Solution of axisymmetric crack problems using distributed dislocation ring dipoles

Abstract

A solution procedure for the calculation of crack tip stress intensity factors arising at the edges of an arbitrarily shaped crack lying on a surface of revolution is described. The cracks are subject to an arbitrary axisymmetric stress field, devoid of torsion, and may be present in either an infinite space or two elastically dissimilar bonded half-spaces, of which one may, as a special case, have vanishing elastic constants. The technique employed is a one-dimensional integral equation approach, in which the kernel is formed from rings of dislocation pairs, arranged to form ring ‘dipoles’. The equation is hypersingular but may readily be inverted using powerful numerical quadratures, providing a computationally efficient solution. Examples of the use of the technique are then described.