A lower-bound model for the deformation of work-hardening polycrystals is proposed. All grains are
assumed to be loaded under the same stress and the stress–strain behavior is found by averaging the
strains in all grains. The shapes of the yield loci have been calculated for textured metals which
deform by {111} 〈110〉 slip (fcc) and by 〈111〉-pencil glide (bcc). As with the corresponding
upper-bound models, the yield loci are best described by an anisotropic yield criterion with an
exponent of 6 to 10 (instead of 2 as in the Hill theory). Also it is shown that a model of polycrystal
deformation 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.
