碳纤维复合材料电导特性和力电耦合行为研究进展

韩朝锋; 薛有松; 张东生; 冯向伟; 陈莉娜; 朱晓伟; 吴海宏; 苏玉恒

doi:10.13801/j.cnki.fhclxb.20230119.004

碳纤维复合材料电导特性和力电耦合行为研究进展

doi: 10.13801/j.cnki.fhclxb.20230119.004

韩朝锋^{1, 3, 5,},
薛有松²,
张东生³,
冯向伟¹,
陈莉娜¹,
朱晓伟⁴,
吴海宏^5, ,,
苏玉恒¹

1.
河南工程学院　纺织工程学院，郑州 450000
2.
东华大学　纺织学院，上海 201620
3.
巩义市泛锐熠辉复合材料有限公司，郑州 450000
4.
河南工业大学　土木建筑学院，郑州 450000
5.
河南工业大学　机电工程学院，郑州 450000

基金项目: 国家自然科学基金委-河南省联合基金重点项目(U1604253)；国家重点研发计划(2016YFB0101602)

详细信息

通讯作者:
吴海宏，博士，教授，博士生导师，研究方向为碳纤维复合材料结构-功能一体化　E-mail：hhwu@haut.edu.cn

中图分类号: TB332
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出版历程
- 收稿日期: 2022-11-25
- 修回日期: 2023-01-06
- 录用日期: 2023-01-19
- 网络出版日期: 2023-01-19
- 刊出日期: 2023-06-15

Research progress on electrical property and electromechanical coupling behaviors of carbon fiber composites

1.
School of Textiles Engineering, Henan University of Engineering, Zhengzhou 450000, China
2.
College of Textiles, Donghua University, Shanghai 201620, China
3.
Gongyi Van-Research Innovation Composite Material CO., LTD., Zhengzhou 450000, China
4.
College of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou 450000, China
5.
School of Mechanical and Electrical Engineering, Henan University of Technology, Zhengzhou 450000, China

Funds: National Natural Science Foundation of China-Henan Province Joint Fund Key Project (U1604253); Supported by the National Key Research and Development Program of China (2016YFB0101602)

摘要

摘要: 碳纤维复合材料具有良好的导电性能，但其作为增强体的树脂基复合材料的导电性能与增强体结构显著相关，且在加载条件下的结构变形触发碳纤维复合材料的导电行为发生改变，这一特性在智能传感器方面具有重要的应用。本文从复合材料电阻法结构健康监测应用出发，着重概述了不同维度增强体碳纤维树脂基复合材料的导电性能和预测模型、表面电势场分布和主要测量技术及力电耦合行为和本构模型，以期为碳纤维复合材料“材料-结构-功能”一体化集成系统的设计提供新方向和新途径。
- 碳纤维 /
- 电导率 /
- 电势场分布 /
- 力电耦合行为
Abstract: Carbon fiber composites have good electrical conductivity, however, the electrical conductivity of the resin matrix composites is significantly related to reinforcement architectures. The structural deformation under external load triggers the modification in the conductive behavior of carbon fiber composites, which has an important application in smart sensors. Based on the utilization of electrical resistance method in structural health monitoring for composites, this paper focuses on the overview of electrical conductivity and predictive models, surface potential field distribution and main measurement technologies, as well as electromechanical coupling behavior and constitutive models of carbon fiber reinforced resin matrix composites with different dimensional architectures. It is expected to provide a new direction and path to design "material-structure-performance" integrated system in carbon fiber composites.
- carbon fiber /
- electrical conductivity /
- potential distribution /
- electromechanical coupling behaviors

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图 1 碳纤维复合材料在结构健康监测(SHM)中的应用：(a) 力电耦合行为；(b) 导电机制；(c) 飞机机翼监测；(d) 桥梁承载监测

Figure 1. Application of carbon fiber composites in structural health monitoring (SHM): (a) Electromechanical coupling behavior; (b) Conductive mechanism; (c) Aircraft wing monitoring; (d) Bridge bearing monitoring

ΔR—Relative resistance change; R₀—Initial resistance; σ₁—Stress; ε₁—Strain

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图 2 复合材料不同维度增强体结构

Figure 2. Different dimensional reinforcement structure of composites

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图 3 复合材料内部电流传导路径示意图

Figure 3. Schematic diagram of internal current conduction path of composites

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图 4 碳纤维复合材料内部三维导电网络示意图^[23]

Figure 4. Schematic diagram of three-dimensional conductive network inside carbon fiber composite^[23]

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图 5 缎纹机织复合材料层压板电导率多尺度均质模型分析^[40]

Figure 5. Multi-scale homogeneous model analysis of electrical conductivity of satin woven composite laminates^[40]

[σ]_yarn—Yarn conductivity; R_x, R_y, R_z—Resistance in the x, y and z directions of Unit 2; R_eq_x, R_eq_y, R_eq_z—Equivalent resistance of single-layer composite materials in the x, y and z directions

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图 6 不同铺层结构碳纤维复合材料层压板电势场和温度场分布^[47]

Figure 6. Distribution of electric potential field and temperature field of carbon fiber composite laminates with different laminate structures^[47]

J—Electrical current; φ^*—Electrical potential field; E^*—Electrical field component; Q^*—Heat flux; T^*—Temperature; T^*_image—Thermal imaging temperature

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图 7 单对电极加载下平纹机织复合材料层压板表面电势场分布^[42]

Figure 7. Surface potential field distributions of plain woven composite laminates under single pair of electrodes^[42]

CFRP—Carbon fiber reinforced plastic; DC—Direct current

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图 8 两对电极加载下平纹机织复合材料层压板表面电势场分布^[42]

Figure 8. Surface potential field distributions of plain woven composite laminate under two pairs of electrodes^[42]

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图 9 3D机织角连锁(AI)织物结构

Figure 9. Architecture of 3D woven angle-interlock (AI) fabric

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图 10 单对电极加载下3D机织AI复合材料表面电势场分布^[56]

Figure 10. Surface potential field distributions of 3D woven AI composites under single pair of electrodes^[56]

AIW—Angle-interlock woven

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图 11 两对电极加载下3D机织AI复合材料表面电势场分布^[56]

Figure 11. Surface potential field distribution of 3D woven AI composites under two pairs of electrodes^[56]

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图 12 应变电压变化与循环次数曲线^[64]

Figure 12. Strain and Potential vs. number of loading cycles curve^[64]

CH 1—Channel 1; CH 2—Channel 2

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图 13 单节点处电阻网路和等效电阻模型^[68]

Figure 13. Electrical network and equivalent electrical circuit around a single node^[68]

δ—Electrical ineffective length; R_i_,_j—Node resistance; R_c—Contact resistance; V_i_,_j—Node voltage

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图 14 等效电阻模型^[70]

Figure 14. Equivalent electrical circuit^[70]

R_L(i)—Longitudinal resistance of the ith lamina; R_Γ(i)—Thickness resistance associated with half of the ith lamina; A—Voltage contact

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图 15 (a) 循环压缩实验；(b) 灵敏度系数与压缩应变曲线^[72]

Figure 15. (a) Cycle compressive test; (b) Gage factor vs compressive strain curve^[72]

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图 16 循环载荷与最大剪切载荷比和相对电阻变化关系^[11]

Figure 16. Relationship between the ratio of cycle load to shear strength and relative resistance change^[11]

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图 17 电阻-循环次数曲线^[14]

Figure 17. Resistance-number of loading cycles curve^[14]

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表 1 单向复合材料层压板电导率预测模型

Table 1. Prediction model for electrical conductivity of unidirectional composite laminates

Model	Electrical conductivity prediction model			Ref.
Model	Longitudinal direction	Transverse direction	Thickness direction	Ref.
Haider model (Composites containing conductive particles)	${\sigma _{{{xx}}}} = {\sigma _{\text{f}}}{V_{\rm{f}}} + {\sigma _{\rm{m}}}(1 - {V_{\rm{f}}})$	${\sigma _{{{yy}}}} = {\sigma _{zz}}{\text{ = }}{\sigma _{\text{m}}}\dfrac{{{\sigma _{\rm{f}}}(1 + {V_{\rm{f}}}) + {\sigma _{\text{m}}}(1 - {V_{\rm{f}}})}}{{{\sigma _{\rm{f}}}(1 - {V_{\rm{f}}}) + {\sigma _{\text{m}}}(1 + {V_{\rm{f}}})}}$		[34]
Penetration model(Unidirectional composite)	${\sigma _{{{zz}}}}{\text{ = }}{\sigma _{\rm{f}}}{\left( {{V_{\rm{f}}} - {V_{\rm{c}}}} \right)^{{p}}}$			[35]
Bueche model(Composites containing conductive particles)	${\sigma _{{{xx}}}} = \dfrac{{{{(1 - {V_{\rm{f}}})} /{{\sigma _{\rm{f}}} + {{{V_{\rm{f}}}{w_{\rm{g}}}} / {{\sigma _{\rm{m}}}}}}}}}{{{1 /{{\sigma _{\rm{m}}}{\sigma _{\rm{f}}}}}}}$			[36]
Fiber contact model(Multidirectional composites containing angle layers)	${\sigma _{ { {xx} } } } = \dfrac{ { {\text{π} } {d^2}X} }{ {4{ \sigma_{\text{f} } }{V_{\rm{p} } }{d_{\rm{c} } }l{\cos^2}\theta } }$	${\sigma _{{\text{yy}}}} = \dfrac{{{\text{π}} {d^2}X}}{{4{\sigma _{{\rm{f}}}}{V_{\rm{p}}}{d_{\rm{c}}}l{\text{si}}{{\text{n}}^2}\theta }}$		[37]
Fiber inclination model(Multidirectional composites containing angle layers)	${\sigma _{ { {xx} } } } = {\sigma _{\rm{f} } }{V_{\text{f} } }\cos{^2}\theta \left(1 - \dfrac{ {L\tan \theta } }{W}\right)$	${\sigma _{ { {yy} } } } = {\sigma _{\rm{f} } }{V_{\text{f} } }{\text{si} }{ {\text{n} }^2}\theta \left(1 - \dfrac{ {L\cot \theta } }{W}\right)$		[37]
Effective medium model(Unidirectional composite)	${\sigma _{{{xx}}}} = {\sigma _{\rm{m}}}\left[ {1 + \dfrac{{{V_{\rm{f}}}({\sigma _{\rm{f}}} - {\sigma _{\rm{m}}})\left[ {({\sigma _{\rm{f}}} - {\sigma _{\rm{m}}})\left( {{S_{11}} + {S_{33}}} \right) + 2{\sigma _{\rm{m}}}} \right]}}{{2{{({\sigma _{\rm{f}}} - {\sigma _{\rm{m}}})}^2}(1 - {V_{\rm{f}}}){S_{11}}{S_{33}} + {\sigma _{\rm{m}}}({\sigma _{\rm{f}}} - {\sigma _{\rm{m}}})(2 - {V_{\rm{f}}})({S_{11}} - {S_{33}})}}} \right]$			[38]
McCullough model(Composites containing conductive particles)	${\sigma _{ { {ii} } } } = {V_{\rm{f} } }{\sigma _{\rm{f} } } + {V_{\rm{m} } }{\sigma _{\rm{m} } } - \dfrac{ { {\lambda _i}{V_{\rm{f} } }{V_{\rm{m} } }{ {({\sigma _{\rm{f} } } - {\sigma _{\rm{m} } })}^2} } }{ { {V_{ { {{\rm{f}}i} } } }{\sigma _{\rm{f} } } + {V_{ { {{\rm{m}}i} } } }{\sigma _{\rm{m} } } } }$ ${V_{{{\rm{f}}}}}_{{i}} = (1 - {\lambda _i}){V_{\text{f}}} + {\lambda _i}{V_{\text{m}}}$,${V_{\text{m}}}_{{i}} = (1 - {\lambda _i}){V_{\text{m}}} + {\lambda _i}{V_{\text{f}}}$, i=1, 2, 3			[39]
Notes: ${\sigma _{\text{f}}}$—Fiber conductivity; ${\sigma _{\text{m}}}$—Resin conductivity; ${V_{\text{f}}}$—Fiber volume fraction; ${V_{\text{c} } }$—Critical fiber volume fraction; p—Critical exponent; ${w_{\text{g} } }$—Conductive particle content; d—Fiber diameter; ${d_{\text{c}}}$—Fiber contact circle diameter; X—Fiber contact coefficient; l—Fiber length; ${V_{\text{p}}}$—Contact fiber volume; L—Sample length; W—Sample width; $\theta $—Fiber inclination angle; S—Shape parameter; x, y, z—Coordinate direction; 1, 2, 3—Principal axis direction; ${\lambda _{{{{i}}} } }$—Fiber contact factor; σ_xx, σ_yy, σ_zz—Electrical conductivity in the x, y and z directions; σ_ii—Conductivity component.

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表 2 单/多向复合材料层压板力电耦合本构模型

Table 2. Electromechanical coupling constitutive model of unidirectional/multi-directional composite laminates

Dimension	Resistance model	Electromechanical coupling constitutive model	Ref.
1D	Considering fiber contact resistance, the basic resistance unit is the electrical ineffective length, which is suitable for unidirectional laminates	$\dfrac{ {\Delta R} }{R} = \dfrac{ {(1 + \alpha \varepsilon )} }{ {\exp\left[ { - \left(\dfrac{ { {\delta _{\rm ec} } } }{ { {L_{\rm{O}}} } }\right)\left(\dfrac{ { {E_{\rm{f} } }\varepsilon } }{ { {\sigma _0} } }\right)} \right]} }{ { - } }1$	[67]
2D	Considering fiber contact resistance, the basic resistance unit is 1/2 of the ineffective length, suitable for unidirectional laminates	$\begin{gathered} \dfrac{{\Delta {R_{11}}}}{{{R_{11}}}} = \dfrac{{1 + K{}_{11}{\varepsilon _{11}}}}{{{{\left( {1 - {F_1}} \right)}^2}}} - 1(0^\circ ) \\ \dfrac{{\Delta {R_{22}}}}{{{R_{22}}}} = \dfrac{{1 + K{}_{22}{\varepsilon _{22}}}}{{1 - {F_2}}} - 1(90^\circ ) \\ \end{gathered} $	[69]
1D	Considering the fiber contact resistance, it follows Weibull statistical distribution; Conductivity, which follows a linear change before fiber fracture and an exponential change after fiber fracture, suitable for multi-directional laminates	$\begin{gathered} \dfrac{ {\Delta R} }{R} = \dfrac{ { {\text{1 + e} } } }{ { {\sigma / { {\sigma _{\rm 0} } } } } } - 1(\varepsilon \leqslant 10\% ) \\ \dfrac{ {\Delta R} }{R} = \dfrac{ { {\text{1 + e} } } }{ {b{ {\rm e}^{ - { {(S - {S_0})}^t} } } }} - 1(\varepsilon \leqslant 10\% ) \\ \end{gathered}$	[71]
2D	Considering Poisson effect, strain effect, and damage effect, suitable for multi-directional laminates	$\begin{gathered}\upsilon = - \dfrac{{{\varepsilon _{11}}}}{{{\varepsilon _{33}}}},{\left( {\dfrac{{\Delta \rho }}{\rho }} \right)_{{\text{reversible}}}} = \alpha {\varepsilon _{33}} \\ \dfrac{{\Delta {R_{33}}}}{{{R_{33}}}} = {\varepsilon _{33}}(1 + \alpha + 2\upsilon ) \\ \dfrac{{\Delta {R_{11}}}}{{{R_{11}}}} = \dfrac{{\Delta {\rho _{11}}}}{{{\rho _{11}}}} - \dfrac{{{{\Delta {R_{33}}} \mathord{\left/ {\vphantom {{\Delta {R_{33}}} {{R_{33}}}}} \right. } {{R_{33}}}}}}{{1 + \alpha + 2\upsilon }} \\ {\left( {\dfrac{{\Delta \rho }}{\rho }} \right)_{{\text{irreversible}}}} = \beta {\varepsilon _{33}} \\ \end{gathered} $	[72]
Notes: $\Delta R$—Resistance change rate; R—Resistance; $\alpha $—Gage factor; $\varepsilon $—Strain; ${\delta _{{\text{ec}}}}$—Slip length; ${E_{\text{f}}}$—Tensile modulus; L—Sample length; ${L_{\text{O}}}$—Reference length; ${\sigma _{\text{0}}}$—Weibull scale factor; K—Strain coefficient; ${F_{\text{1}}}$—Failure probability of series resistor components; ${F_{\text{2}}}$—Probability of failure of parallel resistor components; S—Loading stress; ${S_{\text{0}}}$—Reference stress; $\Delta \rho $—Resistivity change rate; $\rho $—Resistivity; υ—Poisson's ratio; b—Constant, 0.973; t—Constant,8.67; β—Damage effect coefficient.

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