Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media

TL;DR

This paper investigates the behavior of planar tensile cracks in heterogeneous media, revealing how variations in fracture toughness and heterogeneities can lead to instabilities in crack propagation.

Contribution

It introduces a model showing how heterogeneities and the velocity dependence of fracture toughness cause crack front instabilities.

Findings

Existence of a crack front mode with velocity just below Rayleigh wave speed.

Instability occurs when the fracture toughness decreases with velocity.

Heterogeneities induce low-velocity crack front radiation leading to instability.

Abstract

The dynamics of tensile crack fronts restricted to advance in a plane are studied. In an ideal linear elastic medium, a propagating mode along the crack front with a velocity slightly less than the Rayleigh wave velocity, is found to exist. But the dependence of the effective fracture toughness $\Gamma(v)$ on the crack velocity is shown to destabilize the crack front if $(d\Gamma)/(dv)<0$. Short wavelength radiation due to weak random heterogeneities leads to this instability at low velocities. The implications of these results for the crack dynamics are discussed.