Three-dimensional stress fields near notches and cracks

Structures with notches have a tendency to develop critical crack growth because of the stress concentration. The strength of the structures with stress gradient usually shows strong three-dimensional (3D) effects even under in-plane loading. The commonly two-dimensional (2D) models for fracture assessments of bodies with notches and cracks may lead to inaccurate predictions when in-plane loading is applied to certain 3D geometries. In the paper, the recent researches on the 3D effects of stress concentrations at notches and 3D stress fields of cracks are summarized. A new concept of equivalent thickness of the point on the crack front line is proposed based on the detailed analyses of the 3D out-of-plane stress fields of cracks, and then new empirical formulae of the 3D out-of-plane stress constraint factor T_z of I-II mixed-mode cracks are obtained by use of the equivalent thickness. Combining the T_z with the in-plane constraint parameters T or Q, the 3D multi-parameter descriptions of the stress field in front of various types of cracks using K-T_z, J-T_z, K-T-T_z and J-Q-T_z combination can be formulated.