# Field Investigation and Rapid Deterioration Analysis of Heavy Haul Corrugation
## 4 Multi-Crack Expansion Analysis Considering Grinding Marks
### Result Analysis
#### 4.3.3 Circular Curve  
It can be seen from Figure 13a,b that the value of the SIF in the circular curve is much higher than that in a straight line or a transition curve. In terms of distribution state, it is also clear that the adjacent contact patch is prone to crack propagation. For the model without grinding marks, the maximum value of the SIF of type I is 15.05 MPa/mm\({}^{0.5}\). For the model with grinding marks, the SIF is high in the intersection area of grinding marks and the cracks. The maximum value of type I SIF reaches 56.43 MPa/mm\({}^{0.5}\), indicating that poor grinding works easily lead to the rapid progress of type I cracks. For type II crack propagation in the circular curve section, it can be seen from Figure 13c,d that the \(K_{\rm II}\) value is mainly distributed on the contact surfaces of the wheel and rail. For the condition without grinding marks, the maximum value is 11.73 MPa/mm\({}^{0.5}\). For the state with grinding marks, a higher value appears in the intersection area of grinding marks and cracks. The overall maximum value is 65.36 MPa/mm\({}^{0.5}\), and its \(K_{\rm II}\) value is significantly higher than that of the state without grinding marks, indicating that the state of grinding marks can easily lead to the rapid development of type II cracks. As for the results of the SIF values of type III cracks, as shown in Figure 13e,f, the grinding marks significantly enlarge the values of SIF near the intersection point of grinding marks and cracks.  
Figure 12: Results of SIFs at the transition curve: (**a**) SIF of type I cracks without the grinding marks; (**b**) SIF of type I cracks with the grinding marks; (**c**) SIF of type II cracks without the grinding marks; (**d**) SIF of type II cracks with the grinding marks; (**e**) SIF of type III cracks without the grinding marks; (**f**) SIF of type III cracks with the grinding marks.  
From Figure 14, the results of SIFs with grinding marks are higher than in the condition without grinding marks in all three cases. This indicates that grinding marks increase trends in crack propagation in rail surfaces, and it provides a theoretical answer to the question put forward in Section 3.  
Figure 13: Results of SIFs at the circular curve: (**a**) SIF of type I cracks without the grinding marks; (**b**) SIF of type I cracks with the grinding marks; (**c**) SIF of type II cracks without the grinding marks; (**d**) SIF of type II cracks with the grinding marks; (**e**) SIF of type III cracks without the grinding marks; (**f**) SIF of type III cracks with the grinding marks.  
By comparing the results above, it can be seen that the SIF values at the crack tip of the circular curve are higher than they are at the straight line and the transition curve, indicating that it is relatively easy for a crack to expand in the circular curve. This is consistent with experience gathered from the field. The residual surface grinding marks from a poor grinding process accelerate the evolution of cracks on a railhead, thus reducing its plasticity resistance. As such, the deterioration process of plastic flow corrugation enters a rapid progression that advances quickly.  
Therefore, the intersection of grinding marks and fatigue cracks after grinding should be avoided by improving the material, removing the volume of the grinding works to absolutely remove RCF defects, or optimizing grinding quality to reduce grinding marks.