ISIJ International, Vo l. 38 (1998), No. 1, pp. 53-62

Analysis of Mold Wear during Continuous Casting of Slab

Young Mok WON , Tae-jung YEO, Kyu Hwan OH , Joong -kil PARK,') Joo CHOI1) and Chang Hee YIM' J

Scho이 of Materials Science and Eng ineering and Center for Advanced Materials Research, Seoul National Univers ity, San 56-1 , Shinrim-dong, Kwanak -ku , Seoul 151-742, Korea. 1) Iron & Steel Making Research Team , Technical Research Laboratories, POSCO, Pohang, P.O. Box 36, 1, Koedong-dong, Kyungbuk, 790-785, Korea

(Received on June 3, 7997: accepted in final form on Au‘'}ust 18, 1997)

“ '---'

Using a 2-dimensional coupled thermo-elasto-plastic finite element model, the thermo-mechanical behaviours of the strand and mold were analyzed. The calculated geometry and temperature distributions 。f the solidifying shell and mold were compared with experimenta l observations ‘ The calculated geometry around corner region was in good agreement with experimental observations. The mold wear was analyzed by a new dimensionless parameter of "Apparent Wear Parameter" wh ich is inversely proportiona l to yield stress of the mold at service temperature 'and directly proportional to the interfacia l pressure between the strand and mold. The effects of narrow face taper and carbon concentration of cast steel on mold wear were analyzed using the apparent wear parameter. With increasing narrow face taper, the possibility of mold wear increased due to increasing interfacial pressure. With increasing carbon concentration, the width of worn region of 35 mm at 0.05 and 0.1 wt% C steels decreased to 15 mm of 0.2 wt% C steel due to uniform thermal contraction of 0.2 wt% C steel during solidification. The calculated behaviours of mold wear were compared with used mold in industrial operation. The calculated worn region of mold based on the apparent wear parameter were in good agreement with industrial observations.

KEY WORDS: thermo-elasto- plastic finite element model; mold wear; apparent wear parameter; interfacial pressure; narrow face taper; carbon concentration ‘

1. Introduction

The continuous casling proccss has been adopted worldwidely by stecl induslrics over last two decades owing to its inherent advanlagcs of low cost, high yield, tlexibili ty of operation, and abilily 10 ，κhieve a high qllal i~y cast product. In spite 01‘ lhc advantages, the quality 01‘ a Slra nd suffers consiclerably 1‘rOll1 the pres­ence of various dcfeclS, such as break-outs, cracks of

~s인싸lranc떼lC띠d， molcl we않ar ar뼈I ’ ‘ have been c1evelopecl to underSland and investigate the

lhcrmo-mechanical behaviours of lhc solidifying shell and mold during continuous casling. 1 15) Despite such inlcnsc sludics, the thermo-mechanical bchaviours of the Slrand “nd mold during continuous casling of steel are nOl fu lly llnderstood due to the complcx operating conditions of continllOllS casting process, such as mold flllX conditions, supcrhcal of mell, coo ling water f10w ratc 01‘ mo ld ‘ mold taper, slab c1 imc l1sion, steel grade, casling spccd and so on. The formation of air 깡lp be­tween thc slrand and mold, and thc strcss stale of solidifying shcll have been analyzed with lhc cOllpled analysis ofstress and hcat transfer analysis.I-15.30-32.37’ From the viewpoint o f slrand, lhese models have well explai l1cd thc formation of surface and intcrnal cracks, break-olllS, <1nd air gap in continllOllS casting process 01' slab. Howcver, f‘'rOI11 thc vicwpoin t of mold wear, the wea r phenomenon 이、 mol<l has nol bcen flllly studied ye t. G rill el at.2) reported that mold wc“’. due to the physical abrasi.on of mold is relalcd wilh thc normal

53

l‘Orcc which acls againsl lhc mold. And , they reporlcd that wcar oCClIrs in rcgions of thc mold where the air gap is fully c1osed .

The pllrpose of this study is to ana lyze wear phenom­enon 01' the narrow side mold , lIsing a 2-dimensional cOllpled thermo-elasto-plastic fìnitc clcmcnt model to compulc the thermal and mechanical bchaviours 01‘ shc lJ <Il1d oblain the temperature profì le of mold. To prc<licl lhc possibility of mold wear, a new dimensionless pa­ramClcr 0 1' apparcnt wear par“meter has been pro­poscd, which is bascd 011 lhc complex wear mecha­nisms 01' abrasive and adhcsivc wcar. The effects of narrow face taper and carbon conccntratio l1 011 the mold wear were studied . The calclllatcd wca r behaviours of narrow face mold at a conditio l1 01' conlinUOllS casting in il1dllstry were compared with thc cxpcrimentally mcaSLlI‘cd data of used mold in indllstry

2. Mathematical Formulation

2. 1. Calculation of Heat '1‘ransfer during Continuous Casting

Thc lcmpcralure distribution in the transverse slicc 01' slrand is calclllated lIsing <1 11 Eq. (1) for 2-dimen­sional transient heat conduction accompa nying liquid­solid transformation

Ô (. åT\ D (. tJT\ _ [Jt: _ðT I k _- I+ ~. 11< -7- 1+ L -:s = C~~ .. ... (1) tl.,"C \ δx ) ðy \ ðy ) ðl ðt

whcrc Tis thc tcmpcralurc, k is lhe thermal conduclivi ly ‘

‘~) 1998 ISIJ

ISIJ International, Vo l. 38 (1998), No. 1

C is the heat capacity pcr unit volume, λ is the solid fraction and L is the latcnt heat per unit volume. In this sludy‘ lhc cnthalpy mcthod ’ 1) was uscd 10 solvc lhc solidilìcation. Thc initial and houndary condi tions arC as fo l1ows.

'1 ‘= To 、δT

- kn ‘ =ψ .. ...... ........... (2)

on

where TO is the initial casting temperature of molten steel, 11 is the direction norma1 to strand surface and qS is the hcat flux on thc surfacc. Thc hea t conduction equa­lion was solvcd using lhc lìnilC clcmcnl mcthod. 16.18) The following assu l11plio ns wcrc uscd in lhis calculalio l1.

(1) The heat condllction along casting direction is negligible compared with the heat flow to mo1d.

(2) The etTect of convective heat flow in liquid region is taken into account using the effective thermal con­duιt.ivity ， kc((, fo r mollcn stcel. 19J k(T) is’ the thermal conductivity 0 1' liqllid stecl at temperature T.

kcl'f = k(T)[ 1 + 6( 1 -ι?J ................... (3)

(3) Thc hcal lranslèr bClwccn lhc mold and cooling water is characterized with the aid of a heat transfer coefficient, """ determined from lhe following dimension­less correlation. 20)

h없 = 0.023( j’)w?앉 y.ß ( C~W:W y.4 ... (4)

where D is tbc hyd raulic diamctcr, U w is lhc vclocily of cooling walcr, Pw is lhc dcnsily of watcr, μ“. is the viscos­ily of cooling walcr a nd "w is thc hcat transfer coefJìcient between the mo1d and cooling water. Thermo-physical data to calculate hw are given in Table 1. 21)

The therl11al boundary condition between the solidified strand surface ancl mold is modelecl using the interfacial heat transfer coefncient, h,!" which is a function of air gap thickness and surface tcmperature of tbe strand. T he interfacial heal lransfcr cocfTìcicnt c“n bc cxprcsscd as fo Jlows.

"T = 11 RT + " rad .. … ..................... (5)

where hr." is the heat transfer coefficient for the radiative heat flow when the air gap occurs between the strand and 11101d , and Rr is lhe thermal resistance between the strand surface a nd mold cxcept 1‘adiation. The heat transfer coe삐cicn t for radiativc hαIt flow, "'3d' can bc cxprcsscd as fo l1ows.

h""d = O'e(깐+7'.’n)(7~2+'r~~) .............. ... (6)

where 0' is the Stefan- Boltzma n constant , e is the averag­cd cmissiyity 01" shcll and mold surl"accs, 지 is lhc lcm­pcralurc of shcl1 surfacc and Tm is thc tcmpcrature of 11101d. The averaged cmissivily ofshel1 and mold s l1rface was assumed to be 0.8. 22) The thermal resistance, Rr , may be expressed “s follows.

RT = R 1+ R2 + R3 + R4 ............... … .. . (7)

The contact resistance between the mol c1 and mo1d flux film, R1' is given by R, = 1jft ,

‘ where h 1 is the contact

hcal lranst‘CI‘ coclTìcicn t 긴 1 thc 1110ld s l1rl"acc, which was

떼 1998 ISIJ 54

Table 1. Thc I'IIlO.physical data of O1old c()o [ing ‘vater. 211

Propcrly

Specilic hι11 of walcr. C".‘ I)cnSÎly 01‘ walcr ‘ P‘ ThcI'Illal conduc1ivi1y of W3lcr‘ k‘ VÎ~CO~ily of w‘tlcr‘ Jt",

Valuc

4178J/kg C C 998.2kgJm3 0.614 W/mnC 792 X 10- 6 Ns/m2

Tablc 2. Tcmpcrlllurc dcpcndcncc 01‘ hcat tr<l llsfcr coeffi­cicnt bctwccn thc O1old l1 ux and strand surface. B ’

Tcmpcraturc dcscriptiOIl

Mold I1 11X cryslallinc lcmpcratllrc Mold nux soft ening tιc…’mpcr깨a씨1I…III…llrc c M‘c따;1μ띠띠;“씨l니1 501“배i버du“IS‘ lωcmpcωr씨.끼께a씨l ‘u…ure Mclal li‘lllidus tcmpcrat llrc

114, W/m2 K

) 000 2000

10000 20000

’l‘ablc 3. Chcmical ιomposilion 01" carbon Slccl

F.lement C Si Mn P S ClI Ni Cr

wt % 0. 1 0.03 0.4 0.02 0.02 0.06 0.06 0.06

scl 10 3000 Wjm2 K .씨 Thc rcsistance to conduction thro ugh lhe air gap, R 2' is calculalcd by R 2 = d2 /k 2’ where k 2 is the thermal conductivity 01'‘ air and d2 is the thickness of air ga p which is calculated fro l11 the thenno-elasto-plastic stress ana1ysis. The conductivity of ai r was sct to 0. 1 W/m K .21

) Thc resistance to con­duclion lhrough lhc mol<l fl ux fì lm, R3' is calculalcd by R3 = d3/kJ , whcrc k3 is lhc thcrmal condllclivily ofmold flux and d3 is lhc thick ncss of gap 1ì1lcd wilh lhc 11101<1 Ilux. Thc lhcrl11al conduclivity 01' 1110ld liux is uscd 10 bc 1.0 W 1111 K and lhc lhickncss 01‘ 1110ld 11 ux was set tó 100μm I'rom thc 1110ld fl Llx conslImption ancl density 01' 11101d lluX. 24) Thc contact 1‘csistance between the 11101d fl lIx and strand surface is calculated by R4 = 11114, where 114 is the heat tl ‘ansfer coeftìcient between the mold flux and stra nd surface. 1'14 mllst bc dependent on te l11perature

、...

duc 10 lhc 1 <1 1강c changc in viscosities of the mo1d t1ux ‘ over slrand surfacc lcmpcralllrc rangc. Thc tcmperalurc c1ependency 01‘ 114 is givcn in Table 2.23)

The composition of steel used in this study is given in Table 3. Thc liquidlls temperature, TL, and the solidus temperalurc, "5' wcrc calculated using lhc following eqllations. 25)

Tt- = I 536 - 78(wt% C) - 7.6(wt%Si)-4.9(wt%Mn)

- 34.4(wl % P) - 38(wt% S) - 4.7(wt% Cu)

- 3. 1 (wl % N i) - 1.3(wt% Cr) - 3.6(wl % AI) …(8)

Ts= 1 536- 415.5(wt% C) - 12.3(wt%Si)

- 6.8(wtOIcIMn) - 124.5(wt% P) - 183.9(wtO/()S)

-4.3(wt이)N i) - 1.4(wt%Cr) -4.1(wt%Al) .... (9)

The effective coe fl1cicnl of lhcrmal expansion was cal; c111alcd from t.he following cquation. ’

(VI V,.cf) 1{3 - 1 α - ,-,-., ' r . . .....• . . . . .• . .. … ... (1 0) r- Trcf

can occur al lhe interface betwccn the strand and mold whcn the Slrand movcs downward through the mold during casling. Tn adhcsive wear, asperities on the slid­ing $llrface support the frictional load and high st rcss developcd at the asperilies. The high stress Ca llSeS plastic deformalion of the mold at aspcrity and subsequent deformatiO Il give rise 10 wear. Tn abrasivc wear, dU J'ing sliding between hard and soft mctals, thc hard aspcrity 01' hard mClal culs thc soft aspcrity of soft meta1. 27) Typically, sll J'face morph이ogy of abrasivc wear shows thc groove shapc due to lhe penclrating abrasive wcar particlcs. Figurcs 2(a) and 2(b) show the sca nning elec­tron l11icrograph and EDS analysis al the narrow corncr region of strand , respectively. Figures 2(이 and 2(d) show lhe scanning electron micrograph and EDS analysis at thc worn mold surfacc of narrow side, rcspcctively. At thc st rand surface, Cu was found as show l1 in Figs. 2(a) and 2(b), and at the 1110ld surfacc, Fe was found with mold flux as shown in Figs. 2(c) and 2(d). Figure 3 shows the scanning electron micrograph a t lhe worn mold surfacc 01' narrow side. Wcar particlcs and wcar groovcs werc observed in worn surface of mold as shown in Figs. 2 and 3, rcspectivcly. The wcal‘ mech­anisrn 01' ιoppcr mold seems to be a complex we“r of abrasive and ad hesivc wear. The arnO llnt of adhcsive and abrasivc wear in the sliding wear dcpcnds on the mClallurgical , geomelric씨 1 ， tribochcmical and environ-111en l<l 1 propcrtics. 28) Tn these various faclors, wcar phenomenon is signifìcantly inflllenccd by metallurgical properties such as hardness, work hardening and the applied load.

Thc following eqllalion can simply describc lhe Archard’s wca r law28.29) of abrasive and adhcsive wcars.

ISIJ International, Vo l. 38 (1998), No. 1

‘ rablc 4. Spccifìc voluntc 01 ’ ð. , and liquid sleels.“ ’ Spcdfic volulllc‘ cm’fg

1/1.035 O. 1234 +9.38x 10 6(T - 293)

O1225 +9.45 x 10 이T 293) +7.688x 10- (' (wI% C)

Liquid j

/

1000 1100 1200 1300 Temperature , oC

The eftèclivc coelliciclll of Ihcrmal cxp<msion of ().05、0. 1 <ll1d 0.2 wl% C slccls <1$ a f,‘IIlCliO Il of lempcr<l turc.

1500 1400

-0- 0.05wl%C. T,.,=15160C -•:J- O. 1 Owt%C. T .=1495oC ,., -&- 0 2Owl%C. Tf어=1491 0C

7

6

5

A

3

2뼈

nu

”U

AU

nu

nu

”u

。。;，。←x

-

버l「Q @〉;Q@뇨띠

Fig. 1. ’‘-

W" F,… WV IS = . -l-=k ' -_': ... " ................ ( 11) ’ I~ S }{

whcrc •VVIS is the volu l11ctric wear intensity, Wv is the volu l11e loss dllc lo wear, S is the sliding distance, 1’N IS the applied normal load, and H is the hardness 01' lhe worn 111ctal. Since surfacc preSSllrc P1 is givcn as P1 = FN /A al the givcn wearing arca, lincar wear inlcnsity, W L1S•

can be givcn as follows. 29)

W, P. W ,<<. = ... =k'

” ’ S H

where Vre( is the specjfjc volllme of matcrial at the re f'­erence tcmperature, πc(， and V is thc specifì c volumc at tempcralllre T. The cffcctive coeflìcicnl of thermal expansion incllldes volumc changes due to tcmpcratllre change and 8/7 phase transformalion. The spccifìc vol­umcs for liquid, 0 and y steels are given in Table 4.26) Using Eqs. (8) (10) and data in Table 4, the effcctive coeflìcicnts ofthermal cxpansion ofO.05, 0.1 and 0.2 wt % C stecls could be obtaincd as a function 01' temperaturc as shown in Fig. 1. The eOèclive coefficienl of thermal cxpansion at 0.2 wt% C stecl shows almost constan t value in the gi vcn ranges of temperature. Bul, at 0.05 and 0.1 wt% C stccls, with decrcasing temperalllrc below Tref, lhc cffective cocflìcient of lhermal cxpansion sharply increascd and after a maximum valuc, decreascd. ße­cause thcrc is no ðly phasc lransformation at 0.2 wt% C

‘~ sleel, the ellèctivc coefficicnl of thermal cxpansion is almost constan t. Al 0.05 and 0.1 wl % C steels, ðJy phase transformation givcs rise to high value of effcclive co­efficicnl of thermal cxpansion below starting tempcrature 01' c5jy phase trans f、'ormation.

、--

... (12)

whcre WL is lhe linear amount of wear. k is the co­ellìcicnt 0 1' wcar, which is dependcnt on lcmperaturc and cOllld be cvaluated by measuring }"N, P1, WV /S, W1./S and S from the wcar test. BlIl, d ll1'ing CQnli nllous casting, FN' P1, Wv/s, WLíS and S can not be mcasured. Evcn thOllgh malhcmatical 0 1' numerica l analysis can givc FN and P" the values of k. WV /S' WL/S and S can not bc evaluatcd from the numcrical analysis 01' expcrimental observations 01' continuolls casting

111 this stlldy, authors propose “ Apparcnt Wear 씬1-

rameter", Wp, which can describc the mold wear dllring conlinuous casting, assuming that t.he hardness of cop­per mold is proportional to the yicld stress at the tcm­peralllrc during casting.

<<:) 1998 ISIJ 55

2.2. AlIalysis (lf Wcar Phenomenon Thc appropriatc amollnt of mold taper is a very

irnportanl design parameler during operation of con­tinuous casting and typically lhe mold taper of narrow face is larger than that of wide face. At small narrow facc 1μper ， the solidifying shell is prone to hrcak-ollts, bccallse large air gap belween the Slrand and mold causes the hot spot at thc slrancl. At largc narrow facc taper, the high va lue of interfacial pressure bctween the strand and mold is dcveloped and lhc narrow tàcc 1110ld can bc casily worn. Thcrcfore, the optimization of narrow face taper can decreasc break-outs of‘ thc strand and wear phenomcnon of thc mold.

Dllring sliding contacts, wear due to adhesive, abrasive and delamination wear could take place.2기 Mold wear

ISIJ International, Vo l. 38 (1998), No. 1

8.0

F。

4.0 6.0 KeV

mAu

.‘s·mCω‘。-

10.0

4k (/J Q.,

υ 3k 〉、... i m 용 2k 디

i

lk o

Cu

Fe

(b)

2.0

Cu

0.0

5

(a)

、__ , 10.0

(d)

Scannillg elCClron micrograph and ilS EOS resuh. (a) and (b); corncr rcgion of slrand, (c) and (d); worn ll10ld surfacc of narrow side

8.0 4.0 6.0 KeV

2.0 0.0

(c)

Fig. 2.

Figurc 4 shows the initia l finile clcment mesh fOI ca lculating lhc temperature and stress of I 600 x 224 mm slab and lhc temperature of Cu 0. 1 wt%Ag mold. A quartcr scclion was modelcd llsing symmetry conditions. Thc fìnilC clement calclllalion 1‘'01' stress analysis was carricd out at the planc Slrain condition. Thc lhcnnal conductivity of Cu 0.1 wt(Yo^g mold was ‘.\ssumed to be 374 Wjm K. ll ) Tables 5 and 6 give lhc mechanicaI4.7)

and thermal propcrties 7.8) of slra nd as a function of tempera l.urc. Table 7 gives lhc mechanical propcr-ties1 1. 15.301 of Cu- O. I wt%Ag mold as a function 0 1'‘ 、、t

tem pcrature. Calculation was performed at the condi­tion of a casting spccd of 1 m/min. The distance from mcniscus to mold cxit is 770 mm. Thc temperature at mcniscus was takcn as the temperalurc which is super-heated by 20"C such as 1 548, 1 544 and 1 5360 C at thc carbon conccntrations of 0.05, 0.1 and 0.2 wt% C steels. rcspcclivcly. The Coulomb f‘riction law with the friction cocfficicn t of μ = 0‘ I has bcen applied to thc conlact sllrface of strand and mold . The calculations were car-ried oul al lhc variolls narrow face lapcrs of 0.65, 1.30, 1.50 and 1.70 %/m, carbon conccntrations of 0.05, 0.1 “nd 0.2 wt% C steels and slab dimensions of 1 600 x 224 an c1 2 150 x 224 111m.

Calculation 1’rocedurc 3.

Scanning clcclroll miιrograph at ‘hc worn mold sur­fllμ: 01' n“rrow sidc.

Fìg. 3.

l

끼

p t” 。

--lK eS

μ

W --”’ W

RcsuIts and Discussioll

4.1. Analysis 01' Continuous Casting Proccss Figurc 5 shows thc defo l'med geometries 01' lhc shell

and thc air gap near the slab corncr at various distancc bclow mcniscus al the typiιal conditions in indllstrial

4.

56

wherc P1 is thc interfacial preSSll re betwccn thc strand and mold and O' y(T) is thc yicld slress of the worn metal , Î. l' . copper 11101<1 , as a fllnction ot temperature. The apparcnl wcar parameter, W1" is a new dimension­H:!ss wcar paramcter and inversely proporlional 10 thc yicld stress of copper mold and dircclly proportional to the interfacia l pressure bClwccn the strand and mold. The apparent wcar paramcter during continuous casting can be cvalualcd from the I1nite element ana lysis with thcrmo-claSlo-plastic rnodels at the variOllS condilion 0 1、casting. With given yield stl‘css 01' coppcr l11old, inter­facial pressure CH n be easi ly obtained 1‘'rom the calcula­tion at vario LlS opcrating condition. In this study, the effects 01' 1l<lrI'()W race taper and carbon concentration on Lhc l110ld wca r have been studicd llsing Eq . (13) .

... ( 13)

‘c, 1998 IS IJ

I$IJ International, Vo l. 38 (1998), No. 1

(.;oolin l( wa.lcr cha.nnc

facc co"ler Widc facp. orr-cor’‘(! 1"

Coo)lng W a. tCI' pipes

Na rrow sidc lT\old

Fig. 4. Inilial finilc clcl11cnt IT1csh for calιIIlaling the ICll1per써 I lI rc and strcss 01' ~ llI h and Icrnpcralure of rn(l ld.

Table 5. Mcchanic‘11 propcrtics of carbon stccl ‘ .11

TCll1pCralure‘ 。C 900 1 200 1 400 1 450 감 TL

Elastic modulus ‘ GPa 2().46 7.738 4.300 3.385 0.297 (),99 x 10 J Pois~on ‘S ralio 8.23 x 10 5 T + 0.278 0.499 Yield slrcss. MP“ 20.467.738 4,300 3.385 0.297 0.99 x I() -J I’laSliç modulus. MPa 1224 555.6 330.7 278.8 25.0() 2.240

Table 6. Thermal prφerlics 01' carbon sleel.7•M’ k’ --

、 E’l lhalpy ， kJ/kg

Ther l11al conduclivily, Wjm K Lalenl hcat of ~olidificalion ，kJ/kg

11.7+ 0.648 1'‘ 1'S자 228.3+0.268T+ 1.67 x 10-4Tl

’ Ts < T~ ’TL

30 272

Tahlc 7. Mcchanical properlics of Cu 0.1 wt%^g lT1old. 11.1 5.30)

Tcmpcralure . • C 25 100 200 300 400

ElaSlic modllllls、 GP“ 11 7 117 117 11 7 117 Poisson’s rallO 0.36 0.36 0.36 0.36 0.36 Yield slrcss‘ MPa 187.4 183.5 166.7 14 1. 17 119.4

PlaSlic 1l10dlllus. MPa 1 100 1100 1100 1100 1100

operation of 0. 1 wt% C steel, slab width 01' I 600 mm. casting spced of 1 mjmin and narrow facc taper o f 1.50 % jm. Thc deformcd geomctries 01‘ the strand arc magnifìcd by 5 times to see thc formation of air gap.

- rn the initial stage of solidification, the air gap was formed on both wide and narrow side corners as ShOWI1

in this J1gurc. The wide sidc corner of the solidif‘ylng shell separa1cd away from thc mold wall a l1d thc air gap became large with the soliclilication. As solidifìca­~ion proceedcd , the air gap near the l1arrow side corncr äisappca red wi1h the rcductiol1 of slab width by thc rarrow side mold taper. Thc air gap rcduced hcat fiow from strand to mold and gavc I‘ ise to a thinncr shell in thcse regions which has been observed by previous researchers. 2.4.:\ 1) 111 thc lìna l stagc of solidifìcation, lhc air gap ncar narrow side corner complctely dis‘lppeared by the narrow facc taper and the slight surfacc depres­SiO I1 of strand denotcd as “^" can be Scel1 at thc off­corner of narrow face as shown in Fig. 5. These trends correspond 씨th the sevcre wear of narrow side mold observcd in industrial opcration_3!1 Figure 6 shows thc observed gcometry of solidil‘ying shell , which was ob­tained from 1he break-out sh이1 of 0. 1 wt% C steel at a distance below meniscus of 200 mm;' 1) aJ1d the cal-

57

Dlstance from Wlde Corner, mm 40 30 20 10 0

below ~enlscus 50mm

_. __ 300mm _ .. _ .. _ .. - 550mm - -- 770mm

A ~

E E

0 둠 E。ιi

lI: 10 e

‘ -。z E

20 ζ。

@‘J c 30 1 5。;

Fig. 5. DcforlT1cd gcomelrics of Ihe shcll !Ind thc uir gap ncar thc slab corner al vilriolls dislan∞ below menisclls under thc narrow face lapcr of 1.50 %/111. The slab wid lh of 0.1 wl % C slccl is 1 600111111 ‘

A=1524 "c B=1514 'C C=14B5 'C

10mm •---l

Fig. 6. CompariSOJl of the c찌Iculaled !Ind observcd gcomelry of sol idifying shell Ihrough ‘1 brcak-oul shcll “1 a dislancc bc l o、V I11cniscus of 200 1\1111 undcr I bc narrow fucc μlper of 1.50 % jm.

culated prolìle of‘ solidifying shell a1 the distance bclo\ν meniscus 이、 200 mm. The tcmperature lincs of 1 524, I 514 and 1 4850 C corrcsponded 10 thc lempcralures at which thc solid fractions becomc 0.0, 0.6491 and 1.0, respcctively. As shown in lhis figurc ‘ the shape 이‘ cal­culatcd solidi l"ying shcll are in good agreement with thc observcd resul t. This type of defonned gcometry around corner region of slab was called as “ corner rotation" of sol idifying shell. 32) Han el al. 32) showed tha t lhe cornel‘ rota lion of solidifying shell of slab is related with the inhomo상eneolls contraction 01‘ solidifying shcll due to thermal contraction and ðjy phase transronnatiOIl.

f 'jgure 7 shows the variation 0 1" temperature at var-

‘’ 1998 I$IJ

1500 9

1400 φ

‘-그 륨 1300 ‘-@

틀 1200 @

1- 1100

ISIJ International, Vol. 38 (1998) , No. 1

1600

- 0 Wíde Cenler -0- Wide OH-Corner -6- Narrow OH-Corner -흥，_ Narrow Center

1000 o 200 400 600 800

Distance below Meniscus, mm

FiJ:.7. V‘Iriation 01‘ SlIrf;1CC tcmpera 1‘Ire of slab with dis. lance below menisclIs IInder Ihe narrow face taper of 1.50%!rn

잉 210 @ ‘-그 톨 180 ‘-@ g E 150 m 1-프 120 。

E

240 -0- Calculaled al Wide Face -0- Calculated a‘ Narrow Face

• Measured at Wide Fa∞ • Measured at Narrow Face

90 :100 0 100 200 300 400 500 600 700 800 Distance below Meniscus , mm

Fiμ. 8. Comparison of thc calclIlatcd and observed rnold ICfl).

peraturcs with distancc bclow rncniscus IIndcr thc narro\V facc taper 01' 1.50%{II1.

ious positions in strand surface of widc face center, widc face otf-corner, narrow face center and narrow face on、'.comer. The temperatures of wide and narrow face center in strand $ur떠ce decrcascd as lhe solidification procccds and reached about J JOO"C at mold exi t. Thc tcmpcrature of wide facc oO:'corner region in strand surface decreases more sJowJy lhan that of the widc and narrow face center. Thc lemperature of narrow face off. corner region in slrand surface decreascs faSler lhan that of wide face otf-cornc.r region and is nucluating near distance below meniscus of about 200 mm. This fluctua­tion phenomenon results from the intcrmittent contacts bctwccn lhe narrow face corncr 01 ’ solidifying shell and narrow face O1old due to thc thcrmal contraction 01' shcll and narrow face tapcr.

Figurc 8 shows the variations of calculated O1old te01-peralurcs compared with expcrimcnl띠Iy O1easured data. Thc tcmperatures were I11CaslIred along the mold by lwo lhermocouples, which was installed at the diffcrcnt dcpths of 17 and 20 mm from the wide and narrow hot face mold, rcspcctively.3ll The expcrimcntally measured mold tcmperature increases sharply f‘ro01 O1eniscus and dccrcases along the mold. The measured te01peraturc 01' widc face rnold is highcr than that of narrow f‘acc mold, bccause the position of thermocouplc in wide face mold is c10ser to thc strand than that in narrow face mold ,

~) 1998 ISIJ

30

%

m

πQ m

5

EE

-

””@드〉강죠·「

-퍼ζm

-0- Calclllated at Wtde Face -0- Calculated at Narrow Face

• Measured at Wide Face • Measured at Narrow Fac

O o 200 400 600 800

Distance below Meniscus, mm

Fill. 9. Comparison ofthc calclllatcd and obse::rved shell thick. ncss wi!h distancc bclow rncnisclIs IIndcr thc narrow race !aper of 1.50 %/rn ,

Figure 9 shows the varia tions of calculated shell thick­ness compared with measured shell thickness. The shell thickness was measured from the sulfllr print of stop test slab.3’) Kim el 01. 33.34 ) suggcslcd lhat the carbon steels dllring solidification begin lo have strength at the .... ,; temperalure at which the solid fraction becomes a CI‘ itical solid f‘raction. The tempcralure at which steel begins t(l have strength is dcfìncd as ZST (zero strength lcmpcra-tllre) , Moitra ef 씨.35) considered ZST as thc lcmpcratllrc ‘-It the solid fraction 01' 0.7. Kobayashi36) proposed that ZST corrcsponds to the tempcralurc at which the solid fraclion becomes 0.8. Kim el (11,33 ,34) determined 1 hc solid f‘'raction by using micro-scgregation analysis and porous yield function. T n ordcr to determine thc cal-clllalcd shell thickness, Ihc crilical solid fraction is dctcr­mined to be 0.6491 using Ihe method proposed by Kim ('f (11. “,34) 80th measurcd and calculated shellthickncss vallles are in good agrccmen t.

4.2. Analysis of J\I’ old 、iVear4.2. 1. Etfecl of Narrow Face Taper

Brea k-outs in continuous casting process of slab arc closcly related with inadequate a010unl of narrow facc _ι

taper. When the narrow facc laper is small , thc strand ' continues to shrink and for l11S μir gaps. The air gap reduces the heat flow from strand lo mold , and increascs the surface te01peralurc 이、 Slrand and reduces the thick­ness of solidifying shcll. The hot spot at the thin shell can givc risc lo brcak-o Ll ts of the strand . When thc nar-row facc laper is large, the strand contacts with thc 1110ld during continuous c십sting and a high 、.raluc of in\.crfacial pressure between the strand and 1l10ld devclops. This high value of interfacial prcSSllre can give rise to good conlaCl bctwccn thc strand and mold, and increases the hc씨 Oow from strand to 11101d. But, the high valuc of in lcrfacial pressure can give rise to the wear phenomcnon 이‘ narrow face O1old .

The etfect of narrow facc tapers 01' 0.65, 1.30, 1.50 and 1. 70 0;;)101 at the condiliO l1s 01‘ O. J wl'Yo C steel, casting speed of‘ 1 mjmin and slab width 01' 1 600 mm has been analyzcd. Figurcs 10(1\) 낀I1d 10(b) show the deformed gcol11etries of、 the shell and air gap near the slab corner at various distance below meniscus for the narrow facc

58

EE

ζ@E。Q*。」」。zE

。‘←@QCE”-。

m

잉

m

ISIJ International, Vol. 38 (1998), No. 1

Dlslance from Wlde Corner, mm 30 20 10 0

0

below MenJscus 50mm

_ .- - 300mm _ .. _ .. _ .- 550mm - -- 770mm

E E

‘­@

E 。

‘J ~

10 g o z

E 。

20 .t @

u c 。. ” 30 Õ

Dlslance from Wlde Corner, mm 30 20 10 0 40

0

40

below 씨enlscus 50mm

_ ._ .- 300mm _._._ .. - 550mm - -- 770mm

(b) O.2wt%C Sleel f)cforl11<::d ιCOIllC‘ri es II I’ the shcll and thc ail‘ 딩ap neal Ihc slab C(> J"JlCI’ al various ‘listancc bclow mcniscus undcr thc (a) 0.05 and (b) 0.2 wt % C stccl. The slab 씨dth of narro \Y face ‘apcr of 1.50%/m i‘ 1600111111‘

E E 」

@

I

‘­。Q

* ，。 g 。

Z

E 。

20 .t @

‘j I 。

•

” 30 딩

(a) O.OSwt%C sleel

Dlslance from Wlde Corner, mm 30 20 10 0 40

0

below μenlscus 50mm

_.- - 300mm _ .. _ ._ .. - 550mm

--- 770mm

EE

‘L@E

。ugESZ

E

。‘i@uc。;5

m

m

·m

(a) Narrow Face Tapcr ofO.65%/m

D1s•once from Wlde Corner, mm 30 20 10 0 40

0

·、

below 씨eniscus 50mm

_ .- - 300mm _. _. _. - 550mm - - - 770mm

Fi딛. 12.

(b) Narrow Facc Taper of 1.70%/m

Fig. 10. Dcformed gcoll1ctries of thc sh이 1 and Ihc air gap ncar thc shlb comcr at varillUS distance bcJow JllC­nisclIs lInder thc na lTow face μlpc r of (a) 0.65 and (b) 1.70%illl. The sl‘lb width ll r 0. 1 WI% C slceJ is 1600mm.

g“ve rise to no ail‘ gap on narrow face, as shown in Fig. 10(b). As solidilìcation proceeded, lhe air gap near the narrow side corncr nearly disappeared with the rcduction of width by large narrow sidc mold tapcr, and this harcl co ntacts bctween thc slrancl anù mold could give risc Lo scrious wcar of narrow side mold.

Figure 11 shows the apparent wcar paramcler of nar­row side mold from Eq . (13) with distance bclow me­l1iscltS f‘'or the vari ous narrow face tapcr at 90 and 11 0 mm from thc narrow facc center. Al the narrow facc taper of 0.65 %jm, apparcnt wear par“meter was zero during continuous casting, bccause air gap gavc 110 contacl bet.ween lhc strand and molc1. Above thc n<l rrow 1‘acc taper 01' 0.65 %jm , thc apparent wear parameter at 1 10 111m from the l1arrow face centcr increascs sharply from about 350111m below mcnisclls, <ìnd the valuc of apparel1 t wear parameter is higher with larger narrow face tapcr up to 1.70 ‘Yo jm. Al thc 90 mm from the nar­row face cenler, the apparent wear parametcr is lower than that at 110 mm from the narrow face center and increascs from aboul 500111m bclow 111cnisclls

-0-- - • - - 0.65 %/m

-0-- - -. - 1.30 %1m

--.::.- -..._ . 1 .50 %/m

--9- - -.- - 1.70 %/m at 110. 90 mm

0.1 5

0.10

0.05

날 0.25

‘-밍 0.20 Q)

E ro ‘­m α

‘­ro @

르 ‘~ C φ

‘-m a. a. <(

/

200 400 600 800 Distance below Me niscus , mm

c“Icul‘Itcd apI끼lrcnl wcar parlllllCICr wi lh distancc ~1()w menisclIs al 90 (solid symbol) and 110 mm (이)cn symbol) from narrow facc ccnler undcr the various narrnw HICC tapcr.

l o

m nu

Fig. 11.

4.2.2. Effect of Carbon Concentration The cffcct of carbon conccnlrations of 0.05, 0.1 “nd

0.2wt% C steels a t lhe conditions 01、 slab width of

‘, 1998 lSIJ 59

tapcr of 0.65 and 1.70%/m, respeclively. As shown in Fig. I O(a), small narrow facc taper of 0.65 %/ 111 gave rise to the largc air gap on n<lrrow face around olr-corner rcgion as lhc solidification procccùs, because the nar­row face tapcr could nOI compensatc the shrinkage 01' solidifying shell. Large narrow facc taper 01' 1.70%jm could compensatc thc shrinkage of solidifying shcll and

ISIJ International, Vo l. 38 (1998) , No. 1

Figure 14 shows lhc apparent wear parameter wilh distance below mcnisCllS for thc 0.05, 0.1 and 0.2 wt% C sleels at 90 and 110 mm from narrow face center. Al 90 mm from narrow face center, lhe apparent wear paramclcr of 0.2 wt % C steel is smaller than that of 0.05 and 0.1 wl % C stccls and shows almost conslant value dllring casting. ß UI, at 110 mm from llarrow face ccntcr, the apparent wear paramctcr of 0.2 wt% C steel is largcr lhan that of O.Ü5 and 0.2 wt% C slcels and incrcascs fl‘om abollt 200 mm below meniscu$ and shows the maximum va luc at mold exi t. The dilTεrenl wcar behaviours fo r thc diffcrcnt cal‘ bon concentrations secm to be related with thc clfcclive coefficient of thermal expansion ‘ as shown in Fig. 1. The effective coefficient of‘ l.hcrmal expansion ofO.05 and 0.1 wt(Yo C steels shows l씨'gc l‘ valllc bclow reference temperaturc 、 blll that of 0.2 wl‘Yo C Slccl shows the constant value in wholc rangc of tcmpcratul‘ c. Figurc 15 shows the schematic diagram which shows thc difTcrcnt weal‘ behaviour for the 0.05 , 0.1 and O.2wt(Yo C stccls. figures 15(a), 15(b) and 15(c) show the solidifìcalion bchaviours related wilh mold wear for the 0.05 and 0.1 wt% C steel at the initial ’ J

1 600 mrn , casting spccd 01‘ 1 m/min and narrow face taper of 1.50%/m has been ana lyzed. Figure!‘ l2(a) and 12(b) show the deformed geometries of the shell and air gap ncar thc slab corncr at various d istance below meniscus for the carbon conccntration of 0.05 and 0.2 wt% C steels, respectively, and those of 0.1 wt% C sleel can be referred lo Fig. 5. ln ∞mparison with dcfonned geometry of 0. 1 wt% C steel, the aπ gap near narrow sidc corncr for thc concentration of 0.05 wt% C slccl ncarly disappcarcd by thc narrow face taper and the surfacc c1cprcssion 01‘ slrand rcduced at the off­corner of narrow facc as showl1 in Fig. 12(a). However, for the 0.2 wt% C steel, the narrow facc lapcr could sufTìcicntly compensale the shrinkage of solidifying sh이l and gavc risc lo no air gap on na rrow face as shown in Fig. 12(b). And ‘ l.hc slighl surface depression was not formcd on narrow sidc as the solidifìcation proceeds.

Figurc 13 shows lhc va riations of interfacial pressure between thc strand and l110ld al mold exit with distance from narrow facc Ccnlcr for thc 0.05, 0. 1 and 0.2 wt% C steels. With incrcasing thc carbon concentration, the width of worn region dccrcascs from 35 mm at the 0.05 and 0. 1 wt% C steels to 15 mm at the 0.2 wt% C slcel.

-0- - .... - 005wt%C -0- _ ... - o 1 OwI%C -ι- --‘ - 02αN1%C

0.15 13'11 10. 90mm

it·‘κ i*‘윈킷~~μ . .A'

200 400 600 800 Distance below Meniscus, mm

날 0.25

‘-오 0.20 m E m ‘­m α

‘­m m 르 .... ‘ t @

‘-R ooo 웅 0

0.10

0.05

-0- 005wl%C -0- 010wl%C -ó- 02OwI%C

찌

%

때

m

mαE -

@」그mω@」α

-m-Qmt$t

0

Calculatcd apparcnl 、IJcar pararneler wi th d i stancζ

below mcnisc lIs at 90 (sol id symbol) and 110 111m (opcn symbol) from narrow face center IInder the variolls stccl gradcs

liig. 14. o 20 40 60 80 100 120

Dista nce from Na rrow Center, mm Ca lι1I 1a led inlcr‘ facial prcsslIl‘C al mold cxit with dis­tancc I‘rom narrow fact centcr between the slrand and 11101<1 lIn<lcr thc variolls slccl grades.

Fig. 13.

)J

lnitial stage

(d)

Middle stage

- ContracUon

(a)

lnterfacial prc88ure Rotation

“ - - --‘--..，...얘A --------t- 끼 '{I L.... I

II :j1B~그= Taper Mold • ' 11 ' 1 e xit

W 00

Schcmatic diagmm of corncr rolalion of solidifying shcll in continuou‘ ‘:asling slab. (‘1)‘ (b) and (c); 0.05 ilnd 0.1 、，vt% C slccls‘ (d), (c) and (1); 0.2 wt% C slccl.

(e) (b)

60

Fig. 15.

({) 1998 ISIJ

/‘

、-

ISIJ Internationa l. Vo l. 38 (1998). No. 1

Dislur‘ ce be OW Mcniscus , m m

400 /'

(a) Fronl sidc (b) ßOlIom side

Fìμ. 16. Photographs 01' Ihc narJ'ow facc mold wι1 1' <11 Ihc (a) frolll side and (b) bollolll sidc under Ihc narrow face 11Iper of 1.50 %1’”‘ rhc mold was typica l1y lIscd r‘01' l11e cOlllinuolls cílsling of 0.1 wl% C slccl ‘II1d slab widlh 01‘ 2 ) 50 1I111l , after ovel' sevel‘ a) hllndrccl hcats.

Apparenl wear parameler level

딩 100 tl (b) I L (c)

딩 200

1 1

A=0.025 8=0.050 C=O.lOO D=0.160

m :를 400 늦

p。--‘<l) 500 ，。

φ

g 8OO 띠 .....

·m{ 7OO Q

EXIT 0 20 40 0 20 40 0 20 40

Distance from Narrow Corner, mm Fig. 17. Pl'cdiclcd wcar map of na l1'0W siclc rnold we‘11' IIndcl

Ihe narrolV facc taper 01‘ l ‘50%/111 at the (a) s)ab lVidlh 01'2 150 Ill lll alld 0.1 wl% ç slccl ‘ (b) slab widlh 01' 16‘JO lI1m l1nd 0.1 wt% C stccl, :1nd (c) sl“b width

can glve nsc 10 “ depressioll on the surfacc 01‘ S이 idify­ing shell, which was called as “ corner rotation." ‘2) Thus, interfacial prcssu re for the 0.05 and 0.1 wt% C steels shows the largcst peak at thc narrow corner and sec­ond largest pcak around narrow off-corner regioll . ßul‘ for the 0.2 wt 'Yo C stcel‘ the intcrfacia.1 preSSllre al cor­ner shows the largcsl peak and sccond largest pcak found in 0.05 Hnd 0.1 wt % C steels disappears.

4.2.3. Pred iction of Wear Map 01' Narrow Side Mold Figures 16(a) and 16(b) show the photographs 01' ob­

scrvcd mold wear 이、 narrow sidc at the front sidc and botto l1l side at the narrow facc taper 01' 1.50 %/m, respeclivcly. Thc mold was lypic<니 Iy used for thc con­tinuous casling of 0. 1 wt% C Slcel and slab widlh 01‘

2150111111 , ar‘ter over several hundrcd heats. The mold wear al lhc front side started frOI11 about 200 mm from meniscus, and thc width 01' mold wcat‘ a t. the botto ll1

side is observcd “s about 30 mm.

....._ of 1600111111 and 0.2wl% C slecl. Thc caplions "A­[)" denotc thc apparent wear paramctcr.

Figure 17 shows lhe predicted wear map 01‘ ll <l rt‘ow sidc mold at the various conditions in industrial opcra­lion. Ca lculated apparent wcar pa r‘lmeter level al nar­row sidc mold is denoted as “ A, ß , C and 0 ’‘ in lhis figure. Figurc 17(a) shows thc prcdicted wear l11ap at the conditions or 0.1 wt% C steel, narrow face tapcr 1.50 %/m, casting speed of I l11jmin and slab width of 2 150 mm. The 1110ld wcar at the front sidc started 1'1'0111 about 200 l11m from mcnisclls, and thc widlh 01' mold wcar at the bottom sidc is predicted as about 30 mm. This prcdicled wear map arc in good agreemcnl with the observed wcar phenomenon al the same casling conditions as shown in Fig. 16. Figurc 17(b) shows lhc prcdictcd wea r map al thc conditions 01、 0.1 wt끼) C steel, narrow facc laper 1.50%/111, casting speecl 01'‘ Imfmin and slab widlh of 1 600 111m. In lhis case, the mold wcar at the front sidc stHl‘ ted from abolll 350 mm frorn tnC­niscus, and thc widt h of mold wcar al the bottom sidc is prcdicted as about 35mtn. Figu re 17(c) shows the predicted wcar rna.p at the condi\.ions ofO.2 wt'10 C slccl, narrow I'ace μlpcr 1.50 %/m, casling speed of‘ 1 tn/min and slab width 01‘ 1 600 mm. But. in lhís case, the tnold wea r at the front sidc started from ahout 150 mlll from rncniscus, and thc widlh of molcl wcar al lhc bottom sidc is prediclcd as about 15 mm as shown in Fig. 17(c).

middlc stage ancl mold cxit, respectively. Figures 15(cI)‘ 15(c) and 15(f) show thc bchaviollrs for thc 0.2wt% C stee l. The length 이、 arrow in the figurc indicales the amounl of lhcrmal contraclion. For the 0.05, 0.1 and 0.2 wt% C Slccls, at the initial stage of solidilì­calion, lInifonn solidil‘yi ng shell forms as shown in Figs. 15(a) and 15(d). T he thennal contraction 01' 0.05 and 0. 1 wt% C slccls ncar solidilìcalion front is larger lhan that of surl'acc 01' solidifying shell. por the 0.2 wt% C steel, thermal conlraction in the soliclifyi ng shell is uni­|‘orm as shown in Fig. 15(d). At the micldlc stage of so­lidilìcation of 0.2 wt% C slccI‘ lhe thermal contraclion gives rise to aÏl‘ gap arollnd Corllcr region and narrow 1'1Ice taper reduccs lhe air gap around narrow ofl‘-corncr rcgioIl. At the l110ld exit, narrow facc taper gives rise to no air gap arouncl narrow off-corner rcgion as shown in Figs. 15(이 ancl 15(f). Al the 0.05 ancl 0. 1 wt% C stccls、 large thermal conlraction near solidilìcation front

61 :t) 1998 ISIJ

ISIJ Internationa l, Vo l. 38 (1998) , No. 1

5. Conclusions

Using a 2-dimensional coupled thenno-elasto-plastic

finite element model f01‘ the slice of strand in continuous

casling proccss of slab, lhc lhcrmo-mcchanical bchav­

iours 0 1' slrand and mold, and the wεar phenomenon 이‘ narrow face mold has been analyzed. The caIculated

results 0 1' deformed geometries of the strand, tempera­

ture 0 1' the mold , t hickness of the solidifying shell and

wear phenomenon 0 1' the narrow side mold at the typical

condition of continuous casting in indust1'Y al‘e in good

“g 1'eement with the experimenta l obser vation. To p rcdicl lhc possibilily 0 1' mold wear, a ncw di­

mensionless parameter of “ Apparent Wear Parameter", Wp , which is inversely proportional to yield stress of the

mold and d irectly p 1'opo1'tional to the interfacial pressme

between the strand émd mold , was p 1'oposed . The effect

0 1' narrow face taper and ca1'bon concent1'ation on the mold wear has been studied. With inc1'easing nar 1'ow face

tape1' at the conditions of 0. 1 wt% C steel, casting speed of 1 mjmin and slab width of 1 600 mm, mold wear in­

creased, because la1'ge narrow face t.aper gives large inte1'facial pressure between the strand and moJd. Wilh

increasing lhc carbon conccnlralion, lhc width of、 worn

rcgion dccl‘ cascd fr0111 35 111m al 0.05 and 0.1 wl 'Yo C sleel

lO 15111111 al 0.2 wl % C slee l. The smaller wear region of

lhc 0.2 wt% C steel see111S to be related with unifo 1'ming thennal contraction due to constant effective coefficient

of thermal expansion.

Acknowledgments

This work has been financially and technically sup­

ported by POSCO, Pohang, Ko1'ea . Autho1's a 1'e also gr떠atefu비l끼lηfo이'01' the helpful d씨ii써S‘cαω;l씨uss셉S잉io이011μ15 f1'‘'1'01이m Mrι‘' . S. H. Cαho이 )끼 i a떠t Sc이hoα00…o이)서1 0“fM‘at떠e히l'‘띠s Scω;ie히nce and Enginccring, Scoul National Unive 1's ity, Seoul, Korca.

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