## 3 Results and Discussion
### Four-Point Bending Fatigue Test
#### 3.3.3 Fatigue Equation Considering Failure Probability  
According to the above analysis, the fatigue life \(N_{p}\) of CNFPUC obeyed the two-parameter Weibull distribution. Therefore, the failure probability \(F\) should satisfy Equation (2), and the corresponding equivalent fatigue life \(N_{f}\) can be obtained:  
\[N_{f}=N_{a}[\ln{(\frac{1}{1-F})}]^{\frac{1}{b}} \tag{5}\]  
The coefficients \(b\) and \(b\)ln\(N_{a}\) given in Table 10 are substituted into Equation (5), and the fatigue life \(N_{p}\) of given failure probability \(F\) can be obtained by calculation. The calculation results of fatigue life \(N_{p}\) at three stress levels corresponding to different failure probabilities \(F\) are shown in Table 11. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Temperature (\({}^{\circ}\)C)**} & \multicolumn{3}{c}{**Stress Level \(S_{max}\) = 0.60**} & \multicolumn{3}{c}{**Stress Level \(S_{max}\) = 0.70**} & \multicolumn{3}{c}{**Stress Level \(S_{max}\) = 0.80**} \\ \cline{2-10}  & \(b\) & \(\beta\) = \(b\)ln\(N_{a}\) & \(R^{2}\) & \(b\) & \(\beta\) = \(b\)ln\(N_{a}\) & \(R^{2}\) & \(b\) & \(\beta\) = \(b\)ln\(N_{a}\) & \(R^{2}\) \\ \hline \(-\)40 & 7.99 & 105.52 & 0.99 & 5.09 & 62.69 & 0.97 & 3.55 & 39.15 & 0.96 \\ \(-\)20 & 6.66 & 86.19 & 0.99 & 3.34 & 39.48 & 0.97 & 2.51 & 25.19 & 0.98 \\ \(0\) & 5.29 & 66.81 & 0.95 & 2.54 & 29.07 & 0.90 & 2.35 & 22.39 & 0.95 \\ \(20\) & 3.22 & 38.88 & 0.96 & 2.20 & 22.28 & 0.97 & 1.85 & 16.63 & 0.94 \\ \(40\) & 2.63 & 30.59 & 0.97 & 1.92 & 18.12 & 0.92 & 1.36 & 10.59 & 0.98 \\ \hline \hline \end{tabular} Note: \(b\)—regression coefficient, \(R^{2}\)—determination coefficient, \(\beta\)—regression coefficient.  
\end{table} 
Table 10: The results of regression analysis of fatigue test according to Equation (3). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Failure Probability** & **Livability** & \multicolumn{3}{c}{**Stress Levels**} & \multicolumn{3}{c}{**Regression Coefficient**} & \multicolumn{3}{c}{**Determination Coefficient**} \\ \hline
**F** & \(P\) & \(S\) = 0.6 & \(S\) = 0.7 & \(S\) = 0.8 & **1 gA** & \(B\) & \(R^{2}\) \\ \hline
0.10 & 0.90 & 410,389 & 143,514 & 32,672 & 0.41 & 0.11 & 0.96 \\
0.20 & 0.80 & 450,801 & 166,312 & 40,362 & 0.44 & 0.12 & 0.96 \\
0.30 & 0.70 & 478,055 & 182,365 & 46,063 & 0.47 & 0.12 & 0.96 \\
0.40 & 0.60 & 500,037 & 195,700 & 50,968 & 0.49 & 0.12 & 0.96 \\
0.50 & 0.50 & 519,508 & 207,793 & 55,544 & 0.51 & 0.13 & 0.96 \\ \hline \hline \multicolumn{8}{c}{**(A)** Change of fatigue life of CNFPUC with failure probability \(F\) at -20 \({}^{\circ}\)C.} \\ \hline
0.10 & 0.90 & 320,816 & 69,327 & 9314 & 0.23 & 0.08 & 0.97 \\
0.20 & 0.80 & 359,080 & 86,792 & 12,560 & 0.25 & 0.08 & 0.97 \\
0.30 & 0.70 & 385,279 & 99,877 & 15,140 & 0.27 & 0.09 & 0.96 \\
0.40 & 0.60 & 406,629 & 111,218 & 17,470 & 0.29 & 0.09 & 0.96 \\
0.50 & 0.50 & 425,698 & 121,860 & 19,729 & 0.30 & 0.09 & 0.96 \\ \hline \hline \multicolumn{8}{c}{**(B)** Change of fatigue life of CNFPUC with failure probability \(F\) at 0 \({}^{\circ}\)C.} \\ \hline
0.10 & 0.90 & 199,604 & 38,519 & 5271 & 0.20 & 0.08 & 0.98 \\
0.20 & 0.80 & 230,026 & 51,759 & 7255 & 0.21 & 0.08 & 0.97 \\
0.30 & 0.70 & 251,351 & 62,256 & 8857 & 0.24 & 0.08 & 0.96 \\
0.40 & 0.60 & 269,011 & 71,713 & 10,320 & 0.26 & 0.09 & 0.96 \\
0.50 & 0 Based on the actual boundary conditions of the practical and the CNFPUC fatigue tests of the project, a double-logarithm fatigue equation is established:  
\[S=\lg A-B\lg N \tag{6}\]  
The double-logarithm fatigue equation can fit the test results well, and it may exactly satisfy the boundary condition of \(S\to 0\) when the \(N\rightarrow\infty\). The values of coefficients \(A\) and \(B\) depend on the degree of safety that the equation can guarantee [13; 33; 34].