Effect of Graphene Particle Diameter on Mechanical Properties of Graphene Composite Material

In order to improve the mechanical properties of alloys and broaden their application fields, high-performance metal matric composites have received more and more attention. Graphene has excellent mechanical properties and is often used as a reinforcing phase for various composite materials. However, as the reinforcing phase of the composite, the number, shape, and size of graphene have a significant effect on the overall mechanical properties of the composites. Therefore, the influence of graphene particle diameter on the mechanical properties of graphene particle reinforced metal matrix composites was studied in this paper. By establishing a series of finite element models, we simulated the mechanical behaviour of composite materials under static tension loading. The relationship between graphene particle diameter and material mechanical properties is revealed.


Introduction
Composite is the combination of two or more materials which have different phases and the properties superior to the base material.Metal matrix composites (MMCs) are composite materials with a metal matrix as the main structure and ceramic or carbon materials as the reinforcement.MMCs have high strength, enhanced mechanical properties, excellent thermal properties, and ease of forming.Therefore, MMCs are widely used in various fields [1,2,3].
Magnesium (Mg) and its alloys are the lightest structural materials with the density of 1.74 g/cm3.Due to their low density, high specific strength, good castability, and high damping capacity, Mg alloys continue to show promise for structural applications in the automotive and aviation sectors [4,5].In order to further improve the properties of the material, the composite material with the matrix of magnesium alloy and the reinforcement phase of graphene nanoparticles expands the application range of magnesium by improving the strength.In addition, Magnesium based composite materials also have advantages in the manufacturing process.the process involving the synthesis of reinforcement during the composite development (in-situ process) shows improved properties because of a clean reinforcement-matrix interface, thermally stable reinforcement, and better wettability [6].Therefore, magnesium matrix composites have attracted great attention among a variety of MMCs.
In order to investigate the effect of composite structure on its properties, finite element simulation is a commonly method for predicting the mechanical properties.For example, Gao et al [7] used finite element simulation to calculate the influence of random orientation of graphene sheets on strength.Deshpande et al [8] established a new multi-scale process modeling method to accurately predict residual stresses in a unidirectional carbon fiber/epoxy composite and their effect on the strength of composite materials.Therefore, in this paper, we used finite element simulation to build a series of models of graphenereinforced magnesium matrix composites and explored the effect of the diameter of graphene particles on the mechanical properties of the composites.

Finite Element Model
The finite element model (FEM) aimed to simulate the mechanical behaviour of composite materials, has been developed by means of ABAQUS 6.11.The graphene particles are evenly distributed in the composite.In order to simplify the model and reduce the workload, we select a square section containing the largest cross-section of 9 graphene particles.The model of Graphene Composites (MGC) is shown in Figure 1.The side lengths of the squares are uniform at 1500 nm.Six different models were set up, where the diameter of the graphene particles varied between 5nm and 30nm.The volume fraction of graphene in the MGC also varied with the diameter.The particle diameters and corresponding volume fractions in the six finite element models are shown in Table 1.At the same time, each model is stretched by 10% of the tensile strain to observe the effect of particle diameter on the stress state of MGC under the same deformation loading.
In the FEM, the Poisson ratio of graphene particles is 0.16 and the elastic modulus is 1000GPa [9].The Poisson ratio of magnesium alloy ZK60 is 0.3 and the elastic modulus is 50GPa.The contact mode between graphene particles and matrix is tied.

Simulated Results
The simulation results of finite element method are as follows: Figure 2 shows the stress distribution of six types of MGCS.The Mises stress in graphene particles is greater than that in ZK60 matrix.It can be clearly observed that in these models, the Mises stress distribution in the graphene particles is relatively uniform.The stress in the matrix is concentrated in the area between adjacent graphene particles along the tensile direction.This stress concentration phenomenon is more significant when the particle diameter is larger.increasing particle size.In order to reveal the relationship between the Mises stress distribution in MGC and the graphene particle diameter, the variations of Mises stress with particle size are shown in Figure 3,4 based on the finite element simulation results.The two curves in Figure 3 show the range of Mises stress values inside the magnesium alloy matrix and inside the graphene particles, respectively.In the matrix, the range of Mises stress values increases with the increase of the diameter of the graphene particles.The increase in the range of stress values indicates that the stress distribution is more uneven, that is, the stress is more concentrated in some areas of the matrix structure.This leads to a decrease in the strain that the material can withstand as a whole in practice.Similarly, in graphene particles, the range of stress is also larger when the particle diameter is larger.Although the strength of graphene is so high that it is not necessary to consider the effect of stress concentration on the graphene particles, the uneven distribution of stress inside the particles with the increasing particle diameter means that a part of the graphene material is subjected to relatively small loads.Therefore, it is a waste of the excellent mechanical properties of the graphene material.
It is shown in Figure 4 that the difference (D-value) between the maximum Mises stress in the graphene particles and the magnesium alloy matrix decreases with the increasing particle size.This difference is large when the particle diameter is small, and significantly smaller when the particle diameter is large.The difference reflects the strengthening effect of graphene particles.When the Dvalue is small, the maximum stress of the matrix is close to that of the particles.In such a structure with small D-value, the matrix with lower strength is subjected to excessive stress.On the contrary, the large difference indicates that the stress is concentrated in the graphene particles with high strength.The MGCs with large D-value can better play the strengthening role of graphene particles.Therefore, the reduction of particle diameter is more conducive to exerting the strengthening effect of graphene particles on the composite material and reducing the load of the matrix material.These results in Figure 4 are consistent with these in Figure 3.

Summary
The stress in magnesium matrix composites reinforced by graphene particles was calculated by finite element analysis.The distribution of Mises stress in the composites varies with the particle size.With the increase of graphene particle diameter, the stress range in the magnesium alloy matrix is larger, the stress distribution becomes nonuniform, and the maximum stress in the matrix begins to approach the maximum stress in the graphene particles.The results show that the Mises stress distribution in the matrix is increased and the strength of the composite is decreased with the increase of the diameter of the graphene particles.In addition, the large particle diameter could cause the uneven distribution of Mises stress inside the graphene particles.

Figure 2 .
Figure 2. Results of finite element simulation with different particle sizes: (a) Particle diameter 5 nm; (b) Particle diameter 10 nm; (c) Particle diameter 15 nm; (d) Particle diameter 20 nm; (e) Particle diameter 25 nm; (f) Particle diameter 30 nm.Figure2shows the stress distribution of six types of MGCS.The Mises stress in graphene particles is greater than that in ZK60 matrix.It can be clearly observed that in these models, the Mises stress distribution in the graphene particles is relatively uniform.The stress in the matrix is concentrated in the area between adjacent graphene particles along the tensile direction.This stress concentration phenomenon is more significant when the particle diameter is larger.

Figure 3 . 4 .
Figure 3. Variation of stress range with the Figure 4. Variation of D-value with the increasing particle size.increasingparticle size.In order to reveal the relationship between the Mises stress distribution in MGC and the graphene particle diameter, the variations of Mises stress with particle size are shown in Figure3,4 based on the finite element simulation results.The two curves in Figure3show the range of Mises stress values inside the magnesium alloy matrix and inside the graphene particles, respectively.In the matrix, the range of Mises stress values increases with the increase of the diameter of the graphene particles.The increase in the range of stress values indicates that the stress distribution is more uneven, that is, the stress is more concentrated in some areas of the matrix structure.This leads to a decrease in the strain

Table 1 .
Particle diameters and volume fraction in finite element models.