Thermodynamically Founded CDM Models for Creep and Other Conditions

  • J.-L. Chaboche
Part of the International Centre for Mechanical Sciences book series (CISM, volume 399)


The fundamental concepts of Continuum Damage Mechanics are reviewed, with the objective to conform to a sufficiently general thermodynamic framework. The theories are developed at a macroscopic level, with the capability to describe various types of materials, ductile or brittle, metallic, concrete, composites,… etc., in an unique framework. For that, we consider both elasticity coupled with damage, plasticity and viscoplasticity coupled with damage and the damage growth equations themselves. Moreover, we discuss the important but difficult problems associated with the damage deactivation effects that can take place under compressive loadings.

A special attention is focused on the nature of damage state variables, in correspondence with the choices made in the various thermodynamic potentials, and on the various coupling possibilities. Some applications are presented on metallic materials, concerning ductile damage, creep damage and creep-fatigue interaction. We also discuss briefly the different levels for the inelastic/damage structural analysis and the applications of CDM to the Local Approaches to Fracture. Some illustrations are also given for Metal Matrix Composites and Ceramic Matrix Composites.


Effective Stress Kinematic Hardening Creep Damage Creep Crack Growth Tertiary Creep 
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.
    Kachanov L.M.: Time of the rupture process under creep conditions, Isv. Akad. Nauk. SSR. Otd Tekh. Nauk., 8 (1958), pp. 26–31.Google Scholar
  2. 2.
    Murzewski J.W.: The tensor of failure and its application to determination of strength of welded joints, Bull. Acad. Polon. Sci., Série Sci. Tech., VI (1958), pp. 159–164.Google Scholar
  3. 3.
    Rabotnov Y.N.: Creep problems in structural members, North-Holland, 1969.Google Scholar
  4. 4.
    Hayhurst D.R.: Creep rupture under multiaxial state of stress, J. Mech. Phys. Sol., 20 (1972), pp. 381–390.CrossRefGoogle Scholar
  5. 5.
    Leckie F.A. and Hayhurst D.R.: Creep rupture of structures, Proc. Royal Soc. London, 340 (1974), pp. 323–347.CrossRefMATHGoogle Scholar
  6. 6.
    Chrzanowski M.: Use of the damage concept in describing creep-fatigue interaction under prescribed stress, J. Mech. Sci., 18 (1976), pp. 69–73.CrossRefGoogle Scholar
  7. 7.
    Hult J.: Continuum Damage Mechanics. Capabilities limitations and promises, in: Mechanisms of Deformation and Fracture, Pergamon, Oxford, 1979 pp. 233–347.CrossRefGoogle Scholar
  8. 8.
    Murakami S. and Ohno N.: A continuum theory of creep and creep damage, in: Creep in Structures (Edited by A. Ponter and D. Hayhurst), 3rd IUTAM Symp., Springer-Verlag, 1980 pp. 422–443, leicester.Google Scholar
  9. 9.
    Chaboche J.L.: Sur l’utilisation des variables d’état interne pour la description de la viscoplasticité cyclique avec endommagement, in: Problèmes Non Linéaires de Mécanique, 1977 pp. 137–159, symposium Franco-Polonais de Rhéologie et Mécanique, Cracovie.Google Scholar
  10. 10.
    Lemaître J. and Chaboche J.L.: Mécanique des Matériaux Solides, Dunod, Paris, 1985.Google Scholar
  11. 11.
    Lemaître J.: A Continuum Damage Mechanics model for ductile fracture, J. of Engng. Mat. Technol., 107 (1985), pp. 83–89.CrossRefGoogle Scholar
  12. 12.
    Germain P., Nguyen Q.S. and Suquet P.: Continuum Thermodynamics, J. of Applied Mechanics, 50 (1983), pp. 1010–1020.CrossRefMATHGoogle Scholar
  13. 13.
    Krajcinovic D. and Fonseka G.U.: The Continuous Damage theory of brittle materials, Parts 1 and 2, J. of Applied Mechanics, 48 (1981), pp. 809–824.CrossRefMATHGoogle Scholar
  14. 14.
    Krajcinovic D.: Continuum Damage Mechanics, Applied Mechanics Reviews, 37 (1984), pp. 1–6.Google Scholar
  15. 15.
    Ortiz M.: A constitutive theory for the inelastic behavior of concrete, Mech. Mater., 4 (1985), pp. 67–93.CrossRefGoogle Scholar
  16. 16.
    Ju J.W.: On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects, Int. J. Solids Structures, 25 (1989), pp. 803–833.CrossRefMATHGoogle Scholar
  17. 17.
    Chow C.L. and Wang J.: An anisotropic theory of Continuum Damage Mechanics for ductile fracture, Engineering Fracture Mechanics, 27 (1987), pp. 547–558.CrossRefGoogle Scholar
  18. 18.
    Voyiadjis G.Z. and Kattan P.: Damage of fiber reinforced composite materials with micromechanical characterization, Int. J. Solids Structures, 30 (1993), pp. 2757–2778.CrossRefMATHGoogle Scholar
  19. 19.
    Chaboche J.L.: Continuous Damage Mechanics: a tool to describe phenomena before crack initiation, Nuclear Engineering and Design, 64 (1981), pp. 233–247.CrossRefGoogle Scholar
  20. 20.
    Murakami S.: Notion of Continuum Damage Mechanics and its application to anisotropic creep damage theory, J. of Engng. Mat. Technol., 105 (1983), pp. 99.CrossRefGoogle Scholar
  21. 21.
    Hayhurst D.R.: Materials data bases and mechanisms-based constitutive equations for use in design, in: Creep and Damage in Materials and Structures (Edited by H. Altenbach and J. Skrzypek ), Springer, 1999.Google Scholar
  22. 22.
    Krempl E.: Cyclic creep and creep fatigue interaction, in: Creep and Damage in Materials and Structures (Edited by H. Altenbach and J. Skrzypek ), Springer, 1999.Google Scholar
  23. 23.
    Skrzypek J.: Material damage models for creep failure analysis and design of structures, in: Creep and Damage in Materials and Structures (Edited by H. Altenbach and J. Skrzypek ), Springer, 1999.Google Scholar
  24. 24.
    Lemaître J. and Chaboche J.L.: Mechanics of Solid Materials, Cambridge University Press, Cambridge, U.K., 1990.CrossRefMATHGoogle Scholar
  25. 25.
    Jonas J.J. and Baudelet B.: Effect of crack and cavity generation on tensile stability, Acta Metallurgica, 25 (1977), pp. 43–50.CrossRefGoogle Scholar
  26. 26.
    Cailletaud G., Policella H. and Baudin G.: Mesure de déformation et d’endommagement par mesure électrique, La Recherche Aérospatiale, (1980), pp. 69–75.Google Scholar
  27. 27.
    Cordebois J.P and Sidoroff F.: Anisotropie élastique induite par endommagement, Col. Euromech 115, Editions du CNRS, 1982, 1979 Grenoble.Google Scholar
  28. 28.
    Plumtree A. and Nilsson J.O.: Damage mechanics applied to high temperature fatigue, Journées Internationales de Printemps, 1986 Paris.Google Scholar
  29. 29.
    Charewicz A. and Daniel I.M.: Fatigue damage mechanisms and residual properties of graphite/epoxy laminates, Engineering Fracture Mechanics, 25(1986).Google Scholar
  30. 30.
    Chaboche J.L.: Description phénoménologique de la viscoplasticité cyclique avec endommagement, Doctorat d’Etat, Université Pierre et Marie Curie, Paris 6, Paris, 1978.Google Scholar
  31. 31.
    Chaboche J.L.: Une loi différentielle d’endommagement de fatigue avec cumulation non linéaire, Revue Française de Mécanique, (1974), pp. 71–82.Google Scholar
  32. 32.
    Baste S., Guerjouma R. El and Gérard A.: Mesure de l’endommagement anisotrope d’un composite céramique-céramique par une méthode ultrasonore, Revue de Physique Appliquée, 24 (1989), pp. 721–731.CrossRefGoogle Scholar
  33. 33.
    Germain P.: Cours de Mécanique des Milieux Continus, volume I, Masson, Paris, 1973.MATHGoogle Scholar
  34. 34.
    Sidoroff F.: On the formulation of plasticity and viscoplasticity with internal variables, Arch. Mech., Poland, 27 (1975), pp. 807–819.MATHMathSciNetGoogle Scholar
  35. 35.
    Halphen B. and Nguyen Q.S.: Sur les matériaux standards généralisés, J. de Mécanique, 14 (1975), pp. 39–63.MATHGoogle Scholar
  36. 36.
    Chaboche J.L.: Unified cyclic viscoplastic constitutive equations: development, capabilities and thermodynamic framework, Academic Press Inc., 1996 pp. 1–68.Google Scholar
  37. 37.
    Chrysochoos A.: Bilan énergétique en élastoplasticité, grandes déformations, J. Mécanique Théorique et Appliquée, 4(1985).Google Scholar
  38. 38.
    Chrysochoos A.: Dissipation et blocage d’énergie lors d’un écrouissage en traction simple, Doctorat d’Etat, Université de Montpellier, Montpellier, 1987.Google Scholar
  39. 39.
    Leckie F.A. and Onat E.T.: Tensorial nature of damage measuring internal variables, in: Physical Non-Linearities in Structural Analysis, IUTAM Symp., Springer, 1980 Senlis.Google Scholar
  40. 40.
    Lemaître J.: A course on Damage Mechanics, Springer, 1992.Google Scholar
  41. 41.
    Ladevèze P.: Sur une théorie de l’endommagement anisotrope, Rapport Interne 34, Laboratoire de Mécanique et Technologie, Cachan, 1983.Google Scholar
  42. 42.
    Vakulenko A.A. and Kachanov M.L.: Continuum theory of medium with cracks, Mech. of Solids, english transl. of Mekhanika Tverdogo Tela (in Russian), 6 (1971), pp. 145–151.Google Scholar
  43. 43.
    Kachanov M.: Continuum model of medium with cracks, J. of the Engineering Mechanics Division, 106 (1980), pp. 1039–1051.Google Scholar
  44. 44.
    Chaboche J.L.: Le concept de contrainte effective appliqué à l’élasticité et à la viscoplasticité en présence d’un endommagement anisotrope, Col. Euromech 115, Editions du CNRS, 1982, 1979 pp. 737–760, grenoble.Google Scholar
  45. 45.
    Simo J.C. and Ju J.W.: Strain-and stress-based Continuum Damage models–I–Formulation, Int. J. Solids Structures, 23 (1987), pp. 821–840.CrossRefMATHGoogle Scholar
  46. 46.
    Saanouni K.: Sur l’analyse de la fissuration des milieux élasto-viscoplastiques par la théorie de l’endommagement continu, Doctorat d’Etat, Université de Compiègne, 1988.Google Scholar
  47. 47.
    Benallal A.: Thermoviscoplasticité et endommagement des structures, Doctorat d’Etat, Université Pierre et Marie Curie, Paris 6, 1989.Google Scholar
  48. 48.
    Dragon A.: On phenomenological description ofrock-like materials with account for kinetics of brittle fracture, Archivium Mechaniki Stosowanej, 28 (1976), pp. 13–30.Google Scholar
  49. 49.
    Hansen N.R. and Schreyer H.L.: Thermodynamically consistent theories for elastoplasticity coupled with damage, in: Damage Mechanics and Localization, volume 142/AMD, ASME, 1992 pp. 53–67.Google Scholar
  50. 50.
    Zhu Y.Y. and Cescotto S.: Fully coupled elasto-visco-plastic damage theory for anisotropic materials, Int. J. Solids Structures, 32 (1995), pp. 1607–1641.CrossRefMATHGoogle Scholar
  51. 51.
    Allix O., Ladevèze P., Dantec E. Le and Vittecoq E.: Damage Mechanics for composite laminates under complex loading, in: Yielding, Damage and Failure of Anisotropic Solids (Edited by J. Boehler), EGF5, Mechanical Engineering Publications, London, 1990 pp. 551–569.Google Scholar
  52. 52.
    Mazars J.: Mechanical damage and fracture of concrete structures, in: Advances in Fracture Research, volume 4, Pergamon Press, Oxford, 1982 pp. 1499–1506.Google Scholar
  53. 53.
    McClintock F.: A criterion for ductile fracture by the growth of holes, J. of Applied Mechanics, (1968).Google Scholar
  54. 54.
    Rice J.R. and Tracey D.M.: On the ductile enlargement of voids in triaxial stress fields, J. Mech. Phys. Sol., 17 (1969), pp. 201.CrossRefGoogle Scholar
  55. 55.
    Lemaître J.: How to use Damage Mechanics, Nuclear Engng and Design, 80 (1984), pp. 233–245.CrossRefGoogle Scholar
  56. 56.
    Rousselier G.: Finite deformation constitutive relations including ductile fracture damage, in: Three-Dimensional Constitutive Relations and Ductile Fracture (Edited by Nemat-Nasser), North-Holland Publ. Comp.,1981, 1980 pp. 331–355, dourdan.Google Scholar
  57. 57.
    Benallal A., Billardon R., Doghri I. and Moret-Bailly L.: Crack initiation and propagation analyses taking into account initial strain hardening and damage fields, in: Numerical Methods in Fracture Mechanics (Edited by L. et al.), Pineridge Press, 1987 pp. 337–351, san Antonio, Texas.Google Scholar
  58. 58.
    Skrzypek J.: Application of the orthotropic damage growth rule to variable principal directions, Int. J. Damage Mechanics, 7 (1998), pp. 180–206.CrossRefGoogle Scholar
  59. 59.
    Chaboche J.L. and Lesne P.M.: A non-linear continuous fatigue damage model, Fatigue and Fracture of Engineering Materials and Structures, 11 (1988), pp. 1–17.CrossRefGoogle Scholar
  60. 60.
    Gallerneau F.: Etude et modélisation de l’endommagement d’un superalliage monocristallin revêtu pour aube de turbine, Doctorat d’Université, École Nationale Supérieure des Mines de Paris, 1995.Google Scholar
  61. 61.
    Lesne P.M. and Cailletaud G.: Creep-fatigue interaction under high frequency loading, ICM5, 1987 Beijing, Chine.Google Scholar
  62. 62.
    Savalle S. and Cailletaud G.: Microamorçage, micropropagation et endommagement, La Rech. Aérospatiale, (1982), pp. 395–411.Google Scholar
  63. 63.
    Lesne P.M. and Savalle S.: A differential damage rule with microinitiation and micro-propagation, La Rech. Aérospatiale, (1987), pp. 33–47.Google Scholar
  64. 64.
    Benallal A., Billardon R. and Marquis D.: Prévision de l’amorçage et de la propagation des fissures par la mécanique de l’endommagement, Int. Spring Meeting “Fatigue at High Temperature”, 1986 Paris.Google Scholar
  65. 65.
    Savalle S. and Culié J.P.: Méthodes de calcul associées aux lois de comportement cyclique et d’endommagement, La Rech. Aérospatiale, (1978).Google Scholar
  66. 66.
    Lesne P.M. and Savalle S. An efficient “cycles jump technique” for viscoplastic structure calculations involving large number of cycles, 2nd Int. Conf. on “Computational Plasticity”, 1989 Barcelone.Google Scholar
  67. 67.
    Jr. J.C. Newman: Finite element analysis of fatigue crack propagation including the effecte of crack closure, Ph.d. thesis, VPLBlacksburg, 1974.Google Scholar
  68. 68.
    Anquez L. Elastoplastic crack propagation fatigue and failure, La Rech. Aérospatiale, (1983), pp. 15–39.Google Scholar
  69. 69.
    Kruch S., Chaboche J.L. and Prigent P.: A fracture mechanics based fatigue-creepenvironment crack growth model for high temperature, volume 59, 1994 pp. 141–148.Google Scholar
  70. 70.
    Devaux J.C. and Mottet G. Déchirure ductile des aciers faiblement alliés: modèles numériques, Rapport 79–057, Framatome, 1984.Google Scholar
  71. 71.
    Walker K.P. and Wilson D.A.: Constitutive modeling of engine materials, Report FR17911 (AFWAL-TR-84–4073), PWA, 1984.Google Scholar
  72. 72.
    Lemaître J.: Local approach of fracture, Engng. Fracture Mechanics, 25 (1986), pp. 523–537.CrossRefGoogle Scholar
  73. 73.
    Hayhurst D.R., Dimmer P.R. and Chernuka M.W.: Estimates of the creep rupture lifetime of structures using the finite element method, J. Mech. Phys. Sol., 23 (1975), pp. 335.CrossRefMATHGoogle Scholar
  74. 74.
    Saanouni K. and Lesne P.M.: Non-local damage model for creep crack growth prediction, 2nd MECAMAT Int. Seminar, “High Temperature Fracture Mechanisms and Mechanics”, Mech. Engineering Publications, 1987 Dourdan, France.Google Scholar
  75. 75.
    Liu Y., Murakami S. and Kanagawa Y.: Mesh dependence and stress singularity in finite element analysis of creep crack growth by Continuum Damage Mechanics approach, Eur. J. Mech., A/Solids, 13 (1994), pp. 395–417.MATHGoogle Scholar
  76. 76.
    Hall F.R., Hayhurst D.R. and Brown P.R.: Prediction of plane-strain creep crack growth using Continuum Damage Mechanics, Int. J. Damage Mechanics, 5 (1996), pp. 353–402.CrossRefGoogle Scholar
  77. 77.
    Rousselier G., Devaux J.C. and Mottet G.: Ductile initiation and crack growth in tensile specimens. Application of Continuum Damage Mechanics, SMIRT 8, 1985 Brussels.Google Scholar
  78. 78.
    Billardon R.: Fully coupled strain analysis of ductile fracture, 1st MECAMAT Int. Seminar on Local Approaches of Fracture, 1986 Moret-sur-Loing, France.Google Scholar
  79. 79.
    Bazant Z.P. and Belytschko T.: Localization and size effect, 2nd Int. Conf. on Constitutive Laws for Engineering Materials: Theory and Applications, Elsevier, 1987 Tucson.Google Scholar
  80. 80.
    Saanouni K., Chaboche J.L. and Lesne P.M.: On the creep crack growth prediction by a non local damage formulation, Eur. J. Mech., A/Solids, 8 (1989), pp. 437–459.MATHGoogle Scholar
  81. 81.
    Bazant Z.P. and Pijaudier-Cabot G.: Modeling of distributed damage by non local continuum with local straintrain hardening and damage fields, in: Numerical Methods in Fracture Mechanics (Edited by L. et al.), Pineridge Press, 1987 pp. 411–432, san Antonio, Texas.Google Scholar
  82. 82.
    Ladevèze P., Gasser A. and Allix O.: Damage mechanics modelling for ceramic composites, J. of Engng. Mat. Technol., 116(1994).Google Scholar
  83. 83.
    Ladevèze P.: A damage computational approach for composites: Basic aspects and micromechanical relations, Computational Mechanics, 17 (1995), pp. 142–150.CrossRefMATHGoogle Scholar
  84. 84.
    Saanouni K. and Lesne P.M.: Sur la description phénoménologique des déformations anélastiques dans les composites endommageables, C. R. Acad. Sci. Paris, t. 315 (1992), pp. 1165–1170.MATHGoogle Scholar
  85. 85.
    Maire J.F. and Chaboche J.L.: A new formulation of continuum Damage Mechanics for composite materials, Aerospace Science and Technology, 4 (1997), pp. 247–257.CrossRefGoogle Scholar
  86. 86.
    Maire J.F. and Lesne P.M.: A damage model for ceramic matrix composites, Aerospace Science and Technology, 4 (1997), pp. 259–266.CrossRefGoogle Scholar
  87. 87.
    Kruch S., Chaboche J.L. and Pottier T.: Two-scale viscoplastic and damage analysis of a metal matrix composite, in: Danmage and Interfacial Debonding in Composites (Edited by G. Voyiadjis and D. Allen ), Elsevier, 1996 pp. 45–55.CrossRefGoogle Scholar
  88. 88.
    Pottier T., Kruch S. and Chaboche J.L.: Analyse de l’endommagement macroscopique d’un composite à matrice métallique, JNC10, AMAC, 1996 pp. 1361–1371, paris.Google Scholar
  89. 89.
    Chaboche J.L., Lesné O. and Pottier T.: Continuum Damage Mechanics of composites: towards a unified approach, in: Damage Mechanics in Engineering Materials (Edited by G. Voyiadjis, J. Ju and J. Chaboche ), Elsevier Science B.V., 1998 pp. 3–26.CrossRefGoogle Scholar
  90. 90.
    Maire J.F. and Pacou D.: Essais de traction-compression-torsion sur tubes composites céramique-céramique, JNC10, AMAC, 1996 pp. 1225–1234, paris.Google Scholar
  91. 91.
    Legrand N., Rémy L., Dambrine B. and Molliex L.: Etude micromécanique de la fatigue oligocyclique d’un composite à matrice métallique base titane renforcé par des fibres unidirectionnelles de CiC, JNC10, AMAC, 1996 pp. 1349–1360, paris.Google Scholar
  92. 92.
    Chaboche J.L.: Damage induced anisotropy: on the difficulties associated with the active/passive unilateral condition, Int. J. Damage Mechanics, 1 (1992), pp. 148–171.CrossRefGoogle Scholar
  93. 93.
    Chaboche J.L.: Development of Continuum Damage Mechanics for elastic solids sustaining anisotropic and unilateral damage, Int. J. Damage Mechanics, 2 (1993), pp. 311–329.CrossRefGoogle Scholar
  94. 94.
    Curnier A., He Q. and Zysset P.: Conewise linear elastic materials, J. Elasticity, 37 (1995), pp. 1–38.CrossRefMATHMathSciNetGoogle Scholar
  95. 95.
    Halm D. and Dragon A.: A model of anisotropic damage by mesocrack growth–Unilateral effects, Int. J. Damage Mechanics, 5 (1996), pp. 384–402.CrossRefGoogle Scholar
  96. 96.
    Siquiera C.: Développement d’un essai biaxial sur plaques composites et utilisation pour la modélisation du comportement d’un matériau SMC, Doctorat d’Université, Université de Franche-Comté, 1993.Google Scholar

Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • J.-L. Chaboche
    • 1
  1. 1.Office National d’Etudes et de Recherches AérospatialesChâtillonFrance

Personalised recommendations