# Study of the Rotary Bending Fatigue Resistance of 30 MnB5, 41 CrS4 and 30 MnVS6 Steels
## 2 Materials and Methods
Since the initiation of fatigue cracks is a process that takes place preferentially on the surface [38], if there was a poor or uneven preparation of the samples, the results obtained could present a very high dispersion and be inconclusive. The determination of the applied stress in the specimen is carried out using the following equation:  
\[\mathrm{S}=\mathrm{K}\frac{\mathrm{Mc}}{\mathrm{I}} \tag{1}\]  
where K is the stress concentration factor, M the bending moment of the force applied to the specimen, c is the distance perpendicular to the neutral axis from where the maximum stress acts (\(\sigma_{\mathrm{m}}\)) and I the moment of inertia of the cross section. To calculate K, it is taken into account that the relationship between D/d and r/d is 2.2 and 5, respectively (where r is the radius of agreement, 20 mm). The result obtained for K is a value close to 1 [39]. For the type of geometry used, the corresponding standard [27] establishes that the applied force is determined with the following expression:  
\[\mathrm{F}=\mathrm{S}\frac{\pi\mathrm{d}^{3}}{32(\mathrm{L}-\mathrm{x})} \tag{2}\]  
where L is the length from the clamping point of the specimen to the point of application of the load and x is the distance between the clamping point and the midpoint of the sample. For the tested specimens, the distance (\(\mathrm{L}-\mathrm{x}\)) is 52.5 mm. In the rotary-bending fatigue tests carried out, different stress levels have been used. The values used have been chosen as percentages of the yield strength provided by the manufacturer for each type of steel and are shown in Table 5. In none of the cases has 100% of the yield strength been reached to avoid fatigue tests being carried out in the plastic regime of the steels. In order to cover the widest possible range of stresses, values between 40% and 90% of R\({}_{\mathrm{e}}\) have been proposed  
The Wohler curves (S-N), where N is the numbers of cycles, for ferrous alloys show a limiting stress below which fatigue failure does not occur [40,41]. This value, known as the fatigue resistance limit, is the inversion point of the S-N curve and it is normally in the range of 10\({}^{5}\) to 10\({}^{7}\) cycles. Considering this range of values, the decision was made to end the fatigue test in 10\({}^{6}\) cycles. From 10\({}^{6}\) cycles, infinite life fatigue would be considered for the materials under study. The results obtained in the rotary-bending fatigue tests have been refined using the Grubbs statistical analysis [42]. This statistical treatment made it possible to discard atypical or extreme results that presented discordance with the rest of the measurements. The Wohler curve was fitted using the Basquin method [43]. A characteristic of fatigue tests is that, despite their large dispersion, the fatigue resistance data (for a specific stress level) follow a logarithmic distribution (Gaussian distribution). Thus, it is possible to use \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Key** & **B1** & **B2** & **EC** & **MV** \\ \hline
**MPa** & **30 MnB5** & **30 MnB5** & **41 CrS4** & **30 MnVS6** \\ \hline
40\% R\({}_{\mathrm{e}}\) & - & 366 & 393 & - \\
50\% R\({}_{\mathrm{e}}\) & 424 & - & 494 & 324 \\
60\% R\({}_{\mathrm{e}}\) & 511 & 559 & 586 & 388 \\
70\% R\({}_{\mathrm{e}}\) & 596 & 653 & 685 & 452 \\
78\% R\({}_{\mathrm{e}}\) & - & 717 & - & - \\
85\% R\({}_{\mathrm{e}}\) & 723 & 777 & 838 & - \\
90\% R\({}_{\mathrm{e}}\) & - & - & 581 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Values of maximum stress amplitudes, S (MPa), used in the rotary-bending tests for each evaluated steel. the associated half-life curve and the standard deviation to define a calculation S-N curve for any probability of fatigue [44]. This methodology is the one that was used to carry out the comparative analysis of the fatigue results of the four types of steels.