## 4 Evaluation of Quality and Efficiency
### Database  
An extensive database is created for a quality and efficiency evaluation. For this purpose, load-notch-strain curves are determined for different geometries with different load configurations and notch geometries. These geometries can be classified as follows, see Figure 13:  
* Flat specimen with notches on both sides loaded with tension or bending, and stress concentration factors \(\mathrm{K_{t}}\) = 1.5, 3, and 5;
* Circular specimen with notches loaded with tension, bending, or torsion; and stress concentration factors \(\mathrm{K_{t}}\) = 1.5, 3, and 5;
* Planetary carrier loaded with planetary pin forces. In the investigations detailed in the following sections, different parts of the database are utilised. Figure 13: Exemplary specimen geometries and load types of the database: (**A**): flat specimen with \(\mathrm{K_{t,tension}}=1.5\); (**B**) round specimen with \(\mathrm{K_{t,tension}}=1.5\); (**C**) planetary carrier from [69]. As mentioned before, the investigations are limited to the material group of steel. In the FEA, E = 206 GPa is used as the modulus of elasticity. For the tensile strengths, R\({}_{\rm m}\) = 400 MPa, 800 MPa, and 1200 MPa are chosen. The first two values are taken as relevant lower and average strengths for steels, while the upper value corresponds to the upper limit of the range of validity of the FKM guideline nonlinear [25]. As described in Section 4.1, the cyclic properties are estimated from the tensile strength using Equations (4) and (5). The load sequences shown in Figure 12 are varied by using different maximum values of the load spectrum. The height of the maximum values is chosen in such a way that approximately the same service life results in a constant amplitude loading N\({}_{\rm const. }\) for different geometries. In order to compare the data for the different geometries, the loads L are expressed in the form of linear-elastic stresses in the following. Table 1 summarises the number of cycles with the corresponding symbols for the stress range of the linear-elastic stress. For the high load L\({}_{\rm max,3}\), the stress range at constant amplitude loading is \(\Delta\sigma_{\rm el,max,3}\), which, under the previously described boundary conditions, results in a calculated service life of N\({}_{\rm const. }\approx 10^{2}\) cycles. To illustrate the loads, they are plotted on an exemplary load-notch-strain curve; see Figure 14. At the low load L\({}_{\rm max,1}\), the stress range of the theoretical elastic stress \(\Delta\sigma_{\rm el,max,1}\) features a large elastic strain part and a small plastic strain part, whereas at the high load L\({}_{\rm max,3}\), the plastic strain part dominates. The load steps are applied in the simulation in equidistant steps so that the last load step corresponds to the maximum load L\({}_{\rm max}\). The load steps L\({}_{\rm l,k}\) used for determining the load-notch-strain curve for the initial load are based on Equation (20) with the number of load steps n\({}_{\rm I}\) (index I for initial load). Similarly, the load steps L\({}_{\rm H,k}\) used for determining the load-notch-strain curve for the hysteresis branch are based on Equation (21) with the number of load steps n\({}_{\rm H}\). For the specifications of the FKM guideline nonlinear, n\({}_{\rm I}\) = 100 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Maximum Value of the Spectrum L\({}_{\rm max}\)** & **Linear-Elastic Stress Range** & **Cycles N\({}_{\rm const.}\)** \\ \hline Low load L\({}_{\rm max,1}\) & \(\Delta\sigma_{\rm el,max,1}\) & \(\approx\)\(10^{5}\) \\ Medium load L\({}_{\rm max,2}\) & \(\Delta\sigma_{\rm el,max,2}\) & \(\approx\)\(10^{3}\) \\ High load L\({}_{\rm max,3}\) & \(\Delta\sigma_{\rm el,max,3}\) & \(\approx\)\(10^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Examined maximum values of the load spectra. Figure 14: Maximum values of load spectra illustrated on a load–notch-strain curve.