PSI - Issue 43

Sergiy Kotrechko et al. / Procedia Structural Integrity 43 (2023) 228–233 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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1. Introduction The Local Approach (LA) to fracture was introduced in the 1980s. It aimed to solve key problems in fracture mechanics, such as the prediction of the specimen geometry and statistical size effect on fracture toughness (transferability problem), as well as the effects of temperature, degradation of the material after neutron irradiation, etc. The possibility of solving these complicated problems was seen in the application of the statistical local criterion for the initiation of fracture in the vicinity of a crack, because only this approach allows to take into account the most important features of the mechanism of fracture initiation on the microscale. This meant the possibility of establishing a permanent physical basis for fracture mechanics. However, as the results of numerous studies show (Wiesner and Goldthorpe (1996), Gao X., Dodds (2000), Pineau (2006), Wasiliuk et al. (2006), Ruggieri and Dodds (2018)), the LA did not fully meet expectations. First of all, it turned out that the parameters of the Weibull distribution - m and u  - are not constants, but their values depend on temperature, specimen geometry and the plastic strain value. In general, it was found that LA can only be used at low temperatures. However, from the application point of view, the ductile to brittle transition region (DBT) is the most important. The main reason for this state of the art is the unjustified simplification of the local quantitative criterion for fracture initiation. Many works have attempted to overcome this shortcoming (e.g. Pluvinage et al. (1999), Bordet et al. (2005), Gao et al. (2005), Ruggieri et al. (2015), Jivkov et al. (2019), Ruggieri and Jivkov (2019)). In general, two key issues have not been addressed and have been identified as needing to be addressed, namely: (i) the need to consider the effects of temperature and the magnitude of local plastic strai n on the bulk density ρ of the crack nuclei (CN); (ii) the consideration of the value of the threshold stress th  . As far as the latter is concerned, it is indeed a methodological problem. It consists in developing a technique for the experimental determination of th  . Therefore, a simplified method of th  determination for structural steels has been proposed by Kotrechko et al. (2019). Jivkov et al. (2019), Ruggieri and Jivkov (2019) have tried to take into account the effect of plastic strain and test temperature on the number of CN formed in the local plastic zone in front of a macrocrack tip. Ruggieri and Jivkov (2019) proposed suitable approximations to account for the effects of temperature and plastic strain on crack nuclei density and, accordingly, on Weibull stress magnitude. This allowed the critical values of the IC J integral to be predicted with high accuracy for both low and high temperatures within the DBT region. At the same time, Ruggieri and Jivkov (2019) emphasized the importance of clarifying the physical nature of such a significant effect of temperature on the intensity of CN generation. An attempt to develop a physical version of the Local Approach based on a detailed analysis of the processes of crack nuclei formation and unstable equilibrium in a polycrystalline aggregate was made by Kotrechko (2002, 2013), Kotrechko and Mamedov (2016), Kotrechko et al. (2019). This approach made it possible to determine regularities of the influence of both the metal structure and the conditions of its loading on the probability of fracture. However, it proved to be quite demanding for engineering calculations. At the same time, this approach can be used as a tool to analyze the key effects controlling the initiation of cleavage in the vicinity of the macrocrack, in particular to analyze the effects of temperature and the magnitude of plastic strain on the crack nuclei formation rate within the "process zone". This report examines the physical reasons for the influence of plastic strain and temperature on the intensity of CN formation and shows how this affects both the slope of the temperature dependence and the scatter limits of the fracture toughness of structural steels in the ductile to brittle transition region. 2. Theoretical background Inhomogeneity of microplastic deformation, which gives rise to plastic deformation incompatibility on grain or interphase boundaries, is a general reason for the CN formation in polycrystalline solids. Kotrechko (2013), Kotrechko and Mamedov (2016) proposed a generalised model of CN formation in a polycrystalline aggregate. Adapted version of this model for prediction the brittle fracture of structural steels enables to derive the expression for the bulk density of CN formed at a given value of local plastic strain: