Analysis of surface and internal cracl<s in continuously cast beam blanl<

K. Kim, H. N. Han, T. Yeo, Y. Lee, K. H. Oh, and D. N. Lee

I'n a 1‘e、，v recent stlld ics. thc sizc ‘lnd loc씨 iO I1 o[ thc “I1 ga p in lhe mOlllcl \\'crc caJcI.1Jatcd by coupli ng ()f l.hcrmal “nd strcss anal vscs. G rill νf {//s and Killoshila 1-'1 u! ‘’ 딩Ilc lll atcd lhe .:tir gap ai the corner 01‘ sla b. l1sing experirnental rn id face heal tl 11X data. Kristiansson1o dClcr­rnined lhe ail 설a p sizc ft‘ om 5trcss analysis. Thc gap sizc was subscql1Cnlly uscd as a boundary cOlldi lioll fo r the I1CXt SICp 01' lhermal analysi‘ rho l11as el lII. 11 15 anι1 You eI {dU > calclllated lhe l emperaturc and thcrmal strcss 01 sla b llsing a cOllpled analysis 、이lÍch took in lO accol1nl i hc variation of mould tcmpcraturc and l hc con l,lcl 1‘orccs bctwccn thc solidifying shcll Sl.1 r f,iCC ilnd l.he l110uld wall T hcir mcthods μrc l.houghi to be an irnpro 、 e ll1 ent on c“rlicr lllcthods

Figure 1 야lOWS l he shape 01‘ the short cross-scction 01' a beall1 blank. T he intcmal strcss dcvclopmcnt and lhc solidilication mcchanism of thc bcam bla nk during cas(ing arc considcrably diffcrcn l frOITI thosc of slab and billet bcçausc 01' its (;()l1l plica ted casting shape l 7 20 T hl1S‘ to investigate ancl heller understand thc formation o[ cracks. a [her l11omechanical analysis whiçh takcs i nlo ，κcounl the ellect 01‘ an all‘ ga p IS ncccssary ’ | ‘。 d“ tc‘ no such analysis 11<‘S bccn 1‘cpor[cd.

('ontinllOus <':<lsling ha~ been analysed llsing simpli tìcd high lernperat ure mechanic‘tl propcrtics‘ cspc<:ially i l1 thc m llshy zone‘ owing to thc di1lìclllti cs 01' measll remenl U ndcrstanding thc I11cchanical behaviour of lhe mushy zonc during casl.i ng is \'ery irnponan[ 10 obtain good q llali ty casl prodUC1S’ becallse all cracks obscrvcd i l1

CO I1 ‘ i l1u()usly caSl steel except transvcrsc cracks form in t his zone 01' low ducti l i ty.2J 2(’ Thc dUClili[ y loss nf 1 he m llshy zone is associa tcd 、\'i l h microsegreg<l lion of solll [e elements of solidi[ying dçl1drile interraces. T his solu tc elll‘ ichmcnt locally k씨 çrs the solidus lemperature and gi、 csl‘ isc [0 a zcro dUCli lily [ernpera[ure belo\V thc cqll ilibl‘11Im sol idlls lemperal llre‘ as sho\\’n in fig.2. Tcnsilc st rcss applied to the steel in thc 1‘angc bç’‘\'cçn t hc solidus and zero ductil ity tcmpcralurçs can sc.:paral e dendrites. Hot lcars can takt.: placc lInder a small s[ rain “ hcn thc inlcrdcndri li c.: liquid lì lm is lhin enough to 1‘csist fccding 01' lhε sl.Irroll nding li이 uid throllgh thc dcndl‘I(ç 씨 ms. 1I is dillìcul t to modcl this phcnomcl1on sinçe it depends on steel composi[ion. microslrllclure, dendri[e arm spaci ng. and 50 on. Hc씨 CVCI ‘ Ihc malhemalical model clescl‘ibing

A two-dimensional transient cOllpled thermoelastoplastic fini te element model has been developed. The model incorporates the effect of microsegregat ion of solute e l딩ments on hot tearS using a thermomechanical property model of the mushy zone and the two phase zone of Ô and ì'. The model successfully analyses the thermomechanical behaviour of the solidify ing shell of a beam blank during sol idificat ion in the mould. A ir gaps form at the flange t ip corners in the initial stage of sol idification which reduce the heal flow and give rise to hot spots at the flange tip corners. Large tensile stresses develop in the surface layers of the web and the fi llet which can cause surface cracks in the in itial stage of bea m blank casting. The fla nge t ip region is in a brittle temperatu re range during casting because the air gap reduces the heat transfer from the beam blank to the mould. A large tensile stress develops in the internal reg ion ofthe flange t ip from the intermediate stage of casting, which in turn can cause internal cracking in the flange tip reg ion. These analysis results are in good agreement with reported observations. ISí 1234

@ 1997 The tnstitllte 01 Materiats. Manllsçript rcçcived 14 Fcbruary 1996; in (inal lorm 23 May 1996. Dr Kim is wilh the Technology Dp.vetopment Group, M,U Fab. Department, Semiconduçtor R&D, s“msung Eleçtroniçs, Yongin, Or H,lfl is in I!JC Rcscarch Cenler lor Thin Filrn Fabrication and Crystal Growing 01 A<lvanced Matp. riats. Seolll National University, Mr Yeo. Dr Oh‘ and Dr D.N. lee Dre in the Division 01 Materiats Science and Engineerin\), “”이 Rcsc,lfch tnstitllte lor Adv<lnçc(j M“ teriills, SC()ul National Universilv. and Or Y. lce is wilh Ihe Strip Casling Research Team, Research Institute of tndustria l Science and Technoto\}y, Potwn~l， Korc‘’

‘_ , / /

/

Fillet / 、 / ‘、/

48Cmrr. -

Wide foce

Cross-section of continuously cast beam blanl<

... ‘1

INTRODUCTION f he continU()llS casting process has been aιlopted world、~'idc

by steel ind llstrics ovcr thc paSI two dccadçs owing 10 i[s inhcl‘cnt adv씨n lagcs o[ 10“ ços[‘ h igh yiçld. nex il기 li ly of OPC}‘Il lOn‘ and abili ly 10 achieve a high qllali l y caSI prodllct. I)espile [he advantages, the qllality ()f a s‘rand sllfrers considerably from the presence of variolls dclcc[s. Many l11athel11a[ical modcls havc bccn dc\'clopcd [0 lI ndcrstand thc lhcrmomcchaniα11 sl.atçs of lhç solidi fv in !! shcll in con[in\lOllS casling.1 ‘ I)espile such intense sllldies‘

the conlinuolls caslin!2 01‘ steel is not fll llv understood -。、Ning to the complexity 01‘ the continuous cast ing pr‘'0“ccss 、”‘ hi(κc이;h im、\'0이)끼Iv、vcs ‘“1 1<“…1I 설‘C J1l1…111’mbc이r of 0씨pχc띠l ‘“씨l니…ting f，‘ l“κ‘c l끼l“…(l rs、 ’s‘ IHμκ‘<.:h ι l1l l‘01.…1.1비l니i<띠‘d condilion<;, submollld condi liol1s, sleel cO l11posilion, cast ing speed, anι1 SO on. I n particulal’, a cO l11plcxi ty aI‘ISCS in thc fOrl11alion 01、 an ‘lir gap bctwccn sol idi[ying shcll 5111'1‘'acc and l.hc mOllld wa lJ as ‘l rcsult 01‘ thcr l1laJ and Ô-ì’

I. ransformatioll conlraclio l1s. T he size and shape 01‘ the ai r gap depencl upon heat 11nw conditions‘ 씨.rlúch in tu m atrcct thc tcmpçra[ urc and s[rcss disl.ributio l1S 01' t hc solidi fy ing shcll ‘ U nfavo \l μlb lc l:Ombina tio l1s 01' the [ernperalu re and st ress dislrihulions can cause delecls such as longitlldinal slI rfacc CI‘ acks and brcakou{. T hcrcl"orc, it is importanl to takc thc formation 01‘ thc ail‘ gap into accoun[ accura[cly i l1 lhc ana lysis nf cOl1 li l1uOLlS casting

120mm

-’------Web "-,

、

、

í I 、、 Inncr flange | “ tip corner tt<;,.ngc\

lip ‘ 75R /

、、 /

Outer !,fonge 쉰p ~orne'

LE

。Nt-------

,,•

UQ。*~‘。」·、。z

NO. 3 249 Vol. 24 IrOIH)''l(~ki r、(l and Sleelmaking 199ì

1520

10

250 Kim c/ 씨 Analysis of cracks in CC bC""1 blank

08

Z 0.6 。

1-ü 쪼 0.4 LL

0.2

ω 녁 띠 m z 。• I

，or。

g ’,.0119’ h 1

tc,;np, I

IIqu idus ’cmp

Tn‘’ 、、-낌

t

L M

뻐

π

Out lll ll\' --‘ 20 ( ô I ’emp. 1 ‘1.1、 ‘--γ‘--- “ |

SO lidV$ 、、 temp.

mushy zo~~，!

>

‘「-」-」.Q

그 。

70T

1500 0.0

1440 1460

TEMPERATURE. OC

Calculated solid fraction f5 , â-Fe fraction in solid phase “ fs . and y-Fe fraction in solid phase ’ fs as function of temperature for 0'12 wt-%C steel

3

inves tigated thc cOècl of carbon conlcnt in thc range 0.0 15 1 .0 、，\'t- ‘”’ on lhe high tcmpcl씨III‘c Slrcnglh and tOllghnC$s of solidilìed steels. and thcy mcasured the ZST all(r ZDT for cach steel composition. Koh<lyashi29 comparcd thc Schmidtman and Rakoski cxpcrimèl1wl dala with thc rcsllh ‘’f lll icrosegrcgation analysis, and proposcd that ZSl and ZDT COrl'cspond 1.0 the lell1 per~ l llrcs at 、이1i c:h Ihe solid f끼lc tion bccomes 0.8 and 0 ,99, 1‘cspcιt i\'c l y . rrom high tcmpCl‘1\ II r..: I.el써 le testing of ι“ ’ bon sleels‘ Nakagm“‘ er 111:\0 also proposcd Ihat χI)l ‘ cnrrcsponds to t he tcmp응l 낀 l ll rc at 、이lÎch 1 hc snlid 1‘ractlon rcaιhcs 0.98 and Kim (;'1 ‘/I. J 1..\ .\ S l땅gcsted lhat ZST “nd Z I)T COI‘ respond to thc ICmpc l'il lll reS at which thc $oli‘1 frac LÏons bccomc çritical ,olid fraction ~f“lnd 1'0, respξcti\'c l y. from the micrn,egregation analysis of \'ariOllS c‘11‘ bon stccls. h orn the abovc rcslllts. Z I)T seems to bc thc Icmperalllre a‘ which slccl is fully solidified. Thc prcscl1 t allthors took ZDT to bc thc Icmperature at which .I"s - 1. Since (he low dllClilit y of ν) Ii difying steel at higb Icrnpe띠ures is callscd by lhc inlcnJelld ritic liqllid lì lm. the lempcratllrc rangc 01 m l1 ~hy /olle dllring conlÌn\.lolls casling can bc dClcrmined \lsing lI1 icroscgrcgalion <lnalysis.

Thc prcsC l\1 ‘“…씨삐11…씨u…삐삐l니띠삐I1네삐h미삐10씨‘01…ws cαω찌a씨1니I cαωII씨l 1111씨1\…w띠IS샤씨hy :wnc as 끼 |‘urlction of Icmpcrnl l1 re II서 n~_ tl~c I1nÎlc diO‘c rc l1 ιe rnelhod proposcd by Uesh il11a ('1 01.'" “ 、이1ich lake, inlO accolln l solule dill'usion in a solid. The COl11position of Ihc sleel used in thc c써clllalion is Fe-O'1 2C­O' IOSí 1'2Mn- O.OI7P-0'013S. and Ihc lhermophysic씨 daw uscd in thc calculatiol) arc givcn in Tahle 1. Figurc 3 sho“s thc calculated solid fraclions as a function 01' Icmpc’‘llure during solidification. Calculalion was ca rricd ()Ul at a cooling ra(c 01‘ 0'17 K s 1 and at a dcndri lc ‘ 1 1'1끼 spaclng 01' 1 000 μlll. 111 1 hc rìgure,“ is solid fraιlion and ðf~ and ;.1、rcpl‘cscnl (Ì-Fc and '/-Fe 1‘rac(Îons in Ihe solid phasc.3U2

Solid ifì ιôllion is complctcd atf‘ _ I and thc () y 11‘ anslúrl1l ­

atioll is complclcd ‘11 % 二 1. Thc tcmpcraturc 씨 wh ich stecl is flllly solidílìed , i.e. ZDT was ca lclIlaled to bc 1452‘ C which is abollt 40 K lowèr than thc tCll1 pCralUre given hy Ihc fc C binary eq llilíbrill l11 phasc diagram. Thercforc. thc thcrl110rnechanical bch“viOllr of solidifying

Schematic illustration of zero d uctility temperature (ZDT) and zero strength tel1lperature (ZST)

mechan ical bchaviour of (he mllshy Z0 l1C ‘IS a funclio l'l of te ll1pCI‘ alllrc and sleel composition has 10 bc developed (0 calclllll lC lhc I.cmperature alld slrcss dísl ribuliolls in thc solidifyí l1g shell more acçuralcly‘ and 10 ex씨ninc thçil inOucllιe Oll the form‘lIion of ιracks. ln thc c“rlicl “c'o rks、sirnplilied mcchanical properly data bascd on thc cqlli­lihriulll phasc diagram ‘vere employcd to cakulate the s lress at lhc high lernperaturc rangc wilhoul laking the dcform“tíon hehaviollr 이’ thc l1l11shy /one inlo accollnt. 1l0wever. solidification of stccl duríng continllous casting does not ['ollo\V thc cquilibrium solidilìcalion palh bcçause of i(s rapid cooling ra l.c. and hot teal‘s do originatc in lhe Il\Llshy ZO IlC. Thcrc[ore, lhe microscgl‘cgalion phellomenoll and mcchan it:‘tl behavio lll' 01' thc l11l1~hy /.Olle shollld bc modcJIμI to rnake Ihe Hllalysis 1110rc aCιl.l ra te

rhe purpose 0 1' thc presenl sludy is 10 pr이)ose a lhermomcchaniçal l110del which can cxplain the defonna­tion bchaviour of lhe mushy zonc. “I1d to develop a Iwo­dimcnsío l1a l coupled thcnnoclaslopl:"tic ’ìnite clcmcl1 l 1l1odel to cornplllc thc thcrn자11 and rnechanical bchaviOllrs of lhe heam blallk. Lsing lhis model. :tn illvcstigation has heen carricd out inlo the siιe alld 10αItio l1 of the air gap and thc cOèct of the ai r gap on thc tcmpcηllure ‘illld stress distl‘ ibll tíOllS ín bc“’11 hlank casting.

2

MATHEMATICAL MODEL A nμlthcmat í ιal rnodel has bccl1 f0 1' 111 111‘llcd to Irack a tr‘111SVCrSc 、 li ce () [' a beam blank th rough a contilluOllS]Y c‘ISl slra nd as it moves do‘.\'n. ancl 10 calculatc the inleractivc hc씨 o。、，\' and lhe air gap formalio l1 het weell thc solidifying ‘hell surfacc and thc mould wall. To dctcrmine lhe solid fraction in the mushy ιOllC a5 a fllnction of lel11peralllre. the microscgrcgation of sollllc clcm~!)\s has been a‘sessed lIsing thc 1110‘léí of Ueshima er (11.27 Fro l11

lhe relation bctwccn sOlid rraction alld tcmpcralure ‘ a therlllomcchanic비 1l10del 01' thc mushy z.onc is proposed to dcscribc t he defo rrnat ion 01‘ thc mushy /.one

Microsegregation analysis of mus hy zo ne Genera lly. (hc SlIsçcplíbilily to cracking during contin l.lolls cllsting is cxperirnen tally assc~scd by 1 wo characteristic tcmpcralu l'es‘ zero st l'ength Icmpcratll l'e (ZST) Hnd zcr.~ dllctílity Icmpcraturc (7.1)'1'). Schmidtman and Ra)‘oski18

Equilibrium distribution coeffi cients c and diffusion coefficients D of elements in steel used in calculation Table 1

7'61 x 10 6 exp( - 134 557:RTl 30 x 10- b expt- 251458:RTl 55 x 10 G oxp( 249366: RTl 1‘ o x 10-6 eXI1( - 182 841 'RTl 2.4 )< 10 - ‘ exp (- 223 425 .RTl

0 ' , m' $ - ’

1.27 x 10 G cxp( 81379,RTl 8'0 x 10- ' exp( - 248 948,RTl 76 x 10 • exp( 224430,RT) 2'9 x 10 ‘ cxpt 230 120.RTl

4'56 x 10- ‘ p.xpl - 214639 RTl

D‘. fTl2 S 1

1'79 0'68 1'03 0'57 0'70

r. :f‘

No. 3 Vol. 24

0'34 0‘ 52 078 0'13 0'035

ç JI’‘’

lronmaking and Stcchl1aking 1997

0'19 0'77 0'76 0.23 0.05

k‘”‘’ EIOll1enl

C Si Mn p s

1.0

i탁 06C' • 0.1:\(' 〉‘ c그 0 8 (l l8C 口 0.27('

.t! v v 11 0 O.IIC l::, 0.60(;

>- j I + 0.53C X 0.82C 工~ 0 6 ~ t:::::!ÌIIt엠마 eqn. (1)

‘3 z

/: 나」 A

U또3 04 口

나으J 02 口

’~ /“ A ++ 나」 、0:: 0.0

0.5 0.6 0.7 0.8 0.9 1.0

SOLlO FRACTION, fs

Kim f! t ,lf. Analysis of cracks in CC bc‘ IIn blank 251

Thc yicJd fu nction ‘F is used to caJculale lhe plasli<; slra in ilH.;relllcnts dιr;. and lhc matrix notation 01' the stress l11crernems 이σ is eval uatcd as foJ)(l\νs

d씨 = lA j:l;L (! 'σ'.1

l qTCr， ld~ .- d~끼’) ! (‘q ’ lg ‘r) dT ('‘F rrEt p ‘q + 'q 'ctt (J i σ”

dO' = (‘~(d{: - #’ - df IJ ’)

(.1 )

= cιl’(d_!! -d_!! ’ 11)

1-, (‘qTCJ)T(‘q’ tg _ ‘r) d‘’n + 1 ‘g- - l Tl - ; | dE , • • (4)

L ".:: 'I?'q + '{?cr. 'q 1

where

‘l/rCr,('qTcry 4 Re|ative strength of carbon stee|s as fllnctlon of C” - CF - , 3 l 「

soli이 f~:cti~I~"~'" VI '-'OII J.J VII a lLII;;çla aa 'U I l\ ... l.IVI I UI Ip l lq _l_ 'q l(.""'q

sleel should bc l1lodcllcd in lhc tcmpcrilture range fJ'OJ11 lhe liquidus lernperaturc 10 χDT.

Mechanical property model of mushy zone To descrihe the lherl11o lTle<;hani<;“1 bchaviour of Ihc mushy zone between lhe liqll idus lempcraturc and ZDT‘ Lcc ‘Ind Kim‘s yield CI’ iterion.13 (‘0 1' porous I1lct씨s 、μtS lIscd. 1'hc rclati 、 c dcnsi ty, C1‘ itical re lative densilY, and yield slrcss of porous Illcl“1 in lhc crilcl‘ ion havc been replaced by solid fraClion/s , <;riti<;al solid fraClion ~l~ ‘ and yicld strcss y(‘ of the ll1ushy zone ‘ respeclively. Î ‘hus、 Ihc foll owing rclalion is obtained

3.J2= 'I YÕ= Yfs

whcrc

) -( --

11 = [(.r~ ~r~);( 1 - ~1~ Jl ~ ZD1' ‘γl ι ZST

1) = 0 ZSTι ’l

“ here YO is lhc yicld Stl‘css 이‘ a flllly solidified steel, .12 ’‘ lhe quadr<l li<; dcvialoric slrcss invariant, T is tcmper‘ltu re, ZST is zero ’;Iren싣th lemper써 ure al whi<;h .k bccomcs ~r~ ， and ZD1' is zero duClilily l.el1l pe’ ‘Iturc al 、νhidl slcc] is fully solidificd. fo r workhardening rnetals‘ 끼's and YO are lhc now slrcsscs of lhc lllushv zone and fu llv solidifìecl sleels, respecli vel y ’ I hc st rcss is cxpcctcd 10 incrcasc lincarly with increasing solid fraction b비wcen 7.D1' and ZS1'‘

Figure 4 shows lhe relative slrenglh of Ihc l11ushy zo nc as a I‘ unclion of solid fract ion fo r va riolls carhon sleels T he relalive strcnglh is dcfll1cd by thc ra tio 01" strength 0 1' rnushy i'.one 10 slrenglh of fu l1y solidilìcd stccl. Most data show the lineal‘ reJalionship belwecn thc solid fra<;lion and thc strength in the range "f~ ‘':;; J~ ~;; I regardfcss 01' <;arbon conlcnL fl‘om this 1‘csult ‘ the proposed yield crilerion fO I the l1l ushy 7.onc givcs a satisf,‘ctory result The critical soli이 fraction </~ is deler11l incd 10 1χ 0.641.) 1 by thc bcst fitting 01‘ thc lllC“surcd data to eq uation ( 1) as shown in Fig.4. FOI 씨 |‘1111y solidilìcd stccl“I~ = 1, 1';'s = ì~ ‘ and equalion ( 1) become、 Ihe von Miscs yicld nitcrion.

Constitutive equation in thermoelastoplastic fin it e e lement formulation For thc yield condition of equalion (1) ‘ lI nder isotropi<; h씨den i ng‘ Ihc yicld f‘unction F 씨 t tillle I can be expressed as

'F = 파 관， ' , . (2)

WhCl‘C ‘'1 at‘c the slate variahles ‘vhil;h are dcpcndcnl on lhc solid fraction and ‘ ì~ are ‘he Slale varia bles ‘,vhi<;h an; dependcn l on lhc pl<빼

(5)

In lhc ‘tbo、 c cq ualions. d_!; and di:TJJ ,11‘e the ll1alrix noμl l ions 01‘ 10μtl and thCl‘ m“1 strain incremenls. ') is Ihe posilive s<;ala’, 'T is lhc Icmpcrallll‘C‘ and (‘E and c cl’ are lhe elaslic slress- slrain mal rix and clasloplastic stress- strain mal rix, respeclively. T he scala r va ll1c ’r and lhc vcctor values ‘g “ p‘ and '(1 are defìned by lhe rollowing cq l1allOnS

F‘F 2 cI'Y" ‘l ‘ = - = ‘ "ì~)~

c ‘’r 3' " J d‘ I

d CE • - ‘

l y = _• - C" ’ σ : ‘l'’l ‘

(6)

(7)

1.. t: ’F 2 ’'1 EE"‘” ‘ p‘’ = - --=------ η e‘ι:; 3 ι E - Eμ111 ’j

f ’F ’qij= - τ-씨

‘ { ‘O"îj ‘

(8)

(9)

where E, 1:“w , and ‘끼i a re lhc ç)astiι modulus ‘I11d tangenlial rnodulu$ ‘If lhe flllly sol idifìcd slccl, and lhc devia\oric stresses ‘ |‘especlively. SlI띠l니pe히rscωJï니띠pl끼I r de잉n <…‘0씨)Ies 11네lHπC \1'μ‘'a…I I1SpO’S‘c 0이r a vecαto r o r’ matri‘'iαx . The tl대he히’rt‘1끼llla띠I st“ηra‘'a씨l川111 11 1

II1C1ω띠rcn띠ωmcn뻐1

I 0 :"1. I ‘ l샤”= | 」-( ’T T,."r) I 씨’T 1 ô’‘ ’ . • (10) , 1 d’T ' - - ",,, . .. - - 1" ' J

whcl‘C γ is thc cffcctivc thcrlllaJ expansion coelJìciellt which is dcpc l1dcl11 011 lhc tClllpcrature and Ô- ï t ralls('ormalioll‘ and '1;이 ‘Ind ôij ‘Irc Ihc lcmpcralurc at thc strcss f1‘cc sta tc alld lhe Kronecker della, respe<.;lively.

Effective p lastic strain rate and flow stress in carbon steel 1'0 obtain an expression for the !1ow C 1I 1 、 es 01‘ lhe carbo !1

slccl at val‘ JO lIS tcmpcr“t ll res and strain rates ‘ lhe fo llo 、，\'JJlg(.;onslil111ivc cqllalion proposcd by Ha n er ((/“‘~ was lIsed

èf> =;[ cxp( - Q씨T)I sinh (fJ K )11!m

ló= Kε;1

’ --(

( 12)

whcrc, A, IJ“ lnd 111 arc consμI nts， R is the gas constant, Q is Ihe (κli 、!alion cncrgy for dcformation, K is thc strength coellìcien L εl‘ i、 lhe εn'ccl i 、 c plastic slrain , ‘Ind 11 is lhc s train hardening exponen l. The f1 0w slress of fully solidilìed slccl YO al a givcn tcmpcratllre can be caJc lI la led lIsi ng eq lI<l tiO IlS (1 1 ) ‘lI1d (12). 1'hc lcmpcralllrc 띠 thc strand ca n he calcll laled Ih rough ana l 、 sis 0 1' hc써 transfc r.

fig1l1‘e 5a- (' sho、，VS lhe calclIlaled and mcasllrcd II lliaxia l slrcss strain data for a fll lly ’‘olidifìed sleel al v<lrious tcmpcra lurcs and strain ra tes. The experimentaJ d띠aJS

Ironll1aking anrl Steelmaking 1997 Vol. 24 N(I . 3

252 K;m 81 al. Analysis of cracks in CC IJC~11I IJ’‘”’k

50 , i (a) ~< ~ 6.7 x I O'? Is

40

m 울 30 .1

0.02 r% nU

μ 뼈

m

째

OO~

110 .---~- " .. _" (h) .. ι - 6.7xl O' ’ Is

m ι E rfi 20 (j) 나」

g (j) 10

끼

O 000 끼

뼈 뼈

{

S

’” ’ …… ”” 때

25 '-.---~---’

7,() .. (c) ", - 6.7 x IOJI/s

m 울 15

(j)

입 m ￠

• (j)

5

(J.O'I

STRAIN

fI 6'7 x 10 2 S '‘ b 6.7 x 10 3 S '; c 6'7 ‘ 10 • s ’ 5 Measured (.) and calculated lIniaxial stress- strain

délta of steel at various temperatures and given strain rates

(J ()2 (J.()(, (J O!;

、vcrc bc~、I lìlled 10 equ~…ons ( 11 ) and ( 12) hy a non-lincar lìlling melhod 10 ohlain lhc fo llowing paramclcrs: Ih 0.01308 M Pa - 1‘ 11 = 04289, A = 1'047 x 1010 S 1. Q = 326.3 kJ 11\01- 1

, /11 = 0.2008. T hc dcfo rmalion bcha、 iour of a fllll y solidilkd stccl is sccn in Fig, 5 1‘ ) be lVell described by c‘1\"11 ions ( 1 1 ) and ( 12 ) 111 lhe lcm Jìer<l lll re range a hovc ZIYI ‘, lhe sleel ex isls as a 11\1Ishy 201lC. T hc l1o\V stl‘C5S of carbon s‘ccllincarly dccrcascs wilh dc.:crcasing solid 1‘l ‘ICI IO I1

bct\Vccn ~ι l\nd 1, and if lhc solid fr; lclion reaches a critical valllc, lhe strength of the ll1ushy :I.OIIC hecomes zero.

Calculation of heat transfer

Thc Icmpcraturc dislriblllion in thc Iransvcrsc sliα~ of Ihe bcam bl‘ Il1 k wilh …Jit thi<:kncss is <:a lc.;\Ilated \Ising eq ualion ( 13) for Iw‘’-‘iimel1sional Irallsienl heal cond \lction accompanying liquid- solid transformatioll

지 (페) -되 (넷) I flL펀 = 1) ('1 감 ( 13 )

whcre ’/' is lhe (emperalure, " is lhe therll1al concluctivilY, ( ‘l' is lhe heat capacity. (I is thc dcnsily. ‘lnd L is thc lalcn(

Iron fl)~kino and S\ee’ll1aking 1997 Vol. 24 NO. 3

6 Initial finite ele l11ent l110del ’llesh for calculating temperature and thermal stress of beam blank and mOll ld

hc씨. ')‘ hc inilia l hOllnd‘ Iry condilioll a re as fo ll(1wS

T = 77.,; t T

kn τ- = ((

‘” t 14)

whcrι '/0 is Ihe init ial casting tcmpcraturc 01‘ 1l10ltCll stccl‘ 11 is thc d ircclion normal to Ihc bcam bJank S\l rra<:e, and q' is lhc hC:l1 Jl llX on lhc su rfa<:ι t-:q \lal io l1 ( 14 ) is solved \lsing Ihc lìnilc o.:Iemen( melhodJ~ The follo\\’ ll1g assump­(1()I1S arc u“ed in lhis calcul<…on.

(i) the heal condllclion in thc caslin얀 dirc<:tion is ncgligiblc comparcd 、，\'ilh Ihc hCBl I1l)‘\' 10 lhe mould

(i i) thc cll‘ccl of <:O tn’c<: livc hCilt Ilow in lhe liquid pool is takcll inlo ‘1<:<:0 \1 n 1 using Ihe ellecti ve thermal ιQnd llιti 、 ily kcrr for mol(en slecl3t.‘ whcrc 시T) is thc lhιrnlal COllduCl ivity ()f liqllid stccl llt IcmpCral \l 1‘cT‘

kcrf = /;( ', ‘) [ 1 + 6( I _ ./S)2J í J 5)

(i ii ) lhc hcat Iransfcr bCl\Vccn IllQ \1 ld .lIld <:ooling w<)(el is chara<:lcriscd lVilh Ihc aid of a heal lransfer ‘;ocOì<:Ìenl h‘ delermined from Ihe following dimcn­‘iOl1 les‘ correla tion 3‘

띈 -0{)23 (” ;:t‘ t펴rrrlw) 、I' hcrc () is thc hydw lI li<: diamCICr. "w is lhe velocily 1)1' ιQol ing walCI ‘ μ‘.V is 1 hc visco셔ly 0 1' cooli ng watel ‘ ”’ld hw i 、 lhe hea1. transfer coellìcienl between mould alld cl)oling waler. Thermophys ic씨 dala to calcul씨c IJ“. 1\)‘c givcn in Tablc 2 _-1~

Boundary conditions for heat tra nsfe r Thc lhcrmal bO \lndary <:ondilioll hClweel1 lhe ~olid ilìed shell ~lI rrace and the mouJd \\'a ll is modcllcd using thc interfacia l heat t ransfcr cocfficicnl "、h whidl is a fu’Jclion

Table 2 Physical property data of rnOllld cooling water

HYllr<llllic ‘li","oto,' o( çoolin(j chan ，、el，1IFlow vAlor.iIY o( WMAr. Iμ Specific h90t 이 wuter, C"‘、，Tllcrmol condllctivity o( wðler, k‘’ Visr.osity n( WRler. 1'.,

O'025m 2'315 m s ’ 4178J kn ' K 1 0'614 \1\1 m- ’ K- ’ 792 x 10 6Ns m 2

of lIir g“p thickncss ‘Ind slI rfacc ICmpcratllrc 01' bc‘IJll bl“nk. rhe 1.0 ta 1 Iherl1l‘tl resis ta ncc bel wccn t hc st ra nd surl'acc

ancl the rnoll ld “ all ( I). h may be expressed as the Sl.I rrl 0 1' lhosc 01' fillx. ‘111‘ gap, ‘\nd intel‘ faces

l시lsh = (')$h = ω ， +(I)Z +11시 + ‘1)4 ( 17)

The contact I‘esistance bet ween lhe rnoulcl and the !1101l 1d Illlx fì JIl1 (t) , is givcn by (,), = 1/’11 ,. wherc h, is the conlact he씨 1.1 ‘IOsl‘잉 cllcllìcicnl a t thc ll10ll ld sur1'acc. ‘" which w“s sel 10 3000 、V m l K ’‘ l‘he resiSla ncc 10 condUC I.Îon Ihrollgh lhe ai r g‘ ' P (!)l JS ι"ιulatcd by ω1 = d2./k2 ~ \ 1‘ hcrc k~ is the Iherrna l conduclivit.y 01‘ the ;:t ir and 112 i, the lhickncss 0 1' lhc ail‘ 뭘\p “ hich is calcu laled 1‘rorn the prcviO\lS stcp of slrcss ana1ysis. Thc cond llctivity 0 1' thc ai r.\8 was set to 0.1 W rn ‘ K J ’I'he rcsista ncc: (0 conduc­lion thro llgh lhe JllOllld l1 ux {ì lm (，시 is ca lclIla ted by m\ ­d ‘/k\ ‘ whcrc k.! is thc thcrma l cond llclivity 01‘ the Jllollld l1ux ‘Jnd d‘ is (hc (hickncss of I.hc g“p hllcd with 1l101lld 1111x. 1‘he conduc ti 、 ily ‘>1' the l1lould Il ll ,x \Ví‘s uscd “s 1 0 W m 1 K ' and (he Ihickness 이‘ lhe n1<wl‘1 ll ux was sel to 100 μrn frorn the rnoulcl Illlx consurnplion and densily 0 1' Jllollld fi ll x .~(J T he conlacl res istance behveen the Jllollld fillx and lhe stee1 shell is calclIla(ed by (써 = 1 !h~ ， where h~ is Ihc hcal ( 1끼nsfcJ‘ cocllìcicnt bctwccn thc ll10llld nllx and be‘1m bl“ nk slI rfacc; 11 , mlls( bc (cmpcra lurc dcpcndcnt “s a res lIh of the large dlílllge in viscosilics of l1lould Illlx over lhe Slrand surface lempera ll.lre range. T he lern peralure dcpendence 01' Iμ is given in Table 3

RESUL TS AND DISCUSSION Figure 6 shows lhe initial mesh for calcl1 lating Ihe lemper­alll l‘C “nd thcrm“1 strcss 01‘ thc bc“m blank and 1l10uld From lhc symmctry of Ihc mOllld and bcam b1ank, “ 이uar(e r seclion is l110delJe‘1 whidl has 2146 nodcs ‘Jnd 18ú8 elemenlS. ( ‘ ircular holes shown in Ihe lìgure are mould cooling pipes. Calclllat ion was perfol‘ med lI ncler conclilions of a widc facc tapcl‘ of 1 ‘”’-‘I casling spccd ofO'8 m min- ' . 씨 nd a mould lcnglh of 0.6 111.

Fig l.lre 7a- c! shows I.hc I.cl11 pcraturc diSlri bll liOl1s al various dislances below I.he menisc l.lS ‘lS the beam blank rn ()ves down lhrough lhe rnould. Temperal.ures of 15 19, 1504, [485, ancl 1452"( ‘ corresponcl to the tern peratuJ‘es at wh ich Ihe solicl fraction becomes 00, 0, 649 1, 09. ancl 1.0‘

rcspcctivcly. As sho、vn in Fig. 7(/‘ in thc ini tial stagc 01 solidi fJ caliolJ . “ llnifonn solidil‘'ying shcll forms 011 t.hc 씨 holc surface of Ihe hearn blank as a resull of good conlaCl bel씨leerl the mOl1 ld wa l1 ancl the solidifying shell slI rface 1-loWCVCl ‘ “s sol id ilìαIlion procccds, Ihc flan상，c tJ P cort1crs of Ihc bcal11 blank have “ 111 0 re ’apid coo]i ng 1씨C lhan 이her parl、 0 1' Ihe beam blank, the shel1 slarls 10 sh rin k away f‘rorn the fl ange lip corners due to Iherrnal contraclion ‘

and a n air gap f‘o rms. Oncc ('o rmed ‘ alJ‘ gaps red llce the 10ω11 hca t t'low from strand 10 mOllld. This 1‘ aiscs thc ICl11pcral.urc of Ihc Ilangc lip and givcs rise to lhc forma tio l1

이 ho( spols a이jm:cn l (0 bolh 11“ngc tlp corners ‘IS shoW I1

川 Fig. 7h. The <1 ir gap in hi bils lhe fo rrna lion of fully solidifìccl shell in lhe liange lip s l1 rface layer cloW J\ 10 the ll101l1d exit lInder 1 'y,’ 、‘ idc racc 1“pcr condilions as shown in F ig. 7ι I he effecl of lhe 씨 r gap on Ihe lel11 pe’‘J t ll re distribll tio J\ 이 lhe mould is also shO\vn in Fig.7. T he

Table 3 Temperatllre dependence of heat transfer coefficient 114 be1ween mould flux and strand surface

Temperature, 114, Ternper‘,tllre condition C W m - 2 K ’ Mould ’IlJX crystall in p. tp. mpp.raturp. 1030 1000 MOll ld II 11X sotlcllin“ tCITψC， ‘ ，tu re 11 50 2000 Melal soli <l\l$ lemperalure 1452 6000 Metalliqll idus temperature 1519 20 000

Kím el /11. Analysis 01 crilcks in CC beam bJank 253

(0)

‘’ 3 $; b 10 s; c 30 $; d 45 s 7 Calculated ternperature contours in beam blan l< after

given casting times at casting speed of 0'8 m min -1

l1101l1d tcmpera lllrc adjaccnl to Ihc tlangc tip is 10\Vcr tha n ‘’Iher p<l rts of 1l10uld bec(l llsc \hc air ga p rcd llccs \hc hca l Iransfer frorn heam hlank to mould, while lhe le l11pcraLll rc adjacent 10 the fì lle( al ‘、 hich the heHl lransfer JS maX il1l ll l1l

l‘cachcs abo\l t 250ιC at the 1l10uld exit.

Ironmaki ng ilnd Stp.p.lmaking 1997 Vo l. 24 No.3

254 Kim er 1'1/. Ana’ysis 01 cracks in CC heam blank

‘’ 3 s; 1) 10 s; c 30 ß; μ 45 s

Ql r gap

8 Deforrned geometry of bearn blanl< and forrnation of air gap after given casting tirnes 8t casting speed of 0'8 m rnin -1

Figlll‘c 8a d $how~ lhe deformcd gC()mel f') of thc bcam blank al variolls distanccs below Ihc Il1cniscus. '1‘ he dcformed geomclry of lhe beam hlank is lIlagnilìe‘1 x 5 10 see Ihe f'ormalion ()f lhe air gap. ln n wide face lapcl‘ 01、

l μ， ‘ thc “ir ga))s r1 re locatcd in bolh n‘Inge lip corncJ's and J'cll1ain unlil lhe hea ll1 blank arri ves al lhe mould cxi l.

Thcrefore, mOllld t“pCJ' ll1usl be rnodi licd so Ihal ‘I s()und

lronmaking (ln(l Sleelmaking 1997 Vol. 24 NO. 3

1600

1500

。ιj

않 1400

←그〈없aC l300

등~ 120()

J 100 0

/'’"，"'.""'7'，-::::τ-::-:T-:-:=.‘------‘-.. _--------outer tlangc ’ ν ““ IIp corner inner꺼a뺑

IIp corncr

lìlle‘ ‘.~ web

’ ‘

/--악， flange cenlre

----,_-,, 1 -- “ -- _" , - .-.-..-10 20 )0 40 50 (,0

DISTANCE BELQW MENISCUS. cm

9 Variation of beam b’an l< surface temperature with distance below meniscus during casting

solidifying 이lell can fOJ'1l1 in Ihe nange lip rcgion. To ot싸1m

” ’‘’lidifying shcll whiçh Ç()nlai ns Illinimum defecIκ an o))limised mould lapcl “ hich took inlo account Ihc deformed gcomcl rics of Ihe nangc tip corncrs ‘luring casling was proposcd hy K il11 •

41 This oPlimi‘cd l110uld tape J' “ hich compcnsalcd for lhe fOI‘ llla lÎon of lhe <1 ir gap al Ihc fl“ngc lip I;orne l “.teCI‘앙lscd Ihc size ‘)f lhe air gll p and thc slrcss lìcld ,1( Ihe Ih\ng,c li p (,;orners41

Figure 9 sho\ιS lh<.: varialion 01' slIrfa (,;c 1 덩mperalllrc wilh distancc bcl(싸 lhe lllenis(,;lIs. Thc surface tcmpcralllrc ‘)f bOlh the “'eh and lhc tlangc çenlre decreascs as solidilìcalion proçeeds and rcachcs - 1 100‘ C al lhc ll10uld cxi t. Thc Icm f)eratllre of lhc fìllcl ~ lI rface dccrcascs m‘)re slowly than 1 hose 01‘ thc \V이) nnd lhe t1angc (,;cnlrc ‘ bel,;ause the surf:‘I(,;C arc‘1 01‘ lhe rìllel I’egion is smal ler ()wi ng to its (,;011 1;<1 VC

SlId…;c shape. T hc solidifyi l1g shell 01‘ Ihc l1angc li p shrinks ilway from thc mOllld <lnd a gap is I‘'ormcd hcl ween Ihc mould and lhc shdl slIrface al 씨 dislance hclo、\' thc mCll isclIS or ~ 5 (,;111. I'his redllccs Ihc ral o,; of heat n。、\' from lhc strand、 paniclllarly nCélr bOlh wrners 01' thc flélngc lip “’hcrc lhc gap is largcsl as shown in Fig.8. Hot spOIS f,‘)rm on Ihc nange li p s llrfaçc ‘lnd lhe lempcralllrc of lhe nangc lip (,;nrners is main l씨I1cd ahove 1350 C “1 Ihc l1'loll ld exit

「‘ig llre 1 () shows lypical def’'CCIS in cOlllin uollsly casl heam blanks I‘C))‘)rled hy Onishi ('( (//. IH.42 S lI rfacc crack s arc IIS I!씨Iv f,‘>und in lhc 、.\'cb and (j llel rcgions. 、.I' hi lc

Surface Crack in Web and Fillet

Internal Crack in Flange Tip

10 Typical defects in continuously cast beam blan l<

Kím el al. Analysis of cracks in CC beam blank 255

‘'-'-'-γ

--wcb ----- fi llct

.. inncr tlunge t ip

---- outer nangc tip

---- f1ange cemre

(IJ 1.6 a E (f) α1 l니 r::t: f­(f) _J

& o8 ‘j z α

응 0.4 그 E

훌 0.0

1.2

-“ ” 0

DISTANCE BELOW MENISCUS , cm

Variation of maximum principal stress on surface layer of bea ll1 blanl< with distance below meniscus during casting

and fi llet Slll‘I'acc laycrs. Sllch ‘t high Icnsik s tn:ss ‘levelops in thc wcb and lìllct rcgion bccallse lhe ll1011ld inhibils lhe natllral lhcrl1lal con lraction 0 1' tbe beam blank near the Iìllct rcgion. I‘ he Ilange tip sllrface layer is under a tensile stress 0 1' -0.4 MPa during casting and ‘ hcncc, thc possibili l) nl‘ surrace cracking is low. Howcvcl“ thc maioril)' of (hc tlange tip rcgion is wÎ lhin thc l1l11shy zone lemperalure rangc dllring solid ilìιa lion in the moulcl as shown in Fig. 7. rhus ‘ inlernal cracks may be likely to OCCllr in thc inncl‘ Ilange lip region where a tensilc strcss 0('‘ -lMP‘1 dc、c)ops‘as shown in f ig. llc and d. and whcrc lhc $olidifying shell cxists in thc l1111shy sla tc

Figure 12 shows the varia tion 이‘ maXitllllJ1l principal sl.ress 01' lhe surl'ace layel‘ with distance bclo、v thc J1lcnisclls. Large tensile stresscs dcvclop al thc c‘lrly sμ1ge ‘>1' solidifica tion in thc wcb and lìllcl sur[ace layers‘ bu( these strcsscs bccol11c low al lhe 11l0uld exi l.. In l.ernal cracking is mainly dcpcndenl on lhe enlargement 0 1' the mushy zonc in thc Oangc lip region logelher Wilh a high tens ile stl‘css a l lhe n10uld exist (see Fig. 12).

CONCLUSIONS Thc couplcd <l nalysis 01' heat transl'ei‘ and del'ormalion in a 480 x 420 x 120 rnm 0.12 wt-<ι，(' stccl bcam blank Icads 10 lhe 1‘'o llowing CO Jlclllsio Jls.

1. Typical dcfccls of thc bcam bJa nk , sllch as longitudinal SlIl‘ facc cracking in thc \Veb and inlernal cracking in the llangc tip region, can be ‘IIccessl'lI lly predicted llsi Jlg thc thermornechanical model 01‘ the mllshy zonc 、.vh ich incor­porates rnic l'OsegregatioJl 01' sollltc clcmcnls and cOllpJcd thermoelastoplastic lìnitc c1cmcnt ‘lnalysis.

2. An air 팔lp forms in thc Ilange tip corner al lhe initial sμtgc 01' ~olidilìca1.ion. 1‘ he siνze 0 1' 11미he air gap call be cαo이)ntro이)끼lIed bηy‘ i“irn씨lP(‘os“I Jlg a씨l니…pp끼l'‘op、) 1'1’'1μlatκc mOll띠Ik…d tμapcr‘'s. Thc air gap iJlhibits thc hcat fI。、~， and givcs risc to inlcrna l CI 씨ck ing in lhc llangc lip rcgion. ^ large tensile s tress develops in the 、I'eh and fjlle t at the inilial stage of‘ sol idificat ioJl 、vhich

rnay gl 、 e rise to longitlldinal Slll‘ face crackin섣 on thc \Vcb and fillct surfaccs.

0,,)

12

께 ” ” ” ” ”

n u 이

/ / , ‘ 、

(c)

(cl )

11

AC I<NOWLEDGEMENTS This work has bccn suppor(cd by lbc K orea Science and |τ ngincc r i ng Foundalio l1 through the Research Center 1'01 f'hin F il ll1 Fabl‘ ication and C r)'stal Growing 0 1' Advallccd Malerials‘ Seoul National Univcl‘sity, Korcκ Thc allthors ‘11’e also gratcflll fo r lìnancial Sllpport from thc Kan설won lndllslry. Pohan설. Korc“

No.3 Vol. 24 1997 Ironmnking and Steelrnuking

in ternal cracking orten tJp reglon.

Figm‘c 11(1 d sh，씨 S lhe calclIla tecl maximum principa l slress distri butions in the sol idified shell “rtCI‘ var‘ IOllS solidilìcation limes. The calclllation indicatcs thal 씨 tcnsilc stress 01‘ .~ 1 MPa dcvclops in Ihc 、.veb a nd 川le l surface laycrs in t.he inilial stage 01' s이 idifìca tion. SUI‘I'ace cracking can occur in the initial stage of‘ solidification bccallsc thc web and fillet sllrfaccs ar‘c al slIch high tcmpcralures lhat thcv can bc in thc mushv sμlle. When the tensile slress

‘ -cxcccds lhe 1‘ l ‘tcllHe stress 01' l.he ll1 ushy z()ne ‘ cracking is likely 10 ()CCllr along Ihe interclend ritic region 0 1' thc wcb

typically occurs in thc nangc

256 Kim <::1 .1/. AOIllysis 0’ cracks In CC bc‘Ifn b’ank

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2 1. \v. 1. 1 .11κKH)I( I ) 끼('/，，11. 'f'r'lII、" 1972‘ 3. U.< 1 l.ìS7‘

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