# Damage Analysis of Rolling Stock Automatic Coupler under Cyclic Loads
## 4 Discussion and Conclusions
### Nomenclature  
\begin{tabular}{l l} Latin symbols & low-cycle fatigue curves constants describing the first and second half-cycles, respectively [24; 25]; \\ \(C_{1},C_{2},C_{3}\) & low-cycle fatigue curves constants describing strain-controlled loading [24; 25]; \\ \(d,d_{total}\) & total damage; \\ \(d_{e}\) & fatigue damage due to elastic strain; \\ \(d_{p}\) & fatigue damage due to plastic strain; \\ \(d_{Q}\) & cumulated low-cycle quasi-static damage; \\ \(d_{F}\) & cumulated low-cycle fatigue damage; \\ \(E\) & modulus of elasticity (MPa); \\ \(e\) & strain (\%); \\ \(e_{i}\) & strain intensity (\%); \\ \(e_{0}\) & strain intensity of initial loading (\%); \\ \(\overline{e}_{0}\) & initial loading strain normalized to proportional limit strain: \(\overline{e}_{0}=e_{0}/e_{pr}(\%)\); \\ \(e_{a}\) & amplitude of the strain (\%); \\ \(e_{pr}\) & proportional limit strain (\%); \\ \(e_{pk}\) & accumulated unilateral plastic strain (\%); \\ \(\overline{e}_{pk}\) & accumulated unilateral plastic strain over \(k\) half-cycles of loading (\%); \\ \(\overline{e}_{pk,r}\) & accumulated unilateral plastic strain at \(k_{f}\) half-cycles of loading (\%); \\ \(\overline{e}_{u}\) & continuous strain under static loading (\%); \\ \(i=1\ldots n\) & samples number in the rank order; \\ \(k\), \(k\)th, \(k_{N}\) & number of loading half-cycles; \\ \(k_{f}\) & number of loading half-cycles to crack initiation; \\ \(m_{d}\) & strain scale (mm/mm); \\ \(m_{\sigma}\) & stress scale (MPa/mm); \\ \(n\) & number of of measurements; \\ \(N_{ri}\) & number of load cycles determined using the Goodman diagram [15] \\ \(N_{i}\) & number of high-cycle fatigue load cycles; \\ \(q\) & degree indicator equal to 1; \\ \(r\) & coefficient of asymmetry; \\ \(s\) & statistical distribution standard deviation; \\ \(S_{k}\) & cyclic stress for the \(k\)th half-cycle of loading (MPa); \\ \(S_{T}\) & cyclic proportional limit stress calculated from the beginning of the unloading \\  & (MPa); \\ \(\overline{S}_{T},\overline{S}_{k}\) & cyclic stress normalized respectively to proportional limit \\  & stress: \(\overline{S}_{T}=S_{T}/\sigma_{pr}\), \(\overline{S}_{k}=S_{k}/\sigma_{pr}\)(MPa); \\ \(T\) & traction force, (N); \\ \(V\) & coefficient of variation; \\ \(\overline{x}\) & statistical mean; \\ \(x_{i}\) & independent variables; \\ Greek symbols & low-cycle fatigue curves constants describing the materials softening or \\  & hardening [22; 23; 24]; \\  & constants of degree equations of low-cycle fatigue curves by the number of \\  & cycles (half-cycles) before crack initiations [22]; \\ \(\delta_{k}\) & elasto-plastic deformation hysteresis loop width; \\ \(\epsilon_{i}\) & elasto-plastic cyclic strain intensity (\%); \\ \(\epsilon_{k}\) & cyclic strain for the \(k\)th half-cycle of loading (\%); \\ \(\epsilon_{T}\) & cyclic proportional limit strain calculated from the beginning of the unloading \\  & (\%); \\  & cyclic strain normalized respectively to proportional limit \\  & stress: \(\overline{\epsilon}=\epsilon_{i}/\epsilon_{pr}\), \(\overline{\epsilon}_{T}=\epsilon_{T}/\epsilon_{pr}\), \(\overline{\epsilon}_{k}=\epsilon_{k}/\epsilon_{pr}\)(\%); \\ \(\sigma,\sigma_{max}\), \(\sigma_{min}\) & monotonous, maximum and minimum stress, respectively (MPa); \\ \(\sigma_{0}\) & initial loading stress intensity (MPa); \\ \(\sigma_{i}\) & stress intensity (MPa); \\ \(\sigma_{pr}\) & proportional limit stress (MPa); \\ \end{tabular}  
The diagram presented above is based on the results of the experiments. The initial half-cycle is described by key parameters: \(\sigma_{0}\), \(e_{0}\), \(\sigma_{pr}\) and \(e_{pr}\). The initial half-cycle (curve OA) is positioned in coordinates \(\sigma\)-\(e\). First half-cycle (curve AB) and all other half-cycles coordinates are \(\bar{S}e\). Each subsequent half-cycle is described: \(S\), \(\varepsilon\), \(S_{T}\), and \(\delta_{k}\)[22].