Some Unification of Creep Theories Based on Internal Time Concept

  • O. Watanabe
  • S. N. Atluri
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


Among the constitutive equations for high strain rate properties of materials under dynamic loading, the’ Overstress Model’ of Malvern[l] and Perzyna[2] is well known because of its simplicity and ability. This model has been widely extended for describing the quasi-static creep behavior under high temperature environment by Chaboche[3], Robinson[4], Bruhns[5], Krempl, McMahon & Yao[6] and Sahashi, Imatani & Inoue[7]. On the other hand,’ Endochronic Model’ of Valanis[8] received attensions because of its ability to predict time-independent plastic deformation under complex loading histories. This model is applied for time-dependent deformations, such as dynamic loading and quasi-static creep behaviors. Wu & Yip[9] applied this model for the dynamic behavior of materials, and Chang, Sugiura & Lee[10] proposed an alternate theory of high strain rate problems. In this’ Endochronic Model’ for dynamic problems, the current stress exists beyond the yield surface, and inelastic strain becomes larger as the stress goes away from the boundary of the static yield surafce. Watanabe & Atluri[11,12] applied’ Endochronic Model’ for quasi-static creep behaviors, where the current stress is confined within the yield surface, and inelatic strain rate will become infinite as the stress approaches to the boundary of yield surface.

This paper gives some theoretical unification of the rate dependent constitutive modeling for dynamic and quasi-static problems developed in’ Overstress Model’ and’ Endochronic Model’. By introducing a new intrinsic time derived from the fundamental stress-strain relation in the integral form,’ Endochronic Model’ is shown to be general enough to relate closely to the previous’ Overstress Model’.


Constitutive Equation High Strain Rate Yield Surface Creep Strain Inelastic Strain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Malvern, L.E.: The propagation of longitudinal waves of plastic deformation in a bar of material exhibiting a strain-rate effect. J. Appl. Mech., ASME 18 (1951) 203.MathSciNetGoogle Scholar
  2. 2.
    Perzyna, P.: The constitutive equation for rate sensitive plastic materials. Q. Appl. Math., 20 (1963) 321.MathSciNetMATHGoogle Scholar
  3. 3.
    Chaboche, J.L.: Viscoplastic constitutive equations for the description of cyclic and anisotropic behavior of metals. Bull. L’Aca. Pol. Sci., Ser. Sci. Tech., XXV (1977) 33.Google Scholar
  4. 4.
    Robinson, D.N.: A unified creep-palsticity model for structural metals at high temperature. ORNL TM-5969, (1978)Google Scholar
  5. 5.
    Bruhns, O. ed.: Constitutive modeling in the range of inelastic deformation — a state of arts report. INTERATOM Rep. RAP-055-D (B) (1984)Google Scholar
  6. 6.
    Krempl, E.; McMahon, J.J.; Yao, D.: Viscoplasticity based on overstress with a differential growth law for the equilibrium stress. Mech. Mat. 5 (1986) 35.CrossRefGoogle Scholar
  7. 7.
    Sahashi, T.; Imatani, S.; Inoue, T.: A constitutive model accounting for the plasticity-creep interaction condition, and the description of inelastic behavior of 2¼ Cr—1 M o steel. Trans. JSME, A 52-476 (1986) 1126.Google Scholar
  8. 8.
    Valanis, K.C.: Fundamental consequence of a new intrinsic time measure — plasticity as a limit of the endochronic theory. Arch. Mech. 32 (1980) 171.MathSciNetMATHGoogle Scholar
  9. 9.
    Wu, H.C.; Yip, M.C.: Strain rate and strain history effects on the dynamic behavior of metallic materials. Int. J. Solids Struct. 16 (1980) 515.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Chang, K.C.; Sugiura, K.; Lee, G.C.: Rate-dependent material model for structural steel. J. Eng. Mech., ASCE, 115-3 (1989) 465.CrossRefGoogle Scholar
  11. 11.
    Watanabe, O; Atluri, S.N.: Internal time, general internal variable, and multi-yiels-surface theories of plasticity and creep: a unification of concepts. Int. J. Plast. 2 (1986) 37.MATHCrossRefGoogle Scholar
  12. 12.
    Watanabe, O.; Atluri, S.N.: Constitutive modeling of cyclic plasticity and creep, using an internal time concept. Int. J. Plast. 2-2 (1986) 107.CrossRefGoogle Scholar
  13. 13.
    Chaboche, J.L.: Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int. J. Plast. 5 (1989) 247.MATHCrossRefGoogle Scholar
  14. 14.
    Nouailhas, D.; Policella, H.; Kaczmarek, H.: On the description or cyclic hardening under complex loading histories. Int. Conf. Constitutive Laws for Engineering Materials, Tucson, Arizona, Desai & Gallagher ed. (1983)Google Scholar
  15. 15.
    Walker, K.P.: Research and development program for non-linear structural modeling with advanced time-temperature dependent constitutive relationships. Repot PWA-5700-50, NASA CR-165533 (1981).Google Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1991

Authors and Affiliations

  • O. Watanabe
    • 1
  • S. N. Atluri
    • 2
  1. 1.Institute of Engineering MechanicsUniversity of TsukubaTsukuba 305Japan
  2. 2.Georgia Institute of TechnologySchool of Civil EngineeringAtlantaUSA

Personalised recommendations