The Energy Approach of EPFM Applied to the Analysis of a WPS Experiment on a Cracked Cylinder

This document presents the energy approach of elastic-plastic fracture mechanics applied to the analysis of a “warm pre-stress” test on a cylinder made of a 17MoV84mod. steel, artificially degraded by special heat treatment to simulate an irradiated end of life RPV material and submitted to a mechanical loading close to a thermal shock transient. This test has been conducted at the MPA of Stuttgart in the context of the European project SMILE. The influence of the hardening representation (isotropic, kinematics, etc.) as well as the choice of the toughness values of the material are analysed. The numerical analysis was performed at EDF-R&D with the Code-Aster, the finite element code of EDF. First of all, we have identified the critical value G_pc of the G_p parameter at the temperature of failure (T = 35°C). Then we have applied the energy approach and compared the results obtained to experimental one’s. Concerning the global values, the agreement between the results of calculation and the experimental results is good if we consider the values of temperature or COD as well as the values of K_J. Concerning the local values, we have observed a rapid decreasing of the opening stress at the notch tip and a significant influence of the hardening on the Von Mises stress. The curves giving the fracture probability as function of K_J are quite relevant to estimate the predictive capacity of the approach used, as well as the importance of the choice of hardening. We have pointed out a 15% variation of K_J depending on this choice. Using tests on CT specimens at room temperature in order to identify the critical value G_pc of the G_p parameter, the value of 77.7 MPa.m^1/2 is obtained for K_J if we consider the kinematics case, at 95% of fracture probability. This value is the highest and the nearest to the experimental value equal to 90 MPa.m^1/2. It is not a proof that the hardening is completely kinematics but it leads to the question of a more complete identification of the material to know what is the isotropic part and the kinematics part in the hardening. Besides, because the difference between the result obtained with the energy approach and the experimental result is equal to 14% we can conclude to a satisfactory predictive capacity of this approach. The “warm pre-stress” effect, associated with a significant increase of the cleavage fracture toughness at low temperature after a pre-loading at a higher temperature, is clearly predicted by using the energy approach. The comparison between the results obtained with the different approaches used (energy approach, Beremin model, etc.) will be made in another paper. This work is performed in the context of the SMILE European Project.