v3.02.314 SSLP314 — Deviated crack at the interface between two elastic half-planes

Summary:

This test case treats the problem of a deflected crack in 2 dimensions, under the hypothesis of plane stresses. The set consists of two elastic, linear and isotropic materials, material 1 being located in the upper half-plane.

The crack is defined by two branches. The first branch is located horizontally at the interface of the two materials, and is characterized by its length \(c\).

The second is an extension of the first and is inclined at \(45°\) with respect to the horizontal, in the clockwise direction (characteristic length \(a\)). It is the end of this branch, completely included in material 1, that we are studying. The deviated crack (branch 1 and 2) is continuous, in a medium that is assumed to be infinite, and the load applied to this plate is a uniform pull on the upper and lower edges.

For this study, the parameters explored are the Young module ratio \(\mathit{E2}/\mathit{E1}\) equal to \(0.25,1.,4.\) and the \(a/c\) ratio equal to \(0.1\) and \(1.\) There are a total of 6 test cases.

Isostatic boundary conditions block the three plane rigid body modes without causing any reactions to the supports.

Under the action of traction, and considering the angle of the crack, the second branch opens (mode I) and slides (mode II).

This test case validates the use of the operator calculating the energy restoration rate in fracture mechanics for 2D models: CALC_G (G and K options).

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
  • 1.4. Crack size
• 2. Benchmark solution
  • 2.1. Benchmark results
  • 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. E modeling
  • 7.1. Characteristics of modeling E
  • 7.2. Characteristics of the mesh
  • 7.3. Tested sizes and results
• 8. F modeling
  • 8.1. Characteristics of F modeling
  • 8.2. Characteristics of the mesh
  • 8.3. Tested sizes and results
• 9. Summary of results