Continous Casting

Oscillation Mark Formation in Continuous Casting Processes

by Jessica Elfsberg

Casting of Metals Royal Institute of Technology SE-100 44 Stockholm, Sweden

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan framlägges till offentlig granskning för avläggande av Teknologie Licentiatexamen, fredag 31 oktober 2003, kl. 15.00, B2, Brinellvägen 23, Stockholm.

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Oscillation Mark Formation in Continuous Casting Processes by Jessica Elfsberg Casting of Metals Royal Institute of Technology S-100 44 Stockholm, Sweden

Abstract Oscillation marks are ripples formed on the surface of continuously cast material. They may cause cracking and decrease the yield of the process since some material must be grinded away to avoid crack growth. A study of break-out shells, a fullscale water model study and full-scale experiments in four different plants have been performed to analyse the formation of oscillation marks. The hypothesis initiating the studies was that there is an optimal oscillation frequency. Material cast at the optimal frequency will have smaller oscillation marks and fewer cracks and, maybe most important, all marks are of the same character and depth. The optimal oscillation frequency is determined by its relation to casting velocity and interfacial tension between metal and protective medium, e.g. slag: f=

v 2 ⋅a

where a =

2 ⋅ σ metal / surrounding

g ⋅ (ρ metal − ρ surrounding )

The results from the experiments indicate that there is an optimal frequency at which the surface quality gets better. A theoretical analysis has been worked out. The suggestion is that the marks form as the surface tension balance controlling the meniscus shape collapses. The collapses occur when the meniscus grows too high and bulges out towards the mould wall. Calculations were performed to analyse the influence of interfacial tension on the oscillation marks. The results show that the higher the interfacial tension gets the deeper and wider will the marks get. Instead of analysing the friction forces acting in the meniscus region, it was assumed that the oscillation cause a variation of the interfacial tension. In some of the calculations, the interfacial tension was changed from one value to another at some point. The mark shape then becomes a combination of the different cases.

Oscillationsmärkesbildning vid kontinuerliga gjutprocesser av Jessica Elfsberg Metallernas gjutning Kungliga Tekniska Högskolan 100 44 Stockholm, Sverige

Sammanfattning Oscillationsmärken är tvärgående ”räfflor” som bildas på ytan av kontinuerligt gjutet material. Märkena kan orsaka sprickbildning samt minska utbytet av processen eftersom man måste slipa ämnena för att undvika spricktillväxt. En undersökning av genombrottsskal, en fullskalig vattenmodellstudie och fullskaliga experiments vid fyra olika gjutningsanläggningar har genomförts för att analysera bildningen av oscillationsmärken. Hypotesen som initierade arbetet var att det finns en optimal oscillationsfrekvens. Material som gjuts vid den optimala frekvensen får mindre oscillationsmärken och färre sprickor och, kanske viktigast, alla märken kommer att vara av samma typ och vara lika djupa. Den optimala oscillationsfrekvensen bestäms av dess relation till gjuthastighet och gränsytspänningen mellan smälta och omgivande medium, till exempel slagg: f=

v 2 ⋅a

där a =

2 ⋅ σ metal / surrounding

g ⋅ (ρ metal − ρ surrounding )

Resultaten från experimenten indikerar att det finns en optimal frekvens vid vilken ytkvaliteten blir bättre. En teoretisk analys har utarbetats och föreslår att oscillationsmärkena bildas när ytspänningsbalansen som bestämmer meniskens form kollapsar. Kollapsen inträffar när menisken blir för hög och bular ut mot kokillväggen. Inverkan av gränsytspänningen på märkenas profil har analyserats med hjälp av beräkningar. Resultaten visar att högre gränsytspänning ger djupare, och bredare märken. Istället för att analysera de friktionskrafter som uppkommer mellan smälta och slagg i meniskområdet, antogs det att oscillationen orsakar en variation av gränsytspänningen. I några beräkningar ändrades gränsytspänningen från ett värde till ett annat vid en viss tidpunkt. Märkets form förändrades till en kombination av formerna för de olika gränsytspänningarna.

The thesis includes the following supplements: Supplement 1 Thoughts about the Initial Solidification Process during Continuous Casting of Steel Fredriksson, H. and Elfsberg, J. Scandinavian Journal of Metallurgy 2002, Vol. 31, pp. 292-297 I prepared samples and performed microscopy studies. I also took part in writing the report. Supplement 2 Experimental Study of the Formation of Oscillation Marks in Continuous Casting of Steel Billets Elfsberg, J., Widell, B., Fredriksson, H. 4th European Continuous Casting Conference, Oct 14-15 2002, Birmingham, England. I performed the experiments, most of the evaluations and report writing. Supplement 3 Oscillation Mark Formation on Continuously Cast Copper Elfsberg, J., Fredriksson, H. ISRN:KTH:MG-INR-03:02 SE TRITA-MG-2003:02 I performed the experiments, most of the evaluations and report writing. Supplement 4 Oscillation Mark Formation on Continuously Cast Stainless Steel and Carbon Steel Slabs Elfsberg J., Fredriksson H. ISRN:KTH:MG-INR-03:03 SE TRITA-MG-2003:03 I performed the experiments, most of the evaluations and report writing. Supplement 5 Theoretical Study of Oscillation Mark Formation in Continuous Casting Processes Elfsberg J., Fredriksson H. ISRN:KTH:MG-INR-03:04 SE TRITA-MG-2003:04 I did the calculations and the report writing.

Contents 1. Introduction…………………………………………………………………...... 1 2. History and Principles of Continuous Casting…………………………….. History The Principles of Conventional Continuous Casting Casting Powder Oscillation Parameters

1 1 3 4 5

3. Review on the Formation of Oscillation marks……………………………. 6 4. Experimental work………………………………………………………….. Study of break-out shells DDS- Steel Slabs Fundia Special Bar AB – Steel Billets Fundia Armeringsstål A/S – Steel Billets Outokumpu Copper AB – Copper Strips Outokumpu Copper AB – Water Model Why modelling liquid metal flow using water Avesta Polarit AB – Stainless Steel Slabs

10 10 11 11 11 12 12 12 13

5. Experimental Results……………………………………………………….. Study of break-out shells DDS- Steel Slabs Fundia Special Bar AB – Steel Billets Fundia Armeringsstål A/S – Steel Billets Outokumpu Copper AB – Copper Strips Outokumpu Copper AB – Water Model Avesta Polarit AB – Stainless Steel Slabs

14 14 16 17 19 19 20 21

6. Theoretical background……………………………………………………... 6.1 Heat Transfer……………………………………………………………….. Conduction Radiation Convection Heat transport in Continuous Casting Heat transport in the Model for Oscillation Mark Formation The Heat Transfer from the Melt to the Shell The Heat Transfer from the Shell to the Mould Determination of Solid Shell Growth Rate and Shell Tip Radius Solidification in the z-direction

24 24 24 25 25 25 26 27 28 28 29

6.2 Surface Tension Balance and Angles between Phases…………………… 30 6.3 Pressure balance and Meniscus Shape……………………………………. 32

Derivation of the Laplace Capillary Constant Pressure Balance and Angles between the Phases

33 35

7. Theoretical analysis………………………………………………………….. 36 7.1 The Model for the Oscillation Mark Formation…………………………... The First Approach The Second Approach Optimal Oscillation Frequency

36 37 37 38

7.2 Calculation of Oscillation Mark Profile…………………………………… 39 The First Approach 39 The Second Approach 40 8. Results of Calculations………………………………………………………. 40 The First Approach 40 The Second Approach 41 9. Discussion……………………………………………………………………. 44 10. Future Works………………………………………………………………... 46 11. Acknowledgements…………………………………………………………. 47 12. References…………………………………………………………………... 48 Supplements 1-5

1. Introduction All metal manufacturing includes a solidification process. The metal is either atomised to a powder, or it is cast. There is several casting methods used today. Many of the methods use the mould only once, for example sand mould casting, the lost-wax method and precision casting. For larger quantities of liquid metal, there are basically two methods: ingot casting and continuous casting. Ingot casting normally uses a permanent mould made by cast iron isolated by ceramic material. There are limitations with the ingot casting methods. The structure in the centre of the ingot will get coarse which decreases the strength of the metal and when casting larger quantities of metal the handling of the ingots gets very complex. To be able to increase the manufacturing capacity without decreasing the quality, the development of a continuous casting process started in 1856. Since then continuous casting has grown to be the major technique for casting steel. Copper is today continuously cast using a similar design as for steel casting. The heart of a continuous casting machine is the mould. The mould is an openended tube in which the metal is poured. The liquid metal is protected by either a gas, inert or reductive, or some melted compound. For steel the most common protection media are casting powder, i.e. an oxide mixture, or rape-seed oil. In the mould the liquid metal starts to solidify and during the solidification, surface defects called oscillation marks are formed. The oscillation marks appears as grooves perpendicular to the casting direction. They are typically 0.1-1 mm deep. The oscillation marks may work as initiation point for cracks and beneath them there is a zone with higher risk for inclusions, pores and segregation. There may also be cracks on the cast surface formed in the mould. It is clear that the surface quality of the cast material is mainly determined by the process in the mould. The formation of oscillation marks has been extensively examined by many authors and there are several models describing the formation of oscillation marks in continuous casting. To be able to control the formation of marks, the mechanism of the formation must be fully known. This work suggests that there is an optimal oscillation frequency. At the optimal oscillation frequency, it is suggested that no, or very small, oscillation marks form. 2. History and Principles of continuous casting History To be able to increase the casting capacity without decreasing the quality, the development of a continuous casting process started in 1856. Henri Bessemer suggested a model in which liquid metal was poured between to water-cooled rolls.

1

Figure 1. The twin-roll caster suggested by Bessemer [1] The process was by then hard to control and the cast material was of very poor quality. In 1887 R M Daelen suggested a process using a vertical water-cooled mould open in its top and bottom. In this process problems with sticking occurred when casting steel and not until 1933, when Siegfried Junghans introduced the concept of mould oscillation, a functional continuous casting process for steel could be developed. In Junghans development the mould was moved downward at a velocity equal to the casting speed for approximately threequarters of each cycle followed by a rapid return to the starting position. There were therefore no relative motion between the mould and the strand shell during the down-stroke. In 1954 there was a major break-through in continuous casting steel processes. A new oscillation profile, suggested by Concast/Halliday, produced a condition called negative strip. Negative strip is when the down-stroke velocity in each cycle exceeds the casting speed. Sinusoidal oscillation was first used on two Russian slab casters installed in 1959. Presently, sinusoidal is essentially the standard mode of oscillation worldwide. It is relatively simple to design and has the advantage of lower moments of inertia and smaller jerk (the rate of change of acceleration with respect to time). If the jerk is too high, problems related to vibration, noise and wear of moving parts and bearings can occur. However, non-sinusoidal oscillation has received renewed attention and with sophisticated hydraulic oscillators, a wide variety of profiles may come in use. The benefits of continuous casting compared to ingot casting are: ● Higher yield ● Smaller number of necessary manufacturing steps ● More mechanised casting process ● More even composition ● Better surface finish.

2

A lot of development of the continuous casting processes has taken place the last decades. For example different electromagnetic devices have been introduced. Electromagnetic fields can be used for braking and for stirring the liquid metal in the mould. It is also possible to press the melt away from the mould walls with a strong electromagnetic field. Today conventional continuous casting, described in figure 2, is the dominant casting process for steel. In the future, electromagnetic casting may get in common use as well as the twin-roll caster suggested by Bessemer in 1856. Many of the problems can today be handled, but the process is still very expensive [1]. The Principles of Conventional Continuous Casting Figure 2 shows the principal design of a conventional continuous casting machine:

Figure 2. A continuous casting machine [1]. Melt flows from a ladle to a tundish and further to a mould. Between the ladle and the tundish, and from tundish to mould, ceramic tubes protect the melt. Beneath the mould there are a secondary cooling zone and a straightening zone. From a ladle, the liquid metal flows down into a tundish. The tundish acts as distributor if there is more than one mould, it evens the temperature and the composition of the melt and it makes it possible for inclusions to leave the melt. From the tundish the melt flows to the mould/moulds. A mould for steel casting is normally made by copper which is water-cooled; the surface towards the liquid metal is often covered with a protective layer by for example chromium. To avoid sticking in the mould it is oscillated. The casting process is started with the help of a dummy bar on which the metal freezes, so when it is moved downwards a strand can be drawn out from the mould. The velocity of the strand and the cooling must be controlled so that the solid shell is strong enough when the 3

strand leaves the mould. Beneath the mould there is a secondary cooling zone in which water is sprayed on the surface of the strand. Further down in the machine, the strand is bent so it gets horizontal and then straightened. When the strand is solid throughout the whole cross section it can be cut to proper lengths, often with an oxy-gas torch. The casting can be protected or not protected. In protected casting, the melt is not in contact with air at any time before it leaves the mould. In the ladle, a slag layer on the top of the melt protects it. The melt flows through a ceramic tube from the ladle to the tundish, the outlet of the ceramic tube is beneath the surface in the tundish, i.e. the tube is submerged. The melt surface is covered with some oxide mixture in the ladle and flows through one or more nozzles from the tundish to the mould/moulds. These nozzles are submerged in the melt in the mould. In the mould, casting powder, i.e. an oxide mixture, covers the melt surface. The casting powder protects the metal from contact with the air and may act as a lubricant in the meniscus region. In unprotected casting of steel rape-seed oil is often used as protective media. The oil burns and cracks, forming a reducing atmosphere in the mould. In continuous casting of thin copper strips either a salt mixture or a controlled, inert or reducing, atmosphere is used as protection from oxygen. As the melt fills the mould, the following occurs: in the upper part of the mould, a meniscus forms. The meniscus is the melt forming a convex upper surface just at the mould wall. The meniscus is curved because there is an interfacial tension between liquid metal and protective media [2]. Beneath this meniscus, a solid shell forms as the metal gets close to the wall. The solidified shell is continuously pulled downwards, at the same time new melt is poured down into the mould. The moving shell grows and shrinks when it is strong enough to withstand the metallostatic pressure. Then an air gap forms between the shell and the mould. Casting Powder The casting powder can either be a mechanical mixture of fine grain oxides or a pre-melted and granuled mixture. Granuled powders are preferable since they do not get packed and may thus be fed by automatic feeders. The properties considered important are viscosity, basicity, melt temperature, melting rate and degree of crystallisation. These properties can be connected to the composition of the powder. Another important factor is the particle size distribution. Particles of the same size will always have empty space in between. If there are particles of a wide range of sizes, the particles will pack tighter and air passage gets more difficult. The main ingredients of casting powders are CaO, SiO2, Al2O3, MgO, Na2O and CaF2. The acidic oxide SiO2 forms SiO42- which forms a silicate network. This

network will bind up and contain the other oxides. Al2O3, which is an amphoteric 4

oxide, can replace the SiO42- in the network. The Al2O3 molecule can form two negative ions, AlO4-, and will thus increase the viscosity strongly if there is excess oxygen present. The following oxides are basic and decrease the viscosity since they break the silicate network: CaO, MgO, BaO, SrO, Na2O, Li2O, K2O. Also fluoride ions lower the viscosity [4], [5]. Graphite is also included (3-6 %) to control the melt rate. The casting powder has several functions [6], [7], [8], [9], [10], [11], [12]: ● Protect the metal from oxidation ● Thermally isolate the upper surface to prevent meniscus solidification ● Absorb inclusions from the melt and dissolve them ● Lubricate the surface between mould and shell ● Create a homogeneous heat transport ● Determine the meniscus shape by determining the metal/slag interfacial tension. The composition of the casting powder may change throughout the casting due to reactions between steel and slag. As the composition changes, the essential properties of the slag will also change. Reactions between the metal and the slag will result in major mass transport between them. Mass transport across the interface will decrease the surface tension of the liquid metal. Oscillation Parameters The formation of the oscillation marks is regarded to be influenced by the mould oscillation. There are a number of parameters describing the oscillation, for example: Instantaneous mould velocity t   vm = 2π ⋅ s ⋅ f ⋅ cos  2 π ⋅ f ⋅   60 

[m/min]

Equation 1

where s is the stroke length [mm], f is the oscillation frequency [1/min] and t is the cycle time [s]. Average mould velocity v average = 2 ⋅ s ⋅ f

[m/min]

5

Equation 2

Total cycle time tc =

60 f

[s]

Equation 3

The negative strip time, tN, is the time during which the velocity of the downgoing mould is higher than the casting velocity. For the sinusoidal mode of oscillation, tN is calculated by the equation [13]: tN =

60 V  ⋅ arccos c  πf  πsf 

[s]

Equation 4

where VC is the casting velocity [m/min]. The oscillation parameters should be chosen so that the negative strip time is large enough for avoiding sticking. Typical values are 0.2-0.3 seconds [1]. The distance between oscillation marks has been assumed to follow the expression: VG f [3], [6], [13], [14]. p=

[mm]

Equation 5

3. Review on the Formation of Oscillation Marks There is a lot of work done in the field of formation of oscillation marks. Some of the suggestions on formation mechanisms are here reviewed. Sato presented in 1979 [15] the idea of the formation on a “secondary” meniscus formed due to pressure variations caused by the oscillation. He suggests that the marks are formed in two steps, first the solid meniscus shell is lifted by the upward moving mould. This lift causes the formation of two convex surfaces, ab and bc in figure 3b. Then, as the mould turns, the two convex surfaces are forged together and the mark is formed. Figure 3 shows the formation of a mark during casting operation without the use of casting powder. Figure 4 shows the conditions for casting with the use of casting powder. The mechanisms for the two cases are the same, but the presence of the slag will cause a different pressure term [15].

6

Figure 3. The oscillation mark formation during continuous casting without the use of slag. The mark forms during the upstroke. The solid meniscus us lifted by the mould movement [15].

Figure 4. The formation of oscillation marks in continuous casting with the use of casting powder [15]. In 1980 Saucedo et al. [16] performed work from which they deduce that the oscillation marks, or ripples, form because the meniscus solidifies. They suggest 7

that no marks will form if the rate of heat extraction is lowered. In a paper from 1991 Saucedo [17] present the theory more detailed. The oscillation marks are suggested to form when the oscillation forces the liquid metal to regain contact with the mould wall. This can happen in two ways, either an overflow occurs, or the shell is bent towards the mould by the metallostatic pressure. It is also possible that the two processes combine [17]. Figure 5 shows the different ways the liquid metal can get in contact with the mould wall above the frozen meniscus. The left mark is usually termed folding mark, and the mark in the middle is called an overflow mark.

Figure 5. The mark formation starts with solidification of the meniscus. Then the metal can get in contact with the mould wall in different ways: i. the rising liquid pushes the solid shell towards the wall, ii. the liquid overflows the shell or iii. The first two combines. In 1980 Tomono et al. [18] performed experiments with organic substances. They could observe the formation and concluded that the two mark types, i.e. folding marks and overflow marks, are formed of different reasons. They suggest that oscillation marks form when the meniscus is submitted to compressive force by particles sticking to the wall, and that folding marks form independently of the oscillation. They used the Bikerman equation for calculating the meniscus shape and connected the oscillation mark properties to the discrepancy between observed meniscus shape and calculated [18]. In 1984 Takeuchi and Brimacombe [3] described how the pressure in the liquid slag channel varies and draws the meniscus back towards the mould wall during the negative strip. The difference between marks with and without hooks is assumed to be caused by the difference in strength of the meniscus skin. If the skin is strong, an overflow will occur, and a hook forms. If the skin is weaker, the 8

shell is purely pressed against the wall and no overflow is needed, and no hook forms. They describe how the meniscus follows the oscillation [3], [19], [20].

Figure 7. The fluctuation of the meniscus with mould oscillation [3] In 1986 Suzuki et al. [21] presented a theory for the oscillation mark formation. Their model assume that an over-lap mechanism control the formation. The meniscus in surface tension balance with the shell moves upwards as the solid shell grows inwards, see figure 8.

Figure 8. Suzuki et al. suggested in 1986 that the meniscus moves inwards and upwards according to a surface tension balance. Delhalle et al. [22] described, in a work from 1989, three different formation mechanisms for oscillation marks, see figure 9. The three mechanisms are based upon meniscus solidification. The liquid metal may overflow the solid shell or first the liquid metal overflow the shell and then the shell is remelted or the solid shell may be bent back by metallostatic pressure. Solidification of the curved part results in hook formation. The size and shape of the oscillation marks is said to depend on the heat extraction, the oscillation and the interfacial properties [22].

9

Figure 9. A. Mould oscillation and product withdrawal cause liquid steel to overflow the solid hook. The overflowing liquid freezes against the mould wall and a new shell tip forms. B. as A, but here partial or total remelting of the solid shell tip is assumed. C. the metallostatic pressure bends the solid shell back against the mould [22]. Lainez and Busturia [23] performed work to determine exactly when the oscillation marks form. They suggest that solidification do not start at the meniscus, but further down in the mould, namely at the lower part of the solid slag rim. They connect the oscillation mark formation to this region and say that they form at the point where the mould downward speed is at maximum [23]. 4. Experimental Work Experiments have been performed in industrial scale at Danish Steel Works Ltd. (DDS), Fundia Smedjebacken, Fundia Mo-i-Rana, Outokumpu Copper Västerås and AvestaPolarit, Avesta. A surface profilometer was used to get information about the surface topography of the steel slabs and the steel billets. We also performed some metallographic analysis of the materials. In the copper casting case, the flow pattern in the mould has been studied using a water model. We also studied the surface appearance of the cast copper strips for different oscillation frequencies and protective medium. In our first work we studied shell tips from break-out-shells from continuous casting plants in Sweden. A break-out is when the solidifying shell breaks and the liquid metal flows out from it, leaving an empty shell in the mould. Study of Break-Out Shells A number of break-outs from steel casting machines have been analysed. The shape of the marks, the shape of the tip and the microstructure were analysed.

10

DDS – Steel Slabs A steel with 0.119%C, 0.127%Mn, 0.036%Si, 0.013%P and 0.008%S were studied. During this experiment the oscillation frequency was varied, the velocity was kept constant, but the stroke length was varied to keep the negative strip time constant. Later the velocity was varied together with the stroke length while the oscillation frequency was constant. 11 different oscillation frequencies between 74 and 134 min-1 and 5 different velocities, in the range of 0.7-1.1 m/min, were tested. Casting powder was used at the casting. The surface topography was measured with the surface profilometer and the surfaces were photographed, using a digital camera. Some samples were studied in a light optical microscope. The numbers of transversal cracks on the 200 mm long specimens were counted. Fundia Special Bar AB – Steel Billets In Smedjebacken experiments on 5 different heats, A-E, were performed. The alloys used in the four heats A-D contains about 0.16% C, 0.3% Si, 1.2% Mn. The sulphur content were varied between 0,004 and 0,033% and as the sulphur content varied, the Ca and Al contents also varied. The fifth heat, E, was studied because the steel grade shows extremely shallow oscillation marks. The composition of E is 0.55% C, 1.86% Si, 0.85% Mn and 0.017% S. In these castings, casting powders were used. During the experiments 5 different frequencies, in the range of 90-240 min-1, were tested. The stroke length was constant ±3 mm and the casting velocity was 1.6 m/min. The surface profile of one of the narrow sides of the cast strand was measured using the surface profilometer and from heat A, B and E samples from the regions of different oscillation frequency were cut out. In each region one could find deep marks, and more shallow marks. Both types were cut out and metallographically prepared and studied in a light optical microscope. Some of the regions on the billets were photographed using a digital camera. Fundia Armeringsstål A/S – Steel Billets In Mo-i-Rana 3 different heats, M-O, were studied. Two of them were quite similar in composition while the third had considerably lower carbon content. The compositions of M and N were 0.18% C, 0.2% Si, 0.75% Mn. Sulphur contents were 0.023 and 0.036 respectively. The third heat, O, was a steel grade with considerably lower carbon content. The composition was 0.08% C, 0.18% Si, 0.65% Mn and 0.034% S. In these trials rapeseed oil was used as lubricant. The velocity could not be varied, only the oscillation frequency. The stroke length was ±5.2 mm. For the different charges the oscillation 5 frequencies between 90 and 180 1/min were tested. 11

The surface topography was measured with the surface profilometer and the surfaces were photographed, using a digital camera. Outokumpu Copper AB – Copper Strips In the copper experiment two different protective media were used, the oscillation frequency and the velocity, by varying the number of down-lets in the nozzle. Normally the protective media is a carbon carrying gas, but we also used a salt mixture, with the major ingredient Na2B4O7 (borax). The composition of the copper alloy was Cu-0.03%Sn. On these samples we studied the shape of the oscillation mark along the broad side of the strip. The waviness of the oscillation marks was compared to the down-let arrangement. The heat transport to the mould cooling water was registered. Outokumpu Copper AB- Water Model A full-scale water model was used to study how the free surface shape varied with the nozzle arrangement. The nozzle design was not exactly equal to the one in the casting machine, but they were similar enough to give sufficient information about the upper surface. The number and the positions of closed nozzles were varied and the flow pattern was photographed. Why Modelling Liquid Metal Flow using Water? It is common to use water modelling of continuous casting to get information about flow patterns. To compare two systems the following demands are needed: ● Dynamic similarity ● Geometrical similarity ● Kinematic similarity ● Thermally similarity When we use water as a model material, it is of course impossible to achieve thermal similarity but for steel flow the thermal similarity is not so important since there are small temperature differences and the natural convection can be neglected. Geometrical similarity is reached if the model is proper scaled. Kinematic similarity will be reached if geometrical and dynamic similarity can be reached. For dynamic similarity the following dimensionless numbers must be equal in the steel process and in the water model:

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Froudes number v2 Fr = gL

Equation 6

Reynolds number. vL Re = ν

Equation 7

Webers number. ρv 2 L W= σ

Equation 8

v is the velocity of the fluid and L is a characteristic length for the process, ν is the kinematic viscosity for the fluid, ρ is the density of the fluid and σ is the surface tension for the fluid. The dimensionless numbers are tools used in fluid mechanics to compare systems. According to fluid mechanics, two systems with identical dimensionless numbers satisfy the Navier-Stokes equation. The systems are therefore comparable. Data for the different fluids are given in Table 1. Table 1. Data for water, steel and copper [24], [25]. Media Density [kg/m3] Viscosity [Pa·s] Water 1000 0.001 Liquid steel 7000 0.007 Liquid copper 8000 0.004

Surface tension [J/m2] 0.073 1.8 1.3

This means that the kinematic viscosity, ν, are in the cases of water and steel about 1E-6 m2/s and for copper it is 2E-6 m2/s. Reynolds number are thus easy to get equal. Froude’s number is controlled by the scaling. Both the length and the velocity must be chosen correctly. The choice of water to simulate steel makes it impossible to get all the three numbers equal for the two cases. In bulk flow in the mould it is possible to neglect the surface tension and thereby the Weber number [26] Avesta Polarit AB – Stainless Steel Slabs In this experiment the oscillation frequency was varied while the velocity and the stroke length were kept constant. The steel studied was 316L with the composition 11%Ni, 17%Cr, 4.5%Mo and 0.002%S. The sulphur is of interest because it decreases the surface tension of the alloy. According to the literature, the surface tension of this alloy is about 1.7 J/m2 for sulphur contents about 0.002 wt% [27]. The sulphur content of the studied charges is lower than that, so the surface tension will be somewhat higher than 1.7 J/m2. Casting powder was used. 4 different oscillation frequencies between 100 and 180 min-1 were tested. The surface topography was measured with the surface 13

profilometer and the surfaces were photographed, using a digital camera. The purpose of this campaign was to study the appearance of hooks beneath the surface. Samples with a length of 300 mm´s were cut out and on these the marks were very carefully studied. The samples cast at 120 min-1 and at 160 min-1 were studied in a light optical microscope. The dendrite arm spacing and the content of Mo, Ni and Cr was measured in a microprobe around marks from these samples.

5. Experimental Results Study of Break-Out Shells Two different types of oscillation marks were observed on the break-out shells. In the literature these marks are termed overflow marks and folding marks. It was also observed that the top shell does not form a continuous even line around the mould shell and that the shell growth occurs in steps, as shown in figure 10 a and b. The white arrows indicate oscillation marks found just at the level where the shell thickness starts to change.

Figure 10 a. The upper surface does not behave as an even line during the casting. The white arrow points at an oscillation mark.

Figure 10 b. The same sample as in figure 10 a seen from the perpendicular direction. The growth of the shell has occurred in steps.

We examined a number of break-out shells. The shapes of seven shell tips are shown in figure 11.

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Figure 11. Seven observed shell tips from break-outs. One shell tip was studied more carefully. Figure 12 shows the microstructure of that tip. We can identify two different regions, one fine grained on the top and a coarser below.

Figure 12. The microstructure of a shell tip from a break-out. We can see two different regions, a fine-grained to the left, and a coarser grained to the right.

15

DDS – Steel Slabs

Fraction of oscillation marks with cracks

From the experiment on steel slabs at DDS, data on the oscillation mark distances for different frequencies were achieved. The fraction of oscillation marks with cracks on the wide side of the slab could be determined, see figure 13. There is a minimum for 83 min-1. The minimum at 134 min-1 is probably not reliable since the evaluation was harder on that sample. As the surface profiles on both the narrow sides were measured, it is possible to observe that the oscillation marks do not form at the same level around the slab, see figure 14. Figure 14 also shows periods of shallow marks followed by a deep mark; see especially on the higher curve between 6400 and 6600 mm. Figure 15 shows the oscillation mark distance for different frequencies. The curve has a maximum for f=83 min-1. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 70

80

90

100

110

120

130

140

Oscillation frequency [1/min]

Figure 13. Diagram showing the fraction of oscillation marks with cracks as a function of oscillation frequency.

Surface profile [mm]

25 20 15 10 5 0 6400

6600

6800 7000 7200 Distance from start [mm] Figure 14. The oscillation marks on the both narrow sides of the slab, are not identical. The solid line at about 6850 mm is caused by a signal disturbance. 16

Oscillation mark distance [mm]

13 12 11 10 9 8 7 70

80

90

100

110

120

130

140

Oscillation frequency [1/min]

Figure 15. Diagram showing the oscillation mark distance at different oscillation frequencies. Fundia Special Bar AB – Steel Billets In these experiments it was clearly seen that the oscillation mark pattern changes immediately as the oscillation frequency is changed, see figure 17. Further it was observed that the oscillation mark distance decrease when the frequency increases.

f=240 min-1

f=100 min-1

Figure 17. The oscillation marks change appearance immediately when the oscillation frequency is changed. The frequency is changed from 100 min-1 to 240 min-1. The diagram in figure 18 shows the fraction of deeper marks as a function of oscillation frequency for the two heats C and D. The sulphur content was lower for C than for D. Thereby C had a higher interfacial tension. For C a minimum is 17

seen at 137 min-1 and for D a very clear minimum is present at f=150 min-1. When the fraction of deeper marks is zero, all the marks have the same appearance.

Fraction of deeper marks

0.35 0.3 0.25 0.2 0.15 0.1 C D

0.05 0 80

90

100

110

120

130

140

150

160

Oscillation frequency [1/min]

Figure 18. Diagram of the fraction of deep marks as a function of frequency for steel cast with casting powder.

Distance [mm]

Figure 19 shows the distances between the oscillation marks for the two heats A and B who are low in sulphur and high in sulphur respectively. The higher sulphur content reduces the interfacial tension and decreases the distance. 20 18 16 14 12 10 8 6 4 2 0

low sulfur high sulfur

100

120

140

160 180 200 Oscillation frequency [1/min]

220

240

Figure 19. The oscillation mark distances for two heats of the same steel with different sulphur contents.

18

Fundia Armeringsstål A/S – Steel Billets In this study, the oscillation marks formed during casting with rape-seed oil as protection have been examined. It was deduced that oscillation marks are formed in the same way as on materials cast with casting powder. Between the marks, a ripple pattern can be seen, with the mark distance of about 1 mm. The ripples are assumed to form due to vibrations in the machine and are not further analysed. The diagram in figure 20 shows the fraction of deeper marks as a function of frequency. There are maxima at approximately 125 min-1 and 150 min-1 respectively. Fraction of deeper marks 0.6 0.5 0.4 0.3 0.2

Low sulphur High sulphur

0.1 0 0

50

100

150

200

Oscillation frequency [1/min]

Figure 20. Diagram of the fraction of deeper oscillation marks as a function of frequency for steel cast without casting powder, but with rape-seed oil. Outokumpu Copper AB – Copper Strips On the cast copper strips, there are patterns of different types of oscillation marks. The marks on the narrow sides are deeper than the ones on the wide sides. This fact may be due to the deformation of the strip caused by the rolls in the machine, or due to the difference in heat extraction between the narrow and the wide sides. Deeper marks are also found on the strips cast with the use of salt. The salt addition caused a decrease by approximately 10% of the heat extraction from the mould (measured as difference in temperature of mould cooling water), see figure 21. The surface appearances of the copper strips were studied. Figure 22 shows a strip cast with the use of salt, v=1.1m/min and f=150 min-1. A waviness of the 19

oscillation marks is clear. The waviness can be connected to the nozzle arrangement in the down-let system. The ridges in the waves, corresponds to open nozzles and the upwards convex bulge is formed beneath closed nozzles. 100

v=1,1 m/min

Heat transport [kW]

350

Front

90 80

300

70

250

Back

200

60 50

150

40

Salt addition

30

100

Mould level [%]

400

20

50

10

0 0

100

200

300

400

500

600

700

800

0 900 1000

Time [s]

Figure 21. The heat transported to the mould cooling water is shown as a function of time for the two wide sides of the mould. The lowest curve shows the liquid metal level in the mould, in % of some reference.

Figure 22. Photo of the surface of the copper strip cast at v=1.1 m/min and f=150 min-1 and salt used as protection. The marks are wavy as given by the down-let system. Outokumpu Copper AB – Water Model In the water model study it could be seen that the water forms a concave bulge right beneath the closed nozzles. The streams from the nozzles on each side of the closed one/ones will interrupt the bulging when they press the surface downwards. When the profile of the water surface was compared with the oscillation marks on the cast strips, it seemed clear that the same thing happens in the mould. There is one exception, close to the narrow side of the strip there are a recirculation bulge on the cast strip. This one is not so strong in the water model – because there is no shell moving downwards in the water model. 20

Figure 23. Photo of half the water model. We can see how the water forms an upwards convex bulge beneath the closed nozzles and is pressed downwards by the streams from the open nozzles. Avesta Polarit AB – Stainless Steel Slabs On the sample cast with the frequency 120 min-1 marks both with and without hooks were found. On the samples cast at the other frequencies, no hooks were found. The marks with hooks often showed some cracks which the marks without hook did not. The Mo, Ni and Cr content around the oscillation marks with hooks were measured using a microprobe. Figure 24 shows the fraction of deeper oscillation marks and the depth of the deep marks as a function of oscillation frequency. There is a clear minima of the depth for f=160 min-1. Figure 25 shows the microstructure of the material around the oscillation mark. A “hook” which has been flown over by another liquid can clearly be seen. There are some cracks in the bottom of the mark. The structure close to the surface is very fine-grained while it gets coarser further from the surface.

21

0.6 Fraction deep marks

0.35

Fraction deep marks

0.3

Depth of deep marks [mm]

0.5

0.25

0.4

0.2

0.3

0.15 Measurements from 500 mm for each frequency

0.2

0.1

0.1

0.05

0 0

50

100

Depth of deep marks [mm]

0.7

0 200

150

Frequency [1/min]

Figure 24. Diagram of the fraction of deeper marks and depth of deeper marks as a function of oscillation frequency. We see that the fraction of deeper marks decreases as the frequency increases and that the depth shows a minimum for f=160 min-1. During the casting process, the temperature of the mould cooling water was logged. The temperature difference between inlet and outlet water can be used for determining the heat extraction. The differences in mould water temperatures are between 3.25 and 4.25 K and shown in figure 25. To determine the heat extraction, we also need the volume of water flowing through the mould per time unit. These numbers are: for both the narrow sides, 400 l and for the wide sides 5300 and 5400 l respectively. difftemp ÖK difftemp ytter difftemp inner difftemp VK

4.4

Water temperature [°C]

4.2 4 3.8 3.6 3.4 3.2

f=180 /min

f=160 /min

3 50

60

70

f=100/min

f=120/min

80 Cast length [m]

90

100

Figure 25. The mould cooling water temperature difference as a function of cast length. The plus signs represent changed oscillation frequency. 22

Figure 6 shows an oscillation mark with a hook and some cracks in the overflow material.

Figure 26. Photo of oscillation mark with a hook and cracks (indicated by white arrows). The structure close to the surface is much more fine-grained than the structure more far from the surface. The oscillation frequency was 120 min-1.

23

6. Theoretical background Our model of oscillation mark formation is based on a heat balance, a surface tension balance and a pressure balance. A heat balance gives us the growth rate, the surface tension balance gives us the angles between the phases and a pressure balance gives us the shape of the liquid metal meniscus during the process. Below the physical principles needed are described. 6.1 Heat transfer Heat can be transported by conduction, by radiation and by convection. Conduction Conduction is when energy is transported through the material by propagation of vibrations of the atoms. Conductive heat transport is described by Fourier´s first law: dq dT = −k dt dx

Equation 9

q is amount of heat per unit area, t is time, k is heat conductivity [W/mK], T is temperature and x is thickness of layer heat travels through. Heat transfer across an interface is described by the following relation: dq = −h ⋅ (T2 − T1 ) dt

Equation 10

If the heat must travel through several layers, we can treat the layers as connected in series and L/kA as a resistance, the total resistance is: x1 x2 x3 x = + + ... k ⋅ A k 1 ⋅ A1 k 2 ⋅ A 2 k 3 ⋅ A 3

Equation 11

and k⋅A dQ =− ⋅ (T2 − T1 ) dt L

Equation 12

can be used to calculate the heat flown through the system. Q is q times A. A more general relation than the ones above is the general heat conduction equation 24

DT D 2T =α Dt Dx 2

Equation 13

α is the thermal diffusivity which can be determined as: α=

k [m2/s] ρ ⋅ Cp

Equation 14

where k is the heat conduction coefficient of the material with the unit [J/m⋅s⋅K], ρ is the density of the material in [kg/m2] and Cp is the heat capacity in [J/kg⋅K]. Radiation The heat radiation can be determined by:

(

)

dW = ε ⋅ σ ⋅ A ⋅ T 4 − T04 dt

Equation 15

where W is energy [J], ε is emissivity, which is a dimensionless, material dependant factor, σ is the Stefan-Boltzmann constant = 5,67 ⋅ 10−8 [W/m2⋅K4], A is the area, T is the temperature of the body, T0 is the temperature of the surrounding and t is the time. Convection Convection is energy transport caused by movement of the surrounding matter. Natural convection is when media moves because of differences in heat content. Forced convection is when material, e.g. water or air, is forced to pass a body. If the body is warmer it will be cooled by the flowing fluid and vice versa. Convection can be described by the following equation: dQ = h kon ⋅ A ⋅ (T0 − T∞ ) dt

Equation 16

hkon is the convective heat transfer coefficient, [J/m2⋅s⋅K]. Heat Transport in Continuous Casting In the mould, zone 1, the dominant heat transport mechanism is conduction through several layers. The layers are mushy zone, solid metal, air gap, liquid slag, solid slag, chromium layer on mould wall, copper in mould wall and mould 25

cooling water. The conduction through several layers can be treated as heat transfer across a boundary. The heat transported from the steel in the mould can be calculated by using the temperature difference of the mould cooling water. Q=

⋅ ∆Twater Vwater ⋅ ρ water ⋅ C water p

Equation 17

A

Here Vwater is the water flow, ρwater is the density of the water (assumed to be constant and =1 kg/m3, C pwater is the heat capacity of water (=4.184 [kJ/kg⋅K]), ∆T is monitored and A is the contact area between cast material and mould, [m2]. A = (2 ⋅ b + 2 ⋅ d ) ⋅ (length of contact in the mould)

Equation 18

Beneath the mould, in zone 2, the metal is cooled mainly by forced convection when water is sprayed on the surface. In this the radiation and conduction through support rolls dominates the process. The 3rd zone can be said to start as the strand is solid across the entire cross-section. Here in this zone, the heat transfers through radiation, natural convection and through conduction to the support rolls. Heat Transport in the Model for Oscillation Mark Formation In the analysis of the oscillation mark formation, we consider convective heat transfer to be the controlling one in the mould. We further assume that there are two convective steps, heat transfer from the superheated melt, across a laminar boundary layer, to the surface of the solidifying strand and heat transfer across a gap between strand and mould. A conductive component is also include in our analysis but we do not consider radiation apart from the fact that the convective heat transfer coefficient for heat flow across the gap between shell and mould wall, may include radiative transfer. Air gap Mould wall

Solid shell

Laminar boundary layer

Figure 27. The main heat transfer mechanisms at the meniscus are convective heat transfer from the bulk liquid to the shell and convective heat transfer from the shell to the mould. 26

Convective heat transfer is generally described by Equation 16. The first convective step transports the superheat from the melt to the solidified shell. The temperature of the melt outside the boundary layer is the Tsol+∆T, and the temperature of the shell in contact with the melt is Tsol. In this analysis we treat the solidification front as planar. The other convective step transports heat from the solid shell to the mould wall. The temperature of the outside surface of the solid shell is lower than Tsol but in the meniscus region still quite close why we chose to use Tsol in our calculations. The temperature of the mould wall is assumed to be 100°C. This value was chosen because the mould is water cooled. The water channels are of course not at the surface why the temperature of the surface is somewhat higher. Some authors report 350°C. The equations describing the two convective processes in the continuous casting mould: dQ = h lam ⋅ A ⋅ ∆T dt dQ = h air ⋅ A ⋅ (Tsol − Tmould ) dt

Equation 19 Equation 20

The heat transfer from the melt to the shell The heat transfer coefficient, hlam, can be determined as: h lam =

k melt δ lam

Equation 21

where kmelt is the heat conductivity of the melt and δlam is the thickness of the laminar velocity boundary layer at the meniscus. Using an appropriate approximation for the flow, calculation of the thickness of a boundary layer can be done. The flow in our case can be described as flow passing a straight, horizontal, long cylinder and the thickness of the boundary layer is [26]: δ lam =

L = C ⋅ Ra n

L  g ⋅ β ⋅ (TS − T∞ ) ⋅ L3   C ⋅   ν⋅α  

n

Equation 22

The constants C and n depends on the size of the Rayleigh number and are listed in Table 2 [26].

27

Table 2. The constants C and n for different Rayleigh numbers. RaL C n 10-10-10-2 0.675 0.058 10-2-102 1.02 0.148 102-104 0.85 0.188 104-107 0.48 0.25 107-1012 0.125 0.333 The heat transfer from the shell to the mould The heat transfer coefficient at the meniscus will determine the thickness of the shell tip present before the oscillation mark starts to form. In this region, there is only a very narrow air gap, and the heat transfer can be rather high. A slag film is present and perhaps also a solid slag rim. The heat transfer depends on: ● Thickness of air gap ● Thickness of solid slag layer on mould wall ●Thickness of liquid slag layer ●Thermal conductivity of solid and liquid slag One way to determine the heat transfer coefficient across the gap, filled with slag, is to use Equation 21: h=

k gap δ gap

The heat conductivity of the liquid slag is approximately 1 W/mK [8], [28]. In their values, both the actual conduction and the radiation are included. The thickness of the vertical liquid flux layer has been evaluated from the consumption of casting powder. Several authors report average values of 0.2 mm [28]. With these values, we get a heat transfer coefficient of 5000 W/m2·K. In this approximation we assume that there is no air gap or solid slag layer. The maximum heat transfer coefficient has by other authors been reported to be up to 6000 W/m2·K. Determination of Solid Shell Growth Rate and Shell Tip Radius The radius of the initially formed solid shell tip, determines the oscillation mark profile. This radius can be determined from a heat balance. The heat that must be transported to the mould is the heat of solidification and the superheat of the melt and, assuming that Nu<<1 (since the shell is very thin), the heat flux gets:

28

dQ dx dT = A ⋅ ρ metal ⋅ − ∆H ⋅ + V ⋅ ρ metal ⋅ C P ⋅ dt dt dt

Equation 23

To make the superheat easier to treat, we treat it as heat transfer across a laminar boundary layer as described above: dQ dx = A ⋅ ρ metal ⋅ − ∆H ⋅ + A ⋅ h lam ⋅ ∆T dt dt

Equation 24

The heat transported away is assumed to pass across the air gap between strand and mould is given by Equation 20 and the heat transfer coefficient by Equation 21. dQ = A ⋅ h gap ⋅ (Tsol − Tmould ) dt

h gap =

k gap δ gap

We put the transferred heat equal to the heat formed during cooling and solidification and can get an expression for the shell growth rate: dx h gap ⋅ (Tsol − Tmould ) − h lam ⋅ ∆T = dt ρ ⋅ (− ∆H )

Equation 25

The radius of the shell tip can be calculated from this expression assuming that it forms in one time-step. R=

h gap ⋅ (Tsol − Tmould ) − h lam ⋅ ∆T ρ ⋅ (− ∆H )

⋅ timestep

Equation 26

Solidification in the z-direction The solidified shell may conduct heat in the z-direction, causing the shell tip to grow upwards. The shapes of the shell tips indicates that this happens, since the tips often are parabolic instead of half circular or more flat. An accurate analysis of this mechanism would include determining the surface temperature profile and the variation of the shell thickness. Note that with the assumption Nu<<1, no heat transport in the z-direction is possible.

29

6.2 Surface tension balance and angles between phases Surface tension is the physical phenomena that make free drops spherical and razor blades not to sink in water. The surface tension is due to surface atoms not having their bindings occupied in one direction. There will be an excess energy in the surface and as all systems try to minimize its energy, a drop will try to get spherical shape, since a sphere has the smallest area to volume ratio. By definition, surface tension acts between a liquid or solid surface and vapour. When treating surfaces between liquids, or between a liquid and a solid, the property is named interfacial tension. The unit of surface tension and interfacial tension is [J/m2] or [N/m].

β

β

Figure 28. Sessile drops for high and for low surface tensions. β is the wetting angle.

Surface/Interfacial tension [J/m^2]

One common method for determining the surface tension is to measure the shape of sessile drops, see figure 28, the higher surface tension, the more spherical drop. The surface tension and the interfacial tension depend strongly on the content of impurities. Some elements, so-called surface-active agents or surfactants, will concentrate at the surface/interface and reduce the surface/interfacial tension. One important example is the effect of sulphur on the surface tension of liquid iron, see figure 29. 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

0.2

0.4

0.6

0.8

1

Content sulphur in Fe [wt%]

Figure 29. The surface tension of the Fe-S-system decreases as the S-content increases. Similar behaviours are seen for steel and copper. The adsorption process also lowers the surface tension. Adsorption is when a solid or a liquid binds foreign 30

atoms to its surface. The binding may be physical or chemical. In physical adsorption, the adsorbed atoms can easily be removed since the attraction forces are very small. In chemical adsorption the attraction forces are large, and the adsorbed elements are hard to remove. Adsorption can be active at continuous casting of both steel and copper. There might be specimens in the protective media that adsorbs at the surface and thereby reduces the surface tension. Another possible process influencing the surface tension is when there are reactions between metal and slag/salt/atmosphere. A mass transport across a phase boundary will cause a decrease in surface/interfacial tension. The surface/interfacial tension also depend on the temperature, an increasing temperature decreases the surface tension [24], [25]. Three phases in contact will establish a multiphase equilibrium. The Dupré equation describes the equilibrium: γ 23 γ 13 γ = = 12 sin Ω1 sin Ω 2 sin Ω 3

Equation 27

where γii are the surface/interfacial tensions and Ωi the angles between the phases [29]. The present phases will establish a surface/interfacial tension balance, which decides the angles between the phases. The equilibrium surface/interfacial tension balance can be calculated for the principal geometry in Figure 30: V or slag or salt

S

L

σLV γ σSV α β+γ-180°

β σSL

Figure 30. The present phases will establish an interfacial tension balance. For this geometry, the following equations are valid: 31

α + β + γ = 360°  σ σ   σ LV = SV =  SL   β α sin sin  sin γ   σ 2 = σ 2 + σ 2 − σ ⋅ σ ⋅ cos(β + γ − 180°) SV SL SV SL  LV

Equation 28 Dupré equation

Equation 29

Cosine theorem

Equation 30

This system can be solved:  σ Equation 31 β = arcsin SV ⋅ sin α    σ LV   σ σ α + β + γ = α + arcsin SV ⋅ sin α  + γ = 360° → γ = 360° − α − arcsin SV ⋅ sin α     σ LV  σ LV 2 2 σ 2LV = σ SV + σ SL − σ SV ⋅ σ SL ⋅ cos(β + γ − 180°) =

  σ  σ  2 2 = σ SV + σ SL − σ SV ⋅ σ SL ⋅ cos arcsin SV ⋅ sin α  + 360° − α − arcsin SV ⋅ sin α  − 180°  =  σ LV   σ LV    2 2 2 2 = σ SV + σ SL − σ SV ⋅ σ SL ⋅ cos(180° − α ) = σ SV + σ SL + σ SV ⋅ σ SL ⋅ cos α

2 2  σ 2LV − σ SV − σ SL σ SV ⋅ σ SL 

→ α = arccos

   

Equation 32

and 2 2 σ      σ 2 − σ SV − σ SL  β = arcsin SV ⋅ sin  arccos LV    σ LV σ ⋅ σ SV SL    

Equation 33

6.3 Pressure balance and meniscus shape At the upper surface of a liquid metal in any kind of tube, a meniscus is formed. The shape of the meniscus has been described by Bikerman [2]: a a 2 + 2a 2 − z 2 ln z 2

x − x 0 = − 2a 2 − z 2 +

Equation 34

x is the direction perpendicular to the mould wall and z is parallel to the wall. x0 = a −

a

(

)

⋅ ln 2 + 1 ≈ 0.3768a 2 2⋅σ a2 = (ρ metal − ρ surr ) ⋅ g

Equation 35 Equation 36

32

The Laplace capillary constant, a2, is based on a pressure balance. The classical formulation takes metallostatic pressure and surface tension into account but may be completed with other pressure terms, such as pressure caused by movements in the liquid metal or pressure caused by an electromagnetic field. Derivation of Laplace capillary constant The derivation of the Laplace capillary constant starts with putting metallostatic pressure equal to the pressure caused by the interfacial tension: g ⋅ (ρ metal − ρ surr ) ⋅ z =

σ dϕ = σ ⋅ sin ϕ ⋅ R dz

Equation 37

If this expression is integrated, we end up with: g ⋅ (ρ metal − ρ surr ) ⋅ z 2 = 2σ ⋅ (1 − cos ϕ)

Equation 38

The conditions at the wall are that the liquid surface is vertical or: ϕ=

π 2

which means that g ⋅ (ρ metal − ρ surr ) ⋅ z 2 = 2σ

Equation 39

The maximum height of the meniscus is z, i.e. the Laplace capillary constant: z=

2σ g ⋅ (ρ metal − ρ surr )

Equation 40

The density of the protective media of course changes if we change media. The Bikerman profile may also be changed by changing the interfacial tension term or the gravitational acceleration. Figure 31 shows the Bikerman profile for different interfacial tensions and different densities of protective media.

33

z [m]

0

−0.01

Surface tension: 0.7 J/m2 − red line 1.88 J/m2 − blue line 7 J/m2 − green line

Density of surrounding media: 2000 kg/m3

−0.02 0.01

0.02

0.03

0.04

0.05 x [m]

0.06

0.07

0.08

0.09

0.1

Figure 31 a. The meniscus profile for different interfacial tensions between metal and media. The higher interfacial tension, the higher profile.

z [m]

0

−0.01

Density of surrounding media: 1 kg/m3 − red line 2000 kg/m3 − blue line

Surface tension: 1.88 J/m2

−0.02 0

0.01

0.02

0.03

0.04

0.05 x [m]

0.06

0.07

0.08

0.09

0.1

Figure 31 b. The meniscus profiles for iron with different protective media. Different media have different densities. A higher density gives a higher meniscus, the blue curve. The oscillation will cause variation of the meniscus shape [3]. The effect of the oscillation on the Laplace capillary constant can either be considered as a variation of the friction force between steel and protective media of as a variation of the gravitational acceleration. If we choose the friction force approach, we can let the interfacial tension vary since the friction force and the surface tension will act in the same way. As the mould moves upwards, the meniscus height will decrease which corresponds to a low surface tension. The downward movement can in the same way be treated as an increase of the surface tension. A proper analysis of the friction force would include determination of the velocity gradient in the media protecting the steel, e.g. slag. Apart from the velocity profile we need to know the viscosity of the media. In a casting process the viscosity of a slag may change due to reactions between slag and metal. The variation of the gravitational acceleration may be treated in the following way: The position of the mould moving according to a sine function is: y = s ⋅ sin (2 ⋅ π ⋅ f ⋅ t )

Equation 41

The velocity of the oscillating mould is described by the derivative of the sine function, i.e:

34

v = 2 ⋅ π ⋅ f ⋅ s ⋅ cos(2 ⋅ π ⋅ f ⋅ t )

Equation 42

The acceleration of the mould is the derivative of the velocity, i.e. a sine function: acc = − (2 ⋅ π ⋅ f

)2

⋅ s ⋅ sin (2 ⋅ π ⋅ f ⋅ t )

Equation 43

The Laplace capillary constant can thus be written. a2 =

2⋅σ

(ρ L − ρ surr ) ⋅ (g + (− (2 ⋅ π ⋅ f )2 ⋅ s ⋅ sin (2 ⋅ π ⋅ f ⋅ t )))

Equation 44

The time, t, will vary between 0 and the maximum time, which is the period, T: T=

1 f

Equation 45

It is possible to reformulate the Bikerman equation for other cases. We can take liquid metal movement or electromagnetic pressure into account. If we include liquid metal movements in the balance, the final expression will be: ρm ⋅ v2 z=− + 2 ⋅ g(ρ m − ρ surr )

(ρ

2 ⋅ σ L / surr ⋅ v2 ) + 2 (2 ⋅ g(ρ m − ρ surr )) g ⋅ (ρ m − ρ surr ) 2

m

Equation 46

A simplified approximation of the meniscus height, under the influence of an electromagnetic field, was performed by Sundberg [30] and gives: µ ⋅H h≈ 0 2gρ

2

Equation 47

ρ is the density of the melt and for steel with the density 7000 kg/m3 at the field strength H =2 *105 A/m we get the meniscus height [30]: h≈

(

4π ⋅ 10 −7 ⋅ 2 ⋅ 10 5 2 ⋅ 9.81 ⋅ 7000

)

2

= 0.366 m

Pressure Balance and Angles between the Phases The angle between the liquid phase and the solid tip can be determined by derivation of the Bikerman equation:

35

  a a 2 + 2a 2 − z 2 d  − 2a 2 − z 2 + + x0  ln   z 2 dx  =  dt dt

dx = dt

z

+

2a 2 − z 2

a  2 

( 2a

2

)(

−z

− z 2 ⋅ a 2 + 2a 2 − z 2

Equation 48

)

1  dz − ⋅ z  dt

Equation 49

The chain rule for derivatives gives dx dx dz = ⋅ dt dz dt

Equation 50

and thus dx dx dt = = dz dz dt

z 2a − z 2

2

+

a  2 

( 2a

2

)(

−z

− z ⋅ a 2 + 2a − z 2

2

2

)

1 −  z 

Equation 51

The angle β is  dx  β = arc cot  −   dz 

Equation 52

7. Theoretical analysis 7.1 The model for the oscillation mark formation When the liquid metal level is the proper one, the withdrawal of the product starts. To keep the level constant, new melt is constantly poured down into the mould. This simultaneous filling and withdrawal, makes the meniscus height increase until the interfacial tension balance, between the three phases solid, liquid and protective media, collapses and an overflow occur. The overflowing melt will get quite close to the mould wall and a solid shell will immediately form and the process starts over again, see Figure 32. We see that the shell growth occur in steps – this behaviour was also seen on the break-out shell, see figure 10.

36

Figure 32. The height of the meniscus increases until it collapses as the surface tension balance gets unstable. The melt will flow over the shell tip and a mark is formed The first approach First we chose to do the calculations according to a model in which we start with a planar surface and let the liquid meniscus move as determined by the solidification inwards and the withdrawal downwards. We then assumed that a microscopic interfacial tension balance was established between the liquid metal, one dendrite tip and the protective media. The model is described by the figure 33. The shape of the mark calculated according to this model gets concave in its lower part. Liquid

a.

Liquid

Liquid

c.

b. Solid

Liquid

Liquid

e.

d. Solid

Liquid

f.

Liquid

g.

Solid

Solid Solid Figure 33. Our first attempt of calculating the oscillation mark profile was based on the idea of a flat upper surface and a liquid meniscus moving inwards and “upwards”. The second approach In the second approach we chose to start with a shell with a half-circular tip. The radius of the tip was determined by a heat balance using the maximum heat 37

transfer coefficient. This shell with its radius was assumed to move inwards as described by figure 34. The withdrawal of the strand and the constant level in the mould made the shell tip with the constant radius virtually move upwards. The macroscopic interfacial tension balance determines where along the half circular tip the liquid meniscus would be situated after each time step. The meniscus grows higher for each time step and its shape will follow the Bikerman equation why it above its critical height will move towards the mould wall. The distance between the marks will be about the total height of the meniscus taking the oscillation into consideration. In this assumption, a solid shell tip of the same radius is growing upwards and inwards. The shell withdrawal continues which makes the liquid meniscus height to increase until it “bulges” back. The bulge gets in contact with the mould wall and immediately solidifies. A new cycle is started.

Liquid

Liquid

Solid

Solid

Liquid

Liquid

Solid

Liquid

Solid Solid

Figure 34. The model that we based most of our calculations on, assume a halfcircular shell tip. Optimal oscillation frequency The main hypothesis in the work is that there is an optimal oscillation frequency for which the mark formation gets very stable. At this frequency, all the marks have the same depth and there is no pattern of different marks. The oscillation causes a variation of the meniscus height and it may be possible to avoid the mark formation. If the oscillation frequency is chosen so that the maximum meniscus height is never reached, the overflows will not occur. In other words, if the mould is turning to upward movement just as the maximum meniscus height is reached, the overflow will be suppressed. The optimal oscillation frequency is suggested to be: f=

v

Equation 53

2 ⋅a

and Equation 36 gives: 38

a=

2 ⋅ σ metal / surrounding

g ⋅ (ρ metal − ρ surrounding )

Although it may be hard to totally suppress the marks, it is suggested that the surface quality gets considerably improved if an oscillation frequency close to the ideal one is chosen. It may also be advantageously to choose an oscillation frequency that is twice the ideal one. Then every second mark will be “ideal” and the others are deeper and more likely to cause defects. 7.2 Calculation of oscillation mark profile The first approach According to the Bikerman profile, the original height of the meniscus is that where the distance between the meniscus and the wall is as small as possible. A heat balance between the heat transported across the air gap and the heat of solidification gives the growth rate of the shell. The heat transported across the air gap is described by Equation 20: dQ = h ⋅ A ⋅ (Tshell − Tmould ) dt

and the heat of solidification can, according to Equation 23, be written as: dQ dx = A ⋅ ρ ⋅ (− ∆H ) ⋅ dt dt

Assuming that all heat is transported across the gap between the metal and the mould, the two equations must be equal and the following expression for the growth rate of the shell results. dx h ⋅ (Tshell − Tmould ) = dt ρ L ⋅ (− ∆H )

Equation 54

dz , of the strand is known and the assumptions above give z as dt a function of time in Bikerman equation. Putting z into the Bikerman equation and derivate it, gives the angle β. Comparing the angle from the surface tension

The pulling rate,

balance with

∆air gap ∆height

from the Bikerman profile makes it possible to determine

the height of the meniscus and the air gap for each step.

39

When the calculations are begun, it is assumed that the upper surface is almost flat. The shell grows inwards and a surface tension balance is established between the solid and the liquid. The heat flow will be perpendicular to the mould surface. The depth of an oscillation mark was calculated by derivate the Bikerman equation and by solving the other equations numerically for a number of time steps. The second approach The calculation of the marks shape start by assuming that a shell with a halfcircular tip solidifies in one time step. The thickness of this shell is determined by the maximum heat transfer coefficient and the time step length. The radius of the tip is assumed to be half the shell thickness. On top of the shell tip, there will be a liquid meniscus. The shape of the meniscus depends on the interfacial tension between liquid metal and protective media. We treat the frictional forces caused by the oscillation as a variation of the interfacial tension. As soon as the mould changes direction, the interfacial tension changes and so does the shape of the meniscus. The position of the meniscus along the solidified shell tip is determined by the interfacial tension balance. This angle is put into the derivative of the Bikerman equation to get the position along the meniscus. In the next time step, the solid tip has moved inwards and “upwards”. A new surface tension balance is established and since the liquid metal level in the mould is kept constant and the growth “upwards” is slower than the withdrawal, the height of the meniscus will increase until it “bulges” over and gets in contact with the mould wall. A new first shell tip is solidified and the next mark starts to form. 8. Results of calculations The first approach The oscillation mark profile was calculated for two cases: i, No superheat and ii, A superheat of 30°C. The first approach gives concave marks as shown in Figure 35.

40

Figure 35. The oscillation mark profile calculated in our first attempt. The mark gets concave. The second approach The calculations of the oscillation mark profiles shows that the oscillation mark width and depth increases as the interfacial tension increase, see Figures 36, 37 and 39. 1.88 J/m2, is the equilibrium interfacial tension between melt and metal vapour. The lower value, 0.7 J/m2, corresponds to upward mould movement and the higher interfacial tension, 7 J/m2, corresponds to downward mould movement. Marks formed as the mould moves upwards should according to our model get smaller in both width and depth, while marks formed during down strokes get wider and deeper. The calculations show that if the mould changes direction during the formation of the mark, the mark profile will be influenced.

41

OSM depth and width [mm]

width, hlam=600 W/m2K

7

width, hlam=22000 W/m2K

6 5 4 3 2

depth, hlam=600 W/m2K depth, hlam=22000 W/m2K

1 0 0

2

4

6

8

Interfacial tension between melt and surrounding [J/m^2]

Figure 36. The calculations show that the width and the depth of the oscillation marks increase with increasing interfacial tension between liquid and vapour. A lower laminar heat transfer coefficient gives wider and deeper marks. Figures 37 and 38 are for hlam=600 W/m2K which is a guessed value. A first analysis gave hlam=22000 W/m2K and Figures 39 and 40 are for this value. A higher hlam gives smaller width and depth of the marks. In Figures 37-40, the red curves are for no solidification in the z-direction. The green curves are for solidification in the z-direction of half the one in the x-direction. The blue curves are for solidification in the z-direction of the same magnitude as the one in the xdirection.

42

−3

3.5

x 10

S.T. 0.7

−3

x 10 6 S.T.1.88

3

S.T. 0.7; 7

S.T. 7 0.01

5

2.5

S.T. 1.88; 7

0.01

0.01

0.009

0.009

0.009

0.008

0.008

0.008

0.007

0.007

0.007

0.006

3

0.005

0.004

0.003

0.003

0.002

0.002

0.001

0.001

0 0 0.5 1 depth [m] −3 x 10

0 0 1 2 depth [m] −3 x 10

Figure 37. The OSM-profiles for three different interfacial tensions: 0.7, 1.88 and 7 J/m2 and hlam=600 W/m2K.

−3

3

0 0 1 2 depth [m] −3 x 10

5

S.T. 0.7

0 0 1 2 depth [m] −3 x 10

Figure 38. OSM-profiles for increasing interfacial tensions and hlam=600 W/m2K. σLV is suddenly changed from lower to higher at one point. −3

−3

−3

x 10

0.005

0.004

0.001 0 0 5 depth [m] −4 x 10

0.005

0.006

0.003 0.002

1

0.5

0.006

0.004 2 1

height [m]

1.5

height [m]

2

height [m]

height [m]

height [m]

4

x 10

5

0.01

S.T 1.88

x 10

5

S.T 7, 0.7

S.T. 7, 1.88

S.T. 7

x 10

4.5

0.009

4.5

4.5

4

0.008

4

4

3.5

0.007

3.5

3.5

3

0.006

3

3

2.5

0.005

2.5

height

height

2.5

height [m]

1.5

height

height

2

2.5

0.004

2

2

1.5

0.003

1.5

1.5

1

0.002

1

1

0.5

0.001

0.5

0.5

2

1

0.5

0 0 depth [m]−45 x 10

0 0 0.5 1 depth [m] −3 x 10

0 0 1 2 depth [m] −3 x 10

Figure 39. The OSM-profiles for three different interfacial tensions: 0.7, 1.88 and 7 J/m2 and hlam=22000 W/m2K.

43

0 0 0.5 1 depth [m] −3 x 10

0 0 0.5 1 depth [m] −3 x 10

Figure 40. OSM-profiles for decreasing σLV and hlam=22000 W/m2K. σLV is suddenly changed from higher to lower at one point.

9. Discussion There are two types of oscillation marks: overflow marks and folding marks. We suggest that they both are caused by overflows. The difference in their appearance depends on that they form at different places in the oscillation cycle. The overflow marks are formed during the down strokes, and the folding marks during the upstrokes, see Figure 41.

Figure 41. The sinus curve indicates the mould movement and the vertical lines are the overflows. The first two overflows will produce overflow marks, the next two folding marks and the fifth, an overflow mark. The experiments shows that the oscillation marks may form patterns, see Figure 14. One deeper mark is followed by some shallow marks. Then there comes a deep one and so on. It is believed that the deeper marks form when the interfacial tension and the oscillation co-operates as shown in Figure 41. We further suggest that it is possible to avoid the oscillation mark formation by avoiding the overflows. This is because the oscillation causes a variation of the meniscus profile, as described for example by Takeuchi et al. [3]. If the oscillation frequency is chosen so that the maximum meniscus height is never reached, the overflows will not occur. In other words, if the mould is turning to upward movement just as the maximum meniscus height is reached, the overflow will be suppressed. The optimal oscillation frequency is suggested to be: f=

v

Equation 51

2 ⋅a

and Equation 36 gives: a=

2 ⋅ σ metal / surrounding

g ⋅ (ρ metal − ρ surrounding )

This term may be modified taking liquid movement, electromagnetic fields and even mould oscillation into account as described in Chapter 6.3.

44

Figure 42 shows the relation between casting velocity and oscillation frequency for different interfacial tensions. The triangles represent the performed experiments at the billet casting plant at Fundia Special Bar AB in Smedjebacken.

Interfacial tension

2

1.8 1.6 1.4 1.2 1.0

1,5 1 0,5 0 0

50

100 150 200 Frequency [1/min]

250

Figure 42. A diagram showing the ideal relation between oscillation frequency and casting speed can be constructed. The solid lines represent the relation for different interfacial tensions. This curve is for the billet casting at Fundia Special Bar AB in Smedjebacken. The solid triangles represent the experiments performed. The hooks present in some oscillation marks is assumed to be the shell present when the mark forms. The break-out shell study indicates that the shell thickness is a couple of millimetres when the marks form. Close to the ideal oscillation frequency, the fraction of marks with cracks has a minimum (Figure 13), the oscillation mark distance has a maximum (Figure 15), the fraction of deeper marks has a minimum (Figure 18) and the depth of deep marks has a minimum (Figure 24). The surface quality in all gets better and more stable. It is also interesting to see how the heat transfer increases for the optimal oscillation frequency (Figure 26). Together these factors form a strong incentive for trying to optimise the oscillation parameters in industrial continuous casting processes. The calculations performed in the theoretical work shows that the mark shapes changes when the interfacial tension changes. If the oscillation is assumed to cause changes in the interfacial tension, this means that marks formed at different times of the oscillation cycle will have different properties. The calculations is thus also supporting the idea of an optimal oscillation frequency – i.e. by choosing an oscillation frequency that admits the marks to form at the same time in the oscillation cycle, the marks will get more even and less harmful.

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10. Future works The formation of oscillation marks in continuous casting has been thoroughly examined by us and by many other authors. More work may be needed in electromagnetic casting methods and on the function of casting powder. One suggestion is to study the oscillation marks on material cast under influence of an electromagnetic field and use a modified version of the Laplace capillary constant to optimise the oscillation frequency. Another suggestion is a work aiming to connect optimal oscillation frequency to casting powder composition for very crack sensitive steel grades. Casting powder selection is though still a dark field that need some efforts. The shell growth in the mould is interesting, not only for the oscillation mark formation, but for basically all problems concerning continuous casting. An interesting experiment would be to, for different oscillation frequencies, determine the actual shell growth in the mould by adding some element that will deposit at the solidification front and be detectable at a segregation analysis. A bigger study of break-out shells may also give valuable information about the phenomena occurring in the continuous casting mould.

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11. Acknowledgements First I wish to thank my supervisor Professor Hasse Fredriksson for the cooperation, and the administrative staff at the department: Ms Lena Magnusson, for the support throughout my rough times and Mrs Elisabeth Lampén, for keeping everything together at the department. Thanks also the Swedish Iron Masters Association and the Faxén Laboratory for financing and to the companies who let me perform experiments: The former Danish Steel Works Ltd. (DDS), Frederiksvaerk, Denmark – especially Mr Bernt Lodin. Fundia Special Bar AB, Smedjebacken, Sweden – especially Mr Gunnar Hällén. Fundia Armeringsstål A/S, Mo-i-Rana, Norway – especially Mr Arne-Eirik Eide. Outokumpu Copper Partner AB, Västerås, Sweden – especially Dr Karin Hansson, Mr Rolf Grödén, Dr Jafar Mahmoudi and Mr Stieg Andersson AvestaPolarit AB, Avesta, Sweden – especially Mr Tommy Acimovic, Mr Niklas Nilsson and Mr Anders Appell. The Swedish Institute for Metals Research let me use the surface profilometer and taught me how to use it. Thank You – especially to Mr Hans Bruce and Mr Mårten Persson. I would also express my gratitude to: Mr Thomas Bergström for experimental assistance. Mr Björn Widell, who helped me get started with the experiments. Mr José Tinoco and Mr Futsum Hailom Yosef, my roommates, who have to see my messy desk and gladly share their knowledge about their home countries. Members of Casting of Metals, former and present, especially Ms Jenny Kron and Mr Anders Lagerstedt for all our discussions about everything. Further I want to thank all my friends for the good times, particularly Annika Brännström, Patrik Persson and Peter Mattesson for the invaluable friendship. I also wish to thank my mom and dad: Elisabeth and Mats for raising me to an independent person and my brother Mattias and my sister Jenny for always helping me keep courage. Finally I thank my love in life Bernt-Åke for his tolerance, patience and neverending support and our son Hugo for filling my life with extraordinary joy. I love you both!

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12. References 1. Irving, W.R. ”Continuous casting of steel”, The Institute of Materials, London 1993 2. Bikerman J.J. ”Physical surfaces”, Academic press, New York & London 1970 3. Takeuchi E., Brimacombe J.K., Metallurgical Transactions B, Vol. 15 B, September 1984, pp. 493-509 4. Lanyi M. D., Rosa C. J., Metallurgical Transactions B, Vol. 12B, June 1981, pp. 287-298 5. Pinheiro C. A., Samarasekara I.V., Brimacombe J.K., Iron and Steelmaker, November 1994, p. 62 6. Riboud P. V., Larrecq M., Steelmaking Conference Proceedings, Vol. 74, Washington D.C., USA, 1991, pp. 78-82 7. Mills K. C., Steel Technology International, 1994 8. Abratis H., Höfer F., Jünemann M., Sardemann J., Stoffel H., Stahl und Eisen 116 (1996), Nr. 4, pp. 85-91 9. Pinheiro C. A., Samarasekara I.V., Brimacombe J.K., Iron and Steelmaker, October 1994, pp.55-56 10. Branion R.V., Mold Powders for Continuous Casting and Bottom Pour Teeming, Iron and Steel Society, AIME, pp. 3-14 11. Mc Cauley W. L., Apelian D., Iron and Steelmaker, August 1983 12. Gray R., Marston H., Steelmaking Conference Proceedings, Vol. 74, Washington D.C., USA, 14-17 Apr 1991, pp. 93-102 13. Szekeres E. S., Iron and steel Engineer, July 1996, pp. 29-37 14. Wolf M. M., Mold Powders for Continuous Casting and Bottom Pour Teeming, Iron and Steel Society, AIME, pp. 33-44 15. Sato R., Steelmaking proceedings, Vol. 62, Detroit, Michigan, 25-28 Mar, 1979, pp. 48-67 16. Saucedo I.G., Beech J., Davies G. J., Conference on Solidification Technology in the foundry and cast house, Warwick, Coventry, 15-17 September 1980

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17. Saucedo I. G., Steelmaking Conference Proceedings, Vol. 74, Washington D.C., USA, 14-17 Apr 1991, pp. 79-89 18. Tomono H., Ackermann P., Kurz W., Heinemann W., Conf. Continuous Casting of Small Cross Sections, Pittsburgh, Pa., 8 Oct 1980, pp. 524-531 19. Takeuchi E., Brimacombe J.K., Metallurgical Transactions B, Vol. 16B, September 1985, pp. 605-625 20. Samarasekara I.V., Brimacombe J.K., Bommarju R., ISS Transactions, Vol. 5, 1984, pp.79-94 21. Suzuki T., Miyata Y., Kunieda T., J. Japan Inst. Metals, Vol. 50, No.2 (1986), pp.208-214 22. Delhalle A., Larrecq M., Petegnief J., Radot J.P., La Revue de Métallurgie – CIT, June 1989, pp.483-489 23. Lainez E., Busturia J. C., 1st European Conference on Continuous Casting, Florence, Italy 1991, pp. 1.621-1.631 24. Encyclopedia Britannica 25. Iida T., Guthrie R. I. L. ”The Physical Properties of Liquid Metals”, Clarendon Press, Oxford 1988 26. Incropera F. P., DeWitt D. P. “Fundamentals of Heat and Mass Transfer, 4th Ed.”, John Wiley & Sons, Inc., New York 1996, ISBN 0-471-30460-3 27. Grant D. M., Wood J. V., Powder Metallurgy, Vol. 35, No. 1, 1992 28. Yamauchi A., Sorimachi K., Sakuraya T., Fujii T., ISIJ International, Vol. 33 (1993), No. 1, pp. 140-147 29. Murr L.E. “Interfacial phenomena in metals and alloys”, Addison-Wesley, 1975 30. Sundberg Y., “Elektrougnar och induktiva omrörare”, ASEA, Ugnsbyrån, 1978

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