Contact of the lips of an interphase crack in the field of concentrated mass forces

Abstract

We consider a plane problem of the theory of elasticity for a crack located on the boundary of a fixed half plane subjected to the action of an arbitrary concentrated load applied to internal points of the domain. It is assumed that the crack lips contact without friction in the vicinity of the tip. By applying the Fourier integral transformation, we reduce the problem to a system of singular integral equations. In constructing the numerical solution of this system, we take into account the singular behavior of unknown functions near singular points. We establish the dependence of the size of the region of contact of the crack lips on the type of applied load. It is shown that, in this case, the combination of stress intensity factors obtained under the load applied at infinity remains quasiinvariant with respect to the length of the contact region. By using the elastic solution, we approximately determine the boundaries of the plastic domain near the crack tip and analyze their dependence on the intensity of the shearing field.