A COMSOL framework for predicting hydrogen embrittlement -- Part II: phase field fracture

TL;DR

This work advances hydrogen embrittlement research by delivering a generalised, hydrogen-informed phase-field fracture model that couples elastic-plastic deformation with stress-driven diffusion and trapping, implemented in COMSOL and freely available. Building on Part I’s hydrogen uptake/transport, it introduces a unified framework where G_c degrades with hydrogen content via a coverage-based law, and fracture evolution is driven by a phase-field variable φ under an AT2-like regularization. Numerical demonstrations on a 2D notched plate, boundary-layer R-curves, and a 3D vessel reveal how hydrogen concentration, diffusion, and trapping modulate crack initiation and propagation, including rate-dependent effects and the transition between brittle and ductile behavior. The results highlight the model’s ability to reproduce key HE phenomena, including leak-before-break scenarios, while offering practical guidelines for selecting degradation parameters and time-stepping strategies for robust simulations. The openly available codes and methodological clarity provide a valuable tool for engineers to predict hydrogen embrittlement in complex components.

Abstract

Prediction of hydrogen embrittlement requires a robust modelling approach and this will foster the safe adoption of hydrogen as a clean energy vector. A generalised computational model for hydrogen embrittlement is here presented, based on a phase field description of fracture. In combination with Part I of this work, which describes the process of hydrogen uptake and transport, this allows simulating a wide range of hydrogen transport and embrittlement phenomena. The material toughness is defined as a function of the hydrogen content and both elastic and elastic-plastic material behaviour are incorporated, enabling to capture both ductile and brittle fractures, and the transition from one to the other. The accumulation of hydrogen near a crack tip and subsequent embrittlement is numerically evaluated in a single-edge cracked plate, a boundary layer model and a 3D vessel case study, demonstrating the potential of the framework. Emphasis is placed on the numerical implementation, which is carried out in the finite element package COMSOL Multiphysics, and the models are made freely available.

Figures (30)

• Figure 1: Comparison of different degradation functions.
• Figure 2: Enhancing diffusivity through a step function to capture how the rapid fluid (gaseous or electrochemical) hydrogen-containing environment progresses with crack advanced.
• Figure 3: Atomistically-informed hydrogen degradation laws and comparison with the phenomenological law by Yu et al. Yu2016ASteels: (a) influence of the hydrogen degradation coefficient $\chi$ for a segregation energy of $\Delta g_b^0 = 30$ kJ/mol, and (b) influence of the segregation energy for a hydrogen degradation coefficient $\chi=0.6$.
• Figure 4: Numerical experiments on a single-edge cracked plate undergoing uniaxial loading: (a) scheme of the geometry and the boundary conditions, and (b) finite element mesh.
• Figure 5: Validation of the numerical implementation against the behaviour of a linear elastic solid. Comparison against the results by Cui et al.Cui2022AEmbrittlement (symbols). A very good agreement is obtained across a wide range of hydrogen concentrations. The time increment and tolerance are chosen as $\Delta \bar{u} = 10^{-3}$ and $R_{tol}=0.005$.