A COMSOL framework for predicting hydrogen embrittlement -- Part I: coupled hydrogen transport

TL;DR

The paper develops a comprehensive COMSOL-based framework for predicting hydrogen embrittlement by coupling stress-assisted diffusion, multi-trap hydrogen, dislocation transport, and hydrogen-induced softening under realistic boundary conditions. It integrates Oriani-equilibrium and McNabb–Foster kinetic trapping, dislocation-mediated transport, and electrochemical surface uptake, with careful attention to numerical stability and discretisation. The authors validate the approach against classical benchmarks (Sofronis–McMeeking, Krom, Dadfarnia, Charles, Di Leo–Anand, Kotake) and demonstrate robust performance across several scenarios, including complex boundary conditions and material softening. The work culminates in an openly shared COMSOL implementation, providing a solid foundation for hydrogen-aware fracture modeling (to be extended in Part II with crack-growth simulations).

Abstract

Hydrogen threatens the structural integrity of metals and thus predicting hydrogen-material interactions is key to unlocking the role of hydrogen in the energy transition. Quantifying the interplay between material deformation and hydrogen diffusion ahead of cracks and other stress concentrators is key to the prediction and prevention of hydrogen-assisted failures. In this work, a generalised theoretical and computational framework is presented that for the first time encompasses: (i) stress-assisted diffusion, (ii) hydrogen trapping due to multiple trap types, rigorously accounting for the rate of creation of dislocation trap sites, (iii) hydrogen transport through dislocations, (iv) equilibrium (Oriani) and non-equilibrium (McNabb-Foster) trapping kinetics, (v) hydrogen-induced softening, and (vi) hydrogen uptake, considering the role of hydrostatic stresses and local electrochemistry. Particular emphasis is placed on the numerical implementation in COMSOL Multiphysics, releasing the relevant models and discussing stability, discretisation and solver details. Each of the elements of the framework is independently benchmarked against results from the literature and implications for the prediction of hydrogen-assisted fractures are discussed. The second part of this work (Part II) shows how these crack tip predictions can be combined with crack growth simulations.

Figures (23)

• Figure 1: Different hydrogen transport phenomena are modelled and implemented in the present work. Hydrostatic stress ($\sigma_h$) influences not only hydrogen diffusion but also uptake on the crack surface. Trapping effects, considering features such as grain boundaries, dislocations, inclusions or voids, are modelled from a local equilibrium or kinetic exchange between lattice hydrogen (L) and trapped hydrogen (T). In addition, hydrogen transport by dislocations assuming a preferred orientation is modelled.
• Figure 2: Boundary layer model used in all simulations: (a) schematic of the geometry and boundary conditions; and (b) detail of the finite element mesh near the crack tip.
• Figure 3: Capturing the influence of stresses and trapping. (a) Comparison of predictions of lattice hydrogen concentration ahead of the crack tip by the present implementation and the works of Sofronis and McMeeking Sofronis1989NumericalTip and Krom et al. Krom1999HydrogenTip; (b) Contours for normalised hydrogen concentration at lattice sites, $C_L/C_{env}$. The contours in (b) correspond to the maximum loading rate (i.e., after 130 s) and consider the strain rate effect.
• Figure 4: Validation of the strain rate effect at high loading rates. Comparison between lattice hydrogen concentrations predicted ahead of the crack tip by the present implementation and the work by Krom et al. Krom1999HydrogenTip.
• Figure 5: Influence of the discretization scheme on the lattice hydrogen distribution ahead of the crack tip. The results aim at assessing: (a) The role of different p-discretization approaches for the three unknown variables: the displacement field $\mathbf{u}$, the hydrostatic stress $\sigma_h$, and the lattice hydrogen concentration $C_L$; (b) The role of $\sigma_h$ storage approaches in the predictions of lattice hydrogen concentration ahead of the crack tip.