Quasi-static crack propagation in heterogeneous media

TL;DR

This paper investigates the behavior of cracks in heterogeneous media under quasi-static conditions, analyzing their surface roughness and the effects of residual stresses, with implications for understanding experimental observations.

Contribution

It formulates equations of motion for crack fronts in heterogeneous media and analyzes their scaling behavior, highlighting differences between mode I and mode III cracks.

Findings

Mode III cracks are self-affine with a roughness exponent of 1/2.

Mode I cracks are only logarithmically rough due to local mode preference.

Residual stresses may increase crack surface roughness, but elastic wave effects might be necessary to explain experimental data.

Abstract

The dynamics of a single crack moving through a heterogeneous medium is studied in the quasi-static approximation. Equations of motion for the crack front are formulated and the resulting scaling behaviour analyzed. In a model scalar system and for mode III (tearing) cracks, the crack surface is found to be self affine with a roughness exponent of $\zeta=1/2$. But in the usual experimental case of mode I (tensile) cracks, local mode preference causes the crack surface to be only logarithmically rough, quite unlike those seen in experiments. The effects of residual stresses are considered and found, potentially, to lead to increased crack surface roughness. But it appears likely that elastic wave propagation effects may be needed to explain the very rough crack surfaces observed experimentally.