Miskolc, Hungary Miskolc, Hungary April2006 April 2006 Numerical Modelling of Deformation and Fracture Processes of NPP Equipment Elements Моделирование процессов деформирования и разрушения материалов и элементов оборудования АЭС Kharchenko V. Харченко В.В. G.S.Pisarenko Institute for Problems of Strength Институт проблем прочности им. Г.С. Писаренко НАН Украины 1st Hungarian-Ukrainian Joint Conference on 1st Hungarian-Ukrainian Joint Conference on « Safety-Reliability and Risk of Engineering Plants and Components »

About 50% of the electric power produced in Ukraine is generated by the NPPs. Now there are 15 units—13 VVER and 2 VVER-440—operated in Ukraine. But, as seen from Table, half of the units have been operated for over 20 years. So, Extension of the NPP Service Life is one of the most important strategical tasks of the nuclear industry Operating reliability and extension of the NPP service life depend on the solution of the problems concerning the structural strength of equipment

Creation of the scientific fundamentals for determining the strength and life of NPP equipment A great deal has been done by the Institutes of the National Academy of Sciences of Ukraine for the development of the nuclear science and technology including the following: Development of the procedures and unique equipment for testing NPP structural materials, including those under irradiation conditions Development of the procedures and software packages for simulation of NPP equipment elements Investigation of deformation and fracture, determination of the mechanical properties of structural steels under various conditions of thermo-mechanical loading and a complex stress state Investigation of the stress-strain state of materials and NPP equipment elements Development of the strength (fracture) criteria   Now we’ll say about IPS results of numerical modeling

Development of the methods and software for the stress-strain state calculations for complex three-dimensional structures Mixed schemes of the finite- element method (MFEM) for the thermoelasticity and thermoplasticity Original Software RELAX, SPACE, PIPE, ИМПРО, and other packages Tests: Pure bending of the beam Three-point bending of the beam with the edge crack, etc

n Examples of the Test Tasks Solution Error in the SIF determination Error in the stress determination Pure bending of the beam Three-point bending of the beam with the edge crack Our MFEM

Evaluation of the Validity and Accuracy of the Modeling Schemes Different FE Meshes Stresses σZ on the outer surface of the welded joint in the region of strain gage mounting: 1 – numerical calculation (P1/P2 = 16/6 MPa, M = MH  m); 2 – data of full-scale strain measurements Accuracy of Different Software and Meshes Comparison of Calculation and Measurements

Modeling of the Behavior of Materials and Structural Elements Modeling of material testing under static, cyclic and dynamic loadings (tension, compression, impact toughness) Modeling of the strain-stress state kinetics in the processes of manufacture and maintenance (cutting, pipe pressing-in, thermal treatment) Modeling of behavior of NPP equipment elements (reactor pressure vessel, steam generator, protective structures) under service loads

Numerical modeling of material testing. Various schemes of dynamic testing

Calculation scheme Specimens Specimen with concentrator R2 Tension Testing Modelling Smooth cylindrical specimen

Calculation Experiment Charpy Testing Modelling Time variation of the load on the knife-edge

loading unloading The variation of the stress state at the crack (or concentrator) tip indicated that the plastic deformation region changes its shape and the accumulation of residual plastic strains occurs after each cycle. Further investigation will deal with the analysis of damage accumulation at the crack (or concentrator) tip and assessment of the applicability of various fracture criteria under such loading conditions. Repeated Loading Modelling

STRESS-STRAIN STATE FEATURES OF STEAM GENERATOR ELEMENT WITH THE CONCENTRATOR UNDER REPEATED-STATIC LOADING Stress Distribution in the region of a concentrator 1mm in depth under pressures P1 and P2: 1 – radial stresses, 2 – axial stresses, 3 – tangential stresses, 4 – equivalent stresses under loading, 5 – axial stresses under unloading. Modeling scheme for the steam generator component and the fragment of the finite element meshing in the defect region.

- Reactor pressure vessel; - Steam generators; - Pipelines Primary Circuit of WWER NPP MATERIAL TESTING AND NUMERICAL MODELLING FOR INTEGRITY AND LIFETIME ASSESSMENT OF NPP COMPONENT

Conditions of in- service thermomechanical loading, specifically in emergency events – thermal shock STRENGTH AND LIFE CALCULATION of reactor pressure vessels of NPPs Strength of RPVs with cracks - limit state criteria; - postulation of cracks - calculation of SIF K J - fracture toughness K JС Stress state, temperature fields, thermal hydraulics, Neutron fluence in pressure vessel wall Ф(x, y, z) Residual stresses Mechanical properties of base metal, welds, cladding and their in-service degradation Defects (actual and hypothetical) Key issues

Temperature and Stresses in RPV 3D Model Temperature in RPV wall Stress in RPV wall Stress in RPV weld

Stress intensity factor versus crack-tip temperature (plastic calculation), from NUREG/CR-6651, Task T1C2 The SIF value and peculiarities of its variation in time are affected by a large number of factors: sizes and locations of cracks; loading conditions; metal characteristics; accuracy of calculation methods and schemes; and so on. When assessing the RPV structural integrity, the accuracy of determination of changes in the stress intensity factor (SIF) value under thermal shock conditions also plays an important part.

Geometrical model Finite element grid: a)–in the vicinity of the crack; b)– in the cross section of the crack front Crack location area RPV with a built-in crack

Variation in the stress intensity factor KI along the longitudinal half-elliptical crack front under PTS a/c = 2/3, a/t = 1/10 Hoop strains in the zone of the built-in longitudinal half-elliptical crack Crack location area RPV with a built-in crack

Si, Sy, Ey in crack tip: 1 – t=0.3ms, 2 – t=0.5ms, 3 – t=0.66ms, 4 – t=0.83ms. Crack propagation and arrest in RPV wall under PTS Crack velocity.

3D Calculation Scheme -Weld 111 Crack place Experimental Data on-line Integrity and Lifetime Assessment Structural Integrity and Lifetime of Steam Generator Elements Elements with damage: -Heat-change tubes - Collectors Key problems analysis experimental data stress calculation

3-D Models for Stress Modeling of the SG Element

Evaluation of the Validity and Accuracy of the Modeling Schemes Different FE Meshes Stresses σZ on the outer surface of the welded joint in the region of strain gage mounting: 1 – numerical calculation (P1/P2 = 16/6 MPa, M = MH  m); 2 – data of full-scale strain measurements Accuracy of Different Software and Meshes Comparison of Calculation and Measurements

Распределение по окружности патрубка ПГ напряжений  z на стенке кармана на высоте 20 мм от дна. Напряжения  1 -  3 на стенке кармана в области галтельного перехода: 1 – 16/6 МПа + 2,279 МН  м, угол 4,10 рад.; /11 МПа + 1,082 МН  м, угол 4,32 рад.; 3 – 18/8 МПа + 0,977 МН  м, угол 4,32 рад.; 4 -16/6 МПа + 0,827 МН  м, угол 4,32 рад. Local Stress State of Steam Generator Element Ours 3D Schemes Different 2D Schemes

Simulation of the Stress-Strain State Kinetics in Manufacturing and Maintenance Pressing-in of pipes into the steam generator collector Local thermal treatment of the SG shell and collector assembly after maintenance Temperature distribution Schematic of the SG Element and mounting of heating elements: 1 - steam generator shell with heat insulation; 2 – nozzle; 3 – “pocket”; 4 – heat insulation; 5- welded joint; 6 – heating elements; 7 –collector; 8 – heat insulation plugs

Residual Stresses of the SG Element after Local Thermal Treatment Distribution of the residual stresses acting on the “pocket” surface on the side of the nozzle 20 mm away from its bottom (from the results of three-dimensional computations): tangential stresses  (1); axial stresses  Z (2);  i (3) а) - φ = π; b) - φ = 0 Equivalent Stresses Resume: Local Stresses are High Level in SG Element after Local Thermal Treatment and under Service Loads

Conclusions In our opinion the important research directions are as follows : Development and harmonization of standards for the structural integrity and lifetime assessment Development of procedures for structural integrity and lifetime calculation (including those taking into account crack propagation and arrest) Improvement of strength (fracture) criteria Development of experimental methods for determining metal degradation and obtaining additional information Improvement of correlation dependences between mechanical metal characteristics obtained by various methods Improvement of calculation methods for assessment of strain-stress state, fracture mechanics parameters and their application to problems of structural integrity and to risk-based methods

Summary Thank You For Attention !