v3.03.311 SSLA311 — Circular crack subjected to an annular load

Summary:

This test case treats the case of an internal crack located in the center of a circular bar, in axisymmetric mode. The particularity of the load is that the linear load is applied to a ring very close to the crack bottom. The fixed parameter is the radius of the crack \(a\), and the parameter to be explored is the radius of application of the load \(c\). The medium is elastic, linear, homogeneous and isotropic. The geometric domain is assumed to be unlimited in \(r\) and \(z\).

The meshes must therefore take into account the proximity of the load in such a way as to respect the bridge of application of the load.

Since the load is normal to the crack, we calculate the characteristic coefficient of fracture mechanics \(K\) in pure \(I\) mode. Then, we use Irwin’s formula in plane deformation to derive/to establish \(G\).

This is, of course, an approximation.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. reference result
  • 2.2. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling A
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
• 4. B modeling
  • 4.1. Characteristics of B modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. C modeling
  • 5.1. Characteristics of C modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
• 6. D modeling
  • 6.1. Characteristics of modeling D
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
• 7. Summary of results
• 8. notes