A Study Into Crack Growth in a Railway Wheel Under Thermal Stop Brake Loading Spectrum

Stop brakingised FrostDugdale approach has been used to modelling thermal fatigue crack growth.

2012 Elsevier Ltd. All rights reserved.

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induced at the running surface. According to Moyar and Stone, no fatigue damage is induced at the surface during free run-ning of a cold wheel. When the brakes are applied and the temperature rises, the fatigue strength of the material drops. Also,the induced shear stress range and maximum normal stress are increased. This will increase the fatigue damage. Accordingto their paper, the thermal cycles play a fundamental role in crack nucleation and in the growth of the crack until the thresh-old value of the equivalent stress intensity factor is reached. Also, thermal cycles play an important role in the generation of

1350-6307/$ - see front matter 2012 Elsevier Ltd. All rights reserved.

Corresponding author.E-mail address: [email protected] (D. Peng).

Engineering Failure Analysis 25 (2012) 280290

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Engineering Failure Analysishttp://dx.doi.org/10.1016/j.engfailanal.2012.05.018gradually over the wheel rim and plate, depending on the intensity of the heating source [1,2]. The stresses experienced bythe railway wheel during service are due to mechanical and thermal loads.

Rail wheel failures in service have been reported by Michael and Sehitoglu [3], Stone and Carpenter [4], Sakamoto andHirakawa [5], Kwon et al. [6] and Ramanan et al. [7]. The fatigue life of wheel treads has a strong bearing on the economyand safety of rail transportation. An understanding of fatigue mechanisms and a prediction of lifetimes are of interest to bothmanufacturers and operators. The thermal damage caused by braking can be classied into two major categories damagefrom the thermal input distributed around the circumference of the tread from friction during on-tread braking, and thatassociated with the extreme, thermal input that occurs locally between wheels and rails during skids caused by wheelslocking.

Moyar and Stone [8,9] used a multiaxial fatigue criterion developed by Fatemi and Socie [10] to quantify fatigue damageNonlinear stress analysisStress intensity factorFatigue crack growth

1. Introduction

Railway wheels, used in freight seThermal loading has various types, bquite commonly braked by using blotread braking, heat generated by fric, perform three functions: support the cars, steer the cars and serve as brake drums.is generally a product of braking. Railway cars for both passengers and freight aren Australia, which contribute to the thermal load on the rail wheel. During wheell forces is distributed as severe thermal gradients within the near surface or moreA study into crack growth in a railway wheel under thermal stopbrake loading spectrum

D. Peng a,, R. Jones a, T. Constable baCRC for Rail Innovation, Department of Mechanical and Aerospace Engineering, Monash University, P.O. Box 31, Monash University, Victoria 3800, AustraliabAsset Engineering, Operational Excellence, QR National, RC 1-11, 305 Edward Street, Brisbane 4000, Queensland, Australia

a r t i c l e i n f o

Article history:Received 14 November 2011Received in revised form 21 May 2012Accepted 28 May 2012Available online 9 June 2012

Keywords:

a b s t r a c t

This paper provides a method for solving thermal fatigue crack growth in the rail wheelunder stop braking spectrum. The analysis was performed in three stages. In the rst stage,a nite element model of the rail wheel is used for all braking applications. For each appli-cation, a non-linear thermal stress analysis is performed. The second stage of the sequen-tial analysis is carried out to calculate the stress intensity factor of thermal cracks, by usinga semi-analytical solution technique that involves the use of an analytical solution com-bined with a numerical algorithm to assess fracture strength. In the third stage, a general-

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residual stress elds. The same point is also remarked in [11] when thermal loading is the dominant cause of fatigue, theresulting surface cracks tend to be radial. Some tests and experimental studies of hot spotting phenomenon have been re-ported in [12]. In their paper, the damage analysis results based on linear damage rule within braking block have also beenprovided.

A simplied elastic analysis of an idealised braked railcar wheel subjected to periodic brake-shoe thermal shock, railchill and realistic tractive rail contact stresses has been used to demonstrate the important thermal contributions to surfacefatigue cracking using a critical plane fatigue initiation theory [13]. Contact region fatigue of railway wheels under combinedmechanical rolling pressure and thermal loads has been extensively studied by Lunden [14]. This problem has been consid-ered as an axisymmetric model. The mechanical load acting on the wheel was approximated as a time-variant axisymmetricpressure. This pressure was calculated based on the Hertzian contact between the wheel and the rail. The combined mechan-ical and thermal loads are realised in two ways. Specied numbers of mechanical loading cycles are followed by one thermalcycle. Thermal cycles have been applied as disturbances during the execution of a specied mechanical loading programme.However, Lunden [14] has not addressed certain issues in his work. Mechanical load calculations do not account for the lat-eral load that is realised by the wheels due to track irregularities and perturbations. The effect of friction between the wheeland rail during contact and the contact region stress, which promote plastic deformation in the tread surface, have not beenconsidered. Further, the effect of combined thermal and mechanical loads on a three-dimensional model has not been ad-

stress-intensity factors can then be obtained for a variety of cracks using the original nite element analysis quickly and eas-

D. Peng et al. / Engineering Failure Analysis 25 (2012) 280290 281ily. An equivalent block method, based on the Generalised FrostDugdale approach [2639], was used to modelling crackgrowth.

2. Thermal fatigue crack growth model

2.1. Thermal load and stress analysis

During the braking process, the friction generated by the brake-shoe on the moving tread produces a heating rate. Theheat generation at the braking shoe-wheel interface and heat transfer to the rail is shown schematically in Fig. 1. The coef-cient Qwheel(=Qshoe) is the average instantaneous braking (friction) power (kW) and Qrail is indicated the heat into rail fromwheel/rail contact surface.

A spectrum of braking loads that would typically be applied to the wheel will be analysed in this paper over a trip, seeFig. 2. There are 29 applications in this thermal loading spectrum (we have named it spectrum no.1). The further details maybe found in [40].

Rail

Moving

Wheel

Braking shoe

Qrail

QwheelQshoe

Fig. 1. Graphical representation of the rail chill effect.dressed. A fatigue crack propagation prediction models based on fracture mechanics method has been referenced in[15,16]. In these papers, Hertz theory has been used to calculate wheel/rail contact stress eld and an axisymmetric niteelement model has been employed to obtain thermal distribution. A superposition principle [17] has been applied to esti-mate the approximate local maximum stress intensity factor. Then, a cycle by cycle procedure based on Paris law is usedto calculate cracks propagation.

This paper presents the results of a study into methods for estimating the thermal fatigue life of the rail S-shape plate railwheel under braking loading. The thermal crack growth model considered in this approach is focused on the thermal inputdistributed around the circumference of the tread from friction during on-tread braking. This study consists of the followingareas of analysis. For each application in the thermal loading spectrum, a 3D nite element nonlinear transient analysisbased on heat transfer principle has been used for estimating the temperature variation of the rail wheel. The sequentialnonlinear static analysis calculates thermal stress distribution in the rail wheel. A simple and accurate formula [1825]for the stress-intensity factors associated with surface has been employed in the present paper [1825]. Solutions to

approcient

282 D. Peng et al. / Engineering Failure Analysis 25 (2012) 280290applied to the surface, where the area of wheel/rail and wheel/braking shoe is excluded. These temperatures were used tocalculate the resulting thermal stress eld in the wheel following thermal loading.2.2. St

Tha num

Here Klength

A gsented

Whgive ttially)to accximation, the Hertzs theory is used to evaluate contact area [50] in this paper. The rail convection heat transfer coef-is taken from [41,46]. In this approach, the transient cool down with a convection (in the air) boundary condition isAs the wheel rotates, there are heating and cooling periods for the wheel tread. Conduction in the rail wheel itself occursduring wheel tread braking process. The unsteady heat conduction is governed by the equation [41,42]

r2T qcpj

@T@t

_qv 1

In which q = material density, cp = specic heat, j = thermal conductivity _qv = heat generated during the phase transforma-tion from austenite.

As the wheel rotates, there are heating and cooling periods for the wheel tread. The condition of two thermal contactinterfaces of wheelrail and brake-wheel are very complex. Many factors, such as roughness of the surfaces, oxides, lubri-cant, organic material and sand, may cause a nonzero thermal contact (imperfect contact). In this analysis, interface thermalcontact resistance has been ignored and a widely used assumption [8,4348] of perfect thermal contact between the twosurfaces has been accepted. At high Peclet number, the detailed distribution of the fast moving heat sources in the wheeltread is not important. For each application in the thermal spectrum, average braking power load was applied to the treadregion of the wheel around its circumference. The heat source description was based on braking at a constant decelerationrate from initial speed to a full stop. A linear ramp loading pattern is used in non linear transient analysis, similar in [49]. Inthis analysis, a justiable assumption that only 90% of heat generated goes into the railway wheel has been used.

In order to account for the dissipation of thermal heat to the surroundings, a convectional boundary condition is appliedto the surface of the wheel. As the wheel rotates, tread surface is subjected to periodic heating and cooling. A method to ac-count for the cooling inuence from the rail is transformed to convection cooling to the area of wheelrail contact. As a rst

Fig. 2. A spectrum of braking loads.ress intensity factor and crack growth calculation method

e present paper use a semi-analytical solution technique that involves the use of an analytical solution combined witherical algorithm to assess fracture strength.

KI K1I Fe Fs Feeadaq

h i2

1I is the innite body solution developed by Vijayakumar and Atluri [52], ad is constant, q is the local curvature, a is aof the surface elliptical crack; Fe and Fs are the boundary correction factors are taken from Newman and Raju [53].eneralised Frost and Dugdale [54] crack growth law has been used to estimate the surface crack growth. This law pre-in Jones et al. [2639], namely:

da=dN Ca1m=2DKm 3ere C and m are constants. Here it should be noted that da/dN is a function of both a and DK (which when combinedhe crack growth a DK dependence with a correction that makes the crack growth history log-linearly (i.e. exponen-dependent on crack depth). Jones et al. [31] subsequently expanded the generalised Frost and Dugdale law (Eq. (2))ount for R-ratio as follows:

da=dN Ca1n=2 DKgKmax1g n

4

Where C, n and g are constants. Kmax is the maximum value of the stress intensity factor in a block. This formulation hasbeen subsequently supported by measuring the fractal dimension of a wheel specimen supplied by QR National. Here it hasbeen found that the fatigue surface has a fractal dimension D of approximately 1.2. This nding has been further substan-tiated via fractal dimension measurements on cracking, see Fig. 3 and Table 1.

These results are particularly important as they imply that laws based on the Paris based crack growth law are inconsis-tent with the physical processes driving crack growth. The advantage of approaching the problem in this way negates theneed to model the crack explicitly in the nite element model. In this way a crack of any size can be chosen arbitrarily inthe original nite element model. As the crack is not modelled explicitly a coarser mesh can be used minimising the numberof degrees of freedom, and thereby improving analysis time. Solutions to stress-intensity factors can then be obtained for avariety of cracks using the original nite element analysis quickly and easily.

3. FEM model and results analysis

3.1. Mesh, boundary conditions and thermal loads

In this section, two numerical results of a study into methods for estimating the fatigue crack growth in a 920 mm diam-eter rail S-shape plate rail wheel associated with stop braking and drag braking are presented. The inuence on the crack

3.2. Material properties

D. Peng et al. / Engineering Failure Analysis 25 (2012) 280290 283Fig. 3. Location of fractal dimension measurements.In this analysis, the material is assumed to be a high carbon steel wheel AAR grade B. For the initial verication study, thematerial properties are assumed to be equivalent to Microalloyed AAR class B wheel steel and are extracted from [51]. Theroom temperature yield strength of the material is set at 800 MPa, material stiffness at 206 GPa, possions ratio at 0.286 anddensity at 7870 kg/m3. The material thermal properties used are specic heat 490 J/kg C, coefcient of thermal expansion 14 105, thermal conductivity 47.5 W/m C and free convection heat transfer coefcient 25 106 W/C m2.

For the non-linear analysis, the effect of temperature on the stress strain characteristics is considered. The variations ofthe yield strength and the elasticplastic property with temperature have been shown in Fig. 5. The coefcient of thermalexpansion, thermal conductivity and specic heat also varied with temperature.growth in the rail wheel with rail chill effect has been investigated. The half wheel cut face has been constrained to constructthe nite element model. The resultant mesh has 57,980 nine-noded elements and 63,096 nodes (with 189,288 degree offreedom) by using software FEMAP [56], see Fig. 4. A sufcient ne mesh is taken in the vicinity of the wheelrail contactfor putting cool ux to model the rail chill effect. This model uses symmetry boundary conditions in the XY plane. All othersurfaces of the wheel exposed to the atmosphere are considered with convective heat transfer, except for the symmetryboundary condition surface and tread surface.

The thermal load band was 66 mmwide, to reect the use of a brake shoe. In service conditions, a small band of the wheeltread was loaded in short fast repeated cycles. The thermal load corresponds to approximately a gross bogie load of128 tonne.

Table 1Fractal dimension D associated with in-service cracking.

1 2 3 4 5 6 7 8 9 10 11

X 1.194 1.204 1.212 1.167 1.190 1.312 1.342 1.306 1.212 1.202 1.267Y 1.193 1.185 1.286 1.180 1.242 1.323 1.372 1.339 1.179 1.254 1.234

Fig. 4. 3D mesh of the 920 mm rail wheel.

0

100

200

300

400

500

600

700

800

900

200 300 400 500 600 700

Stre

ss (M

Pa)

Temperature (0C)

Yield Strength (MPa)Elastic Modulus (GPa)Plastic Modulus (MPa x 10)

Fig. 5. Variation in stress characteristics over predicted temperature range.

0

20

40

60

80

100

120

140

160

180

200

0 20 40 60 80 100 120 140

Tem

pera

ture

(0C

)

Time (Seconds)

Thermal Transient Analysis LT3LT1LT2LT4LT5LT6LT7LT8LT9LT10LT11LT12LT13LT14LT15LT16LT17LT18LT19LT20LT21

Fig. 6. Maximum tread region temperature of the wheel versus braking time for applications.

284 D. Peng et al. / Engineering Failure Analysis 25 (2012) 280290

D. Peng et al. / Engineering Failure Analysis 25 (2012) 280290 2853.3. Heat transfer transient analysis

The thermal load was applied for a duration time, after which, the temperature variations throughout the wheel werecalculated by using nonlinear transient analysis [57]. The ambient temperature was set at 25 C.

The temperature distribution on the tread throughout the wheel of the current model in different braking time wasshown in Fig. 6. Note that there are eight applications were not included in Fig. 6 as those applications may have a littereffect on the life calculation. Two meshes, with 189,288 (mesh 1) and 729,534 (mesh 2) degree of freedom respectively, wereemployed to check the convergence of the rail wheel temperature under thermal load results. The maximum difference be-tween those meshes for the temperature was less than 1%.

3.4. Non-linear thermal stress analysis

The sequential analysis uses the temperatures in the wheel from nonlinear transient analysis to calculate the resultingthermal stress eld by using a NewtonRaphson method to do nonlinear static stress analysis [57]. In this analysis, 50 incre-ments have been used to carry out non-linear analysis. Fig. 7 shows the rz stress prole through the wheel during the ther-mal loading cycle at periods of cooling to 25 C for application LT1. Add the number of increment to 60, there were almost no

Fig. 7. rz Stress distribution local detail of the temperature cooling to 25 C.

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00-100 -50 0 50 100 150 200 250 300 350 400 450

Dep

th B

elow

Tre

ad S

urfa

ce (m

m)

(MPa)

Thermal Hoop Stress

Average Braking Power = 50.4 KW

Fig. 8. Hoop stress distribution along T to T0 of the temperature cooling to 25 C.


50

100

150

200

250

100 150 200 250 300 350 400 450 500

Tem

pera

ture

(0C

)

Stress (MPa)

Stress viz. Temperature

Fig. 9. Maximum rz stress viz. temperature for applications in the thermal loading spectrum.different from current model. In convergence check, for the Von-Mises stress and maximum principle stress results, differ-ence between mesh 1 and mesh 2 were less than 2%. It was veried that present mesh was sufciently accurate for estimat-ing the thermal stress of the wheel during tread braking.

The thermal loading cycle that the wheel is subject to through its life results in what is termed a stress reversal within thematerial. Over time, the cyclic loading causes the residual stress state of the wheel to change from one of compressive stressto tensile stress. This is due to the small amounts of plastic deformation, which occur during each thermal loading cycle. Thematerial is unable to recover from the plastic deformation, caused through thermal expansion when cooling occurs. As cool-ing occurs from peak temperature down to room temperature, tensile stress occurs in area 1. Whilst in area 2 and 3, tensilestress occurs as temperature progresses from room temperature up to peak level. In area 1, the maximum stress level isaround 400 MPa and in area 2 and 3, the maximum stress level is around 70 MPa.

The stress distribution along T to T0 is represented by Fig. 8. For each application, the maximum temperature and corre-sponding stress at tread is outlined by Fig. 9. Maximum rz stress viz. temperature for applications in the thermal loadingspectrum is shown in Fig. 9. There are eight applications did not occur in this gure as their maximum thermal stress werelower than 50 MPa. Only duty cycles in braking spectrum were thus considered in this paper given there are virtually nodifference in the computed fatigue life and that the running time is markedly reduced. A stress threshold can be appliedto additionally remove applications in the thermal loading spectrum where this estimated stress is below a threshold. Thissets an absolute limit such as a 50 MPa fatigue limit. The results of the duty cycle analysis for the braking spectrum no.1 isprovided in Fig. 10. From this analysis it is observed that some applications can be omitted from the duty cycle analysis asthe damage due to these applications is minimal, i.e. less than 0.03% of the total damage.

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

1 2 3 4 5 6 7 8Loading Distribution (%) 29.4 55.4 67.0 93.0 100.0 71.8 62.7 46.6Repeat Times 1 2 3 1 1 1 1 1

Perc

enta

ge (%

)

Application Number

Braking Loading Spectrum No.1

Fig. 10. Duty cycles for braking loading spectrum no.1.

D. Peng et al. / Engineering Failure Analysis 25 (2012) 280290 2873.5. Fatigue life estimating

The material (micro-alloyed class B) properties [55] have been used to calculate crack growth in this paper is:

n = 3.0. g = 1.0. C = 3.38 1012. Initial crack length: ai = 0.05 mm; ci = 0.2 mm.

Fig. 11. The positions of the postulated cracks.

a

c

ZY

X

P

Qo

Crack PlaneQ

Fig. 12. Semi elliptical surface crack, QQ0 is a free edge.

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500

Cra

ck L

engt

h (m

m)

Number of Block

Crack Length viz. Number of Block

Crack LengthCrack Depth

Fig. 13. Crack propagation results for the wheel under braking loading spectrum no.1 at location 1.

288 D. Peng et al. / Engineering Failure Analysis 25 (2012) 28029010.0

12.0

14.0

16.0

18.0

20.0

ngth

(mm

)

Crack Length viz. Number of Blocks Utilisation = 200,000 km/year (average annual usage). The denitions associated with these RCF induced initial surface defects are shown in Fig. 11. Orientation in this paper: a = b = c = 0 (degree), see Fig. 12.

Three cases of thermal fatigue induced crack growth were considered. The thermal fatigue locations associated with thesethree cases were set at points 1 (case 1), 2 (case 2) and 3 (case 3), see Figs. 1315. Here, one block includes all the duty cyclesin braking loading spectrum no.1. The resultant crack growth results are given in Table 2. These results appear to be in qual-itative agreement with eet experience.

0.0

2.0

4.0

6.0

8.0

0 5000 10000 15000 20000 25000

Cra

ck L

e

Number of Blocks



0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Cra

ck L

engt

h (m

m)

Number of Blocks

Crack Length viz. Number of blocks



Table 2Crack growth results for the wheel under braking loading spectrum no.1.

Case ai (mm) ci (mm) af (mm) cf (mm) NLife (years)

1 0.05 0.2 12.4 20.3 19.41 1 12.4 20.3 11.5

2 0.05 0.2 15.0 18.3 >503 0.05 0.2 15.0 18.2 >50

Alexandropoulos, Greece; 2006.

[36] Molent L, Barter SA, Jones R. Some practical implications of exponential crack growth, multiscale fatigue crack initiation and propagation of

D. Peng et al. / Engineering Failure Analysis 25 (2012) 280290 289engineering materials: structural integrity and microstructural worthiness. In: Sih GC, editor, ISBN 978-1-4020-8519-2, Springer Press; 2008.[37] Jones R, Peng D. Tools for assessing the damage tolerance of primary structural components. In: Farahmand B, editor. Virtual testing and predictive

modeling: fatigue and fracture mechanics allowables, Springer; 2008.[38] Pitt S, Jones R, Farahmand B. Cracking in mil annealed Ti6Al4V. In: Proceedings international conference on fracture, Ottawa; 2009.[39] Jones R, Molent L, Krishnapillai K. An equivalent block method for computing fatigue crack growth. Int J Fatigue 2008;30:152942.[40] Peng D, Jones R. An initial study into crack growth in a railway wheel under thermal brake loading. Australia: Monash University; 2010.[41] Mills AF. Heat transfer. Boston, USA: Richard D. Irwin, inc; 1992. p. 888.[42] Bejan A. Theory of rolling contact heat transfer. J Heat Transfer Trans ASME 1989;111:25763.[43] Donzella G, Scepi M, Trombini F. The effect of block braking on the residual stress state of a solid railway wheel. In: Proceedings of the institution of

mechanical engineers, vol. 212 (2), ProQuest Science Journals pg; 1998. p. 14558.[32] Jones R, Forth SC. Cracking in D6ac steel. In: Proceedings international conference on fracture, Ottawa; 2009.[33] Jones R, Peng D, Pitt S. Thoughts on the physical processes underpinning crack growth. Fatigue Fract Eng Mater Struct 2009;10 (Invited paper).[34] Jones R, Pitt S, Peng D. The generalised FrostDugdale approach to modelling fatigue crack growth. Eng Fail Anal 2008;15:113049.[35] Jones R, Pitt S, Peng D. An equivalent block approach to crack growth, multiscale fatigue crack initiation and propagation of engineering materials:

structural integrity and microstructural worthiness. In: Sih GC, editor. ISBN 978-1-4020-8519, Springer Press; 2008.4. Conclusions

This paper has shown how heat transfer methods and fracture mechanics tools can be used to predict the growth of ther-mal fatigue induced cracks. In the paper we have considered three possible locations of crack growth. It can be concludedthat under service conditions, the alterative thermal stress resulting in tensile circumferential stresses can be enhancedfatigue crack initiation and growth. In area 2 and 3, during pure thermal loading, no failure is likely to occur. It should benoted that no mechanical loading and residual stresses (due to the manufacturing process) are included in this analysis.

Acknowledgement

This work was funded by the Commonwealth Research Centre for Railway Innovation through CRC project BR11.

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A study into crack growth in a railway wheel under thermal stop brake loading spectrum1 Introduction2 Thermal fatigue crack growth model2.1 Thermal load and stress analysis2.2 Stress intensity factor and crack growth calculation method

3 FEM model and results analysis3.1 Mesh, boundary conditions and thermal loads3.2 Material properties3.3 Heat transfer transient analysis3.4 Non-linear thermal stress analysis3.5 Fatigue life estimating

4 ConclusionsAcknowledgementReferences

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A Study Into Crack Growth in a Railway Wheel Under Thermal Stop Brake Loading Spectrum