Intersonic crack growth on an interface

Evidence has accumulated recently that a crack can propagate on an interface 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 the 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 singularity exponents differ from one half, so that the energy release rate is either zero or infinite. The relation of this theory to the experimental observations has been obscure. Specifically, it is unclear what crack speeds are forbidden by the theory. In this paper, we first introduce a unified method to analyse the crack tip field. The crack can be static, subsonic or intersonic; and the two constituent solids can be isotropic or anisotropic. To address 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 structureless point; rather, a distributed stress represents bonding or friction. The model removes both the singular crack tip and the singular shock front. The length of the cohesive zone also characterizes the thickness of the shock front. This length depends on the crack speed. A crack speed is forbidden if it results in a negative cohesive zone length. The predictions of the model are discussed in the light of the experimental observations.