On Nix’s Theorem for two skew dislocations in an anisotropic piezoelectric space, half-space and bimaterial

In a private communication with D. M. Barnett, W. D. Nix presented a series of numerical computations in which he calculated the net interaction force between two skew dislocations separated by a distance h that are parallel to the traction-free surface of an isotropic elastic half-space. Nix drew a series of conclusions from his numerical computations including the independence of the net interaction force on the distance h. In seeking the extension of Nix’s conclusions to half-spaces of arbitrary anisotropy, Barnett called Nix’s original set of results ‘Nix’s Theorem’. In this paper, using the Stroh octet formalism, we derive new explicit and real form expressions for the net interaction force between two skew dislocations with generalized Burgers vectors, separated by a distance h, in an infinite anisotropic piezoelectric space, in a half-space and in a bimaterial. Each dislocation undergoes finite discontinuities in displacements and in electric potential across the slip plane. The net interaction force is yet again found independent of the separation distance. For an infinite space and half-space with a traction-free and charge-free surface, the net interaction force is found independent of the second component of each of the two generalized Burgers vectors and vanishes when only the second component of one generalized Burgers vector is nonzero and the remaining three components are zero.