## 5 Estimating the Fatigue Life of M24 High-Strength Bolts Based on Broken Mechanics
### Estimation of Fatigue Life of M24 Twisted-Shear High-Strength Bolt  
According to the fatigue crack extension parameters determined above, the fatigue life of M24 high-strength bolts is estimated based on the Paris formula, and the results are listed in Tables 10-12. According to the comparison of the predicted life and the test life in the tables above, it is basically feasible to estimate the fatigue life of high-strength bolts by using the Paris formula, which can generally reflect the changing trend of fatigue life. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & \(\sigma_{max}\)**/**MPa** & \(\sigma_{min}\)**/**MPa** & \(\Delta\sigma_{n}\)**/**MPa** & **Predicted Life/Time** & **Test Life/Time** \\ \hline M24-1 & 400 & 240 & 160 & 2,731,721 & 5,100,006 \\ M24-2 & 400 & 240 & 160 & 2,731,721 & 5,100,006 \\ M24-3 & 475 & 285 & 190 & 1,631,306 & 2,273,480 \\ M24-4 & 475 & 285 & 190 & 1,631,306 & 2,352,282 \\ M24-5 & 485 & 291 & 194 & 1,532,467 & 751,375 \\ M24-6 & 500 & 300 & 200 & 1,398,641 & 1,221,394 \\ M24-7 & 500 & 300 & 200 & 1,398,641 & 1,298,395 \\ M24-8 & 512.5 & 307.5 & 205 & 1,298,777 & 1,546,630 \\ M24-9 & 515 & 309 & 206 & 1,279,955 & 492,189 \\ M24-10 & 515 & 309 & 206 & 1,279,955 & 492,189 \\ M24-11 & 525 & 315 & 210 & 1,208,199 & 535,942 \\ M24-12 & 525 & 315 & 210 & 1,208,199 & 567,354 \\ M24-13 & 550 & 330 & 220 & 1,050,820 & 153,563 \\ M24-14 & 550 & 330 & 220 & 1,050,820 & 205,678 \\ M24-15 & 550 & 330 & 220 & 1,050,820 & 196,329 \\ M24-16 & 550 & 330 & 220 & 1,050,820 & 370,241 \\ M24-17 & 550 & 330 & 220 & 1,050,820 & 457,271 \\ M24-18 & 550 & 330 & 220 & 1,050,820 & 457,271 \\ M24-19 & 550 & 330 & 220 & 1,050,820 & 642,275 \\ M24-20 & 550 & 330 & 220 & 1,050,820 & 642,275 \\ M24-21 & 550 & 330 & 220 & 1,050,820 & 441,443 \\ M24-22 & 575 & 345 & 230 & 919,629 & 282,422 \\ M24-23 & 575 & 345 & 230 & 919,629 & 282,422 \\ M24-24 & 600 & 360 & 240 & 809,399 & 195,186 \\ M24-25 & 600 & 360 & 240 & 809,399 & 214,782 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Estimated fatigue life of M24 high-strength bolt (\(a_{0}\) = 0.01 mm). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & \(a_{0}\) & \(a_{c}\) (mm) & \(\alpha\) & \(\mathbf{C}\) & \(\mathbf{m}\) \\ \hline
0.01 mm, 0.02 mm, 0.05 mm & 21.19 & 1.1215 & 7.04 \(\times\) 10\({}^{-12}\) & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The value of parameters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & \(\sigma_{max}\)**/MPa** & \(\sigma_{min}\)**/MPa** & \(\Delta\sigma_{n}\)**/MPa** & \
\begin{tabular}{c} **Predicted** \\ **Life/Time** \\ \end{tabular} &
\begin{tabular}{c} **Test** \\ **Life/Time** \\ \end{tabular} \\ \hline M24-1 & 400 & 240 & 160 & 1,188,130 & 5,100,006 \\ M24-2 & 400 & 240 & 160 & 1,188,130 & 5,100,006 \\ M24-3 & 475 & 285 & 190 & 709,517 & 2,273,480 \\ M24-4 & 475 & 285 & 190 & 709,517 & 2,352,282 \\ M24-5 & 485 & 291 & 194 & 666,528 & 751,375 \\ M24-6 & 500 & 300 & 200 & 608,323 & 1,221,394 \\ M24-7 & 500 & 300 & 200 & 608,323 & 1,298,395 \\ M24-8 & 512.5 & 307.5 & 205 & 564,888 & 1,546,630 \\ M24-9 & 515 & 309 & 206 & 556,701 & 492,189 \\ M24-10 & 515 & 309 & 206 & 556,701 & 492,189 \\ M24-11 & 525 & 315 & 210 & 525,492 & 557,354 \\ M24-13 & 550 & 330 & 220 & 457,042 & 205,678 \\ M24-15 & 550 & 330 & 220 & 457,042 & 205,678 \\ M24-17 & 550 & 330 & 220 & 457,042 & 370,241 \\ M24-19 & 550 & 330 & 220 & 457,042 & 457,271 \\ M24-20 & 550 & 330 & 220 & 457,042 & 642,275 \\ M24-21 & 550 & 330 & 220 & 457,042 & 441,443 \\ M24-22 & 575 & 345 & 230 & 399,982 & 282,422 \\ M24-23 & 600 & 360 & 240 & 352,039 & 214,782 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Estimated fatigue life of M24 high-strength bolt (\(a_{0}=0.02\) mm). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No. ** & \(\sigma_{max}\)**/MPa** & \(\sigma_{min}\)**/MPa** & \(\Delta\sigma_{n}\)**/MPa** & \ \begin{tabular}{c} **Predicted** \\ **Life/Time** \\ \end{tabular}  & \begin{tabular}{c} **Test** \\ **Life/Time** \\ \end{tabular}