PSI - Issue 68

M. Zarazovskii et al. / Procedia Structural Integrity 68 (2025) 391–397

392 2

M. Zarazovskii et al./ Structural Integrity Procedia 00 (2025) 000–000

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(1)

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where K I – stress intensity factor (SIF) in the existing or postulated crack in the RPV, K IC – the critical SIF. The calculations are performed with the understanding that the RPV metal will degrade due to operational factors, such as irradiation and operating temperature. The fracture toughness (FT) curve is represented by an exponential function:

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# #A ! " C C % " = + $ " !

(2)

where A 1 – the lower shelf (asymptote), which is minimum value of FT at low temperatures region; A 2 and – empirical coefficients; T – temperature; T K – the critical brittleness temperature (CBT) of the RPV metal, which is responsible for indexing the FT curve (CTB is WWER’s analogy of western Transition Temperature). To ensure the conservatism of the brittle strength margin estimation, the coefficients of function (2) for the nuclear standards are chosen so that the resulting curve corresponds to the lower limit of all experimental data. A significant part of NPP fleet in the EU, the US, and Ukraine have already exceeded their design life. The lifetime extension beyond the original design life was made possible by a series of technical assessments and the implementation of measures, mainly related to the surveillance specimen (SS) testing. However, the majority of the SS have already been utilised, and there is insufficient irradiated metal for further studies. In this context, the development of methods for the study of miniature samples derived from halves of previously used SS becomes a pertinent area of research. Consequently, over the past few decades, research in this field has been actively pursued. One of the most popular areas of study in the field of FT specimen miniaturisation is the investigation of the potential for obtaining crack resistance in RPV metal through the application of the Master-Curve methodology ASTM E1921-17a (2017), Wallin, K. (1991), Wallin, K. et al. (2001). The Master-Curve concept is to ascertain the crack resistance directly, based on a limited number of samples, utilising a three-parameter Weibull model Wallin, K. (1989). This model establishes a correlation between crack resistance and the probability of overall failure p f . The p f value represents the probability of failure at a given stress intensity value that is less than or equal to K Jc for any specimens selected from a large batch. The p f distribution of ferritic steels with yield strengths in the range from 275 to 825 MPa is similar and depends on the specimen size and test temperature, as well as on the value of the lower asymptote of crack resistance for ferritic steels K min . The shape of this distribution is contingent upon the value of the Weibull exponent b , which is approximately equal to ≈4. The Master-Curve is expressed by the exponential function as follows: 0.5 , T 0 , – reference temperature, which is determined by statistical processing of the FT experimental data as the point at which the median ( р f =0.5) of the Master-Curve corresponds to K Jc =100 MPa∙m 0.5 . The ASTM E1921 outlines two methods for assessing the strength of materials: multi-temperature assessment and single-temperature assessment. 1. Multi-temperature assessment: • The experiment is conducted at varying temperatures in order to ascertain the relationship between the critical stress intensity K Jc on temperature. • The apparatus enables the user to gain a more comprehensive understanding of the material's strength characteristics under varying conditions. • In order to construct a curve of K Jc versus temperature, it is necessary to conduct tests at different temperatures and analyse the data obtained. 2. Single-temperature assessment: • The experiment was conducted at a specific temperature. • It allows us to obtain the value of the critical stress intensity K Jc for a given temperature. ! ( ) ! #&#$%" #&'( )*+ # $$ ,, $ $ -+ ! ! "# $ % & & ! " + " # $ % & ' ( )) * + ,, - . ! = + (3) where K min =20 MPa∙m

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