Bending properties of graphene/Al layered beams under transverse and longitudinal loads
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摘要: 采用分子动力学(MD)方法模拟了石墨烯(GNs)/Al层状梁在横向荷载和纵向压缩下的弯曲变形，探究了层状梁弯曲特性的影响因素。从横向荷载下的弯曲结果可见，由于层间作用的影响，层状梁的弯曲刚度随着GNs层数的增加而不断降低。GNs/Al层状梁的弯曲机制并非由GNs和Al组分特性的简单相加，这使经典连续力学难以适用于高各向异性的层状材料中。在单轴纵向压缩中，GNs使细长的层状梁在塑性变形前更易发生屈曲行为。发生屈曲的临界应力σcr和临界应变εcr主要受层状梁中重复层厚度的影响，尤其在重复层厚度不足2 nm时，σcr和εcr急剧降低。屈曲后的弯曲变形中，位错形核的拉-压不对称性使原子缺陷仅从受压缩的地方产生。随着GNs层数的增加，重复层间距离降低，层状梁的柔韧性随之增加。Abstract: Molecular dynamics (MD) method was used to simulate the bending deformation of graphene (GNs)/Al layered beams under transverse load and longitudinal compression, and the influencing factors of the bending characteristics of the laminated beams were investigated. It can be seen from the bending results under transverse load that the bending stiffness of the layered beam decreases with the increase of the number of GNs layers due to the effect of interlayer action. The bending mechanism of GNs/Al layered beams is not simply the addition of GNs and Al component properties, which makes it difficult to apply classical continuum mechanics to high anisotropy layered materials. In uniaxial longitudinal compression, GNs makes the slender beam more prone to buckling before plastic deformation. The critical stress (σcr) and critical strain (εcr) of buckling are mainly affected by the thickness of the repeating layer in the layered beam, especially when the thickness of the repeating layer is less than 2 nm, the σcr and εcr decrease sharply. In flexural deformation after buckling, the tension-pressure asymmetry of dislocation nucleation causes atomic defects to occur only from the compressed place. As the number of GNs increases and the distance between repeated layers decreases, the flexibility of the layered beam increases.
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Keywords:
- graphene/Al layered beam /
- molecular dynamics /
- bending deformation /
- bending stiffness /
- buckling
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图 1 石墨烯(GNs)/Al层状梁模型
Figure 1. Model of graphene (GNs)/Al layered beam
Gray atom is fixed atom in c-f and c-c; the two atoms before and after the two ends are fixed respectively in s-s; L—Length of GNs/Al layered beam; P—Concentrated load
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图 3 GNs/Al层状梁模型中的原子应力分布
Figure 3. Atomic stress distribution in GNs/Al layered beam models
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图 4 悬臂梁的计算模型
Figure 4. Calculation model of cantilever beam
Nx , Ny and Nz—Number of atomic layers in x, y and z direction; d0—Distance between adjacent atomic layers; a0—Lattice constant of single crystal Al; q—Uniform distributed load; b—Width of GNs/Al layered beam; h—Height of GNs/Al layered beam ; η—Length ratio of the no-load area
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图 5 纯Al梁横截面上原子的应力和位移云图
Figure 5. Stress and displacement nephogram of atoms in cross section of pure Al beam
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图 7 纵向压缩下GNs/Al层状梁的应力-应变曲线
Figure 7. Stress-strain curves of the GNs/Al layered beam under longitudinal compression
σcr—Critical stress; εcr—Critical strain; HCP—Close-packed hexagonal structure
表 1 纯Al梁的横截面尺寸与相应的弯曲刚度
Table 1 Cross-section size and corresponding bending stiffness of pure Al beam
Nx=Ny 9 11 13 15 17 19 21 γ
/%L1 45.30 37.21 31.61 27.51 24.37 21.89 19.88 L2 45.18 37.09 31.49 27.38 24.25 21.77 19.76 L3 45.09 37.01 31.40 27.30 24.16 21.68 19.67 L4 45.02 36.93 31.33 27.23 24.09 21.61 19.61 w
/nmL1 0.318 0.237 0.183 0.146 0.119 0.098 0.083 L2 0.337 0.251 0.194 0.154 0.126 0.104 0.087 L3 0.354 0.264 0.204 0.162 0.132 0.109 0.092 L4 0.370 0.275 0.213 0.169 0.137 0.114 0.095 EB
/10−23 N·m2L1 3.245 4.354 5.625 7.065 8.677 10.468 12.447 L2 4.918 6.599 8.529 10.718 13.239 15.910 18.935 L3 7.043 9.453 12.223 15.370 18.909 22.856 27.225 L4 9.662 12.972 16.784 21.119 26.007 31.454 37.511 Notes: γ—Ratio of the number of atoms on the outermost surface of the model to the total number of atoms in the model; w—Deflection; EB—Bending stiffness. 
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目的
碳基增强体对材料整体弯曲特性的影响以及内在影响因素的报道很少。本文以GNs/Al层状梁为基本结构，采用无须引入尺度参数的MD方法探究在横向荷载和纵向压缩下，碳基体GNs对金属复合层状梁弯曲性能的影响。从而在微观尺度上为工程实际提供相关分析和实验过程中较难发现的机理。
方法在Al基中平行Al晶体(001)面等距离加入1~3层GNs构成GNs/Al层状梁的MD模型。进而模拟模型在横向荷载和纵向压缩下的弯曲过程，并从原子尺度上分析结构演化规律。
结果从横向荷载下的弯曲结果可见，由于层间作用的影响，层状梁的弯曲刚度随着GNs层数的增加而不断降低。GNs/Al层状梁的弯曲机理并非由GNs和Al组分特性的简单相加，这使经典连续力学难以适用于高各向异性的层状材料中。在单轴纵向压缩中，GNs使细长的层状梁在塑性变形前更易发生屈曲行为。发生屈曲的临界应力和临界应变主要受层状梁中重复层厚度的影响，尤其在重复层厚度不足2 nm时，和急剧降低。屈曲后的弯曲变形中，位错形核的拉-压不对称性使原子缺陷仅从受压缩的地方产生。随着GNs层数的增加，重复层间距离降低，层状梁的柔韧性随之增加。
结论本文通过MD模拟，成功地从原子尺度上展现了纳米层状梁的弯曲机理，从而为工程实际起到有益借鉴。具体结论有：(1)GNs/Al层状纳米梁在横向荷载产生的弯曲下，由于较弱的层间作用，GNs层降低了层状梁的弯曲刚度。且层状梁的弯曲机理并不是由GNs和Al的特性简单相加决定的，在性质上不同于单独考虑C和Al组分的弯曲行为。这使得经典连续介质力学难以适用于高度各向异性的层状材料中。层状梁在大比表面积下的高表面原子数占比使存储在结构体内和表面的应变能相当，从而导致这些模型的表面效应十分突出。因此，纳米结构的力学性能具有极大的尺寸依赖性。(2)单轴纵向压缩下，GNs能使细长层状梁在塑性变形前先发生屈曲行为。分层模态下，屈曲部分不能继续承受压缩，使材料发生剧烈弯曲现象。且发生屈曲行为的临界应力和临界应变主要取决于重复层的厚度。重复层厚不足2 nm时，临界应力和临界应变值会显著降低。(3)在纵向压缩产生弯曲变形的过程中，由于位错形核的拉-压不对称性，位错等原子缺陷仅从层状梁弯曲的压缩处产生。且当GNs层数增多时，重复层间距离降低，GNs/Al层状梁的柔韧性随之增强。
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虽然目前关于纳米梁的弯曲研究取得了重大成果，但碳基增强体对材料整体弯曲特性的影响以及内在影响因素的报道却很少。因此本文以石墨烯(GNs)/Al层状梁为基本结构，采用分子动力学(MD)方法探究在横向荷载和纵向压缩下，碳基体GNs对金属复合层状梁弯曲性能的影响。从而在微观尺度上为工程实际提供相关分析和实验过程中较难发现的微观机理。
本文采用分子动力学方法，通过相关变量的曲线图和整个弯曲变形过程中微观结构演化的分析，探索了GNs对层状材料弯曲特性的影响以及造成影响的内在因素。主要创新成果如下：
(1)在层间作用的影响下，GNs层降低了GNs/Al层状梁的弯曲刚度。
(2)单轴纵向压缩GNs/Al层状梁时，GNs的加入使细长的层状梁在塑性变形前更容易发生屈曲行为(如
图1 )，而发生屈曲的临界应力和临界应变主要受金属层厚的影响。当厚度不足2 nm时，临界应力和临界应变急剧下降(如图2 )。(3)由于位错形核具有拉-压不对称性，层状梁屈曲后的弯曲过程中，原子缺陷仅从弯曲受压处产生。且随着GNs层数的增多，层状梁的重复层间距离减小，使层状梁柔韧性增强(如
图3 )。
GNs使细长的层状梁在塑性变形前更易发生屈曲行为
重复层厚度对临界应力和临界应变的重要影响
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