j.k. be - reflections and perspectives - the formation of oscillation marks in the cc of steel slabs

8/3/2019 J.K. be - Reflections and Perspectives - The Formation of Oscillation Marks in the CC of Steel Slabs

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The Formation of Oscillation Marks inthe Continuous Casting of Steel SlabsE. TAKEUCHI and J . K. BRIMACOMBEThe formation of oscillation marks on the surface of continuously cast slabs has been studied bymetallogra phically exam ining slab samples and by performing a set of mathem atical analyses of heatflow, lubrication. and meniscus shape in the meniscus region of the mold. The metallographic studyhas revealed that, in agreem ent with previous work , the oscillation marks can be classified principallyaccording to the presence o r absence of a sm all "hook" in the subsurface structure at the base ofindividual oscillation marks. The depth of the oscillation marks exhibiting subsurface hooks varieswith the carbon content, reaching a maximum at about 0.1 pct carbon, while the oscillation markswithout hooks show no carb on depend ence. The ana lysis of heat flow at the men iscus, which is basedon a measured mold heat-flux distribution, indicates that depending on the level of superheat, themeniscus may partially free ze within the period of a typical mold oscillation cycle. Lub rication theoryhas shown that, owing to the geometry of the mold flux channel between the solidifying shell at themeniscus and the straight mold wall, significant pressure gradients capable of deform ing the meniscuscan be gene rated in the flux by the reciprocating motion of the mold relative to the sh ell. A forc ebalance on the interface between the steel and the mold flux has been applied to compute the shapeof the meniscus as a function of the pressure developed in the lubricating flux at different stages inthe mold oscillation cycle. Th is has demonstra ted that the "contact" point between the me niscus andmold moves out of phase with (by n/2), nd has a greater amplitude than. the mold displacement sothat just at, or near, the end of the negative strip time molten steel can overflow at the meniscu s. Fromthese studies a reasonable mechanism of oscillation-mark formation emerges which involves inter-action between the oscillating mold and the meniscus via pressure gradients in the mold flux, m eniscussolidification, and overflow. The mechanism is consistent with industrial observations.

I. INTRODUCTIONTHEurface of continuo usly cast slabs is characterized bythe prescnce of oscillation marks that form periodically atthe meniscus due to mold reciprocation. A typical exampleof oscillation marks is shown in Figure 1. The oscillationmarks have an importan t influence on the su rface quality ofthe slabs because they are often the site of tran sverse cracks,and therefore influence crack form ation. It has been fo und,for example, that reduction of the depth of the oscillationmarks by increasing the mold oscillation frequency dimin-ishes the severity of transverse cracks.' Improvement ofsurface quality by such means is particularly important at thepresent time as "direct-charge" practices are being devel-oped in which, to minimize energy losses, the slabs aretransferred from the caster to a reheating furnace withoutintermediate cooling for s urface inspection . Clearly. a key toachieving high surface quality is the control of phenomenain the m eniscus region which influence initial solidificationand the formation of oscillation marks.To date surface quality has been improved largely byempirical means such as changing mold fluxes2.jand, asmentioned earlier, raising the frequency of mold oscil-lation. Further gains in surface quality, howe ver, can bemade if the meniscus phenom ena are understood sufficientlywell to predict the influence of variables like mold-fluxcomposition, superheat, steel grade, casting speed, and

E. TAKEUCHI, on study leave from Nippon Steel Corporation, is aGraduate Student, and J . K. BRIM ACOM BE is Stelco Professor of ProcessMetallurgy. both with the Department of Metallurgical Engineering, TheUniversity of British Columbia, Vancouver, B.C. V6T IW5, Canada.Manuscript submitted January 23 . 1984.

mold oscillation characteristics on initial solidification andthe formation of oscillation marks. This is a difficult taskbecause the meniscus phenomena which involve rapid heatextraction, fluid flow, and a complicated interplay of forcesare exceedingly complex. The present study has beenconducted to shed light on these vital aspects of initialsolidification.

11. PREVIOUS WORKHeat flow and solidification in the meniscus region pre-viously have been studied both experimentally and theo-retically. The axial distribution of heat extraction by slabmolds has been determined from temperatures measuredwith thermocouples imbedded in the copper plate(s) of them ~ l d . ' . ~ . ~nfortunately, one-dimensional heat conductionthrough the thickness of the mold wall has been a ssume d inconverting the thermocouple readings to local heat fluxeswhere as, as Sam araseker a and Brimacornbe'' have show n,

the axial component of heat conduction in the meniscusregion is large. Implicit neglect of axial heat conductionmeans that reported data for heat flux at the meniscus arelower than the actual values. Another deficiency, from thestandpoint of characterizing heat flows in the meniscus re-gion, is the absence of heat-flux data over the length of themold wall above and adjacent to the meniscus. Thus, theheat-flux profiles reported in the literature are inadequa te forthe prediction of the temperature distribution in the moldflux and steel at the men iscus. Kno wledg e of the m old-fluxtemperature at the meniscus is very important because itaffects the viscosity and flow of the flux into the gap be-tween the mold wall and solidified shell.


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Fig. I -Appeara nce of oscillation marks on the narrow face of a slab.

Solidification in the meniscus region has been investi-gated theoretically by T omon o et al." and Saucedo et al."The first authors assumed one-dimensional heat conductionin the steel and two-dimensional heat conduction in themold wall, while the latter workers accounted for two-dimensional conduction in the steel but ignored the moldwall and characterized steel-to-mold heat transfer by anassumed heat-transfer coefficient. In both studies the pres-ence of mold flux was ignored. While these simplificationslimit the direct applicability of the mod els. it was show n thatsome solidification of the meniscus is possible, and that apartially solidified meniscus could play a sign ificant role inthe formation of oscillation marks during slab casting.Oscillation marks form on each cycle of m old oscillationso that the pitch of the oscillation marks, 1, depends in-versely on the oscillation frequency*

*Nomenclature is provided at the end of the paper.

Negative-strip time is the time interval in each cy cle of moldoscillation in which the downward velocity of the moldexceeds the withdrawal rate of the stran d. A typical negativestrip time is 0.2 to 0.3 second. The depth of oscillationmarks decreases with increasing oscillat ion f r e q u e n ~ y ' , ~ , ~ , ' ~and increases with increasing oscillation strokeand negative-strip time."-l8 The effects of mold-flux prop-erties and casting spee d on the depth of th e oscillation markshave not been determined clearly.Oscillation marks can be clas sified according to the adja-cent solidified structure. Emi et a/.'' have discerned twotypes of os cillation marks based on the presence or absenceof a small "hook" in the subsurface structure adjacent toeach oscillation mark . It has been reported that non-m etallicinclusions can be concentrated in the vicinity of pronouncedhooks and that positive segregation may be found at thebottom of oscillation marks; the extent of the segregationdepends on the depth of the marks."Several mechanisms have been proposed to explain theformation of oscillation mark s. SatoI9 has sugg ested, as didSavage and Pritchard in 1954,20hat the shell "sticks" to themold wall such that on the upstroke of the mold, the shell

ruptures allowing liquid steel partially to fill the gap created.This event is followed by a "healing" period while the moldmoves downward. This mechanism is difficult to justify,however, because the oscillation marks on a slab surfa ce arerelatively straight and horizontal (Figure I), which wouldhardly be possible if the rupture mechanism predominated.Emi et aI.l4 have proposed a mech anism, in which the topedge of the shell is pushed into the molten steel by liquidflux during the negative strip period of the mold o scillation.The mold flux is "pumped" into the channel between thesteel and the mold by a frozen slag rim attached to the moldwall. At the end of the nega tive-strip period, when the moldand strand are moving downward w ith the same velocity. theflux pressure is released and femostatic pressure eithercauses molten steel to overf low the partially solidified me-niscus to form a hook or the meniscus is pushed back towardthe mold wall such that a hook is not created. Th us, the hookadjacent to oscillation marks is a manifestation of moltensteel overflowing a partially solidified meniscus. Similarconcepts have been invoked by Based onexperimental results obtained with a "mold simulator",Kawakami et aI.l5 have suggested that oscillation marksarise from the interaction of a viscous layer of mold fluxwhich moves with the mold wa ll, and during negative strip,physically bends the top of the solidifying shell. Moltensteel then overflows the bent shell. These mechanisms areessentially conceptual in nature and, to date, have beenapplied only in a qualitative manner to rationa lize the influ-ence of os cillation character istics on the pitch and depth ofoscillation m arks.

111. SCOPE OF PRESENT STUDYThe depth of the oscillation marks has been related pre- In the present study, an attempt is made to overcomeviously to the stroke and fre quency of mold oscillation, and some of the deficiencies of earlier investigations and tomore generally to the negative-strip time, t ~ ,hich can be establish a stronger theoretical foundation f or the formationexpressed as follows: of oscillation marks than hitherto has been reported. The

I approach taken has been to examine oscillation marks met-b =- rc cos(-$) [2] allographically from a large number of slab samples andnf thereby to observ e. at first hand, the geom etry of the ma rks,


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the adjacent subsurface structure, and the influence of cast-ing variables on these metallurgical aspects of oscillationmarks. Next, a series of theoretical analyses has been under-taken to examine three of the phenomena that are importantin the meniscus region:[i] heat flow involving steel, mold flux, and the moldwall;[ii] flow of the molten mold flux into the gap between thesteel and mold wall. and the generation of pressure gradien tsin the flux due to mold oscillation;[iii] deformation of the meniscus as a result of the pressuregradients i n the adjacent molten flux.

This approach reveals the importance of previously un-reported factors such as the geometry of the flux channelnear the meniscus and the deformation of the meniscusshape by oscillation-generated flux pressure. Finally, theanalyses of heat transfer and fluid flow are combined in anoverall model of the meniscus that predicts trends in agree-ment with industrial findings. In the paper the results of eachsubstudy are first presented followed by a discussion of themechanism of oscillation-mark formation and a presentationof the overall model predictions.

IV. METALLURGICALSTUDY OF SLAB SAMPLESA. Casting Conditions

The casting conditions and composition of the slab sam-ples examined are presented in Table I. Note that the carboncontent of the steel ranges from 0.08 to 0.26 pct and thatthe steel has either been Si-killed or Al-killed. The sametype of mold flux was used for all the heats, and m etal-levelcontrol was implemented.Samples for the study were cut from the narrow face ofthe slabs because, unlike the broad face. it is not deformedby ~u pp or t olls in the casting machine.B . Metallographic Technique

The pitch of the oscillation marks was measured at thecenter and comer of the as-cut samples. The steel samplesthen were cut longitudinally perpendicular to the oscillationmarks to reveal the profile of the slab surface and the sub-surface structure. The longitudinal sections so obtainedwere machined flat, polished, and etched with either picricacid or Oberhoffer's etch. The subsurface structure wasexamined and photographed using a standard optical micro-scope. The depth of the oscillation marks was measuredfrom the base of the mark to the level of a rule resting on theslab surface.Table I. Casting Conditions and

C . Appearance and Pitch of Oscillation MarksThe narrow face of a typical slab, exhibiting oscillationmarks, has been shown already in Figure 1. The marks areseen to be evenly spaced and closely parallel across the face.The average value of the measured pitch is about 16 mmwhich corresponds closely to that calculated from Eq. [ I ] ,as expected. The average pitch was not ob served to increasewith casting speed because mold frequency was linked to the

casting speed. The scatter in pitch m easurem ents, expressedas a standard deviation, was found to increase from 0.7 to5.2 mm with increasing casting speed from 0.8 9 to 1.25 mper minute. The results were the same for the center andcomer of the face. Presumably the increased variability ofpitch is caused by sudden small changes in men iscus leveldue to flow variation and turbulenc e, that are more difficultto control at the higher casting speeds.D . Subsu$ace Structure of Oscilla tion Marks

Oscillation marks were found with and without hooks inthe adjacent subsurface structure, as reported by Emiet a1.,I4 although the majority exhibited hooks. Typicalsubsurface structures of the two types of oscillation marksin low-carbon (0.08 - 0. 09 pct) and medium-carbon(0.26 pct) slabs are shown in Figures 2 and 3. It is seen thatoscillation marks accomp anied by hooks in 0 .0 9 pct Cslabs (Figure 2( a)) are deeper and the trough associated witheach mark is longer than those in the 0 .26 pct C slabs(Figure 2(b )). This d ifference is not found in the case ofoscillation marks without hooks (Figure 3). Moreover,hooks in the subsurface of 0.09 pct C slabs form a smallerangle with the surface than in the 0.26 pct C slabs. Thedendrite orientation adjacent to the oscillation marks is simi-lar to that described by Emi et al. I4viz. , that den drites ini-tially grow normal either to the hooks when they are presentor to the curved surface of the oscillation mark when thehooks are absent. In either case, the dendrites then changeorientation within a short d istance to become roughly per-pendicular to the mold wall. Finally, slab samples free ofsubsurface hooks characteristically also contained smallspherical blowholes, that are likely trapped argon gas thatwas injected through the tundish nozzle.E. Depth of Oscillation Marks

Figures 4 and 5 show the depth plotted against thepitch of the oscillation marks measured in the 0.08 and0.2 6 pct carbon slabs, respectively. The oscillation-m arkdepth and its dependence on pitch is the same for marks withand without hooks in the low-carbon slab (Figu re 4) and formarks without hooks in the higher carbon slab (Figure 5).As was also observed in the previous section, the depth ofComposition of the Slab Samples

Chemical 0.08 0.58 0.20 0.007 0.009 0.001Composit ion (Pct) -0.26 -0.89 -0.24 -0.009 -0.019 -0.033Casling conditions: temperature (in tundish ): 1529 to 1549 "C: casting speed: 0.89 to 1.25 m/min; immersion nozzle: bifurcated, 25 d eg dow n; moldsize: 1829 to 1930 mm x 178 to 203 mm; mold oscillation: 12 .7 mm stroke, 4 0 to 90 cpm frequ ency; viscosity of mold flux: 5.45 poise at 1200 "C.2.65 wis e at 1300 "C.


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I 1 I15 2 0 25P~ tc h of Oscillat~on Morks (mm)Fig. 5-Relationship between depth and pitch of oscillation marks in0.26 pct carbon slabs.

Subsurface Hooks I) Absenl 1

Carbon Content of Slo bs I0/0)Fig. 6-Influ ence of carbon content of the slabs on the depth of oscilla-tion marks.

mold wall which accounts for vertical as well as through-thickness heat conduction. Moreover, the mathematicalmodel of heat conduction in the mold flux and steel is alsofully two-dimensional.A . Axial Profile of Mold Heat Flux at the Meniscus

The mold heat-flux profile has been calculated from themold temperatures reported by Nakato and M u ~ h i ~ ~uringthe casting of slabs for heavy plate. Their values of moldtemperature close to the meniscus are shown as closed cir-cles on the left-hand side of Figure 7. The mold heat-fluxprofile was determ ined using the ma thematical model of themold wall reported by S amarasekera and Brimacomb e."The two-dimensional model is based on assumptions ofsteady-state heat conduc tion, negligible transverse heat con-duction, negligible oscillation effects, and cooling water inplug flow . An assumed heat-flux profile, which defines theboundary co ndition at the hot face of the mold, was input tothe model and the two-d imen sional tempe rature distributionwas calculated, then compared to the local values reportedby Nakato and M uchi. The heat-flux profile next was ad-justed to obtain a better fit and the process was repeateduntil predicted and measured mold temperatures were in

Distance From ColdF a c e (m m) Heat Flux (kw/rn2)

0 20 40 0 1000 2000 3000100 I l l 1 1 I IMea s u r e dtemperature IoC)

80 -60 -

Fig . 7-Temperature distribution in the mold wall and the heat flux distri-bution near the meniscus (closed circles are values of mold temperaturereported by Nakato and Muchi14).

close agreement. The results of the temperature fitting andthe heat-flux profile determined are shown in Figure 7 .The mold heat flux is seen to have a maximum value of2500 kW/m2 at 5 mm below the meniscus, while in themold flux region, i t is 700 kW/m2. The peak heat flux isslightly greater than that reported by Nakato and M u ~ h i . ~ ~tis also interesting that the maximum mold temperature islocated at about 35 mm below the meniscus which is 30 mmbelow the level of peak heat flux. This difference resultsfrom the significant vertical heat conduction in the menis-cus region.B. Temperature Distribution in the Mold Flux and Steel

To predict the temperature distribution in the meniscusarea, an approach similar to that of Tomono et al." andSaucedo et al.12 has been adopted in which, due to theinfluence of mold oscillation on local fluid flow, tempera-ture gradients in the mold flux and steel are assumed to bedestroyed periodically. This event is followed by an interv ali n which heat is conducted in unsteady state through thephases. The concept is analogous to the "surface renewal"theory proposed for mass-transfer systems by Higbie25.26many years ago. During the unsteady-state period, thephases are assumed to be stagnant which inclu des neglectingthe downward motion of the steel. In our calculations, thisperiod is assumed to commence at the end of the negative-strip interval of the mold osc illation cycle becau se "overflow "


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.O 2 4 6 8 10Distance From Mold Wall (mm)

Fig. 9-Predicted temperature distribution in the mold flux and fractionsolidified in the steel at the meniscus after a time of 0.3 s. Molten steelassumed to be stagnant. Calculation conditions given in Table 11.

Note that the superheat of the steel is taken to be 5 "C inthe vicinity of the meniscus, and the initial temperature ofthe mold flux is 1500 "C.' Figure 9 shows the resultsof the calculations, expressed as isotherms in the mold fluxand fraction solidified, f,, in the steel. after a period of0.3 seconds. Thus, the solidifying shell is predicted to beonly partially solid with f, = 0.6 located at about 0.1 mmfrom the mold wall and f, = 0.2 situated at about 0.6 -0.7 mm. These positions are similar to those reported bySaucedo et o l . " although they also predicted solidificationfarther along the meniscus. That the region of f, = 1 isnegligibly small does not mean that the semisolid shell hasno rigidity. Saucedo et a l . have sugg ested that the shell mayexhibit rigidity iff, is as low as 0.2 whereas Matsumiyaet a / . 9 have used a value of 0.8 5 for a rigidity criterion. T hecritical J; remains unknown, but it is possible that the shellformed in 0 .3 or 0 .4 seconds could act as a solid. Thissuggests that the overflow mechanism that gives rise tosubsurface hooks is plausible; but because the extent of thepredicted meniscus solidification is considerably less thanthe depth of the observed hooks, 1.5 to 2 mm in Figure 2,it does not, by itself, adequately account for the formationof oscillation marks.These calculations have been performed assuming thatthe molten steel is stagnant which effectively minimizes theextraction of superheat and maximizes the growth of thesolid shell. Convection in the molten steel, however, can begenerated at the meniscus by the input streams dischargingfrom the submerged pouring tube and by inert gas that isinjected into the tundish nozzle and entra ined by the flow ingsteel. These effects have been modeled crudely by in-creasing the thermal conductivity of the stagnant steel by afactor of four. The calculation of the temperature distribu-tion in the meniscus region has been repeated, and the re-

Dis tanc e From Mold Wall (mm)Fig. 10-Predicted temperature distribution in the mold flux and fractionsolidified in the steel at the meniscus after a time of 0. 3 s. Convection inmolten steel incorporated by artificially raising liquid conductivity four-fold. Other calculation conditions given in Table 11.sults are shown in Fig ure 10. The frac tion solid is seen to bediminished significantly and, depending on the correct ri-gidity criterion, the shell formed in 0. 3 seconds may behavemore like a liquid than a solid. Under these conditions, flowof molten steel over a partially solidified rigid meniscuscannot take place as before, and subsurface hooks will notform. Thus, from these calculations it can be argued that thepresence or absence of subsurface hooks depends on thelocal extraction of superheat at the meniscus which is gov-erned by the magnitude of the superheat and the convectionin the molten steel. This argument will be taken up later inthe paper.Another important aspect of the predictions shown inFigures 9 and 10 is the low temperature of the mold fluxadjacent to the mold wall. Since the viscosity of typicalmold fluxes increases sharply with temperature below1000 - 1200 "C," a very thin zone of high viscosity fluxmust exist against the mold w all. As sh all be see n, this highviscosity flux plays an important role in the formation ofoscillation marks.

VI. FLUID PRESSUR E IN THEMOLD FLUX AT THE MENISCUS

It has already been seen that a simple overflow mecha-nism cannot explain the depth of the subsurface hooks, andtherefore other factors must also play a role in the formationof oscillation marks. T he m ost obvious is the mold flux an d,in particular, its behavior as it flows, under the influence ofmold oscillation and strand withdrawal, into the gap be-tween the solidified shell at the meniscus and the mold wall.Previously the action of the flux, specifically its lubric-ity, has been characterized in terms of the shear stress


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Fig. I I -Geometry of mold flux channel at the meniscus.

that acts on the strand. While this may beimportant for overall mold lubrication, i t will be shown herethat the shear stress is not very significant at the meniscusas compared to the pressure generated in the mold flux bythe mold oscillation. This pressure, which has not beenconsidered previously, arises because the flux chan nel nar-rows in width as the me niscus curves toward the mold wall,as shown schematically in Figure 11. In this part of thestudy, the flux pressure has been estimated roughly fromfluid flow principles originally applied to lubrication prob-lems by Reynolds and others.32The following assumptions have been made to predict thepressure and velocity distributions in the flux channel:[i] Steady state is assumed which is equivalent to sayingthat the pressure and velocity gradients are instantaneouslyestablished;[ii] Inertial forces can be neglected because fluid velocitiesare low and the flux viscosity is high;[iii] The flux behaves as a Newtonian fluid;[iv] The meniscus in the region of interest is covered witha rigid "solid" skin, and the shape of the flux channel doesnot change significantly;[v] Flux velocities in the transverse direction (u:) and normalto the steel (u,) are negligible. u, is neg ligible because theangle formed.by the meniscus with the vertical is small;[vi] The density and viscosity of the mold flux are constant.The latter assumption is, admittedly, very restrictive be-cause the large temperature gradients across the flux channelwill result in a correspondingly steep viscosity gradient. Itwould be preferable to couple the heat and fluid flows andsolve simultaneously for the temperature, velocity, andpressure distributions, but at this early stage in the devel-opment of the model, this added complexity is unw arranted.

It does mean , however, that the flux pressures predicted areonly very approximate relative to real values.Under these assumed conditions, fluid flow in the fluxchannel is governed by the following equation of motion:

and equation of continuity

where QR is a relative consumption rate of mold flux. Itshould be noted that, because the rigid meniscus skin ismoving down ward with the strand, u, s a relative velocity,expressed as

where vf and v, are the flux and strand velocities, re- .spectively, both of which are defined relative to a fixedreference frame. T he boundary conditions, subject to whichEqs. [6] and [7] are to be solved, are (see Figure 11 fordefinition of boundaries):

[ i i ] 0 a x 5 I,, y = h(.r), u, = 0

Note that B.C. [i] and [ii] are a statement of the "no slip"condition which is correct provided that the rigid skin as-sumed to cover the meniscus in the flux channel behavesas a solid.The solution to Eqs. [6] and [7] is described briefly in theAppendix. For the case where the part of the m eniscus underconsideration is taken to be linear, and bounded by thecoordinates ( 0, hi) and (l/,.hf), see Figure 11, the pressuregradient in the mold flux 1s given by:

and the velocity distribution isu. = (v. - v.)(l - f ) { 3 b m - v.)

Figure 12 shows the pressure distribution calculated fromEq. [9] for different flux viscosities and for both upward anddownw ard mold v elocities. A mold oscillation frequency of100 cpm, a stroke length of 8 mm, and a casting speed of1.0 m per minute have been assumed for this case. T he length


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100 I I 1 I tdownward motion

f =I00 pmV = 1.0m/min

I upward motion I-60 ' I I I I I0 2 4 6 8 10Distance Down Mold Wall (mm)

Fig. 12-Predicted axial pressure profiles in the flux channel near themeniscus. Flux channel dimensions assumed to be: h, = 0 . 3 5 m m ,h, = 0.05 rnm, 1, = 10 mm .of the flux channel has been determ ined from the pitch of theoscillation marks while the value of the lower channelwidth, hJ ,has been a pproximated from calculated v alues ofthe minimum thickness of mold flux based on m easured fluxconsu mptio n rates.'"n Figure 12 the mold flux is seen todevelop a positive pressure on the downstroke and a nega-tive pressure on the upstroke. A maximum in the flux pres-sure is predicted toward the bottom of the flux channel forboth upward and downward mold velocities. As expected,the magnitude of the peak pressures increases with in-creasing flux viscosity. Interestingly, the maximum value ofnegative pressure on the upstroke is greater than that of thepositive pressure on the downstroke, because on the up-stroke the motion of the mold rela tive to the strand is greater.With a flux viscosity of 10 P, this negative pressure is muchlarger than the local ferrostatic pressure.Figure 13 show s the velocity distribution in the flux ch an-nel, as calculated from Eq . [lo]. at the maximum downw ardvelocity of the mold. The conditions assumed are the sameas applied in the pressure calcu lations, and the flux v iscosityis 5 P. As expected, a downw ard velocity is predicted nearthe mold wall, and a flow reversal is seen near the steel in

Distance From MoldWall (mm)0 0.10 0.20 0.30

Fig. 13-Predicted relative velocity distribution s in the flux channel nearthe meniscus at time of maximum downw ard velocity of the mold. Condi-tions as for Fig. 12 and assumed flux viscosity is 5 P.

distribution in Figure 13, as follows:

The values obtained are an order of magnitude less than thepressure shown in Figure 12, and therefore the shear stresswill have only a minor effect on meniscus behavior.

VII. MENISCUS SHAPEThe shape of the meniscus depends on the presence of asolidified skin and, more conventionally, on the balance offorces acting at the interface between the mold flux andmolten steel. It is clear from the previous section that an

important force that cannot be ignored is the fluid pressuregenerated in the mold flux channel. Thus, in this part of ourstudy, a mathematical relationship has been developed topredict the meniscus shape resulting from the flux pressuredeveloped at different stages of the mold oscillation cycle.A two-dimensional meniscus, as shown in Figure 14. hasbeen considered. To simp lify the calculations, the m eniscusis assumed to be free of a rigid skin and to attain its equi-librium shape instantaneously.* The equ ation governing thethe upper region of the flux channel. *An attempt was made to incorporate a solid skin. but the predictions ofThe shear stress acting on the m eniscus (assumed to have skin deformation, using finite-element analysis, were too uncertain witha rigid skin ) has been calculated from the velocity present knowledge of skin thickness and mechanical properties.


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static shape of the meniscus under the influence of fluid [iii] The newly calculated meniscus profile was approxi-pressure is derived in the Appendix, and is as follows: mated by a new quadratic equation; P(x) and R(x) were

where R (x) = f i P ( x ) - p,gr}dr0 [I31P(x ) is the axial pressure distribution in the mold flux calcu-lated from Eqs. [6] and [7], assuming complete slip at themeniscus, i . e . , at y = h(x) , v, = 0 and y = 0 , v - v,.I -I t may be noted that if R ( x ) = 0 , i . e . , no dynam~c res-sure, Eq. [12] reduces to the analytical solution given byBikerman" and MatijeviCM for a static meniscus

y = - d m

where a * , the capillary constant, is defined as

The "contact" point of the meniscus with the mold wall, x,,as defined by 4 = r / 2 , was calculated from Eq . [A231

The meniscus shape was calculated at selected pointsin the mold oscillation cycle by the following iterativeprocedure:[i ] P(x) and R(x) were computed initially assuming a qua-dratic relationship for the meniscus, Eq. [ I 31, approximatedfrom Eq. [14].[ii] To simplify the calculation R (x) was fitted to a qua-dratic equation, and the m eniscus profile and contact pointwere computed from Eqs. [I21 and [16], respectively.

Fig. 14-Geometry of two-dimensional meniscus system

recalculated; then the meniscus profile and contact pointwere recomputed.[iv] The process was repeated until successive calculationsof the m eniscus shape differed negligibly.In this way the generation of flux pressure, due to moldoscillation, and the meniscus shape have been coupled.

Figure 15 shows the meniscus profiles predicted at d iffer-ent times in a sinusoidal mold oscillation cycle having afrequency of 100 cpm and a stroke length of 8 mm. Theinitial time corre sponds to the mold being at the top of itsstroke when v, = 0. At this time, there is no oscillation-generated pressure in the flux if the meniscus is completelyliquid (or is liqu id-like) because then v, is effectively zero.Thus, at r = 0 , the m eniscus profile shown is that predictedfrom Eq. [14]. At 0.15 second, the mold has reached itsmaximum downw ard velocity and the meniscus profile andcontact point have been depressed by the positive pressuregenerated in the flux. At 0.3 second, the mold has traveledto the bottom of its stroke when v, = 0, and oscillation-generated pressure in the flux has disappeared leaving themeniscus again with an equilibrium shape predicted byEq. [14]. Beyond 0 .3 second, the mold moves upw ard,generating a negative pressure in the flux and drawing themeniscus and contact point also upward.Figure 16 show s the movem ent of the contact point of themeniscus with the mold wall during the mold oscillation. Itis seen that the contact point, which is responding to themold velocity, moves out of the phase with the mold dis-placement by n/2. Moreover, the amplitude of the contactpoint movement is greater than that of the mold displace-ment; and after 0. 3 second the contact point rises above itsinitial level. Thus, at this time, which corresponds to the endof the negative-strip period or just beyond it, the moltensteel surges toward the mold wall; and if a thin rigid skincovers part of the meniscus, overflow may occur.

VIII. MECHANISM OFOSCILLATION-MARK FORMATIONIn order to facilitate the mathematical analyses of fluidflow and meniscus shape in the preceding sections, themeniscus has been assumed, respectively, to be coveredpartially with a rigid solid skin or to behave as a liquid. Theheat-flow analysis has shown that both cases are possibledepending on the superheat and local conv ection, Figures 9and 10. The presen ce of the meniscus skin and the gener-ation of pressure in the flux channel are the bases for themechanism of oscillation-mark formation.Figures 17 and 18 provide a schem atic representation ofthe formation of the two types of oscillation marks, i . e . ,with and w ithout adjacent subsurface hooks, respective ly. In


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A-Mold Wall B- Meniscus Level C - Men~scusD- Mold Flux E - Molten Steel

Time ( s)Fig. 15-Predicted chan ge of menis cus shape with time resulting from sinusoidal mold oscill ation (s = 8 mm. f = 100 cpm, u = 1200 dyne/cm.p, = 7.2 g/cm3. p, = 2.8 g/cm').

--- moldcontoct Doint

Fig. 16-Move ment of "contact point" of meniscus with mold wall duringmold oscillation. See caption to Fig. 15 for oscillation conditions.

both c ases the meniscus responds to the m old oscillation andflux pressure in the same manner. As described earlier,during the nega tive-strip time (Stages 1-3), when the moldis moving downward more rapidly than the strand, the me-niscus is pushed by the positive pressure generated in themold flux, away from the mold wall. Then in the ensuingpositive-strip period (Stages 4-7), the meniscus is drawnback toward the mold wall. It is most unlikely that thepartially solidified meniscus is drawn back un iformly, how-ever, becau se the upper part of the m eniscus skin is farthestfrom the cooling influence of the mold wall and thereforeshould be the hottest and weakest. As a result, the upper partof the skin is expected to be drawn back more by the nega-

Fig. 17-Schematic representation of the formation of an oscillation markwith subsurface hooks.

tive flux pressure and the inertial force of the surg ing liquidsteel. The difference between the two types of oscillationmarks then arises because of differences in the mechanicalstrength of the meniscus skin. In the case of oscillationmarks with subsurface hooks, the skin is relatively strong,owing to a greater thickness (low superh eat, stagna nt liquid)and/or low carbon content. Thus, the top of the skin resists


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Fig. 18-Schematic representation of the formation of an oscillation markwithout subsurface hooks.

h near the top which bends partially back toward the moldbefore overflow occurs. Th at the depth of oscillation marks>m without subsurface hooks does not depend on the carbonI content of the steel (Figure 6) can be explained by a simi-> lar argument based on mechanical properties. In thiscase, ow ing to a high superheat or enhanced convection, the-- meniscus skin is sufficiently thin and weak that it does not

being bent back fully toward the mold wall, and liquid steeloverflows it (Stage 4, Figure 17) to form a subsurface hook.On the other hand, with oscillation marks having no sub-surface hooks, the skin is weak and behaves more like aliquid. Thus, at the beginning of positive strip the top of theskin is easily pulled back with the liquid toward the mold sothat overflow does not occur (Stage 4 , Figure 18).This m echanism is consistent with results from the metal-lurgical study of oscillation marks reported in a previoussection. Turning first to the subsurface hooks, they are sig-nificantly longer (Figure 2) than was predicted by the heat-flow model (Figure 9). T his is explained by the fact thatthe meniscus skin is pushed toward the steel by the fluxpressure (Figure 17) before overflow occurs. The hooks in0.0 9 pct carbon slabs form a smaller angle with the surfacethan hooks in 0.26 pct carbon slabs (Figure 2), probablybecause the m echanical strength of the lower carbon m enis-cus skin is greate9' and more resistant to the flux pressures .Even then it is difficult to rationalize the presence of hooksin the 0.26 pct carbon slabs that are nearly perpendicular tothe slab surface, unless the combination of flux pressu re andoverflow can deform them to this extent. Slabs that do notexhibit subsurface hooks characteristically contained inertgas blowholes. This indicates that convection was createdclose to the meniscus by rising gas bubbles which, as shownin Figure 10, reduces the thickness and strength of the me-niscus skin so that it can be drawn back toward the moldwall without overflow, at the beginning of positive strip.Another finding is that the depth of the oscillation markswith subsurface hooks is greater in 0.09 pct carbon slabsthan in slabs containing 0. 26 pct carbon. A gain, this may berelated to the greater strength expected for the low er carbonmeniscus skin. At the beginning of the positive-strip time,when negative flux pressures are developing, the entire me-niscus skin in the 0.26 pct carbon slab may be sufficientlyweak to be drawn back toward the mold wall. In contrast.the meniscus skin in the 0.1 pct carbon slab may have suf-ficient strength to resist the negative flux pressure except

.IX . MENISCUS MODEL PREDICTIONS

develop the mechanical rigidity of a solid but behaves m orelike a liquid; thus it responds in the same manner to fluxpressure irrespective of the carbon content of the steel.The finding that the depth of oscillation marks with sub-meniscus surface hooks in aluminum-killed steels is slightly greaterthan in silicon-killed steels may be due to an increase in

The final stage in this study has been to combine themathematical analyses of heat flow and flux pressure in afirst-generation meniscus model and to calculate approxi-mately the effect of the following variables on oscilla-tion mark formation: stroke length, oscillation frequency,negative-strip time, mold flux viscosity, and meniscus levelvariation. In the model, the heat flow analysis is applied firstto predict the temperature of the mold flux adjacent to themold wall during the positive-strip period of the oscillationcycle. The average temperature of the flux within 500 pmof the mold wall, a typical depth of oscillation mark, andover a height at the meniscus equivalent to the oscillationstroke length then is calculated since this flux will enterthe flux channel on the succeeding downstroke of the mold.The viscosity of the flux is computed from the empiricalr e l a t i o n ~ h i p ~ ~

mold flux viscosity as alumina, floating out of the steel, is. . absorbed by the flux.'' The inc rease in slag viscosity in-creases the pressure generated in the mold flux (Figure 12),which in turn should increase the deformation of the menis-cus during negative strip and the depth of oscillation marks.

Ilog I-L, = 0.578(104) + 273) - 2.979 [I71Next, the fluid flow analysis is applied to predict the pres-sure generated in the mold flux! assuming that the length ofthe flux channel is equal to the pitch of oscillation marks,and that the top and bottom widths of the channel are 0.35and 0.05 mm, respectively.* The total flux pressure force,

*The top channel width of 0.35 mm is in the range of the depth ofoscillation marks while the bottom width has been estimated fromthe minimum thickness of mold flux film calculated from mold fluxconsumption.integrated over the channel length, has been compu ted at themaximum downward velocity of the mold; this has beenused as a measure of the deformation of the partially solidi-fied meniscus and of the depth of oscillation marks.Figure 19 shows the effect of changing meniscus level,expressed in terms of the pitch of the oscillation marks, onthe total force generated in two mold fluxes having differentviscosities. A sudden rise in meniscus level lengthens thepitch of the oscillation marks and at the same time hasthe effect of raising the mold velocity. Thus. as the pitchof the oscillation marks increases, the total force acting on


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c7 9 I I 13

Pitch of Osci l la t ion Marks ( m m )Fig. 19-Influence of meniscus level variation (sho wn as chan gingpitch of oscillation marks) on total force due to pressure generated in theflux channel.

the partially solidified meniscus increases and the depth ofoscillation marks also should increase. This effect has beenseen in Figures 4 and 5 where the variation in pitch has beenobserved to be greatest at the highest casting speeds. Thisphenomenon also has been reported to be a problem whencasting with high oscillation frequencies.' Also in Figure 19,raising the flux viscosity is predicted to increase the totalflux pressure force, as was suggested earlier with respect tothe casting of aluminum- vs silicon-killed steels.Figure 20 shows the effect of oscillation stroke on thetotal flux pressure force for two oscillation frequencies. Inboth cases the total force increases almost linearly withincreasing stroke length which is in reasonable agreementwith oscillation-m ark depths reported by Em i et a1. l 4 Thisinfluence is caused by the increase of mold speed as thestroke length is increased at constant frequency.Figure 21 shows the effect of oscillation frequency on theflux pressure fo rce for several different stroke lengths. W ithlonger strokes, raising the oscillation frequency stronglyreduces the total pressure force; but when short oscillationstrokes are employed, frequency has only a minor effect.The same tendency, with respect to the depth of oscillationmarks, has been reported by Kuwano et al.I3for the castingof stainless steel and by other^^.^ working with high oscil-lation frequencies. Varying the frequency affects the totalpressure force by changing both the pitch of the oscil lationmarks and the mold velocity. At low frequencies, the hightotal pressure force results from the long pitch of the oscil-lation marks and the correspondingly long flux channel.How ever, because the velocity of the m old is also low. a lowtotal pressure force can be attained at high casting speeds,where v, - v, is small, depending on the stroke length ofthe mold. Such an effect is shown in Figure 22.

0 1 I 10 5 10 15Oscil lat ion Stroke (mm)

Fig. 20-Influence of oscillation stroke on total force due to pressuregenerated in the flux channel. v, = I m/min.

w0 100 2 0 0Oscil lat ion Frequency (cpm)Fig. 21 -Influence of oscillation frequency on total force due to press uregenerated in the flux channel. v , = I rn/min.

The negative-strip time, as defined by Eq. [2], has beencalculated for all se venteen conditions indicated above, andits effect on the total pressure force generated in the fluxchannel, assumin g a casting speed of 1.0 m per minute, isshown in Figure 23. A single correlation thus is found, inwhich with only minor scatter, the total pressure force in-creases with negative strip time. The same relationship,between osc illation-mark depth and t, , has been reported byMcPherson er a1.I6 nd Hashio et a[.'' In view of this good


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t I I I I100 2 0 0Oscillation Frequency (cpm)

Fig. 22- Influence of oscillation frequency on total force due to pressuregenerated in the flux channel. v , = 1.2, I .5 mfmin.

Negotive Strip Time (s )Fig. 23-Influence of negative-strip time on total force due to pressuregenerated in the flux channel (numbers in parentheses indicate oscillationfrequencies). v , = I m/min.

correlation, a series of plots of total pressure force vsnegative-strip time has been calculated fo r different castingspeeds and is shown in Figure 24. The solid lines reveal theeffect of casting speed on the total pressure force. At lowfrequencies and w ith short strokes, the force decrease s withincreasing casting speed, but with higher frequencies andlonger strokes it increases with casting speed.These predictions obviously have value only in reveal-ing trends in the depth of oscillation marks as a functionof oscillation variables. However, the knowledge gainedshould be useful in the selection of mold conditions thatminimize the depth of osc illation marks so that high surfacequality can be assured.

X. SUMMARY AND CONCLUSIONSA study involving a metallurgical examination of slabsamples and a theoretical analysis of meniscus phenomena

Negotive Strip Time (s )Fig. 24-Influence of negative-strip time on total force due to pressuregenerated in the flux channel. v , = 0.8, 1 O. 1.2, 1 .5 m/min.

has been conducted to elucidate the mechanism of oscilla-tion-mark formation. The metallurgical investigation hasrevealed the following:1. As reported by previous w orkers, oscillation marks werefound with and without hooks in the adjacent subsurface

structure.2. Hooks in the subsurface structure of 0 .0 9 pct carbonslabs form a smaller angle with the surface than in0.26 pct carbon slabs.3. Slabs having oscillation marks without sub surface hookscharacteristically also contained inert-gas blowholes.4. The depth of oscillation marks with subsurface hooks isgreater in low-carbon (0.09 pct) than in medium-carbon(0.26 pct) slabs. Oscillation marks without hooks do notshow a carbon dependen ce of depth. In low carbon slabsthe depth of oscillation marks with subsurface hooks wasslightly greater when the steel was killed with aluminumthan when killed with silicon.

The theoretical analyses contributed new knowledge onmeniscus phenom ena.1. Prediction of the temp erature distribution in the meniscusregion, using experimental heat fluxes, showed that par-tial solidification at the men iscus to form a thin rigid skindepen ds strongly on local convection. A low-tem peratureregion was also predicted in the mold flux adjacent to themold wall.2. A fluid-flow ana lysis has shown that, owing to the shapeof the flux channel between the m eniscus and mold wall,pressure is generated in the flux by the mold oscillation .The pressure is positive when the mold is m oving down -ward faster than the strand (neg ative strip) and is neg ativeduring the positive-strip period. The pressure is muchlarger than the shear stress acting in the flux channel.


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3. Calculation of the meniscus shape (in the absence of arigid skin) has indicated that the meniscu s is pushed aw ayfrom the mold w all during the negative-strip period whenpositive pressure is generated in the flux and is drawnback toward the mold wall by negative flux pressuresduring positive strip. Overflow thus may occur at thebeginning of the positive-strip time.The mech anism of oscillation mark-formation is basedupon the generation of pressure in the flux channel and thepresence of a rigid o r semi-rigid skin at the meniscu s. If theskin is rigid, ovefflow at the commencement of positivestrip causes a subsurface hook to form; whereas if the skinis semi-rigid it moves with the meniscus and overflow doesnot occur so that hooks do not form. This m echanism and aresulting first-generation meniscus model can explain ob-servations of oscillation marks made in this work and inother studies.

APPENDIXDynamic pressure in the mold flux channel

The solution to Eqs. [6] and [7] for the pressure profileand velocity distribution in the mold flux channel has beenobtained as follows. Equation [6] was integrated with re-spect to y , with limits set by B. C.'s [i] and [ii], to obtain

Then Eq. [A ll was substituted into Eq. [7] which-was inte-grated and rearranged to give

Q R , the relative flux consumption rate, was evaluated byrearranging Eq. [A21 and integrating from x = 0 to x = 1/(Figure 11)

where

Eqs. [A31 and [A51 were substituted into Eq. [A21 whichwas integrated again, from 0 to x , giving

( ( X I- {pfgb - (P , - Pf) + 6 1 . 4 ~ ~v , ) E ( ~ ) ) -((4)[A61

where E < X ) nd ( ( x ) are defined as in Eqs. [A41 and [A5].

The relative velocity distribution was obtained by com-bining Eqs. [All through [A51 to yield

The expressions for E ( y ) and 5( y) depend on the functionused to approximate the segment of the meniscus underconsideration. If a linear function is adopted, e.g. ,h (.r) = ax + p [A81

then

For the physical system shown in Figure I I

andf l = hi [A 121

Substitution of E qs. [A91 through [A121 into Eqs. [A61 and[A71 leads to Eqs. [9] and [lo], respectively.On the other hand, if a quadratic function for the lowerpart of the meniscus region is chosen, viz.h (x) = a x 2 + bx + c ( a . b , c const.) [A131

the evaluation of E ( X ) nd ((x) depends on the value ofK = 4ac - b 2 . f K > 0

but if K < 0


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This refinement of the fluid flow calculations has not beenpursued further in the present study.Meniscus shape with applied fluid pressure

The meniscus in a continuous-casting mold, shown inFigure 14, is two-dimensional and external; its static shapeis governed by the following equation:

From Figure 14, the following relationship can be derivedeasily:dx- - in 4ds-y = cos 4d s

In the presence of fluid pressure in the flux channelAP = p,gx - P(x) [A211

Equations [A18], [A19], and [A211 can be combined toyieldd 4 - p,gx - P(x')- -dx a sin 4

which may be integrated subject to the boundary condition,x = 0 , 4 = 0:

cos 6 = 1 -where

Finally, Eqs. [A19], [A20], and [A231 can be combined toyield the final result, Eq . [12].

NOMENCLATUREa2 capillary constant (-)Cp,, Cps sG cifii heat of m old flux and steel, respectively(Jlr: C)f frequency of mold oscillation (cycle/s)fi fraction solid [= (T,,, - TS)/(T,,, - T,,)]h(x) width of flux channel (cm)hi , hf width of flux channel at inlet and outlet,respectively (cm )hs-f heat transfer coefficient between steel and mold flux(W/cm2 "C)I pitch of oscillation marks (cm)1 length of flux channel (cm)P(x) axial distribution of pressure in mold flux(dyne/cm2)

pressure difference (dyne/cm2)pressure at inlet and outlet of flux channel,respectively (dyne/cm 2)heat-flux distribution along mold w all (W/c m2)relative consumption of mold flux (cm3/s)integration of pressure in flux channel from x = 0to x = x (dynelcm)distance normal to meniscus (cm)stroke of mold oscillation (cm)distance along meniscus (cm)temperature of flux and steel, respectively ("C)initial temperature of flux and steel, respectively(OC)liquidus and solidus temperature, respectively ("C)negative and positive strip time, respectively (s)relative velocity of mold flux (cm/s)velocity of mold flux (cm/s)velocity of mold (cm/s)velocity of slab (cm/s)contact point of meniscus with mold wall (cm)thermal conductivity of mold flux and steel,respectively (W/cm "C)viscosity of mold flux (poise)interfacial tension between mold flux and steel(dynelcm)shear stress (dyne/cm2)contact angle (radian)

ACKNOWLEDGMENTSThe authors wish to thank Nippon Steel Corp. and theNatural Sciences and Engineering Research Council ofCanada for the provision of a graduate scholarship (to E.Takeuch i) and research support, respectively. The assistanceof Dr. Y. Nishida of the Government Industrial ResearchInstitute (Nagoya, Japan) and of Dr. I. V. Samarasekera ofthe Department of Metallurgical Engineering is gratefullyacknowledged. A large number of steel companies haveprovided slab samples and information; without their helpthis study would not be possible.

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12. I. Saucedo, J . Beech, and G . J . Davies: Metal Tech., 1982. vol. 9.pp. 282-9 1.13. T. Kuwano, N. Shigematsu, F. Hoshi, and H. Ogiwara: Irot~tnakingand Steelmaking, 1983. vol. 10, pp. 75-81.14. T. Emi. H. Nakato, Y. Iida, K. Emoto. R . Tachibana, T. Imai, andH. Bada: Proc. 61st NOH-BOSC. 1978, pp. 350-61.15. K. Kawakami,T. Kitagawa, H. Mizukami, H . Uchibori. S. Miyahara,M. Suzuki, and Y. Shiratani: Tetsu-to-HaganP, 1981. vol. 67,pp. 1190-99.16 . N. A. M cPherson. A. W. Hardie, and G . Patrick: ISS Transactiot~s,1983, vol. 3, pp. 21-36.

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j.k. be - reflections and perspectives - the formation of oscillation marks in the cc of steel slabs

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