On Nix's Theorem for Two Skew Dislocations in Anisotropic Elastic Half-Spaces and Bimaterials

Abstract

In the earlier papers, the net interaction force F between two skew dislocations with Burgers vectors b, b separated by a distance h in an infinite anisotropic elastic space, in a half space, or in a dissimilar bimaterial has been presented. In this paper, the authors employ Green's functions to obtain new explicit expressions of F. The new solutions provide new physical interpretations. The authors show that, for the infinite space and the half-space with a traction-free surface, F is independent of b₂, b₂ and that F = 0 if b or b is along the x2-axis. F is independent of the skew angle Oif the projections of b, b on the plane X2 = 0 lie along a pair of conjugate radii of an ellipse. For other half-spaces and bimaterials, F(on b) = 0 when b and b x v are along the x2-axis where v is the axial vector of a skew-symmetric matrix. Hence b is arbitrary if v = 0, which is the case for the half-space with a slippery surface and for certain bimaterials. F(on b) is independent of 0 when b is along the x2-axis and b is coplanar with v and the xi-axis. More physical interpretations are presented in the paper.