An Approach to Analysis of Fracture of Semi-bounded Body Under Compressing Along Interfacial Near-Surface Crack

The problem of compressing a piece-homogeneous half-plane with forces directed along the near-surface crack located in the interface of two materials is considered. The problem relates to non-classical problems of fracture mechanics, since under such a loading scheme the stress-strain state realized in the body is homogeneous and in the corresponding expressions for stresses and displacements near the crack there are no singular components. Due to the fact that the stress intensity factors are equal to zero, the classical Griffiths-Irwin fracture criteria are inapplicable for the problem under consideration. In this situation, the start of crack propagation is associated with the local stability loss of the equilibrium state of a part of the material in the region adjacent to the crack. Using the approaches of the linearized theory of deformed bodies stability, the mathematical formulation of the problem was carried out.