## 3 Results and Discussion
### Validation of the Calculated Fatigue Strength Results
Figure 13 shows a comparison between the numerically predicted fatigue strength and the stress range, which led to a run-out of the respective specimen. Herein, data points on the right-hand side of the diagonal line represent conservative estimations. Additionally, a scatter band of \(+10\%\) and \(-10\%\) was evaluated. As the majority of derived data points fall within the respective scatter band, the depicted results confirm the sound \begin{table}
\begin{tabular}{c c c} \hline \hline \(R\)\([-]\) & **Specimen** & **Cycles to Failure \([-]\)** \\ \hline \multirow{8}{*}{\(-1\)} & \#02 & 3,335,750 \\  & \#03 & 3,352,772 \\  & \#04 & 13,076 \\  & \#05 & 9,708,502 \\  & \#06 & 2,336,391 \\  & \#07 & 1,135,902 \\  & \#08 & 7,876,634 \\  & \#09 & 540,942 \\  & \#10 & 2,533,432 \\  & \#11 & 5,068,835 \\  & \#12 & 9,526,277 \\  & \#13 & 912,933 \\  & \#14 & 6,880,565 \\  & \#15 & 2,591,440 \\  & \#16 & 3,645,336 \\ \hline \multirow{8}{*}{0} & \#17 & 6,671,185 \\  & \#18 & 954,420 \\  & \#19 & 581,208 \\ \cline{1-1}  & \#20 & 2,789,243 \\ \cline{1-1}  & \#21 & 2,008,825 \\ \cline{1-1}  & \#23 & 8,364,431 \\ \cline{1-1}  & \#25 & 3,232,072 \\ \cline{1-1}  & \#26 & 16,900 \\ \cline{1-1}  & \#34 & 2,616,984 \\ \cline{1-1}  & \#78 & 2,964,118 \\ \cline{1-1}  & \#84 & 195,189 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Number of load cycles to burst failure. applicability of the presented methodology to assess the fatigue strength of defect-afflicted cast steel components. Furthermore, the methodology presented in a preceding study [26] was applied, to assess the fatigue strength of the investigated defect-afflicted specimens based on the theory of critical distances. Utilizing the values of \(a_{0}\) reported in Table 4, the fatigue strength \(\Delta\sigma_{LLF,Defect,TCD}\) was evaluated by the TCD-framework. A comparison between the SED- and TCD-based assessment results is depicted in Figure 14. In contrast to Figure 13, the results of specimens where no run-out was achieved in the experiments are also depicted. Regarding Figure 14, the SED-framework yields slightly reduced values of the predicted fatigue strength compared to the ones derived by the TCD-based methodology, indicating a higher degree of conservatism when utilizing the SED-framework. In order to  
Figure 14: Comparison of SED- and TCD-based long-life fatigue assessment results: (**a**) \(R=-1\); and (**b**) \(R=0\). Figure 13: Comparison of the numerically and experimentally derived endurance limit results: (**a**) \(R=-1\); and (**b**) \(R=0\). quantify the pictured tendencies, the average unsigned deviation \(\Delta_{unsigned}\) and signed deviation \(\Delta_{signed}\) between the numerically and experimentally derived results were evaluated according to Equations (8) and (9), respectively. \[\Delta_{unsigned} =\frac{1}{n}\cdot\sum_{i=1}^{n}\frac{\left|\Delta\sigma_{LLF,Defect,i }-\Delta\sigma_{Exp,Run-out,i}\right|}{\Delta\sigma_{Exp,Run-out,i}}\cdot 100\% \tag{8}\] \[\Delta_{signed} =\frac{1}{n}\cdot\sum_{i=1}^{n}\frac{\Delta\sigma_{LLF,Defect,i}- \Delta\sigma_{Exp,Run-out,i}}{\Delta\sigma_{Exp,Run-out,i}}\cdot 100\% \tag{9}\]  
Table 7 summarizes the resulting deviations obtained by the SED- and TCD-based fatigue assessment methodologies. Regarding Table 7, both applied methodologies led to similar values of \(\Delta_{unsigned}\). As the maximum unsigned deviation takes a value of only 11.3%, the reported results emphasize the sound capability of the applied assessment concepts in predicting reasonable fatigue strength values of defect-afflicted cast steel components. Regarding the depicted values of \(\Delta_{signed}\), both concepts lead to positive deviations, which represent an average overestimation of experimentally derived run-out load levels. However, an improved prediction accuracy of the presented SED-based assessment methodology was observed, as the depicted values of \(\Delta_{signed}\) are significantly smaller than those derived by the TCD-framework.