Coarsening of the Sn-Pb solder microstructure in constitutive model-based predictions of solder joint thermal mechanical fatigue

AbstractAn expression for the coarsening rate of the Pb-rich phase particles was determined through isothermal aging experiments and comparative literature data as: $$\begin{gathered}\lambda=\lambda_0+\{[4.10\times10^{- 5}e^{-11023/T}\hfill\\+15.6\times10^{-8}e^{-3123/T}(d\gamma/dt)]t\}^{0.256}\hfill\\ \end{gathered}$$ where λo and λ are the initial and final mean Pb-rich particle diameters, respectively (mm); T is temperature (°K); t is time (s); and dγ/dt is the strain rate (s−1). The phase coarsening behavior showed good agreement with previous literature data from isothermal aging experiments. The power-law exponent, p, for the Pb-rich phase size coarsening kinetics: $$\lambda ^p - \lambda _0 ^p \approx t$$ increased from a value of 3.3 at the low aging temperature regime (70–100°C) to a value of 5.1 at the high temperature regime (135–170°C), suggesting that the number of short-circuit diffusion paths had increased with further aging. This expression provides an important basis for the microstructurally-based, constitutive equation used in the visco-plastic model for TMF in Sn-Pb solder. The revised visco-plastic model was exercised using a through-hole solder joint configuration. Initial data indicate a satisfactory compatibility between the coarsening expression and the constitutive equation.