The anomalous work hardening observed in the classic Fleck-Muller-Ashby-Hutchinson torsion plastic deformation experiment on small-diameter Cu rods, and in the Stölken-Evans bent thin Ni foils experiments, was explained as being caused by the presence of geometrically necessary (non-redundant dislocations) as opposed to redundant (or statistically stored) dislocations. The anomalous hardening had been attributed to necessary screw dislocations that were oriented parallel to the axis of the torsion specimen. Anomalous hardening, with necessary screw dislocations that lay in planes perpendicular to the torsion axis had been analyzed by Hurtado and Weertman. In the present case, it was shown that it was not possible (in plastically isotropic metals) for the anomalous hardening to arise from twist boundaries formed by combining necessary screw dislocations that were parallel to the torsion specimen axis and necessary screw dislocations that were perpendicular to the axis. This was because the sign of the necessary screw dislocations in one set of dislocations of a cross-grid was opposite to that of the other. Because twist boundaries could not form, it was thought to be unlikely that anomalous hardening arose because the overall (necessary plus redundant) dislocation density was increased by the addition of necessary screw dislocations. The necessary dislocations all moved in the same radial directions (towards the center of the torsion bar) and were thought to be unlikely to hinder each other’s motion significantly. However, the

 condition that the necessary dislocation density was less than or equal to the redundant dislocation density, everywhere within a sample, gave rise to anomalous hardening. That this condition led to anomalous hardening was demonstrated in detail for the simpler problem of a bent foil. The present conclusion was that the necessary dislocation density was always lower than, or equal to, the redundant dislocation density - in the case of anomalous work hardening - rather than the opposite (necessary-dislocation density greater than redundant-dislocation density). That is, in the absence of hardening mechanisms, such as dislocation locks, which could support the latter situation.

Anomalous Work-Hardening, Non-Redundant Screw Dislocations in a Circular Bar Deformed in Torsion, and Non-Redundant Edge Dislocations in a Bent Foil. J.Weertman: Acta Materialia, 2002, 50[4], 673-89