A non-associated flow rule with simple non-branching form representing the apparent non-normality effects after abrupt strain-path change

Abstract

Although the existed ‘corner models’ are capable of reasonably predicting experimental observations of the corner effects including the formation of a sharp vertex on the subsequent yield surface and the apparent non-normality of plastic flows after abrupt strain-path change, these models have not been widely used in metal forming computation due to their complexity. The present work proposes a non-associated flow rule with simple non-branching form to represent the non-normality effects after abrupt strain-path change. Then a stable stress update algorithm for the present rule is developed, based on the fully implicit backward Euler method. The present rule is implemented in ABAQUS and its effectiveness is verified through the FEM simulations of two typical strain-path change experiments. Furthermore, some concerned influencing factors of the non-normality effects after strain-path change are discussed. The results show that the new rule has good prediction performance by comparing with the previous works by Simo, Yoshida et al. and the associated flow rule (AFR). And the combination of the non-associated flow rule and the visco-plastic model can closely reproduce the complete experimental observations of corner effects. Moreover, the plane strain tension simulations reveal that the proposed rule predicts the earlier and sharper strain localization than AFR.