## 2 Materials and Methods
### StressLife\({}_{\rm HCF}\) Method  
In general, the StressLife\({}_{\rm HCF}\) method requires two load increase tests (LIT), with the first LIT being used for the basic characterization of the fatigue behavior of the material. LITs enable an estimation of the fatigue strength and provide initial information about the stress amplitude at which a plastic material response can be expected. In general, LITs are performed with a starting stress amplitude \(\sigma_{a,start}\) that is evidently below the fatigue strength of the material, with a stepwise increase by \(\Delta\sigma_{a}\) after every \(\Delta N\) cycle [44]. To cover a large range of stress amplitudes in a reasonable test time, a large increase in the stress amplitude after a defined number of cycles is selected, which, however, leads to a decreased number of data points in the plastic region, as the material fails more quickly due to the high stresses. Therefore, a second LIT with a lower increase in stress amplitude for a more precise assessment of elastic and plastic material behavior is necessary. The material responses of the second LIT are averaged per load level and displayed in a Morrow equivalent plot together with the respective stress amplitude. In this plot, the material response can be divided into a range in which approximately no material response has taken place (elastic area) and a range in which recognizable material responses have occurred (plastic area). With the slopes of the allometric fit functions of these two ranges, the hardening exponent \(n_{total}\) for the HCF regime is determined from a weighted average of these slopes. The weighting reflects the proportion of data points in the respective regions. This hardening exponent is used to calculate the fatigue strength exponent \(b\) and the fatigue ductility exponent \(c\) according to Equations (3) and (4). In addition, the material response \(M\) at half of the number of cycles to failure (0.5\(\cdot\)N\({}_{f}\)) of two constant amplitude tests (CAT) is required to separate the material response into elastic and plastic portions by applying a generalized Coffin and Manson equation and a generalized Basquin equation. The stress amplitudes of the CATs are selected, with one stress amplitude in the specific plastic range and one stress amplitude in the elastic-plastic range of the already performed LIT. However, in this study, only stress amplitudes from the plastic range could be used for the CATs, as previous tests at the given frequencies in the elastic-plastic range had resulted in reaching the maximum number of cycles for the tests without failure (run-outs). In a further step, the coefficients \(B\) and \(C\) are calculated by Equations (5) and (6). Using a plot based on Ramberg-Osgood, the material response of a calculated constant amplitude test CAT\({}_{\rm calc}\) can be estimated. This CAT\({}_{\rm calc}\) is added in conjunction with the two other CATs to the Morrow equivalent plot and is also fitted with an allometric fit function, which allows us to obtain the remaining required parameters, which are used to describe an S-N curve by Equation (7) according to StressLife\({}_{\rm HCF}\)[25].  
\[b=-\frac{n_{total}}{5\,n_{total}+1} \tag{3}\]  
\[c=-\frac{1}{5\,n_{total}+1} \tag{4}\]  
\[C=\frac{\left(2\ N_{f,CAT1}\right)^{b}\cdot M_{