## 3 Functionality of Key Modules
### Local Fatigue Assessment
#### 3.4.3 Elastic Strain Energy Density
The difference in elastic strain energy distribution between the sub-case method (M2) and the superposition method (M3) was more pronounced when the local stress concentration factor increased. In the case of the circular defect, the superposition method yielded a decrease in ESED of about 8%, while the mean value for the elongated defect exhibited a reduction of up to 20% in the case of sharp notch ESED assessment. If a blunt notch ESED evaluation is required, the calculated curvature volume of each point of the defect does not originate at the defect but, instead, on the vector path dependent on the local curvature value. Figure 28 visualizes the change of ESED values in the blunt notch ESED fatigue assessment. The elastic strain energy density values for the three geometries significantly decreased when blunt notch fatigue assessment was conducted. For the circular hole-in-plate, the mean values of the elastic strain energy density distribution in the blunt notch case were \(\Delta\overline{W}_{blunt,M2.CIR}=1.039\times 10^{-5}\) mJ/mm\({}^{3}\) and \(\Delta\overline{W}_{blunt,M3.CIR}=0.957\times 10^{-5}\) mJ/mm\({}^{3}\); the evaluated standard deviations were again negligible. The elliptical hole led to mean values of \(\Delta\overline{W}_{blunt,M2.ELL}=1.484\times 10^{-5}\) mJ/mm\({}^{3}\) and \(\Delta\overline{W}_{blunt,M3.EHL}=1.290\times 10^{-5}\) mJ/mm\({}^{3}\), and the related standard deviations were obtained as \(\Delta\hat{W}_{blunt,M2.DEF}=0.602\times 10^{-5}\) mJ/mm\({}^{3}\) and \(\Delta\hat{W}_{blunt,M3.DEF}=0.523\times 10^{-5}\) mJ/mm\({}^{3}\). The elongated defect elastic strain energy density mean values were evaluated as \(\Delta\overline{W}_{blunt,M2.DEF}=2.557\times 10^{-5}\) mJ/mm\({}^{3}\) and \(\Delta\overline{W}_{blunt,M3.DEF}=2.170\times 10^{-5}\) mJ/mm\({}^{3}\), and the related standard deviations were \(\Delta\hat{W}_{blunt,M2.DEF}=1.179\times 10^{-5}\) mJ/mm\({}^{3}\) and \(\Delta\hat{W}_{blunt,M3.DEF}=0.936\times 10^{-5}\) mJ/mm\({}^{3}\). The blunt notch ESED fatigue assessment yielded decreased values, compared to the sharp notch study, which is more applicable to blunt defect geometries. Again, the elastic strain energy density result of the superposition  
Figure 28: ESED course for three defect geometries evaluated as blunt notch and with 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 ‘ellipisis_lin_rot0 deg_v1’); and (**c**) Elongated defect (mesh ‘defect_elongated_lin_v1’). Figure 27: ESED course for three defect geometries, evaluated as sharp notch and with 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 ‘ellipisis_lin_rot0 deg_v1’); and (**c**) Elongated defect (mesh ‘defect_elongated_lin_v1’). method was decreased (by about 16%), compared to the more accurate sub-case method. As the control volume was significantly increased in the blunt notch case, the effect of local geometry curvature was diminished, compared to the respective sharp notch ESED results for both methods. In summary, from the elastic strain energy evaluation, it can be stated that the sub-case method provided the most accurate solutions, while the superposition approach provided results that were decreased by about 15%, depending on the defect curvature. In general, the ESED assessment in the sharp notch case yielded higher values than the blunt notch case, reflecting the findings of the N-SIF evaluation for the three defect geometries.