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:
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, and 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:
![Creep Experimental Data [-] at Different Temperatures Used for Curve-Fitting](graphics/gtec_leadfree6.png)
The curve-fitting method is nonlinear, so an iterative process is used to obtain a good fit with the experimental data; therefore, initial values for each material parameter are required. The following input finds the generalized Garofalo material constants:
/COM, Read experimental data saved in dat files TBFT,EADD,1,CREEP,temp218.dat ! Read experimental data at 218 K temperature TBFT,EADD,1,CREEP,temp273.dat ! Read experimental data at 273 K temperature TBFT,EADD,1,CREEP,temp298.dat ! Read experimental data at 298 K temperature TBFT,EADD,1,CREEP,temp348.dat ! Read experimental data at 348 K temperature TBFT,EADD,1,CREEP,temp398.dat ! Read experimental data at 398 K temperature /COM, Perform material curve-fitting operations. TBFT,FADD,1,CREEP,GGAR, ! Define a constitutive model generalized Garofalo TBFT,SET,1,CREEP,GGAR,,1,1e-5 ! Initialize C1 coefficients (C1 > 1) TBFT,SET,1,CREEP,GGAR,,2,1e-5 ! Initialize C2 coefficients TBFT,SET,1,CREEP,GGAR,,3,5.0 ! Initialize C3 coefficients TBFT,SET,1,CREEP,GGAR,,4,0 ! Initialize C4 coefficients TBFT,SET,1,CREEP,GGAR,,tdep,1 ! Set temperature dependency ON TBFT,SET,1,CREEP,GGAR,,tref,all ! Set reference temperature TBFT,SOLVE,1,CREEP,GGAR,,1,5000,0,0 ! Solve for coefficients with 5000 iterations TBFT,FSET,1,CREEP,GGAR, ! Write constants to the material database
Table 35.2: Generalized Garofalo Creep Constants from Curve-Fitting and Reference
| 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 |
Compared to the reference material parameters [3] in Table 35.2: Generalized Garofalo Creep Constants from Curve-Fitting and Reference, the curve-fitting results have disabled the temperature-dependent term of the Garofalo creep equation by setting C4 = 0.0. The automatic curve-fitting then finds a value of C1 that compensates for C4 = 0.0, and the temperature-dependence of the Garofalo creep increment comes from the temperature-dependent C1 value.
For more information, see ???? in the Material Reference.
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.