Anomalous work hardening, non-redundant screw dislocations in a circular bar deformed in torsion, and non-redundant edge dislocations in a bent foil

摘要

The anomalous work hardening observed in the classic torsion plastic deformation experiment on copper rods of small diameter of Fleck, Muller, Ashby and Hutchinson (Acta Metall Mater, 42, (1994) 475), and seen too in the bent thin nickel foils experiments of Stolken and Evans (Acta mater, 46, (1998) 5109), has been explained as caused by the presence of N-dislocations. (Here "N" stands for geometrically necessary or non-redundant dislocations and "R" stands for redundant or statistically stored dislocations.) Gao, Huang, Nix, and Hutchinson (J Mech Phys Solids, 47 (1999) 1239) ascribe the anomalous hardening to N-screw dislocations that are oriented parallel to the axis of the torsion specimen. Hurtado and Weertman (J phys stat sol (a), 149 (1995) 173) analyzed anomalous hardening with N-screw dislocations that lie in the planes perpendicular to the torsion axis. In the present paper it is shown that it is not possible in plastically isotropic metals for the anomalous hardening to arise from twist boundaries formed by combining N-screw dislocations that are parallel to the torsion specimen axis and N-screw dislocations that are perpendicular to the axis because the sign of the N-screw dislocations in one set of dislocations of a cross-grid is opposite that of the other. Because twist boundaries cannot form, it appears unlikely that anomalous hardening arises because the overall N-dislocations plus R-dislocations) dislocation density is increased by the addition of N-screw dislocations. The N-dislocations all move in the same radial directions (towards the center of the torsion bar) and are not likely to hinder significantly each other's motion. However, the condition that the N-dislocation density is less than or equal to the R-dislocation density everywhere in a sample does give rise to anomalous hardening. That this condition does lead to anomalous hardening is shown explicitly and in detail for the simpler problem of the bent foil. This paper comes down on the side of the skimping (N-dislocation density always less than or equal to the R-dislocation density) answer to the origin of anomalous work hardening, rather than the swamping (N-dislocation density greater than R-dislocation density) answer (in the absence of hardening mechanisms, such as dislocation locks, that can rescue the swamping explanation).