S.Mukherjee and A.Dasgupta
Center for Advanced Life Cycle Engineering, University of Maryland, College Park, MD 20742, USA
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The lack of statistical homogeneity in functional SnAgCu (SAC) solder joints due to its coarse grained micro-structure in conjunction with the severe anisotropy exhibited by single crystal Sn renders each joint unique in terms of mechanical behaviour. High-Sn SAC solder joints exhibit significant piece to piece variability in their mechanical response under identical loading conditions in the as-fabricated state. A mechanistic multi scale modelling framework is proposed in this study, using a modified form of Roslerís dislocation detachment model, to capture the influence of the inherent elastic anisotropy in single crystal Sn on the measured secondary creep response of a single crystal of SnAgCu (SAC) solder. Line tension and mobility of dislocations in dominant slip systems of single crystal Sn is captured using elastic crystal anisotropy of body centred tetragonal (BCT) Sn. The anisotropic secondary creep rate of eutectic Sn-Ag phase are then modelled using above inputs and saturated dislocation density in dominant glide systems at 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 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. Secondary creep shear strain rate along  direction is found to be highest and lowest along  direction compared to that of isotropic predictions among three selected most facile slip systems.
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