Skip to main content
Log in

On modelling steady state and transient creep of polycrystalline solids

  • Contributed Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

A constitutive model is proposed to describe creep deformation of polycrystalline materials under complex stress and temperature histories. The concept of piecewise linear effective stress—creep strain rate relationship is utilized. A key assumption in this model is that the back stress under a given stress and temperature reaches a saturation point. This saturation point corresponds to the steady state condition.

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. Besseling, J. F.: A theory of elastic plastic and creep deformation of an initially isotropic material showing anisotropic strain hardening, creep, recovery and secondary creep. J. Appl. Mech.25, 529–536 (1953).

    Google Scholar 

  2. Bodner, S. R., Merzer, A.: Viscoplastic constitutive equations for copper with strain history and temperature effects. ASME J. Engng. Mat. Techn.100, 388–394 (1978).

    Google Scholar 

  3. Cernocky, E. P., Krempl, E.: A theory of thermoviscoplasticity based on infinitesimal total strain. Int. J. Solids and Structures16, 723–741 (1980).

    Google Scholar 

  4. Chaboche, J. L.: Viscoelastic constitutive equations for the description of cyclic and anisotropic behavior of metals. Bull. Acad. Polon. Sci., Ser. Sci. Tech.25, 33 (1977).

    Google Scholar 

  5. Chaboche, J. L., Dang Van, K., Cordier, G.: Modelization of the strain memory effect on the cyclic hardening of 316 stainless steel. Trans. 5th Int. Conf. Struc. Mech. Reactor Tech. (Jaeger, T. A., Boley, B. A., eds.), Amsterdam: North-Holland 1979.

    Google Scholar 

  6. Faruque, M. O.: On the description of cyclic creep and rate dependent plastic deformation. Acta Mechanica55, 123–136 (1985).

    Google Scholar 

  7. Findley, W. N., Lai, J. S.: Creep and recovery of 2618 aluminum alloy under combined stress with a representation by a viscous-viscoelastic model. J. Appl. Mech.45, 507–514 (1978).

    Google Scholar 

  8. Garafalo, F.: Fundamentals of creep and creep-rupture in metals. New York: Macmillan 1965.

    Google Scholar 

  9. Gittus, J. H.: Dislocation creep under cyclic stressing: physical model and theoretical equations. Acta Met.26, 305–317 (1978).

    Google Scholar 

  10. Hart, E. W.: Constitutive relations for the nonelastic deformation of metals. Trans. ASME, J. Engr. Mat. and Tech.98, 193–202 (1976).

    Google Scholar 

  11. Kocks, U. F.: Laws for work-hardening and low-temperature creep. Trans. ASME, J. Engng. Mat. Tech.98, 76–85 (1976).

    Google Scholar 

  12. Krans, H.: Creep analysis. New York: Wiley 1980.

    Google Scholar 

  13. Krempl, E.: Cyclic creep—an interpretive literature survey. Welding Research Council. WRC Bull.195, 63 (1974).

    Google Scholar 

  14. Krieg, R. D.: Numerical integration of some new unified plasticity-creep formulations. Proc. 4th International Conference on Structural Mechanics in Reactor Technology, 1977.

  15. Krieg, R. D., Swearengen, J. C., Rhode, R. W.: A physically-based internal variable model for rate-dependent plasticity, in: Inelastic behavior of pressure vessel and piping components (Chang, T. Y., Krempl, E., eds.), pp. 15–28, New York: ASME 1978.

    Google Scholar 

  16. Kujawski, D., Mroz, Z.: A viscoplastic material model and its application to cyclic loading. Acta Mechanica36, 213–230 (1980).

    Google Scholar 

  17. Laften, J. H., Stouffer, D. C.: An analysis of high temperature metal creep: Part II—A constitutive formulation and verification. Trans. ASME, J. Engng. Mat. Techn.100, 363–380 (1978).

    Google Scholar 

  18. Lagneborg, R.: A theoretical approach to creep deformation during intermittent load. ASME J. Basic Engng.93, 205 (1971).

    Google Scholar 

  19. Lagneborg, R.: A modified recovery-creep model and its evaluation. Met. Sci. J.6, 127–133 (1972).

    Google Scholar 

  20. Lagneborg, R.: Creep: mechanisms and theories, in: Creep and fatigue in high temperature alloys (Bressers, J., ed.), Applied Science publishers 1981.

  21. Larsson, B., Storakes, B.: A state variable interpretation of some rate-dependent inelastic properties of steel. ASME J. Engng. Mat. Techn.100, 395–401 (1978).

    Google Scholar 

  22. Leckie, F. A., Ponter, A. R. S.: On the state variable description of creeping materials. Ing. Archiv.43, 158–167 (1974).

    Google Scholar 

  23. Malinin, N. N., Khadjinsky, G. M.: Theory of creep with anisotropic hardening. Int. J. Mech. Sci.14, 235–246 (1972).

    Google Scholar 

  24. Miller, A.: An inelastic constitutive model for monotonic, cyclic and creep deformation. ASME J. Engng. Mat. Tech.98, 97–113 (1976).

    Google Scholar 

  25. Mroz, Z.: On generalized kinematic hardening rule with memory of maximal prestress. J. Mech. Appl.5, 241–260 (1981).

    Google Scholar 

  26. Mroz, Z., Trampczynski, W. A.: On the creep-hardening rule for metals with a memory of maximal prestress. Int. J. Solids and Structures20, 467–486 (1984).

    Google Scholar 

  27. Murakami, S., Ohno, N.: A constitutive equation of creep based on the concept of a creep-hardening surface. Int. J. Solids and Structures18, 597–609 (1982).

    Google Scholar 

  28. Odqvist, F. K. G.: Mathematical theory of creep and creep rupture. Oxford University Press 1974.

  29. Ohashi, Y., Ohno, N., Kawai, M.: Evaluation of creep constitutive equations for type 304 stainless steel under repeated multiaxial loading. ASME J. Engng. Mat. Tech.104, 159–164 (1982).

    Google Scholar 

  30. Ohnami, M., Motoie, K., Yoshida, N.: Study on the influence of strain history on creep of polycrystalline metallic materials at elevated temperature. Zairyo18, 226 (1969).

    Google Scholar 

  31. Ostrom, P., Lagneborg, R.: A recovery-thermal glide creep model. Trans. ASME, J. Engng. Mat. Tech.98, 114–124 (1976).

    Google Scholar 

  32. Paslay, P. R., Wells, C. H.: Uniaxial creep behavior of metals under cyclic temperature and stress or strain variation. J. Appl. Mech.98, 445–449 (1976).

    Google Scholar 

  33. Ponter, A. R. S., Leckie, F. A.: Constitutive relationships for the time-dependent deformation of metals. J. Engng. Mat. Techn.98, 47–51 (1976).

    Google Scholar 

  34. Rabotonov, Y. N.: Creep problems of structural members. Amsterdam: North-Holland 1969.

    Google Scholar 

  35. Robinson, D. N., Pugh, C. E., Corum, J. M.: Constitutive equations for describing high-temperature inelastic behavior of structural alloys. IAEA Int. Working group on fast reactors specialists—Meeting on high temperature structural design technology, 1976.

  36. Robinson, D. N.: A unified creep-plasticity model for structural metals at high temperature. ORNL/TM-5969, Oak Ridge National Laboratory, 1978.

  37. Swearengen, J. C., Rhode, R. W., Hicks, D. L.: Mechanical state relations for inelastic deformation on iron: the choice of variables. Acta Met.24, 969–975 (1976).

    Google Scholar 

  38. Swearengen, J. C., Rhode, R. W.: Application of mechanical state relations at low and high homologous temperatures. Met. Trans.8 A, 577–582 (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

With 12 Figures

Rights and permissions

Reprints and permissions

About this article

Cite this article

Faruque, M.O., Zaman, M.M. On modelling steady state and transient creep of polycrystalline solids. Acta Mechanica 71, 115–136 (1988). https://doi.org/10.1007/BF01173941

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01173941

Keywords

Navigation