THE SOLUTION OF THE PLANE FRACTURE MECHANICS PROBLEM OF A PIECEWISE-HOMOGENEOUS HALF-PLANE UNDER COMPRESSION ALONG AN INTERFACIAL NEAR-SURFACE CRACK

Abstract

The paper presents an analytic-numerical approach to the study of plane problems on compression of piecewise homogeneous semi-confined bodies by near-surface cracks located at the interface of different media. The approach was developed in the framework of the three-dimensional linearized theory of stability of deformable bodies, when the beginning of the fracture process is initiated by the loss of material stability in a local region near cracks. For the first time the solution of the plane problem of compression of a semi-confined body (base) with a coating layer along a near-surface interfacial crack was obtained. Using representations of general solutions of linearized equilibrium equations through harmonic potential functions and application of Fourier integral expansions, this boundary value problem is reduced to an eigenvalue problem for a system of homogeneous Fredholm integral equations of the first kind, which is investigated numerically using the Bubnov-Galyorkin method. For the case when the base and coating material is described by the Bartenev-Khazanovich elastic potential, the values of critical parameters corresponding to the local loss of stability of the material around the crack at the initial stage of fracture were calculated. To verify the effectiveness of the proposed approach, we compared the values of critical fracture parameters obtained as a result of solving the problem for the considered piecewise homogeneous body with an interfacial crack with the values of critical fracture parameters obtained earlier when considering a similar plane problem for a homogeneous body with a near-surface crack.