Evaluation of the Lazarus-Leblond constants in the asymptotic model of the interfacial wavy crack

TL;DR

This paper connects two analytical methods for modeling interfacial wavy cracks in isotropic materials, providing integral representations and explicit constants to unify previous solutions and improve understanding of stress intensity factors.

Contribution

It derives the explicit Lazarus-Leblond constants and constructs integral representations, bridging the special and general solution methods for interfacial crack analysis.

Findings

Derived closed-form Lazarus-Leblond constants

Constructed integral representations of weight functions

Unified previous analytical approaches

Abstract

The paper addresses the problem of a a semi-infinite plane crack along the interface between two 3D isotropic half-spaces. Two methods of solution have been considered in the past: Lazarus and Leblond (1998) applied the "special" method by Bueckner (1987) and found the expression of the variation of the stress intensity factors for a wavy crack without solving the complete elasticity problem; their solution is expressed in terms of the physical variables, and it involves five constants whose analytical representation was unknown; on the other hand the "general" solution to the problem has been recently addressed by Bercial-Velez et al. (2005), using a Wiener-Hopf analysis and singular asymptotics near the crack front. The main goal of the present paper is to complete the solution to the problem by providing the connection between the two methods. This is done by constructing an integral representation for the Lazarus-Leblond's weight functions and by deriving the closed form representations of the Lazarus-Leblond's constants.