v6.04.166 SSNV166 — Cracked cylinder under multiple loads

Summary

The purpose of this test is to calculate the stress intensity factors along the crack bottom for a cylinder with an axisymmetric crack.

The influence of the degree of the elements and the type of the method is studied through various models.

1. Modeling \(A\) tests \(\mathrm{K1}\) and \(\mathrm{K3}\) with a \(\mathrm{3D}\) linear mesh and a classical finite element method (\(\mathrm{FEM}\)).

2. Modeling \(B\) tests \(\mathrm{K1}\) and \(\mathrm{K3}\) with a \(\mathrm{3D}\) quadratic mesh (Barsoum elements) around the crack bottom and an \(\mathrm{FEM}\).

3. Modeling \(C\) tests \(\mathrm{K1}\) and \(\mathrm{K3}\) with a \(\mathrm{3D}\) linear mesh with a classical resolution but an extraction of intensity factors based on an energy calculation.

In addition, for each model, various load cases are studied:

• traction (stress in \(I\) mode);

• twisting (stress in \(\mathrm{III}\) mode);

• flexure (opening on one side, closing on the other) with and without taking into account contact.

Cases of traction and twisting do not involve contact.

Although symmetries exist in some cases (axisymmetry for case 1, plane symmetry for case 2) the representation is done in \(\mathrm{3D}\) to make the test generalizable under multiple loading.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Bibliographical references
• 3. Modeling A: Linear mesh, classical formulation
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. note
  • 3.4. Test values and results of modeling A
• 4. Modeling B: Quadratic mesh, classical formulation
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Test values and B modeling results
  • 4.4. Changes in K1, K2, K3 along the crack bottom
• 5. C modeling: Linear mesh, classical formulation and energetic method
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested values and results of the C modeling
  • 5.4. Changes in K1 and K3 along the crack bottom
• 6. Summary of results