Effect of Anisotropic Yield Function Evolution on Estimation of Forming Limit Diagram

Abstract

In case of theoretical prediction of the FLD, the variations in yield stress and R-values along different material directions, were long been implemented to enhance the accuracy. Although influences of different yield models and hardening laws on formability were well addressed, anisotropic evolution of yield loci under monotonic loading with different deformation modes is yet to be explored. In the present study, Marciniak-Kuckzinsky (M-K) model was modified to incorporate the change in the shape of the initial yield function with evolution due to anisotropic hardening. Swift’s hardening law along with two different anisotropic yield criteria, namely Hill48 and Yld2000-2d were implemented in the model. The Hill48 yield model was applied with non-associated flow rule to comprehend the effect of variations in both yield stress and R-values. The numerically estimated FLDs were validated after comparing with FLD evaluated through experiments. A low carbon steel was selected, and hemispherical punch stretching test was performed for FLD evaluation. Additionally, the numerically estimated FLDs were incorporated in FE simulations to predict limiting dome heights for validation purpose. Other formability performances like strain distributions over the deformed cup surface were validated with experimental results.