## 3 Results and Discussion  
### Load Increase Test  
In previous applications of StressLife\({}_{\text{HCF}}\), fatigue tests were carried out at a lower test frequency of 5 Hz [25]. Within this research, the fatigue tests were performed at 80 and 260 Hz, leading to a different progression of the material response in the form of a long-lasting and low-expressed elastic material response and a shorter but very highly expressed plastic response in comparison to the tests at 5 Hz. As discussed in 2.2, two LITs need to be performed. For both test frequencies, an initial LIT with a starting stress amplitude of \(\sigma_{a,start}=100\) MPa and a load increase of \(\Delta\sigma_{a}=20\) MPa after each \(\Delta N=1.8\times 10^{5}\) cycles was examined. The increased step length was chosen to ensure comparability of the total duration (in time) to the database of 5 Hz. The same step length was also used for the 260 Hz tests so that no further variations had to be taken into account and to enable a direct correlation of the results.  
As given in Figure 5, a starting stress amplitude of \(\sigma_{a,start}=180\) MPa and a load increase of \(\Delta\sigma_{a}=5\) MPa have been defined for the second LIT for both frequencies. Figure 5 shows the cyclic deformation curves of the LITs considering the change in temperature (red), the directly measured change in electrical resistance (green), and the change in \(R_{corr}\) (blue), which is derived from the total values calculated by Equations (8) and (9).  
Figure 4: Experimental setup of the resonant testing rig for the determination of the electrical resistance temperature behavior: (1) unloaded fatigue specimen; (2) electrodes for electricity feed; (3) Kelvin clamps to measure the voltage drop; (4) heating device with an adaption for the geometry of the fatigue specimen; (5) IR camera; and (6) electrical resistance-temperature hysteresis, including the fitting (sequence: 30 \({}^{\circ}\)C to 200 \({}^{\circ}\)C to 30 \({}^{\circ}\)C).  
Since the change in temperature for the LIT at 260 Hz exceeds the fit of the electrical resistance-temperature hysteresis at the beginning of the load stage at 265 MPa, a correction for \(R_{corr}\) is not possible for that period, and the graph is displayed with an interruption (black bars). The frequency effect can already be seen in these cyclic deformation curves, represented by a shift in the first material response to higher stress amplitudes (220 MPa for 80 Hz and 240 MPa for 260 Hz), resulting in a higher portion of elastic data points. This first material response can be used to estimate the fatigue strength. The increase in the fatigue strength at higher frequencies can be explained by the fact that the dislocation movement is increasingly limited by the reduced time available for their motion, resulting in reduced plastic deformation in the specimen volume or shift of plastic deformation to higher stress amplitudes at high test frequencies [9]. Another reason is the frequency sensitivity of bcc metals (like ferritic-pearlitic SAE 1045), which are more susceptible to deactivated slip systems due to the high critical shear stress and high dislocation activation energy caused by the high test frequencies [12; 13]. At the point where the initial material response occurs, there is no significant change in temperature, indicating that this effect is solely caused by the frequency effect. After the onset of the first material response, both curves show a clear increase in the material response due to the cyclic softening of the material, which is followed by a decrease in the material response in terms of cyclic hardening. In addition, failure of the test frequency of 80 Hz already occurs at 240 MPa, whereas failure at a test frequency of 260 Hz does not occur until 265 MPa.