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1.
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. Different values of parameters controlling the velocity dependence of friction, the strength excess parameter and the length of the nucleation zone, 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. General considerations and observations suggest that the subshear pulse and supershear crack are, respectively, the most and least common modes of earthquake ruptures.  相似文献   

2.
Laser-generated stress wave profiles with rarefaction shocks (almost zero post-peak decay times) have been uncovered in different types of glasses and presented in this communication. The rise time of the pulses was found to increase with their amplitude, with values reaching as high as . This is in contrast to measurements in other brittle crystalline solids where pulses with rise times of and post-peak decay times of were recorded. The formation of rarefaction shock is attributed to the increased compressibility of glasses with increasing pressures. This was demonstrated using a one-dimensional nonlinear elastic wave propagation model in which the wave speed was taken as a function of particle velocity. The technological importance of these pulses in measuring the tensile strength of very thin film interfaces is demonstrated by using a previously developed laser spallation experiment in which a laser-generated compressive stress pulse in the substrate reflects into a tensile wave from the free surface of the film and pries off its interface at a threshold amplitude. Because of the rarefaction shock, glass-modified waves allow generation of substantially higher interfacial tensile stress amplitudes compared with those with finite post-peak decay profiles. Thus, for the first time, tensile strengths of very strong and ultra thin film interfaces can be measured. Results presented here indicate that interfaces of 185-nm-thick films, and with strengths as high as , can be measured. Thus, an important advance has been made that should allow material optimization of ultra thin layer systems that may form the basis of future MEMS-based microelectronic, mechanical and clinical devices.  相似文献   

3.
A laser interferometry-based technique was developed to locally measure the in-plane components of particle velocity in dynamic experiments. This technique was applied in the experimental investigation of dynamic sliding along the incoherent (frictional) interface of a Homalite–steel bimaterial structure. The bimaterial specimen was subjected to uniform compressive stress and impact-induced shear loading. The evolution of the dynamic stress field was recorded by high-speed photography in conjunction with dynamic photoelasticity. The combination of the full-field technique of photoelasticity with the local technique of velocimetry was proven to be a very powerful tool in the investigation of dynamic sliding. A relatively broad loading wave with an eye-like structure emanated from the interface. The particle velocity measurements established that sliding started behind the eye-like fringe pattern. It propagated with supershear speed with respect to Homalite. A shear Mach line originating from the sliding tip is visible in the photoelastic images. A vertical particle velocity measurement revealed the existence of a wrinkle-like pulse traveling along the bimaterial interface. The wrinkle-like pulse followed the initial shear rupture tip and propagated at a specific subshear speed.  相似文献   

4.
The present paper describes results of plate-impact pressure-shear friction experiments conducted to study time-resolved growth of molten metal films during dry metal-on-metal slip under extreme interfacial conditions. By employing tribo-pairs comprising hard tool-steel against relatively low melt-point metals such as 7075-T6 aluminum alloys, interfacial friction stress ranging from 100 to and slip speeds of approximately have been generated. These relatively high levels of friction stress combined with high slip-speeds generate conditions conducive for interfacial temperatures to approach the melting point of the lower melt point metal (Al alloy) comprising the tribo-pair.A Lagrangian finite element code is developed to understand the evolution of the thermo-mechanical fields and their relationship to the observed slip response. The code accounts for dynamic effects, heat conduction, contact with friction, and full thermo-mechanical coupling. At temperatures below the melting point the material is described as an isotropic thermally softening elastic-viscoplastic solid. For material elements with temperatures in excess of the melt point a purely Newtonian fluid constitutive model is employed.The results of the hybrid experimental-computational study provides new insights into the thermoelastic-plastic interactions during high speed metal-on-metal slip under extreme interfacial conditions. During the early part of frictional slip the coefficient of kinetic friction is observed to decrease with increasing slip velocity. During the later part transition in interfacial slip occurs from dry metal-on-metal sliding to the formation of molten Al films at the tribo-pair interface. Under these conditions the interfacial resistance approaches the shear strength of the molten aluminum alloy under normal pressures of approximately 1- and shear strain rates of . The results of the study indicate that under these extreme conditions molten aluminum films maintain a shearing resistance as high as .Scanning electron microscopy of the slip surfaces reveal molten aluminum to be smeared on the tribo-pair interface. Knoop hardness measurements in 7075-T6 Al alloy at various depths from the slip interface indicate that the hardness increases approximately linearly with depth and reaches a plateau at approximately from the surface.  相似文献   

5.
The dynamic behaviour of sharp V-notches which are either symmetric or oblique to the longitudinal boundary of a homogeneous elastic and isotropic strip subjected to an impact plane pulse was studied by the method of caustics. The stress pulse impinging on the flanks of the notch reflects and diffracts in different ways depending on the geometry of the notch relative to the coming pulse. For compressive stress pulses a stress concentration at the bottom of the notch does not create a crack propagation phenomenon, whereas for tensile pulses there is a possibility for an incubation, nucleation and eventual propagation of a crack. A complete experimental study of the incubation nucleation and propagation of cracks from the bottoms of notches in thin strips under tensile stress pulses was undertaken, whereas for compressive stress pulses the stress concentration at the bottom of the notch was evaluated. Interesting results were disclosed concerning the reinforcement of pulses by reflection and caging in, the evolution of stress concentration at the notch and the mode of crack propagation inside the plate. Dynamic stress intensity factors were evaluated all over the paths of crack propagation indicating a close intimacy between crack velocity and values of SIFs.  相似文献   

6.
We study, by experiments and modeling, the linear and geometric nonlinear behavior of thin-film bilayer mechanical structures subjected to thermal loading due to combined creep and stress relaxation. On the experimental side, we designed and fabricated a series of micron-scale gold ( thick)/polysilicon(1.5 and thick) beams and plates and initially thermal cycled them between room temperature and 190°C to stabilize the gold microstructure over this temperature range. After the initial thermal cycle, they are heated to 190°C where they are relatively flat, and then cooled to 120°C. During this temperature drop the thin film structures undergo linear and possibly geometrically nonlinear deformation depending on their size. They are then held at 120°C for about four weeks. During the thermal loading history we measured, using interferometry, full-field deformed shapes of the structures, from which curvature was determined. During the isothermal hold, creep and stress relaxation are observed in all of the structures, as manifested in significant curvature changes. We observe that both material and structural phenomena contribute to the observed deformation response. The interplay between the two is apparent in the plates where the initial cooling caused them to buckle, but the creep and stress relaxation then caused them to substantially unbuckle. We attempted to model the inelastic deformation by assuming simple power-law creep in the gold , and assuming that the polysilicon did not relax at the modest temperature of 120°C. In order to accurately account for the dependence of curvature and stress on position, we carried out the calculations using the finite element method. We find that with such a simple model we can qualitatively describe all of the observed phenomena, however, some quantitative discrepancies exist. Finally, we carried out a parametric study of the effects of the structure shape and the power-law creep constants on the deformation, and studied the evolution of the stress state in the films both through the thickness and in the plane of the beams and plates. Regarding the stress state, initially a significant stress gradient exists through the thickness of the films. Over time it becomes more uniform, and nearly constant in the creeping/relaxing metal film, but the gradient remains in the polysilicon film (that does not creep or relax).  相似文献   

7.
We employ a kinetic Monte Carlo algorithm to simulate the motion of -oriented screw dislocation on a -slip plane in body centered cubic Ta and Ta-based alloys. The dislocation moves by the kink model: double kink nucleation, kink migration and kink-kink annihilation. Rates of these unit processes are parameterized based upon existing first principles data. Both short-range (solute-dislocation core) and long-range (elastic misfit) interactions between the dislocation and solute are considered in the simulations. Simulations are performed to determine dislocation velocity as a function of stress, temperature, solute concentration, solute misfit and solute-core interaction strength. The dislocation velocity is shown to be controlled by the rate of nucleation of double kinks and the dependence of the double kink nucleation rate on stress and temperature are consistent with existing analytical predictions. In alloys, dislocation velocity depends on both the short- and long-range solute dislocation interactions as well as on the solute concentration. The short-range solute-core interactions are shown to dominate the effects of alloying on dislocation mobility. The present simulation method provides the critical link between atomistic calculations of fundamental dislocation and solute properties and large scale dislocation dynamics that typically employ empirical equations of motion.  相似文献   

8.
This study of the dynamic compressive strength properties of metal foams is in two parts. Part I presents data from an extensive experimental study of closed-cell Hydro/Cymat aluminium foam, which elucidates a number of key issues and phenomena. Part II focuses on modelling issues.The dynamic compressive response of the foam was investigated using a direct-impact technique for a range of velocities from 10 to . Elastic wave dispersion and attenuation in the pressure bar was corrected using a deconvolution technique.A new method of locating the point of densification in the nominal stress-strain curves of the foam is proposed, which provides a consistent framework for the definition of the plateau stress and the densification strain, both essential parameters of the ‘shock’ model in Part II. Data for the uniaxial, plastic collapse and plateau stresses are presented for two different average cell sizes of approximately 4 and 14 mm. They show that the plastic collapse strength of the foam changes significantly with compression rate. This phenomenon is discussed, and the distinctive roles of microinertia and ‘shock’ formation are described. The effects of compression rates on the initiation, development and distribution of cell crushing are also examined. Tests were carried out to examine the effects of density gradient and specimen gauge length at different rates of compression and the results are discussed. The origin of the conflicting conclusions in the literature on the correlation between nominal strain rate (ratio of the impact velocity Vi to the initial gauge length lo of the specimen) and the dynamic strength of aluminium alloy foams is identified and explained.  相似文献   

9.
The implementation of the characteristic of compressive plasticity into the Discrete Element Code, DM2, while maintaining its quasi-molecular scheme, is described. The code is used to simulate the shock compression of polycrystalline copper at 3.35 and 11.0 GPa. The model polycrystal has a normal distribution of grain sizes, with mean diameter 14 μm, and three distinct grain orientations are permitted with respect to the shock direction; 〈1 0 0〉, 〈1 1 0〉, and 〈1 1 1〉. Particle velocity dispersion (PVD) is present in the shock-induced flow, attaining its maximum magnitude at the plastic wave rise. PVD normalised to the average particle velocity of and are yielded for the 3.35 and 11.0 GPa shocks, respectively, and are of the same order as those seen in the experiment. Non-planar elastic and plastic wave fronts are present, the distribution in shock front position increasing with propagation distance. The rate of increase of the spread in shock front positions is found to be significantly smaller than that seen in probabilistic calculations on nickel polycrystals, and this difference is attributed, in the main, to grain interaction. Reflections at free surfaces yield a region of tension near to the target free surface. Due to the dispersive nature of the shock particle velocity and the non-planarity of the shock front, the tensile pressure is distributed. This may have implications for the spall strength, which are discussed. Simulations reveal a transient shear stress distribution behind the shock front. Such a distribution agrees with that put forward by Lipkin and Asay to explain the quasi-elastic reloading phenomenon. Simulation of reloading shocks show that the shear stress distribution can give rise to quasi-elastic reloading on the grain scale.  相似文献   

10.
Large electrostrictive actuation of barium titanate single crystals   总被引:1,自引:0,他引:1  
An experimental investigation of the electromechanical behavior of single crystals of the ferroelectric perovskite barium titanate is presented. An experimental setup has been designed to investigate large strain actuation in single crystal ferroelectrics subjected to combined electrical and mechanical loading. Experiments have been performed on initially single domain crystals of barium titanate with (100) and (001) orientation at compressive stresses between 0 and . Global strain and polarization histories have been recorded. The electrostrictive response is shown to be highly dependent on the level of applied stress with a maximum strain of 0.9% measured at a compressive stress of about and electric field of about . This level of strain is about 5 times higher than in typical commercial piezoelectric PZT. Polarized light microscopy has been used to observe the evolution of the domain pattern simultaneously with the strain and polarization measurement. The observations reveal that the observed large strain behavior is the result of 90° domain switching.  相似文献   

11.
We present atomistic simulations of the tensile and compressive loading of single crystal face-centered cubic (FCC) nanowires with and orientations to study the propensity of the nanowires to deform via twinning or slip. By studying the deformation characteristics of three FCC materials with disparate stacking fault energies (gold, copper and nickel), we find that the deformation mechanisms in the nanowires are a function of the intrinsic material properties, applied stress state, axial crystallographic orientation and exposed transverse surfaces. The key finding of this work is the first order effect that side surface orientation has on the operant mode of inelastic deformation in both and nanowires. Comparisons to expected deformation modes, as calculated using crystallographic Schmid factors for tension and compression, are provided to illustrate how transverse surface orientations can directly alter the deformation mechanisms in materials with nanometer scale dimensions.  相似文献   

12.
In order to construct a plate theory for a thick transversely compressible sandwich plate with composite laminated face sheets, the authors make simplifying assumptions regarding distribution of transverse strain components in the thickness direction. The in-plane stresses and σyy (Fig. 1) are computed from the constitutive equations, and the improved values of transverse stress components and σzz need to be computed by integration of pointwise equations of motion in a post-process stage of the finite element analysis. The improved values of the transverse strains can also be computed in the post-process stage by substituting the improved transverse stresses into the constitutive relations. A problem of cylindrical bending of a simply supported plate under a uniform load on the upper surface is considered, and comparison is made between the displacements, the in-plane stress and the improved transverse stresses (obtained by integration of the pointwise equations of motion), computed from the plate theory, with the corresponding values of exact elasticity solutions. In this comparison, a good agreement of both solutions is achieved. In the finite element analysis of sandwich plates in cylindrical bending with small thickness-to-length ratios, the shear locking phenomenon does not occur. The model of a sandwich plate in cylindrical bending, presented in this paper, has a wider range of applicability than the models presented in literature so far: it can be applied to the sandwich plates with a wide range of ratios of thickness to the in-plane dimensions, with both thin and thick face sheets (as compared to the thickness of the core) and to the sandwich plates with both transversely rigid and transversely compressible face sheets and cores.  相似文献   

13.
The purpose of this paper is to determine , the overall homogenized Love-Kirchhoff strength domain of a rigid perfectly plastic multi-layered plate, and to study the relationship between the 3D and the homogenized Love-Kirchhoff plate limit analysis problems. In the Love-Kirchhoff model, the generalized stresses are the in-plane (membrane) and the out-of-plane (flexural) stress field resultants. The homogenization method proposed by Bourgeois [1997. Modélisation numérique des panneaux structuraux légers. Ph.D. Thesis, University Aix-Marseille] and Sab [2003. Yield design of thin periodic plates by a homogenization technique and an application to masonry wall. C. R. Méc. 331, 641-646] for in-plane periodic rigid perfectly plastic plates is justified using the asymptotic expansion method. For laminated plates, an explicit parametric representation of the yield surface is given thanks to the π-function (the plastic dissipation power density function) that describes the local strength domain at each point of the plate. This representation also provides a localization method for the determination of the 3D stress components corresponding to every generalized stress belonging to . For a laminated plate described with a yield function of the form , where σu is a positive even function of the out-of-plane coordinate x3 and is a convex function of the local stress σ, two effective constants and a normalization procedure are introduced. A symmetric sandwich plate consisting of two Von-Mises materials ( in the skins and in the core) is studied. It is found that, for small enough contrast ratios (), the normalized strength domain is close to the one corresponding to a homogeneous Von-Mises plate [Ilyushin, A.-A., 1956. Plasticité. Eyrolles, Paris].  相似文献   

14.
Dynamic crack growth along a polymer composite-Homalite interface   总被引:1,自引:0,他引:1  
Dynamic crack growth along the interface of a fiber-reinforced polymer composite-Homalite bimaterial subjected to impact shear loading is investigated experimentally and numerically. In the experiments, the polymer composite-Homalite specimens are impacted with a projectile causing shear dominated interfacial cracks to initiate and subsequently grow along the interface at speeds faster than the shear wave speed of Homalite. Crack growth is observed using dynamic photoelasticity in conjunction with high-speed photography. The calculations are carried out for a plane stress model of the experimental configuration and are based on a cohesive surface formulation that allows crack growth, when it occurs, to emerge as a natural outcome of the deformation history. The effect of impact velocity and loading rate is explored numerically. The experiments and calculations are consistent in identifying discrete crack speed regimes within which crack growth at sustained crack speeds is possible. We present the first conclusive experimental evidence of interfacial crack speeds faster than any characteristic elastic wave speed of the more compliant material. The occurrence of this crack speed was predicted numerically and the calculations were used to design the experiments. In addition, the first experimental observation of a mother-daughter crack mechanism allowing a subsonic crack to evolve into an intersonic crack is documented. The calculations exhibit all the crack growth regimes seen in the experiments and, in addition, predict a regime with a pulse-like traction distribution along the bond line.  相似文献   

15.
Interface delamination during indentation of micron-scale ceramic coatings on metal substrates is modeled using discrete dislocation (DD) plasticity to elucidate the relationships between delamination, substrate plasticity, interface adhesion, elastic mismatch, and film thickness. In the DD method, plasticity in the metal substrate occurs directly via the motion of dislocations, which are governed by a set of physically based constitutive rules for nucleation, motion and annihilation. A cohesive law with peak stress characterizes the traction-separation response of the metal/ceramic interface. The indenter is a rigid flat punch and plane strain deformation is assumed. A continuum plasticity model of the same problem is studied for comparison. For low interface strengths (e.g. ), DD and continuum plasticity results are quantitatively similar, with delamination being nearly independent of interface strength, and easier for thinner, lower-modulus films. For higher interface strengths (), continuum plasticity predicts no delamination up to very high loads while the DD model shows a smooth increase in the critical indentation force for delamination with increasing interface strength. Tensile delamination in the DD model is driven by the accumulation of dislocations, and their associated high stresses, at the interface upon unloading. The DD model is thus capable of predicting the nucleation of cracks, and its dependence on material parameters, in realms of realistic constitutive behavior and/or small length scales where conventional continuum plasticity fails.  相似文献   

16.
The perceived wisdom about thin sheet fracture is that (i) the crack propagates under mixed mode I & III giving rise to a slant through-thickness fracture profile and (ii) the fracture toughness remains constant at low thickness and eventually decreases with increasing thickness. In the present study, fracture tests performed on thin DENT plates of various thicknesses made of stainless steel, mild steel, 6082-O and NS4 aluminium alloys, brass, bronze, lead, and zinc systematically exhibit (i) mode I “bath-tub”, i.e. “cup & cup”, fracture profiles with limited shear lips and significant localized necking (more than 50% thickness reduction), (ii) a fracture toughness that linearly increases with increasing thickness (in the range of 0.5-). The different contributions to the work expended during fracture of these materials are separated based on dimensional considerations. The paper emphasises the two parts of the work spent in the fracture process zone: the necking work and the “fracture” work. Experiments show that, as expected, the work of necking per unit area linearly increases with thickness. For a typical thickness of , both fracture and necking contributions have the same order of magnitude in most of the metals investigated.A model is developed in order to independently evaluate the work of necking, which successfully predicts the experimental values. Furthermore, it enables the fracture energy to be derived from tests performed with only one specimen thickness. In a second modelling step, the work of fracture is computed using an enhanced void growth model valid in the quasi plane stress regime. The fracture energy varies linearly with the yield stress and void spacing and is a strong function of the hardening exponent and initial void volume fraction. The coupling of the two models allows the relative contributions of necking versus fracture to be quantified with respect to (i) the two length scales involved in this problem, i.e. the void spacing and the plate thickness, and (ii) the flow properties of the material. Each term can dominate depending on the properties of the material which explains the different behaviours reported in the literature about thin plate fracture toughness and its dependence with thickness.  相似文献   

17.
Wave propagation in viscoelastic rods is encountered in many applications including studies of impact and fracture under high strain rates and characterization of the dynamic behavior of viscoelastic materials. For viscoelastic materials, both material and geometric dispersion are possible when the diameter of the rod is of the same order as the wavelength. In this work, we simplify the Pochhammer frequency equation for low and intermediate loss viscoelastic materials and formulate corrections for geometric dispersion for both the phase velocity and attenuation. The formulation is then experimentally verified with measurements of the phase velocity and attenuation in commercial polymethylmethacrylate rods that are 12 and in diameter. Without correcting for geometric dispersion, the usable frequency range for determining the phase velocity and attenuation for the rod is about , and about for the rod. Using the correction procedure developed here, it was possible to accurately determine the phase velocity and attenuation up to frequencies exceeding for the rod and for the rod. These corrections are applicable to many polymers and other viscoelastic materials. From thereon, the viscoelastic properties of the material can be determined over a wide range of frequencies.  相似文献   

18.
The problem of a steady-state slip pulse of finite size between dissimilar materials is studied. It is shown that for a Coulomb friction law, there is a continuous set of possible solutions for any slip propagation velocity and any slip length. These solutions are, however, nonphysical because they show a singular behaviour of the slip velocity at one extremity of the pulse, which implies a crack-like behaviour. In order to regularize these solutions, we introduce a modified friction law due to Prakash and Clifton (Experimental Techniques in the Dynamics of Deformable Solids, Vol. AMD-165, pp. 33-48; J. Tribol. 120 (1998) 97), which consists in introducing in the Coulomb friction law a relaxation time for the response of the shear stress to a sudden variation of the normal stress. Then, we show that even for a slip velocity-dependent characteristic time, the degeneracy of the solutions is not suppressed and a physical pulse is not selected. This result shows the absence of steady state self-healing pulses within the modified friction law and is consistent with recent finite-difference calculations (J. Geophys. Res. 107 (2002) 10).  相似文献   

19.
Atomistic simulations are used to investigate how the stress required for homogeneous nucleation of partial dislocations in single crystal copper under uniaxial loading changes as a function of crystallographic orientation. Molecular dynamics is employed based on an embedded-atom method potential for Cu at 10 and 300 K. Results indicate that non-Schmid parameters are important for describing the calculated dislocation nucleation behavior for single crystal orientations under tension and compression. A continuum relationship is presented that incorporates Schmid and non-Schmid terms to correlate the nucleation stress over all tensile axis orientations within the stereographic triangle. Simulations investigating the temperature dependence of homogeneous dislocation nucleation yield activation volumes of ≈0.5- and activation energies of . For uniaxial compression, full dislocation loop nucleation is observed, in contrast to uniaxial tension. One of the main differences between uniaxial tension and compression is how the applied stress is resolved normal to the slip plane on which dislocations nucleate—in tension, this normal stress is tensile, and in compression, it is compressive. Last, the tension-compression asymmetry is examined as a function of loading axis orientation. Orientations with a high resolved stress normal to the slip plane on which dislocations nucleate have a larger tension-compression asymmetry with respect to dislocation nucleation than those orientations with a low resolved normal stress. The significance of this research is that the resolved stress normal to the slip plane on which dislocations nucleate plays an important role in partial (and full) dislocation loop nucleation in FCC Cu single crystals.  相似文献   

20.
We investigate the linearized response of two elastic half-spaces sliding past one another with constant Coulomb friction to small three-dimensional perturbations. Starting with the assumption that friction always opposes slip velocity, we derive a set of linearized boundary conditions relating perturbations of shear traction to slip velocity. Friction introduces an effective viscosity transverse to the direction of the original sliding, but offers no additional resistance to slip aligned with the original sliding direction. The amplitude of transverse slip depends on a nondimensional parameter η=csτ0/μv0, where τ0 is the initial shear stress, 2v0 is the initial slip velocity, μ is the shear modulus, and cs is the shear wave speed. As η→0, the transverse shear traction becomes negligible, and we find an azimuthally symmetric Rayleigh wave trapped along the interface. As η→∞, the inplane and antiplane wavesystems frictionally couple into an interface wave with a velocity that is directionally dependent, increasing from the Rayleigh speed in the direction of initial sliding up to the shear wave speed in the transverse direction. Except in these frictional limits and the specialization to two-dimensional inplane geometry, the interface waves are dissipative. In addition to forward and backward propagating interface waves, we find that for η>1, a third solution to the dispersion relation appears, corresponding to a damped standing wave mode. For large-amplitude perturbations, the interface becomes isotropically dissipative. The behavior resembles the frictionless response in the extremely strong perturbation limit, except that the waves are damped. We extend the linearized analysis by presenting analytical solutions for the transient response of the medium to both line and point sources on the interface. The resulting self-similar slip pulses consist of the interface waves and head waves, and help explain the transmission of forces across fracture surfaces. Furthermore, we suggest that the η→∞ limit describes the sliding interface behind the crack edge for shear fracture problems in which the absolute level of sliding friction is much larger than any interfacial stress changes.  相似文献   

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