Analysis of bi-material interface cracks with complex weighting functions and non-standard quadrature

TL;DR

This paper develops a boundary element method with complex weighting functions and non-standard quadrature to accurately analyze stress intensity factors at bi-material interface cracks, including complex oscillatory singularities.

Contribution

It introduces a novel boundary element approach that handles oscillating stress singularities using complex weights and specialized quadrature, improving accuracy for interface crack problems.

Findings

Provides highly accurate, mesh-independent solutions for interface crack problems.

Demonstrates the method's effectiveness through comparison with analytical solutions.

Applies the approach to study epoxy-metal joint scaling behavior.

Abstract

A boundary element formulation is developed to determine the complex stress intensity factors associated with cracks on the interface between dissimilar materials. This represents an extension of the methodology developed previously by the authors for determination of free-edge generalized stress intensity factors on bi-material interfaces, which employs displacements and weighted tractions as primary variables. However, in the present work, the characteristic oscillating stress singularity is addressed through the introduction of complex weighting functions for both displacements and tractions, along with corresponding non-standard numerical quadrature formulas. As a result, this boundary-only approach provides extremely accurate mesh-independent solutions for a range of two-dimensional interface crack problems. A number of computational examples are considered to assess the performance of the method in comparison with analytical solutions and previous work on the subject. As a final application, the method is applied to study the scaling behavior of epoxy-metal butt joints.