Application of Multiscale Crystal Plasticity Models to Forming Limit Diagrams

A polycrystal plasticity model is used to conduct parametric studies of forming limit diagrams (FLD) and to compare with experimental data. The Marcinak and Kuczynski [13] method is applied. It is confirmed that the onset of necking is retarded by increases in the ratio of initial band to sheet thickness and material strain rate sensitivity. It was also demonstrated that initial texture plays an important role in FLD response, as has been shown in other recent studies [6,26,7]. It is shown that a texture resulting from plane strain compression to one-tenth of the initial thickness gives a predicted FLD that more closely matches measured data than that based on an initially isotropic texture. The influence of a relatively softer response in terms of effective stress in torsional shear than in compression (i.e., shear softening) on FLDs is investigated with the aid of a hardening surface formulation along with the polycrystal plasticity texture evolution model. It is shown that necking behavior can be significantly affected by shear softening, particularly for initially textured sheets. It is also demonstrated that the hardening surface formulation provides additional flexibility in modeling FLD behavior beyond that afforded by classical polycrystal plasticity.