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Significance Statement
Multiscale mechanistic model has been proposed to capture the anisotropic creep response of SAC (SnAgCu) single crystals, by combining the creep response of the Sn-Ag eutectic phase (from Tier 1) with creep response of pure Sn dendritic lobes at Tier 2, using the anisotropic Mori-Tanaka homogenization theory. The proposed model can predict anisotropic creep response for any single crystal specimen with any random orientation with respect to the loading direction. The proposed model can capture the effect of volume fraction, interparticle spacing, orientation, and aspect ratio of primary Sn phase and IMCs on creep response. The proposed model can also qualitatively capture the effect of isothermal aging and microalloying on creep response of SAC solder joints
Dislocation climb and dislocation detachment in the eutectic Sn-Ag phase are proposed to be the competing rate controlling recovery mechanisms at low (< 12 MPa) and high stress levels (> 12 MPa) respectively and agree with the experimental data. Line tension factor and mobility of edge dislocation is found to vary by one order of magnitude and (2-4) times between the studied slip systems in BCT Sn lattice at RT. Transient creep strain rates along [001] direction of SAC305 single crystal #1 is predicted to be 1-2 orders of magnitude higher than that of along [100]/[010] direction. Predicted transient creep strain and steady state creep rate along global specimen direction is found to vary by a factor of (1-3) orders of magnitude due to change in one of the Euler angles (j1) in SAC305 single crystal #1, which is in agreement with experimental observations. Scatter in the observed experimental data is found to be bounded by the predicted anisotropic steady state creep rates along three most facile slip systems of SAC single crystal.
Journal Reference
International Journal of Plasticity, Volume 78, 2016, Pages 1–25.
S. Mukherjee1, B. Zhou2, A. Dasgupta1, T.R. Bieler2
[expand title=”Show Affiliations”]- CALCE, Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
- Chemical Engineering and Materials Science, Michigan State University, East Lansing, MI 48824, USA
Abstract
The lack of statistical homogeneity in functional SnAgCu (SAC) solder joints due to their coarse grained microstructure, in conjunction with the severe anisotropy exhibited by single crystal Sn, renders each joint unique in terms of mechanical behavior. A mechanistic multi-scale modeling framework is proposed in this study to predict the influence of composition and microstructure on the anisotropic transient creep response of single crystal SnAgCu (SAC) solder. Tier I consist of single-crystal eutectic Sn–Ag alloy, with nanoscale Ag3Sn particles embedded in a single-crystal Sn matrix. Tier II consists of single crystal SAC solder which is composed of Sn dendrites surrounded by the eutectic Sn–Ag phase of Tier I. The Tier I anisotropic transient creep model is based on dislocation mechanics. The Tier II model uses the results of Tier I as an input and is based on anisotropic composite micro-mechanics.
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.
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