Depinning transition in failure of inhomogeneous brittle materials

The dynamics of a crack propagating in an elastic inhomogeneous material is investigated. The variations of the average crack velocity with the external loading are measured for a brittle rock and are shown to display two distinct regimes: Below a given threshold Gc, the crack velocity is well described by an exponential law v ~ exp^{-(C/(G-(Gamma))} characteristic of subcritical propagation, while for larger values of the driving force G > Gc, the velocity evolves as a power law v ~ (G - G_c)^theta with theta = 0.80 $\pm$ 0.15. These results can be explained extending the continuum theory of Fracture Mechanics to disordered systems. In this description, the motion of a crack is analogue to the one of an elastic line driven in a random medium and critical failure occurs when the loading is sufficiently large to depinne the crack front from the heterogeneities of the material.