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Theoretical elastic behaviour of crystals at large strains

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Abstract

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.

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References

  1. R. H. Snow, Powder Technol. 13 (1974) 33.

    Google Scholar 

  2. R. Hill, Math. Proc. Cambridge Phil. Soc. 77 (1975) 225.

    Google Scholar 

  3. F. Milstein and K. Huang, Phys. Rev. B 19 (1979) 2030.

    Google Scholar 

  4. A. Kelly, “Strong Solids” (Clarendon, Oxford, 1966).

    Google Scholar 

  5. A. Kelly, W. R. Tyson and A. A. Cottrell, Phil. Mag. 15 (1967) 567.

    Google Scholar 

  6. P. C. Gehlen, A. R. Rosenfield and G. T. Hahn, J. Appl. Phys. 39 (1968) 5246.

    Google Scholar 

  7. Z. S. Basinski, M. S. Duesbery and R. Taylor, Phil. Mag. 21 (1970) 1201.

    Google Scholar 

  8. M. F. Ashby, S. H. Gelles and L. E. Tanner, ibid. 19 (1969) 757.

    Google Scholar 

  9. L. M. Brown, G. R. Woolhouse and U. Valdre, ibid 17 (1968) 781.

    Google Scholar 

  10. L. M. Brown and G. R. Woolhouse, ibid 21 (1970) 329.

    Google Scholar 

  11. N. H. Macmillan, J. Mater. Sci. 7 (1972) 239.

    Google Scholar 

  12. R. Hill and F. Milstein, Phys. Rev. B 15 (1977) 3087.

    Google Scholar 

  13. F. Milstein and R. Hill, J. Mech. Phys. Solids 25 (1977) 457.

    Google Scholar 

  14. Idem, ibid. 26 (1978) 213.

    Google Scholar 

  15. Idem, ibid. 27 (1979) 215; F. Milstein and R. Hill, Phys. Rev. Lett. 43 (1979) 1411.

    Google Scholar 

  16. K. Huang, F. Milstein and J. A. Baldwin, Jr, Phys. Rev. B 10 (1974) 3635.

    Google Scholar 

  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. E. Esposito, A. E. Carlsson, D. D. Ling, H. Ehrenreich and C. D. Gelatt, Jr, Philosophical Magazine, in press.

  19. M. Born, Proc. Cambridge Phil Soc. 36 (1940) 160.

    Google Scholar 

  20. R. D. Misra, ibid. 36 (1940) 173.

    Google Scholar 

  21. M. Born and R. Fürth, ibid. 36 (1940) 454.

    Google Scholar 

  22. M. Born and R. D. Misra, ibid. 36 (1940) 466.

    Google Scholar 

  23. R. Fürth, ibid. 37 (1941) 34.

    Google Scholar 

  24. Idem, ibid. 37 (1941) 177.

    Google Scholar 

  25. H. W. Peng and S. C. Power, ibid. 38 (1942) 67.

    Google Scholar 

  26. L. A. Girifalco and V. G. Weizer, Phys. Rev. 114 (1959) 687.

    Google Scholar 

  27. Idem, National Aeronautics and Space Administration Technical Report R-5 (1959).

  28. F. Milstein, J. Appl. Phys. 44 (1973) 3825.

    Google Scholar 

  29. Idem, ibid. 44 (1973) 3833.

    Google Scholar 

  30. F. Milstein and K. Huang, Phys. Rev. B 18 (1978) 2529.

    Google Scholar 

  31. F. Milstein, R. Hill and K. Huang, Phys. Rev. B., in press.

  32. F. Milstein, “Theoretical Strength of Perfect Crystalline Materials”, prepared for United States Air Force Project RAND, RM-6379-PR (1970).

  33. F. Milstein, Phys. Rev. B 3 (1971) 1130.

    Google Scholar 

  34. M. Born, Proc. Cambridge Phil. Soc. 39 (1943) 100.

    Google Scholar 

  35. N. H. Macmillan and A. Kelly, Proc. Roy. Soc. Ser. A 330 (1972) 291.

    Google Scholar 

  36. Idem, ibid. 330 (1972) 309.

    Google Scholar 

  37. D. J. Gunton and G. A. Saunders, Proc. Roy. Soc. London A 343 (1975) 63.

    Google Scholar 

  38. G. P. Parry, Q. J. Mech. Appl. Math. 31 (1978) 1.

    Google Scholar 

  39. F. Milstein and B. Farber, Philosophical magazine, in press.

  40. F. Milstein and B. Farber, Phys. Rev. Lett. (1980), in press.

  41. F. Milstein, R. Hill and B. Farber, unpublished work.

  42. F. Milstein and B. Farber, unpublished work.

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Authors and Affiliations

  1. Department of Mechanical and Environmental Engineering, University of California, 93106, Santa Barbara, California, USA

    Frederick Milstein

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  1. Frederick Milstein
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Milstein, F. Theoretical elastic behaviour of crystals at large strains. J Mater Sci 15, 1071–1084 (1980). https://doi.org/10.1007/BF00551795

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