# Review on the Electrical Resistance/Conductivity of Carbon Fiber Reinforced Polymer
## 2 Structure of CFRP and Its Electrical Conductivity
### Conductivity of CFRP and Its Characteristics  
In particular, CFRP exhibits poor electrical conductivity and some other unsatisfactory inherent characteristics. Although carbon fibers are good conductors and epoxy resins show excellent properties for wide applications, the electrical insulation behavior restricts their applications in many industries. The electrical conductivity of CFRP can be enhanced by adding conductive fibers. Electrically conductive channels are randomly distributed within an insulating matrix. The entire CFRP may be electrically conducting or insulating [28; 29]. This fiber directionality determines the electrical anisotropy in CFRP. The electrical conductivity is much higher in the fiber direction and lower in the direction perpendicular to fiber direction [1; 30]. The conductivity of unidirectional CFRP composites is much lower than that of metals by a factor of about 1,000, whereas the conductivity in cross fiber direction is lower by up to more than 100 times [1]. If the coupling capacitance between fibers are not considered in CFRP, under ideal conditions, the current is believed to only flow through individual carbon fibers due to the surrounding insulating polymer. If the carbon fibers were perfectly straight and did not contact adjacent fibers, CFRP would be highly insulating in the non-fiber direction. In fact, the electrical conductivity of CFRPs in the non-fiber direction is not zero since the ideal conditions cannot be met. Carbon fiber itself is not a straight fiber but a wavy fiber (Figure 3). Due to inter-fiber contact points, the current may flow from one fiber to another [31]. The electric conductance shows similar characteristics in the thickness direction. The inter-lamina makes the electric conductance of the out-of-plane direction much smaller than that of 90\({}^{\circ}\) direction. Since the electric conductance of 90\({}^{\circ}\) and out-of-plane is related to fiber contacts, the total electrical impedance of a piece of CFRP composites depends on the impedance of all the fibers [32]. The chance of contact between adjacent fibers increases with the increase in the fiber volume fraction. The area contains rich resin among CFRP, thus decreasing the out-of-plane electrical conductivity [33]. Figure 1: A typical structure of carbon fiber reinforced polymer (CFRP). Figure 2: A laminate formed by stacking single lamina. It is generally believed that unidirectional CFRP laminates shows anisotropic electrical properties. That is to say, the conductivity along the direction perpendicular to fibers is relatively small, whereas the conductivity along the fiber direction of the composite can be calculated with fiber-volume fraction and total single-fiber conductivity [29]. For an ideal unidirectional composite, the composite resistivity parallel to the fibers \(\sigma_{\text{cp}}\) can be calculated as [34]:  
\[\sigma_{\text{cp}}=\sigma_{\text{f}}/v_{\text{f}} \tag{1}\]  
where \(v_{\text{f}}\) is the volume fraction of fibers; and \(\sigma_{\text{f}}\) is the resistivity of carbon fibers. If conductivities in all three directions are considered, the conductivity tensor of the CFRP plate can be expressed as [35; 36]:  
\[\_=\left(\begin{array}{ccc}\_=\ \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\  
sensors [51; 52; 53; 54; 55]. Hence, self-sensing relies on the fibers themselves to act as the sensing elements and minimizes any structural attrition due to sensor incorporations [56]. Significant progress has been made in the multi-functionality of CFRPs. When CFRP composites are applied in the self-sensing technology, only a portion of composites are generally used as the sensor [57; 58; 59; 60; 61; 62]. The electrical resistivity of composites could indicate damage and strain. Resistivity in the fiber's direction could indicate the fiber's breakage damage, whereas the resistivity in the through-thickness direction could indicate the delamination damage [49].