# Upgrade of the Universal Testing Machine for the Possibilities of Fatigue Tests in a Limited Mode
## 9 Cyclic Load Tests
### Experimental Measurements TD1a  
For the planned low-cycle fatigue measurements, it was necessary to ensure that the maximum load values exceeded the yield strength of the material used. The tensile diagram of steel 12 010 (Figure 4a) shows a significant yield strength at the loading force level of 15 kN with a corresponding normal stress level of 318 MPa that had to be overcome. For this test, the loading parameters were set with a lower (minimum) force limit of \(F_{\min}=0\) kN and \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Transducer** & **Scale** & **Loading** & \(x\) & \(y\) & \(a\) & \(b\) & \(R^{2}\) & **Hysteresis** & **Figure** \\  & **Factor** & **Mode** & \(x\) & \(y\) & [**]** & [**]** & [**]** & **[**]** & **No.** \\ \hline TD1 & 40:1 & loading & \(\Delta l_{\text{LARM}}\) & \(\Delta l_{\text{FPZ}}\) & 0.9957 & 0.0450 & 1.0000 & x & Figure 11a \\ \hline TD2 & 2000:1 & loading & \(\Delta l\) [mm] & \(\Delta l_{\text{FPZ}}\) & 0.9558 & \(-0.0008\) & 0.9986 & x & Figure 11b \\ \hline TD1 & 10:1 & loading & \(U_{\Delta l}\) [V] & \(\Delta l\) [mm] & 4.9813 & 2.9473 & 0.9998 & & Figure 12 \\  & 10:1 & unloading & \(U_{\Delta l}\) [V] & \(\Delta l\) [mm] & 5.1021 & 2.2094 & 1.0000 & from & Figure 12 \\ \hline TD1 & 20:1 & loading & \(U_{\Delta l}\) [V] & \(\Delta l\) [mm] & 2.5392 & \(-0.1658\) & 0.9999 & & Figure 12 \\  & 20:1 & unloading & \(U_{\Delta l}\) [V] & \(\Delta l\) [mm] & 2.5463 & \(-0.2930\) & 1.0000 & from & Figure 12 \\ \hline TD1 & 40:1 & loading & \(U_{\Delta l}\) [V] & \(\Delta l\) [mm] & 1.2705 & \(-0.1470\) & 1.0000 & from & Figure 12 \\  & 40:1 & unloading & \(U_{\Delta l}\) [V] & \(\Delta l\) [mm] & 1.2698 & \(-0.1590\) & 1.0000 & from & Figure 12 \\ \hline x & x & loading & \(U_{F}\) [V] & \(F_{\text{FPZ}}\) [kN] & 50.8390 & 1.2317 & 0.9970 & & Figure 13a \\  & x & unloading & \(U_{F}\) [V] & \(F_{\text{FPZ}}\) [kN] & 51.2880 & \(-1.3665\) & 0.9975 & low & Figure 13a \\ \hline TD2 & 500:1 & loading & \(U_{\Delta l}\) [V] & \(\Delta l\) [mm] & 0.1050 & 0.0075 & 0.9998 & & Figure 13b \\  & 500:1 & unloading & \(U_{\Delta l}\) [V] & \(\Delta l\) [mm] & 0.1049 & \(-0.0010\) & 1.0000 & from & Figure 13b \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the calibration process, regression analysis and other related information. an upper (maximum) force limit of \(F_{\max}=17\) kN (in Figure 4a as \(F_{\mathrm{TD1a}}\)) and \(\sigma_{\max}=360\) MPa, respectively. This stress value for the positively vanishing load also corresponded to the normal stress range \(\Delta\sigma\). The Scaling Factor SF was set to 40:1. The specified number of cycles was \(N=500\). The test was terminated after the specified number of cycles. The values obtained were recorded in two files, the first for force and the second for strain. The situation for the analysis of test specimen 12 010 under cyclic loading with the application of transducer TD1 in both TD1a and TD1b mode is shown in Figure 14.  
Subsequently, the obtained signal attributed to the deformation was transformed to real strain values using the transformation dependence calibration curve according to Figure 12. Thus, the time dependence of the strain \(\varepsilon\) obtained for the TD1a measurement is shown in Figure 15.  
The construction of the normal stress vs. strain dependence, i.e., also of the possible hysteresis loops, should be carried out only for certain cycles for better illustration. Standards on fatigue testing methodologies for metallic materials from all cycles recommend the use of selected cycles, preferably \(1\cdot 10^{n}\), \(2\cdot 10^{n}\) and \(5\cdot 10^{n}\) for powers of \(n=0\), \(1\), \(2\), \(3\) and \(4\). In this case, cycles 1-5, 10, 20, 50, 100, 200 and 500 were used (Figure 16). Figure 14: Situation during the analysis of the test specimen of material 12 010 under cyclic loading with the application of transducer TD1 in TD1a and TD1b mode. Figure 15: Time dependence of the relative deformation \(\varepsilon\) when measuring TD1a with the parameters: transducer TD1, Specimen No.