Axisymmetric displacement boundary value problem for a penny-shaped crack
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A solution is derived from equations of equilibrium in an infinite isotropic elastic solid containing a penny-shaped crack where displacements are given. Abel transforms of the second kind stress and displacement components at an arbitrary point of the solid are known in the literature in terms of jumps of stress and displacement components at a crack plane. Limiting values of these expressions at the crack plane together with the boundary conditions lead to Abel-type integral equations, which admit a closed form solution. Explicit expressions for stress and displacement components on the crack plane are obtained in terms of prescribed face displacements of crack surfaces. Some special cases of the crack surface shape functions have been given in the paper.
Key wordspenny shaped crack Abel transforms displacements asymmetry knoop indentation axial symmetry
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- 1.Parihar, K. S.;Krishna Rao, J. V. S.: Axially symmetric stress distribution in the neighbourhood of a penny-shaped crack under general surface loadings. Eng. Fract. Mech. 39 (1991) 1067–1095Google Scholar
- 2.Parihar, K. S.;Krishna Rao, J. V. S.: The axially symmetric problem of a penny-shaped crack under general surface loadings. Int. J. Eng. Sci. 31 (1993) 953–966Google Scholar
- 3.Sneddon, I. N.: The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc. R. Soc. London Ser. A 187 (1946) 229–260Google Scholar
- 4.Olesiak, Z.;Sneddon, I. N.: The distribution of surface stress necessary to produce a penny-shaped crack of prescribed shape. Int. J. Eng. Sci. 7 (1969) 863–873Google Scholar
- 5.Sneddon, I. N.: Fourier transforms. New York: McGraw-Hill 1951Google Scholar
- 6.Sneddon, I. N.;Lowengrub, M.: Crack problems in the classical theory of elasticity. New York: Wiley 1969Google Scholar
- 7.Sneddon, I. N.: Use of integral transforms. New Delhi: Tata McGraw-Hill 1979Google Scholar
- 8.Fett, T.: Fracture of ceramics with surface flaws introduced by knoop indentation. J. Material Sci. 19 (1984) 672–682Google Scholar