Skip to main content
SpringerLink
Log in

Variation of stress intensity factor along the front of a 3D rectangular crack by using a singular integral equation method

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

In this paper a singular integral equation method is applied to calculate the distribution of stress intensity factor along the crack front of a 3D rectangular crack. The stress field induced by a body force doublet in an infinite body is used as the fundamental solution. Then, the problem is formulated as an integral equation with a singularity of the form of r −3. In solving the integral equation, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function, which expresses stress singularity along the crack front in an infinite body. The calculation shows that the present method gives smooth variations of stress intensity factors along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abe, H., Hayashi, K. and Enokida, Y. (1982). Stress intensity factors for a rectangular crack in a semi-infinite solids. Trans. Japan Soc. Mech. Engrs 48, 29-34.

    Google Scholar 

  • Hadamard, J. (1923). Lectures on Caunchy's Problem in Linear Partial Differential Equations, Yale University Press.

  • Isida, M., Yoshida, T. and Noguchi, H. (1982). A rectangular crack in an infinite solid, a semi-infinite solid and a finite-thickness plate subjected to tension. Prelim Proc. Japan Soc. Mech. Engrs. and Japan Soc. Precision Engng., Mie District, No. 823-3, pp. 15-17 (in Japanese).

  • Isida, M., Tsuru, H. and Noguchi, H. (1983). New method of analysis of three-dimensional crack problems. Memoirs of the Faculty of Engineering, Kyushu University, Vol. 43, No.4, pp. 317-334.

    Google Scholar 

  • Isida, M., Yoshida, T. and Noguchi, H. (1991). A rectangular crack in an infinite solid, a semi-infinite solid and a finite-thickness plate subjected to tension. International Journal of Fractures 52, 79-90.

    Google Scholar 

  • Kassir, M.K. (1981). Stress intensity factor for a three-dimensional rectangular crack. Trans. ASME, Sea. E 48, 309-312.

    Google Scholar 

  • Kassir, M.K. (1982). A three-dimensional rectangular crack subjected to shear loading. International Journal Solid and Structures 18, 1075-1082.

    Google Scholar 

  • Mastrojannis, E.N., Keer, L.M. and Mura, T.A. (1979). “Stress Intensity Factor for a Plane Crack under Normal Pressure”, International Journal of Fractures 15, 247-258.

    Google Scholar 

  • Murakami, Y. (1985). Analysis of stress intensity factors of Modes I, II and III inclined surface cracks of arbitrary shape. Engng. Frac. Mech. 22, 101-114.

    Google Scholar 

  • Murakami, Y. and Endo, M. (1983). Quantitative evaluation of fatigue strength of metals containing various small defects or cracks. Engng. Frac. Mech. 17, 1-15.

    Google Scholar 

  • Murakami, Y. and Nemat-Nasser, S. (1983). Growth and stability of interacting surface flaws of arbitrary shape. Engng. Frac. Mech. 17, 193-210.

    Google Scholar 

  • Murakami, Y., Kodama, S. and Konuma, S. (1988). Quantitative evaluation of effects of nonmetallic inclusions on fatigue strength of high strength steel. Trans. Japan Society of Mechanical Engineers 54, 688-696 (in Japanese).

    Google Scholar 

  • Nisitani, H. (1967). The two-dimensional stress problem solved using an electric digital computer. Journal of the Japan Society of Mechanical Engineers 70, 627-632 (in Japanese).

    Google Scholar 

  • Nisitani, H. (1968). Bulletin of Japan Society of Mechanical Engineers 11, 14-23.

    Google Scholar 

  • Nisitani, H. and Murakami, Y. (1974). Stress Intensity Factor of an Elliptical Crack and Semi-Elliptical Crack in Plates Subjected to Tension, International Journal of Fractures 10, 353-368.

    Google Scholar 

  • Noda, N.-A. and Miyoshi, S. (1996). Variation of stress intensity factor and crack opening displacement of a semi-elliptical surface crack. International Journal of Fractures 75, 19-48.

    Google Scholar 

  • Noda, N.-A., Kobayashi, K. and Yagishita, M. (1999). Variation of mixed modes stress intensity factors of an inclined semi-elliptical surface crack, International Journal of Fractures (in press).

  • Weaver, J. (1977). Three-Dimensional crack analysis. International Journal of Solids Structures 13, 321-330.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Kyushu Institute of Technology, Kitakyushu, 804-8550, Japan

    Qing Wang, Nao-Aki Noda, Masa-Aki Honda & Mengcheng Chen

Authors
  1. Qing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nao-Aki Noda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Masa-Aki Honda
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mengcheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, Q., Noda, NA., Honda, MA. et al. Variation of stress intensity factor along the front of a 3D rectangular crack by using a singular integral equation method. International Journal of Fracture 108, 119–131 (2001). https://doi.org/10.1023/A:1007669725341

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007669725341

Search

Navigation