Advertisement

Process modelling and microstructure

  • M. Rappaz
  • CH.-A. Gandin

Abstract

Among the many routes which are used for the processing of high-temperature materials, solidification plays a key role. Several modelling tools are now available for the simulation of the interconnected macroscopic phenomena associated with any casting process (heat exchange, mould filling, convection, stress development, etc.). Based upon finite-difference (FD) or finite-element (FE) techniques, these models solve the continuity equations of mass, energy, momentum, solute species, averaged over the liquid and solid phases. As such, macroscopic models do not account for the detailed phenomena occurring at the scale of the microstructure. For that reason, a stochastic cellular automaton (CA) model has been developed recently for the prediction of the grain structure formation in solidification processes, in particular during the investment casting of superalloys. Such a microscopic model considers the heterogeneous nucleation of grains at the surface of the mould and in the bulk of the liquid, the growth kinetics and preferential growth directions of the dendrites and the microsegregation. The microscopic CA model has been coupled to FE heat flow computations in order to predict the grain structure at the scale of a casting. It is shown that microstructural features and crystallographic textures can be simulated as a function of the casting conditions and alloy composition.

Keywords

Cellular Automaton Investment Casting Mould Filling Chill Surface Microsegregation Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, M. P., Srolovitz, D. J., Grest, G. S. & Sahni, P. S. 1984 Computer simulation of grain growth. I. Kinetics. Acta metal. 32, 783–791.Google Scholar
  2. Bennon, W. D. & Incropera, F. P. 1987 A continuum model for momentum, heat and species transport in binary solid—liquid phase change systems. Int. J. Heat Mass Transfer 30, 2161–2187.CrossRefGoogle Scholar
  3. Chalmers, B. 1964 Principles of solidification. New York: Wiley.Google Scholar
  4. Combeau, H. & Lesoult, G. 1993 Simulation of freckles formation and related segregation during directional solidification of metallic alloys. In Modeling of casting, welding and advanced solidification processes VI (ed. T. S. Piwonka et al.), pp. 201–208. The Minerals, Metals and Materials Society.Google Scholar
  5. Ganesan, S. & Poirier, D. R. 1990 Conservation of mass and momentum for the flow of interdendritic liquid during solidification. Metall. Trans. B 21, 173–181.Google Scholar
  6. Gandin, Ch.-A., Rappaz, Ch. A. & Tintillier, R. 1993 Three-dimensional probabilistic simulation of solidification grain structures: application to superalloys precision castings. Metall. Trans. A 24, 467–479.Google Scholar
  7. Gandin, Ch.-A., Rappaz, M. & Tintillier, R. 1994 Three-dimensional simulation of the grain formation in investment casting. Metall. Trans. A 25, 629–635.Google Scholar
  8. Gandin, Ch.-A. & Rappaz, M. 1994 A coupled finite element—cellular automaton model for the prediction of dendritic grain structures in solidification processes. Acta metall. mater. 42, 2233–2246.CrossRefGoogle Scholar
  9. Gandin, Ch.-A., Rappaz, M., West, D. & Adams, B. L. 1995 Grain texture evolution during the columnar growth of dendritic alloys. Metall. Trans. A 26, 1543–1552.Google Scholar
  10. Hunt, J. D. 1984 Steady state columnar and equiaxed growth of dendrites and eutectic. Mater. Sci. Engng 65, 75–83.CrossRefGoogle Scholar
  11. Kobayashi, S. 1988 Solute redistribution during solidification. J. Cryst. Growth 88, 87–96.CrossRefGoogle Scholar
  12. Kurz, W. & Fisher, D. J. 1989 Fundamentals of solidification. Aedermannsdorf: Trans. Tech. Pub.Google Scholar
  13. Kurz, W., Giovanola, B. & Trivedi, R. 1986 Theory of microstructural development during rapid solidification. Acta metall. mater. 34, 823–830.CrossRefGoogle Scholar
  14. Mo, A. 1994 An internal variable description of solidification suitable for macrosegregation modeling. Metall. Trans. B 25, 597–605.Google Scholar
  15. Ni, J. & Beckermann, C. 1991 A volume-averaged two-phase model for transport phenomena during solidification. Metall. Trans. B 22, 349–361.Google Scholar
  16. Rappaz, M. & Thévoz, Ph. 1987 Solute diffusion model for equiaxed dendritic growth: analytical solution. Acta metall. mater. 35, 2929–2933.CrossRefGoogle Scholar
  17. Rappaz, M. 1989 Modelling of microstructure formation in solidification processes. Int. Mater. Rev. 34, 93–123.Google Scholar
  18. Rappaz, M. & Voller, V. 1990 Modelling of micro-macrosegregation in solidification processes. Metall. Trans. A 21, 749–753.Google Scholar
  19. Rappaz, M. & Gandin, Ch.-A. 1993 Probabilistic modelling of microstructure formation in solidification processes. Acta metall. mater. 41, 345–360.CrossRefGoogle Scholar
  20. Sato, T., Kurz, W. & Ikawa, K. 1987 Experiments on dendrite branch detachment in the succinonitrile—canphor alloy. Trans. Jpn Inst. Metals 28, 1012–1021.Google Scholar
  21. Thévoz, Ph., Rappaz, M. & Desbiolles, J. L. 1990 3-MOS: a general FEM code for the prediction of microstructures in castings. In Light metals (ed. Ch. M. Bickert), pp. 975–984. The Minerals, Metals and Materials Society.Google Scholar
  22. Toffoli, T. & Margolus, N. 1991 Cellular automata machines. MIT Press.Google Scholar
  23. Turnbull, D. 1950 Kinetics of heterogeneous nucleation. J. chem. Phys. 18, 198–203.CrossRefGoogle Scholar
  24. Voller, V. R., Brent, A. D. Si Prakash, C. 1989 The modelling of heat, mass and solute transport in solidification systems. Int. J. Heat Mass Transfer 32, 1719–1731.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • M. Rappaz
  • CH.-A. Gandin

There are no affiliations available

Personalised recommendations