An oblique edge crack and an internal crack in a semi-infinite plane acted on by concentrated force at arbitrary position

Abstract

A semi-infinite plane with an oblique edge crack and an internal crack acted on by a pair of concentrated forces at arbitrary position is studied. The problem can be divided into two particular parts; one is the half plane with the edge crack acted on by the concentrated forces; the other is the half plane with the edge cracked subjected to distributed dislocations on the line of the internal crack. The traction components along the line of the internal crack induced by the distributed dislocations must be of the same magnitude and in the opposite direction to the traction components resulting from the first part, the condition is used to establish the boiunary integral equation of the problem, in which the fundamental solutions of the edge cracked half plane plays an important part, and the dislocation distributions on the line of the internal crack can be determined by solving the boundary integral equation numerically. Since the properties of the half plane and edge crack have been reflected analytically by the fundamental solution of the edge crack have been reflected necessary to perform numerical computation on the surface of the half plane so that the method is presented in this paper is of high precision and less computation.