Determination of interaction forces between parallel dislocations by the evaluation of J integrals of plane elasticity

The Peach–Koehler expressions for the glide and climb components of the force exerted on a straight dislocation in an infinite isotropic medium by another straight dislocation are derived by evaluating the plane and antiplane strain versions of J integrals around the center of the dislocation. After expressing the elastic fields as the sums of elastic fields of each dislocation, the energy momentum tensor is decomposed into three parts. It is shown that only one part, involving mixed products from the two dislocation fields, makes a nonvanishing contribution to J integrals and the corresponding dislocation forces. Three examples are considered, with dislocations on parallel or intersecting slip planes. For two edge dislocations on orthogonal slip planes, there are two equilibrium configurations in which the glide and climb components of the dislocation force simultaneously vanish. The interactions between two different types of screw dislocations and a nearby circular void, as well as between parallel line forces in an infinite or semi-infinite medium, are then evaluated.