On the Path and Area Jx1-Integral Components and their Relationship to the Out-of-Plane Constraint in Elastic Cracked Plates
In this paper, the path and area components of the Jx1-integral, JP and JA, in three dimensional elastic cracked plates under mode-I loading are investigated aiming at relating them to the out-of-plane constraint conditions resulting from different specimen thicknesses. It is concluded that the JP and JA components of the Jx1-integral vary in the region where the out-of-plane constraint extends. Sufficiently far from the crack front, these integrals tend to stabilize, indicating that the thickness constraint vanishes and that a 2D-like stress and strain fields have been reached. A pure plane strain condition is only attained when the specimen thickness is very large when compared to the in-plane dimensions. For thin plates, it is shown that the 2D plane stress condition is impossible in the close neighbourhood of a 3D crack front under elastic behaviour so that the consideration of an equivalent Young modulus E', used to find a simple relation between the J(s)-integral and KI for different constraint levels can be misleading.
M.H Aliabadi, S. Abela, S. Baragetti, M. Guagliano and Han-Seung Lee
A. Fernández Canteli et al., "On the Path and Area Jx1-Integral Components and their Relationship to the Out-of-Plane Constraint in Elastic Cracked Plates", Key Engineering Materials, Vols. 417-418, pp. 421-424, 2010