PSI - Issue 59

Oksana Hembara et al. / Procedia Structural Integrity 59 (2024) 190–197 Oksana Hembara et al. / Structural Integrity Procedia 00 (2019) 000 – 000

191

2

Nomenclature e p

equivalent plastic deformation

hydrogen flux hydrostatic stress

J

σ h N T D L C L

number of hydrogen trapping sites hydrogen diffusion coefficient

hydrogen concentration

1. Introduction Structures operating in hydrogen environments require thorough analysis to prevent premature failure due to hydrogen embrittlement (HE). Currently, various mechanisms of HE has been proposed by Djukic et. al. (2016) and Dwivedi and Vishwakarma (2018). Among them, the most prevalent are HEDE (Hydrogen Enhanced Decohesion) and HELP (Hydrogen Enhanced Localized Plasticity), proposed by Djukic et. al. (2014, 2015, 2019). There is ongoing debate about which mechanism is the most adequate in explaining hydrogen embrittlement. However, it is widely acknowledged that an increased concentration of hydrogen near the crack tip plays a crucial role in hydrogen-induced brittleness. This phenomenon results from the complex interaction between hydrogen and the material (Djukic et. al. (2016) and Mehrer (2007)): hydrogen atoms penetrate and diffuse within the crystal lattice of the material, interact with microstructural defects (acting as traps), and influence the material’s properties and fracture conditions (Andreikiv and Hembara (2022), Capelle et al. (2013); Hembara and Chepil (2022), Ohaeri et al. (2018); Skalskyi et al. (2018)). The issue of hydrogen concentration near various defects in a deformed and hydrogenated body is complex, and an effective analytical solution to this problem has not yet been published in the literature. In global scientific research numerical methods are actively evolving for assessing hydrogen concentration in metals, particularly in the vicinity of fracture zones where the material has been deformed beyond its yield point. Many authors have employed finite element methods to investigate the distribution of hydrogen in the fracture zone for specific cases. Among them Yokobori et. al. (1996), who solved hydrogen diffusion equations, taking into account the influence of stress gradients. In their analysis, they used an analytical form of the elastic-plastic stress field. On the other hand, Sofronis and McMeeking (1989) conducted an analysis of hydrogen diffusion by combining finite element methods for hydrogen diffusion with a finite element program for stress analysis. Krom et. al. (1999) considered the effect of plastic deformation, which was not considered in the Sofronis and McMeeking (1989) model. Subsequently, Sofronis et. al. (2001) proposed a model for hydrogen-induced softening, indicating a reduction in the initial yield strength due to hydrogen absorption, and analyzed the hydrogen-induced localization of plastic flow for a plate under uniform tension. In this analysis Taha and Sofronis (2001) and Liang and Sofronis (2003) obtained only static values of hydrogen concentration, then performed a transient analysis of hydrogen diffusion, accounting for the elastic-plastic stress field around the crack tip, the effect of plastic deformation, and the softening effect induced by hydrogen. Ivanyts’kyi et. al. (2022) constructed distributions of hydrostatic stress and hydroge n concentration along the crack line for three types of steels under tensile loading at the limiting equilibrium state and after unloading. An empirical relationship between hydrogen concentration and material mechanical properties was established. Additionally, results of hydrostatic stress distribution obtained experimentally using digital image correlation under boundary loading were presented. Dmytrakh (2011), Dmytrakh et al. (2018, 2019, 2023); Syrotyuk and Dmytrakh (2014) and Nyrkova (2020) experimentally investigated the influence of hydrogen concentration on crack growth. This article presents the results of a diffusion analysis of hydrogen in the vicinity of the most common types of crack-like defects on the inner surface of a pipe under internal pressure in a hydrogen-containing environment. 2. Formulation of the hydrogen diffusion problem using finite element method The hydrogen diffusion equation utilized in this research is based on studies by Sofronis et. al. (2001) and Taha and Sofronis (2001). In accordance with the positioning of hydrogen atoms in metals, two types of hydrogen are classified: hydrogen atoms within normal interstitial lattice sites (diffusion-mobile or lattice hydrogen) and those located at