Numerical study on rolling contact fatigue in rail steel under the influence of periodic overload

https://doi.org/10.1016/j.engfailanal.2020.104624Get rights and content

Highlights

  • This paper provides a method for solving 3D fatigue crack growth in railway rails.

  • We estimate the behavior of fatigue crack growth in UIC60 rail.

  • A 3D boundary element model has been applied to estimate the fatigue life.

  • Failure of rail was analyzed to identify the cause.

  • Results are in good agreement with those achieved in field measurements.

Abstract

Fatigue crack is one of the most common defects in railway system. Fatigue crack growth may lead to wheel and rail failure and damage to other components. In this paper, by applying the including service conditions of the railway system, first, a 3D nonlinear stress analysis model has been applied to estimate stress fields of the rail under the influence of periodic overloads. For this purpose, an UIC60 rail with accurate geometry using finite element method (FEM) is studied. Next, the results of this model are used for fatigue crack growth and also to estimate the fatigue life in rails using boundary element method (BEM). In this regard, first, the types of cracks and the corresponding factors which cause them were analyzed. In addition to performing stress analysis for different positions of the wheel, different values of the stress intensity factors (SIFs) were also obtained. Using these stress intensity factors, two characteristics of fatigue crack propagation namely, crack growth and direction of its development, were obtained. In this study, Paris Equation is used as a criterion of fatigue crack growth rate and the maximum tangential stress was considered as the crack growth direction. The numerical analysis results showed that the effect of periodic overloads on the fatigue life in rails was significant and could not be ignored.

Introduction

Reliable movement and path will be provided by wheel and rail contact, and this would be dependent on several factors. Various stresses exist in the wheel/rail contact, which create small cracks that may initially grow in a subcritical manner and eventually become large enough to lead to failure. These small cracks could exist in the raw material or may occur during manufacture. In the railway system, one of the objectives is to control and delay the failure of wheel and rail cracks. The fatigue phenomenon in the rails is mainly caused by wheel/rail contact stresses, which are caused by repetitive forces during wheel movement on the rails. The plane where the cracks first start to form and orient along with it is the plane where fatigue occurs [1], [2], [3], [4]. In recent years, many efforts have been made to investigate rolling contact fatigue (RCF) and crack growth in the railway system [5], [6], [7], [8], [9], [10]. Residual stresses that occur without any external loading on the rails are created during the manufacturing process by heat treatment, welding or even grinding and also during repairs [11], [12], [13]. Thermal stresses are caused by the difference between the bias temperature and the operating temperature. Masoudi Nejad [14] estimated the residual stresses caused by heat treatment on the railway mono-block wheel using a three-dimensional elastic–plastic finite element model. The results of this study showed that the amount of residual stresses resulting from heat treatment is significant and cannot be ignored for its effects on crack initiation and fatigue life. A general computational model was developed by Glodez and Ren [15] to model fatigue crack growth under periodic contact loads on mechanical components. The model confidently simulated the subsurface fatigue crack growth under contact loading conditions. A multipurpose approach for analyzing the subsurface cracks in the wheel under Hertz loading was proposed by Guagliano and Vergani [16]. The basis of this approach was the analytical calculations of the displacement field in the wheel and its application as boundary conditions in a finite element analysis of the near-crack area. Lansler and Kabo [17] investigated the deformation of cracks in steel wheels under rolling contact fatigue conditions. In this study, a two-dimensional finite element model of a steel wheel containing a subsurface crack under Hertz contact loads was used in which the elastic–plastic material characteristics with nonlinear hardening were applied. The numerical results of their study showed that the deformations of mode I can be neglected. Furthermore, the load amplitude and contact geometry play a critical role in the tangential displacements of the crack surface. Bogdanski and Trajer [18] introduced the concept of a non-dimensional finite element model that could reduce the number of models required to analyze an RCF problem.

Many studies have been done in the field of investigating parameters affecting fatigue crack growth including initial crack angle and loading type [19], [20], [21], [22], [23]. Extensive research has been done by Massoudi Nejad on fatigue crack growth under the influence of residual stresses in a bandage wheel. Massoudi Nejad et al., have investigated the fatigue crack growth and fatigue life in a railway bandage wheel under contact stresses and thermal residual stresses. The results showed that the fatigue crack growth in railway wheel without residual stress demonstrates the combination of shear modes II and III of crack growth [24], [25], [26], [27], [28]. In another study, the stress field caused by the construction process in the railway wheel is investigated by Massoudi Nejad. For this purpose, a three-dimensional elastic–plastic finite element model is presented to estimate the stress field. Three-dimensional finite element analysis results show good agreement with those achieved in field measurements. [28].

In recent decades, with the advent of numerical methods and non-destructive testing as well as powerful finite element analysis software, extensive research has been conducted on fatigue crack growth as the major cause of mechanical components failure [29], [30], [31], [32], [33], [34]. It is a well-known fact that overloading with fixed load periodicity will reduce of fatigue crack growth rate. This decrease in the fatigue crack growth rate depends on load variables such as the applied stress intensity factor, overload and number of overload, loading rate, sample thickness as well as material parameters such as yield strength, strain hardening and fracture toughness [35].

Mutoh et al. [36], concluded that the effect of overload was more significant only at lower amplitude loads. They also claimed that the amount of overload ratio had a significant effect on its subsequent crack, such that the greater the amount of overload, the delay in cracking growth due to the fatigue load will be greater. Using the Wheeler method, Boljanović [37] investigated the crack growth and overload effects in the combined loading case and was able to predict the crack growth path using the finite element method and the stress intensity factor. Crack closure is identified as a major cause of crack growth retardation in the works of Espinosa [38] and he showed that the gap between successive overloads can affect the crack growth rate. Zheng [39] introduced the plastic zone formed at the crack tip as a criterion for predicting the behavior of the material under the influence of the overload and using this criterion he could make a good prediction of the delay in crack growth. Using circular CT specimens and the Wheeler method to obtain the effective stress intensity factor, Wang [40] investigated the effects of single overload and loading history at different load ratios and concluded that the greater overload ratio would lead to further crack growth retardation and only a significant reduction of crack growth rate can be observed following an overload.

With the development of analytical and numerical methods in solid mechanics, today it is attempted to study quantitatively and more precisely the effects of different parameters rather than qualitative studies. Numerous studies have been conducted with numerical and analytical methods that have addressed various aspects of it. However, the discussion of the effect of overload on fatigue life in rails is less discussed. The purpose of this study is to evaluate fatigue crack growth and fatigue life under the influence of periodic overload in rails. For this purpose, the actual sample of the rail used in the railway system is considered. Three-dimensional elastic–plastic finite element modeling was performed, taking into account the applied loads on rails and considering the resulting stress distribution, crack growth and fatigue life estimation. Field observations in the railway system have also been used to validate the results of the numerical model.

Section snippets

Residual stress field

Sometimes due to problems such as wheel brakes or less adhesion or when the train wants to stop, the wheels stop earlier and they are dragged onto the rails instead of rolling. When the wheel is mounted (the wheel is pulled onto the rails), part of the driver's wheel is removed and a flat surface is formed. When the wheel starts to rotate, an impact load is exerted on the rails in every turn. Sometimes the impact load could have such a high value that may cause the rail to be severely damaged

Stress intensity factors (SIFs)

Analytical solution of stress intensity factors is only possible in simple and specific cases. Generally, in many cases, their exact resolution is either time-consuming or impossible. Another solution is to use numerical methods such as the boundary element method (BEM). In [41], the stress intensity factors for Hertz cracks were calculated by Yingzhi and Hills. The value of the stress intensity factor of mode I for θ ≈ 27° is calculated as:KI=0.028P0a0where,P0=3P2πa0

In the presence of

Evaluation of fatigue crack growth

In recent decades, with the advancement of numerical methods and non-destructive experiments, as well as powerful finite element analysis and boundary element software, extensive research has been done on the growth of fatigue crack as the major cause of mechanical components failure. In this study, after entering the necessary information and calculating the values of the stress intensity factor, the life expectancy of fatigue for an UIC60 rail is calculated. The proposed equations in [43],

Conclusions

In this study, a three-dimensional model was developed for fatigue crack growth and fatigue life estimation of UIC60. Parametric fracture analysis is performed by defining the factors affecting crack growth for two types of surface fractures and using linear fracture mechanics and boundary element method. Also, the effect of periodic overload and stress field resulting from wheel contact with rails and fatigue life were investigated. According to the results of numerical analysis and comparing

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work has been supported by the International Postdoctoral Exchange Fellowship Program (Talent-Introduction Program) of the P. R. China (Fund No. 234384).

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