MiskolcMiskolc , , HungaryHungary

AprilApril 20020066

Numerical Modelling Numerical Modelling of Deformation and Fracture Processes of Deformation and Fracture Processes

of NPP Equipment Elementsof NPP Equipment Elements

Моделирование процессов деформирования и Моделирование процессов деформирования и разрушения материалов и элементов оборудования АЭСразрушения материалов и элементов оборудования АЭС

Kharchenko V. Kharchenko V. Харченко В.В.Харченко В.В.

G.S.Pisarenko Institute for Problems of Strength G.S.Pisarenko Institute for Problems of Strength Институт проблем прочности им. Г.С. Писаренко НАН Институт проблем прочности им. Г.С. Писаренко НАН УкраиныУкраины

1st Hungarian-Ukrainian Joint Conference on1st Hungarian-Ukrainian Joint Conference on ««Safety-Reliability and Risk of Engineering Plants and ComponentsSafety-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-1000 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 equipmentA 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 structuresMixed 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 = 2.279 MHm);•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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

200

400

600

800

1000

1200

1400

1600

1800

Удлинение, мм

Уси

лие, кг

с

Упруго-пластическая модельУпруго-пластическая модель с GTNЭкспериментЭксперимент

Tension Testing Modelling

0 1 2 3 4 5 6 70

200

400

600

800

1000

1200

1400

Удлинение, мм

Усилие, кгс

ЭкспериментЭкспериментУпруго-пластическая модель с GTNУпруго-пластическая модель

Smooth cylindrical specimen

CalculationExperiment

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

-300

-200

-100

0

100

200

300

400

500

0,596 0,597 0,598 0,599 0,6

X (m)

S (МПа)

•2

•3

•4

•1

•5

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

VTT INDUSTRIAL SY STEMS

TEMPERATURE (°C)

FRA

CTU

RE

ME

CH

AN

ICA

LP

AR

AM

ETE

R

Loadingparameter KJ

Safety margin

Fracturetoughness KJC

Transition temperatureshift due to irradiation

KJ < KJC

Safety requirements

Conditions of in-service

thermomechanical loading,

specifically in emergency events – thermal shock

STRENGTH AND LIFE CALCULATIONof reactor pressure vessels of NPPs

Strength of RPVs with cracks- limit state criteria;- postulation of cracks- calculation of SIF KJ

- fracture toughness KJС

Stress state, temperature fields, thermal hydraulics,

Neutron fluence in pressure vessel wall Ф(x, y, z)

Residual stresses

Mechanical propertiesof 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

20

40

60

80

100

120

0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08

Crack front length, m

К1,

МP

а*m

^0

,5

600 s

1000 s

2000 s

3000 s

4000 s

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

•1 •2

•3•4

•1

•2

•3•4

•1

•2

•3

•4

•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

0,00

0,35

0,70

1,05

1,40

Время

Нап

ряже

ние

-Weld 111

Crack placeExperimental 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 = 2.279 MHm);•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 МНм, угол 4,10 рад.; 2 - 25/11 МПа + 1,082 МНм, угол 4,32 рад.; 3 – 18/8 МПа + 0,977 МНм, угол 4,32 рад.; 4 -16/6 МПа + 0,827 МНм, угол 4,32 рад.

Local Stress State of Steam Generator Element Ours 3D Schemes

Different2D

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

0

50

100

150

200

250

300

350

400

450

0 0,5 1 1,5 2 2,5 3

Угол, рад

Напряж

ение, М

Па

1

2

3

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 Levelin SG Elementafter 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 !