1. 2 nd Hungarian-Ukrainian Joint Conference on SAFETY-RELIABILITY AND RISK OF ENGINEERING PLANTS AND COMPONENTS ASSESSMENT OF SUB-CLAD FLAWS, J-INTEGRAL CALCULATION Róbert Beleznai Tibor Köves Péter Kavalyecz BAY-LOGI Bay Zoltán Foundation for Applied Research Institute for Logistic and Production Systems Kyiv 20 th September, 2007

2. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 2 CONTENT Test specimens –Crack type –Crack dimensions –Crack geometry Material properties Residual stress Validation of the model Boundary condition J-integral calculation BAY-LOGI

3. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 3 BAY-LOGI Main objective of the work  WWER Cladded Reactor Pressure Vessel (WWER-440) J-integral calculation based on the report of the Nuclear Research Institute Rez plc, Division of Integrity and Technical Engineering. Introduction

4. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 4 Test specimen Specimen type: 4PB (40x85x670 mm) BAY-LOGI

5. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 5 Material properties WWER reactor pressure vessel steel with austenitic cladding Data arises from the report of the NRI True stress – true plastic strain curve was derived for the FE calculation BAY-LOGI

6. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 6 BAY-LOGI Material properties E=211 GPa  =12.55*10 -6 E=162 GPa  =17.1*10 -6 Poisson ratio: =0.3

7. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 7 Crack types Two different crack lengths were analyzed 1e2 and 1e4: –crack length: 15 mm –upper crack tip located 3 mm under the fusion line of the cladding –both crack tips are sharp 1e7: –crack length: 40 mm –upper crack tip located 3 mm under the fusion line of the cladding –upper crack tip is sharp –lower crack tip is drilled out BAY-LOGI

8. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 8 Crack dimensions Straight crack front were considered in all case. BAY-LOGI 1e2 Cladding thickness10.8 mm Upper crack front69.81 mm Lower crack front55.88 mm Crack length13.93 mm1e4 Cladding thickness11.35 mm Upper crack front70.76 mm Lower crack front55.87 mm Crack length14.89 mm 1e7 Cladding thickness11.25 mm Upper crack front70.63 mm Lower crack front30.78 mm Crack length39.85 mm

9. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 9 Crack geometry BAY-LOGI

10. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 10 Residual stress Residual stress arises from the difference of the thermal expansion coefficients Stress free temperature: T sf =350°C BAY-LOGI

11. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 11 Residual stress BAY-LOGI Comp 11 of stress

12. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 12 Residual stress BAY-LOGI

13. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 13 Validation of the FE model BAY-LOGI

14. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 14 BAY-LOGI NRI The results of NRI and BZF are in very good correlation. BZF

15. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 15 Load-displacement curves BAY-LOGI

16. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 16 FE model  MSC.MARC 2005R3 code  3D model  20 nodes hexahedron elements  J-integral calculation BAY-LOGI Specimen number Number of elements Number of nodes 1E2384018593 1E4415220017 1E7481823134

17. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 17 Boundary conditions Only one quarter of the specimen was simulated. BAY-LOGI Total applied force 2 Total applied force 2 Symmetry condition Specimen number Total applied force [kN] 1E2259.7 1E4339.4 1E7205.5

18. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 18 J-integral calculation J-integral values along the crack front at max loading BAY-LOGI Straight crack front

19. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 19 J-integral calculation J-integral values history plot BAY-LOGI Straight crack front

20. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 20 Real crack front BAY-LOGI 1E2 1E4 1E7

21. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 21 J-integral along the crack front BAY-LOGI Real crack front

22. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 22 J-integral history plot BAY-LOGI Real crack front J-integral values history plot

23. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 23 Conclusion In case of short straight and short real cracks the difference of the J-integral values is not significant. In case of deep crack more accurate J-integral value was resulted, if real crack front was modelled. Residual stress was considered, and this calculation is validated by NRI data. FE models were also validated by LLD curve of NRI. BAY-LOGI

24. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 24 Possibilities for further investigations Weibull stress calculation based on the Beremin-model. T-stress calculation. BAY-LOGI

25. 2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 2007 25 Thank you for your kind attention! BAY-LOGI