The rate-dependent plasticity material behavior is used for solder bumps, while the other parts are assumed to be linear elastic and temperature-independent.
The generalized Garofalo model is used to simulate creep behavior. The creep strain rate of the model is expressed as:
 | (35–1) |
where
 is the change in equivalent creep strain with respect to
time. |
 is the equivalent stress. |
| T is the temperature. |
| C1 through C4 are the constants. |
| t is the time at the end of the substep. |
| e is the natural logarithm base. |
The following experimental data are used with the curve-fitting tool for creep materials to find the creep model constants. For more details, see Material Properties in the Technology Showcase: Example Problems.
Figure 35.8: Creep Experimental Data [4-6] at Different Temperatures Used for Curve-Fitting Procedure
![Creep Experimental Data [-] at Different Temperatures Used for Curve-Fitting Procedure](graphics/gtec_leadfree6.png)
The constants from curve-fitting procedure and the reference [3] listed in the table below fit the experimental data
describing creep behavior even though they have different values of
C4 and consequently, C1. They
calculate equal values for C2 and C3, and
the remaining terms in Equation 35–1 are
equal for every temperature, 
.
Table 35.2: Generalized Garofalo Creep Constants Calculated from Curve Fitting and at Constant Temperature
| Temperature (K) | Constant [units] | Reference [3] | Curve Fitting |
|---|---|---|---|
| 218 | C1 [second-1] | 26.00917 | 7.19E-11 |
| C2 [MPa-1] | 0.037486 | 3.75E-02 | |
| C3 [ ] | 5.5 | 5.50E+00 | |
| C4 [Kelvin] | 5802 | 0.00E+00 | |
| 273 | C1 [second-1] | 17.14286 | 1.01E-08 |
| C2 [MPa-1] | 0.044852 | 4.49E-02 | |
| C3 [ ] | 5.5 | 5.50E+00 | |
| C4 [Kelvin] | 5802 | 0.00E+00 | |
| 298 | C1 [second-1] | 14.19463 | 4.97E-08 |
| C2 [MPa-1] | 0.049251 | 4.93E-02 | |
| C3 [ ] | 5.5 | 5.50E+00 | |
| C4 [Kelvin] | 5802 | 0.00E+00 | |
| 348 | C1 [second-1] | 9.568966 | 5.50E-07 |
| C2 [MPa-1] | 0.061269 | 6.13E-02 | |
| C3 [ ] | 5.5 | 5.50E+00 | |
| C4 [Kelvin] | 5802 | 0.00E+00 | |
| 398 | C1 [second-1] | 6.105528 | 2.85E-06 |
| C2 [MPa-1] | 0.081046 | 8.10E-02 | |
| C3 [ ] | 5.5 | 5.50E+00 | |
| C4 [Kelvin] | 5802 | 0.00E+00 |
The following material properties [3] are used for the thermomechanical analysis of the flip chip:
Table 35.3: Flip Chip Material Properties
| Properties | Solder | Chip | Underfill | Substrate |
|---|---|---|---|---|
| Conductivity (W/m-K) | 33 | 110 | 1.6 | 13 |
| Specific Heat (J/Kg-K) | 226 | 712 | 674 | 879 |
| Density (Kg/m3) | 7400 | 2330 | 6080 | 1938 |
| Young’s Modulus (MPa) | E(T) = 52708 - 67.14T - 0.0587T2 MPa | 162000 | 14470 | 18200 |
| Poisson’s Ratio | 0.4 | 0.28 | 0.28 | 0.25 |
| Coefficients of Thermal Expansion (ppm/K) | 22.36 | 2.3 | 20 | 19 |
Elastic and perfectly plastic material behavior is assumed. Bilinear isotropic hardening is used to define the solder plasticity to compare results.