Exact analysis of mode-III cohesive fracture in layered elastic composites

Abstract

This paper examines the mechanics of mode-III defect initiation and quasi-static growth in a composite consisting of N layers separated by nonuniform nonlinear cohesive surfaces. The exact analysis is based on the elasticity solution to the problem of a single layer of finite width and thickness subjected to arbitrary, nonuniform but equilibrated shear tractions on top and bottom surfaces. The formulation leads to a system of integral equations governing rigid body layer translations and cohesive surface slip fields (tangential jump discontinuities across layer interfaces). Cohesive surfaces are modelled by traction-slip relations (exponential, modified exponential) characterized by a cohesive strength, a force length and possibly friction parameters. Symmetric center, edge and array defects are modeled by cohesive strength functions that vary with surface coordinate. Infinitesimal strain equilibrium solutions are sought by eigenfunction approximation of the solution of the governing integral equations. Solutions indicate that quasi-static defect initiation/propagation occur under increasing applied shear traction. For small values of force length, brittle behavior occurs corresponding to sharp crack growth. At larger values of force length, ductile response occurs similar to linear “spring” cohesive surfaces. Both behaviors ultimately cause abrupt failure of the surface. Results for the stiff, strong cohesive surface with a center defect under a small applied traction agree well with static crack solutions taken from the literature. Detailed results are obtained for (i) an array of symmetric collinear defects accounting for defect–defect interaction, (ii) a symmetric defect in a bilayer with nonuniform material properties/thicknesses, (iii) a center defect accounting for decohesion and friction.