## 3 Results and Discussion
### Evaluation of the Linear-Elastic Design Limit Curve  
In order to describe the control volume governing the aggregated amount of strain energy during fatigue assessment, the control radius \(R_{c}\) was evaluated according to Equations (2) and (3). Additionally to the dependency of the material parameters \(\Delta K_{th,lc}\) and \(\Delta\sigma_{0}\) on \(R\), Equation (2) also includes parameters that rely on the geometry of the utilized notched specimens. Hence, the long-crack growth threshold stress intensity factor range for V-notched specimens \(\Delta K_{1,th}^{V}\) as well as the geometry parameter \(e_{1}\) were evaluated for the notch geometries utilized in the experimental small-scale fatigue tests. The resulting values of \(R_{c}\) are given in Table 4, alongside the calculated values of \(a_{0}\) according to Equation (1). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(R\) [\(-\)] & **2\(\pi\) [\({}^{\circ}\)]** & \(\mathbf{a_{0}}\) [mm] & \multicolumn{2}{c}{\(R_{c}\) [mm]} \\  & & **Equation (1)** & **Equation (2)** & **Equation (3)** \\ \hline \multirow{2}{*}{\(-1\)} & 45 & \multirow{2}{*}{0.146} & 0.138 & \multirow{2}{*}{0.124} \\  & 135 & & 0.133 & \\ \hline \multirow{2}{*}{0} & 45 & \multirow{2}{*}{0.097} & 0.091 & \multirow{2}{*}{0.088} \\  & 135 & & 0.088 & \\ \hline \multirow{2}{*}{0.5} & 45 & \multirow{2}{*}{0.039} & 0.037 & \multirow{2}{*}{0.035} \\  & 135 & & 0.035 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the evaluation of \(R_{c}\) and \(a_{0}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(R\) [\(-\)] & **Number of Specimens [\(-\)]** & \multicolumn{2}{c}{**Mean**} & \(\mathbf{\Delta K_{th,lc}}\) [MPa\(\sqrt{\text{m}}\)] & \multirow{2}{*}{**Maximum**} \\  & & **Mean** & & **Minimum** & **Maximum** \\ \hline \(-1\) & 4 & 13.72 & 13.35 & 14.03 \\ \(0\) & 3 & 7.65 & 7.54 & 7.74 \\ \(0.5\) & 2 & 3.40 & 3.36 & 3.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the evaluation of \(\Delta K_{th,lc}\) for the investigated stress ratios. Regarding the results depicted in Table 4, the calculations according to Equations (2) and (3) result in similar values of the control radius for the investigated stress ratios. Both evaluation methods show decreasing values of \(R_{c}\) as \(R\) increases. Recalling Equation (3), \(R_{c}\) is directly connected to the material intrinsic length \(a_{0}\). Hence, the dependency of \(R_{c}\) upon \(R\) reflects the trend of \(a_{0}\) as reported in the literature [56]. However, calculations of the SED incorporating a control radius that depends on the acting stress ratio resulted in significantly enlarged scattering of the analysed experimental fatigue data. A decrease in \(R_{c}\) resulted in a smaller value of the considered control volume. Due to the stress gradient emanating from the apex of notch-like geometries, a smaller control volume implies an increasing focus on the highly-stressed region in the vicinity of the notch root. Hence, the averaged value of the calculated SED shifts towards higher values, as the size of the control volume decreases. Following this considerations, a larger control volume leads to an underestimation of the calculated averaged SED values. Apart from the variation observed in the calculated SED values, the implementation of a dependency of \(R_{c}\) upon \(R\) also significantly increases the experimental effort necessary to establish the respective relationship. Hence, an averaged value of \(R_{c}\) = 0.083 mm was utilized in the present analysis independent of the stress ratio. Considering Table 4, it should be noted that this average value shows only a small deviation to the evaluated values of \(R_{c}\) at a stress ratio of \(R=0\). As \(\Delta\sigma_{0}\) and \(\Delta K_{th,lc}\) are often reported in the literature for \(R=0\), an appropriate value of the control radius can be conveniently calculated utilizing Equation (3).