Screw dislocations in a holed wedge

Abstract

A numerical code has been designed and implemented to find the stress at any material point in a holed wedge material due to any number of crystal or real screw dislocations in the wedge. The code implements the image dislocation method together with the collocation-point method to find stresses at any material point. We demonstrate that the combined analytical–numerical method (analytical with the image dislocations and numerical with the collocation-point method) is valid in that it produces stress fields giving rise to zero traction on free surfaces as well at an arbitrary number of collocation points on void surfaces. In addition, the method makes it possible to find the Peach–Koehler force (PKF) acting on a real screw dislocation at any point in the wedge, as well as to determine points of equilibrium, where the PKF is zero. Numerous and easy to interpret contour plots reveal the utility of this method which was carried out using the mathematical software MATLAB.