Numerical Material Testing Method for Hexagonal Close-Packed Metals Based on a Strain-Rate-Independent Finite Element Polycrystal Model

The purpose of this study was to develop a numerical material testing method applicable to hexagonal close-packed (hcp) materials that can predict complex material behavior such as biaxial test results from relatively easy-to-perform uniaxial tests. The proposed numerical material testing method consists of a physical model that represents the macroscopic behavior of the material and a means of determining the included crystallographic parameters using macroscopic experimental data. First, as the physical model, the finite element polycrystal model (FEPM) previously applied by the authors for face-centered cubic (fcc) materials was applied and modified for hcp materials. A unique feature of the FEPM is that it avoids the use of strain-rate-dependent coefficients, whose physical meaning is ambiguous, because the deformation analysis can be performed while automatically determining the activity of all slip systems. The applicability of FEPM to numerical material testing methods was verified in hcp materials through this study. Then, a material parameter optimization process was developed using a genetic algorithm (GA). The proposed method was validated using literature values of magnesium alloy AZ31. First, the proposed optimization process was performed on cast AZ31 using uniaxial tensile and compressive stress—strain curves as teaching data to confirm that the stress—strain curves for the biaxial state could be predicted. Then, the proposed method was applied to rolled sheet AZ31, where the pseudo-anisotropic crystal orientations generated by numerical rolling were used as initial values. The prediction of unknown material data showed that, even in the case of sheets, the crystallographic parameters could be reasonably determined by the proposed optimization process.