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Finite-Element Crystal Plasticity on Phase-Field Microstructures: Predicting Mechanical Response Variations in Ni-Based Single-Crystal Superalloys

  • Jean-Briac le GraverendEmail author
  • Rajendran Harikrishnan
Multiscale Computational Strategies for Heterogeneous Materials with Defects: Coupling Modeling with Experiments and Uncertainty Quantification

Abstract

The mechanical response of Ni-based single-crystal superalloys is known to be sensitive to the microstructural state, i.e., the shape and size of the γ′ precipitates when exposed to high-temperature conditions. The magnitude and sign of the natural lattice misfit between the γ and γ′ phases play the most crucial role in establishing a controlled size, shape, and distribution of γ′ precipitates during heat treatments as well as in defining the direction of rafting, viz. the directional coalescence of the γ′ precipitates. In this study, a bottom-up scale bridging strategy of using phase-field informed finite-element (FE) crystal plasticity on realistic microstructures is followed to better understand the effect of the microstructural state on the macro-scale performance of a \( \left\langle {001} \right\rangle \)-oriented Ni-based single-crystal superalloy. Strain-controlled tensile tests using FE crystal plasticity were performed on a set of different microstructural states: cuboidal, rafted, and topologically inverted imported from 3D phase-field simulations. The study revealed that a cuboidal microstructure with a natural lattice misfit of − 0.004 is the most ductile. As observed experimentally, the microstructure with rafts perpendicular to the loading axis (N-type) is more ductile than the cuboidal one. The P-type microstructure, i.e., with rafts parallel to the loading axis, is found to have the lowest ductility, which was attributed to lesser dislocation mobility.

Notes

Acknowledgements

The simulations were performed using the computing resources from Laboratory for Molecular Simulation (LMS) and High Performance Research Computing (HPRC) at Texas A&M University. The authors are grateful to Mr. James Fillerup and the financial support from AFOSR through Award No.: FA9550-17-1-0233 to carry out this study. We also acknowledge Dr. Adrian Loghin and GE Global Research for their support and interest in our research.

References

  1. 1.
    J. Cormier, Behavior of the single crystal superalloy MC2 during high and very-high non-isothermal creep loading (Ph.D. Thesis, ENSMA—Université de Poitiers, France, 2006)Google Scholar
  2. 2.
    J.-B. le Graverend, J. Cormier, F. Gallerneau, S. Kruch, and J. Mendez, Int. J. Fatigue 91, 257 (2016).CrossRefGoogle Scholar
  3. 3.
    P. Caron and T. Khan, Mat. Sci. Eng. 61, 173 (1983).CrossRefGoogle Scholar
  4. 4.
    R.C. Reed, The Superalloys: Fundamentals and Applications (Cambridge: Cambridge University Press, 2006).CrossRefGoogle Scholar
  5. 5.
    J.-B. le Graverend, J. Cormier, F. Gallerneau, S. Kruch, and J. Mendez, Mater. Des. 56, 990 (2014).CrossRefGoogle Scholar
  6. 6.
    H. Long, S. Mao, Y. Liu, H. Wei, Q. Deng, Y. Chen, Z. Zhang, and X. Han, Mater. Des. 167, 107633 (2019).CrossRefGoogle Scholar
  7. 7.
    D. Ayrault, Fluage à haute température de superalliages base nickel monocristallins (France: Ecole Nationale Supérieure des Mines de Paris, 1989).Google Scholar
  8. 8.
    M.V. Nathal and R.A. Mackay, Mater. Sci. Eng. 85, 127 (1987).CrossRefGoogle Scholar
  9. 9.
    S. Li, J. Tao, T. Sugui, and H. Zhuangqi, Mater. Sci. Eng. A 454, 461 (2007).Google Scholar
  10. 10.
    U. Tetzlaff and H. Mughrabi, Enhancement of the high-temperature tensile creep strength of monocrystalline nickel-base superalloys by pre-rafting in compression, ed. T. M. Pollock et al. International Symposium on Superalloys, Seven Springs, PA, TMS, 2000, p. 273Google Scholar
  11. 11.
    M. Ott and H. Mughrabi, Mater. Sci. Eng. A 272, 24 (1999).CrossRefGoogle Scholar
  12. 12.
    R.A. MacKay and L. Ebert, Metall. Mat. Trans. A 16, 1969 (1985).CrossRefGoogle Scholar
  13. 13.
    M. Pessah-Simonetti, P. Caron, and T. Khan, Effect of mu phase on the mechanical properties of a nickel-base single crystal superalloy, ed. S. D. Antolovitch et al. International Symposium on Superalloys, Seven Springs, PA, TMS, 2000), p. 567Google Scholar
  14. 14.
    L. Espié, Etude expérimentale et modélisation numérique du comportement de monocristaux de superalliages (PhD Thesis, Ecole Nationale Supérieure des Mines de Paris, France), 1996Google Scholar
  15. 15.
    A. Gaubert, Modélisation des effets de l’evolution microstructurale sur le comportement mécanique du superalliage monocristallin AM1 (PhD Thesis, Ecole Nationale Supèrieure des Mines de Paris, France, 2009)Google Scholar
  16. 16.
    M. Ott, U. Tetzlaff, and H. Mughrabi, Influence of directional coarsening on the isothermal high-temperature fatigue behaviour of the monocrystalline nickel-base superalloys CMSX-6 and CMSX-4, ed. H. Mughrabi et al., Microstructure and mechanical properties of metallic high temperature materials (Deutsche Forschungsgemeinschaft, Bonn, Germany, 1999), p. 425Google Scholar
  17. 17.
    C.C. Engler-Pinto, C. Noseda, M.Y. Nazmy, and F. Rezai-Aria, Interaction between creep and thermo-mechanical fatigue of CM247LC-DS, ed. R. D. Kissinger et al. (International Symposium on Superalloys, Seven Springs, PA, TMS, 1996), p. 319Google Scholar
  18. 18.
    R. Giraud, J. Cormier, Z. Hervier, D. Bertheau, K. Harris, J. Wahl, X. Milhet, J. Mendez, and A. Organista, Effect of the prior microstructure degradation on the high temperature/low stress non-isothermal creep behavior of CMSX-4 Ni-based single crystal superalloy, ed. R. S. Huron et al. (International Symposium on Superalloys, Seven Springs, PA, TMS, 2012), p. 265Google Scholar
  19. 19.
    D. Arrell, M. Hasselqvist, C. Sommer, and J. Moverare, On TMF damage, degradation effects, and the associated TMIN influence on TMF test results in γ/γ′ Alloys, ed. K. A. Green et al.. (International Symposium on Superalloys, Seven Springs, PA, TMS, 2004), p. 291Google Scholar
  20. 20.
    J.-B. le Graverend, J. Cormier, F. Gallerneau, P. Villechaise, S. Kruch, and J. Mendez, Int. J. Plast 59, 55 (2014).CrossRefGoogle Scholar
  21. 21.
    B. Fedelich, G. Künecke, A.I. Epishin, T. Link, and P.D. Portella, Mat. Sci. Eng. A 510–511, 273 (2009).CrossRefGoogle Scholar
  22. 22.
    T. Tinga, W.A.M. Brekelmans, and M.G.D. Geers, Comp. Mat. Sci. 47, 471 (2009).CrossRefGoogle Scholar
  23. 23.
    R. Desmorat, A. Mattiello, and J. Cormier, Int. J. Plast. 95, 43 (2017).CrossRefGoogle Scholar
  24. 24.
    H.-J. Chang, M.C. Fivel, and J.-L. Strudel, Int. J. Plast. 108, 21 (2018).CrossRefGoogle Scholar
  25. 25.
    R.S. Kumar, A.-J. Wang, and D.L. McDowell, Int. J. Fract. 137, 173 (2006).CrossRefGoogle Scholar
  26. 26.
    M. Okazaki and M. Sakaguchi, Int. J. Fatigue 30, 318 (2008).CrossRefGoogle Scholar
  27. 27.
    W.-P. Wu, Y.-F. Guo, G.-S. Dui, and Y.-S. Wang, Comp. Mat. Sci. 44, 259 (2008).CrossRefGoogle Scholar
  28. 28.
    E.P. Busso, N.P. O’Dowd, and R.J. Dennis, A rate dependent formulation for void growth in single crystal materials, ed. S. Murakami and N. Ohno (IUTAM Symposium on Creep in Structures, Dordrecht, the Netherlands, Springer, 2001), p. 41Google Scholar
  29. 29.
    L. Müller, U. Glatzel, and M. Feller-Kniepmeier, Acta Metall. Mater. 41, 3401 (1993).CrossRefGoogle Scholar
  30. 30.
    R. Harikrishnan and J.-B. le Graverend, Mater. Des. 160, 405 (2018).CrossRefGoogle Scholar
  31. 31.
    I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler, G.J. Schmitz, and J.L.L. Rezende, Physica D 94, 135 (1996).CrossRefGoogle Scholar
  32. 32.
    L. Méric and G. Cailletaud, J. Eng. Mater. Technol. 113, 171 (1991).CrossRefGoogle Scholar
  33. 33.
    I. Steinbach, Model. Simul. Mater. Sci. Eng. 17, 073001 (2009).CrossRefGoogle Scholar
  34. 34.
    M. Cottura, Y. Le Bouar, B. Appolaire, and A. Finel, Acta Mater. 94, 15 (2015).CrossRefGoogle Scholar
  35. 35.
    D. Bellet and P. Bastie, Phil. Mag. B 64, 143 (1991).CrossRefGoogle Scholar
  36. 36.
    J.S. Van Sluytman and T.M. Pollock, Acta Mater. 60, 1771 (2012).CrossRefGoogle Scholar
  37. 37.
    K. Serin, G. Göbenli, and G. Eggeler, Mat. Sci. Eng. A 387–389, 133 (2004).CrossRefGoogle Scholar
  38. 38.
    X.P. Tan, J.L. Liu, T. Jin, Z.Q. Hu, H.U. Hong, B.G. Choi, I.S. Kim, and C.Y. Jo, Mater. Sci. Eng. A 528, 8381 (2011).CrossRefGoogle Scholar
  39. 39.
    R.J. Asaro, Adv. Appl. Mech. 23, 1 (1983).CrossRefGoogle Scholar
  40. 40.
    J.W. Hutchinson, Proc. R. Soc. Lond. A Math. Phys. Sci. 319, 247 (1970)Google Scholar
  41. 41.
    U.F. Kocks, Metall. Mater. Trans. 1, 1121 (1970).CrossRefGoogle Scholar
  42. 42.
    P. Franciosi, Acta Metall. 33, 1601 (1985).CrossRefGoogle Scholar
  43. 43.
    D. Nouailhas, P. Pacou, G. Cailletaud, F. Hanriot, and L. Rémy, Adv. Multiaxial Fatigue 114, 244 (1993).CrossRefGoogle Scholar
  44. 44.
    L. Méric, P. Poubanne, and G. Cailletaud, J. Eng. Mater. Technol. 113, 162 (1991).CrossRefGoogle Scholar
  45. 45.
  46. 46.
    M. Fahrmann, W. Hermann, E. Fahrmann, A. Boegli, T.M. Pollock, and H.G. Sockel, Mater. Sci, Eng. A 260, 212 (1999).Google Scholar
  47. 47.
    D. Siebörger, H. Knake, and U. Glatzel, Mat. Sci. Eng. A 298, 26 (2001).CrossRefGoogle Scholar
  48. 48.
    J.F. Ganghoffer, A. Hazotte, S. Denis, and A. Simon, Scripta Metall. Mater. 25, 2491 (1991).CrossRefGoogle Scholar
  49. 49.
    T.M. Pollock and A.S. Argon, Acta Metall. Mater. 42, 1859 (1994).CrossRefGoogle Scholar
  50. 50.
    H. Yasuda, T. Takasugi, and M. Koiwa, Acta Metall. Mater. 40, 381 (1992).CrossRefGoogle Scholar
  51. 51.
    S.W. Yang, Metall. Trans. A 16, 661 (1985).CrossRefGoogle Scholar
  52. 52.
    L. Müller, U. Glatzel, and M. Feller-Kniepmeier, Acta Metall. Mater. 40, 1321 (1992).CrossRefGoogle Scholar
  53. 53.
    J. Gayda and R.A. MacKay, Scripta Metall. 23, 1835 (1989).CrossRefGoogle Scholar
  54. 54.
    F. Diologent, Comportement en fluage et en traction de superalliages monocristallins a base de nickel (PhD Thesis, Université de Paris sud, Centre d’Orsay, France, 2002).Google Scholar
  55. 55.
    T.M. Pollock and A.S. Argon, Acta Metall. Mater. 40, 1 (1992).CrossRefGoogle Scholar
  56. 56.
    D.W. MacLachlan, G.S.K. Gunturi, and D.M. Knowles, Comp. Mat. Sci. 25, 129 (2002).CrossRefGoogle Scholar
  57. 57.
    A. Fredholm and J.-L. Strudel On the creep resistance of some nickel base single crystals, ed. M. Gell. (International Symposium on Superalloys, Seven Springs, PA, TMS, 1984), p. 211Google Scholar
  58. 58.
    A. Nitz and E. Nembach, Metall. Mat. Trans. A 29, 799 (1998).CrossRefGoogle Scholar
  59. 59.
    M. Demura, D. Golberg, and T. Hirano, Intermetallics 15, 1322 (2007).CrossRefGoogle Scholar
  60. 60.
    F.M. Beremin, A. Pineau, F. Mudry, J.-C. Devaux, Y. D’Escatha, and P. Ledermann, Metall. Trans. A 14, 2277 (1983).CrossRefGoogle Scholar
  61. 61.
    J.-B. le Graverend, Int. J. Plast. (2019).Google Scholar
  62. 62.
    R.C. Reed, N. Matan, D.C. Cox, M.A. Rist, and C.M.F. Rae, Acta Mater. 47, 3367 (1999).CrossRefGoogle Scholar
  63. 63.
    P. Caron, Y. Ohta, Y.G. Nakagawa, and T. Khan: Creep deformation anisotropy in single crystal superalloys, ed. S. Reichman et al. (International Symposium on Superalloys, Seven Springs, PA, TMS, 2000), p. 215Google Scholar
  64. 64.
    J.R. Rice and D.M. Tracey, J. Mech. Phys. Solids 17, 201 (1969).CrossRefGoogle Scholar
  65. 65.
    M. Simonetti and P. Caron, Mater. Sci, Eng. A 254, 1 (1998)Google Scholar
  66. 66.
    A. Misra and R. Gibala, Metall. Mat. Trans. A 28, 795 (1997).Google Scholar

Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  • Jean-Briac le Graverend
    • 1
    • 2
    Email author
  • Rajendran Harikrishnan
    • 1
  1. 1.Department of Aerospace EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Department of Materials Science and EngineeringTexas A&M UniversityCollege StationUSA

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