Advertisement

Metallurgical and Materials Transactions B

, Volume 1, Issue 2, pp 357–361 | Cite as

Competition among basal, prism, and pyramidal slip modes in hcp metals

  • G. Y. Chin
  • W. L. Mammel
Article

Abstract

The competition of slip among\((0001)\left\langle {2\bar 1\bar 10} \right\rangle , \left\{ {01\bar 10} \right\}\left\langle {2\bar 1\bar 10} \right\rangle \), and\(\left\{ {01\bar 11} \right\}\left\langle {2\bar 1\bar 10} \right\rangle \) slip modes of hcp metals has been analyzed geometrically in terms of a critical resolved shear stress, CRSS, criterion. Under the action of an applied stress slip systems of one or more modes may be activated depending on the value of the CRSS and on the orientation of the slip systems with respect to the applied stress. If the CRSS of a given slip mode should exceed a limiting value relative to the CRSS of the other modes, however, the given mode becomes inoperative even under the most favorably stressed conditions. It is found by an examination of the yield loci that basal slip is inoperative if α2 < cos θ; prism slip is inoperative if α2 < α1 sin θ; and pyramidal slip is inoperative if α2 > cos θ + α1 sin θ where\(\alpha _1 = \tau _{01\bar 10} /\tau _{0001} \) and\(\alpha _2 = \tau _{01\bar 11} /\tau _{0001} \) are, respectively, the ratios of CRSS for prism and pyramidal slips relative to basal slip, and ϕ is the angle between the (0001) and\((01\bar 11)\) normals. Since the value of ϕ is a function ofc/a, the limiting values of α1 and α1 depend on thec/a ratio of the crystal structure.

Keywords

Slip System Slip Plane Metallurgical Transaction Volume Crystal Plasticity Yield Locus 
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.
    See C. S. Barrett and T. B. Massalski:Structure of Metals, 3rd ed., pp. 404, 415, McGraw-Hill Book Co., New York, 1966.Google Scholar
  2. 2.
    R. L. Bell and R. W. Cahn:Proc. Roy. Soc. London, 1957, vol. A239, pp. 494–521.Google Scholar
  3. 3.
    J. H. Wernick and E. E. Thomas:Trans. TMS-AIME, 1960, vol. 218, pp. 763–14.Google Scholar
  4. 4.
    P. R. Price:J. Appl. Phys., 1961, vol. 32, pp. 1750–57.CrossRefGoogle Scholar
  5. 5.
    E. Schiebold and G. Siebel:Z. Metallk., 1931, vol. 69, pp. 458–82.Google Scholar
  6. 6.
    R. E. Reed-Hill:Trans. TMS-AIME, 1960, vol. 218, pp. 554–58.Google Scholar
  7. 7.
    F. D. Rosi, C. A. Dube and B. H. Alexander:AIME Trans, 1953, vol. 197, pp. 267–65.Google Scholar
  8. 8.
    E. A. Anderson, D. C. Jillson, and S. R. Dunbar:AIME Trans, 1953, vol. 197, pp. 1191–97.Google Scholar
  9. 9.
    E. J. Rapperport and C. S. Hartley:Trans. TMS-AIME, 1960, vol. 218, pp. 869–76.Google Scholar
  10. 10.
    G. I. Taylor:J. Inst. Met., 1938, vol. 62, pp. 307–24;Stephen Timoshenko 69th Anniversary Volume, pp. 218–24, The MacMillan Co., New York, 1938.Google Scholar
  11. 11.
    J. F. W. Bishop and R. Hill:Phil. Mag., 1951, vol. 42, pp. 414–27, 1298–1307.Google Scholar
  12. 12.
    G. Y. Chin and W. L. Mammel:Trans. TMS-AIME, 1969, vol. 245, pp. 1211–14.Google Scholar
  13. 13.
    U. F. Kocks: The Relation of Polycrystal Deformation to Single Crystal Deformation, Argonne National Laboratory, Argonne, Ill., 1969.Google Scholar
  14. 14.
    G. Y. Chin, W. L. Mammel, and M. T. Dolan:Trans. TMS-AIME, 1967, vol. 239, pp. 1111–12.Google Scholar
  15. 15.
    G. Y. Chin and W. L. Mammel:Trans. TMS-AIME, 1967, vol. 239, pp. 1400–05.Google Scholar
  16. 16.
    G. Y. Chin, W. L. Mammel, and M. T. Dolan:Trans. TMS-AIME, 1967, vol. 239, pp. 1854–55.Google Scholar
  17. 17.
    G. Y. Chin, W. L. Mammel, and M. T. Dolan:Trans. TMS-AIME, 1969, vol. 245, pp. 383–88.Google Scholar
  18. 18.
    G. Y. Chin, W. F. Hosford, and D. R. Mendorf:Proc. Roy. Soc. London, 1969, vol. A309, pp. 433–56.CrossRefGoogle Scholar
  19. 19.
    See for example, R. Hill:The Mathematical Theory of Plasticity, p. 301, Oxford University Press, London, 1950; and F. A. McClintock and A. S. Argon:Mechanical Behavior of Materials, pp. 283–89, Addison-Wesley Co., Reading, Mass., 1966.Google Scholar
  20. 20.
    See, for example, C. S. Barrett and T. B. Massalski:Structure of Metals, 3rd ed., p. 615, McGraw-Hill Book Co., New York, 1966.Google Scholar
  21. 21.
    M. H. Yoo and C. T. Wei:J. Appl. Phys., 1967, vol. 38, pp. 4317–22.CrossRefGoogle Scholar
  22. 22.
    J. D. Eshelby:Phil. Mag., 1949, vol. 40, p. 903.Google Scholar
  23. 23.
    J. E. Dorn and J. B. Mitchell: Proc. 2nd Berkeley Int. Mater. Conf., 1964, V. F. Zackey, ed., Ch. 12, John Wiley & Sons, New York, 1965.Google Scholar

Copyright information

© Metallurgical Society of American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., and American Society for Metals 1970

Authors and Affiliations

  • G. Y. Chin
    • 1
  • W. L. Mammel
    • 1
  1. 1.Bell Telephone LaboratoriesMurray Hill

Personalised recommendations