Comparison of bifurcation and imperfection analyses of localized necking in rate-independent polycrystalline sheets

Plastic flow localization into a narrow band is investigated for a rate-independent polycrystalline sheet. Strain localization is considered to initiate at a point of bifurcation from the homogeneous deformation state or to result from the growth of a preexisting imperfection. Bifurcation analysis based on the rate-independent crystal plasticity model is found to give limit strains at a realistic strain level in the biaxial-stretching range. Limit strains predicted by the imperfection analysis are lower than those for bifurcation analysis and tend to approach those strain levels with decreasing amount of initial imperfection. Then, the bifurcation analysis is applied to the simulation of the forming limit for strongly textured sheets. The bifurcation analysis reveals the same trend of a texture dependence of limit strains as that for the imperfection analysis employing a rate-dependent model reported in the literature.