# Upgrade of the Universal Testing Machine for the Possibilities of Fatigue Tests in a Limited Mode
## 10 Summary Evaluation of the Processes Performed and Results
### Evaluation of Calibration Processes and Regression Analyses  
The integration and functional verification of the extension sensors-extensometers as TD1 and TD2 transducers based on inductive sensors in two different sensitivity levels from the extensive accessories of the FPZ 100/1 required several processes. These were mainly related to their calibration and to the creation of transformation dependencies between the search quantities elongation \(\Delta l\) and load force \(F\) as mechanical quantities and their electrical equivalents in the form of electrical voltage signals \(U_{\Delta l}\) and \(U_{F}\). In addition, single-purpose jigs with integrated industrially produced displacement transducers LARM MSL30.152 PA were designed and manufactured for this purpose.  
In some cases of the specimen-material combination, adjustments were made for calibration purposes to extend the elastic deformation region up to several times the original level. This was achieved by a combination of several procedures. In the first phase, this was firstly by strain hardening by previous plastic deformation. As this solution was not sufficiently effective, subsequent heat treatment of the specimens by hardening and tempering was applied.  
The reliability and validity of the calibration and transformation dependencies were subsequently assessed by regression and simple correlation analyses. The results of the regression analyses confirmed that the selected linear regression models fully represent the calibration dependencies, with the \(R^{2}\) determination value not falling below 0.9970. At the same time, the possibility of hysteresis with hysteresis loops formed by the loading and unloading branches of the process was investigated. The obtained results do not indicate  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline
**TD** & **Steel** & \(\sigma_{y}\) & \(l_{b}\) & \(\phi d\) & \(T\) & \(f\) & \(F_{\text{min}}\) & \(\sigma_{\text{min}}\) & \(F_{\text{max}}\) & \(\sigma_{\text{max}}\) & \(N\) & SF & \(f_{\text{total}}\) & **Figure** \\
**(me.)** & **No.** & **[MPa]** & **[mm]** & **[mm]** & **[s]** & **[Hz]** & **[NN]** & **[MPa]** & **[N]** & **[MPa]** & **[-]** & **[-]** & **[-]** & **[s min.]** & **No.** \\ \hline
**TD1a** & 12 010 & 318 & 50 & 7.75 & 30 & 0.033 & 0 & 0 & 17 & 360 & 500 & 40:1 & 15,000, 250 & Figures 15–17 \\
**TD1b** & 12 010 & 318 & 50 & 7.75 & 30 & 0.033 & 0 & 0 & 20 & 424 & 78 & 40:1 & 2340; 39 & Figures 18 and 19 \\ \hline
**TD2a** & 14 109.3 & 317 & 50 & 7.75 & 30 & 0.033 & 0 & 0 & 17 & 360 & 100 & 50:1 & 3000; 50 & Figures 20 and 21 \\
**TD2b** & 14 109.3 & 317 & 50 & 7.75 & 30 & 0.033 & 0 & 0 & 16 & 339 & 400 & 50:1 & 12,000, 200 & Figures 22 and 23 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of fatigue tests performed.  
any hysteresis. The exception is the regime \(F_{\text{FPZ}}=\text{f}(U_{F})\), which showed a weak hysteresis at a very low level.  
The obtained calibration and transformation dependencies were subsequently used in the evaluation of validation experimental measurements of low-cycle fatigue.