Roughness of Interfacial Crack Front: Correlated Percolation in the Damage Zone

TL;DR

This paper links the roughness of crack fronts in heterogeneous materials to correlated percolation theory, providing a theoretical prediction for the roughness exponent that matches experimental results.

Contribution

It introduces a new elastic brittle model connecting crack front roughness to correlated percolation, predicting the roughness exponent with numerical and analytical methods.

Findings

The roughness exponent zeta is given by nu/(1+nu).

Numerical simulations find nu=1.5, leading to zeta=3/5.

Predicted zeta=0.6 matches experimental observations.

Abstract

We show that the roughness exponent zeta of an in-plane crack front slowly propagating along a heterogeneous interface embeded in a elastic body, is in full agreement with a correlated percolation problem in a linear gradient. We obtain zeta=nu/(1+nu) where nu is the correlation length critical exponent. We develop an elastic brittle model based on both the 3D Green function in an elastic half-space and a discrete interface of brittle fibers and find numerically that nu=1.5, We conjecture it to be 3/2. This yields zeta=3/5. We also obtain by direct numerical simulations zeta=0.6 in excellent agreement with our prediction. This modelling is for the first time in close agreement with experimental observations.