## 2 Materials and Methods
### Testing Setup  
All CATs and LITs are carried out using a resonant testing rig of the type MIKROTRON (Russenberger Prufmaschinen AG, Neuhausen am Rheinfall, Switzerland), with a maximum static loading capacity of 20 kN and a maximum force amplitude of 10 kN. The tests were performed with a stress ratio of R = \(-\)1 at ambient temperature. According to [25], the specimens' surface temperature was measured in three sections using an IR camera of the type thermoIMAGER TIM QVGA-HD (Micro-Epsilon Messtechnik GmbH & Co., KG, Ortenburg, Germany) with a thermal sensitivity of 0.04 K. In order to avoid non-uniform heating of the specimens during the tests due to the load cell, cooling rings were installed on the upper and lower clamping. In order to obtain the direct correlation between the change in temperature as a consequence of frequency-induced self-heating effects during the fatigue tests and the measured electrical resistance, a dependency function of these two variables was determined. Therefore, a load-free specimen was heated up to 200 \({}^{\circ}\)C by a modified heating device, and the associated change in electrical resistance was measured continuously. The heating device consists of a small opening (\(d\) = 7.8 mm) in the center of the gauge length of the specimen. During this procedure, the change in temperature in the middle of the specimen's gauge length was measured by an IR camera, while the electrical resistance \(R_{total}\) was traced by using the four-point measuring method consisting of a current feed (3A DC), two Kelvin clamps to measure the drop in voltage on the gauge length, a data acquisition card type NI-9238 (National Instruments, Munchen, Germany), an isolation plate to prevent the flow of current through the machine, and one DC power supply of the type TOE 8851 (Toellner Electronic Instrumente GmbH, Herdecke, Germany) with a setting resolution of 5 mA and a setting accuracy of 0.2% + 10 mA. After reaching 200 \({}^{\circ}\)C, a cooling cycle to room temperature followed. Based on the recorded data, a correlation function between the electrical resistance and the change in temperature can be derived. A regression function was used in order to describe the heating path as a square approximation of a second-degree polynomial in accordance with [45]. This setup is shown in Figure 4 and differs only slightly from the measurement setup during the fatigue tests. The current for the fatigue tests was supplied directly at the clamping device instead of additional electrodes, as these could start to vibrate during the tests. With the use of this regression function, a temperature-dependent electrical resistance value \(R_{\text{\it{hys}}}\) can be calculated by Equation (8), resulting in \(R_{0}\) as the y-intercept of the regression function. Moreover, \(\Delta T\) characterizes the change in temperature in the middle of the heating spot, whereas \(\alpha\) represents the linear fitting parameter, and \(\beta\) the square fitting parameter. By inserting \(R_{\text{\it{hys}}}\) into Equation (9), a temperature-corrected electrical resistance \(R_{corr}\) can be determined, which is unaffected by the temperature flow and is only dependent on microstructural changes, like the formation of dislocations or changes in grain size and grain boundaries [20]. \[R_{\text{\it{hys}}}=R_{0}+\alpha\cdot\Delta T+\beta\cdot\Delta T^{2} \tag{8}\]  
\[R_{\text{\it{corr}}}=R_{total}-R_{\text{\it{hys}}} \tag{9}\]  
The electrical resistance-temperature setup is illustrated in Figure 4, together with the result of the hysteresis measurement, including the derived parameters used for the correction of the electrical resistance values in the fatigue tests. Figure 4 depicts the direct relation between the change in temperature and electrical resistance in terms of a hysteresis loop (black curve), with an additional fitting function for the heating path (red curve).