Skip to main content
SpringerLink
Log in

Interaction between a spherical inhomogeneity and two symmetrically placed penny-shaped cracks

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

Abstract

Stress analysis is carried out for a three-dimensional elastic solid containing an elastic spherical inhomogeneity and two coplanar penny-shaped cracks. Each of the two cracks is located on either side of the elastic spherical inhomogeneity and the geometry is subjected to uniform tensile stress at infinity. The interaction between the inhomogeneity and the cracks is tackled by the superposition principle of elasticity theory and Eshelby's equivalent inclusion method. Analytical solutions for the stress intensity factors on the boundaries of the cracks and the stress field inside the inhomogeneity are evaluated in series form. Numerical calculations are reported for several special cases, and show the variations of the stress intensity factors and stress field inside the inhomogeneity with the configuration and elastic properties of the solid and the inhomogeneity.

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

  1. O. Tamate, International Journal of Fracture 4 (1968) 257–265.

    Google Scholar 

  2. Y.C. Hsu and V. Shivakumar, International Journal of Fracture 12 (1976) 619–630.

    Google Scholar 

  3. G.P. Sendeckyj, International Journal of Fracture 10 (1974) 45–52.

    Google Scholar 

  4. K.N. Srivastava and R.L. Mahajan, Indian Journal of Technology 8 (1970) 398–404.

    Google Scholar 

  5. H. Hiral and M. Satake, Journal of Applied Mechanics 47 (1980) 806–809.

    Google Scholar 

  6. J.D. Eshelby, in Progress in Solid Mechanics 2, North-Holland, Amsterdam (1961) 89–140.

    Google Scholar 

  7. K. Tanaka and T. Mura, Metallurgical Transactions 13A (1982) 117–123.

    Google Scholar 

  8. S.P. Timoshenko and J.N. Goodier Theory of Elasticity, McGraw-Hill, New York (1934).

    Google Scholar 

  9. T. Mura, Micromechanics of Defects in Solid, Martinus Nijhoff, Boston (1982).

    Google Scholar 

  10. Z.M. Xiao, M.K. Lim and K.M. Liew, International Journal of Engineering Science 32 (1994) 303–311.

    Google Scholar 

  11. M.K. Kassir and G.C. Sih, Three-dimensional Crack Problems, Noordhoff, Leyden (1975).

    Google Scholar 

  12. Z.A. Moschovidis and T. Mura, Journal of Applied Mechanics 42 (1975) 847–852.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, 2263, Singapore

    Z. M. Xiao, K. M. Liew & M. K. Lim

Authors
  1. Z. M. Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. M. Liew
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. K. Lim
    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

Xiao, Z.M., Liew, K.M. & Lim, M.K. Interaction between a spherical inhomogeneity and two symmetrically placed penny-shaped cracks. Int J Fract 70, 305–320 (1994). https://doi.org/10.1007/BF00032449

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00032449

Keywords

Search

Navigation