Computational predictions of hydrogen-assisted fatigue crack growth

TL;DR

The paper addresses hydrogen-assisted fatigue crack growth in metals by developing a phase-field framework that couples fracture, hydrogen diffusion, and fatigue damage. It integrates a Griffith-based phase-field description with an AT2 regularisation, a diffusion law for hydrogen, and fatigue degradation functions, yielding a model where toughness degrades as $f_H(C)$ and $f_F(\bar{\alpha})$, with the crack evolution governed by $f_F(\bar{\alpha})f_H(C)(G_c/\ell)(\phi - \ell^2 \nabla^2\phi) + g'(\phi)\psi_0 = 0$. Importantly, predictions match experimental data across hydrogen pressure, load ratio, and loading frequency without hydrogen-specific calibration, using only air-fatigue behavior and toughness sensitivity to hydrogen. This enables efficient Virtual Testing of infrastructure components in hydrogen environments and provides guidance on conservative testing frequencies and the impact of pre-charging, with potential extensions to capture explicit hydrogen–cyclic damage interactions.

Abstract

A new model is presented to predict hydrogen-assisted fatigue. The model combines a phase field description of fracture and fatigue, stress-assisted hydrogen diffusion, and a toughness degradation formulation with cyclic and hydrogen contributions. Hydrogen-assisted fatigue crack growth predictions exhibit an excellent agreement with experiments over all the scenarios considered, spanning multiple load ratios, H2 pressures and loading frequencies. These are obtained without any calibration with hydrogen-assisted fatigue data, taking as input only mechanical and hydrogen transport material properties, the material's fatigue characteristics (from a single test in air), and the sensitivity of fracture toughness to hydrogen content. Furthermore, the model is used to determine: (i) what are suitable test loading frequencies to obtain conservative data, and (ii) the underestimation made when not pre-charging samples. The model can handle both laboratory specimens and large-scale engineering components, enabling the Virtual Testing paradigm in infrastructure exposed to hydrogen environments and cyclic loading.

Figures (10)

• Figure 1: Experimental fatigue crack growth rates d$a$/d$N$ versus stress intensity factor range $\Delta K$ curves for a ASME SA-723 Grade 1 pressure vessel steel San2017bortot2023effect. The experimental data have been generated for various hydrogen gas pressures ($p_\mathrm{H_2}$), load ratios ($R$), and loading frequencies ($f$). These tests, conducted at SANDIA National Laboratories, are representative of the fatigue crack growth behaviour of pressure vessel steels in hydrogen-containing environments. The curve in air ($p_\mathrm{H_2}=0$) was provided by TENARIS and is representative of the response in air of ASME SA-723 Grade 1 pressure vessel steel.
• Figure 2: Schematic description of phase field fracture. The discrete, sharp crack (left) is regularised by making use of an auxiliary phase field variable $\phi$, with the width of the regularised zone being governed by the magnitude of the phase field length scale $\ell$.
• Figure 3: Testing configuration; Compact Tension (CT) samples are employed with the following: (a) geometry, with dimensions in mm, and (b) finite element mesh, with the zoomed region showing the mesh along the expected crack growth trajectory.
• Figure 4: Degradation of the fracture toughness as a function of the hydrogen concentration. Experimental data for similar pressure vessel steels (taken from Refs. SanMarchi2012Matsumoto2017bortot2023effectSan2017). The data are used to determine the material hydrogen degradation function $f_\mathrm{H} (C) = G_c / G_c (C=0) = J_{Ic} / J_{Ic} (C=0)$.
• Figure 5: Numerical fatigue crack growth experiments: representative results. Contours of (a) phase field variable $\phi$ and (b) hydrogen concentration $C$ with three different stages of crack growth: $a=a_0+2$ mm, $a=a_0+8$ mm, and $a=a_0+16$ mm, where $a_0$ is the initial crack size, as shown in Fig. \ref{['fig: CTspecimen']}a. These representative contours have been computed for a H$_2$ pre-charged sample exposed to a loading frequency of $f=1$ Hz, a hydrogen pressure of $p_\mathrm{H_2}=106$ MPa and a loading ratio of $R=0.1$.