Bruno Barthelet

Influence Coefficients to Calculate Stress Intensity Factors for an Elliptical Crack in a Plate

Crack assessment in engineering structures relies first on accurate evaluation of the stress intensity factors. In recent years, a large work has been conducted in France by the Atomic Energy Commission to develop influence coefficients for surface cracks in pipes. However, the problem of embedded cracks in plates (and pipes) which is also of practical importance has not received so much attention. Presently, solutions for elliptical cracks are available either in infinite solid with a polynomial distribution of normal loading or in plate, but restricted to constant or linearly varying tension. This paper presents the work conducted at EDF R&D to obtain influence coefficients for plates containing an elliptical crack with a wide range of the parameters: relative size (2a/t ratio), shape (a/c ratio) and crack eccentricity (2e/t ratio where e is the distance from the center of the ellipse to the plate mid plane). These coefficients were developed through extensive 3D finite element calculations: 200 geometrical configurations were modeled, each containing from 18000 to 26000 nodes. The limiting case of the tunnel crack (a/c = 0) was also analyzed with 2D finite element calculation (50 geometrical configurations). The accuracy of the results was checked by comparison with analytical solutions for infinite solids and, when possible, with solutions for finite-thickness plates (generally loaded in constant tension). These solutions will be introduced in the RSE-M Code that provides rules and requirements for in-service inspection of French PWR components.Copyright

Progress in the Development of J Estimation Schemes for the RSE-M Code

The RSE-M Code provides rules and requirements for in-service inspection of French Pressurized Water Reactor power plant components. The Code gives non mandatory guidance for analytical evaluation of flaws. To calculate the stress intensity factors in pipes and shells containing semi-elliptical surface defects, influence coefficients are given for a wide range of geometrical parameters. To calculate the J integral for a circumferential surface crack in a straight pipe, simplified methods are available in the present version of the Code (2000 Addenda) for mechanical loads (in-plane bending and torsion moments, pressure), thermal loads as well as for the combination of these loads. This paper presents the recent advances in the development of J-estimation schemes for two configurations: • a longitudinal surface crack in a straight pipe, • a longitudinal surface crack in the mid-section of an elbow.© 2002 ASME

Analytical Method for the Calculation of J Parameter in Cracked Components: Presentation of the RSE-M/RCC-MR Procedure and Benchmark Proposal

RSE-M and RCC-MR codes provide flaw assessment methodologies and related tools for Nuclear Power Plant. For these two codes, AREVA, CEA and EDF developed a large set of compendia for the calculation of the parameter J for various components (plates, pipes, elbows, [[ellipsis]]) and various defect geometries. The last step of these developments deals with the weld joints: since 2004, a methodology have been developed to calculate the J parameter for a defect located in a weld, less conservative than usual methods. This methodology is based on the definition of an equivalent material that leads to the same J value (with same loading conditions and defect geometry) than the bi-material component. The stress-strain curve of this equivalent material is deduced from a combination of the tensile curves of the base metal and of the weld metal. The weigth coefficients applied are specifically defined for the J calculation and generalized to deal with any weld joint geometry.© 2010 ASME

Analytical Method for the Calculation of J Parameter for Surface Cracks in Piping Welds

RSE-M and RCC-MR codes provide flaw assessment methodologies and related tools for Nuclear Power Plant. AREVA, CEA and EDF developed in particular a large set of compendia for the calculation of the parameter J for various components (plates, pipes, elbows, ...) and various defect geometries. The last step of these developments deals with the weld joints : since 2004, the partners are developing a methodology to calculate the J parameter for a defect located in a weld, less conservative than usual methods. This methodology is based on the definition of an equivalent material that leads to the same J value (with same loading conditions and defect geometry) than the bi-material component. The stress-strain curve of this equivalent material is deduced from a combination of the tensile curves of the base metal and of the weld metal. The weigth coefficients applied are specifically defined for the J calculation and generalized to deal with any weld joint geometry.Copyright

Recent Advances for J Simplified Assessment in RSE-M Code

The RSE-M Code [1] provides rules and requirements for in-service inspection of French Pressurized Water Reactor power plant components. Non mandatory guidance is given in the Code for analytical flaw evaluation in a wide range of situations. In Appendix 5.4 of the Code, influence coefficients are provided to calculate stress intensity factors in pipes and shells containing semi-elliptical surface defects. The J assessment method is based on the reference stress concept with two options for reference loads evaluation: “CEP elastic plastic stress” and “CLC modified limit load”. In this paper recent advances concerning J assessment under mechanical loading for a crack located in a pipe-elbow junction are presented. Reference stress evaluation with “CLC” option is developed and mechanical foundations of the equation of large scale yielding under complex loading (pressure, in-plane and out-of-plane bending) are presented.Copyright

Life Management of Reactor Coolant Piping — Probabilistic Calibration of Partial Safety Factors in Flaw Acceptance Criteria: Application to Cast Duplex Stainless Steel Components

The RSE-M Code provides rules and requirements for in-service inspection of the components of the French PWR power plant. The Code gives non mandatory guidance for analytical evaluation of flaws, comprising fracture mechanics analyses based on engineering methods, flaw acceptance criteria and codification of material characteristics. Based on a probabilistic calibration methodology, partial safety factors on the main random variables involved in flaw assessments (loading, crack size, yield strength and material toughness) are given in Appendix 5.5 of the Code for each category of operating conditions (A, C or D) and for the possible failure modes (ductile tearing or brittle fracture). These partial safety factors should be used with the material characteristics specified in Appendix 5.6 of the Code, to insure the consistency of the methodology. The criteria of the RSE-M Code have been implemented for the acceptance of generic flaws in cast duplex stainless steel elbows of the Reactor Coolant System. Statistical analyses of the mechanical properties of the base-metal have been carried out to get their characteristic values consistent with the Code criteria: • tensile properties comprising yield strength, ultimate tensile strength and non dimensional reference true stress - true strain curves taking into account thermal ageing, • value of the J-integral in the ductile regime at the onset of crack extension (J0.2 after 0.2 mm of crack extension), J-Δa curves in the ductile regime taking into account thermal ageing in the hot leg conditions, • fatigue crack growth rates. The results show that the aged cast duplex stainless steel elbows satisfy the Code criteria for each category of operating conditions.Copyright

Development of a J-Estimation Scheme for Surface Cracks in Piping Welds

The RSE-M Code provides rules and requirements for in-service inspection of French Pressurized Water Reactor power plants. The Code gives non mandatory guidance for analytical evaluation of flaws. Flaw assessment procedures rely on fracture mechanics analyses based on simplified methods (i.e. analytical). Analytical methods were developed under a cooperative program between EDF, CEA and AREVA NP to calculate the J integral in various cracked piping components (straight pipe, tapered transition, elbow and pipe-to-elbow junction). These methods are available for mechanical loading (in-plane bending moment, pressure, torsion moment), thermal loading as well as for combined loading. Moreover, they can be used either for materials with Ramberg-Osgood stress-strain curves or for real materials (stainless steels and carbon manganese steels, including those with yield plateaus). However, for the analysis of cracks in welds, they use the tensile properties of the weakest material between the base material and the weld material. This induces some conservatism on the estimated J values. A cooperative program was launched in 2004 to develop a J estimation scheme which takes into account the strength mismatch effects. The scheme relies on the definition of an ‘equivalent’ stress-plastic strain curve, as proposed in the R6 rule (section III.8: allowance for strength mismatch effects). This curve is then used with the analytical methods for homogeneous cracked components. In a first step, the method is developed for circumferential surface cracks in straight buttwelded pipes submitted to mechanical loading. It takes into account the geometry of the weld joint (V-shaped), as well as the location of the crack within the weld. This paper presents the current state of development of this J estimation-scheme.© 2008 ASME

Overview of Flaw Assessment Methods in the RSE-M Code

The RSE-M Code provides rules and requirements for inservice inspection of French Pressurized Water Reactor power plant components. Appendices 5.3 and 5.4 of the Code give non mandatory guidance for analytical evaluation of flaws, i.e. fracture mechanics analyses based on simplified methods. Flaw assessment aims to calculate the initiation and the subsequent propagation of the crack under cyclic loading (fatigue analysis) and then to assess the crack stability, by comparing the applied J integral to the toughness of the material. This paper shows an overview of the R&D work undergone to make possible an analytical approach: • analytical formulas for the elastic stress field in elbows under in-plane, out-of-plane and torsion moments, • stress intensity factors solutions based on the influence coefficient method for surface and embedded cracks in pipes, • simplified methods to estimate the J integral for various configurations of piping, flaws and loading. These methods are shortly presented, including their field of application and their validation.Copyright