Interaction between non-parallel dislocations in piezoelectrics

The total interaction force F12F12 between two crossing (non-intersecting) straight dislocations is found and analyzed for the three types of piezoelectric media of unrestricted anisotropy: an unbounded body, an infinite plate and a half-infinite body. In the latter two cases the dislocations are supposed to be parallel with the surfaces, which are in turn implied to be mechanically free of tractions and electrically closed (metalized). The found force F12F12 is orthogonal to the parallel planes, P and Q  , containing the crossing dislocations. In an unbounded medium the value F12F12 proves to be independent of the distance between P and Q  . On the other hand, it depends on directions of the dislocations and on their Burgers vectors: the force F12F12 may be either attractive or repulsive. In a plate the interaction becomes sensitive to dislocation positions y(1,2)y(1,2) with respect to the surfaces. Only in the situations, when dislocations are much closer to each other than to the both surfaces, their interaction may be approximately described by the solution for an unbounded medium. Otherwise, corrections arising from the image forces due to the plate surfaces become essential. The dislocation in the vicinity of a surface strongly acts on its counterpart only until the latter situates even closer to the same surface than the first one. When the second dislocation leaves this narrow zone, the interaction force on it abruptly decreases to a very small level. With an increase in the thickness of the plate, this behavior becomes more and more pronounced. In a half-infinite medium the interaction between the dislocations is exactly described by a Heaviside step-like dependence F12∝H(y(1)-y(2)F12∝H(y(1)-y(2)) valid for any y(1,2)y(1,2). It is shown that we deal here with an analog of the plane capacitor effect.