## 3 Functionality of Key Modules
### Local Fatigue Assessment  
The local fatigue assessment code block was applied for the sub-case method (compare to Figure 2b) and the superposition method of derived load cases (compare to Figure 2c) in the same manner. The principal difference between the two methods is how the result input database for each evaluation load angle, denoted as '_<File>_#.mat'_, was generated. As the investigated local fatigue approaches evaluate the nodal stress distribution, it is important to study whether numerical model parameters, such as the load angle step \(\Delta\varphi\), the mesh-seed, and the mesh bounding box size, affect the stress results. Thus, the evaluation of nodal stress values along the defect contour was first investigated. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Points on Circle** & **Average Mesh-Seed** & **Sharp Notch Study 1** & **Blunt Notch Study 1** \\ \hline
42 & 0.15 mm & 0.062 mm\({}^{2}\) & 0.185 mm\({}^{2}\) \\
78 & 0.10 mm & 0.061 mm\({}^{2}\) & 0.183 mm\({}^{2}\) \\
98 & 0.08 mm & 0.061 mm\({}^{2}\) & 0.185 mm\({}^{2}\) \\
131 & 0.06 mm & 0.060 mm\({}^{2}\) & 0.186 mm\({}^{2}\) \\
196 & 0.04 mm & 0.060 mm\({}^{2}\) & 0.185 mm\({}^{2}\) \\
392 & 0.02 mm & 0.060 mm\({}^{2}\) & 0.187 mm\({}^{2}\) \\ \hline \hline \end{tabular} \({}^{\dagger}\) Standard value of control radius \(R_{c}=0.19\) mm is consequently used.  
\end{table} 
Table 4: Effect of mesh-seed on evaluated control volume for sharp and blunt notch assessment of circular hole-in-plate geometry. Figure 11: Fraction of cells at starting point for three defect geometries: (**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’). The comparative notch stress evaluation was carried out for both numerical methods using the three basic geometries: Circular hole-in-plate (Figure 7a), elliptical hole-in-plate (Figure 7b), and elongated defect (Figure 7d). In addition, as a reference for the circular hole-in-plate model, the maximum principle stress at the notch tip for the bilateral blunt notched plate in Figure 1b was obtained as \(\sigma_{tip}=3.03\) MPa. As the sub-case method requires the definition of the load angle increment \(\Delta\varphi\) before pre-processing, the following rule of thumb can be applied to estimate this value. The initial load angle increment \(\Delta\varphi_{init}\) is the ratio of the circumference of the cells of the defect contour to the product of their number and mean defect radius. As the sub-case (as well as the superposition method) requires incremental steps divided within \(90^{\circ}\), common values include \(\Delta\varphi=1,\ 3,\ 5,\ 10,\ 15,\ 30,\ \text{and}\ 45^{\circ}\). Values below \(1^{\circ}\) are also requestable, but the computation effort increases accordingly. \[\Delta\varphi_{init}\sim\frac{\sum_{j=0}^{n}d_{j,j+1}}{n}\frac{2}{D_{avg}} \tag{11}\]  
The linear mesh of the hole-in-plate model shown in Figure 7a has 41 points in the defect loop, the computed circumference is 6.28 mm, and the mean extent is 2 mm. This equates to a value of \(\Delta\varphi\sim 8.8^{\circ}\), implying that an incremental load angle of \(\Delta\varphi=5^{\circ}\) should be well-applicable. The stress distribution along the circular defect contour is shown as level plots in Figure 12a for both methods. Figure 12b depicts the maximum principle stress course for selected load angle values of \(\varphi=0^{\circ},\ 45^{\circ},\ 90^{\circ},\ \text{and}\ 135^{\circ}\). As the investigated mesh is quite coarse, the notch tip stress was not reached. The maximum stress along the defect contour was evaluated as \(\sigma_{FE,M2,max}=2.91\) MPa for the sub-case method, labeled with the index M2. For the superposition method, indexed by M3, the maximum stress was evaluated as \(\sigma_{FE,M3,max}=2.86\) MPa.