Active microwave thermography (AMT) is an integrated nondestructive testing (NDT) technique that utilizes a microwave-based thermal excitation and subsequent thermal measurement. AMT has shown potential for applications in the transportation, infrastructure, and aerospace industries. This paper investigates the potential of AMT for detection of defects referred to as flat-bottom holes (FBHs) in composites with high electrical conductivity such as carbon fiber-based composites. Specifically, FBHs of different dimensions machined in a carbon fiber reinforced polymer (CFRP) composite sheet are considered. Simulation and measurement results illustrate the potential for AMT as a NDT tool for inspection of CFRP structures. In addition, a dimensional analysis of detectable defects is provided including a radius-to-depth ratio threshold for successful detection.

## Introduction

Nondestructive testing (NDT) of infrastructure is important to many industries including aeronautics and transportation as it relates to the inspection of carbon fiber reinforced polymer (CFRP) structures. Several NDT methods including microwave, ultrasound, X-ray, and thermography (active and passive) have been applied to the aeronautical and transportation industries (with varying levels of success) for inspection of infrastructure and composites [17]. Among these methods, microwave NDT is very limited for inspection of subsurface defects in conductive materials due to the lack of penetration of microwave energy into such materials. Additionally, while surface inspections of conductive materials are feasible, often the inspection time may be significant due to the need for raster scanning of the area of interest. Acoustic methods are successful in many arenas and are well-established. However, they often require operator expertise and contact with the material/structure under test. X-ray or computed tomography is also quite promising for many applications but brings significant safety requirements and precautions [4]. Thermography, both active and passive, is another well-established and successful technique. Passive thermography utilizes natural sources of thermal energy such as solar energy, structural loading, moisture evaporation, and air movement. On the other hand, active thermography utilizes an active source of thermal energy such as a flash lamp (as is used in traditional thermography), quartz lamp, electromagnetic, and acoustic. Passive thermography implies no control of the applied energy; rather, simply observing with an infrared camera, whereas active thermography implies control of the applied energy (for the purpose of inspection). Active thermography has been successfully applied to a number of NDT needs including defect detection in composite materials [57].

Active microwave thermography (AMT) is a relatively new NDT technique that is based on the integration of microwave and thermographic NDT [815]. In AMT, microwave energy is utilized to heat a structure of interest, and the resulting surface thermal profile is monitored via a thermal camera. Compared to traditional (flash lamp) thermography, AMT does not require substantial amounts of power [12], and several (electromagnetic) parameters can be optimized in order to tailor the inspection to a specific material including frequency and polarization. Recently, AMT has been utilized for detection of corrosion on steel [11], evaluation of steel-fiber reinforced concrete [12], and inspection of structures strengthened with unidirectional CFRP [1315], with promising results.

In general, when using a microwave-based thermal excitation, there are two possible heating mechanisms that may take place: dielectric heating and Joule heating. Dielectric heating takes place when the structure under test contains (lossy) dielectric materials. In general, the ability of a dielectric to generate heat is determined by its loss factor (ε″) which appears as the imaginary part of its complex dielectric constant (ε = ε′jε″). Due to the lossy electromagnetic properties of the material, microwave energy is absorbed and converted into heat. The real part of dielectric constant, on the other hand, represents the ability of the material to store electromagnetic energy. The other heating mechanism, Joule heating, occurs when conductive materials are present in the structure. When a conductor is exposed to electromagnetic radiation, depending on its electrical conductivity (σ), currents are induced on the surface of the conductive material. These currents serve as a secondary thermal excitation, as ohmic losses (which cause a subsequent thermal increase) occur when currents flow in a conductive material. In addition to direct ohmic losses, these induced currents may also serve as a secondary source of (reradiated) electromagnetic energy which can be subsequently absorbed by other nearby lossy dielectrics (such as the epoxy in CFRP materials).

In all cases, the heat generated from the electromagnetic energy diffuses throughout the material. Since defects and discontinuities affect the heat diffusion, a temperature difference on the surface of the structure will result if a defect is present. Analyzing the surface temperature profiles captured during an AMT inspection allows the defects to not only be detected, but also be characterized. As such, this paper investigates a new application of AMT as an NDT tool for inspecting defects in conductive (specifically CFRP) composites. The defects are modeled as cylindrical holes that are referred to as flat-bottom holes (FBHs) [16]. Representative simulated and measurement results are provided, showing the applicability of AMT for such inspections.

## Simulation and Analysis

In order to investigate the utility of AMT for inspection of FBHs in conductive materials, numerical modeling was conducted. More specifically, a finite slab containing an FBH under plane wave excitation is considered, as is illustrated in Fig. 1. The height of the dielectric slab is denoted as h, and the radius and depth of the defect are given as r and d, respectively.

Upon contact with the structure under inspection, portions of the incident plane wave will be reflected, absorbed by, and transmitted through the material. The absorbed energy is converted to heat, and therefore, can be considered as a thermal source. For a highly conductive material, there will not be any energy transmitted through the material. Thus, the incident energy is either reflected or absorbed. Further, for highly conductive materials, most of the incident energy will be reflected. The energy that is not reflected is absorbed within a very thin layer (essentially the surface) of the material. This layer is dimensionally on the order of the material's skin depth, $δ$, which is defined as $δ=1/πfμσ$, where f and μ are the incident wave frequency and material permeability, respectively. A CFRP laminate with electrical conductivity of σ = 50,000 S/m, for example, has a skin depth of $∼46μm$ at f = 2.4 GHz. As such, the thermal source can be considered as a uniform (due to the plane wave excitation) surface heat source, Qs, on the surface of the structure. Specifically, Qs may be quantified as
$Qs=Pinc−Pref=Pinc1−Γ2$
(1)
where Pinc and Pref are the incident and reflected wave power densities, respectively, and $Γ$ denotes the electromagnetic wave reflection coefficient of the air-structure interface and is defined at $Γ=η−η0/η+η0$. In this formula, η is the characteristic impedance (ratio of electric to magnetic fields of any electromagnetic wave in the medium) of the conductive material and is given by $η≅ωμ/σ$, and η0 is the characteristic impedance of freespace (i.e., 120π) [17].
The heat source of Eq. (1) generates thermal energy which extends throughout the structure volume over time. To calculate the time-dependent temperature distribution, T, the source-free heat equation given in Eq. (2) should be solved. The volumetric heat source in Eq. (2) is considered to be zero since there is no heat source inside the structure and the surface heat source over the inspection surface will be applied as an inflow heat flux boundary condition
$ρcp∂T∂t=∇·k·∇T$
(2)
Here ρ, cp, and k are the density, specific heat, and thermal conductivity tensor, respectively. The thermal conductivity, k, is considered a tensor due to the potential anisotropy of the structure. For example and as it relates to this work, the thermal conductivity for a CFRP laminate differs for the in-plane and along-the-depth (or transverse) directions (i.e., parallel and perpendicular to its embodied fibers, respectively). However, the same thermal conductivity is assumed along any in-plane direction. This assumption is valid for multidirectional fiber-reinforced composites as their fibers are oriented in several in-plane directions, rendering the same electrical and thermal behavior along these directions. Unidirectional composites, on the other hand, have different behaviors along the two in-plane normal directions of parallel- and perpendicular-to-the-fibers, requiring assignment of different values to the electrical and thermal conductivities in these directions. Taking this into consideration and assuming a cylindrical coordinate system with the z-axis being the axis of the FBH (modeled as a cylinder), the in-plane isotropy of thermal conductivity leads to angular symmetry of temperature (i.e., ∂T/∂φ = 0). As such, Eq. (2) can be expressed in cylindrical coordinates as [18]
$ρcp∂T∂t=1r∂∂rrkr∂T∂r+∂∂zkz∂T∂z$
(3)

where T is a function of space and time, and material properties ρ, cp, kr, and kz are a function of space (due to the inhomogeneity of CFRP and air). The values used in simulation for these parameters are provided in Table 1 [19,20].

Discretizing space and time as r = iΔr, z = jΔz, and t = kΔt, where i, j, and k are discretized coordinates, and Δr, Δz, and Δt are space and time steps, and using a forward-time centered-space scheme, finite difference approximations to each term in Eq. (3) may be written as
$ρcp∂T∂t≃ρi,jcpi,jTk+1i,j−Tki,jΔt$
(4)

$1r∂∂rrkr∂T∂r≃1iΔr×1Δr{i+1/2Δrkri+1/2,jTki+1,j−Tki,jΔr−i−1/2Δrkri−1/2,jTki,j−Tki−1,jΔr}$
(5)

$∂∂zkz∂T∂z≃1Δz{kzi,j+1/2Tki,j+1−Tki,jΔz−kzi,j−1/2Tki,j−Tki,j−1Δz}$
(6)
Also, boundary conditions are incorporated as
${kn∂T∂n=Qs−hc(T−Ta)top surface∂T∂n=0all other surfaces$
(7)
where n, hc, and Ta denote the direction normal to the boundary, convective heat transfer coefficient, and ambient temperature, respectively. The top surface boundary condition of Eq. (7) represents the heat generated by the microwave excitation and thermal energy loss due to convection. The remaining surfaces utilize the adiabatic boundary condition, meaning that the heat flux from these boundaries is assumed zero. A stable solution of Eqs. (4)(6) satisfies the stability condition [21] given as
$Δt≤12αmax1/Δr2+1/Δz2$
(8)

where αmax denotes the maximum thermal diffusivity of the materials involved.

The numerical model given above provides the temporal evolution of temperature in the material/structure. The temperature is subsequently analyzed over the inspection surface of the structure to predict the thermal profiles captured in practice by a thermal camera during an AMT inspection. Using this numerical technique is advantageous over commercial electromagnetic/thermal simulation software packages since it utilizes an analytical electromagnetic solution given in Eq. (1), instead of a time-consuming full-wave numerical solution. Specifically, due to the small skin depth (micrometers or less) of conductive materials, the mesh size should be taken comparably small and subsequently require a huge memory resource and processing time. Furthermore, the spatial two-dimensional heat transfer equation given in Eq. (3) (which has two spatial coordinates, r and z) is used rather than a three-dimensional simulation. Therefore, the simulations may run remarkably faster while providing accurate results (as will be shown later). The simulation time becomes specifically important when evaluating defects by a reverse approach. In such cases, the simulation is iteratively solved with swept values for dimensions in order to find the best match between the simulation and measurement results.

To quantify the temperature variation over the structure's inspection surface (in order to evaluate potential defects), the temporal temperature increase, ΔT(x,y,t), is defined as
$ΔTx,y,t=Tx,y,t−Tx,y,0$
(9)
where T(x, y, t) is the temperature distribution on the surface under inspection at a given time t, and T(x, y, 0) is the initial temperature distribution. Using ΔT instead of the absolute temperature, T, eliminates the effect of the initial temperature distribution over the surface and represents the temperature change resulting only from the microwave excitation. Another important parameter, referred to as the thermal contrast, (TC), is defined (temporally) as
$TCt=ΔTx,y,tD−ΔTx,y,tS$
(10)

where $·S$ and $·D$ denote the average over a given sound and defective area, respectively. Defective and sound areas refer to areas on the inspection surface above the location of defective and sound areas within the structure (as most defects are located beneath the surface). Therefore, the TC, as defined in Eq. (10), represents the temperature difference caused by the defect and can be used to evaluate the defect.

For an air-filled defect such as an FBH, a positive TC is expected as the air is a good thermal insulator, and therefore, reduces the loss of thermal energy through diffusion. As it relates to heat diffusion, FBHs with larger cross section and smaller depths will result in less radial and transverse heat diffusion, as compared to smaller or deeper FBHs. Therefore, the TC is expected to increase with FBH radius and decrease with depth. To verify these expectations and further study the detectability of FBHs as a function of dimensions, the TC obtained using the numerical technique discussed earlier and a coupled electromagnetic/thermal model created in CST MPHYSICS STUDIO (CST MPS) are shown as a function of depth for FBHs with 10, 15, and 20 mm radii in Fig. 2. The structure's height (h) is assumed to be 5 mm and the microwave excitation is applied for 420 s. Also, the frequency and power level of the incident energy are 2.4 GHz and 50 W (respectively) in all simulations (to be consistent with the measurement results given in Measurement Results Section).

The results of Fig. 2 show good agreement between those of the previously-mentioned numerical model and those obtained via CST MPS. As a result, the numerical approach developed for this work is used for all simulations hereafter. As is also evident in Fig. 2, the TC is dependent on the depth and radius of the FBHs. This quantity can be used to estimate the detection likelihood of a FBH with a certain r and d. To this end, TC is provided as isothermal contours versus r and d in Fig. 3. From this, it is noticeable that the TC decreases from the top-left corner of the r-d plane, which represents high r/d ratios, to the right-bottom corner, where r/d ratios are small. This ratio, called aspect ratio, is often used to estimate the detectability of a defect in traditional thermography [16]. Similarly, this ratio can be used as an estimate of defect detectability in AMT.

Theoretically, the minimum TC required for a successful detection is equal to the sensitivity of thermal camera used for measurement. As such, for any given structure, microwave excitation, and thermal camera, a region in the r-d plane exists which yields any combination of r and d for which FBHs are likely not detectable. In Fig. 3, this undetectable region occurs when TC falls below 30 mK, the sensitivity of the thermal camera used for measurements. However, in order to improve detection of such defects, the power level or frequency of the microwave excitation can be increased in order to increase the TC or using a thermal camera with lower sensitivity. In fact, according to Eq. (1), the surface heat source (Qs) is linearly proportional to the incident power (Pinc). Also, the intrinsic impedance of a conductor increases with frequency ($ωμ/σ$) and becomes more similar to that of freespace, thereby reducing the amount of reflected energy and increasing the absorbed energy. Therefore, as the TC is proportional to the absorbed power, it would also increase with increased excitation power and frequency. To verify this, Fig. 4 shows the TC after applying 420 s of microwave excitation as a function of frequency (in the operational band of the AMT system used for measurements) and excitation power for an FBH with r = 8 and d = 4 mm (an undetectable FBH per Fig. 3). According to Fig. 4, the TC meets the measurement threshold for a 75 W microwave excitation operating at a frequency greater than 3 GHz, or with a 100 W excitation and a frequency greater than 1.7 GHz. Therefore, for detection of any given FBH and temperature measurement sensitivity, there is a combination of minimum excitation power and frequency that must be met. However, practically speaking, this threshold may not be achievable, as increasing the power level and frequency both increase system cost. In addition, safety risks may also result as the power is increased. More specifically, for normal environmental conditions and for incident electromagnetic energy of frequencies from 10 MHz to 100 GHz, the radiation protection guide regulated by the Occupational Safety and Health Administration (OSHA) is 10 mW/cm2 as averaged over any possible 0.1 h period [22]. In this work, compliance with the OSHA radiation standard is achieved at least ∼80 cm from the horn antenna aperture. As it relates to the safety of the operator, if the operator remains outside of this area, OSHA compliance is achieved. Furthermore, utilization of specific frequencies may be restricted by the U.S.' Federal Communications Commission (FCC) or similar regulatory bodies in other countries. To comply with FCC regulations, the operating frequency of 2.4 GHz is used, which is in the unlicensed frequency band allocated for industrial, scientific, and medical (ISM) applications.

## Measurement Results

In order to further illustrate the potential for AMT to inspect CFRP structures, representative measurements on a CFRP sample, shown in Fig. 5, were made. The sample has a thickness (h) of 5 mm and includes nine FBHs with radii of 10, 15, and 20 mm, each with depths of 2, 3, and 4 mm. The other side of the sample is intact and is the interrogation and viewing side (i.e., surface that is excited by microwave energy and subsequently viewed with the thermal camera). The CFRP sample consists of a number of thin carbon fiber layers placed at various angles with respect to each other. Thus, the overall sample consists of fibers that can be assumed to be located at all angles (from 0 deg to 180 deg). As such, the thermal and electrical properties of the sample are identical along any in-plane direction (as discussed earlier for CFRP of this type). However, the fibers are transverse to the sheet normal direction which causes the along-the-depth properties differ from those of the in-plane.

The measurement setup is shown in Fig. 6 and consists of a microwave source and amplifier, horn antenna, thermal camera, and control and data acquisition unit. The thermal camera used in this work is the FLIR T430sc, with the specifications shown in Table 2. The control and data acquisition units synchronize the microwave and thermal segments of the AMT system. All measurements are conducted at a frequency of 2.4 GHz and a power level of 50 W. The horn antenna faces directly toward the sample surface to maximize the microwave-induced heat over the surface. The sample was placed at a distance of 17 cm from the antenna's aperture (herein referred to as the lift-off distance). This distance was chosen to ensure that the microwave excitation was sufficiently uniform over the inspection area but also allowed viewing of the sample surface with the thermal camera. More specifically, as a result of the electric field distribution of the horn antenna at the location of the sample, the energy is mostly focused over an area commensurate with the aperture size (23 × 17 cm2). The camera has a skewed view of the sample surface. The measurement setup is fixed during the entire measurement process. The thermal profiles taken by the thermal camera are subsequently rotated by postprocessing in order to remove the effect of the skew angle. The sample is placed on a thermal insulator (Styrofoam) to avoid thermal losses from the bottom surface.

The measurements were conducted for a total excitation time of 420 s (as in simulations). In order to observe the effect of defects on the thermal profile over the sample surface, Fig. 7 illustrates the surface thermal profile for an FBH with r = 20 mm and d = 2 mm at three instances of time within the excitation period.

The temperature increase is evident in both the defective and sound areas in Fig. 7. However, the temperature increases more rapidly over the defective area (the middle point of each image), resulting in a finite TC and a detectable FBH. This is significant in that while microwaves do not interact with the FBH directly, the FBH can still be detected due the effect of the FBH on thermal diffusion. This property of AMT is unique among microwave-based inspections, as traditional microwave NDT relies on the direct interaction of microwaves and materials, therefore finding application for subsurface defect detection in dielectric materials, but only surface inspections of conductive materials (such as CFRP). The variations in the background are partly due to the proximity of other FBHs and the sample edges to the main FBH under inspection. Furthermore, noise from environment (e.g., thermal energy from undesired sources reflected by the sample and captured by thermal camera), emissivity variations over the inspection surface, thermal camera noise, etc. show up in the thermal profiles. As the temperature values are small, the temperature variations are significant and easily seen.

To illustrate the effect of FBH radius and depth on the TC, measurement results for three FBHs with a 20 mm radius and depths of 2, 3, and 4 mm are shown in Fig. 8(a), and measurement results of three additional FBHs with a depth of 2 mm and radii of 20, 15, and 10 mm are shown in Fig. 8(b). Each measurement is repeated three times and the results are averaged. The TC is calculated based on the average measured temperature over 100 pixels for both defective and sound areas, in addition to a temporal average that is calculated over 100 frames. These averaging processes highly suppress temperature fluctuations due to noise. As seen in Fig. 8(a), the TC increases at a slower rate for deeper FBHs. In addition, the asymptotic maximum TC is also inversely proportional to depth. Similarly, as is evident in Fig. 8(b), the rate of increase of the TC is also proportional to FBH radius (i.e., larger radius, larger rate of increase). Both of these behaviors are as expected, per the results of simulations. Specifically, the TC at t = 420 s for the curves of Fig. 8(a) are roughly 260, 160, and 110 mK and they are 260, 150, and 90 mK for the curves given in Fig. 8(b). These values are in good accordance with the corresponding simulated TC values given in Fig. 2 for the simulated FBHs with the same radius and depth. This validates the presented simulation model as well as illustrates the potential of AMT for detection of FBHs in electromagnetically conductive structures.

To investigate the effect of sample distance and orientation with respect to the antenna on the AMT inspection results, Fig. 9 illustrates the TC versus time for an FBH of r = 20 mm and d = 2 mm for two different lift-offs and two orthogonal polarizations (referred to as P1 and P2). The polarization refers to the orientation of the incident electric field. Since the antenna is linearly polarized, the sample was rotated 90 deg with respect to the antenna to see the effect of polarization. As is evident in Fig. 9, a smaller lift-off results in a larger TC due to the increase in incident power level impinging on the sample surface (i.e., reduced free-space losses). In addition, for a given lift-off, the TC is independent of polarization. This is due to the multidirectional nature of the fibers within the CFRP sample (discussed earlier), causing the same electrical and thermal properties for all in-plane directions. Hence, selection of the polarization of the microwave excitation is not a concern for this sample. However, if the fibers are oriented in a single direction (i.e., unidirectional CFRP), the optimum electric field polarization is perpendicular to the fiber orientation so that the incident energy can penetrate into the sample and generate more heat, thereby providing a better TC (as is shown in Ref. [13]).

In AMT inspections, the temperature distribution is subject to nonideal temporal and spatial variations due to noise from the environment, emissivity variations over the inspection surface, internal noise of thermal camera, etc. Because of the relatively low temperature increase for AMT measurements of CFRP materials (on the order of 30-300 mK for the current CFRP sample), the level of noise is expected to be nontrivial relative to the thermal contrast caused by defects. To quantify and evaluate the effect of noise on the measurement results, the signal-to noise (SNR) is defined as [23]
$SNRt=10log10TC2tσS2t$
(11)
where $σS2$(t) is the noise power (variance of temperature distribution over sound area) and is calculated as
$σS2t=ΔTx,y,t−ΔTx,y,tS2S$
(12)

In Fig. 10, the SNR for three different FBHs is shown as a function of time. As expected, the SNR in Fig. 10 is higher for the FBHs with larger r or smaller d due to higher level of TC. More importantly, this quantity experiences a considerable rate of change during the first 60 s of microwave excitation. In addition, the SNR (in all cases) saturates (i.e., reaches an asymptotic value) after ∼120 s of microwave excitation. With this in mind, there is a maximum effective heating time of ∼120 s after which continued excitation does not improve the SNR. Therefore, the optimum (fastest inspection without loss of quality) inspection time can be considered ∼120 s for this application.

The SNR as defined in Eq. (11) uses the thermal contrast between defective and sound areas to evaluate the signal level. The SNR can also be considered from an image point-of-view (i.e., similar to the thermal images of Fig. 7) in order to observe its saturation and evaluate the noise level throughout the inspection surface. Thus, the SNR over the whole inspection surface may be defined as
$SNRx,y,t=10log10ΔTx,y,t−ΔTx,y,tS2σS2t$
(13)

Using Eq. (13), SNR images are presented in Fig. 11 for three different excitation times. As can be seen in Fig. 11, the defective area appears after only an excitation time of ∼30 s due to the steep increase in the signal (TC) level relative to noise shown in Fig. 10. Also, the SNR saturation evident in Fig. 11 can also be observed here by comparing the images at 120 and 420 s. In other words, the equivalence of the images at 120 and 420 s illustrates the SNR saturation and subsequently the maximum effective heat time.

## Conclusion

Active microwave thermography is an integrated nondestructive testing tool with strong potential in numerous aerospace and infrastructure applications. To this end, this work considers AMT as a potential inspection approach for detection of FBH defects in conductive composites (specifically, CFRP). Specifically, the effect of radius and depth, or combined as radius-to-depth ratio of FBH on its detection likelihood was studied through simulation and measurement. By considering the thermal contrast (i.e., difference between the temperature increase of a defective area and that of a sound/healthy area), it has been shown that detection likelihood can be improved by increasing the operating frequency of the microwave excitation or power level. AMT measurements were conducted for a number of FBHs machined in a multidirectional CFRP sheet showing practical possibility of detecting defects in conductive composites. The results showed that TC is independent of polarization selection for multidirectional (unlike unidirectional) CFRP due to its in-plane symmetrical structure. Ultimately, monitoring the SNR over time showed that a high level of defect information relative to background noise (>20 dB) is achievable after ∼60 s of microwave excitation and a maximum effective heat time of 120 s.

## Funding Data

• Division of Electrical, Communications and Cyber Systems National Science Foundation under (Grant No. 1609470).

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