r7.02.10 Simplified defect toxicity analysis using the K-beta method

Summary:

The analysis method presented (K-beta method) is applied to the analysis of the harmfulness of a defect located under the lining of pressurized water reactor tanks, implemented by the command POST_K_BETA.

The K-beta reference method is codified in RSE -M and aims to evaluate, from a study carried out in the context of linear elasticity and in which the defect is not explicitly meshed, the elasto-plastic stress intensity factor (also qualified as « plastically corrected » in the context of this methodology) at the level of each of the different points of the defect, i.e. at the level of the defect point located on the side of the coating (called point A) and at the level of the tip of the defect located in the base metal (called point B).

To do this, the elastic stress intensity factor at the two points of the defect is first calculated, using the stresses at the nodes resulting from the mechanical resolution and the residual stresses given by the user. Then, in a second step, the plastically corrected stress intensity factor is calculated from its elastic equivalent via the so-called « beta correction » method. At each moment of the analysis and at the level of each of the points of the defect, the obtained ratio of the critical toughness to the plastically corrected stress intensity factor determines the instantaneous margin factor and then makes it possible to deduce the minimum margin factor with respect to failure.

The theoretical aspects of the K-beta method and its computational implementation are the subject of the following paragraphs.

This method corresponds to the Rupt1D approach in the nomenclature of the EDF Epicure project.

Table of contents

• 1. General description of the method
  • 1.1. Principle of the calculations carried out
  • 1.2. Method validity framework \({K}_{\beta }\)
  • 1.3. Geometric treatment of the offset for the elliptical defect
• 2. Step 1: calculation of the strength factor of the elastic stresses of the elliptical defect
  • 2.1. Intensity factor of the elastic stresses of a band defect in an infinite plate
  • 2.2. Change of frame of reference
  • 2.3. Numerical determination of the strength factor of the elastic stresses of the band defect
  • 2.4. Geometric correction factors for an elliptical surface defect
• 3. Step 1: calculation of the strength factor of the elastic stresses of the semi-elliptical defect
  • 3.1. Definition of defect
  • 3.2. Calculation of the elastic stress intensity factor
  • 3.3. Determination of influence coefficients
  • 3.4. Change of frame of reference
• 4. Step No. 2: calculation of the elasto-plastic stress intensity factor by the « correction b » method
  • 4.1. Plastic correction factor for a load phase considered in isolation
  • 4.2. Plastic correction during a transition
• 5. Validation
• 6. Bibliographical references
• 7. Description of document versions