Rapid Fracture Behaviour of Rolling Contact Fatigue Cracks

under High Axle Load Conditions

S.A. Ranjha1, K. Ding1, P. Mutton2 &A. Kapoor1

1Faculty of Engineering and Industrial Sciences, Swinburne University of Technology,

Hawthorn, Melbourne, Australia; 2/nstitute of Railway Technology, Department of

Mechanical and Aerospace Engineering, Monash University, Melbourne, Australia

SUlllD1alY : The probability of catastrophic rail failure as a result of the propagation of surface-initiated rolling contact fatigue (RCF) cracks to form transverse defects (TDs) is of ongoing concern to the rail industry, especially since the Hatfield incident in the UK in 2000. The heavy haul sector is not immune to such concerns, as the combination of improved rail steels and optimisation of the wheel-rail interface

has reduced the extent to which rail wear influences rail life.

The purpose of this paper is to investigate the growth behaviour of gauge corner cracking ( GCC), and in particular, the tendency for rails to break with a rapid fracture, under the high axle load conditions typical of those that exist in Australian heavy haul operations. Previous work has shown that the occurrence of

tension spikes as a result of localised vertical and lateral head bending on the web were significant in the understanding of this behaviour, which is exacerbated with increasing rail head wear (HW), such that the occurrence of the rapid fracture associated with this behaviour correlates with the extent of rail HW

This behaviour was examined using finite element (FE) modelling, which had previously been validated

by comparison with in-track measurements to verify the prediction of the tension spikes. The FE model used a single rail on a discrete elastic foundation to parametrically study the growth behaviour of RCF damage subjected to changes in the rail HW; the contact patch offset (CPO) from the rail centreline,

the (IJV) ratio of lateral (L) to vertical (V) loads, foundation stiffness and the thermal stresses. The FE results reveal that existing GCC, when subjected to high tensile stresses at the underhead radius (UHR) and the gauge corner region, can contribute to the development of rapid (unstable) fracture. The results of this work can be used to examine the influence of wheel-rail interaction behaviour and rail HW on the probability of catastrophic rail failure from RCF damage.

1. INTRODUCTION

Rolling contact fatigue (RCF) is a typical fatigue failure in the railway industry, and is associated with rail defects such as head checks, squats and transverse defects (TDs). In order to provide an uninterrupted and safe operation, it is vital that the railway industry maintains rails in good condition. However, rail maintenance is costly. In the United States alone, the estimated total annual cost of replacing and repairing worn out and degraded rails for

382

the railroad is approximatelyUS$2 billion [1], and other countries spend similar high amounts.

Wear and RCF formation in wheel-rail contact has been extensively studied by many researchers [2-6]. The hypotheses of the studies generally focus on the theory of plasticity with a suitable fatigue criterion for rail life prediction. Rings berg et al [7] investigated RCF behaviour in terms of the cyclic ratcheting material response of a pearlitic rail steel. The ratcheting material model

lOlL Ima ·• .... 1 H--v IW." • a• ... C s .... 2013

..........Jalod .... pluiiA ........ ... lluo .....- ...r.... .....tu-dillaoalo.--...au . l-.RCP d·=·p do; 'ope wiLeD ihe •ooomn1•t-d llr1lia ..,.-+...1 • afttal..l-.. &zt 1D na mmfta1. An u ..... ·6 ,I DE falipe ...- i•iri • io the rail bcC ...... the fllicloe �pq p,; .. m.d.....boEdo.....W-..ora...a .....

I 4 IJv.J fi otol[l],�....&i j.!� map · 'P"" riof the C.,. v ... tbea:Y· Tile fllicloe �-·a sodlv""'P>l•holl '-d:., .. "· � had .J.a 1-n me 1 J ad in tL. pu/ .. .adaL ..,. .. ·;,...t..tllyRiapboqecai[9J.ll'sp eclludo..­•ol [lo.IZJ ...a .. _.!led "M.oooLil'o Jlai.Mcdol• (WLilM) ... ;.., 'c;o> .. Hw!Sold ""'""- n.. maolol �the crook�-clmiorthe.lilio oEthe RCl' .,..!. .r.- . . . . ..... Saal ,._ n.. ...... �,;,. pLuu d_.,.'!.d ia tl.o _. jpiiWih ......Jal-: P.,.l (craci:jpiiWI!. Jv�mec' ·""'),pl!.o2 (cnck -"' b:r - •• ...) ... pUoo II' (cnok .,...,nJ. dam• I 1 Jv �ill ). Ia pll..ll, doo � 1iEe i1 \ iF •ty + F1:C:r dwl pla&M 2. A rapid r.. e �&am TDo ....J.u tlod ol.awaia F'or.l [1.!] ""!Y -i!·--�(CCC)II!moclawn .. ..

........ dopdo&a...d>erailloud, u. illr.triftAllytbo ......,.._a,., .........

J.llpn lo n-·----·olopcd-Ral'� [II]

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lmpont bd.o &am � ...!uooLo ... wlo.ol "llo.ioo" ,.. ·d ed.lup wbecl 111111...,.--. ' "'"'

1vtv t. a i-:nnw ill nit.._dinr � 6o:aP d. � wL..l&d pn amaEn • .. ia mnt:d'

.......... Hccce. tbo ;,p-.. Gil falipe.,..!. .-Ill­mizu;u:. Ia� JILe .._d;"'.._wualllljorocr a

.. ........ •tloo IDo.ol.�

TJ.a otooD,y _.: • ..� t1oo .....J. .-11. r ... .,. andno at tllo ,.,..,. -- oE nil _,]..,. r.o.. coc. w!bch aop phooelloEd.o WLll.M[lO.ll], 'II:Ioid­r4toaailo'-d!naota "*""'.....looloaodndmo(UHIQ,

• • 7 f with 1' et kiMI �with &CGtD\.!.e • � tbo lo..t -p " r4 tloe loooo! Mnclinr..,...., ....a., ...d doo lol.onl � ... doo loooo! [11·19] ...... inolpdod Pdofo<blllllc�loool>coa<I_..,...,Cl'&Cioo.w!bch opps da.,;,iool oradr'-tk...d""''Yropid!yps: a ... ..uh ia nil t.ihnroo [12]. Ia i -- tho .....!. s-<!> iauu ·,. .. ""lly l'hodurecoll20.J aAII C..,.Vm .. oll,l!l] clicJ - • a .. ........ .r tloe .,.;llooocl on tbo ,.,.,. d...... a, J. ooa#wr&ID.d.,: dB. .&'.at;. ol iDcr ttd ie'l ee �hip .d kiM eon r · •

""""" • od 1>oaa ._.. (HW), 'l1uo • r r o1< ...

I I 7 J wiih tDJ.L.Kn.r.,.af-ipDS inl'L... ! alll>o..p � .a= Ill lllp .r ...... � t.. • .....�<-a..,..,. .,...,n�o- • dt1 a • .,. ...!.otbritilclzl_, ljydoo �-�� Ia tho....­iae ··prM. a I� llltE&ec Cftck wM iatft:i W U iM - - 'l'loo cnok-"' w .... udor­djfF &d: == ,. J amdaa& Ja.d� to 1Im nilJ:..d t.t the ·-· • 1M':· .. WI& � wilb ftiiPt:C:t to diS uatrdw.Dp ftL

.Z. CRACK.IIIODJ!ILDBYELOPMENI'

A mom • I .....dal 1D jno t.lipa .....J. -"' ... ,. I tho WI ....!. ABAQtJ8 6.11·2. n.. .....dol -• tal a! a Qllqp'm rail 'Orislo f m l...p. blol= ... olootin r .... u.. 'l'loo liE ......Jal _....._. .. .mp ..-.1.. w1W6, ,._in iJ. 1:1:--t-W c;" I t• ..dial ... " • • .. oiJopo 1luod ... tllo vP<aJII.cad ciJCdoo t�.ot ....... ....a.. �o.-y 1oow1 -,... (F'or.I). 'lh.....J. ohoopo ..... d ., I II)' lluo oomicin:claO' ndDoo R, ... a cnck _,_ �oq��a a <Pillo 21), Tile .....J.Iallll> 'II." will. ........ 8 to tbo 111(1 ....r- .r tloa ...a ��. .,.. ..1 ol"" n8ioot o£21 mm lrum tloo I I' • oE a ...a ��cad a I •• :1bn u u..... in For:tc. Tile� ill� e ... .- �ill ==•&4 Bnm' , • d w iDtl.u.&f 8 wph. 'l'loo I !wllia!loo olwn- modood (X•FBM) or!elo::: ...... ,. td to the ......It I ... wiOc:ll .... olincoL !£ ..., .... J � .. UHil ........... 1-ri .. ol.awa ia F'>!f.2o.c,;tlooa olndoroEtloo.....loi-FBM.Le f

Tile :X.l"'!Zol psofdu oipfioat ..m....,.. ....,. 011= app:: ·+ .... llJC1l .. Lc..nd"7 e1 q1 1 1.221,.,. "'"Mrs a•l k (Cut.r .. ol 1,2.5]; .MaJisa.. ot ol CM]), ad eJemtnt ddaiaD m ,. t (lbceMI ct a1 D&J> .. m •" .... camp ·,. •• .,.. .. ��-

Contact patch

Crack front

�f�����:1��c· "\! '""'q;j Crack

UHR

� : ,.

(a) (b) (c)

r....,21 A.,;,p ....Sa t1uo.....,........, (e) cntk oll.ope (c:nckJ...stla llllllll....&coloorjjda.2R); (b) ....S..U..IIIIIaoa (8 ·10<>); (<>) ..... ��u:t pllcla olliet (Cl'O), IJV .m. mu1 poo1t1aa ar tJuo <nd..r.-..., -oE ...a luood u ..-a:m

inaetlicm oC ubitra�y ctaclao. Oompuod to 1he1ftditio!W PB lpJil'01ICh. tile cnck WU mba,.....! by additiODal E..m:tioa. that .....- the lliDplariliu at the ond. front, ADd .u- A llloOl'e elr� azul _.. ca�Dula�ical of the �tic wlu ... In ...JdilioQo tile diaplocancnt; .IWd � wu divid8d into eatinuoua and d;.......m,...,. portL TJ... X-FEM .!_...,.. fm tile ond. rePza pnmde the crack� ...bich � the ��CII ia the d!qla.....,..,. field alcar tile ..-..:1.. 'l'lmoe lliDplal' E.mctiamo .n.... the uympluli.: diaplace���eo.t at the cnck &oat to be talaol mto acccmo.1: for the _.deli "if o£ <ftd.a whooe ....,.my ia iDdepcadart o£ the .... Jmite eleznem nPm [M].

A rirJP wheelJa.d ir. oimul.m.J. "Pplyiq & &.lly odippiDjJ HerdzaD eomact pllldl em tile rail contact �. The --- load. iaclud.. latm.d (L) ... a vertical (V) load.

384

(!.JV .r.uio oCWual to� load),& COiltact pa1d. cdbet (CPO) &om tile rall � ..,. FiB .2e.and di8iert1lt � paatinna � to the po.;ticm oC the d'llclr, -

Fig S. The pMiiDjJ wheelwu timalated by� the .....- I� at mp 1, tha. otep .2, d.e otep 3 and ao

Cllo The .- immeity s-a (SIF•) m .Mode I. II and m (K,. K, ....d K111 �) ,..,.... � aL:mr tile crack &wit foreachofthelooerion• Siae of the crack ..,a tile rail HW.....,..., ...Kd ...ith tile crad< �Ria a

ranp of6mmtoliOmmudHWiallla.ranpofiOmm to 22 mm. .r411p41C!iftl,y. Cnck cm-ti.ou of 60'>, 70' u.d !10' ...,_ CODIIAideftd.. The .... alta ..., ued far the IMiluaaiDa of l'adpo C!ftdo 8"'"''h or a.IODjJ lllt!lule crack ill the rail.

The preoiou otudiea [18, 19] haw revealed tl.at 1he ae11on•l � ...nation &om ambi.em (26-C) to cold (lO'C) ...,. pmdua: 1111 &dditioaal temoile .-

of about ..fO MPa at tl:o.e UHR n:sicm· A� elastic foundation at the location of mepen wu uaed to aupport the raiL The mcrl! daaiLo reprdinfr theee panmderll are given in Table 1. Therefore, allowa.nce has been made in the CUft'ellt model Cor the dl'ed o£ foUAdaticm ms:.:-. and the thermal *-• � from variationa around. the nominal atre-&ee or neutral temperature, i n order to determine the applicabJe ltreN limite. '111e �ual ltreNea (renhiDg from the rail m.aDu&ctwing proceaa and repeated roJliD& contact between wheel and rail)

Model Parameters Rail span, S (mm) Vertical stiffness, Kv (KN/mm} La teral stiffness. Kt. (MN/mm) Vertical load, v (kN) LN ratio worn rail profile HW (mm) Contact patch offset CPO (mm) Contact patch area (mm2) Major semi axis, a (mm) Minor semi axis, b (mm) Thermal expansion coefficient, a (•C·') Young's modulus, E (MPa) Poisson's ratio. v Density, tl (g/cm 3)

Value 6000 35 2800 171.7 0, 0.2 10,15,22 15,20 125.6 10 4 1.2x10·S 209,000 0.3 7.8

will alao inluenoe the craek pwth beha-viour. Even though tl:o.e reeidual stn eeee are apected to redistn"'bute the atreea .tate in rail aa a reault of HW and durintJ crack pl'Op'lption, the imluence of residualatre!IM8 on the iinaJ. &acture hemm""' cumheraame. Thua, the rellidwd atre111H were not considered for this atudy and the c:orreeponding

- · - HH - l<tc; - -LAHT3 • IGe -- HE3· K.c

75

55 -cPO = 15 mm, lJV = o -----CPO : 20 mm. lN: 02

I � •• ••

dl\:c:b will be minimi•ecl The invea�ation of tl:o.e rapid fracture iDfl.uenc:ed by the t2Daile .lacal 'bendiJJ& meaaea aa a remit of HW; which i a uaoclated with an ecx:entricity o£ contact loads, will be the main focu.e.

3. RESULTS AND DISCUSSION

u sa- iD.teDSiw laccor (SD') em the� .&om The X-FEM .amlyaia ccmsider. a ��iD«le � c:nu:k at the puae corner of the rail. The crack ia in the � orientation of ansfe e with a eemicircular ebape apprnVm•ting a 9Piad he.d check (F't,g. 1), with crack radiwo R. and c:raclr. aurface l� 2R. The potriticm on the crack front ia normalized by the totod � of tl:o.e crack front, with pomion 0 correap�to the UHRneD the lower gauge cornerpointandpoeiUon 1atapointattl:o.etcp aar£ace of tl:o.e rail (Fig • .2a). The SlPa (K, K11 and KrJ at tl:o.e c:rac:kfrontwen u aed. to ezamjne tl:o.e growtl:o. behaviour of thia c:raS in l'e!!pODJIC to tl:o.e lll:reu distribution renllin« from the combmation of conte.ct load., bending, and the aeaaoDall,y-dependent thermal atreeeea. Fractun: tougbneaa lema for tl:o.rcc rail sradee commQD)y uaed. in lteavy haul .appliwione: a plain CMn Head. Hardened (HH) sracJe [27], a I...aw � Hut "1\oNt.ed (LAHT) sracJe [2B], and lf;nlelwtectoid (HE) Hea »wed grade [29], were uaed to ezamine the poui.bility of rapid c:raclr. growth.

Fig. 4 ahowa tl:o.e mazimum (owr the entire c:raS front) Made I SIF �-) under conte.ct load. of UV � 0 and 0.2 when appliecl to cli8'erent loading politiona Cor crack I� R • 18 111m, e. 90o and HW 15 111111.. The reaulta reveal that rapid &a.:ture could occur when the contact load ia � impcMoed ahove tl:o.e c:raS aa the Kr- > KIC (KIC • 36.4 MPaVm for HE rails, KIC • 39.1 MPaVm for LAH1'3 rails, and KJC • ..f5 MPaVm for HH rails). Thia ia

HW 15mm

•• - . - . - . - . - . - . - . - . - . - 1:- . - . - . - . - . - . - . - . - . -••

-35 � :. � ¥: 15

-25

--------- - ·------------------------- �---------------•• •• It • t H , . I 4 . ' • I

• •

� / I � .

·--� v·· ............. ,'

, . I

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500

L011ding position reletive to the position of crack (mm)

38S

lOth International Heavy Haul Association Conference, 2013

because of the local tensile bending stress which occurs as a short-duration spike in the UHR region (Fig. 2c) where the crack front (R = 18 mm) is located. Compared to the loading case when UV = 0.0 at an offset (CPO •

15 mm),the loads with the high CPO provide high tensile bending stress due to the localised bending of the rail head on the web [18, 19]. The K1"""" is up to 71MPav'm, which is almost four times higher than the loading case when UV = O.and CPO =15 mm. When the loads are positioned away from the crack, the K1...., reduces as the local bending stresses are absent at the crack front and the global bending stresses are only small.

Under the same conditions (CPO = 20 mm, UV = 0.2, 6= 90" and HW • 15 mm), the K1 ,_value is dependent on the crack length R Fig. 5 shows that the crack with a length R = 18 mm produces the highest value of K1 ,_ compared with a crack length R = 5 mm and 30 mm. This is because

the crack front for an 18 mm crack goes through the region of high UHR stresses, whereas smaller or bigger cracks have their crack fronts away from this highly stressed region. For extreme loading conditions (CPO • 20 mm and UV = 0.2); the crack may not extend to 30mm, as the probabili1)' is high for a rapid failure at R=l8mm. Another possibility exists, if the loads are lower, then the SIFs would be smaller as well. Fig. 4 suggests that a crack with a length R =18 mm produces a value of K1...., < K1c for the loading case of CPO = 15 mm and UV =0. The crack will not grow by rapid fracture and will pass through this region by gentle fatigue crack growth.

70 - • - HH ·IGc: - --· LAHT3 · 1<.c -- HE3-Ktc

60 -.-R=5mm ----R =18 mrn

50 -R=30mrn

SIFs (K1 K11 and Km) around the crack front with various crack lengths, crack orientation, wheel-rail contact and HW conditions were studied to investigate any possible rapid fractures due to the effect of local bending stresses. The critical crack length for these conditions can be estimated. As the HW changes the rail profile, the crack length R needs to be shortened in order to keep the crack in the critical UHR region (as shown in Fig. 2c). There are three crack lengths with respect to HW ((a) R • 23 mm for HWlO mm; (b) R- 18 mm for HW 15 mm; (c) R = 10 mm for HW 22 mm) that are considered in the analyses. It can be seen from Fig. 6 that a smaller HW 10 mm presents lower SIFs, particularly for Knr At the UHR region for the normalised crack front position of 0 to 0.2, K1 and K11 are positive and higher than the rest of the positions, but K1 is less than the K1c individually provided for the HH, HE3 and LAHT3 rail grades. Fig. 6 (c) shows that for a crack with a heavily worn rail profile (HW22 mm), K1 exceeds the fracture toughness of the HH, HE3 and LAHT3 grades &om the normalised crack front position of 0 to 0.3 in the UHR region. Hence, rapid (unstable) crack propagation will be expected for these combination of the crack length and HW (i.e. R = 18 mm for HW 15 mm; and R = 10 mm for HW 22 m.m see Fig 6 b-e).

The effect of crack orientation on SIFs was also studied. For this investigation the crack angle was varied to 60o and 70°. Compared to Fig. 6 (c) where the crack orientation was 6 = 90", Fig. 7 shows a clear reduction of K1 at the crack front position of 0 to 0.2 for the crack orientation

HW15tmm,

•• II

II - 4 - II - • - II - .. - II - II - .. _. II - ·•t II - ... - II - 4 - II - II - II - II - Iii - II - i"

:II -�

---------------------------- �. ----------------------------

---------------- fi--�-------------

� 30 � �

20

10

0

·10 ·2e00 -2000 ·1&00 · 1000

tri I ' I I I I ll ,. It •• • I II • I I ' I I I

•

1000 2000

Fipre 5: K1- at the crack front as a function crack length R (8 • 90o) under the loads of UV -0.2 at CPO • 20 mm

386

2800

erE 9 •liD' (Fis. l".o), ami 0 tD 0.6 fix the .....k ariematiom erE e • TO' or'l!· 1\o). 1a tLo UHR. ,..;- &;. - ;. -�""""' the ...-ad< ............ io..........! ... the q. lllllfMe ol .. niL .mel !he rapid &..taze 'lm/1 be cltma by .M..do LA �1.1. rapid r.:..:ta.. ....,,],l ....,.,

(o)R·21....., 120 100

80 60

HW10mm - · -HH· l<,c :-.: · :te��3� K,c -- K c

--K', -- K ... � 40 · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - ·

--------------------------------------------------------------------------------

of 20 :!!. ... 0 iii

-20 -40

..... _______ _ "-

-60 -80

0 0.2 0.4 0.6 0.8

(b)R-llmm Normalised crack front poaition

120 .--------------------------------------.H'-WU71°5�m�m�--, 100 - · - HH·K,c ----LAHT3 .K,c

00 . - - H �-I<,c

-- K" 60

h.

==�·

� 40 .::.-;.: =-=-_; �-;,.=-=·-;�--=-:.;-_ _;. �-

·:. ::.,;_:;�=-=-�.;:::.�.:,;.�-of 20 :!!. I ������--� � 0 � --

·20

-40

·60 ·60 L---------------------------------------------�

0 0.2 0.4 0.6 0.8 1 (o)R•lOmm

NonnaUaed crack front position

140 c---------------------------------------���-----, HW22mm

120 -· -HH·K.c

100 ---·LAHT3 • K,c - - HE3 • K,c --K, --K --K"

•

- 80 � .. ll. 60 :!!. � 40 ;. · - · - · - · - · l'--.:-.:-:.-:.-.:-.: -:.-:. --------------------------------------

---------------------

-20 L-----------------------------------------------� 0 0.2 0.4 0.6 0.8 1

Normalised crack front position

38'7

00 · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - - · ---= -.: ':.-:. -.: -.: ':.-:.-.: -.: ':.-:.-.: -.: ':."':.-.: -.: ':.-:.-.: -.: ':.-:.-.: -.:

$-.so : !. HW22mm �-100

- . ·HH-f<tc ····LAHT3·i<oe

-- HE3· 1<oe ·1$0 -K,

-K, -Ko .m L---�------------------------� 0 02 OA 0.6 0.8

Nonn�iMd crtc:k front poeition

5.2 Pftdj_.:l asdl:...,..,. 'l1.e predicb:d cr.cl< � ia caleulmd uaiDs the Paria .b.w [30], aee Eq. (1):

da dN=C4� (1)

Where N ia pftdicted &ligue li&, Me ia the .._, ime...ity r.np; C and n...., the ...-tial co- TL.: aperimemal cr.cl< sr-tb data Cor the rail ateel UIC pde 900A;wu reporb:d by Sl!;yttehol t.t J [14], and ia � uaed. here wilh c =2.47 z 10"9 (growth rate in mm/� ad slftu iD. MPa) ad expwocut n � 3.33. 'l1lia il a .pecl&c eumple to show c:rac:k sr-tb behaviOUJ:' in 1Le UHR..,. wid! the rail grade�� 1he C aud.n wbw. uaeclforthe CllM'!DI;�.mar;y be �compared to the in-eerorice rail snde-far the hu'71wd opuatiau reporb:d by Ueda et al [31] where C =1 z let' (srawth rate in mm/� and an.. in .MPa) n:pnnent n = 3 and *-• raDp of 20 .MPa. That would. be a pal:tU:uW-b' pod. evmple, th� the e£Fm oE the �grade. It ia poeoaible 1o �der - advulced � by comhinina I!Jl1 MC8 and I!Jl111 in AK,. to detennine c:radt pwth rate. However /JJI.8 and M"m are

IWl ,,.dm1 c-:k.d.e...J. ...,me amdhlcm • ........ , •• dma

BJl' UY CPO B. 9 (-) ,..,;. (-) (-) rJ

10 0 16 23 90 10 0.2 16 23 90 10 0.2 20 23 90

0 16 18 90 16

0.2 20 18 90

22 0.2 20 10 70

90

00

30

1 10

HW22mm · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - · - · ­

--------------------------------------------------------------------------

: ·10 � - • •HH · I<,e a -30

····LAHT3 · l<,e -- HE3 ·l<oe ·!!0 -K -K� :ro -K.

·90 0 0. 2 O A 0.6 0.8

Nomallttd ertck front potldon

mucll amalltr llODlp8ftd to /JJI.1 for the � renlta <F'i8· 6). With thia the C!ll1'ftllt aimpli6ed approadl whidl ued anJ.y M1 ia .fJW.V accuram. The � sr-tb ia dependent CID �=�-,which ....dae. the Krc reported &r all thr.:e mm:rial srade-in. the rail./1111he maimum o£ the cr.cl< opening WI*'*.PO"d. to 1he mazimlJDl (owr 1l:ae entin: ctacl.: &cmt) Mode I SIP QI,-) of the 1mlaile local hendinaa�.

Table 2 eL.ow. the prcdicb:d faPpe life Nf fot- die pt\>­eDtina crad.a unM:r the dill'erent lcwlina condi1iou. A poabbll. rapid fraetun: coald 000111' ...hen the ctacl.:a are poaitiDned. in the UHR ftfion, with an ana}e 8 o£ maTe 1han 10", ander a � wilh an otDet on the heaviJ.y worn nUl profile. It can alao 'be IHIIID tlw 1he .Ie. worn rail will mDit rapid (liDitlhle) Eatipe era propapion. Thae ob.� caDDOt produce � between the HW limit. of a r.il and the lmGwn defect t;ype.s �b. 1111 allowahJe HW limit af rail Lat. b.een .tiWi fly DIJftl etal (.32] to be in the .... af 16 to 20 mm. in ClllrYN o£ demoeuins radii. Marid1 [5.'5] found. an� HW limit to \e 21mm. far 6110-800 m. l'WWI CU1'VIIII at m UV ntio of 0.3 fot- nUl material wid! a latipe a�Rn�th o£ 2<10 .MPa, bul the aecepl&ble HWiimit wuld red1we 1o 20 mm. if 1111 addi1ional telulile -. o£ 80 MPa wu .dded. d..e tn

PftoUmd :a-ha

4/Cr·�- N, Ml'a{m (:Uf!qe!N) -19..64 <Is-< 0) In5n.i.t. IAfe

8.81 6.64 21.29 0.362 10.36 5.03

11 0 (K.-> Km) Rapid Fraeture

39.68 0 (for HE, LAliT grade) 0.0194 (for HH grade}

122.98 0 l.L->X,..) R.md Fracture

388

lOth International Heavy Haul Association Conference, 2013

the differential thermal stresses. Typically, HW = 20 mm is allowed for Deutche Bahn (DB) as reported by Zerbst et al [34].The calculations indicated in Table 2 consider rail HW of 10 to 22 mm under extreme loading.

4. CONCLUSIONS

This paper discusses the prediction of the rapid fracture behaviour for rail associated with local bending of the rail head on the web. Gauge corner cracking (GCC) was considered corresponding to Phase 3 of the WLRM. The X-FEM model was used to investigate the stress intensity factor near the crack front that results from contact loads, bending and seasonally-dependent thermal stresses. A single crack was modelled at different lengths and orientations, over a range of HW conditions.

The results of this analysis showed that the highest K1 """" occurs when the contact loading was directly applied above the crack location; due to the stresses resulting from the localised bending response of the rail head on the web. K1"""" was more significant in terms of rapid fracture than K11 and K11r Pre-existing GCC at the gauge corner region with crack lengths extending to the UHR region could cause a rapid (unstable) fracture if high tensile stresses at the UHR region result from extreme contact loading conditions. However, in practice, the rail gauge corner often develops multiple cracks in which case the stress state could be more complex. Further work is therefore required to examine the growth behaviour of multiple RCF cracks under more realistic service conditions.

5. ACKNOWLEDGEMENT

The first author thanks Swinburne University of Technology for the provision of funding through a SUPRA scholarship. The data on measured rail stresses under heavy haul conditions was based on research activities undertaken by the Institute of Railway Technology, Monash University for Rio Tinto Iron Ore.

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