The effect of deformation-induced disorientations on the work-hardening of metals is modelled based on dislocation dynamics. Essentially, Kocks’ dislocation model describing stage III hardening is extended to stage IV by incorporation of excess dislocations related to the disorientations. Disorientations evolving from purely statistical reasons — leading to a square root dependence of the average disorientation angle on strain — affect the initial work-hardening rate (and the saturation stress) of stage III only slightly. On the other hand, deterministic contributions to the development of disorientations, as differences in the activated slip systems across boundaries, cause a linear increase of the flow stress at large strains. Such a constant work-hardening rate is characteristic for stage IV.
Materials Science and Engineering A: Structural Materials: Properties, Microstructures and Processing, 2004, Vol 387-389, p. 257-261