Modelling the Elasto-Plastic Material Behavior of Textured Hexagonal Close-Packed Metals

This study examines and models the three-dimensional anisotropic and asymmetric plastic behavior of hexagonal closed packed (HCP) metals, with focus on basal textured magnesium (Mg) alloys. Both experimental and numerical methods were employed. Uniaxial, pure shear, and equibiaxial tests were conducted, accompanied by in-situ strain field measurements using digital image correlation (DIC) throughout the tests. Strong strain localization is observed during uniaxial and equibiaxial compression tests due to the formation of macroscopic bands of twinned grains (BTGs). Within the BTGs, the evolution of the lateral plastic strains exhibited strong anisotropy. For instance, the results of the uniaxial compression tests yield plastic Poisson’s ratios of \(v_{12}^{{{\text{p}}1}} \approx 0\) and \(v_{13}^{{{\text{p}}1}} \approx 1\) . In contrast, the uniaxial tensile tests result in a homogeneous strain field with an almost isotropic material behavior. Cyclic tests with compressive load ratios show that the strain localization still applies. Furthermore, the initial macroscopic cracks originated within the BTGs. For fatigue modeling, such as with the presented concept of the highly strained volume, it is important to consider the stress-strain states exclusively within these areas. Hence, a multiaxial constitutive model is presented and implemented in the finite element method (FEM) software CalculiX via a user-defined material subroutine (UMAT). The model successfully describes anisotropic yield stresses, tension-compression asymmetry, strong strain localization, and anisotropy in lateral plastic strains. The FEM simulation results for a uniaxial compression specimen indicates that the model could accurately calculate the fatigue parameter for the concept of highly strained volume.