## 4 Evaluation of Quality and Efficiency
### Summary and Recommendations for the User  
In Section 3, methods for improving the efficiency of the determination of load-notch-strain curves in an FEA with elastic-plastic material behaviour were described; these were subsequently examined in Section 4 using a database with regard to their quality and efficiency. In this section, a summary of the results and a resulting recommendation for the user are given. The correlation between the load-notch-strain curve for the hysteresis branch and the initial load must always be taken into account. With these, the efficiency of the load-notch-strain curve determination can be increased without a loss of quality, as the determination of the load-notch-strain curve for the initial load by means of FEA is no longer necessary. The material behaviour is entered in the FE software as a discretised curve. The investigations in Section 4.4 show that the number of support points used for the description of the material behaviour influences the quality and efficiency of the load-notch-strain curve determination, and thus also the service life estimation. In addition, a decrease in quality is observed with an increasing load height at the same number of support points. As a good compromise between quality and efficiency, the recommended number of support points for the material law is \(\mathrm{n_{M}}=50\) up to a stress range of twice the tensile strength \(\Delta\sigma=2\cdot\mathrm{R_{m}}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Constraint** & **Specimen** & **Load** & \(\mathrm{n_{H}}\) \\ \hline \multirow{4}{*}{\(\left|\begin{matrix}\mathrm{N_{var,n_{H}}}\\ \mathrm{N_{var,300}}\end{matrix}-1\right|\leq 1\%\)} & Flat specimen & Tension & 5 \\  & Bending & 5 \\ \cline{1-1}  & & Tension & 5 \\ \cline{1-1}  & Round specimen & Bending & 4 \\ \cline{1-1}  & Torsion & 5 \\ \cline{1-1}  & & Planet carrier & - & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of load steps \(\mathrm{n_{H}}\) for different geometries with spline interpolation. Figure 21: Number of load steps \(\mathrm{n_{H}}\) for different geometries with spline interpolation. The type of evaluation of the node results in the FEA with elastic-plastic material behaviour has a great influence on the efficiency and quality of the load-notch-strain curve determination. The standard procedure of many FE programs is to copy the results at the Gauss points to the element nodes. An example calculation on a flat specimen notched on both sides shows that the load-notch-strain curves generated in this way do not converge to a constant service life even with fine meshing, and the service lives are on the unsafe side. When using an extrapolation method, as is common in calculations with elastic material behaviour, a converged service life can be achieved in the example even with coarser meshing. In the case where only the stresses and strains on the surfaces of components are of interest, the use of shell elements on the component surface brings immense advantages for increasing efficiency. Due to the shell elements, Gauss points are available on the component surface, whereby load-notch-strain curves with the same quality can be calculated with a significantly coarser meshing. The simulations on a notched flat specimen show that (at least with the ANSYS Workbench program used) copying the results of the Gauss points to the element nodes is preferable to extrapolation. In Section 4.6, methods for estimating the load-notch-strain curve from only a few simulated load steps are presented and compared. The linear interpolation method is mentioned only because of its simplicity. In order to exclude the influence of the load-notch-strain curve on the service life, a relatively high number of load steps must be applied in the simulation compared to the other methods, meaning that the efficiency is only increased to a small extent. The regression of the load-notch-strain curve with the power function has advantages and disadvantages.