## 3 Experimental Results and Discussion
### Ratcheting Strain Rate and Ratcheting Boundary for SAF2507 Steel  
In order to arrest the ratcheting behavior of the material, [PERSON] et al. [40] attempted to determine zero ratcheting strain rate with specified mean stress and stress amplitude. If the material was loaded under zero ratcheting strain rate conditions with specified mean stress and stress amplitude, ratcheting strain could be suppressed and would not increase further. The ratcheting strain rate represented the incremental ratcheting strain during each cycle and was denoted by \(d\epsilon_{r}/dN\), where \(N\) was the number of cycle weeks.  
Figure 7a showed the correlation between stress amplitude and ratcheting strain rate at a constant mean stress of 400 MPa. The correlation between the ratcheting strain rate and the mean stress at a constant stress amplitude of 300 MPa are shown in Figure 7b. Based on the least squares method, Equation (2) is used to regress. The slope and vertical intercept of Equation (2) are listed in Table 3, and the corresponding mean stress and stress amplitude were calculated when the ratcheting strain rate was zero, as shown in Table 3.  
\[y=mx+c \tag{2}\]  
Figure 6: Uniaxial ratcheting tests with constant stress control and different pre-strains.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Figure** & **Slope** & **Intercept** & \multicolumn{2}{c}{**Zero Ratcheting Strain Rate**} \\ \cline{3-6}  & **No.** & **m** & **c** & **Mean Stress** & **Stress Amplitudes** \\ \hline \multirow{2}{*}{SAF2507} & Figure 7a & 0.0467 & \(-\)12.725 & 400 & 272.48 \\ \cline{2-6}  & Figure 7b & 0.024 & \(-\)6.8 & 283.33 & 300 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Slope, intercept, and stress values at zero ratcheting strain.  
Figure 7: (**a**) Ratcheting strain rate vs. stress amplitude; (**b**) ratcheting strain rate vs. mean stress.  
The ratcheting effect was significantly impacted by both mean stress and stress amplitude. [PERSON] et al. [40] provided the correlation among the ratcheting strain rate, the constant mean stress accompanied by the varying stress amplitude, and the constant stress amplitude along with the varying mean stress, which is presented in Equation (3).  
\[\dot{\epsilon}_{r}=(m_{1}a_{1}+m_{2}a_{2}+c_{1}+c_{2})/2 \tag{3}\]  
where the parameter \(m_{1}\) denoted the slope of the stress amplitude and material ratcheting strain rate at constant mean stress, and the parameter \(m_{2}\) denoted the slope of the mean stress and material ratcheting strain rate at constant stress amplitude. Parameter \(c_{1}\) was the vertical intercept of stress amplitude and material ratcheting strain rate when the mean stress was constant, and parameter \(c_{2}\) was the vertical intercept of mean stress and material ratcheting strain rate when the stress amplitude was constant.  
According to Equation (3), Figure 8 gives the three-dimensional ratcheting surface zone generated by the mathematical equation. It is shown that the ratcheting strain of SAF2507 stainless steel could be found for different sets of applied mean and amplitude stress. The three-dimensional surface zone was constructed with certain boundary limits of maximum mean and amplitude stresses were applied in the experiment. The boundaries can be increased by extending the trend line without changing the slopes and intercepts.