The problem of stress concentration in the vicinity of the crack tip of finite length perpendicularly located to the interface between two elastic half-planes was reviewed. The usage of integral discontinuous solutions method enabled us to reduce the problem to solving a singular integral equation of the first kind with Cauchy kernel. We reviewed the limiting case of the problem when the half-plane without the crack is absent and the boundary of the body under review is free from stress. The solution of the integral equation is constructed in the form of an asymptotic expansion with respect to the small parameter characterizing the relative distance between the crack and the interface. In order to determine the effectiveness of obtained expansions we construct the solution of the same problem by collocation method. It was executed a comparison of the results with the known ones, previously obtained by numerical methods. The values of the normal stress intensity factor in the vicinity of the crack tip for various combinations of geometrical and physical parameters of the problem were obtained.

В данной работе решена задача о концентрации напряжений в окрестности вершины трещины конечной длины, расположенной перпендикулярно границе раздела двух упругих полуплоскостей. На основе уравнений равновесия задача сведена к решению сингулярного интегрального уравнения первого рода с ядром Коши с помощью метода разрывных решений. Интегральное уравнение было решено методами малого параметра и коллокации. Проведен анализ сходимости методов, получены численные результаты.