Universal Aspects of Dynamic Fracture in Brittle Materials

We present an experimental study of the dynamics of rapid tensile fracture in brittle amorphous materials. We first compare the dynamic behavior of “standard” brittle materials (e.g. glass) with the corresponding features observed in “model” materials, polyacrylamide gels, in which the relevant sound speeds can be reduced by 2-3 orders of magnitude. The results of this comparison indicate universality in many aspects of dynamic fracture in which these highly different types of materials exhibit identical behavior. Observed characteristic features include the existence of a critical velocity beyond which frustrated crack branching occurs1, 2 and the profile of the micro-branches formed. We then go on to examine the behavior of the leading edge of the propagating crack, when this 1D “crack front” is locally perturbed by either an externally introduced inclusion or, dynamically, by the generation of a micro-branch. Comparison of the behavior of the excited fronts in both gels and in soda-lime glass reveals that, once again, many aspects of the dynamics of these excited fronts in both materials are identical. These include both the appearance and character of crack front inertia and the generation of “Front Waves”, which are coherent localized waves 3-6 which propagate along the crack front. Crack front inertia is embodied by the appearance of a “memory” of the crack front, which is absent in standard 2D descriptions of fracture. The universality of these unexpected inertial effects suggests that a qualitatively new 3D description of the fracture process is needed, when the translational invariance of an unperturbed crack front is broken. INTRODUCTION The study of dynamic fracture is a subject that has been under intensive study for over 50 years. This subject is not only of practical interest, but is of considerable fundamental interest. The existence of even a single small crack in a material under stress gives rise to a significant decrease in the material’s strength. This reduction in strength, predicted by linear elasticity, is due to singular behavior of the stress field at the tip of a crack. Each component of the stress field behaves as r -1/2, in the near vicinity of the crack tip, where r is the distance from the tip. One can, therefore, view a crack as a rapidly propagating singularity, whose speed of propagation is on the order of the speed of information (acoustic velocities) within the surrounding material. Thus, understanding the dynamic behavior of a moving crack may shed light on the physics of a large family of nonlinear problems, which are typified by propagating singular fronts. There are a number of important and still open problems related to the study of dynamic fracture. Experiments have shown 9 that as long as the fracture process is described by a single propagating crack, the equation of motion for a dynamic crack, derived by balancing the energy flow into a crack’s tip with the dissipative processes contained within the near-tip region, provides an excellent quantitative description of a crack’s motion. This successful description of a crack’s dynamics has two “formal” conditions. The first (the assumption of “small-scale yielding”) is that all dissipative processes are contained within a small region surrounding the crack tip, coined the process zone, which itself is surrounded by the singular stress field mentioned above. The second condition is tha t the medium in which the crack is propagating is effectively two-dimensional (i.e. that a crack can be viewed as a branch cut whose tip is point-like).