Effect of Composition and Thermal–Mechanical History on the Creep Behavior of Sn–Ag–Cu Solders—Part II: Model

The microstructure of Sn-Ag-based solders undergoes continuous evolution during service due to isothermal and strain-enhanced aging. The precipitate particle size and interparticle spacing increase during service, resulting in the evolution of mechanical properties. In the accompanying paper (Part I), the effects of thermal-mechanical history on the microstructure and creep behavior of Sn-3Ag-0.5Cu and Sn-1Ag-0.5Cu were studied experimentally. The creep response of solders under all microstructural conditions follows a power law, with the stress exponent and activation energy being independent of composition and microstructural condition. However, the preexponent depends on the alloy composition and thermal/mechanical history, and is related to the precipitate size (or spacing) within the eutectic. The solder creep rate increased linearly with increasing particle size for the solder with higher alloy content (e.g., Sn-3Ag-0.5Cu) but nonlinearly for the solder with lower alloy content (Sn-1Ag-0.5Cu). In this paper, a composite model for creep of solders, explicitly accounting for both the eutectic and proeutectic constituents of the microstructure, is developed to rationalize this experimental observation. The creep rate of the eutectic microconstituent is proportional to the precipitate size. Hence in Sn-3Ag-0.5Cu, where creep is controlled by the continuous network of eutectic in the microstructure, the creep rate is nominally proportional to the precipitate size. In Sn-1Ag-0.5Cu, where the eutectic is discontinuous and a large proportion of proeutectic β is present, the creep rate increases at a less-than-linear rate with increasing precipitate size. The analytical composite model is shown to predict the creep behaviors of both solders well.