Three-dimensional assessments of crack tip constraint

Abstract

Crack tip constraint can be used as a means to relate the stresses at the crack tip to a measure of fracture toughness of a material. Current technique to determine crack tip constraint demonstrated in structural integrity standards are based on two-dimensional plane strain approach. This paper explores the possibility of extending the current two-dimensional crack tip constraint solutions to three-dimensional crack problems through an investigation of the asymptotic structure of three-dimensional crack tip stress fields under elastic-plastic non-hardening responses. Analysis was based on three-dimensional boundary layer formulations, combined with full-field solutions of single edge notched bend bars and centre cracked tension panels having a range of thicknesses. The fields along the crack front were examined as a function of load level and thickness. From the results, it is demonstrated that, at the crack tip (r = 0), a family of asymptotic fields develop which feature a constant stress sector directly at the crack tip. Within this sector the fields differ hydrostatically while being similar in respect of the maximum stress deviator. At the intersection with the free surface, an elastic perfectly-plastic corner field which differs from the plane stress field is shown to develop. It is shown that in these fields the level of constraint is parameterised by J/zσo, where z is the distance from the free surface. J/zσo unifies both the change in the maximum principal stress and the mean stress, as a function of thickness and deformation level from all sections of different geometry and thickness specimens. An explicit expression has been developed which demonstrated the constraint loss due to in-plane and out-of plane crack tip constraint effects, allowing a two-parameter fracture mechanics methodologies in a modified form to be extended to fully three-dimensional fields.