Advertisement

Plastic Flow Properties in Relation to Localized Necking in Sheets

  • A. K. Ghosh
Chapter

Abstract

Considerable interest exists in understanding the levels of maximum useful strains achievable prior to localized necking (forming limits) and their dependence on the imposed stress-state. Marciniak’s model of imperfection growth has successfully explained the rise in forming limit as the imposed strain-ratio (ε21) is increased from zero (plane strain) toward unity (balanced biaxial tension). Experimental studies on formability of various materials have, however, revealed basic differences in behavior, such as the “brass-type” and the “steel type”, exhibiting respectively, zero and positive dependencies of forming limit upon the strain-ratio. Such results cannot be reconciled without proper attention to the details of strain hardening and strain-rate hardening behaviors of these materials, particularly as functions of strain and strain-ratio. A review of these properties for several materials will be presented in an attempt to show their importance on the necking behavior. Furthermore, the dependence of the patterns of behavior upon the mode of stretching (in-plane and punch stretching) is discussed. Some results of a Marci niak-type model of material imperfection are also considered.

Keywords

Plane Strain Limit Strain Form Limit Diagram Localize Necking Form Limit Curve 
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]
    Z. Marciniak and K. Kuczyński, Int. J. Mech. Sci., 9 (1967), 609.CrossRefGoogle Scholar
  2. [2]
    S. P. Keeler and W. A. Backofen, Trans. ASM, 56 (1963), 25.Google Scholar
  3. [3]
    M. Azrin and W. A. Backofen, Metall. Trans., 1 (1970), 2857.Google Scholar
  4. [4]
    A. K. Ghosh and W. A. Backofen, Metall. Trans., 4 (1973), 1113.CrossRefGoogle Scholar
  5. [5]
    S. S. Hecker, J. Eng. Mater. Technol. (Trans. ASME, H), 97 (1975), 66.CrossRefGoogle Scholar
  6. [6]
    R. Hill, J. Mech. Phys. Solids, 1 (1952), 19.CrossRefGoogle Scholar
  7. [7]
    H. van Minh, R. Sowerby and J. L. Duncan, Int. J. Mech. Sci., 17 (1975), 339.CrossRefGoogle Scholar
  8. [8]
    Y. Yamaguchi and P. B. Mellor, Int. J. Mech. Sci., 18 (1976), 85.CrossRefGoogle Scholar
  9. [9]
    S. Stören and J. R. Rice, J. Mech. Phys. Solids, 23 (1975), 421.CrossRefGoogle Scholar
  10. [10]
    R. Hill, J. Mech. Phys. Solids, 6 (1958), 236.CrossRefGoogle Scholar
  11. [11]
    A. K. Ghosh and S. S. Hecker, Metall. Trans., 6A (1975), 1065.Google Scholar
  12. [12]
    A. K. Ghosh and S. S. Hecker, Metall. Trans., 5 (1974), 2161.Google Scholar
  13. [13]
    M. J. Painter and R. Pearce, J. Phys. D: Appl. Phys., 7 (1974), 992.CrossRefGoogle Scholar
  14. [14]
    A. K. Ghosh, Met. Trans., 8A (1977), 1221.Google Scholar
  15. [15]
    Z. Marciniak, K. Kuczyński and T. Pokora, Int. J. Mech. Sci., 15 (1973), 789.CrossRefGoogle Scholar
  16. [16]
    A. K. Ghosh, Metall. Trans., 7A (1976), 523.Google Scholar
  17. [17]
    S. S. Hecker, Met. Eng. Q., 14 (1974), 30.Google Scholar
  18. [18]
    L. E. Malvern, J. Appl. Mech. (Trans. ASME) 18 (1951), 203.Google Scholar
  19. [19]
    R. Pearce, Int. J. Mech. Sci., 13 (1971), 299.CrossRefGoogle Scholar
  20. [20]
    K. Yoshida, K. Yoshii, H. Komorida, M. Usuda and H. Watanabe, Scientific Papers, Inst, of Physical and Chemical Research, Tokyo, 64 (1970), 24.Google Scholar
  21. [21]
    H. J. Kleemola and A. J. Ranta-Escola, Metall. Trans., 7A, (1976), 595.Google Scholar
  22. [22]
    D. J. Lloyd, B. D. McLaughlin and H. Sang, Scr. Metall., 11 (1977), 297.CrossRefGoogle Scholar
  23. [23]
    J. L. Duncan and W. Johnson, Sheet Met. Ind., 42 (1965), 271.Google Scholar
  24. [24]
    A. Needleman and N. Triantafyllidis, Brown University Report NSF-ENG76-16421/1, June 1977 (to be published in J. Eng. Mater. Technol.).Google Scholar

Copyright information

© Plenum Press, New York 1978

Authors and Affiliations

  • A. K. Ghosh
    • 1
  1. 1.Rockwell InternationalThousand OaksUSA

Personalised recommendations