Skip to main content
SpringerLink
Log in

Stress intensity factors for an elliptical crack approaching the surface of a semi-infinite solid

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

Abstract

Stress intensity factors for an embedded elliptical crack approaching the free surface of the semi-infinite solid that is subjected to uniform tension perpendicular to the plane of crack are presented in a nondimensional form for various crack aspect ratios and crack distances from the free surface. Stress intensity factors are determined numerically using an alternating technique with two solutions. The first solution involves an elliptical crack in a solid and subjected to normal loading expressible in a polynomial of x and y. The second solution involves stresses in the half space due to prescribed normal and shear stresses on the surface. Effect of the Poisson's ratio on these stress intensity factors is also investigated. Stress intensity factors for a semi-elliptical surface crack in a tinite thickness plate are then estimated in a nondimensional form for various crack aspect ratios and crack depth to plate thickness ratios.

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. C. F. Tiffany and J. N. Masters, applied Fracture Mechanics, Fracture Toughness and Its Application, ASTM Special Technical Publication No. 381 (1965) 249–278.

  2. A. E. Green and I. N. Sneddon, The Distribution of Stress in the Neighborhood of a Flat Elliptical Crack in an Elastic Solid, Proceedings of the Cambridge Philosophical Society, 46 (1950) 159–163.

    Google Scholar 

  3. G. R. Irwin, Crack Extension Force for a Part-Through Crack in a Plate, Journal of Applied Mechanics, 29, Trans. ASME, 84 (1962) 651–654.

    Google Scholar 

  4. C. F. Tiffany, P. M. Lorenz, and L. R. Hall, Investigation of Plane Strain Flaw Growth in Thick-Walled Tanks, NASA CR-54837 (February 1966).

  5. L. R. Hall, Plane Strain Cyclic Flaw Growth in 2014-T62 Aluminum and 6A1-4V(ELI) Titanium, NASA CR-72396 (November 1968)

  6. J. N. Masters, W. P. Haese and R. W. Finger, Investigation of Deep Flaws in Thin-Walled Tanks, NASA CR-72606 (December 1969)

  7. A. S. Kobayashi and W. L. Moss, Stress Intensity Magnification Factors for Surface-Flawed Tension Plate and Notched Round Tension Bar, Proceedings of the Second International Conference on Fracture, Brighton, England (1968)

  8. Private communication with R. W. Thresher, Department of Mechanical Engineering. Oregon State University, Corvallis, Oregon.

  9. F. W. Smith A. F. Emery and A. S. Kobayashi, Stress Intensity Factors for Semi-circular Cracks, Part 2 -Semi-Infinite Solid, Journal of Applied Mechanics, 34, Trans. ASME, 89 (1967) 953–959.

    Google Scholar 

  10. L. A. Wigglesworth, Stress Distribution in a Notched Plate, Mathematika, 4 (1957) 76–96

    Google Scholar 

  11. A. S. Kobayashi, M. Ziv and L. R. Hall, Approximate Stress Intensity Factor for an Embedded Elliptical Crack Near Two Parallel Free Surfaces, International Journal of Fracture Mechanics, 1, No. 2 (1965) 81–95.

    Google Scholar 

  12. F. W. Smith and M. J. Alavi, Stress Intensity Factors for a Penny Shaped Crack in a Half Space, Journal of Engineering Fracture Mechanics, 3, no. 2 (1971) 241–255

    Google Scholar 

  13. F. W. Smith and M. J. Alavi, Stress Intensity Factors for a Part Circular Surface Flaw, Proceedings of the First International Conference on Pressure Vessel Technology, Delft, Holland (1969)

  14. R. W. Thresher, and F. W. Smith, Stress Intensity Factors for a Surface Crack in a finite Solid, Journal of Applied Mechanics, 39th Trans. of ASME, 95 (1972) 195–200

    Google Scholar 

  15. R. C. Shah, and A. S. Kobayashi, Stress Intensity Factor for an Elliptical Crack Under Arbitrary Normal Loading, Journal of Engineering Fracture Mechanics, 3, no. 1 (1971) 71–96

    Google Scholar 

  16. A.E.H. Love, On Stress Produced in a Semi-Infinite Solid by Pressure on Part of the Boundary, Philosophical Transactions of the Royal Society, Series A, 228 (1929) 378–395

    Google Scholar 

  17. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York (1944) 241–245.

    Google Scholar 

  18. C. M. Segedin, A Note on Geometric Discontinuities in Elastostatics, International Journal of Engineering Science, 6 (1968) 309–312

    Google Scholar 

  19. G. R. Irwin, Analytical Aspects of Crack Stress Field Problems, T. and A. M. Report No. 213, University of Illinois, March 1962

  20. M. K. Kassir and G. C. Sih, Geometric Discontinuities in Elastostatics, Journal of Mathematics and Mechanics, 16, No. 9 (1967) 927–948

    Google Scholar 

  21. R. C. Shah and A. S. Kobayashi, Stress Intensity Factors for an Elliptical Crack Approaching the Surface of Semi-Infinite Solid, Boeing Company Document No. D-180-14494-1, (1971)

  22. M. Isida and Y. Itagaki, The Effect of Longitudinal Stiffeners in a Cracked Plate under Tension, Proceedings of the 4th U.S. National Congress of Applied Mechanics (June 1962) 955–969

Download references

Author information

Authors and Affiliations

  1. The Boeing Company, Aerospace Group, Seattle, Washington

    R. C. Shah (Specialist Engineer) & A. S. Kobayashi (Professor)

  2. Department of Mechanical Engineering, University of Washington, Seattle, Washington

    A. S. Kobayashi (Professor)

Authors
  1. R. C. Shah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Kobayashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Specialist Engineer, Aerospace Group, The Boeing Company, Seattle, Washington.

Professor, Department of Mechanical Engineering, University of Washington, Seattle, Washington, and also Aerospace Group, The Boeing Company, Seattle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shah, R.C., Kobayashi, A.S. Stress intensity factors for an elliptical crack approaching the surface of a semi-infinite solid. Int J Fract 9, 133–146 (1973). https://doi.org/10.1007/BF00041855

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00041855

Keywords

Search

Navigation