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Article

Atomistic Investigation of the Effects of Different Reinforcements on Al Matrix Composite

by
Yongchao Zhu
1,*,
Na Li
2,
Lan Zhang
2,
Jidong Zhang
2,
Liwei Niu
1,
Wei Li
1 and
Songtao Li
1
1
Department of Railway Engineering, Zhengzhou Railway Vocational and Technical College, Zhengzhou 451460, China
2
School of Mechanics and Engineering Science, Zhengzhou University, Zhengzhou 450001, China
*
Author to whom correspondence should be addressed.
Metals 2022, 12(8), 1252; https://doi.org/10.3390/met12081252
Submission received: 19 May 2022 / Revised: 22 July 2022 / Accepted: 22 July 2022 / Published: 26 July 2022
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Abstract

:
In this work, we studied the effects of different reinforcements on a metal matrix composite (MMC) using molecular dynamics (MD) simulations, where graphene was chosen as the two-dimensional (2D) material and diamond was selected as the three-dimensional (3D) material. Sintering and tensile processes were conducted on the MMC models containing reinforcements of various sizes, and the effects of reinforcements with the same surface area were compared. The results indicated that the 2D material was more beneficial for sintering at the heating stage, producing a higher-density structure. The volume of Al atoms fell from 752 to 736 nm3 as the graphene size in the composite system increased. However, a slight increase from 749 to 755 nm3 was observed when the diamond radius was small. Converted to relevant metrics in the experiments, the density of the composite reached 2.84 g/cc with a 3.3 wt.% addition of single-layer graphene (SLG) and 2.87 g/cc with a 15.4 wt.% addition of diamond, and the results were slightly higher than the experimental reports. Both SLG and diamond could reduce the number of arranged Al atoms from 43,550 to approximately 35,000, and bilayer graphene (BLG) with the largest size could further decrease the number of arranged atoms to nearly 30,000, implying that grain refinement could be obtained by increasing the surface area of reinforcements. Considering the scale of these models, the reinforcement size and pore location in the initial structures were deemed to have an impact on the mechanical properties. The composite with the largest proportion of SLG showed an increase of more than 1.6 GPa in tensile strength; however, BLG showed a significant drop of 1.9 GPa when stretched in the normal direction, as the large interlayer space acted as a large hole in tension. The diamond size did not appear to affect the strengthening effects. Nevertheless, the elongation values of composites with graphene were generally 35% higher than the Al-diamond composites.

1. Introduction

The preparation of advanced composite materials is a scientific research hot spot. Specifically, metal matrix composite (MMC) materials exhibit a superior wear resistance, a high specific strength, and a good dimensional stability. Hence, many efforts have been made to investigate various reinforcements to improve the properties of MMCs. Recently, more emphasis has been placed on the preparation of Al matrix composite with Al2O3, SiC, or B4C particles using powder metallurgical processing [1,2,3].
Generally, it is believed that the addition of three-dimensional (3D) ceramic nanoparticles can improve the mechanical properties of composites by increasing the dislocation density, diminishing the grain size, and slowing down the propagation of cracks. Sharma et al. prepared Al–Si3N4 composites by a conventional stir casting route, which improved the ultimate tensile strength by 25% [4]. Kumar et al. fabricated Al6O63–Si3N4 composites by following the stir casting method of the liquid metallurgy technique, displaying an increase of approximately 90% in tensile strength with a 10% addition of reinforcement [5]. Chu et al. investigated the structures of Al-diamond composites fabricated by spark plasma sintering, indicating that the reinforcement with a smaller size was helpful in increasing the density [6]. Wang et al. studied the mechanical properties of Al-SiC composites prepared by powder metallurgy combined with hot extrusion and found that a 0.5 vol.% of SiC resulted in a 10% increase in ultimate tensile strength [7].
Furthermore, two-dimensional (2D) reinforcements such as graphene have also been widely studied to promote the properties of MMCs, which have shown to be more effective [8]. Yang et al. studied Al-graphene composites prepared by the pressure infiltration method, which showed an increase in tensile strength of 45% after the addition of only 0.54 wt.% graphene nanoplates [9]. Shin et al. produced Al2024-graphene composites by ball milling and hot rolling, and the tensile strength of the composite containing a 0.7 vol.% of graphene was two times higher than that of monolithic Al2024 [10]. Wang et al. sintered Al–graphene composites under 40 MPa of pressure, showing an increase of 30.6% in tensile strength when the graphene content was 0.5 wt.% [11]. In general, the optimal amount of graphene was less than 1 wt.%, while the addition of up to a 20 wt.% 3D reinforcement could sustainably improve the properties of the MMC, and the strengthening mechanism of the 2D nanosheets was generally considered the same as the role of 3D nanoparticles [12,13]. Thus, it has been typically argued that 2D reinforcement is more advantageous for mechanical properties.
MMCs with excellent properties can be also prepared with one-dimensional (1D) reinforcements such as carbon nanotubes (CNTs). Jiang et al. produced a 2 vol.% CNT-reinforced Al composite by flake powder metallurgy, with a tensile stress of 435 MPa, which was almost two times higher than the unreinforced Al matrix [14]. Kwon et al. achieved a 300% increase in tensile strength by adding just 1 vol.% of CNTs to the Al matrix [15]. Esawi et al. observed a tensile strength increase of up to 50% in an Al–CNT composite containing 2 wt.% CNTs [16]. However, there has been no reasonable comparison of the enhanced effects between 1D, 2D, and 3D materials because the problems of homogeneous dispersion, quantity control, and size control have been difficult to adequately control using currently available experimental methods. A comparison can only be provided for the actual performance of composites with the same reinforcement content, regardless of the disparity in particle size. For example, Shin et al. found that an increment in yield stress versus a reinforcement volume fraction for FLG was 3.5 times higher than that of CNTs, but FLG had a specific surface area that was 12.8 times larger per volume than CNTs [17]. Meysam et al. synthesized 1 wt.% graphene- and 5 wt.% Al2O3-reinforced Al composites with an average particle size of 47 nm and average platelet diameter of 5 μm [18]. Therefore, it has been difficult to study the effects of different reinforcements precisely through experimental methods. Nevertheless, a comparison between the different types of reinforcements is helpful for experimentalists to select reinforcing agents, especially for nano MMCs, and the strengthening mechanisms should be further studied for comparison.
Molecular dynamics (MD) simulations offer a promising approach for conducting a comparison between different reinforcements and have been widely used for the monitoring of the structural evolution in the loading or heating processes. Srivastava et al. and Silvestre et al. analyzed graphene and CNTs separately embedded in Al bulk under a compressive strain rate and found that the compressive strength of the nanocomposite material was substantially larger than that of pure Al [19,20]. Choi et al. investigated the mechanical behavior of Al–CNT composites, which showed that CNTs with a larger pipe diameter led to a greater yield stress [21]. Han et al. gained insights into the interaction mechanism between dislocation and graphene in graphene/aluminum composites, finding that the hardness of the composites decreased when the lateral gap between the graphene sheets increased [22]. Kumar et al. observed the Al–graphene interface after a cooling process and found that Al atoms were organized in the {111} facet of the face-centered cubic structure [23]. He et al. simulated the sintering process of Al–graphene systems, and the mechanical properties of the sintered composites were greatly increased with the addition of graphene [24]. Huo et al. modeled the sintering process of Al–SiC composites, and a significant enhancement in the strength was found with finer SiC particles [25]. However, a comparison between the different patterns of reinforcements has not been made in these models, let alone the rationality of comparison.
In this study, we designed models for powder sintering to discuss the influence of graphene and diamond in Al matrix composites, which were compared on the same surface areas of the reinforcements, as the function of the reinforced phase was achieved through the interface to affect the motion and arrangement of metal atoms [26]. As the model of the metal–CNT composite was built in [20], CNTs with the same surface area would be very long for achieving a large length–diameter ratio that was even as high as 375 in experiments [16], forming a cuboid structure with a very long side. Thus, 1D materials were not assessed in the models in this study, where composites with a cubic structure were sintered. Then, structural analysis and tensile measurements were performed on the composite models after the same sintering process, to reveal the differences in strengthening effects between the 2D and 3D materials.

2. Model Methods

The powder metallurgy method has the most important advantages of a low processing temperature and the ability to incorporate high volume fractions of reinforcements [7]. The reinforcing phases could be well mixed with the metal powders by various dispersing technologies such as ultrasonic dispersion and ball-milling. Then, the mixed powder was condensed by cold or hot extrusion combined with the sintering process, which was assisted by an electromagnetic field and spark plasma. During the sintering step, the metal particles became gradually bonded through plastic deformation and material transfer under the drive of temperature and pressure. To gain insight into the role of reinforcements in MMCs, an initial model of an Al matrix composite was employed for modeling the sintering process by MD simulations, where graphene served as a 2D reinforced phase or diamond acted as a 3D reinforced phase. As shown in Figure 1, the models consisted of eight spherical Al nanoparticles with a radius of 28 Å, where the adjacent Al particles were 2 Å apart from each other, and a square nanoplatelet of graphene held the center of the models as well as a spherical diamond. Of note, the surface area of the reinforcements was chosen as the key variable in this study to ensure the rationality of comparison between the 2D and 3D reinforced phases. The side lengths (ls) of the graphene sheets, including both single-layer graphene (SLG) and bilayer graphene (BLG), ranged from 32 Å to 96 Å, while the radius (R) values of the diamond particles changed from 8 Å to 28 Å, and the other characteristic parameters of these reinforcements are presented in Table 1.
All models were taken as the representative volume elements (RVE) inside the composite systems by applying the periodic boundary condition (PBC) box in the three dimensions of the global simulations. Before sintering, the isothermal–isobaric (NPT) ensemble was adopted to relax the system at 300 K and 1 atm, which updated the position and velocity of the atoms to control the temperature and pressure with volume changes. The relaxation process lasted for 100 ps, causing the Al particles to gather, wrapping the graphene nanoplatelets or diamond particles. Subsequently, the integrated structure was sintered in three stages under the NPT ensemble, and every stage was held for 300 ps. First, the temperature was heated from 300 K to 773 K, while external pressure was applied from 1 atm to 500 atm (50 MPa). Then, the system maintained the temperature and pressure. Finally, the conditions of the simulation were returned to 300 K and 1 atm after a cooling stage. All of the parameter settings mentioned above, such as the heating and cooling rates, were based on similar modeling studies [23,27].
To explore the effects of different reinforcements on the mechanical behavior, the tensile process was used for the sintered RVEs. By separately changing the shapes of the simulation boxes in both the plane and normal directions, quasi-static tension was operated under the NVE ensemble, while the temperature was reset by explicitly rescaling the velocities.
In all MD simulations, the eam potential was applied to the interactions between the Al atoms [28], which was comprised of the embedding energy that was a function of the atomic electron density and pair potential interactions. The tersoff potential was used to link the carbon atoms in graphene or diamond [29], which consisted of two and three body interaction terms, and has been commonly applied in the simulations of carbon materials [30,31]. Al–C interactions used the style of the morse potential [32], which consisted of a pair potential obtained by curve fitting of the ab initio data, and this potential was expected to be more suitable for modeling the interface [33]. The velocity Verlet algorithm was used to solve Newton’s equations of motion and the time step was set to 1.0 femtosecond. All MD simulations in this study were carried out by LAMMPS, where the potential file was obtained from the LAMMPS library. The generated data from the simulations were visualized using VMD software.

3. Results and Discussion

3.1. Effects of Different Reinforcements on the Sintered Structure

MD simulations were employed to investigate the sintering process in powder metallurgy, and structural evolutions were discussed in depth by observing the atomic configuration, analyzing the lattice structure, and computing the radial distribution function. Thus, the emphasis of this study was on identifying the disparity in the results, which arose from different reinforcements in the Al matrix composites. To facilitate comparison, only the models containing different reinforcements with the largest sizes were used to observe changes in the atomic structures, and the surface areas of the two reinforcements were fairly similar. As shown in Figure 2, the sintering processes of the composite systems were visualized to monitor the changes in the surface morphologies. In the beginning, the surface energy was sufficient to form a sintering neck in both systems after the systems were relaxed. However, atomic migration appeared more clearly on the Al particles around graphene because the interspace of the Al particles was not fully filled by the 2D reinforcements; thus, the plastic deformation of the Al particles was not restricted in space. As the sintering process started, Al atoms could migrate a larger distance under the action of thermal energy, pores that arose from the interspace of the Al particles grew smaller, and the system volume decreased rapidly in the heating stage. When the temperature and pressure were kept constant, the system volume became stable in a short time, and a slight drop in volume appeared with cold shrinkage in the cooling stage. Lastly, there were no significant differences between the sintered systems in appearance, which became a densified bulk. However, as indicated in Figure 2c, graphene was more favorable for sintering because the volume curve of Al–SLG fell faster in the early stage. The densification of the composite systems mainly finished during the constant temperature and pressure stage, and the sintered structures were finally achieved after cold shrinkage.
To obtain deeper insight into the effects of different reinforcements on sintered structures, more models with reinforced particles of various sizes were obtained and the volumes of Al in the composites were determined. Based on Figure 3a, the sintered structure of the pure Al system occupied a volume of 760 nm3, the Al volume with the same number of atoms in the Al–SLG composite decreased from 752 nm3 to 736 nm3, and BLG decreased the Al volume as well. However, the Al volume in the Al–diamond system increased from 749 nm3 to 755 nm3, and then finally decreased to 740 nm3. It should be noted that the singularity marked by the yellow circle was ascribed to the rolled graphene. Thus, we could determine that the growing size of the graphene could promote the densification of Al atoms, and the Al structures would be more compact only if the diamond was sufficiently large. Overall, this suggested that the 2D materials were more beneficial than the 3D materials in compressing the Al structures at the same surface area values. This conclusion could be drawn again by the changes in the pore volumes, as depicted in Figure 3b, which exactly matched the curves of the Al volumes, except for the point labeled by a green circle, where the increase in pore volume was attributed to the interlayer space of BLG with the largest size. Moreover, the total volume of the composites could be computed and the densities could be calculated, as shown in Figure S1. The density of the composite with a 3.3 wt.% SLG addition was as high as 2.84 g/cc, while the density of the composite with a 15.4 wt.% diamond addition was up to 2.87 g/cc. In general, the density values of the composites in the models were only slightly (0.02 to 0.05 g/cc) higher than most experimental results [4,5,15], where the composite densities increased with an increasing weight percentage of the reinforcement that was greater than 1%, and graphene could give rise to a faster increase in density. However, a high BLG content possibly led to a slight drop in density, which was in accordance with the increase in pore volume stage.
To directly show the inner structures sintered with different reinforcements, the local lattice disorder was determined on the basis of the centro-symmetry parameter (CSP) analysis. Al atoms with a bulk lattice were colored in blue, where the atoms on the surface were painted in red, implying internal pores, and defects such as atoms in dislocations or grain boundaries were tinted in green. As shown in Figure 4a–d, pores could be easily found in the pure Al structure, and fewer pores appeared in the Al–diamond system, while there were no visible pores in the Al–graphene models. Furthermore, a large area containing a perfect lattice was observed in the sintered structure; however, the arrangements of Al atoms around the reinforcements were heavily disturbed, due to lattice mismatch. Quantitative analysis was conducted by the common neighbor analysis (CNA) method to count the number of atoms arranged in a perfect lattice, which included atoms in both a face-centered cubic (f.c.c.) order and a hexagonal close-packed (h.c.p.) order. As depicted in Figure 4e, a pure Al structure had 43,550 atoms in a perfect lattice, which decreased to 34,381 with an increasing size of the SLG and further dropped to 30,273 with an increasing size of the BLG. Of note, the diamond appeared to have a similar influence on the Al arrangement, compared to SLG at the same surface area value. To a certain extent, we could conclude that the grain refinement caused by the reinforcements was mainly determined by their surface areas, where BLG was possibly more conducive to the reduction of grain size. Moreover, Figure 4e was redrawn as a function of the weight percentage in Figure S2, which indicated that the increase in graphene content could prepare composites with smaller metal grains. Thus, it was safely suggested that MMCs with finer grains could be prepared by the addition of reinforcement with a larger size, especially larger 2D sheets. Thus, the size of the reinforcement should be taken into account, as an excessive number of nanoparticles added to a composite will lead to serious agglomeration.

3.2. Effects of Different Reinforcements on Tensile Properties

Commonly, it has been believed that the improvement in the mechanical properties of MMCs can be attributed to the grain refinement and high density of dislocations, as verified in studies with a variety of reinforcements [4,5,6,7,8,9,10,11,12,13]. In this work, uniaxial tensile simulations were performed to compare the effects of 2D and 3D materials on tensile properties. Every sintered RVE was stretched along the Y and Z axes. Then, CSP analysis of the Al atoms was used again to trace the changes of the inner structure, and the atomic configurations under maximum stress are detailed in Figure 5. As expected, the dislocations piled up during the tensile process, and the green belts around graphene and diamond were obviously enlarged. With dislocation motion, the inner pores grew quickly, compared to the details in Figure 4. Furthermore, the interlayer space of BLG was also identified as a pore. However, the Al–SLG system appeared to be more stable because no pores were visible in the initial structure. Finally, the pores formed a crack propagating along the interface between Al and the reinforcements, as shown by the stress–strain curves in Figure 6c,d. Therefore, we maintained that the pores played a very crucial role in the tensile process.
To confirm the findings of the strengthening mechanism, the stress changes of all models were drawn, as shown in Figure 6, which were slightly (1.0 to 1.5 GPa) lower than the similar models of the Al–SiC system on a larger scale [25]. Of note, the grain refinement was possibly not in favor of improving the tensile strength on the scale of the simulations [34,35], and only a piece of reinforcement in the RVE could not hinder development of the pores away from the reinforcements. Therefore, there was no clear law in most results. For example, the addition of diamonds with various sizes appeared to make no clear difference in the tensile strength, which fluctuated in the range from 5.0 to 5.6 GPa. Unsurprisingly, the largest pore was found in the lowest point, as indicated by the yellow circle in Figure 6a, and as discussed above. However, we determined that the composite containing a square SLG with 96 Å on each side had the best mechanical properties, with improvements in tensile strength of 6.6 GPa and 6.9 GPa, respectively, in the Y and Z directions, as marked by the green circle where graphene nearly covered the entire section. Although BLG gave rise to a similar effect as SLG on the tensile properties along the Y axis, the large pores led to a clear reduction in the tensile stress of the composite containing BLG with a large size. However, the stress curve of the Al–BLG system that stretched along the Z axis presented a certain rule due to the different paths of the cracks. The pores near BLG with a small size led to a crack along the side of graphene, while the interlayer space of BLG with a large size gave rise to a crack between the graphene layers, as circled in Figure 6b, where the tensile strength dropped to 3.1 GPa. Furthermore, the composites with graphene displayed an advantage in ductility, which was approximately 35% higher than the Al–diamond composite for elongation at failure. This was because most ceramic particles will lead to a reduction in ductility [4,5,6,7] under elongation, while graphene will result in a slight increase during elongation [10]. Based on Figure S3a,b, which depicted the changes in stress as a function of weight percentage, there was a big difference from the experimental studies, where an apparent increase in tensile stress could be observed with the increasing addition of reinforcement. Because the increase in reinforcement content here was due to the increase in size rather than in quantity, the changes of tensile stress were irregular, particularly at small sizes. Thus, we assumed that SLG with a sufficiently large size could increase the tensile strength, while the composite with BLG exhibited directivity in mechanical properties, and the 3D particle size appeared to have no obvious influence on direct enhancement.
Therefore, based upon the results from the MD simulations, it can be preliminarily suggested that increasing the reinforcement size offers a promising way to produce MMCs with finer grains and a higher density, especially when the excessive addition of reinforcement particles will lead to serious agglomeration. If only the direct effect of the reinforcement is considered, increasing the 3D nanoparticle size may not be beneficial for tensile strength, and 2D nanosheets with a larger size may be able to improve mechanical performance. However, multilayer 2D nanosheets may lead to a decrease in tensile properties perpendicular to the nanosheet.

4. Conclusions

MD simulations of the sintering and tensile processes were employed to study the effects of different reinforcements on MMCs. Graphene was more beneficial for sintering than diamond in the heating stage. An increase in graphene size could promote the densification of Al atoms, and the volume decreased from 752 to 736 nm3, while the small-sized diamond was unable to improve the density clearly, with a slight increase from 749 to 755 nm3. In general, 2D materials may help to achieve a more compact structure at the same surface area value compared to 3D materials. Under ideal conditions in models, the density of a composite with a 3.3 wt.% addition of SLG was as high as 2.84 g/cc, while the density of the composite with a 15.4 wt.% diamond addition was up to 2.87 g/cc, and the results were slightly higher than the experimental reports. The arrangement of Al atoms was also largely affected by the growing surface area of reinforcements, which could reduce the number of the arranged Al atoms from 43,550 to the minimum of 30,000, implying a decrease in the grain size. Considering the model scale, the size of the reinforcement and the location of the initial pores were regarded as a major influence on the mechanical properties. SLG with a sufficiently large size could truly produce an increase of at least 1.6 GPa in the tensile strength, and BLG could lead to a significant drop of 1.9 GPa when stretched in the normal direction. However, the diamond size appeared to have no clear effects on strengthening. In addition, the ductility of the composites was improved by graphene, with an increase in elongation of approximately 35%.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/met12081252/s1, Figure S1: Calculated density as a function of the weight percentage of reinforcement. Figure S2: Total number of Al atoms arranged in the face-centered cubic (f.c.c.) and hexagonal close-packed (h.c.p.) lattices as a function of weight percentage of reinforcement. Figure S3: Tensile strength as a function of the weight percentage of reinforcement in the different systems, which were separately stretched in the (a) Y direction and (b) Z direction.

Author Contributions

Conceptualization, Y.Z.; formal analysis, N.L.; investigation, J.Z.; resources, S.L.; writing—original draft preparation, L.N.; writing—review and editing, Y.Z.; supervision, L.Z.; project administration, W.L. All authors have read and agreed to the published version of the manuscript.

Funding

This work was funded by the key scientific research projects of colleges and universities in Henan Province, 21B560018.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Details of the atomistic models: (a) Al–graphene system; (b) Al–diamond system.
Figure 1. Details of the atomistic models: (a) Al–graphene system; (b) Al–diamond system.
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Figure 2. Atomic configurations of the composite systems containing (a) a square single-layer graphene (SLG) with ls = 96 Å and (b) a diamond with R = 28 Å at different sintering times; (c) volumes of the composite systems as a function of sintering time.
Figure 2. Atomic configurations of the composite systems containing (a) a square single-layer graphene (SLG) with ls = 96 Å and (b) a diamond with R = 28 Å at different sintering times; (c) volumes of the composite systems as a function of sintering time.
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Figure 3. Al (a) and pore volumes (b) as a function of the surface areas of the different systems.
Figure 3. Al (a) and pore volumes (b) as a function of the surface areas of the different systems.
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Figure 4. Inner structures of different systems containing (a) no reinforcement, (b) a square single-layer graphene (SLG) with ls = 96 Å, (c) a square bilayer graphene (BLG) with ls = 96 Å, and (d) a diamond with R = 28 Å. Atoms in (a–d) are colored according to centro-symmetry parameter (CSP) values; (e) the total number of Al atoms arranged in f.c.c. and h.c.p. lattices as a function of surface area.
Figure 4. Inner structures of different systems containing (a) no reinforcement, (b) a square single-layer graphene (SLG) with ls = 96 Å, (c) a square bilayer graphene (BLG) with ls = 96 Å, and (d) a diamond with R = 28 Å. Atoms in (a–d) are colored according to centro-symmetry parameter (CSP) values; (e) the total number of Al atoms arranged in f.c.c. and h.c.p. lattices as a function of surface area.
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Figure 5. Inner structures under maximum stress in the tensile process of different systems containing (a) no reinforcement, (b) a square single-layer graphene (SLG) with ls = 96 Å, (c) a square bilayer graphene (BLG) with ls = 96 Å, and (d) a diamond with R = 28 Å. Atoms in (a–d) are colored according to centro-symmetry parameter (CSP) values, and the arrows indicate the tensile directions.
Figure 5. Inner structures under maximum stress in the tensile process of different systems containing (a) no reinforcement, (b) a square single-layer graphene (SLG) with ls = 96 Å, (c) a square bilayer graphene (BLG) with ls = 96 Å, and (d) a diamond with R = 28 Å. Atoms in (a–d) are colored according to centro-symmetry parameter (CSP) values, and the arrows indicate the tensile directions.
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Figure 6. Tensile strength as a function of the surface area of different systems stretched in (a) the Y direction and (b) the Z direction; The stress–strain curves of sintered models containing single-layer graphene (SLG), bilayer graphene (BLG), and diamond with the largest sizes, which are stretched separately in (c) the Y direction and (d) the Z direction.
Figure 6. Tensile strength as a function of the surface area of different systems stretched in (a) the Y direction and (b) the Z direction; The stress–strain curves of sintered models containing single-layer graphene (SLG), bilayer graphene (BLG), and diamond with the largest sizes, which are stretched separately in (c) the Y direction and (d) the Z direction.
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Table
Table 1. Characteristic parameters of the reinforcements.
Table 1. Characteristic parameters of the reinforcements.
GrapheneDiamond
Side Length
(Å)		Surface Area
(Å2)		Content a
(wt.%)		Radius
(Å)		Surface Area
(Å2)		Content
(wt.%)
3210240.3688040.34
4823040.831218091.23
6440961.501632152.87
8064002.282050245.62
9692163.262472359.66
///28984715.41
a Graphene content was calculated according to single-layer graphene (SLG), and bilayer graphene (BLG) content should be doubled.
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Zhu, Y.; Li, N.; Zhang, L.; Zhang, J.; Niu, L.; Li, W.; Li, S. Atomistic Investigation of the Effects of Different Reinforcements on Al Matrix Composite. Metals 2022, 12, 1252. https://doi.org/10.3390/met12081252

AMA Style

Zhu Y, Li N, Zhang L, Zhang J, Niu L, Li W, Li S. Atomistic Investigation of the Effects of Different Reinforcements on Al Matrix Composite. Metals. 2022; 12(8):1252. https://doi.org/10.3390/met12081252

Chicago/Turabian Style

Zhu, Yongchao, Na Li, Lan Zhang, Jidong Zhang, Liwei Niu, Wei Li, and Songtao Li. 2022. "Atomistic Investigation of the Effects of Different Reinforcements on Al Matrix Composite" Metals 12, no. 8: 1252. https://doi.org/10.3390/met12081252

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