Intersonic crack growth on an interface

Evidence has accumulated recently that a crack can propagate on an interfac e between dissimilar solids at speeds between the smallest and the largest sonic speeds of the constituent solids. Such an intersonic crack has posed several challenges to the existing theory. Assuming that the crack tip is a structureless point, and the solids are linearly elastic all the way to th e crack tip, the theory shows that the stress field is singular not only at the crack tip, but also along the shock front. Furthermore, the singularit y exponents differ from one half, so that the energy release rate is either zero or infinite. The relation of this theory to the experimental observat ions has been obscure. Specifically, it is unclear what crack speeds are fo rbidden by the theory. In this paper, we first introduce a unified method t o analyse the crack tip field. The crack can be static, subsonic or interso nic; and the two constituent solids can be isotropic or anisotropic. To add ress the problem of forbidden crack speeds, we extend a cohesive zone model to intersonic cracks. In this model, the crack tip is no longer a structur eless point; rather, a distributed stress represents bonding or friction. T he model removes both the singular crack tip and the singular shock front. The length of the cohesive zone also characterizes the thickness of the sho ck front. This length depends on the crack speed. A crack speed is forbidde n if it results in a negative cohesive zone length. The predictions of the model are discussed in the light of the experimental observations.