A nonlinear symmetry breaking effect in shear cracks

TL;DR

This paper develops a weakly nonlinear elastic theory for shear cracks, revealing a symmetry breaking effect that causes tensile deformation at the crack tip, with implications for understanding interfacial failure.

Contribution

It introduces a general nonlinear elastic framework for shear cracks, quantifies the symmetry breaking effect, and applies it to various materials, advancing the understanding of crack tip behavior.

Findings

Shear cracks experience tensile-mode deformation at the tip.

The symmetry breaking effect is quantified by an explicit inequality.

Elastic nonlinearities may influence frictional crack dynamics.

Abstract

Shear cracks propagation is a basic dynamical process that mediates interfacial failure. We develop a general weakly nonlinear elastic theory of shear cracks and show that these experience tensile-mode crack tip deformation, including possibly opening displacements, in agreement with Stephenson's prediction. We quantify this nonlinear symmetry breaking effect, under two-dimensional deformation conditions, by an explicit inequality in terms of the first and second order elastic constants in the quasi-static regime and semi-analytic calculations in the fully dynamic regime. Our general results are applied to various materials. Finally, we discuss available works in the literature and note the potential relevance of elastic nonlinearities for frictional cracks.