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Analysis of a flat annular crack under shear loading

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An annular crack in an infinite isotropic elastic solid under shear loading is analyzed. General solution to the Navier's equilibrium equation is expressed in terms of three harmonic functions. Employing the Hankel transform the harmonic functions are represented by the solution of a pair of triple integral equations. The triple integral equations are reduced to a pair of mixed Volterra-Fredholm integral equations, which are numerically solved. The stress intensity factors of the annular crack under various shear loadings such as uniform radial shear, linearly varying radial shear, uniform shear and linearly varying shear are calculated as the Poisson's ratio ν anda/b (a; inner radius,b; outer radius) vary.

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  1. Choi, I. and Shield, R. T., 1982, “A Note on a Flat Toroidal Crack in an Elastic Isotropic Body,” Int. J. Solids Structures, Vol. 18, pp. 479–486.

  2. Cooke, J. C., 1963, “Triple Integral Equations,” Quart. J. Mech. Appl. Math., Vol. 16, pp. 193–203.

  3. Danyluk, H. T. and Singh, B. M., 1986, “Problem of an Infinite Solid Containing a Flat Annular Crack under Torsion,” Engng Fracture Mech., Vol. 24, pp. 33–38.

  4. Kassir, M. K. and Sih, G. C., 1975, “Three-Dimensional Crack Problems,” In Mechanics of Fracture (Edited by G. C. Sih), Vol. 2, Noordhoff International Publishing, Leyden.

  5. Kim, M. U. and Kim, J. U., 1985, “Slow Rotation of an annular Disk in a Viscous Fluid,” J. Phys. Soc. Jpn., Vol. 54, pp. 3337–3341.

  6. Moss, L. W. and Kobayashi, A. S., 1971, “Approximate Analysis of Axisymmetric Problems in Fracture Mechanics with Application to a Flat Toroidal Crack,” Int. J. Fracture Mech., Vol. 7, pp. 89–99.

  7. Panasyuk, V. V., Andrejkiv, A.E. and Stadnik, M. M., 1981, “Theree-Dimensional Static Crack Problems Solution (a Review),” Engng Fracture Mech., Vol. 14, pp. 245–260.

  8. Selvadurai, A. P. S. and Singh, B. M., 1985, “The Annular Crack Problem for an Isotropic Elastic Solid,” Quart. J. Mech. Appl. Math., Vol. 38, pp. 233–243.

  9. Smetanin, B. I., 1968, “Problem of Extension of an Elastic Space Containing a plane Annular Slit,” PMM, J. Appl. Math. Meth., Vol. 32, pp. 458–462.

  10. Sneddon, I. N., 1946 “The Distribution of stress in the Neighborhood of acrack in an Elastic Solid,” Proc. Roy. Soc. (London) A, Vol. 187, pp. 229–260.

  11. Watson G. N., 1944, “Theory of Bessel Functions” Cambridge University Press, London.

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Correspondence to Hyeon Gyu Beom.

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Beom, H.G., Earmme, Y.Y. Analysis of a flat annular crack under shear loading. KSME Journal 7, 35–47 (1993). https://doi.org/10.1007/BF02953143

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Key Words

  • Annular Crack
  • Hankel Transform
  • Triple Integral Equation
  • Mixed Volterra-Fredholm Integral Equation
  • Stress Intensity Factor
  • Shear Loading