## 2 Materials and Methods  
Mechanical stress-strain measurements within cyclically loaded total strain-controlled constant amplitude (CAT) and strain-increase tests (SIT) in air, as well as under distilled water media conditions, were performed using an extensometer with an initial length of \(L_{0}=89\) mm, mounted on the specimen shafts and measuring the deformation, allowing the resulting total strain amplitude \(\varepsilon_{a,t}\) to be determined during the fatigue test. Since this extensometer setup measures deformation along the minimum cross-section and the transitions of the specimen's shafts, the calibration to the strain values within the minimum cross-section is essential. A second extensometer was, therefore, applied in the minimum cross-section, allowing a correlated total strain amplitude \(\varepsilon_{a,t,cor}\) to be used as the controlled value. All fatigue tests were performed with a strain ration of \(R=-1\) and a constant strain rate of \(\varepsilon_{a,t,cor}=4\times 10^{-3}/\) s using triangular strain-time functions. Additionally, a special in situ cell for fatigue tests performed in distilled water was developed, allowing additional measurement techniques to be included (Figure 1a). It should be noted that in tests with AISI 347 steel, distilled water does not cause any corrosion effects on the material. However, comprehensive, well-adhering oxide layers are formed, which are locally broken up due to surface damage, e.g., by micro cracks, followed by macro cracking along the further process. In this context, the electrochemical open-circuit potential (\(E_{OCP}\)) can be used to describe these effects occurring at the material's surface on the specimen, and thus enables further fatigue-related damage mechanisms to be separated. For this purpose, a pump-driven water circuit is used to circulate the water through the cell, and a thermostat continuously cools the medium to a temperature of 22 \({}^{\circ}\)C. For electrochemical measurement, a reference electrode (silver chloride) and a counter electrode (graphite) are used in the cell, and the fatigue specimen serves as the working electrode. Fatigue tests at elevated temperatures up to 300 \({}^{\circ}\)C were carried out using a custom-built furnace for the servo hydraulic testing machine and a high-temperature extensometer (Figure 1b). Furthermore, fatigue tests were performed under reactor pressure vessel boiling water (BWR) conditions at 70 bar and 240 \({}^{\circ}\)C in a specially designed autoclave (Figure 1c). The high-temperature water used in the fatigue tests was provided by a water treatment plant and had a conductivity of about 0.055 \(\mu\)S/cm. The impurities due to chloride ions were generally below 5 \(\mu\)g/kg, which is in accordance with the VGB guidelines [23] for the quality of reactor water in BWR plants in normal operation according to the guidelines. Figure 1: Experimental setup at (**a**) room temperature in distilled water; (**b**) higher temperatures; (**c**) reactor pressure vessel boiling water conditions. The oxygen content in the fluid was set to 400 \(\mathrm{\SIUnitSymbolMicro g}\)/kg (0.4 ppm), which is the upper limit for BWR plants and is mainly used in international laboratory studies to simulate BWR conditions. To measure the change in electrical resistance, a high constant current (\(I=8\) A) was applied to the specimens using a DC potential probe. During loading, the change in voltage and the thereon-dependent change in electrical resistance along the specimen was measured via wires mounted at the transitions between the gauge length and the shafts using adapted copper clamps and connected to a voltage measurement card with a maximum voltage range of \(\pm\)500 mV. The change in electrical resistance depends, on the one hand, on the change in specimen geometry (which can be neglected for a load ratio of \(R=-1\)). The deciding factor, however, is the change in the specific electrical resistance, from which direct conclusions can be drawn about the change in the defect density of the materials.