Effective toughness of heterogeneous brittle materials

TL;DR

This paper investigates how the effective toughness of heterogeneous brittle materials depends on the correlation length of local toughness variations, revealing regimes of weak and strong pinning affecting crack propagation.

Contribution

It introduces a perturbative approach to estimate effective toughness and identifies different regimes based on correlation length, highlighting the transition from average toughness to enhanced toughness due to pinning effects.

Findings

Weak pinning regime where effective toughness equals average local toughness.

Transition to strong pinning regime with higher effective toughness.

Crack propagation characterized by jumps between pinning configurations.

Abstract

A heterogeneous brittle material characterized by a random field of local toughness Kc(x) can be represented by an equivalent homogeneous medium of toughness, Keff. Homogenization refers to a process of estimating Keff from the local field Kc(x). An approach based on a perturbative expansion of the stress intensity factor along a rough crack front shows the occurrence of different regimes depending on the correlation length of the local toughness field in the direction of crack propagation. A `"weak pinning" regime takes place for long correlation lengths, where the effective toughness is the average of the local toughness. For shorter correlation lengths, a transition to "strong pinning" occurs leading to a much higher effective toughness, and characterized by a propagation regime consisting in jumps between pinning configurations.