Advertisement

Large Plastic Deformation of Polycrystals

  • C. Stolz
Part of the International Centre for Mechanical Sciences book series (CISM, volume 376)

Abstract

This paper is devoted to the description of the general relationships between micro- and macroscales in non-linear mechanics. After a thermodynamical presentation of these relations, we point out some particular cases of non-linearities, especially the case of polycrystalline aggregates in finite strain. In the case of the single crystal, the energy is well defined in the frame of the crystal lattice, the deformation of which is essentially reversible. The plastic deformation preserves the orientation and the structure of the lattice. In the case of the polycrystal, the constitutive law has the same form as the single-crystal orne, the evolution of a triad of vectors is necessary to describe the evolution of the microstructure and to ensure uniqueness of the decomposition of the deformation gradient in a reversible and a plastic part.

The problem of the evolution of the internal state of a single crystal and of a polycrystal is investigated, including the symmetry of the rate boundary-value problem.

Keywords

Free Energy Density Large Plastic Deformation Concentration Tensor Comptes Rendus Acad Normality Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bui, H. D.: Etude de l’évolution de la frontière du domaine élastique avec l’écrouissage et relation de comportement élastoplastique des métaux cubiques, Thèse de Doctorat, Paris V I, 1969.Google Scholar
  2. [2]
    Francfort, G., Nguyen, Q. S. et Suquet, P.: Thermodynamique et lois de comportement thermomécanique, Comptes Rendus Acad. Sci. de Paris, II, 296 (1983), 1007–10.Google Scholar
  3. [3]
    Germain, P., Nguyen, Q. S. and Suquet, P.: Continuum thermodynamics, J. Appl. Mech., 50 (1983), 1010–1020.CrossRefGoogle Scholar
  4. [4]
    Halphen, B.: Sur le champ des vitesses en thermoplasticité finie, Int. J. Solids Struct., 11 (1975), 947–60.CrossRefGoogle Scholar
  5. [5]
    Hashin, Z.: Analysis of composite materials, J. Appl. Mech., 50 (1983), 481–485.CrossRefGoogle Scholar
  6. [6]
    Hill, R.: Generalised constitutive relations for incremental deformation of metal crystals by multislip, J. Mech. Phys. Solids, 14 (1966), 95–102.CrossRefGoogle Scholar
  7. [7]
    Hill, R.: The essential structure of constitutive laws of metal composites and polycristals, J. Mech. Phys. Solids, 15 (1967), 79–95.CrossRefGoogle Scholar
  8. [8]
    Hill, R. and Rice, J.: Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. Mech. Phys. Solids, 20 (1972), 401–413.CrossRefGoogle Scholar
  9. [9]
    Kremer, E.: Linear properties of random media, Proc. 15th Colloq. Groupe Français de Rhéologie, 1980.Google Scholar
  10. [10]
    Mandel, J.: Contribution théorique à l’étude de l’écrouissage et des lois de l’écoulement plastique, Proc. 11th Int. Congr. Appl. Mech., Springer-Verlag, Berlin, 1964.Google Scholar
  11. [11]
    Mandel, J.: Plasticité Classique et Viscoplasticité, CISM, Udine, Springer-Verlag, 1971.Google Scholar
  12. [12]
    Mandel, J.: Sur la définition d’un repère privilegié pour l’étude des transformations anélastiques d’un polycristal, J. Mécanique Théorique et Appliquée, 1 (1982), 7–23.Google Scholar
  13. [13]
    Nguyen, Q. S.: Bifurcation et stabilité des systèmes irréversibles obéissant au principe de dissipation maximale, J. Mécanique Théorique et Appliquée, 3 (1984), No. 7, 41–61.Google Scholar
  14. [14]
    Rice, J.: Inelastic constitutive relations for solids: an internal variable theory and its application to crystal plasticity, J. Mech. Phys. Solids, 19 (1971), 433–455.CrossRefGoogle Scholar
  15. [15]
    Sanchez Palencia, E.: Comportement local et macroscopique d’un type de matériaux plastiques hétérogènes, Int. J. ENGNG. SCi., 12 (1974), 331–351.CrossRefGoogle Scholar
  16. [16]
    Stolz, C.: Contribution à l’étude des grandes transformations en élastoplasticity, Doctorat ENPC, Paris, 1982.Google Scholar
  17. [17]
    Stolz, C.: Etude des milieux à configuration physique et applications, Comptes Rendus Acad. Sci. de Paris, II, 299 (1984), 1153–1155.Google Scholar
  18. [18]
    Stolz, C.: On relationships between micro-and macro-scales for particular cases of non linear behavior in heterogeneous media, in Yielding Damage and Failure of Anisotropic Solids, EGF5 (Ed. J.P. Boehler), 1989, Mechanical Engineering Publication, London.Google Scholar
  19. [19]
    Stolz, C.: Study of the constitutive law for a polycristal and analysis of rate boundary value problem in finite elastoplasticity, in Large Deformations of Solids, Ed. Zarka, Gittus and Nemat Nasser, Elsevier Applied Science, 1985.Google Scholar
  20. [20]
    Stolz, C.: General relationships between micro and macro scales for the non linear behavior of heterogneous media, in Modelling Small Deformations of Polycrystals, Ed J. Zarka and J. Gittus, Elsevier Science Publishers, 89–115, 1983.Google Scholar
  21. [21]
    Willis, J. 1.: Overall Properties of Composites, in Advances in Applied Mechanics, Vol. 21, C. S. Yih (Ed.), Academic Press, New York, 1981.Google Scholar
  22. [22]
    Zarka, J.: Etude du comportement des monocristaux métalliques, J. Mécanique Théorique et Appliquée, 12, (1973).Google Scholar

Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • C. Stolz
    • 1
  1. 1.CNRS-URA 317PolytechnicPalaiseauFrance

Personalised recommendations