A cyclic small-strain plasticity model for wrought Mg alloys under multiaxial loading: Numerical implementation and validation

Basal-textured wrought magnesium alloys are inherently prone to mechanical twinning/de-twinning during cyclic deformation at room temperature. They, subsequently, exhibit distinctive flow curve attributes, which are impossible to describe using conventional plasticity models developed for symmetric/isotropic metals, deforming mainly by slip. A continuum plasticity model is herein proposed, in such way that accounts for various asymmetric/anisotropic aspects of cyclic flow response of wrought magnesium alloys. The proposed model entails an isotropic von Mises yield function which evolves in stress space according to a generalized anisotropic kinematic hardening rule, based on Ziegler's rule. The phenomenological concept of plastic moduli matrix introduced in the proposed kinematic rule is viewed as the key factor in representing material yield/hardening behaviour in different directions. The components of this matrix can independently be calibrated by conducting uniaxial cyclic experiments along each direction. An efficient and stable numerical algorithm is developed and then coded into UMAT to use within Abaqus (R)/Standard finite element software. Thereafter, model validation has been successfully done using proportional and non-proportional biaxial axial-torsional cyclic tests on AZ31B, AZ61A, and AM30 Mg alloy extrusions.