Forming limit diagrams for kinematically hardened voided sheet metals

A model to predict forming limit diagrams for kinematically hardened voided sheet metals is established. The model is based on von Mises yield criterion for a void-free matrix material, Gurson–Tvergaard yield criterion for voided solids, and a kinematic-hardening rule due to Prager–Ziegler. A complete formulation of plasticity constitutive laws is given, e.g. yield function, flow rule and void growth law. A computer program is developed using the above model and containing all parameters involved in the process of biaxial stretching of sheet metals. The model which considers only rigid plastic behavior has been then applied to investigate the influence of various material parameters on the prediction of limit strains. These include strain-hardening exponent “n”, strain-rate sensitivity “m”, average ratio of normal anisotropy “r̄”, initial void volume fraction “Cv0”, and the initial sheet imperfection “f0”. Comparisons among theoretical predictions and experiments existing in the literature show that reasonable agreements are realized. This has been done by using realistic material data for various metallic alloys of steel, aluminum, brass, and copper.