Effect of void growth on predicting forming limit strains for planar isotropic sheet metals

Formability of biaxially stretched sheet metals is limited by the occurrenc e of localized necking. The theoretical determination of limit strains in b iaxial stretching, i.e. the forming limit diagram assumes the presence of i nitial local thickness inhomogeneities in the sheet metal. This analysis du e to Marciniak and Kuczynski often assumes an exaggerated value of thicknes s inhomogeneity in order to arrive at reasonable agreement between the pred icted and experimental forming limit diagrams. In this work the forming lim it diagram is predicted assuming that necking is initiated due to the prese nce of initial heterogeneous distribution of void-like defects in the sheet metal, which grow with straining. These voids may already exist initially in the material or it may initiate earlier with deformation due to the pres ence of second-phase hard particles. A modified constitutive model for void ed materials based on Green's yield function is developed. This model with its flow rule and the derived void growth characteristics are used to predi ct the forming limit diagram. Work-hardening ability of the material, strai n-rate sensitivity and normal anisotropy of the sheet metal are taken into consideration. The predicted forming limit curves are compared with that ob tained experimentally For steel, copper and aluminum sheets of known mechan ical propel ties and density change characteristics with strain. Reasonable values of initial void volume fraction together with thickness inhomogenei ty as that expected from rolling gauge control are used. Results show that consideration of void growth into a model to predict forming limit diagrams gives better agreement with experiments. (C) 2000 Elsevier Science Ltd. Al l rights reserved.