## 2 Materials and Methods  
### Materials  
The investigated material is SAE 1045 (C45E, 1.1191) steel in normalized conditions (\"+N\"), where the heat treatment is characterized by an austenitization at \(T_{ust.}\) = 860 \({}^{\circ}\)C for \(t_{ust.}\) = 45 min. Table 1 summarizes the chemical composition according to our own measurements obtained by spectrometric element analysis, along with specified limit values according to DIN EN ISO 683-1 [43]. Mechanical properties from tensile tests that were averaged over a total of five tests are summarized in Table 2. For assessing the hardness HV 10 values, nine indents were analyzed, and an average hardness of 178 HV 10 was determined.  
Figure 1 displays micrographs of the specimens' cross-sections (longitudinal and transverse direction) etched with nil by using an Axio Imager.M1m microscope (Carl Zeiss AG, Oberkochen, Germany), showing a ferritic-peariltic microstructure. The longitudinal section corresponds to the microstructure along the loading axis, while the transversal section is perpendicular to it. Ferrite can be observed as clear, bright grains. Pearlite reveals dark cementite lamellas with bright ferrite in between them. The average grain size obtained by the linear intercept method is approx. \(d_{grain}\) = 11 \(\upmu\)m. In the longitudinal direction, microstructural banding can be observed (Figure 1a,b), where ferrite and pearlite bands run parallel to the direction of rolling. This banded structure results from a low cooling rate after heat treatment.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Material** & **C** & **Si** & **Mn** & **S** & **Cr** & **Mo** & **Ni** \\ \hline \multirow{2}{*}{SAE 1045} & DIN EN ISO 683-1 & 0.420–0.500 & 0.100–0.400 & 0.500–0.800 & \(\leq\)0.045 & \(\leq\)0.400 & \(\leq\)0.100 & \(\leq\)0.400 \\ \cline{2-8}  & Own analysis (+N) & 0.427 & 0.232 & 0.742 & 0.007 & 0.070 & 0.020 & 0.078 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Chemical composition in wt.-% of the SAE 1045 steel according to DIN EN ISO 683-1 and own analysis.  
Figure 1: Light micrographs of cross-sections of SAE 1045 specimen in a longitudinal direction with (**a**) 200\(\times\) magnification and (**b**) 1000\(\times\) magnification; in a transverse direction with (**c**) 200\(\times\) magnification and (**d**) 1000\(\times\) magnification.  
To complement the light microscopy images, Figure 2 showcases high-resolution secondary electron (SE) images of the specimens obtained by scanning electron microscopy (SEM) using the TESCAN Clara Mark III (TESCAN, Brno, Czech Republic). The enhanced magnification focuses on the fine alternating ferrite and cementite layers that are characteristic of pearlite, which define its morphology and were not that discernible in the previous light microscopy images.  
The geometry of the fatigue specimens and their dimensions (in mm) are given in Figure 3. A fatigue specimen with a cylindrical gauge length of 15 mm and a gauge diameter of 5.6 mm was chosen to ensure a homogeneous stress distribution in the gauge section and to minimize stress concentrations at the transitions.  
Figure 3: Geometry and dimensions of fatigue specimens.  
Figure 2: Scanning electron microscopy (SEM) image in secondary electron (SE) mode of cross-sections of SAE 1045 specimen in longitudinal direction with **(a)**\(5580\times\) magnification and **(b)**\(20\),\(300\times\) magnification; in traverse direction with (e) \(5580\times\) magnification and **(d)**\(20\),\(300\times\) magnification.