# Damage Analysis of Rolling Stock Automatic Coupler under Cyclic Loads
## 1 Introduction
For practical damage summation, an equation treating elastic and plastic damage separately is proposed:  
\[d_{total}=d_{e}+d_{p}+d_{Q} \tag{1}\]  
Under the respective conditions (heavy cargo, frequent shunting, track unevenness, etc. ), the automatic coupler housing develops stresses that exceed the proportionality limit of the material. This is usually caused by random overloading [13]. Figure 1: General view of an automatic coupler type SA3: main parts, dimensions (units in mm), and action–reaction forces \(T\) (the housing is a hollow casting consisting of a head subjected by tensile force and fixed tail 6. The head has big tooth 1 and little tooth 4, which come together to form the gills. The lock mechanism part 3 and the lock holder 2 extend from the gills. The front part of the housing has a support 5 for transmitting compression forces to the wagon body frame in the event of deformation of the fully damping apparatus and coupling device). It is imperative that historical load data for the automatic coupler is available for the identification of the possible damage to the automatic coupler and determination of the remaining service life. In ref. [1], researchers use statistical data available for the rolling stock fleets to determine the load levels and frequencies. The force acting on the automatic coupler was measured during the operation. Further calculations are carried out in the studies above for the full range of operating forces developing during the operation of the automatic coupler over a year, as shown in Table 1[1]. In an American-type automatic coupler, the strain is measured at respective points during the carriage of coal on a defined railway section [14]. Measurements were made for full versus empty rolling stocks. The distribution of stress levels and cycles obtained was generalized as a linear summation was used, not accounting for the effects of history and consistency. Tensile test results for steels used for automatic couplers have already been presented in other works. The mechanical characteristics obtained are yield strength \(\sigma_{y}=464\) MPa and strength limit \(\sigma_{u}=651\) MPa. Steel properties are determined based on the set of chemical elements, and Table 2 summarizes the results of the chemical analysis of an automatic coupler [14]. In ref. [14], fatigue curves were obtained in the experiment referring to the cycle asymmetry coefficient \(r=0.05\) and the constant load amplitude. The fatigue damage was calculated using [PERSON]'s linear dependence:  
\[d=\sum_{i=1}^{N_{i}}\frac{1}{N_{ri}} \tag{2}\]  
where \(N_{ri}\) was determined using the Goodman diagram [15] for the corresponding loading case. The Goodman diagram was used to recalculate conditional stresses using an experimental curve with the coefficient of asymmetry \(r=0.05\). The high density of micropores in the material of the automatic coupler housing is considered an important factor. Micropores are mainly distributed at the edges of the cuts, particularly in the defect areas. This microporosity may be a key factor in lower fatigue resistance. In ref. [16], the defects were quantified using a computer technique. As the pores of the casting are very irregular in shape, it was simplified for the modeling. The aim was to affect the location and size of the pair so that, despite the irregularity of their shape, the pair was idealized into a sphere with an appropriate diameter. The computational results showed that the closer the pair is to the surface of the body, the higher the stress concentration. If the pair crosses the outer surface, it produces the highest stress concentrations. The results also show that the size of the pore has a significant effect on the stress concentration, regardless of how close the pore is to the surface [16]. Researchers [17] have demonstrated the influence of the mechanical and cyclic characteristics of different steels on the durability of automatic couplers.