Penny-shaped crack in a plate of finite thickness subjected to a uniform shearing stress

This paper contains an analysis of the stress distribution in a plate of finite thickness of an elastic material containing a penny-shaped crack when it is deformed by the application of a uniform shearing stress on the surface of the plate. The crack lies on the central plane of the plate with its surface parallel to those of the plate and is stress-free. By making a suitable representation of the stress function for the problem, the problem is reduced to the solution of a pair of Fredholm integral equations of the second kind. This pair of Fredholm integral equations of the second kind is solved numerically, and the increase in the stress intensity magnification factor due to the effect of the finite thickness of the plate is presented for various values of the thickness.