# Reliability Prediction of Mixed-Signal Module Based on Multi-Stress Field Failure Mechanisms
## 6 Reliability Prediction of the Communication Module Under the Mission Profile
### Functional Failure Reliability Prediction of Key Components  
Functional failure specifically results from solder joint fatigue in the communication module under the spacecraft mission profile. Given that the solder joints of FPGA and SRAM are relatively more prone to failure, this section focuses on the reliability prediction of solder joint fatigue in both FPGA and SRAM. This section employs the Engelmaier model, which is based on plastic deformation, to analyze the fatigue life of solder joints. The Engelmaier model assumes that solder joint fatigue is driven by cyclic plastic deformation under thermal and mechanical stress, making it suitable for low-cycle fatigue conditions. It is applicable to lead-free and eutectic solder alloys within the temperature range of the spacecraft. The model is expressed as follows [38]:  
\[N_{\text{f}}=\frac{1}{2}\left(\frac{\Delta\gamma}{2\varepsilon_{\text{f}}} \right)^{\frac{1}{\varepsilon}} \tag{8}\]  
\[\Delta\gamma=\sqrt{3}\Delta\varepsilon_{\text{P}} \tag{9}\]  
\[c=-0.442-6\times 10^{-4}T_{\text{m}}+1.74\times 10^{-2}\ln(1+f) \tag{10}\]  
\[t=\frac{N_{\text{f}}}{f} \tag{11}\]  
where \(\Delta\gamma\) represents the range of plastic shear strain, \(\Delta\varepsilon\) is the range of plastic strain, and \(\varepsilon_{\text{f}}\) is the material fatigue coefficient. The fatigue ductility exponent is denoted as \(c\), while \(T_{\text{m}}\) is the average temperature of the temperature cycle. The temperature cycle frequency is represented by \(f\), in cycles per day. In Section 4.3, the equivalent plastic strain of the critical FPGA and SRAM solder joints under temperature cycling is analyzed. From the simulation results, the equivalent plastic strain range for the critical FPGA solder joint is 0.00264, while for the critical SRAM solder joint, it is 0.000443. Using Equation (9), the range of plastic shear strain for the critical FPGA solder joint is calculated to be 0.004573. Based on the temperature variation with time in Figure 17, the average temperature of the FPGA solder joint during the temperature cycle is 27.77 \({}^{\circ}\)C, with a temperature cycle frequency \(f\) of 24 cycles/day. Substituting \(T_{\text{m}}\) and \(f\) into Equation (10), the fatigue ductility exponent \(c\) is calculated to be \(-0.40265\). According to [39], for the solder material SAC305, considering uncertainties in the manufacturing process, the fatigue coefficient \(\varepsilon_{\text{f}}\) is assumed to follow a normal distribution \(\varepsilon_{\text{f}}\)-N(0.325,0.005). For SRAM, the calculation method for each parameter is the same as for FPGA. After completing the calculations, the parameters used in the solder joint fatigue model are summarized in Table 6.  
After substituting all the parameters into Equation (8), the number of cycles \(N_{\text{f}}\) required for the fatigue failure of 10,000 FPGA solder joints is calculated based on the distribution of the fatigue coefficient \(\varepsilon_{\text{f}}\). Using Equation (11), the fatigue life of the critical FPGA solder joint is calculated, and the histogram of the FPGA solder joint lifetimes is plotted, as shown in Figure 25. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Plastic Strain** & **Plastic Shear** & **Fatigue Ductility** & **Fatigue** \\  & **Range \(\Delta\varepsilon_{\text{P}}\)** & **Strain Range \(\Delta\gamma\)** & **Exponent \(c\)** & **Coefficient \(\varepsilon_{\text{f}}\)** \\ \hline FPGA & 0.00264 & 0.00457 & \(-\)0.40265 & N(0.325,0.005) \\ SRAM & 0.00054 & 0.00094 & \(-\)0.40206 & N(0.325,0.005) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The parameters used in the solder joint fatigue model. The lifetime data are then fitted, and the reliability \(R_{\text{FPGA-sj}}\) of the FPGA solder joint is calculated, with the reliability curve plotted as shown in Figure 26. This trend aligns with the physical nature of fatigue failure, where the bearing capacity of the solder joint gradually decreases as the fatigue process progresses, ultimately leading to failure.