Structural Reconstruction of Solidification Kinetics in Cast Iron with Spherical Graphite

Transcription

1 ISIJ International, Vol. 56 (2016), ISIJ International, No. 5 Vol. 56 (2016), No. 5, pp Structural Reconstruction of Solidification Kinetics in Cast Iron with Spherical Graphite Simon Naumovich LEKAKH* Missouri University of Science and Technology, 223 McNutt Hall, 1400 N. Bishop Street, Rolla, MO, USA. (Received on November 14, 2015; accepted on January 20, 2016) A novel method for the structural reconstruction of solidification kinetics in cast iron with spherical graphite (SGI) is described in this paper. The method includes an automated SEM/EDX analysis of different micro-features in SGI structure, separation of graphite nodule statistics from non-metallic inclusions, and conversion to a three dimensional Population Density Function (PDF exp ). A structure integrator was developed to simulate the PDF sim for the arbitrary nucleation and growth rate functions. Structural reconstruction of the solidification kinetics in the industrial castings was done by inverse optimization and matching both PDF functions at unique parameters of graphite nodule nucleation and growth. It was shown that SGI solidification kinetics in industrial castings significantly differ from those predicted by basic nucleation models. The cooling rate and inoculation have large effects on the kinetics of graphite nodule nuclei formation during solidification. It was proved that the observed bi-modal PDF function in inoculated SGI is related to the second nucleation wave. The suggested method provides insight into the nucleation process in SGI casting and can be used as a tool for process control. Reconstructed solidification kinetics can help in the design of effective inoculants and melt treatment methods. Knowledge about nucleation parameters can be also used for improving simulations of casting solidification. KEY WORDS: solidification; nucleation; cast iron; spherical graphite; casting. 1. Introduction The modern experimental science of solidification began in 1879 when Russian metallurgist Chernov published a monograph named Research into the structure of the steel slabs. 1) Chernov described the major crystalline structures in steel and one type of steel crystal (dendrite) was named after him. The development of analytical methods to describe casting solidification processes began from Chvorinov s pioneering works to predict solidification time and shrinkage defects. 2) Analytical analysis of micro-structure formation in cast metals started from fundamental Chalmers s book Principle of Solidification published in ) The next decades of research activity in solidification science was summarized in books written by Flemings, 4) Kurz and Fisher, 5) Dantzig and Rappaz, 6) and Stefanescu. 7) The analytical analysis of the solidification of cast iron with different shapes of graphite phases was the focus of many publications. Stefanescu described defining moments of the studies of solidification of iron-base materials with lamella (GI), compacted (CGI) and spherical (SGI) graphite. 8) Theoretical studies were used together with experiments to determine the nucleation and growth kinetics in cast iron castings. Figure 1 schematically presents theoretical approaches and experimental methods that have been used to study cast iron solidification. Heterogeneous nucleation. Homogeneous nucleation will not occur in industrial cast irons since the nucleation event requires the presence of a substrate that will initiate graphite solidification. The necessity of effective heterogeneous nucleation of graphite phases is determined by the * Corresponding author: lekakhs@mst.edu DOI: Fig. 1. Theoretical and experimental approaches used to study solidification in cast irons ISIJ 812

2 thermodynamic nature of the iron-carbon equilibrium diagram, which has a stable (iron-graphite) and a metastable (iron-cementite) liquid-solid types of transformations. Only a small temperature gap divides the stable from the metastable solidification. Many factors can lead to undesirable undercooling of the melt and promote cementite formation, referred to as a chill tendency. Various studies have discussed the nucleation mechanisms of the graphite eutectic from the point of view of changing the nucleation energy and a possible ranking of nucleants is as follows: graphite (highest least energy required), silicate, oxides, sulfides, carbides, nitrides, and austenite (lowest). 9) Skaland 10) described different categories of non-metallic inclusions experimentally observed in SGI after Mg treatment. Angular faceted sulfide (Mg, Ca)S and oxide MgO SiO 2 particles were found in the center of the graphite nodules, as well as in the matrix. Igarashi and Okada, 11) who studied the structure of spheroidal graphite in thin plates, found a spherical sulfide (Mg, Ca)S of about 1 μm diameter near the center of the graphite spheroids and it is thought to be a nucleus for the graphite. They also found a spherical MgO of about 0.2 μm diameter inside the sulfide and it is considered to be a nucleus for the sulfide. From a thermodynamic point of view, MgO precipitates will form first because this oxide has the higher value of free energy of formation and MgS would co-precipitate later. For determination of the chemical nature of heterogeneous nuclei, the soft quenching technique was applied to develop small graphite nodules and increase the probability to reveal non-metallic heterogeneous nuclei using automated SEM/EDX analysis. 12) Statistical analysis of the hundreds of non-metallic inclusions showed significant partitioning inclusions between metal matrix and graphite nucleus. Inclusions found inside small graphite nodules had higher concentration of Ca and S when compared to inclusions located in the matrix. The real mechanism of heterogeneous nucleation in inoculated SGI could be more complicated. It was suggested 13,14) that the nucleation process has several steps: (i) a formation of prime non-metallic substrates in the melt by chemical reactions between active components (Al, Ca, Ba) in FeSi inoculants and S and O impurities in the melt and (ii) activation of their surface by carbon. When the ferrosilicon particle dissolves in the iron melt, regions in the form of nearly concentric rings with different silicon concentration will arise around the particles. The melt composition in these regions varies from eutectic composition to hypereutectic Fe C Si alloy, where the liquid composition is highly supersaturated with respect to the melt-hypereutectic graphite equilibrium. In these FeSi dissolution regions, favorable conditions for carbon activation of existing nonmetallic inclusions are created. The experimentally proved strong inoculation effect just after melt treatment (carbonactivated substrates survived during late inoculation) and the fading effect after minutes melt holding (C substrates dissolved back in homogenized melt) both support this hypothesis. These complications make it difficult to describe nucleation kinetics in inoculated SGI by applying classical instantaneous, continuous (JMAK), or undercooling models: 4 8,15,16) -instantaneous (athermal) nucleation: N = const... (1) -isothermal solidification with time (τ) dependent rate nucleation (dn/dτ): dn / dτ = 1 + βτ... (2) N o ( ) -heterogeneous nucleation activated in undercooled (ΔT) melt: N = α T 2... (3) -Weibull distribution of heterogeneous nuclei: N N exp γ / T... (4) = s ( ) where: N s is the maximum possible nuclei number, α, β, and γ are constants, some of which could be estimated from the homogeneous nucleation barrier (ΔG homo ) and factor f(θ) related to the contact angle (θ) between the melt and the sold substrate. Several experimental methods (Fig. 1), including insitu X-ray radiography 17) and solidification interrupted by quenching 18) were used to verify the real kinetics of the nucleation of graphite nodules in cast irons. This experimental data did not follow known theoretical models (Eqs. (1) (4)). Direct observation of solidification kinetics in high temperature melt has serious limitations. For example, X-ray radiography of thin samples does not allow researchers to distinguish between surface and body nucleation events, and quenching experiments do not fully suppress additional nucleation during rapid cooling. An in-direct analysis of nucleation kinetics can be performed by comparing experimental cooling curves with simulated (Fig. 1). The experimental and simulated cooling curves were compared by varying the assumptions of nucleation and growth kinetics in simulations. It was shown that a disagreement with classical nucleation theory takes place because melt treatment and pouring temperature changed the nodule count 19) significantly. The new complex model that was proposed in that article better predicted the average nodule count. Moreover, the larger disagreements between experimentally measured nodule diameter distribution and the values predicted from simulations were noticed when a three dimensional analysis of nodule diameter distribution was performed. These structural analyses were done by applying two different methods for calculating the three dimensional nodule size from random two dimensional structure slices: (i) Finite Difference Method (FDM) 20) and (ii) inverse simulations, suggested by author. 21,22) Both methods provided a not monotonic size distribution in industrial castings. For example, a bi-modal size distribution was observed when a set of small nodules co-exists with a near normally distributed set of large nodules. These results indicate an existence of a second nucleation wave at the end of solidification, which cannot be predicted from theoretical models of heterogeneous nucleation. These small fresh formed graphite nodules at the end of solidification play an important role in the formation of interdendritic micro-shrinkage. Control of the nucleation kinetics can be used for self-healing microporosity because graphite precipitations increase the specific volume of the alloy. Small graphite nodules formed at the second nucleation wave will also promote ferrite formation during the eutectoid reaction, This reaction is controlled ISIJ

3 by carbon diffusion from austenite to neighboring graphite nodules. The fine structure will also decrease Si and Mn segregations, formed during solidification, with potential in lowering the ductile to brittle transition temperature. The goal of this article is to develop and test a novel method of structural reconstruction of solidification kinetics in SGI. The method includes automated SEM/EDX quantitative and qualitative analysis of SGI structure in casting. The post-processing data allowed us to determine the values of unique parameters of graphite nodule nucleation and growth. This methods is differ from previous simulations and experimental approaches (Fig. 1). 2. Methodology of Structural Reconstruction of Solidification Kinetics 2.1. Three-dimensional Representation of Graphite Nodule Distribution Establishing the real three-dimensional geometrical topology of all precipitates in SGI and distinguishing one from the other (graphite vs non-metallic inclusions) are important steps in the structural reconstruction of solidification kinetics. There are several possible ways to obtain the real threedimensional distribution of phases: (i) to employ true three-dimensional instrumental methods or (ii) to convert two-dimensional experimental statistics, obtained from a random section, into a three-dimensional distribution. The known methods of true three-dimensional structure analysis belong to three major group: extraction methods, 23) based on observations of not dissolved solid features, micro-city scanning 24) (X-ray or synchrotron radiation), and 3D-reconstruction of sequential slices. 25) However, all these methods are time-consuming and have dimensional limitations of the studied objects. In comparison to true three-dimensional laboratory techniques, advanced two-dimensional methods, such as an automated SEM/EDX analysis, are very productive and actively used in the metallurgical practice for gathering large statistics of different micro-features (non-metallic inclusions, phases, micro-porosity) ) In comparison to traditional quantitative optical metallography, automated SEM/EDX analysis provides a combination of precise morphological and chemical statistics of micro-structural features using two-dimensional observations of large random sections. An example of the features statistics collected with automated SEM/EDX analysis (ASPEX PICA 1020 system) in industrial 25 mm cast plate made from pearlitic near eutectic composition SGI, low alloyed by 0.5% Cu, is shown in Fig. 2. Automated feature analysis was used to separate non-metallic inclusions from graphite nodules Fig. 2. (a) Optical image of etched microstructure and automated SEM/EDX analysis of industrial 25 mm wall thickness SGI plate: (b) map of micro-features distribution, (c) joint ternary diagram of non-metallic inclusions, and (d) particle size (D 2) distributions ISIJ 814

4 applying special rules (Table 1). The map in Fig. 2(a) shows the distribution of graphite and non-metallic inclusions in a random section, Fig. 2(b) presents the chemistries of nonmetallic inclusion families using a joint ternary diagram, 28) and graphs on Fig. 2(c) illustrate the importance of automated SEM/EDX analysis to separate other features from small graphite nodules. Recently, several methods were suggested to convert twodimensional statistics from observations of a random section to the real three-dimensional volume distribution ,29) These methods have several limitations for non-spherical phases; however, they are well suited for poly-dispersed near-spherical graphite nodules. The method to convert twodimensional graphite nodules into three-dimensions 21,22) was used in this study. The probability (P) of observing circular sections with radius r of a sphere with radius R in a random two-dimensional slice is given in Eq. (5): 30,31) ϕ( r) = r ; 2 2 R r 1 2 Pr ( 1 < r < r2) = R r R R r ( 1 ) (5) It was assumed that the three dimensional particle distributions D 3i consisted of k narrow overlapped normal distributions (k=12 was used in this simulation). For an arbitrary set of fraction m i of each normal distribution (0<m i <1) in the total particle population ( m i =1), the sum of probabilities of visible diameters D 2i distribution in the slice was numerically simulated for each groups (g) of diameters in normal distributions (g =12) and slices (s) of each diameter (s=5) using Eq. (5). The generated two dimensional set consisted of k*g*s=12*12*5=720d 2i was distributed into size classes. This procedure provided a frequency function Table 1. Automated SEM/EDX analysis of micro-features in industrial 25 mm cast SGI. Micro-features Average D 2, μm Area, ppm Number (N 2), 1/mm 2 Graphite Non-metallic inclusions φ(d 2i ) for an arbitrary set of m i. In the final step, the generated distribution of diameters D 2i for the arbitrary set of m i was compared and fitted to an experimentally measured distribution of particle diameters D 2exp by applying an inverse simulation. Automated SEM/EDX analysis separated the statistics of non-metallic inclusions from graphite nodules and revealed a bi-modal character of distribution of graphite nodules. Figure 3(a) illustrates the probability for the three-dimensional distribution of non-metallic inclusions and graphite nodules for two dimensional slice shown in Fig. 2. Because the shape of the distribution curve φ(d 3i ) depends on the selected bin size (ΔD 3i ), the independent from bin size Population Density Function (PDF) was used 32) for comparison of different distributions (Fig. 3(b)): 4 PDF D / D 1 / mm... (6) ( ) = ϕ ( 3i) 3i( ) 2.2. Microstructure Integrator The assumption that the three dimensional graphite nodule PDF function uniquely reflects both nucleation and growth of graphite phases was used for structural reconstruction of SGI solidification kinetics. The equiaxed solidification kinetics of SGI are described by a combination of functions: functions f(τ), describes the nucleation the rate (n) in the remaining melt, and function ψ(τ) describes the growth velocity of graphite nodules (V), surrounded by austenite shell, with respect to solidification time (0<τ<1): n = dn / dτ = f ( τ )... (7) V = dr/ dτ = ψ( τ )... (8) Equations (7) and (8) were integrated numerically together over an equal 20 time steps (0.05τ solidification ) for arbitrary values of nucleation rates (n i ) and growth velocity (V i ) at each step (τ i ). Based on published experimental observations, 17 19) a two-step growth model was chosen: (i) free growth in the melt with constant velocity until D 3critical =2 μm and (ii) parabolic decline graphite growth, controlled by carbon diffusion through the austenite shell, for D 3 >D 3critical. Numerically integrating Eqs. (7) and (8) produced a simulation of the solidification kinetics at each time step. The nodule number N sim (1/mm 3 ), PDF sim Fig. 3. Recalculated three dimensional graphite nodule distribution in industrial 25 mm wall thickness SGI plate: (a) probability of three-dimensional diameter (D 3) and (b) Particle Distribution Function (PDF) ISIJ

5 (1/mm 4 ), D 3max-sim (μm), and total volume of graphite phase W sim (parts) were calculated at the end of solidification for any arbitrary functions f(τ) and ψ(τ). The structure integrator was built in Microsoft EXCEL applying a Solver for the inverse optimization of these two nucleation and growth functions by matching the simulated PDF sim to the experimental PDF exp. The weighted error function was minimized under several constrains: Error = PDF i ( exp PDF stm i 2 ) i Di W N sim sim W N exp exp min... (9) D3sim D3exp Figure 4 illustrates the reconstructed solidification kinetics using the experimental PDF function (25 mm thickness wall cast plate, case from Fig. 3). Two hubs on the nucleation rate curve were predicted at the initial stage and near the end of solidification. Bi-modal nodule type distribution was observed in the casting (Fig. 3). 3. Industrial and Laboratory Cases To illustrate the practical application of this novel method Fig. 4. Reconstructed solidification kinetics in a 25 mm wall thickness inoculated industrial SGI casting. of the structural reconstruction of solidification kinetics, industrial and laboratory produced SGI castings made by different processes were analyzed. In all cases, SGI with a near eutectic carbon equivalent was used Effect of Wall Thicknesses Step plates with thicknesses of steps of 5 mm and 30 mm were cast from inoculated SGI. In this case, the effect of the cooling rate on solidification kinetics in sand casting was verified. Figure 5 illustrates PDF for graphite and non-metallic inclusions in a cast step plate. The portions of small non-metallic inclusions in a total population density of counted features in thin and medium wall thickness casting were significantly different. This indicates that only thresholding optical image 20) without using automated SEM/ EDX analysis will create a larger error. Both PDF functions showed bi-modal nodule size distribution. Figure 6 illustrates reconstructed nucleation kinetics with two nucleation waves. The amplitude of a second nucleation wave was relatively more significant for a heavier section Continuous Castings The effect of the cooling rate was verified on continuously cast, large diameter bars (200 mm). Samples were taken at 3 radial locations: (a) near rapidly cooled surface, when SGI solidified inside the graphite mold, (b) on approximately ½ radius, where a melt partially solidified inside the mold and partially solidified later outside a mold at a lower cooling rate, and (c) on the middle of the cast bar, which directly solidified from the liquid core outside the mold (Fig. 7). The shape of the PDF curves for these samples were significantly different: close to normal distribution was in the sample taken near the casting wall and well defined bi-modal distributions in the middle of the continuously cast bar (Fig. 8(a)). Reconstructed solidification kinetics near the casting wall had close to log-normal distribution, while two nucleation waves were predicted at ½R and at the bar center (Fig. 8(b)). This nucleation kinetics could be related to changing heat extraction rate when casting solidified inside and outside the mold Inoculation The effect of melt inoculation by FeSi additions with active elements (Ba, Ca) on reconstructed solidification Fig. 5. PDF for graphite and non-metallic inclusions in a cast step plate from inoculated SGI: (a) 5 mm and (b) 30 mm wall thicknesses ISIJ 816

6 Fig. 6. Nucleation rate (a) and development of graphite nodule number (b) during solidification of cast step plate from inoculated SGI. Fig. 7. Etched microstructures of continuously cast bar Ø200 mm at: (a) near surface, (b) ½ radius and (c) center. Fig. 8. (a) PDF of graphite nodule and (b) nucleation rate at different radial locations in a Ø200 mm continuously cast bar from near eutectic SGI. kinetics was studied in laboratory heats with pouring vertical plates of 15 mm wall thickness. Thermocouples were installed on the middle of the walls. Inoculation had a large effect on the graphite nodule number per unit of volume ( /mm 3 vs /mm 3 ) and the shape of the PDF curve. The non-modified melt had a bell type PDF curve while the modified PDF curve was bi-modal (Fig. 9(a)). Reconstructed solidification kinetics indicated that inoculation promoted a formation of large second nucleation wave (Fig. 9(b)). To verify the existence of two nucleation waves in inoculated SGI, a computer assisted thermal analysis was performed. 33,34) Applied single thermocouple analysis has some limitations; however, can provide qualitative information about latent heat liberation and solid fraction evolution during solidification. In this method, the liquid and solid states were used as a reference to plot the Z-curve assuming a Newtonian approximation of heat transfer. The solid fraction was estimated as an area between the first derivative of the cooling curve and Z-curve. The rate of the solid fraction evolution during solidification estimated in such a way for the base and inoculated SGI is shown in Fig. 9(c). The solidification rate (df/dt) curve obtained from thermal analysis and nucleation rates (dn/dt) curve reconstructed from structure both had a similar trends ISIJ

7 Fig mm wall thickness plate cast from non-inoculated and inoculated SGI: (a) PDF of graphite nodule, (b) reconstructed nucleation rate, and (c) rate of solid fraction evolution computed from experimental cooling curve. 4. Discussion To compare reconstructed solidification kinetics in castings with predicted from classical models, a structural integrator was used to build a virtual PDF vir assuming that solidification followed one of the classical models (Eqs. (1) (4)). For adequate comparisons of these PDF vir to the computed from structures, the virtual simulations were done under similar constrains: the same volume part of graphite nodules (W=0.1) and maximum nodule diameter (D 3 =50 μm). The nodule number per unit volume (N) was not constrained because used kinetics models provided different N-values after inverse simulations. Four simulated models included: (i) instantaneous nucleation at constant growth velocity (model A), (ii and iii) declined growth velocity, which is typical for graphite nodule growth inside austenite shells (model B instantaneous nucleation and model C - increased nucleation rate), and (iv) a nucleation rate was related to the degree of melt undercooling in model D. For the last case, heat balance was included in the structural integrator to calculate undercooling (ΔT) at each time step by balancing the generated latent heat with heat losses, assuming that the melt cooling rate was 1 C/s. To provide more freedom for inverse simulations, the virtual nucleation rate was fitted to Eq. (10): Fig. 10. PDF vir curves integrated for basic kinetics models. N = No + γ T + ε T 2... (10) Figure 10 illustrates the generated PDF vir. Model A predicts a flat PDF curve, while models B and C have opposite trends. The shape of the PDF curve for model D, where the nucleation rate depended on melt undercooling, is closer to observed in some experimental cases (faster cooled SGI shown in Figs. 8 and 9). At the same time, this model does not predict the second nucleation wave observed in inoculated SGI ISIJ 818

8 The goal of this article was limited by description of suggested method of structural reconstruction of solidification kinetics in SGI. Detailed analysis on specific trends of the experimental PDF curves and reconstructed nucleation kinetics needs additional experimental studies. The suggested methodology can be used as stand-alone tool for design the effective inoculants and melt treatment processes. Knowledge about nucleation parameters can also be used for improving the simulations of casting solidification. 5. Conclusions A novel method of structural reconstruction of solidification kinetics in cast iron with spherical graphite (SGI) was suggested and tested for castings produced by different processes. It was shown the importance of an automated SEM/ EDX analysis to separate the graphite nodule statistics from the other micro-structural features. The suggested method to build a three dimensional Population Density Function (PDF exp ) provides a unique function, characterized graphite nodules dimensional population. The structure integrator used the PDF exp to simulate a unique set of nucleation and growth parameters. It was shown that the real SGI solidification kinetics significantly differs from predicted by basic nucleation models. Cooling rate and inoculation have large effects on the kinetics of graphite nodule nuclei formation during solidification. It was proven that the observed bi-modal PDF function in inoculated SGI is related to the second nucleation wave. Suggested method provides insight into the nucleation process in SGI castings and can be used as a tool for design an effective inoculants and process control. Knowledge about nucleation parameters can also be used for the improving the simulations of casting solidification. REFERENCES 1) A. F. Golovin: Met. Sci. Heat Treat., 10 (1968), ) P. Jelinek and T. Elbel: Arch. Foundry Eng., 10 (2010), 77. 3) B. Chalmers: Principles of Solidification, Wiley, New York, (1964). 4) M. C. Flemings: Solidification Processing, McGraw-Hill, New York, (1974). 5) W. Kurz and D. J. Fisher: Fundamentals of Solidification, Trans. Tech. Publ., Zuerich, Switzerland, (1998). 6) J. A. Dantzig and M. Rappaz: Solidification, EPFL Press, Lausanne, (2009). 7) D. M. Stefanescu: Science and Engineering of Casting Solidification, Kluwer Acad., New York, (2002). 8) D. M. Stefanescu: Mat. Sci. Eng. A, (2005), ) C. R. Loper: AFS Trans., 107 (1999), ) T. Skaland: Proc. AFS Cast Iron Inoculation Conf., American Foundry Society, Schaumburg, IL, (2005), ) Y. Igarashi and S. Okada: Int. J. Cast Met. Res., 11 (1998), ) S. Lekakh, V. Richards and K. Peaslee: Int. J. Metalcast., 3 (2009), ) C. H. Wang and H. J. Fredriksson: Proc. 48th Int. Foundry Cong., Organizing Committee of the 48th Int. Foundry Cong., Varna, Bulgaria, (1981), ) S. Lekakh and C. R. Loper: AFS Trans., 111 (2003), ) F. Carazo, P. Dardati, D. Celentamo and L. Godoy: Metall. Mater. Trans. B, 12 (2012), ) K. Barmak: Metall. Mater. Trans. B, 9 (2010), DOI: /s ) K. Yamane, H. Yasuda, A. Sugiyama, T. Nadira, M. Yoshita, K. Morishita, K. Uesugi, T. Takeuchi and Y. Suzuki: Metall. Mater. Trans. A, 46 (2015), ) G. Alonso, D. M. Stefanescu, P. Larranaga and R. Suarez: Int. J. Cast Met. Res., 6 (2015), DOI: / Y ) S. C. Murcia, E. A. Ossa and D. J. Celentano: Metall. Mater. Trans. B, 45 (2014), ) K. M. Pedersen and N. S. Tiedjie: Mater. Charact., 59 (2008), ) S. Lekakh, J. Qing, V. Richards and K. Peaslee: AFS Trans., 121 (2013), ) S. Lekakh, V. Thapliyal and K. Peaslee: 2013 AISTech Conf. Proc., AIST, Warrendale, PA, (2013), ) J. Lu, D. Ivey and H. Henein: 2013 AISTech Conf. Proc., AIST, Warrendale, PA, (2013), ) L. Babout, E. Maire, J. Buffiere and R. Fougeres: Acta Mater., 49 (2001), ) J. Konrad, S. Zaefferer and D. Raabe: Acta Mater., 54 (2006), ) E. Martinez, K. Peaslee and S. Lekakh: AFS Trans., 119 (2011), Paper ) K. Peaslee, V. Singh and S. Lekakh: Proc. Richard J. Fruehan Symp., AIST, Warrendale, PA, (2011), 6. 28) M. Harris, O. Adaba, R. O Malley, S. Lekakh and V. Richards: AIST Proc., AIST, Warrendale, PA, (2015), ) C. Basak and A. Sengupta: Scr. Mater., 51 (2004), ) D. Sahagian and A. Proussevitck: J. Volcanol. Geotherm. Res., 84 (1998), ) S. Saltykov: Sterometric Metalurgy, Moscow, USSR, (1958). 32) M. Van Ende, M. Guo, E. Zinngrebe, B. Blanpain and I. Jung: ISIJ Int., 53 (2013), No. 11, ) D. M. Stefanescu: Int. J. Met. Cast., 1 (2015), 7. 34) S. Lekakh and V. Richards: AFS Trans., 115 (2011), Paper ISIJ