# Damage Analysis of Rolling Stock Automatic Coupler under Cyclic Loads
## 3 Results  
### Finite Element Modeling of an Automatic Coupler and Estimation of Stress and Strain  
The forces acting on the housing are distributed in the front loop of the automatic coupling. The maximum force (2500 kN) corresponds to the movement of the train. The remaining forces correspond to a certain level of loading of the wagons at the maximum permissible train speed. Typical operational forces (950 kN, 1550 kN, 2350 kN, 2500 kN) have been used in the calculations, and even higher forces (3150 kN) may occur in the event of overloading or incorrect operation [1; 11].  
The FE model is based on the technical drawings of an automatic coupler SA3. To reduce the complexity of the calculations, the body of the automatic coupler has been divided into two parts in the horizontal plane of symmetry. Although the body is not perfectly symmetrical, the geometric differences are limited to the lock mechanism and do not affect the stress-strain behavior of the automatic coupling. Therefore, by adopting  
Figure 8: Accumulated unilateral plastic strain during the asymmetric cycle.  
Figure 7: Low-cycle fatigue curves under the strain-controlled loading (1\(-\)\(\overline{z}\); 2\(-\)\(\overline{\delta}\)).  
a conditional plane of symmetry and describing the necessary boundary conditions, it is sufficient to study half of the automatic coupler.  
During its operation, the automatic coupler housing is subjected to forces \(T\) of different magnitudes, depending on the mass of the wagons, as already mentioned. To study the automatic coupler using the Ansys Classic FEM model, the load is distributed on the front surface of the automatic coupler housing head (see Figure 1, parts 1-4) and six degrees of freedom were constrained in the tail bore (see Figure 1, part 6). The FEM mesh was generated automatically. The selected finite element is a second-order tetrahedral element with 10 nodes (SOLID 187 Ansys element). The finite element model used consists of 66,358 tetrahedral elements and 113,907 nodes. At sufficiently high loads, stresses and strains exceed the limit of proportionality, and elastic-plastic deformation begins. In this case, the stress-strain relationship is non-linear. Therefore, a five-part polygonal approximation of the stress-strain diagram was used in the calculation. For this purpose, a multilinear material deformation curve was used.  
The most dangerous zones of the automatic coupler (Figure 9) and the intensities of the stresses \(\sigma_{i}\) and strains \(e_{i}\) have been identified through the application of a finite element model of the automatic coupler (Table 5). The automatic coupler housing was evaluated taking into account longitudinal force \(T\). It can be seen from Table 5 that the maximum force induces stresses \(\sigma_{i}\) that exceed the proportionality limit of steel 20 GL \(\big{(}\sigma_{pr}=230\) MPa\(\  
As can be seen in Table 5, at a load of \(T=3150\) kN, the stress intensity at the transition between the head and the tail (zone 2) is not only higher than the material's proportionality limit but also higher than the yield strength (\(\sigma_{y}=320\) MPa). Thus, this zone is subject to low-cycle deformation. For other loads in the operating range, the stress intensity in the automatic coupler housing is below the material proportionality limit and, therefore, is less dangerous. The stress intensity distribution at \(T=3150\) kN for the automatic coupler housing is shown in Figure 9. The figure shows that the stress intensity is highest in the transition between the head and tail. There is also a significant increase in the stress intensity of the small tooth, big tooth, and tail zones.  
Only the numerical values of the results change as a function of the load level, and the nature of the results remains the same. The highest stress intensities were obtained in all cases in the transition between the head and tail. This is due to the high stress concentration at the dimensional change locations where the dimensions change in two planes.