (e.g., Rosakis et al., 2007). In our study, the interface is partially glued, in order to confine the rupture before it reaches the ends of the specimen. The specimens are painted with a speckle pattern to provide the surface with characteristic features for image matching. Images of the specimens are taken before and after dynamic rupture with a 4 Megapixels resolution CCD camera. The digital images are analyzed with two software packages: VIC-2D (Correlated Solutions Inc.) and COSI-Corr (Leprince et. al, 2007). Both VIC-2D and COSI-Corr are able to characterize the full-field static displacement of a dynamic crack. For example, in a case with secondary mode I cracks, the correlation analysis performed with either software clearly shows (i) the relative displacement (slip) along the frictional interface, (ii) the rupture arrest on the glued boundaries, and (iii) the presence of two wing cracks. The obtained displacement measurements are converted to strains, using de-noising techniques. The digital image correlation method is then used in combination with high-speed photography. We will report our progress on the study of a spontaneously expanding sub-Rayleigh shear crack advancing along an interface containing a patch of favorable heterogeneity, such as a preexisting subcritical crack or a patch with higher prestress. According to the predictions of Liu and Lapusta (2008), intersonic transition and propagation can be achieved in the presence of a
The near-field ground motion signatures associated with sub-Rayleigh and supershear ruptures are investigated using the laboratory earthquake experiment originally developed by Rosakis and co-workers (Xia et al., 2004, 2005; Lu et al., 2007; Rosakis et al., 2007). Heterodyne laser interferometers enable continuous, high-bandwidth measurements of fault-normal (FN), fault-parallel (FP), and vertical (V) particle velocity ``ground motion" records at discrete locations on the surface of a Homalite-100 test specimen as a sub-Rayleigh or a supershear rupture sweeps along the frictional fault. Photoelastic interference fringes, acquired using high-speed digital photography, provide a synchronized, spatially resolved, whole field view of the advancing rupture tip and surrounding maximum shear stress field. The first phase of experimental investigations examine and verify the ground motion signatures of supershear ruptures. Experimental results demonstrate that a shear Mach front produced by a stable supershear rupture is characterized by a dominant FP velocity component. The situation is shown to reverse in the sub-Rayleigh rupture speed regime whereby the FN particle velocity component dominates the ground motion record. Additional distinguishing particle velocity signatures, consistent with theoretical and numerical predictions, and repeatedly observed in experimental records are, (1) a pronounced peak in the FP velocity record induced by the leading dilatational field, which sweeps the measurement station in advance of the shear Mach front, and (2) a pronounced velocity swing in the FN record associated with the arrival of a trailing Rayleigh sub-Rayleigh (secondary) rupture, which follows the arrival of the shear Mach front. Analysis of the particle velocity records also confirms 2D steady-state theoretical predictions pertaining to the separation, attenuation, and radiation partitioning of the shear and dilatational portions of the rupture velocity field components
Templeton, E. L.; Baudet, A.; Bhat, H. S.; Dmowska, R.; Rice, J. R.; Rosakis, A. J.; Rousseau, C. E.
The study of dynamically propagating shear cracks along geometrically complex paths is important to understanding the mechanics of earthquakes. Recent laboratory fracture studies of Rousseau and Rosakis examined a branched configuration, analogous to their study of rupture along a bent fault path [Rousseau and Rosakis, JGR, 2003], to enhance understanding of the behavior of a shear rupture approaching the intersection of two paths. Whereas crack motion along a simple bent path is readily explained by means of the energy available to sustain the propagating crack, or through a crack tip stress field criterion, the behavior of multiple paths displays more intricate variations featuring the inability of the crack to extend along secondary paths situated at shallow angles with respect to the initial direction of propagation. Secondary paths located at larger angles, on the extensional side, generally promote simultaneous extension along both paths beyond the junction, in contrast to preferred motion along the straight path, which is favored when secondary paths are situated on the compressional side. The experiments involve impact loading of thin plates of Homalite-100, a photoelastic polymer, which are cut along branched paths and weakly glued back together everywhere except along a starter notch near the impact site. High-speed photography of isochromatic fringe patterns (lines of constant difference between in-plane principal stresses) characterized the transient deformation field associated with the impact and rupture propagation. We adapted the ABAQUS/Explicit dynamic finite element program to analyze the propagation of shear cracks along such branched weakened paths. Two configurations for weakened paths, branches at 35° to the compressional side and the extensional side, were analyzed. We implemented a linear slip-weakening failure model as a user-defined constitutive relation within the ABAQUS program, where weakening could be included in either or both of (1
Lu, X.; Lapusta, N.; Rosakis, A. J.
Friction laws are typically introduced either based on theoretic ideas or by fitting laboratory experiments that reproduce only a small subset of possible behaviors. Hence it is important to validate the resulting laws by modeling experiments that produce spontaneous frictional behavior. Here we simulate experiments of spontaneous rupture transition from sub-Rayleigh to supershear done by Xia et al. (Science, 2004). In the experiments, two thin Homalite plates are pressed together along an inclined interface. Compressive load P is applied to the edges of the plates and the rupture is triggered by an explosion of a small wire. Xia et al. (2004) link the transition in their experiments to the Burridge-Andrews mechanism (Andrews, JGR, 1976) which involves initiation of a daughter crack in front of the main rupture. Xia et al. have measured transition lengths for different values of the load P and compared their results with numerical simulations of Andrews who used linear slip-weakening friction. They conclude that to obtain a good fit they need to assume that the critical slip of the slip-weakening law scales as P-1/2, as proposed by Ohnaka (JGR, 2003). Hence our first goal is to verify whether the dependence of the critical slip on the compressive load P is indeed necessary for a good fit to experimental measurements. To test that, we conducted simulations of the experiments by using boundary integral methodology in its spectral formulation (Perrin et al., 1995; Geubelle and Rice, 1995). We approximately model the wire explosion by temporary normal stress decrease in the region of the interface comparable to the size of the exploding wire. The simulations show good agreement of the transition length with the experimental results for different values of the load P, even though we keep the critical slip constant. Hence the dependence of the critical slip on P is not necessary to fit the experimental measurements. The inconsistency between Andrews' numerical results