## 3 Results and Discussion  
### Fatigue Test  
Figure 6a presents an S-N diagram showing the fatigue test data at a room temperature of about 20 \({}^{\circ}\)C. The logarithm of the number of cycles to failure is on the X-axis, and stress amplitude is on the Y-axis. When 200 MPa stress amplitude was applied to the center of the specimen, fatigue failure did not occur until 10\({}^{9}\) cycles, which means that the axle material had typical carbon steel properties with a fatigue limit. However, the fatigue limit was not \(2\times 10^{6}\) cycles. Some specimens fractured in the \(2\times 10^{6}\) to \(1\times 10^{7}\) cycle range. The fracture surfaces in Figure 6b,c show the fracture surfaces at 213,000 and \(1.02\times 10^{6}\) cycles, respectively. A crack occurred on the surface, gradually grew elliptically, and then reached an unstable state at a certain crack size. The specimen was finally broken. Some inclusions were found on the fracture surface. According to [1], inclusions found in axles are typically aluminates, sulfides, silicates, oxides, etc. The specification [4] specifies the acceptable size and quantity of inclusions. Figure 7a presents an S-N diagram at \(-30\)\({}^{\circ}\)C. Fatigue failure in four specimens occurred in the \(2\times 10^{6}\) to \(1\times 10^{7}\) cycle range, beyond the 2 million cycles traditionally regarded as the infinite life of steel. Figure 7b-e shows the fracture surfaces; cracks formed on the surface as in the room temperature case and gradually progressed. Once they reached a certain size, they entered an unstable growth mode. Some black voids or inclusions were observed on the fracture surface. Figure 8a presents an S-N diagram at \(-60\)\({}^{\circ}\)C. Similar to at \(-30\)\({}^{\circ}\)C, fatigue failure in five specimens occurred in the \(2\times 10^{6}\) to \(1\times 10^{7}\) cycle range, beyond the 2 million cycles. Figure 8b,c shows the fracture surfaces; cracks formed on the surface as in the room temperature case and gradually progressed. Once they reached a certain size, they entered an unstable growth mode. Some black voids or inclusions were observed on the fracture surface. Further, it was observed that long, white ridges were decreased in the stable crack propagation region. Figure 9 compares fatigue test data for 20, \(-30\), and \(-60\)\({}^{\circ}\)C. It can be seen that the fatigue strength increases with decreasing temperature. In general, for metals, the lower the temperature, the higher the hardness, the tensile, and yield strengths. Fatigue strength is proportional to hardness and tensile strength. When the amplitude of the acting stress is S\({}_{\text{a}}\) and the number of cycles to failure under a given stress amplitude \(\Delta\)S is N, the straight section of the S\({}_{\text{a}}\)-N diagrams at each temperature can be expressed as Equations (1)-(3). R is the coefficient of determination. The fatigue strengths at 2 million cycles for +20, \(-30\), and \(-60\)\({}^{\circ}\)C were 210.1, 225.2, and 251.9 MPa, respectively. Fatigue strength at \(-30\) and \(-60\)\({}^{\circ}\)C increased by 7.1 and 19.9%, respectively, compared to the fatigue strength at room temperature. Statistical analysis of the S-N curves was performed using the Excel program. The results are summarized in Table 3.  
\[+20\text{ }^{\circ}\text{C: S}_{\text{a}} =-25.786\text{ log(N)}+372.57,\text{ R}^{2}=0.895 \tag{1}\] \[-30\text{ }^{\circ}\text{C: S}_{\text{a}} =-28.946\text{ log(N)}+407.61,\text{ R}^{2}=0.931\] (2) \[-60\text{ }^{\circ}\text{C: S}_{\text{a}} =-34.207\text{ log(N)}+467.43,\text{ R}^{2}=0.888 \tag{3}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Coefficient of Determination** & **Standard Deviation** & **Standard Error of the Mean** \\ \hline \(+20\)\({}^{\circ}\)C & 0.895 & 27.95 & 6.58 \\ \hline \(-30\)\({}^{\circ}\)C & 0.931 & 20.03 & 5.78 \\ \hline \(-60\)\({}^{\circ}\)C & 0.888 & 36.19 & 10.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical analysis of the S–N curves.