An equilibrium internal transverse crack in a composite elastic half-plane

The problem of the stress concentration in the vicinity of the crack tips for a crack of finite length located perpendicular to the interface of two elastic bodies – a half-plane and a strip – is considered. Using the method of generalized integral transforms, the problem reduces to solution of a singular integral equation with a Cauchy kernel. Limit cases of the problem are considered when the thickness of the strip is relatively small, equal to zero (free boundary of the half-plane), or indefinitely large (a composite plane). The solution of the integral equation is constructed by the collocation method and the small parameter method. With the aim of increasing the efficiency of the numerical method, an approximation of the regular part of the kernel in a special form is used. Values of the stress intensity factors of the normal stresses in the vicinity of crack tips are obtained for different combinations of the geometrical and physical parameters of the problem.