Research and Analysis of Carbon Fiber-Reinforced Polymer Prepreg Detection Based on Electromagnetic Coil Sensors

Abstract

In response to the challenges posed by the complexity and potential hazards of traditional chemical methods for detecting the surface density of carbon fiber prepreg materials, this paper explores the use of eddy current testing principles. It establishes the relationship between coil impedance variation and the surface density of carbon fiber prepreg materials and designs a quadrupolar excitation eddy current detection probe. This probe can detect the surface density of both single-line and woven carbon fiber prepreg structures. The overall structure and dimensions of the designed quadrupolar probe were optimized using finite element simulation software. The results show that the number of coil turns significantly affects the sensor performance, with more turns leading to increased sensitivity. Moreover, with the same number of coil turns, smaller inner diameters and larger outer diameters of the coil enhance sensor sensitivity. A comprehensive comparison between unidirectional and woven carbon fiber models suggests that woven structures have superior electrical conductivity at identical excitation frequencies, while unidirectional models show more pronounced electrical anisotropy. These findings provide valuable insights for analyzing electrical properties, numerical simulations, and eddy current testing in composite materials.

1. Introduction

Carbon fiber-reinforced polymer (CFRP), as a continuously evolving composite material, exhibits numerous advantageous properties, including high specific strength, elevated specific modulus, exceptional fatigue resistance, and remarkable corrosion resistance [1]. It possesses excellent stability and strong acid resistance and is capable of withstanding the corrosion and immersion of concentrated hydrochloric acid and sulfuric acid, among its other merits [2]. The CFRP prepreg is composed of reinforcing fibers and matrix resin and serves as an intermediate product of CFRP articles. Carbon, as the reinforcing agent, exhibits preferable stiffness and tensile properties, undertaking the majority of the load. Epoxy resin, as the matrix, adheres the carbon fibers together through the adhesive effect, thereby facilitating uniform load transfer throughout the entire CFRP. Despite the numerous outstanding characteristics of CFRP, the complexity of its processing technology, production process factors, and external environmental factors may result in the occurrence of defects in CFRP components [3]. Low molecular impurities, solvents, and moisture in the prepreg can easily cause changes in the carbon content and resin content of the CFRP prepreg. Nevertheless, the carbon content and resin content within the CFRP prepreg will exert an influence on various properties of CFRP, resulting in the CFRP failing to reach the prescribed performance standards [4]. In their experiments, Park et al. discovered that the resistivities in the longitudinal, transverse, and thickness directions of the unidirectional carbon fiber plate would increase significantly with the decrease in the fiber volume fraction. Moreover, the growth rate of the conductivities in the transverse and thickness directions was faster than that in the longitudinal direction [5]. Since the quantity of carbon content can influence the performance of CFRP, carbon content detection is a very crucial link in the production process of prepreg. The performance of the composite material can be enhanced by controlling the quality of the prepreg.

The traditional matrix acid etching method is a carbon fiber surface density detection approach based on the chemical differences in components. However, it suffers from drawbacks such as complex processes, high randomness of results, and operational hazards, which are unfavorable for the improvement of the CFRP prepreg production process. Hence, the development of a novel, reliable, simple, and safe carbon fiber surface density detection technology that does not damage raw materials represents an important development direction in the CFRP preparation industry. The development of nondestructive testing technologies for CFRP materials is of significant importance. CFRP prepreg is composed of carbon fibers and a resin matrix, demonstrating multiphase and anisotropic properties. Therefore, it is impossible to infer the rules of the internal eddy current distribution and coil impedance variation based on experience. It is necessary to conduct research through a combination of test analysis and numerical calculation. In recent years, numerous scholars have conducted significant work on electrical property analysis, numerical analysis, and eddy current detection in composite materials. To enhance the sensitivity of the detection coil, various coil structures have been designed for the nondestructive testing of carbon fiber-reinforced composites. Lukaszuk et al. employed a testing system featuring differential sensors with two pairs of vertically oriented excitation coils and utilized a central pickup coil for inspecting anisotropic structural materials. To identify a device applicable for detecting hidden defects in such materials, a sample fabricated from quadrupolar woven carbon fiber-reinforced composite material with two artificial defects (the maximum relative depths of the notches were 30% and 70%, respectively, with a thickness of 0.4 mm and a length of 5 mm) was adopted to evaluate this system [6]. Miguel A. Machado adopted a pair of 45° parallelogram coils in the experiments to test the carbon fiber-reinforced polymer (CFRP) with low electrical conductivity, and was capable of clearly detecting the slightest side cuts (0.2 times the width) and fiber fractures. The experiments demonstrated an excellent signal-to-noise ratio [7]. For the detection of curved pipes with natural concave defects, Daura, L. U. put forward a transmitter–receiver flexible printed coil (FPC) array employing the Wireless Power Transfer (WPT) method. An experimental study was carried out on the material surface using a single excitation coil and multiple receiving coils based on the WPT principle. The experiment utilized 21 scanning points to measure the depressions on the dedicated concave samples. The experimental data were used for training and evaluating the dual resonance response. Feature selection and feature fusion were conducted through deep learning to map and reconstruct the defective depressions for quantitative nondestructive testing [8]. Olivier Lefebvre et al. designed and fabricated a rectangular planar inductive coil with a wire diameter that could be reduced to 10 μm. Subsequently, they carried out a simulation analysis of the magnetic field surrounding the coil with the aid of FEM software (ANSYS^® version 12.1). Eventually, they successfully utilized this coil to capture and manipulate magnetic particles [9]. To overcome the lift-off effect that occurs during magnetic field measurement, Wu Dehui et al. designed a probe composed of an “8”-shaped transmitting coil and a circular receiving coil. This probe is not only insensitive to the variation in lift-off distance but also exhibits a high degree of sensitivity when detecting defects. In the quantitative experimental tests for planar wave detection and crack detection, the scanning images clearly display the cracks, and the length and location of the cracks can be estimated from the scanning images [10]. Yang Fan et al. put forward the method of pulsed eddy current thermal imaging for detecting low-frequency defects in carbon fiber-reinforced plastics. By utilizing eddy current loss to characterize the thermal power of eddy currents in carbon fiber-reinforced plastics, detection results with a frequency of up to 750 kHz can be provided [11]. The special conductive principle of CFRP makes the design scheme of the related probe required for its eddy current testing one of the research hotspots. Mizukami et al. devised a coil group in which the excitation coil and the receiving coil are mutually quadrupolar for the purpose of reducing the influence of the excitation magnetic field on the detection coil. This probe can be utilized for detecting the external waviness of CFRP plates [12]. Pasadas, Dario J et al. guided Lamb wave tomography and eddy current testing (ECT) techniques were combined to locate and evaluate fiber breaks in carbon fiber-reinforced plastic (CFRP) structures. Guided wave testing (GWT) and computed tomography (CT) imaging were employed to quickly locate fiber breaks in the CFRP plate [13]. Dehui Wu et al. proposed a self-resonance ECT method for non-contact detection of CFRP and developed an ECT system capable of detecting CFRP defects at low frequencies while maintaining a relatively high signal-to-noise ratio. The results indicate that the detection effect of the self-resonance ECT system at 500 kHz is similar to that at low frequencies. In comparison with the performance of traditional ECT systems at 10 MHz, a frequency of 500 kHz is sufficient to provide satisfactory detection results for the aforementioned CFRP samples [14].

Based on the above background, the eddy current nondestructive testing technology for CFRP is mainly employed for defect detection, while studies on the carbon fiber areal density of CFRP prepreg are limited. This paper builds on experience in CFRP defect detection and addresses the shortcomings of the traditional matrix acid etching method for detecting carbon fiber areal density, such as its complex process, highly variable results, and operational hazards. By analyzing the eddy current conductivity and numerical model of CFRP prepreg, the “8”-shaped structure probe is improved. Through finite element numerical analysis of the quadrupolar coil group, the impact of different coil parameters and excitation frequencies on impedance is investigated. Models of unidirectional strip and braided carbon fibers are established. The distribution laws of conduction current density in the x, y, and z directions are simulated, and the relationship between the areal density of different structural carbon fibers and coil impedance variation is verified. The organization of this paper is as follows: Section 2 introduces the numerical model of CFRP prepregs, analyzes the material’s electromagnetic properties in detail, and establishes the electromagnetic relationship between the probe and the material. Section 3 further validates the effectiveness of the numerical model through finite element simulations and optimizes the geometric parameters of the probe to improve detection sensitivity and accuracy. Section 4 presents the detection results of the surface density of CFRP prepregs and discusses the performance differences between woven and unidirectional carbon fiber structures. Finally, Section 5 summarizes the main contributions of this paper and suggests directions for future research.

2. Numerical Model

Eddy Current Testing (ECT) is a nondestructive testing method based on the principle of electromagnetic induction. Usually, a coil with alternating current is employed to generate an alternating magnetic field. When the alternating magnetic field passes through the tested conductor, circular currents, known as eddy currents, are induced within the conductor. The other magnetic field generated by the eddy current affects the original magnetic field, resulting in variations in the magnetic flux in the detection coil. This variation can be measured through the change in impedance in the detection coil. By measuring the change in the impedance in the detection coil, variations in the physical properties of the conductor material can be inferred, including parameters like the carbon content and areal density in CFRP prepreg.

The equivalent impedance of a coil can generally be represented by the function in Equation (1) [15]:

$$Z=F(\sigma ,\mu ,f,x,\lambda )$$

(1)

where $\sigma$ and $\mu$ are the electrical conductivity and magnetic permeability of the measured conductor, $f$ is the frequency of the excitation signal, $x$ is the distance between the coil and the conductor, and $\lambda$ is the size factor of the coil.

CFRP prepreg mainly constitutes of carbon fibers and resin that are unevenly and longitudinally arrayed. When the CFRP prepreg is placed within a constant electric field, the majority of electrons shift along the direction of the fibers, while only a small quantity of electrons leap to another fiber via the contact points among the carbon fibers. As a result, it features an extremely complex geometric structure and anisotropy of electrical conductivity. The anisotropy and the complex geometry bring about challenges when it comes to numerical simulation. To circumvent these difficulties, numerous works employ homogenized mathematical expressions to simulate these materials [16]. The electrical conductivity tensor of carbon fiber composite materials is represented in Equation (2) [17].

$$[\sigma ]=\left[\begin{array}{ccc}{\sigma }_{\mathrm{L}}co{s}^2(\theta )+{\sigma }_{\mathrm{T}}si{n}^2(\theta )& {\displaystyle \frac{{\sigma }_{\mathrm{L}}-{\sigma }_{\mathrm{T}}}{2}}sin(2\theta )& 0\\ {\displaystyle \frac{{\sigma }_{\mathrm{L}}-{\sigma }_{\mathrm{T}}}{2}}sin(2\theta )& {\sigma }_{\mathrm{L}}si{n}^2(\theta )+{\sigma }_{\mathrm{T}}co{s}^2(\theta )& 0\\ 0& 0& {\sigma }_{\mathrm{cp}}\end{array}\right]$$

(2)

where ${\sigma }_{\mathrm{L}}$ denotes the conductivity along the fiber direction, ${\sigma }_{\mathrm{T}}$ represents the conductivity in the transverse direction of the fiber, and ${\sigma }_{\mathrm{cp}}$ represents the conductivity in the thickness direction of the plate. $\theta$ represents the fiber orientation angle. The electromagnetic problem is formulated in terms of the electric vector potential T and the scalar magnetic potential $\phi$, which are governed by Equations (3) and (4), involving the conductivity tensor of the CFRP plate, the magnetic permeability of free space ${\mu }_0$, and the angular frequency ω. $H$ is the magnetic field intensity. Hereinafter, V_s and V_c signify the volumes of the excitation coil and the CFRP plate region, respectively, and V_c is delineated by the boundary. Bold letter are used to represent vectors throughout the article.

$$\nabla \times {\sigma }^{-1}\nabla \times T+j\omega {\mu }_0(T-\nabla \phi )=-j\omega {\mu }_{0}H$$

(3)

$$\nabla \cdot (H+T-\nabla \phi )=0$$

(4)

The current density $J$ in V_c is given by Equation (5):

$$J=\nabla \times T$$

(5)

In order to eliminate the normal component of the current density at the V_c boundary, a boundary condition is required, such as that in Equation (6):

$$n\times T=0{/}_{\mathsf{\Gamma }}$$

(6)

The magnetic field $H$ in Equation (3) is calculated using the Biot–Savart Equation (7), where $\parallel r-r^{\prime }\parallel$ is the distance between a source of excitation in V_s and V_c.

$$H(s)={\displaystyle \frac{1}{4\pi }}{{\displaystyle \int }}_{V_S}{\displaystyle \frac{J_s(r^{\prime })\times (r-r^{\prime })}{\parallel r-r^{\prime }{\parallel }^3}}dV$$

(7)

The principle of studying the system is based on the fact that only the parts carrying the source current or induced current are discretized. The excitation coil Hs is evaluated at each node of the finite difference grid through the average value of Equation (7).

Due to the eddy currents generated in the CFRP plate, the coil impedance changes. This change is calculated by Equation (8), where the source current and the magnetic field scattered by the CFRP plate are calculated using the Biot–Savart Equation (9).

$$\mathsf{\Delta }\mathrm{Z}={\displaystyle \frac{-1}{{\mathrm{I}}_{\mathrm{s}}^2}}{{\displaystyle \int }}_{{\mathrm{V}}_{\mathrm{S}}}{\mathrm{E}}_{\mathrm{i}}{\mathrm{J}}_{\mathrm{s}}\mathrm{d}\mathrm{V}$$

(8)

$$H_i\left(r\right)={\displaystyle \frac{-j\omega {\mu }_0}{4\pi }}{{\displaystyle \int }}_{V_C}{\displaystyle \frac{J\left(r^{\prime }\right)}{r-r^{\prime }}}dV, \left(r^{\prime }\in V_C\right)$$

(9)

We need to measure the relationship between the average value of the modulus of the current density within a certain area in the plane ${\rho }_{\mathrm{A}}$ and $H_i$. Therefore, Equation (9) can be written as Equation (11).

$$H_i={\displaystyle \frac{-j\omega {\mu }_{0}s}{4\pi }}{\rho }_{\mathrm{A}}{\displaystyle \int \frac{J\left(r^{\prime }\right)}{r-r^{\prime }}}dr$$

(10)

The definition is as follows:

$${\rho }_{\mathrm{A}}={\displaystyle \frac{{\displaystyle \underset{S}{\iint }JdS}}{S}}={\displaystyle \frac{{\displaystyle \underset{S}{\iint }\frac{1+j}{\sqrt{2}}\sqrt{\omega {\mu }_0\sigma }HdS}}{S}}$$

(11)

In Equation (11), $\omega$ represents the frequency control and $S$ represents the specific cross-sectional area used to calculate the current density and magnetic field strength during the detection process. $S$ is controlled by the test sample, $H$ is controlled by the excitation, and $\sigma$ is related to the areal density of carbon content (denoted as ${\rho }_c$). Hence, the relationship between the coil impedance variation and the areal density of carbon content can be accounted for by Equation (12).

$$\Delta Z=F({\rho }_c)$$

(12)

3. Finite Element Simulation Analysis of Electromagnetic Field

3.1. Model Establishment

In order to investigate the electromagnetic coupling between the sensors and CFRP materials, we utilized the COMSOL6.1 software package (Stockholm, Sweden) to establish an FEM simulation model. The simulation geometric model is depicted in Figure 1 (the air domain is not shown in the figure). Four identical coils form an excitation coil group in the same plane. The current in the adjacent coils is of equal magnitude but flows in the opposite direction, causing these four coils to form an 8-shaped structure in pairs. Its top view is presented in Figure 2. The total magnetic flux generated by the excitation coils within the area of point a, which is located on the perpendicular bisector of the center connection lines of coil 1, coil 3, and coil 2, coil 4, is zero. That is, under this design, the magnetic field generated by the excitation coils does not have an impact on the detection coils [12]. The detection coil is placed above the center point of the excitation coil group and is enlarged to cover the plane of the tested CFRP prepreg sample. The parameters of the coils and the carbon fiber test material are listed in

Table 1. Parameters of coils and carbon fiber materials.

Geometric Parameters	Values
Inner diameter of the T-coil	10 (mm)
Outside diameter of the T-coil	30 (mm)
Height of the T-coil	1 (mm)
Number of turns of the T-coil	50
Inner diameter of the R-coil	30 (mm)
Outside diameter of the R-coil	110 (mm)
Height of the R-coil	1 (mm)
Number of turns of the R-coil	100
The distance between neighboring transmit Coil centers	50 (mm)
Detachment distance	5 (mm)
Plate volume	50 × 50 × 2 (mm)
Air domain volume	1000 × 1000 × 1000 (mm)

.

In the AC/DC module of the COMSOL6.1 software, the physical field is selected as the magnetic field and solved in the frequency domain. The relative magnetic permeability and relative dielectric constant of this model are both set to 1. The conductivity of the air domain is set to 1 S/m, which simplifies the model and reduces the computational complexity without exerting a significant influence on the results. The excitation coil and the receiving coil are set to copper, with the conductivity set at 5.998 MS/m. The conductivity of the carbon fiber composite material varies in each direction, presenting a distinct electrical anisotropy, and its conductivity is represented by the conductivity tensor Equation (2), where (${\sigma }_L,{\sigma }_T,{\sigma }_{cp}$) = (5000, 200, 50) S/m. The meshing of the geometric model is depicted in Figure 3. The coil domain and CFRP domain are meshed using adaptive meshing, where the meshing becomes increasingly dense until the change in energy is below the predefined value (e.g., 0.1%) [18], while the air domain is meshed with refined tetrahedral meshes. A 1A quadrupolar current is passed through the excitation coil, inducing eddy currents in the CFRP prepreg. The number of nodes is approximately 250,000. The magnetic field produced by the eddy currents leads to variations in the magnetic flux in the detection coil, based on which the material properties of the CFRP prepreg can be deduced.

3.2. Material Attributes

Eddy current simulation analyses were conducted, respectively, for the isotropic copper plates and the anisotropic CFRP plates, and the results are presented as follows. Figure 4a depicts the eddy current distribution of the isotropic plate. It can be observed that the arrowheads of the eddy currents are evenly distributed, and their trajectories almost imitate the effect produced by the circular coil, presenting as regular and symmetrical. In this case, the direction and intensity of the eddy currents are the same in all directions of the plate, which indicates the homogeneity of the internal structure of the material and the consistency of the influence of the external magnetic field. Conversely, the eddy current distribution in the anisotropic plate shows completely different characteristics. As shown in Figure 4b, in anisotropic materials such as carbon fiber-reinforced plastic (CFRP) plates, the trajectories of the eddy currents exhibit a distinct divergence pattern, revealing significant non-uniformity. The reason behind this non-uniform distribution is the significant difference in electrical conductivity in different directions within the material. This difference in electrical conductivity between the longitudinal and transverse directions causes eddy currents to encounter varying resistances as they pass through the material, forming complex and variable trajectories. This reflects the intricate physical structure within the anisotropic material and provides direct evidence of how the current path is influenced by the material properties under an external magnetic field.

3.3. Research on Geometric Parameters of the Probe

The structure and parameter design of eddy current detection sensors is of paramount importance for ensuring efficient and accurate nondestructive testing. As the design of the sensor directly determines its capacity for detecting material defects, its sensitivity, and its penetration depth. In the detection of CFRP prepregs in this paper, considering the properties of CFRP, the expected detection accuracy, and the convenience of practical operation, parameters such as the geometric parameters of the coil and the lift-off height between the probe and the tested material are optimized. Based on this model, the relationship between the coil impedance and the working frequency, number of turns, diameter, inner diameter, height of the excitation coil, and the lift-off height between the probe and the tested material is studied. Hereby, the influence of the coil’s geometric parameters on the sensor’s sensitivity and linear range is investigated.

Separate simulation experiments were conducted by varying the number of coil turns (from 20 to 100 with a step of 10) at excitation frequencies ranging from 1 to 10 MHz (with a step of 1 MHz). The experimental results are depicted in Figure 5. When the excitation frequency is 1 MHz, the impedance difference between a 20-turn coil and a 50-turn coil is 0.53 Ω, and the impedance difference between a 20-turn coil and a 100-turn coil is 2.38 Ω. When the excitation frequency is 10 MHz, the impedance difference between a 20-turn coil and a 50-turn coil is 48.93 Ω, and the impedance difference between a 20-turn coil and a 100-turn coil is 223.61 Ω. Apparently, with the increase in the excitation frequency and the number of coil turns, the gradient of the coil impedance change gradually increases. In particular, when the number of coil turns exceeds 50, the coil impedance change becomes more significant. The coil inductance Equation (13) helps to improve our understanding of the conclusions related to coil design. However, an increase in the number of coil turns will enhance the magnetic field strength, and excessive turns may lead to signal attenuation.

$$L={\displaystyle \frac{\mu \cdot N^2\cdot \mathrm{Area}}{\mathrm{length}}}$$

(13)

In Equation (13), $L$ is the inductance of the coil, $\mu$ is the magnetic permeability, $N$ is the number of turns in the coil, area is the cross-sectional area of the coil, and length is the length of the coil.

Figure 6 presents the distribution diagrams of the magnetic flux density modulus at excitation frequencies of 1 MHz and 10 MHz, respectively. By comparing the two diagrams, we can see that low-frequency signals penetrate the inspected material more deeply, making them suitable for detecting deep defects. In contrast, high-frequency signals are better for detecting surface or small defects. By Equation (14), we can better understand that as frequency increases, the standard penetration depth decreases. This relationship highlights how higher frequencies cause the current to concentrate near the surface of the material, a phenomenon known as the skin effect. The skin depth δ is inversely proportional to the square root of the frequency, meaning that as frequency f increases, δ becomes smaller. This effect is crucial in applications such as nondestructive testing, where changes in penetration depth impact the accuracy of subsurface evaluations. Our method of detecting carbon fiber prepregs can only achieve depths of 1–2 mm, which is considered surface detection. Therefore, the simulation experiments in the following text use an excitation frequency of 10 MHz.

$$\delta ={\displaystyle \frac{1}{\sqrt{\pi \cdot \mu \cdot \sigma \cdot f}}}$$

(14)

$\delta$ is the skin depth, $\mu$ is the magnetic permeability of the material, $\sigma$ is the electrical conductivity, and $f$ is the frequency of the alternating current.

Figure 6. Distribution map of magnetic flux density magnitude: (a) 1 MHz magnetic flux density magnitude; (b) 10 MHz magnetic flux density magnitude.

Figure 6. Distribution map of magnetic flux density magnitude: (a) 1 MHz magnetic flux density magnitude; (b) 10 MHz magnetic flux density magnitude.

The number of fixed coil turns is set at 50, with an excitation frequency of 10 MHz. Parametric scanning is conducted on the inner diameter (d) of the coil (5–15 mm, with a step size of 5 mm), the outer diameter (D) (20–30 mm, with a step size of 5 mm), and the height of coil (H) (1–3 mm, with a step size of 1 mm), as they vary with the lift-off distance (0.6–1.5 mm, with a step size of 0.1 mm). The finite element model is solved to obtain the effects of each parameter on the coil impedance and the performance of the probe.

The influence of the inner diameter of the coil on the probe is depicted in Figure 7. When the inner diameter of the coil is 5 mm and the lift-off distance is increased by 0.1 mm, the maximum difference in coil impedance is 4.81 Ω. When the inner diameter of the coil is 15 mm and the lift-off distance is increased by 0.1 mm, the maximum difference in coil impedance is 22.32 Ω. The smaller the inner diameter of the probe, the smaller the gradient of the coil impedance variation with the lift-off height. Therefore, a smaller inner diameter coil can increase the density of the magnetic field and enhance the ability to detect local defects. The influence of the outer diameter of the coil on the probe is illustrated in Figure 8. When the outer diameter of the coil is 20 mm and the lift-off distance is increased by 0.1 mm, the maximum difference in coil impedance is 4.93 Ω. When the outer diameter of the coil is 30 mm and the lift-off distance is increased by 0.1 mm, the maximum difference in coil impedance is 18.51 Ω. The larger the outer diameter of the coil, the greater the gradient of the impedance variation with the lift-off height. Thus, it can be seen that a larger outer diameter can expand the detection range. The influence of the height of the coil on the probe is presented in Figure 9. When the height of the coil is 1 mm and the lift-off distance is increased by 0.1 mm, the maximum difference in coil impedance is 12.7 Ω. When the height of the coil is 3 mm and the lift-off distance is increased by 0.1 mm, the maximum difference in coil impedance is 12.63 Ω. The gradient of the coil impedance variation with the lift-off height is not significant. From Figure 7, Figure 8 and Figure 9, it is evident that the coil impedance shows a decreasing trend as the lift-off distance increases.

4. Detection of Surface Density of CFRP Prepreg

4.1. Simulation Model of CFRP Prepreg Materials

In CFRP prepreg, carbon fibers are arranged in diverse manners, such as unidirectionally (in which all carbon fibers are aligned parallel to the resin in the same direction), and in a woven formation (in which carbon fibers and resin are interlaced in a specific pattern), to meet specific application demands. The arrangement of fibers directly influences the mechanical and electrical properties of the material. Unidirectional arrangement offers the maximum strength and rigidity, while woven arrangement enhances the material’s impact resistance and electrical conductivity. In this section, we propose two distinct models, as shown in Figure 10, to address the simulation challenges brought about by the woven and unidirectional carbon fiber structures and the anisotropy of electrical conductivity of CFRP prepreg.

4.2. Simulation Outcomes and Discussion

By observing the distribution map of conductive current density in Figure 11 and exploring the distribution of conductive current density along the x, y, and z axes in the unidirectional carbon fiber model and the braided carbon fiber model in Figure 11a–c, it can be seen that the conductivity of the unidirectional carbon fiber is mainly concentrated in the direction of the fiber. Therefore, the current density along the y-axis is larger, the current density along the x-axis is smaller, and the conduction of current along the z-axis will encounter certain impedance; thus, the current density is relatively lower. This unidirectional structure enables the material to have a very high electrical conductivity in the direction of the fiber, while the electrical conductivity perpendicular to the fiber direction is significantly reduced. Therefore, the electrical conductivity of the unidirectional carbon fiber exhibits a strong anisotropy. By observing Figure 11d–f, it can be found that the distribution of conductive current density along the x, y, and z axes of the braided carbon fiber is relatively uniform. Along the x-axis, the conductivity of braided carbon fiber is similar to that of unidirectional carbon fiber. However, due to the interweaving of fibers in multiple directions, its conductivity is higher than that of unidirectional carbon fiber. Along the z-axis, the conduction path is relatively short, leading to a larger current density in this direction. This braided structure offers a more uniform distribution of electrical conductivity, making the conductivity in various directions more similar and reducing anisotropy.

We analyze Figure 12a,b to compare the variations in coil impedance and current density modulus of the braided and unidirectional models when the excitation frequency changes. With the increase in the excitation frequency, the real part of the coil impedance and the current density modulus increase accordingly. Under the same excitation frequency, the current density modulus of the braided model is approximately four times that of the unidirectional model. We analyze the real part of the coil impedance and the current density modulus independently, as shown in Figure 13. The conductivity of the braided carbon fiber model is superior to that of the strip carbon fiber model. Under the same excitation frequency gradient, the measured real part of the impedance of the braided carbon fiber plate is much larger than that of the strip carbon fiber model. It can be seen that the sensor probe designed in this paper is more sensitive to the surface density detection of the braided model.

5. Conclusions

The electrical conductivity within anisotropic materials exhibits remarkable differences when flowing in various directions. The disparity in electrical conductivity between the longitudinal and transverse directions causes eddy currents to encounter distinct resistances when traversing the material, thereby forming complex and variable trajectories. This reflects the intricate physical structure within anisotropic materials. Low-frequency signals can penetrate the inspected material more deeply to detect deep-seated defects, while high-frequency signals are more applicable to the detection of surface or minor defects. An increase in the number of coil turns enhances the magnetic field strength and elevates the sensitivity. The smaller the inner diameter of the coil, the smaller the gradient of the coil impedance variation with the lift-off height. The larger the outer diameter of the coil, the greater the gradient of the impedance variation with the lift-off height. A larger outer diameter can expand the detection range. The electrical conductivity of the braided carbon fiber model surpasses that of the unidirectional carbon fiber model. Under the same excitation frequency gradient, the measured real part of the coil impedance of the braided carbon fiber plate is considerably larger than that of the strip-shaped carbon fiber model.

Future research will validate the simulation model and design method proposed in this paper through experiments. The relationship between impedance changes obtained from simulations and actual detection results will be verified. CFRP samples with different structures, such as unidirectional and braided carbon fibers, will be compared in experiments to further validate the predicted current density distribution and electromagnetic response of the materials. Additionally, the effects of skin effect and proximity effect on the detection results will be considered. Probes with different frequencies and numbers of turns will be selected in the experiments to evaluate their impact on sensitivity and signal strength. These experimental validations will help optimize probe design, improve detection accuracy, and provide more reliable practical evidence for nondestructive testing technologies of CFRP materials.