Dynamic crack deflection and penetration at interfaces in homogeneous materials: experimental studies and model predictions

Abstract

We examine the deflection/penetration behavior of dynamic mode-I cracks propagating at various speeds towards inclined weak planes/interfaces of various strengths in otherwise homogeneous isotropic plates. A dynamic wedge-loading mechanism is used to control the incoming crack speeds, and high-speed photography and dynamic photoelasticity are used to observe, in real-time, the failure mode transition mechanism at the interfaces. Simple dynamic fracture mechanics concepts used in conjunction with a postulated energy criterion are applied to examine the crack deflection/penetration behavior and, for the case of interfacial deflection, to predict the crack tip speed of the deflected crack. It is found that if the interfacial angle and strength are such as to trap an incident dynamic mode-I crack within the interface, a failure mode transition occurs. This transition is characterized by a distinct, observable and predicted speed jump as well as a dramatic crack speed increase as the crack transitions from a purely mode-I crack to an unstable mixed-mode interfacial crack.

Introduction

When cracks propagate in homogeneous, brittle solids, they can only do so under locally mode-I conditions and at sub-Rayleigh wave speeds typically below the crack branching speed (Freund,1990; Broberg, 1999). Indeed, even if the applied far-field loading is asymmetric, the dynamically growing crack will curve and follow the path that will result to locally opening (mode-I) conditions at its tip making mix-mode and pure mode-II crack growth in homogeneous materials a physical impossibility. In addition, as the crack accelerates, under increasing far-field loading, it reaches a critical speed beyond which it becomes energetically more favorable to propagate with multiple, branched crack tips rather than as a single entity. This is called the branching speed which for a material like Homalite-100 is approximately equal to 0.35c_S.

The situation is entirely different if a crack is constrained to propagate along a weak preferable path in an otherwise homogeneous solid. In this case and depending on the bond strength, the weak crack path or bond often traps the crack, suppresses any tendency of branching or kinking out of the weak plane and permits very fast crack growth much beyond the speeds observable in monolithic solids (Rosakis et al., 1999). Indeed, when mode-I cracks propagate in both isotropic and orthotropic solids containing weak crack paths (Washabaugh and Knauss, 1994; Coker and Rosakis, 2002), they can reach speeds as high as the Rayleigh wave speed of the solid. On the other hand, when mode-II cracks are made to propagate along such weak cracks, they tend to go even faster with speeds that are clearly within the intersonic regime of the solid (Rosakis et al., 1999; Gao et al., 1999; Geubelle and Kubair, 2001; Coker and Rosakis, 2002).

Although the extreme mode-I and mode-II cases have recently been studied experimentally and theoretically, very little is known about the dynamic mixed-mode crack growth along weak paths, a situation that has only recently been analyzed by Geubelle and Kubair (2001), and about the transition of an incident dynamic mode-I crack into a mixed-mode crack as it encounters a weak plane or interface. In the present work, we examine the incidence of dynamically growing cracks at inclined interfaces of various strengths. Our first goal is to observe this phenomenon experimentally and to establish and validate a dynamic deflection/penetration criterion. We then concentrate on the deflection behavior and examine mixed-mode crack growth along an interface.

It should be noted that static deflection/penetration behavior at an interface has been the subject of numerous research efforts in the past years and that many significant results for various kinds of materials have been obtained (Cook and Gordon, 1964; He and Hutchinson, 1989; Gupta et al., 1992; Evans and Zok, 1994; Martinez and Gupta, 1994; Ahn et al., 1998; Leguillon et al., 2000; He et al., 2000; Qin and Zhang, 2000). For quasi-statically growing cracks, the fracture toughness ratio of the interface and the matrix material has been identified as the most important parameter governing the crack deflection/penetration phenomenon and has formed the basis of a highly successful crack deflection/penetration criterion (Hutchinson and Suo, 1992). To authors’ knowledge and with very few notable exceptions (Siegmund et al., 1997), the equivalent dynamic problem has remained unexplored. In this paper we deal only with an important subset of this problem. In particular, we consider weakly bonded systems composed of identical constituent solids so that the resulting material remains constitutively homogeneous. However, the existence of a weak bond (bond of lower fracture toughness) makes this material inhomogeneous regarding its fracture resistance behavior. By doing so we avoid the complication of the material property and wave speed mismatch across the interface, while retaining the essential properties of a weak path or bond whose strength can be experimentally varied and analytically modeled.

Motivation for studying this basic problem comes from our recent experimental observations of dynamic failure mechanisms in bonded Homalite layers subjected to projectile impact (Xu and Rosakis, 2002a). A visual example of the interaction of a fan of dynamically moving mode-I branches incident on a weak interface is shown in Fig. 1 (dynamic equivalent of the Cook–Gordon mechanism). The horizontal line in this picture represents an interface between two weakly bonded Homalite layers. As the subsonic mode-I cracks approach the interface, one central shear-dominated interfacial crack is nucleated and propagates along the bond at intersonic speeds providing an illustrative example of failure mode transition. This nucleation and growth of a symmetrically growing intersonic shear crack along a straight-line path is extensively discussed in the book by Broberg (1999). Fig. 1 is the direct evidence that such cracks exist and may be nucleated through remote interaction of incoming mode-I cracks with weak interfaces. Another example of the interaction between mode-I crack growth and an interface is given in the post-mortem picture of Fig. 2(a). Here two mode-I branches are incident onto the same vertical interface at approximately the same speed. The two cracks meet the interface at two different incident angles (angle between the crack path and the interface). As evident form the picture, the crack that meets the interface at 78° penetrates the interface while the other one is trapped by it (incident angle is 50°). Another motivation comes from the question of dynamic crack propagation in brittle heterogeneous solids (composed of large grains bonded together by weak grain boundaries). Examples of such solids include marble (Rosakis, 2000) or certain classes of high explosives (Dienes, 1996). Fig. 2(b) shows a dynamic crack propagating towards a grain boundary, which it may penetrate or follow depending on the incident crack speed, incident crack angle as well as the relative toughnesses between the grain and the grain boundary.