Asymptotic behaviour of the elastic solution near the tip of a crack situated at a nonideal interface (Q2775656)

The purpose of this paper is to investigate accurately the nonideal interface with an interface crack for all possible combinations of material parameters as well as for different geometries of the interface zone for modes I and II. The thickness of a nonideal interface between two bonded materials is \(h(r)=h_0r^\alpha (\alpha\geq 0)\). The formulation of the model problem is based on the field equations of \(2D\) elasticity and the corresponding transmission conditions (thin spring approach). Using the Mellin transformation, a system of functional equations is derived. The existence and uniqueness of solutions to the functional equations obtained are proven and the solutions are given for different values of the parameter \(\alpha\). The asymptotic analysis of solutions in the vicinity of the crack tip is also presented. Some numerical examples illustrate the calculation of the stress singularity exponent.