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

  • A. DíazEmail author
  • I. I. Cuesta
  • E. Martinez-Pañeda
  • J. M. Alegre
Original Paper


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.


Hydrogen diffusion Permeation test Finite element simulation Grain boundary trapping 



The authors gratefully acknowledge financial support from the project MINECO Refs: MAT2014-58738-C3-2-R and RTI2018-096070-B-C33. E. Martínez-Pañeda acknowledges financial support from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA Grant Agreement No. 609405 (COFUNDPostdocDTU).


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Structural Integrity GroupUniversidad de BurgosBurgosSpain
  2. 2.Department of EngineeringUniversity of CambridgeCambridgeUnited Kingdom
  3. 3.Department of Civil and Environmental EngineeringImperial College LondonLondonUK

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