Multiphysics and multiscale modelling of ductile cast iron solidification

• Autorzy: Gurgul D. , Burbelko A. , Fraś E. , Guzik E.
• Języki publikacji: EN

Abstrakty

EN

The presented model of ductile cast iron solidification is a typical sample of multiphysics and multiscale engineering system. This model takes into consideration the different time and spatial scales of accounted phenomenon of microstructure formation: heat diffusion, components mass diffusion in the liquid and solid phases, thermodynamic of phase transformation under the condition of inhomogeneous chemical composition of growing and vanishing phases, phase interface kinetics and grains nucleation. The results of two-dimensional modelling of the microstructure formation in the ductile cast iron (so called - Ductile Iron - DI) are presented. The cellular automaton model (CA) was used for the simulation. Six states of CA cells were adopted to three phases above mentioned (liquid, austenite and graphite) and to three two-phase interfaces. For the modelling of concentration and temperature fields the numerical solution was used. The parabolic nonlinear differential equations with a source term were solved by using the finite difference method and explicit scheme. The overlapping lattices with the same spatial step were used for the concentration field modelling and for the CA. The time scale of the temperature field for this lattice is about 10⁴ times shorter. Due to above reasons the another lattice was used with a multiple spatial step and the same time step.

Słowa kluczowe

EN

cellular automaton; ductile iron; solidification process; dendrite of austenite; spheroidal graphite

PL

automat komórkowy; żeliwo ADI; proces krzepnięcia; żeliwo sferoidalne

• Wydawca: Komisja Odlewnictwa Polskiej Akademii Nauk Oddział w Katowicach
• Czasopismo: Archives of Foundry Engineering
• Rocznik: 2010
• Tom: Vol. 10, iss. 1 spec.
• Strony: 35--40
• Opis fizyczny: Bibliogr. 27 poz., rys., tab.

Twórcy

autor

Gurgul D.

• AGH - University of Science and Technology, Reymonta 23, 30-059 Krakow, Poland

autor

Burbelko A.

• AGH - University of Science and Technology, Reymonta 23, 30-059 Krakow, Poland

autor

Fraś E.

• AGH - University of Science and Technology, Reymonta 23, 30-059 Krakow, Poland

autor

Guzik E.

• AGH - University of Science and Technology, Reymonta 23, 30-059 Krakow, Poland

Bibliografia

• [1] Rafii-Tabar H., Chirazi A.: Multi-scale computational modelling of solidification phenomena, Physics Reports-Review Section of Physics Letters, 365(3), (2002) pp. 145-249.
• [2] Lee P.D., Chirazi A.: Atwood R.C., Wang W.: Multiscale modelling of solidification microstructures, including microsegregation and microporosity, in an Al-Si-Cu alloy, Materials Science and Engineering A, 365(1-2), (2004) pp. 57-65.
• [3] Umantsev A.R., Vinogradov V.V., Borisov V.T.: Mathematical Modeling of the Dendrite Growth in the Undercooled Melt, Kristallografia, 30(3), (1985) pp. 455-460. (In Russian).
• [4] Umantsev A.R., Vinogradov V.V., Borisov V.T.: Modeling of the Dendrite Structure Evolution, Kristallografia, 31(5), (1986) pp. 1002-1008. (In Russian).
• [5] Rappaz M., Gandin Ch.A.: Probabilistic Modeling of Microstructure Formation in Solidification Processes, Acta Metallurgica et Materialia, 41(2), (1993) pp. 345-360.
• [6] Pan S., Zhu M.: A three-dimensional sharp interface model for the quantitative simulation of solutal dendritic growth, Acta Materialia, 58(1), (2010) pp. 340-352.
• [7] Mosbah S., Bellet M., Gandin Ch.A.: Simulation of Solidification Grain Structures with a Multiple Diffusion Length Scales Model, Modeling of Casting, Welding and Advanced Solidification Processes - XII, S.L. Cockcroft, D.M. Maijer eds., TMS, Vancouver, Canada, (2009) pp. 485-493.
• [8] Guillemot G., Gandin Ch.A., Bellet M.: Interaction Between Single Grain Solidification and Macro Segregation: Application of a Cellular Automaton - Finite Element Model, Journal of Crystal Growth, 303 (1), (2007) pp. 58-68.
• [9] Beltran-Sanchez L., Stefanescu D.M.: A Quantitative Dendrite Growth Model and Analysis of Stability Concepts, Metallurgical and Materials Transactions A, 35A(8), (2004) pp. 2471-2485.
• [10] Pavlyk V., Dilthey U.: Simulation of Weld Solidification Microstructure and its Coupling to the Macroscopic Heat And Fluid Flow Modelling, Modelling and Simulation in Materials Science and Engineering, 12(1), (2004) pp. S33-S45.
• [11] Zhu M.F., Hong C.P.: A Three Dimensional Modified Cellular Automaton Model for the Prediction of Solidification Microstructures, ISIJ International, 42(5), (2002) p. 520-526.
• [12] Jarvis D.J., Brown S.G.R., Spittle J.A.: Modelling of Non-Equilibrium Solidification in Ternary Alloys: Comparison of 1D, 2D, and 3D Cellular Automaton-Finite Difference Simulations, Materials Science and Technology, 16(11-12), (2000) pp. 1420-1424.
• [13] Burbelko A.A., Fraś E., Kapturkiewicz W.: Modelling of Dendritic Growth During Unidirectional Solidification by the Method of Cellular Automata, Materials Science Forum, 649, (2010) pp. 217-222.
• [14] Burbelko A.A., Fraś E., Kapturkiewicz W., Olejnik E.: Nonequilibrium Kinetics of Phase Boundary Movement in Cellular Automaton Modelling, Materials Science Forum, 508, (2006) pp. 405-410.
• [15] Brown S.G.R., Bruce N.B.: Three-Dimensional Cellular Automaton Models of Microstructural Evolution During Solidification, Journal of Materials Science, 30(5), (1995) pp. 1144-1150.
• [16] Zhu MF., Hong CP.: Modeling of microstructure evolution in regular eutectic growth, Physical Review B, 66(15), (2002) art. No. 155428.
• [17] Zhu M.F., Hong C.P.: Modeling of microstructure evolution in eutectic and peritectic solidification, Modeling of Casting, Welding and Advanced Solidification Processes - X, D.M. Stefanescu, J.A. Warren, M.R. Jolly, M.J.M. Krane eds., TMS, Warrendale, Pennsylvania, (2003) pp. 91-98.
• [18] Zhu M.F., Hong C.P., Stefanescu D.M., Chang, Y.A.: Computational modeling of microstructure evolution in solidification of aluminum alloys, Metall. Mater. Trans. B, 38B(4), (2007) pp. 517-524.
• [19] Chopard B., Droz M.: Cellular automata modeling of physical systems, Cambridge University Press, Cambridge, UK, (2005).
• [20] Hoyt J., Asta M.: Atomistic computation of liquid diffusivity, solid-liquid interfacial free energy, and kinetic coefficient in Au and Ag, Phys. Rev. B., 65, (2002) art. No. 214106, 1–11.
• [21] Burbelko, A.: Mezomodeling of Solidificatnion Usin a Cellular Automaton, UWND AGH, (2004) Krakow (in Polish).
• [22] Mullins W.W., Sekerka R.F.: Morphological stability of a particle growing by diffusion or heat flow, Journ. of Applied Phys., 34, (1963) pp. 323-329.
• [23] Dilthley U., Pavlik V.: Numerical simulation of dendrite morphology and grain growth with modified cellular automata, Modeling of Casting, Welding and Advanced Solidification Processes VIII, B.G. Thomas and C. Beckermann eds., TMS, Warrendale, (1998) pp. 589-596.
• [24] Burbelko A.A., Kapturkiewicz W., Gurgul D.: Analysis of causes and means to reduce artificial anisotropy in modelling of the solidification process on cellular automaton, Solidification Processing 2007: Proceedings of the 5th Decennial International Conference on Solidification Processing. H. Jones eds., The University of Sheffield, UK, (2007) pp. 31-35.
• [25] Kubaschewski O.: Iron – Binary Phase Diagrams, Springer-Verlag, (1985) Berlin.
• [26] Rivera G., Boeri R., Sikora J.: Revealing and characterising solidification structure of ductile cast iron, Materials Science and Technology, 18(7), (2002) pp. 691-697.
• [27] Rivera G., Calvillo P.R. Boeri R., Houbaert Y., Sikora J.: Examination of the solidification macrostructure of spheroidal and flake graphite cast irons using DAAS and ESBD", Materials Characterization, 59, (2008) pp. 1342-1348.