It was shown that the independence of the total interaction force, with regard to separation, remained valid for 2 skew straight dislocations in an anisotropic linear elastic half-space; with each dislocation parallel to the traction-free half-space boundary. Upon referring to the dislocation closest to the half-space boundary as I and to the other as II, the remarkable result was obtained that the total interaction force of I on II vanished, while the total interaction force of II on I was precisely twice the net interaction force which II exerted on I in an infinite medium. The fact that the net interaction forces in the half-space problem were unequal and opposite (unless they both vanished) was attributed to a lack of translational invariance normal to the half-space boundary. The Orlov-Indenbom result for 2 skew dislocations in an infinite anisotropic medium was then derived, and a Green's function method was used to calculate a suitable so-called image field. When this was added to that used to produce the Orlov-Indenbom result, it accounted for the presence of the free boundary of a dislocated half-space. Integration of the appropriate image Peach-Koehler force over each of the 2 skew dislocations then predicted the above dislocation interaction behavior.

The Net Interaction Force between Two Skew Dislocations in an Elastically Anisotropic Half-Space D.M.Barnett: Scripta Materialia, 1998, 39[4-5], 371-8