Lower Bound Yield Locus Calculations

A lower-bound model for the deformation of work-hardening polycrystals is proposed. All grains areassumed to be loaded under the same stress and the stress–strain behavior is found by averaging thestrains in all grains. The shapes of the yield loci have been calculated for textured metals whichdeform by {111}  〈 110 〉slip (fcc) and by〈 111 〉 -pencil glide (bcc). As with the correspondingupper-bound models, the yield loci are best described by an anisotropic yield criterion with anexponent of 6 to 10 (instead of 2 as in the Hill theory). Also it is shown that a model of polycrystaldeformation in which the grains are loaded to the same stress ratio (but not the same level of stresses)violates normality and is not a lower bound.