Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition

We derive here a linear elastic stochastic description for slow crack growth in heterogeneous materials. This approach succeeds in reproducing quantitatively the intermittent crackling dynamics observed recently during the slow propagation of a crack along a weak heterogeneous plane of a transparent Plexiglas block [M{aa}l{o}y {it et al.}, PRL {bf 96} 045501]. In this description, the quasi-static failure of heterogeneous media appears as a self-organized critical phase transition. As such, it exhibits universal and to some extent predictable scaling laws, analogue to that of other systems like for example magnetization noise in ferromagnets.