A parametric study into the influence of Taylor-type scale-bridging artifacts on accuracy of multi-level crystal plasticity finite element models for Mg alloys

Abstract

Meshing grain structures explicitly to incorporate microstructure dependent material behavior in modeling tools for metal forming processes and structural components is unfeasible. Grain-to-polycrystal meso-level homogenization theories are employed to embed polycrystal plasticity constitutive laws in finite element (FE) frameworks, which hence relate the meso-scale to the macro-scale response. A Taylor-type polycrystal plasticity (T-CP) theory is often used at the meso-scale within FE frameworks (T-CPFE) owing to its simplicity and computational efficiency. The theory relies on the iso-strain constraint imposed over constituent grains at each integration point. The constraint can be relaxed by spreading orientation distributions over finite elements in a mesh. This work seeks to establish an optimal number of crystal orientations to spread over integration points for accurate modeling of Mg alloys. Quasi-static and high strain-rates simulations of tension, compression, simple-shear, and plane strain deformation conditions are performed and post-processed to reveal the differences in predicted mechanical fields between T-CPFE and an explicit polycrystalline grain microstructure of an AZ31 Mg alloy. Moreover, several flow stress curves of the alloy are simulated and compared with measured data. A range of meshes with variable degree of relaxed constraints at integration points are suitably designed and used in the simulations. The performance of the six crystals per integration point is established to be an optimum in smoothing local deformation while allowing heterogenous deformation over the mesh. As such, the relaxed Taylor homogenization can provide tractable part level simulations of Mg alloys.