## 3 Functionality of Key Modules
### Local Fatigue Assessment
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Load Angle Stepping \(\Delta\varphi\)** & **Evaluation Method** & **Max Notch Tip Stress** & **Exceedance Limit 97.5\%**1  \\ \hline \hline \(3^{\circ}\) & Sub-case (M2) & 2.91 MPa & 2.67 MPa/0.07 MPa \\  & Superposition (M3) & 2.86 MPa & 2.74 MPa/0.05 MPa \\ \hline \(5^{\circ}\) & Sub-case (M2) & 2.91 MPa & 2.67 MPa/0.07 MPa \\  & Superposition (M3) & 2.86 MPa & 2.74 MPa/0.05 MPa \\ \hline \(10^{\circ}\) & Sub-case (M2) & 2.90 MPa & 2.67 MPa/0.06 MPa \\  & Superposition (M3) & 2.85 MPa & 2.71 MPa/0.07 MPa \\ \hline \(15^{\circ}\) & Sub-case (M2) & 2.90 MPa & 2.67 MPa/0.06 MPa \\  & Superposition (M3) & 2.86 MPa & 2.70 MPa/0.07 MPa \\ \hline \(30^{\circ}\) & Sub-case (M2) & 2.90 MPa & 2.68 MPa/0.06 MPa \\  & Superposition (M3) & 2.82 MPa & 2.74 MPa/0.05 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Effect of load angle step on evaluated stress distribution of coarse-meshed circular hole-in-plate (refer to Figure 7a) for sub-case and superposition methods. As the major axis of the ellipse was aligned horizontally (compare to Figure 7b for the finite element model), the load angles of \(\varphi=0^{\circ}\) and \(\varphi=90^{\circ}\) were mutually included for all models. However, the evaluated stress course along the defect contour ought to be affected by the value of the load angle stepping \(\Delta\varphi\) and its corresponding local curvature. Table 6 details the effect of load angle stepping on the notch stress results. In detail, the maximum notch tip stress is depicted, as well as the mean and standard deviation over all load vectors exceeding a probability level of 97.5%. Although the maximum notch tip stress values varied slightly, the exceedance limits were still quite unaffected. This can be explained by the comparably smooth change in the local curvature of the ellipse. The course of the local stress field is depicted in Figure 14 for the elongated defect shape. The stress distribution is more irregular, but the maximum stress level was in the same order as that of the elliptical defect. No significant changes in the evaluated maximum stress or stress exceedance limits were observed for the elongated defect, as detailed in Table 7. It can be reasoned that even the lowest applied angle step value of \(3^{\circ}\) is too large to cover the effect of small notches on singular notch tip peak values: the defect contour node loop covered 178 points, and the average diameter of the elongated defect was equal to about \(D_{agg}=16.2\) mm, leading to a recommended stepping angle of \(\Delta\varphi_{init}=2^{\circ}\), below the investigated lowest angle of \(3^{\circ}\). Again, both methods presented similar values for the maximum notch tip stress and stress exceedance limits. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Load Angle Stepping \(\Delta\varphi\)** & **Evaluation Method** & **Max Notch Tip Stress** & **Exceedance Limit 97.5\% \({}^{1}\)** \\ \hline \multirow{2}{*}{\(3^{\circ}\)} & Sub-case (M2) & 8.18 MPa & 4.58 MPa/2.04 MPa \\  & Superposition (M3) & 8.06 MPa & 4.96 MPa/2.21 MPa \\ \hline \multirow{2}{*}{\(5^{\circ}\)} & Sub-case (M2) & 8.18 MPa & 4.59 MPa/2.05 MPa \\  & Superposition (M3) & 8.03 MPa & 4.96 MPa/2.21 MPa \\ \hline \multirow{2}{*}{\(10^{\circ}\)} & Sub-case (M2) & 8.13 MPa & 4.59 MPa/2.04 MPa \\  & Superposition (M3) & 8.02 MPa & 4.97 MPa/2.21 MPa \\ \hline \multirow{2}{*}{\(15^{\circ}\)} & Sub-case (M2) & 8.18 MPa & 4.58 MPa/2.04 MPa \\  & Superposition (M3) & 8.02 MPa & 4.98 MPa/2.21 MPa \\ \hline \multirow{2}{*}{\(30^{\circ}\)} & Sub-case (M2) & 7.60 MPa & 4.57 MPa/2.05 MPa \\  & Superposition (M3) & 8.02 MPa & 4.97 MPa/2.25 MPa \\ \hline \end{tabular} \({}^{1}\) The exceedance limit is evaluated as a data tuple of mean value and standard deviation.  
\end{table} 
Table 6: Effect of load angle stepping on evaluated stress distribution of coarse-meshed elliptical hole-in-plate (refer to Figure 7b) for sub-case and superposition methods.