Theory of Dislocation Cells. III. Simple Cells Constructable from Multipoles

Abstract

Infinitely tall dislocation cells such as may be constructed from assemblies of similar dislocation multipoles are investigated. The long-range stress fields of these are shown to be the same as those of the corresponding dislocation multipoles, while the short-range stress fields are those of the corresponding infinitely extended tilt walls, except for disturbances in the immediate vicinity of corners. It is shown that the stresses of a cell of given shape, cross-sectional area, and angle of relative misorientation, decrease in magnitude the more closely the dislocations in its walls are spaced. In the limit of continuous dislocation distributions all cell stresses vanish identically. Terminated cells are briefly considered, and a method for the simple construction of two-grid tilt boundaries, composed of parallel edge dislocations involving two arbitrarily oriented Burgers vectors, is presented.