Criterion for crack formation in disordered materials

Crack formation is conventionally described as a nucleation phenomenon despite the fact that the temperatures necessary to overcome the nucleation barrier are far too high. In this paper we consider the possibility that cracks are created due to the presence of frozen disorder (e.g., heterogeneities or frozen dislocations). In particular we calculate the probability for the occurrence of a critical crack in a quasi-two-dimensional disordered elastic system. It turns out that this probability takes the form of an Arrhenius law (as for thermal nucleation) but with the temperature T replaced by an effective disorder temperature T-eff which depends on the strength of the disorder. The extension of these results to d = 3 dimensions is briefly discussed.