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

TL;DR

This paper models slow crack growth in heterogeneous materials as a self-organized critical phase transition, successfully reproducing crackling dynamics and revealing universal scaling laws similar to those in magnetic systems.

Contribution

It introduces a linear elastic stochastic model that captures crackling dynamics and characterizes slow crack growth as a self-organized critical phase transition.

Findings

Reproduces crackling dynamics observed in experiments

Identifies universal scaling laws in crack growth

Models failure as a self-organized critical phase transition

Abstract

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.