Multiscale modeling of the anisotropic transient creep response of heterogeneous single crystal SnAgCu solder

In Tier I, creep deformation is governed by dislocation impediment and recovery at nanoscale Ag3Sn particles, with recovery being the rate controlling mechanism. Dislocation climb and dislocation detachment at the Ag3Sn particles are proposed to be the competing rate controlling recovery mechanisms. Line tension and mobility of dislocations in dominant slip systems of single crystal Sn are estimated based on the elastic crystal anisotropy of body centered tetragonal (BCT) Sn. The anisotropic transient creep rate of the eutectic Sn-Ag phase of Tier I is then modeled using above inputs and the evolving dislocation density calculated for dominant glide systems during the transient stage of creep. The dominant slip systems are determined based on the dislocation mobility and on the orientation angle between the crystal principal axes and the loading direction. The creep response of the eutectic phase (from Tier 1) is combined with the creep response of Sn lobes at Tier 2, using the anisotropic Mori-Tanaka homogenization theory, to obtain the transient creep response of a SAC305 single crystal along global specimen directions. This model has been calibrated using experimentally obtained transient creep response of a SAC305 single crystal specimen. The above multiscale calibrated model is then used to predict (i) the transient creep response of another SAC305 single crystal specimen and (ii) the effect of orientation (by changing one of the Euler angles) on the transient creep response of SAC305 single crystal. The grain orientation of above two SAC single crystal specimens (with respect to loading direction) were identified with orientation image mapping and then utilized in the model to estimate the resolved shear stress along the dominant slip directions. Parametric studies have also been conducted to predict the effects of the volume fraction, aspect ratio, and orientation of ellipsoidal Sn inclusions on the anisotropic transient creep response of SAC single crystals.