An Anisotropic Model with Non-associated Flow Rule to Predict HCP Sheet Metal Ductility Limit

Abstract

In this paper, an anisotropic plasticity model is coupled with Marciniak and Kuczynski localized necking criterion to predict the ductility limit of hexagonal closed packed (HCP) crystal structure sheet metals submitted to uniaxial and biaxial stretching. The anisotropic plastic evolution at room temperature is in fact described by the constitutive model using the non-associated flow rule (non AFR). In the current investigation, the plastic potential and the yield function are independently defined by taking into account the quadratic anisotropic yield criterion Hill48 which leads to the accurate prediction of the progressive plastic anisotropy as well as the material behavior using a minimal set of material parameters. To predict forming limit diagrams (FLDs), An efficient implicit algorithm is developed to solve the necessary constitutive equations to provide the coupling between Marciniak and Kuczynski instability approach and the anisotropic plasticity model with non-AFR. The numerical simulations are compared with several reference results from the literature to validate the mechanical behavior of the particular HCP magnesium alloy AZ31. Then, the ductility limit of this particular HCP magnesium alloy is numerically predicted and compared with analytical results of forming limit diagrams from the literature based on the associated and non-associated flow rule.