Abstract:

The piece-to-piece variation among Sn-based lead-free solder joints is commonly attributed to stochastic variations in grain structure and the anisotropy inherent in the body-centered tetragonal (BCT) β-Sn lattice structure, especially for micron-scale joints that contain only a few grains. Parametric simulations of different microstructures, using grain-scale modeling, offer a convenient approach to estimate the degree of variability. Thus, although it is impossible to accurately predict the response of a given joint without knowing the microstructure, the best-case and worst-case limits of its behavior can be estimated. A crystal viscoplasticity approach has been developed to describe the anisotropic steady-state creep behavior of SAC single crystals and calibrated with results from literature and with in-house testing. The overall response of a single crystal has been characterized by a corresponding homogenized continuum-scale creep model based on Hill's anisotropic potential, in conjunction with Norton power-law model for creep rates. In this study, the Hill-Norton model described above is applied to analyze the effect of grain orientation on the viscoplastic response and durability of a singlecrystal solder joint under the combined action of compressive and thermal cyclic loading. The predicted lifetime, based on volume-averaged creep dissipation energy density, shows 31% variation for best-case and worst-case grain orientations.