An asymptotic analysis of the solution in the neighbourhood of the corner point of a crack along the kinked interface of two media

The asymptotic behaviour of an elastic field in the neighbourhood of the corner point of a crack at the interface of different materials is investigated within the framework of plane elasticity, taking into account the contact of its surfaces and the possibility of their mutual slippage with dry friction. The problem is solved by the method of complex Kolosov-Muskhelishvili potentials. The results obtained enable one to estimate the angular range of existence of contact zones and the singularity of the stresses close to the corner point of the crack. It is shown that the formation of contact zones, taking into account the friction forces accompanying slippage, depends essentially on the magnitude of the angle of the interface kinking the elasticity moduli of the materials and the friction coefficient. Numerical calculations are carried out and the stress and displacement distributions in the neighbourhood of the corner point are obtained.