A temperature-dependent elasto-plastic constitutive model for magnesium alloy AZ31 sheets

For warm forming simulations of magnesium alloy sheets, a constitutive model is proposed for describing the temperature-dependent asymmetric cyclic behavior of magnesium alloy sheets. The asymmetric hardening behavior is classified into three modes − twinning (T), untwinning (U), and slip (S) − depending on the corresponding dominant deformation mode. The yield criterion uses two separate yield functions that correspond to the twinning/untwinning and slip dominant deformation modes. Though this model is phenomenological, it adopts the concept of the deformation mechanism as magnesium alloy sheets exhibits significantly different behavior by the active deformation mechanisms for a wide range of temperatures. To obtain the model parameters, the constitutive model requires cyclic behavior at room temperature and tensile behavior at high temperatures. A numerical algorithm for efficiently integrating the constitutive equations is presented for switching deformation paths and active deformation modes. For verification, the predictions by the proposed constitutive model are compared with measurements for the simple shear behavior and the high temperature cyclic behavior.