## 4 Results and Discussion  
### Microstructural Evolution  
The simulation illustrates that the effective elastic modulus degrades with the accumulation of shock cycles. In order to study the cause of performance degradation, the microstructural evolution is characterized from autocorrelation functions.  
The specific surface, marked as s, of two-phase media is defined as the two-phase interface area per unit total volume, which can be obtained from the slope of the two-point autocorrelation function [27]. In this study, \(s\) of original images and reconstructed models is conducted from Equation (18):  
\[\frac{d}{dt}S_{2}(r)\bigg{|}_{r=0}=\left\{\begin{array}{l}-s/\pi,D=2\\ -s/4,D=3\end{array}\right.. \tag{18}\]  
Specific surface can be used to estimate the hydraulic diameter (\(D_{H}\)) of porous media [28], which is calculated in Equation (19). \(V\) is the volume fraction of the medium:  
\[D_{H}=\frac{4V}{s} \tag{19}\]  
The captured autocorrelation functions of original SEM images from Figure 5 changes with thermal shocks are shown in Figure 15. There is an increase in the slope at the origin and a decrease in the correlation length. Changes of the mean particle size, hydraulic diameter and specific surface in SEM pictures and reconstructed models are calculated as shown in Table 4.  
It can be seen that the average micron-silver particle size decreases, while this is in contrast to a slight increase in the size of silver grains (-45 \({}^{\circ}\)C-250 \({}^{\circ}\)C) reported in [29]. It should be noted that the surface diffusivity of silver is relatively lower at 125 \({}^{\circ}\)C [30] than the melting point and  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Thermal Shock (Cycles)** & \(D_{P2D}\) **(um)** & \(D_{P3D}\) **(um)** & \(D_{H2D}\) **(um)** & \(D_{H3D}\) **(um)** & \(s_{2D}\) **(um\({}^{-1}\))** & \(s_{3D}\) **(um\({}^{-1}\))** \\ \hline
0 & 4.30 & - & 3.16 & - & 1.10 & - \\
50 & 3.03 & 2.88 & 1.88 & 2.0 sintering temperature. Meanwhile the soak of \(-170\)\({}^{\circ}\)C seems to prevent particle recrystallization growth and even reverse-driven particles from dispersing. The hydraulic diameter of the medium declines with fluctuation. If the porous medium is regarded as an interconnected pipeline network, the above situation can be interpreted as the rise of pore density and pore nucleation growth induced by cyclic loading, which is consistent with the measured increase in average pore size and porosity [31]. The whole tendency of the specific surface goes up, which physically means that the total surface area of pores increases. The results demonstrate that damage gradually accumulates with thermal shock testing, resulting in the increase in porosity and the role of pores as grain growth inhibitors. The contact area between adjacent grains and the size of the medium decreases. The medium particles tend to disperse. In Figure 15 autocorrelation functions slightly oscillate after 50 thermal shocks, which reflects in the influence of the roundness of micron silver particles. Furthermore, another important finding from visual the view of pores (Figure 8) is that the pore distribution area becomes uneven and the local density changes, which will further promote the initiation of cracks.