PSI - Issue 28

Casper Versteylen et al. / Procedia Structural Integrity 28 (2020) 1918–1929 Versteylen/ Structural Integrity Procedia 00 (2020) 000–000

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1.1. PTS

The effect of thermal stresses due to a PTS event in a RPV wall with a postulated crack in it can be calculated using FEM analyses. The stress intensity factor of a crack in a reactor pressure vessel can be calculated and compared to the critical stress intensity factor (fracture toughness). Choi et al. calculated stress intensity factors for a uniform cooling rate of 100 °C/hour uniformly distributed on the RPV inner surface Choi et al. (2019). In this analysis the cooling effect of the fluid flow is simplified significantly. In reality the pressurized hot and cold water affects the RPV wall temperature in complex ways. The thermal mixing of the fluid inside the RPV has been modelled by several authors Sharabi et al. (2016), Jaros et al. (2017), and Boyd (2008). The influence that the fluid flow has on stress intensity of a postulated crack has been analyzed by Mora et al. (2019), by modelling fluid flow using CFD techniques and using a sub-model in an region of the RPV with high stresses. The sub-model is used to calculate the critical stress intensity for cleavage. The fluctuation of the stress intensity in time is due to the fluid mixing. A similar stepped CFD and FEM approach was applied by Uitslag-Doolaard et al. (2019). In this approach several crack locations were analyzed and a LOCA of 200 seconds was analyzed, compared to 37 by Mora et al. (2019). The character of failure for body centered cubic (BCC) steels depends on the temperature at which the deformation takes place. At lower temperatures the plastic deformation cannot be accommodated by dislocation movement and failure is sudden and occurs without much energy dissipation by cleavage fracture. At higher temperatures the failure mode tends to be ductile. The transition between those modes depends on the temperature, because the dislocation slip modes are thermally activated. In the brittle domain, the probability of brittle failure should be evaluated using statistics. Commonly, brittle cleavage failure for a certain stress level follow the Weibull distribution. The materials response to a stress intensity is captured in the materials fracture toughness. Relevant for the nuclear industry is the fact that the fracture toughness of the RPV material decreases due to irradiation. The probability of forming a critical cleavage crack depends on the weakest link of the material. Therefore the thickness of the specimen is inversely proportional to the fracture toughness. The IAEA defines the critical stress intensity factor �� as �� � 2� � �11 � �� � �����.�1��� � � � �� � � 25 .4 � � � � ��� � 1 � 1 � � �� � � � � �1� with T as the temperature, T � is a reference temperature (both in degrees Celsius), B the thickness of the specimen (the RPV wall in this case) in mm and P � is the cumulative probability of brittle fracture Uitslag-Doolaard et al. (2019). This equation is derived from the model developed by Beremin (1983), in which the probability of forming a cleavage fracture is related to some materials properties and an applied stress. Beremin also considered that a crack inside the material causes a stress concentration and a plastic zone which has its effect on the local stress state. This allow for a link between fracture toughness and the probability of failure. The proportionality between probability of failure and stress concentrations is P � ~K � due to the plastic zone around a pre-existing crack Ritchie et al. (1973). The constants in equation (1) represent K ��� and K ������ , the minimum fracture toughness and the critical fracture toughness at the reference conditions respectively. Their values are chosen such that the prediction for K �� is conservative Wallin (2002). In the case of small scale yielding (SSY) for a plane strain specimen, the relationship between the J integral (J) and the stress intensity factor (K) is straightforward. 1.2. Critical stress intensity for cleavage