## 5 Comparative Calculation  
Finally, in comparative calculations on a notched specimen, four procedures for determining the service life at variable amplitudes are compared:  
1. As a reference for the calculation time, the load-notch-strain curves are determined as described in Section 2.3 without taking into account the methods described for increasing efficiency in Section 3. The load-notch-strain curves for the initial load and the hysteresis branch are determined separately in FEA. This means that for the 100 classes recommended by the FKM guideline nonlinear [25], \(n_{\text{I}}\) = 100 load steps are simulated for the load-notch-strain curve of the initial load, and \(n_{\text{H}}\) = 200 load steps are simulated for the load-notch-strain curve of the hysteresis branch. The material law is modelled with \(n_{\text{M}}\) = 200 support points. Section 4.5 demonstrated that the procedure of copying the results at the Gauss points to the element nodes does not give a converged result even with a fine mesh. Therefore, stresses and strains at the element nodes are determined by extrapolation, whereby a mesh with \(\rm n_{E}=30\) is sufficient. Outside the notch area, the meshing deviates from Section 4.5; see Figure 15. There, the specimen is meshed with hexahedral elements outside the notch. Tetrahedral elements are used for the comparison, which means that the meshing in the rest of the specimen is almost independent of the meshing in the notch. 2. In Section 2.2, it is claimed that the general use of load-notch-strain curves, as opposed to recalculating the complete load sequence in an FEA with elastic-plastic material behaviour, results in an immense time advantage. To substantiate this, 0.01% of the reversal points of the load sequence from Section 4.1 are applied to the flat specimen and the CP-time is then extrapolated linearly. The section of the load sequence is chosen to include the maximum value of the spectrum; this is shown in Figure 12B. Since the complete load sequence is not calculated, no life estimation can be performed afterwards. The material law is deposited with \(\rm n_{M}=50\) interpolation points, and the meshing and evaluation of the node results are selected as in the first case. 3. In the third case, load-notch-strain curves are determined for the service life estimation with the methods mentioned without the use of shell elements on the surface. This means that the load-notch-strain curve for the hysteresis branch is calculated from \(\rm n_{H}=5\) load steps with spline interpolation, and the load-notch-strain curve is derived from this. The material law is deposited with \(\rm n_{M}=50\) support points, and the meshing and evaluation of the node results are selected as in the first case. 4. In the fourth case, the procedure is the same as that used in the third case, except that shell elements are used on the component surface, which means that a coarser mesh with \(\rm n_{E}=5\) can be used. For these four cases, the load-notch-strain curves and subsequently the service lives are determined on a flat specimen with \(\rm R_{m}=800\) MPa and \(\rm K_{t}=3\), and a high collective maximum value \(\rm L_{max3}\). Table 5 summarises the boundary conditions of the individual cases examined. The comparison of the CP-Times is used to evaluate the efficiency. These are related to the CP-Time of the direct load-notch-strain curve determination (1 st case). The time taken to perform the spline interpolation is neglected, as this is \(<\)0.1 s. It is obvious that due to the calculation time, the calculation reversal point to reversal point cannot be applied for longer load time histories. By using the presented methods without shell elements, the CP-Time can be reduced to 0.023 times the original time. With the use of shell elements, even a reduction to 0.005 times is possible. A comparison of the three calculated service lives (point 1, 3, and 4) shows only a minor deviation.