Stresses on secondary systems due to piled-up groups of dislocations of arbitrary orientation

Abstract

Stress-fields around piled-up groups of dislocations of arbitrary orientation have been calculated by replacing the discrete dislocations by a continuous distribution of infinitesimal dislocations. Previous calculations by Mitchell (1964) have been performed on edge and screw dislocation pile-ups. In the present paper the case of 60° dislocations has been considered in particular, since in face-centred cubic crystals the dislocations will lie parallel to the intersection of the primary and conjugate or critical slip planes. It is shown that the stress-fields on many secondary slip systems are large and are capable of producing secondary slip over distances of the order of the pile-up length. Considerable reduction of long-range stresses is possible by the formation of tangles of primary and secondary dislocations whose Burgers vectors add up to zero and by the formation of small angle tilt boundaries. It is necessary that the primary and secondary dislocation densities should be of the same order, as is observed experimentally. The amount of secondary strain necessary for such high dislocation densities is small and is compatible with experimental observations.