Perturbation of Mode III interfacial cracks

TL;DR

This paper develops asymptotic formulas for the first-order perturbation of stress intensity factors in Mode III interfacial cracks, considering geometrical deviations of the crack faces and interface, with numerical illustrations and discussions on extending to finite bodies.

Contribution

It introduces a method to derive asymptotic formulas for Mode III interfacial crack perturbations, emphasizing the importance of skew-symmetric weight functions.

Findings

Derived first-order asymptotic formulas for stress intensity factor perturbations.

Numerical results demonstrate the method's application to various geometrical perturbations.

Discussion on extending the approach to finite-sized structures.

Abstract

We consider the perturbation problem of a Mode III interfacial crack. The perturbation is of geometrical type and can be both perturbation of the crack faces and perturbation of the interface, which can deviate from the initial straight line configuration. Asymptotic formulae are derived for the first-order perturbation of the stress intensity factor. It is shown that, due to the unsymmetrical nature of the problem, the Mode III skew-symmetric weight function derived in Piccolroaz et al. (2009) is essential for the derivation of the correct asymptotic formulae. To illustrate the method, we present the numerical results for different geometrical perturbations of a half-plane interfacial crack in an infinite bimaterial structure. Discussion on the extension of the method to finite bodies is also presented.