Investigation of compression of a piecewise homogeneous half-plane with a fixed boundary along an interface crack

A two-dimensional problem of fracture mechanics about the compression of a piecewise-homogeneous semi-bounded body with a boundary fixed in a special way along an interface near-surface crack is studied. The analytical-numerical approach proposed within the framework of the three-dimensional linearized stability theory of deformable bodies consists in reducing the original boundary value problem to an eigenvalue problem for a system of Fredholm integral equations of the first kind. For the case when the constituent materials of the body are described by the Bartenev–Khazanovich elastic potential, and the ratio of their rigidities does not exceed a certain value, the value of the critical load parameters corresponding to the local loss of stability of the material in the vicinity of the crack at the initial stage of fracture is calculated