Stress Field Near a Dislocation Slip Plane in an Orthotropic Medium

Abstract

The elastic stress field in the vicinity of a dislocation slip plane in an infinite orthotropic medium subjected to uniform shear at infinity is determined using a formulation in integral equations. It is assumed that a slip plane is different from a traction-free surface crack in that it has uniform shear on its surface and remains closed under the applied stress field. However, the use of these mixed boundary conditions under the restrictions of plane stress in linear elasticity is found to give the same stress distribution as that for a shear crack. Although a shear crack under an applied uniform shear opens up into an ellipse, the opening per unit length is shown to be so small that for most engineering applications it can be considered closed and the equivalence of a shear crack and a slip plane is established. It is pointed out that this correspondence is not valid between a shear crack in a thick elastic plate and a slip plane in an infinite elastic medium. Results for an isotropic body are given as a limiting case of an orthotropic body.