Abstract
We develop a phase-field model for the simulation of chemical diffusion limited microstructure evolution. The model is applied to γ′-precipitation under the influence of realistic multi-step aging treatments in multi-component nickel-based superalloys with industrially relevant chemical complexity. The temperature-dependent thermodynamic and kinetic input parameters are obtained from CALPHAD calculations using ThermoCalc. Further, the model accounts for the lattice-misfit between the precipitate- and the matrix-phase. The required temperature-dependent elastic stiffness and lattice-misfit can be measured using resonance ultrasound spectroscopy and high temperature X-ray diffraction, respectively. This allows to account for realistic shaping of γ′-particles in the simulation. The comparison to shapes of γ′-particles in experimental microstructures serves as an important cross validation of the model. The application of the model to investigate the effect of the subsequent aging treatment on the precipitation microstructure after a brazing process is discussed.
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References
Reed, R.C.: The Superalloys Fundamentals and Applications, 1st edn. Cambridge University Press, New York (2006)
Fleischmann, E., Konrad, C.H., Preußner, J., Völkl, R., Affeldt, E., Glatzel, U.: Influence of solid solution hardening on creep properties of single-crystal nickel-based superalloys. Metal. Mater. Trans. A 46, 1125 (2015)
Holzinger, M., Schleifer, F., Glatzel, U., Fleck, M.: Phase-field modeling of γ′ -precipitate shapes in nickel-base superalloys and their classification by moment invariants. Eur. Phys. J. B 92, 208–217 (2019)
Völkl, R., Glatzel, U., Feller-Kniepmeier, M.: Measurement of the unconstrained misfit in the nickel-base superalloy CMSX-4 with CBED. Scripta Mater. 38, 893–900 (1998)
Slama, C., Servant, C., Cizeron, G.: Aging of the Inconel 718 alloy between 500 and 750°C. J. Mater. Res. 12, 2298–2316 (1997)
Safari, J., Nategh, S.: On the heat treatment of Rene-80 nickel-base superalloy. J. Mater. Process. Tech. 176, 240–250 (2006)
Böttger, B., Altenfeld, R., Laschet, G., Schmitz, G.J., Stöhr, B., Burbaum, B.: An ICME process chain for diffusion brazing of alloy 247. Integr. Mater. Manufac. Innov. 7, 70–85 (2018)
Böttger, B., Apel, M., Daniels, B., Dankl, L., Göhler, T., Jokisch, T.: Systematic phase-field study on microstructure formation during brazing of Mar-M247 with a Si-based AMS4782 filler. Metal. Mater. Trans. A 50, 1732–1747 (2019)
Lifshitz, I.M., Slyosov, V.V.: The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Sol. 19, 35 (1961)
Wagner, C.: Theory of the aging of precipitates by dissolution-reprecipitation (Ostwald ripening). Zeitsch. f. Elektrochem. 65, 581 (1961)
Mushongera, L.T., Fleck, M., Kundin, J., Querfurth, F., Emmerich, H.: Phase-field study of anisotropic γ′-coarsening kinetics in Ni-base superalloys with varying Re and Ru contents. Adv. Eng. Mater. 17, 1149–1157 (2015)
Fleck, M., Schleifer, F., Holzinger, M., Glatzel, U.: Phase-field modeling of precipitation growth and ripening during industrial heat treatments in Ni-base superalloys. Metall. Mater. Trans. A 49, 4146–4157 (2018)
Thompson, M.E., Su, C.S., Voorhees, P.W.: The equilibrium shape of a misfitting precipitate. Acta Metall. Mater. 42, 2107–2122 (1994)
Jokisaari, A.M., Naghavi, S.S., Wolverton, C., Voorhees, P.W., Heinonen, O.G.: Predicting the morphologies of γ′ precipitates in cobalt-based superalloys. Acta Mater. 141, 273–284 (2017)
Siebörger, D., Knake, H., Glatzel, U.: Temperature dependence of the elastic moduli of the nickel-base superalloy CMSX-4 and its isolated phases. Mater. Sci. Eng. A 298, 26–33 (2001)
Bhadak, B., Sankarasubramanian, R., Choudhury, A.: Phase-field modeling of equilibrium precipitate shapes under the influence of coherency stresses. Metall. Mater. Trans. A 49, 5705–5726 (2018)
Wang, Y., Banerjee, D., Su, C.C., Khachaturyan, A.G.: Field kinetic model and computer simulation of precipitation of L12 ordered intermetallics from FCC solid solution. Acta Mater. 46, 2983–3001 (1998)
Zhu, J.Z., Wang, T., Ardell, A.J., Zhou, S.H., Liu, Z.K., Chen, L.Q.: Three-dimensional phase-field simulations of coarsening kinetics of γ′ particles in binary Ni-Al alloys. Acta Mater. 52, 2837–2845 (2004)
Pang, Y., Li, Y.S., Wu, X., Liu, W., Hou, Z.: Phase-field simulation of diffusion-controlled coarsening kinetics of γ′ phase in Ni-Al alloy. Int. J. Mater. Res. 106, 108–113 (2015)
Bhaskar, M.S.: Quantitative phase field modelling of precipitate coarsening in Ni-Al-Mo alloys. Comp. Mater. Sci. 146, 102–111 (2018)
Cottura, M., Le Bouar, Y., Appolaire, B., Finel, A.: On the role of elastic inhomogeneity in the development of cuboidal microstructures in Ni-based superalloys. Acta Mater. 94, 15–25 (2015)
Andersson, J.O., Helander, T., Höglund, L., Shi, P., Sundman, B.: Thermo-Calc & DICTRA, computational tools for materials science. Calphad 26, 273–312 (2002)
Finel, A., Le Bouar, Y., Dabas, B., Appolaire, B., Yamada, Y., Mohri, T.: Sharp phase field method. Phys. Rev. Lett. 121, 25501 (2018)
Fleck, M., Schleifer, F., Glatzel, U.: Frictionless motion of marginally resolved diffuse interfaces in phase-field modeling. https://arxiv.org/abs/1910.05180. Accessed 25 Jan 2020
Schleifer, F., Holzinger, M., Lin, Y.-Y., Glatzel, U., Fleck, M.: Phase-field modeling of γ/γ" microstructure formation in Ni-based superalloys with high γ" volume fraction. Intermetallics 120, 106745 (2020)
Fleck, M., Querfurth, F., Glatzel, U.: Phase field modeling of solidification in multi-component alloys with a case study on the Inconel 718 alloy. J. Mater. Res. 32, 4606–4615 (2017)
Ardell, A.J., Ozolins, V.: Trans-interface diffusion-controlled coarsening. Nature Mater. 4, 309 (2005)
Acknowledgements
We thank the German Federal Ministry for Economics and Energy (BMWi) for financially supporting the project COORETEC: ISar 03ET7047D and the German Federal Ministry of Education and Research (BMBF) for financial support in the project ParaPhase 01IH15005B. Further, this work is funded by the Deutsche Forschungsgemeinschaft (DFG) within the projects 387117768 and 431968427. Finally, we are very thankful to our collaboration partners at ACCESS, MTU Aero Engines AG and Siemens AG for the fruit-full discussions within the joint research project COORETEC: ISar.
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Fleck, M., Schleifer, F., Holzinger, M., Lin, YY., Glatzel, U. (2021). Phase-Field Modeling of Precipitation Microstructure Evolution in Multicomponent Alloys During Industrial Heat Treatments. In: Reisgen, U., Drummer, D., Marschall, H. (eds) Enhanced Material, Parts Optimization and Process Intensification. EMPOrIA 2020. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-70332-5_7
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