Effect of the yield surface evolution on the earing defect prediction

Abstract

Although the prediction of earing in the cup drawing process is considerably related to the yield surface shape, the yield surface evolution is also essential for the final ear form. The bending-unbending issue is a fundamental subject occurring on the die and punch shoulders. Since the yield stress is loading path dependent in reversal loadings, the conventional hardening models used in the monotonic loading conditions bring about inaccurate outcomes for predicting the ultimate earing profile, and a kinematic hardening model should be incorporated into the constitutive equations. This study elucidates the yield surface evolution effect involving expansion and translation simultaneously on the ear formation. A sixth-order polynomial yield function was employed to precisely characterize the yield surface shape, while a combined isotropic-kinematic hardening model was implemented to represent the evolution of the yield surface. The translation of the yield surface position was defined by the Armstrong-Frederic hardening model. Punch force-stroke responses and the ear form profiles were predicted by the implemented plasticity model in Marc using the Hypela2 user subroutine and compared with the experimental results. The combined hardening assumption yielded an increase in the mean cup height when compared to the isotropic hardening assumption. Moreover, The HomPol6 coupled with the combined hardening showed a better agreement with the experimental results.