Effect of Poisson’s ratio mismatch on brittle interfacial cracking between two dissimilar elastic layers

Abstract

Previous work by the authors (Harvey et al., 2015) on brittle interfacial cracking between two dissimilar elastic layers is extended to accommodate Poisson’s ratio mismatch in addition to the existing capability for elastic modulus mismatch. Under crack tip bending moments and axial forces, it is now possible to use a completely analytical 2D elasticity-based theory to calculate the complex stress intensity factor (SIF) and the crack extension size-dependent energy release rates (ERRs). To achieve this, it is noted that for a given geometry and loading condition, the total ERR and bimaterial mismatch coefficient are the two main factors affecting the partitions of ERR. Based on this, equivalent material properties are derived for each layer, namely, an equivalent elastic modulus and an equivalent Poisson’s ratio, such that both the total ERR and the bimaterial mismatch coefficient are maintained in an alternative equivalent case. Cases for which no analytical solution for the SIFs and ERRs currently exist can therefore be ‘transformed’ into cases for which the analytical solution does exist. The approach is verified against results from 2D finite element method simulations in which excellent agreement is observed for cases of plane stress and plane strain with a variety of loading conditions.