## 3 Functionality of Key Modules
### Local Fatigue Assessment
#### 3.4.2 Theory of Critical Distances  
Local fatigue assessment utilizing the TCD requires the stress results along the vector path for each point in the defect loop. To check the accuracy of the implemented interpolation method for nodal stresses, coarse- and fine-meshed circular hole-in-plate models were evaluated along the TCD vector path. The coarse-meshed circular hole-in-plate model is depicted in Figure 7a, possessing an average arc-length of the points within the defect loop of \(\overline{d}_{CIR,coarse}=153\) um, while the fine-meshed circular defect possesses an edge length of \(\overline{d}_{CIR,fine}=8\) um. Figure 19 depicts the statistical evaluation of the stress course along the vector path evaluated as the maximum TCD stress value for each load vector. The applied incremental load step was set to \(\Delta\varphi=3^{\circ}\). As the fine mesh captures the stress gradient near the surface, the fatigue-characterizing stress was increased for the coarse mesh. The reference TCD stress value of the bilateral blunt notched V-plate is given in Table 2, as \(\sigma_{TCD,CIR,ref}=2.44\) MPa, and the evaluated Point Method stress values for the hole-in-plate model in Figure 19 were satisfyingly close for both simulation methods. As previously noticed in the nodal stress evaluation at the defect loop, the superposition approach led to a minor exceedance of the computed TCD stress, by about 2%, compared to the sub-case method. Figure 18: PSM peak stress course for three defect geometries 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 ‘ellip-sis_lin_rot0 deg_v1’); and (**c**) Elongated defect (mesh ‘defect_elongated_lin_v1’). The depicted Point Method stress maps were evaluated with 10\({}^{\circ}\) as the incremental load angle step. Figure 20 characterizes the Point Method stress at a distance \(L_{m}=a_{0}/2\). No significant differences between the sub-case method and the superposition approach were observed; although, when considering the superposition of the derived load cases, the TCD stress maps were slightly increased. The TCD stresses were computed along each normal path (compare Figure 10), and the maximum Point Method stress was stored for each load angle. The 97.5% exceedance limit of the Point Method stresses of all evaluated load angles was subsequently determined. For the circular hole-in-plate, the mean values were \(\overline{\sigma}_{TCD,M2,CIR}=2.35\) MPa and \(\overline{\sigma}_{TCD,M3,CIR}=2.40\) MPa, while the standard deviations were \(\hat{\sigma}_{TCD,M2,CIR}=0.06\) MPa and \(\hat{\sigma}_{TCD,M3,CIR}=0.05\) MPa (note: the results are designated with label M2 for the sub-case method and label M3 for the superposition method). Both methods matched the reference value of \(\sigma_{TCD,CIR,ref}=2.44\) MPa quite well for the circular hole-in-plate, even though coarse meshes were applied. In the case of the elliptical hole-in-plate, the mean values were \(\overline{\sigma}_{TCD,M2,ELL}=3.18\) MPa and \(\overline{\sigma}_{TCD,M3,ELL}=2.83\) MPa, while the standard deviations were \(\hat{\sigma}_{TCD,M2,ELL}=0.99\) MPa and \(\hat{\sigma}_{TCD,M3,ELL}=0.74\) MPa. Thus, the Point Method-based fatigue limit of the elliptical defect was lower than for the circular defect, which is in agreement with the N-SIF results. The elongated defect led to mean values of \(\overline{\sigma}_{TCD,M2,DEF}=3.89\) MPa and \(\overline{\sigma}_{TCD,M3,DEF}=3.98\) MPa, while the standard deviations were \(\hat{\sigma}_{TCD,M2,DEF}=0.94\) MPa and \(\hat{\sigma}_{TCD,M3,DEF}=0.98\) MPa. The elongated defect contour presented the highest Point Method stress distribution and, therefore, the lowest fatigue strength endurance limit of the three geometries. Figure 23: ESED evaluation of fine-meshed circular hole-in-plate (mesh ‘circle_fine_quad_R1 mm_v17) by sub-case method and incremental load step of \(\Delta\varphi=3^{\circ}\): (a) Level plot; and (b) Plots along defect contour.