Grinfeld instability on crack surfaces

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 numerically that die energy of a wavy crack becomes smaller than the energy of a straight crack if the crack length exceeds a critical length L-c =5.18L(G) (L-G is the Griffith length). We analyze the dynamic evolution of this instability, governed by surface diffusion or condensation and evaporation. It turns out that the curvature of the crack surface becomes divergent near the crack tips. This implies that the widely used condition of the disappearance of K-II, the stress intensity factor of the sliding mode, is replaced by the more general requirement of matching chemical potentials of the crack surfaces at the tips. The results are generalized to situations of different external loading.