PSI - Issue 5

Jesús Toribio et al. / Procedia Structural Integrity 5 (2017) 1291–1298

1292

Toribio and Kharin / Structural Integrity Procedia 00 (2017) 000 – 000

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1. Introduction

Hydrogen embrittlement (HE) of metals is the problem that has gained again much importance due to emerging hydrogen technologies, in particular those that operate with H 2 gas. This stimulates the efforts towards better understanding, modelling and predictive simulation of hydrogenous environment (gas H 2 ) assisted fracture (HEAF), certain aspects of which are the subject matter of the present contribution. Irrespectively of hydrogen source, hydrogen assisted fracture (HAF) results from the synergic action of the stress, strain and hydrogen in metal. Every material damaging is associated with crystal imperfections, e.g., dislocations according to the schemes of Zener-Stroh, Cottrell, etc. As well, lattice imperfections in metals afford deeper potential wells for hydrogen than ordinary interstitial sites of a regular lattice, and so they act as attractors (traps) of the species in the course of its thermally activated random walking in metal. Materials contain various kinds of traps (solution impurities, vacancies, dislocations, interfaces, etc.) having different trapping capabilities, see, e.g., Hirth (1980). Dissimilar interstitial positions in crystal form a set of the site types  comprising the regular lattice sites L and a subset of different trap types { T }, and have their respective number concentrations N A ( A   ) per unit volume. The total amount of hydrogen in a material unit is represented by its atom number volume concentration C , which is fractioned between dissimilar sites from a set  , so that C =  A   C A , where C A is the partial concentration of hydrogen allocated to A -type positions. In continuum physics terms, HAF event occurs in material volume element d 3 x at a point identified by position vector x when the concentration C X ( x , t ) of hydrogen accumulated over time t in X -type sites ( X  { T }   ), which are responsible for the operating mechanism of fracture, reaches the stress-strain dependent critical value ( , ) p cr X C σ ε   , where ( , ) t x σ  and ( , ) t p x ε  are the tensors of stress and plastic strain, in some critical location x = x cr at the instant of local fracture t = t cr : (x , ) (x , ) cr cr cr X cr cr X t t C C  . Advancement of HAF is then rate-limited by the species delivery to the fracture process zone (FPZ) to meet the requirements of the operating damaging mechanism, so that hydrogen transport to damage loci is the key component of HE. Accordingly, the modelling of hydrogen transport that can specify hydrogen partitioning between distinct microstructural positions is crucial for HE analysis, prediction and control. Hydrogen delivery to prospective damage loci in material-environment systems in general comprises a series of kinetic processes, see, e.g., Nelson (1983) or Gao and Wei (1985), such as ( i ) delivery of H-containing molecules (H 2 or other) in the surrounding gas towards the proximities of FPZs in metal; ( ii ) atomic H discharge from gas molecules at the gas-metal interface and entry of into metal, ( iii ) H movement trough metal bulk towards fracture loci by diffusion. According to certain indications (mainly, the correlations between the effects of gas pressure and temperature on the rates of HEAF and of certain transport steps), each of these transport mechanisms can control the rate of hydrogen arrival in fracture loci, which gives place to models relating the kinetics of HEAF with individual transport process on the basis of corresponding theories of gas flow, surface physics, or diffusion in solids, cf., e.g., Williams and Nelson (1970), Lu et al. (1981), Gao and Wei (1985), and Kharin (1987). The capability of a particular transport step to really dominate the kinetics of HEAF should be expected to rely on the circumstances of a particular HEAF case. Nevertheless, lack of independent knowledge about intrinsic parameters of the transport processes apart from mere fitting to the HEAF data depreciates the conclusiveness of the observed correlations. At any rate, description of the entire journey of hydrogen from surrounding gas to the harmful position in metal with account for all involved kinetic processes would be valuable for understanding of HEAF and for grounded extrapolations of observed behaviours to other conditions (Nelson (1983)). An attempt to construct such coupled model of hydrogen delivery to potential damage sites in metals is undertaken in this contribution.

2. 2. Hydrogen transport in metal-environment system: the flux equations

The three key sequential steps and the energy landscape of hydrogen journey towards fracture sites in metals are depicted schematically in Fig. 1. Certainly, every involved transport step is a quite complicated process per se . Specific hydrogen flux descriptions for each of them are provided in the following subsections.