# Damage Analysis of Rolling Stock Automatic Coupler under Cyclic Loads
## 2 Materials and Methods
### Static and Low-Cycle Results for the Automatic Coupler Steel  
The recorded static tension curve was used for reference to produce the static strain (tensile) diagram (Figure 3). The diagram shall be produced considering both the strain \(e\) (\(m_{d}=0.00117\) mm/mm) and stress \(\sigma\) (\(m_{\sigma}=5.37\) MPa/mm) scales. The mean arithmetic value \(\overline{x}\), statistical distribution standard deviation \(s\), and coefficient of variation \(V\) were calculated for the normal distribution law using the equation below [21]:  
\[\overline{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\sum}}x_{i},\ s=\sqrt{ \frac{1}{n-1}\underset{i=1}{\overset{n}{\sum}}(x_{i}-\overline{x})^{2}},\ V= \frac{s}{\overline{x}}. \tag{3}\]  
The obtained mechanical characteristics of steel 20 GL and the results of the calculations are shown in Table 4.  
Failure is influenced by various metallographic or geometric defects in the structure. The main internal defects and heterogeneities in the microstructure of metals occur during the metallurgical and heat treatment processes. Surface defects (surface roughness, hardening), which occur during the production of the specimens and are of a statistical nature, are also highly important. Some errors are due to non-uniform test conditions. All \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \(\sigma_{pr}\), MPa & \(\sigma_{pr}\), MPa & \(\sigma_{n}\), MPa & \(S_{k}\), MPa & \(\psi\), \% & \(e_{m}\), \% & \(e_{pr}\), \% & \(E\), MPa \\ \hline
1 & 242 & 333 & 516 & 785 & 39.16 & 19.14 & 0.117 & 206,500 \\
2 & 188 & 306 & 526 & 701 & 31.11 & 22.62 & 0.156 & 150,500 \\
3 & 215 & 269 & 505 & 638 & 32.76 & 22.94 & 0.165 & 180,200 \\
4 & 279 & 371 & 532 & 654 & 27.75 & 20.14 & 0.117 & 238,700 \\ \hline \(\overline{x}\) & **231** & **319** & **519** & **694** & **32.69** & **21.21** & **0.1387** & **193,900** \\ \hline \(s\) & 38 & 43 & 12 & 65 & 4.79 & 1.8628 & 0.025 & 37,581 \\ \(V\) & 0.165 & 0.139 & 0.023 & 0.094 & 0.146 & 0.0878 & 0.183 & 0.194 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mechanical characteristics of steel 20 GL. Figure 3: Tensile diagram of steel 20 GL; I—first specimen, II—second specimen, III—third specimen, IV—fourth specimen, V—mean value. of the above errors are specific to a single batch of metal. For a metal of the same grade but different batches, the dispersion of properties between batches will be even greater due to the dispersion of the chemical composition and metallurgical process conditions of the different batches. All factors discussed above influence the dispersion of both static and cyclic material characteristics. The automatic coupler of a rolling stock is subjected to cyclic loading, that is, when the stresses in the cross-section of the part vary periodically from \(\sigma_{max}\) to \(\sigma\approx 0\). Therefore, material tests were also carried out on the specimen under symmetric and asymmetric loads. The low-cycle loading was chosen for the investigation of the cyclic properties of the material since the automatic couplers of a rolling stock are subjected to variable forces and, as shown above, produce stresses that exceed the proportionality limit. Two types of load cycles were chosen for the low-cycle fatigue study, asymmetric (pulsating cycle, \(r=0\)) and symmetric (reversed cycle \(r=-1\)), because the automatic coupler operates under asymmetric load, while the symmetrical load cycle gives a better indication of the cyclic strain parameters of the material, which is needed for the calculation of the damage caused by low-cycle strain. In this investigation, the strain scale \(m_{d}=0.00148\) mm/mm and the stress scale \(m_{\sigma}=4.52\) MPa/mm were determined for the low-cycle stress-controlled load. For strain-controlled loading, the strain scale \(m_{d}=0.001099\) mm/mm and the stress scale \(m_{\sigma}=5.43\) MPa/mm. Under stress-controlled loading, the strain is unconstrained and free to develop; therefore, the mode of failure depends on the level of loading.