Safe equilibrium and crack growth in inhomogeneous materials as a variational problem

TL;DR

This paper formulates a variational principle for safe equilibrium in inhomogeneous cracked materials, linking energy reduction rates to crack growth and validating criteria for crack propagation directions.

Contribution

It introduces a variational framework for predicting crack growth in inhomogeneous materials based on energy reduction rates, extending existing criteria.

Findings

Crack remains in safe equilibrium when energy reduction rate is negative.

Crack growth initiates when the energy reduction rate reaches zero.

Application to bimaterial interface cracks demonstrates the criterion's predictive capability.

Abstract

The variational principle of safe equilibrium for inhomogeneous elastic cracked bodies is formulated. Using the standard calculus of variations, we show that the crack remains in safe equilibrium as long as the maximum energy reduction rate of the virtually growing crack is negative. The crack starts to grow in the direction of the maximum energy reduction rate when the latter becomes zero. This energetic criterion implies the criteria proposed by He and Hutchinson (1989). As an application we use this criterion to predict the growth direction of an interface crack in a bimaterial.