Orynyak I.V., Borodii M.V. , Batura A . S .

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

2. IPSNASU 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. IPSNASU Softwareadvantages • 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. IPSNASU 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. IPSNASU Q’ s x • SIF calculation by Point Weight Function Method !!! The contribution in SIF 1/800 area nearbyQ’ point correspondent to 1/4 value of SIF Q’- pointon the front; - valueSIF; -weightfunction; - loading; - cracksurface;Q – load applicationpoint

6. IPSNASU We search weight functionin the form - asymptotic WF (ellipticcrackin infinite body) - correction coefficient, basic solution is used

7. IPSNASU Using our Point Weight Function Methodin 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. IPSNASU Using our Point Weight Function Methodin 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. IPSNASU Check of the PWFM accuracy for semi-elliptic cracks SIF along crack front (angle), homogeneous loading 90 0

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12. IPSNASU Dependence SIF from ratio a/l

13. IPSNASU Dependence SIF from ratio a/l

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

15. IPSNASU Complex damage 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. IPSNASU Using stable form crack growth

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

18. IPSNASU Input Data 2) Temperature field for time Table arbitrary size

19. IPSNASU weld seam heat-affected zone basematerial cladding crack base material cladding crack Input Data 3) Crack types a)Axialwith weld seam b)circumferential

20. IPSNASU 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 Atakes from coordinates of first point

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

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

23. IPSNASU 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-lengthl -40 мм., depth a - 50 мм.

24. IPSNASU a)Dependences of the calculated and critical SIF from temperature for time = 3000 sec SIFfor base material --//-- forwelding seam Critical SIFfor base material --//-- for welding seam --//-- forheat-affected area

25. IPSNASU b)History of the dependences calculated SIF fromtemperature forsome points and all times intervals andcritical SIF T historyforbase material --//-- for welding seam criticalSIFforbase material --//-- forwelding seam --//-- forheat-affected area

26. IPSNASU 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. IPSNASU d) Figure of the calculated margin calculated temperature margin shift of the temperature by user table shift of the temperature by analytical model

28. IPSNASU Calculated temperature margin Results for other crack geometries New geometry for axial crack Half lengthl - 60мм Depth a - 40 мм

29. IPSNASU Calculated temperature margin New geometry for axial crack Half lengthl - 40мм Depth a - 60 мм

30. IPSNASU calculated temperature margin New geometry for circumferential crack Half lengthl - 60мм Depth a - 30 мм

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

32. IPSNASU Result for main scenario Time point t4= 3000 sec- the most dangerous time step Axial crack half lengthl -40 мм., depth a - 50 мм. For timeDT =0 failure probability equal 1.07*10-05 SIF dependences on angle

33. IPSNASU Dependences of logarithm probability on DT

34. IPSNASU Probability density forDT = 50

35. IPSNASU 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.