## 3 Results and Discussion
### Evaluation of the Linear-Elastic Design Limit Curve
However, from a scientific point of view, the study of the relationship between \(R_{c}\) and \(R\) depicts an interesting topic for future research work. As an appropriate value of \(R_{c}\) was defined, the results of the experimental investigations reported in Section 2.1 were evaluated in terms of the linear-elastic strain energy density range \(\Delta\overline{\text{W}}^{(e)}\). Notched specimens were evaluated in accordance to the analytical framework presented by [PERSON] and [PERSON] [27]. The evaluation of the fatigue test results of the utilized plain specimens was carried out according to Equation (5). The effect of the stress ratio was accounted for by the implementation of the factor \(c_{w}\), given by Equation (6). Statistical evaluation of the fatigue data was conducted following the standard ASTM E739 [57] in the finite-life region, where the fatigue limit in the high-cycle fatigue regime was determined according to the \(arcsin\sqrt{P}\) approach [58]. Figure 8 depicts the assessed fatigue data in terms of the linear-elastic SED. Figure 8 summarizes the experimentally derived fatigue data into a uniform scatter band, combining the results of three different specimen geometries tested at stress ratios of \(R=-1,0\) and 0.5. The statistically evaluated fatigue limit curve for a probability of survival of \(P_{S}=50\%\) was plotted, alongside the scatter band representing probabilities of survival of \(P_{S}=10\) and \(90\%\). Furthermore, the probability of survival of \(P_{S}=97.5\%\) was evaluated, serving as a design limit curve in accordance to the commonly utilized guideline FKM [12]. Concerning the scatter band index of the depicted data points, the linear-elastic fatigue assessment gave a value of \(1:T_{\Delta\overline{\text{W}}^{(e)}}=4.32\). It should be noted, that the energy-based fatigue assessment implies an increased scatter index of fatigue data compared to stress-based concepts, due to the quadratic relationship between the stress and strain energy density. By calculating the square root of the energy-based scatter index, the scatter index in terms of stresses was computed as a value of \(1:T_{\sigma}=2.08\). This comparably high value was mainly caused by the fatigue data evaluated at a stress ratio of \(R=0.5\). Regarding Figure 8, the experimental results at stress ratios of \(R=-1\) and 0 revealed an overall match. Only the evaluated SED values of notched specimens tested at \(R=0.5\) diverged significantly from the remaining data points. As the notched specimens exhibited stress concentration at the notch apex, the high values of maximum stresses during cyclic loading at \(R=0.5\) resulted in plastic deformation in the vicinity of the notch root. This plastic deformation caused mean stress relaxation [59; 60], leading to cyclic testing under an effective stress ratio of \(R<0.5\), following the initial loading. Hence, as the effect of the stress ratio was implemented in the fatigue assessment by consideration of the factor \(c_{w}\) given by Equation (6), the linear-elastic SED was overestimated. This overestimation  
was traced back to the value of \(c_{w}\), which takes a value of 3 at \(R=0.5\), implying that the linear-elastic SED is three times larger than the one at \(R=0\). In order to improve the prediction accuracy even at high stress ratios, the implementation of the elastic-plastic material behaviour should be considered in further work.