Frictional sliding modes along an interface between identical elastic plates subject to shear impact loading

Frictional sliding along an interface between two identical isotropic elastic plates under impact shear loading is investigated experimentally and numerically. The plates are held together by a compressive stress and one plate is subject to edge impact near the interface. The experiments exhibit both a crack-like and a pulse-like mode of sliding. Plane stress finite element calculations modeling the experimental configuration are carried out, with the interface characterized by a rate and state dependent frictional law. A variety of sliding modes are obtained in the calculations depending on the impact velocity, the initial compressive stress and the values of interface variables. For low values of the initial compressive stress and impact velocity, sliding occurs in a crack-like mode. For higher values of the initial compressive stress and/or impact velocity, sliding takes place in a pulse-like mode. One pulse-like mode involves well-separated pulses with the pulse amplitude increasing with propagation distance. Another pulse-like mode involves a pulse train of essentially constant amplitude. The propagation speed of the leading pulse (or of the tip of the crack-like sliding region) is near the longitudinal wave speed and never less than times the shear wave speed. Supersonic trailing pulses are seen both experimentally and computationally. The trends in the calculations are compared with those seen in the experiments.     

Dynamic crack growth along a polymer composite-Homalite interface

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.     

Wave propagation in porous media as a function of fluid saturation

An experimental investigation is conducted using dynamic photoelasticity and high speed photography to study the wave propagation due to blast loading in porous media as a function of fluid saturation. The porous media have been modeled as a continuous solid containing particular arrays of holes or voids. The study has focused mainly on the effect of the porous structure on transient pulse propagation as well as the effect of the moisture in the pores on wave propagation. A series of experiments have been conducted using a sheet of Homalite 100 with different geometry of the periodic array of holes. A small amount of explosive was used to generate the stress wave. Dynamic photoelastic photographs were taken with the high speed camera as the wave propagated across the holes. These data are analyzed to obtain the wave velocity as well as the stress-wave attenuation in the porous media.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Quasi-static and dynamic crack growth along bimaterial interfaces: A note on crack-tip field measurements using coherent gradient sensing

The paper presents a preliminary experimental investigation of crack-tip deformation fields near quasistatically and dynamically growing cracks in bimaterial interfaces. A three-point-bend bimaterial specimen with a relatively large stiffness mismatch between the two materials is studied. A recently developed optical method of coherent gradient sensing (CGS) is used to map crack-tip deformation fields.The quasi-static measurements are interpreted using plane-stress, singular-field solution for the interface crack tip. Results are compared with two-dimensional finite-element computations performed on identical specimen geometries and material mismatch.³² Impact studies conducted with bimaterial specimens provide the first experimental results of deformation fields near dynamically growing cracks along interfaces. Very high crack velocities, up to 80 percent of the Rayleigh wave speed for the less stiffer material of the two, are observed.     

Mechanism of shear attenuation near the interface under combined compression and shear impact loading

We investigate the compressional/shear coupling plastic wave propagation characteristics analytically for ideal elastic–plastic materials in both stress and particle velocity spaces, focusing on the shear wave attenuation near the interface occurring in pressure–shear plate impact experiments. The results show that the shear attenuation is strongly associated with the wave propagation characteristics of the coupling waves. In the stress space, as the shear stress increases, an adjustment of the stress components is observed and the final stress state along the wave path is a combined pure shear- and hydrostatic pressure-state. In the particle velocity space, the wave structures with different loading and maximal transverse particle velocity are obtained. The maximal transverse particle velocity varies with the longitudinal velocity and forms a boundary line. Once the loading transverse velocity exceeds this line, a transverse particle velocity discontinuity occurs at the impact interface. If the bonding strength is sufficiently high, there will be a shear band in the target in the extreme vicinity of the interface.     

Dynamic crack kinking from a PMMA/Homalite interface

The behavior of a pre-existing, dynamically loaded, interfacial crack kinking away from the interface separating two materials was experimentally investigated under dynamic loading conditions. Dynamic fracture experiments were performed on pre-cracked bimaterial panels of PMMA bonded with Homalite-100 impact loaded using a high-speed gas gun. By varying the location of impact, a large range of mixed mode loading at the crack tip was produced. Information about the stress state surrounding the crack tip was obtained through use of the lateral shearing interferometer of coherent gradient sensing in conjunction with high-speed photography. The high-speed interferogram corresponding, to the time of crack initiation was analyzed in each case to find the preinitiation mode mixity at the crack tip. Measurement of both the local initiation mode mixity and the crack kink angle allows for possible extension of existing quasi-static interface crack kinking criteria, such as maximum opening stress or maximum energy release rate, to the case of dynamic loading. It was found that for bimaterial systems with small material property mismatch, such as the PMMA/Homalite system, the maximum opening stress criterion accurately predicts the relation between crack tip mode mixity and resulting kink angle for small initial crack kinking speeds.     

Scattering of SH-waves by an interacting interface linear crack and a circular cavity near bimaterial interface

An analytical method is developed for scattering of SH-waves and dynamic stress concentration by an interacting interface crack and a circular cavity near bimaterial interface. A suitable Green‘s function is contructed, which is the fundamental solution of the displacement field for an elastic half space with a circular cavity impacted by an out-plane harmonic line source loading at the horizontal surface. First, the bimaterial media is divided into two parts along the horizontal interface, one is an elastic half space with a circular cavity and the other is a complete half space. Then the problem is solved according to the procedure of combination and by the Green‘s function method. The horizontal surfaces of the two half spaces are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at the linking section, or with some forces to recover cracks by means of crack-division technique. A series of Fredholm integral equations of first kind for determining the unknown forces can be set up through continuity conditions as expressed in terms of the Green‘s function. Moreover, some expressions are given in this paper, such as dynamic stress intensity factor (DSIF) at the tip of the interface crack and dynamic stress concentration factor (DSCF) around the circular cavity edge. Numerical examples are provided to show the influences of the wave numbers, the geometrical location of the interface crack and the circular cavity, and parameter combinations of different media upon DSIF and DSCF.     

Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113–2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent ?1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.     

Subsonic interfacial fracture using strain gages in isotropic–orthotropic bimaterial

An experimental study has been conducted in which strain fields were used to investigate the behavior of subsonic crack propagation along the interface of an isotropic–orthotropic bimaterial system. Strain field equations were developed from available field equations and critically evaluated in a parametric study to identify optimum strain gage location and orientation. Bimaterial specimens were prepared with PSM-1 polycarbonate and Scotchply^® 1002 unidirectional, glass-fiber-reinforced, epoxy composite. Dynamic experiments were conducted using these specimens with strain gages mounted on the composite half to obtain values of the dynamic complex stress intensity factor, K=K₁+iK₂, in the region of the crack tip while photoelasticity was used on the PSM-1 half. Results show that the trend and magnitude of K obtained using strain gages compare favorably with those obtained using photoelasticity.     

Contact Zone Approach for a Moving Interface Crack in a Piezoelectric Bimaterial under Thermoelectromechanical Loading

An interface crack of a finite length moving with a constant subsonic speed v along an interface of two semi-infinite piezoelectric spaces is considered. It is assumed that the bimaterial compound is loaded by a remote mixed mode mechanical loading and a thermoelectrical field and that a frictionless contact zone arises at the leading crack tip. Electrically permeable and electrically insulated cases of the open part of the crack are involved into the consideration. By introducing a moving coordinate system at the crack tip the problem is reduced to a combined Dirichlet–Riemann boundary value problem which is solved exactly. For both cases of the electrical conditions the transcendental equations are obtained for the determination of the real contact zone length, and moreover, the associated closed form asymptotic formulas are found for small values of this parameter. Variations of the contact zone length and the stress intensity factor with respect to the crack speed and the loading have been investigated both for electrically permeable and electrically insulated cases.     

压剪复合平板冲击加载技术进展及其应用

自20世纪70年代末发明压剪炮以来, 压剪复合冲击加载实验技术和诊断技术有了长足进展, 应用也日益广泛.由于压剪联合加载波直接反映了材料的动态剪切特性, 对于认识材料的屈服、损伤演化、失效、相变、界面滑移等动态行为和机理, 构筑更全面的本构模型能够提供必要的附加信息.本文主要讨论气炮实验中压剪复合应力波的产生方式, 诊断技术, 以及在压剪复合塑性波和动高压本构模型、聚合物压剪冲击行为、剪切波跟踪法(SWT)和水泥基复合材料的损伤和失效、界面动摩擦行为、冲击相变、动态损伤和断裂等方面的研究与应用进展.      

Remarks on the energy release rate for an antiplane moving crack in couple stress elasticity

This paper is concerned with the steady-state propagation of an antiplane semi-infinite crack in couple stress elastic materials. A distributed loading applied at the crack faces and moving with the same velocity of the crack tip is considered, and the influence of the loading profile variations and microstructural effects on the dynamic energy release rate is investigated. The behavior of both energy release rate and maximum total shear stress when the crack tip speed approaches the critical speed (either that of the shear waves or that of the localized surface waves) is studied. The limit case corresponding to vanishing characteristic scale lengths is addressed both numerically and analytically by means of a comparison with classical elasticity results.     

Subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone

A recent experimental study has demonstrated the attainability of intersonic shear crack growth along weak planes in otherwise homogeneous, isotropic, linear elastic solids subjected to remote loading conditions (Rosakis et al., Science 284 (5418) (1999) 1337). The relevant experimental observations are summarized briefly here and the conditions governing the attainment of intersonic crack speeds are examined. Motivated by experimental observations, subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone is subsequently analyzed. A cohesive law is assumed, wherein the cohesive shear traction is either a constant or varies linearly with the local sliding rate. Complete decohesion is assumed to occur when the crack tip sliding displacement reaches a material-specific critical value. Closed form expressions are obtained for the near-tip fields. With a cohesive zone of finite size, it is found that the dynamic energy release rate is finite through out the intersonic regime. Crack tip stability issues are addressed and favorable speed regimes are identified. The influence of shear strength of the crack plane and of a rate parameter on crack propagation behavior is also investigated. The isochromatic fringe patterns predicted by the analytical solution are compared with the experimental observations of Rosakis et al. (1999) and comments are made on the validity of the proposed model.     

Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes

Advances in computing as well as measurement instrumentation have recently allowed for the investigation of a wider spectrum of physical phenomena in dynamic failure than previously possible. With increasing demand for specialized lightweight, high strength structures, failure of inhomogeneous solids has been receiving increased attention. Such inhomogeneous solids include structural composites such as bonded and sandwich structures, layered and composite materials as well as functionally graded solids. Many of such solids are composed of brittle constituents possessing substantial mismatch in wave speeds, and are bonded together with weak interfaces, which may serve as sites for catastrophic failure (Rosakis and Ravichandran (2000)).In the present study numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes is presented. A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covariance structure with finite set of the internal state variables. A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic non-normality; (ii) softening generated by microdamage mechanisms; (iii) thermomechanical coupling (thermal plastic softening and thermal expansion); (iv) rate sensitivity.To describe suitably the time and temperature dependent effects observed experimentally during dynamic loading processes the kinetics of microdamage has been modified. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent elastic–plastic response can be obtained. The identification procedure is developed basing on the experimental observations. The finite difference method for regularized elasto-viscoplastic model is used. The edge-cracked bimaterial specimen is considered. In the initial configuration, the height of the specimen is equal to 30 cm, width is 12.5 cm and the length of the initial crack is equal to 2.5 cm. The length of the boundary over which impact is applied is equal to 5 cm, the rise time is fixed at 0.1 μs and the impact velocity is varied. The impact area is localized symmetrically or asymmetrically to the shorter axis of the specimen (symmetry axis of the cohesive band). Basing on the available data of recent experimental observation Rosakis et al. (1999) that have been carried out for relatively thin specimens both the plane stress and plane strain conditions are considered. The material of the specimen is AISI 4340 steel, while PMMA is the cohesive band, both modelled by thermo-elasto-viscoplastic constitutive equations with effects of isotropic hardening and softening generated by microdamage mechanisms and thermomechanical coupling. Fracture criterion based on the evolution of microdamage is assumed. Both, isothermal and adiabatic processes are considered.Particular attention is focused on the investigation of the interactions and reflections of stress waves and the influence of these waves on the propagation of macrocrack within the interface band. The propagation of the macroscopic crack within the material of the interface band for both symmetrical and asymmetrical impact cases has been investigated. It has been found that macrocrack-tip speeds vary from the shear wave speed to the dilatational wave speed of the material and is higher than the Rayleigh surface wave speed. This result is in accord with the experimental observations performed by Rosakis et al. (1999).     

Close-field optical analysis of an explosive-loading function

This research program was conducted to study the formation of a stress wave resulting from the detonation of an explosive charge in a circular hole in a large thin plate. Dynamic photoelasticity methods were employed. The isochromatic-fringe patterns were recorded with a Cranz-Schardin multiple-spark camera operating at a framing rate of 500,000 exposures/second. Experimental procedures developed during the course of the investigation eliminated fracturing of the model in the vicinity of the explosive and permitted recording of the dynamic fringe patterns at the boundary of the hole during the entire period of loading. Results of the study provide a realistic pulse shape for use with theoretical solutions to wave-propagation problems when comparisons are made with experimental solutions to the same problems obtained by dynamic photoelasticity means. Propagation and attenuation characteristics of the stress wave in the close field were obtained and compared with previous results obtained by extrapolation from farfield information. An explanation is provided for the high degree of reproducibility of explosive loadings and for the uniformity in amplitude of the stress wave produced in photoelastic models by different amounts of explosive.     

Finite element analysis of a bimaterial interface crack

In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems.     

含偏置裂纹三点弯曲梁的动态断裂行为研究

采用动态焦散线方法，对含偏置裂纹三点弯曲梁承受横向冲击的弯曲断裂行为进行了一系列动态断裂力学实验研究，分析了无量纲量ａ／ｌ的改变（ａ——初始裂纹偏离梁中心线的距离；ｌ——梁长度的一半）对于裂纹动态扩展行为（裂纹起始状态、裂纹尖端的复合应力强度因子、裂纹扩展速度、裂纹扩展轨迹）的影响，并借助动态光弹性应力分析，对应力波与扩展裂纹的相互作用以及应力波传播规律进行探讨．给出了裂纹尖端复合应力强度因子、裂纹扩展速度的变化、裂纹曲裂轨迹以及方向与梁中应力波传播的相互关系     

Dynamic photoelastic study of wave fields in elastic plates with stress concentrators

The method of dynamic photoelasticity is used to study the dynamic failure of structural members in the form of plates with a curvilinear (circular or elliptic) hole and an isolated crack under impulsive loading. The time-dependences of the stress intensity factors and the crack tip velocity are investigated for two types of models __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 84–92, December 2005.     

Sudden deceleration or acceleration of an intersonic shear crack

Sudden jumps in the crack tip velocity were revealed by numerical simulation (in both continuum/cohesive element and molecular dynamics approaches) and experiments for rapid shear cracking. The cracking velocity may accelerate from a sub-Rayleigh speed to the intersonic range, or from an intersonic speed to a higher one, when the reflected impact wave reloads the crack tip. On the other hand, the cracking velocity may decelerate from an intersonic speed to a lower one or recede to the sub-Rayleigh range when the fracture driving force declines. The velocity change encountered during intersonic cracking plays a different role from that in the acceleration or deceleration of a subsonic crack. A crack propagating at an intersonic speed would leave a shear wave trailing behind. When the crack decelerates or accelerates, the effect of the trailing wave will lead to a transition period from one steady-state solution of crack tip singularity to another. This investigation aims at quantifying these processes. The full field solution of an intersonic mode II crack whose speed changed suddenly from one velocity (intersonic or subsonic) to another (intersonic or subsonic) is given in closed form. The solution is facilitated via superposing a series of propagating crack problems that are loaded by dislocations to seal the unwanted crack-face sliding or by concentrated forces moving at various speeds to negate the crack-face traction. In contrast to the subsonic solution, the results in the intersonic case indicate that the elastic fields around the crack tip depend on the deceleration or acceleration history that is traced back over a long time. Singularity matching dictates the jump that may actually take place.     

Electromagnetic velocity-transducer studies of plastic waves in aluminum bars

In this investigation, annealed aluminum rods were subjected to dynamic compressive impact loading of duration of the order of 560 μsec to study the propagation of longitudinal plastic waves, using an electromagnetic transducer to record particle velocities at four stations approximately three inches apart. Test results indicate that any given level of particle velocity propagates along the bar with a constant speed, not affected by the strain rate, within the range of strain rates encountered. Good agreement was found between the propagation speeds observed for different levels of velocity (averaged over all tests) and predictions of the von Kármán rate-independent plastic-wave-propagation theory based on a single dynamic stress-strain curve almost coinciding with the static curve.