## 3 Results and Discussion
### Validation of the Calculated Fatigue Strength Results
This improved accuracy may be the result of the averaging procedure over a finite volume when applying the SED concept. Rather than assessing the fatigue life based on a single stress value at a dedicated point, as conducted in terms of the TCD, the SED-framework also considers the strains present in the control volume, yielding an improved contribution regarding size-effect. This increase in accuracy also justifies the slightly enhanced numerical effort of the sub-model-based SED-framework compared to the utilization of the TCD. Concerning fatigue assessment in the finite-life region, the application of the SED depicts a more straight-forward approach compared to the TCD. [PERSON] and [PERSON] presented an extension of the TCD to facilitate the fatigue assessment of notched components in the medium-cycle regime, introducing a relationship between the critical distance and the number of cycles to failure [63]. This dependency is described by a power law, where the corresponding parameters are dependent on the material and the investigated load ratio. Hence, application of this methodology requires a calibration procedure in order to evaluate the corresponding material parameters. The subsequent fatigue assessment of defect-afflicted components is based on an iterative loop which increases numerical effort when dealing with arbitrarily shaped spatial imperfections. Considering the SED concept, the fatigue assessment in the finite-life regime takes advantage of the design limit curve evaluated in Section 3.1. Utilizing the derived parameter \(\Delta\overline{W}^{(e)}_{97.5\%}\), the corresponding defect structure loaded under an arbitrary stress range \(\Delta\sigma_{i}\) can be assessed following Equation (10). \[\Delta\overline{W}^{(e)}_{DEF,97.5\%}=c_{w}\cdot\Delta\overline{W}^{(e)}_{97.5\%}\cdot\left(\frac{\Delta\sigma_{i}}{\Delta\sigma_{g}}\right)^{2} \tag{10}\]  
In order to also validate the presented methodology in the finite-life region, the stress ranges of all conducted experiments reported in Section 2.2 were considered according to \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\(R\)\([-]\)} & \multicolumn{2}{c}{\(\Delta_{unsigned}\) [\%]} & \multicolumn{2}{c}{\(\Delta_{signed}\) [\%]} \\  & **SED** & **TCD** & **SED** & **TCD** \\ \hline \(-1\) & 8.6 & 11.3 & +2.9 & +9.2 \\ \(0\) & 7.0 & 7.4 & +2.4 & +5.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average deviations obtained by the applied assessment methodologies. Equation (10), yielding corresponding values for the linear-elastic SED range \(\Delta\overline{W}_{DEF,97.5\%}^{(c)}\). Figure 15 depicts the numerical assessment results of the defect-afflicted cast steel specimens, where the data points from Figure 8 are plotted as a reference. Regarding the results of the defect-afflicted specimens, it should be mentioned, that there are two data points reported for each value of \(N\), constituting the results based on the X- and Y-view of the corresponding specimen, respectively. As nearly all evaluated SED values fall within the derived scatter band, the depicted data points in Figure 15 exhibit satisfying fatigue assessment results. Looking closely in the region of \(N=10^{4}\), four data points can be observed, that are clearly outside the depicted scatter band. These data points represent the assessment results of specimens #04 tested at \(R=-1\) and #26 tested at \(R=0\), while the fatigue strength of both specimens was accurately predicted by the presented methodology, the assessment of the respective stress ranges \(\Delta\sigma_{Exp,Failure}\) underestimates the SED value suggested by the evaluated scatter band. A possible explanation for the observed deviation could be a geometrical feature, representing a notch-like shape of high acuity, not visible on the two perpendicularly assessed radiographs. The utilization of three-dimensional finite element analyses could possibly improve the prediction accuracy, while simultaneously increasing the computational effort and associated costs.