Journal of Materials Science

, Volume 15, Issue 5, pp 1071–1084 | Cite as

Theoretical elastic behaviour of crystals at large strains

  • Frederick Milstein


Current knowledge in the subject of the theoretical mechanical behaviour of perfect single crystals under load is reviewed. Examples of computations of load, lattice deformation, elastic moduli, and elastic stability are discussed, and qualitatively interesting (and sometimes surprising) phenomena are noted. Although computational techniques are reviewed briefly, the emphasis is upon the collation and interpretation of various computational results that have appeared in the literature. Special consideration is given to the topics of lattice stability and the definition and computation of elastic moduli of crystals under load, as well as branching from one path of deformation to another under a prescribed mode of loading. Possible applications in materials science include deformation of whiskers, twinning, martensitic transformations, very rapid shock deformation, powder technology and size reduction, and mechanical properties of small structures such as metallized integrated circuits.


Mechanical Behaviour Computational Result Material Science Martensitic Transformation Integrate Circuit 
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.


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  1. 1.
    R. H. Snow, Powder Technol. 13 (1974) 33.Google Scholar
  2. 2.
    R. Hill, Math. Proc. Cambridge Phil. Soc. 77 (1975) 225.Google Scholar
  3. 3.
    F. Milstein and K. Huang, Phys. Rev. B 19 (1979) 2030.Google Scholar
  4. 4.
    A. Kelly, “Strong Solids” (Clarendon, Oxford, 1966).Google Scholar
  5. 5.
    A. Kelly, W. R. Tyson and A. A. Cottrell, Phil. Mag. 15 (1967) 567.Google Scholar
  6. 6.
    P. C. Gehlen, A. R. Rosenfield and G. T. Hahn, J. Appl. Phys. 39 (1968) 5246.Google Scholar
  7. 7.
    Z. S. Basinski, M. S. Duesbery and R. Taylor, Phil. Mag. 21 (1970) 1201.Google Scholar
  8. 8.
    M. F. Ashby, S. H. Gelles and L. E. Tanner, ibid. 19 (1969) 757.Google Scholar
  9. 9.
    L. M. Brown, G. R. Woolhouse and U. Valdre, ibid 17 (1968) 781.Google Scholar
  10. 10.
    L. M. Brown and G. R. Woolhouse, ibid 21 (1970) 329.Google Scholar
  11. 11.
    N. H. Macmillan, J. Mater. Sci. 7 (1972) 239.Google Scholar
  12. 12.
    R. Hill and F. Milstein, Phys. Rev. B 15 (1977) 3087.Google Scholar
  13. 13.
    F. Milstein and R. Hill, J. Mech. Phys. Solids 25 (1977) 457.Google Scholar
  14. 14.
    Idem, ibid. 26 (1978) 213.Google Scholar
  15. 15.
    Idem, ibid. 27 (1979) 215; F. Milstein and R. Hill, Phys. Rev. Lett. 43 (1979) 1411.Google Scholar
  16. 16.
    K. Huang, F. Milstein and J. A. Baldwin, Jr, Phys. Rev. B 10 (1974) 3635.Google Scholar
  17. 17.
    Z. S. Basinski, M. S. Duesbuery and R. Taylor, Proceedings of the Second International Conference on Strength of Metals and Alloys, Vol. 1 (American Society for Metals, Cleveland, 1971) p. 118.Google Scholar
  18. 18.
    E. Esposito, A. E. Carlsson, D. D. Ling, H. Ehrenreich and C. D. Gelatt, Jr, Philosophical Magazine, in press.Google Scholar
  19. 19.
    M. Born, Proc. Cambridge Phil Soc. 36 (1940) 160.Google Scholar
  20. 20.
    R. D. Misra, ibid. 36 (1940) 173.Google Scholar
  21. 21.
    M. Born and R. Fürth, ibid. 36 (1940) 454.Google Scholar
  22. 22.
    M. Born and R. D. Misra, ibid. 36 (1940) 466.Google Scholar
  23. 23.
    R. Fürth, ibid. 37 (1941) 34.Google Scholar
  24. 24.
    Idem, ibid. 37 (1941) 177.Google Scholar
  25. 25.
    H. W. Peng and S. C. Power, ibid. 38 (1942) 67.Google Scholar
  26. 26.
    L. A. Girifalco and V. G. Weizer, Phys. Rev. 114 (1959) 687.Google Scholar
  27. 27.
    Idem, National Aeronautics and Space Administration Technical Report R-5 (1959).Google Scholar
  28. 28.
    F. Milstein, J. Appl. Phys. 44 (1973) 3825.Google Scholar
  29. 29.
    Idem, ibid. 44 (1973) 3833.Google Scholar
  30. 30.
    F. Milstein and K. Huang, Phys. Rev. B 18 (1978) 2529.Google Scholar
  31. 31.
    F. Milstein, R. Hill and K. Huang, Phys. Rev. B., in press.Google Scholar
  32. 32.
    F. Milstein, “Theoretical Strength of Perfect Crystalline Materials”, prepared for United States Air Force Project RAND, RM-6379-PR (1970).Google Scholar
  33. 33.
    F. Milstein, Phys. Rev. B 3 (1971) 1130.Google Scholar
  34. 34.
    M. Born, Proc. Cambridge Phil. Soc. 39 (1943) 100.Google Scholar
  35. 35.
    N. H. Macmillan and A. Kelly, Proc. Roy. Soc. Ser. A 330 (1972) 291.Google Scholar
  36. 36.
    Idem, ibid. 330 (1972) 309.Google Scholar
  37. 37.
    D. J. Gunton and G. A. Saunders, Proc. Roy. Soc. London A 343 (1975) 63.Google Scholar
  38. 38.
    G. P. Parry, Q. J. Mech. Appl. Math. 31 (1978) 1.Google Scholar
  39. 39.
    F. Milstein and B. Farber, Philosophical magazine, in press.Google Scholar
  40. 40.
    F. Milstein and B. Farber, Phys. Rev. Lett. (1980), in press.Google Scholar
  41. 41.
    F. Milstein, R. Hill and B. Farber, unpublished work.Google Scholar
  42. 42.
    F. Milstein and B. Farber, unpublished work.Google Scholar

Copyright information

© Chapman and Hall Ltd 1980

Authors and Affiliations

  • Frederick Milstein
    • 1
  1. 1.Department of Mechanical and Environmental EngineeringUniversity of CaliforniaSanta BarbaraUSA

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