On the Extension of Creep-Damage Theories for Isotropic Materials to the Case of Anisotropic Materials

Conference paper
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 9)


For many applications the isotropic creep-damage description of the material behaviour at elevated temperatures, but moderate and approximately constant loading conditions is accurate enough for the life-time estimation and the prediction of the macroscopic failure initiation. In contrast, from tests it is known that for various materials the creepdamage process is anisotropic from the beginning even in the case of initially isotropic materials. Due to this fact anisotropic creep-damage models must be developed.

Various possibilities of the extension isotropic creep-damage models to the case of anisotropic materials are presented in the literature. Firstly, the extension of the classical Kachanov-Rabotnov concept will be introduced. This model can be used if the material behaviour is the same for tensile and compressive loading states. Since some materials show a behaviour depending on the stress state so-called non-classical models can be formulated. The second part is devoted to other concepts in anisotropic creep-damage modelling.


Anisotropic creep damage induced anisotropy stress-state dependent material behaviour 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Altenbach, H. (1999a). Classical and nonclassical creep models, in H. Altenbach and J. Skrzypek (eds), Creep and Damage in Materials and Structures, Springer, Wien, New York, pp. 45–95. CISM Lecture Notes No. 399.Google Scholar
  2. Altenbach, H. (1999b). Creep-damage behaviour of plates and shells, Mech. Time-Dependent Mat. 3: 102–123.Google Scholar
  3. Altenbach, H. (2001a). Consideration of stress state influences in the material modelling of creep and damage, in S. Murakami and N. Ohno (eds), IUTAM Symposium on Creep in Structures, Kluwer, Dordrecht, pp. 141–150.Google Scholar
  4. Altenbach, H. (2001b). A generalized limit criterion with application to strength, yielding, and damage of isotropic materials, in J. Lemaitre (ed.), Handbook of Materials Behavior Models, Academic Press, San Diego, pp. 175–186.CrossRefGoogle Scholar
  5. Altenbach, H. (2002). Creep analysis of thin-walled structures, ZAMM 82(8): 507–533.MathSciNetzbMATHCrossRefGoogle Scholar
  6. Altenbach, H., Altenbach, J. and SchieBe, P. (1990). Konzepte der Schadigungsmechanik und ihre Anwendung bei der werkstoffmechanischen Bauteilanalyse, Techn. Mech. 11(2): 81–93.Google Scholar
  7. Altenbach, H., Altenbach, J. and Zolochevsky, A. (1995). Erweiterte Deformationsmodelle und Versagenskriterien der Werkstoffmechanik, Deutscher Verlag fur Grundstoffindustrie, Stuttgart.Google Scholar
  8. Altenbach, H. and Blumenauer, H. (1989). Grundlagen und Anwendungen der Schadigungsmechanik, Neue Hiitte 34(6): 214–219.Google Scholar
  9. Altenbach, H., Dankert, M. and Zolocevskij, A. (1990). Anisotrope mathematisch mechanische Modelle fur Werkstoffe mit von der Belastung abhangigen Eigenschaften, Techn. Mech. 11(1): 5–13.Google Scholar
  10. Altenbach, H., Huang, C. X. and Naumenko, K. (2001). Modelling of the creep-damage under the reversed stress states by considering damage activation and deactivation, Techn. Mech. 24(4): 273–282.Google Scholar
  11. Altenbach, H., Huang, C. X. and Naumenko, K. (2002). Creep-damage predictions in thin-walled structures by use of isotropic and anisotropic damage models, J. Strain Anal. 37(3): 265–275.CrossRefGoogle Scholar
  12. Altenbach, H., Morachkovsky, O., Naumenko, K. and Sychov, A. (1997). Geometrically nonlinear bending of thin-walled shells and plates under creep-damage conditions, Arch. Appl. Mech. 67: 339–352.zbMATHCrossRefGoogle Scholar
  13. Altenbach, H., SchieBe, P. and Zolochevsky, A. A. (1991). Zum Kriechen isotroper Werk-stoffe mit komplizierten Eigenschaften, Rheol. Acta 30: 388–399.CrossRefGoogle Scholar
  14. Altenbach, H. and Zolochevsky, A. (1991). Kriechen diinner Schalen aus anisotropen Werkstoffen mit unterschiedlichem Zug-Druck-Verhalten, Forschung im Ingenieurwe-sen 57(6): 172–179.CrossRefGoogle Scholar
  15. Altenbach, H. and Zolochevsky, A. (1996). A generalized failure criterion for three-dimen­sional behaviour of isotropic materials, Eng. Fracture Mech. 54(1): 75–90.CrossRefGoogle Scholar
  16. Altenbach, H. and Zolochevsky, A. A. (1994). Eine energetische Variante der Theorie des Kriechens und der Langzeitfestigkeit fiir isotrope Werkstoffe mit komplizierten Eigen­schaften, ZAMM 74(3): 189–199.zbMATHCrossRefGoogle Scholar
  17. Altenbach, H. and Zolocevskij, A. (1992). Zur Anwendung gemischter Invarianten bei der Formulierung konstitutiver Beziehungen für geschadigte anisotrope Kontinua, ZAMM 72(8): 375–377.zbMATHCrossRefGoogle Scholar
  18. Altenbach, J. and Altenbach, H. (1994). EinfUhrung in die Kontinuumsmechanik, Teubner Studienbücher Mechanik, Teubner, Stuttgart.Google Scholar
  19. Avula, X. (1987). Mathematical modelling, Encyclopedia Phys. Sci. Tech. 7: 719–728.Google Scholar
  20. Backhaus, G. (1983). Deformations gesetze, Akademie-Verlag, Berlin.Google Scholar
  21. Bassani, J. L. and Hawk, D. E. (1990). Influence of damage on crack-tip fields under small-scale-creep conditions, Int. J. Fracture 42: 157–172.CrossRefGoogle Scholar
  22. Bertram, A. (1993). What is the general constitutive equation?, in A. Cassius, G. Godert, U. Gorn, R. Parchem and J. Villwock (eds), Beitrage zur Mechanik: Festschrift zum 65. Geburtstag Rudolf Trostel, TU Berlin, Berlin, pp. 28–37.Google Scholar
  23. Betten, J. (1982). Zur Aufstellung einer Integritatsbasis fiir Tensoren zweiter und vierter Stufe, ZAMM 62(5): T274–T275.MathSciNetzbMATHGoogle Scholar
  24. Betten, J. (1993). Kontinuumsmechanik, Springer-Verlag, Berlin, Heidelberg, New York.zbMATHGoogle Scholar
  25. Betten, J. (1998). Anwendungen von Tensorfunktionen in der Kontinuumsmechanik anisotroper Materialien, ZAMM 78(8): 507–521.MathSciNetzbMATHCrossRefGoogle Scholar
  26. Betten, J. (2001). Mathematical modelling of materials behaviour under creep condition, Appl. Mech. Rev. 54(2): 107–132.MathSciNetCrossRefGoogle Scholar
  27. Betten, J. (2002). Creep Mechanics, Springer-Verlag, Berlin, Heidelberg, New York.Google Scholar
  28. Betten, J., El-Magd, E., Meydanli, S. C. and Palmen, P. (1995). Untersuchnung des anisotropen Kriechverhaltens vorgeschadigter Werkstoffe am austenitischen Stahl X8CrNiMoNb 1616, Arch. Appl. Mech. 65: 121–132.CrossRefGoogle Scholar
  29. Billington, E. W. (1985). The Poynting-Swift effect in relation to initial and post-yield defor­mation, Int. J. Solids Struct. 21(4): 355–372.zbMATHCrossRefGoogle Scholar
  30. Bodnar, A. and Chrzanowski, M. (1991). A non-unilateral damage in creeping plates, in M. Życzkowski (ed.), Creep in Structures, Springer, Berlin, Heidelberg, pp. 287–293.CrossRefGoogle Scholar
  31. Boyle, J. T. and Spence, J. (1983). Stress Analysis for Creep, Butterworth, London.zbMATHGoogle Scholar
  32. Cane, B. J. (1981). Creep fracture of dispersion strengthened low alloy ferritic steels, Acta Metall. 29: 1581–1591.CrossRefGoogle Scholar
  33. Chen, W. F. and Zhang, H. (1991). Structural Plasticity, Springer-Verlag, Berlin, Heidelberg, New York.CrossRefGoogle Scholar
  34. da C. Andrade, E. N. (1910). On the viscous flow of metals, and allied phenomena, Proc. Royal Soc. London ALXXXIV: 1–12.Google Scholar
  35. Dyson, B. F. (1992). Material data requirements, creep damage machanisms, and predictive models, in L. H. Larson (ed.), High Temperature Structural Design, Mechanical Engineering Publications, London, pp. 335–354.Google Scholar
  36. El-Magd, E., Betten, J. and Palmen, P. (1996). Auswirkung der Schadigungsanisotropie auf die Lebensdauer von Stahlen bei Zeitstandbeanspruchung, Mat.-wiss. u. Werkstofftechn. 27: 239–245.CrossRefGoogle Scholar
  37. Finnie, I. and Heller, W. R. (1959). Creep of Engineering Materials, McGraw-Hill, New York.Google Scholar
  38. Gorev, B. V., Rubanov, V. V. and Sosnin, O. V. (1979). O postroenii uravnenii polzuchesti dlya materialov s raznymi svoistvami na rastyazhenie i szhatie (On the formulation of creep equations for materials with different properties in tension and compression, in russ.), Zhurnalprikladnoi mekhaniki i tekhnicheskoi fiziki (4): 121–128.Google Scholar
  39. Haupt, P. (2000). Continuum Mechanics and Theory of Materials, Springer- Verlag, Berlin, Heidelberg, New York.zbMATHGoogle Scholar
  40. Hyde, T. H., Sun, W. and Becker, A. A. (2000). Failure prediction for multi-material creep test specimens using steady-state creep rupture stress, Int. J. Mech. Sci. 42: 401–23.zbMATHCrossRefGoogle Scholar
  41. Hyde, T. H., Sun, W., Becker, A. A. and Williams, J. A. (1997). Creep continuum damage constitutive equations for the base, weld and heat-affected zone materials of a service-aged l/2Crl/2Mol/4V:2 l/4CrlMo multipass weld at 640°C, J. Strain Anal. 32(4): 273–285.CrossRefGoogle Scholar
  42. Hyde, T. H., Sun, W. and Tang, A. (1998). Determination of material constants in creep continuum damage constitutive equations, Strain 34(August): 83–90.CrossRefGoogle Scholar
  43. Hyde, T. H., Sun, W. and Williams, J. A. (1999). Prediction of failure life of internally pressurised thick walled crmov pipes, Int. J. Pressure Vessel & Piping 76: 925–933.CrossRefGoogle Scholar
  44. Johnson, A. E. and Frost, N. E. (1951). Fracture under combined stress creep conditions of 0.5% molybdenum steel, Engineer 191: 434.Google Scholar
  45. Kerr, D. C, Staubli, M., Nazmy, M., Nikbin, K. M. and Webster, G. A. (1997). Effects of the state of stress on the tensile and creep properties of 7-T1AI, J. Strain Anal. 32(2): 97–105.CrossRefGoogle Scholar
  46. Konkin, V. N. and Morachkovskij, O. K. (1987). Polzuchest’ i dlitel’naya prochnost’ legkikh splavov, proyavlyayushchikh anizotropnye svoistva (Creep and long-term strength of light alloys with anisotropic properties, in russ.), Probl. Prochnosti (5): 38–12.Google Scholar
  47. Kowalewski, Z. L. (1996). Creep rupture of copper under complex stress state at elevated temperature, Design and life assessment at high temperature, Mechanical Engineering Publ., London, pp. 113–122.Google Scholar
  48. Kowalewski, Z. L., Hayhurst, D. R. and Dyson, B. F. (1994). Mechanisms-based creep con­stitutive equations for an aluminium alloy, J. Strain Anal. 29(4): 309–316.CrossRefGoogle Scholar
  49. Krajcinovic, D. (1996). Damage Mechanics, Applied Mathematics and Mechanics Vol. 41, North-Holland, Amsterdam.Google Scholar
  50. Lemaitre, J. (1996). A Course on Damage Mechanics, Springer-Verlag, Berlin, Heidelberg, New York.zbMATHCrossRefGoogle Scholar
  51. Liu, Y. and Murakami, S. (1998). Damage localization of conventional creep damage models and proposition of a new model for creep damage analysis, JSME Int. J. 41: 57–65.CrossRefGoogle Scholar
  52. Malinin, N. N. (1981). Raschet na polzuchesf konstrukcionnykh elementov (Creep calcula­tions of structural elements), Mashinostroenie, Moskva, (in Russian).Google Scholar
  53. Murakami, S. (1983). Notion of continuum damage mechanics and its application to aniso­tropic creep damage theory, ASME J. Engng. Mat. Tech. 105: 99–105.CrossRefGoogle Scholar
  54. Murakami, S. and Ohno, N. (1981). A continuum theory of creep and creep damage, in A. R. S. Ponter and D. R. Hayhurst (eds), Creep in Structures, Springer, Berlin, pp. 422–444.CrossRefGoogle Scholar
  55. Murakami, S. and Sanomura, Y. (1985). Creep and creep damage of copper under multi-axial states of stress, in A. Sawczuk and B. Bianchi (eds), Plasticity Today-Modelling, Methods and Applications, Elsevier, London, New York, pp. 535–551.Google Scholar
  56. Murakami, S., Sanomura, Y. and Hattori, M. (1986). Modelling of the coupled effect of plastic damage and creep damage in Nimonic 80A, Int. J. Solids Struct. 22(4): 373–386.CrossRefGoogle Scholar
  57. Odqvist, F. K. G. and Hult, J. (1962). Kriechfestigkeit metallischer Werkstoffe, Springer-Verlag, Berlin, Heidelberg, New York.Google Scholar
  58. Othman, A. M., Dyson, B. F., Hayhurst, D. R. and Lin, J. (1994). Continuum damage me­chanics modelling of circumferentially notched tension bars undergoing tertiary creep with physically-based constitutive equations, Acta Metall. Mater. 42(3): 597–611.CrossRefGoogle Scholar
  59. Othman, A. M., Hayhurst, D. R. and Dyson, B. F. (1993). Skeletal point stresses in circumfer­entially notched tension bars undergoing tertiary creep modelled with physically-based constitutive equations, Proc. Royal Soc. London A441: 343–358.Google Scholar
  60. Penny, R. K. and Mariott, D. L. (1995). Design for Creep, Chapman & Hall, London.CrossRefGoogle Scholar
  61. Perrin, I. J. and Hayhurst, D. R. (1994). Creep constitutive equations for a 0.5Cr-0.5Mo-0.25V ferritic steel in the temperature range 600–675°C, J. Strain Anal. 31(4): 299–314.CrossRefGoogle Scholar
  62. Plewa, M. and Osipiuk, W. (1998). Creep of tubular test pieces in a complex state of stress, Int. J. Pressure Vessel & Piping 75: 63–66.CrossRefGoogle Scholar
  63. Qi, W. and Bertram, A. (1998). Damage modeling of the single crystal superalloy srr99 under monotonous creep, Comp. Mater. Sci. 13: 132–141.zbMATHCrossRefGoogle Scholar
  64. Qi, W. and Bertram, A. (1999). Anisotropic continuum damage modeling for single crystals at high temperatures, Int. J. of Plasticity 15: 1197–1215.zbMATHCrossRefGoogle Scholar
  65. Rabotnov, Y N. (1969). Creep Problems in Structural Members, North-Holland, Amsterdam.zbMATHGoogle Scholar
  66. Rodin, G. J. and Parks, D. M. (1986). Constitutive models of a power-law matrix containing aligned penny-shaped cracks, Mech. Mater. 5: 221–228.CrossRefGoogle Scholar
  67. Saanouni, K., Chaboche, J. L. and Lense, P. M. (1989). On the creep crack-growth prediction by a non-local damage formulation, European J. of Mech., A/Solids 8(6): 437–459.zbMATHGoogle Scholar
  68. Sdobyrev, V. P. (1959). Kriterij dlitel’noj prochnosti dlya nekotorykh zharoprochnykh splavov pri slozhnom napryazhennom sostoyanii (Criterion of long term strength of some high-temperature alloys under multiaxial stress state, in russ.), Izv. AN SSSR. Otd. tekh. nauk. MM (6): 93–99.Google Scholar
  69. Skrzypek, J. J. (1993). Plasticity and Creep, CRC Press, Boca Raton.zbMATHGoogle Scholar
  70. Skrzypek, J. and Ganczarski, A. (1998). Modelling of Material Damage and Failure of Structures, Foundation of Engineering Mechanics, Springer-Verlag, Berlin, Heidelberg, New York.Google Scholar
  71. Sluzalec, A. (1992). Introduction to Nonlinear Thermomechanics, Springer-Verlag, Berlin, Heidelberg, New York.zbMATHCrossRefGoogle Scholar
  72. Sosnin, O. V. (1974). Energeticheskii variant teorii polzuchesti i dlitel’noi prochnosti. Polzuchest’ i razrushenie neuprochnyayushikhsya materialov (Energetic variant of the creep and long-term strength theories. Creep and fracture of nonhardening materials, in russ.), Probl. Prochnosti (5): 45–9.Google Scholar
  73. Sosnin, O. V., Gorev, B. V. and Nikitenko, A. F. (1986). Energeticheskii variant teorii polzuchesti (Energetic variant of the creep theory), Institut Gidrodinamiki, Novosibirsk. (in Russian).Google Scholar
  74. Trunin, I. I. (1965). Kriterii prochnosti v usloviyakh polzuchesti pri slozhnom napryazhennom sostoyanii (Failure criteria under creep conditions in multiaxial stress state, in russ.), Prik. Mekhanika 1(7): 77–83.Google Scholar
  75. von Mises, R. (1928). Mechanik der plastischen Formanderung von Kristallen, ZAMM 8(3): 161–185.zbMATHCrossRefGoogle Scholar
  76. Życzkowski, M. (1981). Combined Loadings in the Theory of Plasticity, PWN-Polish Scientific Publisher, Warszawa.zbMATHGoogle Scholar
  77. Życzkowski, M. (2000). Creep damage evolution equations expressed in terms of dissipated power, Int.J.Mech. Sci. 42: 755–769.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Lehrstuhl für Technische Mechanik, Fachbereich IngenieurwissenschaftenMartin-Luther-Universität Halle-WittenbergGermany

Personalised recommendations