The net interaction force between two skew dislocations in an anisotropic linear elastic bimetallic medium

Barnett, in 1998, considered the problem of two skew dislocations in an anisotropic elastic half-space, each dislocation being parallel to the half-space boundary (which was taken as traction-free). He showed that the net interaction force of one dislocation on the other is independent of the separation of the dislocations. Rather incredibly, if the dislocation closest to the half-space boundary is denoted as (1) and the other skew dislocation is denoted as (2), Barnett deduced that the net interaction force of (1) on (2) vanishes, while the total interaction force of (2) on (1) is exactly twice the net force which (2) exerts on (1) in an infinite medium! The present work examines two skew dislocations in two perfectly bonded anisotropic half-spaces (one half-space may be doubly dislocated or each half-space may contain one dislocation). We show that there is an additional contribution (beyond that given by the half-space result) to the net interaction force exerted by one dislocation on the other, which is also separation-independent; essentially each dislocation experiences an additional contribution to the net interaction force which is the same as if the other dislocation were located at the interface between the two half-spaces. This additional contribution to the net force is ‘almost’ explicit, requiring only a computation of the admittance matrices of the Stroh formalism for each half-space.