Temperature dependence of Beremin-modell parameters for RPV steel

1. Temperature dependence of Beremin-modell parameters for RPV steel Gyöngyvér B. Lenkey Róbert Beleznai Szabolcs Szávai

2. Objectives • Parameter study on the effect of material properties (Ry, n) • To determine the temperature dependence of Beremin-modell parameters (PERFECT EU Integrated project: Prediction of Irradiation Damage Effects in Reactor Components)

3. Stress-strain curve for JRQ reference RPV material • ASTM A533 grade B class 1 • D=6mm cylindrical specimens • with strain measurement on the specimen • -70 °C

4. 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. Beremin-modell • Failure probability - Weibull distribution: • Weibull-stress: • where - major principal stress in Vi

6. Weibull-parameter calculation • Fixed m: m=10 (temperature independent) • su was determined from the master curve: • at Jmed the probability of failure is Pf=0.5:

7. FEM model • 2D plain strain • Different models for different crack length values of the specimens • Refined mesh size at the crack tip: 10 mm • Blunted crack tip: 2.5 mm

8. FEM results – process zone Von Mises stress Eq. plastic strain

9. Performed analysis • Sensitivity analyses: • Three different values of yield strength (Ry measured ±25 MPa) • Three different values of strain hardening exponent. • Further analyses: • Temperature dependence of su (from –110 to –60 °C) – using artificially generated stress-strain curve based on measured yield strength values • Effect of strain hardening exponent

10. Yield strength variation

11. Effect of yield strength variation

12. su, MPa Effect of yield strength • 10 % variation in yield strength causes 5% change in su. • appr. linear relationship.

13. Hardening exponent variation

14. Effect of hardening exponent variation

15. su, MPa Effect of hardening exponent • not linear relationship. • larger effect for the higher n value.

16. Determine the temperature dependence of su • Master curve describe the T dependence of Kmed  Jmed • From FEM calculation: su(Jmed)  su(T) formal relationship – for a given material law • From the calculation: su(Jmed)  su(T) formal relationship for different material law (Ry variation, n variaton) • Knowing the T dependence of Ry su(T) can be determined

18. Determine the temperature dependence of su • Master curve describe the T dependence of Kmed (T) Jmed(T) • From FEM calculation: su(Jmed)  su(T) – for a given material law • From the calculation: su(Jmed)  su(T) for different material law (Ry variation, n variation!) • Knowing the T dependence of Ry su(T) can be determined

19. Ry - increasing

20. n - increasing

21. Determine the temperature dependence of su • Master curve describe the T dependence of Kmed  Jmed • From FEM calculation: su(Jmed)  su(T) – for a given material law • From the calculation: su(Jmed)  su(T) for different material law (Ry variation) • From the T dependence of Ry su(T) can be determined

22. Temperature dependence of the yield strength Slope: 16 MPa/10 °C Material law was generated based on measured Ry

25. Temperature dependence of su for JRQ reference RPV material

27. Conclusions • Both Ry and n have significant effect on the Beremin-modell parameter (su) with fix m value • If the master curve describes well the material behaviour, it is possible to formulate the temperature dependence of su - based on fracture toughness values measured at one temperature and the temperature dependence of the stress-strain curve