Abstract
Applying external stress during aging can effectively regulate the precipitation process in magnesium alloys, thereby influencing their strength-ductility synergy. In this work, a three-dimensional phase-field model coupled with external loading was employed to quantitatively investigate the precipitation behavior of β′ phase in Mg–0.5 at.% Nd alloys under various stress conditions. The simulation results accurately predicted the habit planes and growth directions of the three variants of β′ phase, showing good agreement with experimental observations. It was found that compressive stress along the 〈0001〉α direction (CSA1) and tensile stresses along the 〈112¯0〉α and 〈11¯00〉α directions (TSA2, TSA3) promoted the cooperative growth of all three variants. In contrast, shear stress applied to the {0001}α basal plane favored the preferential growth of only one variant, leading to a pronounced orientation effect. This phenomenon was well explained by introducing the interaction energy under applied stress. Furthermore, the strengthening contribution under different stress conditions was quantified based on the Orowan mechanism, and the loading mode corresponding to the optimal mechanical properties was identified. This study reveals the underlying mechanism of external stress in modulating precipitation behavior and provides theoretical guidance for the design of stress-assisted aging processes for high-performance Mg–Nd alloys.