The significance of the zone melting theory for the electron beam multi-chamber furnace

The significance of the zone melting theory for the electron beam multi-chamber furnace H Fiedler, G Scharf, and F Esser, VEB Qualitats und Edelstahlkombinat,Edelstahlwerk,821 Freital, Huttenstrasse1, GDR

The postulates of the zone melting theory do not adequately cover the concentration distributions observed in steel or alloy ingots obtained from electron beam mufti-chamber furnaces. A model system based on the segregation and diffusion processes was developed to give an improved description of the segregation process and the system was programmed for a digital computer. The results indicate that the solidification rate is the most important factor in the melting conditions investigated and that, in the water cooled moulds, only a relatively small area is capable of an increase in concentration. The build-up of ingots in water-cooled copper moulds in the electron beam furnace has a similar mechanism to that of the zone melting process. It is thus apposite to represent the segregation processes occurring during solidification by the equations already known for the zone melting theory 1. If the practical results of remelting in vacuum arc and electron beam furnaces a r e then examined, there are indications that the liquations of t h e most important accompanying elements occurring therein obey different laws. It was established by Bungardt and Tr~Smel=that the practical distribution coefficient k, calculated from the equations mentioned above, reaches values near to 1 and cannot therefore be covered by the postulates on the zone melting effect alone. It has been established from a large number of chemical investigations on ingots of various steels and alloys from a 200 kW electron beam multi-chamber furnace that the typical concentration curve of the zone melting process does not occur for the various accompanying elements. It was thus necessary to design a model of the system for further scientific investigation of the fundamentals of remelting in electron beam furnaces. The model was conceived to describe the theory of the segregation process more fully than the present equations and was programmed for a digital computer. The model system was designed to examine two processes to begin with, namely the primary segregation process according to the equation cs= o • c s, and the diffusion process according to the equation C

C=

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I I I,(~ -~

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, cil'-~--Id~

(Cm,

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Bilonzglelchung_n,l

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Figure 1. Diagram of the calculated curve. Konzentration= concentration; erstarrter Bereich=solidified zone; Schmelze = melt; Bilanzgleichung=equation of balance; Ortschritt-Teilung = stepwise division.

c==koc,a so that the liquation components of the concentration (cm,--c=) can also be ordered in the manner described above at the phase boundary. The concentrations occurring in the solid and liquid phases can be determined by the rate of solidification at any instant

The partial differential equation is used in the model as a difference equation. It can be seen from Figure 1 that the model is so constructed that the solid phase always increases by the thickness h during solidification. The concentration c~ is calculated for the initial liquation process by c~= k o . co

"'

for the solidified element of the layer h, so that (Co--Cl) can be regarded as a measure of the liquation component accumulating in front of the solidification front. This calculation of the concentrations in the liquid phase assumes the presence of a boundary concentration cR at the solid/liquid interface, for which the equation of balance

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o,2

i

o,4

!

!

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C o - - C 1= E ( C m - - C o ) m=l

must be valid. For the next step, when a further degree of solidification has taken place, the concentration of this area can be calculated from the concentration value Cmi, which derives from the previous calculation cycle, i.e,

Figure 2. Carbon precipitation in zone melting with a solidification rate of I era/hr. Konzentrationsverh~iltnis=contentratio; berechnete Werte= calculated values for; Versuchsergebnisse nach= test results after.

Vacuum/volume 19/number 4. PergamonPress Ltd/Printedin GreatBritain

205

H Fiedler, G Scharfand F Esser: The significance of the zone melting theory for the electron beam multi-chamber furnace and the resulting expansion of the melt bath and by the diffusion capacity of the precipitating components. The model used presupposes the presence of interfaces. It requires a knowledge only of the theoretical distribution coefficients, since the effect of the rate of solidification is implicit.

0

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t,r 1,o

0

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-~'0-;"--I "8"" ,-~.=-!- 0 . • CkfSO e.2,8 k W h / ~ ' ~ • Ck~$O e.1,$ kWh/kg * Or 80 e . U kW~/~ ¢00 ZOO 300 Blockl~nfe in m m

o400

Figure 3. Carbon content in the ingot build-up direction with various solidification rates. berechnete Erstarrungsgeschwindigkeit = calculated solidification rate; Konzentrationsverh~iltnis = content ratio; Blockliinge= length of ingot. Data on the precipitations of carbon in zoned melts are given in Figure 2. It can be seen that if a diffusion coefficient De=0.001 cm-°/s is used, the test data of Fischer and UberoP can be reproduced fairly exactly with an algorithm. This means that the model embraces the zoned melting process as well as residual melt solidification. Figure 3 (lower part) includes the typical concentration curve over the length of the core zone of an ingot of steel with higher content of carbon, remelted in the EMO 200 furnace with various rates of solidification. The upper part of the figure shows the concentration curve obtained with the model; different rates of solidification at the start of the ingot are taken into account. It can be concluded from the concentration curves obtained for zoned melting that only a small area of the bath will

206

obtain an increase in concentration during iiquation, since the actual diffusion coefficient used in the calculation (D =0.001 cm/s ~) is very close to the theoretical one. If zoned melting is conducted with a solidification rate of 1 cm/hr, the calculated bath depth which undergoes the 10 per cent increase in concentration will be about 40 ram. By transferring to the higher rate of solidification in the EMO 200, the enriched area at the crystallization front becomes smaller, and according to tests on the model at 25 cm/hr is only about 7 mm. There is also good agreement here between the test and the calculated concentrations with values for D Oof about 10-3cmVs. It can thus be stated that in previous calculations a low extensive volume of bath was considered as accumulative store for segregated components 2. With the low rates of solidification occurring at the top of the ingot, the calculations are in agreement with the experimental values in giving concentration ratios (Figure 3, top) which would be expected from the zone melting theory. The transition to higher solidification rates, corresponding to an ingot length of 100-300 ram, brings about a reduction in the layer thickness and thus in the volume of precipitate. Our investigations enable us to conclude that, in contrast to the zone melting theory, the use of the model system under varied remelting conditions shows that only a relatively small area of the bath is capable of an increase in concentration. The decisive factor for the melting conditions in the EMO 200 is the rate of solidification. The liquation phenomena occurring during solidification in water-cooled moulds used in the special remelting process or during normal ingot solidification can only be dealt with in detail in the very limited area of constant solidification rates with the known equations. The model system employed is suitable for temporarily variable rates of solidification and also for the calculation of liquation during zone melting.

References 1 W A Fischer, H Spitzer and M Hishinuma, Archivfiir Eisenhiittenwesen, 31 (6), 1960, 365-71. 2 K Bungardt and K Tr~mel, Archivfiir Eisenhiittenwesen, 35 (7), (1964), 725-37. a W A Fischer and R Uberoi, Archly fiir Eisenhiittenwesen, 33, 1962, 661-69.