Mathematical Model for Prediction of Composition of Inclusions Formed during Solidification of Liquid Steel

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1 , pp Mathematical Model for Prediction of Composition of Inclusions Formed during olidification of Liquid teel. K. CHOUDHARY 1) and A. GHOH 2) 1) Research and Development Division, Tata teel, Jamshedpur , India. 2) Formerly Professor in the Department of Materials and Metallurgical Engineering, Indian Institute of Technology. Now Visiting cientist, Research & Development Division, Tata teel, Jamshedpur , India. (Received on March 16, 2009; accepted on eptember 17, 2009) Non-metallic inclusions originate mainly during secondary steelmaking due to deoxidation and other exogenous sources. Additional inclusions form during cooling and subsequent freezing of liquid steel. Rejection of solutes by the solidifying dendrites causes segregation of solutes in the interdendritic liquid with consequent build-up of their thermodynamic supersaturation. The work reported in the present paper was undertaken to develop a computation procedure for prediction of inclusion compositions formed during cooling and solidification of liquid steel. The model has been applied to an inclusion sensitive grade of steel. egregation of various solutes with progress of freezing has been calculated using the Clyne Kurz microsegregation equation. A sequential computation procedure involving segregation equation and thermodynamic equilibrium calculations by the Factsage thermodynamic software has been developed. Compositions of inclusions at various solid fractions have been determined. Model predictions have been compared with literature as well as with inclusion compositions determined in continuously cast billet samples using EM-ED. Reasonably good correspondence between model predictions and observed inclusions have been obtained. KEY WORD: steelmaking; continuous casting; steel billets; solidification; segregation models; inclusions. 1. Introduction Non-metallic inclusions are mostly (primary endogenous inclusions) generated during the ladle deoxidation of steel. Additional (secondary) inclusions are formed at all subsequent stages of liquid steel processing viz., during the holding period of the melt, transport operation from ladle to tundish and from tundish to mold, and finally during solidification. Inclusion formation is usually associated with its removal by flotation in the liquid steel. Therefore, the overall inclusion content of steel depends upon a dynamic balance between the inclusion formation and inclusion removal from the liquid steel. Due to detrimental effects on steel properties, an important task of steelmakers is to control the formation non-metallic inclusions during liquid steel processing as well as casting. For effective inclusion control it is important to know the conditions required for formation of various inclusions in steel quantitatively. Towards this, thermodynamics has been proved to be an important tool, and it is widely applied for the evaluation and control of inclusions formation during steelmaking and casting. During casting, inclusions form in the residual liquid steel due to rejection of solute elements by the solidifying dendrites (microsegregation) and consequent build-up of their supersaturation in the interdendritic liquid. Depending upon the thermodynamic conditions, segregated elements in the interdendritic spaces may react amongst them and may give rise to various inclusions (oxides and sulfides). uch inclusions are difficult to remove and may have adverse influence on the mechanical properties of the finished steels. For example, fine inclusions, which mostly precipitate during solidification, are harmful to the magnetic properties of silicon steel. It is almost impossible to achieve complete removal of inclusions from liquid steel. Only large inclusion particles are removed by flotation in the liquid steel. Finer ones are difficult to float out. One of the possible solutions to control the inclusions in steel is to modify them, chemically and/or physically, so that their potentially harmful effects can be minimized, and beneficial effects to steel properties can be enhanced. One of the examples of inclusion control during solidification is, precipitation of hard crystalline inclusions can be prevented, and a glassy ductile inclusion can be produced, which is much less harmful for subsequent deformation processing and for the end application of steel. 1,2) An inclusion with undesired properties and morphology can also be coated with another softer inclusion, the result being a less harmful composite inclusion. Chemistries and shapes of inclusions formed during solidification can also be used for controlling the steel microstructure through grain refinement of steel. During solidification of Mn i killed steel, specific oxide inclusions are allowed to precipitate first on which sulfide (Mn) inclusions are precipitated subsequently. uch inclusions provide heterogeneous nucleation sites for the formation acicular ferrite, which enhances the strength of steel significantly. Control of microstructure through such technique has been termed as

2 Oxides Metallurgy, and has become one of the active areas of research in Inclusion Engineering in recent years. 3,4) Precise evaluation of inclusion formation during solidification calls for the solution of a combination of microsegregation and thermodynamic models. everal studies have been reported in literature. 5 15) Investigators have employed various types of microsegregation models for calculating the amount of solutes rejected by dendrites with progress of solidification. For thermodynamic calculations some of them have employed indigenously developed multi-phase multi-component thermodynamic model, 5 11) whereas others have used commercially available thermodynamic software packages (ChemApp, Factsage, Thermocalc etc.) ) In recent years application of such software has gained wide acceptance in inclusion research. In addition, mass balance has been an integral part of these software packages. This facilitates calculation of the amount of inclusions as well, besides predicting the types of inclusions. Both coupled and uncoupled microsegregation and thermodynamic models have been employed in various studies, 5 15) although coupled model has been claimed to be superior to the uncoupled one. 11) Present work has been undertaken to develop an effective thermodynamic computation procedure for prediction of inclusion formation during liquid steel solidification. A methodology of calculation incorporating microsegregation and thermodynamic model has been developed. Based on relevant solidification parameters, segregation of various solutes during freezing has been calculated. Composition of inclusions at various solid fractions has been calculated using a commercial thermodynamic software based on liquid steel compositions data obtained from the segregation model. Model predictions have been compared with literature as well as with inclusion observed in EM-ED examination of continuously cast billet samples collected from the plant. The computational procedure developed in the present work is expected to be quite helpful in improving the cleanliness of existing as well as futuristic grades of steels produced at Tata teel. 2. Theoretical Analysis 2.1. Microsegregation Models Microsegregation is caused by the redistribution of solutes during solidification, as solutes are generally rejected into the liquid owing to their difference between the equilibrium solubility in the liquid and solid phases that coexist in the mushy region during solidification. Due to the short freezing times and small diffusion coefficients, complete diffusion of solutes in the solid phase is not possible. This inhibits attainment of homogenization on completion of solidification. Depending on the degree of solute diffusion in the solid, several approximations have been made for the description of microsegregation. Local thermodynamic equilibrium at the solid liquid ( L) interface and complete mixing of solutes in the liquid phase have mostly been assumed in various models. Many analytical equations of microsegregation with different assumptions and simplifications have been developed to predict solute redistribution and related phenomena ) Numerous studies on microsegregation have been carried out for binary alloys. 22) The heart of most of the simple microsegregation models is the assumed relationship between solute concentrations in interdendritic liquid as function of solid fraction. The starting point of the microsegregation model was the Lever-rule model, an equilibrium solidification model, which assumes complete mixing of all solute elements in both the liquid and the solid phases at every stage of freezing, as follows: Where C L is the concentration of a given solute element in the liquid at the solid liquid interface, C 0 is the initial (nominal) liquid concentration, k ( C /C L ) is the equilibrium partition coefficient for that element, and f is the solid fraction. This model is usually not valid because diffusion in the solid phases is too slow, especially for larger solute atoms such as manganese. Also, industrial solidification processing hardly operates close to the equilibrium. The opposite limiting case to the equilibrium solidification model is the cheils equation 16) which assumes no diffusion in the solid phase, and is as follows: C L C 0 (1 f ) (k 1)...(2) However, the cheils equation does not adequately estimate the final solute concentration, because C L becomes infinite at f 1. This model is only useful for very rapid solidification processes such as laser welding, where the cooling rates exceed 10 C/s. In order to predict microsegregation during solidification of metals realistically, in industrial casting processes, finite non-zero diffusion must be considered in the solid phase. Many simple microsegregation models have been proposed, which assume fixed dendrite arm spacing, constant physical properties, thermodynamic equilibrium at the solid liquid interface, and straight liquidus or/and solidus lines in the equilibrium phase diagram. Brody and Flemings 17) was the pioneer to propose a general form of this model that assumes complete diffusion in the liquid phase and incomplete back-diffusion in the solid phase, as follows: C C [ 1 ( 1 2αk) f ] L C0 CL...(1) [ 1 ( 1 k) f ] 0 where a is a back-diffusion parameter, defined as: Dt f α 2 (. 05λ )...(3)...(4) Where D is the diffusion coefficient of solute in the solid phase in cm 2 s 1, t f is the local solidification time in seconds, and l is the secondary dendrite arm spacing in cm. The Brody Flemings equation reduces to cheils equation as back diffusion becomes negligible, i.e. a 0, as expected. But it does not converge to Eq. (1) for very fast diffusion in solid, i.e., when a tends to infinity. ubsequently, Clyne and Kurz 18) modified the back diffusion parameters in the equation of Brody Flemings and proposed the following equation, replacing the solidification parameter a ( k 1) ( 1 2αk )

3 with W: Where W is defined as: C C [ 1 ( 1 2Ωk) f ] L 0...(5) Ω α 1 exp...(6) α exp 2 2α W tends to 1/2 as a tends to infinity; that is, diffusion is complete and Eq. (5) becomes Eq. (1). This can be arrived at from the infinite series: exp(x) 1 x. Also, W tends to a and then to 0, as a approaches 0. That is, Eq. (5) tends to Eq. (3) and then to Eq. (2). Therefore, Eq. (5) qualitatively covers all situations ranging from complete-to-zero mixing in the solid phase during solidification, and the model is relatively closer to the real situation. In the present work, applicability of both Brody Flemings 17) as well as Clyne Kurz 18) models to a billet casting situation have been critically assessed for comparison. But the Clyne Kurz equation was employed to estimate the extent of microsegregation of various solute elements in a plain low carbon steel. Local solidification time (in seconds) in Eq. (4) is defined as follows: t f TL T C...(7) Where T L and T are liquidus and solidus temperature ( C) of steel, and C R ( C/s) is the cooling rate Estimation of Liquidus and olidus Temperatures of teel everal correlations between liquidus and solidus temperatures with steel compositions have been reported in literature. 11,23 25) ome of those correlations were examined critically and it was found that the most of them estimated the liquidus temperature of steel fairly well for all carbon ranges. However, none of the correlations gave reasonable estimate of the solidus temperature for all carbon contents. Large discrepancies were observed, particularly in the steels where carbon contents were close to the peritectic transformation (i.e. 0.18%C). Due to this reason, calculations were restricted in the present work to the given low carbon steel composition only (Table 1) and the correlations reported recently by Diederichs and Bleck 26) were used for the estimation of the liquidus as well as the solidus temperatures. T L [%C] 31.5[%] 32[%P] 5[%Mn %Cu] 7.8[%i] 3.6[%Al] 1.5[%Cr] 2[%Mo] 4[%Ni] 18[%Ti] 2[%V]...(8) R ( k 1) ( 1 2Ωk ) T [%C] 183.5[%] 124.5[%P] 6.8[%Mn] 12.3[%i] 4.1[%Al] 1.4[%Cr] 4.3[%Ni]...(9) Above correlations estimated the liquidus and solidus temperature fairly well for the given steel composition (Table 1) Estimation of econdary Dendrite Arm pacing for Various Carbon Ranges In order to extend the model to various carbon content of steel, DA needs to be evaluated. everal correlations and measurements of DA are reported in literature. 27,28) Won and Thomas 22) have critically analyzed some of them and proposed the following correlations. The investigators 22) have demonstrated the applicability of their correlations over a wide range of carbon concentration. For 0 [%C] 0.15 λ For [%C] ( C 0 ) C...(10) ( C λ C R C 0 ) 0...(11) where C R is the cooling rate ( C/s) and C 0 is the carbon content (in mass percent) of steel and l is secondary dendrite arm spacing in micron Estimation of Cooling Rate for the Billet Caster In the present work, the inclusion formation model has been developed for various plain carbon steels cast through billet casters at Tata teel. The required average cooling rate of one of the caster has been estimated through measurements of average secondary dendrite arm spacing of billet samples collected from the caster. Measured DA values were subsequently used for the estimation of average cooling rate of the billet caster using Eqs. (11) and (12). 3. Thermodynamic Considerations of Inclusion Forming Reactions In the present work, attempt has been made to develop a generalized calculation methodology for inclusion precipitation during solidification of steel. To start with, the methodology has been developed for the plain carbon calcium treated Mn i killed steel, typically used in a wide range of engineering applications, particularly for the long products. Following deoxidation equilibria have been considered Formation of Oxide Inclusions Commonly, in Mn i deoxidation of steel Fe i and/or Fe Mn is added to the liquid steel first just after the tapping from the basic oxygen furnace (BOF). Inclusions originating during this process involve the concurrent Mn i Al deoxidation represented by the following reactions [Mn] [O] (MnO)...(12) [i] 2[O] (io 2 )...(13) 2[Al] 3[O] (Al 2 O 3 )...(14) R Table 1. Nominal composition of liquid steel measured at the end of LF treatment.

4 Table 2. Equilibrium partition coefficients (k) of solute elements between solid and liquid steel, and their diffusion coefficients (D) in d and g phases. 13,22,24) Ferro-alloy addition is the main source of aluminum in steel. That is why reaction (14) also gets involved in the deoxidation process. ubsequently, the liquid steel is treated with calcium to get rid of solid inclusions (Al 2 O 3, io 2 ). Therefore, before calcium treatment inclusions belong primarily to MnO io 2 Al 2 O 3 system. On calcium treatment or by interaction of liquid steel with CaO bearing ladle slag, reaction (12) gets replaced partially or fully by the following reaction depending upon the effectiveness of calcium treatment. [Ca] [O] (CaO)...(15) In addition, liquid steel may contain traces of magnesium as well. Ferro-alloys, ladle lining and slag are the potential sources of Mg during ladle treatment of steel. Therefore, the following reaction also needs to be considered. [Mg] [O] (MgO)...(16) imilarly, in steels containing Ti, inclusions formed from deoxidation may contain small quantity of TiO x as well by the following reaction: [Ti] x[o] (Ti X O)...(17) Therefore, in actual situation, inclusions originating from deoxidation reactions (12) to (17) are essentially a multicomponent solution of oxides or slag. In addition, some solid phases (e.g. Al 2 O 3, io 2 etc.) may also appear depending upon the liquid steel composition. In addition, steel invariably contains some amount of sulfur. Therefore, following sulfide forming reactions have also been considered. [Ca] [] (Ca)...(18) [Mn] [] (Mn)...(19) 3.2. Tools for Thermodynamic Calculations In order to calculate inclusion composition as well as its amount in liquid steel, FACTAGE thermodynamic software has been used ) The software contains Equilib as one of the modules, which is based on the Gibbs free energy minimization technique for calculation of various multicomponent-multiphase reaction equilibria. In order to calculate steel-inclusions equilibria using equilib module, the various data bases have been used. For example, for liquid steel FACT-FeLQ database was employed. This data base is based on the associated solution model proposed by Pelton and coworkers. 31,32) For activity composition relationship of slag FACT-LAGA data base was employed in addition to the solid stoichiometric compounds data bases. A sequential calculation procedure involving microsegregation model and Factsage was adopted for the prediction of inclusion formation during solidification. Composition of residual interdendritic liquid at various solid fractions during freezing was calculated first using the microsegregation model. ubsequent to this thermodynamic calculation was performed using the composition of segregated liquid. In order to perform calculations at various solid fractions, composition of interdendritic liquid was duly modified to take care of the solutes already consumed in precipitated inclusions in the preceding solid fractions. The calculation procedure predicted the types of inclusions as well as their amount precipitating in 100 g of solidifying liquid steel. 4. Results and Discussion 4.1. Assessment of Validity of egregation Model Brody Flemings as well as Clyne Kurz model have been tested in the present work by comparison with literature. Calculations using both the models had been carried out for a low carbon steel by Won and Thomas. 22) Data of equilibrium partition coefficients and diffusivity of various solute elements in a and g iron employed by Won et al. were accepted in the present study, and reported in Table 2. Figures 1(a) and 1(b) show the results for variation of manganese and carbon segregations respectively in the interdendritic liquid with progress of solidification. It may be noted that the calculations by both Won and Thomas as well as in the present work are based on the Clyne Kurz model, and they are in agreeing with each other. But those calculated by Brody Flemings equation are giving different values. It

5 Fig. 2. (a) Cast structure of a billet sample and (b) variation of secondary dendrite arm spacing (DA) from surface to center of a 125 mm square steel billet. Fig. 1. Comparison of variation of (a) manganese and (b) carbon concentration in the inter-dendritic liquid with progress of solidification predicted by both Brody Flemings as well as Clyne Kurz equations (for 0.13% C steel). is evident from the plots that Brody Flemings equation over-estimates back-diffusion. Consequently, the amount of segregation predicted by the same is less in comparison to Clyne Kurz equation. As a matter of fact, Brody Flemings equation predicted almost no carbon segregation with increasing solid fractions, which is totally unrealistic. This is another reason as to why Brody Flemings equation was abandoned and Clyne Kurz equation was employed in all subsequent work Estimation of Cooling Rate (C R ) As stated earlier, in order to apply the segregation model to a particular casting situation, data of cooling rate is required for determination of t f. In the present case, this has been done through measurement of secondary dendrite arm spacing of billet samples of different grades of steel collected from one of the billet casters of Tata teel. A typical variation of DA from surface to centre of the billet is shown in Fig. 2. Using Eqs. (13) and (14) and the measured secondary dendrite arm spacing (Fig. 2), cooling rate at 50 mm from the surface was estimated to be approximately 0.25 C s 1. Therefore, the average cooling rate of 0.25 C s 1 has been employed in all subsequent calculations of microsegregation. Fig. 3. Formation of Mn during dendritic freezing of 0.25% C, 1.5% Mn and 0.05% steel Application of the Mathematical Model for Prediction of Mn Inclusion Formation Reaction involved in Mn formation [Mn] [] (Mn)...(20) olubility product (K Mn ) K Mn [h Mn ][h ]...(21) log K Mn /T (22) where [h Mn ] and [h ] are the Henrian activity of Mn and respectively in liquid steel with respect to 1 mass% standard state. Condition for precipitation of pure Mn (a Mn 1) f Mn f [%Mn][%] K Mn...(23) where f and f Mn are the activity coefficients of and Mn respectively in 1 mass% standard state. Figure 3 presents the variation of the product of

6 [%Mn] [%] for the interdendritic liquid and equilibrium solubility products with solid fraction in low carbon 0.05% steel. It is evident that Mn inclusions in steel form exclusively due to segregation of Mn and towards the end of solidification ( f 0.9). Here the chosen composition of the steel is the same as that of Turkdogan and Grange. 6) The latter used different thermodynamic data and did calculations of Mn inclusion formation during freezing employing cheils equation of segregation. As Fig. 3 shows that their values were much higher than the present calculations. This is because the cheils equation assumes no diffusion in solid, and hence over-predicts solute concentrations in the interdendritic liquid Prediction of Inclusion Formation during Cooling of Liquid teel Oxide inclusions in molten steel precipitate and grow during cooling of molten steel from the end of the ladle treatment up to teeming, and then to the liquidus temperature in the mold, and finally during solidification from the liquidus to the solidus temperatures. In the present work, the model has been applied for the predictions in one of the low carbon inclusion sensitive grades of steel typically used in making welding electrodes. The nominal composition of the above grade is shown in Table 1. In the current deoxidation practice, final liquid steel composition and temperature are at the end of treatment in the ladle furnace (LF). Due to continuous drop in temperature from LF to caster this gives rise to additional/secondary inclusions in steel. Also, in order to estimate microsegregation during solidification, nominal composition of liquid steel must be known close to the liquidus temperature. This has been estimated using Factsage based calculations at various temperatures from the LF up to the liquidus temperature for the data shown in Table 1. uch calculations predicted the composition of liquid steel in equilibrium with inclusions precipitated at various temperatures during cooling. Figure 4 presents predicted variation of inclusion composition and its amount during cooling from the ladle treatment temperature up to the liquidus (1 513 C) temperatures. It is evident, only liquid inclusions precipitated for the composition of steel considered in the present case under the current deoxidation practice. Deoxidation inclusions contained primarily CaO, io 2 and Al 2 O 3 with small quantity of MgO ( 3%) and MnO ( 5%). In addition, there was an increase in the amount of inclusions with decreasing temperature. It can be seen that the inclusion composition varied only over a narrow range during cooling (Fig. 4). Calculations showed such inclusions arose mainly due to variation in the aluminum and oxygen content of the liquid steel in comparison to its other constituents during cooling. In order to validate the model prediction for inclusion precipitation during cooling of liquid steel from LF up to the liquidus temperatures, inclusion characterization of liquid steel samples from LF and billet samples have been carried out using EM-ED. Few such typical inclusions are shown in Fig. 5 along with their ED spectrum. Figure 6 presents characteristic X-ray map of constituent elements of one of such inclusions. Those inclusions composed essentially of io 2, Al 2 O 3 and CaO and contain small amounts of MgO and MnO. They were liquid when precipitated and, consequently, have spherical shapes upon freezing. A pseudo-ternary CaO io 2 Al 2 O 3 diagram was drawn using the FIG module of the Factsage, and position of the measured and the predicted inclusion composition were projected over it, as shown in Fig. 7. cales in the ternary diagram is in mass fraction of oxide constituents of the ternary CaO io 2 Al 2 O 3 system. It is evident from the figure that the measured inclusion composition of LF samples varied relatively over a wide range in the ternary with respect to their predicted equilibrium value, indicating liquid steelinclusion equilibrium was only partially attained during the ladle treatment. In comparison to this, similar inclusions observed in billet samples were distributed relatively over a narrow range, and were located close to their equilibrium value. This indicated that liquid steel-inclusion equilibrium Fig. 4. Inclusion composition and amount from ladle treatment temperature up to close to liquidus temperature of a low carbon steel. Fig. 5. Inclusions observed in liquid steel sample.

7 Fig. 6. Characteristic X-ray map of constituent elements of one of the typical inclusions observed in the liquid steel sample. Fig. 7. Predicted and measured inclusion composition in liquid steel. was not readily attained during the ladle treatment under the given practice; rather it took some time (longer residence time). Also, the inclusions containing CaO Al 2 O 3 io 2 MgO MnO observed in billet samples were essentially unfloated deoxidation product originated in the upstream ladle deoxidation as well as during cooling of liquid steel. Clearly, Inclusions predicted by the present methodology for the given grade of steel have shown close correspondence with the EM-ED measurements of the same for the liquid as well as cast steel samples Prediction of Inclusions during olidification of teel As stated earlier, a sequential calculation procedure involving microsegregation and Factsage was adopted for predicting inclusion formation during solidification of the given steel. Using Factsage nominal composition of liquid Fig. 8. Predicted inclusion types and their amount formed during solidification. steel close to the liquidus was estimated first from the measured composition in the LF. Using this data and other casting parameters viz., DA, cooling rate of billet samples and composition of the interdendritic liquids were estimated first for the various solid fractions using Clyne Kurz model and other auxiliary correlations (Eqs. (4) to (12)). ubsequently, thermodynamic calculations using Factsage were performed for the given solid fraction. First calculation was performed for the composition and temperature of liquid steel close to the liquidus temperature i.e. for very small solid fractions. Calculation resulted in liquid steel composition in equilibrium with inclusions. For calculations at higher solid fractions, composition of segregated liquid was modified by deducting the amount of solutes already consumed in the formation of inclusions at the preceding solid fraction before its use in the Factsage calculations. Figure 8 presents predicted inclusions formed during solidification of the given low carbon i Mn killed steel at

8 Fig. 9. Variation in composition of liquid MnO io 2 Al 2 O 3 inclusions with progress of solidification. various solid fractions. It may be noted that a variety of inclusions precipitated in the given steel during solidification. uch inclusions included: ( i ) a continuous precipitation of liquid MnO io 2 Al 2 O 3 from the beginning to end of solidification (ii) solid alumina and alumina rich liquid MnO io 2 Al 2 O 3 inclusions precipitated during the initial stage of solidification, consuming most of the dissolved Al of the segregated liquid (iii) solid io 2 (cristobalite) and io 2 enriched liquid MnO io 2 Al 2 O 3 inclusions precipitated later towards the end of solidification due to attainment of (iv) io 2 close to saturation solid Mn inclusions formed only towards the end of the solidification. CaO and MgO were absent in the above inclusions, as almost whole of the dissolved Ca and Mg was already consumed in inclusion formation during cooling, i.e. prior to solidification, due to their very high reactivity. Variation in composition of liquid MnO io 2 Al 2 O 3 inclusions with progress of solidification is shown in Fig. 9. It may be noted that inclusions precipitating at the beginning are enriched in Al 2 O 3 content and close to alumina saturation, causing precipitation of solid alumina phase (Fig. 8). Precipitation of these inclusions consumed most of the aluminum content of the segregated interdendritic liquid. Inclusions precipitating at final stage practically contained very small quantity of alumina. io 2 and MnO content of inclusions progressively increased with solid fraction due to increasing segregation of i and Mn Validation of Model As mentioned already, for model validation, inclusion characterization of cast billet samples were carried out using EM-ED. Figure 10 presents some of the inclusions identified in billet samples. Inclusions were mostly fine size (1 4 microns). It is evident from Fig. 10, the measured inclusion characteristics matched well with those predicted by the methodology developed in the present work. This essentially confirms the adequacy of the methodology adopted for inclusion predictions. It has been planned to extend its application to other important grades of steel produced at Tata teel in future. Fig. 10. Types of inclusions observed in low carbon steel billet samples. 5. Conclusions A methodology of calculation for prediction of inclusion formation during freezing of liquid steel has been developed. This involved sequential microsegregation and thermodynamic equilibrium calculations Clyne Kurz model and other critically assessed auxiliary correlations were employed for estimating the interdendritic microsegregation. The commercial Factsage software was used for thermodynamic calculations. Model predictions were compared against inclusion types and their composition measured in liquid steel as well as cast billet samples collected from the plant. Reasonable agreements between the measured and the predicted inclusions were obtained both for the inclusions originating during cooling of liquid steel, as well as for those formed during solidification of steel. Therefore, it is planned to utilize this model in future at Tata teel for other grades of steel. Present work has revealed a variety of endogenous inclusion formation in the given grade of steel. Following types of inclusions were predicted as well as identified in cast billet samples:

9 (1) Unfloated inclusions of ladle deoxidation, composed of CaO, io 2 and Al 2 O 3, containing small amounts of MgO and MnO. They were liquid when precipitated in the liquid steel during cooling from the ladle treatment temperature up to the liquidus temperature. (2) During the initial stages of freezing, solid Al 2 O 3 inclusions precipitated in association with alumina-rich liquid MnO io 2 Al 2 O 3 inclusions. CaO and MgO were practically absent in those inclusions as almost all Ca and Mg content of liquid steel had been fully consumed in the precipitation of deoxidation inclusions during upstream deoxidation processing and cooling of liquid steel. (3) Towards the final stages of solidification, precipitation of liquid MnO io 2 Al 2 O 2 close to silica saturation occured, along with formation of solid Cristobalite (io 2 ). Those inclusions were mainly MnO io 2 containing only a small quantity of Al 2 O 3. In addition, Mn inclusions, isolated or in association with oxides, which formed exclusively during the last stage of solidification, were also present in the cast samples. Acknowledgements The authors would like to thank the Management of Tata teel, India, for giving permission to publish the work. The help rendered by Mr. Vikram harma, In-charge Metallography laboratory, in carrying out extensive EM-ED analysis of steel samples, is also gratefully acknowledged. REFERENCE 1). Maeda, T. oejima and T. aito: teelmaking Conference Proceedings, Vol. 72, I, Warrendale, PA, (1989), ) G. M. Faulring: Iron teelmaker, 26 (1999), 29. 3) M. Wakoh, T. awai and. Mizoguchi: IIJ Int., 36 (1996), No. 8, ) H.. Kim, H. G. Lee, K.. Oh: Metall. Mater. Trans. A, 32A (2001), ) E. T. Turkdogan: Trans. Metall. oc. AIME, 233 (1965), ) E.T. Turkdogan and R. A. Grange: J. Iron teel Inst., (1970), May, ) M. Imagumbai and T. Takedaji: IIJ Int., 34 (1994), No. 7, ). Ovtchinnikov,. Kazakov and D. Janke: Ironmaking teelmaking, 30 (2003), ) M. Wintz, M. Bobadilla, J. Lehmann and H. Gaye: IIJ Int., 35 (1995), ) H. Gaye, P. Rocabois, J. Lehmann and M. Wintz: Proc. McLean ymposium, I-AIME, Warrendale, PA, (1998), ) Z. Liu, J. Wei and K. Cai: IIJ Int., 42 (2002), ) Y. B. Kang and H. G. Lee: IIJ Int., 44 (2004), ) W. Yamada, T. Matsumiya and A. Ito: Proc. 6th Int. Iron and teel Congress, IIJ, Tokyo, (1990), ) L. Holappa, M. Hamalainen, M. Liukkonen and M. Lind: Ironmaking teelmaking, 30 (2003), ) T. Matsumiya: J. Phase Equilibria Diffusion, 26 (2005), ) W. Kurz and D. J. Fisher: Fundamentals of olidification 3rd ed., Trans Tech Pub., witzerland, (1992), ) H. D. Brody and M. C. Flemings: Trans. TM-AIME, 236 (1966), ) T. W. Clyne and W. Kurz: Metall. Trans. A, 12A (1981), ) I. Ohnaka: Trans. Iron seed Inst. Jpn., 26 (1986), ). Kobayashi: IIJ Int., 39 (1999), No. 7, ) Y. H. hin, M.. Kim, K.. Oh, E. P. Yoon and C. P. Hong: IIJ Int., 41 (2001), ) Y. M. Won and B. G. Thomas: Metall. Mater. Trans. A, 32A (2001), ) M. uzuki, R. Yamaguchi, K. Murakami and M. Nakada: IIJ Int., 41 (2001), ) Y. Ueshima,. Mizoguchi, T. Matsumiya and H. Kajioka: Metall. Trans. B, 17B (1986), ) B. G. Thomas, I. V. amarasekera and J. K. Brimacombe: Metall. Trans. B, 18B (1987), ) R. Diederichs and W. Bleck: teel Res. Int., 77 (2006), ) H. Jacobi and K. chwerdtfeger: Metall. Trans A, 7A (1976), ) B. Weisgerber, M. Hecht and K. Harste: teel Res., 70 (1999), ) C. W. Bale, P. Chartrand,. A. Degterov, G. Eriksson, K. Hack, R. B. Mahfoud, J. Melançon, A. D. Pelton,. Petersen: Factage Thermochemical oftware and Databases, Calphad, 26 (2002), ) Factage: Montreal. 31) I. H. Jung,. A. Decterov and A. D. Pelton: IIJ Int., 44 (2004), ) I. H. Jung,. A. Decterov and A. D. Pelton: Metall. Mater. Trans. B, 35B (2004), 493.