Green’s functions for the T-stress of small kink and fork cracks

Abstract

Green’s functions for T-stresses used so far are restricted to symmetric crack problems, for instance, edge cracks normal to the free surface of a rectangular plate. In the case of more complicated cracks, component geometries, and loading cases, a more general formulation of the Green’s function has to be used. Such a relation was recently proposed by the authors. As an example, Green’s functions for T-stresses acting at the tip of a kinked crack were determined by extending the Cotterell–Rice procedure. Application to the edge-cracked plate revealed an excellent agreement of local T-stress with results obtained directly from FE computations. A simple approximate relation with a high accuracy for kink angles of up to 30° is proposed that allows an estimate of the T-stress from the stress field of the unkinked crack. It is shown that the T-stress of a kinked crack under pure mode-I loading can be computed roughly as the difference of the radial and tangential stresses of the unkinked crack at the tip of the kink.