## 1 Introduction  
Turnouts are essential components of railway facilities. A turnout consists of a switch panel, a closure panel and a crossing panel [1]. In order to achieve vehicle transfer, the switch rail and point rail are designed as variable cross-section rails, transferring the wheels between the stock rail and switch rail and between the wing rail and nose rail. During this process, skipping wheel-rail contact points can cause strong dynamic wheel-rail interaction, which is also a main reason for wear, rolling contact fatigue (RCF) and accumulated plastic deformation [2; 3; 4] of turnout rail. The surface initiated RCF is mainly characterized by surface cracks (see Figure 1). These are caused by long-term accumulation and development of RCF under wheel loads, and the position and size of rail damage caused by each pass of vehicle wheels are related to the dynamic parameters of the vehicle-track system [1; 3]. Therefore, it is necessary to analyze the RCF behaviors of turnout rails and the main parameters influencing the rail RCF in order to guide the simulation and prediction of rail damage in turnouts. Wheel-rail RCF is a longstanding worldwide problem, and has been one of the research topics of international academic conferences such as the Conference on Contact Mechanics (CM) and the International Association for Vehicle System Dynamics (IAVSD). Researchers have presented many numerical and experimental studies on wheel-rail RCF in sectional lines, which form the basis for studying rail RCF in turnouts. However, considering the complicated structure of turnouts, the research is more difficult. [PERSON] et al. [5] presented a method for simulating the wear, RCF and plastic deformation of turnout switch/crossing panel rails, and used the method to evaluate the effects before and after the turnout geometric size and rails are optimized. [PERSON] et al. [3] presented a numerical method for calculating the accumulated wear and RCF of turnout switch panel rails, for which, the random process of vehicle motion was simulated through discretizing the dynamic parameters of the vehicle-turnout system, the Archard model was used to predict the rail wear, and the rail RCF was predicted according to the Palmgren-Miner rule and a model deduced based on the Shakedown theory. In addition, they also evaluated the structural design of turnout switches based on this method. [PERSON], [PERSON] and [PERSON] et al. [6; 7; 8] optimized the track stiffness and rail profiles in order to reduce the dynamic wheel-rail interaction at turnout zones and solve problems such as rail wear and fatigue of turnout rails. [PERSON] et al. [9] presented a finite element model for crossing with a single running wheel according to the wheel-rail vibration, elastic wheel deformation and plastoelastic rail deformation, in order to calculate the dynamic wheel-rail interaction, then they also presented a simplified finite element model for calculating the dynamic wheel-crossing interaction [10], according to the influence of grid precision and calculation time, through setting appropriate grid sizes. Based on this model, they performed a contrast analysis on the properties of three materials used for crossings, Manganese steel, Hardox and Marage300 according to the generation and development of RCF cracks. [PERSON] et al. [4] presented a finite element model with regard to crossing with a single running wheel-set in order to calculate the dynamic wheel-rail interaction, and studied the generation and fatigue process of RCF cracks of crossing rails based on their model. Researchers from Yanshan University of China [11; 12; 13] analyzed the wear and fatigue properties of high manganese steel/austenitic steel and bainitic steel materials used for crossings through material tests in order to realize good wear and fatigue resistance. At present, for the calculation of wheel-rail contact information of turnout switches, researchers usually consider a switch rail and a stock rail as a combined part.