It was noted that the non-redundant dislocation density was larger than the redundant dislocation density in parts of the plastically deformed region, of a circular bar that had been deformed in torsion, if it was assumed that stress gradients (and gradients of the rotation pseudo-stress) did not affect the constitutive equation of an elastic-plastic solid. It was unclear whether the anomalous hardening that was seen in small-diameter torsion bars arose because the added non-redundant dislocations increased the work hardening in a manner that was similar to the hardness which was produced by redundant dislocations. An alternative explanation was that the increased hardening occurred because it was physically impossible for the non-redundant dislocation density ever to be greater than the redundant dislocation density, and the solid adjusted to this requirement in the affected regions by increasing the number of redundant dislocations or by eliminating both redundant and non-redundant dislocations. An analysis of torsional plastic deformation was presented here which was based upon the second possibility.

J.A.Hurtado, J.Weertman: Physica Status Solidi A, 1995, 149[1], 173-86