Electromechanical-Mode Coupling Model and Failure Prediction of CFRP under Three-Point Bending

: Carbon ﬁber reinforced polymer materials (CFRP) cause CFRP to bend or fail when subjected to external loads or impacts. In the case of static three-point bending, using the conductive properties of the carbon ﬁber inside the CFRP, the overall damage detection and failure prediction can be carried out by electromagnetic methods. The eddy current coil is used to realize real-time monitoring of damage, and the measured voltage value can be mapped to obtain the load of the sample. This paper conducts theoretical analysis and experimental veriﬁcation, and obtains the relationship between CFRP stress damage and spatial conductivity change, and proposes a CFRP electromechanical coupling model under quasistatic three-point bending. Combined with the theory of electrically ineffective length, the CFRP three-point bending electromechanical coupling model was revised. Experimental results prove that the revised model can describe the load-conductivity change trend of three-dimensional braided CFRP more accurately, which provides a theoretical basis for monitoring the structural health of CFRP through electromagnetic methods.


Introduction
Currently, carbon fiber reinforced polymer materials (CFRP) have been widely used in industrial fields, such as aerospace, military manufacturing, and transportation [1]. After years of development, CFRP has gradually become the main load-bearing structural material in the abovementioned fields. The application of CFRP not only maintains strength and rigidity but also ensures overall safety and prolongs the service life of structural parts. In engineering applications, composite carbon fibers mainly bear loads and resist material deformation and damage caused by external forces. Carbon fibers are prone to matrix cracking, fiber fracture, and delamination [2], which degrades the overall structural mechanical properties.
With the wide application of CFRPs in aerospace, industrial, civil life, etc., composite materials show less damage during use, which is difficult to see with the naked eye. To ensure safety and stability during service, nondestructive testing of CFRPs has attracted wide attention [3], and nondestructive testing technology has been used to detect hidden potential damage without damaging the structure itself. Common detection technologies include ultrasonic detection, radiographic detection, laser ultrasound, and infrared thermal wave detection [4][5][6][7], but these technologies usually require couplants, and the detection equipment is relatively large, which is not suitable for fast scanning.
Most nondestructive testing techniques are usually applied to the study of static damage, while the methods mentioned above for the study of dynamic damage of composite real-time in situ monitoring and conducts a dynamic mechanical damage experiment of 3DAWF in quasi-static three-point bending. The experimental results prove that the FBC model has higher accuracy than the LBC model. We expect to be able to monitor the changes in the material state in real-time. Under the condition that the structural parts are known to bear the maximum load, the conductivity model is combined with the eddy current detection technology to perform full-cycle online health monitoring of the sample structure to realize the prediction of the remaining life of the structural parts.

Conductivity Change Model of CFRP under Three-Point Bending
Under the condition of quasi-static three-point bending, the CFRP material first undergoes bending deformation and interlayer cracks, and then the internal fibers break sequentially from bottom to top until the fiber completely breaks and fails. In the whole process, the conductivity change of CFRP is composed of two parts: 1. Macroscopically, the conductivity change of bending strain is caused by bearing load σ str . 2. Microscopically, after the fibers are broken, the conductive path is formed again, resulting in the conductivity change σ e f f . Therefore, the electrical conductivity σ t at time t using the mathematical expression is: a.
Load bending-conductivity σ str (LBC model) The piezoresistance change of the carbon fiber composite material under continuous stress is, the relevant parameters are shown in Figure 1a,b: where ∆R str is the change in resistance due to strain, R 0 is the initial resistance, and k is the strain sensitivity, where ε(x) represents the distribution of strain along the fiber, which depends on boundary conditions and loading methods. Normal stress F usually satisfies the following three mechanical relations: N is the axial force on the cross section, M y is the coupling moment on the y-axis, and M z is the coupling moment on the z-axis. Assuming that there is no extrusion between the layers parallel to the neutral layer, combined with the geometric relationship before and after deformation, the physical relationship satisfies Hooke's law: (4) where is the modulus of elasticity, is the distance between the fiber bottom layer and the neutral layer, and is the radius of curvature of the neutral axis after deformation.
From (3) and (4), the strain in the middle of the template can be obtained as: Combining (2) and (5) can get: Equation (6) establishes the relationship between the resistance change rate and the external load , the loading position, and the distance between the fiber bottom layer and the neutral layer. Usually, , , , ℎ, , and are constant values in the elastic zone. Therefore, the resistance change rate changes with the size of the load. Introducing a sensitivity coefficient , the equation can be simplified as: The sensitivity coefficient is constant when the position of the applied load is determined. In this paper, the position where the load is applied is always at 1/2, the sensitivity coefficient is constant, and the impedance change can be monitored in real-time under different load sizes, and Equation (7) shows that as the load increases, the rate of change of resistance also increases, and the two are in a linear relationship.
For carbon fiber composite materials, the volume fraction of internal conductive carbon fibers and the size of the material need to be considered: Assuming that there is no extrusion between the layers parallel to the neutral layer, combined with the geometric relationship before and after deformation, the physical relationship satisfies Hooke's law: where E is the modulus of elasticity, b is the distance between the fiber bottom layer and the neutral layer, and r is the radius of curvature of the neutral axis after deformation. From (3) and (4), the strain in the middle of the template can be obtained as: Combining (2) and (5) can get: Equation (6) establishes the relationship between the resistance change rate ∆R str R 0 and the external load P, the loading position, and the distance b between the fiber bottom layer and the neutral layer. Usually, E, k, l, h, ω, and are constant values in the elastic zone. Therefore, the resistance change rate changes with the size of the load. Introducing a sensitivity coefficient K x , the equation can be simplified as: The sensitivity coefficient K x is constant when the position of the applied load is determined. In this paper, the position where the load is applied is always at 1/2, the sensitivity coefficient is constant, and the impedance change can be monitored in real-time under different load sizes, and Equation (7) shows that as the load increases, the rate of change of resistance also increases, and the two are in a linear relationship.
For carbon fiber composite materials, the volume fraction of internal conductive carbon fibers and the size of the material need to be considered: From Equations (8) and (9), the initial resistance and the resistance R 0 and R t at time t can be obtained, where L x , L y is the length of the fiberboard along the x, y axis, e 0 is the thickness of the fiberboard, σ t , σ 0 are the electrical conductivity and initial electrical conductivity along the direction at time t, respectively, and V f is the volume fraction of the fiber. Bring these terms into Equation (7) to get: Thus, Equation (10) can be obtained at time t. When an external load P is applied, the relationship between the conductivity value and the load size, that is, σ t and P, is inversely proportional. As the load increases, the conductivity decreases.

b.
Fiber break-conductivity σ e f f (FBC model) The mechanical structure of CFRP can be regarded as a connection of multiple tiny springs, and its electrical structure can be regarded as a series-parallel network of multiple small resistances. As shown in Figure 2b,c, the left half is the schematic model of the micro spring of the mechanical fiber, and the right half is the electrical resistance change model. with the application of load, the mechanical structure of CFRP changes after the carbon fiber breaks. The load-bearing capacity is reduced, its electrical structures are connected to each other due to the broken fibers, and a new conductive network is formed again.
The conductivity of the broken fiber can be derived from the rate of change of the resistance of the broken fiber, which is similar to the derivation process of Equation (10) Based on the concept of electrically ineffective length proposed by Park, a model was proposed to predict the change in electrical resistance due to sample degradation and fiber breakage. Therefore, we added the electrical conductivity change caused by fiber damage to the overall electrical conductivity model. In the series/parallel array model, the overall failure resistance change rate can be expressed as: l ec is the electrically ineffective length; that is, due to the fracture and damage of the carbon fiber, the original conductive path can no longer carry current, and the adjacent contact fiber is a new conductive path, so the electrically ineffective length is the distance between adjacent contact points, as shown in Figure 2d. As shown, the value of l ec is the average length of the fiber contact point, E f is the overall Young's modulus, and χ, m are the material failure parameters of the Weibull distribution. Therefore, the overall conductivity change is affected by the bending strain of the specimen and the fiber fracture. Combining Equations (11) and (12) to modify the previous LBC model (10), we obtain: From Equation (13), as the load P increases, the electrical conductivity decreases. From a macroscopic point of view, the bending of the sample leads to a change in the electrical conductivity of the overall resistance. From a microscopic point of view, the fracture of internal fibers rebuilds new conductive paths and will continue to affect the electrical properties of CFRP. The bending strain will be the main influencing factor for changes in electrical conductivity. This model is applicable to all CFRP samples.

Experimental Materials
The experimental sample uses two three-dimensional angle interlocking woven carbon fiber composite materials (3DAWFs), a three-dimensional weave (PTW) structure, and a twill three-dimensional weave structure (TTW), and the carbon fiber is T800-12K. To damage the outer surface of the sample only by bending, according to the sample preparation guide D5687/D5687M, the standard span-thickness ratio of the sample is 32:1, the thickness of the standard sample is 3.8 mm, and the width is 13 mm. The length of the specimen is 20% longer than the supporting span. The span of the bending machine support roller is 121.6 mm, and the sample length is approximately 146 mm. The overall layup is 4 layers.
During the layup process, 5284 high-temperature epoxy resin is inserted between the prepregs to control the internal contact and fiber volume fraction of the CFRP laminate. The carbon fiber content is 55 ± 3%. Standard ASTMD7264 was used to test the three-point bending performance of the two structural layer interwoven composite materials.
Both structural lining warp layers on-line woven fabrics are composed of three sets of system yarns. The stuffer warp yarn (red) is stretched along the fabric forming direction. The layers are connected along the forming direction, and the yarns are sinusoidal in the interior as knotted warps (blue). The weft yarn (yellow) perpendicular to the fabricforming direction is generally straightened inside the fabric. Therefore, the overall conductivity change is affected by the bending strain of the specimen and the fiber fracture. Combining Equations (11) and (12) to modify the previous LBC model (10), we obtain: From Equation (13), as the load P increases, the electrical conductivity decreases. From a macroscopic point of view, the bending of the sample leads to a change in the electrical conductivity of the overall resistance. From a microscopic point of view, the fracture of internal fibers rebuilds new conductive paths and will continue to affect the electrical properties of CFRP. The bending strain will be the main influencing factor for changes in electrical conductivity. This model is applicable to all CFRP samples.

Experimental Materials
The experimental sample uses two three-dimensional angle interlocking woven carbon fiber composite materials (3DAWFs), a three-dimensional weave (PTW) structure, and a twill three-dimensional weave structure (TTW), and the carbon fiber is T800-12K. To damage the outer surface of the sample only by bending, according to the sample preparation guide D5687/D5687M, the standard span-thickness ratio of the sample is 32:1, the thickness of the standard sample is 3.8 mm, and the width is 13 mm. The length of the specimen is 20% longer than the supporting span. The span of the bending machine support roller is 121.6 mm, and the sample length is approximately 146 mm. The overall layup is 4 layers.
During the layup process, 5284 high-temperature epoxy resin is inserted between the prepregs to control the internal contact and fiber volume fraction of the CFRP laminate. The carbon fiber content is 55 ± 3%. Standard ASTMD7264 was used to test the three-point bending performance of the two structural layer interwoven composite materials.
Both structural lining warp layers on-line woven fabrics are composed of three sets of system yarns. The stuffer warp yarn (red) is stretched along the fabric forming direction. The layers are connected along the forming direction, and the yarns are sinusoidal in the interior as knotted warps (blue). The weft yarn (yellow) perpendicular to the fabric-forming direction is generally straightened inside the fabric.
Compared with TTW three-dimensional materials, the knotted warp yarn of PTW passes through two weft yarns in one cycle, and TTW three-dimensional woven material passes through four warp yarns in one cycle, as shown in Figure 3a,b. The two materials connect the two layers of carbon fiber woven fabric through the knotted warp yarn, thereby obtaining better high delamination resistance and high strength in the thickness direction. The relevant parameters of carbon fiber are shown in Table 1. Compared with TTW three-dimensional materials, the knotted warp yarn of PTW passes through two weft yarns in one cycle, and TTW three-dimensional woven material passes through four warp yarns in one cycle, as shown in Figure 3a,b. The two materials connect the two layers of carbon fiber woven fabric through the knotted warp yarn, thereby obtaining better high delamination resistance and high strength in the thickness direction. The relevant parameters of carbon fiber are shown in Table 1. The change in CFRP resistance is greatly affected by the size, and the conductivity is between 5 10 ~5 10 S/m. Therefore, to accurately measure the resistance of the sample, it is necessary to avoid and reduce contact resistance as much as possible. We polished the upper and lower surfaces of the sample along the width and thickness directions, removed the surface resin to expose the fibers, and then applied conductive silver glue to the surface evenly. After static air-drying, conductive copper tape was used to stick to the surface of the silver glue to increase the contact area between the positive and negative chucks of the impedance analyzer and the sample, thereby reducing the contact resistance, as shown in Figure 3c.

Simulation
According to the difference between the structure of plain weave and twill weave, modeling with COMSOL Multiphysics finite element analysis software, in the modeling, the state of binding warp yarn is simulated by sweeping a parameterized curve, and the  The change in CFRP resistance is greatly affected by the size, and the conductivity is between 5 × 10 3 ∼ 5 × 10 4 S/m. Therefore, to accurately measure the resistance of the sample, it is necessary to avoid and reduce contact resistance as much as possible. We polished the upper and lower surfaces of the sample along the width and thickness directions, removed the surface resin to expose the fibers, and then applied conductive silver glue to the surface evenly. After static air-drying, conductive copper tape was used to stick to the surface of the silver glue to increase the contact area between the positive and negative chucks of the impedance analyzer and the sample, thereby reducing the contact resistance, as shown in Figure 3c.

Simulation
According to the difference between the structure of plain weave and twill weave, modeling with COMSOL Multiphysics finite element analysis software, in the modeling, the state of binding warp yarn is simulated by sweeping a parameterized curve, and the warp yarn and weft yarn are arranged in an array. Consistent size and related parameters, reflecting only the CFRP structure caused by differences in the weave samples, are necessary for simulation.

Three-Point Bending Solid Mechanics Part
To explore the situation of the two structures under a three-point bending force, the length of the middle part of the model is 3 mm to simulate the width of the lower indenter, and two cylinders with a span of 122 mm are placed under the sample as fixed constraints to simulate the supporting roller. Set the downward force on the upper surface of the middle part to simulate the applied load P. PTW and TTW bending deflection curves under force as shown in Figure 4. The relevant mechanical setting parameters are shown in Table 2.
reflecting only the CFRP structure caused by differences in the weave samples, are necessary for simulation.

Three-Point Bending Solid Mechanics Part
To explore the situation of the two structures under a three-point bending force, the length of the middle part of the model is 3 mm to simulate the width of the lower indenter, and two cylinders with a span of 122 mm are placed under the sample as fixed constraints to simulate the supporting roller. Set the downward force on the upper surface of the middle part to simulate the applied load P. PTW and TTW bending deflection curves under force as shown in Figure 4. The relevant mechanical setting parameters are shown in Table 2.  The load P on the PTW and TTW three-dimensional braided structure is increased from 100 N to 500 N to obtain the load-strain curve. From Figure 5 of the force bending deflection curve, as the load increases, the deflection growth rate of the PTW sample is greater than the deflection growth rate of the TTW structure sample. Under the same stress, the TTW structure should change less.  The load P on the PTW and TTW three-dimensional braided structure is increased from 100 N to 500 N to obtain the load-strain curve. From Figure 5 of the force bending deflection curve, as the load increases, the deflection growth rate of the PTW sample is greater than the deflection growth rate of the TTW structure sample. Under the same stress, the TTW structure should change less. For the PTW structure, the top view of the stress distribution shows that along the length of the template, the support roller and the stress area are the reddest. In the middle position between the support rollers, the red color is concentrated on the knotted warp yarn and the stuffer warp yarn. In the areas on both sides of the support roller, the red color is concentrated on the knotted warp yarn, indicating that the knotted warp and the stuffer warp mainly bear most of the stress in the z-axis direction. For the top view of the stress distribution of the TTW structure, the dark red part appears as an oblique stripe, indicating that the knotted warp yarn bears most of the stress in the z-axis direction.
The similarity between the two structures is that the warp yarns bear greater stress. Because the knotted warp yarns are laid into the weft yarn system at a certain buckling change angle along the thickness direction, they present a wavy state. The buckling and fluctuating knotted warp yarns effectively transfer the bending load to other areas in the thickness direction, while the weft yarns are distributed flatly in the yarn system, and there is no special stress distribution area. The difference is that the twill weave structure can withstand a higher level of stress load than the plain weave structure because of its high fabric density, and the knotted warp yarns bear most of the stress.

Electromagnetic Simulation
A dual-coil sensor is designed as shown in Figure 6. A small coil is placed in the large coil, where the large coil is the excitation coil and the small coil is the collection coil, and the sensor is placed in the center of the sample. In the simulation, the two types of structures choose to use the LBC model to solve the conductivity value within the average load pressure range. For the PTW structure, the top view of the stress distribution shows that along the length of the template, the support roller and the stress area are the reddest. In the middle position between the support rollers, the red color is concentrated on the knotted warp yarn and the stuffer warp yarn. In the areas on both sides of the support roller, the red color is concentrated on the knotted warp yarn, indicating that the knotted warp and the stuffer warp mainly bear most of the stress in the z-axis direction. For the top view of the stress distribution of the TTW structure, the dark red part appears as an oblique stripe, indicating that the knotted warp yarn bears most of the stress in the z-axis direction.
The similarity between the two structures is that the warp yarns bear greater stress. Because the knotted warp yarns are laid into the weft yarn system at a certain buckling change angle along the thickness direction, they present a wavy state. The buckling and fluctuating knotted warp yarns effectively transfer the bending load to other areas in the thickness direction, while the weft yarns are distributed flatly in the yarn system, and there is no special stress distribution area. The difference is that the twill weave structure can withstand a higher level of stress load than the plain weave structure because of its high fabric density, and the knotted warp yarns bear most of the stress.

Electromagnetic Simulation
A dual-coil sensor is designed as shown in Figure 6. A small coil is placed in the large coil, where the large coil is the excitation coil and the small coil is the collection coil, and the sensor is placed in the center of the sample. In the simulation, the two types of structures choose to use the LBC model to solve the conductivity value within the average load pressure range. The lift-off height of the dual-coil sensor is 0.3 mm from the sample surface, and the coil current is set to 1A. To make the impedance of the sample appear inductive and allow the current to pass through the sample better, the frequency is set to a high frequency of 1 MHz in the simulation.
The height of the two coils is 8.6 mm, and the number of turns is 100 r. The model is shown in Figure 6. To obtain a strong signal as a whole, the radius of the excitation coil is set to 6.2 mm.
For the selection of the radius of the collection coil, to obtain the size of the collection coil most sensitive to defects, a series of internal diameter values of the collection coil with a radius of 5~2.8 mm was tested in the simulation, and coils with different radii were placed in intact and defective tests. In the sample, the voltage difference between the two conditions is measured.
From Figure 7b, a series of coils with different radius are tested, and it can be found that as the coil radius decreases, the overall signal also decreases. However, the difference between the voltage values in the non-damaged and damaged state is found to be the largest when the radius is 4.6 mm, indicating that the radius of 4.6 mm is the most sensitive to damage response.
When the coil radius is determined and the thickness of the coil is optimized, Figure  7c, it can be found that as the thickness of the coil increases, the overall signal is in a state of decreasing. Similarly, the voltage difference between the non-damaged and damaged state is made. When the thickness is 1 mm, the voltage difference at this time is the largest.
As shown in Figure 7d, when the size of the collection coil is 4.6 mm, the voltage value changes most obviously, which is better than the other 6 groups of coil sizes, and the sensitivity is 46% higher than the average.
Simultaneously, the thickness of the coil was simulated. The diameter of the coil copper wire was 0.2 mm, so it increased from 0.2~1.2 mm with a step length of 0.2 mm. As shown in Figure 7e, when the coil was 1 mm thick, the sensitivity to damage was the best compared to the overall average increase of 278%. The lift-off height of the dual-coil sensor is 0.3 mm from the sample surface, and the coil current is set to 1 A. To make the impedance of the sample appear inductive and allow the current to pass through the sample better, the frequency is set to a high frequency of 1 MHz in the simulation.
The height of the two coils is 8.6 mm, and the number of turns is 100 r. The model is shown in Figure 6. To obtain a strong signal as a whole, the radius of the excitation coil is set to 6.2 mm.
For the selection of the radius of the collection coil, to obtain the size of the collection coil most sensitive to defects, a series of internal diameter values of the collection coil with a radius of 5~2.8 mm was tested in the simulation, and coils with different radii were placed in intact and defective tests. In the sample, the voltage difference between the two conditions is measured.
From Figure 7b, a series of coils with different radius are tested, and it can be found that as the coil radius decreases, the overall signal also decreases. However, the difference between the voltage values in the non-damaged and damaged state is found to be the largest when the radius is 4.6 mm, indicating that the radius of 4.6 mm is the most sensitive to damage response.
When the coil radius is determined and the thickness of the coil is optimized, Figure 7c, it can be found that as the thickness of the coil increases, the overall signal is in a state of decreasing. Similarly, the voltage difference between the non-damaged and damaged state is made. When the thickness is 1 mm, the voltage difference at this time is the largest.
As shown in Figure 7d, when the size of the collection coil is 4.6 mm, the voltage value changes most obviously, which is better than the other 6 groups of coil sizes, and the sensitivity is 46% higher than the average.
Simultaneously, the thickness of the coil was simulated. The diameter of the coil copper wire was 0.2 mm, so it increased from 0.2~1.2 mm with a step length of 0.2 mm. As shown in Figure 7e, when the coil was 1 mm thick, the sensitivity to damage was the best compared to the overall average increase of 278%. Electronics 2021, 10, x FOR PEER REVIEW 11 of 18 In the simulation, we use the LBC and FBC models to determine the conductivity. We choose a 500-N load and observe the trends of the two models, as shown in Figure 8. The results show that the FBC model is used to solve the conductivity. The parameters are shown in Table 3. The change trend is greater than the change trend of the LBC model, but the difference between the two is not large, showing that the damage caused by the fiber load will affect the electrical conductivity. Table 3. Related parameters of the electromagnetic simulation.

Coil
Parameter Excitation coil radius 6.2 mm Collection coil radius 4.6 mm Number of turns 100 r In the simulation, we use the LBC and FBC models to determine the conductivity. We choose a 500-N load and observe the trends of the two models, as shown in Figure 8. The results show that the FBC model is used to solve the conductivity. The parameters are shown in Table 3. The change trend is greater than the change trend of the LBC model, but the difference between the two is not large, showing that the damage caused by the fiber load will affect the electrical conductivity. The displacement field change of the mechanical simulation is divided into three parts according to the different colors, as shown in the displacement field deflection change cloud diagram in Figure 9a. C1 is the dark red area with the maximum strain part, the length is approximately 30 mm; C2 is the medium strain part from red to light blue, and the total length is approximately 56 mm; and C3 is the dark blue part, which has the lowest strain, and the length is approximately 60 mm.
The conductivity values of the two structures are set within the average load pressure range. The different load sizes of the two structures are the average load that the two structures can withstand in the reference experiment. The PTW is 450 N and the TTW structure is 670 N. After calculating the LBC model and the FBC model separately, the coil voltage curves of the two structures are obtained, as shown in Figure 9c. The coil voltages of the two structures have the same change trend, and they decrease exponentially with increasing load.
The predicted value of the FBC model is lower than the predicted value of the LBC model, and the overall downward trend is faster, but the difference between the two is not very large, indicating that the bending strain is the main reason for the change in electrical conductivity.
The bottom carbon fiber is cracked due to bending, and then the broken fiber is reconnected. The new conductive path formed has an impact on the overall conductivity change, but it is not the main factor.   The displacement field change of the mechanical simulation is divided into three parts according to the different colors, as shown in the displacement field deflection change cloud diagram in Figure 9a. C1 is the dark red area with the maximum strain part, the length is approximately 30 mm; C2 is the medium strain part from red to light blue, and the total length is approximately 56 mm; and C3 is the dark blue part, which has the lowest strain, and the length is approximately 60 mm.
The conductivity values of the two structures are set within the average load pressure range. The different load sizes of the two structures are the average load that the two structures can withstand in the reference experiment. The PTW is 450 N and the TTW structure is 670 N. After calculating the LBC model and the FBC model separately, the coil voltage curves of the two structures are obtained, as shown in Figure 9c. The coil voltages of the two structures have the same change trend, and they decrease exponentially with increasing load.
The predicted value of the FBC model is lower than the predicted value of the LBC model, and the overall downward trend is faster, but the difference between the two is not very large, indicating that the bending strain is the main reason for the change in electrical conductivity.
The bottom carbon fiber is cracked due to bending, and then the broken fiber is reconnected. The new conductive path formed has an impact on the overall conductivity change, but it is not the main factor.

Experimental Methods and Equipment
This section discusses a 3DAWF sample, an electromagnetic eddy current real-time monitoring system, and a universally powerful machine. In the experiment, a single longitudinal load was applied to the carbon fiber sample through a universal strength machine, and a three-point bending experiment was carried out until the sample fractured. During this process, an electromagnetic eddy current real-time monitoring system was used to monitor the sample throughout the whole cycle.
As shown in Figure 10, in the experiment, the sample was placed in the middle of the supporting roller, and both ends were fixed on the supporting roller to prevent the sample position from shifting during the bending process. To obtain the most obvious change trend, the monitoring probe is fixed directly under the applied load of the sample, and the probe and the load nose are in the same straight line. The AG1KNE model universal strength machine produced by the Shimadzu Corporation was used to apply the load at a loading rate of 1 mm/min, and the load was applied until the sample broke. For realtime monitoring, a DMET multichannel digital electromagnetic tomography online imager is selected to detect the electromagnetic characteristics of the sample.
During the experiment, due to the application of external force, the sample was bent, the fibers were broken, and the original conductive network was destroyed, which caused the conductivity of the sample to change.
Thus, the mapping can be utilized with the dependence of the conductivity of the load to explore the relationship between the load voltage signal and the eddy current coil.

Experimental Methods and Equipment
This section discusses a 3DAWF sample, an electromagnetic eddy current real-time monitoring system, and a universally powerful machine. In the experiment, a single longitudinal load was applied to the carbon fiber sample through a universal strength machine, and a three-point bending experiment was carried out until the sample fractured. During this process, an electromagnetic eddy current real-time monitoring system was used to monitor the sample throughout the whole cycle.
As shown in Figure 10, in the experiment, the sample was placed in the middle of the supporting roller, and both ends were fixed on the supporting roller to prevent the sample position from shifting during the bending process. To obtain the most obvious change trend, the monitoring probe is fixed directly under the applied load of the sample, and the probe and the load nose are in the same straight line. The AG1KNE model universal strength machine produced by the Shimadzu Corporation was used to apply the load at a loading rate of 1 mm/min, and the load was applied until the sample broke. For real-time monitoring, a DMET multichannel digital electromagnetic tomography online imager is selected to detect the electromagnetic characteristics of the sample.
During the experiment, due to the application of external force, the sample was bent, the fibers were broken, and the original conductive network was destroyed, which caused the conductivity of the sample to change.
Thus, the mapping can be utilized with the dependence of the conductivity of the load to explore the relationship between the load voltage signal and the eddy current coil.

Experimental Results
As shown in Figure 11, the resistance value of the TTW and PTW weave samples before and after the load is bent is measured using an impedance analyzer to obtain the resistance change rate ΔR/R , which is divided by the load applied to it to obtain the K . After calculation, the value ranges of PTW and TTW are 7.3 10 ~9.1 10 and 8.5 10 ~12.1 10 , respectively.
In the experiment, the constant pressing rate of the universal strength machine is set to 1 mm/min. To prevent the sample from slipping, a 2 N preload is applied. Figure 12 shows the deflection-load curve of the two structures. The average loads of the PTW structure and TTW structure samples are 465.98 N and 671.98 N, respectively. The figure shows that before fracture, the load increases linearly with the deflection. When the deflection reaches 10 mm, the load decreases rapidly. The specimens of the two structures fail. At this time, a large number of fibers break, and the matrix cracks.

Experimental Results
As shown in Figure 11, the resistance value of the TTW and PTW weave samples before and after the load is bent is measured using an impedance analyzer to obtain the resistance change rate ∆R/R 0 , which is divided by the load applied to it to obtain the K x . After calculation, the value ranges of PTW and TTW are 7.3 × 10 −3 ∼ 9.1 × 10 −3 and 8.5 × 10 −4 ∼ 12.1 × 10 −4 , respectively. In the experiment, the samples of the two structures were monitored for the whole cycle. To reduce the error, we averaged every 100 data values measured to obtain a new average data value and made a scatter plot of the final multiple average values. The TTW structure can bear greater stress, the measurement time is longer, and the voltage average In the experiment, the constant pressing rate of the universal strength machine is set to 1 mm/min. To prevent the sample from slipping, a 2 N preload is applied. Figure 12 shows the deflection-load curve of the two structures. The average loads of the PTW structure and TTW structure samples are 465.98 N and 671.98 N, respectively. The figure shows that before fracture, the load increases linearly with the deflection. When the deflection reaches 10 mm, the load decreases rapidly. The specimens of the two structures fail. At this time, a large number of fibers break, and the matrix cracks. Figure 11. Impedance analyzer measures the rate of change of resistance.
In the experiment, the samples of the two structures were monitored for the whole cycle. To reduce the error, we averaged every 100 data values measured to obtain a new average data value and made a scatter plot of the final multiple average values. The TTW structure can bear greater stress, the measurement time is longer, and the voltage average scatter diagram of the TTW structure is relatively denser than the voltage average scatter diagram of the PTW structure. When the sample breaks, the full cycle data collection stops. Due to the stretching of the fibers in the early stage and the breakage of the fibers in the later stage and reattachment, the electrical resistance of the material itself continues to In the experiment, the samples of the two structures were monitored for the whole cycle. To reduce the error, we averaged every 100 data values measured to obtain a new average data value and made a scatter plot of the final multiple average values. The TTW structure can bear greater stress, the measurement time is longer, and the voltage average scatter diagram of the TTW structure is relatively denser than the voltage average scatter diagram of the PTW structure. When the sample breaks, the full cycle data collection stops.
Due to the stretching of the fibers in the early stage and the breakage of the fibers in the later stage and reattachment, the electrical resistance of the material itself continues to increase, but the growth rate decreases, so the electrical conductivity of the material also decreases and tends to be flat. This is because matrix cracking occurs in the early stage itself. The greater the applied load, the smaller the stress or strain ratio, and the faster the damage development. In the later stage, the carbon fiber in the matrix will gradually break with increasing load, which means that the crack density tends to be saturated. The measured average voltage value of the coil changes significantly at the end, and the overall trend decays exponentially.
We normalize the average coil voltage measured in the experiment, use the same coefficient to normalize the coil voltage value obtained in the simulation using the two models of LBC and FBC, and compare the two, as shown in Figure 13. The LBC model has a large gap, but the simulation results of the FBC model fit well with the experimental results. a large gap, but the simulation results of the FBC model fit well with the experimental results.
In summary, the FBC model is used for prediction. The effect is better, and it can more accurately describe the stress-conductivity change trend of three-dimensional braided CFRP. Therefore, we can use the electromechanical coupling relationship obtained by the FBC model to reflect the physical damage changes during the bending process of the sample. Figure 13. Normalized comparison between the simulation and experimental results. The (left) picture shows the PTW structure, and the (right) picture shows the TTW structure.

Conclusions
1. Due to the unique binding warp yarn embedded in the thickness direction of the three-dimensional angle interlocking structure, the material has better high delamination resistance and high strength in the in-plane direction and the thickness direction than the ordinary two-dimensional woven structure material. The buckling and fluctuating binding warp yarns effectively transfer the bending load to other areas in the thickness direction, while the weft yarns are distributed flatly in the yarn system, and there is no special stress distribution area. The difference is that TTW has a high fabric density, and the binding warp yarn bears most of the stress. Therefore, when a quasistatic load is applied, the TTW structure can withstand a higher level of load than the PTW structure when it breaks. 2. When the specimen is bent, matrix cracking occurs first. The greater the applied load, the smaller the stress or strain ratio, and the faster the damage will develop. In the latter half, when the carbon fiber in the matrix gradually breaks with the increase of the load, it means that the crack density tends to be saturated, and at this time, the damage of the material becomes slow. In the bending test, due to changes in the internal fibers, such as stretching and breaking, the electrical resistance of the material itself increases, so the electrical conductivity of the material also decreases accordingly. The electrical conductivity of the material changes so that the magnetic field In summary, the FBC model is used for prediction. The effect is better, and it can more accurately describe the stress-conductivity change trend of three-dimensional braided CFRP. Therefore, we can use the electromechanical coupling relationship obtained by the FBC model to reflect the physical damage changes during the bending process of the sample.

1.
Due to the unique binding warp yarn embedded in the thickness direction of the threedimensional angle interlocking structure, the material has better high delamination resistance and high strength in the in-plane direction and the thickness direction than the ordinary two-dimensional woven structure material. The buckling and fluctuating binding warp yarns effectively transfer the bending load to other areas in the thickness direction, while the weft yarns are distributed flatly in the yarn system, and there is no special stress distribution area. The difference is that TTW has a high fabric density, and the binding warp yarn bears most of the stress. Therefore, when a quasistatic load is applied, the TTW structure can withstand a higher level of load than the PTW structure when it breaks.

2.
When the specimen is bent, matrix cracking occurs first. The greater the applied load, the smaller the stress or strain ratio, and the faster the damage will develop. In the latter half, when the carbon fiber in the matrix gradually breaks with the increase of the load, it means that the crack density tends to be saturated, and at this time, the damage of the material becomes slow. In the bending test, due to changes in the internal fibers, such as stretching and breaking, the electrical resistance of the material itself increases, so the electrical conductivity of the material also decreases accordingly. The electrical conductivity of the material changes so that the magnetic field excited by the excitation coil in the material changes accordingly. Therefore, using the principle of electromagnetic induction, the voltage collected by the fabricated coil probe can indirectly indicate the physical damage change during the bending process of the sample.

3.
Combined with the theory of electric ineffective length, the previous three-point bending electromechanical coupling model (LBC) of three-dimensional braided CFRP was revised. Experimental results prove that the revised FBC model can more accurately describe the stress-conductivity change trend of three-dimensional braided CFRP, which provides a theoretical basis for monitoring the structural health of CFRP through electromagnetic methods.