Anisotropic Strain Rate Sensitive and Continuum Damage Coupled Plasticity Model: An Application for Magnesium A Z31B

Abstract

In this work, an anisotropic and time-dependent damage-coupled plasticity model is written under finite strain formulation to describe the mechanical behavior of ductile materials. The model is formulated in arbitrary coordinate space to accommodate simulation of proportional and non-proportional 3D loadings. A phenomenological continuum damage mechanics approach is suggested to model the material mechanical behavior and anisotropic damage beyond the post-necking region up to fracture. The developed mathematical model scheme captures the strain rate effect on the material’s mechanical response and better approximates the yield stress, ultimate tensile strength and the strain to fracture. This thesis also presents an implicit time integration method for the anisotropic time-dependent model. Magnesium alloys are the lightest structural metals and therefore are potential candidates for use in stamped automotive panels. Thus, the prediction capability of the model is validated by comparing the numerical predictions to the uniaxial tensile experiments of TRC sheets of Mg AZ31B Alloy. The comparisons between the numerical predictions and the experimental results show fair agreement over a multitude of strain rates and temperatures.