A dislocation-based model for all hardening stages in large strain deformation

Abstract

A new model is presented to describe the hardening behaviour of cell-forming crystalline materials at large strains. Following previous approaches, the model considers a cellular dislocation structure consisting of two phases: the cell walls and the cell interiors. The dislocation density evolution in the two phases is considered in conjunction with a mechanical analysis for the cell structure in torsional deformation in which the cell walls are lying at 45° with respect to the macroscopic shear plane and are strongly elongated in the direction perpendicular to the applied shear direction. Guided by recent results on the volume fraction of cell walls [Müller, Zehetbauer, Borbély and Ungár, Z. Metallk. 1995, 86, 827], the cell-wall volume fraction is considered to decrease as a function of strain. Within a single formulation, all stages of large strain behaviour are correctly reproduced in an application for copper torsion. Moreover, strain rate and temperature effects are accounted for correctly and the predicted dislocation densities are in accord with experimental measurements. It is suggested that the factor responsible for the occurrence of hardening Stages IV and V is a continuous decrease of the volume fraction of the cell walls at large strains. A significant effect of the deformation texture variation on strain hardening is also discussed.