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

Abstract

Formability of biaxially stretched sheet metals is limited by the occurrence of localized necking. The theoretical determination of limit strains in biaxial stretching, i.e. the forming limit diagram assumes the presence of initial local thickness inhomogeneities in the sheet metal. This analysis due to Marciniak and Kuczynski often assumes an exaggerated value of thickness inhomogeneity in order to arrive at reasonable agreement between the predicted and experimental forming limit diagrams. In this work the forming limit diagram is predicted assuming that necking is initiated due to the presence 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 presence of second-phase hard particles. A modified constitutive model for voided materials based on Green's yield function is developed. This model with its flow rule and the derived void growth characteristics are used to predict the forming limit diagram. Work-hardening ability of the material, strain-rate sensitivity and normal anisotropy of the sheet metal are taken into consideration. The predicted forming limit curves are compared with that obtained experimentally for steel, copper and aluminum sheets of known mechanical properties and density change characteristics with strain. Reasonable values of initial void volume fraction together with thickness inhomogeneity 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.