1. Stress State Simulation for Reactor and Steam Generator Pressure Vessels
Kharchenko V.
G.S.Pisarenko Institute for Problems of Strength
2nd Hungarian-Ukrainian Joint Conference on
«Safety-Reliability and Risk of Engineering Plants and Components»
Kiev, Ukraine
19-21 September 2007

2. INTEGRITY AND LIFETIME ASSESSMENT OF NPP COMPONENTS
- Reactor pressure vessel; - Steam generators; - Pipelines
Primary Circuit of WWER NPP

3. When assessing the RPV or SG structural integrity,
the accuracy of determination of changes in the stress state and stress intensity factor (SIF) values under thermo-mechanical loading also plays an important part.
Stress intensity factor versus crack-tip temperature (plastic calculation) for RPV under PTS, from NUREG/CR-6651, Task T1C2
The stress and SIF values and peculiarities of its variation in space and time are affected by a large number of factors: loading conditions; sizes and locations of cracks; metal characteristics; accuracy methods and schemes for calculations; and so on.
Not only materials characteristics are big scatter, stress state and FM parameters often have big differences too

4. 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 2D and 3D Software
RELAX, SPACE, PIPE, and other packages
Various Tests:
Pure bending of the beam
Three-point bending of the beam with the edge crack, etc
Comparisons with commercial software (ANSYS and so on), analytical and exp. results

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

6. Structural Integrity and Lifetime of Steam Generator Elements
Elements with damage:
Heat-change tubes
Collectors
узел соединения “горячего” коллектора и патрубка ПГ
Crack place
Experimental Data
on-line
3D Stress Calculation
Key problems analysis experimental data stress calculation
Integrity and Lifetime Assessment

7. 3-D calculation models

8. Evaluation of the Validity and Accuracy of the Schemes for Modeling
Accuracy of Different Software and Meshes
Different FE Meshes
Comparison of Calculation
and Measurements
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

9. Comparison of calculations results
Distribution of the stresses acting on the “pocket” surface on the side of the nozzle 20 mm away from its bottom under hydrotest
•- EDO Gidropress, software ANSYS
- our results, software SPACE

10. Local Stress State of Steam Generator Element
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.
Ours 3D Schemes
Different2D Schemes

11. Stress state under different loading
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.

12. Influence of structural design on stresss state
Рис. 1. Схемы подсоединения к ПГ «горячей» ветки ГЦТ в случае блоков «малой» (а) и «большой» (б) серий (вид сверху и сбоку): 1 – ПГ; 2 – труба «горячей» ветки ГЦТ; 3 – КР, 4 – опорный бурт; 5 – патрубок «холодной» ветки; А – место разрушения а б
Распределение по окружности патрубка ПГ напряжений z в стенке «кармана» на высоте 20 мм от его дна, вызванное совместным действием теплоносителя и изгибающего момента при НУЭ (а) и ГИ на плотность (б): - «малая» серия; - «большая» серия

13. Residual stresses (φ = π)
Modelling of stress-strain state of a Welded Joint of Hot Collector to Nozzle of SG PGV-1000 during Local Heat Treatment after Repair
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 (φ = π)
Temperature
distribution

14. Residual Stresses of the SG Element after Local Thermal Treatment
Equivalent Stresses
а) - φ = π; b) - φ = 0
Resume: Local Stresses are High Level in SG Element after Local Thermal Treatment and under Service Loads
Distribution of the residual stresses acting on the “pocket” surface on the side of the nozzle 20 mm away from its bottom

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

16. Stress State in RPV under PTS
We use original 2D and 3D Software RELAX, SPACE and schemes with and without built-in cracks
We analysed accuracy of stress and FM parameters ( SIF, COD) determination for linear and non-linear cases
3D FE Model
Input data for 3D accidents cases
as function of time and space:
coolant temperature in the downcomer
heat transfer coefficient
primary circuit pressure

17. To calculate the SIF, we considered two basic options :
SIF Calculations
To calculate the SIF, we considered two basic options :
engineering methods, whereby use is made of analytic formulae or tabulated collections of stress intensity values for given defect and vessel geometries;
cracked body finite element analyses, in which the crack is directly modelled in the mesh and subjected to the appropriate loadings

18. RPV with a built-in crack
Crack location area
WWER 1000 RPV FEM model with surface or sub cladding crack
(a=11 or 19 mm, a/c=1/3 or 2/3) in weld 4

19. Temperature and Stress State
Comparison of Temperature in RPV wall
(EDO Gidropress, Marc and IPS, SPACE)
3D Distribution of Temperature at t=500 s
Comparison of Stresses in RPV wall for Different FE Meshes

20. with and wthout residual stress
Stress Distributions
with and wthout residual stress

21. SIF Distribution along 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
SIF comparisons by different procedures (WPF and EVI)

22. Comparison of SIF calculations ( EDO Gidropress, Marc and IPS, SPACE)
Intermediate Primary Leak (Break of SG Collector Head). Weld 4.
Circumferential cracks,
a=11 and 19 mm, а/с=2/3 .
Small Primary Leak (D36 mm). Weld 4.
Circumferential cracks,
a=11 and 19 mm, а/с=2/3 .

23. Crack Open Displacement
Elastic case
Elasto-plastic case
Elasto-plastic case with residual stresses

24. Conclusions
Methods and software have been improved for the calculation of the stress state of complex spatial structures with cracks, which is based on the mixed schemes of the finite element method;
Various numerical and engineering procedures for determining the stress intensity factors for a reactor pressure vessel have been compared
Comparison of the results of the stress state calculation for RPV and SG elements obtained by the authors and at the Design Bureau “GIDROPRESS” revealed a good correspondence and confirmed the applicability of the developed computational schemes, calculation procedures, and software;
The development of 3D models for the SG welded joint and their application for calculations made it possible to establish a nonmonotonic stress distribution along the circumference of the welded joint with two maxima. The maximum (comparable to the yield stress) levels of tensile stresses are reached in the local region at the fillet for various regimes of post-repair heat treatment and operation conditions. The level of the maximum stress is influenced appreciably by the bending moment induced by thermal expansion of the Main Circulation Pipeline

25. Thank You For Attention !