"SAC" Creep Data Analysis and Modeling

Fit of Kariya and Schubert Models

Figure 26: Plot of SAC creep data and isothermal lines of Schubert / Wiese et al.'s model.

Isothermal lines representing the Kariya and Schubert creep models are plotted in Figure 25 and 26, respectively. The test data is shown as in Figure 23. The Kariya model is a power-law model that did fit the Kariya et al.'s Sn-3.0Ag-0.5Cu and Sn-3.8Ag-0.7Cu data equally well. The Kariya model gives steady state strain rates as a function of stress s and absolute temperature T (R =8.314 J/mole):

with: E(MPa) = 76087 - 109 x T(°K)

Schubert / Wiese et al., 2001, proposed the following power-law breakdown / hyperbolic sine model with model constants obtained by regression of their Sn-3.8Ag-0.7Cu bulk solder creep data:

From Figure 25:

• The Kariya model fits the Kariya and Neu datasets nicely except for a slight departure from the data at -55°C and strain rates above 10-3/sec. This shows consistency between the SAC and Castin data.
• The Kariya model does not fit the Schubert data.

From Figure 26:

• As expected, the Schubert model fits the Schubert / Wiese Sn-3.8Ag-0.7Cu data well.
• The Schubert model also fits the 125°C Kariya and Neu data well.
• The Schubert model is at a significant departure from the Kariya and Neu datasets at temperatures of 70-75°C and below.

Assuming that the models apply to all SAC alloys under study, one of the main differences between the Kariya and Schubert models is that the models attempt to fit data in different stress regions, mostly under 10-20 MPa for the Schubert data and above 10 MPa for the Kariya's data. Based on Sn-Pb experience, solder joints stresses in Sn-Pb assemblies are typically under in the range 1 to 10 MPa. This suggests the need to gather SAC creep data in the lower stress range (< 10 MPa).

In the next sub-sections, the above data is reviewed further and we attempt to fit a simple hyperbolic sine model to the Kariya et al., Neu et al. and Schubert et al.'s datasets. The intent of this exercise is to bridge the datasets with points below and above the 10 MPa stress level. Because the alloys under consideration have slightly different compositions, and because some of the data points are treated as outliers (as discussed below), the proposed empirical model is later tested against additional, independent creep data.

Review of SAC Data

The publications by Kariya et al., Neu et al. and Schubert / Wiese et al. provide a wealth of data that, taken together, covers a wide range of stress, strain rate and temperature conditions. Looking at the data plotted in Figure 23, the following empirical observations are made:

• The 150°C Schubert et al. dataset shows continuity with the Neu et al. and Kariya et al. datasets at 125°C.
• To a first order, the 70°C Schubert al. shows approximate continuity with the Neu et al. data and Kariya et al. "strength" data at 75°C.
• However, the 75°C Kariya et al. creep data does not seem to show continuity with the 70°C Schubert et al. data.

• The 75°C Kariya et al. "creep" dataset is thus treated as an outlier and is not included in the development of the power-law breakdown model.

• The 20°C Schubert et al. data does not show continuity with the other datasets at 23°C (Neu et al.) and 22°C (Kariya et al.). It is also not understood why the 20°C Schubert et al. data points at 5, 10 and even 20 MPa give creep rates fairly close to those at 70°C.

• Because of the above apparent discrepancies, the 20°C Schubert et al. dataset is also treated as an outlier and is not included in the analysis.

• The last two datasets, i.e. the -10°C Kariya et al. data and the -55°C Neu et al. data, seem to fit the general temperature trends of the other Kariya et al. and Neu et al. datasets.

In summary:

• Out of the 12 isothermal datasets shown in Figure 22, two of them (the 20°C Schubert et al. data and the 75°C Kariya et al. "creep" data) are treated as outliers and are not included in the subsequent analysis.
• The other 10 datasets show first order consistency and are preserved for regression analysis and development of the power-law breakdown creep model. The 37 points from those 10 datasets are given in Table B.2. The corresponding data covers:

• Temperatures in the range -55°C to 150°C.
• Stresses in the range 2 MPa to 100 MPa.
• Strain rates in the range 3.8 x 10^-9 /sec to 1 x 10^-3 /sec.

Regression Analysis

Figure 27: Fit of power-law breakdown model to the SAC creep data.

Non-linear regression of the data in Table B.2 gives the following equation of the power-law breakdown model:

The dashed lines are "lower" and "upper" bounds of the correlation band that are an arbitrary factor 1 0 or aproximately 3.16 times above and 10 or approximately 3.16 times below the master curve. Most of the data fall within or close to the bounds of the correlation band. The power-law breakdown model gives an activation energy Q = 67.9kJ/mole (=0.70eV) which compares to 61 kJ/mole in the Kariya et al. power-law model. The exponent of the hyperbolic sine function is n = 6, higher than the exponent n = 3 in the Schubert / Wiese et al. powerlaw
breakdown model.

Figure 28: Plot of SAC creep data and isothermal lines of first-order SAC creep model.

The raw data and isothermal lines of the hyperbolic sine model are plotted in Figure 28. Figures 27 and 28 suggest that, to a first order, the simplified SAC creep model provides for a reasonable fit of the data somewhat independent of the SAC alloy composition.