Surface Instabilities in Cracks

Abstract

The surface of a propagating crack is shown to be morphologically unstable because of the nonhydrostatic stresses near the surface (Asaro-Tiller-Grinfeld instability). We find that the energy of a wavy crack becomes smaller than the energy of a straight crack if the crack length is a few times larger than the Griffith length. The local dispersion relation is derived assuming that the instability develops via mass transport by surface diffusion. We also argue that the widely used condition of the vanishing of $K_{\mathrm{II}}$, the stress-intensity factor of the sliding mode, appears in a natural way in our description as an effective boundary condition at the tip of the crack.