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A new approach to modelling of phase boundary migration is presented. In particular, a meso-scale model of alloy solidification, which can resolve solid grain boundaries as they grow through the diminishing liquid phase, has been developed. The initial condition is of a superheated, but cooling, liquid alloy in a domain with a mixed thermal boundary condition. After activation via nucleation of solid, the model tracks the phase boundaries as discrete fronts across a fixed computational grid, and the kineticsof motion are derived from theories of dendritic growth. Each interface is formed by interpolation between representative computational markers, and is the boundary between liquid and partial solid with a dendritic morphology. The model simulates the non-equilibrium growth of both a columnar front and equiaxed grains, and can thus be used to predict the final grain structure in metallic alloy castings. The evolution of microstructure and heat are fully coupled in the formulation. The method is illustrated by the example of the simulation of Al-Cu alloy solidification.
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Tom
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25--36
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Bibliogr. 19 poz.,
Bibliografia
- [1] CARTER, P., Cox, D. C., GANDIN, CH.-A., REED, R. C.: Process modelling of grain selection during the solidification of single crystal superalloy castings, Mater. Sci. Eng. A280(2000), 233-246.
- [2] WARREN, J. A., BOETTINGER, W. J.: Prediction of dendritic microsegregation pat- terns using a diffuse interface phase field model, [in] Modelling of Casting, Welding and Advanced Solidification Processes VII (Eds. M. Cross and J. Campbell), TMS, Warrendale, PA, USA, 601-607, 1995.
- [3] KRILL III, C. E., CHEN, L.-Q.: Computer simulation of 3-D grain growth using a phase-field model, Acta Mater. 50(2002), 3057-3073.
- [4] JURIC, D., TRYGGVASON, G.: A front-tracking method for dendritic solidification, J. Comp. Phys. 123(1996), 127-148.
- [5] LAKEHAL, D., MEIER, M., FULGOSI, M.: Interface tracking towards the direct simulation of heat and mass transfer in multiphase flows, Int. J. Heat and Fluid Flow, 23(2002), 242-257.
- [6] Cox, R.C. (ED.): Robert Mallet (1810-1881), Centenary Seminar Papers, Institu- tion of Engineers of Ireland and The Royal Irish Academy, Dublin, Ireland, 1982.
- [7] MALLET, R.: On the Physical Conditions Involved in the Construction of Artillery, Longman, Brown, Green, Longmans and Roberts, London 1856.
- [8] CAMPBELL J.: Castings, Butterworth Heinemann, Oxford, UK, 1991.
- [9] BURDEN M. H., HUNT J.D.: Cellular and dendritic growth, J. of Crystal Growth 22(1974), 99-116.
- [10] HUNT, J. D., Lu, S.-Z.: Numerical modelling of cellular/dendritic array growth: spacing and structure predictions, Metall. Mater. Trans. 27A (1996), 611-623.
- [11] BROWNE D. J., HUNT, J. D.: A model of columnar growth using a front-tracking technique, Modeling of Casting, Welding and Advanced Solidification Processes IX, IX (Eds. P.R. Sahm, P.N. Hansen and J.G. Conley), Shaker Verlag, Aachen, Ger- many, 437-444, 2000.
- [12] BROWNE, D. J.: Modelling columnar and equiaxed growth, D.Phil. thesis, University of Oxford, UK, 2002.
- [13] O'MAHONEY, D., BROWNE, D. J.: Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process, Experimental Thermal and Fluid Science 22(2000), 111-222.
- [14] BROWNE, D. J., O'MAHONEY, D.: Interface heat transfer in investment casting of aluminum alloys, Metall. Mater. Trans. 32A (2001), 3055-3063.
- [15] FLEMINGS, M. C.: Solidification Processing, McGraw Hill, New York 1974. [16] TURNBULL, D. AND FISHER, J. C.: Rate of nucleation in condensed systems, J. Chem. Phys. 17(1949), No. 1, 71-73.
- [17] BANASZEK, J., BROWNE, D. J., FURMANSKI, P.: Eulerian equilibrium and non- equilibrium macroscopic modelling of binary system solidification, Arch. of Thermo- dynamics, 24(2003), No. 1, 37.
- [18] JACKSON K. A., HUNT J. D., UHLMANN D. R., SEWARD III T. P.: On the origin of the equiaxed zone in castings, Trans. Met. Soc. AIME 236(1966), 149-158.
- [19] SHYY W, UDAYKUMAR H. S., RAO M. M., SMITH, R. W.: Computational fluid dynamics with moving boundaries, Taylor & Francis, Washington, DC, USA, 1996.
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Bibliografia
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bwmeta1.element.baztech-article-BGPK-0638-2762