## 3 Functionality of Key Modules
### Local Fatigue Assessment
As this peak value is affected by the mesh density and applied load vector, it is recommended to evaluate the exceedance limit of the maximum principal course along the defect contour for each load angle. An exceedance probability of 97.5% was chosen, as suggested in [66]. This led to a mean value \(\overline{\sigma}_{FE,M2,\Delta\varphi 5^{\circ}}=2.67\) MPa and standard deviation \(\bar{\sigma}_{FE,M2,\Delta\varphi 5^{\circ}}=0.07\) MPa in the sub-mesh-method case. For the superposition method, the corresponding mean and standard deviation values for the same level of exceedance probability were \(\overline{\sigma}_{FE,M3,\Delta\varphi 5^{\circ}}=2.74\) MPa and \(\bar{\sigma}_{FE,M3,\Delta\varphi 5^{\circ}}=0.05\) MPa. To check the convergence of the maximum notch tip stress, a refined mesh with quadratic elements was used for the circular hole-in-plate model. This increased the number of vertices within the circular defect to 800, including mid-nodes. The fine-meshed model possessed an average cell edge length of \(d_{j,j+1}=3.9\)\(\mu\)m within the defect node loop. The maximum notch tip stress of the fine-meshed hole-in-plate model for the sub  
Figure 12: Notch tip stress evaluation of circular hole-in-plate (mesh ‘circle_lin_R1 mm_v1’) by sub-case and superposition methods for incremental load step of \(\Delta\varphi=5^{\circ}\): (**a**) Level plots; and (**b**) Course along defect contour. case method was \(\sigma_{FE,M2,max}=3.01\) MPa, and that for the superposition method was \(\sigma_{FE,M3,max}=3.17\) MPa. The mean and standard deviation for the sub-case method were \(\overline{\sigma}_{FE,M2,\Delta\varphi^{5}}=2.98\) MPa and \(\delta_{FE,M2,\Delta\varphi^{5}}=0.01\) MPa, whereas the superposition method yielded \(\overline{\sigma}_{FE,M2,\Delta\varphi^{5}}=3.02\) MPa and \(\delta_{FE,M2,\Delta\varphi^{5}}=0.06\) MPa. The numerical simulation results of both methods matched the previously calculated notch tip stress \(\sigma_{tip}=3.03\) MPa of the bilaterally V-notched plate satisfactorily (see Figure 1b as model reference). Comparing the scatter bands and maximum peak values for both methods, it is evident that, in the case of the superposition method, the overall stress peak and scatter index were slightly enhanced. The maximum single stress peak increased up to 5%, in the case of the superposition method, while the mean value was almost unaffected. To illustrate the effect of the load step increment \(\Delta\varphi\), the stress distributions of the circular hole-in-plate models were evaluated according to the notch tip exceedance limits in Table 5. As tension unity load was applied to the hole-in-plate model, the maximum notch tip stress can also be interpreted as the stress concentration factor. It is recognizable that the calculated initial load stepping value \(\Delta\varphi\), compared to Equation (10), is well-applicable. The further refined load stepping increments of \(\Delta\varphi=3^{\circ}\) and \(\Delta\varphi=5^{\circ}\) did not increase the accuracy of the notch tip stress evaluation. Even a coarse load step increment of \(\Delta\varphi=10^{\circ}\) led to similar results, as the circular defect possesses a constant curvature value. In addition, the change in stress distribution in the case of the elliptical hole-in-plate was studied. Both methods presented a similar stress distribution, as depicted in Figure 13, for a constant load step angle of \(\Delta\varphi=5^{\circ}\). Figure 13: Notch tip stress evaluation of elliptical hole-in-plate (mesh ‘ellipsis_lin_rot0 ddeg_v1’) by sub-case and superposition methods for incremental load step of \(\Delta\varphi=5^{\circ}\): (**a**) Level plots; and (**b**) Course along defect contour.