Abstract
As in the two-dimensional case, we shall find considerable similarities in the formulation and solution of contact and crack problems. In particular, we shall find that problems for the plane crack can be reduced to boundary-value problems which in the case of axisymmetry can be solved using the method of Green and Collins developed in ยง22.2.
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Notes
I.N. Sneddon, The distribution of stress in the neighbourhood of a crack in an elastic solid, Proc.Roy.Soc. (London), Vol. A187 (1946), 226โ260.
More generally, any problem involving a crack of arbitrary cross-section A on the plane z = 0 and loaded by a uniform tensile stress ฯzz at z = ยฑโ has the same symmetry and can also be formulated using Solution F. In the general case, we obtain a two-part boundary-value problem for the half-space z > 0, in which conditions (23.6) and (23.7) are to be satisfied over A and ฤ respectively, where ฤ is the complement of A in the plane z = 0.
This problem was first solved by A.L.Florence and J.N.Goodier, The linear thermoelastic problem of uniform heat flow disturbed by a penny-shaped insulated crack, Int.J.Engng.Sci., Vol. 1 (1963), 533-540.
The other constant of integration leads to a term which is singular at the origin and has therefore been set to zero.
This is known as the Reissner-Sagoci problem.
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ยฉ 1992 Springer Science+Business Media Dordrecht
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Barber, J.R. (1992). The Penny-Shaped Crack. In: Elasticity. Solid Mechanics and Its Applications, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2454-6_23
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DOI: https://doi.org/10.1007/978-94-011-2454-6_23
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