Analysis of hydrogen permeation tests considering two different modelling approaches for grain boundary trapping in iron

Abstract

The electrochemical permeation test is one of the most used methods for characterising hydrogen diffusion in metals. The flux of hydrogen atoms registered in the oxidation cell might be fitted to obtain apparent diffusivities. The magnitude of this coefficient has a decisive influence on the kinetics of fracture or fatigue phenomena assisted by hydrogen and depends largely on hydrogen retention in microstructural traps. In order to improve the numerical fitting of diffusion coefficients, a permeation test has been reproduced using FEM simulations considering two approaches: a continuum 1D model in which the trap density, binding energy and the input lattice concentrations are critical variables and a polycrystalline model where trapping at grain boundaries is simulated explicitly including a segregation factor and a diffusion coefficient different from that of the interior of the grain. Results show that the continuum model captures trapping delay, but it should be modified to model the trapping influence on the steady state flux. Permeation behaviour might be classified according to different regimes depending on deviation from Fickian diffusion. Polycrystalline synthetic permeation shows a strong influence of segregation on output flux magnitude. This approach is able to simulate also the short-circuit diffusion phenomenon. The comparison between different grain sizes and grain boundary thicknesses by means of the fitted apparent diffusivity shows the relationships between the registered flux and the characteristic parameters of traps.

Simulation of hydrogen permeation through pure iron for trapping and surface phenomena characterisation

“…Following the previous work of the authors [34], a 2D polycrystal model is used to explicitly simulate grain boundary trapping. Slabs of 𝐿 × 1000 µm 2 are modelled, where 𝐿 is equal to 580 µm for the 925ºC/40min sample and 480 µm for 1100ºC/5min.…”

“…However, the goal of the present work is to provide a usable model considering the Mass Diffusion module and automatized by python scripts without the need of subroutines so grain boundaries are designed with a given thickness that reproduces a layer where hydrogen is trapped due to the misorientation, geometrically necessary dislocations (GND) [38] and the likely carbon segregation. In the present calculations, an intermediate thickness of 𝑡 𝑔𝑏 = 100 nm is considered [34].…”

“…Following this procedure, since 𝐷 𝑎𝑝𝑝 varies depends on concentration, 𝐷 𝑔𝑏 is implemented in ABAQUS by considering a concentration-dependent diffusivity table. Solubility properties are assigned following the approach from [34]: solubility of grains is taken as 1 and a segregation is defined as the grain boundary solubility introduced in the corresponding material properties. To determine the segregation magnitude, a low lattice occupancy is assumed, 𝜃 𝐿 ≪ 1, and Equation ( 9) is rearranged considering 𝐶 𝑔𝑏 = 𝜃 𝑇 𝑁 𝑇 .…”

Influence of charging conditions on simulated temperature-programmed desorption for hydrogen in metals

“…Both strong and weak traps are full for input lattice concentration 𝐶 𝐿,0 > 1.0 wt ppm; however, the order of magnitude of 𝐶 𝑇 highly depends on binding energy for low lattice concentrations. In order to assess the possible influence of 𝐶 𝐿,0 on TDA spectra, as done before in a previous study on hydrogen permeation modelling [41], a weak trapping phenomenon (𝐸 𝑏 = 30 kJ/mol) is simulated; for low binding energy and room temperature uniform charging, the segregation regime plotted in Figure 7 hints a possible high influence of initial concentration 𝐶 𝐿,0 . Thus, due to the wider range of lattice concentration for which saturation is not achieved, only weak traps are here considered.…”

Cohesive zone modelling of hydrogen assisted fatigue crack growth: the role of trapping

“…Following ingress, atomic hydrogen diffuses through the crystal lattice and resides at either interstitial lattice sites or microstructural trapping sites (e.g., dislocations, grain boundaries, voids, carbides and interfaces). Whether embrittlement is governed by the hydrogen content in lattice or by the one in trap sites is still a matter of debate [9][10][11][12][13], and trapping characteristics vary from one material to another [14][15][16].…”