In this paper, the anisotropic mechanical properties of rolled AZ31 magnesium alloys are investigated using nanoindentation tests at room temperature. Nanoindentation was carried out at four angles, including the rolling direction (0°), diagonal direction (45°), transverse direction (90°), and vertical direction (ND). Experimental results show that hardness increases as the rolling angle increases from 0° to 90° and is lowest in the ND direction. The hardness independent of the effect of indentation depth is obtained by analyzing the indentation size effect and then converting hardness values into yield strengths. A new criterion is proposed on the basis of the Hill48 yield criterion. The data obtained through the above experiments are used to determine the parameters in the new criterion. Finally, a solution to the challenge of modeling a function that accurately describes the anisotropic yielding behavior of AZ31 magnesium alloys is proposed using the nanoindentation technique to solve the requirements of specimen size and experimental methods of the macro test.

Accurate calibration of the Preston–Tonks–Wallace (PTW) model is a nonlinear, multimodal optimization problem. Root mean square error (RMSE) is the sole optimization objective, with average absolute relative error (AARE) used only as a diagnostic. The primary comparison jointly calibrates one seven-parameter vector across all temperatures within each fixed strain-rate group; the 0.1, 3000, and 5000 s⁻¹ groups are calibrated separately. A secondary transfer assessment imposes the stricter constraint of one unchanged vector across all 11 temperature-strain-rate conditions. The adaptive GA-BO strategy combines diversity-dependent mutation, periodic and stagnation safeguards, elite-envelope Bayesian optimization (BO), and BO-to-population reinjection. Genetic algorithm (GA), BO, and GA-BO each receive exactly 1000 constitutive-model evaluations and 20 paired seeds. In the primary comparison, GA-BO gives median RMSE values of 8.06, 7.94, and 21.69 MPa and significantly improves on GA at all three rates, while remaining statistically comparable to BO and requiring substantially less serial time in the present implementation. The shared-vector assessment gives a GA-BO median global RMSE of 45.54 MPa and quantifies the accuracy-transfer trade-off created by enforcing one vector over the full rate range. Bootstrap, held-out-temperature, ablation, and one-factor setting analyses further quantify parameter coupling, calibration-transfer uncertainty, component contributions, and setting robustness. The resulting workflow therefore improves the accuracy-efficiency balance of reproducible PTW calibration while explicitly reporting the parameter-transfer cost across rate regimes.