## 4 Experimental Program
### Cyclic Loading  
The test configuration for cyclic loading was the same compared to monotonic loading. Each test series contained three test specimens for gathering possible scatter. The load amplitudes \(\Delta\sigma^{t}_{\text{st}}\) varied between 5% and 80% of the reference tensile strength \(f_{\text{st}}\), according to Table 1. The testing machine's electromechanical drive limited the frequency to approximately 0.85 Hz. Table 3 lists the most critical parameters of the experimental program for cyclic tensile loading. Besides general test parameters, Table 3 also contains basic results (load cycles leading to failure \(N_{\text{um}}\)) of the cyclic loaded fibre tests. Except for the test series VFZ-7 and VFZ-8, all fibres fractured within the test area, i.e., between the cannulas. However, in one test of VFZ-7 and VFZ-8, the fibre crack occurred in the cannulas. This crack location could indicate higher scatter of ultimate load cycles \(N_{\text{um}}\). The specimen's manufacturing process might have caused additional damage while pressing and gluing the filigree steel fibre into the cannulas. The additional damage might be responsible for the lesser fatigue resistance of the steel fibres. Nevertheless, the test results and the number of load cycles lie within the usual scatter range for fatigue tests [17; 18]. \begin{table}
\begin{tabular}{c c c c} \hline
**Name** & \(\mathcal{O}_{\text{f}}\) & **Tensile Strength\(f_{\text{st},\text{m}}^{t}\)** & **Standard Deviation** & **5\%-Quantile of \(f_{\text{st},\text{m}}^{t}\)** \\ \hline [-] & [mm] & [N/mm\({}^{2}\)] & [N/mm\({}^{2}\)] & [N/mm\({}^{2}\)] \\ VFS-A & 0.19 & 3575.8 & 80.2 & 3462.4 \\ VFS-B & 0.13 & 4250.4 & 95.2 & 4080.7 \\ \hline \end{tabular}
\end{table} 
Table 2: Characteristic values for the theoretical stress–strain relationship of high-strength micro steel fibres. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Name** & **Quantity** & **Upper Stress** & **Lower Stress** & **Load Amplitude** & **Load Amplitude** & **Load Cycles** \\  & **Level** \(\Delta\sigma^{t}_{\text{st},\text{o}}\) & **Level** \(\Delta\sigma^{t}_{\text{st},\text{u}}\) & \(\Delta\sigma^{t}_{\text{st}}\) & \(\Delta\sigma^{t}_{\text{st}}\) & \(N_{\text{um}}\) \\ \hline [-] & [num.] & [-] & [-] & [-] & [N/mm\({}^{2}\)] & [num.] \\ VFZ-1 & 3 & 0.90 & 0.10 & 0.80 & 2860.7 & 962\({}^{\pm 5}\) \\ VFZ-2 & 3 & 0.80 & 0.10 & 0.70 & 2503.1 & 1008\({}^{\pm 46}\) \\ VFZ-3 & 3 & 0.70 & 0.10 & 0.60 & 2145.5 & 1593\({}^{\pm 344}\) \\ VFZ-4 & 3 & 0.60 & 0.10 & 0.50 & 1787.9 & 2382\({}^{\pm 260}\) \\ VFZ-5 & 3 & 0.50 & 0.10 & 0.40 & 1430.3 & 4240\({}^{\pm 880}\) \\ VFZ-6 & 3 & 0.40 & 0.10 & 0.30 & 1072.7 & 3364\({}^{\pm 40}\) \\ VFZ-7 & 3 & 0.30 & 0.10 & 0.20 & 715.2 & 7986\({}^{\pm 1963}\) \\ VFZ-8 & 3 & 0.20 & 0.10 & 0.10 & 357.6 & 57,375\({}^{\pm 10,073}\) \\ VFZ-9 & 3 & 0.15 & 0.10 & 0.05 & 178.8 & 1,000,000\({}^{\pm 0}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Experimental programme of tensile tests subjected to cyclic loading. The load cycles \(N_{\text{um}}\) and load amplitudes \(\Delta\sigma_{\text{st}}^{\text{f}}\) were plotted on an S/N-diagram, and the corresponding regression curve was determined. Equation (1) gives the formulae of the regression curve:  
\[\Delta\sigma_{\text{st}}^{\text{f}}=5\cdot 10^{4}\cdot N^{-0.44} \tag{1}\]  
where \(\Delta\sigma_{\text{st}}^{\text{f}}\) is the load amplitude and \(N\) is the number of load cycles. Figure 6 shows the S/N curve of the high-strength micro steel fibre and the plotted test results. For load amplitudes smaller than \(\Delta\sigma_{\text{st}}^{\text{f}}<3500\) N/mm\({}^{2}\), the regression curve (red dashed line) equals the short-term strength. The red arrows pointing to the right Figure 6 mark so-called \"run-outs\". Furthermore, Figure 6 shows the S/N curve for prestressing steel according to Model Code 2010 (2010) (dashed black line).