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Article

Study on Grain Boundary Mechanical Behaviors of Polycrystalline γ-TiAl Using Molecular Dynamics Simulations

by
Wenjuan Zhao
1,*,
Maoqing He
1,
Chunliang Li
2 and
Wei Chen
1
1
School of Mechanical Engineering and Mechanics, Xiangtan University, Xiangtan 411105, China
2
Hunan Aerospace Chengyuan Precision Machinery Co., Ltd., Changsha 410205, China
*
Author to whom correspondence should be addressed.
Metals 2024, 14(7), 779; https://doi.org/10.3390/met14070779
Submission received: 11 May 2024 / Revised: 18 June 2024 / Accepted: 24 June 2024 / Published: 1 July 2024
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Abstract

:
In this study, the molecular dynamics (MD) method was used to study the tensile deformation of polycrystalline γ-TiAl with complex and random grain orientations. Firstly, the tensile deformation was simulated with different average grain sizes (8.60 nm, 6.18 nm, and 4.50 nm) and strain rates (1 × 108 s−1, 5 × 108 s−1, and 1 × 109 s−1). The results show that the peak stress increases with an increase in tensile strain rate, and the peak stress decreases as the grain size decreases, showing an inverse Hall–Petch effect. Upon observing atomic configuration evolution during tensile deformation, it is found that the grain boundary is seriously distorted, which indicates obvious grain boundary sliding occurring. With a further increase in the loading, some dislocations nucleate at the grain boundaries and propagate towards the interior of the grains along the grain boundaries, which demonstrates that dislocation motion is the primary coordination of the mechanical process of the grain boundaries. The dislocation density near the grain boundaries continues to increase, leading to the generation of micro-cracks and eventually causing material failure. Another interesting phenomenon is that the grains rotate, and the specific rotation angle values of each grain are quantitatively calculated. Grain rotation relaxes the stress concentration near the grain boundaries and plays a toughening role. Consequently, the plastic deformation behaviors of polycrystalline γ-TiAl are achieved through the grain boundary mechanical process, that is, grain boundary sliding and grain rotation.

1. Introduction

TiAl-based metal compounds exhibit low density (only half that of Ni-based superalloys), high specific stiffness, and excellent high-temperature creep and oxidation resistance [1,2,3]. γ-TiAl alloys have been considered to be the preferred material for making certain aerospace structural components and can achieve significant improvements in thrust-to-weight ratio and fuel efficiency [4,5,6]. To improve turbine speed and fuel efficiency, new-generation aero-engines (such as gear turbofan engines) have higher requirements for harsh service conditions under high stress. However, the application of γ-TiAl alloys in aero-engines is limited due to its disadvantages of poor plasticity at room temperature and fast crack growth rate [7,8]. Therefore, it is urgent to investigate the plastic deformation behavior of γ-TiAl in depth to expand its application potential.
The typical structure of TiAl alloys is a lamellar structure composed of two layered phases, in which the γ-TiAl phase with an L10 structure is one of its main constituent phases [9]. A large number of complexly oriented interfaces in its microstructure have a significant impact on its mechanical properties [10]. Polysynthetically Twinned (PST) TiAl crystals are used in experimental investigations to study the influence of interface orientation, and in situ transmission electron microscopy (TEM) experiments on the deformation behavior and fracture mechanism of PST-TiAl have shown that different interfaces play different roles in the deformation process, and this effect is strongly dependent on the lamellar orientation of PST crystals. The fracture mechanism and crack propagation behavior of crystals are also closely related to the lamellar orientation. Appel et al. [11] found in a fracture study of a (γ + α2) TiAl alloy that in the laminar structure, microcracks were initiated at the interface and stress concentration was easily generated. Therefore, cracks expanded at a fast rate to fracture the crystal, and it was found that the interface hindered the dislocation motion. Meier and his colleagues [12] observed the microstructures of TiAl alloys with different grain sizes under superplastic tensile deformation using optical microscopy (OM) and TEM. It was found that interface slip was the primary mechanism underlying superplastic deformation for fine-grained materials. Therefore, the mechanical behavior of the interface plays a crucial role in influencing the plastic deformation and fracture mechanism of TiAl alloys, whereas it is difficult to understand the deformation mechanism and the effects of interfaces of TiAl alloys by experimental means, because the actual polycrystalline TiAl crystal has a more complex interface than PST TiAl crystal.
The interface structure and mechanical behavior of γ-TiAl alloys are microscopic processes at an atomic scale, especially for nanocrystals. If the microscopic mechanism of the grain boundary mechanical behavior in the tensile deformation of polycrystalline γ-TiAl can be investigated at the atomic scale, our understanding of the properties of γ-TiAl alloy will be deepened. MD simulation has been proven to be an efficient and convenient way of studying the plastic deformation mechanisms of nanocrystalline materials, and it can accurately observe the atomic motion and structural evolution process within the nanoscale range, which contributes to deepening our insight into these deformation mechanisms, especially for processes that are impossible or difficult to reach experimentally [13,14]. Many scholars have effectively explained the relationship between plastic deformation mechanisms and grain boundary mechanical behavior using the MD method. Our previous study [15] reported that the tensile deformation of γ-TiAl twin crystals containing <110> symmetrical inclined grain boundaries at different temperatures and strain rates was simulated by the MD method, and it was concluded that the grain orientation difference and the atomic structure of grain boundaries were the main factors affecting the critical shear stress of dislocation nucleation. Swygenhoven et al. [16] used the MD method to study the relationship between the dislocation slip and grain boundary structure of face-centered cubic metal Al nanocrystals. The results showed that dislocation generally nucleates at grain boundaries, and dislocation slip is hindered by grain boundaries. Cao et al. [17] investigated the effect of supersonic fine particle bombardment (SFPB) on the mechanical properties of γ-TiAl alloys with different grain sizes using the MD method. They found that when the grain size was less than 9.96 nm, its tensile strength decreased with a decrease in grain size, showing a reverse Hall–Petch relation. Furthermore, deformation mechanisms such as grain boundary migration, grain rotation, and dislocation motion were observed. Therefore, the MD method is used in this study to assist in exploring the plastic deformation behavior of polycrystalline γ-TiAl from a microscopic perspective. In this paper, based on the actual polycrystalline structure, a polycrystalline γ-TiAl model with complex orientation is established by the MD method to simulate tensile deformation behavior. The plastic deformation behavior of polycrystalline γ-TiAl at the atomic-scale is analyzed by observing and quantitatively calculating the evolution of atomic configuration. At the same time, the interaction between the grain boundary and dislocation during the process of plastic deformation is also investigated, and we reveal the influence of the grain boundary mechanical behavior of the polycrystalline γ-TiAl alloy on its plastic deformation mechanism during the tensile process.

2. Modeling and Simulation

The polycrystalline γ-TiAl models were generated using the Voronoi geometric algorithm [18], with which the central location and orientation of each grain were randomly selected. The dimensions of γ-TiAl models were 16 nm × 12 nm × 12 nm. Then, the polycrystalline γ-TiAl models for three different average grain sizes ranging from 8.60 nm to 6.18 nm to 4.50 nm, and each polycrystalline γ-TiAl model contained between 140,000 and 150,000 atoms. The deformation of polycrystalline γ-TiAl was simulated using the embedded-atom method (EAM) potential developed by Zope and Mishin [19]. Periodic boundary condition was employed in the tensile direction (X-direction), and free boundary conditions were employed in the Y-direction and Z-direction. For example, the atomic configuration of polycrystalline γ-TiAl with an average grain size of 6.18 nm is shown in Figure 1.
Static calculations were employed to determine the minimum energy of the atomic configurations through a nonlinear conjugate gradient method. After this step, the polycrystalline γ-TiAl models were relaxed using the MD method in the NVT ensemble at a pressure of 0 bar and temperature of 1 K. A Nosé–Hoover thermostat was applied for temperature control. Uniaxial tensile tests were then simulated at the constant strain rates of 1 × 108 s−1, 5 × 108 s−1 and 1 × 109 s−1, which was applied in the X direction with a time step of 10−15 s. The MD simulations were carried out by a code based on the open-source code of LAMMPS 3 Mar 2020 [20]. The AtomEye version 3 (2012) [21] and Ovito 3.4.0 [22] software were employed for the visualization of atomic configurations of the polycrystalline γ-TiAl models.

3. Results and Discussion

3.1. Behaviors of Stress versus Strain

The engineering stress–strain curves of the polycrystalline γ-TiAl with an average grain size of 6.18 nm deformed at three sets of different strain rates are presented in Figure 2. It can be observed that the peak stress of the polycrystalline γ-TiAl increases with the increasing tensile strain rate. This is because at low tensile strain rates, the atoms have sufficient time to constantly move and adjust their positions, allowing the system to gradually approach equilibrium. However, when the strain rate increases, there is not enough time for the atoms to adjust their position, preventing the system from restoring equilibrium. Consequently, the higher the strain rate, the more difficult for the system to equilibrate, which increases the peak stress.
Figure 3 illustrates the tensile engineering stress–strain curves of polycrystalline γ-TiAl alloys with average grain sizes of 8.60 nm, 6.18 nm and 4.50 nm, it is found that the peak stress decreases as the grain size decreases. The main reason for this is that when the grain size decreases to the nanoscale, the proportion of grain boundaries increases significantly. With the continued reduction in grain size of the polycrystalline γ-TiAl, the grain deformation mechanism becomes dominated by grain boundaries. This dominance facilitates grain boundary sliding and grain rotation more easily, resulting in a reduction in peak stress. Therefore, the polycrystalline γ-TiAl begins to soften, and the inverse Hall-Petch (H-P) effect appears [23]. It should be noted that the inverse H-P effect has been studied by many researchers through extensive experiments and simulations. This phenomenon has been observed in various polycrystalline materials, including TiAl alloys [17,24,25]. The inverse H-P effect may be attributed to a change in the plastic deformation mechanism from dislocation-mediated plasticity to grain boundary sliding and grain rotation when the grain size is below a critical value. Ding et al. [24] studied the effect of grain size on the mechanical properties of polycrystalline γ-TiAl, and found that the inverse H-P effect occurred when the grain size was smaller than 8 nm. This was due to the deformation mechanism changing from the plasticity dominated by dislocation slip and deformation twins to grain boundary migration and grain rotation.
As seen in Figure 2 and Figure 3, the engineering stress–strain curves of polycrystalline γ-TiAl with different strain rates and grain sizes exhibit similar variation tendencies. Therefore, polycrystalline γ-TiAl with an average grain size of 6.18 nm was chosen as research object to study the evolution of atomic configurations with the strain rate of 1 × 109 s−1.

3.2. Grain Boundary Sliding and Grain Rotation

It is further shown in Figure 3 that the strains corresponding to points A, B, C, and D on the tensile engineering stress–strain curve of polycrystalline γ-TiAl with a grain size of 6.18 nm are 0, 0.040, 0.070, and 0.125, respectively. As the strain increases, the stress continues to increase and accumulate, leading to the creation of numerous dislocations and other defects. When the strain gradually reaches 0.070 (point C), the peak stress is reached. In addition, with the further increase in loading, microcracks form at the grain boundaries where stress concentration is significant, leading to grain necking along the grain boundaries. Therefore, the stress of each model decreases with the growth in strain. In order to explore the evolution of grain boundaries and grains during the tensile deformation, Figure 4 shows the atomic configuration and corresponding shear stress distribution of polycrystalline γ-TiAl with average grain sizes of 6.18 nm under strain corresponding to points A–D in Figure 3. To facilitate observation and description, the boundaries of grains are traced with thin solid black lines. The seven grains are also numbered 1–7 in sequence, and black thick lines are used to indicate the orientation of grains 1–7 in the X-Y plane. Because the tensile direction uses periodic boundary conditions, the two grain 3 in the diagram represent two parts of the same grain. At the same time, the shear stress distribution in the X-Y plane of the grain under different strains was calculated during the simulation shown in Figure 4(a2–d2).
Comparing the changes in atomic configurations illustrated in Figure 4(a1–d1), it can be seen that some grain boundaries have been distorted to varying degrees (as indicated by arrows in Figure 4(b1–d1)). From Figure 4(a1–d1), the strain increases from 0 to 0.125, and the grain boundaries of grains 1 and 5 first become flat from local bending and then distort again. In addition, the grain boundaries between grains 3, 4, and 5 gradually began to be local distortion. Specifically, the movement of atoms is hindered by grain boundaries, causing them to slip along the grain boundaries. In the light of this, the observed grain boundary distortions are attributed to the grain boundaries sliding during plastic deformation. Through observation of the triple junction of grain boundary in Figure 4(a1–d1), it can be found that the grain boundary between grain 2 and grain 5 gradually slide towards the interior of grain 2. This movement causes the intersection of triple junction of grain boundary between grain 1, 2 and 5 to gradually shift directly upwards (as shown by the ellipses in Figure 4(b1–d1)). Additionally, during the deformation process, the intersection of triple junction of grain boundary between grains 4, 5 and 6 gradually slide towards the lower boundary of the model. This results in the gradual contraction of grain 6 (as shown by the rectangle in Figure 4(a1,d1)), and the lower end of the grain 5 can be observed sliding towards the interior of the grain 6. During the process of increasing strain, atoms near the grain boundaries diffuse from one grain to another, causing the grains to continue to grow or shrink. This phenomenon can be attributed to grain boundaries sliding and atomic diffusion. At the strain of 0.125, the grain boundary between grains 3 and 7 exhibits a noticeably larger sliding amplitude, and the grain boundaries become thinner and thinner, ultimately leading to gradual disappearance of the grain boundary. Figure 4(a2–d2) display shear stress distribution with 0, 0.040, 0.070, and 0.125 strain, respectively. As the strain gradually increased to 0.070, it can be found that the shear stress presents a trend of increasing. A significant concentration of stress occurred at the grain boundary illustrated in Figure 4(c2) circled in black, when the stress reaches its peak state (corresponding to point C in Figure 3). Microcracks are initiated at this location and gradually necked along the grain boundaries (as shown by the curve at the edge of Figure 4(c2)). Li et al. [26] studied the tensile deformation behavior of polycrystalline Mo nanowires through molecular dynamics simulations and found that polycrystalline Mo necked and fractured at the grain boundaries during tensile deformation. This is because stress is highly concentrated at the grain boundaries, causing distortion of the nearby lattice and resulting in structural transformation. Interestingly, it can be seen that the positions with uneven distribution of shear stress corresponds to the position of grain boundary slip (as shown by the black arrows in Figure 4). This suggests that the distribution of shear stress at the grain boundary is uneven, causing local stress concentration at these points, which in turn promotes further grain boundary slip. The grain boundary atoms slide relative to the action of load, which leads to the rotation of grain orientation (as indicated by the curved arrow in Figure 4(d4)).
To better reveal the phenomenon of grain rotation, the in-plane rotation angles of grain 1–5 at the three stages of tensile strain (0–0.040, 0.040–0.070, and 0.070–0.125) were calculated, and the results are shown in Table 1. As observed from the table, during the increasing of tensile strain from 0 to 0.125, grains 1, 2 and 4 rotate 7.76°, 7.57° and 7.54° in a clockwise direction, respectively, while grains 3 and 5 rotate 1.94° and 1.41° in a counterclockwise direction, respectively. The grain boundary atoms and the grain atoms move in inconsistent directions leading to mutual slip when the applied load is applied, resulting in forced slip of grain boundaries and forced rotation of grains. Furthermore, with further increasing of strain, many grain boundaries slide, leading to an increase in grain rotation angle, which indicates that grain boundary slip promotes grain rotation during deformation. Zhou et al. [27] and Mao et al. [28] found that grain boundary sliding and migration were accompanied by grain rotation, which has been verified through experimental observation of grain rotation in Al [29], Ni [30] and Pt [31] using in situ TEM. Interestingly, comparing the rotation angles of each grain, it can also be found that the rotation amplitude of the border grain is greater than that of the center grains in the γ-TiAl polycrystal cell. The reason can be explained by combining the shear strain distribution in Figure 4(a2–d2). Grains 1, 2 and 4 at the boundary experience no surface binding force, and the grain boundaries are subjected to large but uneven shear stress, and the necking also occurs along the grain boundaries. In contrast, the grains in the central position are subjected to the torque caused by the rotation of the surrounding grains in different directions. The rotation torque on the boundary of the center grains 3 and 5 will offset a part of the applied torque. As a result, the boundary grains rotate at a greater angle than the intermediate grains.

3.3. The Interaction of the Dislocation and Grain Boundary

Figure 5 shows the process of dislocation emission and slip of polycrystalline γ-TiAl under different strains. The seven grains are numbered 1–7 in sequence. As can be seen from the black elliptic position in Figure 4(b2), when the strain is 0.040, large shear stress appears at the triple junction of grain boundary between grains 3, 4 and 5, where the polycrystalline γ-TiAl emits dislocations. Further analysis reveals that the dislocation is a Schokley dislocation (called dislocation 1) in the crystal plane of ( 1 1 ¯   1 ¯ ) , slipping to the inside of grain 3 in the form of a dislocation ring. With a further increase in strain, the stress gradually approaches its peak, and dislocations are also emitted from another triple junction of grain boundary between grains 2, 3 and 5 (as shown by the red ellipse in Figure 5d). It can be found that the dislocation is the Schokley dislocation (called dislocation 2) in the crystal plane of ( 1 ¯   1   1 ¯ ) , which also slips to the inside of grain 5 in the form of a dislocation ring. When the strain increases to 0.068, dislocation 2 approaches the grain boundary on the other side and is eventually absorbed by the grain boundary. Through analysis, it can be seen that it slides along the crystal plane of ( 1 ¯   1   1 ¯ ) . As the tensile deformation progresses, it can be seen from Figure 5e,f that some grains successively emitted dislocations to coordinate the deformation of the unit cell, but the dislocation density of the whole cell remains low (as shown by the black arrow in Figure 5e,f). As discussed above, grain boundary sliding and grain rotation occur during the increase im tensile strain from ε = 0 to ε = 0.040, and the first dislocation 1 starts to emission when the strain is 0.040. This indicates that the grain boundary sliding and grain rotation are conducive to inducing dislocation emission from grain boundaries at the initial stage of tensile deformation, providing the conditions of orientation and shear stress. Dislocation slip only plays the role of coordinating deformation during plastic deformation, which is also hindered by grain boundaries. Researchers have also reported on this phenomenon through experimental means. Zhao et al. [32] observed severe distortion of some grain boundaries in the microstructure evolution diagram of Ti-6Al-4V alloy during superplastic deformation, and dislocations were only emitted from the grain boundaries. Therefore, they proposed that grain boundary sliding coordinated by dislocations is the main mechanism of tensile plastic deformation in Ti-6Al-4V alloy. Kim et al. [33] also observed obvious distortion of grain boundaries during the tensile deformation process of Ti-6Al-4V alloy, and concluded that grain boundary sliding is the main plastic deformation mode. In addition, they observed that the dislocation only emitted from the grain boundary, suggesting that dislocation slip played a coordinating role in tensile deformation.

4. Conclusions

In this study, the MD simulation was used to study the plastic deformation behavior of polycrystalline γ-TiAl under uniaxial tensile loading. By establishing a numerical model of polycrystalline γ-TiAl, the effect of grain boundary mechanical behavior of polycrystalline γ-TiAl on the plastic deformation mechanism is revealed from the microscopic perspective. Based on the research results, the main conclusions can be obtained:
(1)
From the tensile engineering stress–strain relationship of polycrystalline γ-TiAl, it is found that the peak stress of polycrystalline γ-TiAl increases with an increase in tensile strain rate (1 × 108 s−1, 5 × 108 s−1, 1 × 109 s−1). However, the peak stress decreases during the tensile process with decreasing grain size (8.60 nm, 6.18 nm, 4.50 nm), showing a visible inverse Hall-Petch relationship.
(2)
Grain boundary sliding and grain rotation occur throughout the tensile deformation process of polycrystalline γ-TiAl, with grain boundary sliding dominating the plastic deformation. The rotation angle of the border grains is larger than that of the center grains, which is caused by the combined effect of the uneven distribution of shear stress at the grain boundaries and the relative rotation of each grain.
(3)
During the process of tensile deformation, it is difficult to form a dislocation source inside the polycrystalline γ-TiAl grain, and the dislocation is only emitted from the grain boundary and slips into the grain interior. Dislocation slip is hindered by the grain boundary on the other side, resulting in local stress concentration at the grain boundary. The nucleation and slip of the dislocations occur after the grain boundary sliding and grain orientation rotation begin, indicating that the grain boundary sliding and grain orientation rotation in the early stage of tensile deformation play an important role in the emission of dislocations, providing conditions for orientation and shear stress.

Author Contributions

Conceptualization, W.Z.; methodology, M.H.; software, M.H. and W.C.; validation, C.L.; formal analysis, W.Z.; investigation, W.C.; resources, W.Z.; data curation, C.L.; writing—original draft preparation, M.H.; writing—review and editing, W.Z.; visualization, M.H. and C.L.; supervision, W.C.; project administration, W.Z.; funding acquisition, W.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Natural Science Foundation of Hunan Province (2020JJ4584).

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

Author Chunliang Li was employed by the company Hunan Aerospace Chengyuan Precision Machinery Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. (a) A 3D view of polycrystalline γ-TiAl models; (b) schematic diagram of tensile loading, and the atomic color represents the coordination number.
Figure 1. (a) A 3D view of polycrystalline γ-TiAl models; (b) schematic diagram of tensile loading, and the atomic color represents the coordination number.
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Figure 2. Engineering stress–strain curve of polycrystalline γ-TiAl with grain sizes of 6.18 nm at different strain rates (1 K).
Figure 2. Engineering stress–strain curve of polycrystalline γ-TiAl with grain sizes of 6.18 nm at different strain rates (1 K).
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Figure 3. Engineering stress–strain curve of polycrystalline γ-TiAl with different grain sizes (1 K, 1 × 109 s−1), and the strains at the four points A to D on the curve are 0, 0.040, 0.070 and 0.125, respectively.
Figure 3. Engineering stress–strain curve of polycrystalline γ-TiAl with different grain sizes (1 K, 1 × 109 s−1), and the strains at the four points A to D on the curve are 0, 0.040, 0.070 and 0.125, respectively.
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Figure 4. (a1–d1) Atomic configuration and (a2–d2) corresponding atomic shear stress distribution in tensile deformation of γ-TiAl polycrystal with an average grain size of 6.18 nm. (a1,a2) ε = 0; (b1,b2) ε = 0.040; (c1,c2) ε = 0.070; (d1,d2) ε = 0.125 (projected in the direction [001]. In (a1–d1), the yellow atoms indicate that the coordination number is 12, and the other colors atoms indicate that the coordination number is not 12. The atomic colors in (a2–d2) indicate stress values (unit: GPa)) (1 K, 1 × 109 s−1).
Figure 4. (a1–d1) Atomic configuration and (a2–d2) corresponding atomic shear stress distribution in tensile deformation of γ-TiAl polycrystal with an average grain size of 6.18 nm. (a1,a2) ε = 0; (b1,b2) ε = 0.040; (c1,c2) ε = 0.070; (d1,d2) ε = 0.125 (projected in the direction [001]. In (a1–d1), the yellow atoms indicate that the coordination number is 12, and the other colors atoms indicate that the coordination number is not 12. The atomic colors in (a2–d2) indicate stress values (unit: GPa)) (1 K, 1 × 109 s−1).
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Figure 5. Microscopic atomic configurations of dislocation emission and slip under different strains during the tensile deformation of polycrystalline γ-TiAl (Projected in the direction [001], the green atoms indicate that the coordination number is 12, and the other colors atoms indicate that the coordination number is not 12).
Figure 5. Microscopic atomic configurations of dislocation emission and slip under different strains during the tensile deformation of polycrystalline γ-TiAl (Projected in the direction [001], the green atoms indicate that the coordination number is 12, and the other colors atoms indicate that the coordination number is not 12).
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Table 1. Comparison of rotation angles of grain 1–5 (clockwise/anticlockwise refers to the direction in which the grain rotates in the X-Y plane).
Table 1. Comparison of rotation angles of grain 1–5 (clockwise/anticlockwise refers to the direction in which the grain rotates in the X-Y plane).
StrainGrain 1Grain 2Grain 3Grain 4Grain 5
0–0.040
(A-B)		Clockwise 2.50°Anticlockwise 2.01°Clockwise 0.90°Anticlockwise 2.02°Clockwise 0.40°
0.040–0.070
(B-C)		Clockwise 2.10°Anticlockwise 2.42°Clockwise 0.49°Anticlockwise 2.98°Clockwise 0.53°
0.070–0.125
(C-D)		Clockwise 3.16°Anticlockwise 3.14°Clockwise 0.55°Anticlockwise 2.54°Clockwise 0.48°
0–0.125
(A-D)		Clockwise 7.76°Anticlockwise 7.57°Clockwise 1.94°Anticlockwise 7.54°Clockwise 1.41°
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Zhao, W.; He, M.; Li, C.; Chen, W. Study on Grain Boundary Mechanical Behaviors of Polycrystalline γ-TiAl Using Molecular Dynamics Simulations. Metals 2024, 14, 779. https://doi.org/10.3390/met14070779

AMA Style

Zhao W, He M, Li C, Chen W. Study on Grain Boundary Mechanical Behaviors of Polycrystalline γ-TiAl Using Molecular Dynamics Simulations. Metals. 2024; 14(7):779. https://doi.org/10.3390/met14070779

Chicago/Turabian Style

Zhao, Wenjuan, Maoqing He, Chunliang Li, and Wei Chen. 2024. "Study on Grain Boundary Mechanical Behaviors of Polycrystalline γ-TiAl Using Molecular Dynamics Simulations" Metals 14, no. 7: 779. https://doi.org/10.3390/met14070779

APA Style

Zhao, W., He, M., Li, C., & Chen, W. (2024). Study on Grain Boundary Mechanical Behaviors of Polycrystalline γ-TiAl Using Molecular Dynamics Simulations. Metals, 14(7), 779. https://doi.org/10.3390/met14070779

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