On the -integral and the out-of-plane constraint in a 3D elastic cracked plate loaded in tension

In this study, the behaviour of the J x 1 -integral and its components J P -integral and J A -integral is numerically investigated for 3D linear elastic cracked plates of different thicknesses loaded in tension. Unlike the path-independent J x 1 -integral, the components J P and J A are shown to be path dependent in a region that coincides with the out-of-plane constrained zone due to the thickness effect, enabling the characterization of this zone with such integrals. The distribution of the out-of-plane components σ 33 and ε 33 in the vicinity of the crack front is also analyzed for different thicknesses and confronted to 2D solutions. In addition, a novel tensor concept of the stress intensity k ij is introduced, showing a unique structure depending on K I irrespective of the specimen thickness. It is confirmed that a pure plane strain condition close and far from the crack front is only asymptotically reached when the specimen thickness is very large when compared to the in-plane dimensions. For thin plates, it is confirmed that the 2D plane stress condition is meaningless in the neighborhood of a 3D crack front under elastic behaviour.