On the Jx1-Integral and the Out-of-Plane Constraint in a 3D Elastic Cracked Plate Loaded in Tension Articles uri icon

publication date

  • April 2010

start page

  • 934

end page

  • 946


  • 7-8


  • 47

international standard serial number (ISSN)

  • 0020-7683

electronic international standard serial number (EISSN)

  • 1879-2146


  • In this study, the behaviour of the Jx1-integral and its components JP-integral and JA-integral is numerically investigated for 3D linear elastic cracked plates of different thicknesses loaded in tension. Unlike the path-independent Jx1-integral, the components JP and JA 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 sigma33 and epsilon33 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 kij is introduced, showing a unique structure depending on K;SUB/SUB; 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.