Anisotropic Microstructural Evolution in Eutectic Sn–Bi Solders Under Isothermal Aging and Cyclic Loading: A Phase-Field Perspective
摘要
Sn–Bi eutectic solders are widely used in flexible electronics, yet their long-term reliability is compromised by microstructural evolution under thermomechanical loads. To address this, a novel phase-field modeling framework is developed that uniquely couples thermal aging and mechanical cycling effects to predict microstructural degradation. The model integrates the Cahn–Hilliard and Allen–Cahn formulations with elastic energy contributions to simulate coarsening, solute redistribution, and stress-driven grain boundary migration in the lamellar microstructure. The results indicate that under isothermal aging alone, microstructural coarsening is primarily governed by interfacial energy minimization and asymmetric solubility behavior, where Bi atoms preferentially diffuse into Sn-rich domains. When cyclic mechanical loading is introduced, coarsening becomes faster, and grain alignment appears, especially in Bi-rich regions, due to stress-driven diffusion and grain boundary migration. Moreover, analysis of grain orientation using the von Mises distribution shows that Bi-rich grains progressively align with the loading direction. This anisotropic alignment becomes more pronounced with increasing stress amplitude but eventually reaches a saturation point. This grain realignment is closely linked to strain energy redistribution within the microstructure, where Bi-rich regions exhibit noticeable stress relaxation through reorientation, while the Sn-rich domains remain comparatively unaffected.