Dynamic stability of crack fronts: Out-of-plane corrugations

TL;DR

This paper investigates the out-of-plane stability of crack fronts in linear elastic fracture mechanics, identifying conditions under which corrugations emerge and their potential link to crack branching.

Contribution

It applies the Willis-Movchan 3D perturbation formalism to analyze crack front corrugations and predicts their propagation speed relative to Rayleigh waves.

Findings

Corrugations emerge above a critical crack speed.

Corrugations propagate near Rayleigh wave-speed.

Potential link between corrugations and crack branching.

Abstract

The dynamics and stability of brittle cracks are not yet fully understood. Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys. Solids {\bf 45}, 591 (1997)] to study the out-of-plane stability of planar crack fronts in the framework of linear elastic fracture mechanics. We discuss a minimal scenario in which linearly unstable crack front corrugations might emerge above a critical front propagation speed. We calculate this speed as a function of Poisson's ratio and show that corrugations propagate along the crack front at nearly the Rayleigh wave-speed. Finally, we hypothesize about a possible relation between such corrugations and the long-standing problem of crack branching.