Investigation of the Fracture of a Semibounded Body Compressed Along a Near-Surface Interface Crack

Abstract

We consider the problem of compression of a piecewise homogeneous half plane by forces directed along a near-surface crack located on the interface of two materials. This problem belongs to the class of nonclassical problems of fracture mechanics because, for the analyzed loading scheme, the stressstrain state realized in the body is homogeneous and the corresponding expressions for stresses and displacements in the vicinity of the crack do not contain singular components. Due to the fact that the stress intensity factors are equal to zero, for the analyzed problem, the classical Griffith–Irwin fracture criteria are inapplicable. In the indicated situation, the onset of crack propagation is associated with the local loss of stability of the equilibrium state of a part of the material located in the region adjacent to the crack. By using the approaches of the three-dimensional linearized theory of stability of deformable bodies, we propose a mathematical statement of the problem and an approach to its investigation. By using the representations of stresses and displacements in terms of complex potentials, we analyze the case where the roots of the corresponding characteristic equation are identical for each material.