Effects of post-necking hardening behavior and equivalent stress–strain curves on the accuracy of M–K based forming limit diagrams

Abstract

A rate dependent Taylor type crystal plasticity formulation is employed to study the effects of post-necking hardening behavior on the Marciniak–Kuczynski (M–K) based forming limit diagram predictions. Three uniaxial stress–strain curves, identical up to the necking region, with three different post-necking hardening behaviors are generated using crystal plasticity formulation. The three curves are obtained by curve fitting the simulated uniaxial true stress–strain curve to the experimental curve for the CC AA5754. In the first curve the true stress strain curve saturates after necking while the other two curves demonstrate post-necking hardening. A representative volume element obtained from Electron Backscatter Diffraction (EBSD) data is considered for the analysis. Numerical simulations of forming limit diagrams based on the classical M–K approach are performed with the same initial texture and the three different stress–strain curves. Analysis with the numerical model demonstrates that the post-necking behavior significantly affects the predicted FLDs. A new calibration approach is presented to accurately capture the post-necking behavior of metals. Predicted FLDs with this new approach are compared to the experimental FLD for the CC AA5754. In order to further characterize the process of finding the accurate post-necking hardening behavior, a method based on using equivalent stress–strain curve is presented. It is shown that the FLD, calculated using experimental uniaxial tensile data as input, is comparable with a FLD arising from equivalent stress–strain data.