Mode III crack propagation in a bimaterial plane driven by a channel of small line defects

TL;DR

This paper analyzes the quasi-static propagation of a Mode III crack along a bimaterial interface containing a finite array of small line defects, providing analytical formulas for crack advancement and potential applications in composite material failure analysis.

Contribution

It introduces an asymptotic analytical approach to model crack propagation influenced by microdefects arranged as a channel in a bimaterial interface.

Findings

Analytical formulas for incremental crack advance are derived.

Numerical examples demonstrate the approach's application to composite failure.

Extension to infinite defect arrays is discussed.

Abstract

We consider the quasi-static propagation of a Mode III crack along the interface in a bimaterial plane containing a finite array of small line defects (microcracks and rigid line inclusions). The microdefects are arranged to form a channel around the interface that can facilitate (or prevent) the crack propagation. The two dissimilar elastic materials are assumed to be weakly bonded, so that there is no kinking of the main crack from the straight path. On the basis of asymptotic formulae obtained by the authors, the propagation is analysed as a perturbation problem and the incremental crack advance is analytically derived at each position of the crack tip along the interface relative to the position of the defects. Numerical examples are provided showing potential applications of the proposed approach in the analysis of failure of composite materials. Extension to the case of infinite number of defects is discussed.