# Evaluation of Structural Behavior and Fatigue Performance of a KR-Type Rail Clip
## 3 Finite Element Analysis
### Results of Analysis  
The results obtained through FEA were first verified by comparing it with the experimental results. Figure 10 provides a comparison of the maximum principal strains between the strain measurements in the laboratory assembly test and the FEA results in step 1. Figure 10a-c show a comparison of the strains along the circumference at the three different cross sections of the rail clip, which are denoted by \"Left\", \"Center\", and \"Right\" in Figure 10d. The boundary position marked in Figure 10b is near the region contacted between the rail clip and the guide plate. The plot of the strains obtained from the analysis is shown through the black solid lines. The red dots are the strains measured from the assembly test. A comparison of strains revealed a good correlation with an average error of about 14%. Table 2 shows the natural frequencies and their associated mode shapes obtained through the frequency analysis performed in Abaqus. The natural frequencies are also compared with the measured ones from the laboratory modal test in this table. The comparison of natural frequencies indicated a good correlation, with an error of about 15%.  
The global response in the two loading steps is plotted in Figure 11. The vertical axis represents the vertical force applied to the torque location while the horizontal axis represents the vertical displacement at the clip end in step 1. As shown in Figure 11, although the global response typically exhibits elastic behavior, a slight plastic behavior is also observed as the applied force approaches closer to the tightened end (i.e., the initial straight line gets inclined a little toward the tightened end).  
Figure 12 depicts the contours of the maximum principal stress. While Figure 12a shows the contours after the completion of step 1 (which simulates the assembly process), Figure 12b shows the contours for steps 1-2 (which simulates the vertical movement of the rail clip from the train passage) (i.e., the contours in Figure 12b represent the stress range). It should be noted that the stresses were relieved due to the train passage, because the downward vertical movement of the rail reduced the clamping force of the rail clip. Since both mean stress (or maximum stress) and stress amplitude affect fatigue performance, the locations where the maximum stress or the stress amplitude were high can potentially represent fatigue crack initiation. These locations were identified in the red color of the stress contours in Figure 12.  
Figure 9: Loading steps of finite element analysis.  
Figure 10: Comparison of test results and those obtained through Abaqus (maximum principal strains) in step 1: (**a**) left section; (**b**) center section; (**c**) right section; (**d**) strain gauge locations.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & **Test** & **Abaqus** & **Error** & **Mode Shape** \\  & **(Hz)** & **(Hz)** & **(\%)** & **Mode Shape** \\ \hline
1 st & 871 & 999 & 14.7 & \\
2 nd & 1025 & 1181 & 15.2 & \\
3 rd & 1272 & 1478 & 16.2 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of natural frequencies (test vs. Abaqus).  
A fatigue test was conducted at Hybrid Structural Testing Center at Myongji University using a 100 kN dynamic actuator with the loading frequency of 5 Hz. The rail clips were tested for various constant displacement ranges from 0.8 mm to 4 mm. Irrespective of the constant displacement ranges, KR-type rail clips have revealed that fatigue cracks occur at two different locations and propagate along different paths. Figure 13 shows the failure modes (failure modes 1 and 2) from the fatigue test, which were compared with the ones obtained through FEA. From Figure 13, it can be observed that the crack initiation points identified from the fatigue tests are similar to the stress concentration locations obtained through FEA.