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Tensile response of (1 1 0) twist grain boundaries in tungsten: A molecular dynamics study
Computational Materials Science 159 (2019) 265–272
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Tensile response of (1 1 0) twist grain boundaries in tungsten: A molecular dynamics study Ya-Xin Fenga, Jia-Xiang Shanga, , Sheng-Jian Qinb, ⁎
a b
T
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School of Materials Science and Engineering, Beihang University, Beijing 100191, China School of Materials Science and Engineering, Shijiazhuang Tiedao University, Shijiazhuang, Hebei Province 050043, China
ARTICLE INFO
ABSTRACT
Keywords: Molecular dynamics simulation Twist grain boundary Tensile response Dislocation Tungsten
Molecular dynamics simulations are performed to investigate the tensile behavior of W bicrystals with different twist grain boundaries (TGBs): the low-angle grain boundary (LAGB), the ordinary high-angle grain boundary (HAGB) and the 3 TGB. Owing to the initial hexagonal dislocation network (HDN), the LAGB can directly emit 1 dislocations without dislocation nucleation: the 2 1 1 1 dislocations in HDN are pinned by bilateral nodes or 0 0 1 dislocations and form Frank-Rend dislocation sources, which continually emit dislocations and remain the structure of HDN under tensile loading. Once the HDN become disordered, Frank-Rend dislocation sources are broken and dislocations in HDN can be directly emitted. In the ordinary HAGB and 3 TGB, dislocations are nucleated from interfaces accompanied with apparent stress decrease at nucleation sites. Supplied with enough stress, emitted dislocations can freely pass through adjacent boundaries. By measuring dislocation densities, we find that the 3 TGB becomes more active at high temperature and easier to nucleate dislocations, while the 1 LAGB and ordinary HAGB are less affected by temperature. Besides, it is found that 2 1 1 1 dislocations play a dominate role in the plastic deformation of W bicrystals regardless of TGB structures and temperature.
1. Introduction It is well known that the character and distribution of grain boundaries (GBs) in polycrystalline metals play a prominent role in many material properties. Plastic deformation in polycrystalline materials are assisted by GB sliding, migration and nucleation of dislocations from GB structures [1–3]. In addition to governing mechanical strength of polycrystalline materials, GBs also act as sinks for certain kind of point defects [4]. Tungsten (W) is regarding as a promising candidate for plasma facing materials due to its high melting temperature, high thermal conductivity and low sputtering erosion [5–7]. Understanding the deformation behaviors of GBs in W is essential for its application in nuclear reactor. To date, considerable experimental and theoretical studies have been carried out to explore GB responses in polycrystalline materials under different mechanical conditions. Wang et al. [8] conducted in situ nanomechanical experiments in W bicrystal nanowires and observed reversible deformation twinning under [1 1 0] compression. Spearot et al. [9–11] investigated the dislocation nucleation form 1 0 0 and 1 10 tilt GBs in Cu and Al and found that boundaries containing the E structure unit can emit dislocations at comparatively low stress ⁎
magnitudes. Song et al. [12] studied the tensile behavior of Cu bicrystals and tricrystals with the tensile direction parallel to tilt GBs and reported that the plasticity of bicrystalline Cu with a high tilt angle is much better than that of structure with low tilt angle, while the plasticity of trifurcate crystal Cu is better in low tilt angle structure. Recently, Singh et al. [13] simulated the plastic deformation of Nb bicrystals containing symmetric and asymmetric tilt GBs by using molecular dynamics (MD) simulations. It was demonstrated that the yield strength increases with increasing misorientation angle for higher misorientation angle between crystals provides greater resistance to the movement of dislocations thus delaying the onset of plasticity. Besides, the dislocation density was found to be higher for the high value of tilt angle and this trend was independent of temperature. Among different GBs, twist grain boundaries (TGBs) draw more and more attention for their unique GB structures. In our previous work, the energy and structure of (1 1 0) TGBs in W have been systematically investigated [14]. According to the analysis of dislocation, (1 1 0) TGBs can be divided into three types: low-angle grain boundaries (LAGBs), intermediate-angle grain boundaries (IAGBs) and high-angle grain boundaries (HAGBs). The LAGBs contain a regular dislocation network 1 consisting of 2 1 1 1 and 0 0 1 screw dislocations. In the IAGBs, the
Corresponding author. Corresponding author. E-mail addresses: [email protected] (J.-X. Shang), [email protected] (S.-J. Qin).
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https://doi.org/10.1016/j.commatsci.2018.12.028 Received 17 October 2018; Received in revised form 14 December 2018; Accepted 14 December 2018 0927-0256/ © 2018 Elsevier B.V. All rights reserved.
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Fig. 1. (a) Bicrystal interface model used in this work. (b–c) Twist grain boundary (TGB) structure for different twist angles: (b) low-angle grain boundary (LAGB), = 3° ; (c) ordinary high-angle grain boundary (HAGB), = 34.38°; (d) 3 TGB, = 70.53° . Atoms are colored according to the potential energy, as indicated by the color bar (unit: eV). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
interaction was described by a modified version of the Ackland-Theford potential [18] developed by Juslin and Width [19]. Before performing MD simulations, the reliability of the potential was carefully verified by reproducing results from experiments, density functional theory (DFT) calculations and other interatomic potentials [20–29]. It has also been shown in previous studies [30–32] that this potential provides good descriptions of defect properties and strain field. The construction of TGB models has been detailedly described in previous works [14,33]. To study the interaction between TGBs and defects, a bicrystal cell with two TGBs was considered, as shown in Fig. 1a. The middle and bilateral sections of a single crystal rotated clockwise and counterclockwise, reabout the [1 1 0] direction by 2 spectively. After rotation, the GB structures were first optimized via the combination of conjugate gradient energy minimization and quasi-dynamic quenching, and then equilibrated at desired temperature for 10 ps with a timestep of 0.5 fs. Periodic boundary conditions were applied along all sides. To investigate the effect of TGB structures, three typical TGBs were studied: the LAGB with = 3° (Fig. 1b), the ordinary HAGB with = 34.38° (Fig. 1c) and the 3 TGB with = 70.53° (Fig. 1d). The crystal orientations, dimensions and number of atoms in each model are presented in Table 1. Upon completion of the equilibration process, the TGB models were deformed as a whole at a constant engineering strain rate of 1 × 10 8 s 1 along the z direction with constant temperature between 10 and 1200 K. The strain rate considered here is much higher than the typical experimental strain rate due to the inherent time-scale limitation of MD simulation. To relieve the influence of high strain rate, engineering strain was applied incrementally with a step of 5 × 10 5 and then the models were relaxed for 1 ps at desired temperature. During loading, temperature was maintained as a constant and stresses on all directions except the loading direction are allowed to relax using the isothermal-isobaric
Table 1 Model parameters: crystal orientations, dimensions (nm) and the number of W atoms. Model type
Crystal orientation x
LAGB Ordinary HAGB 3 TGB
y
Dimensions
No. of W atoms
z
27, 27, ± 1 16, 16, ± 7
1, 7,
1, 54 7, 32
110 110
12.1 × 17.1 × 17.9 15.0 × 10.6 × 17.9
233,440 179,520
1, 1, ± 1
1,
1, 2
110
11.0 × 15.5 × 17.9
192,000
dislocation network becomes disordered and gradually disappears with increasing twist angle. The HAGBs, where no dislocation is observed, can be divided into three sub-types further: special boundaries with low , boundaries in their vicinity with similar structures as the corresponding special boundary in local regions as well as ordinary HAGBs consisting of periodic patterns. So far, researches about mechanical responses of TGBs focus on the LAGB [15,16]. There still lacks a comprehensive understanding of the deformation behavior of different TGBs under mechanical loading. In this work, we focus on the deformation behavior of different TGBs under uniaxial tensile loading. In the following, we will first describe the simulation method in Section 2. The tensile response of TGBs at 10 K is presented in Section 3, followed by the effect of temperature given in Section 4. The final conclusion is presented in Section 5. 2. Method The open source code LAMMPS [17] was adopted to perform MD simulations of the tensile response of TGBs in W. The interatomic
Fig. 2. (a) Tensile stress-strain curves of TGBs at 10 K. (b) The dislocation density of TGBs as a function of tensile strain.
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Fig. 3. Atomic snapshots and dislocations taken from the LAGB model showing (a) before yielding; (b) nucleation of {1 1 0} stacking faults; (c–e) emission and 1 1 absorbtion of 2 1 1 1 full dislocations between dislocation networks. The arrows between (b) and (c) indicate the 2 1 1 1 dislocations are emitted along the {1 1 0} stacking faults. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
deformation stage, jagged stress-strain curves are observed with different flow stress magnitudes. By comparing with the variation of dislocation densities (Fig. 2b), it can be found that the dislocation densities rapidly increase and decrease during the drop of stress, while they nearly remain unchanged during the rise of stress, which indicates the W bicrystals release stress by the motion, multiplication and annihilation of dislocations. Previously, Zepeda-Ruiz et al. [36] investigated the dislocation activity in Ta under compressive loading and reported that dislocations move in a stay-and-go fashion, which is consistent with our results. Variable flow stress magnitudes mainly result from different interface stress distributions and dislocation states, e.g., when there are stress concentrations at the interface or pre-existing dislocations, the stress required for dislocation nucleation or multiplication will be easy to reach and hence the flow stress will be low. But when stress distributes uniformly at the interface or no dislocation exists, the dislocation nucleation or multiplication will be relatively difficult, leading to a higher flow stress. The specific dislocation activities will be discussed below. Since GB structures can significantly influence deformation behaviors of nanocrystalline materials, we will discuss the tensile behavior of each TGB respectively.
Fig. 4. The length variation of dislocations with different Burgers vectors in the LAGB during yielding.
(NPT) ensemble. Analysis and visualization of the simulation results were performed with the Atomeye [34]. Dislocation analysis was achieved using the dislocation extract algorithm (DXA) [35].
3.1. Deformation behavior of the LAGB Fig. 3 shows the yielding behavior of the LAGB under tensile loading at 10 K. The LAGB contains a hexagonal dislocation network (HDN) 1 composed of 0 0 1 and 2 1 1 1 screw dislocations (Fig. 3a). As yielding begins, a number of stacking faults along {1 1 0} planes are nucleate 1 1 from the 2 1 1 1 screw dislocations in HDNs (Fig. 3b), and then 2 1 1 1 dislocations are emitted along these stacking faults with slip systems of [1 1 1](1 0 1) and [1 1 1](0 1 1) (Fig. 3c). It should be noted that emitted dislocations are produced through dislocation multiplication rather HDNs simply emit parts of them, because HDNs are not broken after dislocation emission, as circled in Fig. 3c. When meeting with adjacent LAGB, emitted dislocations interact with the HDN and then become part of it. With increasing strain, more dislocations are emitted from HDNs accompanied with the abrupt drop of stress. After yielding, the dislocation networks become disordered as a result their interaction with absorbed dislocations (Fig. 3d). Previously, Sainath et al. [15] simulated the tensile behavior of 100 TGB ( = 2°) in Fe nanowire, which contains a square dislocation network composed of 0 0 1 screw dislocations. It was found that
3. Tensile response at 10 K Fig. 2a and b show the tensile stress-strain curves and dependencies of dislocation density with strain of TGBs at 10 K, respectively. As shown in Fig. 2a, the stress-strain curves behave similarly for all TGBs, which can be characterized by initial elastic deformation up to the peak stress, following abrupt stress drop and progressive plastic deformation. The tensile strength obtained for the LAGB, ordinary HAGB and 3 TGB is 28.2, 28.5 and 29.2 GPa respectively, which is influenced by GB structures. Because of the symmetric GB structure, the 3 TGB is stable and difficult to nucleate dislocations. The structure of ordinary HAGB is disordered and dislocation nucleation is relative easier here. Owing to the initial dislocation network, the LAGB has no need for dislocation nucleation and dislocations can be easily emitted. It can also be inferred from these stress-strain curves that the young’s modulus of the W bicrystals is almost constant, irrespective to TGB structures. In the plastic 267
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Fig. 5. Atomic snapshots and dislocations taken from the LAGB model showing the dislocation emission process during plastic deformation. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Atomic snapshots taken from the ordinary HAGB model showing (a) before yielding; (b) dislocation nucleation; (c–d) emission and absorbtion of
1 2
1 1 1 full
dislocations between GBs. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
emitted dislocations are produced by splitting 0 0 1 sessile screw dis1 locations into two 2 1 1 1 glissile screw dislocations. Similar phenomenon was observed by Liu et al. [16] in the tensile process of (1 0 0) TGB ( = 6°) of Cu nanowire, where emitted dislocations are produced 1 1 1 1 2 1 + 6 2 1 1 . It’s through dislocation dissociation: 2 1 1 1 6 wondering that whether dislocation multiplication is achieved through dislocation dissociation in the LAGB. To verify this, we measure the length variation of dislocations with different Burgers vectors during 1 yielding. As shown in Fig. 4, the total length 2 1 1 1 dislocations first significantly increases and then decreases, while that of 0 0 1 dis1 locations slightly increases, indicating the emitted 2 1 1 1 dislocations are not produced by splitting 0 0 1 dislocations. Combined with the yielding behavior shown in Fig. 3, we find another possible way to 1 achieve dislocation multiplication that the 2 1 1 1 dislocations in HDNs are pinned by bilateral nodes or 0 0 1 dislocations and thus form 1 Frank-Rend dislocation sources, which continually emit 2 1 1 1 dislocations under tensile loading. There are two evidences to support it:
first, the nucleation sites for {1 1 0} stacking faults manifest that the 1 emitted dislocations are produced from the 2 1 1 1 dislocations rather than 0 0 1 dislocations in HDNs; second, after dislocation emission, the 1 1 1 1 dislocations in HDNs are not missing because the Frank-Rend 2 sources will leave a dislocation at the original position after each 1 emission. Therefore, we think that the emitted 2 1 1 1 dislocations are produced from the Frank-Rend dislocation sources, which consist of 1 1 1 1 dislocations and bilateral nodes or 0 0 1 dislocations in HDNs. 2 During following plastic deformation process, due to disordered 1 dislocation networks, some 2 1 1 1 dislocations are no longer pinned by bilateral nodes or 0 0 1 dislocations and can be directly emitted from dislocation networks once stress reaches the value needed for dislocation emission. Fig. 5 shows a dislocation emission process in the LAGB during plastic deformation. As shown in Fig. 5, when the required stress is reached, part of the dislocation network elongates, emitted and finally absorbed by another dislocation network. After emission, this part is missing in the dislocation network (circled in Fig. 5a and d),
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Fig. 7. Atomic snapshots taken from the ordinary HAGB model showing the dislocation emission process during plastic deformation. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Atomic snapshots taken from the 3 TGB model showing (a) before yielding; (b) nucleation of {1 1 0} stacking faults; (c–e) emission and absorbtion of 2 1 1 1 1
full dislocations between GBs. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
implying the emitted dislocations are parts of the dislocation network and further verifying the dislocation multiplication mechanism we inferred above.
nucleation sites for next dislocation emission. Fig. 7 shows a dislocation emission process in the ordinary HAGB during plastic deformation. The 1 1 1 1 dislocations are nucleated from the stress concentration area of 2 interface. After emission, dislocations pass through the middle grain, absorbed by adjacent GB and then reemitted, indicating the absorbed dislocations are just be trapped by GBs rather than annihilation; supplied with enough stress, they can freely pass through the ordinary HAGB.
3.2. Deformation behavior of the ordinary HAGB Fig. 6 shows the yielding behavior of the ordinary HAGB at 10 K. As 1 shown in Fig. 6, 2 1 1 1 dislocations are clearly nucleated form the interface and apparent stress drop can be observed at the nucleation sites. Although no stacking faults are formed, the primary slip systems can still be confirmed as [1 1 1](0 1 1) and [1 1 1](0 1 1) . Afterwards, the ordinary HAGB reduces stress rapidly by continually emitting dislocations. When meeting with adjacent GBs, dislocations are absorbed and induce local stress concentrations in the interface, which become the
3.3. Deformation behavior of the 3 TGB The tensile behavior of the 3 TGB is similar to that of the ordinary HAGB but with some differences, as shown in Fig. 8. Prior to dislocation emission, stacking faults along (1 0 1) and (1 0 1) planes are nucleated
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Fig. 9. (a) The tensile stress-strain curve of the 3 TGB at 10 K. (b–e) Atomic snapshots taken from the 3 TGB model showing the dislocation emission and motion during plastic deformation. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
from the 3 TGB, leading to local stress decrease. Then straight 2 1 1 1 dislocations are emitted and absorbed by adjacent TGBs accompanied with rapid stress decrease. The slip systems of dislocation in the 3 TGB are identified as [1 1 1](1 0 1) and [1 1 1](1 0 1) . Although the slip systems in each TGB are different, their schmid factors are all 0.404. Combined with the yield strength, the critical resolved shear stress (CRSS) required to nucleate dislocations for the LAGB, ordinary HAGB and 3 TGB is calculated as 11.4, 11.5 and 11.8 GPa respectively, which coincides with the structure character of each TGB. After yielding, the 3 TGB become crooked as a result of dislocation emission, owing to its stripy structure. The plastic deformation process of 3 TGB is close to that of ordinary HAGB but with a larger flow stress variation, which should be attributed to different interface stress distributions and dislocation states, as shown in Fig. 9. During the plastic deformation stage b–c (marked in Fig. 9a), the stress can be easily released by the dislocation nucleation and emission from the stress concentration area of interface as well as the motion of the pre-existing dislocation, as circled in Fig. 9b–c. However, during the plastic deformation stage d-e (marked in Fig. 9a), the stress distributes uniformly along the interface without apparent stress concentration and hence the stress for dislocation nucleation and emission is difficult to reach, resulting in the abundant dislocation nucleations from the whole interface and a high flow stress (Fig. 9d–e). 1
4. Effects of temperature Fig. 10a–c present the tensile stress-strain curves of each TGB at different temperatures. It is found that the LAGB first yields followed by the ordinary HAGB and finally the 3 TGB at same temperature. With increasing temperature, yield stresses decrease due to the enhanced atomic mobility, while yield strains first increase and then decrease, which is affected by both enhanced atomic mobility and dislocation slip mechanism. In BCC structures, full dislocations can be regarded as 1 1 leading 6 1 1 1 partial and trailing 3 1 1 1 partial dislocations. As
temperature increases, the strain energy need for nucleation of
1 6
Fig. 10. Tensile stress-strain curves of TGBs at different temperatures.
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and ordinary HAGB are less affected by temperature. Fig. 12b shows the 1 average density of 2 1 1 1 dislocations is oblivious higher than that of
0 0 1 dislocations at all conditions, indicating 2 1 1 1 dislocations take a dominated role during plastic deformation regardless of TGB structures and temperatures. 1
5. Conclusion The tensile behaviors of TGBs in W at different temperatures are studied using MD simulations. Three typical TGBs are investigated in this work: the low-angle grain boundary (LAGB) with a hexagonal dislocation network (HDN), the ordinary high-angle grain boundary (HAGB) consisting of periodic patterns and the 3 TGB with good symmetry. Owing to the initial HDN, the LAGB has no need for dislocation nucleation and emitted dislocations are produced through dislocation 1 multiplication: the 2 1 1 1 dislocations in HDN are pinned by bilateral nodes or 0 0 1 dislocations and thus form Frank-Rend dislocations 1 sources, which continually emit 2 1 1 1 dislocations and keep the structure of HDN unchanged under tensile loading. Once the HDN become disordered, Frank-Rend dislocation sources are broken and dislocations in HDNs can be directly emitted. In the ordinary HAGB, dislocations are nucleated from the interface and apparent stress decrease can be observed at nucleation sites. The emitted dislocations are then absorbed by adjacent TGB and induce local stress concentrations, which become the nucleation sites for next dislocation emission. It is found that dislocations can freely pass through the ordinary HAGB supplied with enough stress. The tensile behavior of 3 TGB is similar to that of the ordinary HAGB but with some differences. The dislocations emitted during yielding are almost straight at 10 K and the interface become crooked after yielding, which should be attributed to the stripy structure of 3 TGB. Besides, a large flow stress variation is also observed during the plastic deformation of 3 TGB for different interface stress distributions and dislocation states. With increasing temperature, tensile behaviors of TGBs do not apparently change. By measuring dislocation densities, we find that the 3 TGB becomes more active at high temperature and easier to nucleate dislocations, while the LAGB and ordinary HAGB are less affected by 1 temperature. Besides, it is found that 2 1 1 1 dislocations take a majority in all dislocations and dominate the tensile behavior of TGBs regardless of GB structures and temperature.
Fig. 11. Yield stress of each TGB as a function of temperature.
1
partial dislocations is less affected, while that of 3 1 1 1 decreases rapidly, which has been proved in our previous work [37]. Hence, yield strains first increase for the enhanced atomic mobility and then decrease for the decreased energy barrier for partial dislocation nucleation. The same variation trend of yield strain is also found in other cases dominated by dislocation slip mechanism [38,39]. Fig. 11 shows the yield stresses of TGBs at different temperatures. It can be clearly seen that the 3 TGB has the highest yield stress followed by the ordinary HAGB and finally the LAGB at same temperature. The same order of yield stress and strain among TGBs is decided by their GB structures, which has been explained above. The tensile behavior of investigated TGBs does not apparently change with increasing temperature and therefore is not listed here. Fig. 12a-b show the temperature dependence of average dislocation density of total dislocations and dislocations with different Burgers vectors in each TGB during yielding respectively, which are averaged over 10 ps since yielding. As shown in Fig. 12a, the dislocation densities of the LAGB and ordinary HAGB fluctuate within a certain range at all temperatures, while that of the 3 TGB significantly improve at temperatures higher than 300 K, implying the 3 TGB becomes more active at high temperature and easier to nucleate dislocations, while the LAGB
Fig. 12. Average dislocation densities of (a) total dislocations and (b) dislocations with different Burgers vectors in TGBs during yielding as a function of temperature.
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Data availability
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All data included in this study are available upon request by contact with the corresponding author. CRediT authorship contribution statement Ya-Xin Feng: Investigation, Methodology, Data curation, Visualization, Writing - original draft, Writing - review & editing. JiaXiang Shang: Funding acquisition, Project administration, Resources, Supervision. Sheng-Jian Qin: Methodology, Formal analysis, Writing review & editing. Acknowledgements The authors acknowledge the financial support from the National Magnetic Confinement Fusion Program under Grant No. 2013GB109002. The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1(A). References [1] D. Terentyev, X. He, A. Serra, et al., Structure and strength of 110 tilt grain boundaries in bcc Fe: an atomistic study, Comput. Mater. Sci. 49 (2010) 419–429. [2] X.H. Tong, H. Zhang, D.Y. Li, effects of mis-orientation and inclination on mechanical response of 110 tilt grain boundaries in -Fe to external stresses, Modell. Simul. Mater. Sci. Eng. 22 (2014) 065016. [3] L. Zhang, L. Cheng, K. Tieu, Atomistic simulation of tensile deformation behavior of 5 tilt grain boundaries in copper bicrystal, Sci. Rep. 4 (2014) 5919. [4] B. Li, X.J. Long, Z.W. Shen, S.N. Luo, Interactions between displacement cascades and 3 110 tilt grain boundaries in Cu, J. Nucl. Mater. 481 (2016) 46–52. [5] V. Barabash, G. Federici, R. Matera, et al., Armour materials for the ITER Plasma Facing Components, Phys. Scr. T81 (1999) 74–83. [6] G. Federici, R.A. Anderl, P. Andrew, et al., In-vessel tritium retention and removal in ITER, J. Nucl. Mater. 266–269 (1999) 14–29. [7] G. Federici, H. Wuerz, G. Janeschitz, R. Tivey, Erosion of plasma-facing components in ITER, Fusion Eng. Des. 61–62 (2002) 81–94. [8] J.W. Wang, Z. Zeng, C.R. Weinberger, In situ atomic-scale observation of twinningdominated deformation in nanoscale body-centred cubic tungsten, Nat. Mater. 14 (2015) 594–600. [9] D.E. Spearot, K.I. Jacob, D.L. McDowell, et al., Nucleation of dislocations from [001] bicrystal interfaces in aluminum, Acta Mater. 53 (2005) 3579–3589. [10] D.E. Spearot, M.A. Tschopp, K.I. Jacob, et al., Tensile strength of 100 and 110 tilt bicrystal copper interfaces, Acta Mater. 55 (2007) 705–714. [11] D.E. Spearot, K.I. Jacob, D.L. McDowell, et al., Dislocation nucleation from bicrystal interfaces with dissociated structure, Int. J. Plast. 23 (2007) 143–160. [12] H.Y. Song, Y.L. Li, M.R. An, Atomic simulations of the effect of twist grain boundaries on deformation behavior of nanocrystalline copper, Comput. Mater. Sci. 84 (2014) 40–44. [13] D. Singh, A. Parashar, Effect of symmetric and asymmetric tilt grain boundaries on the tensile behaviour of bcc-Niobium, Comput. Mater. Sci. 143 (2018) 126–132. [14] Y.X. Feng, J.X. Shang, Z.H. Liu, et al., The energy and structure of (110) twist grain
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Tensile response of (1 1 0) twist grain boundaries in tungsten: A molecular dynamics study Ya-Xin Fenga, Jia-Xiang Shanga, , Sheng-Jian Qinb, ⁎
a b
T
⁎⁎
School of Materials Science and Engineering, Beihang University, Beijing 100191, China School of Materials Science and Engineering, Shijiazhuang Tiedao University, Shijiazhuang, Hebei Province 050043, China
ARTICLE INFO
ABSTRACT
Keywords: Molecular dynamics simulation Twist grain boundary Tensile response Dislocation Tungsten
Molecular dynamics simulations are performed to investigate the tensile behavior of W bicrystals with different twist grain boundaries (TGBs): the low-angle grain boundary (LAGB), the ordinary high-angle grain boundary (HAGB) and the 3 TGB. Owing to the initial hexagonal dislocation network (HDN), the LAGB can directly emit 1 dislocations without dislocation nucleation: the 2 1 1 1 dislocations in HDN are pinned by bilateral nodes or 0 0 1 dislocations and form Frank-Rend dislocation sources, which continually emit dislocations and remain the structure of HDN under tensile loading. Once the HDN become disordered, Frank-Rend dislocation sources are broken and dislocations in HDN can be directly emitted. In the ordinary HAGB and 3 TGB, dislocations are nucleated from interfaces accompanied with apparent stress decrease at nucleation sites. Supplied with enough stress, emitted dislocations can freely pass through adjacent boundaries. By measuring dislocation densities, we find that the 3 TGB becomes more active at high temperature and easier to nucleate dislocations, while the 1 LAGB and ordinary HAGB are less affected by temperature. Besides, it is found that 2 1 1 1 dislocations play a dominate role in the plastic deformation of W bicrystals regardless of TGB structures and temperature.
1. Introduction It is well known that the character and distribution of grain boundaries (GBs) in polycrystalline metals play a prominent role in many material properties. Plastic deformation in polycrystalline materials are assisted by GB sliding, migration and nucleation of dislocations from GB structures [1–3]. In addition to governing mechanical strength of polycrystalline materials, GBs also act as sinks for certain kind of point defects [4]. Tungsten (W) is regarding as a promising candidate for plasma facing materials due to its high melting temperature, high thermal conductivity and low sputtering erosion [5–7]. Understanding the deformation behaviors of GBs in W is essential for its application in nuclear reactor. To date, considerable experimental and theoretical studies have been carried out to explore GB responses in polycrystalline materials under different mechanical conditions. Wang et al. [8] conducted in situ nanomechanical experiments in W bicrystal nanowires and observed reversible deformation twinning under [1 1 0] compression. Spearot et al. [9–11] investigated the dislocation nucleation form 1 0 0 and 1 10 tilt GBs in Cu and Al and found that boundaries containing the E structure unit can emit dislocations at comparatively low stress ⁎
magnitudes. Song et al. [12] studied the tensile behavior of Cu bicrystals and tricrystals with the tensile direction parallel to tilt GBs and reported that the plasticity of bicrystalline Cu with a high tilt angle is much better than that of structure with low tilt angle, while the plasticity of trifurcate crystal Cu is better in low tilt angle structure. Recently, Singh et al. [13] simulated the plastic deformation of Nb bicrystals containing symmetric and asymmetric tilt GBs by using molecular dynamics (MD) simulations. It was demonstrated that the yield strength increases with increasing misorientation angle for higher misorientation angle between crystals provides greater resistance to the movement of dislocations thus delaying the onset of plasticity. Besides, the dislocation density was found to be higher for the high value of tilt angle and this trend was independent of temperature. Among different GBs, twist grain boundaries (TGBs) draw more and more attention for their unique GB structures. In our previous work, the energy and structure of (1 1 0) TGBs in W have been systematically investigated [14]. According to the analysis of dislocation, (1 1 0) TGBs can be divided into three types: low-angle grain boundaries (LAGBs), intermediate-angle grain boundaries (IAGBs) and high-angle grain boundaries (HAGBs). The LAGBs contain a regular dislocation network 1 consisting of 2 1 1 1 and 0 0 1 screw dislocations. In the IAGBs, the
Corresponding author. Corresponding author. E-mail addresses: [email protected] (J.-X. Shang), [email protected] (S.-J. Qin).
⁎⁎
https://doi.org/10.1016/j.commatsci.2018.12.028 Received 17 October 2018; Received in revised form 14 December 2018; Accepted 14 December 2018 0927-0256/ © 2018 Elsevier B.V. All rights reserved.
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Fig. 1. (a) Bicrystal interface model used in this work. (b–c) Twist grain boundary (TGB) structure for different twist angles: (b) low-angle grain boundary (LAGB), = 3° ; (c) ordinary high-angle grain boundary (HAGB), = 34.38°; (d) 3 TGB, = 70.53° . Atoms are colored according to the potential energy, as indicated by the color bar (unit: eV). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
interaction was described by a modified version of the Ackland-Theford potential [18] developed by Juslin and Width [19]. Before performing MD simulations, the reliability of the potential was carefully verified by reproducing results from experiments, density functional theory (DFT) calculations and other interatomic potentials [20–29]. It has also been shown in previous studies [30–32] that this potential provides good descriptions of defect properties and strain field. The construction of TGB models has been detailedly described in previous works [14,33]. To study the interaction between TGBs and defects, a bicrystal cell with two TGBs was considered, as shown in Fig. 1a. The middle and bilateral sections of a single crystal rotated clockwise and counterclockwise, reabout the [1 1 0] direction by 2 spectively. After rotation, the GB structures were first optimized via the combination of conjugate gradient energy minimization and quasi-dynamic quenching, and then equilibrated at desired temperature for 10 ps with a timestep of 0.5 fs. Periodic boundary conditions were applied along all sides. To investigate the effect of TGB structures, three typical TGBs were studied: the LAGB with = 3° (Fig. 1b), the ordinary HAGB with = 34.38° (Fig. 1c) and the 3 TGB with = 70.53° (Fig. 1d). The crystal orientations, dimensions and number of atoms in each model are presented in Table 1. Upon completion of the equilibration process, the TGB models were deformed as a whole at a constant engineering strain rate of 1 × 10 8 s 1 along the z direction with constant temperature between 10 and 1200 K. The strain rate considered here is much higher than the typical experimental strain rate due to the inherent time-scale limitation of MD simulation. To relieve the influence of high strain rate, engineering strain was applied incrementally with a step of 5 × 10 5 and then the models were relaxed for 1 ps at desired temperature. During loading, temperature was maintained as a constant and stresses on all directions except the loading direction are allowed to relax using the isothermal-isobaric
Table 1 Model parameters: crystal orientations, dimensions (nm) and the number of W atoms. Model type
Crystal orientation x
LAGB Ordinary HAGB 3 TGB
y
Dimensions
No. of W atoms
z
27, 27, ± 1 16, 16, ± 7
1, 7,
1, 54 7, 32
110 110
12.1 × 17.1 × 17.9 15.0 × 10.6 × 17.9
233,440 179,520
1, 1, ± 1
1,
1, 2
110
11.0 × 15.5 × 17.9
192,000
dislocation network becomes disordered and gradually disappears with increasing twist angle. The HAGBs, where no dislocation is observed, can be divided into three sub-types further: special boundaries with low , boundaries in their vicinity with similar structures as the corresponding special boundary in local regions as well as ordinary HAGBs consisting of periodic patterns. So far, researches about mechanical responses of TGBs focus on the LAGB [15,16]. There still lacks a comprehensive understanding of the deformation behavior of different TGBs under mechanical loading. In this work, we focus on the deformation behavior of different TGBs under uniaxial tensile loading. In the following, we will first describe the simulation method in Section 2. The tensile response of TGBs at 10 K is presented in Section 3, followed by the effect of temperature given in Section 4. The final conclusion is presented in Section 5. 2. Method The open source code LAMMPS [17] was adopted to perform MD simulations of the tensile response of TGBs in W. The interatomic
Fig. 2. (a) Tensile stress-strain curves of TGBs at 10 K. (b) The dislocation density of TGBs as a function of tensile strain.
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Fig. 3. Atomic snapshots and dislocations taken from the LAGB model showing (a) before yielding; (b) nucleation of {1 1 0} stacking faults; (c–e) emission and 1 1 absorbtion of 2 1 1 1 full dislocations between dislocation networks. The arrows between (b) and (c) indicate the 2 1 1 1 dislocations are emitted along the {1 1 0} stacking faults. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
deformation stage, jagged stress-strain curves are observed with different flow stress magnitudes. By comparing with the variation of dislocation densities (Fig. 2b), it can be found that the dislocation densities rapidly increase and decrease during the drop of stress, while they nearly remain unchanged during the rise of stress, which indicates the W bicrystals release stress by the motion, multiplication and annihilation of dislocations. Previously, Zepeda-Ruiz et al. [36] investigated the dislocation activity in Ta under compressive loading and reported that dislocations move in a stay-and-go fashion, which is consistent with our results. Variable flow stress magnitudes mainly result from different interface stress distributions and dislocation states, e.g., when there are stress concentrations at the interface or pre-existing dislocations, the stress required for dislocation nucleation or multiplication will be easy to reach and hence the flow stress will be low. But when stress distributes uniformly at the interface or no dislocation exists, the dislocation nucleation or multiplication will be relatively difficult, leading to a higher flow stress. The specific dislocation activities will be discussed below. Since GB structures can significantly influence deformation behaviors of nanocrystalline materials, we will discuss the tensile behavior of each TGB respectively.
Fig. 4. The length variation of dislocations with different Burgers vectors in the LAGB during yielding.
(NPT) ensemble. Analysis and visualization of the simulation results were performed with the Atomeye [34]. Dislocation analysis was achieved using the dislocation extract algorithm (DXA) [35].
3.1. Deformation behavior of the LAGB Fig. 3 shows the yielding behavior of the LAGB under tensile loading at 10 K. The LAGB contains a hexagonal dislocation network (HDN) 1 composed of 0 0 1 and 2 1 1 1 screw dislocations (Fig. 3a). As yielding begins, a number of stacking faults along {1 1 0} planes are nucleate 1 1 from the 2 1 1 1 screw dislocations in HDNs (Fig. 3b), and then 2 1 1 1 dislocations are emitted along these stacking faults with slip systems of [1 1 1](1 0 1) and [1 1 1](0 1 1) (Fig. 3c). It should be noted that emitted dislocations are produced through dislocation multiplication rather HDNs simply emit parts of them, because HDNs are not broken after dislocation emission, as circled in Fig. 3c. When meeting with adjacent LAGB, emitted dislocations interact with the HDN and then become part of it. With increasing strain, more dislocations are emitted from HDNs accompanied with the abrupt drop of stress. After yielding, the dislocation networks become disordered as a result their interaction with absorbed dislocations (Fig. 3d). Previously, Sainath et al. [15] simulated the tensile behavior of 100 TGB ( = 2°) in Fe nanowire, which contains a square dislocation network composed of 0 0 1 screw dislocations. It was found that
3. Tensile response at 10 K Fig. 2a and b show the tensile stress-strain curves and dependencies of dislocation density with strain of TGBs at 10 K, respectively. As shown in Fig. 2a, the stress-strain curves behave similarly for all TGBs, which can be characterized by initial elastic deformation up to the peak stress, following abrupt stress drop and progressive plastic deformation. The tensile strength obtained for the LAGB, ordinary HAGB and 3 TGB is 28.2, 28.5 and 29.2 GPa respectively, which is influenced by GB structures. Because of the symmetric GB structure, the 3 TGB is stable and difficult to nucleate dislocations. The structure of ordinary HAGB is disordered and dislocation nucleation is relative easier here. Owing to the initial dislocation network, the LAGB has no need for dislocation nucleation and dislocations can be easily emitted. It can also be inferred from these stress-strain curves that the young’s modulus of the W bicrystals is almost constant, irrespective to TGB structures. In the plastic 267
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Fig. 5. Atomic snapshots and dislocations taken from the LAGB model showing the dislocation emission process during plastic deformation. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Atomic snapshots taken from the ordinary HAGB model showing (a) before yielding; (b) dislocation nucleation; (c–d) emission and absorbtion of
1 2
1 1 1 full
dislocations between GBs. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
emitted dislocations are produced by splitting 0 0 1 sessile screw dis1 locations into two 2 1 1 1 glissile screw dislocations. Similar phenomenon was observed by Liu et al. [16] in the tensile process of (1 0 0) TGB ( = 6°) of Cu nanowire, where emitted dislocations are produced 1 1 1 1 2 1 + 6 2 1 1 . It’s through dislocation dissociation: 2 1 1 1 6 wondering that whether dislocation multiplication is achieved through dislocation dissociation in the LAGB. To verify this, we measure the length variation of dislocations with different Burgers vectors during 1 yielding. As shown in Fig. 4, the total length 2 1 1 1 dislocations first significantly increases and then decreases, while that of 0 0 1 dis1 locations slightly increases, indicating the emitted 2 1 1 1 dislocations are not produced by splitting 0 0 1 dislocations. Combined with the yielding behavior shown in Fig. 3, we find another possible way to 1 achieve dislocation multiplication that the 2 1 1 1 dislocations in HDNs are pinned by bilateral nodes or 0 0 1 dislocations and thus form 1 Frank-Rend dislocation sources, which continually emit 2 1 1 1 dislocations under tensile loading. There are two evidences to support it:
first, the nucleation sites for {1 1 0} stacking faults manifest that the 1 emitted dislocations are produced from the 2 1 1 1 dislocations rather than 0 0 1 dislocations in HDNs; second, after dislocation emission, the 1 1 1 1 dislocations in HDNs are not missing because the Frank-Rend 2 sources will leave a dislocation at the original position after each 1 emission. Therefore, we think that the emitted 2 1 1 1 dislocations are produced from the Frank-Rend dislocation sources, which consist of 1 1 1 1 dislocations and bilateral nodes or 0 0 1 dislocations in HDNs. 2 During following plastic deformation process, due to disordered 1 dislocation networks, some 2 1 1 1 dislocations are no longer pinned by bilateral nodes or 0 0 1 dislocations and can be directly emitted from dislocation networks once stress reaches the value needed for dislocation emission. Fig. 5 shows a dislocation emission process in the LAGB during plastic deformation. As shown in Fig. 5, when the required stress is reached, part of the dislocation network elongates, emitted and finally absorbed by another dislocation network. After emission, this part is missing in the dislocation network (circled in Fig. 5a and d),
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Fig. 7. Atomic snapshots taken from the ordinary HAGB model showing the dislocation emission process during plastic deformation. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Atomic snapshots taken from the 3 TGB model showing (a) before yielding; (b) nucleation of {1 1 0} stacking faults; (c–e) emission and absorbtion of 2 1 1 1 1
full dislocations between GBs. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
implying the emitted dislocations are parts of the dislocation network and further verifying the dislocation multiplication mechanism we inferred above.
nucleation sites for next dislocation emission. Fig. 7 shows a dislocation emission process in the ordinary HAGB during plastic deformation. The 1 1 1 1 dislocations are nucleated from the stress concentration area of 2 interface. After emission, dislocations pass through the middle grain, absorbed by adjacent GB and then reemitted, indicating the absorbed dislocations are just be trapped by GBs rather than annihilation; supplied with enough stress, they can freely pass through the ordinary HAGB.
3.2. Deformation behavior of the ordinary HAGB Fig. 6 shows the yielding behavior of the ordinary HAGB at 10 K. As 1 shown in Fig. 6, 2 1 1 1 dislocations are clearly nucleated form the interface and apparent stress drop can be observed at the nucleation sites. Although no stacking faults are formed, the primary slip systems can still be confirmed as [1 1 1](0 1 1) and [1 1 1](0 1 1) . Afterwards, the ordinary HAGB reduces stress rapidly by continually emitting dislocations. When meeting with adjacent GBs, dislocations are absorbed and induce local stress concentrations in the interface, which become the
3.3. Deformation behavior of the 3 TGB The tensile behavior of the 3 TGB is similar to that of the ordinary HAGB but with some differences, as shown in Fig. 8. Prior to dislocation emission, stacking faults along (1 0 1) and (1 0 1) planes are nucleated
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Fig. 9. (a) The tensile stress-strain curve of the 3 TGB at 10 K. (b–e) Atomic snapshots taken from the 3 TGB model showing the dislocation emission and motion during plastic deformation. Atoms are colored according to the tensile stress per atom, as indicated by the color bar (unit: GPa). The perfect BCC atoms are removed for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
from the 3 TGB, leading to local stress decrease. Then straight 2 1 1 1 dislocations are emitted and absorbed by adjacent TGBs accompanied with rapid stress decrease. The slip systems of dislocation in the 3 TGB are identified as [1 1 1](1 0 1) and [1 1 1](1 0 1) . Although the slip systems in each TGB are different, their schmid factors are all 0.404. Combined with the yield strength, the critical resolved shear stress (CRSS) required to nucleate dislocations for the LAGB, ordinary HAGB and 3 TGB is calculated as 11.4, 11.5 and 11.8 GPa respectively, which coincides with the structure character of each TGB. After yielding, the 3 TGB become crooked as a result of dislocation emission, owing to its stripy structure. The plastic deformation process of 3 TGB is close to that of ordinary HAGB but with a larger flow stress variation, which should be attributed to different interface stress distributions and dislocation states, as shown in Fig. 9. During the plastic deformation stage b–c (marked in Fig. 9a), the stress can be easily released by the dislocation nucleation and emission from the stress concentration area of interface as well as the motion of the pre-existing dislocation, as circled in Fig. 9b–c. However, during the plastic deformation stage d-e (marked in Fig. 9a), the stress distributes uniformly along the interface without apparent stress concentration and hence the stress for dislocation nucleation and emission is difficult to reach, resulting in the abundant dislocation nucleations from the whole interface and a high flow stress (Fig. 9d–e). 1
4. Effects of temperature Fig. 10a–c present the tensile stress-strain curves of each TGB at different temperatures. It is found that the LAGB first yields followed by the ordinary HAGB and finally the 3 TGB at same temperature. With increasing temperature, yield stresses decrease due to the enhanced atomic mobility, while yield strains first increase and then decrease, which is affected by both enhanced atomic mobility and dislocation slip mechanism. In BCC structures, full dislocations can be regarded as 1 1 leading 6 1 1 1 partial and trailing 3 1 1 1 partial dislocations. As
temperature increases, the strain energy need for nucleation of
1 6
Fig. 10. Tensile stress-strain curves of TGBs at different temperatures.
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and ordinary HAGB are less affected by temperature. Fig. 12b shows the 1 average density of 2 1 1 1 dislocations is oblivious higher than that of
0 0 1 dislocations at all conditions, indicating 2 1 1 1 dislocations take a dominated role during plastic deformation regardless of TGB structures and temperatures. 1
5. Conclusion The tensile behaviors of TGBs in W at different temperatures are studied using MD simulations. Three typical TGBs are investigated in this work: the low-angle grain boundary (LAGB) with a hexagonal dislocation network (HDN), the ordinary high-angle grain boundary (HAGB) consisting of periodic patterns and the 3 TGB with good symmetry. Owing to the initial HDN, the LAGB has no need for dislocation nucleation and emitted dislocations are produced through dislocation 1 multiplication: the 2 1 1 1 dislocations in HDN are pinned by bilateral nodes or 0 0 1 dislocations and thus form Frank-Rend dislocations 1 sources, which continually emit 2 1 1 1 dislocations and keep the structure of HDN unchanged under tensile loading. Once the HDN become disordered, Frank-Rend dislocation sources are broken and dislocations in HDNs can be directly emitted. In the ordinary HAGB, dislocations are nucleated from the interface and apparent stress decrease can be observed at nucleation sites. The emitted dislocations are then absorbed by adjacent TGB and induce local stress concentrations, which become the nucleation sites for next dislocation emission. It is found that dislocations can freely pass through the ordinary HAGB supplied with enough stress. The tensile behavior of 3 TGB is similar to that of the ordinary HAGB but with some differences. The dislocations emitted during yielding are almost straight at 10 K and the interface become crooked after yielding, which should be attributed to the stripy structure of 3 TGB. Besides, a large flow stress variation is also observed during the plastic deformation of 3 TGB for different interface stress distributions and dislocation states. With increasing temperature, tensile behaviors of TGBs do not apparently change. By measuring dislocation densities, we find that the 3 TGB becomes more active at high temperature and easier to nucleate dislocations, while the LAGB and ordinary HAGB are less affected by 1 temperature. Besides, it is found that 2 1 1 1 dislocations take a majority in all dislocations and dominate the tensile behavior of TGBs regardless of GB structures and temperature.
Fig. 11. Yield stress of each TGB as a function of temperature.
1
partial dislocations is less affected, while that of 3 1 1 1 decreases rapidly, which has been proved in our previous work [37]. Hence, yield strains first increase for the enhanced atomic mobility and then decrease for the decreased energy barrier for partial dislocation nucleation. The same variation trend of yield strain is also found in other cases dominated by dislocation slip mechanism [38,39]. Fig. 11 shows the yield stresses of TGBs at different temperatures. It can be clearly seen that the 3 TGB has the highest yield stress followed by the ordinary HAGB and finally the LAGB at same temperature. The same order of yield stress and strain among TGBs is decided by their GB structures, which has been explained above. The tensile behavior of investigated TGBs does not apparently change with increasing temperature and therefore is not listed here. Fig. 12a-b show the temperature dependence of average dislocation density of total dislocations and dislocations with different Burgers vectors in each TGB during yielding respectively, which are averaged over 10 ps since yielding. As shown in Fig. 12a, the dislocation densities of the LAGB and ordinary HAGB fluctuate within a certain range at all temperatures, while that of the 3 TGB significantly improve at temperatures higher than 300 K, implying the 3 TGB becomes more active at high temperature and easier to nucleate dislocations, while the LAGB
Fig. 12. Average dislocation densities of (a) total dislocations and (b) dislocations with different Burgers vectors in TGBs during yielding as a function of temperature.
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Data availability
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All data included in this study are available upon request by contact with the corresponding author. CRediT authorship contribution statement Ya-Xin Feng: Investigation, Methodology, Data curation, Visualization, Writing - original draft, Writing - review & editing. JiaXiang Shang: Funding acquisition, Project administration, Resources, Supervision. Sheng-Jian Qin: Methodology, Formal analysis, Writing review & editing. Acknowledgements The authors acknowledge the financial support from the National Magnetic Confinement Fusion Program under Grant No. 2013GB109002. The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1(A). References [1] D. Terentyev, X. He, A. Serra, et al., Structure and strength of 110 tilt grain boundaries in bcc Fe: an atomistic study, Comput. Mater. Sci. 49 (2010) 419–429. [2] X.H. Tong, H. Zhang, D.Y. Li, effects of mis-orientation and inclination on mechanical response of 110 tilt grain boundaries in -Fe to external stresses, Modell. Simul. Mater. Sci. Eng. 22 (2014) 065016. [3] L. Zhang, L. Cheng, K. Tieu, Atomistic simulation of tensile deformation behavior of 5 tilt grain boundaries in copper bicrystal, Sci. Rep. 4 (2014) 5919. [4] B. Li, X.J. Long, Z.W. Shen, S.N. Luo, Interactions between displacement cascades and 3 110 tilt grain boundaries in Cu, J. Nucl. Mater. 481 (2016) 46–52. [5] V. Barabash, G. Federici, R. Matera, et al., Armour materials for the ITER Plasma Facing Components, Phys. Scr. T81 (1999) 74–83. [6] G. Federici, R.A. Anderl, P. Andrew, et al., In-vessel tritium retention and removal in ITER, J. Nucl. Mater. 266–269 (1999) 14–29. [7] G. Federici, H. Wuerz, G. Janeschitz, R. Tivey, Erosion of plasma-facing components in ITER, Fusion Eng. Des. 61–62 (2002) 81–94. [8] J.W. Wang, Z. Zeng, C.R. Weinberger, In situ atomic-scale observation of twinningdominated deformation in nanoscale body-centred cubic tungsten, Nat. Mater. 14 (2015) 594–600. [9] D.E. Spearot, K.I. Jacob, D.L. McDowell, et al., Nucleation of dislocations from [001] bicrystal interfaces in aluminum, Acta Mater. 53 (2005) 3579–3589. [10] D.E. Spearot, M.A. Tschopp, K.I. Jacob, et al., Tensile strength of 100 and 110 tilt bicrystal copper interfaces, Acta Mater. 55 (2007) 705–714. [11] D.E. Spearot, K.I. Jacob, D.L. McDowell, et al., Dislocation nucleation from bicrystal interfaces with dissociated structure, Int. J. Plast. 23 (2007) 143–160. [12] H.Y. Song, Y.L. Li, M.R. An, Atomic simulations of the effect of twist grain boundaries on deformation behavior of nanocrystalline copper, Comput. Mater. Sci. 84 (2014) 40–44. [13] D. Singh, A. Parashar, Effect of symmetric and asymmetric tilt grain boundaries on the tensile behaviour of bcc-Niobium, Comput. Mater. Sci. 143 (2018) 126–132. [14] Y.X. Feng, J.X. Shang, Z.H. Liu, et al., The energy and structure of (110) twist grain
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