Mechanistic Modeling of the Anisotropic Steady State Creep Response of SnAgCu Single Crystal

A multiscale modeling framework is proposed in this study to capture the influence of the inherent elastic anisotropy of single crystal Sn and the inherent heterogeneous microstructure of a single crystal SnAgCu (SAC) solder grain on the secondary creep response of the grain. The modeling framework treats the SAC microstructure as having several distinct length scales. The smallest length scale (Tier 0) consists of the Sn BCT lattice. The eutectic Sn-Ag micro-constituent, consisting of nanoscale Ag₃Sn IMC particles embedded in the single crystal BCT Sn matrix, is termed Tier 1. The single-crystal SAC microstructure, consisting of Sn dendrites and surrounding eutectic Sn-Ag phase, is termed Tier 2. Dislocation recovery mechanisms, such as Orowan climb and detachment from nanoscale Ag₃Sn particles, are found to be the rate controlling mechanisms for creep deformation in the eutectic Sn-Ag phase (Tier 1) of a SAC single crystal. The anisotropic secondary creep rate of eutectic Sn-Ag phase (Tier 1), is then modeled using the above inputs and the saturated dislocation density calculated for dominant glide systems during secondary stage of creep. Saturated dislocation density is estimated as the equilibrium saturation between three competing processes: (1) dislocation generation; (2) dislocation impediment caused by back stress from pinning of dislocations at IMCs; and (3) dislocation recovery due to climb/detachment from IMCs. Secondary creep strain rate of eutectic Sn-Ag phase in three most facile slip systems is calculated and compared against the isotropic prediction. At low stress level secondary steady state creep rate along (110)[001] system is predicted to be ten times the creep rate along (100)[0-11] system. However, at high stress level, secondary steady state creep rate along (110)[001] system is predicted to be ten thousand times the creep rate along (100)[0-11] system. The above predictions are in strong agreement with (1–4) orders of magnitude of anisotropy observed in steady state secondary creep response in SAC305 solder joints tested under identical loading conditions in experiments conducted by several authors. The above model is then combined with Eigen-strain methods and average matrix stress concepts to homogenize the load sharing between the Sn dendrites and the surrounding eutectic Ag-Sn matrix. The resulting steady state creep rates are predicted for a few discrete single crystal SAC305 specimens. Very good agreement is observed between the predicted steady state creep rate and the measured creep rates for two SAC305 single crystal specimens.