Prediction of Accurate Mixed Mode Fatigue Crack Growth Curves using the Paris’ Law

  • S. Sajith
  • K. S. R. Krishna MurthyEmail author
  • P. S. Robi
Original Contribution


Accurate information regarding crack growth times and structural strength as a function of the crack size is mandatory in damage tolerance analysis. Various equivalent stress intensity factor (SIF) models are available for prediction of mixed mode fatigue life using the Paris’ law. In the present investigation these models have been compared to assess their efficacy in prediction of the life close to the experimental findings as there are no guidelines/suggestions available on selection of these models for accurate and/or conservative predictions of fatigue life. Within the limitations of availability of experimental data and currently available numerical simulation techniques, the results of present study attempts to outline models that would provide accurate and conservative life predictions.


Mixed mode Fatigue Crack growth Paris’ law Stress intensity factor 



The authors are thankful to Cornell Fracture Group, Cornell University, New York for allowing authors to use the FRANC2D software.


  1. 1.
    R.J. Sanford, Principles of Fracture Mechanics (Prentice Hall, Upper Saddle River, NJ, 2003)Google Scholar
  2. 2.
    T. Swift, in Structural Integrity of Aging Airplanes, ed. by S.N. Atluri, S.G. Sampath, P. Tong (Springer, Berlin, 1991), p. 433CrossRefGoogle Scholar
  3. 3.
    F.C. Campbell, Fatigue and Fracture: Understanding the Basics (ASM International, Materials Park, Ohio, 2012)Google Scholar
  4. 4.
    J. Qian, A. Fatemi, Mixed mode fatigue crack growth: a literature survey. Eng Fract Mech 55, 969–990 (1996)CrossRefGoogle Scholar
  5. 5.
    D. Rozumek, E. Macha, A survey of failure criteria and parameters in mixed-mode fatigue crack growth. Mater Sci 45, 190–210 (2009)CrossRefGoogle Scholar
  6. 6.
    G.C. Sih, Strain-energy-density factor applied to mixed mode crack problems. Int J Fract 10, 305–321 (1974)CrossRefGoogle Scholar
  7. 7.
    L.P. Borrego, F.V. Antunes, J.M. Costa, J.M. Ferreira, Mixed-mode fatigue crack growth behaviour in aluminium alloy. Int J Fatigue 28, 618–626 (2006)CrossRefzbMATHGoogle Scholar
  8. 8.
    K. Tanaka, Fatigue crack propagation from a crack inclined to the cyclic tensile axis. Eng Fract Mech 6, 493–507 (1974)CrossRefGoogle Scholar
  9. 9.
    W.R. Chen, L.M. Keer, Fatigue crack growth in mixed mode loading. J Eng Mater Technol 113, 222–227 (1991)CrossRefGoogle Scholar
  10. 10.
    Y. Xiangqiao, D. Shanyi, Z. Zehua, Mixed-mode fatigue crack growth prediction in biaxially stretched sheets. Eng Fract Mech 43, 471–475 (1992)CrossRefGoogle Scholar
  11. 11.
    S.B. Biner, Fatigue crack growth studies under mixed-mode loading. Int J Fatigue 23, 259–263 (2001)CrossRefGoogle Scholar
  12. 12.
    T. Tamilselvan, K. Lo, Y. Gong, M. Zhao, A model for mixed-mode fatigue. J Test Eval 33, 188–196 (2005)CrossRefGoogle Scholar
  13. 13.
    H.A. Richard, F.G. Buchholz, G. Kullmer, M. Schöllmann, 2D- and 3D-mixed mode fracture criteria. Key Eng Mater 251–252, 251–260 (2003)CrossRefGoogle Scholar
  14. 14.
    A.C.O. Miranda, M.A. Meggiolaro, J.T.P. Castro, L.F. Martha, Path and life predictions under mixed mode I-mode II complex loading. in Proceedings of Mechanics solids Brazil, p. 421–432 (2007)Google Scholar
  15. 15.
    A.C.O. Miranda, M.A. Meggiolaro, J.T.P. Castro, L.F. Martha, T.N. Bittencourt, Fatigue life and crack path predictions in generic 2D structural components. Eng Fract Mech 70, 1259–1279 (2003)CrossRefGoogle Scholar
  16. 16.
    S. Boljanović, S. Maksimović, Analysis of the crack growth propagation process under mixed-mode loading. Eng Fract Mech 78, 1565–1576 (2011)CrossRefGoogle Scholar
  17. 17.
    M. Blažić, S. Maksimović, Z. Petrović, I. Vasović, D. Turnić, Determination of fatigue crack growth trajectory and residual life under mixed modes. J Mech Eng 60, 250–254 (2014)CrossRefGoogle Scholar
  18. 18.
    S. Ma, X.B. Zhang, N. Recho, J. Li, The mixed-mode investigation of the fatigue crack in CTS metallic specimen. Int J Fatigue 28, 1780–1790 (2006)CrossRefGoogle Scholar
  19. 19.
    P. Reimers, Simulation of mixed mode fatigue crack growth. Comput Struct 40, 339–346 (1991)CrossRefGoogle Scholar
  20. 20.
    K.S. Kim, H.S. Lee, An incremental formulation for the prediction of two-dimensional fatigue crack growth with curved paths. Int J Numer Methods Eng 72, 697–721 (2007)CrossRefzbMATHGoogle Scholar
  21. 21.
    I. Varfolomeev, M. Burdack, S. Moroz, D. Siegele, K. Kadau, Fatigue crack growth rates and paths in two planar specimens under mixed mode loading. Int J Fatigue 58, 12–19 (2014)CrossRefGoogle Scholar
  22. 22.
    A. Ingraffea, G. Blandford, J. Liggett, Automatic modelling of mixed-mode fatigue and quasi-static crack propagation using the boundary element method. Proceeding of Fracture Mechanics: Fourteenth Symposium, ASTM STP 791, pp. 407–426 (1983)Google Scholar
  23. 23.
    A. Portela, M.H. Aliabadi, D.P. Rooke, Dual boundary element incremental analysis of crack propagation. Comput Struct 46, 237–247 (1993)CrossRefzbMATHGoogle Scholar
  24. 24.
    A.M. Yan, H. Nguyen-Dang, Multiple-cracked fatigue crack growth by BEM. Comput Mech 16, 273–280 (1995)CrossRefzbMATHGoogle Scholar
  25. 25.
    X. Yan, Automated simulation of fatigue crack propagation for two-dimensional linear elastic fracture mechanics problems by boundary element method. Eng Fract Mech 74, 2225–2246 (2007)CrossRefGoogle Scholar
  26. 26.
    G. Sih, B. Barthelemy, Mixed mode fatigue crack growth predictions. Eng Fract Mech 13, 439–451 (1980)CrossRefGoogle Scholar
  27. 27.
    J.M. Alegre, M. Preciado, D. Ferreño, Study of the fatigue failure of an anti-return valve of a high pressure machine. Eng Fail Anal 14, 408–416 (2007)CrossRefGoogle Scholar
  28. 28.
    F. Erdogan, G.C. Sih, On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85, 519–525 (1963)CrossRefGoogle Scholar
  29. 29.
    S.K. Maiti, R.A. Smith, Criteria for brittle fracture in biaxial tension. Eng Fract Mech 19, 793–804 (1984)CrossRefGoogle Scholar
  30. 30.
    S.H. Sajjadi, M.J. Ostad Ahmad Ghorabi, D. Salimi-Majd, A novel mixed-mode brittle fracture criterion for crack growth path prediction under static and fatigue loading. Fatigue Fract Eng Mater Struct 38, 1372–1382 (2015)CrossRefGoogle Scholar
  31. 31.
    J. Weertman, Rate of growth of fatigue cracks calculated from the theory of infinitesimal dislocations distributed on a plane. Int J Fract Mech 2, 460–467 (1966)CrossRefGoogle Scholar
  32. 32.
    R.W. Lardner, A dislocation model for fatigue crack growth in metals. Philos Mag 17, 71–82 (1968)CrossRefGoogle Scholar
  33. 33.
    G. Irwin, Analysis of stresses and strains near the end of a crack transversing a plate. J Appl Mech 24, 361–370 (1957)Google Scholar
  34. 34.
    H. Pathak, A. Singh, I.V. Singh, Numerical simulation of 3D thermo-elastic fatigue crack growth problems using coupled FE-EFG approach. J Inst Eng India Ser C 98, 295–312 (2017)CrossRefGoogle Scholar
  35. 35.
    M. Hussain, S. Pu, J. Underwood, Strain energy release rate for a crack under combined mode I and mode II. Fract Anal ASTM STP 560, 2–28 (1974)Google Scholar
  36. 36.
    FRANC2D, A Crack Propagation Simulator (Cornell University, New York, 1998)Google Scholar
  37. 37.
    MATLAB. The MathWorks, Inc., Natick, Massachusetts, US (2000)Google Scholar
  38. 38.
    M.A. Pustejovsky, Fatigue crack propagation in titanium under general in-plane loading—I: experiments. Eng Fract Mech 11, 9–15 (1979)CrossRefGoogle Scholar

Copyright information

© The Institution of Engineers (India) 2017

Authors and Affiliations

  • S. Sajith
    • 1
  • K. S. R. Krishna Murthy
    • 1
    Email author
  • P. S. Robi
    • 1
  1. 1.Department of Mechanical EngineeringIndian Institute of Technology GuwahatiGuwahatiIndia

Personalised recommendations