v7.01.311 HPLA311 - Murakami 11.39. Circular crack in the center of a sphere subjected to a uniform temperature on the lips

Summary:

This test is the result of the independent validation of version 3 in fracture mechanics.

It is a basic static test in axisymmetry under stationary thermal loading calculated by finite elements on the same mesh of a limited domain.

The behavior is isotropic linear thermoelastic.

It includes two axisymmetric models for which the a/b ratio is varied, a being the radius of the circular internal crack in the horizontal plane xoy and b radius of the sphere. The stress intensity factors K and the energy recovery rate are calculated by the theta method (operator CALC_G).

• 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. Uncertainty about the solution
  • 2.4. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested features
  • 3.4. Definition of crown radii
  • 3.5. Benchmark solutions
  • 3.6. Tested sizes and results
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Features tested
  • 4.4. Definition of crown radii
  • 4.5. Reference solutions
  • 4.6. Tested sizes and results
• 5. Summary of results