Experimental and simulational study on tensile mechanical property of carbon nanotubes/epoxy resin composite
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摘要: 由于具有优异的力学、电学和热学性能，碳纳米管(Carbon nanotubes，CNTs)被广泛用于高性能复合材料制备研究。然而，CNTs具有高长径比、高比表面能和强范德华力，在制备过程中易团聚，在高填料浓度下导致复合材料力学性能的降低。为了准确表征碳纳米管增强环氧树脂纳米复合材料(CNTs enhanced epoxy nanocomposite，CNTs/EP)的拉伸力学性能，通过实验和有限元模拟分析，表征了不同类型CNTs增强的CNTs/EP的拉伸力学性能。在考虑团聚对环氧树脂材料参数影响的情况，提出了折减团聚区域树脂材料参数的方法，改进了团聚分布数值分析方法。结果表明，在0.5wt%的低含量下，均匀分布数值分析方法可以准确预测CNTs/EP的拉伸强度和弹性模量；团聚分析方法准确预测了CNTs/EP在1.5wt%高浓度下的拉伸力学性能，弹性模量和拉伸强度的预测误差不超过5%。Abstract: Due to the excellent mechanical, electrical and thermal properties, carbon nanotubes (CNTs) are widely used in the research and preparation of high-performance composite. However, with the high aspect ratio, high specific surface energy and strong van der Waals force, CNTs intend to form agglomeration during the preparation process, causing a decrease in the mechanical property of the composite material at high concentration. In order to accurately characterize the tensile mechanical property of CNTs enhanced epoxy nanocomposite (CNTs/EP) nanocomposite, the tensile mechanical properties of different kinds of CNTs/EP were characterized by experiment and finite element analysis. Considering the influence of agglomeration on the material parameter of epoxy, a method for reducing the materials parameter of epoxy in the agglomeration region was proposed to improve the numerical analysis method of agglomeration distribution model. The results show that the uniform distribution numerical analysis method can accurately predict the tensile strength and elastic modulus of CNTs/EP at a low content of 0.5wt%. The agglomeration analysis method accurately predicts the tensile mechanical property, the error of elastic modulus and tensile strength of CNTs/EP are no more than 5% at a high concentration of 1.5wt%.
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Key words:
- carbon nanotubes /
- epoxy resin /
- dispersion property /
- mechanical property /
- finite element method
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图 1 碳纳米管增强环氧树脂纳米复合材料(CNTs/EP)纳米复合材料模型：(a)拉伸试样；(b) CNTs分布图；(c)模型图；(d)基体、碳纳米管与界面
Figure 1. Carbon nanotubes enhanced epoxy nanocomposite (CNTs/EP) nanocomposite model: (a) Tensile specimen; (b) Microscopic distribution of CNTs; (c) Finite element model; (d) Matrix, carbon nanotube and interphase
图 3 EP轴拉伸性能：(a)应力-应变曲线；(b)断裂图；(c)延性材料；(d)塑性参数
Figure 3. Uniaxial tensile property of pure EP: (a) Stress-strain curve; (b) Fracture image; (c) Ductile material; (c) Plasticity parameter
$ \bar \varepsilon _0^{{\text{pl}}} $—Equivalent plastic strain at the onset of damage; $ \bar \varepsilon _0^{{\text{pl}}} $—Equivalent plastic strain at failure; $ {\sigma _0} $—Elastic limit for tension; $ {\sigma _{{\text{y}}0}} $—Yield stress; $ E $—Elastic modulus; $ D $—Damage variable; $ \bar \sigma $—Stress without damage
图 4 均匀分布CNTs纳米复合材料建模流程图
Figure 4. Modeling flowchart for nanocomposite with uniformly distributed CNTs nanocomposites
图 5 团聚分布CNTs纳米复合材料示意图
Figure 5. Diagram of micro CNTs nanocomposite with agglomerate
${r_0}$—Radius of agglomeration; l—Distance from the center of the agglomerate to the material point
图 6 团聚CNTs纳米复合材料建模流程图
Figure 6. Modeling flowchart for CNTs nanocomposite with agglomeration
图 7 网格独立性分析：(a)模型尺寸的影响；(b)网格尺寸的影响
Figure 7. Mesh independence analysis: (a) Effect of model size; (b) Effect of mesh size
图 8 图均布纳米复合材料网格独立性分析
Figure 8. Mesh independence analysis of uniformly distributed nanocomposite
图 9 图均布纳米复合材料模型示意图
Figure 9. Model diagram of nanocomposite with uniformly distributed CNTs
图 10 均匀分布CNTs/EP纳米复合材料数值模拟应力-应变曲线
Figure 10. Numerical simulation of stress-strain curves for uniformly distributed CNTs/EP nanocomposite
图 11 CNTs/EP纳米复合材料拉伸力学性能：(a)弹性模量；(b)拉伸强度
Figure 11. Tensile mechanical properties of CNTs/EP nanocomposites: (a) Elastic modulus; (b) Tensile strength
图 12 均布纳米复合材料应力云图((a)~(d)分别是纯环氧树脂、C-CNTs/EP、g-CNTs/EP和p-CNTs/EP；单位：GPa)
Figure 12. Stress contour for uniform micro nanocomposite ((a)-(d) are pure epoxy, C-CNTs/EP, g-CNTs/EP and p-CNTs/EP, respectively.Unit: GPa)
图 13 团聚CNTs/EP纳米复合材料MT理论预测结果：(a) 0.5wt%；(b) 1.0wt%；(c) 1.5wt%
Figure 13. Prediction result of CNTs/EP nanocomposite with agglomerate via MT method: (a) 0.5wt%; (b) 1.0wt%; (c) 1.5wt%
图 14 团聚环氧树脂试样件光学图像：(a)和(b)是深埋团聚试样；(c)和(d)是表面团聚试样
Figure 14. Optical images of epoxy samples with agglomerate: (a) and (b) are samples with deep-buried agglomerate; (c) and (d) are samples with surface agglomerate
图 15 团聚EP拉伸实验结果：(a)弹性模量；(b)拉伸强度
Figure 15. Tensile test result of EP with agglomerate: (a) Elastic modulus; (b) Tensile strength
图 16 团聚区域单元的材料赋予示意图
Figure 16. Schematic diagram of mesh material assignment of the agglomeration region
图 18 团聚环氧树脂力学性能：(a)拉伸强度；(b)弹性模量
Figure 18. Mechanical properties of epoxy with agglomerate: (a) Tensile strength; (b) Elastic modulus
图 20 团聚CNTs/EP纳米复合材料拉伸力学性能
Figure 20. Tensile mechanical properties of CNTs/EP nanocomposite with agglomerate
图 21 团聚纳米复合材料应力云图((a)~(d)分别是团聚环氧树脂、p-CNTs/EP、g-CNTs/EP和C-CNTs/EP；单位：GPa)
Figure 21. Stress contour for nanocomposite with agglomerate: ((a)~(d) are pure epoxy, p-CNTs/EP, g-CNTs/EP and C-CNTs/EP, respectively.Unit: GPa)
Material Modulus
/GPaPoisson's ratio Strength/GPa EP 3.112 0.3 0.0524 CNT 1000 0.2 20 
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表 2 纳米材料界面参数
Table 2. Interface parameters of nanomaterials
Nanomaterial Stiffness/
(GPa·μm−1)Interfacial strength/GPa Fracture energy/
(10−4 GPa·μm)C-CNTs 3000 0.3 7.5 g-CNTs 1000 0.1 2.5 p-CNTs 360 0.036 9.0 Notes: C-CNTs—Carboxylated carbon nanotubes; g-CNTs—Gelatin functionalized CNTs; p-CNTs—Pristine CNT
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