Surface dislocation model of a finite stressed solid

Abstract

A surface dislocation model using the discrete dislocation method has been applied to a finite solid subjected to either an applied stress or an internal stress. It has been shown that the state of stress in a finite body can be obtained by isolating the finite body with the aid of the surface arrays of dislocations such that the surface boundary conditions are satisfied on the surfaces of the finite body. The surface dislocations in general consist of two arrays: one whose Burgers vector is large and whose presence on the surface leads to a major relaxation of the surface and one whose Burgers vector is small and whose presence on the surface leads to a minor relaxation of the surface. The surface arrays are determined by minimizing the total energy of the configuration which corresponds to the free surface boundary conditions. The surface dislocation model has been utilized for a finite solid subjected to compression, shear and rotation. It has also been employed for a solid containing either a screw dislocation or an edge dislocation. The advantages of employing the surface dislocation model over other methods are illustrated.