The penny crack beneath the surface of a half-space: with application to the blister test

The crack tip stress intensities are found for a penny shaped crack lying beneath the free surface of a half-space, and parallel with it. This is done by employing a novel distributed dislocation approach using axi-symmetric Somigliana dislocations as the kernel of an integral equation, and provides a precise solution at the expense of little computing cost. A comparison is made with the crack tip stress intensity factors for a simple plane crack, and predictions are made for the preferred crack extension direction.