Numerical simulation model for the competition between short crack propagation and wear in the wheel tread

Highlights

• A numerical model is developed to simulate the competition between crack propagation and wear.

• The model is shown to operate properly when applied to the results of twin disc tests.

• When a 1000 km straight run is simulated, the wheel tread is hardly damaged.

• If the rolling direction of the wheel is reversed, the delamination wear becomes dominant.

Abstract

A numerical model is developed to simulate the competition between RCF-initiated short crack propagation and wear in a wheel tread. The crack is assumed to initiate when the total accumulated plastic shear strain reaches the critical value. In the early crack growth simulations, the two-stage short crack growth model proposed by Hobson is applied. With regard to wear, the Archard model is adopted as the basis. The model is shown to operate properly when applied to the results of unidirectional twin disc tests. When an outward route comprising a 1000 km straight run is simulated based on the Shinkansen routes, it is found that the tread is hardly damaged. The results obtained from the rolling reversal fatigue tests show that if the rolling direction of the wheel is reversed, the delamination wear becomes dominant.

Introduction

Railway systems involve contact between rolling wheels and rail. The demand for higher train speed and greater wheel loads have led to increased contact pressure and tangential traction between the wheel and the rail. Under a cyclic wheel passage, these lead to the perpetual initiation of cracks known as “rolling contact fatigue” (RCF), and wear in both surfaces and these are major damages for wheels and rails. For example, the railway wheel turning data [1] indicated that the majority of wheels were turned due to RCF or tread/flange wear.

In the initiation and early propagation stages of cracks, crack propagation competes with wear [2]. The mechanism that initiates cracks depends on factors such as the geometry of the rail and the wheel, properties of their steels, type of traffic, and lubrication. At the same time, wear changes the shape of both surfaces, thereby altering the wheel–rail contact region and associated contact stresses. Both crack propagation and wear are driven by stress, strain, and traction, which are all related to the forces in the contact region. When the wear rate is much greater than the crack growth rate, cracks cannot propagate and, in some cases, are eliminated. In contrast, very low wear rates have negligible influence on crack growth. Consequently, wear rate must be considered to estimate the net crack growth rate.

The pioneering research on the competition between RCF crack propagation and wear in a wheel/rail system was carried out by Franklin et al. [[3], [4], [5]], who developed a “brick model” that employs a formulation based on the incremental plasticity by ratcheting within a number of sections (or bricks) within a cross section through a rail. If the bricks reach their critical shear strain, they are considered to fail and are marked as weak. Franklin et al. designed many patterns of weak and non-failed healthy bricks as scenarios in which a brick might be removed. Doing so can indicate situations in which bricks either are removed at the surface as wear debris or form crack-like defects inside the rail.

Burstow [[6], [7], [8]] developed a “whole life rail model” that considers the competition between RCF crack propagation and wear in a rail. In this model, he proposed a “damage function” that describes the relationship between the wear number Tγ and the RCF crack initiation fatigue damage, where T is the shear force and γ is the creepage at the wheel–rail interface. The damage function comprises four regions: (i) a threshold below which RCF damage does not occur, (ii) a region where RCF damage linearly increases, (iii) the amount of damage falls as wear increases, and (iv) a region where damaged material is entirely removed by wear.

Mazzù [[9], [10], [11]] proposed an integrated model that considers multiple interacting damage mechanisms in railway wheels. The procedure is based on models for wear, cyclic plasticity, and surface and subsurface fatigue cracks, all integrated in an algorithm that exchanges input and output data between each failure model. The wear is assessed by means of the Archard model of adhesive wear. The cracks are evaluated by means of linear elastic fracture mechanics (LEFM) terms such as stress intensity factors (SIFs), threshold SIFs, and a Paris-type law.

Karttunen et al. [12,13] provided an engineering “meta-model” to predict gauge corner and flange root degradation concerning RCF and wear from measured rail, wheel, and track geometries. The RCF impact is quantified by a shakedown based dimensionless “fatigue index” (FI) [14]. Deterioration due to wear is quantified using Tγ.

Dirks and Enblom [15] introduced a model that can predict both wear and RCF of railway wheels and rails. Two existing RCF prediction models were analyzed and compared in a parametric study, the first being an FI model and the other being a “damage function” model. For the wear model, the Archard model was applied.

Bevan et al. [16] developed a damage model to predict the deterioration rate of a wheel tread in terms of wear and RCF damage. This model uses a description of a fleet's route diagram to characterize the duty cycle of the vehicle. Using this duty cycle and a combination of the Archard and Tγ damage models, many vehicle dynamics simulations were conducted to calculate the wheel and rail contact forces and predict the formation of wear and RCF damage.

Brouzoulis [17] presented a two-dimensional (2D) finite element (FE) model to simulate the growth of a single RCF crack in a rail. This model accounts for wear and allows crack curving. The Archard wear model was adopted along with a Paris-type crack propagation law whose crack driving force is based on the concept of material forces.

Jun et al. [18] studied the minimum size at which a crack would grow in a rail, which being defined as the size of the smallest crack that grew fast enough to stay ahead of removal by wear and periodic grinding. They used the Archard wear model and the “2.5D” fatigue crack growth model developed by Fletcher and Kapoor [19].

Trummer et al. [20] developed a predictive model for RCF crack initiation at the surface of rails and wheels, referred to as the “wedge model.” In this “wedge model”, both surface RCF crack initiation and delamination wear are deemed to be governed by the growth of the microscopic cracks in a severely shear deformed layer near the surface.

Hiensch and Steenbergen [21] extended the concept of a “damage function” from a conventional rail to a premium pearlite rail. This was done both by simulating the dynamic train–track interaction and by using field observations. Values of the RCF damage index were established for the rails, describing the behavior of the associated “damage function.”

Akama et al. [22] developed a numerical simulation model to study the competition between RCF-initiated short crack propagation and wear in a carbon steel having ferrite–pearlite structure under the RCF conditions. The crack is assumed to initiate when the total accumulated plastic shear strain reaches the critical value. In the early crack growth simulations, the two-stage short crack growth model proposed by Hobson is applied. With regard to wear, the Archard model is adopted as the basis. The model was applied to the railhead of the actual Shinkansen site, and the behavior of each function was confirmed.

Herein, we use the developed model to study the competition between the RCF-initiated crack propagation and the wear in a railway wheel tread. Further, we have added to the model a new function to the model that accounts for the crack initiation caused because of the MnS present inside the steel. None of the aforementioned references considered the initiation of cracks from non-metallic inclusions even though several cracks are observed to be initiated from them. We begin by applying the model to the results of twin disc fatigue tests to assess its capabilities and accuracy. Further, we apply it to obtain the realistic stress, strain, and slip-velocity states associated with the wheel tread. Finally, based on the twin disc fatigue tests, we study the manner in which reversing the wheel rolling direction affects the crack propagation and wear. This effect cannot be ignored because majority of the trains operate as a shuttle service; however, this important subject has not yet been addressed in the references.