Fracture and the Grinfeld instability

We present a continuum theory that describes the fast growth of notches in a solid phase which are induced by nonhydrostatic stresses (Grinfeld instability). This mechanism overcomes the usual cusp singularity by a self-consistent selection of the tip radius. It connects the Grinfeld instability to fracture mechanics, predicts the saturation of the steady state crack velocity appreciably below the Rayleigh speed and tip blunting. Furthermore, it includes the possibility of a tip splitting instability for high applied tensions.