Recent advances in three-dimensional fracture mechanics

Some basic three-dimensional (3D) problems in fracture mechanics are discussed in this paper. Firstly, the interaction between the stress-strain fields and the out-of-plane constraint is analyzed. The weaker singularities of stresses at the crack border in both linear elastic and elastic-plastic materials are shown to be confined to an infinite small zone at the intersection point of the crack front line and the free surface of the cracked body. Therefore, the K-based linear elastic fracture mechanics theory and J-based nonlinear fracture mechanics theory can be extended to 3D cracked bodies. The influence of the out-of-plane constraint factor Tz on the crack tip fields was analyzed and the variations of some important fracture parameters from plane stress to plane strain state are summarized. Then, in consideration the influences of both the in-plane and out-of-plane constraints, a general J-Q(T)-Tz or J-A(2)-Tz theory is proposed and proven to be more effective. Finally, the 3D effect on fracture of engineering materials is outlined.