Stochastic Nature of the Casting Solidification Displayed by Micro-Modelling and Cellular Automata Method

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Abstract:

Some aspects of stochastic nature of the solidification processes are described. Firstly, the influence of the random grains nucleation on the cooling curves repeatability in the thin wall casting is presented. Secondly, the foundations of an average shape prediction for geometry of ele¬mentary diffusion field (concept of the Averaged Voronoi Polyhedron, AVP) are shown for the mi¬cro-modelling of the diffusion limited growth. Stochastic nature of the grains nucleation and growth is taken into account in the solidification modelling based on the Cellular Automaton technique (CA).

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Solid State Phenomena (Volume 197)

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101-106

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February 2013

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[1] A.R. Umantsev, V.V. Vinogradov, V.T. Borisov, Mathematical modeling of the dendrite growth during the solidification from undercooled melt, Kristallografia 30 (1985) 455-60 (in Russian).

Google Scholar

[2] M. Rappaz, Ch.A. Gandin, Probabilistic Modelling of Microstructure Formation in Solidification Processes, Acta Met. Mater. 41 (1993) 345-360.

DOI: 10.1016/0956-7151(93)90065-z

Google Scholar

[3] L. Nastac, D.M. Stefanescu, Stochastic modelling of microstructure formation in solidification processes, Modelling Simul. Mater. Sci. Eng. 5 (1997) 391-420.

DOI: 10.1088/0965-0393/5/4/008

Google Scholar

[4] D.J. Jarvis, S.G.R. Brown, J.A. Spittle, Modelling of non-equilibrium solidification in ternary alloys: comparison of 1D, 2D, and 3D cellular automaton-finite difference simulations, Mat. Sci. Techn. 16 (2000) 1420-1424.

DOI: 10.1179/026708300101507389

Google Scholar

[5] M.F. Zhu, C.P. Hong, A three dimensional modified cellular automaton model for the prediction of solidification microstructures, ISIJ Int. 42 (2002) 520-526.

DOI: 10.2355/isijinternational.42.520

Google Scholar

[6] L. Beltran-Sanchez, D.M. Stefanescu, A Quantitative dendrite growth model and analysis of stability concepts, Metall. Mat. Trans. A 35 (2004) 2471-2485.

DOI: 10.1007/s11661-006-0227-3

Google Scholar

[7] V. Pavlyk, U. Dilthey, Simulation of weld solidification microstructure and its coupling to the macroscopic heat and fluid flow modelling, Model. Simul. Mater. Sci. Eng. 12 (2004) 33-45.

DOI: 10.1088/0965-0393/12/1/s03

Google Scholar

[8] G. Guillemot, Ch.A. Gandin, M. Bellet, Interaction between single grain solidification and macrosegregation: Application of a cellular automaton-finite element model, J. Cryst. Growth 303 (2007) 58-68.

DOI: 10.1016/j.jcrysgro.2006.12.076

Google Scholar

[9] P.D. Lee, A. Chirazi, R.C. Atwood, W. Wang, Multiscale modelling of solidification microstructures, including microsegregation and microporosity in an Al-Si-Cu alloy, Mat. Sci. Eng. A 365 (2004) 57-65.

DOI: 10.1016/j.msea.2003.09.007

Google Scholar

[10] A.A. Burbelko, E. Fraś, W. Kapturkiewicz, D. Gurgul, Modelling of dendritic growth during unidirectional solidification by the method of cellular automata, Mat. Sci. Forum 649 (2010) 217-222.

DOI: 10.4028/www.scientific.net/msf.649.217

Google Scholar

[11] H.L. Zhao, M.F. Zhu, D.M. Stefanescu, Modeling of the divorced eutectic solidification of spheroidal graphite cast iron, Key Eng. Mat. 457 (2011) 324-329.

DOI: 10.4028/www.scientific.net/kem.457.324

Google Scholar

[12] A.A. Burbelko, D. Gurgul, W. Kapturkiewicz, M. Górny, Cellular automaton modelling of ductile iron microstructure in the thin wall casting, IOP Conference Series: Mat. Sci. Technol. 33 (2012) 012083.

DOI: 10.1088/1757-899x/33/1/012083

Google Scholar

[13] Ch.A. Gandin, M. Rappaz, A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes, Acta Metall. Mater. 42 (1994) 2233-2246.

DOI: 10.1016/0956-7151(94)90302-6

Google Scholar

[14] D.M. Stefanescu, A. Catalina, X. Guo, L. Chuzhoy, M.A. Pershing, G.L. Biltgen, Prediction of room temperature microstructure and mechanical properties in iron castings, in: B.G. Thomas, C. Beckerman (Eds. ), Modeling of Casting, Welding and Advanced Solidification Process - VIII, TMS, Warrendale, PA, 1998, pp.455-462.

Google Scholar

[15] S. Chang, D. Shangguan, D. Stefanescu, Modeling of the liquid/solid and the eutectoid phase transformation in spheroidal graphite cast iron, Metal. Trans. A 23A (1992) 1333-1346.

DOI: 10.1007/bf02665065

Google Scholar

[16] T. Skaland, O. Grong, T. Grong, A model for the graphite formation in ductile cast iron, Metal. Trans. A. 24A (1993) 2347-2353.

DOI: 10.1007/bf02648606

Google Scholar

[17] S.M. Yoo, A. Ludwig, P.R. Sahm, Numerical simulation of nodular cast iron in permanent moulds, in: J. Beech, H. Jones (Eds. ), Solidification Processing, Renmor House, Univ. of Sheffield, 1997, pp.494-497.

Google Scholar

[18] M.I. Onsoien, O. Grong, O. Gundersen, T. Skaland, A process model for the micro-structure evolution in ductile cast iron: part I, Metall. Mat. Trans. A 30A (1999) 1053-1068.

DOI: 10.1007/s11661-999-0158-x

Google Scholar

[19] A.A. Burbelko, J. Początek, M. Królikowski, Application of Averaged Voronoi Polyhedron in the modelling of crystallisation of eutectic nodular graphite cast iron, Arch. of Foundry Eng. 13 (2013) 134-140.

DOI: 10.2478/afe-2013-0026

Google Scholar

[20] A.N. Kolmogorov, On the Statistical Theory of Metal Crystallisation, Bull. Acad. Sci. USSR. 3 (1937) 355-359 (in Russian).

Google Scholar

[21] G. Lesoult, M. Castro, J. Lacaze, Solidification of spheroidal graphite cast iron, Acta Mater. 46 (1998) 983-1010.

DOI: 10.1016/s1359-6454(97)00281-4

Google Scholar

[22] E. Fraś, W. Kapturkiewicz, A.A. Burbelko, H.F. Lopez, Modeling of graphitization kinetics in nodular cast iron casting, in: P. Sahm, P.N. Hansen, J.G. Conley (Eds. ), Modeling of Casting, Welding and Advanced Solidification Processes IX, Shaker, Aachen, 2000, pp.885-892.

Google Scholar

[23] W. Brostow, V.M. Castano, Voronoi polyhedra as a tool for dealing with spatial structures of amorphous solids, liquids and dense gases. J. Mater. Ed. 21 (1999) 297-304.

Google Scholar