r7.02.05 Calculation of stress intensity factors in linear thermoelasticity

Summary:

The method for calculating stress intensity factors \({K}_{I}\), \({K}_{\mathrm{II}}\) and \({K}_{\mathrm{III}}\) in linear thermoelasticity is presented. The formulation considers the energy restoration rate as a symmetric bilinear form of the displacement field \(u\) and uses the explicit expressions of the known singular displacement fields in plane linear elasticity.

This method can be used using option CALC_K_G of the CALC_G command, both for a meshed crack (classical finite elements) and for a non-meshed crack (rich finite elements: method X- FEM).

This method can also be used to calculate the stress intensity factors associated with the natural vibration modes of a structure.

• 1. Expressions of stress intensity factors in linear thermoelasticity
  • 1.1. Presentation in plane linear thermoelasticity
  • 1.2. Extension to the 3D case
  • 1.3. IRWIN formula and energy return rate G
  • 1.4. Decoupling of disruptive modes
• 2. Implantation of KI, KII and KIII in linear thermoelasticity in Code_Aster
  • 2.1. Types of items and loads
  • 2.2. Environment required for the calculation of KI, KII and KIII
  • 2.3. Symmetric bilinear form g (.,.)
  • 2.4. Singular displacement fields and their derivatives
  • 2.5. Post-processing of KI results and KII
• 3. Bibliography
• 4. Description of document versions