TRIB 2004-64374 SLIDING OF FRCITIONALLY HELD INCOHERENT INTERFACES UNDER DYNAMIC SHEAR LOADING

An experimental investigation was conducted to study the nature of dynamic rupture caused by shear loading, through impact, of interfaces which are held together by friction under external pressure. The dynamic stress field developed during rupture propagation was recorded in real time by a high-speed camera in conjunction with a classical dynamic photoelasticity set-up. Visual evidences of different dynamic propagating rupture modes were recorded. Unlike classical shear cracks in coherent interfaces of finite strength, rupture in frictional interfaces seems to grow without noticeable acceleration phases and at various discreet speeds. At low impact velocities a cracklike rupture mode occurs which becomes super-shear with the increase of the impact speed and a shear Mach cone emanates from the rupture point. For higher impact speeds super-shear and super-sonic Mach lines are observed formatting an unstable slip pulse which subsequently vanishes whereas evidences for extended stick and slip regions are recorded. Increasing the external applied pressure the observed features are intensified. INTRODUCTION Rupture of frictionally held, incoherent, interfaces subjected to shear loading is a basic problem in engineering and often occurs dynamically, for example, during materials processing, deformation and failure of fiber reinforced composites. In Geophysics, dynamic rupture of adjoining slabs causes the generation of earthquakes. There are two widely accepted approaches describing dynamic shear rupture (Rice [1]). The most classical approach uses elastodynamic shear crack models (behind the leading edge of sliding, the surfaces continuously slide and interact through contact and friction). More recently, models that describe ruptures as ‘self-healing’ slip pulses have been introduced (behind the leading edge of sliding, there is sliding for a finite length behind which sliding stops and the surfaces are locked). The question of whether ruptures assume a ‘crack-like’ or a ‘pulse-like’ mode and under what circumstances they do so is currently at the center of research activity. When two surfaces are in contact, their relative motion is resisted by frictional force. The ratio of the tangential force to the normal force is called the coefficient of friction. However, the mechanics of contact and friction is actually quite complex. The interaction of elastic waves with friction has been the subject of many recent investigations. The possible interface waves in unbonded frictionless contact between two different bodies in which separation does not occur have been investigated by Achenbach and Epstein [2]. These “smooth contact Stonely waves” (also known as slip waves or generalized Rayleigh waves) are qualitatively similar to those of bonded contact and occur for a wider range of material combinations. Slip waves with interface separation were found by Comninou and Dundurs [3]. They also investigated the possibility of separation waves and /or stick slip waves in the sliding of two identical half–planes with friction, (Comninou and Dundurs [4]). Their analysis showed that such waves could exist only with singularities at the tips of the slip zones. Comninou and Dundurs [5] also investigated the possible sliding motion of two identical bodies without interface slipping (carpet analogous). Weertman [6] has shown that a coupling between slip and normal stress exists in a frictional interface between dissimilar materials. He concluded that a self healing pulse can propagate along the frictional interface between dissimilar elastic solids, when the remote shear stress is less than the frictional stress of the interface. Adams [7, 8] showed that the steady sliding, under Coulomb friction law, of two elastic half-planes which are not very dissimilar is dynamically unstable for arbitrary small values of friction. The instability mechanism is due to destabilization of interfacial slip waves and gives rise to a dynamic instability in the form of self excited motion. These self excited oscillations are generally confined to a region near the sliding interface. He also investigated the sliding, under Coulomb friction law, of two dissimilar bodies due to periodic regions of slip and stick propagating along the interface. He was able to show that stickand-slip waves can propagate along the interface. The numerical results of Adams [7] suggest a connection between the existence of the generalized Rayleigh waves and the illposedness. Ranjith and Rice [8] have shown that when the 1 Copyright © 2004 by ASME material pair is such that the generalized Rayleigh wave speed is defined (modest mismatch in material properties), the problem is ill-posed for any value of the friction coefficient, whereas when it is not defined (large mismatch in material properties) the problem remains ill-posed for values of the friction coefficient larger than a critical value. Numerical studies of the nucleation and propagation of slip pulses using Coulomb friction law at the interface, by Andrews and Ben Zion [9], Ben Zion and Andrews [10] encountered numerical problems. Cochard and Rice [11] found that the Adams instability was responsible for those numerical problems since the cases studied by Andrews and Ben Zion fall in the range in which the generalized Rayleigh wave speed is defined and are thus ill-posed. They showed that the same method gives results which converge with parameter choices in the well-posed range. In order to regularize the problem, Cochard and Rice [11] replaced the Coulomb friction law by an experimentally based friction law due to Prakash and Clifton (Prakash and Clifton [12], Prakash [13]). This friction law, incorporating memory dependence, transforms the instantaneous variation of shear strength that would follow from an instantaneous variation of normal stress if the Coulomb law was used to a smooth function. The Prakash and Clifton law conserves the main futures of the problem originally studied using the Coulomb law at least qualitatively, e.g. the rupture still occurs as self healing pulses. Ranjith and Rice [8] have shown that this law provides also regularization for the linear stability analysis. However, Ben-Zion and Huang [9] showed that the self sharpening and divergent behavior found earlier by Cochard and Rice [11] with Coulomb friction law exists also with regularized friction for large enough propagation distance or equivalently for long times. Coker et al. [14] analyzed numerically the frictional sliding along a planar interface between identical elastic solids under impact shear loading. The interface is characterized by a rate and state dependent frictional law. They report crack-like, pulse-like and mix rupture modes, depending on the loading conditions. As we see there is a debate about the different high rate phenomena that occur at the interface of two incoherent halfplanes which are subject to dynamic shear loading and until now there are no experimental evidences which would help to analyze the problem. There is a huge literature about experimental work on frictional sliding. However, there is practically nothing on real time observations of sliding in the μsec regime. The majority of the existing experimental studies use a large time scale and they are concerned with developing qualitative and/or quantitative relationships between time averaged friction data and various governing parameters and conditions, for example the properties of bulk and surface layer materials, the roughness of the surface in contact, the normal stress level, the rate of application of stress, the interfacial slip speed, the history of loading, the temperature and so on. Unfortunately, most dynamic friction laws obtained using various experimental configurations and apparatus, lack the reproducibility of friction data (surveys by Martins et all., [15], Ibrahim [16, 17]). The results of these experiments are multibranched friction versus slip velocity curves, which even for the same material and the same experimental apparatus depend not only on the properties of the frictional interface but also on the dynamic properties of the apparatus, such as mass, stiffness and damping. This suggests that the friction data obtained in the course of stick-slip motions are not an intrinsic property of the surfaces in contact but they are greatly affected by several of the dynamic variables involved in each particular experiment set up. Prakash [18] employs a plate-impact pressure-shear friction experiment. The use of this experimental configuration allows the investigation of intrinsic dynamic frictional response of a sliding interface on a microsecond time-scale and without the problems associated with the dynamic parameters of the various frictional apparatus. Moreover, the experimental configuration allows critical frictional parameters such as the applied normal pressure, the transmitted shear stress and the interfacial slip velocity to be interpreted using the framework of one-dimensional wave analysis. The experimental results, deduced from the response to step changes imposed on the normal pressure at the frictional interface, reinforce the importance of including frictional memory in the development of the rate-dependent state variable friction models. However, this set-up is not able to bring information about the stress field developed in the specimen and to shed light on the phenomena occurring on the interface. The purpose of the present work is to study experimentally the high rate events which occur during rupture of incoherent interfaces by applying an asymmetric impact loading experiment and to obtain some information about the nature of rupture. Using dynamic photoelasticity we investigated dynamic rupture in a micro-second time-scale without the problems associated with the dynamic parameters of the apparatus and we were able to capture in real time significant effects like loading pulses, rupture propagation, slip pulses and s