PSI - Issue 59

Oleksandr Andreykiv et al. / Procedia Structural Integrity 59 (2024) 182–189 O. Andreykiv et al. / Structural Integrity Procedia 00 (2023) 000 – 000

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and material degradation parameters, must be utilized in assessing possible failures in the continued operation of power plants. The most detrimental factors threatening the safety of nuclear and thermal power plants are hydrogen embrittlement and radiation creep. The issue of hydrogen embrittlement in metallic materials has long been a focal point for scientists and engineers, and various aspects of this problem have been extensively researched. Notably, there are results from experimental studies on the impact of hydrogen on the degradation of metallic materials (Babii et al. (2007), Tsyrul’nyk et al. (2007), Murakami (2008), Zagórski et al. (2008 ), Student (2010)) and methods for determining the residual life of structural elements operating in hydrogen-containing environments (Panasyuk et al. (2000), Hembara et al. (2017, 2022), Jiang et al. (2019), Krechkovska et al. (2023)). However, the effects of hydrogen on the propagation of high-temperature creep cracks (Andreikiv et al. (2023)), which often represent the primary mechanism of loss of durability in energy infrastructure components, have not yet been thoroughly studied. Radiation creep of materials has been intensively studied by materials scientists since the 1980s. Numerous works have addressed the issue of radiation creep and its connection with material characteristics. The rate of radiation creep has been investigated, with some studies, such as those by Jung et al. (1986) and Ibragimov et al. (1989), exploring the correlation between creep rate and the yield strength of unirradiated material. Nevertheless, this approach has faced criticism from other authors who claim that the creep rate is governed by the continuously evolving structure under radiation. They propose building relationships between creep rate and the energy of defect production (Gilbert et al. (1972), Reiley (1981), Fukumoto et al. (2013), Kuramoto et al. (2013)). Most researchers, however, tend to agree that the most accurate representation of radiation creep rate is through dependence on radiation dose (fluence) or flux density (flux) (Olszta et al. (2012), Palmer et al. (2014)). Since radiation creep is predominantly driven by the movement of dislocations stimulated by stress, theoretical researches in this direction inevitably encompass processes involving dislocation glide due to the absorption of point defects. Theoretical models have been developed in this regard (Kirsanov et al. (1981) and Pyatiletov et al. (1981)). In our view, for engineering practice, a more important case is when both of the above-mentioned mechanisms are in effect, leading to the degradation and failure of metallic structures, particularly in nuclear power plants. We are not aware of any studies addressing such scenarios. Therefore, in this publication, we propose a computational model for crack propagation in high-temperature creep in metallic materials subjected to hydrogen-containing environments and neutron irradiation. 2. Statement of the Problem and Solution Method Let us consider a plate with a straight macroscopic crack of length 2 l 0 , subjected to tensile loads perpendicular to the defect location line with an intensity p , which is uniformly heated to a temperature T 0 (creep temperature (Garofalo (1970))), irradiated by a neutron flux with an intensity Ф 0 , and becomes saturated with a hydrogen concentration C 0 , which is formed during the dissociation of hydrogen molecules on the metal surfaces of the equipment. The problem consists of finding the time t = t * , when the crack reaches a critical value l = l * , beyond which further plate failure is considered instantaneous. Since we are dealing with slow crack growth, i.e., with stepwise crack propagation, we will write the energy balance for the elementary act of crack jump in the following form:   A W . (1) Here A is the work of external forces;  is the fracture energy; W is the deformation energy:

( ) (2) (1) W W W l W t pl pl s    , ( )

(2)

( )

(1) W l pl

s W is the elastic component,

is the part of the plastic deformation energy that depends on the crack

where

length l ; ( ) (2) W t pl is the part of the plastic deformation energy expended on plastic deformation at a constant crack length during the incubation period c t t  preparing for its jump. It depends on time t , neutron intensity Ф 0 , hydrogen concentration C 0 and is generated by the body itself. By differentiating equation (1) with respect to time, we obtained the equation for the rate of energy change in the plate: