## 3 Results and Discussion
### Fatigue Limits  
Based on the principles of [PERSON]'s method, to obtain a more accurate solution, the selected S-N curves must be as close as possible to the real ones. In the present study, the S-N curves (for turning and polishing and for DB) were selected based on our previous studies. The mechanical properties of the studied 316 CTASS are similar to those of the 304 CTASS investigated in [6]. The difference in the tensile strength and yield limit values for these two steel types is approximately 304 MPa. Their elongations are 45% and 41%, respectively. The S-N curves in [6] for 304 steel have fatigue limits of 440 MPa due to turning and polishing and 540 MPa due to the smoothing DB process. Since the 316 steel in the present study has lower strength (the yield limit and tensile strength are 60 MPa lower than the corresponding values of 304 steel [6]), the main S-N curves for 316 steel in a double-logarithmic coordinate system have fatigue limits of 380 MPa for turning and polishing and 420 MPa for the smoothing DB processes (Figure 10). The difference \(\Delta\sigma\) in the stress amplitudes between any two adjacent levels is 20 MPa, and the number of cycles n for each step is \(10^{5}\) (see Figure 10). \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Specimens**} \\ \multicolumn{2}{c}{} & \multicolumn{2}{c}{**F**} & \multicolumn{2}{c}{**A**} & \multicolumn{2}{c}{**N**} & \multicolumn{2}{c}{**D**} \\ \hline
**Depth** & \multicolumn{2}{c}{**Error, MPa**} & \multicolumn{2}{c}{**Depth**} & \multicolumn{2}{c}{**Error, MPa**} & \multicolumn{2}{c}{**Depth**} & \multicolumn{2}{c}{**Error, MPa**} & \multicolumn{2}{c}{**Depth**} & \multicolumn{2}{c}{**Error, MPa**} \\
**mm** & **Axial** & **Hoop** & **mm** & **Axial** & **Hoop** & **mm** & **Axial** & **Hoop** & **mm** & **Axial** & **Hoop** \\ \hline
0 & 110.8 & 30.4 & 0 & 130.6 & 37.6 & 0 & 84.9 & 53.2 & 0 & 130.1 & 88.7 \\
0.02 & 77.6 & 28.5 & 0.02 & 29.2 & 33.5 & 0.02 & 60.8 & 70.2 & 0.02 &  
The fatigue limit experimental results are listed in Table 7. All four DB processes significantly increase the fatigue limit of the specimens compared to turning and polishing. The largest increase from 365 MPa to 419 MPa (i.e., 14.79%) is observed in the samples from group F (flood lubrication), while the smallest increase from 365 MPa to 405 MPa (i.e., 10.96%) is recorded in the samples from group D (dry DB without cooling). Dry DB with air cooling or nitrogen cooling (groups A and N) results in an increase of 14.25% and 14.52%, respectively, which is essentially the same as that achieved by DB under flood lubrication. The fatigue limits of the samples that underwent DB under dry conditions increase with decreasing temperature. The smaller fatigue limit increase observed from dry DB without cooling (group D) can be explained by the resulting microstructure of the surface and subsurface layers. As noted in Section 3.2.1, dry DB processes form a submicro-crystalline structure with high atomic density in these layers, with correspondingly higher second-order microstresses. These microstresses lead to greater internal energy in these layers. These structural changes are most pronounced for group D specimens, in which the internal energy is highest. The introduced residual compressive macrostresses delay fatigue macrocrack formation. The increased internal energy is released as the macrocrack develops and the resistance to fatigue macrocrack growth in the affected layers is accordingly lowest for the dry DB process without cooling (group D). However, dry DB without cooling also leads to a surface texture with the largest negative skewness and a kurtosis significantly greater than three (see Table 5). This combination of shape roughness parameters has been demonstrated to significantly favor the tribological behavior of the surface in boundary friction and mixed lubrication friction conditions [46; 59; 60; 61].