Atomistic simulations of hydrogen effects on tensile deformation behaviour of [0 0 1] twist grain boundaries in nickel

Computational Materials Science 159 (2019) 12–23

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Atomistic simulations of hydrogen effects on tensile deformation behaviour of [0 0 1] twist grain boundaries in nickel

T

⁎

Jiaqing Lia, Cheng Lua, , Linqing Peia,b, Che Zhanga, Rui Wanga, Kiet Tieua a b

School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW 2522, Australia College of Mechanical Engineering, Chongqing University, Chongqing 400044, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Hydrogen embrittlement Atomic mechanism Twist grain boundaries Fracture

Hydrogen (H) embrittlement of metals is a common phenomenon but the exact atomic mechanisms responsible for H-induced plasticity process and ultimate failure are not clarified. In this work, the impacts of H on tensile deformation behaviour of different types of twist grain boundaries (TGBs) have been systematically studied by molecular dynamics (MD) simulations. Different deformation mechanisms are reported, depending on grain boundary types and bulk H concentrations, including easier dislocation nucleation due to the presence of H, Henhanced dislocation dissociation, and H-induced slip planarity. The simulations indicate that the interactions between H-enhanced dislocation plasticity and TGBs play a crucial role in the ultimate fracture path. The decohesion of the TGBs is considerably promoted by the presence of H under conditions where dislocation accommodation and emission process on the TGBs causes the changes of grain boundary structures and local stress state. Our results advance a mechanistic understanding for experimentally-observed H embrittlement and provide a viable path to engineering microstructure with high resistance to H embrittlement in new materials.

1. Introduction Hydrogen (H) embrittlement, referred to as a phenomenon in which the ingress of H into metallic systems causes the degradation of the mechanical properties (e.g., toughness and plasticity) and further leads to an unexpected catastrophic fracture, has been reported intensively for decades [1–5]. In some metallic systems, H-induced failure can occur by a sharp transition from ductile transgranular mode to brittle intergranular mode, which is commonly interpreted that H segregation weakens the cohesive strength of grain boundaries (GBs) and encourages GB separation based on H-enhanced decohesion (HEDE)-like mechanism [6–9]. However, a plasticity-mediated decohesion model was recently proposed by Martin and Wang [10,11], who explained Henhanced intergranular fracture within the framework of H-enhanced local plasticity (HELP) concept [12–14]. Through the analysis of the evolved dislocation microstructure it has been suggested that H-induced plasticity process including the change in GB structures and local H concentrations as well as the increased local stress related to dislocation pile-up is essential for creating conditions for the onset of fracture [15]. Unfortunately, more details considering how the dynamic plasticity process occurs on an atomic scale cannot be directly observed with experimental techniques. Atomistic simulation was effective in probing GB-mediated ⁎

plasticity process, such as dislocation nucleation [16–18], GB sliding [19–20] and coupled GB motion [21–23]. For example, Spearot et al. [17,24] conducted a series of molecular dynamics (MD) simulations to investigate the nucleation events from GBs with 〈1 0 0〉 and 〈1 1 0〉 tilt axes over a wide range of misorientation angels, finding that the tensile stress for dislocation nucleation was directly correlated to the grain orientations and certain structural units of GBs. Tschopp et al. [16] and Spearot et al. [25] studied the dislocation nucleation from bicrystal GBs with dissociated structure. According to their simulation results, the dissociated structure served as the sites for dislocation nucleation and promoted the nucleation events on secondary slip systems from the GBs. Cahn and Mishin [21,26] took advantage of atomistic simulation on [0 0 1] symmetric tilt GBs to examine the shear-induced coupled motion. Two distinct coupling modes (positive and negative branches) were predicted based on the proposed geometric model of coupling. They revealed that the GB migration was achieved by deformation of structural units and collective glide of lattice dislocations on corresponding slip planes. In parallel efforts, many researchers have attempted to investigate the various H embrittlement mechanisms, by using simulation approaches [27–31]. For example, Tehranchi and Curtin [27] calculated the reduction of theoretical strength on the various symmetric tilt GBs, concluding that the theoretical strength was not significantly reduced

Corresponding author. E-mail address: [email protected] (C. Lu).

https://doi.org/10.1016/j.commatsci.2018.11.048 Received 4 October 2018; Received in revised form 26 November 2018; Accepted 26 November 2018 0927-0256/ © 2018 Elsevier B.V. All rights reserved.

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by the presence of H atoms for all studied GBs. Within thermodynamic framework, Wang and Martin [32] reported the H segregation and the impacts of H coverage, GB types and H gas pressure on the GB cohesive property, and found that the reduction of GB cohesive energy can reach 37% under charging condition where H-induced intergranular fracture occurred, directly supporting the HEDE mechanism. Curtin’s group examined the H-triggered ductile-to-brittle transition in bulk Ni and Fe via finite-temperature coupled atomistic/discrete dislocation (CADD) multiscale method and MD simulations [31,33,34]. It was claimed that the formation of nano-hydride due to substantial accumulation of H around the crack tip promoted brittle fracture by preventing crack-tip dislocation emission. Later on, they further investigated the effect of H on modifying the crack tip behaviour (competition between dislocation emission and cleavage fracture) along different symmetric tilt GBs in Ni. The simulation results showed that H created no ductile-to-brittle transition for the predicted ductile cracks along any of considered GBs [35]. In addition, the interactions between H and vacancies were proved to be critical for failure [36–38]. H and vacancies preferred to accumulate as defect complexes near GBs, thereby producing damage and causing brittle fracture along the GBs [39]. As mentioned before, significant dislocation plasticity was found beneath the fracture surfaces, regardless of quasi-brittle or intergranular [10,11,15,40–46], overwhelmingly backing up the HELP mechanism. As the basis of HELP mechanism, H shielding concept has been used to explain the early stage of fracture. H attachment to the dislocations modifies the stress field of dislocations so as to enhance the local plasticity via moving dislocations at lower stress levels in some directions, ultimately leading to the fracture [47]. However, recently Xie et al. [48] demonstrated that H hampered the mobility of moving dislocations in quantitative mechanical tests. This phenomenon was further attributed to that hydrogenated vacancies segregating to the dislocation core can strongly lock the mobile dislocations. In addition, Song and Curtin [49] proposed that Cottrell atmospheres following dislocations produced resistance to dislocation motion, and found that H provided no shielding effect on dislocation-dislocation interactions. As a result, these observations have made the HELP mechanism controversial and suggested the necessity of further studies. In addition, how the localized plasticity at different GBs being influenced by the presence of H and its contribution to the underlying qusi-cleavage/intergranular fracture along GBs on an atomic scale are still not fully understood. Therefore, the focus of this work is to investigate the impacts of H on the plastic deformation process associated with dislocation nucleation/reaction at GBs as well as void nucleation and coalescence that causes the ultimate failure. Herein, atomistic simulations were employed to study the tensile deformation behaviour of Ni bicrystal models with different twist grain boundaries (TGBs) under varying H concentrations.

Fig. 1. Schematic diagram of a bicrystal model rotated around the [0 0 1] direction (Z axis), and the GCMC swap region is indicated by dash lines. Atoms are coloured according to the CSP value.

boundary plane at a rate of 200 per 0.5 ps. The imposed chemical potential, calculated by the bulk H concentration [52,53], was kept constant according to a stochastic algorithm throughout the system. During the charging process, the thermal motion was modelled with the canonical NVT ensemble every 0.1 ps, and the time increment of simulation was set 1 fs. In order to obtain a stable H configuration, the MD/ GCMC model was equilibrated for a total of 5 ns. Then, the tensile deformation was applied along Z axis for each considered case to investigate the H effect on tensile response of the TGBs. Atoms within 10 Å of the top and bottom were frozen. The simulation cell was subjected to a successive incremental loading by displacing frozen atoms (top and bottom) in opposite directions. After each increment, the frozen atoms were held fixed, while all other atoms were relaxed by a conjugate gradient method. Note that the H segregation into TGBs was performed at 300 K but the tensile deformation was executed at 0.1 K to avoid H diffusion and other thermally activated behaviour during the simulation. Illustration of all simulation results was achieved by tracking the common neighbour analysis (CNA) parameter [54], centro-symmetry parameter (CSP) [55] as well as coordination numbers of all atoms at each snapshot during tensile deformation. The local stress distribution was calculated by the Virial theorem [56], and the Voro + + code was used to obtain the average atomic volume component in stress calculation [57]. In addition, the Dislocation Extraction Algorithm (DXA) in Ovito [58] was adopted to identify dislocation motions and reactions during the deformation process.

2. Methods The simulations in this work were implemented with molecular dynamics simulator LAMMPS [50] utilizing the widely-used embeddedatom-method (EAM) interatomic potentials for Ni-H [51]. The bicrystal model was constructed by rotating grain-A above the interface plane about the Z axis by θ/2 clockwise, while rotating grain-B underneath the grain boundary by θ/2 counterclockwise, as shown in Fig. 1. The simulation cell was modelled with periodic boundaries along X and Y directions and free boundary condition in Z direction. Table 1 lists three cases with different misorientation angles (θ), representing both lowangle and high-angle TGBs. For all cases, the system was first relaxed with the minimum energy procedure, and then equilibrated with the isobaric-isothermal (NPT) ensemble at desired temperature and pressure for 0.1 ns (i.e., T = 300 K , σxx = σyy = 0 ). Herein, we adopted the MD/grand canonical Monte Carlo (GCMC) technique to simulate Ni-H interactions. H atoms were repeatedly added or deleted from a region extending ± 40 Å perpendicular to the

3. Results 3.1. TGB structure and H segregation Atomic structures of three TGBs in the absence of H are shown in Fig. 2(a)–(c). Two types of TGBs are formed: dislocation network and planar defect. For low-angle TGBs (θ≤ 15.19°), a square dislocation network consisting of screw dislocations with Burgers vector b1 = 1/2[1 1 0] and b2 = 1/2[1¯ 1 0] is observed. Comparing Fig. 2(a) with Fig. 2(b), the density of square dislocation network increases and the spacing between screw dislocations decreases with increasing twist angles. In terms of θ > 15.19°, the decrease of dislocation grid and the increase of dislocation interaction with each other contribute to the disappearance of square dislocation network and formation of planar defect, as shown in Fig. 2(c). During GCMC relaxation process, H atoms 13

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Table 1 Model parameters for the three considered TGBs after energy minimization. Twist angle θ (°)

X direction (mn0)A /(mn¯0)B

Model size X × Y × Z (Å)

γGB (mJ·m−2)

GB atoms (%)

6.73° 14.25° 36.87°

Σ145 (17 1 0)/(17–1 0) Σ65 (8 1 0)/(8–1 0) Σ5 (3 1 0)/(3–1 0)

119.7 × 119.7 × 240.1 113.4 × 113.4 × 227.4 111.2 × 111.2 × 222.1

597.6 761.5 850.2

2.2 3.0 3.2

exhibit a strong tendency segregating into the TGBs, consistent with favourable trapping properties of GBs [59,60]. It is apparent from Fig. 2(d) and (e) that, at low bulk H concentration, H atoms occupy exclusively at the intersections of dislocation networks, which can be attributable to the fact that high hydrostatic stress at dislocation intersections drives more H atoms to segregate (see Fig. 2(a) and (b)). For Σ5 TGB with planar defect, H atoms distribute along the TGB plane. Owing to the presence of H, TGBs have larger distorted environment and local atomic structures are significantly more disordered (see circled regions in Fig. 2(d) and (e)). Further inspection indicates that the dislocation network structures disappear when the local H concentration reaches a high level. This structural change simply due to the presence of H can play an important role in plastic deformation process and ultimate decohesion of GBs [15,61]. Table 2 sums up the excess H concentrations at three investigated TGBs with different bulk H concentrations. The specific calculation details are displayed in Section S1 of Supplementary material. At low bulk H concentration, Σ5 GB has the highest level of H segregation. Recall that this TGB with planar defect has higher GB atom fraction and GB energy in Table 1, and more preferential sites of H segregation exist along the TGB plane. Compared to the Σ145 TGB, Σ65 TGB has a higher excess H concentration due to higher density of screw dislocation network where H atoms favourably occupy. As the bulk H concentration increases, Σ5 TGB is becoming saturated, while the atomic structure of Σ65 GB changes from dislocation network to planar defect, evidenced by a sudden increase of excess H concentration at Cbulk = 1.2 × 10−3 . Similar transition is also observed in Σ145 GB, corresponding to Cbulk = 5.2 × 10−3 .

Table 2 Excess H concentrations at three investigated TGBs with various bulk H concentrations. Bulk H concentration Cbulk

Excess H concentrationCH Σ145GB

−5

3.0 × 10 1.5 × 10−4 6.0 × 10−4 1.2 × 10−3 3.0 × 10−3 5.2 × 10−3

0.012 – 0.045 0.069 0.107 0.322

Σ65GB

± 0.002 ± ± ± ±

0.005 0.007 0.010 0.008

a

0.021 0.051 0.107 0.349 0.509 –

± ± ± ± ±

Σ5GB 0.009 0.009 0.010 0.012 0.017

0.074 0.110 0.132 0.154 0.223 –

± ± ± ± ±

0.015 0.012 0.010 0.011 0.019

3.2. Tension response The stress-strain curves obtained with different bulk H concentrations are demonstrated in Fig. 3. All MD simulations suggest that H segregation can dramatically influence the tensile deformation behaviour of TGBs. One can see that, for all considered cases, the tensile stress initially rises with the imposed strain, reaches a peak value, and then drops dramatically. We denote the peak value as the effective yield stress in this work. Fig. 4 shows that the addition of H into the Σ65 and Σ5 TGBs results in a decrease in the yield stress, while the yield stress of Σ145 TGB rises significantly with increasing bulk H concentration. As a high-angle TGB, Σ5 has no pre-existing dislocations. Thus the reduction in yield stress due to the presence of H suggests that H facilitates dislocation nucleation and enhances local plasticity around the TGB. However, for low-angle TGBs (Σ65 and Σ145), it is invalid for

Fig. 2. Atomic structures of three TGBs: (a) and (d) Σ145 (θ = 6.73°), (b) and (e) Σ65 (θ = 14.25°), (c) and (f) Σ5 (θ = 36.87°). (a)-(c) and (d)-(f) represent the atomic structures without H and with H (Cbulk=3.0 × 10−5), respectively. Atoms are coloured by hydrostatic stress value, and H atoms are assigned in pink. 14

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Stress (GPa)

10

12

Pure Ni -5 3.0x10 -4 6.0x10 -3 1.2x10 -3 3.0x10 -3 5.2x10

(a)

8 6

10

Stress (GPa)

12

4 2 0.1

0.2

8 6 4 2

Fracutre

0 0.0

Pure Ni -5 3.0x10 -4 1.5x10 -4 6.0x10 -3 1.2x10 -3 3.0x10

(b)

0.3

0 0.00

0.4

0.05

12 10

Stress (GPa)

0.10

0.15

0.20

Strain

Strain Pure Ni -5 3.0x10 -4 1.5x10 -4 6.0x10 -3 1.2x10 -3 3.0x10

(c)

8 6 4 2 0 0.00

0.05

0.10

0.15

0.20

Strain Fig. 3. Stress-strain curves of bicrystal models with different bulk H concentrations: (a) Σ145 TGB, (b) Σ65 TGB and (c) Σ5 TGB.

Yield stress (GPa)

12

common to (1 1¯ 1) and (1¯ 1 1) two slip planes, which makes it possible for dislocation dissociation to happen on both planes, marked as points 1 and 2. Similarly, the dissociation from 1/2[1¯ 1 0] perfect screw dislocation into partials occurs on (1 1 1) and (1 1 1¯) planes at points 3 and 4. As deformation proceeds, continued tensile stress leads to the further dislocation dissociation and the expansion of intrinsic stacking fault. At a strain of 3.04% in Fig. 5(b), dislocation dissociation at point 2 has been fully completed, and dissociated partial dislocations will no longer glide away from the TGB into lattice regions. The above reaction can be expressed in vector form:

145 TGB 65 TGB 5 TGB

11 10 9 8 7

0

-3

1x10

-3

2x10

-3

3x10

-3

4x10

1 /2[1 1 0](1¯11) → 1/6[2 1 1](1¯11) + 1/6[1 2 1¯](1¯11)

-3

5x10

Cbulk

(1)

To mediate the additional tensile strain, the leading partial dislocation further splits into a stair-rod dislocation and a Shockley dislocation as shown in Fig. 5(c). This dissociation process is given as:

Fig. 4. Yield stress vs. bulk H concentration for all models.

1/6[2 1 1](1¯11) → 1/6[1 1¯ 0](001) + 1/6[1 2 1](11¯1)

predicting H-induced local plasticity simply based on the decrease/increase of the yield stress, as the equilibrium structures of these TGBs are accommodated by dislocation networks. Therefore, a closer examination of dislocation activities and atomic movement is required to identify the role of H in the plastic deformation process at different TGBs.

(2)

The formed Shockley partial 1/6[1 2 1] glides on the cross-slip plane (1 1¯ 1), while the produced stair-rod partial 1/6[1 1 0] lies on the (0 0 1) plane. This dislocation is sessile as (0 0 1) plane is not a slip plane. But later on, the trailing partial dislocation on the primary plane catches up and reacts with the stair-rod dislocation at the intersection of the (1 1¯ 1) and (1¯ 1 1) planes, with another Shockley partial formed on the cross-slip plane. This reaction is summarised as:

3.3. Dislocation activity and atomic mechanism

1/6[1 1¯ 0](001) + 1/6[1 2 1¯](1¯11) → 1/6[2 1 1¯](11¯1)

3.3.1. Σ145 (θ = 6.73°) TGB Fig. 5 shows the dislocation activities and atomic configurations for Σ145 (θ = 6.73°) TGB with and without H during tensile deformation process. Dislocation activities at point 2 from Fig. 5(b)–(e) are circled for further analysis. Fig. 5(a) shows the initial configuration prior to tensile deformation in the absence of H. Clearly, the screw dislocations have already split into two partials separated by a stacking fault in each square network unit. For example, a 1/2[1 1 0] pure screw dislocation dissociates into two Shockley partials (1/6[1 2 1] and 1/6[2 1 1]) residing on (1 1¯ 1) plane at point 1, bounding an intrinsic stacking fault. It should be noted that the 1/2[1 1 0] perfect screw dislocation is

(3)

The interaction process is energetically favourable from the perspective of Frank energy criteria. In addition, the elastic energy is further released by the swipe of the trailing partial dislocation eliminating the bounded intrinsic stacking fault. A new extended dislocation has transferred totally to the cross-slip plane in Fig. 5(d), and is free to glide on this plane in Fig. 5(e). This observed cross-slip involving a stair-rod dislocation in Ni is a new finding in MD simulations, which can approve the model proposed by Fleischer [62]. As shown in Fig. 5(f)–(h), the presence of H can make a difference during the tensile deformation process. At low bulk H concentration, an 15

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Fig. 5. Dislocation activities and atomic configurations for Σ145 (θ = 6.73°) TGB with various bulk H concentrations during tensile deformation process: (a)–(e) without H, and (f)–(h) with H of Cbulk = 3.0 × 10−5 . All images are coloured by DXA. The blue lines are the perfect dislocations, the green lines represent the Shockley dislocations, the pink lines are the stair-rod dislocaitons, and the red lines are other types of dislocaitons. Stacking-fault atoms are shown in red, and H atoms are assigned in pink.

3.3.2. Σ65 (θ = 14.25°) TGB The detailed deformation process of Σ65 (θ = 14.25°) TGB in the presence and absence of H is presented in Fig. 6. In the absence of H, the equilibrium TGB structure is composed of two series of screw dislocations b1 = 1/2[1 1 0] and b2 = 1/2[1¯ 1 0], as marked in Fig. 6(a). Prior to yielding point, it is found that dislocation dissociation events occur onto {1 1 1} planes in network units as shown in Fig. 6(b), i.e. 1/ 2[1 1 0] pure screw dislocation dissolves in its glide plane (1¯ 1 1) into two Shockley partial dislocations: 1/6[2 1 1] and 1/6[1 2 1]; 1/ 2[1¯ 1 0 ] screw dislocation dissociates into 1/6[1¯ 2 1] and 1/6[2¯ 1 1¯] partials on plane (1 1 1¯) . The atomic mechanism responsible for this dislocation dissociation is illustrated in Fig. 6(e). Four groups of atoms have been marked, specifically, atoms L ∼ P reside on one (1¯ 1 1) plane; atoms A ∼ F rest in the second (1¯ 1 1) plane; the third takes the positions Q ∼ R, and atoms F ∼ K are located at (1 1 1¯) plane. It’s worth noting that atom A is common to planes (1¯ 1 1) and (1 1 1) , while atom F lies in the intersection line [1 0 1] between planes (1¯ 1 1) and (1 1 1¯) . With the increase of the imposed tensile stress, the hydrostatic stress of all atoms increase, and atoms A ∼ C and F ∼ I have the highest stress values (see Fig. 6(e2)). Driven by high hydrostatic stress, atoms B, C, G and H make movement to find stable positions, while atoms A, F and I are sessile due to coplanar constrains. This can

H-enhanced dislocation dissociation (local plasticity) is observed at the elastic stage (see Fig. 5(f) and (g)), which will be discussed in detail in Section 3.3.2. Analogous to the H-free case, continued tensile strain causes the leading partial to dissolve into a star-rod dislocation and a Shockley partial dislocation (see Fig. 5(h)), shown as following:

1/6[1 2 1¯](1¯11) → 1/6[1¯ 1 0](001) + 1/6[2 1 1¯](11¯1)

(4)

However, in contrast to H-free case, the trailing partial 1/6[2 1 1] on the primary plane cannot ‘catch’ the produced stair-rod dislocation to form a new partial on cross-slip plane. This observed H-induced slip planarity at the expense of cross-slip is interpreted that H reduces the stacking-fault energy [63], which decreases the tendency for cross-slip by increasing the separation distance between the trailing partial and stair-rod dislocation. Moreover, H-enhanced dislocation dissociation on the (1 1 1) plane blocks the movement of newly-dissociated Shockley partial 1/6[2 1 1] on cross-slip plane. Consequently, stair-rod dislocation1/6[1¯ 1 0], trailing dislocation 1/6[2 1 1] and newly-dissociated Shockley partial 1/6[2 1 1] form a stable and sessile arrangement (Lomer-Cottrell lock), acting as a strong barrier to the further glide of dislocations on the (1 1¯ 1) and (1¯ 1 1) planes. This exactly explains that the higher tensile stress is required to activate the onset of yielding in the presence of H, compared to the H-free case. 16

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Fig. 6. Dislocation activities and atomic configurations for Σ65 (θ = 14.25°) TGB with various bulk H concentrations during tensile deformation process: (a–e) without H and (f–j) with H of Cbulk = 3.0 × 10−5 . All images are coloured by DXA, the same as described in Fig. 5, except (e) and (j) coloured by the hydrostatic stress value.

intersections of dislocation network, as shown in Fig. 6(f). It is very interesting to notice that dislocation dissociation events occur at a much lower tensile strain (ε = 2.04%), compared to H-free case, implying that H can promote earlier dislocation dissociation and enhance dislocation plasticity around the TGB. To explain this phenomenon, atomic configuration of ∑65 TGB in the presence of H is illustrated in Fig. 6(j). It is clearly seen that introduction of H (atoms A and E) into TGBs has the profound effect of changing local stress state and atomic structure: H increases local stress (see atom B in Fig. 6(j1)) and promotes the generation of vacancy (see Fig. 6(j3)). Due to the high hydrostatic stress, atom B attempts to move to the nearby stable position, even though at low tensile stress. Meanwhile, the H-generated vacancy facilitates the motion of atom D as indicated by black arrow in Fig. 6(j3), which in turn accelerates the motion of atom B. Finally, the zigzag motion of atoms B and D releases their stresses to a lower level (see Fig. 6(j2)) and causes the screw dislocation to dissociate into two Shockley partial dislocations (see Fig. 6(g)). Following the same mechanism, the motion of atoms F and I makes the dislocation dissociation happen on the (1 1 1) plane. Note that, even though H-enhanced dislocation dissociation exists at the elastic stage, the onset of yielding of H-charged cases at low bulk H concentration is still correlated to

be clued that, after dislocation dissociation, atoms B, C, G and H change in colour from near-red in Fig. 6(e2) to near-yellow in Fig. 6(e3), while the colours of atoms A, F and I are nearly kept the same. The movement path of atoms B and C has been indicated by black arrows in Fig. 6(e4). Instead of jumping from the site B to the site C over the top of the atom → M (vector BC ), atom B moves to the nearby site R along the ‘valley’ → between the atoms M and O (vector BR ). Likewise, atom C attempts to jump to the new site Q via a valley between the atoms N and P (vector → → CQ ) rather than vector CF . This zig-zag motion results in dislocation dissociation from a pure screw dislocation into two Shockley partial dislocations onto {1 1 1} planes (see Fig. 6(b)). However, further dissociation no longer continues as the movement of atom B from site R to → → site C (vector RC ) and atom C from site Q to site F (vector QF ) is blocked by the sessile atom F. When the strain increases to yielding point of 9.64%, the dissociated partials begin to interact with other dislocations in the neighbouring network units and further dislocation emission are observed in Fig. 6(d). Fig. 6(f)–(j) show the dislocation activities and atomic mechanisms during tensile deformation process at low bulk H concentration (Cbulk = 3.0 × 10−5 ). Initially, H atoms segregate exclusively to the 17

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Fig. 6. (continued)

free cases (see Fig. 7(a)–(c)), the boundary composed of planar defect gradually becomes coarsened before reaching the yielding point as the tensile deformation proceeds. In Fig. 7(b), the onset of plasticity is activated by an array of nucleation of partial dislocation loops with edge and screw characters from the interface plane into grain-A and grain-B simultaneously. It can be seen that dislocation slip occurs on four {1 1 1} planes, leading to four nucleated partial dislocations (1/6[1¯ 1 2], 1/6[1 1 2], 1/6[1¯ 1¯ 2] and 1/6[1 1 2]) linked back to the TGB plane by extrinsic stacking faults. According to Schmid factor analysis, they are all the favourable slip planes with the maximum max max max max Schmid factor SF(11 ¯ 1) = SF(1¯11) = SF(111) = SF(111¯) = 0.471. As the tensile strain carries on, the intersection of operative slip systems leads to dislocation interactions. Furthermore, the presence of abundant extrinsic stacking faults in bicrystal model also blocks the movement of newly nucleated partial dislocations from the TGB plane, as shown in Fig. 7(c). For H-charged cases (see Fig. 7(d)–(i)), different tensile deformation mechanisms are observed. As shown in Fig. 7(d) and (g), some ledges occur within the boundary planes, and the spacing between ledges decreases as the bulk H concentration is increased, which arises as a

dissociated dislocation interactions as well as dislocation emission, like the H-free case. Therefore, the initial yield stress is reduced slightly with the increase of bulk H concentration (Cbulk ≤ 6.0 × 10−4 ), as shown in Figs. 3 and 4. However, at high bulk H concentration, a totally different tensile deformation mechanism is displayed in Fig. S1(d)–(f). Here, no H- enhanced dislocation dissociation events can be observed at the elastic stage. When the yielding point is reached (ε = 8.44%), 1/6[1¯ 1 2] and 1/6[1 1 2] Shockley partials directly nucleate from the TGB plane into the grain-A and grain-B, with an extrinsic stacking fault left behind. In summary, as the H content is increased, planar defect is gradually formed at the expense of dislocation network, leading to a change in plasticity mode from one dominated by dissociated dislocation interactions to the other controlled by dislocation nucleation from the boundary plane. This H-induced plasticity mode change is the main reason why the yield stress of Σ65 TGB at high bulk H concentration is much lower than that at low bulk H concentration and H-free case. 3.3.3. Σ5 (θ = 36.87°) TGB Fig. 7 shows the dislocation activities for Σ5 (θ = 36.87°) TGB with and without H at different deformation stages, respectively. For the H18

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Fig. 7. Dislocation activities and atomic configurations for Σ5 (θ = 36.87°) TGB with various bulk H concentrations during tensile deformation process: (a)–(c) without H, (d)–(f) with H of Cbulk = 6.0 × 10−4 , and (g)–(i) with H of Cbulk = 3.0 × 10−3 . The insertions of (d) and (g) are coloured by the CSP value. All other images are coloured by CNA, where atoms with a perfect fcc structure are blue, the red atoms organize the TGB plane and the dislocation core, the continuous light blue atoms represent the stacking fault, and H atoms are assigned in green.

19

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the boundary plane, and the number of vacancies is increased. As the H concentration further increases, besides a higher dislocation density, some voids nucleate and grow at the boundary region (see Fig. 8(c)). Continued H coverage results in void growth and coalescence, clued by a series of voids with significant sizes in Fig. 8(d) and (e). As expected, a quasi-brittle fracture is ultimately initiated along the TGB via void growth and coalescence during the plastic straining stage. Fig. 9 qualitatively demonstrates the effect of H coverage on the dislocation density and total volume of nucleated voids along the Σ145 TGB as the tensile deformation proceeds. It is found that dislocations are emitted from TGBs at an increased rate, causing a higher dislocation density existing in the H-charged cases, being consistent with the HELP mechanism [15]. Also, it is evident from Fig. 9(b) that the nucleation and growth of voids is sensitive to the bulk H concentration, which clearly supports the embrittling effect of H in this model. It is noted in Fig. 8(c)–(e) that the nucleation of voids originates from the regions of high dislocation plasticity where there are extensive dislocation accommodation/emission events at TGBs in the presence of H. It is therefore very likely that the dislocation-TGB interactions via dislocation accommodation/emission at TGBs are responsible for the ultimate decohesion. To uncover this, we further demonstrate the key atomic configurations of H-enhanced dislocation-TGB interaction process for Σ145 TGB with bulk H concentration (Cbulk = 6.0 × 10−4 ) at different tensile deformation stages in Fig. 10. These snapshots are captured from a region extending ± 40 Å perpendicular to the boundary plane. At each tensile strain, atoms are coloured according to CSP value (a)–(d), coordination number (e)–(h) and hydrostatic stress value (i)–(l). It can be seen from Fig. 10(a)–(d) that dislocation network intersections mainly provide the sites for dislocation nucleation/emission events. This can be attributed to that H segregates into the intersections of dislocation network, and promotes local plasticity by changing the local stress state (see Fig. 10(i)) and atomic structure of TGBs (see Fig. 10(a)). With H-enhanced dislocation emission/accommodation events on the TGB, local atomic configuration of the boundary at intersections is much more disordered (see Fig. 10(b)). Meanwhile, local stress at dislocation network intersections is significantly increased as

result of heterogeneous distribution of H atoms along TGB plane. The formation of GB ledges related to dislocation nucleation is already reported [16]. At low bulk H concentration (Cbulk = 6.0 × 10−4 ), when the yield stress is reached (ε = 9.08%), a series of Shockley dislocations with the Burgers vector of 1/6[1¯ 1 2] and 1/6[1¯ 1¯ 2] nucleate from H-induced GB ledges and slip on (1 1¯ 1) and (1 1 1) planes in grain-A and grain-B, respectively. Continued tensile strain leads to dislocation nucleation events on other possible slip systems (see Fig. 7(f)). Theoretically, dislocation slip should occur on four {1 1 1} planes simultaneously as the maximum Schmid factor is identical on different slip systems, whereas, in the presence of H, partial dislocations nucleate on one certain slip system earlier than other slip planes. Moreover, the tensile stress/strain for dislocation nucleation is lower than that of Hfree case. This implies that the configuration of H-induced GB ledges facilitates easier dislocation nucleation event. Further evidence supporting this point is presented in Fig. 7(g)–(i). More GB ledges created by high H concentration trigger the nucleation of 1/6[1¯ 1¯ 2] and 1/6[1¯ 1 2¯] partials from the boundary plane at a lower tensile strain, with an array of extrinsic stacking faults left behind. To accommodate additional tensile deformation, another two groups of partial dislocations (1/6[1 1 2] and 1/6[1 1 2]) on (1 1 1¯) and (1 1¯ 1) slip planes are also activated from dislocation interaction sites, as shown in Fig. 7(i).

3.4. Void formation and fracture initiation In Fig. 3(a), ultimate fracture occurs along Σ145 TGB at high bulk H concentration (Cbulk = 5.2 × 10−3 ). Careful examination of exact mechanism for the failure process and its correlation with the H-enhanced dislocation plasticity needs to be taken. Fig. 8 shows the key dislocation configurations for void nucleation and fracture initiation along the Σ145 TGB deformed 40% for various bulk H concentrations. In the absence of H, the boundary has low dislocation density and a few vacancies can be identified, as illustrated in Fig. 8(a). With the bulk H concentration (Cbulk = 3.0 × 10−5 ) in the model, a significant local plasticity with a high dislocation density can be observed directly along

Fig. 8. Void nucleation and fracture initiation observed in Σ145 (θ = 6.73°) TGB deformed 40% with various bulk H concentrations. Different colours of atoms and dislocaitons represent the same as described in Fig. 5. The surface of voids is identified in yellow. 20

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occur in network units at the elastic stage during the tensile deformation process without H, as shown in Fig. 6(b). The exact atomic mechanism of this dislocation dissociation is the zig-zag motion of atoms. For the H-charged case, the zig-zag atomic motion is accelerated owing to H increasing local stress and promoting the generation of vacancy, which results in an earlier dislocation dissociation with respect to a much lower tensile strain. Herein, we propose the observed ‘H-enhanced dislocation dissociation’ as a new mechanism to illuminate the HELP theory, parallel to two commonly-postulated mechanisms: (i) H increases dislocation motion [69] and (ii) H reduces dislocation-dislocation interactions [70]. In the case of Σ145 TGB, asides from the Henhanced dislocation dissociation, the presence of H also causes a transition from dislocation cross-slip to coplanar slip. Wen et al. [71] investigated the effect of H on cross-slip process in Ni and reported that H could reduce the stacking-fault energy and thereby inhibit dislocation cross-slip process by the increase in the separation distance between partial dislocations. It is also found that the interactions between H-enhanced dislocation plasticity and TGBs are directly linked to the ultimate H-induced failure via the two notable factors: (i) the accommodation and emission process causes structural changes of TGBs, making the local atomistic state much more disordered; (ii) the local stress field increased by the dislocation-TGB interactions at dislocation network intersections can trigger the void nucleation and growth, leading to the ultimate quasibrittle fracture. One needs to keep in mind that the ultimate H-induced

shown in Fig. 10(j). With these conditions considered, the decohesion of atoms around the intersections is facilitated by the presence of H. As a result, the nucleation and growth of voids are triggered (see Fig. 10(g) and (h)), with the local stress relieved to a lower level.

4. Discussion The present results in this work comprehensively elucidate the effects of bulk H concentrations on the tensile deformation mechanisms and fracture responses of various Ni bicrystal models. It can be concluded that, during MD simulations, the introduction of H causes an enhanced localized plasticity around the TGBs and quasi-brittle fracture, which is firmly supported by experimentally-observed fractographs and microstructures beneath H-embrittled fracture surfaces [3,10,11,42–46]. Quasi-brittle fracture can be achieved via void nucleation and coalescence triggered by significant dislocation interactions with GBs [44,64–68], like the case in Fig. 10. Atomic mechanisms responsible for H-enhanced local plasticity at different types of TGBs are systematically studied. For Σ5 TGB, the formation of GB ledges due to H serves as a determining step for easier dislocation nucleation from the boundary plane. This structural change of GBs simply due to the presence of H has been confirmed to increase the local plasticity and reduce the cohesive strength of GBs [15,61]. In contrast, the influence of H on deformation mechanism of Σ65 TGB is much more complex. It is found that dislocation dissociation events

Fig. 10. The atomic configurations of H-enhanced dislocation-TGB interaction process for Σ145 TGB with bulk H concentration (Cbulk = 6.0 × 10−4 ) at different tensile deformation stages. At each tensile strain, atoms are coloured according to CSP value (a)–(d), coordination number (e)–(h) and hydrostatic stress value (i)–(l). 21

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fracture process itself is by decohesion of TGBs, although the environments for achieving it are via the dislocation-TGB interactions. Therefore we are motivated to directly calculate the H-induced reduction of TGB cohesive strength with two factors: disordered boundary structure and local stress state. The detailed calculation methods and results have been presented in Section S2 of Supplementary material. As shown in Fig. S2 of Supplementary material, it is proposed that the embrittling effect of H in metals can be significantly facilitated with disordered boundary structure and local stress state created by the dislocation-TGB interactions. Previously, Wang et al. [72] calculated the ideal tensile strength with the ‘activated GBs’. It was revealed that the activation of GBs segregated with H severely reduced the cohesive strength and the work of separation. Unfortunately, the factor of local stress state was not taken into consideration. It is confirmed that in this work, for TGBs segregated with H, the local stress state combined with disordered boundary structure together can dramatically weaken the cohesion of the TGBs.

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CRediT authorship contribution statement Jiaqing Li: Methodology, Software, Writing - original draft. Cheng Lu: Conceptualization, Supervision, Project administration. Linqing Pei: Writing - review & editing. Che Zhang: Visualization, Investigation. Rui Wang: Software, Validation. Kiet Tieu: Supervision, Funding acquisition. Acknowledgements This work is supported by Australia Research Council Discovery Project (DP170103092) and National Natural Science Foundation of China (NSFC51701030). This research is undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government. J.L. and R.W. greatly acknowledge support from China Scholarship Council (CSC). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.commatsci.2018.11.048. References [1] S.M. Myers, M. Baskes, et al., Hydrogen interactions with defects in crystalline solids, Rev. Mod. Phys. 64 (1992) 559. [2] W. Xie, X. Liu, W. Chen, H. Zhang, Hydrogen hardening effect in heavily deformed single crystal α-Fe, Comput. Mater. Sci. 50 (2011) 3397–3402. [3] W.-S. Ko, J.B. Jeon, J.-H. Shim, B.-J. Lee, Origin of hydrogen embrittlement in vanadium-based hydrogen separation membranes, Int. J. Hydrogen Energy 37 (2012) 13583–13593. [4] A. Pundt, R. Kirchheim, Hydrogen in metals: microstructural aspects, Annu. Rev. Mater. Res. 36 (2006) 555–608. [5] Y. Fukai, The Metal-Hydrogen System, Springer, 2004. [6] R.A. Oriani, Ber Bunsenges, A mechanistic theory of hydrogen embrittlement of steels, Phys. Chem. 76 (1972) 848–857. [7] S. Lynch, Hydrogen embrittlement phenomena and mechanisms, Corros. Rev. 30 (2012) 105–123. [8] I. Scheider, M. Pfuff, W. Dietzel, Simulation of hydrogen assisted stress corrosion cracking using the cohesive model, Eng. Fract. Mech. 75 (2008) 4283–4291. [9] D.E. Jiang, E.A. Carter, First principles assessment of ideal fracture energies of materials with mobile impurities: implications for hydrogen embrittlement of metals, Acta Mater. 52 (2004) 4801–4807. [10] M.L. Martin, B.P. Somerday, R.O. Ritchie, P. Sofronis, I.M. Robertson, Hydrogeninduced intergranular failure in nickel revisited, Acta Mater. 60 (2012) 2739–2745. [11] S. Wang, M.L. Martin, P. Sofronis, S. Ohnuki, N. Hashimoto, I.M. Robertson, Hydrogen-induced intergranular failure of iron, Acta Mater. 69 (2014) 275–282. [12] Y. Murakami, The effect of hydrogen on fatigue properties of metals used for fuel cell system, Int. J. Fract. 138 (2006) 167–195. [13] P. Sofronis, I.M. Robertson, Transmission electron microscopy observations and micromechanical/continuum models for the effect of hydrogen on the mechanical behaviour of metals, Philos. Mag. a-Phys. Condens. Matter Struct. Defects Mech. Prop. 82 (2002) 3405–3413.

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