A numerical study on effects of friction-induced thermal load for rail under varied wheel slip conditions

Abstract

A finite element-based simulation was carried out to investigate the effects of friction-induced thermal load on rail under varied wheel slip conditions. The surface temperature rise from six different percentage slips (1%, 1.5%, 2%, 5%, 8.5%, and 10%) at the contact interface was examined for eight-wheel pass. The residual stresses and accumulated plastic strains evolved by the effect of localized temperature rise are estimated. Analytical formulation for conduction mode of heat transfer at the contact patch is used to estimate the temperature distribution. The interaction of thermal-elastic-plastic field conditions is obtained by a proposed simulation model. This is implemented in commercial finite element software ANSYS 14.0. In order to capture the steep thermal gradient beneath the contact surface, refined mesh is used in the upper layers up to a depth of 2 mm of the simulation domain. For better manifestation of thermally affected material layers, a temperature dependent bilinear-kinematic hardening material condition is applied. Results indicate the maximum temperature rise at about 0.6a from the trailing end in the contact ellipse of semi-major axis a. At higher slippage conditions the initial pearlitic rail steel gets converted to martensite which is often observed on rail surface as white etching layer known to be associated with rolling contact fatigue. The study reveals the mechanisms of thermally induced defects observable on rail surface. The outcomes, in addition, can provide useful information for the development of thermo-mechanically superior rail steels.

Keywords

Rail–wheel contact slip frictional heat thermal softening martensite formation rolling contact fatigue

1. Introduction

The rail–wheel system operation utilizes friction to transmit power. These friction/traction forces generate heat due to changes in relative slip between the contacting wheel–rail surfaces. Rise in temperature over the contact region is of critical importance to understand the accompanying queries. It can lead to material softening,¹ together with deterioration of rail–wheel profiles by promoting plastic flow in the material.² This may help initiate crack and subsequent propagation in either of the contacting elements.^3–5 Often wheel slip protection systems are used to control the available traction and minimize slippage. Variation in speed and braking schedule are common the in rail-operation process. All these cause changes in the contact stress distribution. Further, variations in environmental conditions and track irregularities make the involved contact phenomenon more complex. Slip between wheel and rail for even a fraction of a second can intensify heat at the tiny rail–wheel material volume surrounding the touching region to several hundred degrees. Existing conditions develop a thermal state sufficient to produce observable damage on the rail in the form of rail burn, white etching layer (WEL), etc. These are localized metallurgical transformations over a small material volume. With the progress of time and subsequent rail-pass this damage gives rise to easy crack formation or corrosion cracking (see Figures 1 –3). The presence of such damage endangers the safety of the transport system in particular. Thus, it is imperative to study the effect of thermal load, arising from variation in train speed, braking, and traction modifications, on rail material response.

Figure 1.

Rail edge damage due to thermal softening and accumulated material due to plastic flow at field end. Snapshot taken from around Dhanbad, India.

Figure 2.

Rail surface damage due to martensite formation and disintegration by corrosion crack propagation. Snapshot taken from around Dhanbad, India.

Figure 3.

Rail burn at higher slippage. Snapshot taken from around Dhanbad, India.

A result of axle load transfer from wheel to rail is local elastic deformation over an elliptical area of contact. This contact zone embodies the stick and slip regions evolved from the velocity difference of the touching elements, shown in Figure 4. In the leading part of the contact ellipse forms the stick/adhesion zone while slip region appears at the trailing end. This slippage (occurring at the trailing end of the contact ellipse) is interchangeably called creepage or microslippage. Under varying traction and braking conditions microslippage occurs. In effect this increases the temperature of the dynamic wheel–rail contact interface by several 100 degrees kelvin.⁶ The slip frequency increases significantly in the event of wheel lockup, hunting oscillations and in negotiating curved track/rail. With the increase in tractive force, the slip region increases reducing thereby the stick region. This results in a rolling-sliding contact condition. Once the tractive force reaches its saturation value, the stick region disappears, and the entire contact area turns into a state of pure sliding. Slippage variation at the wheel–rail interface increases due to improper track gradients, wrong driving practices (impulsive acceleration and braking), insufficient locomotive/traction power, and by contamination of the rail surface (like, oil, dust, dead leaves, etc.). All these can unfavorably reduce the available friction to an undesirable level that promotes skidding.

Figure 4.

Rail–wheel contact mechanics showing contact zone, distribution of pressure, and shear stress over stick-slip region.

Moderate heat generation, evolved from the microslippage, in presence of a high-strain rate, induced by instantaneous increase in traction, often leads to the formation of shiny white surface on rail head popularly known as WEL.⁷ Sudden braking raises the interface temperature impulsively to cause metallurgical transformation of the upper layer of rail head material’s microstructure, effective only to a film depth, from initial pearlite to martensite. The initial pearlite steel austenitizes at a favorable temperature to form a face centered cubic crystal structure that on rapid quenching further transforms to hard martensite of body centered tetragonal (BCT) crystal structure.⁸ WEL is a martensite layer. During this conversion in the contact patch material, a volume expansion of about 0.5% is observed that induce residual tensile thermal stresses.⁹ These residual thermal stresses in combination with rolling contact load cycle can promote crack initiation in hard and brittle martensite.

Heat transfer at the dynamic wheel–rail contact interface is an instantaneous process. It is, therefore, difficult to capture the value of the instantaneous temperature rise of the dynamic wheel–rail interface through any conventional experimental process. Progress on estimation of frictional heating by rubbing surfaces has a long history. The surface heat accumulation by sliding may easily be transferred by conduction into sliding bodies one being almost at ambient temperature. This effect has been studied by many researchers using analytical and numerical methods.^6,10–16 The problem of temperature rise due to sliding contact was pioneered by Jaeger and coworkers and by Blok.^17–20 Jaeger stated his theory on the frictional heating from rubbing surfaces, assuming that steady-state temperatures are achieved rapidly in the slider and most of the heat generated enter the stationary half of the contacting surfaces. Blok proposed highest temperature to develop at the sliding interface and specified it as flash temperature. The mathematical formulation with minor modifications is used to date to tackle contact (wheel–rail) problems.^17–20 A detailed review in this respect was provided by Srivastava et al.²¹

Tanvir approximated a fast moving heat source as an instantaneous static source and estimated the rise in temperature due to wheel slip on rail using the Laplace transform method.⁶ Knothe and Liebelt analyzed contact temperatures for components in relative sliding motion combining Laplace transforms and Green’s function methods.²² They identified that thermal stresses greatly affect the shakedown limit, expressed as the maximum contact pressure P_o at the onset of yielding in the presence of residual stresses in wheel–rail contact. Fischer et al.,²³ who extended the work of Knothe and Liebelt,²² presented thermal stresses for frictional contact in wheel–rail systems. Ahlström and Karlsson described a one-dimensional analytical model of heat conduction for the thermally affected zone formed during railway wheel skid.¹² Sawley estimated the temperature developed in the sliding wheel and discussed the consequences of the rate of change of temperature on metallurgical means of avoiding spall type defect formation.²⁴ Gupta et al. used the finite element method to estimate the frictional heat across the contact patch for different combinations of creep and adhesion.¹³ Widiyarta et al. proposed a computer model to simulate and predict wear and crack initiation in rails induced by thermal effects leading to ratchetting failure.¹⁶ They predict frictional heating to increase the rate of damage accumulation by ratchetting.

The presence of damaged rails, caused by thermal stress, imparts noise, premature rail replacement, enhances the possibility of damage on wheels rolling on it, and has the potential to cause derailment. Thus, an assessment of the thermal response of rail material induced by variation in microslippage incorporated by different wheel slip percentage promises to be a very important way to understand different damage mechanisms occurring at the rail surface. An analytical solution limits its applicability only for idealized geometry and material parameters. Numerical simulation, on the other hand, is more versatile than analytical methods in terms of adaptability of varying material properties and wheel–rail geometry combinations. In this paper, a two-dimensional thermo-elasto-plastic finite element model of a rail section is used in the ANSYS 14.0 platform to simulate the problem. Six different slip percentages and up to eight wheel-pass conditions are considered to determine their effect on temperature distribution across the contact zone of rail section, residual thermal stress distribution, and the accumulated plastic strain developed therein.

The main objective of this study is to explore and expose the influence of thermal load in developing rail-surface damages and their possible range of penetration. The results from this study clarify the influence of slip percentage on temperature rise, thermal stress, and strain accumulation that will help to decide strategies for minimizing rail surface damage states. It may also be used to design contact surface materials to minimize maintenance and operating hazards on the basis of layers of materials being influenced by thermal effects.

2. Numerical modeling

The actual wheel–rail contact condition involves several loads acting simultaneously. These are dynamic load, impulsive load, together with traction and frictional load. These load systems are responsible for defect evolution mechanisms like material transformation, thermal softening, plastic deformation, and crack initiation and its propagation. The present study focuses on the effects of frictional heat introduced by varying slip percentages, thereby increasing the temperature level. Wheel slippage varies with the contact patch size, speed, curve tracking, and braking. This is the major source of temperature rise-induced thermal stresses in rail material. In the section to follow the analytical method for calculation of temperature rise is discussed. This formulation is used later for the finite element model validation.

2.1 Analytical method for calculating the temperature rise at the wheel–rail contact

Estimation of temperature rise in the contact region is an essential component in formulating the thermal stress evolved from microslippage. The major source of heat, in general, is considered to be the wheel temperature attained from a brake application condition and sink is the rail stock at ambient temperature. During rolling-sliding condition, on the other hand, the friction coefficient varies according to stick-slip zone distribution present. This, in turn, raises the temperature of the contact interface. The rail–wheel functional pattern introduces the contact dynamics that directs the heat transfer condition to be predominantly in conduction mode. Accordingly, the general heat transfer equation is used to govern the temperature field estimation in wheel–rail contact:

κ \frac{\partial^{2} T}{\partial x^{2}} + κ \frac{\partial^{2} T}{\partial y^{2}} + κ \frac{\partial^{2} T}{\partial z^{2}} = \frac{\partial T}{\partial t}

(1)

where x, y, z, and t are the spatial coordinates, T is temperature, and $κ$ is thermal diffusivity.

The wheel remains in contact with a location on the rail surface for a very short span of time. Frictional heat generated at the contact interface acts as a fast-moving heat source and the heat transfer is able only to affect a very thin layer of rail surface material. The thickness of the affected zone, termed as thermal penetration depth (δ), depends on the semi contact length (a) and the non-dimensional Peclet number (P_e) and is defined as follows:

δ = \frac{a}{\sqrt{P_{e}}}

(2)

The Peclet number is a function of the wheel/forward velocity (V) and the thermal diffusivity, $κ$ .¹⁰ Thermal diffusivity has embedded effects of material properties like thermal conductivity, λ, density, ρ, and specific heat capacity, c:

P_{e} = \frac{aV}{2 κ}; κ = \frac{λ}{ρ c}

(3)

Ertz and Knothe suggested that for $P_{e} > 10$ ,¹⁰ the heat conduction occurs only in a direction perpendicular to the contact plane, i.e., along the depth (z-direction) of rail. An operating speed of 90 km/h with an axle load of 17 ton (166.7 kN) is considered in this paper. This evaluates the magnitude of P_e to be 5142, much greater than the suggested threshold value of 10. Accordingly, the heat conduction in longitudinal (x) and lateral (y) directions can be neglected. This reduces Equation (1) to:

κ \frac{\partial^{2} T}{\partial z^{2}} = \frac{\partial T}{\partial t}

(4)

This second-order partial differential equation specifies the temperature to change with rail depth and time. A review of literature by the authors indicates that different methodologies can be adopted to solve this equation.²¹ The approach of Ertz and Knothe for temperature estimation arising from pressure distribution on smooth surfaces is considered in this study and discussed here briefly.¹⁰ The model follows a modified heat transfer relation given by Carslaw and Jaeger.^17,18 The frictional contact pressure problem is treated to be a semi-infinite solid subjected to a moving heat source q(t) applied at a reference point on the surface, z = 0 at t≥ 0. The initial and boundary conditions for the Fourier heat conduction Equation (4) are as follows:

T (z, t = 0) = 0

(5)

- λ \frac{\partial T}{\partial z} (z = 0, t) = q (t)

(6)

The general solution of Equation (4), shown by Carslaw and Jaeger,¹⁷ is:

T = \frac{1}{β_{r} \sqrt{π}} \int_{0}^{t} q (t - t') \exp (- \frac{z^{2}}{4 κ t'}) \frac{dt'}{\sqrt{t'}}

(7)

Ertz and Knothe modified this solution by introducing non-dimensional contact patch coordinates $ξ = \frac{x}{a}$ , $ζ = \frac{z}{δ}$ ,¹⁰ shown in Figure 5, which changes the temperature distribution relation in Equation (7) to:

T_{w, r} (ξ, ζ) = \frac{1}{β_{r}} \sqrt{\frac{a}{π V}} \int_{- 1}^{ξ} q_{r} (ξ') \exp (- \frac{ζ^{2}}{2 (ξ - ξ')}) \frac{d ξ'}{\sqrt{ξ - ξ'}}

(8)

Figure 5.

Non-dimensional coordinate system.

The analytical solution for this integral equation with constant heat flow rate q_r at the rail surface ( $ζ = 0$ ) within the contact patch (i.e., $- 1 \leq ξ \leq 1$ ) is given as follows¹⁰:

T_{r} (ξ) = \frac{2 q_{r}}{β_{r}} \sqrt{\frac{a}{π V}} \sqrt{ξ + 1}

(9)

The result from this relation is used to validate the proposed finite element model.

3. Heat flux calculation

Hertzian contact theory, developed by Heinrich Hertz in 1882, considers two elastic nonconforming bodies. If pressed together the contact area assumes an elliptical shape with a semi-major axis a and semi-minor axis b. Similar is the condition in a rail–wheel contact.²⁵ The distribution of the contact pressure in this elliptical contact area is as follows:

P (x, y) = P_{o} \sqrt{1 - \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}}}

(10)

In the above, $P_{o}$ is the maximum pressure occurring at the center of the elliptical area (shown in Figure 6(a)):

P_{o} = \frac{3 F}{2 π ab}

(11)

where F is the axle load. The semi-axes a and b can be obtained from the following:

a = m {[\frac{3 π}{4} \frac{F (K_{1} + K_{2})}{(A + B)}]}^{1 / 3}

(12)

b = n {[\frac{3 π}{4} \frac{F (K_{1} + K_{2})}{(A + B)}]}^{1 / 3}

(13)

where K₁ and K₂ are constants given by $K_{1} = \frac{1 - ν_{1}^{2}}{π E_{1}}$ and $K_{2} = \frac{1 - ν_{2}^{2}}{π E_{2}}$ , where ν₁, ν₂ are Poisson’s ratios and E₁, E₂ are Young’s moduli of respective bodies. The m and n are Hertzian coefficients obtained by regression analysis.²⁶A and B are the geometrical constants depending on the principal relative radii of wheel and rail profile curvatures. The detailed derivation can be found in the literature.^26,27 By Coulomb’s law of friction, the interfacial shear stress distribution is given by:

τ_{zx} (x, y) = μ P (x, y)

(14)

where µ is the coefficient of friction. During pure sliding condition, the heat flux rate $(\overset{\cdot}{q} (x, y))$ within the contact patch is proportional to the product of pressure ( $P (x, y)$ ), coefficient of friction (µ), and the sliding velocity ( $V_{s}$ ). This is given by:

\overset{\cdot}{q} (x, y) = μ V_{s} P (x, y)

(15)

Figure 6.

(a) Three-dimensional contact pressure distribution on Hertzian elliptical contact patch. (b) Simplified two-dimensional rail simulation domain taken from the middle of the rail section along the line of contact.

The nature and distribution of the evolved heat and the temperature fields at the interface are to satisfy thermodynamic equilibrium. For this, a heat partition factor, suggested previously,²¹ is introduced to maintain the continuity of temperature and conservation of heat fluxes between the wheel and rail surfaces. In the present model, a constant heat partition factor ( $ε$ ) is taken as 0.5. Then the heat flux distribution in wheel ( $q_{w})$ and in rail ( $q_{r}$ ) can be written as follows:

q_{w} = ε \overset{\cdot}{q} (x, y)

(16)

q_{r} = (1 - ε) \overset{\cdot}{q} (x, y)

(17)

while the total heat flux is given by:

q = q_{w} + q_{r}

(18)

4. Finite element model

Simulation of thermal effect due to percentage slip variation at wheel–rail contact is carried out for a 105 mm long rail segment. For all computations, vehicle running at a speed (V) of 90 km/h is considered. The semi-major axis (7.32 mm) of the contact stress ellipse is obtained from Hertz contact theory. Sequentially coupled thermal–structural stress analysis is adopted to obtain temperature field and associated thermal stresses across the wheel–rail contact interface by the model, as shown in Figure 7.

Figure 7.

Finite element analysis model for the current simulation using ANSYS 14.0.

The heat flux distribution along the contact patch, shown in Figure 6(b), is translated on the rail surface for eight wheel passes. Rail surface other than the contact patch is subjected to convection mode of heat transfer. The heat transfer coefficient $h_{c}$ is chosen to be 12 W/ $m^{2} K$ ,²⁸ while the ambient temperature is 30°C. Heat flux distribution is assumed to be parabolic in shape. Commercial finite element software ANSYS 14.0 is used for the current investigation. For transient thermal analysis, the simulation domain is meshed with Plane 77 to obtain the temperature field. This element is defined by eight nodes having one degree of freedom, i.e., temperature, at each node. For transient structural analysis Plane 183 element is used to get the thermal stress and strain fields. This element is defined by eight nodes having two degrees of freedom at each node: translation in the nodal x and z direction. A refined mesh, shown in Figure 8, is used for the upper layers up to a depth of 2 mm in the simulation domain. This helps to capture the results more accurately within the objective depth. The smallest element size used in the mesh model is of 0.053 mm along depth and 1mm along the length. To reduce the simulation time, regions below the finer mesh are taken gradually coarser along the depth. In order to stabilize the targeted results the depth of the simulation domain is set to four times the semi contact length.²⁹ The finite element model includes 5140 elements with 15,695 nodes after proper convergence study.

Figure 8.

Two-dimensional finite element model for the problem domain.

5. Material model

A bilinear kinematic hardening material law is applied to simulate plasticity effect in the rail material.³⁰ For completeness of the presentation, the mechanics involved is briefly stated. The yield criterion has the form:

F (\bar{σ}) - σ_{y} = 0

(19)

where $F (\bar{σ})$ is a scalar function of the relative stress $\bar{σ}$ and $σ_{y}$ is the yield stress. The relative stress is given by:

\bar{σ} = σ - α

(20)

where the backstress $α$ is the shift in the center location of the yield surface in stress space and evolves during plastic deformation shown in Figure 9. Backstress is proportional to shift strain, $ε^{sh}$ , given by:

α = 2 G ε^{sh}

(21)

where G is elastic shear modulus and the shift strain is numerically integrated from the incremental plastic strain:

d ε^{sh} = \frac{C}{2 G} d ε^{pl}, where, C = \frac{2}{3} \frac{E E_{T}}{E - E_{T}}

(22)

Here E is Young’s modulus and E_T is the kinematic hardening parameter (also called tangent modulus or hardening modulus). The evolution of plastic strain can then be determined by the plastic flow rule:

d ε^{pl} = d γ \frac{\partial Q}{\partial σ}

(23)

where $d γ$ is the magnitude of the plastic strain increment and Q is the plastic potential.

Figure 9.

Stress–strain behavior of bilinear kinematic hardening material model.

This material condition is used in the finite element model. Temperature-dependent thermal and mechanical properties are used for the rail material and the same are given in Tables 1 and 2, respectively.

Table 1.

Thermal properties of rail material.^31,32

Temperature,T (°C)	Specific heat,C (J/kg °C)	Thermal conductivity,λ (W/m °C)
0	419.5	59.71
350	629.5	40.88
703	744.5	30.21
704	652.9	30.18
710	653.2	30.00
800	657.7	25.00
950	665.2	27.05
1200	677.3	30.46

Table 2.

Mechanical properties of rail material.^31,32

Temperature (°C)	Young’smodulus(GPa)	Poisson’sratio	Yield strength, $σ_{y}$ (MPa)	Coefficient of thermalexpansion,α, (× $1 0^{- 6} C^{- 1}$ )	Kinematic hardeningparameter, $E_{T}$ (GPa)
24	213	0.295	483	9.89	22.7
230	201	0.307	485.1	10.82	26.9
358	193	0.314	418.8	11.15	21.3
452	172	0.320	332.4	11.27	15.6
567	102	0.326	151.1	11.31	6.2
704	50	0.334	45.0	11.28	1.0
900	43	0.345	13.4	11.25	0.1

6. Simulation cases

In order to simulate the contact conditions, six different slip rates are applied. The positions of the axles are shown in Figure 10. To obtain a more realistic manifestation of desired outputs, the frequency of loading over a contact region is applied in correspondence with wheel locations in Figure 10. The input parameters applied in the simulation are given in Table 3.

Figure 10.

Schematic drawing for axle distance of the wagon used in the simulation.

Table 3.

Parameters used.³³

Parameters	Symbol	Value	Unit
Wagon wheel diameter	D	0.915	m
Wagon tonnage per axle	M	17	tons
Semi axes rail–wheel contact ellipse	a, b	7.32^†, 3.61^†	mm
Normal maximumcontact pressure	$P_{0}$	1510^†	MPa
Ambient temperature	T_o	30	°C
Heat partition factor	ε	0.5	-
Environment	-	Dry	-
Train forward speed	V	90	km/h
Axle bogie distance	L	1830	mm

Magnitudes with superscript ‘†’ are evaluated from appropriate relations.

The friction coefficient and wheel sliding velocity acting along with the contact pressure (arising from axle load) produces the heat flux. This dynamic heat flux moves with contact location. Its schematic illustration is demonstrated in Figure 11 for a single wheel pass.

Figure 11.

Schematic representation of wheel passes.

This flux is treated as frictional load over the contact patch. The wheel running condition is simulated by repeatedly translating the heat flux on rail surface from left to right of the domain shown in Figure 11. Traction/friction coefficients for six different slip percentages are taken from the literature.³³ Sliding velocities are calculated for the chosen six slip percentages. The parameters used in six simulation cases are presented in Table 4.

Table 4.

Simulation cases.

Case	Percentageslip	Tractioncoefficient, µ^33,34	Sliding velocity, $V_{s}$ (m/s)
1	1	0.3875	0.2502
2	1.5	0.42	0.375
3	2	0.4	0.5
4	5	0.38	1.25
5	8.5	0.38	2.125
6	10	0.38	2.5

7. Model validation

The mesh density in contact region is found to have a direct influence on the accuracy of the solution.³⁵ In an earlier study by the authors,²⁶ it was observed that for 1 mm element size in the contact zone, the numerical results could replicate the contact pressure distribution obtained from Hertzian contact theory. In order to re-affirm the analysis of the contact region, mesh with an element size of 1 mm (in the longitudinal direction) is chosen. The maximum temperature obtained from present FEA simulation compares well with the results from analytical model of Ertz and Knothe,¹⁰ thus validates our FEA model. These authors categorically commented that for transient thermal analysis, finite element solutions are more reliable. The results are presented in Table 5.

Table 5.

Comparison of maximum temperature obtained through the analytical model and present finite element model.

Slippage (%)	Present FEAsimulation (°C)	Analytical modelresult (°C)	Difference inthe result (%)
1.00	147.66	137.0521	7.183995
1.50	222.22	222.6421	−0.18994
2.00	275.09	282.7201	−2.77368
5.00	633.4	671.4603	−6.00889
8.50	1120.6	1141.482	−1.86351
10.00	1390.3	1342.921	3.407856

8. Results and discussion

In order to estimate the effect of slippage on temperature rise and its effect on residual thermal stress and plastic strain a numerical simulation of the wheel–rail contact conditions are presented. A thermal-elastic-plastic finite element model is proposed for evaluation. Firstly, transient temperature field is obtained for various percentage slip conditions. Then this temperature field is used for the calculation of thermal strains and thermal stresses. Results are presented graphically to view their intensity variations along the contact patch and the rail depth represented in Figure 6(b). The temperature distribution along the depth for six different slip percentages for an instantaneous contact patch is shown in Figure 12(a) to (f). Noticeably, the maximum temperature occurs at higher slip percentage. The location of maximum heat flux is at the center of the contact ellipse, specified by ξ = 0. The leading edge and trailing edge of the ellipse are at ξ = −1 and ξ = 1, respectively. The peak temperatures are found at just prior to the trailing edge (around at ξ = 0.66) of the contact surface. After first wheel pass, the rail temperature does not reduce to the initial rail temperature. Accordingly, the residual heat accumulates by adding heat produced by succeeding wheel passes. This results in incremental temperature rise in the rail material. Residual temperature distribution across the rail depth after eight wheel passes for different slip rates is shown in Figure 13. It is observable that percentage slip variations do not produce any change in temperature distribution in rail section depth beyond 15mm. However, with higher slip rates specifically beyond 5% cognizable stiffer temperature gradient can be noticed up to 15 mm of rail depth.

Figure 12.

Temperature distribution along the contact patch at different depths for different slip percentages: (a) slip rate = 1%; (b) slip rate = 1.5%; (c) slip rate = 2%; (d) slip rate = 5%; (e) slip rate = 8.5%; (f) slip rate = 10%.

Figure 13.

Residual temperature after eight wheel passes along the rail depth for different slip rates.

The layer material temperature once reaches 500°C, as can be seen in Figure 12(d)–(f), and for percentage slip above 5%, the thermal softening phenomenon initiates. This occurs by spheroidization of the cementite phase existing in initial pearlitic structure as lamellar cementite.¹ Spheroidization is also activated by plastic deformation in high-temperature surrounding. Thermal softening favors plastic flow of material and also brings in a reduction in fatigue life of rail material.¹

Figure 14 describes the residual effective plastic strain variation with the depth of the rail material after eight-wheel pass. Since the attained temperatures are more for higher slip rates (5%, 8.5%, and 10%) in regions close to rail surface, the effective plastic strains are also higher for these instances eased by thermal softening of the material. The variations of the effective plastic strain at the rail surface with the increase in wheel passes number for different slip rates are given in Figure 15. This clarifies that the accumulation of plastic strain at the rail surface does not change significantly for a given slip rate and up to eight number of wheel passes considered in this study.

Figure 14.

Variation of residual equivalent plastic strains along the rail depth for different slip rates.

Figure 15.

Variation of equivalent plastic strain at rail surface with increasing wheel passes for different slip rates.

Figure 12(e) and (f) correspond to the evolution of maximum temperatures crossing rail material’s lower critical temperature of 723°C for 8.5% and 10% slip rates. At such high temperatures, initial pearlitic rail material transforms to martensite with a BCT crystal structure,⁸ which is naturally hard and brittle. During this transformation in the contact patch, about 0.5% volume expansion is observed that induce residual stresses.⁹ These residual stresses in combination with rolling contact loading cycle promote crack initiation in hard and brittle martensite. Figures 16 and 17 describe the variation of residual von Mises stresses, along the rail depth, arising from the thermal effects caused by different slip rates after eight wheel passes. These figures indicate that for slip rates up to 2%, the location of maximum von Mises stress occurs at a depth of about 0.1 mm. For higher slip rates (5%, 8.5%, 10%), the location of maximum von Mises stress shifts to a deeper zone of around 0.2 mm. The position and level of von Mises stress signify the onset of plastic flow or condition of material’s ability to resist any crack initiation. Due to higher stress at these locations of rail surfaces, these sites are more prone to crack initiation.

Figure 16.

Variation of residual von Mises stresses along the rail depth for lower slip rates (1%, 1.5%, and 2%).

Figure 17.

Variation of residual von Mises stresses along the rail depth for higher slip rates (5%, 8.5%, and 10%).

9. Conclusions

Two-dimensional transient thermal and elastic–plastic finite element analysis based solutions are provided to examine the effect of frictional heat generated by change in slip percentage at the dynamic wheel–rail contact interface. Six different slip percentages (1%, 1.5%, 2%, 5%, 8.5%, and 10%) are considered to illustrate their influence in terms of temperature rise, residual thermal stress and plastic strain on the surface and subsurface of the rail material. Surface temperatures of several hundred degrees Celsius are observed. Results indicate that the heat penetration below the surface is shallow and the thermal gradients are steep up to 15 mm. The incremental growth in temperature rise with each rolling pass of the wheel on rail causes thermal softening and hence fosters plastic flow of rail surface material. For higher slip rates, the temperature rises beyond the lower critical temperature. This promotes microstructural transformation of the rail material to martensite formation at outer layer interchangeably stated as WEL. Percentage slip variation is significantly high at curved segments of rail. For reducing wear from wheel–rail flange contact appropriate lubricants are necessary. This study can guide in selection of lubricants to sustain thermal loads. Rail surface damage characterization from friction induced thermal load can be studied in succession. The findings of this research may also help railway operators and maintenance engineers to estimate a priori the thickness of damage on the rail surface and the depth of grinding needed to eliminate it. The study is limited by a specified number of wheel passes considered in the analysis.

Footnotes

Appendix 1 Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Author biographies

Jay Prakash Srivastava is an Assistant Professor at the S R Engineering College, Warangal, India. He received his PhD in Mechanical Engineering from the Indian Institute of Technology (ISM) Dhanbad, India. His doctoral research was based on Modelling and simulation of rail material response under rolling-sliding contact. His research interests are in rolling contact fatigue in railways, rail-wheel interface and its contact mechanics. Jay Prakash is also interested in associated phenomena like residual stresses, phase transformations, fatigue and fracture of rail materials. The research aims to create knowledge to improve the railway system integrity, their reliability, reduce maintenance costs, and extend better safety with comfort.

Prabir Kumar Sarkar is a Professor at the Indian Institute of Technology (ISM) Dhanbad in the Department of Mechanical Engineering and up to April 2020, was Reader at the Mechanical Engineering Department of IIT, Banaras Hindu University, Varanasi, India.

M V Ravi Kiran had completed his M.Tech from IIT(ISM), Dhanbad, India. Presently, he is working as Sr. Engineer (Mechanical Design), Tata Power SED, Bangalore. He is engaged in design and development of Missile Launchers. His research areas include: rail wheel contact dynamics and electro mechanical load transfer systems.

Vinayak Ranjan received his PhD in Mechanical Engineering from IIT (BHU) Varanasi, India in 2006. He is Professor and Head, Department of Mechanical and Aerospace Engineering, Bennett University, Greater Noida, India. His current research interests include vibro-acoustic behavior of plate structures, finite element analysis, biomechanics, structural optimization and wheel rail contact modelling.

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