## 3 Functionality of Key Modules
### Local Fatigue Assessment
#### 3.4.1 Notch Stress Intensity Factor  
The course of the notch stress intensity factor, as a local fatigue approach, was studied for the three basic geometries. The N-SIF can be used to assess either a sharp or blunt notch. In the case of sharp notch assessment, two adjacent nodes of the defect loop define the notch opening angle. In blunt notch assessment, the previously calculated curvature values are used (Figures 8 and 9). As the N-SIF result \(K_{I}^{V}\) depends on the corresponding notch opening angle, the subsequent plots were consistently evaluated as peak stresses in terms of \(\sigma_{PS,I}=K_{I}^{V}/\left(K_{FE,I}^{*}\ d^{1-\lambda_{1}}\right)\). The sharp notch and blunt notch N-SIF assessments used the interpolated stress path values to calculate the boundary values for each case, according to Equations (1) and (3). In \begin{table}
\begin{tabular}{c c c c} \hline
**Load angle Stepping \(\Delta\varphi\)** & **Evaluation Method** & **Max notch Tip Stress** & **Exceedance Limit 97.5\% 1** \\ \hline \multirow{3}{*}{\(3^{\circ}\)} & Sub-case (M2) & 6.80 MPa & 4.03 MPa/1.04 MPa \\  & Superposition (M3) & 6.89 MPa & 4.20 MPa/1.07 MPa \\ \hline \multirow{3}{*}{\(5^{\circ}\)} & Sub-case (M2) & 6.79 MPa & 4.03 MPa/1.04 MPa \\  & Superposition (M3) & 6.89 MPa & 4.21 MPa/1.08 MPa \\ \hline \multirow{3}{*}{\(10^{\circ}\)} & Sub-case (M2) & 6.79 MPa & 4.03 MPa/1.04 MPa \\  & Superposition (M3) & 6.89 MPa & 4.21 MPa/1.08 MPa \\ \hline \multirow{3}{*}{\(15^{\circ}\)} & Sub-case (M2) & 6.79 MPa & 4.02 MPa/1.06 MPa \\  & Superposition (M3) & 6.85 MPa & 4.24 MPa/1.05 MPa \\ \hline \multirow{3}{*}{\(30^{\circ}\)} & Sub-case (M2) & 6.79 MPa & 4.03 MPa/1.00 MPa \\  & Superposition (M3) & 6.62 MPa & 4.20 MPa/0.97 MPa \\ \hline \end{tabular}
\end{table} 
Table 7: Effect of load angle step on evaluated stress distribution of coarse-meshed elongated defect in a plate (refer to Figure 7d) for sub-case and superposition methods. Figure 15: Assessment of maximum notch tip stress of circular hole-in-plate with increased bounding box (mesh list ‘circle_lin_R1 mm_v1_v2...v7’) for incremental load step of \(\Delta\varphi=10^{\circ}\): (**a**) Sub-case method; (**b**) Superposition method; and (**c**) Difference between these methods. the case of the PSM, only the nodal stress at each point of the defect contour was evaluated. Figure 16 displays the computed results for sharp notch peak stress assessment of the three geometries. The incremental load step angle was set to a value of \(\Delta\varphi=10^{\circ}\) for these calculations. The computations were performed for the sub-case and the superposition method, and each method is visualized according to the course of the computed peak stress along the defect contour. The assessed N-SIF values for sharp notches corresponded to the curvature course. For example, the elongated defect exhibited the highest curvature as well as the highest peak stress. The N-SIF results for the blunt notch study are shown in Figure 17. Although the tendency for each geometry was similar to the sharp notch results, the evaluated peak stress values were significantly decreased when the stress concentration was assessed for the blunt notch. The PSM-based fatigue assessment is shown in Figure 18, evaluating only the stress values at the defect loop, which led to similar results as the blunt notch study. As the peak stress method takes only the adjacent elements of each node within the defect loop into account, the corresponding opening angles were evaluated according to a sharp notch case. Figure 16: N-SIF peak stress course for three defect geometries, assuming a sharp notch and incremental load step of \(\Delta\varphi=10^{\circ}\): (**a**) Circular hole-in-plate (mesh ‘circle_lin_R1 mm_v1’); (**b**) Elliptical hole-in-plate (mesh ‘ellipsis_lin_rot0 deg_v1’); and (**c**) Elongated defect (mesh ‘defect_elongated_lin_v1’).