Question 9.2: In flip-chip interconnections using 95 Pb-5 Sn solder, suppo...
In flip-chip interconnections using 95 Pb-5 Sn solder, suppose that stresses encountered in service fluctuate between σ/G=7×10^{-4} \ and \ 1×10^{-3} at temperatures between 25 and 35 °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 Eqn (9.21) as opposed to Eqn (9.22)?
\frac{d\varepsilon }{dt}=A \ \sigma^n \exp\left[-\frac{E_{c}}{RT}\right] (9.21)
\frac{d\varepsilon }{dt}=C\left(\frac{G}{T}\right)\sinh\left(\frac {a \sigma}{G} \right)^n \exp\left[- \frac{E_{c}}{RT}\right] (9.22)
We refer to the high stress/temperature state as 2 and the low stress/temperature state as 1. In the case of Eqn (9.21), noting that n = 7.0 and E_c = 27.7 \ kcal/mol.
\frac{\varepsilon _{2}}{\varepsilon _{1}}=\frac{A\sigma_2^n \exp[-E_c/RT_2]}{A\sigma_1^n \exp[-E_c/RT_1]}=\frac{(1\times10^{-3})^7\exp[-27,700/(1.99(308))]}{(7\times10^{-4})^7\exp[-27,700/(1.99(298))]}=55.3In contrast, the use of Eqn (9.22), where a = 1000 and n = 7.0, yields:
\frac{\varepsilon _{2}}{\varepsilon _{1}}=\frac{(298)(\sinh \ 1)^7\exp[-27,700/(1.99(308))]}{(308)(\sinh \ 0.7)^7\exp[-27,700/(1.99(298))]}=9.4Therefore, depending on which constitutive equation is chosen, a difference by a factor of 5.9 can result in estimating strain acceleration.