Metallurgical Transactions

, Volume 1, Issue 4, pp 877–884 | Cite as

Peierls-Nabarro hardening in the presence of point obstacles

  • Kanji Ono
  • Alfred W. Sommer


In light of the controversy that has existed between proponents of Peierls-Nabarro hardening and dispersed barrier hardening with regard to possible low temperature deformation mechanisms in bee and hep metals, this paper examines the effect of point obstacles on Peierls-Nabarro hardening. The statics of double kink nucleation over Peierls barrier on finite dislocation segments are studied in detail. Point obstacles such as interstitial impurity atoms are considered to limit the length of the dislocation segments. Adopting the rate theory approach, temperature dependence of the yield stress is then investigated as a function of the concentration of point obstacles. It is found that point obstacles have little or no effect on double kink nucleation processes, when the applied stress is near the Peierls stress or at low test temperatures. At lower applied stresses or at higher test temperatures, the present results are significantly different from predictions of the Dorn-Rajnak calculation. In the present theory, the applied stress on the dislocation, τ, is found to be finite and independent of test temperature in dilute solid solutions at elevated temperatures where the Dorn-Rajnak theory predicts vanishing τ. This apparent “athermal” component of τ increases linearly with the concentration of point obstacles, whereas temperature dependent part of τ decreases. These predictions are consistent with experimental observations on iron-base alloys.


Metallurgical Transaction Volume Loop Length Dislocation Segment Minimum Energy Configuration Point Obstacle 
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  1. 1.
    R. L. Fleischer and W. R. Hibbard:Relation between Structure and Strength in Metals and Alloys, p. 262, HMSO, London, 1963.Google Scholar
  2. 2.
    H. Conrad:Relation between Structure and Strength in Metals and Alloys, p. 476, HMSO, London, 1963.Google Scholar
  3. 3.
    P. Guyot and J. E. Dorn:Canad. J. Phys., 1967, vol. 45, p. 983.Google Scholar
  4. 4.
    J. E. Dorn:Dislocation Dynamics, p. 27, McGraw Hill Book Co., New York, 1968.Google Scholar
  5. 5.
    P. B. Hirsch: Proc. Int’l. Conf. on the Strength of Metals and Alloys, Suppl.Trans. Japan Inst. Metals, 1968, vol. 9, p. XXX.Google Scholar
  6. 6.
    R. L. Fleischer:Scripta Met., 1968, vol. 2, p. 113;Acta Met., 1967, vol. 15, p. 1513. R. J. Arsenault:Scripta Met., 1968, vol. 2, p. 99.CrossRefGoogle Scholar
  7. 7.
    J. Dorn and S. Rajnak:Trans. TMS-AIME, 1964, vol. 230, p. 1052.Google Scholar
  8. 8.
    V. Celli, M. Kabler, T. Ninomiya, and R. Thomson:Phys. Rev., 1963, vol. 131, p. 58.CrossRefADSGoogle Scholar
  9. 9.
    A. Seeger:Phil. Mag., 1956, vol. 1, p. 651.CrossRefADSGoogle Scholar
  10. 10.
    W. Mason:J. Acoust. Soc. Am., 1955, vol. 27, p. 643.CrossRefADSGoogle Scholar
  11. 11.
    R. J. Arsenault:Acta Met., 1966, vol. 14, p. 831.CrossRefGoogle Scholar
  12. 12.
    J. Lothe and J. Hirth:Phys. Rev., 1959, vol. 115, p. 543.MATHCrossRefADSGoogle Scholar
  13. 13.
    A. Seeger and P. Schiller:Acta Met., 1962, vol. 10, p. 348.CrossRefGoogle Scholar
  14. 14.
    A. Seeger and P. Schiller:Physical Acoustics, p. 361, IIIA, Academic Press, 1966.Google Scholar
  15. 15.
    H. Conrad and R. Jones: Int’l. Conf. on Titanium, London, May, 1968.Google Scholar
  16. 16.
    K. Ono:J. Appl. Phys., 1968, vol. 39, p. 1803.CrossRefADSGoogle Scholar
  17. 17.
    K. Nakada and A. S. Keh:Acta Met., 1968, vol. 16, p. 903.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society - ASM International - The Materials Information Society 1970

Authors and Affiliations

  • Kanji Ono
    • 1
  • Alfred W. Sommer
    • 1
    • 2
    • 3
  1. 1.Materials Department, School of Engineering and Applied ScienceUniversity of CaliforniaLos Angeles
  2. 2.MetallurgyNorth American AviationLos Angeles
  3. 3.North American Rockwell CorporationLos Angeles

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