The relation between polycrystal deformation and single-crystal deformation

Abstract

A phenomenological description of crystallographic slip and pencil glide in single crystals is outlined, with emphasis on the behavior under prescribed strains. Theoretical relations are established between these single-crystal properties and the behavior of quasi-homogeneous, quasi-isotropic polycrystals deforming uniformly on a macroscopic scale, at subdiffusive temperatures. Experimental comparisons between single crystals and polycrystals are reviewed, considering flow stress, work hardening, temperature and strain rate effects, and various effects of grain size.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    L. A. Johnson, U. F. Kocks and B. Chalmers:Scripta Met., 1968, vol.2, pp.265–70. la. L. A. Johnson:Trans. TMS-AIME, 1969, vol. 245, pp. 275–82.

    Article  Google Scholar 

  2. 2.

    E. Schmid:Proc. Int’l. Cong. Appl. Mech. (Delft), 1924, p. 342.

  3. 3.

    F. A. McClintock and A. S. Argon:Mechanical Behavior of Materials, Addison-Wesley, 1966.

  4. 4.

    G. Y. Chin, R. N. Thurston and E. A. Nesbitt:Trans. TMS-AIME, 1966, vol.236, p. 69.

    Google Scholar 

  5. 5.

    T. H. Lin:J. Franklin Inst, 1960, vol.270, pp. 291–300.

    Article  Google Scholar 

  6. 6.

    U. F. Kocks: Ph.D. thesis, 1959, Harvard Univ., Cambridge, Mass.

    Google Scholar 

  7. 7.

    J. F. W. Bishop:Phil. Mag., 1953, vol.44, pp. 51–64.

    Article  Google Scholar 

  8. 8.

    A. V. Hershey:J. Appl. Mech., 1954, vol.21, pp. 241–49.

    Google Scholar 

  9. 9.

    U. F. Kocks and T. J. Brown:Acta Met., 1966, vol.14, pp. 87–98.

    Article  Google Scholar 

  10. 10.

    U. F. Kocks:Acta Met., 1958, vol.6, pp. 85–94.

    Article  Google Scholar 

  11. 11.

    W. F. Hosford, Jr.:Trans. TMS-AIME, 1965, vol.233, pp. 329–33.

    Google Scholar 

  12. 1la.

    G. Y. Chin, E. A. Nesbitt and A. J. Williams:Acta Met., 1966, vol.14, pp. 467–76.

    Article  Google Scholar 

  13. 11b.

    E. W. Kelley and W. F. Hosford, Jr.:Trans. TMS-AIME, 1968, vol.242, pp. 5–13, 654–60.

    Google Scholar 

  14. 12.

    U. F. Kocks:Acta Met., 1960, vol.8, pp. 345–52.

    Article  Google Scholar 

  15. 13.

    G. I. Taylor:J. Inst. Met., 1938, vol.62, pp. 307–24;S. Timoshenko Anniversary Volume, pp. 218–24, Macmillan, 1938;Deformation and Flow of Solids, pp. 3–12, Springer, 1956.

    Google Scholar 

  16. 14.

    G. Y. Chin, W. L. Mammel and M. T. Dolan:Trans. TMS-AIME, 1967, vol.239, pp. 1854–55.

    Google Scholar 

  17. 15.

    W. F. Hosford, Jr.:Acta Met., 1966, vol.14, pp. 1085–94.

    Article  Google Scholar 

  18. 16.

    U. F. Kocks:Phil. Mag., 1964, vol.10, pp. 187–93.

    Article  Google Scholar 

  19. 17.

    H. R. Piehler:Met. Trans., 1970, vol. 1, in press.

  20. 18.

    W. E Hosford, Jr.: private communication, Univ. of Michigan, Ann Arbor, Mich.

  21. 19.

    U. F. Kocks:Trans. TMS-AIME, 1964, vol.230, pp. 1160–67.

    Google Scholar 

  22. 20.

    B. Ramaswami, U. F. Kocks and B. Chalmers:Trans. TMS-AIME, 1965, vol.233, pp. 927–31.

    Google Scholar 

  23. 21.

    O. Krisement, G. F. de Vries and F. Bell:Phys. Stat. Sol, 1964, vol.6, pp. 73–81.

    Article  Google Scholar 

  24. 22.

    Y. Nakada and A. S. Keh:Acta Met., 1966, vol.14, p. 961.

    Article  Google Scholar 

  25. 23.

    P. J. Jackson and Z. S. Basinski:Can. J. Phys., 1967, vol.45, pp. 707–35.

    Article  Google Scholar 

  26. 24.

    E. J. H. Wessels and P. J. Jackson:Acta Met., 1969, vol.17, pp. 241–8.

    Article  Google Scholar 

  27. 25.

    U. F. Kocks and D. G. Westlake:Trans. TMS-AIME, 1967, vol.239, pp. 1107–09.

    Google Scholar 

  28. 26.

    E. Kröner:Z. Physik., 1958, vol.151, pp. 504–18.

    Article  Google Scholar 

  29. 27.

    E. Kröner:Acta Met., 1961, vol.9, pp. 155–61.

    Article  Google Scholar 

  30. 28.

    J. D. Eshelby:Proc. Roy. Soc., 1957, vol.A241, p. 376.

    Article  Google Scholar 

  31. 29.

    R.E. Hook, J. P. Hirth:Acta Met., 1967, vol.15, pp. 535–51, 1099–1110.

    Article  Google Scholar 

  32. 30.

    J. R. Willis:Quart. J. Mech. Appl. Math., 1964, vol.17, p. 157.

    Article  Google Scholar 

  33. 31.

    R. Hill:J. Mech. Phys. Sol., 1965, vol.13, pp. 89–101.

    Article  Google Scholar 

  34. 32.

    H. Payne, S. J. Czyzak, J. H. Greiner, and T. H. Lin:J. Mech. Phys. Sol., 1958, vol.6, pp. 314–20.

    Article  Google Scholar 

  35. 33.

    B. Budiansky and T. T. Wu: Proc. 4th Cong. Appl. Mech., 1962, p. 1175.

  36. 34.

    J. W. Hutchinson:J. Mech. Phys. Sol., 1964, vol.12, pp. 11–24.

    Article  Google Scholar 

  37. 35.

    W. Voigt:Wied. Ann., 1889, vol.38, p. 573.

    Article  Google Scholar 

  38. 36.

    A. Reuss:Z. Angew. Math. Mech., 1929, vol.9, p. 49.

    Article  Google Scholar 

  39. 37.

    R. Hill:Proc. Phys. Soc. London, 1952, vol.A65, p. 351.

    Google Scholar 

  40. 38.

    D. C. Drucker, H. J. Greenberg, and W. Prager:J. Appl Mech., 1951, vol.18, pp. 371–78.

    Google Scholar 

  41. 39.

    R. Hill:Phil. Mag., 1951, vol.42, pp. 868–75.

    Article  Google Scholar 

  42. 40.

    R. svon Mises:Z. Angew. Math. Mech., 1928, vol.8, pp. 161–85.

    Article  Google Scholar 

  43. 41.

    A. Kochendörfer:Plastische Eigenschaften, 1941, Springer.

  44. 41a.

    G. Y. Chin and W. L. Mammel:Trans. TMS-AIME, 1969, vol.245, p. 1211.

    Google Scholar 

  45. 42.

    J. F. W. Bishop and R. Hill:Phil. Mag, 1951, vol.42, pp. 414–27, 1298–1307.

    Article  Google Scholar 

  46. 43.

    R. Hill:J. Mech. Phys. Sol, 1967, vol.15, pp. 79–95.

    Article  Google Scholar 

  47. 44.

    F. R. N. Nabarro, Z. S. Basinski, and D. B. Holt:Adv. Phys., 1964, vol.13, p.193.

    Article  Google Scholar 

  48. 45.

    H. Tresca:Mem. Sav. Acad. Sci. Paris, 1872, vol.20, p. 281.

    Google Scholar 

  49. 46.

    R. von Mises:Göttinger Nachr., Math-Phys., 1913, p. 582.

  50. 47.

    U. Dehlinger:Z. Metallic., 1943, vol.35, p. 182.

    Google Scholar 

  51. 48.

    U. Dehlinger, J. Diehl, and J. Meissner:Z. Naturf, 1956, vol.1 la, pp. 37–41.

    Google Scholar 

  52. 49.

    G. I. Taylor:Proc. Roy. Soc, 1934, vol.A145, p. 1.

    Article  Google Scholar 

  53. 50.

    M. Roš and A. Eichinger: Proc. 2nd Int’l. Cong. Appl. Mech., Zürich, 1926, p. 315; see also J. L. M. Morrison:Proc. Inst. Mech. Eng., 1942, vol. 144, p. 33.

  54. 51.

    R. Hill:Math. Theory of Plasticity, Clarendon Press, Oxford, 1950.

    Google Scholar 

  55. 52.

    W. Sautter, A. Kochendörfer, and U. Dehlinger:Z. Metallk., 1953, vol.44, pp.442–553.

    Google Scholar 

  56. 53.

    V. S. Lensky: in Plasticity, 2nd Symp. Nav. Struct. Mech., Brown Univ., E.H. Lee, ed., Pergamon Press, 1960.

  57. 54.

    G. I. Taylor: inDeformation and Flow of Solids, pp. 3–12, IUTAM Colloq. Madrid, 1955, Springer, 1956.

    Google Scholar 

  58. 55.

    J. W. Hutchinson:J. Mech Phys. Sol., 1964, vol.12, pp. 25–33.

    Article  Google Scholar 

  59. 56.

    G. Y. Chin and W. L. Mammel:Trans. TMS-AIME, 1967, vol.239, pp. 1400–05.

    Google Scholar 

  60. 57.

    U. E Kocks:Can. J. Phys., 1967, vol.45, p. 1134.

    Article  Google Scholar 

  61. 58.

    J. F. W. Bishop:J. Mech Phys. Sol., 1954, vol.3, pp. 130–42.

    Article  Google Scholar 

  62. 59.

    T. H. Lin and B. Lieb:J. Mech. Phys. Sol., 1962, vol.10, pp. 65–72.

    Article  Google Scholar 

  63. 60.

    See I. L. Dillamore and W. T. Roberts:Met. Rev., 1965, vol.10, pp. 271–380.

    Article  Google Scholar 

  64. 61.

    G. Y. Chin: inTextures in Research and Practice, J. Grewen and G. Wassermann, eds., pp. 51–80, Springer, 1969.

  65. 62.

    G. Sachs:Z. Verein Deut. Ing., 1928, vol.72, p. 734.

    Google Scholar 

  66. 63.

    H. L. Cox and D. G. Sopwith:Proc. Phys. Soc. London, 1937, vol.49, p. 134.

    Article  Google Scholar 

  67. 64.

    A. Kochendörfer and M. Swanson:Arch. Eisenhüttenw., 1960, vol.31, pp.549–53.

    Article  Google Scholar 

  68. 65.

    Ch. Schwink:phys. stat. sol., 1965, vol.8, pp. 457–74.

    Article  Google Scholar 

  69. 66.

    Ch. Schwink and W. Vorbrugg:Z. Naturforsch, 1967, vol.22a, pp. 626–42.

    Google Scholar 

  70. 67.

    U. F. Kocks: Diplom Thesis, Univ. of Göttingen, 1954.

  71. 68.

    G. Masing:Lehrbuch der Allgemeinen Metallkunde, p. 388, Springer, 1950.

  72. 69.

    G. Zankl:Z. Naturforsch., 1963, vol.18a, p. 795.

    Google Scholar 

  73. 70.

    H. Wilsdorf and D. Kuhlmann-Wilsdorf:Z. Angew. Physik., 1952, vol.4, p.409.

    Google Scholar 

  74. 71.

    U. Essmann, M. Rapp, and M. Wilkens:Acta Met., 1968, vol.16, pp. 1275–87.

    Article  Google Scholar 

  75. 72.

    U. F. Kocks, H. S. Chen, D. A. Rigney, and R. J. Schaefer: inWork Hardening, pp. 151–75, Gordon and Breach, 1968.

  76. 73.

    A. S. Keh:Phil. Mag., 1965, vol.12, p. 9.

    Article  Google Scholar 

  77. 74.

    E. Schmid and W. Boas: Plasticity of Crystals, p. Hughes, London, (original published in 1935).

  78. 75.

    J. Diehl:Z. Metallk., 1956, vol.47, pp. 331–43.

    Google Scholar 

  79. 76.

    H. Knöll and E. Macherauch:Z. Metallk., 1964, vol.55, pp. 638–45.

    Google Scholar 

  80. 77.

    S. Howe and C. Elbaum:Phil. Mag, 1961, vol.6, pp. 37–8.

    Article  Google Scholar 

  81. 78.

    F. P. Bullen and C. B. Rogers:Phil. Mag., 1964, vol.9, pp. 401–12.

    Article  Google Scholar 

  82. 78a.

    F.P. Bullen, S. McK. Cousland:phys. stat. sol., 1968, vol.27, pp. 501–12.

    Article  Google Scholar 

  83. 79.

    P. Derner and E. Kappler:Z. Naturforsch., 1959, vol.14a, pp. 1080–81, 1082.

    Google Scholar 

  84. 80.

    R. S. Davis, R. L. Fleischer, J. D. Livingston, and B. Chalmers:Trans. AIME, 1957, vol.209, pp. 136–40.

    Google Scholar 

  85. 81.

    J. D. Livingston and B. Chalmers:Acta Met., 1957, vol.5, pp. 322–27.

    Article  Google Scholar 

  86. 82.

    R. L. Fleischer and B. Chalmers:Trans. Met. Soc. AIME. 1958, vol.212, pp.265–74.

    Google Scholar 

  87. 83.

    J. J. Häuser and B. Chalmers:Acta Met., 1961, vol.9, pp. 802–18.

    Article  Google Scholar 

  88. 84.

    D. A. G. Bruggeman: Doctoral Dissertation, Utrecht, 1930.

  89. 85.

    F. Rhines:Met. Trans., 1970, vol.1, pp. 1105–20.

    Article  Google Scholar 

  90. 86.

    F. R. N. Nabarro: inSome Recent Developments in Rheology, p. 38, London, The British Rheologists’ Club, 1950.

    Google Scholar 

  91. 87.

    J. C. M. Li:Trans. Met. Soc. AIME, 1963, vol.227, p. 239.

    Google Scholar 

  92. 88.

    E. Macherauch:Z. Metallk., 1964, vol.55, pp. 60–82.

    Google Scholar 

  93. 89.

    R. Armstrong, I. Codd, R. M. Douthwaite, and N. J. Petch:Phil. Mag., 1962, vol.7, pp. 45–58. (See also this issue.)

    Article  Google Scholar 

  94. 90.

    S. Mader:Z. Phys., 1957, vol.149, p. 73.

    Article  Google Scholar 

  95. 91.

    R. P. Carreker and W. R. Hibbard:Acta Met., 1953, vol.1, pp. 654–63.

    Article  Google Scholar 

  96. 92.

    R. P. Carreker and W. R. Hibbard:Trans. AIME, 1957, vol.209, p. 112.

    Google Scholar 

  97. 93.

    R. P. Carreker and W. R. Hibbard:Trans. AIME, 1957, vol.209, p. 1157.

    Google Scholar 

  98. 94.

    H. Conrad, S. Feuerstein, and L. Rice:Mat. Sci. Eng., 1967, vol.2, pp. 157–68.

    Article  Google Scholar 

  99. 95.

    U. E Kocks:Phil. Mag., 1966, vol.13, pp. 541–66.

    Article  Google Scholar 

  100. 96.

    D. McLean:Mechanical Properties of Metals, pp. 303–07, Wiley, 1962.

  101. 97.

    J. Washburn and E. R. Parker:Trans. AIME, 1952, vol.194, p. 1076.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kocks, U.F. The relation between polycrystal deformation and single-crystal deformation. Metall and Materi Trans 1, 1121–1143 (1970). https://doi.org/10.1007/BF02900224

Download citation

Keywords

  • Slip System
  • Slip Plane
  • Yield Surface
  • Metallurgical Transaction Volume
  • Yield Locus