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The interaction of crack fronts with asperities is central to fracture criteria in heterogeneous materials and for predicting fracture surface formation. It is known how dynamic crack fronts respond to small, 1st-order, perturbations. However, large and localized disturbances to crack motion induce dynamic and geometric nonlinear effects beyond the existing linear theories. Because the determination of the 3D elastic fields surrounding perturbed crack fronts is a necessary step toward any theoretical study of crack front dynamics, we develop a 2nd-order perturbation theory for the asymptotic fields of planar crack fronts. Based on previous work, we consider two models of fracture: (1) Fracture in a scalar elastic solid which is an analog of antiplane shear fracture (Mode III). In this model, the near-crack fields are obtained via matched asymptotic expansions. (2) Tensile Mode I fracture, in which a self-consistent expansion is used to resolve the fields near the crack front. These methods can be readily extended to higher perturbation orders. The main results of this work are the explicit 2nd-order expressions of the local dynamic energy-release-rates for arbitrary perturbations of straight fronts. The formulae recover the known energy-release-rates of curved quasi-static fronts and of simple 2D cracks. We show that the expressions are separable as a product of a dynamical prefactor that only depends on the instantaneous local normal front velocity, and a history functional that integrates past front configurations. To gain insight, the energy-release-rates in the two models are computed for a traveling wave perturbation. While similar at low wave velocities, the two theories behave differently for fast waves. In scalar elasticity, the 2nd-order contributions are always sub-dominant. However, in the Mode I theory, the 2nd-order correction becomes the dominant term at the crack front wave velocity, where the 1st-order term is zero. We discuss employing the energy-release-rate expressions to predict crack front dynamics via energy balance with dissipation. [ABSTRACT FROM AUTHOR]

• Unstable crack propagations violate the fundamental quasi-static hypothesis. • Unrightfully neglecting inertial effects can lead to unsafe failure predictions. • Ignoring the diffusion of mechanical information yields unphysical crack patterns. • Not following the unstable crack growth weakens the irreversibility condition. • All insights above hold for the most common variational approaches to fracture. The present work is devoted to prove that unstable crack propagation events do not comply with quasi-static hypotheses and thus should be modelled by dynamic approaches. Comprehensive supporting evidence is provided on the basis of three different analyses conducted on multi-ligament unstable fracture conditions, including a simplified Spring-Mass model, detailed quasi-static and dynamic Phase Field fracture models, and bespoke experiments with 3D printed specimens. The obtained results unequivocally show that neglecting the inertial effects can lead to unsafe predictions in the presence of energetic barriers for the development of fracture. Likewise, quasi-static Phase Field fracture models are proven to yield crack patterns that disagree with the experimental evidence because they overlook the progressive diffusion of the mechanical information within the continuum. Moreover, the inability of quasi-static approaches to follow unstable crack propagation is shown to weaken the crucial irreversibility condition of fracture. Overall, these experimentally backed insights should be gravely reckoned with, for they are not exclusive to Phase Field fracture models but common to (almost) any variational approach to fracture, inter alia Cohesive Zone Models or Continuum Damage Mechanics. [ABSTRACT FROM AUTHOR]

Dynamic crack growth is analyzed numerically for a planar bimaterial block with an initial edge crack subject to mode II impact loading along the side of the block. The crack is constrained to grow along a weak interface directly ahead of the initial crack tip. A cohesive constitutive relation, that relates tractions and displacement jumps, is specified across the weak interface. The normal traction along the interface is taken to be a linear function of the normal displacement across the interface while the shear traction is taken to be a nonlinear function with the shear traction approaching zero for large displacement jumps, thus allowing mode II crack propagation. The material on the impact side of the interface is taken to be a linear elastic (actually hypoelastic) solid while the material on the other side of the interface is taken to be an isotropically hardening elastic-viscoplastic solid. Both plastically incompressible and plastically compressible solids are considered. Results are presented for the effects of plastic deformation on the evolution of near crack tip fields, on the crack speed history, and on the tractions that develop at the interface. The effects of various parameter variations are also explored. It is found that plasticity can result in tensile normal tractions developing on the interface in the crack tip vicinity and that the transition to an intersonic crack speed via a daughter crack mechanism can take place in the presence of small amounts of plastic straining. [ABSTRACT FROM AUTHOR]

Dynamic crack initiation, growth and branching phenomena are comprehensively investigated in soda-lime glass using a vision-based method, Digital Gradient Sensing (DGS), in conjunction with digital ultrahigh-speed photography. Being a high-stiffness and low-toughness structural material, soda-lime glass poses enormous temporal and spatial challenges to opto-mechanical measurements using legacy techniques. Unlike the past works on indirect evaluation of instantaneous stress intensity factors in glass via crack speed, DGS is capable of direct quantification of both crack-tip fields and crack speeds. This is useful for examining the dynamic fracture characteristics such as pre- and post-crack initiation histories, crack initiation toughness, energy release rate ( G d )-apparent velocity ( V ) variation, and to shed light on crack bifurcation phenomenon. Accordingly, directly measured mixed-mode stress intensity factor histories and crack-tip velocity histories at branching and subsequent growth are reported. These are supplemented with G d – V plots which show certain unique signatures at branching. From the measured fracture parameters, a material length characteristic based on microcracking due to normal stress in the crack growth direction ahead of the propagating crack that triggers branching is advanced. [ABSTRACT FROM AUTHOR]

The conventional gradient enhancement regularizes structural responses during material failure. However, it induces a spurious damage growth phenomenon, which is shown here to persist in dynamics. Similar issues were reported with the integral averaging approach. Consequently, the conventional nonlocal enhancement cannot adequately describe the dynamic fracture of quasi-brittle materials, particularly in the high strain rate regime, where a diffused damage profile precludes the development of closely spaced macrocracks. To this end, a homogenization theory is proposed to translate the micro processes onto the macro scale. Starting with simple elementary models at the micro scale to describe the fracture mechanisms, an additional kinematic field is introduced to capture the variations in deformation and velocity within a unit cell. An energetic equivalence between micro and macro is next imposed to ensure consistency at the two scales. The ensuing homogenized microforce balance resembles closely the conventional gradient expression, albeit with an interaction domain that decreases with damage, complemented by a micro inertia effect. Considering a direct single pressure bar example, the homogenized model is shown to resolve the non-physical responses obtained with conventional nonlocal enhancement. The predictive capability of the homogenized model is furthermore demonstrated by considering the spall tests of concrete, with good predictions on failure characteristics such as fragmentation profiles and dynamic tensile strengths, at three different loading rates. [ABSTRACT FROM AUTHOR]

We consider parallel splitting of a strip composed of two different chains . As a waveguide, the dissimilar-chain structure radically differs from the well-studied identical-chain system. It is characterized by three speeds of the long waves, c 1 and c 2 for the separate chains, and c + = ( c 1 2 + c 2 2 ) / 2 for the intact strip where the chains are connected. Accordingly, there exist three ranges, the subsonic for both chains (0, c 2 ) (we assume that c 2 < c 1 ), the intersonic ( c 2 , c + ) and the supersonic, ( c + , c 1 ) . The speed in the latter range is supersonic for the intact strip and at the same time, it is subsonic for the separate higher-speed chain. This fact allows the splitting wave to propagate in the strip supersonically. We derive steady-state analytical solutions and find that the splitting can propagate steadily only in two of these speed ranges, the subsonic and the supersonic, whereas the intersonic regime is forbidden. In the case of considerable difference in the chain stiffness, the lowest dynamic threshold corresponds to the supersonic regime. The peculiarity of the supersonic mode is that the supersonic energy delivery channel, being initially absent, is opening with the moving splitting point. Based on the discrete and related continuous models we find which regime can be implemented depending on the structure parameters and loading conditions. The analysis allows us to represent the characteristics of such processes and to demonstrate strengths and weaknesses of different formulations, quasi-static, dynamic, discrete or continuous. Analytical solutions for steady-state regimes are obtained and analyzed in detail. We find the force-speed relations and show the difference between the static and dynamic thresholds. The parameters and energy of waves radiated by the propagating splitting are determined. We calculate the strain distribution ahead of the transition point and check whether the steady-state solutions are admissible. [ABSTRACT FROM AUTHOR]

This work presents a numerical investigation into the dynamic crack penetration vs. deflection at a material interface, for materials exhibiting strain rate dependent damage evolution. The rate dependence of damage manifests as an increased strength and fracture energy (or toughness) at higher strain rates. For this purpose, a strain rate dependent continuum damage mechanics (CDM) based model is considered, which scales the material point softening damage law as a function of the strain rate. The investigations consider two materials, viz. the bulk and the interface, both modeled via the foregoing rate dependent damage model. Attention is focused on a mode I dynamic bulk crack impinging the interface at right angles, for the case where the interface is more strain rate sensitive than the bulk. The model is calibrated and validated with experimental data, and found to predict well the penetration/deflection behavior of a dynamic crack at an interface. Despite this, the predicted crack trajectory approaching the specimen boundary appears to be affected in some cases. The model is then used to conduct a sensitivity analysis for a wide range of bulk and interface properties (moduli, strengths, and fracture energy). The analyses reveal that dynamic crack impingement at the interface is accompanied by sharp changes in the local strain rates, thus altering the local bulk and interface strengths and toughnesses. So, a weak interface can become stronger and tougher than the bulk, locally and instantaneously, if it exhibits a higher strain rate sensitivity than the bulk. This implies that when damage evolution is rate dependent, there is an increased tendency for crack penetration. Due to the local and instantaneous rate dependence of strength and toughness, the previously established criteria in terms of the quasistatic property ratios are shown to be inapplicable. Alternatively, modeling is deemed inevitable for which the main source of uncertainty comes from the boundary conditions, which are shown to significantly affect the predicted cracking behavior. [ABSTRACT FROM AUTHOR]

A numerical scheme is proposed for simulating dynamic antiplane fracture at an interface between a layer and a half-plane. The scheme is a spectral boundary integral equation method which relates the shear stress and the displacement discontinuity at the interface in the spectral domain. In previous studies, numerical schemes have been developed for fracture problems in unbounded solids. This is the first work where a spectral boundary integral equation method has been developed for a system one of whose constituents is a finite solid, namely, a layer. The spectral scheme involves performing time convolution of the spectral amplitude of the shear stress at the interface of the layer and half-space. Numerically, conversion between the spectral domain and spatial domain is done by the Fast Fourier Transform. The numerical scheme is validated through comparison with known solutions of model problems. Use of the numerical method is illustrated by simulating 2D antiplane slip rupture propagation wherein the spectral boundary integral equation is coupled with a slip-weakening friction law. We illustrate the role of initial stress distribution on the modes of rupture propagation at the interface, which can be crack-like or pulse-like. The effect of the layer thickness on the critical nucleation size for dynamic rupture propagation is also studied numerically. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic crack-interface interactions and the related mechanics of crack penetration vs. branching at a weak interface are studied experimentally. The interface is oriented perpendicular to the incoming mode-I crack in an otherwise homogeneous bilayer. The focus of this investigation is on the effect of interface location and the associated crack-tip parameters within the bilayer on the mechanics of the ensuing fracture behavior based on the optical methodologies laid down in Ref. Sundaram and Tippur (2016). Time-resolved optical measurement of crack-tip deformations, velocity and stress intensity factor histories in different bilayer configurations is performed using Digital Gradient Sensing (DGS) technique in conjunction with high-speed photography. The results show that the crack path selection at the interface and subsequently the second layer are greatly affected by the location of the interface within the geometry. Using optically measured fracture parameters, the mechanics of crack penetration and branching are explained. Counter to the intuition, a dynamically growing mode-I approaching a weak interface at a lower velocity and stress intensity factor penetrates the interface whereas a higher velocity and stress intensity factor counterpart gets trapped by the interface producing branched daughter cracks until they kink out into the next layer. An interesting empirical observation based on measured crack-tip parameters for crack penetration and branching is also made. [ABSTRACT FROM AUTHOR]

The object of this work is to simulate the dynamic fracture propagation in fibre-reinforced cementitious composites, in particular, in steel fibre reinforced concrete (SFRC). Beams loaded in a three-point bend configuration through a drop-weight impact device are considered. A single cohesive crack is assumed to propagate at the middle section; the opening of this crack is governed by a rate-dependent cohesive law; the fibres around the fracture plane are explicitly represented through truss elements. The fibre pull-out behaviour is depicted by an equivalent constitutive law, which is obtained from an analytical load–slip curve. The obtained load–displacement curves and crack propagation velocities are compared with their experimental counterparts. The good agreement with experimental data testifies to the feasibility of the proposed methodology and paves the way to its application in a multi-scale framework. [ABSTRACT FROM AUTHOR]

We present three-dimensional finite-element simulations showing the propagation of slip fronts at striped heterogeneous interfaces. The heterogeneous area consists of alternating stripes of weaker and stronger frictional properties, which is equivalent to a lower and higher fracture energy, respectively. By comparing the slip front propagation at interfaces that differ solely by the length scale of the heterogeneous pattern, we illustrate that two different propagation regimes exist. Interfaces with wide stripes present slip fronts with propagation speeds that transition from sub-Rayleigh to inter-sonic. Thinner stripes are, however, characterized by the propagation of sub-Rayleigh slip fronts, which are preceded by slip pulses of negligible slip in the weaker stripes. From a macroscopic point of view, an interface with a smaller heterogeneous pattern appears to be stronger than the equivalent coarser interface even though both have the same average properties. The numerical results as well as a theoretical approach based on fracture-mechanics considerations suggest that the origin of these two distinct propagation mechanisms lies in the interaction between the length scales of the cohesive zone and the heterogeneous configuration. We further show by estimating the relevant length scales that the occurring propagation mechanism is influenced by the friction weakening rate of the interface as well as the shear modulus of the bulk material. [ABSTRACT FROM AUTHOR]

Micromechanics based damage models, such as the model presented in Part I of this 2 part series ( Tonge and Ramesh, 2015 ), have the potential to suggest promising directions for materials design. However, to reach their full potential these models must demonstrate that they capture the relevant physical processes. In this work, we apply the multiscale material model described in Tonge and Ramesh (2015) to ballistic impacts on the advanced ceramic boron carbide and suggest possible directions for improving the performance of boron carbide under impact conditions. We simulate both dynamic uniaxial compression and simplified ballistic loading geometries to demonstrate that the material model captures the relevant physics in these problems and to interrogate the sensitivity of the simulation results to some of the model input parameters. Under dynamic compression, we show that the simulated peak strength is sensitive to the maximum crack growth velocity and the flaw distribution, while the stress collapse portion of the test is partially influenced by the granular flow behavior of the fully damaged material. From simulations of simplified ballistic impact, we suggest that the total amount of granular flow (a possible performance metric) can be reduced by either a larger granular flow slope (more angular fragments) or a larger granular flow timescale (larger fragments). We then discuss the implications for materials design. [ABSTRACT FROM AUTHOR]

The damage and failure of brittle plates subjected to projectile impact is investigated through large-scale three-dimensional simulation using the DG/CZM approach introduced by Radovitzky et al. [Comput. Methods Appl. Mech. Eng. 2011; 200(1–4), 326–344]. Two standard experimental setups are considered: first, we simulate edge-on impact experiments on Al 2 O 3 tiles by Strassburger and Senf [Technical Report ARL-CR-214, Army Research Laboratory, 1995]. Qualitative and quantitative validation of the simulation results is pursued by direct comparison of simulations with experiments at different loading rates and good agreement is obtained. In the second example considered, we investigate the fracture patterns in normal impact of spheres on thin, unconfined ceramic plates over a wide range of loading rates. For both the edge-on and normal impact configurations, the full field description provided by the simulations is used to interpret the mechanisms underlying the crack propagation patterns and their strong dependence on loading rate. [ABSTRACT FROM AUTHOR]

Fracture toughness of brittle amorphous polymers (e.g. polymethyl methacrylate (PMMA)) has been reported to decrease with loading rate at moderate rates and increase abruptly thereafter to close to 5 times the static value at very high loading rates. Dynamic fracture toughness that is much higher than the static values has attractive technological possibilities. However, the reasons for the sharp increase remain unclear. Motivated by these observations, the present work focuses on the dynamic fracture behavior of polycarbonate (PC), which is also an amorphous polymer but unlike PMMA, is ductile at room temperature. Towards this end, a combined experimental and numerical approach is adopted. Dynamic fracture experiments at various loading rates are conducted on single edge notched (SEN) specimens with a notch of radius 150 μ m , using a Hopkinson bar setup equipped with ultra high-speed imaging ( > 10 5 fps ) for real-time observation of dynamic processes during fracture. Concurrently, 3D dynamic finite element simulations are performed using a well calibrated material model for PC. Experimentally, we were able to clearly capture the intricate details of the process, for both slowly and dynamically loaded samples, of damage nucleation and growth ahead of the notch tip followed by unstable crack propagation. These observations coupled with fractography and computer simulations led us to conclude that in PC, the fracture toughness remains invariant with loading rate at J frac = 12 ± 3 kN / m for the entire range of loading rates ( J ̇ ) from static to 1 × 10 6 kN / m − s . However, the damage initiation toughness is significantly higher in dynamic loading compared to static situations. In dynamic situations, damage nucleation is quickly followed by initiation of radial crazes from around the void periphery that initiate and quickly bridge the ligament between the initial damaged region and the notch. Thus for PC, two criteria for two major stages in the failure process emerge. Firstly, a mean stress based defect initiation is suggested. The value of the critical mean stress for defect initiation under dynamic loading is found to be 115±5 MPa, which is significantly higher than its static value of 80 MPa. The critical normal plastic stretch needed for crazes to nucleate from the nucleated defect is estimated to be about 1.78±0.2. [ABSTRACT FROM AUTHOR]

Here, we report measurements of detailed dynamic cohesive properties (DCPs) beyond the dynamic fracture toughness of a bicontinuously nanostructured copolymer, polyurea, under an extreme loading rate, from deep-learning analyzes of a dynamic big-data-generating experiment. We first describe a new Dynamic Line-Image Shearing Interferometer (DL-ISI), which uses a streak camera to record optical fringes of displacement-gradient vs time profile along a line on sample's rear surface. This system enables us to detect crack initiation and growth processes in plate-impact experiments. Then, we present a convolutional neural network (CNN) based deep-learning framework, trained by extensive finite-element simulations, that inversely determines the accurate DCPs from the DL-ISI fringe images. For the measurements, plate-impact experiments were performed on a set of samples with a mid-plane crack. A Conditional Generative Adversarial Networks (cGAN) was employed first to reconstruct missing DL-ISI fringes with recorded partial DL-ISI fringes. Then, the CNN and a correlation method were applied to the fully reconstructed fringes to get the dynamic fracture toughness, 12.1 k J / m 2 , cohesive strength, 302 M P a , and maximum cohesive separation, 80.5 μ m , within ± 0.4 % , ± 2.7 % , and ± 2.2 % differences, respectively. For the first time, the DCPs of polyurea have been successfully obtained by the DL-ISI with the pre-trained CNN and correlation analyzes of cGAN-reconstructed data sets. The dynamic cohesive strength is found to be nearly three times higher than the dynamic-failure-initiation strength. The high dynamic fracture toughness is found to stem from both high dynamic cohesive strength and high ductility of the dynamic cohesive separation. These experimental results fill a gap in the current understanding of nanostructured copolymer's cooperative-failure strength under extreme local loading conditions near the crack tip. This experiment demonstrates the advantages of a big-data-generating experiment to extract unprecedented details of nanostructured material's dynamic fracture characteristics with deep-learning algorithms. [ABSTRACT FROM AUTHOR]

Abstract: The new theory presented in the preceding paper, which models the dynamic comminution of concrete due to very high shear strain rate, is now compared to recent test data on the penetration of projectiles through concrete walls of different thicknesses, ranging from 127 to 254mm. These data are analyzed by an explicit finite element code using the new microplane constitutive model M7 for concrete, which was previously shown to provide the most realistic description of the quasi-static uni-, bi- and tri-axial test data with complex loading path and unloading. Model M7 incorporates the quasi-static strain rate effects due viscoelasticity and to the rate of cohesive crack debonding based on activation energy of bond ruptures, which are expected to extend to very high rates. Here model M7 is further enhanced by apparent viscosity capturing the energy dissipation due to the strain-rate effect of comminution. The maximum shear strain rates in the computations are of the order of 105 s−1. The simulations document that, within the inevitable uncertainties, the measured exit velocities of the projectiles can be matched quite satisfactorily and the observed shapes of the entry and exit craters can be reproduced correctly. [Copyright &y& Elsevier]

Abstract: The modeling of high velocity impact into brittle or quasibrittle solids is hampered by the unavailability of a constitutive model capturing the effects of material comminution into very fine particles. The present objective is to develop such a model, usable in finite element programs. The comminution at very high strain rates can dissipate a large portion of the kinetic energy of an impacting missile. The spatial derivative of the energy dissipated by comminution gives a force resisting the penetration, which is superposed on the nodal forces obtained from the static constitutive model in a finite element program. The present theory is inspired partly by Grady's model for expansive comminution due to explosion inside a hollow sphere, and partly by analogy with turbulence. In high velocity turbulent flow, the energy dissipation rate gets enhanced by the formation of micro-vortices (eddies) which dissipate energy by viscous shear stress. Similarly, here it is assumed that the energy dissipation at fast deformation of a confined solid gets enhanced by the release of kinetic energy of the motion associated with a high-rate shear strain of forming particles. For simplicity, the shape of these particles in the plane of maximum shear rate is considered to be regular hexagons. The particle sizes are assumed to be distributed according to the Schuhmann power law. The condition that the rate of release of the local kinetic energy must be equal to the interface fracture energy yields a relation between the particle size, the shear strain rate, the fracture energy and the mass density. As one experimental justification, the present theory agrees with Grady's empirical observation that, in impact events, the average particle size is proportional to the (−2/3) power of the shear strain rate. The main characteristic of the comminution process is a dimensionless number B a (Eq. (37)) representing the ratio of the local kinetic energy of shear strain rate to the maximum possible strain energy that can be stored in the same volume of material. It is shown that the kinetic energy release is proportional to the (2/3)-power of the shear strain rate, and that the dynamic comminution creates an apparent material viscosity inversely proportional to the (1/3)-power of that rate. After comminution, the interface fracture energy takes the role of interface friction, and it is pointed out that if the friction depends on the slip rate the aforementioned exponents would change. The effect of dynamic comminution can simply be taken into account by introducing the apparent viscosity into the material constitutive model, which is what is implemented in the paper that follows. [Copyright &y& Elsevier]

Abstract: Shear cracks propagation is a basic dynamical process that mediates interfacial failure. We develop a general weakly nonlinear elastic theory of shear cracks and show that these experience tensile-mode crack tip deformation, including possibly opening displacements, in agreement with Stephenson''s prediction. We quantify this nonlinear symmetry breaking effect, under two-dimensional deformation conditions, by an explicit inequality in terms of the first and second order elastic constants in the quasi-static regime and by semi-analytic calculations in the fully dynamic regime. Our general results are applied to various materials. Finally, we discuss related works in the literature and note the potential relevance of elastic nonlinearities for various problem, including frictional sliding. [Copyright &y& Elsevier]

Abstract: Continuum mechanics predicts that the propagation speed of non-equilibrium information in solids is limited by the longitudinal wave speed, so is crack propagation. However, solids are essentially discrete systems. In this paper, via theoretical analysis and numerical simulations, it is demonstrated in a straightforward way that non-equilibrium disturbance (e.g. force, displacement, energy, and so on) can propagate at a supersonic speed in discrete systems, although the magnitude of the disturbance attenuates very quickly. In dynamic fracture, a cascade of atomic-bond breaking events provides an amplification mechanism to counterbalance the attenuation of the disturbance. Therefore, supersonic crack propagation can be realized in a domino way. Another key factor for supersonic crack propagation is to ensure sufficient energy flowing into the crack tip. Since most energy can only be transferred at a speed limited by the longitudinal wave speed, the conditions for the occurrence of supersonic crack propagation are not easily met in most situations, unless there is high pre-stored energy along the crack path or continuous energy supply from the loading concomitantly moving with the crack tip. A quantitative relation between supersonic crack propagation speed and material properties and parameters is given, which implies that knowing all the classical macroscopic quantities is not enough in determining the supersonic crack propagation speed, and the microstructure does play a role. Moreover, it is interesting to note that fracture toughness affects the crack propagation speed in the subsonic regime, but not in the supersonic regime, because the deformation/stress is uniform in front of a supersonic crack where strength criterion dominates. [Copyright &y& Elsevier]

Abstract: The major objective of this work has been to develop, within a continuum framework, a microstructurally-based computational theory to investigate dynamic failure in metals. To model the nucleation and propagation of failure surfaces at the microstructural scale, under large deformations and dynamic loading conditions, general finite-deformation theory, as relating to the decomposition of the deformation gradient, was tailored to monitor displacement incompatibilities and fracture in crystalline solids subjected to large deformations. Based on this proposed decomposition, a general fracture criterion for finitely deforming crystals, using the integral law of incompatibility, was developed. The analyses indicate that this newly proposed fracture formulation and criterion can be validated with experimental results, and can be used to accurately predict brittle and ductile failure modes for the large deformation of single crystals. As part of the newly proposed decomposition of the deformation gradient, sub-problems can also be solved for lattice distortions, such as twinning and geometrically necessary dislocation (GND) densities. Accordingly, the interactions of GND densities with cracks were investigated for single crystals. GND densities were shown to form as loops for stationary crack tips, but no loops formed for propagating cracks. [Copyright &y& Elsevier]

Abstract: A nonuniform crack growth problem is considered for a homogeneous isotropic elastic medium subjected to the action of remote oscillatory and static loads. In the case of a plane problem, the former results in Rayleigh waves propagating toward the crack tip. For the antiplane problem the shear waves play a similar role. Under the considered conditions the crack cannot move uniformly, and if the static prestress is not sufficiently high, the crack moves interruptedly. For fracture modes I and II the established, crack speed periodic regimes are examined. For mode III a complete transient solution is derived with the periodic regime as an asymptote. Examples of the crack motion are presented. The crack speed time-period and the time-averaged crack speeds are found. The ratio of the fracture energy to the energy carried by the Rayleigh wave is derived. An issue concerning two equivalent forms of the general solution is discussed. [Copyright &y& Elsevier]

Abstract: A thermal–mechanical multiresolution continuum theory is applied within a finite element framework to model the initiation and propagation of dynamic shear bands in a steel alloy. The shear instability and subsequent stress collapse, which are responsible for dynamic adiabatic shear band propagation, are captured by including the effects of shear driven microvoid damage in a single constitutive model. The shear band width during propagation is controlled via a combination of thermal conductance and an embedded evolving length scale parameter present in the multiresolution continuum formulation. In particular, as the material reaches a shear instability and begins to soften, the dominant length scale parameter (and hence shear band width) transitions from the alloy grain size to the spacing between micro-voids. Emphasis is placed on modeling stress collapse due to micro-void damage while simultaneously capturing the appropriate scale of inhomogeneous deformation. The goal is to assist in the microscale optimization of alloys which are susceptible to shear band failure. [Copyright &y& Elsevier]

Abstract: We describe a method of constructing exact solutions of the equations of molecular dynamics in non-equilibrium settings. These solutions correspond to some viscometric flows, and to certain analogs of viscometric flows for fibers and membranes that have one or more dimensions of atomic scale. This work generalizes the method of objective molecular dynamics (OMD) (). It allows us to calculate viscometric properties from a molecular-level simulation in the absence of a constitutive equation, and to relate viscometric properties directly to molecular properties. The form of the solutions is partly independent of the form of the force laws between atoms, and therefore these solutions have implications for coarse-grained theories. We show that there is an exact reduction of the Boltzmann equation corresponding to one family of OMD solutions. This reduction includes most known exact solutions of the equations of the moments for special kinds of molecules and gives the form of the molecular density function corresponding to such flows. This and other consequences leads us to propose an addition to the principle of material frame indifference, a cornerstone of nonlinear continuum mechanics. The method is applied to the failure of carbon nanotubes at an imposed strain rate, using the Tersoff potential for carbon. A large set of simulations with various strain rates, initial conditions and two choices of fundamental domain (unit cell) give the following unexpected results: Stone–Wales defects play no role in the failure (though Stone–Wales partials are sometimes seen just prior to failure), a variety of failure mechanisms is observed, and most simulations give a strain at failure of 15–20%, except those done with initial temperature above about 1200K and at the lower strain rates. The latter have a strain at failure of 1–2%. [Copyright &y& Elsevier]

Abstract: Material failure by crack propagation essentially involves a concentration of large displacement-gradients near a crack''s tip, even at scales where no irreversible deformation and energy dissipation occurs. This physical situation provides the motivation for a systematic gradient expansion of general nonlinear elastic constitutive laws that goes beyond the first order displacement-gradient expansion that is the basis for linear elastic fracture mechanics (LEFM). A weakly nonlinear fracture mechanics theory was recently developed by considering displacement-gradients up to second order. The theory predicts that, at scales within a dynamic lengthscale from a crack''s tip, significant displacements and displacement-gradient contributions arise. Whereas in LEFM the singularity generates an unbalanced force and must be discarded, we show that this singularity not only exists but is also necessary in the weakly nonlinear theory. The theory generates no spurious forces and is consistent with the notion of the autonomy of the near-tip nonlinear region. The J-integral in the weakly nonlinear theory is also shown to be path-independent, taking the same value as the linear elastic J-integral. Thus, the weakly nonlinear theory retains the key tenets of fracture mechanics, while providing excellent quantitative agreement with measurements near the tip of single propagating cracks. As is consistent with lengthscales that appear in crack tip instabilities, we suggest that this theory may serve as a promising starting point for resolving open questions in fracture dynamics. [Copyright &y& Elsevier]

The dynamic strength for a broad range of materials with different microstructures exhibits surprisingly similar behavior. Two distinct regimes are observed with a sharp transition between them. At low loading rates, the strength has a weak linear dependence on the log loading rate until a critical rate above which a dramatic increase is observed. We explain this behavior by considering material failure as a bond-breaking process driven by external loading and thermal fluctuation within a Langevin dynamics framework. The analysis leads to nondimensional measures for which the dynamic response collapses onto a universal curve, independent of material properties, describing both loading rate regimes and the transition between them. A simple approximate model is derived that provides an excellent fit to experimental data for a broad range of materials, including concrete, ceramics, and metals. [ABSTRACT FROM AUTHOR]

This work addresses the interrelationship among dissipative mechanisms—material separation in the fracture process zone (FPZ), nonelastic deformation in the surrounding background material and kinetic energy—and how they affect the macroscopic dynamic fracture toughness as well as the limiting crack speed in strain rate sensitive materials. To this end, a micromechanics-based model for void growth in a nonlinear viscous solid is incorporated into a microporous strip of cell elements that forms the FPZ. The latter is surrounded by background material described by conventional constitutive relations. In the first part of the paper, the background material is assumed to be purely elastic. Here, the computed dynamic fracture toughness is a convex function of crack velocity. In the second part, the background material as well as the FPZ are described by similar rate-sensitivity parameters. Voids grow in the strain rate strengthened FPZ as the crack velocity increases. Consequently, the work of separation increases. By contrast, the inelastic dissipation in the background material appears to be a concave function of crack velocity. At the lower crack velocity regime, where dissipation in the background material is dominant, toughness decreases as crack velocity increases. At high crack velocities, inelastic deformation enhanced by the inertial force can cause a sharp increase in toughness. Here, the computed toughness increases rapidly with crack velocity. There exist regimes where the toughness is a non-monotonic function of the crack velocity. Two length scales—the width of the FPZ and the ratio of the shear wave speed to the reference strain rate—can be shown to strongly affect the dynamic fracture toughness. Our computational simulations can predict experimental data for fracture toughness vs. crack velocity reported in several studies for amorphous polymeric materials. [Copyright &y& Elsevier]

The energy flux integral and the energy-momentum tensor for studying the crack driving force in electroelastodynamic fracture are formulated within the framework of the nonlinear theory of coupled electric, thermal and mechanical fields based on fundamental principles of thermodynamics. This formulation lays a foundation for in-depth understanding of the fracture behavior of piezoelectric materials. Remarkably, the dynamic energy release rate thus obtained has an odd dependence on the electric displacement intensity factor for steady-state propagation of a conventional (unelectroded) crack with exact, electrically permeable, semi-permeable, or impermeable crack surface condition, which is in agreement with experimental evidence. [Copyright &y& Elsevier]

When a crack in a thermally non-diffusive material is impact loaded—or propagates at high speed—a cohesive process which resists slow crack extension may itself cause decohesion by adiabatic heating. By assuming that decohesion ultimately occurs by low-energy disentanglement within a melt layer of critical thickness, the fracture resistance of craze-forming crystalline polymers can be estimated quantitatively. Previous estimates used a simple, thermomechanically linear representation of craze fibril drawing. This paper presents a more physically realistic, numerical formulation, and demonstrates it for constant craze thickening rate (as imposed by an ideal full-notch tension test) and for linearly increasing thickening rate (as at the tip of an impact-loaded or rapidly propagating crack). For a linear material, the numerical formulation gives results which asymptotically approach those from analytical solutions, as craze density approaches zero. In more realistic model polymers, the enthalpy of fusion increasingly delays decohesion as impact speed increases, although the temperature distribution of an endotherm appears to have little effect. Increasing molecular weight, heuristically associated with decreasing craze density and increasing structural dimension, increases the predicted impact fracture resistance. In every case, fracture resistance passes through a minimum as impact speed increases. The conclusions encourage the use of impact fracture tests, and discourage the use of the full-notch tension test, to assess the dynamic fracture resistance of a craze-forming polymer. [Copyright &y& Elsevier]

Abstract: A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical. [Copyright &y& Elsevier]

Abstract: The phenomena occurring during rapid crack propagation in brittle single crystals was studied by cleaving strip-like silicon specimens along the {111} low-energy cleavage plane under bending. The experiments reveal phenomena associated with rapid crack propagation in brittle single crystals not previously reported, and new crack path instabilities in particular. In contrast to amorphous materials, the observed instabilities are generated at relatively low velocity, while at high velocity the crack path remains stable. The experiments demonstrate that crack velocity in single crystals can attain the theoretical limit. No evidence for mirror, mist, and hackle instabilities, typical in amorphous materials, was found. The important role played by the atomistic symmetry of the crystals on controlling and generating the surface instabilities is explained; the importance of the velocity and orientation-dependent cleavage energy is discussed. The surface instabilities are generated to satisfy minimum energy dissipation considerations. These findings necessitate a new approach to the fundamentals of dynamic crack propagation in brittle single crystals. [Copyright &y& Elsevier]

Abstract: Understanding sub-Rayleigh-to-intersonic transition of mode II cracks is a fundamental problem in fracture mechanics with important practical implications for earthquake dynamics and seismic radiation. In the Burridge–Andrews mechanism, an intersonic daughter crack nucleates, for sufficiently high prestress, at the shear stress peak traveling with the shear wave speed in front of the main crack. We find that sub-Rayleigh-to-intersonic transition and sustained intersonic propagation occurs in a number of other models that subject developing cracks to intersonic loading fields. We consider a spontaneously expanding sub-Rayleigh crack (or main crack) which advances, along a planar interface with linear slip-weakening friction, towards a place of favorable heterogeneity, such as a preexisting subcritical crack or a small patch of higher prestress (similar behavior is expected for a small patch of lower static strength). For a range of model parameters, a secondary dynamic crack nucleates at the heterogeneity and acquires intersonic speeds due to the intersonic stress field propagating in front of the main crack. Transition to intersonic speeds occurs directly at the tip of the secondary crack, with the tip accelerating rapidly to values numerically equal to the Rayleigh wave speed and then abruptly jumping to an intersonic speed. Models with favorable heterogeneity achieve intersonic transition and propagation for much lower prestress levels than the ones implied by the Burridge–Andrews mechanism and have transition distances that depend on the position of heterogeneity. We investigate the dependence of intersonic transition and subsequent crack propagation on model parameters and discuss implications for earthquake dynamics. [Copyright &y& Elsevier]

Abstract: A weight function matrix is developed for obtaining the stress singularity coefficients at the edge of a plane crack, moving uniformly at an intersonic speed while subjected to arbitrary shear loading. This is then utilised for deriving, to first order, the perturbations of these coefficients associated with a small spatially and temporally varying perturbation of its edge. The perturbation solution is employed, in conjunction with a simple fracture criterion, to investigate the stability of a uniformly moving intersonic crack, subjected to following loads. [Copyright &y& Elsevier]

Abstract: High-speed holographic microscopy is applied to take three successive photographs of fast propagating cracks in Homalite 100 or in Araldite B at the moment of bifurcation. Crack speed at bifurcation is about 540m/s on Homalite 100, and about 450m/s on Araldite B. From the photographs, crack speeds immediately before and after bifurcation are obtained, and it is found that discontinuous change of crack speed does not exist at the moment of bifurcation in the case of Homalite 100, but exists in the case of Araldite B. From the photographs, crack opening displacement (COD) is also measured along the cracks as a function of distance r from the crack tips. The measurement results show that the CODs are proportional to √r before bifurcation. After bifurcation, the CODs of mother cracks are proportional to √r, though the CODs of branch cracks are not always proportional to √r. The energy release rate is obtained from the measured CODs, and it is found that energy release rate is continuous at bifurcation point in both cases of Homalite 100 and Araldite B. Energy flux that shows the energy flow toward a crack tip is also obtained. [Copyright &y& Elsevier]

Abstract: The speed of Rayleigh surface waves, denoted C R, is the accepted upper limit for Mode I crack velocity in monolithic solids. In the current contribution, we discuss several critical issues associated with the velocity of Rayleigh surface waves and crack velocity in single crystal (SC) brittle solids, and the global and local influence of C R on crack path selection in particular. Recent cleavage experiments in SC silicon showed that crack velocity at certain cleavage planes and crystallographic orientations cannot exceed a small fraction of C R, and thereafter the crack deflects to other cleavage planes. Indeed, C R defined by the continuum mechanics ignores atomistic phenomena occurring during rapid crack propagation, and therefore is limited in predicting the crack velocity. Examination of these anomalies shows that this limitation lies in microstructural lattice arrangement and in anisotropic phonon radiation during rapid crack propagation. Globally, C R has no influence on the crack deflection phenomenon. However, the misfit in C R between the original plane of propagation and the deflected plane generates local instabilities along the deflection zone. [Copyright &y& Elsevier]

Abstract: In this comment, it is pointed out that the paper [Li and Mataga, 1996. J. Mech. Phys. Solids 44, 1799–1830], which presents original and valid solution strategy for an important problem of dynamic crack propagation in piezoelectric materials, contains ultimate quantitatively and qualitatively incorrect expressions, conclusions and plots due calculation errors. The correct calculations and corresponding correct conclusions and plots are presented. [Copyright &y& Elsevier]

Abstract: Yoffe''s linear theory of dynamic brittle fracture suggests that crack motion will be unstable beyond ∼70% of the Rayleigh speed, a prediction that is not supported by experiment. We show by atomistic simulations that hyperelasticity, the elasticity of large strains, plays a governing role in the instability dynamics of brittle fracture. A simple, yet remarkable, scaling model based on an effective elastic modulus (the secant modulus at the stability limit) gives successful predictions for the onset speed of the crack instability. [Copyright &y& Elsevier]

Abstract: We develop a general solution method for a dynamically accelerating crack under anti-plane shear conditions along the interface between two different homogeneous isotropic elastic materials. The crack is initially at rest, and after loading is applied the crack-tip speed which may accelerate up to the shear wave speed of the more compliant material. The analysis includes an exact, closed-form expression for the stress intensity factor for an arbitrary time-dependent crack-face traction, as well as expressions for computing the crack-face displacements and the stress in front of the crack. We also present some numerical examples for fixed loads and for loads moving with the crack tip, using a stress intensity factor fracture criterion, in order to examine the predicted effect of material mismatch on interfacial fracture. [Copyright &y& Elsevier]

Abstract: The field of dynamic fracture has been enlivened over the last 5 years or so by a series of remarkable accomplishments in different fields—earthquake science, atomistic (classical and quantum) simulations, novel laboratory experiments, materials modeling, and continuum mechanics. Important concepts either discovered for the first time or elaborated in new ways reveal wider significance. Here the separate streams of the literature of this progress are reviewed comparatively to highlight commonality and contrasts in the mechanics and physics. Much of the value of the new work resides in the new questions it has raised, which suggests profitable areas for research in the next few years and beyond. From the viewpoint of fundamental science, excitement is greatest in the struggle to probe the character of dynamic fracture at the atomic scale, using Newtonian or quantum mechanics as appropriate (a qualifier to be debated!). But lively interest is also directed towards modeling and experimentation at macroscales, including the geological, where the science of fracture is pulled at once by fundamental issues, such as the curious effects of friction, and the structural, where dynamic effects are essential to proper design or certification and even in manufacture. [Copyright &y& Elsevier]

The dynamic propagation of a bifurcated crack under arbitrary loading is studied. Under plane loading configurations, it is shown that the model problem of the determination of the dynamic stress intensity factors after branching is similar to the anti-plane crack branching problem. By analogy with the exact results of the mode III case, the energy release rate immediately after branching under plane situations is expected to be maximized when the branches start to propagate quasi-statically. Therefore, the branching of a single propagating crack under mode I loading should be energetically possible when its speed exceeds a threshold value. The critical velocity for branching of the initial single crack depends only weakly on the criterion applied for selecting the paths followed by the branches. However, the principle of local symmetry imposes a branching angle which is larger than the one given by the maximum energy release rate criterion. Finally, it is shown that an increasing fracture energy with the velocity results in a decrease in the critical velocity at which branching is energetically possible. [Copyright &y& Elsevier]

Cleavage fracture in ferritic steels is often initiated in brittle carbides randomly distributed in the material. The carbides break as a result of a fibre loading mechanism in which the stress levels in the carbides are raised, as the surrounding ferrite undergoes plastic deformation. The conditions in the vicinity of the nucleated micro-crack will then determine whether the crack will penetrate or be arrested by the ferrite. The ferrite is able to arrest nucleated cracks through the presence of mobile dislocations, which blunt and shield the microcrack and thus lowers the stresses at the crack tip. Hence, the macroscopic toughness of the material directly depends on the ability of the ferrite to arrest nucleated micro-cracks and in turn on the plastic rate sensitivity of the ferrite. The initiation of cleavage fracture is here modelled explicitly in the form of a micro-crack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder or in a few cases an elastic sphere and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, where the tractions are governed by a modified exponential cohesive law. It is shown that the critical stress, required to propagate a microcrack from a broken carbide, increases with decreasing plastic rate sensitivity of the ferrite. The results also show that a low stress triaxiality and a high aspect ratio of the carbide promote the initiation of cleavage fracture from a broken carbide. [Copyright &y& Elsevier]

A set of cleavage experiments with strip-shaped single-crystal silicon specimens subjected to three-point bending is reported. The experiments enabled examination of the relationships between the dynamic energy release rate, the velocity, the orientation-dependent cleavage energy, and the cleavage plane of propagation.Dynamic crack propagation experiments show that when a [0 0 1] silicon single crystal is fractured under three-point bending at ‘parallel’ velocity (directly measured at the bottom surface of the specimen) of up to 1500 m/s, it prefers to cleave along the vertical (1 1 0) plane, while when the specimen is fractured under the same conditions but at a velocity higher than 2900 m/s, it cleaves along the inclined (1 1 1) plane. At intermediate velocities, the crack will deflect from the (1 1 0) plane to the (1 1 1) plane. Crack velocity was determined by the initial notch length. The local (calculated) velocity of deflection between the cleavage planes ranges from 2900 m/s, for a crack propagating on the (1 1 0) plane in the [1 &1macr; 0] direction, to about 30 m/s, for a crack on the (1 1 0) plane, but in the [0 0 1] direction.It is suggested that the cause of the deflection phenomenon is the anisotropic, velocity-dependent cleavage energy, resulted phonon radiation caused by anisotropic, velocity-dependent lattice vibrations. We have studied the effect of material properties and propose selection criteria to explain the deflection phenomenon: the crack will deflect to the plane of least-energy, for which G-Γi(V)=max, or to the plane with maximum crack tip velocity, Vi(Γ)=max. [Copyright &y& Elsevier]

The dynamic propagation of a bifurcated crack under antiplane loading is considered. The dependence of the stress intensity factor just after branching is given as a function of the stress intensity factor just before branching, the branching angle and the instantaneous velocity of the crack tip. The jump in the dynamic energy release rate due to the branching process is also computed. Similar to the single crack case, a growth criterion for a branched crack is applied. It is based on the equality between the energy flux into each propagating tip and the surface energy which is added as a result of this propagation. It is shown that the minimum speed of the initial single crack which allows branching is equal to 0.39c, where c is the shear wave speed. At the branching threshold, the corresponding bifurcated cracks start their propagation at a vanishing speed with a branching angle of approximately 40°. [Copyright &y& Elsevier]

While fragmentation of brittle materials is a phenomenon that occurs commonly, a consistent theoretical description of this process is not yet available. In this paper, we introduce a one-dimensional micromechanics-based statistical model for fragmentation in a brittle material and analyze the model using two different approaches, namely, an exact numerical method based on the method of characteristics and a dynamic mean-field theory. The mean-field theory is derived by averaging the equations that govern the dynamics of flaws in a self-consistent manner and explicitly accounts for both the statistical nature of flaw distributions and the stress-wave-mediated communication between flaws. It is shown that the mean-field theory provides an accurate description of the damage evolution process that takes place during fragmentation and predicts fragment sizes that are in close quantitative agreement with the numerical calculations. [Copyright &y& Elsevier]

In this study, the dynamic fracture analysis of finite cracks in anisotropic elastic solids subjected to incident horizontally polarized shear waves is investigated. The influence of finite length of the crack on the dynamic stress intensity factor will be discussed in detail. A linear coordinate transformation is introduced to simplify the problem. The linear coordinate transformation reduces the anisotropic finite crack problem to an equivalent isotropic problem. An alternative methodology different from the conventional superposition method is developed to construct the diffracted fields. The transient solutions are determined by superposition of two proposed fundamental solutions in the Laplace transform domain. For stationary cracks, the exact analytical solutions of dynamic stress intensity factors for two crack tips are obtained in explicit forms and have accounted for the contributions of all the diffracted waves. For a step-stress wave, the maximum dynamic overshot of stress intensity factor is 4/π for any combination of material constants and incident angles. If the stress intensity factor reaches the fracture toughness of the material, the two crack tips are assumed to propagate along the crack tip line with constant subsonic velocities. The influence of the diffracted waves generated from the other crack tip on the propagating crack tip is analyzed. It is shown in this study that the diffracted waves from the other crack tip have significant influence on the stress intensity factors for propagating cracks. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

Results are reported for pressure-shear plate impact experiments designed to study the competition between dynamic shear fracture and dynamic shear band formation for a crack subjected to plane wave loading in Mode III. Experiments showing the propagation of a shear band ahead of the main crack are analyzed by using methods developed previously by others for the diffraction of an elastic shear wave by a semi-infinite crack. Based on measured, room-temperature flow stresses, the predicted speed of propagation of the tip of the band is found to be substantially less than that corresponding to the measured extension of the shear band in the experiments. Possible reasons for differences between predicted and measured shear band speeds are discussed. Reduced shearing resistance in the shear band, presumably due to thermal softening, is viewed as the likely explanation for the relatively long shear bands observed. [Copyright &y& Elsevier]

We present a new method for determining the elasto-dynamic stress fields associated with the propagation of anti-plane kinked or branched cracks. Our approach allows the exact calculation of the corresponding dynamic stress intensity factors. The latter are very important quantities in dynamic brittle fracture mechanics, since they determine the crack path and eventual branching instabilities. As a first illustration, we consider a semi-infinite anti-plane straight crack, initially propagating at a given time-dependent velocity, that changes instantaneously both its direction and its speed of propagation. We will give the explicit dependence of the stress intensity factor just after kinking as a function of the stress intensity factor just before kinking, the kinking angle and the instantaneous velocity of the crack tip. [Copyright &y& Elsevier]

A thermally dissipative cohesive zone model is developed for predicting the temperature increase at the tip of a crack propagating dynamically in a nominally brittle material exhibiting a cohesive-type failure such as crazing. The model assumes that fracture energy supplied to the crack tip region that is in excess of that needed for the creation of new free surfaces during crack advance is converted to heat within the cohesive zone. Bulk dissipation mechanisms, such as plasticity, are not accounted for. Several cohesive traction laws are examined, and the model is then used to make predictions of crack tip heating at various crack propagation speeds in the nominally brittle amorphous polymer PMMA, observed to fail by a crazing-type mechanism. The heating predictions are compared to experimental data where the temperature field surrounding a high speed crack in PMMA was measured. Measurements are made in real time using a multi-point high speed HgCdTe infrared radiation detector array. At the same time as temperature, simultaneous measurement of fracture energy is made by a strain gauge technique, and crack tip speed is monitored through a resistance ladder method. Material strength can be estimated through uniaxial tension tests, thus minimizing the need for parameter fitting in the stress-opening traction law. Excellent agreement between experiments and theory is found for two of the cohesive traction law temperature predictions, but only for the case where a single craze is active during the dynamic fracture of PMMA, i.e. crack tip speed up to approximately 0.2cR. For higher speed fracture where subsurface damage becomes prominent, the line dissipation model of a cohesive zone is inadequate, and a distributed damage model is needed. [Copyright &y& Elsevier]

A dynamic damage growth model applicable to brittle solids subjected to biaxial compressive loading is developed. The model incorporates a dynamic fracture criterion based on wing-crack growth model with a damage evolution theory based on a distribution of pre-existing microcracks in a solid. Influences of lateral confinement pressure (dynamic or static) as well as frictional coefficient on the rate dependence of fracture strength of basalt-rock are investigated systematically. It is found that the failure strength, damage accumulation and wing-crack growth rate are strongly influenced by the nature and the magnitude of confinement pressure. It is also verified that the effect of strain rate on fracture strength of brittle solids is independent of confinement pressure in a certain range of strain rate. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]