Skip to main content
SpringerLink
Log in

Polycrystalline strengthening

  • Published:
Metallurgical Transactions A Aims and scope Submit manuscript

Abstract

The strength of polycrystalline specimens can be related to interaction phenomena taking place during elastic and plastic deformation. Such phenomena are reviewed in term of macroscopic and microscopic strain accommodation processes required to maintain strain continuity across the grain boundaries. The strength-grain size relationships can be described in a number of empirical equations relating the yield stress and the flow stress in tension to various structural parameters. A number of such equations are reviewed and their predictive capability is discussed. Structural information of importance for the understanding of polycrystalline strengthening is obtained mainly from surface relief patterns and from bulk structures observed by transmission electron microscopy of thin foils. The results obtained by these methods are discussed and correlations are proposed. A number of features characterizing the deformed structure are summarized and the behavior of a number of metals and alloys is reviewed with emphasis on the structural changes in the interior of the grains and in the vicinity of the grain boundaries. The models for strain accommodation during deformation are discussed on the basis of the microstructures found, and this structural information is correlated with a number of strength structural equations. Finally, the flow stress of fcc and bcc polycrystalline specimens is related to the occurrence of microstructures formed by macroscopic and microscopic strain accommodation processes during plastic straining, and it is concluded that macroscopic processes may be strength determining at larger strains whereas microscopic effects may be of importance at small strains.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Kochendörfer:Physikalische Grundlagen der Formänderungsfestigkeit der Metalle, Verlag Stahleisen, Düsseldorf, 1963, 55 pp.

    Google Scholar 

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

    CAS  Google Scholar 

  3. U.F. Kocks:Metall. Trans., 1970, vol. 1, pp. 1121–43.

    Google Scholar 

  4. R.W. Armstrong:Metall. Trans., 1970, vol. 1, pp. 1169–76.

    CAS  Google Scholar 

  5. T. L. Johnston and C.E. Feltner:Metall. Trans., 1970, vol. 1, pp. 1161–67.

    CAS  Google Scholar 

  6. J.P. Hirth:Metall. Trans., 1972, vol. 3, pp. 3047–67.

    Article  CAS  Google Scholar 

  7. A. W. Thompson:Work Hardening in Tension and Fatigue, A. W. Thompson, ed., AIME, New York, NY, 1977, pp. 89–126.

    Google Scholar 

  8. D. McLean:Strength of Metals and Alloys, E.N. S. M.I. M., Nancy, France, 1976, pp. 958–75.

    Google Scholar 

  9. H. Mecking:Strength of Metals and Alloys, P. Haasen et al., eds., Pergamon Press, Oxford, 1980, pp. 1573–94.

    Google Scholar 

  10. H. Mecking:Deformation of Polycrystals: Mechanisms and Microstructures, N. Hansenet al., eds., Risø National Laboratory, Roskilde, Denmark, 1981, pp. 73–86.

    Google Scholar 

  11. T. Leffers:Deformation of Polycrystals: Mechanisms and Microstructures, N. Hansenet al., eds., Risø National Laboratory, Roskilde, Denmark, 1981, pp. 55–71.

    Google Scholar 

  12. R. W. Armstrong:Yield, Flow and Fracture of Polycrystals, T. N. Baker, ed., Applied Science Publishers, London, 1983, pp. 1–31.

    Google Scholar 

  13. N. Hansen:Yield, Flow and Fracture of Polycrystals, T. N. Baker, ed., Applied Science Publishers, London, 1983, pp. 311–50.

    Google Scholar 

  14. G. Sachs:Z. Verein. Deut. Ing., 1928, vol. 72, pp. 734–36.

    Google Scholar 

  15. G.I. Taylor:J. Inst. Metals, 1938, vol. 62, p. 307–24.

    Google Scholar 

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

    Article  Google Scholar 

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

    CAS  Google Scholar 

  18. B. Budianski and T. T. Wu:Fourth U.S. National Congress of Applied Mechanics, ASME, New York, NY, 1962, pp. 1175–85.

    Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  21. U.F. Kocks and G. R. Canova:Deformation of Polycrystals: Mechanisms and Microstructures, N. Hansenet al., eds., Risø National Laboratory, Roskilde, Denmark, 1981, pp. 35–44.

    Google Scholar 

  22. T. Leffers:Textures in Research and Practice, J. Grewen and * G. Wassermann, eds., Springer Verlag, Berlin, 1969, pp. 120–29.

    Google Scholar 

  23. T. Leffers:A. Kinematical Model for the Plastic Deformation of Face Centred Cubic Polycrystals, 1975, Risø Report No. 302, 114 pp.

  24. T. Leffers:Textures of Materials, G. Gottstein and K. Lücke, eds., Springer Verlag, Berlin, 1978, vol. 1, pp. 277–87.

    Google Scholar 

  25. H. Honeff and H. Mecking:Textures of Materials, G. Gottstein and K. Lücke, eds., Springer Verlag, Berlin, 1978, vol. 1, pp. 265–75. 1

    Google Scholar 

  26. U.F. Kocks and H. Chandra:Acta Metall., 1982, vol. 30, pp. 695–709.

    Article  CAS  Google Scholar 

  27. G.R. Canova, U.F. Kocks, and J.J. Jonas:Acta Metall., 1984, vol. 32, pp. 211–26.

    Article  CAS  Google Scholar 

  28. T. Leffers and O.B. Pedersen:Strength of Metals and Alloys, R. C. Gifkins, ed., Pergamon Press, Oxford, 1982, pp. 75–82.

    Google Scholar 

  29. T. Tabata, H. Fujita, M. Hiraoka, and S. Miyake:Phil. Mag. A, 1982, vol. 46, pp. 801–16.

    Article  CAS  Google Scholar 

  30. Y. Kawasaki and T. Takeuchi:Scripta Metall., 1980, vol. 14, pp. 183–88.

    Article  CAS  Google Scholar 

  31. P. Ambrosi, E. Göttler, and Ch. Schwink:Scripta Metall., 1974, vol. 8, pp. 1093–98.

    Article  CAS  Google Scholar 

  32. W.L. Price and J. Washbum:J. Austral. Inst. Met., 1963, vol. 8, pp. 1–7.

    CAS  Google Scholar 

  33. P. Ambrosi, W. Homeier, and Ch. Schwink:Scripta Metall., 1980, vol. 14, pp. 325–29.

    Article  CAS  Google Scholar 

  34. A. Kochendörfer:Plastische Eigenschaften von Kristallen und metallischen Werkstoffen, Springer Verlag, Berlin, 1941, pp. 203–53.

    Google Scholar 

  35. F. R. N. Nabarro:Some Recent Developments in Rheology, V. G. W. Harrison, ed., United Trade Press, London, pp. 38–52.

  36. W. Boas:Helvetica Phys. Acta, 1950, vol. 23, pp. 159–66.

    CAS  Google Scholar 

  37. M. F. Ashby:Phil. Mag., 1970, vol. 21, pp. 399–424.

    Article  CAS  Google Scholar 

  38. M. F. Ashby:Strengthening Methods in Crystals, A. Kelly and R.B. Nicholson, eds., Wiley, New York, NY, 1971, pp. 137–92.

    Google Scholar 

  39. A. H. Cottrell:The Mechanical Properties of Matter, Wiley, New York, NY, 1964, pp. 277–83.

    Google Scholar 

  40. B. Chalmers:Proc. R. Soc. Land., 1937, vol. A162, pp. 120–27.

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  42. J.J. Hauser and B. Chalmers:Acta Metall., 1961, vol. 9, pp. 802–18.

    Article  CAS  Google Scholar 

  43. R.E. Hook and J.P. Hirth:Acta Metall., 1967, vol. 15, pp. 535–51.

    Article  CAS  Google Scholar 

  44. R.E. Hook and J.P. Hirth:Acta Metall., 1967, vol. 15, pp. 1099–1110.

    Article  CAS  Google Scholar 

  45. C. Elbaum:Trans. TMS-AIME, 1969, vol. 218, pp. 444–48.

    Google Scholar 

  46. R.L. Fleischer and W. A. Backofen:Trans. TMS-AIME, 1969, vol. 218, pp. 243–51.

    Google Scholar 

  47. P. R. Howell, A. R. Jones, A. Horsewell, and B. Ralph:Phil. Mag., 1976, vol. 33, pp. 21–31.

    Article  CAS  Google Scholar 

  48. D.J. Dingley and R.C. Pond:Acta Metall., 1979, vol. 27, pp. 667–82.

    Article  CAS  Google Scholar 

  49. E. S.P. Das and M.J. Marcinkowski:J. Mat. Sci. Eng., 1971, vol. 8, pp. 189–97.

    Article  Google Scholar 

  50. E. S.P. Das:Grain Boundaries in Engineering Materials, J.L. Walteret al., eds., AIME, New York, NY, 1974, pp. 319–26.

    Google Scholar 

  51. J.P. Hirth and R. W. Baluffi:Acta Metall., 1973, vol. 21, pp. 929–42.

    Article  CAS  Google Scholar 

  52. C. T. Forwood and L. M. Clarebrough:Phil. Mag. A, 1981, vol. 44, pp. 31–41.

    Article  CAS  Google Scholar 

  53. C.T. Forwood and L. M. Clarebrough:Strength of Metals and Alloys, R.C. Gifkins, ed., Pergamon Press, Oxford, 1982, pp. 27–32.

    Google Scholar 

  54. B. Ralph and N. Hansen:Deformation of Polycrystals: Mechanisms and Microstructures, N. Hansen,et al., eds., Risø National Laboratory, Roskilde, Denmark, 1981, pp. 473–78.

    Google Scholar 

  55. J.C.M. Li:Trans. TMS-AIME, 1963, vol. 227, pp. 239–47.

    CAS  Google Scholar 

  56. G. Bäro, H. Gleiter, and E. Hornbogen:Mater. Sci. Eng., 1968/69, vol. 3, pp. 92–104.

    Article  Google Scholar 

  57. H. Gleiter, E. Hornbogen, and G. Bäro:Acta Metall., 1968, vol. 16, pp. 1053–67.

    Article  CAS  Google Scholar 

  58. C.W. Price and J.P. Hirth:Mater. Sci. Eng., 1972, vol. 9, pp. 15–18.

    Article  CAS  Google Scholar 

  59. L.E. Murr:Metall. Trans. A, 1975, vol. 6A, pp. 505–13.

    CAS  Google Scholar 

  60. T. Malis and K. Tangri:Acta Metall, 1979, vol. 27, pp. 25–32.

    Article  CAS  Google Scholar 

  61. L.E. Murr:Mater. Sci. Eng., 1981, vol. 51, pp. 71–79.

    Article  CAS  Google Scholar 

  62. E.O. Hall:Proc. Phys. Soc., 1951, vol. B64, pp. 747–53.

    CAS  Google Scholar 

  63. N.J. Petch:J. Iron Steel Inst., 1953, vol. 174, pp. 25–28.

    CAS  Google Scholar 

  64. G.Y. Chin:Work Hardening in Tension and Fatigue, AW. Thompson, ed., AIME, New York, NY, 1977, pp. 45–66.

    Google Scholar 

  65. R. Penelle:Textures of Materials, G. Gottstein and K. Lücke, eds., Springer Verlag, Berlin, 1978, pp. 129–53.

    Google Scholar 

  66. C. Tome, G. R. Canova, U. F. Kocks, N. Christodoulou, and J. J. Jonas:Acta Metall, 1984, vol. 32, pp. 1637–53.

    Article  CAS  Google Scholar 

  67. J. D. Eshelby, F. C. Frank, and F. R. N. Nabarro:Phil. Mag., 1951, vol. 42, pp. 351–64.

    Google Scholar 

  68. J.C.M. Li and Y. T. Chou:Metall. Trans., 1970, vol. 1, pp. 1145–59.

    Google Scholar 

  69. N. Hansen:Acta Metall, 1977, vol. 25, pp. 863–69.

    Article  CAS  Google Scholar 

  70. N. Hansen:Strength of Metals and Alloys, P. Haasenet al., eds., Pergamon Press, Oxford, 1979, pp. 849–54.

    Google Scholar 

  71. J.D. Meakin and N.J. Petch:Phil. Mag., 1974, vol. 29, pp. 1149–56.

    Article  CAS  Google Scholar 

  72. R. Jago and N. Hansen: unpublished research.

  73. R. Armstrong, I. Codd, R.M. Douthwaite, and N.J. Petch:Phil. Mag., 1962, vol. 7, pp. 45–58.

    Article  CAS  Google Scholar 

  74. J. T. Al-Haidary, N. J. Petch, and E. R. De Los Rios:Phil. Mag. A, 1983, vol. 47, pp. 869–90 and pp. 891–902.

    Article  CAS  Google Scholar 

  75. N. Hansen and B. Ralph:Acta Metall, 1982, vol. 30, pp. 411–17.

    Article  CAS  Google Scholar 

  76. W. L. Phillips and R. W. Armstrong:Metall Trans., 1972, vol. 3, pp. 2571–77.

    Article  CAS  Google Scholar 

  77. N.J. Petch:Phil. Mag., 1956, vol. 1, pp. 331–37.

    Article  CAS  Google Scholar 

  78. H. H. Tjerkstra:Acta Metall, 1961, vol. 9, pp. 259–63.

    Article  CAS  Google Scholar 

  79. Y. Bergström and H. Hallen:Met. Sci., 1983, vol. 17, pp. 341–47.

    Article  Google Scholar 

  80. W. Roberts and Y. Bergström:Z. Metallkde., 1971, vol. 62, pp. 752–57.

    CAS  Google Scholar 

  81. M. J. Marcincowski and H. A. Lipsitt:Acta Metall, 1962, vol. 10, pp. 95–110.

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  83. G.W. Greenwood and A. G. Quarrell:J. Inst. Met., 1953-54, vol. 82, pp. 551–60.

    Google Scholar 

  84. N.J. Petch and E. Wright:Proc. R. Soc. Lond., 1980, vol. A370, pp. 29–39.

    Google Scholar 

  85. R.W. Armstrong:Canad. Met. Quart., 1974, vol. 13, pp. 187–202.

    CAS  Google Scholar 

  86. A.W. Thompson and M.I. Baskes:Phil. Mag., 1973, vol. 28, pp. 301–08.

    Article  CAS  Google Scholar 

  87. S. Riegger, O. Vöhringer, and E. Macherauch:Metall, 1979, vol. 33, pp. 1139–47.

    CAS  Google Scholar 

  88. E. Macherauch:Z. Metallk., 1968, vol. 59, pp. 669–88.

    CAS  Google Scholar 

  89. N. Ono and S. Karashima:Scripta Metall, 1982, vol. 16, pp. 381–84. 90. N. Hansen and D. Juul Jensen: unpublished research.

    Article  CAS  Google Scholar 

  90. J. E. Bailey and P. B. Hirsch:Phil. Mag., 1960, vol. 5, pp. 485–97.

    Article  CAS  Google Scholar 

  91. J.E. Bailey:Phil Mag., 1963, vol. 8, pp. 223–36.

    Article  CAS  Google Scholar 

  92. J. Meakin and N. J. Petch:Role of Substructure in Mechanical Behavior of Metals, Report ASD-TDR-63-324, U.S. Air Force W-P. AFB, OH, 1963, pp. 243–51.

    Google Scholar 

  93. H. Conrad and B. Christ:Recovery and Recrystallization of Metals, L. Himmel, ed., Interscience, New York, NY, 1963, pp. 124–30.

    Google Scholar 

  94. H. Conrad:Electron Microscopy and Strength of Crystals, G. Thomas and J. Washburn, eds., Interscience, New York, NY, 1963, pp. 299–300.

    Google Scholar 

  95. J.W. Edington and R. E. Smallman:Acta Metall, 1964, vol. 12, pp. 1313–28.

    Article  CAS  Google Scholar 

  96. D.J. Dingley and D. McLean:Acta Metall, 1967, vol. 15, pp. 885–901.

    Article  CAS  Google Scholar 

  97. J.-P. Bailon, A. Loyer, and J.-M. Dorlot:Mater. Sci. Eng., 1971, vol. 8, pp. 288–98.

    Article  CAS  Google Scholar 

  98. A. S. Keh and S. Weissman:Electron Microscopy and Strength of Crystals, G. Thomas and J. Washburn, eds., Interscience, New York, NY, 1963, pp. 231–300.

    Google Scholar 

  99. R.L. Jones and H. Conrad:Trans. TMS-AIME, 1969, vol. 245, pp. 779–89.

    CAS  Google Scholar 

  100. A.W. Thompson, M.I. Baskes, and W.F. Flanagan:Acta Metall., 1973, vol. 21, pp. 1017–28.

    Article  CAS  Google Scholar 

  101. Y.D. Chuang and H. Margolin:Metall. Trans., 1973, vol. 4, pp. 1905–17.

    Article  CAS  Google Scholar 

  102. H. Margolin and M.S. Stanescu:Acta Metall, 1975, vol. 23, pp. 1411–18.

    Article  CAS  Google Scholar 

  103. W. Boas and M. E. Hargreaves:Proc. R. Soc. Lond., 1948, vol. A 193, pp. 89–97.

    Article  Google Scholar 

  104. V.M. Urie and H.L. Wain:J. Inst. Metals, 1952-53, vol. 81, pp. 153–59.

    CAS  Google Scholar 

  105. W. Boas and G. J. Ogilvie:Acta Metall., 1954, vol. 2, pp. 655–59.

    Article  CAS  Google Scholar 

  106. G. J. Ogilvie:J. Inst. Metals, 1952-53, vol. 81, pp. 491–95.

    Google Scholar 

  107. T. Bretheau and D. Caldemaison:Deformation of Polycrystals: Mechanisms and Microstructure, N. Hansenet al., eds., Risø National Laboratory, Roskilde, Denmark, 1981, pp. 157–61.

    Google Scholar 

  108. C. Barlow, B. Bay, and N. Hansen:Phil. Mag., A, 1985, vol. 51, pp. 253–75.

    CAS  Google Scholar 

  109. H. Margolin and A.W. Thompson:Deformation of Polycrystals: Mechanisms and Microstructures, N. Hansenet al., eds., Risö National Laboratory, Roskilde, Denmark, 1981, pp. 197–203.

    Google Scholar 

  110. J.A. Ewing and W. Rosenhain:Trans. R. Soc. Lond., 1900, vol. A 193, pp. 353–75.

    Article  CAS  Google Scholar 

  111. E. S. Heidenreich and W. Schockley:J. Appl. Phys., 1947, vol. 18, pp. 1029–31.

    Article  CAS  Google Scholar 

  112. R. D. Heidenreich and W. Schockley:Strength of Solids, Phys. Soc. Lond., 1947, pp. 57–75.

  113. H. Wilsdorf and D. Kuhlmann-Wilsdorf:Z. Angew. Phys., 1952, vol. 4, pp. 361–70, 409–18, 418–24.

    CAS  Google Scholar 

  114. D. Khlmann-Wilsdorf and H. Wilsdorf:Acta Metall., 1953, vol. 1, pp. 394–413.

    Article  Google Scholar 

  115. J.L. Wlter and E.F. Koch:Acta Metall, 1963, vol. 11,pp. 923–38.

    Article  Google Scholar 

  116. H. Hu:Acta Metall, 1962, vol. 10, pp. 1112–16.

    Article  CAS  Google Scholar 

  117. I. L. Dillamore, P. L. Morris, C. J. E. Smith, and W. B. Hutchinson:Proc. R. Soc. Lond., 1972, vol. A 329, pp. 405–20.

    CAS  Google Scholar 

  118. R.D. Heidenreich:J. Appl. Phys., 1949, vol. 20, pp. 993–1010.

    Article  CAS  Google Scholar 

  119. J. Gil Sevillano, P. van Houtte, and E. Aernoudt:Progress in Materials Science, 1981, vol. 25, pp. 69–412.

    Article  Google Scholar 

  120. B. J. Duggan, M. Hatherly, W. B. Hutchinson, and P. T. Wakefield:Metal Sci., 1978, vol. 12, pp. 343–51.

    Article  CAS  Google Scholar 

  121. F. Bourelier and J. LeHéricy.Ecrouissage, Restauration, Recristallation, Presses Universitaires de France, Paris, 1963, pp. 33–39.

    Google Scholar 

  122. A.S. Malin and M. Hatherly:Metals Sci., 1979, vol. 13, pp. 463–72.

    Article  CAS  Google Scholar 

  123. M. Hatherly:Strength of Metals and Alloys, R. C. Gifkins, ed., Pergamon Press, Oxford, 1982, pp. 1181–95.

    Google Scholar 

  124. B. Bay and N. Hansen:Deformation of Polycrystals: Mechanisms and Microstructures, N. Hansenet al., eds., RisøS National Laboratory, Roskilde, Denmark, 1981, pp. 137–44.

    Google Scholar 

  125. M.E. Hargreaves:J. Austral. Inst. Metals, 1956, vol. l,pp. 125–33.

    Google Scholar 

  126. P.R. Swarm:Acta Metall., 1966, vol. 14, pp. 900–03.

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  128. V.G. Zankl:Z. Naturforschg., 1963, vol. 18a, pp. 795–809.

    CAS  Google Scholar 

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

    Google Scholar 

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

    Article  CAS  Google Scholar 

  131. C. Rey and A. M. Vroux:Non-Microscopical Techniques, N. H. Andersenet al., eds., Risø National Laboratory, Roskilde, Denmark, 1984, pp. 451–55.

    Google Scholar 

  132. M.R. Staker and D.L. Holt:Acta Metall, 1972, vol. 20, pp. 569–79.

    Article  CAS  Google Scholar 

  133. H. Margolin, K. Hashimoto, and H. Yagushi:Scripta Metall., 1981, vol. 15, pp. 181–84.

    Article  CAS  Google Scholar 

  134. L. E. Murr and S.S. Hecken.Scripta Metall, 1979, vol. 13, pp. 167–71.

    Article  Google Scholar 

  135. N. Hansen and B. Bay:Strength of Metals and Alloys, R. C. Gifkins, ed., Pergamon Press, Oxford, 1982, pp. 401–06.

    Google Scholar 

  136. J. B. Bilde-Sørensen and N. Hansen:Strength of Metals and Alloys, H.J. McQueenet al., eds., Pergamon Press, Oxford, 1985, pp. 141–46.

    Google Scholar 

  137. F.N. Rhines, R. A. Elis, Jr., and A.B. Gokhale:Scripta Metall, 1981, vol. 15, pp. 783–85.

    Article  CAS  Google Scholar 

  138. N. Hansen, B. Bay, D. Juul Jensen, and T. Leffers:Strength of Metals and Alloys, H.J. McQueenet al., eds., Pergamon Press, Oxford, 1985, pp. 317–22.

    Google Scholar 

  139. L. M. Clarebrough, M. E. Hargreaves, and M. H. Loretto:Recovery and Recrystallization of Metals, L. Himmel, ed., Interscience, New York, NY, 1963, pp. 63–130.

    Google Scholar 

  140. R.M. Douthwaite and N.J. Petch:Acta Metall., 1970, vol. 18, pp. 211–16.

    Article  CAS  Google Scholar 

  141. B. Ralph, R. C. Ecob, A. J. Porter, C. Y. Barlow, and N. R. Ecob:Deformation of Polycrystals: Mechanisms and Microstructures, N. Hansenet al., eds., Risø National Laboratory, Roskilde, Denmark, 1981, pp. 111–24.

    Google Scholar 

  142. B. Bay and N. Hansen:Recrystallization and Grain Growth of Multiphase and Particle Containing Materials, N. Hansenet al., eds., Risø National Laboratory, Roskilde, Denmark, 1980, pp. 51–56.

    Google Scholar 

  143. A. W. Thompson:Strength of Metals and Alloys, E.N.S.M.I.M., Nancy, France, 1976, pp. 405–10.

    Google Scholar 

  144. A.R. Rosenfield and G.T. Hahn:Metall. Trans., 1970, vol. 1, pp. 1080–81.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Risø National Laboratory, 4000, Roskilde, Denmark

    Niels Hansen (Head of the Metallurgy Department)

Authors
  1. Niels Hansen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper is based on a presentation made at the symposium “50th Anniversary of the Introduction of Dislocations” held at the fall meeting of the TMS-AIME in Detroit, Michigan in October 1984 under the TMS-AIME Mechanical Metallurgy and Physical Metallurgy Committees.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hansen, N. Polycrystalline strengthening. Metall Trans A 16, 2167–2190 (1985). https://doi.org/10.1007/BF02670417

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02670417

Keywords

Search

Navigation