Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-27T07:28:31.520Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  26 October 2017

Michael Fleck*
Affiliation:
Metals and Alloys, University of Bayreuth, Bayreuth 95447, Bavaria, Germany
Frank Querfurth
Affiliation:
Teconsult Precision Robotics, Bayreuth 95448, Bavaria, Germany, and Materials and Process Simulation, University of Bayreuth, Bayreuth 95447, Bavaria, Germany
Uwe Glatzel
Affiliation:
Metals and Alloys, University of Bayreuth, Bayreuth 95447, Bavaria, Germany
*
a) Address all correspondence to this author. e-mail: michael.fleck@uni-bayreuth.de
Get access

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.

Type
Articles
Copyright
Copyright © Materials Research Society 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Contributing Editor: Mathias Göken

References

REFERENCES

Reed, R.C.: The Superalloys Fundamentals and Applications (Cambridge University Press, New York, New York, 2006).CrossRefGoogle Scholar
Ivantsov, G.P.: Temperature field around a spherical, cylindrical and acicular crystal growth in a supercooled melt. Dokl. Akad. Nauk USSR 58, 567 (1947).Google Scholar
Brener, E.A. and Mel’nikov, V.I.: Pattern selection in two-dimensional dendritic growth. Adv. Phys. 40, 53 (1991).CrossRefGoogle Scholar
Danzig, J.A. and Rappaz, M.: Solidification (EPFL Press, Lausanne, Switzerland, 2009). Available at: http://www.solidification.org/.Google Scholar
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).Google ScholarPubMed
Ben Amar, M. and Brener, E.A.: Parity-broken dendrites. Phys. Rev. Lett. 75, 561564 (1995).CrossRefGoogle Scholar
Ihle, T. and Müller-Krumbhaar, H.: Fractal and compact growth morphologies in phase transitions with diffusion transport. Phys. Rev. E 49, 29722991 (1994).Google Scholar
Turnbull, D.: Metastable structures in metallurgy. Metall. Trans. A 12, 695 (1981).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).Google Scholar
Kupferman, R., Kessler, D.A., and Ben-Jacob, E.: Coexistence of symmetric and parity-broken dendrites in a channel. Physica A 213, 451464 (1995).Google Scholar
Sabouri-Ghomi, M., Provatas, N., and Grant, M.: Solidification of a supercooled liquid in a narrow channel. Phys. Rev. Lett. 86, 50845087 (2001).CrossRefGoogle Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
Ma, Y. and Plapp, M.: Phase-field simulations and geometrical characterization of cellular solidification fronts. J. Cryst. Growth 385, 140 (2014).Google Scholar
Boettinger, W., Warren, J., Beckermann, C., and Karma, A.: Phase-field simulation of solidification. Annu. Rev. Mater. Res. 32, 163 (2002).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
Karma, A. and Rappel, W-J.: Quantitative phase-field modeling of dendritic growth in two and three dimensions. Phys. Rev. E 57, 43234349 (1998).Google Scholar
Almgren, R.F.: Second-order phase field asymptotics for unequal conductivities. SIAM J. Appl. Math. 59, 2086 (1999).Google Scholar
Echebarria, B., Folch, R., Karma, A., and Plapp, M.: Quantitative phase-field model of alloy solidification. Phys. Rev. E 70, 061604 (2004).Google Scholar
Folch, R. and Plapp, M.: Quantitative phase-field modeling of two-phase growth. Phys. Rev. E 72, 011602 (2005).Google Scholar
Kim, S.G.: A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties. Acta Mater. 55, 4391 (2007).Google Scholar
Plapp, M.: Remarks on some open problems in phase-field modelling of solidification. Philos. Mag. 91, 14786435 (2011).CrossRefGoogle Scholar
Brener, E.A. and Boussinot, G.: Kinetic cross coupling between nonconserved and conserved fields in phase field models. Phys. Rev. E 86, 060601 (2012).Google Scholar
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).Google Scholar
Calculated with thermocalc using TTNi8 and MobNi1 (http://www.thermocalc.com).Google Scholar
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).Google Scholar
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).Google Scholar
Eggleston, J.J., McFadden, G.B., and Voorhees, P.W.: A phase-field model for highly anisotropic interfacial energy. Physica D 150, 91103 (2001).Google Scholar
Debierre, J-M., Karma, A., Celestini, F., and Guérin, R.: Phase-field approach for faceted solidification. Phys. Rev. E 68, 041604 (2003).Google Scholar
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).CrossRefGoogle Scholar
Heulens, J., Blanpain, B., and Moelans, N.: A phase field model for isothermal crystallization of oxide melts. Acta Mater. 59, 2156 (2011).CrossRefGoogle Scholar
Plapp, M.: Unified derivation of phase-field models for alloy solidification from a grand-potential functional. Phys. Rev. E 84, 031601 (2011).CrossRefGoogle ScholarPubMed
Kassner, K., Misbah, C., Müller, J., Kappey, J., and Kohlert, P.: Phase-field modeling of stress-induced instabilities. Phys. Rev. E 63, 036117 (2001).Google Scholar
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.Google Scholar
Pottlacher, G., Hosaeus, H., Wilthan, B., Kaschnitz, E., and Seifter, A.: Thermophysikalische Eigenschaften von festem und flüssigem Inconel 718. Thermochim. Acta 382, 255 (2002).CrossRefGoogle Scholar
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).Google Scholar