Symmetric and skew-symmetric weight functions in perturbation models of 2D interfacial cracks

TL;DR

This paper develops a comprehensive method using symmetric and skew-symmetric weight functions to analyze stress intensity factors in 2D interfacial cracks, enhancing perturbation analysis accuracy.

Contribution

It introduces a novel approach combining symmetric and skew-symmetric weight functions for detailed perturbation analysis of interfacial cracks.

Findings

Derived integral formula for stress intensity factors.

Solved Wiener-Hopf equation for symmetric weight functions.

Established asymptotic procedure for perturbation analysis.

Abstract

In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as high-order terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener-Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution. The weight function matrices are then used in the perturbation analysis of a crack advancing quasi-statically along the interface between two dissimilar media. A general and rigorous asymptotic procedure is developed to compute the perturbations of stress intensity factors as well as high-order terms.