On the problem of a transversely isotropic half-space weakened by a penny-shaped crack filled with a gas

An axially-symmetric problem of a penny-shaped crack situated in a position parallel to the boundary of a semi-infinite transversely isotropic solid is formulated with due regard for the presence of an ideal gas in the crack. The method of the Hankel integral transforms is used to solve this problem. The dual integral equations obtained are reduced to a set of integral equations which are solved numerically. The graphs presented illustrate the influence of the gas on the stress intensity factors of Mode I and Mode II.