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Initiation, evolution, and saturation of coupled grain boundary motion in nanocrystalline materials
Computational Materials Science 112 (2016) 289–296
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Initiation, evolution, and saturation of coupled grain boundary motion in nanocrystalline materials Peng Wang, Xinhua Yang ⇑, Di Peng Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
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Article history: Received 30 July 2015 Received in revised form 23 October 2015 Accepted 30 October 2015 Available online 19 November 2015 Keywords: Nanocrystal Coupled grain boundary motion Saturation Molecular dynamics
a b s t r a c t Coupled grain boundary (GB) motion in sheared nanocrystalline materials composed of Ni, Al, or Cu is investigated by atomistic simulation methods, and the effects of grain size and temperature are evaluated. Due to the pinning effect of triple junctions, saturation of coupled GB motion is observed in all the nanocrystals except Cu. The two components of coupled GB motion, normal migration (NM) and tangential motion (TM), initiate and saturate at nearly equivalent nominal shear strains. Accompanied with coupled GB motion, massive dislocations and stacking faults are found to form within some grains, and the elementary structure units in the observed GBs transform from in-order to out-of-order. Compared with nanocrystalline Ni, the coupled GB motion in nanocrystalline Al has a reduced shear strain threshold and saturated NM displacement. The effects of grain size and temperature are similar in both NM and TM, so that their influence on coupled GB motion is slight. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Grain size has a significant effect on the deformation behavior of nanocrystalline materials. In general, the deformation of a polycrystalline material is dominated by dislocations for grain sizes of hundreds of microns, but mediated by grain boundaries (GBs) for grain sizes of a few nanometers [1–3]. Accordingly, GBs play a key role in determining the mechanical properties and deformation behaviors of nanocrystalline materials, which are remarkably different from their coarse-grained counterparts. An extraordinary deformation behavior involving grain growth has been observed in both experimental studies [4–6] and atomistic simulations [7,8]. Recently, numerous investigations have been conducted to reveal the mechanism of grain growth in nanocrystals [9–12], and some elaborate experiments were also employed for clarifying the role of shear stress as the driving force for mechanically induced GB migration and grain growth [13]. It was found that grain growth generally scales with the applied stress. Moreover, GBs are mobile during deformation, rather than acting as stationary obstacles, so that deformation involving grain growth is always accompanied by GB motion. However, both experiments and theoretical predictions have presented an interesting complexity regarding GB motion [14,15]. In a bicrystal or nanocrystal, normal GB migration (NM) perpendicular to the GB plane is often coupled to tangential motion (TM) parallel to the ⇑ Corresponding author. Tel.: +86 027 87540153. E-mail address: [email protected] (X. Yang). http://dx.doi.org/10.1016/j.commatsci.2015.10.049 0927-0256/Ó 2015 Elsevier B.V. All rights reserved.
GB plane. The coupling factor characterizing coupled GB motion is defined as the ratio of TM to NM. For a bicrystal, this ratio can be geometrically related to the GB misorientation angle according to a theoretical model [14]. However, the predictions of this model are slightly larger than experimental results when applied to a nanocrystalline material [16]. This is possibly because GB motion in a nanocrystal is easily affected by triple junctions and intragranular defects [17,18]. Triple junctions always act as obstacles to GB motion, while intragranular defects not only change the local stress distribution, but also interact with the GBs. In contrast to the sustained NM occurring in a bicrystal, NM in a nanocrystal becomes saturated due to the pinning effect of triple junctions and the impact from dislocations [17,18]. However, the saturation behavior of coupled GB motion in nanocrystals has not been carefully studied yet. A more comprehensive study is required to uncover the mechanisms underlying this phenomenon. Grain growth is widespread in nanocrystals, but rare in coarse-grained materials [2]. This indicates that grain growth is a grain-size related process. Therefore, it can be safely assumed that GB motion also depends on the grain size. In addition, grain growth was found to dominate the plastic deformation of gradient nanograined Cu [19], but no grain growth was observed in gradientstructured interstitial free steel [20]. These conflicting results seemingly imply that the phenomenon of grain growth is multitudinous. The present study focuses on coupled GB motion in metal nanocrystals. A series of face-centered-cubic (FCC) models respectively composed of nanocrystalline Ni, Al, and Cu with R9h1 1 0i
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{2 2 1} symmetric tilt GBs are respectively constructed as the objects of observation. Their shear responses are evaluated by atomistic simulation methods, and the initiation, evolution, and saturation processes of coupled GB motion are subjected to careful analysis. Finally, the effects of grain size, material, and temperature are discussed. 2. Models and computational method A series of quasi-three-dimensional FCC nanocrystalline models 0 texture were constructed. The nanocrystalline with idealized ½1 1 Ni, Cu, and Al models all have the same grain orientations, and have a horizontal R9h1 1 0i{2 2 1} symmetric tilt GB with a misorientation angle of 38.94° [21] and two component grains lying in the middle of the models. This GB was considered as the observation object. The remaining grains were oriented randomly. Among these models, the nanocrystalline Ni models were constructed with grain sizes of 10 nm, 20 nm, 30 nm, 40 nm, and 70 nm to evaluate the effect of grain size on the coupled GB motion. Their outline dimensions are 2 nm along the h1 1 0i texture direction, and vary respectively from 16.5 nm 16.5 nm to 115.5 nm 115.5 nm in the plane perpendicular to the texture direction when the grain sizes increase from 10 nm to 70 nm. The nanocrystalline Cu and Al models were constructed with grain sizes of 30 nm for comparison with the coupled GB motion of the nanocrystalline Ni model having an equivalent grain size. In addition, a bicrystal model with a R9h1 1 0i{2 2 1} symmetric tilt GB was also constructed as a reference for comparison. Molecular dynamics (MD) simulations were performed using LAMMPS [22] with embedded atom method potentials for Ni [23], Al [23], and Cu [24]. Periodic boundary conditions were 1 0 directions, while the boundimposed in the X ½1 1 4 and Z ½1 direction. Before application of a aries were free in the Y ½2 2 1 shear strain, the models were relaxed at 300 K for 100 ps to obtain equilibrium configurations. Subsequently, the models were slowly adjusted to the desired temperature and relaxed for another 100 ps. The simulation temperature employed was 10 K, unless otherwise stated. Two slabs that were 2 nm in thickness were fixed at the top and bottom of each model. The shear strain was applied by deforming the model as a whole in the X direction at a strain rate of 2 108 s1. The canonical ensemble (NVT) with a constant number of atoms, volume, and temperature was employed to trace the atomic trajectories. The MD integration step was 1.0 fs. The common neighbor analysis method was employed to identify the crystalline structures during the visualization [25]. Atoms were colored according to their profiles in the atomic configurations. In what follows, FCC atoms are marked blue, hexagonal close packed (HCP) atoms are marked light blue, and the remainder are marked red. Visualization of the atomistic simulation data was performed by the three-dimensional visualization software OVITO [26]. 3. Characteristics of coupled GB motion in nanocrystalline Ni The location coordinates of the middle point of the observed GB during deformation were captured, and the respective normal and tangential displacements dn and dt of the GB were obtained. The NM displacement versus nominal shear strain curve of the nanocrystalline Ni model with a grain size of 30 nm is plotted in Fig. 1. An examination of Fig. 1 indicates that the NM displacement curve can be obviously separated into three stages. During Stage I, the GB does not migrate until experiencing a nominal shear strain of about 1.00%, which is denoted as the threshold shear strain for NM. When the nominal shear strain exceeds this threshold value, the GB begins to migrate stably during Stage II, and the NM
Fig. 1. NM displacement versus nominal shear strain curves of a Ni bicrystal and nanocrystal.
displacement curve exhibits a stepped character denoted as stick–slip [21], where the term ‘‘stick” corresponds to the shear strain applied to the nanocrystal, while the term ‘‘slip” is related to the resulting NM displacement. Moreover, most of the slip events represent very similar displacements. After the nominal shear strain reaches about 6.60%, the NM progresses into Stage III, where the GB motion is saturated. GB motion in a sheared bicrystal has been observed [14,21]. Therefore, the NM displacement versus nominal shear strain curve of a Ni bicrystal is also plotted in Fig. 1 for comparison. As shown in the figure, GB motion saturation is not observed in the case of a bicrystal, so that the curve exhibits only two stages. Stage I occurs until attaining a threshold shear strain of slightly less than 1.00%, after which the GB motion in Stage II corresponds to a stick–slip character similar to that observed in the nanocrystal. To analyze the underlying mechanism of GB motion saturation in the nanocrystal, the nanocrystal configurations at nominal shear strains of 0%, 6.80%, and 12.00%, corresponding to the three stages, are shown in Fig. 2(a)–(c), respectively. The horizontal and vertical marker lines represent the geometrical symmetry centers, and are drawn to track the NM and TM displacements. The observed GB is initially located at the center of the nanocrystal model, and lies along the horizontal marker line, as shown in Fig. 2(a). With increasing nominal shear strain, the atoms in the model are progressively relocated so that both the horizontal and vertical marker lines are spatially altered. Fig. 2(b) shows that the observed GB is obviously separated from the horizontal marker line, but its two ends are pinned by triple junctions. Therefore, the GB becomes distorted as a result of shear deformation, indicating the occurrence of uneven NM. While the NM displacement increases with increasing shear deformation, it eventually reaches saturation because of the pinning effect of the triple junctions, as shown in Fig. 2(c). A slight unpinning effect of the triple junctions is observed owing to the dislocation activities near the triple junctions. This suggests that the triple junctions are relatively immobile compared to the GB [18]. However, slight unpinning does not significantly affect the distorted GB shape and the onset of NM saturation. Due to the restricted deformation between neighboring grains, massive dislocations and stacking faults are formed within some grains, which is in accordance with experimental evidence [27]. In addition, it is also observed in Fig. 2(b) that the vertical marker line inclines abruptly between the observed GB and the horizontal marker line. This shows that NM is accompanied by TM. The coupled GB motion can be further confirmed by the distribution of the von Mises local shear strain invariant shown in Fig. 2(d). In addition to the dislocation and stacking fault regions, the area over which the GB motion occurs exhibits a larger shear strain invariant.
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Fig. 2. Configurations at nominal shear strains of 0%, 6.80%, and 12.00% (a)–(c), where the von Mises local shear strain invariant contour of the Ni nanocrystal given in (c) is shown in (d). Configurations and contour for the bicrystal are given in (e)–(h) for equivalent nominal shear strains.
For comparison, the configurations of the Ni bicrystal at nominal shear strains of 0%, 6.80%, and 12.00% are also shown in Fig. 2(e)– (g), respectively. The GB initially overlaps with the horizontal marker line. However, in striking contrast with the nanocrystal, the bicrystal GB migrates equally along the normal direction to the GB plane as a whole, so that it does not distort after deformation. In contrast to the distorted GB motion saturation occurring in the nanocrystal, non-distorted GB motion is always retained in the bicrystal during loading, as shown in Fig. 2(f) and (g). Moreover, the vertical marker lines remain perpendicular to the horizontal marker lines outside the coupled GB motion region, while vertical marker lines are tilted inside the region. This indicates that shear deformation takes place only in the NM region, which is also demonstrated by the distribution of the von Mises local shear strain invariant shown in Fig. 2(h). The respective NM and TM displacements dn and dt are labeled in Fig. 2(g) for clarity. To investigate the microscopic mechanism of GB motion saturation in the nanocrystal, the atomistic configurations of the nanocrystal GB at nominal shear strains of 1.36%, 1.92%, 2.00%, 6.80%, and 12.00% are shown in Fig. 3(a)–(e), respectively. The FCC atoms are deleted and all the atoms are colored according to their Y coordinates. Fig. 3(a)–(c) shows the GB configurations before and after the initiation of NM. With the initiation of NM, some GB disconnections (marked by the arrows in Fig. 3(b)) nucleate in advance, and then expand through the GB plane (see Fig. 3 (c)) in the GB with initially perfect jEEj structural unit periodicity similar to the case in the bicrystal [21,28]. The enlarged atomic representations show that elementary structure unit transformation occurs during GB motion. Although the ordered structural units remain in the middle portion of the GB after the elementary structure unit transformation, the GB structures near the triple junctions at the two ends are disordered. The disordered region expands with increasing NM displacement, as shown in Fig. 3 (d) and (e). However, elementary structure unit transformation cannot occur in the disordered GB region, so that the GB is pinned by the triple junctions. The GB atomistic configurations of the bicrystal at nominal shear strains of 1.20%, 1.28%, 1.36%, 7.00%, and 12.00% are also shown in Fig. 3(f)–(j). Similar to the nanocrystal, both GB disconnections and elementary structure unit transformation take place in the sheared bicrystal. Fig. 3(f)–(h) shows the GB configurations before and after the onset of NM displacement. Owing to uniform NM, in distinct contrast to that of the nanocrystal, the ordered structural units remain within the GB after elementary structure unit transformation, as shown in Fig. 3(i) and (j). As a microscopic deformation mechanism, coupled GB motion can have an important influence on the macroscopic mechanical response. To evaluate this influence, the stress–strain curves of both the Ni nanocrystal and bicrystal are plotted in Fig. 4. The
points at which coupled GB motions are initiated are marked by hollow circles. It can be seen from the enlarged stress–strain curve for the nanocrystal given in the inset of Fig. 4 that the nominal shear stress undergoes a nearly linear increase with increasing nominal shear strain before and after the onset of coupled GB motion. This is in striking contrast with the stress–strain curve of the bicrystal, in which the nominal shear stress drops dramatically and enters a fluctuation stage after the onset of coupled GB motion. To uncover the microscopic deformation mechanism corresponding with the macroscopic stress–strain response, the virial stress contours of the nanocrystal at nominal shear strains of 0% and 12.00% and the bicrystal at 12.00% are plotted in Fig. 5. The figure shows that the residual stress in the nanocrystal is negligible at a nominal shear strain of 0%, which indicates that the condition of energy minimization was reached. Due to uneven NM, stress relief is limited to within a small region neighboring the middle segment of the observed GB in the nanocrystal, but the stress is almost entirely relieved in the bicrystal. The observed stress relief nearby the GB validates an earlier experimental observation that GB motion could be a plastic relaxation mechanism [29]. In addition, defect nucleation and propagation may also relieve local stress [17,30]. To clarify the mechanism, the percentage of HCP atoms in the nanocrystal is plotted in Fig. 4. The increment in the percentage of HCP atoms is closely related to the number of defects nucleating during deformation. The percentage of HCP atoms is nearly zero below a nominal shear strain of 2.56%, but, after that, it begins to increase at a variable rate. This indicates that defect initiation is unsynchronized with coupled GB motion, which is expected because the shear resistance of GB motion is usually lower than the resistance of intragranular dislocation nucleation [29,30]. After the defects nucleate, the behavior of the percentage of HCP atoms is fairly consistent with that of the stress–strain curve. As indicated by the five vertical dotted lines in Fig. 4, a rapid increase in the percentage of HCP atoms is always accompanied by a sharp decrease in the shear stress. It is noteworthy that GB motion was determined to be significantly affected by the misorientation angle of the symmetric tilt GB [18]. A R17(5 3 0) GB was found to move spontaneously, while a R5(2 1 0) GB exhibited the stick–slip behavior like that of the presently presented nanocrystalline models with R9h1 1 0i{2 2 1} GBs. Due to the pinning effect of triple junctions, the disordered GB segments neighboring the triple junctions migrate with great difficulty, so that the observed GBs become distorted in these nanocrystals, and GB motion saturation occurs. However, compared with the case of R9h1 1 0i{2 2 1} GBs, the nanocrystal with a R5(2 1 0) GB exhibited a more obvious unpinning effect of triple junctions, possibly because of its higher GB mobility and lower intragranular dislocation resistance.
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Fig. 3. GB atomistic configurations of the Ni nanocrystal at nominal shear strains of (a) 1.36%, (b) 1.92%, (c) 2.00%, (d) 6.80%, and (e) 12.00%, and those of the bicrystal at nominal shear strains of (f) 1.20%, (g) 1.28%, (h) 1.36%, (i) 7.00%, and (j) 12.00%.
Fig. 4. Stress–strain curves of the Ni bicrystal and nanocrystal, and the percentage of HCP atoms in the nanocrystal.
4. The effects of grain size, material, and temperature on the characteristics of coupled GB motion 4.1. The effect of grain size To evaluate the effect of grain size on coupled GB motion and its saturation, five sheared Ni nanocrystalline models with common grain orientations but different grain sizes from 10 nm to 70 nm were simulated. Their NM displacement versus nominal shear strain curves are plotted in Fig. 6. An approximately equivalent threshold shear strain of about 1.00% is observed for all grain sizes. However, the models exhibit considerable differences after the onset of NM. The curves obviously have different general slopes,
where the slope is observed to increase with increasing grain size. Moreover, with increasing grain size, the saturated NM displacement increases and the onset of NM saturation occurs at an increasingly lower shear strain. The saturated NM displacement increases from about 7.91 Å to 16.69 Å when the grain size increases from 10 nm to 70 nm. Once the GB motion resistance exceeds the dislocation slip resistance, dislocations will dominate the plastic deformation, and NM saturation occurs. Consequently, GB motion saturation occurs at a lower shear strain for larger grain size models with a smaller dislocation slip resistance [2]. In addition, due to the combined effect of triple junctions and grain size, the saturated NM displacement exhibits only slight increases with increasing grain size when the grain size exceeds 30 nm. The observed effect of grain size on coupled GB motion can be partly explained by the pinning effect of the triple junctions at the ends of the GB because the distance between the two triple junctions increases as the grain size increases. Due to the pinning effect, the GB looks just like a skipping rope. Although the distance between the triple junctions does not alter the shear stress at which NM is initiated, it affects the evolution and saturation of NM. Further insight into the effect of grain size on the saturated NM displacement can be gained by evaluating the evolution of the atomistic configuration during GB motion. The atomistic configurations of the 30 nm grain size Ni model at NM displacements of 1.28 Å, 6.44 Å, and 13.32 Å are plotted in Fig. 7(a). An ordered jEEj structural unit periodicity is observed in the middle segments of the GBs, while the GB structures near the triple junctions at the two ends are disordered. As NM displacement increases, the disordering gradually develops from the GB ends to the middle segment, as shown by the vertical dotted lines in Fig. 7(a). The atomistic configurations of models with grain sizes of 20 nm, 30 nm, 40 nm, and 70 nm at an NM displacement of 6.44 Å are plotted in Fig. 7(b). Comparison of the four models with different grain sizes reveal
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Fig. 5. Nominal shear stress contours of the Ni nanocrystal at (a) 0%, (b) 12.00% nominal shear strain, and (c) the bicrystal at a nominal shear strain of 12.00%.
Fig. 6. NM displacement versus nominal shear strain curves for Ni nanocrystals of different grain sizes.
that they have nearly the same disordered GB length at an NM displacement of 6.44 Å, as shown by the two dotted lines in Fig. 7(b). This suggests that the disordered GB length is directly related to the NM displacement, and not to the distance between the two triple junctions. Therefore, a longer GB can endure more elementary structure transformation from in-order to out-of-order, so that the saturated NM displacement increases with increasing grain size.
Fig. 8. TM displacement versus nominal shear strain curves for Ni nanocrystals with different grain sizes.
The tangential displacement component of coupled GB motion of the middle point of the observed GB was captured as the TM displacement. The TM displacement versus nominal shear strain curves of the five models with different grain sizes are plotted in Fig. 8. Similar to the case of NM, TM initiates at a nominal shear strain of about 1.00%. During the stable TM stage, all the curves maintain a fairly constant general slope, and the slope is observed to increase with increasing grain size. An obvious TM saturation is
Fig. 7. Atomistic configurations (a) for the 30 nm grain size Ni model at NM displacements of 1.28 Å, 6.44 Å, and 13.32 Å, and (b) for Ni models with grain sizes of 20 nm, 30 nm, 40 nm, and 70 nm at an NM displacement of 6.44 Å.
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relative to that of the TM displacement curve during Stage II leads to the observed increase in b with increasing nominal shear strain shown in Fig. 9. This was also found in previous research [18]. Cahn et al. [14] proposed the expression b = 2 tan (h/2) = 0.71 for the coupling factor of bicrystals, where h is the GB misorientation angle. The predicted value of b is also drawn with a dotted line in Fig. 9 for the nanocrystals. The simulation results for the Ni nanocrystals are observed to be smaller than the theoretical prediction at small nominal shear strain values, but are larger than the theoretical prediction at large nominal shear strain values. This finding can provide an explanation for the discrepancy obtained in previous simulations of coupled GB motion in nanocrystals, namely, an either smaller [17] or larger [18] value of b than that obtained by the theoretical prediction. For a nanocrystal, b increases with increasing nominal shear strain, so that b could be either larger or smaller than the theoretical prediction when it is measured at different shear strains. Fig. 9. The coupling factor b = dt/dn versus nominal shear strain for Ni nanocrystals with different grain sizes.
4.2. Coupled GB motion in different materials
Fig. 10. NM and TM displacement curves of the 30 nm grain size Ni model.
observed, and the saturated TM displacement increases with increasing grain size as well. This indicates that the effect of grain size on TM is very similar to that on NM. Coupled GB motion can be characterized by the coupling factor b = dt/dn [21]. For comparison, b versus nominal shear strain curves of the five Ni models with different grain sizes are plotted in Fig. 9. The figure indicates that b is only slightly affected by the grain size, but generally increases with increasing nominal shear strain. To place this phenomenon in perspective, both the NM and TM displacement versus nominal shear strain curves of the 30 nm grain size Ni model are plotted in Fig. 10. Apparently, the NM and TM not only initiate at the same nominal shear strain of about 1.00%, but also saturate at an equivalent nominal shear strain of about 6.60%. In addition, the larger slope of the NM displacement curve
Generally, materials with different stacking fault energies have different energy barriers for dislocation and twin formation [31,32], as well as for nucleation and motion of GB disconnections [33,34]. It has been determined that Cu, Al, and Ni bicrystals have obviously different GB motion behaviors [21]. Naturally, variations in the coupled GB motions of nanocrystalline Cu, Al, and Ni should be investigated. To compare coupled GB motions in the different materials, the atomistic configurations of nanocrystalline Cu, Al, and Ni with grain sizes of 30 nm at nominal shear strains of 12.00% are plotted in Fig. 11. It is surprising that massive dislocations and stacking faults are observed in nanocrystalline Cu and Ni, while only a few twins nucleate in the nanocrystalline Al. The NM displacement versus nominal shear strain curves of the nanocrystalline Cu, Al, and Ni are plotted in Fig. 12. The figure shows that coupled GB motion occurs in the nanocrystalline Al and Ni but not in the nanocrystalline Cu, which provides results equivalent to that of a bicrystal [21]. Compared with the nanocrystalline Ni, the coupled GB motion in the nanocrystalline Al exhibits a reduced shear strain threshold and saturated NM displacement. Nevertheless, the nanocrystalline Al and Ni models exhibit a nearly equivalent general slope for their NM displacement versus nominal shear strain curves. 4.3. The effect of temperature Temperature also has an important effect on coupled GB motion in nanocrystals. To evaluate this effect, the sheared nanocrystalline Ni model with a grain size of 30 nm was simulated at temperatures of 1 K, 10 K, 100 K, 300 K, and 600 K. The NM displacement versus nominal shear strain curves are plotted in Fig. 13. The figure shows that NM initiates earlier at higher temperatures, as marked by the black arrow in Fig. 13. This is because thermal fluctuation is enhanced at elevated temperature, which promotes the elemen-
Fig. 11. Configurations of nanocrystalline Cu, Al, and Ni at nominal shear strains of 12.00%.
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contributes to its initiation. This partly demonstrates that elevated temperature does not affect the GB motion mechanism [35]. GB motion as well as grain growth is a deformation-induced and thermally-activated process [36]. Fig. 14 plots b versus nominal shear strain curves at different temperatures. The values are considerably intertwined, which indicates that temperature has little influence on b. 5. Conclusions Coupled GB motion in sheared nanocrystals was simulated using the MD method, and the results were compared with those in a sheared bicrystal. The following conclusions can be drawn.
Fig. 12. NM displacement versus nominal shear strain curves of nanocrystalline Cu, Al, and Ni.
Fig. 13. NM displacement versus nominal shear strain curves for nanocrystalline Ni at different temperatures.
(1) In contrast to the coupled GB motion in a sheared bicrystal, the coupled GB motion in a sheared nanocrystal can be separated into three stages denoted as initiation, evolution, and saturation. Saturation of the coupled GB motion was observed due to the pinning effect of the triple junctions, and uneven NM distorted the GB in sheared Ni nanocrystals. (2) Due to restricted deformation between neighboring grains, massive dislocations and stacking faults are formed within some grains. Accompanied with the initiation, evolution, and saturation phases of coupled GB motion, the elementary structure units in the observed GB transformed from inorder to out-of-order in the sheared nanocrystals. (3) NM and TM in the nanocrystals exhibited nearly equivalent threshold shear strains, and saturated at approximately equivalent nominal shear strains. Both NM and TM are significantly affected by the grain size, but the slight effect of the grain size on b indicates that coupled GB motion is only slightly influenced by the grain size. (4) Coupled GB motion was also observed in the nanocrystalline Al but not in the nanocrystalline Cu. Compared with the nanocrystalline Ni, the coupled GB motion in the nanocrystalline Al exhibited a reduced shear strain threshold and saturated NM displacement. (5) NM initiates at a lower nominal shear strain at higher temperature. The NM displacement versus nominal shear strain curves at different simulation temperatures exhibited nearly equivalent general slopes. Temperature also demonstrated little influence on b.
Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant No. 11572135). References [1] [2] [3] [4] [5]
Fig. 14. Coupling factor versus nominal shear strain curves for nanocrystalline Ni at different temperatures.
tary structure transformation. The curves exhibit nearly equivalent general slopes, and the saturated NM displacements vary only slightly. It is therefore obvious that microstructure transformation is driven by external loading, although thermal fluctuation
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Initiation, evolution, and saturation of coupled grain boundary motion in nanocrystalline materials Peng Wang, Xinhua Yang ⇑, Di Peng Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
a r t i c l e
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Article history: Received 30 July 2015 Received in revised form 23 October 2015 Accepted 30 October 2015 Available online 19 November 2015 Keywords: Nanocrystal Coupled grain boundary motion Saturation Molecular dynamics
a b s t r a c t Coupled grain boundary (GB) motion in sheared nanocrystalline materials composed of Ni, Al, or Cu is investigated by atomistic simulation methods, and the effects of grain size and temperature are evaluated. Due to the pinning effect of triple junctions, saturation of coupled GB motion is observed in all the nanocrystals except Cu. The two components of coupled GB motion, normal migration (NM) and tangential motion (TM), initiate and saturate at nearly equivalent nominal shear strains. Accompanied with coupled GB motion, massive dislocations and stacking faults are found to form within some grains, and the elementary structure units in the observed GBs transform from in-order to out-of-order. Compared with nanocrystalline Ni, the coupled GB motion in nanocrystalline Al has a reduced shear strain threshold and saturated NM displacement. The effects of grain size and temperature are similar in both NM and TM, so that their influence on coupled GB motion is slight. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Grain size has a significant effect on the deformation behavior of nanocrystalline materials. In general, the deformation of a polycrystalline material is dominated by dislocations for grain sizes of hundreds of microns, but mediated by grain boundaries (GBs) for grain sizes of a few nanometers [1–3]. Accordingly, GBs play a key role in determining the mechanical properties and deformation behaviors of nanocrystalline materials, which are remarkably different from their coarse-grained counterparts. An extraordinary deformation behavior involving grain growth has been observed in both experimental studies [4–6] and atomistic simulations [7,8]. Recently, numerous investigations have been conducted to reveal the mechanism of grain growth in nanocrystals [9–12], and some elaborate experiments were also employed for clarifying the role of shear stress as the driving force for mechanically induced GB migration and grain growth [13]. It was found that grain growth generally scales with the applied stress. Moreover, GBs are mobile during deformation, rather than acting as stationary obstacles, so that deformation involving grain growth is always accompanied by GB motion. However, both experiments and theoretical predictions have presented an interesting complexity regarding GB motion [14,15]. In a bicrystal or nanocrystal, normal GB migration (NM) perpendicular to the GB plane is often coupled to tangential motion (TM) parallel to the ⇑ Corresponding author. Tel.: +86 027 87540153. E-mail address: [email protected] (X. Yang). http://dx.doi.org/10.1016/j.commatsci.2015.10.049 0927-0256/Ó 2015 Elsevier B.V. All rights reserved.
GB plane. The coupling factor characterizing coupled GB motion is defined as the ratio of TM to NM. For a bicrystal, this ratio can be geometrically related to the GB misorientation angle according to a theoretical model [14]. However, the predictions of this model are slightly larger than experimental results when applied to a nanocrystalline material [16]. This is possibly because GB motion in a nanocrystal is easily affected by triple junctions and intragranular defects [17,18]. Triple junctions always act as obstacles to GB motion, while intragranular defects not only change the local stress distribution, but also interact with the GBs. In contrast to the sustained NM occurring in a bicrystal, NM in a nanocrystal becomes saturated due to the pinning effect of triple junctions and the impact from dislocations [17,18]. However, the saturation behavior of coupled GB motion in nanocrystals has not been carefully studied yet. A more comprehensive study is required to uncover the mechanisms underlying this phenomenon. Grain growth is widespread in nanocrystals, but rare in coarse-grained materials [2]. This indicates that grain growth is a grain-size related process. Therefore, it can be safely assumed that GB motion also depends on the grain size. In addition, grain growth was found to dominate the plastic deformation of gradient nanograined Cu [19], but no grain growth was observed in gradientstructured interstitial free steel [20]. These conflicting results seemingly imply that the phenomenon of grain growth is multitudinous. The present study focuses on coupled GB motion in metal nanocrystals. A series of face-centered-cubic (FCC) models respectively composed of nanocrystalline Ni, Al, and Cu with R9h1 1 0i
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{2 2 1} symmetric tilt GBs are respectively constructed as the objects of observation. Their shear responses are evaluated by atomistic simulation methods, and the initiation, evolution, and saturation processes of coupled GB motion are subjected to careful analysis. Finally, the effects of grain size, material, and temperature are discussed. 2. Models and computational method A series of quasi-three-dimensional FCC nanocrystalline models 0 texture were constructed. The nanocrystalline with idealized ½1 1 Ni, Cu, and Al models all have the same grain orientations, and have a horizontal R9h1 1 0i{2 2 1} symmetric tilt GB with a misorientation angle of 38.94° [21] and two component grains lying in the middle of the models. This GB was considered as the observation object. The remaining grains were oriented randomly. Among these models, the nanocrystalline Ni models were constructed with grain sizes of 10 nm, 20 nm, 30 nm, 40 nm, and 70 nm to evaluate the effect of grain size on the coupled GB motion. Their outline dimensions are 2 nm along the h1 1 0i texture direction, and vary respectively from 16.5 nm 16.5 nm to 115.5 nm 115.5 nm in the plane perpendicular to the texture direction when the grain sizes increase from 10 nm to 70 nm. The nanocrystalline Cu and Al models were constructed with grain sizes of 30 nm for comparison with the coupled GB motion of the nanocrystalline Ni model having an equivalent grain size. In addition, a bicrystal model with a R9h1 1 0i{2 2 1} symmetric tilt GB was also constructed as a reference for comparison. Molecular dynamics (MD) simulations were performed using LAMMPS [22] with embedded atom method potentials for Ni [23], Al [23], and Cu [24]. Periodic boundary conditions were 1 0 directions, while the boundimposed in the X ½1 1 4 and Z ½1 direction. Before application of a aries were free in the Y ½2 2 1 shear strain, the models were relaxed at 300 K for 100 ps to obtain equilibrium configurations. Subsequently, the models were slowly adjusted to the desired temperature and relaxed for another 100 ps. The simulation temperature employed was 10 K, unless otherwise stated. Two slabs that were 2 nm in thickness were fixed at the top and bottom of each model. The shear strain was applied by deforming the model as a whole in the X direction at a strain rate of 2 108 s1. The canonical ensemble (NVT) with a constant number of atoms, volume, and temperature was employed to trace the atomic trajectories. The MD integration step was 1.0 fs. The common neighbor analysis method was employed to identify the crystalline structures during the visualization [25]. Atoms were colored according to their profiles in the atomic configurations. In what follows, FCC atoms are marked blue, hexagonal close packed (HCP) atoms are marked light blue, and the remainder are marked red. Visualization of the atomistic simulation data was performed by the three-dimensional visualization software OVITO [26]. 3. Characteristics of coupled GB motion in nanocrystalline Ni The location coordinates of the middle point of the observed GB during deformation were captured, and the respective normal and tangential displacements dn and dt of the GB were obtained. The NM displacement versus nominal shear strain curve of the nanocrystalline Ni model with a grain size of 30 nm is plotted in Fig. 1. An examination of Fig. 1 indicates that the NM displacement curve can be obviously separated into three stages. During Stage I, the GB does not migrate until experiencing a nominal shear strain of about 1.00%, which is denoted as the threshold shear strain for NM. When the nominal shear strain exceeds this threshold value, the GB begins to migrate stably during Stage II, and the NM
Fig. 1. NM displacement versus nominal shear strain curves of a Ni bicrystal and nanocrystal.
displacement curve exhibits a stepped character denoted as stick–slip [21], where the term ‘‘stick” corresponds to the shear strain applied to the nanocrystal, while the term ‘‘slip” is related to the resulting NM displacement. Moreover, most of the slip events represent very similar displacements. After the nominal shear strain reaches about 6.60%, the NM progresses into Stage III, where the GB motion is saturated. GB motion in a sheared bicrystal has been observed [14,21]. Therefore, the NM displacement versus nominal shear strain curve of a Ni bicrystal is also plotted in Fig. 1 for comparison. As shown in the figure, GB motion saturation is not observed in the case of a bicrystal, so that the curve exhibits only two stages. Stage I occurs until attaining a threshold shear strain of slightly less than 1.00%, after which the GB motion in Stage II corresponds to a stick–slip character similar to that observed in the nanocrystal. To analyze the underlying mechanism of GB motion saturation in the nanocrystal, the nanocrystal configurations at nominal shear strains of 0%, 6.80%, and 12.00%, corresponding to the three stages, are shown in Fig. 2(a)–(c), respectively. The horizontal and vertical marker lines represent the geometrical symmetry centers, and are drawn to track the NM and TM displacements. The observed GB is initially located at the center of the nanocrystal model, and lies along the horizontal marker line, as shown in Fig. 2(a). With increasing nominal shear strain, the atoms in the model are progressively relocated so that both the horizontal and vertical marker lines are spatially altered. Fig. 2(b) shows that the observed GB is obviously separated from the horizontal marker line, but its two ends are pinned by triple junctions. Therefore, the GB becomes distorted as a result of shear deformation, indicating the occurrence of uneven NM. While the NM displacement increases with increasing shear deformation, it eventually reaches saturation because of the pinning effect of the triple junctions, as shown in Fig. 2(c). A slight unpinning effect of the triple junctions is observed owing to the dislocation activities near the triple junctions. This suggests that the triple junctions are relatively immobile compared to the GB [18]. However, slight unpinning does not significantly affect the distorted GB shape and the onset of NM saturation. Due to the restricted deformation between neighboring grains, massive dislocations and stacking faults are formed within some grains, which is in accordance with experimental evidence [27]. In addition, it is also observed in Fig. 2(b) that the vertical marker line inclines abruptly between the observed GB and the horizontal marker line. This shows that NM is accompanied by TM. The coupled GB motion can be further confirmed by the distribution of the von Mises local shear strain invariant shown in Fig. 2(d). In addition to the dislocation and stacking fault regions, the area over which the GB motion occurs exhibits a larger shear strain invariant.
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Fig. 2. Configurations at nominal shear strains of 0%, 6.80%, and 12.00% (a)–(c), where the von Mises local shear strain invariant contour of the Ni nanocrystal given in (c) is shown in (d). Configurations and contour for the bicrystal are given in (e)–(h) for equivalent nominal shear strains.
For comparison, the configurations of the Ni bicrystal at nominal shear strains of 0%, 6.80%, and 12.00% are also shown in Fig. 2(e)– (g), respectively. The GB initially overlaps with the horizontal marker line. However, in striking contrast with the nanocrystal, the bicrystal GB migrates equally along the normal direction to the GB plane as a whole, so that it does not distort after deformation. In contrast to the distorted GB motion saturation occurring in the nanocrystal, non-distorted GB motion is always retained in the bicrystal during loading, as shown in Fig. 2(f) and (g). Moreover, the vertical marker lines remain perpendicular to the horizontal marker lines outside the coupled GB motion region, while vertical marker lines are tilted inside the region. This indicates that shear deformation takes place only in the NM region, which is also demonstrated by the distribution of the von Mises local shear strain invariant shown in Fig. 2(h). The respective NM and TM displacements dn and dt are labeled in Fig. 2(g) for clarity. To investigate the microscopic mechanism of GB motion saturation in the nanocrystal, the atomistic configurations of the nanocrystal GB at nominal shear strains of 1.36%, 1.92%, 2.00%, 6.80%, and 12.00% are shown in Fig. 3(a)–(e), respectively. The FCC atoms are deleted and all the atoms are colored according to their Y coordinates. Fig. 3(a)–(c) shows the GB configurations before and after the initiation of NM. With the initiation of NM, some GB disconnections (marked by the arrows in Fig. 3(b)) nucleate in advance, and then expand through the GB plane (see Fig. 3 (c)) in the GB with initially perfect jEEj structural unit periodicity similar to the case in the bicrystal [21,28]. The enlarged atomic representations show that elementary structure unit transformation occurs during GB motion. Although the ordered structural units remain in the middle portion of the GB after the elementary structure unit transformation, the GB structures near the triple junctions at the two ends are disordered. The disordered region expands with increasing NM displacement, as shown in Fig. 3 (d) and (e). However, elementary structure unit transformation cannot occur in the disordered GB region, so that the GB is pinned by the triple junctions. The GB atomistic configurations of the bicrystal at nominal shear strains of 1.20%, 1.28%, 1.36%, 7.00%, and 12.00% are also shown in Fig. 3(f)–(j). Similar to the nanocrystal, both GB disconnections and elementary structure unit transformation take place in the sheared bicrystal. Fig. 3(f)–(h) shows the GB configurations before and after the onset of NM displacement. Owing to uniform NM, in distinct contrast to that of the nanocrystal, the ordered structural units remain within the GB after elementary structure unit transformation, as shown in Fig. 3(i) and (j). As a microscopic deformation mechanism, coupled GB motion can have an important influence on the macroscopic mechanical response. To evaluate this influence, the stress–strain curves of both the Ni nanocrystal and bicrystal are plotted in Fig. 4. The
points at which coupled GB motions are initiated are marked by hollow circles. It can be seen from the enlarged stress–strain curve for the nanocrystal given in the inset of Fig. 4 that the nominal shear stress undergoes a nearly linear increase with increasing nominal shear strain before and after the onset of coupled GB motion. This is in striking contrast with the stress–strain curve of the bicrystal, in which the nominal shear stress drops dramatically and enters a fluctuation stage after the onset of coupled GB motion. To uncover the microscopic deformation mechanism corresponding with the macroscopic stress–strain response, the virial stress contours of the nanocrystal at nominal shear strains of 0% and 12.00% and the bicrystal at 12.00% are plotted in Fig. 5. The figure shows that the residual stress in the nanocrystal is negligible at a nominal shear strain of 0%, which indicates that the condition of energy minimization was reached. Due to uneven NM, stress relief is limited to within a small region neighboring the middle segment of the observed GB in the nanocrystal, but the stress is almost entirely relieved in the bicrystal. The observed stress relief nearby the GB validates an earlier experimental observation that GB motion could be a plastic relaxation mechanism [29]. In addition, defect nucleation and propagation may also relieve local stress [17,30]. To clarify the mechanism, the percentage of HCP atoms in the nanocrystal is plotted in Fig. 4. The increment in the percentage of HCP atoms is closely related to the number of defects nucleating during deformation. The percentage of HCP atoms is nearly zero below a nominal shear strain of 2.56%, but, after that, it begins to increase at a variable rate. This indicates that defect initiation is unsynchronized with coupled GB motion, which is expected because the shear resistance of GB motion is usually lower than the resistance of intragranular dislocation nucleation [29,30]. After the defects nucleate, the behavior of the percentage of HCP atoms is fairly consistent with that of the stress–strain curve. As indicated by the five vertical dotted lines in Fig. 4, a rapid increase in the percentage of HCP atoms is always accompanied by a sharp decrease in the shear stress. It is noteworthy that GB motion was determined to be significantly affected by the misorientation angle of the symmetric tilt GB [18]. A R17(5 3 0) GB was found to move spontaneously, while a R5(2 1 0) GB exhibited the stick–slip behavior like that of the presently presented nanocrystalline models with R9h1 1 0i{2 2 1} GBs. Due to the pinning effect of triple junctions, the disordered GB segments neighboring the triple junctions migrate with great difficulty, so that the observed GBs become distorted in these nanocrystals, and GB motion saturation occurs. However, compared with the case of R9h1 1 0i{2 2 1} GBs, the nanocrystal with a R5(2 1 0) GB exhibited a more obvious unpinning effect of triple junctions, possibly because of its higher GB mobility and lower intragranular dislocation resistance.
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Fig. 3. GB atomistic configurations of the Ni nanocrystal at nominal shear strains of (a) 1.36%, (b) 1.92%, (c) 2.00%, (d) 6.80%, and (e) 12.00%, and those of the bicrystal at nominal shear strains of (f) 1.20%, (g) 1.28%, (h) 1.36%, (i) 7.00%, and (j) 12.00%.
Fig. 4. Stress–strain curves of the Ni bicrystal and nanocrystal, and the percentage of HCP atoms in the nanocrystal.
4. The effects of grain size, material, and temperature on the characteristics of coupled GB motion 4.1. The effect of grain size To evaluate the effect of grain size on coupled GB motion and its saturation, five sheared Ni nanocrystalline models with common grain orientations but different grain sizes from 10 nm to 70 nm were simulated. Their NM displacement versus nominal shear strain curves are plotted in Fig. 6. An approximately equivalent threshold shear strain of about 1.00% is observed for all grain sizes. However, the models exhibit considerable differences after the onset of NM. The curves obviously have different general slopes,
where the slope is observed to increase with increasing grain size. Moreover, with increasing grain size, the saturated NM displacement increases and the onset of NM saturation occurs at an increasingly lower shear strain. The saturated NM displacement increases from about 7.91 Å to 16.69 Å when the grain size increases from 10 nm to 70 nm. Once the GB motion resistance exceeds the dislocation slip resistance, dislocations will dominate the plastic deformation, and NM saturation occurs. Consequently, GB motion saturation occurs at a lower shear strain for larger grain size models with a smaller dislocation slip resistance [2]. In addition, due to the combined effect of triple junctions and grain size, the saturated NM displacement exhibits only slight increases with increasing grain size when the grain size exceeds 30 nm. The observed effect of grain size on coupled GB motion can be partly explained by the pinning effect of the triple junctions at the ends of the GB because the distance between the two triple junctions increases as the grain size increases. Due to the pinning effect, the GB looks just like a skipping rope. Although the distance between the triple junctions does not alter the shear stress at which NM is initiated, it affects the evolution and saturation of NM. Further insight into the effect of grain size on the saturated NM displacement can be gained by evaluating the evolution of the atomistic configuration during GB motion. The atomistic configurations of the 30 nm grain size Ni model at NM displacements of 1.28 Å, 6.44 Å, and 13.32 Å are plotted in Fig. 7(a). An ordered jEEj structural unit periodicity is observed in the middle segments of the GBs, while the GB structures near the triple junctions at the two ends are disordered. As NM displacement increases, the disordering gradually develops from the GB ends to the middle segment, as shown by the vertical dotted lines in Fig. 7(a). The atomistic configurations of models with grain sizes of 20 nm, 30 nm, 40 nm, and 70 nm at an NM displacement of 6.44 Å are plotted in Fig. 7(b). Comparison of the four models with different grain sizes reveal
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Fig. 5. Nominal shear stress contours of the Ni nanocrystal at (a) 0%, (b) 12.00% nominal shear strain, and (c) the bicrystal at a nominal shear strain of 12.00%.
Fig. 6. NM displacement versus nominal shear strain curves for Ni nanocrystals of different grain sizes.
that they have nearly the same disordered GB length at an NM displacement of 6.44 Å, as shown by the two dotted lines in Fig. 7(b). This suggests that the disordered GB length is directly related to the NM displacement, and not to the distance between the two triple junctions. Therefore, a longer GB can endure more elementary structure transformation from in-order to out-of-order, so that the saturated NM displacement increases with increasing grain size.
Fig. 8. TM displacement versus nominal shear strain curves for Ni nanocrystals with different grain sizes.
The tangential displacement component of coupled GB motion of the middle point of the observed GB was captured as the TM displacement. The TM displacement versus nominal shear strain curves of the five models with different grain sizes are plotted in Fig. 8. Similar to the case of NM, TM initiates at a nominal shear strain of about 1.00%. During the stable TM stage, all the curves maintain a fairly constant general slope, and the slope is observed to increase with increasing grain size. An obvious TM saturation is
Fig. 7. Atomistic configurations (a) for the 30 nm grain size Ni model at NM displacements of 1.28 Å, 6.44 Å, and 13.32 Å, and (b) for Ni models with grain sizes of 20 nm, 30 nm, 40 nm, and 70 nm at an NM displacement of 6.44 Å.
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relative to that of the TM displacement curve during Stage II leads to the observed increase in b with increasing nominal shear strain shown in Fig. 9. This was also found in previous research [18]. Cahn et al. [14] proposed the expression b = 2 tan (h/2) = 0.71 for the coupling factor of bicrystals, where h is the GB misorientation angle. The predicted value of b is also drawn with a dotted line in Fig. 9 for the nanocrystals. The simulation results for the Ni nanocrystals are observed to be smaller than the theoretical prediction at small nominal shear strain values, but are larger than the theoretical prediction at large nominal shear strain values. This finding can provide an explanation for the discrepancy obtained in previous simulations of coupled GB motion in nanocrystals, namely, an either smaller [17] or larger [18] value of b than that obtained by the theoretical prediction. For a nanocrystal, b increases with increasing nominal shear strain, so that b could be either larger or smaller than the theoretical prediction when it is measured at different shear strains. Fig. 9. The coupling factor b = dt/dn versus nominal shear strain for Ni nanocrystals with different grain sizes.
4.2. Coupled GB motion in different materials
Fig. 10. NM and TM displacement curves of the 30 nm grain size Ni model.
observed, and the saturated TM displacement increases with increasing grain size as well. This indicates that the effect of grain size on TM is very similar to that on NM. Coupled GB motion can be characterized by the coupling factor b = dt/dn [21]. For comparison, b versus nominal shear strain curves of the five Ni models with different grain sizes are plotted in Fig. 9. The figure indicates that b is only slightly affected by the grain size, but generally increases with increasing nominal shear strain. To place this phenomenon in perspective, both the NM and TM displacement versus nominal shear strain curves of the 30 nm grain size Ni model are plotted in Fig. 10. Apparently, the NM and TM not only initiate at the same nominal shear strain of about 1.00%, but also saturate at an equivalent nominal shear strain of about 6.60%. In addition, the larger slope of the NM displacement curve
Generally, materials with different stacking fault energies have different energy barriers for dislocation and twin formation [31,32], as well as for nucleation and motion of GB disconnections [33,34]. It has been determined that Cu, Al, and Ni bicrystals have obviously different GB motion behaviors [21]. Naturally, variations in the coupled GB motions of nanocrystalline Cu, Al, and Ni should be investigated. To compare coupled GB motions in the different materials, the atomistic configurations of nanocrystalline Cu, Al, and Ni with grain sizes of 30 nm at nominal shear strains of 12.00% are plotted in Fig. 11. It is surprising that massive dislocations and stacking faults are observed in nanocrystalline Cu and Ni, while only a few twins nucleate in the nanocrystalline Al. The NM displacement versus nominal shear strain curves of the nanocrystalline Cu, Al, and Ni are plotted in Fig. 12. The figure shows that coupled GB motion occurs in the nanocrystalline Al and Ni but not in the nanocrystalline Cu, which provides results equivalent to that of a bicrystal [21]. Compared with the nanocrystalline Ni, the coupled GB motion in the nanocrystalline Al exhibits a reduced shear strain threshold and saturated NM displacement. Nevertheless, the nanocrystalline Al and Ni models exhibit a nearly equivalent general slope for their NM displacement versus nominal shear strain curves. 4.3. The effect of temperature Temperature also has an important effect on coupled GB motion in nanocrystals. To evaluate this effect, the sheared nanocrystalline Ni model with a grain size of 30 nm was simulated at temperatures of 1 K, 10 K, 100 K, 300 K, and 600 K. The NM displacement versus nominal shear strain curves are plotted in Fig. 13. The figure shows that NM initiates earlier at higher temperatures, as marked by the black arrow in Fig. 13. This is because thermal fluctuation is enhanced at elevated temperature, which promotes the elemen-
Fig. 11. Configurations of nanocrystalline Cu, Al, and Ni at nominal shear strains of 12.00%.
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contributes to its initiation. This partly demonstrates that elevated temperature does not affect the GB motion mechanism [35]. GB motion as well as grain growth is a deformation-induced and thermally-activated process [36]. Fig. 14 plots b versus nominal shear strain curves at different temperatures. The values are considerably intertwined, which indicates that temperature has little influence on b. 5. Conclusions Coupled GB motion in sheared nanocrystals was simulated using the MD method, and the results were compared with those in a sheared bicrystal. The following conclusions can be drawn.
Fig. 12. NM displacement versus nominal shear strain curves of nanocrystalline Cu, Al, and Ni.
Fig. 13. NM displacement versus nominal shear strain curves for nanocrystalline Ni at different temperatures.
(1) In contrast to the coupled GB motion in a sheared bicrystal, the coupled GB motion in a sheared nanocrystal can be separated into three stages denoted as initiation, evolution, and saturation. Saturation of the coupled GB motion was observed due to the pinning effect of the triple junctions, and uneven NM distorted the GB in sheared Ni nanocrystals. (2) Due to restricted deformation between neighboring grains, massive dislocations and stacking faults are formed within some grains. Accompanied with the initiation, evolution, and saturation phases of coupled GB motion, the elementary structure units in the observed GB transformed from inorder to out-of-order in the sheared nanocrystals. (3) NM and TM in the nanocrystals exhibited nearly equivalent threshold shear strains, and saturated at approximately equivalent nominal shear strains. Both NM and TM are significantly affected by the grain size, but the slight effect of the grain size on b indicates that coupled GB motion is only slightly influenced by the grain size. (4) Coupled GB motion was also observed in the nanocrystalline Al but not in the nanocrystalline Cu. Compared with the nanocrystalline Ni, the coupled GB motion in the nanocrystalline Al exhibited a reduced shear strain threshold and saturated NM displacement. (5) NM initiates at a lower nominal shear strain at higher temperature. The NM displacement versus nominal shear strain curves at different simulation temperatures exhibited nearly equivalent general slopes. Temperature also demonstrated little influence on b.
Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant No. 11572135). References [1] [2] [3] [4] [5]
Fig. 14. Coupling factor versus nominal shear strain curves for nanocrystalline Ni at different temperatures.
tary structure transformation. The curves exhibit nearly equivalent general slopes, and the saturated NM displacements vary only slightly. It is therefore obvious that microstructure transformation is driven by external loading, although thermal fluctuation
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