Lower Bound Yield Locus Calculations

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Abstract
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 stressstrain 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.

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