Modeling the localized necking in anisotropic sheet metals

Localized necking is one of the most frequently observed failure mechanisms in sheet forming processes. The forming limit diagram (FLD) characterizes the sheet metal formability, and the prediction of FLD is of significant importance to industry. In this paper, the process of deformation and localized necking is modeled to predict the FLD of anisotropic sheet metals. The sheet is assumed to have no initial geometric defects and a localized neck is assumed to develop in two stages. A Considère-type criterion is proposed to determine the critical strains for an initial neck to form. An energy-based hypothesis is proposed to quantify the defect ratio at the neck formation. The evolution of the initial neck is then considered in the second stage. It is demonstrated that, rather than the initial defects, localized geometric softening at a certain stage of deformation can be the main cause of localized necking. As a result, the forming limit curves are found to exhibit different characteristics in different regions of FLD. The predicted forming limit curve for 2036-T4 aluminum is mostly in good agreement with experimental results. The sheet thickness, the strain hardening behavior, and plastic anisotropy are found to affect the sheet metal formability. The present work provides an alternative view of localized necking in anisotropic sheet metals. More realistic yield criteria and strain hardening models can be implemented to enhance the proposed model.