Metallurgical Transactions

, Volume 2, Issue 4, pp 1113–1127 | Cite as

On grain boundary sliding and diffusional creep

  • R. Raj
  • M. F. Ashby
Mechanical Behavior


The problem of sliding at a nonplanar grain boundary is considered in detail. The stress field, and sliding displacement and velocity can be calculated at a boundary with a shape which is periodic in the sliding direction (a wavy or stepped grain boundary): a) when deformation within the crystals which meet at the boundary is purely elastic, b) when diffusional flow of matter from point to point on the boundary is permitted. The results give solutions to the following problems. 1) How much sliding occurs in a polycrystal when neither diffusive flow nor dislocation motion is possible? 2) What is the sliding rate at a wavy or stepped grain boundary when diffusional flow of matter occurs? 3) What is the rate of diffusional creep in a polycrystal in which grain boundaries slide? 4) How is this creep rate affected by grain shape, and grain boundary migration? 5) How does an array of discrete particles influence the sliding rate at a grain boundary and the diffusional creep rate of a polycrystal? The results are compared with published solutions to some of these problems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. l.
    R. Raj: Ph.D. Thesis, Harvard University, Feb. 1971, tobe published.Google Scholar
  2. 2.
    H. Gleiter, E. Hornbogen, and G. Baro:ActaMet, 1964, vol. 16, p. 1053.Google Scholar
  3. 3.
    M. F. Ashby:ScriptaMet., 1969, vol. 3, p. 837.CrossRefGoogle Scholar
  4. 4.
    C. Zener:Phys. Rev., 1941, vol. 60, p. 906.CrossRefGoogle Scholar
  5. 5.
    T. S. Ke.Phys. Rev., 1947, vol. 71, p. 533.CrossRefGoogle Scholar
  6. 6.
    R. C. Gifkins and K. U. Snowdon:Nature, 1966, vol. 212, p. 916.CrossRefGoogle Scholar
  7. 7.
    M. F. Ashby, R. Raj, and R. C. Gifkins:ScriptaMet, 1970, vol. 4, p. 737.CrossRefGoogle Scholar
  8. 8.
    C. Herring:J. Appl. Phys., 1950, vol. 21, p. 437.CrossRefGoogle Scholar
  9. 9.
    R. L. Coble:J. Appl Phys., 1963, vol. 34, p. 1679.CrossRefGoogle Scholar
  10. 10.
    L. M. Lifshitz:Soviet Phys. JETP, 1963, vol. 17, p. 909.Google Scholar
  11. 11.
    G. B. Gibbs:Mem. Sci. Rev. Met., 1965, vol. 62, p. 78l;Mater. Sci. Eng., 1967-68, vol. 2, p. 269.Google Scholar
  12. 12.
    H. W. Green:J. Appl. Phys., 1970, vol. 41, p. 3899.CrossRefGoogle Scholar
  13. 13.
    A. H. Gottrell:Mechanical Properties of Matter, p. 202, John Wiley & Sons, New York, 1964.Google Scholar
  14. 14.
    M. F. Ashby and R. Raj: Harvard University Report No. 2, June 1970.Google Scholar
  15. 15.
    R. N.Stephens:Met. Rev., 1966, vol. 11, p. 129.Google Scholar
  16. 16.
    S. P. Timoshenko and J. N. Goodier:Theory of Elasticity, Ch. 3, pp. 35–64, McGraw Hill, New York, 1970.Google Scholar
  17. 17.
    J. R. Reitz and F. F. Milford:Foundations of Electromagnetic Theory, Ch. 7, Addison Wesley, Reading, Mass., 1964.Google Scholar
  18. 18.
    R. C. Gifkins:J. Inst. Metals, 1967, vol. 95, p. 373.Google Scholar

Copyright information

© The Metallurgical Society of American Institute of Mining 1971

Authors and Affiliations

  • R. Raj
    • 1
  • M. F. Ashby
    • 2
  1. 1.Chase Brass and Copper Co.Cleveland
  2. 2.Division of Engineering and Applied PhysicsHarvard UniversityUSA

Personalised recommendations