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Phase field modeling of solidification in multi-component alloys with a case study on the Inconel 718 alloy

  • Michael Fleck (a1), Frank Querfurth (a2) and Uwe Glatzel (a1)
Abstract

We develop a phase field model for the simulation of chemical diffusion-limited solidification in complex metallic alloys. The required thermodynamic and kinetic input information is obtained from CALPHAD calculations using the commercial software-package ThermoCalc. Within the case study on the nickel-base superalloy Inconel 718, we perform simulations of solidification with the explicit consideration of 6 different chemical elements. The stationary dendritic tip velocities as functions of the constant undercooling temperature obtained from isothermal solidification are compared with the stationary tip temperatures as functions of the imposed pulling velocity obtained during directional solidification. We obtain a good quantitative agreement between the two different velocity—undercooling functions. This indicates that the model provides a self consistent description of the solidification. Finally, the simulation results are discussed in light of experimental solidification conditions found in single crystalline casting experiments of Inconel 718.

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Corresponding author
a) Address all correspondence to this author. e-mail: michael.fleck@uni-bayreuth.de
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Contributing Editor: Mathias Göken

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References
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1. Reed, R.C.: The Superalloys Fundamentals and Applications (Cambridge University Press, New York, New York, 2006).
2. Ivantsov, G.P.: Temperature field around a spherical, cylindrical and acicular crystal growth in a supercooled melt. Dokl. Akad. Nauk USSR 58, 567 (1947).
3. Brener, E.A. and Mel’nikov, V.I.: Pattern selection in two-dimensional dendritic growth. Adv. Phys. 40, 53 (1991).
4. Danzig, J.A. and Rappaz, M.: Solidification (EPFL Press, Lausanne, Switzerland, 2009). Available at: http://www.solidification.org/.
5. Brener, E.A., Boussinot, G., Huter, C., Fleck, M., Pilipenko, D., Spatschek, R., and Temkin, D.E.: Pattern formation during diffusional transformations in the presence of triple junctions and elastic effects. J. Phys.: Condens. Matter 21, 464106 (2009).
6. Ben Amar, M. and Brener, E.A.: Parity-broken dendrites. Phys. Rev. Lett. 75, 561564 (1995).
7. Ihle, T. and Müller-Krumbhaar, H.: Fractal and compact growth morphologies in phase transitions with diffusion transport. Phys. Rev. E 49, 29722991 (1994).
8. Turnbull, D.: Metastable structures in metallurgy. Metall. Trans. A 12, 695 (1981).
9. Huitema, H.E.A., Vlot, M.J., and van der Eerden, J.P.: Simulations of crystal growth from Lennard-Jones melt: Detailed measurements of the interface structure. J. Chem. Phys. 111, 4714 (1999).
10. Bragard, J., Karma, A., Lee, Y.H., and Plapp, M.: Linking phase-field and atomistic simulations to model dendritic solidification in highly undercooled melts. Interface Sci. 10, 121 (2002).
11. Kupferman, R., Kessler, D.A., and Ben-Jacob, E.: Coexistence of symmetric and parity-broken dendrites in a channel. Physica A 213, 451464 (1995).
12. Sabouri-Ghomi, M., Provatas, N., and Grant, M.: Solidification of a supercooled liquid in a narrow channel. Phys. Rev. Lett. 86, 50845087 (2001).
13. Fleck, M., Hüter, C., Pilipenko, D., Spatschek, R., and Brener, E.A.: Pattern formation during diffusion limited transformations in solids. Philos. Mag. 90, 265 (2010).
14. Fleck, M., Brener, E.A., Spatschek, R., and Eidel, B.: Elastic and plastic effects on solid-state transformations: A phase field study. Int. J. Mater. Res. 4, 462 (2010).
15. Kassner, K., Guérin, R., Ducousso, T., and Debierre, J-M.: Phase-field study of solidification in three-dimensional channels. Phys. Rev. E 82, 021606 (2010).
16. Gurevich, S., Karma, A., Plapp, M., and Trivedi, R.: Phase-field study of three-dimensional steady-state growth shapes in directional solidification. Phys. Rev. E 81, 011603 (2010).
17. Ma, Y. and Plapp, M.: Phase-field simulations and geometrical characterization of cellular solidification fronts. J. Cryst. Growth 385, 140 (2014).
18. Boettinger, W., Warren, J., Beckermann, C., and Karma, A.: Phase-field simulation of solidification. Annu. Rev. Mater. Res. 32, 163 (2002).
19. Asta, M., Beckermann, C., Karma, A., Kurz, W., Napolitano, R., Plapp, M., Purdy, G., Rappaz, M., and Trivedi, R.: Solidification microstructures and solid-state parallels: Recent developments, future directions. Acta Mater. 57, 941 (2009).
20. Karma, A. and Rappel, W-J.: Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys. Rev. E 57, 43234349 (1998).
21. Almgren, R.F.: Second-order phase field asymptotics for unequal conductivities. SIAM J. Appl. Math. 59, 2086 (1999).
22. Echebarria, B., Folch, R., Karma, A., and Plapp, M.: Quantitative phase-field model of alloy solidification. Phys. Rev. E 70, 061604 (2004).
23. Folch, R. and Plapp, M.: Quantitative phase-field modeling of two-phase growth. Phys. Rev. E 72, 011602 (2005).
24. Kim, S.G.: A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties. Acta Mater. 55, 4391 (2007).
25. Plapp, M.: Remarks on some open problems in phase-field modelling of solidification. Philos. Mag. 91, 14786435 (2011).
26. Brener, E.A. and Boussinot, G.: Kinetic cross coupling between nonconserved and conserved fields in phase field models. Phys. Rev. E 86, 060601 (2012).
27. Boussinot, G., Brener, E.A., Hüter, C., and Spatschek, R.: Elimination of surface diffusion in the non-diagonal phase field model. Continuum Mech. Thermodyn. 29, 969976 (2017).
28. Calculated with thermocalc using TTNi8 and MobNi1 (http://www.thermocalc.com).
29. Mushongera, L.T., Fleck, M., Kundin, J., Wang, Y., and Emmerich, H.: Effect of Re on directional γ′-coarsening in commercial single crystal Ni-base superalloys: A phase field study. Acta Mater. 93, 60 (2015).
30. Mushongera, L.T., Fleck, M., Kundin, J., Querfurth, F., and Emmerich, H.: Phase-field study of anisotropic γ′-coarsening kinetics in Ni-base superalloys with varying Re and Ru contents. Adv. Eng. Mater., 17, 11491157 (2015).
31. Eggleston, J.J., McFadden, G.B., and Voorhees, P.W.: A phase-field model for highly anisotropic interfacial energy. Physica D 150, 91103 (2001).
32. Debierre, J-M., Karma, A., Celestini, F., and Guérin, R.: Phase-field approach for faceted solidification. Phys. Rev. E 68, 041604 (2003).
33. Fleck, M., Mushongera, L.T., Pilipenko, D., Ankit, K., and Emmerich, H.: On phase-field modeling with a highly anisotropic interfacial energy. Eur. Phys. J. Plus 126, 95 (2011).
34. Heulens, J., Blanpain, B., and Moelans, N.: A phase field model for isothermal crystallization of oxide melts. Acta Mater. 59, 2156 (2011).
35. Plapp, M.: Unified derivation of phase-field models for alloy solidification from a grand-potential functional. Phys. Rev. E 84, 031601 (2011).
36. Kassner, K., Misbah, C., Müller, J., Kappey, J., and Kohlert, P.: Phase-field modeling of stress-induced instabilities. Phys. Rev. E 63, 036117 (2001).
37. Fleck, M.: Solid-state transformations and crack propagation: A phase field study. Ph.D. thesis, RWTH Aachen, Aachen, Germany (2011). Available at: http://darwin.bth.rwth-aachen.de/opus3/volltexte/2011/3511.
38. Pottlacher, G., Hosaeus, H., Wilthan, B., Kaschnitz, E., and Seifter, A.: Thermophysikalische Eigenschaften von festem und flüssigem Inconel 718. Thermochim. Acta 382, 255 (2002).
39. Nestler, B., Danilov, D., and Galenko, P.: Crystal growth of pure substances: Phase-field simulations in comparison with analytical and experimental results. J. Comput. Phys. 207, 221 (2005).
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Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
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