Nonlinear focusing in dynamic crack fronts and the micro-branching transition

TL;DR

This paper investigates the transition from faceting to micro-branching in crack fronts of brittle materials, revealing that nonlinear dynamic localization and rate-dependent dissipation drive this transition.

Contribution

It introduces a first-principles nonlinear equation of motion for crack fronts, elucidating the role of nonlinear focusing in the micro-branching transition.

Findings

Nonlinear focusing governs the transition to micro-branching.

Rate-dependent dissipation influences crack front dynamics.

Derived a nonlinear equation of motion for crack fronts.

Abstract

Cracks in brittle materials produce two types of generic surface structures: facets at low velocities and micro-branches at higher ones. Here we observe a transition from faceting to micro-branching in polyacrylamide gels that is characterized by nonlinear dynamic localization of crack fronts. To better understand this process we derive a first-principles nonlinear equation of motion for crack fronts in the context of scalar elasticity. Its solution shows that nonlinear focusing coupled to rate-dependence of dissipation governs the transition to micro-branching.