PSI - Issue 72

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

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properties of reactor pressure vessel steel change due to different effects. Most important of those for brittle fracture is the irradiation embrittlement. The increase in the transition temperature can cause problems during loss of coolant accidents in which cold water is injected into the primary circuit. The goal of this paper is to show a method with which parameters for the Beremin model can be determined, which can be used for the probabilistic assessment of brittle cleavage fracture. The model originally developed in 1983 by F.M. Beremin in Beremin (1983) is a widely used method to describe brittle fracture probability based on Weibull statistics. This can be later used to determine a theoretical T 0 reference temperature. The groundwork for the numerical characterization of brittle fracture was laid down by F.M. Beremin in Beremin (1983), who performed experiments on steels to determine the mechanical conditions for fracture cleavage. He theorized the material science background for the numerical evaluation based on Weibull statistics and made finite element analysis and material testing to compare the results of his work. Several others implemented his ideas and iterated on them with different versions. Andrieu et al. (2012) applied Beremin’s theories for ferritic steels and Jin et al. (2022) used size scaling for ferritic steels in nuclear power plants. Moattari et al. (2016) investigated the ductile crack growth before cleavage fracture and calibrated the Weibull parameters using scaling method and two types of specimens, CT and SEB. Najafabadi et al. (2019) provides a calibration method for the Weibull parameters based on different constraint levels using T-stresses. Barbosa and Ruggieri (2020) developed a toughness scaling method for parameter determination. Tiryakioğl u (2008) describes the parameter determination using moments and maximum likelihood models. An important part of this work was to study the usability of sub-sized compact tensile test specimens for parameter optimization. Normal 1T-CT specimens are standardized to use in the determination of fracture toughness, but the availability of irradiated versions is limited due to scarcity in the surveillance programs in nuclear power plants. There’s an option for accelerated, artificial irradiation, however it’s ex pensive and the capacity is strongly limited. Hence it would be advantageous if sub-sized, 0.16T-CT (MCT) specimens could be used that can be cut from the half part of a used Charpy specimen. CT specimen (1T and 0.16T) fracture toughness measurement data was taken for three different RPV steels (15Kh2MFAA, 73W, JRQ) on multiple temperatures. Finite element simulations provide the base of this work, using previously determined flow curves for the CT specimens. These together with measurements can be used for the Weibull stress calculation, and later the optimization of the Beremin parameters m (shape parameter) and σu (scale parameter) for the two-parameter version of the method. 2. Modelling methods First, finite element models had to be built in MSC Marc for both normal and mini CT. As mentioned above, flow curves determined in a previous task were used. Due to symmetries, an 8th model was sufficient. The mesh, seen on Fig. 1, was used during a previous benchmark in the project, in which all important results were validated between partners, for example: J-integral, load line displacement, load, stress fields, plastic volumes, etc. The mesh was made with J-integral calculation in mind, hence the circular shape around the crack front. J-integral calculation was done in-software, and with an Excel-based tool using the ASTM E1921-21 standard. Weibull stress calculation is not implemented in MSC Marc, so a method and corresponding scripts had to be developed, that could do that. The theoretical background was provided by the original work of Beremin (1983). The two-parameter version was used in the end, without strain correction. The Weibull stress is calculated as = √∑ ( 1 ) 0 , (1) where V j is the plastic volume, V 0 is the reference volume, 1 is the first principal stress of the j -th element and m is the Weibull modulus. Not all finite elements are considered in this calculation, only those that exceed a certain limit. In the end, this was chosen as the elements, in which the equivalent plastic strain reaches 0.002 . The failure probability can be then calculated as