Stress-Strain State of a Half Plane with Internal Subsurface Cracks

Abstract

The elastic and elastoplastic (within the framework of the model of plastic bands) problems of elasticity theory and fracture mechanics for a half plane with internal smooth and piecewise smooth cracks are solved by the method of singular integral equations. The numerical solutions of the integral equations are obtained by the method of mechanical quadratures. The stress intensity factors at the tips of piecewise smooth subsurface cracks are determined and their dependences on the geometric parameters of the problem are investigated under the conditions of action of internal pressure upon the crack faces and tension of the half plane at infinity. For the elastoplastic problem, we study the influence of the free edge of the half plate, level of loading, and the shape of the crack on the crack tip opening displacement, length, and the angles of orientation of the rectilinear plasticity bands originating from the crack tips.