Penny-shaped crack in a long circular cylinder subjected to a uniform shearing stress

This paper contains an analysis of the stress distribution in a long circular cylinder of elastic material containing a penny-shaped crack when it is deformed by the application of a uniform shearing stress. The crack with its center on the axis of the cylinder lies on the plane perpendicular to that axis, and the cylindrical surface 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 second kind. These are solved numerically, and the percentage increase in the stress intensity factor due to the effect of the finite radius of the cylinder is presented in graphical form for various proximity ratios.