Acta Mechanica Solida Sinica

, Volume 30, Issue 1, pp 51–63 | Cite as

Simulation of plastic deformation induced texture evolution using the crystallographic homogenization finite element method

  • Y. P. Chen
  • Y. Y. Cai


A semi-implicit elastic/crystalline viscoplastic finite element (FE) method based on a “crystallographic homogenization” approach is formulated for a multi-scale analysis. In the formulation, the asymptotic series expansion is introduced to define the displacement in the micro-continuum. This homogenization FE analysis is aimed at predicting the plastic deformation induced texture evolution of polycrystalline materials, the constituent microstructure of which is represented by an assembly of single crystal grains. The rate dependent crystal plasticity model is adopted for the description of microstructures. Their displacements are decomposed into two parts: the homogenized deformation defined in the macro-continuum and the perturbed one in the micro-continuum. This multi-scale formulation makes it possible to carry out an alternative transition from a representative micro-structure to the macro-continuum. This homogenization procedure satisfies both the compatibility and the equilibrium in the micro-structure. This developed code is applied to predict the texture evolution, and its performance is demonstrated by the numerical examples of texture evolution of FCC polycrystalline metals.


Homogenization Local periodicity Crystalline plasticity Texture Finite element 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H.J. Bunge, Texture Analysis in Material Science, Butterworths, London, 1982.Google Scholar
  2. 2.
    H.J. Bunge, Experimental Techniques of Texture Analysis, DGM Informationsgesellschaft, Oberursel, Germany, 1986.Google Scholar
  3. 3.
    U.F. Kocks, et al., Texture and Anisotropy, Preferred Orientations, and Their Effect on Materials Properties, Cambridge University Press, 1998.Google Scholar
  4. 4.
    J. Adam, et al., Electron Backscatter Diffraction in Materials Science, Kluwer Academic Press, 2000.Google Scholar
  5. 5.
    D. Peirce, R.J. Asaro, A. Needleman, An analysis of nonuniform and localized deformation in ductile single crystals, Acta Metall. 30 (1982) 1087–1119.CrossRefGoogle Scholar
  6. 6.
    D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metall. 31 (1983) 1951–1976.CrossRefGoogle Scholar
  7. 7.
    R.J. Asaro, A. Needleman, Texture development and strain hardening in rate dependent polycrystal, Acta Metall. 33 (1985) 923–953.CrossRefGoogle Scholar
  8. 8.
    E. Nakamachi, X. Dong, Elastic/crystalline viscoplastic finite element analysis of dynamic deformation of sheet metal, Int. J. Comput.-Aided Eng. Softw. 13 (1996) 308–326.CrossRefzbMATHGoogle Scholar
  9. 9.
    W. Yang, W.B. Lee, Mesoplasticity and Its Applications, Springer-Verlag, 1993.CrossRefGoogle Scholar
  10. 10.
    C. Miehe, J. Schroder, J. Schotte, Computational homogenization analysis in finite plasticity. Simulation of texture development in polycrystalline materials, Comput. Methods Appl. Mech. Eng. 171 (1999) 387–418.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    C. Miehe, J. Schotte, M. Lambrecht, Homogenization of inelastic solid materials at finite strains based on incremental minimization principle, Application to the texture analysis of polycrystals, J. Mech. Phys. Solids 50 (2002) 2123–2167.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    K. Terada, K. Yuge, N. Kikuchi, Elasto-plastic analysis of composite materials by using the homogenization method (I): formulation, J. Japan Soc. Mech. Eng. A 61 (590) (1995) 91–97.Google Scholar
  13. 13.
    N. Takano, M. Zako, The formulation of homogenization method applied to large deformation problem for composite materials, Int. J. Solids Struct. 37 (2000) 6517–6535.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    N. Ohno, D. Okumura, H. Noguchi, Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation, J. Mech. Phys. Solids 50 (2002) 1125–2153.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    K. Terada, K. Yuge, N. Kikuchi, Elasto-plastic analysis of composite materials by using the homogenization method (II), J. Japan Soc. Mech. Eng. A 62 (601) (1996) 110–117.Google Scholar
  16. 16.
    I. Babuska, Homogenization approach in engineering, Computing Methods in Applied Sciences and Engineering, vol. 134(134), Springer Berlin Heidelberg, 1976, pp. 137–153.Google Scholar
  17. 17.
    E. Sanchez-Palencia, Non-homogeneous Media and Vibration Theory, vol. 127, Springer, Berlin, 1980.zbMATHGoogle Scholar
  18. 18.
    N. Bakhvalov, Panasenko, G. Homogenization, Averaging Processes in Periodic Media, Kluwer Academic Pub., 1984.Google Scholar
  19. 19.
    J. Guedes, N. Kikuchi, Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Comput. Methods Appl. Mech. Eng. 83 (1990) 145–198.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    L. Anand, M. Kothari, A computational procedure for rate-independent crystal plasticity, J. Mech. Phys. Solids 44 (4) (1996) 525–558.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    P. Van Houtte, A comprehensive mathematical formulation of an extended Taylor–Bishop–Hill model featuring relaxed constraints, the Renouard–Wintenberger theory and a strain rate sensitivity model, Textures Microstruct. 8–9 (1988) 313–350.CrossRefGoogle Scholar
  22. 22.
    Y. Zhou, K.W. Neale, L.S. Toth, A modified model for simulating latent hardening during the plastic deformation of rate-dependent FCC polycrystals, Int. J. Plast. 9 (1993) 961–978.CrossRefGoogle Scholar
  23. 23.
    A.M. Maniatty, P.R. Dawson, Y.S. Lee, A time integration algorithm for elasto-viscoplastic cubic crystals applied to modelling polycrystalline deformatiuon, Int. J. Numer. Methods Eng. 35 (1992) 1565–1588.CrossRefzbMATHGoogle Scholar
  24. 24.
    G. Sarma, T. Zacharia, Integration algorithm for modelling the elasto-viscoplastic response of polycrystalline materials, J. Mech. Phys. Solids 47 (1999) 1219–1238.CrossRefzbMATHGoogle Scholar
  25. 25.
    S.V. Harren, The finite deformation of rate-dependent polycrystals (II): a comparison of the self-consistent and Taylor methods, J. Mech. Phys. Solids 39 (3) (1991) 361–383.MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    C.A. Bronkhorst, S.R. Kalidindi, L. Anand, Polycrystalline plasticity and the evolution of crystallographic texture in f.c.c. metals, Philos. Trans. R. Soc. Lond. A 341 (1992) 443–477.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  1. 1.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations