Skip to main content
SpringerLink
Log in

Mathematical description of the mechanical behaviour of metallic materials under creep conditions

  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

The metallic materials creep behaviour has been described and a complete model is presented. The basic constitutive equation, as well as the structure parameters, have been derived from a mathematical analysis that represents the dominant physical procedures and mechanisms. The model is very general because it is referred to all stages of creep and describes the creep behaviour of all metallic materials, including those strengthened by a dispersion of second-phase particles. A creep function has been derived from the constitutive equation describing all three stages of creep under constant loading. The function has the minimum possible number of fitting, parameters. The dependence of the fitting parameters on the loading conditions has been described using very simple mathematical relations. Applications and predictions have been carried out in a wide range of metallic materials. Good agreement has been shown by a comparison made also between the creep curves determined experimentally, and those obtained from creep function and determined fitting parameters.

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. T. B. KERMANIDIS, S. G. PANTELAKIS and N. D. BATSOULAS, Metall. 31 (1990) 1167.

    Google Scholar 

  2. S. G. PANTELAKIS, N. D. BATSOULAS and T. B. KERMANIDIS, Steel Res. 62 (1991) 272.

    CAS  Google Scholar 

  3. S. G. PANTELAKIS, T. KERMANIDIS and N. BATSOULAS, in “Proceedings of the 5th Cairo University MDP Conference” edited by I. Fawzy and M. A. Shirlaby, Cairo, Egypt (Cairo Univ., 1991) p. 23.

  4. T. B. KERMANIDIS, S. G. PANTELAKIS and N. D. BATSOULAS, Theor. Appl. Fract. Mech. 17 (1992) 7.

    Article  CAS  Google Scholar 

  5. N. D. BATSOULAS, Steel Res. 65 (1994) 114.

    CAS  Google Scholar 

  6. Idem, ibid. 65 (1994) 163.

    Google Scholar 

  7. E. OROWAN, J. W. Scotland Iron Steel Inst. 54 (1946) 45.

    Google Scholar 

  8. N. J. FROST and M. F. ASHBY, Division of Engineering and Applied Science, Harvard University, Internal report (1972).

  9. D. J. LOOYD and J. D. EMBORY, Metall. Sci. J. 4 (1970) 6.

    Google Scholar 

  10. C. N. AHLQUIST, R. CASCA-NERI and W. D. NIX, Acta Metall. 19 (1970) 663.

    Google Scholar 

  11. C. N. AHLQUIST and W. D. NIX, ibid. 19 (1971) 373.

    Article  Google Scholar 

  12. A. ORLOVA, M. PAHUTOVA and J. CADEK, Philos. Mag. 25 (1972) 865.

    CAS  Google Scholar 

  13. C. J. BOLTON, “Internal stress: a review with special reference to high temperature creep”, Berkeley Nuclear Laboratories, UK, RD/N2300 (1973).

    Google Scholar 

  14. J. C. GIBELING and W. D. NIX, Mater. Sci. Eng. 11 (1977) 453.

    CAS  Google Scholar 

  15. M. A. ABDOU, in “Proceedings of the 1st Cairo University MDP Conference” edited by I. Fawzy, Cairo, Egypt (Cairo Univ., 1979) p. 13.

  16. M. A. MORRIS and J. L. MARTIN, Acta Metall. 32 (1984) 1609.

    Article  CAS  Google Scholar 

  17. E. EL-MAGD and T. KAISER, in “Proceedings of the 3rd International Conference on Creep and Fatigue” edited by B. Wilshire and D. R. J. Owen (Institute of Metals, London, 1987) p. 130.

    Google Scholar 

  18. E. EL-MAGD and A. D. MEGAHED, in “Proceedings of the 4th Cairo University MDP Conference” edited by M. M. Megahed, Cairo, Egypt, (Cairo Univ., 1988) p. 35.

  19. E. EL-MAGD and C. SHAKER, in “Proceedings of the 4th International Conference on Creep and Fracture of Engineering Materials and Structures” edited by B. Wilshire and R. Evans (Institute of Metals, London 1990) p. 119.

    Google Scholar 

  20. J. WEERTMAN, Acta Metall. 25 (1977) 1393.

    Article  CAS  Google Scholar 

  21. J. J. JONAS, ibid. 17 (1969) 1393.

    Google Scholar 

  22. A. A. SOLOMON and W. D. NIX, ibid. 18 (1970) 863.

    Article  CAS  Google Scholar 

  23. F. DODES and F. CADEK, Phys. Status Solidi(a) 35 (1976) 123.

    Google Scholar 

  24. P. FELTHAM, ibid. 30 (1968) 135.

    CAS  Google Scholar 

  25. Idem, J. Phys. D6 (1973) 2048.

    Google Scholar 

  26. J. H. GITTUS, J. Mech. Phys. Solids 13 (1965) 69.

    Article  CAS  Google Scholar 

  27. G. SAADA, in “Electron Microscopy and Strength of Crystals“, edited by G. Thomas and J. Washburn (Interscience, New York, 1963) p. 53.

    Google Scholar 

  28. R. LAGNEBORG, B. H. FORSEN and J. WIBERY, “Creep Strength in Steel and High Temperature Alloys” (The Metals Society, London, 1974).

    Google Scholar 

  29. F. DOBES, Acta Metall. 28 (1980) 377.

    Article  CAS  Google Scholar 

  30. R. K. HAM, Philos. Mag. 6 (1961) 1183.

    Google Scholar 

  31. A. ORLOVA, Scripta Metall. 16 (1982) 633.

    Article  CAS  Google Scholar 

  32. E. OROWAN, Proc. Phys. Soc. 52 (1940) 8.

    Article  Google Scholar 

  33. Idem, Nature149 (1942) 643.

    Google Scholar 

  34. U. F. KOCKS, ASME J. Eng. Mater. Tech.98 (1976) 76.

    CAS  Google Scholar 

  35. M. BRAUM, “Differential Equations and their Applications” (Springer, New York, 1978).

    Google Scholar 

  36. J. HALE, “Studies in Ordinary Differential Equations” (Mathematical Association of America, New York, 1977).

    Google Scholar 

  37. B. F. DYSON and M. McLEAN, Acta Metall. 31 (1983) 17.

    Article  CAS  Google Scholar 

  38. G. GREENWOOD, Philos. Mag. 17 (1978) 423.

    Google Scholar 

  39. Idem, in “Proceedings of the International Congress on Metals“, Cambridge (The Metals Society, Cambridge, 1973) p. 91.

  40. B. F. DYSON and D. McLEAN, Metal Sci. J. 2 (1977) 37.

    Google Scholar 

  41. Y. N. RABOTNOV, “Creep Problems in Structural Members” (North-Holland, Amsterdam, 1969).

    Google Scholar 

  42. M. RIDES, A. C. COCKS and D. R. HAYHURST, ASME J. Appl. Mech. 56 (1989) 493.

    Article  Google Scholar 

  43. E. EL-MAGD, S. PANTELAKIS and K. JAGER, Res. Mech. 21 (1987) 55.

    CAS  Google Scholar 

  44. F. A. LECKIE, Eng. Fract. Mech. 25 (1986) 501.

    Google Scholar 

  45. F. A. LECKIE and D. R. HAYHURST, Acta Metall. 25 (1977) 1059.

    Article  Google Scholar 

  46. L. M. KACHANOV, “Theory of Creep” (Boston Spa, Wetherby, 1960).

    Google Scholar 

  47. Idem, in “Problems of Continuum Mechanics, Contributions in Honor of 70th Birthday of N. I. Muskhelishvili”, edited by J. R. M. Radok, (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1961) p. 100.

    Google Scholar 

  48. P. W. DAVIES and P. W. EVANS, Acta Metall. 13 (1965) 353.

    Article  CAS  Google Scholar 

  49. P. W. DAVIES and R. DUTTON, ibid. 15 (1967) 1365.

    Article  CAS  Google Scholar 

  50. M. R. SITZER and A. TROOST, Z. Werkstofftech.15 (1984) 264.

    Article  Google Scholar 

  51. A. TROOST, ibid. 14 (1983) 336.

    Article  Google Scholar 

  52. J. MARIN, Proc. SESA 11 (1970) 207.

    Google Scholar 

  53. Y. ESTRIN and H. MECKING, Acta Metall. 32 (1984) 57.

    Article  Google Scholar 

  54. W. V. GREEN, in “Techniques of Metals Research”, edited by R. F. Bunsaw, (Interscience, New York, 1971) p. 39.

    Google Scholar 

  55. R. LAGNEBORG, in “Creep and Fatigue in High Temperature Alloys” edited by J. Bressers (Applied Science, London, 1980) p. 41.

    Google Scholar 

  56. K. R. WILLIAMS and B. WILSHIRE, Mater. Sci. Eng. 47 (1981) 151.

    Article  CAS  Google Scholar 

  57. A. J. KENNEDY, “Processes of Creep and Fatigue in Metals” (Wiley, New York, 1963).

    Google Scholar 

  58. B. C. HOSKIN, “Phenomenological Theories of Time Effects in Metals at High Temperatures with Special Reference to Primary Creep”, Brown University, Division of Engineering Research, 562(20)/7 (1958).

  59. S. BHATTACHARYA, J. Inst. Metals 81 (1952-1953) 83.

    CAS  Google Scholar 

  60. A. H. COTTREL, J. Mech. Phys. Solids 1 (1952) 53.

    Article  Google Scholar 

  61. J. MARIN, Proc. SESA 11 (1970) 207.

    Google Scholar 

  62. A. D. SCHWOPE and L. R. JACKSON, “A Survey of Creep in Metals”, NACA TN 2516 (1951).

  63. A. E. JOHNSON and A. E. FROST, J. Inst. Metals 81 (1952-53) 93.

    CAS  Google Scholar 

  64. F. GAROFALO, ASME J. Basic. Eng. 82 (1960) 867.

    CAS  Google Scholar 

  65. Y. H. PAO and J. MARIN, ASME J. Appl. Mech. 20 (1953) 245.

    Google Scholar 

  66. Y. N. RABOTNOV, “Some Problems of the Theory of Creep” (translation), NACA TN 13567 (1953).

  67. K. SCHAAR, Materialprufung 6 (1964) 130.

    Google Scholar 

  68. C. E. PUGH, in “Advances in Design for Elevated Temperature Environment”, edited by S. Y. Zamrik and R. J. Jeffer (ASME, NEW YORK, 1975) p. 137.

  69. O. D. SHERBY and J. WADSWORTH, “Deformation, Processing and Structure”, (ASM, Metals Park, OH, 1984).

    Google Scholar 

  70. P. W. DAVIES and R. DUTTON, Acta Metall. 15 (1967) 1365.

    Article  CAS  Google Scholar 

  71. P. W. DAVIES and K. R. WILLIAMS, ibid. 17 (1969) 897.

    Article  CAS  Google Scholar 

  72. A. GRAHAM and F. K. A. WALLES, J. Iron Steel Inst. 193 (1955) 105.

    Google Scholar 

  73. R. W. EVANS, J. P. PARKER and B. WILSHIRE, in “Recent Advances in Creep and Fracture of Engineering Materials and Structures”, edited by B. Wilshire and D. R. J. Owen, (Pinieridge Press, Swansea, 1982) p.135.

    Google Scholar 

  74. B. WILSHIRE and D. R. J. OWEN, “Engineering Approaches to High Temperature Design”, (Pineridge Press, Swansea, 1983).

    Google Scholar 

  75. R. W. EVANS, I. BEDEN and B. WILSHIRE, in “Proceedings of the 2nd International Conference on Creep and Fracture of Engineering Materials and Structures” (Pineridge Press, Swansea, 1984) p. 1277.

    Google Scholar 

  76. R. W. EVANS and B. WILSHIRE, “Creep of Metals and Alloys” (Institute of Metals, London, 1985).

    Google Scholar 

  77. N. CHRISTODOULOU, Scripta Metall. 20 (1986) 1041.

    Article  Google Scholar 

  78. S. L. SEMIATIN, A. K. GHOSH and J. J. JONAS, Metall. Trans. 16A (1985) 2291.

    Google Scholar 

  79. J. LEMAITRE and J. L. CHABOCHE, “Mechanics of Solids Materials” edited by Engins (Cambridge University Press, London, 1990).

    Google Scholar 

  80. N. TAYLOR, B. TWADDLE and R. C. HURST, in “Proceedings of the 4th International Conference on Creep and Fracture of Engineering Materials and Structures” edited by B. Wilshire and R. Evans (Institute of Metals, London, 1990) p. 985.

    Google Scholar 

  81. F. GAROFALO, “Fundamentals of Creep and Creep-rupture in Metals” (Macmillan, New York, 1965).

    Google Scholar 

  82. R. H. ERICKSEN and G. J. JONES, Metall. Trans. 3A (1972) 1735.

    Google Scholar 

  83. O. D. SHERBY, T. A. TROZERA and J. E. DORN, Proc. ASTM 56 (1956) 784.

    Google Scholar 

  84. D. MCLEAN and K. F. HALE, in “Proceedings of the Symposim on Structural Processes in Creep” (Iron and Steel Institute, London, 1961) p. 19.

    Google Scholar 

  85. P. FELTHAM and J. D. MEAKIN, Acta Metall. 7 (1959) 614.

    Article  CAS  Google Scholar 

  86. E. R. PARKER, Trans. ASM 50 (1958) 85.

    Google Scholar 

  87. L. RAYMOND and J. E. DORN, ibid. 230 (1964) 560.

    CAS  Google Scholar 

  88. G. BRINSON and B. ARGENT, J. Inst. Metals 91 (1963) 293.

    CAS  Google Scholar 

  89. R. P. CARREKAR, J. Appl. Phys. 21 (1950) 1289.

    Article  Google Scholar 

  90. W. J. EVANS and B. WILSHIRE, Met. Sci. J. 4 (1970) 89.

    CAS  Google Scholar 

  91. D. SIDEY and B. WILSHIRE, ibid. 3 (1969) 56.

    CAS  Google Scholar 

  92. K. E. AMIN, A. K. MUKHERJEE and J. E. DORN, J. Mech. Phys. Solids 18 (1970) 413.

    Article  CAS  Google Scholar 

  93. H. BARTH, Dr-Ing Dlss, Thecnischen Hochschule Darmstadt, Darmstadt (1984).

  94. D. R. HAYHURST, P. R. DIMMER and M. W. CHERNUKA, J. Mech. Phys. Solids 23 (1975) 333.

    Google Scholar 

  95. J. L. CHAHOCHE, “Description thermodynamique et phenomenologiique de la viscoplasticite cyclique avec endommagement”, (ONERA, Paris, 1978).

    Google Scholar 

  96. D. KRAJCINOVIC and S. SELVARAJ, ASME J. Eng. Mater. Technol. 106 (1984) 405.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, School of Engineering, University of Patras, Patras, Greece

    N. D BATSOULAS

Authors
  1. N. D BATSOULAS
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

BATSOULAS, N.D. Mathematical description of the mechanical behaviour of metallic materials under creep conditions. Journal of Materials Science 32, 2511–2527 (1997). https://doi.org/10.1023/A:1018533930076

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018533930076

Keywords

Search

Navigation