Stress singularities in the generalised Comninou frictional contact model for interface cracks in anisotropic bimaterials

Abstract

Characterisation of the singular asymptotic solution at the tip of interface cracks between dissimilar materials is essential for assessing the structural integrity of heterogeneous material systems. In the present article, the Comninou contact model, one of the most relevant and widely used models, originally introduced for isotropic bimaterials, is generalised for the first time to any anisotropic linear elastic bimaterial under generalised plane strain, considering a frictional sliding contact zone adjacent to the crack tip. The classical Coulomb friction law is considered. A novel procedure, based on the Stroh formalism of linear anisotropic elasticity, is developed to derive a system of two new coupled nonlinear eigenequations given in closed form for two unknown parameters of such singular solutions, the singularity exponent $\lambda$ and the sliding angle $\omega$ in the contact zone. In general, this eigensystem is solved by an iterative method, although in some cases, closed-form solutions are provided. Parametric studies of the influence of material orientations and the friction coefficient value on variations of $\lambda$ and $\omega$ reveal several surprising features of this asymptotic solution. The present approach is successfully verified by comparing some of the results obtained with those reported in previous studies, wherever possible. Note that previous studies essentially focused on bimaterials with specific orientations, considerably simplifying the problem. The singular solutions obtained can also be used in the asymptotic analysis of elastic fields at the boundary between stick and slip zones in partial slip contact problems for anisotropic materials.