Molecular Statics Simulation of the Effect of Hydrogen Concentration on {112}<111> Edge Dislocation Mobility in Alpha Iron

Abstract

To clarify the whole picture of hydrogen embrittlement (HE), an understanding of the elementary processes occurring during the fracture process is important. As one of the most important elementary processes of HE crack growth, the role of dislocation motion has been intensively studied. In this study, we performed molecular statics calculations to simulate the dislocation velocity in the presence of absorbed hydrogen atom from a gaseous hydrogen atmosphere. The dislocation motion was assumed to be a stress-dependent thermal activation process, and the energy barriers were investigated using the nudged elastic band method for the {112}<111> edge dislocation in alpha iron. In addition to the energy barrier for dislocation motion, those for hydrogen diffusion were also computed to evaluate the competitive motion of dislocations and hydrogen atoms. The hydrogen concentration was also evaluated using the hydrogen trap energy concept. The results indicate that an extremely low hydrogen concentration yields contradictory results such as softening or hardening depending on the applied stress. In contrast, with increasing hydrogen concentration, the dislocation velocity always decreases and results in hardening independent of the applied stress. Focusing on the dislocation motion, we propose a simplified classification map of hydrogen embrittlement mechanisms, which suggests the importance of the environment and stress conditions on the dominant mechanism of HE.

1. Introduction

Concerns over global warming and energy scarcity issues have led to the global promotion of a hydrogen energy society. Assurance of the strength reliability of structural elements used for hydrogen gas stations and/or hydrogen gas pipelines, particularly for steel from an economical viewpoint, are becoming an important issue. Hydrogen embrittlement (HE) is a phenomenon in which absorbed hydrogen causes marked reduction of the mechanical properties in steel.¹⁾ Recent studies on HE have supported the following distinctive HE mechanisms: (a) hydrogen-enhanced decohesion^2,3,4) (HEDE), in which hydrogen reduces the cohesive strength between metallic bonds and yields brittle fracture; (b) hydrogen-enhanced localized plasticity^5,6,7) (HELP), in which absorbed hydrogen affects the dislocations and locally enhances the plastic deformation; and (c) hydrogen-enhanced strain-induced vacancies^8,9) (HESIV), in which hydrogen enhances the formation and accumulation of vacancies accompanied by plastic deformation, which facilitates ductile fracture. These mechanisms were considered to be proposed based on experimental and/or numerical results obtained under relatively limited conditions for individual researchers despite HE primarily being a phenomenon induced by a wide range of boundary conditions. The whole picture of the HE fracture mechanism remains unclear even for pure iron. Therefore, the view that HE results from the competition of these individual HE mechanisms has recently been supported; i.e., it is impossible to explain the whole picture of HE using one specific mechanism. Because the formation of each HE mechanism progresses near the crack tip, the combination of conditions (environment, material, and stress, as illustrated in Fig. 1) is important, similar to in stress corrosion cracking. Therefore, clarification of the elementary processes that competitively develop as leading fracture processes is important. As one of the most important elementary processes of HE crack growth, the role of dislocation emitted from the crack tip has been intensively studied. For example, it has been reported that the pile-up distance between dislocations decreases under gaseous hydrogen conditions based on transmission electron microscopy observations.¹⁰⁾ This decrease of pile-up distance is considered to be attributed to the increase of dislocation mobility. However, concerning the plastic deformation, the macroscopic stress–strain relation suggests contradictory results, such as hydrogen-induced softening¹¹⁾ and hardening,¹²⁾ even for the same material. This contradiction suggests that the progress of the lattice defects, including dislocations, changes depending on the environment and stress conditions. Atomistic simulations could be effective for clarification of the distinctive elementary process of dislocation motion under a hydrogen atmosphere; however, classical molecular dynamics cannot be used because of the long-time scale needed to calculate the dislocation motion and accompanying hydrogen diffusion. Therefore, molecular statics¹³⁾ and density functional theory¹⁴⁾ investigations have been conducted based on certain assumptions for the dislocation motion. Our previous studies^13,15,16) indicated an increase or decrease of the dislocation velocity depending on the applied stress conditions. These contradictions are attributed to the decrease of the first Peierls potential and increase of the second Peierls potential in the presence of hydrogen atom. However, the hydrogen concentrations adopted in these studies were extremely low compared with those in actual hydrogen gas situations. Thus, evaluation of the dislocation mobility for higher hydrogen concentration conditions is needed. In this study, we evaluated the dislocation velocity for higher hydrogen concentration by calculating the stress-dependent thermal activation energy. Molecular statics analyses were also used to investigate the thermal activation energy in order to clarify the effect of the hydrogen concentration on the dislocation mobility.

Fig. 1.

Schematic of the conditions leading to HE.

2. Analysis Method

2.1. Analysis Model

In the analysis model, we placed an edge dislocation on the {112} slip plane in the <111> slip direction for alpha iron, similar to in our previous studies.^13,15,17) The analysis model is shown in Fig. 2. The size of the analysis model was 11.5, 4.2, and 0.8–8 nm along the x-, y-, and z-directions, respectively. The differences of the model size along z direction are used to control the hydrogen concentration within the analysis model. When we investigate the effect of hydrogen concentration on hydrogen trap energy in section 3.1, the analysis model with 8 nm along z axis is used. 0.8 nm model is used to investigate the dislocation velocity in section 3.2. The iron atoms were arranged to the {112} plane to be the xz plane, and the <111> direction was set as the x-axis. To introduce a 1b (b: the length of a Burger’s vector) edge dislocation, one atomic plane was initially removed followed by structural relaxation, such that a 1b edge dislocation with the dislocation line along the z-direction was introduced in the same manner as in our previous studies.^13,15,17) The three upper-most and bottom-most atomic layers were fixed as boundary atoms. Periodic boundary conditions were adopted along the x- and z-directions. The obtained dislocation structure and the positions of the constituting atoms are shown in Fig. 2(b). Common neighbor analysis¹⁸⁾ (CNA) was performed; the bcc structures are depicted as gray spheres, and the non-crystalline structure is shown in black. We perform nudged elastic band (NEB) calculations^19,20) to investigate the applied shear stress dependence of the minimum energy path (MEP) and the energy barrier of edge dislocation motion (Peierls barrier) with a distance of 1b. Moreover, the diffusion path and energy barrier for hydrogen diffusion accompanying the dislocation motion were also investigated to evaluate the dislocation velocity, which also transported the hydrogen atmosphere. The hydrogen concentration of the analysis model was evaluated using the hydrogen trap energy. A higher hydrogen concentration was required compared with our previous study¹³⁾ to consider actual hydrogen gas storage system conditions. In this study, we adopted a hydrogen concentration of C_H = 1.24/nm (the number of hydrogen atoms per unit length of the dislocation line). The embedded atom method atomic potential developed by Wen et al.²¹⁾ to describe the Fe–H system was used in this study. The conjugate gradient method was used for molecular statics structural relaxation.

Fig. 2.

Analysis model of {112}<111> edge dislocation in alpha iron: (a) crystallographic orientation of the analysis model and (b) magnification of atomic distribution near the dislocation core.

2.2. Edge Dislocation Motion as a Stress-dependent Thermal Activation Process

In this study, the edge dislocation motion was assumed to be a simplified process, as shown in Fig. 3. In the initial state, the dislocation lies in the Peierls valley with the shape of a straight line, as illustrated in Fig. 3(a). Then, part of the dislocation line moves forward to a neighboring Peierls valley, as illustrated in Fig. 3(b). Here the length of the dislocation line that moves forward is l^*; then, the edge dislocation line generates two kinks at both ends of the bulged line. The energy barrier of kink migration is considered to be lower than that of edge dislocation motion needed to surmount the Peierls barrier; thus, the kinks easily move, as illustrated in Fig. 3(c) and result in movement of the edge dislocation by 1b. According to our previous study,¹³⁾ l^* is obtained based on the continuum dislocation theory:²²⁾   

$$l^{*}={\left(\frac{\mu b^2}{8\pi \tau }\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.},$$(1)

where μ is the shear modulus (68.6 GPa) and τ is the shear stress exerted on the dislocation. Because the dislocation motion is approximated as a stress-dependent thermal activation process, as illustrated in Fig. 3, the stress dependence of the energy barrier for dislocation motion and hydrogen diffusion were investigated. Displacements were applied on the boundary atoms, and the work performed by the applied force was calculated using the following equation:   

$${\mathrm{\Phi }}_F=\mathrm{\Phi }-F\mathrm{\Delta }x,$$(2)

where Φ_F is the potential energy of the system including the applied work, Φ is the potential energy of the atomic system, F is the applied force on boundary atoms, and Δx is the displacement of the boundary atoms from the initial equilibrium positions.

Fig. 3.

Schematic illustrations of the approximated edge dislocation motion.

We evaluated the stress-dependent energy barrier (Peierls barrier of unit length of dislocation line: ΔE). The dislocation velocity of the thermal activation process, v_D, is approximately   

$$v_{\mathrm{D}}\approx Q(\mathrm{\Delta }E{l}^{*})b,$$(3)

where Q(ΔE) corresponds to the frequency needed to surmount the energy barrier ΔE and is thus written in the form of the following Arrhenius equation:   

$$Q(\mathrm{\Delta }E)=v_{\mathrm{d}}exp\left(-\frac{\mathrm{\Delta }E}{k_{B}T}\right).$$(4)

Here, ν_d is the attempt frequency obtained using the string model of a dislocation line same as our previous study,¹³⁾ which is also assumed to be a function of the length of dislocation line l^*; ν_d = ν_D(b/l^*), where, ν_D is the Debye frequency.

2.3. Hydrogen Trap Energy and Equilibrium Hydrogen Concentration

The existence probability of hydrogen atoms around the edge dislocation core increases because of the large lattice distortion. Therefore, quantitative evaluation of the hydrogen concentration near the dislocation core should be pivotal for discussion of a realistic hydrogen atmosphere. We adopted the hydrogen trap energy concept.¹⁷⁾ The hydrogen trap energy near the dislocation core is determined by the following equation:   

$$\mathrm{\Delta }{E}_{\mathrm{d}}(\mathbf{r})=\left({\mathrm{\Phi }}_{\mathrm{d}}+\frac{1}{2}{\mathrm{\Phi }}_{\mathrm{H}2}+H^{\mathrm{T}}\right)-{\mathrm{\Phi }}_{\mathrm{d},\mathrm{H}}(\mathbf{r}),$$(5)

where Φ_d is the potential energy of the system in the absence of hydrogen, Φ_H2 is the potential energy of the hydrogen molecule, H^T is the heat of solution of the hydrogen atom to the T-site within a non-deformed perfect lattice, and Φ_d,H(r) is the potential energy of the system when a hydrogen atom is located at a specific site r. Equation (5) indicates that a larger trap energy results in a higher probability of occupation. Examining the hydrogen trap energy distribution around a {112}<111> edge dislocation,¹⁷⁾ the hydrogen occupation site has a trap energy of 0.49 eV as a maximum within the core and are found periodically along the dislocation line every 0.40 nm. Here, we can evaluate the equilibrium hydrogen concentration near the dislocation core based on the obtained distribution of the hydrogen trap energy. The hydrogen occupancy at T-sites within alpha iron under a gaseous hydrogen atmosphere at pressure p (Pa) and temperature T (K) is given by Sieverts’ law:²³⁾   

$$c_{\mathrm{T}-\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}}=0.9686\times {10}^{-6}\sqrt{p}exp\left(-\frac{3\mathrm{\hspace{0.17em} }440}{T}\right).$$(6)

Where, some unit conversions are performed from the original equation in order to convert atomic fraction of hydrogen to the hydrogen occupancy for each site. Using c_T-site, the hydrogen occupancy at a specific trap site with a hydrogen trap energy ΔE_d(r) is given by the following equation:²⁴⁾   

$$\frac{c_i}{1-c_i}=\frac{c_{\mathrm{T}-\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}}}{1-c_{\mathrm{T}-\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}}}exp\left(\frac{\mathrm{\Delta }{E}_d(\mathbf{r})}{k_{B}T}\right),$$(7)

where k_B is Boltzmann’s constant. These occupancies for each trap site takes value between 0 to 1, thus, the total number of trapped hydrogen atoms, N_Total, can be obtained by adding the occupancies of all the trap sites using the following equation based on the hydrogen occupancy at the ith trap site, c_i:   

$$N_{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=\sum _i{c}_i$$(8)

3. Analysis Results

3.1. Effect of Hydrogen Concentration on Hydrogen Trap Energy Near Dislocation Core

Let us first consider the hydrogen concentration adopted in the previous study and this analysis. As in the previous study,^13,15,17) structural relaxation was performed after introducing one hydrogen atom into the trap site near the dislocation core. The hydrogen trap energy was calculated from the energy of the relaxed system. By comparing the trap energy with that of other trap sites, we can find the site where the hydrogen atoms will first be introduced (the hydrogen existence probability is the highest), which is the most stable condition. The same procedure was performed for the second hydrogen atom, and the number of hydrogen atoms was increased from 1 to 20 (C_H = 0.12 to 2.47/nm). The results indicate that the strongest hydrogen trap energies for 1–20 hydrogen atoms were 0.49 eV for all cases; therefore, the maximum trap energy was almost independent of the hydrogen concentration. Because there was no change in the hydrogen trap energy with increasing hydrogen concentration, the hydrogen trap energy was considered to be independent of the hydrogen concentration in this concentration range, and the hydrogen trap energy distribution for one hydrogen atom was used to determine the hydrogen position and concentration in this study. The distribution of the hydrogen trap energy adopted in this study is shown in Fig. 4. Whole hydrogen atoms are located at Position A in Fig. 4 from the 1st to 20th atoms. Thus, the hydrogen atoms are periodically located along the dislocation line. Over 20 hydrogen atoms are periodically located at Position B in Fig. 4. The hydrogen concentration adopted in this study was 1.24/nm, such that all the hydrogen atoms were considered to be located at the Position A.

Fig. 4.

Hydrogen trap energy distribution around an edge dislocation core. Position A has the strongest trap energy of 0.49 eV, and Position B is the next most stable site. The red dotted circle denotes the dislocation core region detected by CNA. (Online version in color.)

3.2. Dislocation Velocity

The relationship between the dislocation position from the hydrogen atom and the potential energy surface (energy curve for dislocation motion) at zero applied stress is shown in Fig. 5. The energy when a hydrogen atom is located at a stable position within the dislocation core was set to zero. For comparison, the energy curve in the absence of hydrogen is also shown in Fig. 5. The existence of hydrogen clearly affects the energy curve of dislocation motion. Here, the energy barrier when the dislocation moves from 0b to 1b is defined as ΔE_0→1. The position 1b from the hydrogen atom is clearly not locally stable, and the dislocation must move from 0b to 2b at once. The energy barrier ΔE_0→2 is extremely large. Moreover, the energy barrier from 2b to 3b is also larger than that without hydrogen. In contrast, the dislocation is very stable at the 3b position and becomes stable next to 0b. This finding is attributed to the existence of a hydrogen occupation site with a high trap energy (B in Fig. 4) in a small distance on the same slip plane from the most stable Position, Position A, in Fig. 4. Thus, it is suggested that the dislocation would be trapped again after moving away from the hydrogen trap at 0b. The energy barrier after 3b increases as ΔE_3→4 < ΔE_4→5 < ΔE_5→6 and then gradually decreases and converges to the energy barrier in the absence of hydrogen. The exact values of the energy barriers for dislocation motion under 0.49 and 1.24/nm are listed in Table 1.

Fig. 5.

Potential energy surface for edge dislocation motion.

Table 1. Dependence of hydrogen concentration on energy barrier for dislocation motion.

Number of hydrogen atoms per unit length of dislocation line	Energy barrier per unit length of dislocation line [eV/nm]
[/nm]	ΔE0→1	ΔE1→2	ΔE2→3	ΔE3→4	ΔE4→5	ΔE5→6
0	0.082
0.49	0.079	0.153	0.092	0.108	0.098	0.085
1.24	0.374		0.210	0.082	0.127	0.140

Next, the energy barrier of dislocation motion under the applied shear stress condition was investigated to evaluate the frequency of dislocation motion. The relationship between the energy barrier for dislocation motion from 0b to 3b and the applied stress is shown in Fig. 6 as an example. With increasing applied stress, both ΔE_0→2 and ΔE_2→3 decreased. The position of 1b was no longer a local minimum within the applied stress range of 0 to 200 MPa adopted in this study.

Fig. 6.

Dependence of applied shear stress on the potential energy surface for edge dislocation motion.

Here, the dislocation is stable at the position of 3b compare to the other positions as shown in Figs. 5 and 6. First, let us consider the dislocation motion from 0b to 3b. To consider the competitive motion of a dislocation and a hydrogen atom, both the dislocation motion and hydrogen diffusion must be considered. First, we introduced a hydrogen atom at a position −1b away from the dislocation core and searched for the MEP of hydrogen diffusion toward the preceding dislocation. The MEP of hydrogen diffusion from −1b to 0b is shown in Fig. 7(a). The MEP was obtained by calculating the energy barrier for all combinations of trap sites using the NEB method. The highest energy barrier in this MEP was 0.25 eV from B to C in Fig. 7(a). Similarly, the MEP of hydrogen diffusion from −2b to 0b is also shown in Fig. 7(b). The highest energy barrier in this MEP was 0.35 eV from D to C in Fig. 7(b). We used these two values to represent the energy barrier of hydrogen diffusion. Similarly, the energy barriers of hydrogen diffusion from −3b to −5b were calculated. Because there was almost no stress dependence on the hydrogen diffusion barrier, the diffusion barrier was approximated as being constant with respect to the applied stress.

Fig. 7.

Magnified illustration of dislocation core and location of hydrogen occupation sites around the core. The MEP is depicted as a red line for the diffusion of a hydrogen atom from (a) −1b and (b) −2b to the dislocation core. The maximum energy barrier through the MEP was (a) 0.25 eV and (b) 0.35 eV. (Online version in color.)

The correlation between the applied shear stress and the frequencies of dislocation motion and hydrogen diffusion based on Eq. (4) are presented in Fig. 8(a). The frequency of dislocation motion in the absence of hydrogen, Q(ΔE_{w/0 H}), is also shown as a reference. When the applied shear stress was smaller than 82 MPa, both the frequency of dislocation motion from 0b to 2b, Q(ΔE_0→2), and that from 2b to 3b, Q(ΔE_2→3), were lower than the frequency of hydrogen diffusion from −2b to 0b, Q(ΔE_{H-diff, −2b}). Thus, the dislocation is considered to continue to move with the trapping of hydrogen determined by the frequency of Q(ΔE_0→2). However, when the applied stress was higher than 82 MPa, the dislocation is considered to move away from a hydrogen atom to the position of 3b. The maximum energy barrier of dislocation motion beyond 3b was ΔE_5→6, as indicated in Table 1; the frequencies of dislocation motion and hydrogen diffusion beyond 3b are shown in Fig. 8(b). Above a shear stress of 82 MPa, the frequency of dislocation motion is always higher than that of hydrogen diffusion; thus, the dislocation would never continue to exist at the position of 3b.

Fig. 8.

Correlation between the frequency of motion and applied shear stress at 300 K for a dislocation moving from (a) 0b to 3b and (b) 3b to 6b. (Online version in color.)

In other words, when the applied shear stress is 82 MPa or less, because the dislocation and hydrogen atom continue to compete, the effect of hydrogen on the dislocation velocity is observed. With further applied stress, the dislocation motion will be affected until the dislocation moves away from hydrogen atom; however, after that, the dislocation can move without any effects of hydrogen. The correlations between the dislocation velocity and shear stress for hydrogen concentrations of 0.49/nm,¹³⁾ 1.24/nm, and 0/nm are presented in Fig. 9. The dislocation velocity increased compare to the hydrogen-free condition when the hydrogen concentration was 0.49/nm and applied shear stress was below 30 MPa. In contrast, the dislocation velocity decreased for all cases with a higher hydrogen concentration of 1.24/nm. The contradictive behavior attributes the shape of the energy barrier for dislocation motion as shown in Fig. 5. The softening under low hydrogen concentration and applied stress occurs due to the reduction of energy barrier for dislocation motion.¹³⁾ Our previous study²⁵⁾ showed those reductions can be observed below about 0.8/nm of hydrogen concentration. Over 0.8/nm, the energy barrier for dislocation motion typically increases since the 1b position is no longer a local stable.

Fig. 9.

Dislocation velocity of stress-dependent thermal activation process at 300 K.

3.3. Equilibrium Hydrogen Concentration Near the Dislocation Core

The dependence of the number of hydrogen atoms within the analysis model on the hydrogen gas pressure and temperature is shown in Fig. 10; the hydrogen trap-energy distribution in Fig. 4 was used with dimensions of 6.4 and 6.5 nm in the x- and y-directions to evaluate the equilibrium hydrogen concentration in the vicinity of dislocation core. The hydrogen concentration adopted here is the number of equilibrium hydrogen atoms obtained using Eq. (8) divided by the length of the dislocation line. The equilibrium hydrogen concentration decreased with increasing temperature; in contrast, the hydrogen concentration increased with increasing gas pressure. The results indicate that the dislocation traps 6/nm of hydrogen atoms under 300 K and 0.01 MPa hydrogen gaseous conditions. Considering the realistic hydrogen gas conditions in a hydrogen gas tank, this value would increase to 144/nm at 300 K and 70 MPa. As previously described in section 3.1, hydrogen atoms stably exist at site A in Fig. 4 until reaching a hydrogen concentration of 2.47/nm; however, the stable site changes to site B in Fig. 4 with higher concentrations. The analysis of the hydrogen diffusion accompanying the dislocation motion thus becomes extremely complex; in this case, the number of combinations of hydrogen diffusion will increase. However, the hydrogen atoms trapped at site B in Fig. 4 are considered not to increase the dislocation mobility (a hydrogen atom at B does not show a significant trend to decrease the first Peierls barrier, as suggested by Table 1: Only lower hydrogen concentration case, hydrogen atom trapped at site A, yield in the reduction of energy barrier.²⁵⁾ On the other hand, the energy barrier increases with increasing the hydrogen concentration and its magnitude is extremely large. Hydrogen positions other than A are far from the crystalline disordered dislocation core so the effect on energy barrier is considered to be small.). The dislocation mobility is considered to decrease even under a more realistic hydrogen concentration condition.

Fig. 10.

Correlation of the number of hydrogen atoms along the dislocation line and (a) gas pressure, (b) temperature under thermal equilibrium.

4. Discussion

In this study, we evaluate the energy barrier for dislocation motion using molecular statics calculations. Molecular statics analyses deal the stable atomic configuration under 0 K, thus, the effects of atomic vibration at finite temperature was eliminated. However, we discussed the dislocation velocity at constant temperature, so that we think the hydrogen effect on dislocation mobility at constant temperature is qualitatively in good agreement with the realistic dislocation behavior. Anyway, our investigations adopted some assumptions for dislocation motion, therefore, experimental data with high accuracy are pivotal to conduct the quantitative discussions. On the other hand, we focused on dislocation motion as one of the most important elementary processes of HE. The actual fracture process of HE is more complex; however, the leading process of crack propagation would be dislocation emission and motion. Focusing only on emitted dislocation motion as an elementary process, our simulation results indicate that the HE mechanism can be classified based on the hydrogen concentration and applied stress as shown in Fig. 11. The dislocation velocity increases under lower hydrogen concentration and lower applied stress, which results in an enhancement of the dislocation motion and/or vacancy formation. These phenomena are somehow related to HELP and/or HESIV mechanisms. However, the dislocation velocity decreases under higher hydrogen concentration, which results in a decrease of the dislocation motion near the crack tip, preventing additional emission of dislocations. Here, the local plastic deformation could also induce vacancies. These phenomena are somehow related to HEDE and/or HESIV mechanisms. Furthermore, the fracture mechanism will be the same as that in the absence of hydrogen under higher applied stress conditions even though the initial state of motion is affected by pinning of solute hydrogen. The classification map proposed here strongly suggests the importance of the environment and stress boundary conditions for HE.

Fig. 11.

Schematic of the transition of the HE mechanism for different hydrogen concentrations and applied stress conditions.

5. Conclusions

The energy barriers of dislocation motion and hydrogen diffusion under different hydrogen concentration conditions were evaluated, and the results were compared with those of our previous study to clarify the effects of hydrogen concentration on the mobility of edge dislocations in alpha iron caused by a stress-dependent thermal activation process. The following conclusions were drawn:

(1) The Peierls potential is affected by the hydrogen concentration, and the hydrogen concentration of 1.24/nm resulted in no softening in our calculations.

(2) The dislocations interacted with solute hydrogen atoms under a lower applied stress condition for the 1.24/nm hydrogen concentration. The interaction led to a decrease of dislocation mobility, resulting in hardening. With increasing applied stress, dislocations were pinned in the initial state of motion; however, hydrogen had no effect on the steady-state dislocation motion.

(3) Focusing on the dislocation motion as an elementary process of HE, we proposed a simplified classification map for HE mechanisms. The validation and verification of this classification map including comparison with experimental results will be the topic of future work.

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