Analysis of electro-permeation of hydrogen in metallic alloys

A reaction-diffusion type modelling framework is presented to analyse both electro-permeation (EP) and thermal desorption spectrometry (TDS) measurements of hydrogen in metallic alloys. It is assumed that the kinetics of hydrogen motion is governed by diffusion through the lattice, along with trapping/detrapping at specific sites such as dislocations, grain boundaries, etc. It is shown that the trapping and detrapping rates are typically much faster than the diffusion rate, and consequently a simplification of the governing equations suffices such that local equilibrium exists between lattice and trapped hydrogen. Using this local equilibrium assumption, we then present an asymptotic analysis of the governing kinetic equation for the EP test. This asymptotic analysis reveals that four regimes of behaviour exist, ranging from negligible trapping to the complete filling of deep traps. The analysis suggests that EP tests should be so-arranged that three regimes of behaviour are spanned, in order to extract the relevant material properties associated with hydrogen transport. The numerical solutions presented in this study support the asymptotic analysis. The hydrogen kinetics framework is also deployed to analyse both EP and TDS tests on the same martensitic steel. The EP measurements all lie in regime I and are thus insufficient to uniquely determine both the trap density and binding energy. Reasonable agreement is obtained between measurements and numerical predictions of TDS tests using parameters estimated from the EP tests. Further improvements in measurements are required to confirm the fidelity of this modelling approach.This article is part of the themed issue 'The challenges of hydrogen and metals'.