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Investigation into the effect of nucleation parameters on grain formation during solidification using a cellular automaton-finite control volume method

  • X. Yao (a1), M.S. Dargusch (a1), A.K. Dahle (a1), C.J. Davidson (a2) and D.H. StJohn (a1)...


A cellular automation (CA) model has successfully been used to model the development of microstructure of an aluminum alloy during solidification to produce detailed structure maps for the solidified alloys. More recently, the application of CA models to practical castings/solidification conditions has attracted increasing research interest. However, the determination of the calculation parameters of any model associated with nucleation is difficult. Accordingly, this work investigates the detailed effect of the six parameters of nucleation on microstructure formation and morphology as well as the grain size by cellular automaton-finite control volume method (CAFVM). The nucleation parameters can be determined or estimated by comparing the calculated and experimental results, which enables a more practical prediction of the microstructure (morphology and grain size).


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1Bennon, W.P.Incropera, F.P.: A continuum model for momentum, heat and species transport in binary solid liquid-phase change system 1: Model formation. Int. J. Heat Mass Transfer 30, 2161 1987
2Voller, V.R., Brent, A.D.Prakash, C.: The modelling of heat, mass and solute transport in solidification systems. Int. J. Heat Mass Transfer 32, 1719 1989
3Ganesan, S.Poirier, D.R.: Conservation of mass and momentum for the flow of interdentritic liquid during solidification. Metall. Trans. B 21, 173 1990
4Ni, J.Beckermann, C.: A volume-averaged 2-phase model for transport phenomena during solidification. Metall. Trans. B 22, 349 1991
5Anderson, M.P., Srolovitz, D.J., Grest, G.S.Sahni, P.S.: Computer-simulation of grain-growth 1: Kinetics. Acta Metall. 32, 783 1984
6Srolovitz, D.J., Anderson, M.P., Sahni, P.S.Grest, G.S.: Computer-simulation of grain-growth 2: Grain size distribution, topology and local dynamics. Acta Metall. 32, 793 1984
7Srolovitz, D.J., Anderson, M.P., Grest, G.S.Sahni, P.S.: Computer-simulation of grain-growth 3: Influence of a particle dispersion. Acta Metall. 32, 1429 1984
8Hesselbarth, H.W.Gobel, I.R.: Simulation of recrystallzation by cellular automata. Acta Metall. Mater. 39, 2135 1991
9Maxwell, I.Hellawell, A.: Simple model for grain refinement during solidification. Acta Metall. 23, 229 1975
10Charbon, Ch., Jacot, A.Rappaz, M.: 3D stochastic modelling of equiaxed solidification in the presence of grain movement. Acta Metall. Mater. 42, 3953 1994
11Lee, S.Y., Lee, S.M.Hong, C.P.: Numerical modeling of deflected columnar dendritic grains solidified in a flowing melt and its experimental verification. ISIJ Int. 40, 48 2000
12Thevoz, Ph., Desbiolles, J.L.Rappaz, M.: Modeling of equiaxed microstructure formation in casting. Metall. Trans. A 20, 311 1989
13Stefanescu, D.M., Moitra, A.Bandyopadhyay, D.: Heat transfer-solidification kinetics modelling of solidification of castings. Metall. Trans. A 21, 997 1990
14Gandin, Ch.A.Rappaz, M.: A coupled finite-element cellular-automaton model for the prediction of dendritic grain structures in solidification processes. Acta Metall. Mater. 42, 2233 1994
15Rafii-Tabar, H.Chirazi, A.: Multi-scale computational modelling of solidification phenomena. Phys. Rep. 365, 145 2002
16Stefanescu, D.M.: Solidification and modeling of cast iron–A short history of the defining moments. Mater. Sci. Eng., A 413–414, 322 2005
17Rappaz, M.Gandin, Ch-A.: Probabilistic modeling of microstructure formation in solidification processes. Acta Metall. 41, 345 1993
18Kurz, W.Fisher, D.J.: Fundamentals of Solidification Trans Tech Publications Aedermannsdorf, Switzerland 1989
19Chalmers, B.: Principles of Solidification Wiley New York 1964
20Boettinger, W.J., Warren, J.A., Bechermann, C.Karma, A.: Phase-field simulation of solidification. Annu. Rev. Mater. Res. 32, 163 2002
21Karma, A.Rappel, W.J.: Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys. Rev. E 57, 4323 1998
22Granasy, L., Pusztai, T., Borzsonyi, T., Toth, G., Tegze, G., Warren, J.A.Douglas, J.F.: Phase field theory of crystal nucleation and polyerystalline growth: A review. J. Mater. Res. 21, 309 2006
23Spittle, J.A.Brown, S.G.R.: Computer-simulation of the effects of alloy variables on the grain structures of castings. Acta Metall. 37, 1803 1989
24Brown, S.G.R.Spittle, J.A.: Modelling of Casting, Welding and Advanced Solidification Processes, edited by M. Rappaz, M. Ozgu, and K. Mahin TMS Warrendale, PA 1991 395
25Echebarria, B., Folch, R., Karma, A.Plapp, M.: Quantitative phase-field model of alloy solidification. Phys. Rev. E 70, 061604 2004
26Folch, R.Plapp, M.: Quantitative phase-field modeling of two-phase growth. Phys. Rev. E 72, 011602 2005
27Greenwood, M., Haataja, M.Provatas, N.: Crossover scaling of wavelength selection in directional solidification of binary alloys. Phys. Rev. Lett. 93, 246101 2004
28Yao, X., Wang, H., He, B.Zhou, X.: Modeling of columnar-to-equiaxed transition in solidified Al–Si alloys. Mater. Sci. Forum 457–479, 3141 2005
29Nastac, L.: Numerical modeling of solidification morphologies and segregation patterns in cast dendritic alloys. Acta Mater. 47, 4253 1999
30Zhu, M.F.Hong, C.P.: A modified cellular automaton model for the simulation of dendritic growth in solidification of alloys. ISIJ Int. 41, 436 2001
31Yao, X., Davidson, C.J., Dahle, A.K.StJohn, D.H.: Modelling of microstructure formation and evolution during solidification. Int. J. Cast Met. Res. 15, 219 2002
32Yao, X., He, B., Wang, H.Zhou, X.: Numerical simulation of dendrite growth during solidification. Int. J. Non-Linear Sci. Numer. Simulat. 7, 171 2006
33Ping, W.S., Liu, D.R., Guo, J.J., Li, C.Y., Su, Y.Q.Zhi, F.H.: Numerical simulation of microstructure evolution of Ti–6Al–4V alloy in vertical centrifugal casting. Mater. Sci. Eng., A 426, 240 2006
34Ito, K., Shara, R., Farjami, S., Marutama, T.Kubo, H.: Evolution of solidification structures in Fe–Mn–Si–Cr shape memory alloy in centrifugal casting. Mater. Trans. 47, 1584 2006
35Cho, S-H., Okane, T.Umeda, T.: CA-DFD analysis of nucleation parameter effects on the grain structures of castings. Int. J. Cast Met. Res. 13, 327 2001
36Backerud, L., Gistafson, P.Johnsson, M.: Grain refining mechanism as a result of addition of titanium and boron. Aluminium 67, 910 1991
37Hutt, J.: The origin of equiaxed crystals and the grain size transition in aluminum-silicon alloys. Ph.D. Thesis, The University of Queensland, 2001
38Easton, M.: Grain refinement mechanisms in aluminum and its alloys and the effect of grain refinement on castability. Ph.D. Thesis, The University of Queensland, 1999
39Croft, D.R.Lilley, D.G.: Heat Transfer Calculation Using Finite Difference Equations Applied Science London 1977
40Yao, X., McDonald, S.D., Dahle, A.K., Davidson, C.J.StJohn, D.H.: Modeling of grain refinement: Part I. Effect of the solute for aluminum. J. Mater. Res. 23(5), 1282 2008
41Kurz, W., Giovanola, B.Trivedi, R.: Theory of microstructural development during rapid solidification. Acta Metall. 34, 823 1986
42Pehlke, R.D., Jeyrajan, A.Wada, H.: Summary of Thermal Properties for Casting Alloys and Mold Materials, University of Michigan, 1982
43Tondel, P.A.: Grain refinement of hypoeutectic Al-Si foundry alloys. Ph.D. Thesis, Norwegian Institute of Technology, Trondheim, Norway, 1994
44Yao, X., McDonald, S.D., Dahle, A.K., Davidson, C.J.StJohn, D.H.: Modeling of grain refinement: Part II. Effect of nucleant particles-TiB2 additions for aluminum. J. Mater. Res. 23(5), 1292 2008



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