Skip to main content
SpringerLink
Log in

A survey of failure criteria and parameters in mixed-mode fatigue crack growth

  • Published:
Materials Science Aims and scope

From the present survey of the mixed-mode crack growth criteria based on the fracture toughness K Ic (critical J-integral), it follows that this concept is very extensively and variously used by different authors. The criteria discussed in the work are based on the parameters K, δ, W, and J. The most extensively applied models include the mixed mode I + II described by the stress intensity factor K. The criteria presented in the work are based on the factors affecting the fatigue crack growth during testing, namely stress, crack-tip displacement, or energy dissipation. In the case of mixed-mode cracking, special attention should be paid to the energy approach (application of the J-integral and strain energy density), which seems to be very promising for elastoplastic materials. Under mixed-mode cracking, two things should be taken into account: the rate and direction of fatigue-crack growth. Moreover, the nonproportional loading, crack closure, or overloads strongly affect the process of fatigue crack growth in the case of mixed-mode cracking.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Suresh, Fatigue of Materials, Cambridge University Press, Cambridge, UK (1991).

    Google Scholar 

  2. S. Kocańda, Fatigue Failure of Metals, WNT, Warsaw (1985).

    Google Scholar 

  3. H. A. Richard, M. Fulland, and M. Sander, “Theoretical crack path prediction,” Fatigue & Fract. Eng. Mater. Struct., 28, 3–12 (2005).

    Article  Google Scholar 

  4. K. N. Smith, P. Watson, and T. H. Topper, “A stress-strain function for the fatigue of metals,” J. Metals JMLSA, 5, 767–778 (1976).

    Google Scholar 

  5. J. R. Rice, “A path independent integral and the approximate analysis of strain concentration by notches and cracks,” J. Appl. Mech., 35, 379–386 (1968).

    Google Scholar 

  6. G. R. Irwin, “Analysis of stress and strain near the end of crack traversing a plate,” J. Appl. Mech., 24, 361–364 (1957).

    Google Scholar 

  7. S. lida and A. S. Kobayashi, “Crack propagation rate in 7075-T6 plates under cyclic tensile and transverse shear loading,” J. Bas. Eng. ASME Trans., 91, 764–769 (1969).

    Google Scholar 

  8. J. R. Yates and K. J. Miller, “Mixed mode (I + III) fatigue thresholds in a forging steel,” Fatigue Fract. Eng. Mater. Struct., 12, 259–270 (1989).

    Article  Google Scholar 

  9. E. M. Wu, “Application of fracture mechanics to anisotropic plates,” J. Appl. Mech., ASME Trans., 34, 967–974 (1967).

    Google Scholar 

  10. F. Erdogan and G. C. Sih, “On the crack extension in plates under plane loading and transverse shear,” J. Bas. Eng., ASTM Trans., 85, 519–525 (1963).

    Google Scholar 

  11. H. M. Westergaard, “Bearing pressures and cracks,” J. Appl. Mech., 61, 49–53 (1939).

    Google Scholar 

  12. J. R. Yates, “Fatigue thresholds under mixed-mode (I + III) loading,” Int. J. Fatigue, 13, 383–388 (1991).

    Article  CAS  Google Scholar 

  13. L. P. Pook, “The fatigue crack direction and threshold behaviour of mild steel under mixed-mode I and III loading,” Int. J. Fatigue, 7, 21–30 (1985).

    Article  Google Scholar 

  14. L. P. Pook, “The significance of mode I branch cracks for combined mode failure,” in: J. C. Radon (editor), Fracture and Fatigue, Elastoplasticity, Thin Sheet, and Micromechanism Problems, Pergamon Press, Oxford (1980), pp. 143–153.

    Google Scholar 

  15. M. Schöllmann, G. Kullmer, M. Fulland, and H. A. Richard, “A new criterion for 3d crack growth under mixed-mode (I + II + III) loading,” in: Proc. of 6th Internat. Conf. on Biaxial/Multiaxial Fatigue & Fracture, Lisboa, Portugal (2001), pp. 589–596.

  16. H. A. Richard, M. Schöllmann, M. Fulland, and M. Sande, “Experimental and numerical simulation of mixed-mode crack growth,” in: Proc. of 6th Internat. Conf. on Biaxial/Multiaxial Fatigue & Fracture, Lisboa, Portugal (2001), pp. 623–630.

  17. H. A. Richard, “Theoretical crack path determination,” in: A. Carpinteri (editor), Internat. Conf. on Fatigue Crack Paths, University of Parma, Parma, CD (2003), p. 8.

    Google Scholar 

  18. S. C. Forth, W. D. Keat, and L. H. Favrow, “Experimental and computational investigation of three-dimensional mixed-mode fatigue,” Fatigue Fract. Eng. Mater. Struct., 25, 3–15 (2002).

    Article  Google Scholar 

  19. K. Tanaka, “Fatigue crack propagation from a crack inclined to the cyclic tensile axis,” Eng. Fract. Mech., 6, 493–507 (1974).

    Article  CAS  Google Scholar 

  20. P. C. Paris and F. Erdogan, “A critical analysis of crack propagation laws,” J. Basic Eng., Trans. ASME, 85, 528–534 (1960).

    Google Scholar 

  21. A. J. Pokluda, “Intrinsic thresholds of long fatigue cracks,” in: XX Symp. on Fatigue and Fracture Mechanics, Akademia Techniczno-Rolnicza, Bydgoszcz-Pieczyska, Poland (2004), pp. 327–337.

  22. X. Yan, S. Du, and Z. Zhang, “Mixed-mode fatigue crack growth prediction in biaxially stretched sheets,” Eng. Fract. Mech., 43, 471–475 (1992).

    Article  Google Scholar 

  23. R. A. Bloch and M. W. Brown, “Crack closure analysis for the threshold of fatigue crack growth under mixed-mode I/II loading,” in: H. P. Rossmanith and K. J. Miller (editors), Mixed-Mode Fatigue and Fracture, ESIS 14, Mechanical Eng. Publ., London (1993), pp. 125–137.

    Google Scholar 

  24. A. A. Wells, “Critical tip opening displacement as fracture criterion,” in: Proc. Crack Propagation Symp., Cranfield (1961), pp. 210–221.

  25. V. V. Panasyuk, Mechanics of Quasibrittle Fracture of Materials [in Russian], Naukova Dumka, Kiev (1991).

    Google Scholar 

  26. C. Li, “Vector CTD criterion applied to mixed-mode fatigue crack growth,” Fatigue Fract. Eng. Mater. Struct., 12, 59–65 (1989).

    Article  Google Scholar 

  27. G. R. Irwin, “Plastic zone near a crack and fracture toughness,” in: Proc. Seventh Sagamore Advance Materials Research Conf., Syracuse University Press, Syracuse, USA (1960), pp. 63–78.

    Google Scholar 

  28. M. A. Sutton, X. Deng, F. Ma, Jr., J. C. Newman, and M. James, “Development and application of a crack-tip opening displacement-based mixed-mode fracture criterion,” Int. J. Solids Struct., 37, 3591–3618 (2000).

    Article  MATH  Google Scholar 

  29. R. J. Nuismer, “An energy release rate criterion for mixed-mode fracture,” Int. J. Fract., 11, 245-250 (1975).

    Article  Google Scholar 

  30. B. Cotterell and J. R. Rice, “Slightly curved or kinked cracks,” Int. J. Fract., 16, 155–169 (1980).

    Article  Google Scholar 

  31. J. B. Sha, P. Zhu, Z. J. Deng, and H. J. Zhou, “Strip model plasticity analysis of mixed-mode crack opening displacement in aluminum alloy LY12,” Theor. Appl. Fract. Mech., 26, 13–21 (1997).

    Article  CAS  Google Scholar 

  32. A. Pirondi and C. Dalle Donne, “Characterization of ductile mixed-mode fracture with the crack-tip displacement vector,” Eng. Fract. Mech., 68, 1385–1402 (2001).

    Article  Google Scholar 

  33. M. M. I. Hammouda, A. S. Fayed, and H. E. M. Sallam, “Simulation of mixed-mode I/II cyclic deformation at the tip of a short kinked inclined crack with frictional surfaces,” Int. J. Fatigue, 25, 743–753 (2003).

    Article  Google Scholar 

  34. D. Rozumek and E. Macha, “A description of fatigue crack growth in elastoplastic materials under proportional bending with torsion,” in: Multiaxial Random Fatigue of Machine Elements and Structures. Part IX, Opole University of Technology, Opole, Poland (2006).

  35. G. C. Sih, “Energy-density concept in fracture mechanics,” Eng. Fract. Mech., 5, 1037–1040 (1973.).

    Article  CAS  Google Scholar 

  36. G. C. Sih, “Strain-energy density factor applied to mixed-mode crack problems,” Int. J. Fract., 10, 305–321 (1974).

    Article  Google Scholar 

  37. T. K. Hellen and W. S. Blackburn, “The calculation of stress intensity factors for combined tensile and shear loading,” Int. J. Fract., 11, 605–617 (1975).

    Article  Google Scholar 

  38. S. A. Hamoush and M. Reza Salami, “Analyzing a mixed-mode plane problem by using J k integrals,” Int. J. Fatigue, 12, 441–446 (1990).

    Article  Google Scholar 

  39. J. W. Eischen, “An improved method for computing the J 2 integral,” J. Eng. Fract. Mech., 26, 691–700 (1987).

    Article  Google Scholar 

  40. H. Kimachi, K. Tanaka, Y. Akiniwa, and H. Yu, “Elastic-plastic fatigue crack propagation under mixed-mode (I + III) cyclic torsion and axial loading,” Internat. Conf. on Fatigue Crack Paths (FCP 2003), Parma, CD (2003), p. 8.

  41. D. Rozumek, “Application of ∆J-integral range for fatigue crack growth rate in mixed modes I and III,” in: Proc. of the Seventh Internat. Conf. on Biaxial/Multiaxial Fatigue and Fracture (ICBMFF), DVM, Berlin (2004), pp. 489–494.

  42. G. Gasiak and D. Rozumek, “∆J-integral range estimation for fatigue crack growth rate description,” Int. J. Fatigue, 26, 135–140 (2004).

    Article  CAS  Google Scholar 

  43. R. Döring, J. Hoffmeyer, T. Seeger, and M. Vormwald, “Short fatigue crack growth nonproportional multiaxial elastic-plastic strains,” Int. J. Fatigue, 28, 972–982 (2006).

    Article  Google Scholar 

  44. W. Ramberg and W. R. Osgood, “Description of stress-strain curves by three parameters,” in: NACA, Technical Note (1943), p. 402.

  45. N. E. Dowling and J. A. Begley, “Fatigue crack growth during gross plasticity and the J-integral in mechanics of crack growth,” ASTM STP 590 (1976), pp. 82–103.

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Opole University of Technology, Opole, Poland

    D. Rozumek & E. Macha

Authors
  1. D. Rozumek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Macha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Rozumek.

Additional information

Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 45, No. 2, pp. 47–62, March–April, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rozumek, D., Macha, E. A survey of failure criteria and parameters in mixed-mode fatigue crack growth. Mater Sci 45, 190–210 (2009). https://doi.org/10.1007/s11003-009-9179-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11003-009-9179-2

Keywords

Search

Navigation