Avalanches and clusters in planar crack front propagation

TL;DR

This paper investigates avalanche behavior in a model of planar crack propagation in disordered media, revealing power-law distributions of local clusters and deriving a key scaling relation, with implications for understanding experimental observations.

Contribution

It introduces a model capturing long-range interactions in crack avalanches, deriving a novel scaling relation between local and global avalanche exponents.

Findings

Avalanches consist of spatially disconnected local clusters with power-law size distribution.

Derived the scaling relation =2-1 between local cluster and global avalanche exponents.

Results explain experimental observations of crack avalanches in Plexiglas and are relevant to other long-range systems.

Abstract

We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a power law with an exponent $\tau_{a}=1.5$. We derive a scaling relation $\tau_a=2\tau-1$ between the local cluster exponent $\tau_a$ and the global avalanche exponent $\tau$. For length scales longer than a cross-over length proportional to the Larkin length, the aspect ratio of the local clusters scales with the roughness exponent of the line model. Our analysis provides an explanation for experimental results on planar crack avalanches in Plexiglas plates, but the results are applicable also to other systems with long-range interactions.