Skip to main content
Log in

On grain and subgrain rotations in two dimensions

  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

Computer simulations of subgrain growth by coalescence in two dimensions have been carried out. The model governing the dynamics allows the subgrains to rotate in order to reduce the sub-boundary energies. The purpose of the model is to study this mechanism separately; thus, the sub-boundaries are not allowed to migrate out of their initial positions. Hence, a coarsening of the subgrain structure occurs due to coalescence only. Results from several simulations are discussed. It was found that the mean subgrain size increased as an exponential function of time. The effect of the initial distribution of orientations and angles of misorientation has also been studied. It was found that the width of the distribution of orientations is important for the evolution of the mean subgrain size. The model and, consequently, the simulations concern subgrain rotations leading to coalescence. Based on these results, the general case of grain rotations in two dimensions has been discussed. It has been suggested that grain rotations depend on the grain boundary energy as a function of the misorientation.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. C.S. Smith:Trans. AIME, 1948, vol. 175, pp. 15–51.

    Google Scholar 

  2. J.E. Burke:Trans. AIME, 1949, vol. 180, pp. 73–91.

    Google Scholar 

  3. W.W. Mullins:J. Appl. Phys., 1956, vol. 27, pp. 900–04.

    Article  Google Scholar 

  4. M. Hillert:Acta Metall., 1965, vol. 13, pp. 227–38.

    Article  CAS  Google Scholar 

  5. N.P. Louat:Acta Metall., 1974, vol. 22, pp. 721–24.

    Article  CAS  Google Scholar 

  6. F.N. Rhines and K.R. Craig:Metall. Trans., 1974, vol. 5, pp. 413–25.

    Article  CAS  Google Scholar 

  7. O. Hundert, N. Ryum, and H. Westengen:Acta Metall., 1979, vol. 27, pp. 161–65.

    Article  Google Scholar 

  8. W.W. Mullins:Acta Metall., 1989, vol. 37, pp. 2979–84.

    Article  Google Scholar 

  9. G. Abbruzzese, I. Heckelmann, and K. Lücke:Acta Metall. Mater., 1992, vol. 40, pp. 519–32.

    Article  CAS  Google Scholar 

  10. K. Lücke, I. Heckelmann, and G. Abbruzzese:Acta Metall. Mater., 1992, vol. 40, pp. 533–42.

    Article  Google Scholar 

  11. R. Sandström:Acta Metall., 1977, vol. 25, pp. 905–11.

    Article  Google Scholar 

  12. H. Fujita:J. Phys. Soc. Jpn., 1961, vol. 16, pp. 397–06.

    Article  CAS  Google Scholar 

  13. H. Hu:Trans. AIME, 1962, vol. 224, pp. 75–84.

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  15. H. Hu: inRecovery and Recrystallization of Metals, L. Himmel, ed., Interscience, New York, NY, 1963, pp. 311–78.

    Google Scholar 

  16. J.C.M. Li:J. Appl. Phys., 1962, vol. 33, pp. 2958–65.

    Article  CAS  Google Scholar 

  17. P. Faivre and R.D. Doherty:J. Mater. Sci., 1979, vol. 14, pp. 897–19.

    CAS  Google Scholar 

  18. A.R. Jones, B. Ralph, and N. Hansen:Proc. R. Soc. London A, 1979, vol. 368, pp. 345–57.

    CAS  Google Scholar 

  19. R. Sandstrom:Acta Metall., 1917, vol. 25, pp. 897–04.

    Google Scholar 

  20. R.D. Doherty and J.A. Szpunar:Acta Metall., 1984, vol. 32, pp. 1789–98.

    Article  CAS  Google Scholar 

  21. F.J. Humphreys:Mater. Sci. Technol., 1992, vol. 8, pp. 135–43.

    CAS  Google Scholar 

  22. F.J. Humphreys:Mater. Sci. Forum, 1993, vol. 113–115, pp. 329–34.

    Google Scholar 

  23. C.S. Nichols, R.F. Cook, D.R. Clarke, and D.A. Smith:Acta Metall. Mater., 1991, vol. 39, pp. 1657–65.

    Article  Google Scholar 

  24. C.S. Nichols, R.F. Cook, D.R. Clarke, and D.A. Smith:Acta Metall. Mater., 1991, vol. 39, pp. 1667–75.

    Article  Google Scholar 

  25. W.T. Read, Jr. and W. Shockley:Phys. Rev., 1950, vol. 78, pp. 275–89.

    Article  CAS  Google Scholar 

  26. D. Wolf:Scripta Metall., 1989, vol. 23, pp. 1713–18.

    Article  Google Scholar 

  27. D. Wolf:Scripta Metall., 1989, vol. 23, pp. 1913–18.

    Article  CAS  Google Scholar 

  28. T.O. Saetre and N. Ryum: inRecrystallization ’90, T. Chandra, ed., TMS, Warrendale, PA, 1990, pp. 267–72.

    Google Scholar 

  29. T.O. Saetre, N. Ryum, and E. Evangelista:Metall. Trans. A, 1991, vol. 22A, pp. 2257–63.

    CAS  Google Scholar 

  30. T.O. Saetre and N. Ryum:Mater. Sci. Forum, 1992, vol. 94–96, pp. 373–78.

    Google Scholar 

  31. T.O. Saetre and N. Ryum:Mater. Sci. Forum, 1993, vol. 113–115, pp. 367–72.

    Google Scholar 

  32. T.O. Saetre and N. Ryum:Proc. COMMP93, Iron and Steel Institute of Japan, Tokyo, 1993, pp. 355–61.

    Google Scholar 

  33. C.S. Nichols, C.M. Mansuri, S.J. Townsend, and D.A. Smith:Acta Metall. Mater., 1993, vol. 41, pp. 1861–68.

    Article  CAS  Google Scholar 

  34. C.S. Nichols and D.A. Smith: inModeling of Coarsening and Grain Growth, C.S. Pande and S.P. Marsh, eds., TMS, Warrendale, PA, 1993, pp. 235–44.

    Google Scholar 

  35. J.P. Hirth and J. Lothe:Theory of Dislocations, 2nd ed., Wiley, New York, NY, 1982, pp. 701–09.

    Google Scholar 

  36. F.R.N. Nabarro: inDislocations and Mechanical Properties of Crystals, Lake Placid Conf., John Wiley & Sons Inc., New York, NY, 1957, pp. 521–33.

    Google Scholar 

  37. J.C.M. Li:Recrystallization, Grain Growth and Textures, ASM, Metals Park, OH, 1966, pp. 86–92.

    Google Scholar 

  38. D. Turnbull and R.E. Hoffman:Acta Metall., 1954, vol. 2, pp. 419–26.

    Article  CAS  Google Scholar 

  39. R.W. Balluffi:Metall. Trans. A, 1982, vol. 13A, pp. 2069–95.

    Google Scholar 

  40. Q. Ma, C.L. Liu, J.B. Adams, and R.W. Balluffi:Acta Metall. Mater., 1993, vol. 41, pp. 143–51.

    Article  CAS  Google Scholar 

  41. G. Hasson and C. Goux:Compt. Rend. Acad. Sc. Paris, 1970, vol. 271, Ser. C, pp. 1048–51.

    CAS  Google Scholar 

  42. G.C. Hasson, J.B. Guillot, B. Baroux, and C. Goux:Phys. Status Solidi A, 1970, vol. 2, pp. 551–58.

    Article  CAS  Google Scholar 

  43. G.C. Hasson and C. Goux:Scripta Metall., 1971, vol. 5, pp. 889–94.

    Article  CAS  Google Scholar 

  44. C. Goux:Can. Metall. Q., 1974, vol. 13, pp. 9–31.

    CAS  Google Scholar 

  45. A.P. Sutton and V. Vitek:Phil. Trans. R. Soc. London A, 1983, vol. 309, pp. 1–68.

    Article  CAS  Google Scholar 

  46. Y. Oh and V. Vitek:Acta Metall., 1986, vol. 34, pp. 1941–53.

    Article  Google Scholar 

  47. M. Dechamps, F. Baribier, and A. Marrouche:Acta Metall., 1987, vol. 35, pp. 101–07.

    Article  CAS  Google Scholar 

  48. A.P. Sutton and R.W. Balluffi:Acta Metall., 1987, vol. 35, pp. 2177–01.

    Article  CAS  Google Scholar 

  49. K.L. Merkle:Ultramicroscopy, 1991, vol. 37, pp. 130–152.

    Article  Google Scholar 

  50. A.H. King:Metall. Trans. A, 1991, vol. 22A, pp. 1177–83.

    Google Scholar 

  51. G. Gottstein and F. Schwarzer:Mater. Sci. Forum, 1992, vol. 94–96, pp. 187–08.

    Article  Google Scholar 

  52. L. Merkle and D. Wolf:Phil. Mag. A, 1992, vol. 65, pp. 513–30.

    Article  Google Scholar 

  53. I. Sinitsky, A. Men, and D.G. Brandon:Acta Metall. Mater., 1993, vol. 41, pp. 3525–34.

    Article  CAS  Google Scholar 

  54. J.G. Sevillano, P. van Houtte, and E. Aernoudt: inProgress in Materials Science, J.W. Christian, P. Haasen, and T.B. Massalski, eds., Pergamon Press, Oxford, 1982, vol. 25, pp. 222–71.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Formerly with the Hydro Aluminum a.s. R&D Center, Karmöy, Norway

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saetre, T.O., Ryum, N. On grain and subgrain rotations in two dimensions. Metall Mater Trans A 26, 1687–1697 (1995). https://doi.org/10.1007/BF02670755

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02670755

Keywords

Navigation