## 4 Experimental Program
### Cyclic Loading
In comparison, prestressing steel shows no good agreement with the fatigue behaviour of high-strength micro steel fibres in \"low-cycle fatigue\" (\(N\leq 10^{4}\) LW) and \"high-cycle fatigue\" (\(N>10^{4}\) LW). The non-agreement could be the reason for comparing the characteristic values (for prestressing steel) and mean values (high-strength steel fibre) with each other. This is why modification of the steel fibre S/N curve (conversion of the mean values into characteristic values) is necessary. Additionally, the typical ranges of the fatigue life in S/N curves for conventional reinforcing bars and prestressing steel are not transferable to high-strength micro steel fibres and need adjustment. While fatigue loads in reinforcing bars and prestressing steel strands are precisely calculable, the stresses in randomly distributed fibres of UHPFRC components might differ vastly from each other. Some fibres in UHPFRC components obtain higher stresses than others, although they lie right next to each other. Therefore, the beginning of the fatigue endurance limit starts earlier at \(N=10^{5}\) LW load cycles (instead of \(10^{6}\)). The other limits of the S/N curve remain equal to conventional reinforcing bars and prestressing steel (Table 4). The calculation goal is a bilinear S/N curve for the high-strength steel fibre under consideration of the 5% quantile values. Therefore, the S/N curve of finite-life fatigue \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Reinforcing Steel Bars:**} & \multicolumn{2}{c}{**High-Strength Micro Steel Fibre:**} \\ \hline \(\bullet\) & Low cycle fatigue & \(N\leq 10^{3}\) & \(N\leq 10^{3}\) \\ \(\bullet\) & Finite-life fatigue strength & \(10^{3}<N<10^{6}\) & \(10^{3}<N<10^{5}\) \\ \(\bullet\) & Fatigue endurance limit & \(N\geq 10^{6}\) & \(N\geq 10^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Modified ranges of fatigue life for high-strength micro steel fibres. Figure 6: Mean and characteristic S/N curve of high-strength micro steel fibres. strength between \(10^{3}\) and \(10^{5}\) load cycles needs a conversion of the mean values into the characteristic values. This conversion requires the test series results with the highest scattering in terms of ultimate load cycles. All the other test series remain disregarded for the calculation at first. The 5% quantile of the test series with the highest scattering (VFZ-7) is:  
\[N_{0.05\mathrm{VFZ-7}}=5615 \tag{2}\]  
The 5% quantile \(N_{0.05\mathrm{VFZ-7}}\) of the test series VFZ-7 belongs to a load amplitude of 715.2 N/mm\({}^{2}\). Two points (\(P_{1}\) and \(P_{2}\)) are added to the S/N diagram: Point \(P_{1}\) (7986/715.2) is equal to the load cycles and load amplitude of the mean S/N curve. Point \(P_{2}\) (5615/715.2) corresponds to the 5% quantile of the test series VFZ-7. If the mean S/N curve (red line) is moved parallel until it intersects point \(P_{2}\) (5615/715.2), the characteristic S/N-curve is formed and is shown in Figure 6 by the blue line. Equation (3) expresses the characteristic S/N curve determined by regression with:  
\[\Delta\sigma_{\mathrm{st}}^{\mathrm{f}}=2.69\cdot 10^{4}\cdot N^{-0.425}\text{ for }N <10^{5} \tag{3}\]  
Equation (3) is consequently only valid for ultimate load cycles between \(10^{3}\) and \(10^{5}\), i.e., the finite-life fatigue strength. For higher ultimate load cycles, Equation (3) shows no good accordance, and modification would be useful. The test series VFZ-9 has not been included in the calculation so far. It shows three run-outs at a load amplitude of \(\sigma_{\mathrm{st}}^{\mathrm{f}}=178.8\) N/mm\({}^{2}\) (cf. Table 3). Thus, the characteristic S/N curve (blue line in Figure 6) changes its direction and obtaines a reduced inclination and crosses the \"run-outs\". The redirection of the S/N curve requires another regression to assign an equation.