Creep Fracture: Creep Laws and Elementary Microscopic-Fracture Models

  • Dominique P. Miannay
Part of the Mechanical Engineering Series book series (MES)

Abstract

This chapter begins with some background on the theory of creep-flow behavior by dislocation motion, by defect motion, or by the combined effect of both. This elementary knowledge allows for the establishment of laws and rules of creep flow on a macroscopic scale. Then the application to a smooth body introduces the notions of skeletal-point and reference stresses.

Keywords

Fatigue Titanium Porosity Carbide Argon 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. J. Frost and M. F. Ashby. “Deformation-mechanism maps, The plasticity and creep of metals and ceramics,” Pergamon Press, Oxford, (1982).Google Scholar
  2. 2.
    W. D. Nix, J. C. Eartham, G. Eggeler and B. Ilschner. “The principal facet stress as a parameter for predicting rupture under multiaxial stresses,” Acta Metall., 37, 4, pp. 1067–1077 (1989).CrossRefGoogle Scholar
  3. 3.
    W. Beere. “Stress redistribution due to grain boundary sliding during creep,” Metal Science, 16, pp. 223–227 (1982).CrossRefGoogle Scholar
  4. 4.
    K. H. Hsia, D. M. Parks and A. S. Argon. “Effects of grain boundary sliding on creep-constrained boundary cavitation and creep deformation,” Mech. Mater., 11, pp. 43–62 (1991).CrossRefGoogle Scholar
  5. 5.
    P. M. Anderson and J. R. Rice. “Constrained creep cavitation of grain boundary facets,” Acta Metall., 33, pp. 409–422 (1985).CrossRefGoogle Scholar
  6. 6.
    G. J. Rodin. “Stress transmission in polycrystals with frictionless grain boundaries,” Trans. ASME, J. Appl. Mech., 62, pp. 1–6 (1995).MATHCrossRefGoogle Scholar
  7. 7.
    R. W. Evans and B. Wilshire. “Creep of metals and alloys,” Institute of Metals, London, (1985).Google Scholar
  8. 8.
    J. Lemaitre et J. L. Chaboche. “Mécanique des matériaux solides,” Dunod, Paris, 2ND edition (1988). “Mechanics of Solid Materials,” Cambridge University Press (1990).Google Scholar
  9. 9.
    G. A. Webster and R. A. Ainsworth. “High temperature component life assessment,” Chapman & aI., eds., London (1984).Google Scholar
  10. 10.
    M. F. Ashby and B. F. Dyson. “Creep damage mechanics and micromechanics,” in “Advances in fracture research-Proceedings of ICF6, Vol.1,” Valluri et al., eds., Pergamon Press, Oxford, pp. 3–30 (1984).Google Scholar
  11. 11.
    M. F. Ashby, C. Gandhi and D. M. R. Taplin. “Fracture-mechanisms maps and their construction for FCC metals and alloys,” Acta Metall., 27, pp. 699–729 (1979).CrossRefGoogle Scholar
  12. 12.
    C. Gandhi and M. F. Ashby. “Fracture-mechanism maps for materials which cleave: FCC, BCC and HCP metals and ceramics,” Acta Metall., 27, pp. 1565–1602 (1979).CrossRefGoogle Scholar
  13. 13.
    D. Miannay. “Fracture Mechanics,” Springer-Verlag, New York (1998).CrossRefGoogle Scholar
  14. 14.
    R. Raj and M. F. Ashby. “Intergranular fracture at elevated temperature,” Acta Metall., 23, pp. 653–656 (1975).CrossRefGoogle Scholar
  15. 15.
    H. C. Chang and N. J. Grant. “Mechanism of inter granular fracture,” Trans. AIME, 206, pp.544–551 (1956).Google Scholar
  16. 16.
    B. F. Dyson. “Continuous cavity nucleation and creep fracture,” Scripta Metall., 17, 1, pp. 31–37 (1983).CrossRefGoogle Scholar
  17. 17.
    A. S. Argon. “Mechanisms and mechanics of fracture in creeping alloys,” in “Recent advances in creep and fracture of engineering materials and structures,” Wilshire and Owen, eds., Pineridge Press, Swansea, UK, pp. 1–52 (1982).Google Scholar
  18. 18.
    A. C. F. Cocks and M. F. Ashby. “On creep fracture by void growth,” Progress in Mat. Sc., 27, pp. 189–244 (1982).CrossRefGoogle Scholar
  19. 19.
    V. Tvergaard. “Influence of grain boundary sliding on material failure in the tertiary creep range,” Int. J. Solids and Structures, 21,3, pp. 279–293 (1985).CrossRefGoogle Scholar
  20. 20.
    D. Hull and D. E. Rimmer. “The growth of grain-boundary voids under stress,” Phil. Mag., 4, pp. 673–689 (1959).CrossRefGoogle Scholar
  21. 21.
    A. Needleman and J. R. Rice. “Plastic creep flow effects in the diffusive cavitation of grain boundaries,” Acta Metall., 28, pp. 1315–1332 (1980).CrossRefGoogle Scholar
  22. 22.
    T. J. Chuang and J. R. Rice. “The shape of intergranular creep cracks growing by surface diffusion,” Acta Metall., 21, pp. 1625–1637 (1973).CrossRefGoogle Scholar
  23. 23.
    T. J. Chuang, K. I. Kagawa, J. R. Rice and L. B. Sills. “Non-equilibrium models for diffusive cavitation of grain interfaces,” Acta Metall., 27, pp. 265–284 (1979).CrossRefGoogle Scholar
  24. 24.
    A. C. F. Cocks and M. F. Ashby. “Intergranular fracture during power-law creep under multiaxial stresses,” Metal Sci., 14, pp. 395–402 (1980).CrossRefGoogle Scholar
  25. 25.
    E. Van der Giessen, M. W. D. Van der Burg, A. Needleman and V. Tvergaard. “Void growth due to creep and grain boundary diffusion at high triaxialities,” J. Mech. Phys. Solids, 43, 1, pp. 123–165 (1995).MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    B. Budianski, J. W. Hutchinson and S. Slutski. “Void growth and collapse in viscous solids,” in “Mechanics of solids: The Rodney Hill 60th anniversary volume,” Hopkins and Sewell, eds., Pergamon Press, Oxford, pp. 607–652 (1982).Google Scholar
  27. 27.
    H. M. Shih and H. H. Johnson. “A model calculation of the Nelson curves for hydrogen attack,” Acta Metall., 30, pp. 537–545 (1982).CrossRefGoogle Scholar
  28. 28.
    A. C. F. Cocks. “Inelastic deformation of porous materials,” J. Mech. Phys. Solids, 37,pp. 693–715 (1989).MATHCrossRefGoogle Scholar
  29. 29.
    P. Sofronis and R. M. McMeeking. “Creep of power-law material containing spherical voids,” Trans. ASME, J. Appl. Mech., pp. S88–S95 (1992).Google Scholar
  30. 30.
    W. D. Nix and J. C. Gibeling. “Flow and fracture at elevated temperature,” Raj, ed., Amcrican Society for Metals, pp. 1–63 (1983). aupoothaGoogle Scholar
  31. 31.
    W. Beere and M.V. Speight. “Creep cavitation by vacancy diffusion in plastically deforming solid,” Metall. Sci., 12, 172, pp. 172–176 (1978).Google Scholar
  32. 32.
    I.W. Chen and A.S. Argon. “Diffusive growth of grain boundaries cavities,” Acta Metall., 29, pp. 1759–1768 (1982).Google Scholar
  33. 33.
    T.L. Sham and A. Needleman. “Effects of triaxial stressing on creep cavitation of grain boundaries,” Acta Metall., 31, pp. 919–926 (1983).Google Scholar
  34. 34.
    B.F. Dyson. “Constrained on diffusional cavity growth rates,” Metall. Sci., 10, pp. 349–353 (1976).Google Scholar
  35. 35.
    H. Riedel. “Fracture at high temperatures,” Springer-Verlag (1987).Google Scholar
  36. 36.
    J.R. Rice. “Constraints on the diffusive cavitation of isolated grain boundary facets in creep polycrystals,” Acta Metall., 29, pp. 675–681 (1981).Google Scholar
  37. 37.
    J.W. Hutchinson. “Constitutive behavior and crack tip fields for materials undergoing creep-constrained grain boundary cavitation,” Acta Metall., 31, pp. 1079–1088 (1983).Google Scholar
  38. 38.
    M.Y. He and J.W. Hutchinson. “The penny-shaped crack and the plane strain crack in an infinite body of power-law material,” J. Appl. Mech., 48, pp. 830–840 (1981).Google Scholar
  39. 39.
    M.Y. He and J.W. Hutchinson. “Penny-shaped crack in a round bar of power-law hardening material,” in “Elastic-plastic fracture, Second Symposium, Vol. 1 Inelastic Crack Analysis, ASTM STP 803,” Shih and Gudas, eds., American Society for Testing and Materials, Philadelphia, pp. I–291–I–305 (1983).Google Scholar
  40. 40.
    K.H. Hsia, A.S. Argon and D.M. Parks. “Modeling of creep damage evolution around blunt notches and sharp cracks,” Mech. Mater., 11, pp. 19–42 (1991).Google Scholar
  41. 41.
    V. Tvergaard. “On the creep constrained diffusive cavitation of grain boundary facets,” J. Mech. Phys. Solids, 32, pp.373–393 (1984).Google Scholar
  42. 42.
    V. Tvergaard. “Analysis of creep crack growth by grain boundary cavitation,” Int. J. Fracture, 31, pp. 183–209 (1986).Google Scholar
  43. 43.
    V. Tvergaard. “Analysis of creep rupture in a notched tensile bar,” Mechanics of Materials, 4, pp. 181–196 (1985).Google Scholar
  44. 44.
    A.S. Argon. “Mechanics and mechanisms of fracture in creeping alloys,” in “Recent advances in creep and fracture of engineering materials and structures,” Wilshire and Owen, eds., Pineridge Press, Swansea, UK, pp. 1–52 (1982).Google Scholar
  45. 45.
    A.S. Argon, C.W. Lau, B. Özmat and D.M. Parks. “Creep crack growth in ductile materials,” in “Fundamentals of deformation and fracture,” Miller et al., eds., Cambridge University Press, pp. 189–243 (1985).Google Scholar
  46. 46.
    B. Özmat, A.S. Argon and D.M. Parks. “Growth modes of cracks in type 304 stainless steel,” Mech. Mater., 11,pp.1–19 (1991).Google Scholar
  47. 47.
    F.A. Leckie and D.R. Hayhurst. “Constitutive equations for creep rupture,” Acta Metall., 25, pp. 1059–1070 (1977).Google Scholar
  48. 48.
    J.B. Conway. “Stress rupture parameters: Origin, calculation and use,” Gordon and Breach, New York (1969).Google Scholar
  49. 49.
    F.C. Monkman and N.J. Grant. “An empirical relationship between rupture life and minimum creep rate in creep rupture tests,” Proc. Am. Soc. Testing Materials, 56, pp. 593–620 (1956).Google Scholar
  50. 50.
    J.E. Dom. “Mechanical behavior of materials at elevated temperatures,” McGrawHill Inc., New York (1961).Google Scholar
  51. 51.
    F.R. Larson and J. Miller. “A time-temperature relationship for rupture and creep stress,” Trans. ASME, 74, p. 765–775 (1952).Google Scholar
  52. 52.
    F.A. Leckie and D.R. Hayhurst. “Creep rupture of structures,” Proc. Roy. Soc. Lond. A, 340, pp. 323–347 (1974).Google Scholar
  53. 53.
    D.R. Hayhurst and F.A. Leckie. in “Mechanical Behavior of materials, Proceedings of ICM 4,” Vol. 2, Carlsson and Ohlson, eds., Pergamon Press, Oxford, pp. 1195–1212 (1984).Google Scholar
  54. 54.
    W.D. Nix, J.c. Eartham, G.Eggeler and B. Ilschner. “The principal facet stress as a parameter for predicting creep rupture under multiaxial stresses,” Acta Metall., 37,4, pp. 1066–1077 (1989).Google Scholar
  55. 55.
    W.D. Nix. “Grain boundary sliding and creep fracture of metals under multiaxial stresses,” in “Advances in Fracture Research, ICF 7, Vol. 2,” Salama et al., eds, Pergamon Press, pp. 1481–1493 (1989).Google Scholar
  56. 56.
    B. AI-Abed, R. Timmins, G.A. Webster and M.S. Loveday. “Validation of a code of practiced for notched bar creep rupture testing: procedures and interpretation of data for design,” Materials at High Temperatures, 16,3, pp. 143–158 (1999).Google Scholar
  57. 57.
    Piques and A. Pineau. “Global and local approaches to creep crack initiation and growth applied to an austenitic stainless steel and an aluminium alloy,” in “Advances in fracture research, Proceedings of ICF 7, Vol. 2,” Salama et al., eds, Pergamon Press, pp.1707–1714 (1989).Google Scholar
  58. 58.
    Yoshida, C. LevailIant, R. Piques and A. Pineau. “Quantitative study of intergranulardamage in an austenitic stainless steel on smooth and notched bars,” in “High temperature fracture mechanisms and mechanies, ESF 6,” Bensussan, ed., Mechanical Engineering Publications, London, pp. 3–21 (1990).Google Scholar
  59. 59.
    L. Robinson. “Effect of temperature variation on the long-time rupture strength of steels,” Trans. Am. Inst. Min. Engrs., 7A, pp 777–781 (1952).Google Scholar
  60. 60.
    K.G. Odqvist. “Mathematical theory of creep and creep rupture, 2nd edn.,” Clarendon Press, Oxford, Ch.12 (1974).Google Scholar
  61. 61.
    Yu N. Rabotnov. “Creep problems in structural members,” Leckie, ed., North Holland, Amsterdam (1969).Google Scholar
  62. 62.
    M. Kachanov. “Introduction to continuum damage mechanics,” Kluwer Academic Publishers, Dordrecht, Netherlands (1986).Google Scholar
  63. 63.
    F. Dyson and F.A. Leckie. “Damage equations for physically-based creep life,”in “Advances in Fracture Research-ICF 7,” Vol.3, Salama et al, eds., Pergamon Press, pp. 2169–2176 (1989).Google Scholar
  64. 64.
    D.R. Hayhurst, P.R. Dimmer and C.J. Morrison. “Development of continuum damage in the creep rupture of notched bars,” Phil. Trans. R. Soc. (London), A 311, pp. 103–129 (1984).Google Scholar
  65. 65.
    Hayhurst, P. R. Brown and C. J. Morrison. “The role of continuum damage in creep crack growth,” Phil. Trans. R. Soc. (London), A 311, pp. 131–158 (1984).CrossRefGoogle Scholar
  66. 66.
    J. Le Ber, V. Cotoni, J. Nicolas and C. Sainte-Catherine. “IDENT lD-A novel software tool for an easy identification of material constitutive parameters,” Nuclear Engng. and Design, 186, pp. 343–352 (1998).CrossRefGoogle Scholar
  67. 67.
    G. J. Rodin and D. M. Parks. “On consistency relations in nonlinear fracture mechanics,” J. Appl. Mech., 108, pp. 834–838 (1986).CrossRefGoogle Scholar
  68. 68.
    G. J. Rodin and D. M. Parks. “Constitutive models of a power-law matrix containing aligned penny-shaped cracks,” Mech. Mater., 5, pp. 221–228 (1986).CrossRefGoogle Scholar
  69. 69.
    G. J. Rodin and D. M. Parks. “A self consistent analysis of a creeping matrix with aligned cracks,” J. Mech. Phys. Solids, 36, 2, pp. 237–249 (1988).MATHCrossRefGoogle Scholar
  70. 70.
    D. M. Parks. “Mechanics and mechanisms of creep deformation and damage,” Nucl. Engng. and Design, 105, pp. 11–18 (1987).CrossRefGoogle Scholar
  71. 71.
    M. Sester, R. Mohrmann and H. Riedel. “A micromechanical model for creep damage and its application to crack growth in a 12% Cr steel,” in “Elevated temperature effects on fatigue and fracture, ASTM, STP 1297,” Piascik, Gangloff, and Saxena, eds., American Society for Testing and Materials, pp. 37–53 (1997).Google Scholar
  72. 72.
    V. Tvergaard. “On the creep constraint diffusive cavitation of grain boundary facets,” J. Mech. Phys. Solids, 33, pp. 447–469 (1985).MATHCrossRefGoogle Scholar
  73. 73.
    M. Capano, A. S. Argon and I. W. Chen. “Intergranular cavitation during creep in Astroloy,” Acta Metall., 37, pp. 3195–(1989).Google Scholar
  74. 74.
    A.S. Argon, K. J. Hsia and D. M. Parks. “Growth of cracks by intergranular cavitation in creep,” in “Topics in Fracture and Fatigue,” Argon, ed., Springer-Verlag, NY, pp. 234–270 (1992).CrossRefGoogle Scholar
  75. 75.
    A. Chakraborty and J. C. Earthman. “Numerical models of creep cavitation in single phase, dual phase and fully lamellar titanium aluminide,” Acta Mater., 45, 11, pp. 4615–4626 (1997).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Dominique P. Miannay
    • 1
  1. 1.Departement d’Evaluation de SureteInstitut de Protection et de Surete NucleaireFrance

Personalised recommendations