Probabilistic Description of Fatigue Crack Growth in a Titanium Alloy Notched Member

  • D. Kocańda
  • S. Kocańda
  • H. Tomaszek
Chapter
Part of the NATO Science Series book series (NAII, volume 11)

Abstract

This paper deals with the prediction of short and long fatigue crack growth in notched members using linear elastic fracture mechanics (LEFM) and includes the stochastic nature of the fatigue process. The probabilistic approach to modelling of crack growth in the depth of components links up with the authors’ previous work, which considered surface crack growth in notched and unnotched samples. The capability of the discussed method in terms of crack growth prediction and lifetime estimation has been verified using experimental data gained for the (a+ß) Ti-6Al-SMo-2Cr (Vt3-1) alloy tested under reversed torsion and reversed bending, at room temperature, and in the range of high cycle fatigue (HCF). Characteristic features of crack initiation and propagation in the examined titanium alloy components with a circumferential notch are shown. Micro-observations of fracture surfaces using both a SEM and TEM allowed us to establish the mechanism of cracking.

Keywords

Fatigue Titanium Furnace Argon Propa 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Neuber, H., (1957) Kerbspannungslehre, Springer, Berlin.Google Scholar
  2. 2.
    Neuber, H. (1961) Theory of stress concentration for shear strained prismatic bodies with arbitrary nonlinear stress-strain law, Trans. ASME, J. Appl. Mechs 28, 544–550.MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Williams, M.L. (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mechs 19, 526–528.Google Scholar
  4. 4.
    Peterson, R.E. (1974) Stress concentration factors, N.-Y. John Wiley&Sons.Google Scholar
  5. 5.
    Kuhn, P. (1970) Residual tensile strength in the presence of through cracks or surface cracks, NASA TND-5432.Google Scholar
  6. 6.
    Hardrath, H.F. and Ohman, L. (1953) A study of elastic and plastic stress concentration factors due to notches and fillets in flat plates. NASA Rep. 1117.Google Scholar
  7. 7.
    Creager, M. and Paris, P. C. (1967) Elastic field equations for blunt cracks with reference to stress corrosion cracking. Int. J. Fract. Mech. 3, 247–252.Google Scholar
  8. 8.
    Raju, I. S. and Newman, J. C., Jr. (1979) Stress intensity factors for a wide range of semi-elliptical surface cracks in finite thickness plates, Engng Fracture Mech. 2, 817–829.CrossRefGoogle Scholar
  9. 9.
    Carpinteri, A. and Brighenti, R. (1998) Stress field near a notch root under pure bending, J. Physicochem. Mechs Mater. 5, 43–48.Google Scholar
  10. 10.
    Oryniak, I.V., Borodii, M.V. and Krasowskyj, A. Ya (1998) Method of the stress intensity factor calculation for cracks emanating from notches, J. Physicochem. Mechs Mater. 5, 69–74.Google Scholar
  11. 11.
    Noda, N.A. and Takase, Y. (1999) Stress concentration formulae useful for any shape of notch in a round test specimen under tension and under bending, Fatigue Fract. Engng Mater. Struct. 22, 1071–1082.CrossRefGoogle Scholar
  12. 12.
    Atzori, B., Lazzarin, P. and Tovo, R. (1997) Stress distribution for V-shaped notches under tensile and bending loads, Fatigue Fract. Engng Mater. Struct. 20, 1083–1092.CrossRefGoogle Scholar
  13. 13.
    Xu, R.X., Topper, T.H. and Thompson, J.C (1997) Mode I stress intensity factor equations for cracks at notches and cavities, Fatigue Fract. Engng Mater. Struct. 20, 1351–1361.CrossRefGoogle Scholar
  14. 14.
    Chien, C.H. and Coffin, L.F. (1998) A new method for predicting fatigue life in notches geometries, Fatigue Fract. Engng Mater. Struct. 21, 1–15.CrossRefGoogle Scholar
  15. 15.
    McEvily, A.J., Eifler, D. and Macherauch, E. (1991) An analysis of the growth of short fatigue cracks. Engng Fracture Mechs 40, 571-548.Google Scholar
  16. 16.
    Shingai, K. (1999) Elastic-plastic strain concentrations and plastic zones of notched specimens under tensile load, in J.H. Beynon, M.W. Brown, T.C. Lindley, R.A. Smith& B. Tomkins (eds.), Engineering Against Fatigue, A.A. Balkema, Rotterdam/Brookfield, pp. 423–430.Google Scholar
  17. 17.
    Kadi, M. and Pluvinage, G. (1999) Effective stress range in fatigue initiation emanating from notch, in X.R. Wu& Z.G. Wang (eds.), Fatigue’99, Proc. 7th Intern. Fatigue Congress, EMAS Higher Education Press, Beijing, P.R. China, pp. 1175–1179.Google Scholar
  18. 18.
    Navarro, A., Vallellano, C. and de los Rios, E.R. (1999) Notch sensitivity and size effects described by a short crack propagation model, in J.H. Beynon, M.W. Brown, T.C. Lindley, R.A. Smith& B Tomkins (eds.), Engineering Against Fatigue, A.A. Balkema, Rotterdam/Brookfield, pp. 423–430.Google Scholar
  19. 19.
    Hoshide, T. and Kusuura, T. (1998) Life prediction by simulation of crack growth in notched components with different microstructures and under multiaxial fatigue, Fatigue Fract. Engng Mater. Struct. 21, 201–213.CrossRefGoogle Scholar
  20. 20.
    Wurm, B., Pham, V.B. and Sähn, S. (1999) Fatigue crack propagation at sharp notches, in X.R. Wu & Z.G. Wang (eds.), Fatigue’99, Proc. 7th Intern. Fatigue Congress, EMAS Higher Education Press, Beijing, P.R. China, pp. 1163–1168.Google Scholar
  21. 21.
    Jago, G. and Bechet, J. (1999) Influence of microstructure of (a+ß) Ti-6.2.4.6 alloy on high-cycle fatigue and tensile test behaviour, Fatigue Fract. Engng Mater. Struct. 22, 647–655.Google Scholar
  22. 22.
    Ritchie, R.O., Davidson, D.L., Boyce, B.L., Campbell, J.P. and Roder, O. (1999) High-cycle fatigue of Ti-6A1-4V, Ibidem, 621–631.Google Scholar
  23. 23.
    Niinomi, M., Fukunaga, K., Akahori, T., Ozeki, A. and Wang, L. (1999) Small fatigue crack initiation and propagation characteristic of Ti-6Al-7Nb, in X.R. Wu& Z.G. Wang (eds.), Fatigue’99, Proc. 7th Intern. Fatigue Congress, EMAS Higher Education Press, Beijing, P.R. China, pp. 353–358.Google Scholar
  24. 24.
    Haung, H. and Liu, S. (1999) Small crack growth and growth rate predictions for titanium alloy TC 11, Ibidem, pp. 371–376.Google Scholar
  25. 25.
    Choi, S.D., Mayama, H., Misava, H., Akita, K. And Lee, J.H. (1999) Characteristic of fatigue crack initiation and propagation on Ti-6A1-4V alloy heat treated in beta field, Ibidem, pp. 427–432.Google Scholar
  26. 26.
    Lesterling, S., Sarrazin-Baudoux, C. and Petit, J. (1999) Mechanisms of fatigue crack propagation in titanium alloys at elevated temperature: Environmental influence, in J.H. Beynon, M.W. Brown, T.C. Lindley, R.A. Smith& B. Tomkins (eds.), Engineering Against Fatigue, A.A. Balkema, Rotterdam/Brookfield, pp. 521–529.Google Scholar
  27. 27.
    Shanyavsky, A.A. and Stepanov, N.V. (1995) Fractographic analysis of fatigue crack growth in engine compressor disks of Ti-6Al-3Mo-2Cr titanium alloy, Fatigue Fract. Engng Mater. Struct. 18, 539–550.CrossRefGoogle Scholar
  28. 28.
    Shanyavsky, A.A., Losev, A.I. and Banovf, M.D. (1998) Development of fatigue cracking in aircraft engine compressor disks of Ti6AL3Mo2Cr titanium alloy, Fatigue Fract. Engng Mater. Struct., 21, 297–313.CrossRefGoogle Scholar
  29. 29.
    Kocanda, D, Kocanda S. and Tomaszek, H. (1996) Probabilistic evaluation of fatigue life in short crack range on the grounds of linear fracture mechanics, in G. Lütjering& H. Nowack (eds), Fatigue’96, Sixth Int. Fatigue Congress, Pergamon, pp. 1275–1280.Google Scholar
  30. 30.
    Kocanda, D, Kocanda S. and Tomaszek, H. (1998) Fatigue crack growth and fatigue life estimation of notched members in a short crack range, in K.-T. Rie& P.D. Portella (eds), Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials”, Fourth Int. Conf., Elsevier Science, pp.547–552.Google Scholar
  31. 31.
    Kocanda, D, Kocanda S. and Tomaszek, H. (1999) Experimental and theoretical investigations of short fatigue crack growth in laser hardened medium carbon steel, in J.H. Beynon, M.W. Brown, T.C. Lindley, R.A. Smith& B Tomkins (eds.), Engineering Against Fatigue, A.A. Balkema, Rotterdam/Brookfield, pp. 501–507.Google Scholar
  32. 32.
    Kocanda, D, Kocanda S. and Tomaszek, H. (1998) Deterministic and probabilistic description of fatigue crack short crack growth in notched members, J. Physicochem. Mechs Mater. 5, 61–68.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • D. Kocańda
    • 1
  • S. Kocańda
    • 1
  • H. Tomaszek
    • 1
  1. 1.Military University of TechnologyWarszawaPoland

Personalised recommendations