Stress singularities of contact problems with a frictional interface in anisotropic bimaterials

This paper develops an effective approach to analyse the asymptotic displacement and stress fields near the singular points in laminated anisotropic composite joints with a fictional contact along the interface. The Ting's theory, extended from the Stroh's formulation for anisotropic elasticity problems, is employed to represent the asymptotic fields near the singular points of the contact problems. The characteristic equations of the contact problems are constructed from the boundary conditions, where the continuity conditions at the frictional interface governed by the Coulomb's law of friction are considered. The order of stress singularities and the asymptotic fields near the singular points are determined by solving the developed non-linear coupled characteristic equations for the general contact problems of friction in anisotropic bimaterials from an iterative procedure. Only real values of root representing the order of stress singularities are found for the general frictional contact problems. In the special case when the frictional contact exists in two half plane composite laminates, stress singularities may appear if the material constants satisfy certain requirements. Explicit solutions for the root of the characteristic equations and the asymptotic fields for the special case can be directly obtained without requiring the iterative procedure. The theoretical and numerical results show that both the friction coefficient within the slip interface and the wedge angle of anisotropic materials have significant effects on the stress singularities for the frictional contact problems. Further investigations are undertaken for several special cases, including studies for isotropic materials that are confirmed by existing theoretical results and experimental data available.