Acta Mechanica Solida Sinica

, Volume 19, Issue 1, pp 75–85 | Cite as

Prediction of yield functions on BCC polycrystals

  • Mojia Huang
  • Mingfu Fu
  • Chaomei Zheng


By the nonlinear optimization theory, we predict the yield function of single BCC crystals in Hill’s criterion form. Then we give a formula on the macroscopic yield function of a BCC polycrystal Ω under Sachs’ model, where the volume average of the yield functions of all BCC crystallites in Ω is taken as the macroscopic yield function of the BCC polycrystal. In constructing the formula, we try to find the relationship among the macroscopic yield function, the orientation distribution function (ODF), and the single BCC crystal’s plasticity. An expression for the yield stress of a uniaxial tensile problem is derived under Taylor’s model in order to compare the expression with that of the macroscopic yield function.

Key words

yield function the ODF BCC polycrystal single BCC crystals anisotropy 


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  1. [1]
    Bunge, H.J., Texture Analysis in Material Science: Mathematical Methods, London: Butterworths, 1982.Google Scholar
  2. [2]
    Roe, R.J., Description of crystallite orientation in polycrystalline materials: III, General solution to pole figures, J. Appl. Phys., Vol.36, 1965, 2024–2031.CrossRefGoogle Scholar
  3. [3]
    Roe, R.J., Inversion of pole figures for materials having cubic crystal symmetry, J. Appl. Phys., Vol.37, 1966, 2069–2072.CrossRefGoogle Scholar
  4. [4]
    Zheng, Q.-S. and Fu, Y.B., Orientation distribution functions for microstructures of heterogeneous materials: Part II. Applied Mathematics and Mechanics, Vol.22 2001, 885–903.CrossRefGoogle Scholar
  5. [5]
    Biedenharn, L.C. and Louck, J.D., Angular Momentum in Quantum Physics, Cambridge University Press, Cambridge, 1984.CrossRefGoogle Scholar
  6. [6]
    Man, C.-S., On the constitutive equations of some weakly-textured materials, Arch. Rational Mech., Vol.143, 1998, 77–103.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Morris, P.R., Averaging fourth-rank tensors with weight functions, J. Appl. Phys., Vol.40, 1969, 447–448.CrossRefGoogle Scholar
  8. [8]
    Sayers, C.M., Ultrasonic velocities in anisotropic polycrystalline aggregates, J. Phys. D., Vol.15, 1982, 2157–2167.CrossRefGoogle Scholar
  9. [9]
    Morris, P.R., Elastic constants of polycrystals, Int. J. Engng. Sci., Vol.8, 1970, 49–61.CrossRefGoogle Scholar
  10. [10]
    Huang, M., Elastic constants of a polycrystal with an orthorhombic texture, Mechanics of Materials, Vol.36, 2004, 623–632.CrossRefGoogle Scholar
  11. [11]
    Huang, M., Perturbation approach to elastic constitutive relations of polycrystals, J. Mech. Phys. Solids Vol.52 2004, 1827–1853.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Sachs, G., Zur ableilung einer fleissbedingung, Z. Verein Deut. Ing., Vol.72, 1928, 734–736.Google Scholar
  13. [13]
    Taylor, G.I., Plastic strain in metals, J. Inst. Met., Vol.62, 1938, 307–324.Google Scholar
  14. [14]
    Man, C.-S., On the correlation of elastic and plastic anisotropy in sheet metals, J. Elasticity, Vol.39, 1995, 165–173.MathSciNetCrossRefGoogle Scholar
  15. [15]
    Man, C.-S. and Huang, M., Identification of material parameters in yield functions and flow rules for weakly textured sheets of cubic metals, International Journal of Non-linear Mechanics, Vol.36, 2001, 501–514.CrossRefGoogle Scholar
  16. [16]
    Khan, A.S. and Huang, S., Continuum Theory of Plasticity, John Wiley & Sons, Inc., New York, 1995.zbMATHGoogle Scholar
  17. [17]
    Hosford, W.F., The Mechanics of Crystals and Textured Polycrystals, Oxford University, New York, 1993.Google Scholar
  18. [18]
    Huang, M., Lan, Z., and Liang, H., Constitutive relation of an orthorhombic polycrystal with the shape coefficients, Acta Mechanica Sinica, Vol.21, 2005, 608–618.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Gambin, W., Plasticity and Texture, Kluwer Academic Publishers, The Netherlands, 2001.CrossRefGoogle Scholar
  20. [20]
    Hill, R., The Mathematical Theory of Plasticity, Clarendon press, Oxford, 1950.Google Scholar
  21. [21]
    Huang, M. and Man, C.-S., Constitutive relation of elastic polycrystal with quadratic texture dependence, J. Elasticity, Vol.72, 2003, 183–212.MathSciNetCrossRefGoogle Scholar
  22. [22]
    Huang, M. and Zheng, C., Green’s function and effective elastic stiffness tensor for arbitrary aggregates of cubic crystals, Acta Mechanica Solida Sinica, Vol.17, No.4, 2004, 337–346.Google Scholar
  23. [23]
    Gass, S., Linear Programming Methods and Applications, McGraw-Hill, New York, 1985.zbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  • Mojia Huang
    • 1
  • Mingfu Fu
    • 1
  • Chaomei Zheng
    • 2
  1. 1.Institute of Engineering MechanicsNanchang UniversityNanchangChina
  2. 2.Computer CenterNanchang UniversityNanchangChina

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