Skip to main content
Log in

Stress intensity factors for the inner generative crack induced by the out-of-plane stress in front of the main through-the-thickness crack

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

The problem of the inner generative crack induced by the out-of-plane stress in front of the main through-the-thickness crack is discussed. The crack front of the inner generative crack is usually perpendicular to that of the main crack in the high strength pipeline steel. A three-dimensional (3D) semi-analytical method to estimate the stress intensity factor (SIF) of the inner generative crack has been proposed, based on the 3D two-parameter K–T z approach and Bueckner’s principle of superposition. Detailed comparison of the 3D semi-analytical, finite element (FE) and the corresponding plane strain solutions has been performed. It was shown that the 3D semi-analytical solutions agree well with the 3D FE results and they both are less conservative than the planar solutions. The influence of the inner generative crack on the SIF of the main crack was also analyzed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Irwin, G.R.: Fracture dynamics. Fracturing of metals, pp. 147–166. American Society for Metals, Cleveland (1948)

  2. Irwin G.R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. Trans. ASME 24: 361–364

    Google Scholar 

  3. Rooke D.P. and Cartwright D.T. (1976). Compendium of stress intensity factors. Her Majesty’s Stationery Office, London

    Google Scholar 

  4. Newman J.C. and Raju I.S. (1981). An empirical stress intensity factor equation for the surface crack. Engng. Fract. Mech. 15: 185–192

    Article  Google Scholar 

  5. Murakami Y. (1987). Stress intensity factors handbook. Pergamon Press, Oxford

    Google Scholar 

  6. Fett T. (1991). An analysis of the three-point bending bar by use of the weight function method. Engng. Fract. Mech. 40: 683–686

    Article  Google Scholar 

  7. Tada, H., Paris, P.C., Irwin, G.R.: The stress analysis of crack handbook. The American Society of Mechanical Engineers (2000)

  8. Guo W., Dong H., Lu M. and Zhao X. (2002). The coupled effects of thickness and delamination on cracking resistance of X70 pipeline steel. Int. J. Press. Vessels Pip. 79: 403–412

    Article  Google Scholar 

  9. Dong H.R., Guo W. and Luo J.H. (2003). Mechanism analysis on delamination of pipeline steel and its effect on fracture. Mat. Mech. Engng. 27: 9–12

    Google Scholar 

  10. Yang Z., Huo C.Y. and Guo W. (2005). The charpy notch impact test of X70 pipeline steel with delamination cracks. Key Engng. Mater. 297–300: 2391–2396

    Article  Google Scholar 

  11. Li H., Kurtz R.J. and Jones R.H. (1998). Effect of thickness and loading mode on the fracture properties of V-4Cr-4Ti at room temperature. J. Nucl. Mater. 258–263: 1386–1391

    Article  Google Scholar 

  12. She C. and Guo W. (2007). The out-of-plane constraint of mixed-mode cracks in thin elastic plates. Int. J. Solids Struct. 44: 3021–3034

    Article  MATH  Google Scholar 

  13. Nakamura T. and Parks D.M. (1988). Three-dimensional stress field near the crack front of a thin elastic plate. J. Appl. Mech. 55: 805–813

    Article  Google Scholar 

  14. Bueckner H.F. (1958). The propagation of cracks and the energy of elastic deformation. J. Appl. Mech. Trans. ASME 80: 1225–1230

    Google Scholar 

  15. Guo W. (1993). Elastoplastic three-dimensional crack border field-I. Singular structure of the field. Engng. Fract. Mech. 46: 93–104

    Article  Google Scholar 

  16. Guo W. (1993). Elastoplastic three-dimensional crack border field-II. Asymptotic solution for the field. Engng. Fract. Mech. 46: 105–113

    Article  Google Scholar 

  17. Guo W. (1995). Elastoplastic three-dimensional crack border field-III. Fracture parameters. Engng. Fract. Mech. 51: 51–71

    Article  Google Scholar 

  18. Henshell R.D. and Shaw K.G. (1975). Crack tip finite elements are unnecessary. Int. J. Numer. Meth. Engng. 9: 495–507

    Article  MATH  Google Scholar 

  19. Barsoum R.S. (1976). On the use of isoparametric finite elements in linear fracture mechanics. Int. J. Numer. Meth. Engng. 10: 25–37

    Article  MATH  Google Scholar 

  20. Williams M.L. (1957). On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24: 109–114

    MATH  MathSciNet  Google Scholar 

  21. Levy N., Marcal P.V. and Rice J.R. (1971). Progress in three-dimensional elastic–plastic stress analysis for fracture mechanics. Nucl. Engng. Des. 17: 64–75

    Article  Google Scholar 

  22. Kassir, M.K., Sih, G.C.: Three dimensional crack problems. In: Sih, G. (ed.) Mechanics of fracture, vol. II. Noordhoff International Publishing, Leyden (1974)

  23. ASTM E561–81: Standard test method for R-curve measurement (1981)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chongmin She.

Rights and permissions

Reprints and permissions

About this article

Cite this article

She, C., Guo, W. Stress intensity factors for the inner generative crack induced by the out-of-plane stress in front of the main through-the-thickness crack. Acta Mech 200, 45–57 (2008). https://doi.org/10.1007/s00707-007-0577-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-007-0577-y

Keywords

Navigation