Research progress on electrical property and electromechanical coupling behaviors of carbon fiber composites
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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。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.
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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
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; Rx, Ry, Rz—Resistance in the x, y and z directions of Unit 2; Reqx, Reqy, Reqz—Equivalent resistance of single-layer composite materials in the x, y and z directions
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
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. Longitudinal direction Transverse direction Thickness direction 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; σxx, σyy, σzz—Electrical conductivity in the x, y and z directions; σii—Conductivity component. 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 modelRef. 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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