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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
Germain, P., Nguyen, Q. S. and Suquet, P.: Continuum thermodynamics, J. Appl. Mech., 50 (1983), 1010–1020.
Halphen, B.: Sur le champ des vitesses en thermoplasticité finie, Int. J. Solids Struct., 11 (1975), 947–60.
Hashin, Z.: Analysis of composite materials, J. Appl. Mech., 50 (1983), 481–485.
Hill, R.: Generalised constitutive relations for incremental deformation of metal crystals by multislip, J. Mech. Phys. Solids, 14 (1966), 95–102.
Hill, R.: The essential structure of constitutive laws of metal composites and polycristals, J. Mech. Phys. Solids, 15 (1967), 79–95.
Hill, R. and Rice, J.: Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. Mech. Phys. Solids, 20 (1972), 401–413.
Kremer, E.: Linear properties of random media, Proc. 15th Colloq. Groupe Français de Rhéologie, 1980.
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.
Mandel, J.: Plasticité Classique et Viscoplasticité, CISM, Udine, Springer-Verlag, 1971.
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.
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.
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.
Sanchez Palencia, E.: Comportement local et macroscopique d’un type de matériaux plastiques hétérogènes, Int. J. ENGNG. SCi., 12 (1974), 331–351.
Stolz, C.: Contribution à l’étude des grandes transformations en élastoplasticity, Doctorat ENPC, Paris, 1982.
Stolz, C.: Etude des milieux à configuration physique et applications, Comptes Rendus Acad. Sci. de Paris, II, 299 (1984), 1153–1155.
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.
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.
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.
Willis, J. 1.: Overall Properties of Composites, in Advances in Applied Mechanics, Vol. 21, C. S. Yih (Ed.), Academic Press, New York, 1981.
Zarka, J.: Etude du comportement des monocristaux métalliques, J. Mécanique Théorique et Appliquée, 12, (1973).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Wien
About this chapter
Cite this chapter
Stolz, C. (1997). Large Plastic Deformation of Polycrystals. In: Teodosiu, C. (eds) Large Plastic Deformation of Crystalline Aggregates. International Centre for Mechanical Sciences, vol 376. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2672-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2672-1_3
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82909-7
Online ISBN: 978-3-7091-2672-1
eBook Packages: Springer Book Archive