Planar distributions of dislocations II. Arrays of superlattice and partial dislocations

Abstract

Dislocation pile-ups were considered in an earlier paper, and a procedure introduced whereby the majority of the dislocations in a pile-up are smeared into a continuous distribution, while those intimately concerned with a particular physical phenomenon are allowed to remain discrete. The main advantages of this approach, as compared with those based on the extreme assumptions that all the dislocations are either discrete or are smeared into a continuous distribution, are that a high degree of physical reality is preserved and a simple solution may be obtained; its accuracy was demonstrated by considering particular pile-up problem sand comparing, where possible, the results for the distance between the dislocations at the head of a pile-up with those obtained by assuming all the dislocations to be discrete. The earlier work is here extended to a consideration of planar distributions of dislocations that are either split into their component partials or are of the superlattice type, thereby necessitating the introduction of an energy parameter describing the fault associated with each complete dis­location. Results have also been obtained by assuming that the smeared dislocations are replaced by a super-dislocation of appropriate Burgers vector; both approaches give similar results, which are also in good agreement with those determined in special situations by other workers employing computational procedures. The predictions of the superlattice dis­location model are used in a brief discussion related to the cleavage fracture characteristics of ordered alloys.