Matched Asymptotic Expansions of Unbalanced Adhesive Joints

Abstract

A matched asymptotic expansion analysis is used to determine the dependence of shear stress boundary layer thickness on adhesive properties in unbalanced single-lap joints. A uniformly accurate expansion of shear stress, in a small and positive dimensionless parameter ε, is shown to contain a pair of adhesive edge boundary layers and an outer zone where the stress is slowly varying between the two layers. An overlap constraint is also found, and if it can be satisfied for ε≪1, then there is sufficient overlap and a single boundary layer of width the order of ε1/2 at either adhesive end. The analytic results are presented in a generic format allowing their application and/or extension to similar problems. All results are numerically verified using a finite difference approximation.