Acta Mechanica

, Volume 225, Issue 11, pp 3059–3072 | Cite as

Elasto-plastic analysis of critical fracture stress and fatigue fracture prediction

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Abstract

The purpose of this investigation is to obtain the critical fracture stress, σf, in a cracked elasto-plastic plate subjected to mixed-mode loading. A new model estimating the magnitude of critical fracture stress based on the plastic zone during crack propagation is developed. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Apart from the obvious and ideal benefits of being able to quantify crack propagation rates without the necessity to determine empirical coefficients and exponents experimentally, such an approach would lead to a better understanding of the factors which affect the crack growth rate.

Keywords

Fracture Toughness Fatigue Crack Stress Intensity Factor Plastic Zone Crack Growth Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    King A., Ludwig W., Herbig M., Buffière J.-Y., Khan A.A., Stevens N., Marrow T.J.: Three-dimensional in situ observations of short fatigue crack growth in magnesium. Acta Mater. 59(17), 6761–6771 (2011)CrossRefGoogle Scholar
  2. 2.
    Mirsalimov V.M., Rustamov B.E.: Interaction of prefracture zones and crack-visible cavity in a burning solid with mixed boundary conditions. Acta Mech. 223(3), 627–643 (2012)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Souza F.V., Allen D.H.: Modeling the transition of microcracks into macrocracks in heterogeneous viscoelastic media using a two-way coupled multiscale model. Int. J. Solids Struct. 48(22–23), 3160–3175 (2011)CrossRefGoogle Scholar
  4. 4.
    Konstantinos I.: Tserpes strength of graphenes containing randomly dispersed vacancies. Acta Mech. 223(4), 669–678 (2012)CrossRefMATHGoogle Scholar
  5. 5.
    Griffith A.A.: The phenomena of rupture and flow in solids. Trans. R. Soc. Lond. A-221, 163–198 (1920)Google Scholar
  6. 6.
    Hussain M.A., Pu S.L., Underwood J.: Strain energy release rate for a crack under combined mode I and mode II. Fract. Anal. ASTM STP 560, 2–28 (1974)Google Scholar
  7. 7.
    Erdogan F., Sih G.C.: On the crack extension in plates under plane loading and transverse shear. ASME J. Basic Eng. 85, 519–527 (1963)CrossRefGoogle Scholar
  8. 8.
    Sih G.C.: Strain–energy–density factor applied to mixed mode crack problems. Int. J. Fract. 10(3), 305–321 (1974)CrossRefGoogle Scholar
  9. 9.
    BS 5447, k 1c Fracture Toughness Testing, British StandardsInstitution (2000)Google Scholar
  10. 10.
    Paris P.C., Erdogan F.: A critical analysis of crack propagation laws. ASME J. Basic Eng. Ser. D 85, 528–539 (1963)CrossRefGoogle Scholar
  11. 11.
    Cooke R.J., Irving P.E., Booth G.S., Beevers C.J.: The slow fatigue crack growth and threshold behaviour of a medium carbon alloy steel in air and vacuum. Eng. Fract. Mech. 7(1), 69–77 (1975)CrossRefGoogle Scholar
  12. 12.
    Jaubert A., Marigo J.J.: Justification of Paris-type fatigue laws from cohesive forces model via a variational approach. Contin. Mech. Thermodyn. 18(1–2), 23–45 (2006)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Bian L.: Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials. Int. J. Solids Struct. 44(25–26), 8440–8456 (2007)CrossRefMATHGoogle Scholar
  14. 14.
    Bian L., Fawaz Z., Behdinan K.: An improved model for predicting the crack size and plasticity dependence of fatigue crack propagation. Int. J. Fatigue 30(7), 1200–1210 (2008)Google Scholar
  15. 15.
    Bian L.: Crack growth prediction and non-linear analysis for an elasto-plastic solid. Int. J. Eng. Sci. 47, 325–341 (2009)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Sih, G.C.: Three dimensional crack problems. In: Mechanics of Fracture 2 Noordhoff, Netherlands (1975)Google Scholar
  17. 17.
    Gillemot L.F.: Criterion of crack initiation and spreading. Eng. Fract. Mech. 8(1), 239–253 (1976)CrossRefGoogle Scholar
  18. 18.
    Irwin G.R.: Linear fracture mechanics. Eng. Fract. Mech. 1, 241–287 (1968)CrossRefGoogle Scholar
  19. 19.
    Liebowitz H., Rice J.R.: Fracture, vol. II. Academic Press, New York (1968)Google Scholar
  20. 20.
    Schwalbe K.H.: Comparison of several fatigue crack propagation laws with experimental results. Eng. Fract. Mech. 6(2), 325–341 (1974)CrossRefGoogle Scholar
  21. 21.
    Kanazawa T., Machida S., Itoga K.: On the effect of cyclic stress ratio on the fatigue crack propagation. Eng. Fract. Mech. 7(3), 445–455 (1975)CrossRefGoogle Scholar
  22. 22.
    Pilkey W.D.: Formulas for Stress, Strain, and Structural Matrices. A Wiley-Interscience Publication, New York (1994)MATHGoogle Scholar
  23. 23.
    Qian J., Fatemi A.: Fatigue crack growth under mixed mode I and II loading. Fatigue Fract. Eng. Mater. Struct. 19(10), 1277–1284 (1996)CrossRefGoogle Scholar
  24. 24.
    Jeong D.Y.: Application of effective stress intensity factor crack closure model to evaluate train load sequence effects on crack growth rates. Theor. Appl. Fract. Mech. 22, 43–50 (1995)CrossRefGoogle Scholar
  25. 25.
    Khen R., Altus E.: Effect of static-mode on fatigue-crack growth by a unified micromechanic model. Mech. Mater. 21(3), 169–189 (1995)CrossRefGoogle Scholar
  26. 26.
    Bulloch J.H.: Effects of mean stress on the threshold fatigue crack extension rates of two spheroidal graphite cast irons. Theor. Appl. Fract. Mech. 18, 15–30 (1992)CrossRefGoogle Scholar
  27. 27.
    Bian L., Taheri F.: A proposed maximum ratio criterion applied to mixed mode fatigue crack propagation. Mater. Des. 32(4), 2066–2072 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures of Hebei ProvinceYanshan UniversityQinhuangdaoPeople’s Republic of China
  2. 2.Department of Civil EngineeringDalhousie UniversityHalifaxCanada

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