Inelastic Constitutive Equations and Phenomenological Laws of Damage Accumulation for Structural Metals

  • E. Krempl
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


During inelastic deformation the mechanical properties of metals can change considerably. Examples of such changes are given. It is argued that these changes are not necessarily a reliable indicator of damage. Residual strength or residual lifetime are proposed as alternate relative measures. For the case of residual lifetime a method of assessing damage is proposed. This method yields the Palmgren-Miner rule as a special case.


Constitutive Equation Structural Metal Residual Strength Endurance Limit Cyclic Creep 
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  1. [1]
    Bodner, S.R.; Partom, Y.: Constitutive equations for elastic-viscoplastic strain hardening materials. J. Applied Mechanics, 42 (1975) 385.CrossRefADSGoogle Scholar
  2. [2]
    Eisenberg, M.A.; Lee, C.W.; Phillips, A.: Observations on the theoretical and experimental foundations of thermoplasticity. Int. J. Solids and Structures, 13 (1977) 1239–1255.CrossRefGoogle Scholar
  3. [3]
    Hart, E.W.: Constitutive equations for the non-elastic deformation of metals. Trans. ASME, J. Engineering Materials and Technology, 98H (1976) 193.CrossRefGoogle Scholar
  4. [4]
    Miller, A.K.: An inelastic constitutive model for monotonic, cyclic and creep deformation - Part I and II. Trans. ASME, J. Engineering Materials and Technology, 98H (1976) 97.CrossRefGoogle Scholar
  5. [5]
    Swearengen, J.C.; Rhode, R.W.: Application of mechanical state relations at low and high homologous temperatures. Met. Trans., 8A (1977) 577.CrossRefGoogle Scholar
  6. [6]
    Valanis, K.C.: On the foundations of the endochronic theory of viscoplasticity. Archives of Mechanics, 27 (1975) 857.MATHMathSciNetGoogle Scholar
  7. [7]
    Cernocky, E.P.; Krempl, E.: A theory of viscoplasticity based on infinitesimal total strain. Acta Mechanica, 36, No. 3–4 (1980).Google Scholar
  8. [8]
    Liu, M.C.M.; Krempl, E.: A uniaxial viscoplastic model based on total strain and overstress. J. Mechanics and Physics of Solids, 27 (1979) 377–391.CrossRefMATHADSGoogle Scholar
  9. [9]
    Walker, K.P.; Krempl, E.: An implicit functional theory of visco-plasticity. Mechanics Research Communications, 4 (1978) 179–190.CrossRefMathSciNetGoogle Scholar
  10. [10]
    Krempl, E.: Viscoplasticity based on total strain. The modelling of creep with special considerations of initial strain and aging. Trans. ASME, J. Engineering Materials and Technology, 101 (1979) 380–386.CrossRefGoogle Scholar
  11. [11]
    Chaboche, J.L.: Continuous damage mechanics. A tool to describe phenomena before crack initiation. Paper presented at SMiRT-5 post-conference seminar on inelastic analysis and life-prediction in high temperature environment, Berlin (August 1979) to appear in Nuclear Eng. and Design.Google Scholar
  12. [12]
    Krempl, E.: On the interaction of rate and history dependence in structural metals. Acta Mechanica 22 (1975) 53–90.CrossRefMATHGoogle Scholar
  13. [13]
    Feltner, C.E.; Laird, C.: Cyclic stress-strain response of fee metals and alloys. Parts I and II. Acta Metallurgica, 15 (1967) 1621–1653.CrossRefGoogle Scholar
  14. [14]
    Nahm, H.; Moteff, J.; Diercks, D.R.: Substructural development during low-cycle fatigue of AISI type 304 stainless steel at 649°C, Acta Metallurgica, 27 (1977) 107–116.CrossRefGoogle Scholar
  15. [15]
    RDT Standard RDT F 9-5T, Division of Reactor Research and Development, U.S. Atomic Energy Commission (Sept. 1974), Fig. A. 35.Google Scholar
  16. [16]
    Krempl, E.: An experimental study of room temperature rate-sensitivity, creep and relaxation of type 304 stainless steel. J. Mechanics and Physics of Solids, 27 (1979) 363–375.CrossRefADSGoogle Scholar
  17. [17]
    Kujawski, D.; Kallianpur, V.; Krempl, E.: Uniaxial creep, cyclic creep and relaxation of AISI type 304 stainless steel at room temperature. To appear J. Mechanics Physics of Solids.Google Scholar
  18. [18]
    Krempl, E.: Cyclic creep. An interpretive literature survey. Welding Research Council Bulletin No. 195, Welding Research Council, New York, NY (1974).Google Scholar
  19. [19]
    Stouffer, D.C.; Strauss, A.M.: A theory of material divagation. Int. J. of Eng. Science, 16 (1978) 1019–1028.CrossRefMATHMathSciNetGoogle Scholar
  20. [20]
    Webster’s New Twentieth Century Dictionary of the English Language, unabridged, 2nd edition, William Collins Publishers inc. (1979).Google Scholar
  21. [21]
    Frost, N.E.; Marsh, K.J.; Pook, L.P.: Metal fatigue. Clarendon Press, Oxford (1974).Google Scholar
  22. [22]
    Lemaitre, J.; Cordebois, J.-P.; Dufailly, J.: Sur le couplage endommagement-élasticité. C.R. Acad. Se. Paris, t.288, Série B (25 Juin 1979 ) 391–394.Google Scholar
  23. [23]
    Lemaitre, J.; Chaboche, J.-L.: Aspect phénoménologique de la rupture par endommagement. J. de Mecanique applicquée, 2 (1978) 317–365.Google Scholar
  24. [24]
    Leckie, F.A.: The constitutive equations of continuum creep damage mechanics. Phil. Trans. R. Soc., London, A288 (1978) 27–47.CrossRefADSGoogle Scholar
  25. [25]
    Forrest, P.G.: Fatigue of metals. Pergamon Press (1962).Google Scholar
  26. [26]
    Ostergren, W.J.; Krempl, E.: A uniaxial damage accumulation law for time-varying loading including creep-fatigue interaction. Trans. ASME, J. Pressure Vessel Technology, 101 (1979) 118–124.CrossRefGoogle Scholar
  27. [27]
    Goldhoff, R.M.; Woodford, D.A.; The evaluation of creep damage in a Cr-Mo-V steel, American Society for Testing and Materials, STP 515 (1972) 89–106.Google Scholar
  28. [28]
    Burbach, J.: The physical justification of the term “state of fatigue of materials” under cyclic loading. American Society for Testing and Materials, STP 519 (1973) 185–212.Google Scholar

Copyright information

© Springer-Verlag, Berlin, Heidelberg 1981

Authors and Affiliations

  • E. Krempl
    • 1
    • 2
  1. 1.Department of Mechanical EngineeringRensselaer Polytechnic InstituteTroyUSA
  2. 2.Aeronautical Engineering & MechanicsRensselaer Polytechnic InstituteTroyUSA

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