To crack, or not to crack: How hydrogen favors crack propagation in iron at the atomic scale

Abstract

Steel is a key structural material because of its considerable strength and ductility. However, when exposed to hydrogen, it is prone to embrittlement. Mechanistic understanding of the origin of hydrogen embrittlement is hampered by the lack of reliable interatomic potentials. Here, we perform large-scale molecular dynamics simulations of crack propagation after having developed and validated an efficient yet density-functional-theory-accurate machine-learning potential for hydrogen in iron. Simulations based on our potential reveal that in the absence of H, iron is intrinsically ductile at finite temperatures with crack-tip blunting assisted by dislocation emission. By contrast, minute (part-per-million) hydrogen concentrations can switch the crack-tip behavior from ductile blunting to brittle propagation. Detailed analysis of our molecular dynamics results reveals that the combination of fast hydrogen diffusion and diminished surface energy is at the origin of embrittlement. Our results set the stage for a modified Griffith's criterion for hydrogen-induced brittle fracture, which closely captures the simulations and that can be used to assess embrittlement in iron-based alloys.

Figures (9)

• Figure 1: Hydrogen-induced crack propagation.a, Critical stress intensity factor as a function of the bulk hydrogen concentration. MD simulation results obtained using the FeH ACE potential are compared with predictions from the proposed embrittlement theory, Eq. \ref{['Eq:theory']}. The theory predictions are based on local hydrogen content ahead of the crack tip extracted from MD simulations (Fig. \ref{['bonds_and_h_atoms']}), which determines the "fresh" crack surface coverage. The saturation level is the theoretical lower bound for a fully H-saturated fresh surface. Theory predictions (bright red circles and solid lines) include pure iron lattice trapping (second term in Eq. \ref{['Eq:theory']}). As hydrogen weakens the iron-iron bonds, the lattice trapping becomes weaker as wellTEHRANCHI_curtin_LT_2017150. Evaluating the impact of hydrogen on its strength is beyond the scope of this study, however, theory predictions without lattice trapping are shown as well and represent a lower bound (light red circles and dotted line). Indeed, MD simulation results lie between theory predictions with and without the (pure iron) lattice trapping. Notably, as hydrogen concentration increases, MD results approach theory predictions without lattice trapping. All results are presented as mean values of at least three simulations with 95% confidence intervals. For the simulation results of pure iron, the confidence interval is smaller than the marker size. b, Experimental observations of the crack tip under mode-I loading, at varying hydrogen concentrations. Pure iron exhibits extensive dislocation emission at the crack tip. Note that dislocation traces appear as lines emanating at an angle from the crack surfaces. Increasing hydrogen concentration (hydrogen pressures of 0.7, 10, and 100 Pa) induces a transition from emission to predominant cleavage. Figure 1b refers to Fig. 6.16 in ref. Vehoff1997.
• Figure 2: Performance of Fe-H Atomic Cluster Expansion (ACE) potential.a, The ACE computational speed compared to neural network potentialNNP_PRM_Ogata_2021 (NNP), as MD steps per day as a function of the number of atoms and cores. The corresponding computational times (expressed in microseconds per timestep per atom) are 0.15, 0.15, and 0.14 for ACE; and 2.34, 2.34, and 2.29 for NNP. b, c, d, Primary validation tests against density functional theory (DFT) and NNP: b, The bcc energy versus volume (E-V) curves; the NNP produces the E-V curve with a spurious local minimum at small volumes, and it fails to converge at even smaller volumes, resulting in an error (cross). c, Energies of the H-free (left) and fully H-saturated (right) $\text{\{}110\text{\}}$ surfaces. DFT clean surface energies are shown as average values from refs. surf_ener_1_JIN2022110029 and jiang_carter_ActaMat_2004_compute_surf_ener_with_H; energies of the covered surfaces were computed following the procedure described in ref. jiang_carter_ActaMat_2004_compute_surf_ener_with_H, see Supp. Info. S3 "Validation of the ACE FeH potential against benchmark properties". DFT surface energies, both clean and covered, are reported with the corresponding 95% confidence intervals. d, Traction--separation (T-S) curves for $\text{\{}110\text{\}}$ crack surfaces; notably, ACE captures the peak height, which limits the maximum stress that the material can withstand. More validation tests are in Supp. Info. S3 "Validation of the ACE FeH potential against benchmark properties".
• Figure 3: The number of iron-iron chemical bonds at the crack tip and the number of hydrogen atoms on the nucleating crack surfaces.a, A schematic illustrating the crack tip geometry and an inset with the atoms (highlighted in grey) ahead of the crack tip. b, Results of the MD simulations at various hydrogen bulk concentrations (0.05, 5, and 200 appm), showing the number of Fe-Fe bonds (top) and of H atoms approaching the newly forming crack surface, as a function of the increasing applied stress intensity factor. For each concentration, simulations were repeated at least trice, Here, representative cases are shown (see Supp. Info. S6 "Hydrogen atoms count at crack tip and its relation to surface energy" for the remaining cases). Light gray lines represent the actual data, while the thick black lines indicate the moving averages (see Supp. Info. S6 "Hydrogen atoms count at crack tip and its relation to surface energy"). Cleavage points are marked where there is a sharp drop in the number of iron-iron bonds and are identified automatically by convolution with a step functionconvolution_smith1997scientist. We employed the OVITO package to count hydrogen atoms and bonds, setting a cutoff distance of 3.25 $\mathring{\mathrm{A}}$ for the largest bond (Fig. \ref{['basic_tests_fe']}d); See the details of counting bonds and hydrogen atoms in Supp. Info. S6 "Hydrogen atoms count at crack tip and its relation to surface energy".
• Figure S1: Reference data and model complexity vs. accuracy and speed. a, DFT reference database for ACE training. The database contains 22,305 structures, including 21,917 structures from the NNP database (see ref. NNP_PRM_Ogata_2021), 20 structures from the bcc E-V curve for the low and high volumes (or nearest-neighbor distances), and 368 structures from traction-separation curves. b Accuracy and computational cost versus the complexity of our ACE. By increasing the number of basis functions (bf), accuracy improves in terms of the radial mean square errors (RMSE) for energies and forces for the testing dataset. However, the increased accuracy is accompanied by a higher computational cost, as illustrated by the incremental rise in the number of bf, reaching 1,300 in one of the trained models. Based on the trade-off between accuracy and computational cost, we choose an ACE with 300 b.f. for our final model (denoted by labels with curly hats).
• Figure S2: Fe-H Atomic Cluster Expansion (ACE) validation tests for bcc Fe. a, Elastic constants. b, Solution energies of the hydrogen interstitial atoms for tetrahedral (T) and octahedral (O) sites in the bcc lattice. c, Energy profiles of diffusion paths between different interstitial sites. DFT data from ref. diffusion_paths_Hirata2018. d, Traction-Separation curve for the 100 surface. e, Phonon density of states (DOS) for pure iron (DFT data from ref. zk_liu_dft_phonons_bcc_fe_HANG201494). f, Phonon density of states (DOS) for iron with interstitial hydrogen at the tetrahedral (T) and octahedral (O) sites obtained with ACE; the positions of the peaks due to hydrogen are compared to the DFT results from ref. phonons_with_h_dft_ALVAREZ2024107590. DFT solution energies are presented as the average values from refs. Carter_2004_PhysRevB.70.064102, jiang_carter_ActaMat_2004_compute_surf_ener_with_H, wolverton_h_sol_energies_COUNTS20104730, and sol_ener_ZHU202238445 with 95% confidence intervals.