Neck growth and forming limits in sheet metals

Abstract

An analytical model that is capable of predicting the development of nonuniform flow in sheet metals under various plane-stress loading conditions is presented. The model is based on the previously formulated idea that the neck grows from the initial geometric or material inhomogeneity. Applying a rate-dependent flow theory of plasticity and a simplified constitutive equation to the nonuniform section where the state of stress is assumed to be uniform, successive stages of neck profile are computed under an imposed state of strain. The computation of the detailed neck growth is then repeated over a wide range of proportional loading conditions to establish the forming limit diagram. The specific magnitude of the initial inhomogeneity that is used in the analysis has been estimated from the measured variations in sheet thickness in a representative sheet of AK steel. The necessary input material parameters have also been determined from the same sheet material. Predicted forming limit diagrams based on these input parameters compare favorably with the general trend observed in the published data on AK steel. Some discrepancies are observed between the predicted and experimental forming limits for 2036 aluminum alloy when the published material parameters are used in the neck growth model. Based on these results, some of the limitations of the analytical model are discussed in light of available experimental observations.