Depinning transition in the failure of inhomogeneous brittle materials.

The dynamics of cracks propagating in elastic inhomogeneous materials is investigated experimentally. The variations of the average crack velocity with the external driving force are measured for a brittle rock and shown to display two distinct regimes: an exponential law characteristic of subcritical propagation at a low driving force and a power law above a critical threshold. This behavior can be explained quantitatively by extending linear elastic fracture mechanics to disordered systems. In this description, the motion of a crack is analogous to the one of an elastic line driven in a random medium, and critical failure occurs when the external force is sufficiently large to depin the crack front from the heterogeneities of the material.