Question 9.2: In flip-chip interconnections using 95Pb-5Sn solder, suppose...
In flip-chip interconnections using 95Pb-5Sn solder, suppose that stresses encountered in service fluctuate between \sigma/G=7×10^{-4} and 1×10^{-3} at temperatures between 50^{\circ }C and 35^{\circ }C. A measure of contact degradation is taken as the ratio of creep strains at the two stress levels. What is the difference in the predicted strain ratio using Eq. 9-19 as opposed to Eq. 9-20?
We refer to the high stress/temperature state as 2 and the low stress/temperature state as 1. In the case of Eq. 9-19, noting that n = 7.0 and E_{c} = 27.7 kcal /mol,
\frac{d\epsilon}{dt}=A \sigma^{n}\exp\left[ -\frac{E_{c}}{RT} \right] (9-19)
\frac{\epsilon_{2}^\cdot }{\epsilon_{1}^\cdot }=\frac{A\mathrm{\sigma}_{2}^{n}\exp\left[ -E_{c}/RT_{2}\right]}{A \mathrm{\sigma}_{1}^{n}\exp\left[ -E_{c}/RT_{1} \right]}=\frac{\left( 1×10^{-3}\right)^{7}\exp\left[ -27,700/\left( 1.99 \left( 308 \right) \right)\right]}{\left( 7×10^{-4}\right)^{7}\exp\left[ -27,700/\left( 1.99\left( 298 \right) \right) \right]}=55.3.In contrast, the use of Eq. 9-20 where \alpha= 1000 and n = 7.0, yields
\frac{d\epsilon}{dt}=C\left( \frac{G}{T}\right)\sinh\left( \frac{\alpha\sigma}{G}\right)^{n} \exp\left[ -\frac{E_{c}}{RT}\right], (9-20)
\frac{\epsilon_{2}^\cdot }{\epsilon_{1}^\cdot }=\frac{\left( 298\right)\left( \sinh 1 \right)^{7}\exp\left[ -27,700/\left( 1.99 \left( 308 \right) \right)\right]}{\left( 308 \right)\left( \sinh 0.7\right)^{7}\exp\left[ -27,700/\left( 1.99\left( 298 \right) \right) \right]}=9.4.Therefore, depending on which constitutive equation is chosen, a difference by a factor of 5.9 can result in estimating strain acceleration.