## 3 Results and Discussion
### Validation of the Calculated Fatigue Strength Results  
Validation of the proposed fatigue assessment methodology was conducted utilizing the results of the high-cycle fatigue experiments presented in Section 2.2. The fatigue strength of corresponding specimens was evaluated according to the procedure described in Section 3.2 and compared to the load levels investigated in the experiments. Figure 12 summarizes the validation results for stress ratios of \(R=-1\) and 0, respectively. Herein, the abscissa depicts the individual specimens in terms of the utilized radiographs denoted as X- and Y-view, which were assessed by the presented methodology. The parameter \(\Delta\sigma_{Exp\_Failure}\) represents the stress range, which led to burst failure in the corresponding experiment. \(\Delta\sigma_{Exp\_Run-out}\) depicts the stress range, where a run-out of the respective specimen at ten million load cycles was achieved. \(\Delta\sigma_{LLF\_Defect}\) represents the assessed fatigue strength of the defect-afflicted specimen, evaluated by the established SED-framework. All depicted stress ranges were normalized with respect to the fatigue strength \(\Delta\sigma_{0,R=-1}\) of the parent material at a stress ratio of \(R=-1\). Considering the depicted results, the presented energy-based fatigue assessment methodology leads to a sound agreement of estimated fatigue strength values and experimental results, as \(\Delta\sigma_{LLF\_Defect}\) is either smaller than \(\Delta\sigma_{Exp\_Run-out}\) or takes a value between \(\Delta\sigma_{Exp\_Run-out}\) and \(\Delta\sigma_{Exp\_Failure}\). Regarding the second case, it should be noted, that the depicted values of \(\Delta\sigma_{Exp\_Run-out}\) are not necessarily the highest possible load levels to achieve a run-out of the corresponding specimens, as the specimens were re-inserted to provoke burst failure after a run-out was  
Figure 12: Validation results of the SED analysis of defect-afflicted cast steel specimens: (**a**) Specimens tested at \(R=-1\); and (**b**) specimens tested at \(R=0\). observed. Hence, values of \(\Delta\sigma_{LLF,Defect}\) that lie in between \(\Delta\sigma_{Exp,Run-out}\) and \(\Delta\sigma_{Exp,Failure}\) depict plausible fatigue strength estimations of the respective specimens. Taking a closer look at Figure 12, one obtains a few specimens, where no run-out was achieved. These supposedly non-conservative assessment results are also reported in Table 6.  
Regarding specimens #05, #12 and #23, the achieved numbers of cycles where burst failure occurred were quite close to ten million cycles, which serves as a criterion of a run-out. As the deviations between \(\Delta\sigma_{LLF,Defect}\) and \(\Delta\sigma_{Exp,Run-out}\) were quite small, the presented values of \(\Delta\sigma_{LLF,Defect}\) depict plausible estimations of the fatigue strength. Considering specimens #14 and #78, the numbers of cycles to failure show values of approximately 6.88 and \(2.96\cdot 10^{6}\) and therefore a higher divergence to the run-out criterion. However, the depicted values of \(\Delta\sigma_{LLF,Defect}\) regarding the X-view of specimen #14 as well as the Y-view of specimen #78 propose a fatigue strength, that is quite below the observed stress range at burst failure. Hence, the presented values of \(\Delta\sigma_{LLF,Defect}\) also depict reasonable fatigue strength estimations, as experiments utilizing a stress range of \(\Delta\sigma_{LLF,Defect}\) could have achieved run-outs of the respective specimens. As exemplified by specimens #14 and #78, the fatigue strength simulation results based on the X- and Y-view of the corresponding specimens differ from each other in some cases. Hence, the derived values of \(\Delta\sigma_{LLF,Defect}\) can be classified in two groups, namely, lower and higher predictions of the fatigue strength. Figure 13 presents these two groups for the investigated stress ratios of \(R=-1\) and 0. It should be noted, that only these numerical results are depicted, where a run-out was achieved in the corresponding experiments.