Advertisement

Journal of Materials Science

, Volume 29, Issue 13, pp 3527–3534 | Cite as

The limits of Poisson's ratio in polycrystalline bodies

  • P. S. Theocaris
Article

Abstract

While it has been established that the elastic moduli and compliances of anisotropic and isotropic materials should be positive for thermodynamic reasons, no condition related to the values of Poisson's ratio has yet been established. However, it is generally accepted that for isotropic materials Poisson's ratio should vary between — 1.0 and 0.5, whereas for orthotropic materials various conditions have been introduced relating the different components of the anisotropic Poisson's ratio with the remaining elastic constants of the material. In this paper, limits for Poisson's ratio of body-centred cubic (bcc) polycrystalline materials are determined, based on the modes of deformation of a typical unit cell of the material subjected to a uniform external loading arbitrarily oriented relative to the principal axes of the crystal. It is shown that the values of Poisson's ratio thus established correlate satisfactorily with experimental values of this constant. The procedure can be readily applied to other structural units of polycrystalline bodies.

Keywords

Polymer Elastic Constant Material Processing Structural Unit External Loading 
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.
    P. S. Theocaris, Proc. Nat. Acad Athens 64 (1989) 80–100.Google Scholar
  2. 2.
    P. S. Theocaris and Th. Philippides, Acta Mechanica 85 (1990) 13–26.CrossRefGoogle Scholar
  3. 3.
    P. S. Theocaris, “Constantin Caratheodory: an international tribute”, edited by Th. Rassias, Vol. II, (World Scientific, Singapore, 1991) 1354–1377.CrossRefGoogle Scholar
  4. 4.
    P. S. Theocaris and Th. Philippides, Zeitsch. Angew-Math. Mech. 71 (1991) 161–171.Google Scholar
  5. 5.
    R. A. Eubanks and E. Sternberg, J Ration. Mech. Analysis 3 (1954) 89–101.Google Scholar
  6. 6.
    B. M. Lempriere, AIAA J. 6 (1968) 2226–2227CrossRefGoogle Scholar
  7. 7.
    R. M. Jones, “Mechanics of composite materials” (McGraw-Hill, Kogakusha, Tokyo, 1975).Google Scholar
  8. 8.
    Idem., J Strain Anal. 27 (1992) 43–44.CrossRefGoogle Scholar
  9. 9.
    A. H. Cottrell, “The mechanical properties of matter” (Wiley, New York 1964).Google Scholar
  10. 10.
    R. F. Almgren, J. Elasticity 15 (1985) 427–430.CrossRefGoogle Scholar
  11. 11.
    R. M. Christensen, “Mechanics of composite materials” (J. Wiley, New York, 1979).Google Scholar
  12. 12.
    S. Timoshenko, “History of strength of materials” (McGraw-Hill, New York 1953).Google Scholar

Copyright information

© Chapman & Hall 1994

Authors and Affiliations

  • P. S. Theocaris
    • 1
  1. 1.National Academy of AthensAthensGreece

Personalised recommendations