Skip to main content
Log in

An anisotropic micromechanical model for calculation of effective elastic moduli of Ni-based single crystal superalloys

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

An anisotropic micromechanical model based on Mori-Tanaka method is developed to calculate the effective elastic moduli of Ni-based single crystal superalloys. In the micromechanical model, the γ' precipitate with very high volume fraction is regarded as matrix, γ phase is divided into three parts as three different kinds of inclusions, and the actual cubic structure and orthogonal anisotropy properties of γ phase and γ′ precipitate are taken into account. Based on this anisotropic micromechanical model, the effective elastic moduli of Ni-based single crystal superalloys composite materials is obtained, and the influences of volume fraction and elastic constants of γ′ precipitate on the effective elastic moduli are also discussed. The results provide useful information for understanding mechanical behavior of composite materials in Ni-based single crystal superalloys and other anisotropic polygonal inclusion problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hershey A V. The elasticity of an isotropic aggregate of anisotropic cubic crystals. J Appl Mech, 1954, 21: 236–241

    MATH  Google Scholar 

  2. Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J Mech Phys Solids, 1965, 13: 89–101

    Article  MATH  Google Scholar 

  3. Hill R. A self-consistent mechanics of composite materials. J Mech Phys Solids, 1965, 13: 213–222

    Article  Google Scholar 

  4. Hutchinson J W. Elastic-plastic behaviour of polycrystalline metals and composites. Proc R Soc A-Math Phys Eng Sci, 1970, 319: 247–272

    Article  Google Scholar 

  5. Budiansky B. On the elastic moduli of some heterogeneous materials. J Mech Phys Solids, 1965, 13: 223–227

    Article  Google Scholar 

  6. Weng G J. Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int J Eng Sci, 1984, 22: 845–856

    Article  MATH  Google Scholar 

  7. Benveniste Y. A new approach to the application of Mori-Tanaka’s theory in composite materials. Mech Mater, 1987, 6: 147–157

    Article  Google Scholar 

  8. Mori T, Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall, 1973, 21: 571–574

    Article  Google Scholar 

  9. Eshelby J D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc A-Math Phys Eng Sci, 1957, 241: 376–396

    Article  MathSciNet  MATH  Google Scholar 

  10. Eshelby J D. Elastic inclusions and inhomogeneities. Prog Solid Mech, 1961, 2: 89–140

    MathSciNet  Google Scholar 

  11. Wang H, Li Q. Prediction of elastic modulus and Poisson’s ratio for unsaturated concrete. Int J Solids Struct, 2007, 44: 1370–1379

    Article  MATH  Google Scholar 

  12. Gong S, Li Z, Zhao Y Y. An extended Mori-Tanaka model for the elastic moduli of porous materials of finite size. Acta Mater, 2011, 59: 6820–6830

    Article  Google Scholar 

  13. Puchi-Cabrera E S, Staia M H, Iost A. A description of the composite elastic modulus of multilayer coated systems. Thin Solid Films, 2015, 583: 177–193

    Article  Google Scholar 

  14. Zhu Y, Dui G. Micromechanical modeling of the stress-induced superelastic strain in magnetic shape memory alloy. Mech Mater, 2007, 39: 1025–1034

    Article  Google Scholar 

  15. Zhu Y, Yu K. A model considering mechanical anisotropy of magnetic- field-induced superelastic strain in magnetic shape memory alloys. J Alloys Compd, 2013, 550: 308–313

    Article  Google Scholar 

  16. Zhu Y, Dui G. Model for field-induced reorientation strain in magnetic shape memory alloy with tensile and compressive loads. J Alloys Compd, 2008, 459: 55–60

    Article  Google Scholar 

  17. Chang J C, Allen S M. Elstic energy changes accompanying gamma-prime rafting in nickel-base superalloys. J Mater Res, 1991, 6: 1843–1855

    Article  Google Scholar 

  18. Miyazaki T, Nakamura K, Mori H. Experimental and theoretical investigations on morphological changes of ?' precipitates in Ni-Al single crystals during uniaxial stress-annealing. J Mater Sci, 1979, 14: 1827–1837

    Article  Google Scholar 

  19. Ratel N, Bruno G, Bastie P, et al. Plastic strain-induced rafting of precipitates in Ni superalloys: Elasticity analysis. Acta Mater, 2006, 54: 5087–5093

    Article  Google Scholar 

  20. Wu W P, Guo Y F, Dui G S, et al. A micromechanical model for predicting the directional coarsening behavior in Ni-based superalloys. Comp Mater Sci, 2008, 44: 259–264

    Article  Google Scholar 

  21. Li S Y, Wu W P, Chen M X. An anisotropic micromechanics model for predicting the rafting direction in Ni-based single crystal superalloys. Acta Mech Sin, 2016, 32: 135–143

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhou L, Li S X, Chen C R, et al. Three-dimensional finite element analysis of stresses and energy density distributions around ?' before coarsening loaded in the [110]-direction in Ni-based superalloy. Mater Sci Eng-A, 2003, 352: 300–307

    Article  Google Scholar 

  23. 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, 2001, 298: 26–33

    Article  Google Scholar 

  24. Fahrmann M, Hermann W, Fahrmann E, et al. Determination of matrix and precipitate elastic constants in Ni-base model alloys, and their relevance to rafting. Mater Sci Eng-A, 1999, 260: 212–221

    Article  Google Scholar 

  25. Mura T. Micromechanics of Defects in Solids. 2nd Edition. Dordrecht: Kluwer Academic Publishers, 1987

    Book  MATH  Google Scholar 

  26. Onaka S, Kobayashi N, Kato M. Two-dimensional analysis on elastic strain energy due to a uniformly eigenstrained supercircular inclusion in an elastically anisotropic material. Mech Mater, 2002, 34: 117–125

    Article  Google Scholar 

  27. Pan E. Eshelby problem of polygonal inclusions in anisotropic piezoelectric full- and half-planes. J Mech Phys Solids, 2004, 52: 567–589

    Article  MathSciNet  MATH  Google Scholar 

  28. Ting T C T. Anisotropic Elasticity: Theory and Applications. Oxford: Oxford University Press, 1996

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to WenPing Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, S., Wu, W., Li, Y. et al. An anisotropic micromechanical model for calculation of effective elastic moduli of Ni-based single crystal superalloys. Sci. China Technol. Sci. 60, 452–458 (2017). https://doi.org/10.1007/s11431-016-0101-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-016-0101-5

Keywords

Navigation