Roughness of tensile crack fronts in heterogenous materials

TL;DR

This paper investigates the roughness of tensile crack fronts in heterogeneous materials using a stochastic model, revealing a phase transition to a rough phase with a specific roughness exponent, influenced by nonlinear effects and history dependence.

Contribution

It introduces a nonlinear stochastic equation of motion for crack fronts and identifies a phase transition to a rough phase with a universal roughness exponent of 1/2.

Findings

A continuous phase transition between flat and rough crack front phases.

The roughness exponent is at least 1/2 and may depend on the history of crack propagation.

Nonlinear effects destabilize linear modes, leading to roughness in crack fronts.

Abstract

The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysis is carried for a moving front in the quasi-static regime using the Self Consistent Expansion. A continuous dynamical phase transition between a flat phase and a dynamically rough phase, with a roughness exponent $\zeta=1/2$, is found. The rough phase becomes possible due to the destabilization of the linear modes by the nonlinear terms. Taking into account the irreversibility of the crack propagation, we infer that the roughness exponent found in experiments might become history-dependent, and so our result gives a lower bound for $\zeta$.