Quasi-static crack front deformations in cohesive materials

TL;DR

This paper develops a theoretical framework to understand how crack fronts deform in heterogeneous cohesive materials, considering the effects of a process zone on stability and shape, which explains experimental observations beyond classical fracture mechanics.

Contribution

It introduces a new equation for 3D coplanar crack propagation that accounts for the process zone's influence on crack front deformations in heterogeneous materials.

Findings

Process zone increases crack front compliance to small perturbations.

Process zone smooths out heterogeneities in fracture energy.

Theory predicts diverse crack front profiles observed experimentally.

Abstract

When a crack interacts with material heterogeneities, its front distorts and adopts complex tortuous configurations that are reminiscent of the energy barriers encountered during crack propagation. As such, the study of crack front deformations is key to rationalize the effective failure properties of micro-structured solids and interfaces. Yet, the impact of a localized dissipation in a finite region behind the crack front, called the process zone, has often been overlooked. In this work, we derive the equation ruling 3D coplanar crack propagation in heterogeneous cohesive materials where the opening of the crack is resisted by some traction in its wake. We show that the presence of a process zone results in two competing effects on the deformation of crack fronts: (i) it makes the front more compliant to small-wavelength perturbations, and (ii) it smooths out local fluctuations of strength and process zone size, from which emerge heterogeneities of fracture energy. Their respective influence on front deformations is shown to strongly impact the stability of perturbed crack fronts, as well as their stationary shapes when interacting with arrays of tough obstacles. Overall, our theory provides a unified framework to predict the variety of front profiles observed in experiments, even when the small-scale yielding hypothesis of linear elastic fracture mechanics breaks down.