Figure 18: Fit of Sn3.5Ag solder joint data to Sn3.5Ag lap shear and plug & ring correlation band.

Figure 18 shows Darveaux's solder joint data on the plot of the Sn-3.5Ag lap shear and plug & ring master curve (Figure 15). The Darveaux's data is within or fairly close to the 10 X correlation band. However, the Darveaux's dataset also shows some curvature that is more pronounced than that of the master curve for the lap shear and plug & ring data. This suggests careful consideration of lap or plug and ring joint data before it can be applied to actual solder joints of electronic assemblies.

Regression of Darveaux's CCC Shear Data

In Darveaux et al. (1995), the CCC solder joint data was fitted to a hyperbolic sine model such as given by equation (32). The corresponding equation in Darveaux et al. (1995) is equation (13.3) and the regression constants are given in Table 13.1 of the same publication. After conversion of stresses from psi to MPa, Darveaux's creep rate equation is written as:

Analysis of the CCC data with the Datafit program gives the following regression constants:

• LNA = ln(A) = 12.84 ± 1.158 (from which the central value of A is: A = 3.77e5)
• B = 0.0983 ± 0.0072
• n = 5.548 ± 0.270
• Q_a = 8957 ± 371 (from which the central value of Q is: Q = 74.5 kJ/mole ~ 0.77 eV)

The equation of the best-fit line is obtained as:

The ratios of constants in the creep rate equations (34) and (35) are:

• For the creep rate constant, A: 3.77e5/2.46e5 = 1.53.
• For the stress multiplicative factor, B: 0.0983/0.0913 = 1.0766.
• For Q_a, or for the activation energy: 8957/8721 = 1.027.
• For the exponent, n, of the sinh() functions: 5.548 / 5.5 = 1.009.

Figure 19: Fit of Darveaux's Sn-3.5Ag data to regression models using equations (34) and (35). The primary Y-axis (to the left) uses activation energy Q1 from the Datafit regression. The secondary Y-axis (to the right) uses activation energy Q2 from Darveaux's regression.

The largest difference in the regression parameters is by a factor 1.53 X for the creep rate constants, A. This may not show on plots of strain rates vs. stress on log-log scales because the vertical axis covers several orders of magnitude. In terms of graphical curve-fitting, either model appears to work well as seen in Figure 19 where we plotted the data and master curves for the two types of regression. The regression in Darveaux's paper was reportedly done by "trial and error". The Datafit software uses a non-linear solver. However, the 1.53X difference in the constants A is large enough to have an impact on solder joint stress/strain analysis results.