Crack propagation as a free boundary problem

TL;DR

This paper introduces a sharp interface model for crack propagation as a free boundary problem, revealing steady state behaviors, velocity saturation, tip blunting, and splitting instabilities through numerical solutions.

Contribution

It presents a novel phase transition-based model for crack growth and provides numerical analysis of steady states and instabilities considering elastodynamic effects.

Findings

Steady state crack velocity saturates below Rayleigh speed.

Tip blunting increases with driving force.

Above a critical force, tip splitting instability occurs.

Abstract

A newly developed sharp interface model describes crack propagation by a phase transition process. We solve this free boundary problem numerically and obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady state crack velocity below the Rayleigh speed, tip blunting with increasing driving force and a tip splitting instability above a critical driving force.