Elastic Field of a Point Defect in a Cubic Medium and its Interaction with Defects

Abstract

Three equal orthogonal double forces without moment aligned along the cubic axes are used as a model for a point defect in a cubic medium. The method of Fourier transforms is used to obtain the solution for the displacement and stress fields. The solution is presented in a polynomial form. The elastic interaction between a point defect and an edge dislocation is computed for copper by making the displacement of the edge dislocation against the stress field of the defect. The interaction with the physically significant [112̄] edge dislocation on the (111) plane in copper is presented. The computer program was verified by the agreement of its results with those for the hypothetical [001] edge dislocation on the (010) plane, for which the stresses can be calculated in closed form. Near the slip plane, the calculated anisotropic interaction was almost twice that of a corresponding isotropic one. The elastic interaction between two point defects in copper is calculated, indicating regions of attraction of like defects along the cube axes and repulsion along the cube diagonals. Eshelby's perturbation analysis for materials with slight anisotropy predicts qualitatively similar effects, but the repulsion is much greater than that predicted by his approximate analysis.