r7.02.08 Calculation of stress intensity factors by extrapolation of the displacement field

Summary:

Here we describe a method for calculating \(\mathit{K1}\), \(\mathit{K2}\) and \(\mathit{K3}\) in 2D (plane and axisymmetric) and 3D by extrapolating the jumps in movements on the lips of the crack. It can be used using the POST_K1_K2_K3 command, both for a meshed crack (classical finite elements) and for a non-meshed crack (enriched finite elements: method X- FEM).

If the crack is meshed, it must be plane; if the crack is not meshed (method X- FEM), it may be non-planar (but sufficiently regular). In both cases, the method is only applicable for linear, homogeneous and isotropic elastic materials.

The method used is theoretically less accurate than the calculation based on the bilinear form of the energy restoration rate and the singular displacements [R7.02.01 et R7.02.05] (operator CALC_G). However, it makes it easy to obtain relatively reliable values of stress intensity factors. Comparing the various calculation methods is useful for estimating the precision of the results obtained.

The accuracy of the results of the method for extrapolating displacement jumps is significantly improved if the mesh is quadratic. For a mesh crack, it is recommended to use so-called « Barsoum » elements at the bottom of the crack (elements whose middle nodes are located a quarter of the edges). For a non-meshed crack, it is recommended to enrich several layers of elements around the crack bottom.

• 1. Problem position
• 2. Implementation of extrapolation methods
• 3. Precision of the proposed methods
  • 3.1. Test SSLP313: 2D C_ PLAN (mesh crack)
  • 3.2. Test SSLV134: 3D (mesh crack)
  • 3.3. Test SSLV134: 3D (unmeshed crack)
• 4. Conclusion
• 5. Bibliography
• 6. Description of document versions