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

2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 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

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

2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 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

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

2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 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

2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 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

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

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

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

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

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

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

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

2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 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 1E E E

2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 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] 1E E E7205.5

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

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

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

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

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

2 nd Hungarian-Ukrainian Joint Conference – Kyiv, 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

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

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