1. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Temperature dependence of Beremin-modell parameters for RPV steel Gyöngyvér B. Lenkey Róbert Beleznai Szabolcs Szávai

2. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Objectives Parameter study on the effect of material properties (R y, n) To determine the temperature dependence of Beremin-modell parameters (PERFECT EU Integrated project: Prediction of Irradiation Damage Effects in Reactor Components)

3. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Stress-strain curve for JRQ reference RPV material ASTM A533 grade B class 1 D=6 mm cylindrical specimens with strain measurement on the specimen -70 °C

4. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Fracture toughness results and master curve data provided by KFKI AEKI JRQ reference RPV material (pre-cracked Charpy specimens): at –60, -70, -90, -110 °C

5. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Failure probability - Weibull distribution: Weibull-stress: –where - major principal stress in V i Beremin-modell

6. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Weibull-parameter calculation Fixed m: m=10 (temperature independent)  u was determined from the master curve: –at J med the probability of failure is P f =0.5:

7. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI FEM model 2D plain strain Different models for different crack length values of the specimens Refined mesh size at the crack tip: 10  m Blunted crack tip: 2.5  m

8. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI FEM results – process zone Von Mises stressEq. plastic strain

9. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Performed analysis Sensitivity analyses: –Three different values of yield strength (R y measured ±25 MPa) –Three different values of strain hardening exponent. Further analyses: –Temperature dependence of s u (from –110 to –60 °C) – using artificially generated stress- strain curve based on measured yield strength values –Effect of strain hardening exponent

10. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Yield strength variation

11. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Effect of yield strength variation

12. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Effect of yield strength 10 % variation in yield strength causes 5% change in  u. appr. linear relationship.  u, MPa

13. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Hardening exponent variation

14. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Effect of hardening exponent variation

15. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Effect of hardening exponent not linear relationship. larger effect for the higher n value.  u, MPa

16. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Determine the temperature dependence of  u Master curve describe the T dependence of K med  J med From FEM calculation:  u (J med )   u (T) formal relationship – for a given material law From the calculation:  u (J med )   u (T) formal relationship for different material law (R y variation, n variaton) Knowing the T dependence of R y   u (T) can be determined

17. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI

18. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Determine the temperature dependence of  u Master curve describe the T dependence of K med (T)  J med (T) From FEM calculation:  u (J med )   u (T) – for a given material law From the calculation:  u (J med )   u (T) for different material law (R y variation, n variation!) Knowing the T dependence of R y   u (T) can be determined

19. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI R y - increasing

20. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI n - increasing

21. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Determine the temperature dependence of  u Master curve describe the T dependence of K med  J med From FEM calculation:  u (J med )   u (T) – for a given material law From the calculation:  u (J med )   u (T) for different material law (R y variation) From the T dependence of R y   u (T) can be determined

22. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Temperature dependence of the yield strength Slope: 16 MPa/10 °C Material law was generated based on measured R y

23. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI

24. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI

25. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Temperature dependence of  u for JRQ reference RPV material

26. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI

27. Bay Zoltán Foundation for Applied Research Institute for Logistics and Production Systems BAY-LOGI Conclusions Both R y and n have significant effect on the Beremin-modell parameter (  u ) with fix m value If the master curve describes well the material behaviour, it is possible to formulate the temperature dependence of  u - based on fracture toughness values measured at one temperature and the temperature dependence of the stress- strain curve