1. Orynyak I.V., Borodii M.V., Batura A.S.
IPS NASU
SOFTWARE FOR ASSESSMENT OF BRITTLE FRACTURE OF THE NPP REACTOR PRESSURE VESSEL USING THE FRACTURE MECHANICS METHODOLOGY
Orynyak I.V., Borodii M.V., Batura A.S.
Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine
National Academy of Sciences of Ukraine 

2. IPS NASU
Software “REACTOR”
This program is intended for calculation of reactor pressure vessel residual life and safety margin with respect to brittle fracture.
Residual life is calculated deterministically and probabilistically (MASTER CURVE approach) for various points of crack front

3. IPS NASU
Software advantages
The sizes of stress and temperature fields' aren't bounded
Number of time moments is bounded only by the computer memory size
Cladding is taken into account
Welding seam and heat-affected area are taken into account
Deterioration is taken into account not only as shift of the material fracture toughness function but also as its inclination
Original feature of the software is using of the author variant of the weight function method. It allows to set loading on the crack surface in the form of table.

4. IPS NASU
Report sections
Theoretical background and verification of the SIF calculation methods.
Kinetics of the crack growth by fatigue or stress-corrosion mechanism.
Software description and residual life calculation of the NPP pressure vessel using fracture mechanics methods

5. SIF calculation by Point Weight Function Method
IPS NASU
SIF calculation by Point Weight Function Method s x Q’
!!! The contribution in SIF 1/800 area nearby Q’ point correspondent to 1/4 value of SIF
Q’- point on the front; value SIF; weight function;
- loading; crack surface; Q – load application point

6. IPS NASU We search weight function in the form
- asymptotic WF (elliptic crack in infinite body)
- correction coefficient, basic solution is used

7. Using our Point Weight Function Method in engineering applications
IPS NASU
Using our Point Weight Function Method in engineering applications
Software for fracture design of the complex turbine engine component (Southwest Research Institute, San Antonio, USA, 2004)
Our approach is used completely

8. Using our Point Weight Function Method in engineering applications
IPS NASU
Using our Point Weight Function Method in engineering applications
2. Modeling of elliptical crack in a infinite body and in a pressured cylinder by a hybrid weight function approach (France, Int. J. Pressure Vessel and Piping. 2005)
Our approach to take for a basis

9. SIF along crack front (angle), homogeneous loading
IPS NASU
Check of the PWFM accuracy for
semi-elliptic cracks 
SIF along crack front (angle), homogeneous loading 90

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12. Dependence SIF from ratio a/l
IPS NASU
Dependence SIF from ratio a/l

13. Dependence SIF from ratio a/l
IPS NASU
Dependence SIF from ratio a/l

14. 2. Kinetics of the crack growth by fatigue or
IPS NASU
2. Kinetics of the crack growth by fatigue or
stress-corrosion mechanism
1. Fatigue
2. Stress-corrosion

15. Complex damage IPS NASU where C1, C2 , v1 , v2 , - material constants
t, - time,
N – loading cycles,
H – wall thickness
T – unit time,
k – number of cycles in unit of time  

16. Using stable form crack growth
IPS NASU
Using stable form crack growth

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3. Residual Life calculation of the NPP pressure vessel using fracture mechanics methods
Input Data
1) Stress field for time
Table arbitrary size

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Input Data
2) Temperature field for time
Table arbitrary size

19. Input Data IPS NASU 3) Crack types a) Axial with weld seam weld seam
heat-affected zone
base material
cladding
crack
b) circumferential
base material
cladding
crack

20. 4) The basic material characteristics
IPS NASU
4) The basic material characteristics
1. Arctangents
2. Exponent
3. User (pointed) function
Common shape of the crack growth resistance function is
for user function A takes from coordinates of first point

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5) Shift and inclination conceptions
1. Shift
2. Shift + Inclination

22. 6) Dependence of shift on radiation
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6) Dependence of shift on radiation
a)Analytical form
b)Table form

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Results
Scenario – Break of the Steam Generator Collector WWER-1000 operated at full power
It is given : stress field,
- temperature field,
= 1000, 2000, 2800, 3000, 3160, 3600, 4000 sec - time points
Axial crack Half-length l мм.,
depth a мм.

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a) Dependences of the calculated and critical SIF from temperature for time = 3000 sec
SIF for base material
--//-- for welding seam
Critical SIF for base material
--//-- for heat-affected area

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b) History of the dependences calculated SIF from temperature for some points and all times intervals and critical SIF T
history for base material
--//-- for welding seam
critical SIF for base material
--//-- for heat-affected area

26. c) Table of the calculated temperature margin
IPS NASU
c) Table of the calculated temperature margin
for all points of crack front and time points
fields for chosen history points
minimal margin
margin for time points

27. d) Figure of the calculated margin
IPS NASU
d) Figure of the calculated margin
calculated temperature margin
shift of the temperature by user table
shift of the temperature by analytical model

28. Results for other crack geometries
IPS NASU
Results for other crack geometries
New geometry for axial crack
Calculated temperature margin
Half length l мм
Depth a мм

29. IPS NASU New geometry for axial crack Half length l - 40мм
Calculated temperature margin
Half length l мм
Depth a мм

30. IPS NASU New geometry for circumferential crack Half length l - 60мм
calculated temperature margin
Half length l мм
Depth a мм

31. Implementation MASTER CURVE Conception
IPS NASU
Implementation MASTER CURVE
Conception
1. Failure probability calculation for structural element
2. Failure probability calculation for crack
3. Calculation parameters
Pf = 63,2% Кmin = 20 В0 = 25 мм b = 4
4. In addition
Кmin , K0(Т), В0, b - arbitrarily

32. Result for main scenario
IPS NASU
Result for main scenario
Time point t4 = 3000 sec - the most dangerous time step
Axial crack half length l мм.,
depth a мм.
For time DT =0 failure probability equal 1.07*10-05
SIF dependences on angle

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Dependences of logarithm probability on DT

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Probability density for DT = 50

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CONCLUSION
1. Efficient method of stress intensity factor (SIF)
calculation is developed.
2. The computer software which reflected all modern requirements for brittle strength analysis of Reactor Pressure Vessel is created.
3. The program application were demonstrated by prediction residual life and temperature margins under modeling of the incident scenario.