Determination of stress intensity factors for semielliptical surface cracks in the WWER-1000 reactor pressure vessel from the results of solving thermoelasticity boundary value problems based on the mixed mesh-projection scheme of the finite element method

Abstract

Results of numerical analysis of stress intensity factors K I for semielliptical surface cracks in the WWER-1000 reactor pressure vessel by emergency cooling simulation with known engineering procedures, the equivalent spatial integration and direct methods are presented. Engineering procedures employ the results of numerical solution of axially symmetric boundary value problems of thermoelasticity based on the mixed mesh-projection scheme of the finite element method implemented in the RELAX software. The three-dimensional K I computations were performed with the SPACE software.Keywords: finite element method, mixed mesh-projection scheme, stress intensity factor, equivalent spatial integration method, direct method, semielliptical crack, reactor pressure vessel.One of the conditions of reliable service of nuclear power plant equipment is the reactor pressure vessel (RPV) integrity both in normal operation and in an emergency. Under RPV operation conditions caused by an emergency, in particular by thermal shock, the basic strength criterion for the RPV material is assumed to be its ability to resist brittle fracture. Stress intensity factor calculations are an appropriate basis for this.The present study cites the results of comparing calculated K I values for a longitudinal semielliptical surface crack in the WWER-1000 RPV obtained by engineering and numerical procedures. Among the first ones are the procedures employing approximate formulas [1, 2] and dimensionless K I values calculated by the method of weight functions [3,4], among the second ones are the procedures making use of the equivalent spatial integration method [5] and the direct method [6] based on solving the boundary value problem of thermoelasticity with the mixed mesh-projection scheme of the finite element method (FEM) [7], which provides a higher accuracy of determining thermostress and strain fields as compared to the classical finite element displacement method.The stress intensity factor by engineering procedures [1-4] is determined from the relationwhere σ is the calculated stress and Y is the dimensionless function for different points of the crack front allowing for crack dimensions and the RPV wall thickness. The stressed state on the crack surface ( Fig. 1) is expressed in terms of stresses (Eq. 1), which are proposed to calculate along the crack with different approximating functions from stress-strain state calculation results for the integral structure. 1380039-2316/07/3902-0138

Calculation of stress intensity factors based on mode I crack opening integral parameters

“…1 and 4) for the known solutions [6]. In case of the nonuniform heating temperature on the crack surface is The proposed method is used for the comparative analysis of K I calculations by means of the volume integral method and formulas while defining stress-strain state of the main components of the nuclear power units in WWER-1000 reactor vessels [11,12].…”

Lineal Elastic Fracture Mechanics Analysis Applied for the Evaluation of the Structural Integrity of a Boiling Water Reactor Vessel Considering Neutronic Irradiation

“…González and coworkers [4] analyzed the loading and unloading conditions generated by a pressurized thermal shock (PTS) with the FEM. Karchenko and collaborators [5] determined the SIF of a semi-elliptical crack in a WWER-1000 reactor. Jhung and collaborators [6] assessed the structural integrity of a reactor vessel.…”

The influence of thermomechanical loading history on the stress level in WWER NPP reactor pressure vessels under thermal shock

“…The relevant publications [1][2][3][4][5][6][7][8][9][10][11][12][13][14] present numerous data that reflect the accumulated experience and various aspects of computational substantiation of strength of WWER and PWR reactor vessels. They also discuss the standard approaches, the acting service loads and loads occurring during the reactor core emergency core cooldown and design accidents.…”

“…The calculation of SSS kinetics for a reactor pressure vessel can be reduced to a successive solution of transient thermal conduction problems and a nonlinear thermomechanical boundary-value problem. To provide an adequate description of variations of a stress level in RPV under real operating conditions including emergency core cooldown (thermal shock), one should take into account the combined influence of various factors such as loading history, nonuniformity of heating and cooling, plastic deformation, inhomogeneity of physical-mechanical properties.The relevant publications [1][2][3][4][5][6][7][8][9][10][11][12][13][14] present numerous data that reflect the accumulated experience and various aspects of computational substantiation of strength of WWER and PWR reactor vessels. They also discuss the standard approaches, the acting service loads and loads occurring during the reactor core emergency core cooldown and design accidents.…”