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Survey of Formulas Used to Describe the Fatigue Crack Growth Rate

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Materials Science Aims and scope

We present a survey of formulas for the fatigue crack growth rate. The equations are split into three groups according to the used parameters of fatigue damage, i.e. stress, strain or displacement, and energy. The parameter K or its range ΔK corresponds to brittle materials and to the initial stage of cracking of elastic-plastic materials. The parameter ε or CTOD is used in elastic-plastic materials and plastic materials to describe the yield strength. The energy approach is based on the parameter J or the strain-energy density W and corresponds to the entire range of the curve of crack growth rate.

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References

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

  2. D. Rozumek and E. Macha, “J-integral in the description of fatigue crack growth rate induced by different ratios of torsion to bending loading in AlCu4Mg1,” Materialwissenschaft Werkstofftechnik, 40, 743–749 (2009).

    Article  Google Scholar 

  3. D. Rozumek and E. Macha, “A survey of failure criteria and parameters in mixed-mode fatigue crack growth,” Mater. Sci., 45, No. 2, 190–210 (2009).

    Article  Google Scholar 

  4. L. Toth and A. J. Krasowsky, Material Characterization Required for Reliability Assessment of Cyclically Loaded Engineering Structures, P. 2: Fatigue Application. Reliability Assessment of Cyclically Loaded Engineering Structures, Kluwer, Dordrecht, 1997, 225–272.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  7. M. Klesnil and P. Lukas, “Influence of strength and stress history on growth and stabilization of fatigue cracks,” Eng. Fract. Mech., 4, 77–92 (1972).

    Article  Google Scholar 

  8. D. Rozumek, “Empirical formulas for description of the fatigue crack growth rate,” Materialwissenschaft Werkstofftechnik, 41, 89–94 (2010).

    Article  Google Scholar 

  9. P. Lazzarin, R. Tovo, and G. Meneghetti, “Fatigue crack initiation and propagation phases near notches in metals with low notch sensitivity,” Int. J. Fatigue, 19, 647–657 (1997).

    Article  Google Scholar 

  10. H. M. Nykyforchyn, “Effect of hydrogen on the kinetics and mechanism of fatigue crack growth in structural steels,” Mater. Sci., 33, No. 4, 504–515 (1997).

    Article  Google Scholar 

  11. D. Rozumek and Z. Marciniak, “Fatigue crack growth in AlCu4Mg1 under nonproportional bending-with-torsion loading,” Mater. Sci., 46, No. 5, 685–694 (2010).

    Article  Google Scholar 

  12. W. Elber, “Einfluss der plastischen Zone auf die rissausbreitung unter schwingbelastung,” Materialprufung, 6, 189–193 (1970).

    Google Scholar 

  13. J. F. Bonnen and T. H. Topper, “The effect of bending overloads on torsional fatigue in normalized 1045 steel,” Int. J. Fatigue, 21, 23–33 (1999).

    Article  Google Scholar 

  14. J. Schijve, M. Skorupa, A. Skorupa, et al., “Fatigue crack growth in the aluminum alloy D16 under constant and variable amplitude loading,” Int. J. Fatigue, 26, 1–15 (2004).

    Article  Google Scholar 

  15. E. K. Priddle, Some Equations Describing the Constant Amplitude Fatigue Crack Propagation Characteristics of a Mild Steel, Berkeley Nuclear Laboratories, RD/B/N2390 (1972).

  16. A. J. McEvily, “On closure in fatigue crack growth,” in: ASTM STP 982 (1988), pp. 35–43.

  17. S. Ya. Yarema, “Stages of fatigue fracture and their consequences,” Mekh. Mater., 6, 66–72 (1973).

    Google Scholar 

  18. J. M. Krafft and W. H. Cullen, “Organizational scheme for corrosion—fatigue crack propagation data,” Eng. Fract. Mech., 10, 609–650 (1978).

    Article  Google Scholar 

  19. R. G. Forman, V. E. Kearney, and R. M. Engle, “Numerical analysis of crack propagation in cyclic-loaded structures,” J. Basic Eng. Trans. ASME, 459–464 (1967).

  20. R. Roberts and F. Erdogan, “The effect of mean stress on fatigue crack propagation in plates under extension and bending,” J. Basic Eng. Trans. ASME, 885–892 (1967).

  21. G. P. Cherepanov, “On the growth of cracks under cyclic loading,” Prikl. Mekh. Tech. Fiz., 6, 64–75 (1968).

    Google Scholar 

  22. R. W. Lander, “A dislocation model for fatigue growth in metals,” Philosophy Magazin, 71–77 (1968).

  23. F. Erdogan and A. Ratwani, “Fatigue and fracture of cylindrical shells containing a circumferential crack,” Int. J. Fract. Mech., 4, 379–392 (1970).

    Google Scholar 

  24. E. M. Morozov, “Crack propagation in elastoplastic and hereditary plastic bodies,” in: Mechanics of Deformed Bodies and Structures [in Russian], Mashinostroenie, Moscow (1975), pp. 304–312.

    Google Scholar 

  25. M. Parry, R. W. Hertzberg, and H. Nordberg, “Fatigue crack-propagation in A514 base plate and welded-joints,” Welding J., 51, 485–490 (1972).

    Google Scholar 

  26. S. Pearson, “The effect of mean stress on fatigue crack propagation in half-inch thick specimens of aluminum alloys of high and low fracture toughness,” Eng. Fract. Mech., 4, 9–14 (1972).

    Article  Google Scholar 

  27. L. P. Pook and E. A. Forst, “Fatigue crack growth theory,” Int. J. Fract. Mech., 9, 38–42 (1975).

    Google Scholar 

  28. C. M. Branco, J. C. Radon, and L. E. Culver, “Influence of mean stress intensity on fatigue crack growth in an aluminum alloy,” J. Mech. Eng. Sci., 17, 199–205 (1975).

    Article  Google Scholar 

  29. A. J. McEvily and R. P. Wei, “Fracture mechanics and corrosion fatigue,” Inst. Mater. Sci., Univ. Connecticut, 381–395 (1977).

    Google Scholar 

  30. K. J. Miller, “The two thresholds of fatigue behavior,” Fatigue Fract. Eng. Mater. Struct., 16, 931–939 (1993).

    Article  Google Scholar 

  31. S. S. Manson, “Interfaces between fatigue, creep, and fracture,” Int. J. Fract. Mech., 2, 327–363 (1966).

    Article  Google Scholar 

  32. B. Tomkins, “Fatigue failure in high strength metals,” Philosophical Magazine, 23, 687–703 (1971).

    Article  Google Scholar 

  33. K. Werner, Analysis of Semielliptic Fatigue Crack Growth [in Polish], Politechnika Częstochowska, Częstochowa (2000).

    Google Scholar 

  34. S. V. Serensen and N. A. Makhutov, “The conditions low cycle fatigue,” Internat. Congr. on Fracture, T. VI, Ref. V-334, München (1973).

    Google Scholar 

  35. C. H. Wang, “Effect of stress ratio on short fatigue crack growth,” Trans. ASME, 118, 362–366 (1996).

    Google Scholar 

  36. A. J. McEvily and T. L. Johnston, “The role of gross slip in brittle fracture and fatigue,” in: Internat. Conf. Fracture, Sendai, Japan (1965), pp. 73–81.

    Google Scholar 

  37. F. Gillemot, “Effect of the material properties on fatigue crack growth at ambient and elevated temperatures,” in: Internat. Conf. on Creep and Fatigue at Elevated Temperatures. Applications, Philadelphia (1973), p. 147.

  38. S. Taira and K. Tanaka, “Mechanical behavior of materials,” Soc. Mater. Sci., 1, 48–58 (1972).

    Google Scholar 

  39. R. J. Donahue, H. Clark, P. Atanmo, et al., “Crack opening displacement and the rate of fatigue crack growth,” Int. J. Fract. Mech., 8, 209–219 (1972).

    Article  Google Scholar 

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

    Article  Google Scholar 

  41. Y. L. Lu and H. Kobayashi, “An experimental parameter J max in elastic-plastic fatigue crack growth,” Fatigue Fract. Eng. Mater. Struct., 19, 1081–1091 (1996).

    Article  Google Scholar 

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

    Article  Google Scholar 

  43. D. Rozumek, “Influence of the slot inclination angle in FeP04 steel on fatigue crack growth under tension,” Materials & Design, 30, 1859–1865 (2009).

    Article  Google Scholar 

  44. D. Rozumek and E. Macha, “Elastic-plastic fatigue crack growth in 18G2A steel under proportional bending with torsion loading,” Fatigue Fract. Eng. Mater. Struct., 29, 135–145 (2006).

    Article  Google Scholar 

  45. D. Rozumek, “J-integral in the description of elastic-plastic crack growth kinetics curve,” Archive Mech. Eng., LIII, 211–225 (2006).

  46. 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 

  47. A. B. Patel and P. K. Pandey, “Fatigue crack growth under mixed mode loading,” Fatigue Fract. Eng. Mater. Struct., 4, 65–77 (1981).

    Article  Google Scholar 

  48. J. Jeleńkowski and J. Wawszczak, “Analiza wpływu czynnika strukturalnego na szybkość propagacji szczeliny zmęczeniowej w stali eutektoidalnej,” in: VIII Symp. Doświadczalnych Badań w Mechanice Ciała Stałego, Warszawa (1978), pp. 288–394.

    Google Scholar 

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Authors and Affiliations

  1. Opole University of Technology, Opole, Poland

    D. Rozumek

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Correspondence to D. Rozumek.

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Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 49, No. 6, pp. 18–27, November–December, 2013.

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Rozumek, D. Survey of Formulas Used to Describe the Fatigue Crack Growth Rate. Mater Sci 49, 723–733 (2014). https://doi.org/10.1007/s11003-014-9667-x

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