PSI - Issue 72

Péter Ungár et al. / Procedia Structural Integrity 72 (2025) 265–269

267

= 1 − [− ( ) ] ,

(2)

where σ u is the normalisation stress, at which 63.2 % of the specimens fail. A Python script was developed that’s used to calculate the Weibull stress es from the finite element results. The advantage of this language over Fortran was the direct access to the result files, and that it can run independently from the FEM analysis. The disadvantage of this method is that the two libraries bundled with MSC Marc, py_post and py_mentat that were used to access the FEM results cannot gain data directly from integration points, only nodal values and element results are available, which is a detriment to accuracy. The code was verified and validated by comparing results with partners.

Fig. 1. Finite element mesh, left: normal CT, right: mini CT.

Another Python script was developed to optimize the two Beremin parameters m and σ u based on measurements. Both Linear Regression and Maximum Likelihood calculations were implemented, in the end Linear Regression had a better convergence and gave better results. The optimisation is based on the correlation between the experimental data, for which rank probability was used and the Weibull stress calculation from the finite element model. The corresponding fracture toughness values needed to be found in the calculated stress intensity factors from the simulations. An Excel based tool was used to determine the J-integral and then stress intensity factors from the finite element results, based on the ASTM E1921-21 standard, using load line displacement and loads. Due to the timesteps of the FEM model, exact matches can’t be found between the fracture toughness values and the calculated stress intensity factors, so interpolation had to be used. Several sensitivity studies were done to analyse the effects of different Weibull stress computational methods. These included the equation using strain correction, element selection criteria (plastic strain, stresses, triaxiality), censoring, load increments, convergence criteria and different arithmetical and data handling in Python. In the last version, strain correction was not used, the element selection was based on equivalent plastic strain only. Censoring according to the standard wa s used, and it’s important to note that even though the censored fracture toughness values are not used for the optimisation, the rank probability is still affected by them. 3. Results During this work three RPV steels were analyzed: 15Kh2MFAA, 73W, JRQ. These included irradiated specimens on a few temperatures. In general, it can be said that optimization gave physically sensible results mainly for 15Kh2MFAA. For the other two materials, while the Beremin parameters using linear regression were obtained, the agreement with the measurements was not acceptable. The reason for this might be the high degree of plasticity in the specimens, but these questions are still open. For the 15Kh2MFAA, a parameter combination was obtained for -130°C ( m = 23.1 and σ u = 2656MPa ) and -120°C ( m = 20.96 and σ u = 2656MPa ) respectively. The comparison, along with the censoring limit can be seen on Fig. 2, where the simulations show good agreement with the measurements.