## 2 Experimental Methods
### Fatigue S-N Curve  
In total, 25 satisfactory constant amplitude fatigue tests of the M24 twisted-shear high-strength bolts were carried out. The results of fatigue tests are shown in Tables 5-8. It is seen that M24-1 and M24-2's had more than 5 million stress cycles, while M24-13, M24-14, and M24-15 with prestress relaxation during secondary loading had a significantly shorter fatigue life. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{3}{c}{**Loading Stress/MPa**} & \multicolumn{3}{c}{**Stress Amplitude/MPa**} &
\begin{tabular}{c} **Fatigue** \\ **Life/Time** \\ \end{tabular} \\ \cline{2-7}  & \(\sigma_{max}\) & \(\sigma_{min}\) & \(\sigma_{m}\) & \(R\) & \(\Delta\sigma\) & \(N\) \\ \hline M24-8 & 512.5 & 307.5 & 410 & 0.6 & 205 & 1,546,630 \\ M24-9 & 515 & 309 & 412 & 0.6 & 206 & 492,189 \\ M24-10 & 515 & 309 & 412 & 0.6 & 206 & 492,189 \\ M24-11 & 525 & 315 & 420 & 0.6 & 210 & 535,942 \\ M24-12 & 525 & 315 & 420 & 0.6 & 210 & 567,354 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Constant amplitude fatigue test results of M24 torsional shear-type high-strength bolt with prestension (\(\sigma_{max}\) = 512.5–525 MP). Generally, the relationship between the external load and its corresponding fatigue life is described by the S-N curve. The empirical equation of the S-N curve in the form of a power function is given by  
\[N\cdot(\Delta\sigma)^{m}=C \tag{4}\]  
The S-N curve in logarithmic form can be expressed as follows:  
\[\lg N=-m\lg(\Delta\sigma)+\lg C \tag{5}\]  
Under the 97.72% reliability probability, the formula obtained is as follows:  
\[\lg N=-m\lg(\Delta\sigma)+\lg C-2s \tag{6}\]  
Combined with the data in the fatigue test process analysis in Tables 4-7, M24-13-15 were considered as abnormal data points and eliminated due to the prestress relaxation of the secondary loading. Furthermore, over 5 million stress cycle data points of the bolts M24-1 and M24-2 also did not participate in fitting the S-N curve. Therefore, the valid data of the other 20 bolts were used to fit the power multiplier S-N curves. Taking the stress amplitude as the parameter, the constant amplitude power regression curve and fatigue S-N curve are presented in Figures 8 and 9, respectively, where the logarithmic equation for the corresponding part of the oblique line of the S-N curve in Figure 9 can be developed as Equation (7). \[\lg N=32.365-11.419\lg(\Delta\sigma) \tag{7}\]  
It can be seen from Figures 8 and 9 that the fatigue life of the specimens is relatively scattered at the same stress amplitude, but in total the fitting correlation coefficient of the bolt test data is highly satisfied, the value of which is about 0.8. Moreover, the test data follow the trend that the lower the stress range, the longer the fatigue life. Additionally, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{4}{c}{**Loading Stress/MPa**} & \multicolumn{2}{c}{**Stress Amplitude/MPa**} & \multicolumn{2}{c}{**Fatigue Life/Time**} \\ \cline{2-7}  & \(\sigma_{max}\) & \(\sigma_{min}\) & \(\sigma_{m}\) & \(R\) & \(\Delta\sigma\) & \(N\) \\ \hline M24-13 & 550 & 330 & 440 & 0.6 & 220 & 153,563 \\ M24-14 & 550 & 330 & 440 & 0.6 & 220 & 205,678 \\ M24-15 & 550 & 330 & 440 & 0.6 & 220 & 196,329 \\ M24-16 & 550 & 330 & 440 & 0.6 & 220 & 370,241 \\ M24-17 & 550 & 330 & 440 & 0.6 & 220 & 457,271 \\ M24-18 & 550 & 330 & 440 & 0.6 & 220 & 457,271 \\ M24-19 & 550 & 330 & 440 & 0.6 & 220 & 642,275 \\ M24-20 & 550 & 330 & 440 & 0.6 & 220 & 642,275 \\ M24-21 & 550 & 330 & 440 & 0.6 & 220 & 441,443 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Constant amplitude fatigue test results of M24 torsional shear-type high-strength bolt with pretension (\(\sigma_{max}=550\) MP).