International Journal of Fracture

, Volume 9, Issue 2, pp 133–146 | Cite as

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

  • R. C. Shah
  • A. S. Kobayashi
Article

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.

Keywords

Shear Stress Mechanical Engineer Free Surface Civil Engineer Stress Intensity Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [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.Google Scholar
  2. [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. [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. [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).Google Scholar
  5. [5]
    L. R. Hall, Plane Strain Cyclic Flaw Growth in 2014-T62 Aluminum and 6A1-4V(ELI) Titanium, NASA CR-72396 (November 1968)Google Scholar
  6. [6]
    J. N. Masters, W. P. Haese and R. W. Finger, Investigation of Deep Flaws in Thin-Walled Tanks, NASA CR-72606 (December 1969)Google Scholar
  7. [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)Google Scholar
  8. [8]
    Private communication with R. W. Thresher, Department of Mechanical Engineering. Oregon State University, Corvallis, Oregon.Google Scholar
  9. [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. [10]
    L. A. Wigglesworth, Stress Distribution in a Notched Plate, Mathematika, 4 (1957) 76–96Google Scholar
  11. [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. [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) 241–255Google Scholar
  13. [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)Google Scholar
  14. [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) 195–200Google Scholar
  15. [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) 71–96Google Scholar
  16. [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) 378–395Google Scholar
  17. [17]
    A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York (1944) 241–245.Google Scholar
  18. [18]
    C. M. Segedin, A Note on Geometric Discontinuities in Elastostatics, International Journal of Engineering Science, 6 (1968) 309–312Google Scholar
  19. [19]
    G. R. Irwin, Analytical Aspects of Crack Stress Field Problems, T. and A. M. Report No. 213, University of Illinois, March 1962Google Scholar
  20. [20]
    M. K. Kassir and G. C. Sih, Geometric Discontinuities in Elastostatics, Journal of Mathematics and Mechanics, 16, No. 9 (1967) 927–948Google Scholar
  21. [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)Google Scholar
  22. [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) 955–969Google Scholar

Copyright information

© Noordhoff International Publishing 1973

Authors and Affiliations

  • R. C. Shah
    • 1
  • A. S. Kobayashi
    • 1
    • 2
  1. 1.The Boeing CompanyAerospace GroupSeattleWashington
  2. 2.Department of Mechanical EngineeringUniversity of WashingtonSeattleWashington

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