Quantitative Exploration of Cooling Rate-Driven Solidification Microstructure Evolution in Mg–Al Alloys

The non-uniform wall thickness of castings leads to substantial differences in cooling rates, which results in diverse solidified microstructures and ultimately affects mechanical properties. This study systematically investigates the effect of cooling rates spanning four orders of magnitude (10⁻² to 10² K/s) on the solidified microstructural characteristics of Mg–Al alloy series (Mg–3Al to Mg–15Al). Through combining experiments and multivariate nonlinear regression analysis, a general power function relationship is established between the morphological characteristic parameters (equiaxed grain size λ₁, specific surface area S_S, dimensionless perimeter P_d, fractal dimension F_d, etc.), the alloy composition (C), and the cooling rate (R). λ₁ follows λ₁ = 61.05C^−0.45R^−0.31, decreasing with the increase of cooling rate; S_s conforms to S_s = 0.01C^0.068R^0.95, where high-Al content and rapid cooling can inhibit microstructure coarsening and significantly increase S_s; P_d follows P_d = 2.60C^0.14R^0.045 + 0.00014C^0.41R^2.19, and F_d satisfies F_d = 1.12 + 0.19C^0.25R^0.32. The step-quenching experiments are further employed to reveal the dynamic evolution law of solidification microstructures: the morphological complexity increases in the early stage of solidification but decreases in the later stage due to the dominance of coarsening. Meanwhile, a series of reliable predictive models are established to accurately predict the evolution of microstructural morphological parameters during solidification. Hardness analysis confirms that the hardness under different solidification conditions is significantly correlated with morphological characteristic parameters, providing a key basis for constructing the composition-microstructure-property relationship. The research results offer important theoretical support for the microstructure regulation and performance optimization of cast Mg–Al alloys.