## 3 Results and Discussion
### Use of StressLife\({}_{\text{HCF}}\) Within Increased Frequency Fatigue Testing  
In this work, the mentioned LPM is applied twice for both test frequencies, once based on the change in temperature and once based on the change in \(R_{corr}\). By using the information from the LIT (Section 3.1), the average material responses of each load level can be obtained and plotted in a Morrow equivalent plot for each test frequency with the respective stress amplitudes, as shown exemplary for \(R_{corr}\) in Figure 7.  
Using the slope of the allometric fits of the elastic (green) and plastic ranges (black) in Figure 7, \(n_{total}\) can be calculated for each test frequency by a weighted averaging of the two determined exponents of the fit functions. From the mathematical description given in Equations (3) and (4), the parameters can be determined in the form of the fatigue strength exponent \(b\) and the fatigue ductility exponent \(c\)[25]. Furthermore, the separation of material response in elastic portions and plastic portions, with the use of a generalized Basquin equation (elastic), a generalized Coffin and Manson equation (plastic), and the fatigue data of two CATs per test frequency from Section 3.2, coefficients \(B\) and \(C\) are determined according to Equations (5) and (6). This allows the estimation of the material response of a theoretically calculated CATcalc. The further final steps for calculating an S-N curve according to StressLife\({}_{\text{HCF}}\) can be found in [24; 25; 50]. To enable better comparability of the S-N curve based on the change in temperature with the S-N curve based on \(R_{corr}\), both curves are given in Figure 8a for 80 Hz and in Figure 8b for 260 Hz. Noticeably, both curves in Figure 8a show a precise accuracy with regard to the description of the CAT data points. Furthermore, the fatigue limit, which indicates the maximum stress amplitude under which the material can withstand cyclic loading without failure, can be estimated by the horizontal progression of the curves. This is in line with the observations in Section 3.1, where the fatigue limit is at around 220 MPa for 80 Hz and 240 MPa for 260 Hz according to the load step of the first occurring material response from the LITs in Figure 5[51]. Furthermore, while the curves in the cycle range from approx. \(10^{5}\) cycles for 80 Hz show a very similar course, the curves for 260 Hz differ more clearly. This can be observed from the fatigue lifetime deviation \(L_{D}\) in Table 3, which was determined according to  
Figure 7: Stress amplitudes vs. average values for the material responses of each load step, including the elastic material responses of both constant amplitude tests (CAT) and the total material responses for a calculated CATcalc according to the StressLife\({}_{\text{HCF}}\) of SAE 1045 +N steel based on the change in temperature-corrected electrical resistance for (**a**) f = 80 Hz and (**b**) f = 260 Hz. Equation (10) using the mean fatigue lifetime per stress level \(N_{f,val}\) of the validation tests and the calculated fatigue lifetime \(N_{f,val}\) according to StressLife\({}_{\text{HCF}}\). Especially at higher stress amplitudes, the curve based on \(R_{corr}\) shows significantly smaller deviations from the validation data points. This can be explained by the different temperatures in 80 Hz (with a max. temperature change in the range of just 100 K) and 260 Hz tests (with a max. temperature change in the range of 250 K). At 260 Hz, temperature changes occur rapidly and may not immediately reflect the microstructural damage due to the material's thermal inertia, which may cause the measured temperature to lag behind the actual microstructural change. As a result, the sensitivity of \(R_{corr}\) to local microstructural changes compared to the direct temperature measurement is significantly higher here, offering a more precise correlation with material damage and thus improving the accuracy of the LPM.