Sudden twisting of a flat annular crack

Abstract

The problem of a torque applied suddenly to the surface of a flat annular crack in an infinite elastic body is considered. The singular solution is equivalent to that of the sudden appearance of a crack in a body under torsion. Laplace and Hankel transforms are used to reduce the problem to a pair of triple integral equations. The solution to the triple integral equations is expressed in terms of a singular integral equation of the first kind with kernel IMproved by means of a contour integration on the Riemann surface. The singular stress distributions near the crack tip are obtained in closed form and the influences of the inertia, the ratio of the inner radius to the outer one and their interactions upon the dynamic stress-intensity factors are shown graphically.