Three-dimensional constraint based fracture mechanics

The structure of three-dimensional crack tip fields has been examined under elastic perfectly plastic conditions using both three-dimensional boundary layer formulations and full-field solution of single edge notched bend bars and centre cracked tension panels. The nature of the stress fields was examined at the crack tip (r = 0) and at a distance of r = 2J/sigmao as a function of load level and thickness. The three-dimensional nature of the crack tip fields has been compared with the limiting cases of plane strain and plane stress. The proximity to plane strain has been assessed using a parameter related to the out-of-plane stress deviator. The proximity to plane stress has been assessed using a parameter related to the radial stress deviator. At the intersection of the free surface and the crack tip, an elastic perfectly-plastic comer field which is different to the plane stress field is shown to develop. Along the crack front, in specimens of different thickness, a family of asymptotic fields develop which feature a constant stress sector. Within this sector the fields differ both hydrostatically and deviatorically but are similar in respect of the maximum stress deviator. This allows the level of the constraint to be assessed by a single parameter which quantifies both the change in the maximum principal stress and the mean stress. A simple expression for out-of-plane constraint loss in SENB and CCP specimens is proposed. In CCP specimens, constraint loss arises from both in-plane and out-of-plane effects. In-plane constraint loss can be estimated using the T-stress and this effect is then combined with out-of-plane constraint loss. At any given section, constraint loss in any thickness specimen can be unified into a single relationship. This allows the quantification of out-of-plane constraint loss through a parameter based on J and the plate thickness. Finally, a three-dimensional constraint based failure methodology based on Failure Assessment Diagrams has been proposed using the analytical expression for constraint loss. The failure assessment scheme has been validated using experimental data on the effect of thickness on toughness