Skip to main content

Abstract

In this chapter we will first present a synopsis of the theoretical foundation of linear and nonlinear fracture mechanics. In recent years a number of monographs, textbooks and conference proceedings have been published on the subject of fracture mechanics (see for example [1–10] where further references are listed). Our objective is not to present a review of these works, but to provide sufficient background so that the treatment of crack growth — the main objective of this chapter — can be followed with relative ease. In pursuing this objective we have been heavily influenced by general articles and book chapters by Rice [11, 12] and Hutchinson [13, 14]. In particular, Hutchinson’s booklet [15] provides a remarkably concise but full treatment of nonlinear fracture mechanics. Since some aspects of nonlinear fracture mechanics are a straightforward generalization of linear elastic fracture mechanics (LEFM) we will begin this chapter with a brief summary of the foundation of LEFM. No attempt is made to give either a historical account of earlier contributions, or to provide a guide to the existing comprehensive literature. (An interested reader could consult some of the major works such as Liebowitz’s Advanced Treatise on Fracture in seven volumes [1], or more recent monographs and review articles [4, 8–10].)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Liebowitz, H. (ed.) (1968) Fracture-Advanced Treatise in 7 volumes, Academic Press, New York.

    Google Scholar 

  2. Tada, H., Paris, P. and Irwin, G. (1973) The Stress Analysis of Cracks Handbook, Del Research Corporation, Hellertown, PA.

    Google Scholar 

  3. Sih, G.C. (1973) Handbook of Stress-Intensity Factors for Researchers and Engineers, Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, PA.

    Google Scholar 

  4. Erdogan, F. (1983) Stress intensity factors. J. Appl. Mech., Trans. ASME, 50th anniversary issue, 103, 992–1002.

    Article  Google Scholar 

  5. Barsom, J.M. and Rolfe, S.T. (1987) Fracture and Fatigue Control in Structures, 2nd edn, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  6. Knott, J.F. (1973) Fundamentals of Fracture Mechanics, Butterworths, London.

    Google Scholar 

  7. Broek, D. (1986) Elementary Engineering Fracture Mechanics, 4th revised edn, Martinus Nijhoff, Dordrecht, Netherlands.

    Google Scholar 

  8. Kanninen, M.F. and Popelar, C.H. (1985) Advanced Fracture Mechanics, Oxford University Press, New York.

    MATH  Google Scholar 

  9. Shih, C.F. and Gudas, J.P. (eds) (1983) Elastic-Plastic Fracture: Second Symposium, in two volumes, ASTM STP 803, American Society for Testing and Materials, Philadelphia, PA.

    Google Scholar 

  10. Anderson, T.L. (1991) Fracture Mechanics: Fundamentals and Applications, CRC Press, Boca Raton, FL.

    Google Scholar 

  11. Rice, J.R. (1967) Mechanics of crack tip deformation and extension by fatigue, in Fatigue Crack Propagation, ASTM STP 415, American Society for Testing and Materials, Philadelphia, PA, pp. 247–311.

    Google Scholar 

  12. Rice, J.R. (1968) Mathematical analysis in the mechanics of fracture, in Fracture, vol. 2, Mechanical Fundamentals (ed. H. Liebowitz), Academic Press, New York, pp. 191–311.

    Google Scholar 

  13. Hutchinson, J.W. (1979) Recent Developments in Nonlinear Fracture Mechanics. Proc. 7th Canadian Cong, of Appl. Mech., Sherbrooke, PQ, vol. 1 (eds F. Ellyin and K.W. Neale), pp. 24–36.

    Google Scholar 

  14. Hutchinson, J.W. (1983) Fundamentals of the phenomenological theory of nonlinear fracture mechanics. J. Appl. Mech., Trans. ASME, 50th anniversary issue, 103, 1042–51.

    Article  Google Scholar 

  15. Hutchinson, J.W. (1979) Nonlinear Fracture Mechanics, Dept. of Solid Mechanics, Tech. Univ. of Denmark, Lyngby, Denmark.

    Google Scholar 

  16. Muskhelishvili, N.I. (1953) Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff, Holland.

    MATH  Google Scholar 

  17. Irwin, G.R. (1960) Fracture Mechanics, in Structural Mechanics (Proc. 1st Symp. Naval Struct. Mech., 1958) (eds J.N. Goodier and N.J. Hoff), Pergamon Press, New York, pp. 557–91.

    Google Scholar 

  18. Paris, P.C. and Erdogan, F. (1963) A critical analysis of crack propagation laws. J. Basic Engng., Trans. ASME, 85, 528–34.

    Google Scholar 

  19. Barenblatt, G.I. (1962) Mathematical theory of equilibrium cracks in brittle fracture, in Advances in Applied Mathematics, Vol. VII, Academic Press, New York, pp. 55–129.

    Google Scholar 

  20. Dugdale, D.S. (1960) Yielding of steel sheets containing slits. J. Mech. Phys. Solids, 8, 100–4.

    Article  Google Scholar 

  21. Goodier, J.N. (1968) Mathematical theory of equilibrium cracks, in Fracture vol. 2 (ed. H. Liebowitz), Academic Press, New York, pp. 1–66.

    Google Scholar 

  22. Rice, J.R. (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech., Trans. ASME, 35, 379–86.

    Google Scholar 

  23. Hutchinson, J.W. (1968) Singular behaviour at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids, 16, 13–31.

    Article  MATH  Google Scholar 

  24. Rice, J.R. and Rosengren, G.F. (1968) Plain-strain deformation near a crack tip in a power-law hardening material. J. Mech. Phys. Solids, 16, 1–12.

    Article  MATH  Google Scholar 

  25. Huit, J.A. and McClintock, F.A. (1956) Elastic-Plastic Stress and Strain Distribution Around Sharp Notches Under Repeated Shear. Proc. 9th Int. Congr. of Appl. Mech., Brussels, Vol. 8, pp. 51–8.

    Google Scholar 

  26. Rice, J.R. (1967) Stresses due to a sharp notch in a work-hardening elasticplastic material loaded by longitudinal shear. J. Appl. Mech., Trans. ASME, 34, 287–98.

    Google Scholar 

  27. McClintock, F.A. (1961) Discussion of fracture testing of high strength sheet materials. Mater. Res. Standards, 1, 277–9.

    Google Scholar 

  28. Kujawski, D. and Ellyin, F. (1986) On the size of plastic zone ahead of a crack-tip. Engng. Fract. Mech., 25, Elsevier Science Ltd, Oxford, 229–36.

    Google Scholar 

  29. Ellyin, F. (1986) Crack growth rate under cyclic loading and effect of different singularity fields. Engng. Fract. Mech., 25, Elsevier Science Ltd, Oxford, 463–73.

    Google Scholar 

  30. Shih, C.F. and German, M.D. (1981) Requirements for a one parameter characterization of crack-tip field by HRR singularity. Int. J. Fract., 17, 27–43.

    Google Scholar 

  31. Irwin, G.R. (1960) Plastic Zone Near a Crack and Fracture Toughness. Proc. 7th Sagamore Ordnance Materials Conf., Syracuse Univ., New York, Vol. IV, pp. 63–78.

    Google Scholar 

  32. Lies, B.N., Brust, F.W. and Scott, P.M. (1991) Development and Validation of a Ductile Flaw Growth Analysis for Gas Transmission Line Pipe. Report to the American Gas Association (AGA) NG-18 Report No. 193, Bettle Memorial Institute, Columbus, OH, June 1991.

    Google Scholar 

  33. American Society for Testing and Materials (1973) Fracture Toughness Evaluation by R-Curve Methods, ASTM STP 527, Philadelphia, PA.

    Google Scholar 

  34. Paris, P.C., Tada, H., Zahoor, A. and Ernst, H. (1979) Instability of the Tearing Modulus of Elastic-Plastic Crack Growth in Elastic-Plastic Fracture, ASTM STP 668 (eds J.D. Landes et al.), American Society for Testing and Materials, Philadelphia, PA, pp. 5–36.

    Chapter  Google Scholar 

  35. Rice, J.R., McMeeking, R.M., Parks, D.M. and Sorensen, E.P. (1979) Recent finite element studies in plasticity and fracture mechanics. Computer Methods in Appl. Mech. and Engng., 17/18, 411–42.

    Article  Google Scholar 

  36. Shih, CF. (1981) Relationships between the J-integral and the crack opening displacement for stationary and extending cracks. J. Mech. Phys. Solids, 29, 305–26.

    Article  MATH  Google Scholar 

  37. Kitagawa, H. and Takahashi, S. (1976) Applicability of Fracture Mechanics to Very Small Cracks. Proc. Int. Conf. Mech. Behaviour of Materials (ICM2), Amer. Soc. Metals, pp. 627–31.

    Google Scholar 

  38. Miller, K.J. (1987) The behaviour of short fatigue cracks and their initiation, Part I-A review of two recent books, and Part II-A general summary. Fatigue Fract. Engng. Mater. Struct., 10, 73–113.

    Google Scholar 

  39. Schijve, J. (1988) Fatigue crack closure: Observations and technical significance, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C. Newman and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 5–34.

    Chapter  Google Scholar 

  40. Topper, T.H., Yu, M.T. and DuQuesnay, D.L. (1988) Mechanics and Mechanisms of Fatigue Crack Initiation and Growth. Proc. Int. Symp. on Fracture Mechanics (eds W.R. Tyson and M. Mukherjee), Pergamon Press, pp. 81–94.

    Google Scholar 

  41. Laird, C. and Smith, G.C. (1963) Initial stages of damage in high stress fatigue in some pure metals. Phil. Mag., 8, 1945–63.

    Article  Google Scholar 

  42. Neumann, P. (1974) New experiments concerning the slip processes at propagating fatigue cracks. Acta Metall, 22, 1155–65.

    Article  Google Scholar 

  43. McEvily, A.J. (1983) On the quantitative analysis of fatigue crack propagation, in Fatigue Mechanisms; Advances in Quantitative Measurement of Physical Damage, ASTM STP 811 (eds J. Lankford et al.), American Society for Testing and Materials, Philadelphia, PA, pp. 283–312.

    Chapter  Google Scholar 

  44. Baïlon, J.-P. and Antolovich, S.D. (1983) Effect of microstructure on fatigue crack propagation: A review of existing models and suggestions for further research, ASTM STP 811 (eds J. Lankford et al.), American Society for Testing and Materials, Philadelphia, PA, pp. 313–49.

    Google Scholar 

  45. Paris, P.C., Gomez, M.P. and Anderson, W.E. (1961) A rational analytical theory of fatigue, The Trend in Engineering, 13 (Univ. of Washington, Seattle, WA), 9–14.

    Google Scholar 

  46. Head, A.K. (1956) The propagation of fatigue cracks. J. Appl. Mech., Trans. ASME, 23, 407–10.

    MATH  Google Scholar 

  47. McClintock, F.A. (1963) On the plasticity of the growth of fatigue cracks, in Fracture of Solids (eds D.C. Drucker and J.J. Gilman). Interscience, New York, pp. 65–102.

    Google Scholar 

  48. Liu, H.W. (1964) Fatigue crack propagation and the stress and strain in vicinity of a crack. Appl. Mat. Res., 3 (4), 229–37.

    Google Scholar 

  49. Frost, N.E. and Dugdale, D.S. (1958) The propagation of fatigue cracks in sheet specimens. J. Mech. Phys. Solids, 6 (2), 92–110.

    Article  Google Scholar 

  50. Rice, J.R. (1965) Plastic Yielding at a Crack Tip. Proc. 1st Int. Conf. on Fracture, Sendai, Japan, part A-17, Japan Soc. for Strength and Fract. Mater., pp. 283–308.

    Google Scholar 

  51. Weertman, J. (1966) Rate of growth of fatigue cracks as calculated from the theory of dislocations distributed on a plane. Int. J. Fract., 2, 460–7.

    Article  Google Scholar 

  52. Ellyin, F. and Li, H.-P. (1984) Fatigue crack growth in large specimens with various stress ratios. J. Pressure Vessel Technol., Trans. ASME, 106 (3), 255–60.

    Article  Google Scholar 

  53. Weertman, J. (1979) Fatigue crack propagation theories, in Fatigue and Microstructure,, pp. 279–306.

    Google Scholar 

  54. Yokobori, T., Konosu, S. and Yokobori, A.T. Jr. (1977) Micro and Macro Fracture Mechanics Approach to Brittle Fracture and Fatigue Crack Growth. In Fracture 1977, Proc. ICF4, Waterloo, Canada, Vol.1 (ed. D.M.R. Taplin), Pergamon, pp. 665–81.

    Google Scholar 

  55. Yokobori, T. (1979) A critical evaluation of mathematical equations for fatigue crack growth with special reference to ferrite grain size and monotonic yield strength dependence, in Fatigue Mechanisms, ASTM STP 675 (ed. J.T. Fong), American Society for Testing and Materials, Philadelphia, PA, pp. 683–706.

    Chapter  Google Scholar 

  56. Kocanda, S. (1978) Fatigue Failure of Metals, Sijthoff and Noordhoff, Amsterdam.

    Google Scholar 

  57. Knott, J.F. (1986) Models of fatigue crack growth, in Fatigue Crack Growth-30 Years of Progress (ed. R.A. Smith), Pergamon Press, Oxford, pp. 31–52.

    Google Scholar 

  58. Blom, A.F. (1989) Modelling of fatigue crack growth, in Advances in Fatigue Science and Technology (eds C. Moura Branco and L. Guerra Rosa), Kluwer Academic, Dordrecht, Netherlands, pp. 77–110.

    Google Scholar 

  59. Davidson, D.L. and Lankford, J. (1992) Fatigue crack growth in metals and alloys: Mechanisms and micromechanics. Int. Mater. Rev., 37, 45–76.

    Google Scholar 

  60. Kujawski, D. and Ellyin, F. (1984) A fatigue crack propagation model. Engng. Fract. Mech., 20, 695–704.

    Article  Google Scholar 

  61. Chitaley, A.D. and McClintock, F.A. (1971) Elastic-plastic mechanics of steady crack growth under anti-plane shear. J. Mech. Phys. Solids, 14, 147–63.

    Article  Google Scholar 

  62. McMeeking, R.M. and Parks, D.M. (1979) On criteria for J-dominance of cracktip fields in L.S.Y., in Elastic-Plastic Fracture, ASTM STP 668 (eds J.D. Landes, J.A. Begley and G.A. Clarke), American Society for Testing and Materials, Philadelphia, PA, pp. 175–94.

    Chapter  Google Scholar 

  63. Lanteigne, J. and Bailon, J.-P. (1981) Theoretical model for FCGR near the threshold. Metall. Trans., 12A, 459–66.

    Google Scholar 

  64. Glinka, G. (1982) Cumulative model of fatigue crack growth. Int. J. Fatigue, 4, 59–67.

    Article  Google Scholar 

  65. Radon, J.C. (1982) A model for fatigue crack growth in a threshold region. Int. J. Fatigue, 4, 161–6.

    Article  Google Scholar 

  66. Fine, M.E. and Davidson, D.L. (1983) Quantitative measurement of energy associated with a moving fatigue crack, in Fatigue mechanisms: Advances in Quantitative Measurement of Physical Damage, ASTM STP 811 (eds. D.L. Davidson et al.), American Society for Testing and Materials, Philadelphia, PA, pp. 350–70.

    Chapter  Google Scholar 

  67. Ellyin, F. and Fakinlede, C.O.A. (1984) Crack-tip growth rate model for cyclic loading, in Modelling Problems in Crack Tip Mechanics (ed. J.T. Pindera), Martinus Nijhoff, Dordrecht, pp. 224–37.

    Google Scholar 

  68. McCartney, L.N. and Irving, P.E. (1977) Comment on a correlation for fatigue crack growth rate. Scripta Metall, 11, 181–3.

    Article  Google Scholar 

  69. Niccols, E.H. (1976) A correlation for fatigue crack growth rate. Scripta Metall, 10, 295–8.

    Article  Google Scholar 

  70. Tanaka, S., Ichikawa, M. and Akita, S. (1981) Variability of m and C in fatigue crack propagation law. Int. J. Fract., 17, R121–4.

    Article  Google Scholar 

  71. Boller, C.H.R. and Seeger, T. (1987) Materials Data for Cyclic Loading, Elsevier, Amsterdam.

    Google Scholar 

  72. Broberg, K.B. (1982) The foundation of fracture mechanics. Engng. Fract. Mech., 16, 497–515.

    Article  Google Scholar 

  73. Gurland, J. (1972) Correlation Between Yield Strength and Microstructure of some Carbon Steels in Stereology and Quantitative Metallography, ASTM STP 504, American Society for Testing and Materials, Philadelphia, PA, pp. 108–18.

    Google Scholar 

  74. Kirby, B.R. and Beevers, C.J. (1979) Slow fatigue crack growth and threshold behaviour in air and vacuum of commercial aluminum alloys. Fatigue Engng. Mater. Struct., 1, 203–15.

    Article  Google Scholar 

  75. Klesnil, M. and Lukas, P. (1972) Effect of stress cycle asymmetry on fatigue crack growth. Mater. Sci. Engng., 9, 231–40.

    Article  Google Scholar 

  76. Masounave, J. and Ballon, J.P. (1976) Effect of grain size on the threshold stress intensity factor in fatigue of a ferritic steel. Scripta Metall, 10, 165–70.

    Article  Google Scholar 

  77. Tanaka, K., Nakai, Y. and Yamashita, M. (1981) Fatigue growth threshold of small cracks. Int. J. Fract., 17, 519–33.

    Google Scholar 

  78. Masounave, J. and Baïlon, J.P. (1975) The dependence of the threshold stress intensity factor on the cyclic stress ratio of the fatigue of ferritic-perlitic steels. Scripta Metall, 9, pp. 723–30.

    Article  Google Scholar 

  79. Beevers, C.J. (1977) Fatigue crack growth characteristics at low stress intensities of metals and alloys. Metal Sci, 11, 362–7.

    Google Scholar 

  80. Ritchie, R.O. (1977) Influence of microstructure on near-threshold fatiguecrack propagation in ultra-high strength steel. Metal Sci., 11, 368–81.

    Article  Google Scholar 

  81. Ritchie, R.O. (1977) Near-threshold fatigue crack propagation in ultra-high strength steel: Influence of load ratio and cyclic strength. J. Engng. Mater. TechnoL, Trans. ASME, 99, 195–204.

    Article  Google Scholar 

  82. Usami, S. and Shida, S. (1979) Elastic-plastic analysis of the fatigue limit for a material with small flaws. Fatigue Engng. Mater. Struct., 1, 471–81.

    Article  Google Scholar 

  83. Stephens, R.I. et al. (1984) Constant and variable amplitude fatigue behaviour of five cast steels at room temperature and — 45°C. J. Engng. Mater. TechnoL, Trans. ASME, 106, 25–37.

    Article  Google Scholar 

  84. Staal, H. V. and Elen, J.D. (1979) Crack closure and influence of cyclic ratio R on fatigue crack growth in type 304 stainless steel at room temperature. Engng. Fract. Mech., 11, 275–83.

    Article  Google Scholar 

  85. King, J.E. (1982) Surface damage and near threshold fatigue crack growth in a Ni-base superalloy in vacuum. Fatigue Engng. Mater. Struct., 5, 177–88.

    Article  Google Scholar 

  86. Taylor, D. and Knott, J.F. (1982) Growth of fatigue cracks from casting defects in nickel-aluminum bronze. Metals Tech., 9, 221–8.

    Google Scholar 

  87. Elber, W. (1971) The significance of fatigue crack closure, in Damage Tolerance in Aircraft Structures, ASTM STP 486, American Society for Testing and Materials, Philadelphia, PA, pp. 230–42.

    Google Scholar 

  88. Urangst, K.D., Shih, T.T. and Wei, R.P. (1977) Crack closure in 2219-T851 aluminum alloy. Engng. Fract. Mech., 9, 725–34.

    Article  Google Scholar 

  89. Macha, D.E., Corbly, D.M. and Jones, J.W. (1979) On the variation of fatiguecrack-opening load with measurement location. Proc. Soc. Exp. Stress Anal., 36, 207–13.

    Google Scholar 

  90. Shin, C.S. and Smith, R.A. (1985) Fatigue crack growth from sharp notches. Int. J. Fatigue, 7, 87–93.

    Article  Google Scholar 

  91. Kiesnil, M. and Lukas, P. (1972) Influence of strength and stress history on growth and stabilization of fatigue cracks. Engng. Fract. Mech., 4, 77–92.

    Article  Google Scholar 

  92. Davenport, R.T. and Brook, R. (1979) The threshold stress intensity range in fatigue. Fatigue Engng. Mater. Struct., 1, 151–8.

    Article  Google Scholar 

  93. Radon, J.C (1982) A model for fatigue crack growth in a threshold region. Int. J. Fatigue, 4, 161–6.

    Article  Google Scholar 

  94. Liaw, P.K. (1988) Overview of crack closure at near-threshold fatigue crack growth levels, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 62–92.

    Chapter  Google Scholar 

  95. Radon, J.C. and Guerra Rosa, L. (1989) Fatigue threshold behaviour, Parts I and II, in Advances in Fatigue Science and Technology (eds C Moura Branco and L. Guerra Rosa), Kluwer Academic, Dordrecht, Netherlands, pp. 129–56.

    Google Scholar 

  96. Elber, W. (1970) Fatigue crack closure under cyclic tension. Engng. Fract. Mech., 2, 37–45.

    Article  Google Scholar 

  97. Kujawski, D. and Ellyin, F. (1987) A fatigue crack growth model with load ratio effects. Engng. Fract. Mech., 28 (4), Elsevier Science Ltd, Oxford, 367–78.

    Article  Google Scholar 

  98. Forman, R.G. (1972) Study of fatigue crack initiation from flaws using fracture mechanics theory. Engng. Fract. Mech., 4, 333–45.

    Article  Google Scholar 

  99. McEvily, A.J. and Wei, R.P. (1972) Fracture mechanics and corrosion fatigue, in Corrosion-Fatigue: Chemistry, Mechanics and Microstructure, Vol. NACE-2 (eds O.F. Devereux, A.J. McEvily and R.W. Staehle), National Association of Corrosion Engineers, Houston, TX, pp. 381–95.

    Google Scholar 

  100. Nicholson, CE. (1973) Influence of Mean Stress and Environment on Crack Growth. Proc. Conf. on Mechanics and Mechanisms of Crack Growth, Cambridge, UK, British Steel Corp., pp. 226–43.

    Google Scholar 

  101. Hoeppener, D.W. and Krupp, W.E. (1974) Prediction of component life by application of fatigue crack growth knowledge. Engng. Fract. Mech., 6, 47–70.

    Article  Google Scholar 

  102. Paris, P.C. et al. (1972) Extensive study of low fatigue crack growth rates in A533 and A508 steels, in Stress Analysis and Growth of Cracks, Part I, ASTM STP 513, American Society for Testing and Materials, pp. 141–76.

    Google Scholar 

  103. Glinka, G. (1985) A notch stress-strain analysis approach to fatigue crack growth. Engng. Fract. Mech., 21, 245–61.

    Article  Google Scholar 

  104. McEvily, A.J. (1988) On crack closure in fatigue crack growth, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C. Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 35–43.

    Chapter  Google Scholar 

  105. Bowles, C.Q. and Schijve, J. (1983) Crack tip geometry for fatigue cracks grown in air and vacuum, in Fatigue Mechanisms: Advances in Qualitative Measurement of Physical Damage, ASTM STP 811 (eds J. Lankford et al.), American Society for Testing and Materials, Philadelphia, PA, pp. 400–26.

    Chapter  Google Scholar 

  106. Hudak, S.J. and Davidson, D.L. (1988) The dependence of crack closure on fatigue loading variables, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C. Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 121–38.

    Chapter  Google Scholar 

  107. Hertzberg, R.W., Newton, C.H. and Jaccard, R. (1983) Crack closure: Correlation and confusion, in Fatigue Mechanisms: Advances in Qualitative Measurement of Physical Damage, ASTM STP 811 (eds J. Lankford et al.), American Society for Testing and Materials, Philadelphia, PA, pp. 139–48.

    Google Scholar 

  108. Williams, J.F. and Lam, Y.C. (1986) The quantification of crack closure based on a contact stress intensity factor. Theor. Appl. Fract. Mech., 6, 21–8.

    Article  Google Scholar 

  109. Elber, W. (1976) Equivalent constant-amplitude concept for crack growth under spectrum loading, in: Fatigue Crack Growth Under Spectrum Loading, ASTM STP 595, American Society for Testing and Materials, Philadelphia, PA, pp. 236–47.

    Chapter  Google Scholar 

  110. Schijve, J. (1980) Prediction methods for fatigue crack growth in aircraft material, in Fracture Mechanics, Twelfth Conf., ASTM STP 700, American Society for Testing and Materials, Philadelphia, PA, pp. 3–34.

    Chapter  Google Scholar 

  111. Ellyin, F. and Wu, J. (1992) Elastic-plastic analysis of a stationary crack under cyclic loading and effect of overload. Int. J. Fract., 56, Kluwer Academic Publishers, Dordrecht, 182–208.

    Article  Google Scholar 

  112. Ward-Close and Ritchie, R.O. (1988) On the effect of crack closure mechanisms in influencing fatigue crack closure following tensile overloads in a titanium alloy: near threshold versus higher ΔK behaviour, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C. Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 93–111.

    Google Scholar 

  113. Allison, J.E., Ku, R.C. and Pompetzki, M.A. (1988) A comparison of measurement methods and numerical procedures for the experimental characterization of fatigue crack closure, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C. Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 171–85.

    Chapter  Google Scholar 

  114. Williams, J.F. and Stouffer, D.C. (1979) An estimate of the residual stress distribution in the vicinity of a propagating fatigue crack. Engng. Fract. Mech., 11,547–57.

    Article  Google Scholar 

  115. Suresh, S. (1983) Micromechanisms of fatigue crack retardation following overloads. Engng. Fract. Mech., 18, 577–93.

    Article  Google Scholar 

  116. Tokaji, K., Ando, Z. and Kojima, T. (1984) Fatigue crack retardation of low carbon steel in salt water. J. Engng. Mater. TechnoL, Trans. ASME, 106, 38–42.

    Article  Google Scholar 

  117. Fleck, N.A. (1988) Influence of stress state on crack growth retardation, in Basic Questions in Fatigue, Vol. 1, ASTM STP 924 (eds J.T. Fong and R.J. Fields), American Society for Testing and Materials, Philadelphia, PA, pp. 157–83.

    Chapter  Google Scholar 

  118. Kim, S. and Tai, W. (1992) Retardation and arrest of fatigue crack growth in A151 4140 steel by introducing rest periods and overloads. Fatigue Fract. Engng. Mater. Struct., 15, 519–30.

    Article  Google Scholar 

  119. Fatigue Crack Growth Under Spectrum Loads (1996), ASTM STP 595, American Society for Testing and Materials, Philadelphia, PA.

    Google Scholar 

  120. Vandar, O. and Yildirim, N. (1990) Crack growth retardation due to intermittent overloads. Int. J. Fatigue, 12, 283–7.

    Article  Google Scholar 

  121. Topper, T.H. and Yu, M.T. (1985) The effect of overloads on the threshold and crack closure. Int. J. Fatigue, 7(3), Elsevier Science Ltd, Oxford, 159–64.

    Article  Google Scholar 

  122. Marissen, R., Trautmann, K.H. and Nowack, H. (1984) The influence of compression loads and of dK/da on the crack propagation under variable amplitude loading. Engng. Fract. Mech., 19, 863–79.

    Article  Google Scholar 

  123. Stephens, R.I., Chen, D.K. and Horn, B.W. (1976) Fatigue crack growth with negative stress ratio following single overloads in 2024-T3 and 7075-T6 aluminum alloys, in Fatigue Crack Growth Under Spectrum Loads, ASTM STP 595, American Society for Testing and Materials, Philadelphia, PA, pp. 27–40.

    Chapter  Google Scholar 

  124. Yu, M.T., Topper, T.H., DuQuesnay, D.L. and Levin, M.S. (1986) The effect of compressive peak stress on fatigue behaviour. Int. J. Fatigue, 8, 9–15.

    Article  Google Scholar 

  125. Chang, J.B. and Hudson, CM. (eds) (1981) Methods and Models for Predicting Fatigue Crack Growth Under Random Loading, ASTM STP 748, American Society for Testing and Materials, Philadelphia, PA.

    Google Scholar 

  126. Petit, J., Davidson, D.L., Suresh, S. and Robbe, P. (eds) (1988) Fatigue Crack Growth Under Variable Amplitude Loading, Elsevier, London.

    Google Scholar 

  127. Newman, J.C, Jr., Wu, X.R., Venneri, J.L. and Li, CG. (1994) Small Crack Effects in High-Strength Aluminum Alloys. NASA Reference Publication 1309, NASA Langley Research Center, Hampton, VA, May 1994, 118 pp.

    Google Scholar 

  128. Budiansky, B. and Hutchinson, J.W. (1978) Analysis of closure in fatigue crack growth. J. Appl. Mech., Trans. ASME, 45, 267–76.

    Article  MATH  Google Scholar 

  129. Führing, H. and Seeger, T. (1979) Dugdale crack closure analysis of fatigue cracks under constant amplitude loading. Engng. Fract. Mech., 11, 99–122.

    Article  Google Scholar 

  130. Newman, J.C, Jr. (1981) A crack-closure model for predicting fatigue crack growth under aircraft spectrum loading, in Methods and Models for Predicting Fatigue Crack Growth under Random Loading, ASTM STP 748 (eds J.B. Chang and CM. Hudson), American Society for Testing and Materials, Philadelphia, PA, pp. 53–84.

    Chapter  Google Scholar 

  131. de Koning, A.V. and Liefting, G. (1988) Analysis of crack opening behaviour by application of a discretized strip yield model, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C. Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 437–59.

    Chapter  Google Scholar 

  132. Ibrahim, F.K., Thompson, J.C and Topper, T.H. (1986) A study of the effect of mechanical variables on fatigue crack closure and propagation. Int. J. Fatigue, 8, 135–42.

    Article  Google Scholar 

  133. Newman, J.C, Jr. and Armen, H., Jr. (1975) Elastic-plastic analysis of a propagating crack under cyclic loading. AIAA Journal, 13, 1017–23.

    Article  MATH  Google Scholar 

  134. Ohji, K., Ogura, K. and Ohkubo, Y. (1975) Cyclic analysis of a propagating crack and its correlation with fatigue crack growth. Engng. Fract, Mech., 7, 457–64.

    Article  Google Scholar 

  135. Newman, J.C, Jr. (1976) A finite-element analysis of fatigue crack closure, in Mechanics of Crack Growth, ASTM STP 590, American Society for Testing and Materials, Philadelphia, PA, pp. 281–301.

    Chapter  Google Scholar 

  136. Ogura, K. and Ohji, K. (1977) FEM analysis of crack closure and delay effect in fatigue crack growth under variable loading. Engng. Fract. Mech., 9, 471–80.

    Article  Google Scholar 

  137. Nakagaki, M. and Atluri, S.N. (1979) Fatigue crack closure and delay effect under Mode I spectrum loading: An efficient elastic-plastic analysis procedure. Fatigue Engng. Mater. Struct., 1, 421–9.

    Article  Google Scholar 

  138. Blom, A.F. and Holm, D.K. (1985) An experimental and numerical study of crack closure. Engng. Fract. Mech., 22, 997–1011.

    Article  Google Scholar 

  139. Kobayashi, H. and Nakamura, H. (1987) Investigation of fatigue crack closure (Analysis of plasticity induced crack closure), in Current Research on Fatigue Crack, The Society of Material Science, Kyoto, Japan, pp. 229–47.

    Google Scholar 

  140. Fleck, N.A. and Newman, J.C, Jr. (1988) Analysis of crack closure under plane strain condition, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C. Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 319–41.

    Chapter  Google Scholar 

  141. Lalor, P.L. and Sehitoglu, H. (1988) Fatigue crack closure outside a small-scale yielding regime, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 342–60.

    Chapter  Google Scholar 

  142. Anquez, L. and Baudin, G. (1988) Correlation between numerically predicted crack opening load and measured load history dependent crack growth threshold, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C. Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 380–97.

    Chapter  Google Scholar 

  143. Chermahini, R.G., Shivakumar, K.N. and Newman, J.C, Jr. (1988) Three-dimensional finite-element simulation of fatigue crack growth and closure, in Mechanics of Fatigue Crack Closure, ASTM STP 982 (eds J.C. Newman Jr. and W. Elber), American Society for Testing and Materials, Philadelphia, PA, pp. 398–413.

    Chapter  Google Scholar 

  144. Chermahini, R.G., Palmberg, B. and Blom, A.F. (1993) Fatigue crack growth and closure behaviour of semicircular and semielliptical surface flaws. Int. J. Fatigue, 15, 259–63.

    Article  Google Scholar 

  145. Fawkes, A.J., Owen, D.R.Y. and Luxmore, A.R. (1979) An assessment of crack tip singularity models for use with isoparametric elements. Engng. Fract. Mech., 11, 143–59.

    Article  Google Scholar 

  146. Bathe, K.-J. (1996) Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  147. Wu, J. (1995) Nonlinear analysis of cracked bodies. Doctoral dissertation, University of Alberta.

    Google Scholar 

  148. Michel, D. (1987) Elevated Temperature Fatigue Crack Propagation. Fatigue 87, Proc. 3rd Int. Conf. on Fatigue and Fatigue Threshold, Virginia, vol. II (ed. R.O. Ritchie), EMAS, London, pp. 1077–85.

    Google Scholar 

  149. Bassani, J.L. and McClintock, F.A. (1981) Creep relaxation of stress around a crack tip. Int. J. Solids Struct., 17, 479–92.

    Article  MATH  Google Scholar 

  150. Riedel, H. (1981) Creep deformation at crack tips in elastic-viscoplastic solids. J. Mech. Phys. Solids, 29, 35–44.

    Article  MATH  Google Scholar 

  151. Riedel, H. and Rice, J.R. (1980) Tensile cracks in creeping solids, in Fracture Mechanics, Twelfth Conf., ASTM STP 700, American Society for Testing and Materials, Philadelphia, PA, pp. 112–30.

    Chapter  Google Scholar 

  152. Ehler, R. and Riedel, H. (1981) A finite element analysis of creep deformation in a specimen containing a macroscopic crack, in Advances in Fracture Research, Proc. 5th Int. Conf. on Fracture, Cannes, France, Vol. 2 (ed. D. Francois), Pergamon, Oxford, pp. 691–8.

    Google Scholar 

  153. Bassani, J.L., Hawk, D.E. and Saxena, A. (1989) Evaluation of the Ct parameter for characterizing creep crack growth rate in the transient regime, in Nonlinear Fracture Mechanics: Vol. 1-Time-dependent Fracture, ASTM STP 995 (eds A. Saxena, J.D. Landes and J.L. Bassani), American Society for Testing and Materials, Philadelphia, PA, pp. 7–26.

    Google Scholar 

  154. Bensussan, P., Piques, R. and Pineau, A. (1989) A critical assessment of the global mechanical approach to crack initiation and creep crack growth in 316L steel, in Nonlinear Fracture Mechanics: Vol. 1-Time-dependent Fracture, ASTM STP 995 (eds A. Saxena, J.D, Landes and J.L. Bassani), American Society for Testing and Materials, Philadelphia, PA, pp. 27–54.

    Google Scholar 

  155. Hui, C.Y. and Riedel, H. (1981) The asymptotic stress and strain field near the tip of a growing crack under creep conditions. Int. J. Fract., 17, 409–25.

    Article  Google Scholar 

  156. Bassani, J.L., Hawk, D.E. and Wu, F.-H. (1989) Crack growth in small-scale creep, in Nonlinear Fracture Mechanics, Vol. I: Time-Dependent Fracture, ASTM STP 995 (eds A. Saxena, J.D. Landes and J.L. Bassani), American Society of Testing and Materials, Philadelphia, PA, pp. 68–95.

    Google Scholar 

  157. Sadananda, K. and Shahinian, P. (1981) Review of the fracture mechanics approach to creep crack growth in structural alloys. Engng. Fract. Mech., 15, 327–42.

    Article  Google Scholar 

  158. Sadananda, K. and Shahinian, P. (1981) Creep-fatigue crack growth, in Cavities and Cracks in Creep and Fatigue (ed. J. Gittus), Elsevier, London, pp. 109–95.

    Google Scholar 

  159. Koterazawa, R. and Mori, T. (1977) Applicability of fracture mechanics parameters of crack propagation under creep condition. J. Engng. Mater. Technol., Trans. ASME, 99, 298–305.

    Article  Google Scholar 

  160. Riedel, H. (1987) Fracture at High Temperature, Springer-Verlag, Berlin.

    Google Scholar 

  161. Ohtani, R. (1987) Substance of creep-fatigue interaction examined from the point of view of crack propagation mechanics, in Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials (ed. K.-T. Rie), Elsevier, London, pp. 211–22.

    Google Scholar 

  162. Ellyin, F. and Fakinlede, C.O.A. (1987) A dislocation model for workhardening material and cyclic J-integral. Int. J. Fract., 33, 95–110.

    Google Scholar 

  163. Jaske, CE. (1995) Life prediction in high-temperature structural materials. J. Pressure Vessel Technol., Trans. ASME, 117, 1–6.

    Article  Google Scholar 

  164. James, L.A. (1995) Environmentally-assisted cracking behaviour of a lowalloy steel under non-isothermal conditions, in Fatigue and Crack Growth: Environmental Effects, Modeling Studies, and Design Considerations, PVP 306 (eds S. Yukawa, D.P. Jones and H.S. Mehta), American Society of Mechanical Engineers, New York, pp. 19–27.

    Google Scholar 

  165. Wei, R.P. and Gangloff, R.P. (1989) Environmentally assisted crack growth in structural alloys: Perspectives and new directions, in Fracture Mechanics: Perspectives and Directions (20th Symp.), ASTM STP 1020 (eds R.P. Wei and R.P. Gangloff), American Society for Testing and Materials, Philadelphia, PA, pp. 233–64.

    Chapter  Google Scholar 

  166. Gangloff, R.P. (1990) Corrosion Fatigue Crack Propagation in Metals. Proc. Environment-Induced Cracking of Metals (eds R.P. Gangloff and M.B. Ives), NACE-10, National Association of Corrosion Engineers. Houston, Texas, pp. 55–109.

    Google Scholar 

  167. Garud, Y.S. (1991) Quantitative evaluation of environmentally assisted cracking: A survey of developments and application of modeling concepts. J. Pressure Vessel Technol., Trans. ASME, 113, 1–9.

    Article  Google Scholar 

  168. Yukawa, S., Jones, D.P. and Mehta, H.S. (eds) (1995) Fatigue and Crack Growth: Environmental Effects, Modeling Studies, and Design Considerations, PVP 306, American Society of Mechanical Engineers, New York.

    Google Scholar 

  169. American Society of Mechanical Engineers (1993) ASME Boiler and Pressure Vessel Code, Section XI: Rules for Inervice Inspection of Nuclear Power Plant Components.

    Google Scholar 

  170. Suresh, S. and Ritchie, R.O. (1982) Mechanistic dissimilarities between environmentally influenced fatigue-crack rates in lower strength steels. Metal Sci., 16, 529–38.

    Article  Google Scholar 

  171. Zhiqiang, X., Yujiu, S. and Mingjing, T. (1991) Crack closure induced by corrosion products and its effect in corrosion fatigue. Int. J. Fatigue, 13, 69–72.

    Article  Google Scholar 

  172. Henaff, G., Petit, J. and Bouchet, B. (1992) Environmental influence on the near-threshold fatigue crack propagation behaviour of a high strength steel. Int. J. Fatigue, 14, 211–18.

    Article  Google Scholar 

  173. Ellyin, F. and Wu, J. (1994) Effect of hydride precipitation on the elastoplastic stress field near a crack tip. Acta Metallurgica et Materialia, 42, 2709–17.

    Article  Google Scholar 

  174. Bartlett, M.L. and Hudak, S.J., Jr. (1990) The influence of frequency-dependent crack closure on corrosion fatigue crack growth, in Fatigue 90, Vol. Ill (eds H. Kitagawa and T. Tanaka), Materials and Components Engineering. Publications Ltd., UK, pp. 1783–8.

    Google Scholar 

  175. Chalant, G., Petit, J. and Suyitno, B. (1990) An environmental fatigue crack propagation model for structural steels, in Fatigue 90, Vol. III (eds H. Kitagawa and T. Tanaka), Materials and Components Engineering Publications Ltd., Birmingham, UK, pp. 1771–6.

    Google Scholar 

  176. Turnbull, A. (1993) Modelling of environment assisted cracking. Corrosion Sci., 34, 921–60.

    Article  Google Scholar 

  177. Shoji, T., Takahashi, H., Suzuki, M. and Kondo, T. (1981) A new parameter for characterizing corrosion fatigue crack growth.J. Engng. Mater. Technol, Trans. ASME, 103, 298–304.

    Article  Google Scholar 

  178. Shoji, T. and Takahashi, H. (1983) Role of Loading Variables in Environmental Enhanced Crack Growth for Water-Cooled Nuclear Reactor Pressure Vessel Steels. Proc. IAEA Specialists’ Meeting on Subcritical Crack Growth, NUREG/CP-0044, May 1983, pp. 143–71.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Chapman & Hall

About this chapter

Cite this chapter

Ellyin, F. (1997). Fatigue crack growth. In: Fatigue Damage, Crack Growth and Life Prediction. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1509-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-1509-1_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7175-8

  • Online ISBN: 978-94-009-1509-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics