Delamination Localization in Multilayered CFRP Panel Based on Reconstruction of Guided Wave Modes

: Multi ‐ layered composite materials are being used in various engineering fields, such as aerospace, automobile, and wind energy, because of their superior material properties. Due to var ‐ ious impact loads during the service life of composite structures, different types of defects can occur, such as matrix cracking, fiber breakage, delaminations


Introduction
Multilayered composite materials are extensively used in aerospace and other engineering fields because of their impressive material properties, such as high stiffness, low weight, and corrosive resistance. As a result, the implementation of these materials contributes to reducing aircraft weight, improving fuel economy, and decreasing flight operation costs [1][2][3][4][5]. Various failure mechanisms can affect composite structures during manufacturing due to design errors or overheating or during service due to static overload, shock, and fatigue. Common defects in composites are fiber failure, buckling, matrix cracking, and delamination [6][7][8][9][10]. If these defects are not detected in composite materials, they can lead to catastrophic structural failure. Fiber failure is relatively straightforward to detect when the composite structure experiences static and dynamic loads. Matrix damage takes different forms, such as voids or cracks within the fibers of the lamina or as a single intralaminar defect within a composite layer. Buckling is another form of failure, commonly appearing as a shear or compression failure.
Delamination is a crucial failure mechanism and represents one of the significant vulnerabilities in multilayered composites. If these types of defects are not detected, delamination can propagate through the composite laminates. Delamination in composite structures can significantly compromise their stiffness, potentially leading to complete of A mode. Then the analytical GW modes were reconstructed following different propagation scenarios such as reflected, converted, and overlapped modes. By selecting the A mode, analytical modeling, numerical simulation, and experiments were performed to detect and estimate the location of the delamination. The objective of this research is to present a novel analytical model to locate the delamination in the presence of reflected, converted, overlapped, and low-amplitude GW modes. A phase velocity reconstruction approach was proposed to reconstruct the velocity of unknown materials from the baseline reference data. An efficient SHM technique was developed to detect and localize the delamination in the multi-layered CFRP material with a minimum number of sensors.
Theoretical analysis of GW interaction with delamination analytical, numerical, and experimental analysis of GWs to increase the probability of detection in CFRP material was used. The quantitative and qualitative analysis for the estimation of delamination position is assessed.

Modeling Setup
For inspection, a multilayered CFRP plate measuring 450 mm in length and 3.5 mm in thickness was selected. The investigated sample was manufactured from 18 plies of carbon fiber, and the orientation of the plies are (-45°, 0°, +45°, 0°, 90°, 0°, -45°, 0°, and +45°) 2 . The mechanical properties of the CFRP used in the numerical simulation are presented in Table 1. Here, E is Young's modulus, G is the shear modulus, is the Poisson's ratio, is the density of CFRP, and is the ply thickness. In this 2D model, the x-axis is along the fibers, the y-axis is along the thickness of the CFRP plate, and the z-axis is assumed to be infinitely long. The location of delamination was analyzed in two cases by placing the receivers before and after the delamination. In case 1, two receivers were placed at distances of 10 mm and 20 mm from the leading edge of the delamination. In case 2, three receivers were placed at distances of 10 mm, 20 mm, and 30 mm from the trailing edge of the delamination. The through-thickness location of the delamination (Xh) was 1.7 mm. The cases studied, the delamination and receiver position, and distances are presented in Table 2.  1  250  230  20  1-2  250  240  10  2-1  250  280  10  2-2  250  290  20  2-3  250  300  30 The 2D simulation was performed to analyze a GW interaction with a delaminationtype defect with a length of 20 mm. The delamination was located at 250 mm along the longitudinal direction and 1.7 mm in the thickness direction, as shown in Figure 1. The transmitter-receiver configuration was used to perform the inspection. A normal force was applied at the point-type excitation source to propagate the A0 mode. To minimize the distortion of guided waves, a point-type excitation was selected. The excitation source was placed at 70 mm from the leading edge of the CFRP plate.

Guided Wave Dispersion Curves
Obtaining dispersion curves is an important task for the selection of appropriate GW modes and the excitation frequency for the inspection. The SAFE method is a fundamental technique used to compute the dispersion curves of guided waves. In this method, a 2D arbitrary plate is divided into elements in the thickness direction, and the x-axis corresponds to the wave propagation direction, as shown in Figure 2. The governing equation of the plain strain model for wave propagation in an elastic medium using the SAFE method can be represented by the following equation [56]: where is the Lamé constant, μ is the shear modulus, is the density, and t is the time. The , , and are symmetric, shear horizontal, and asymmetric displacement vectors.
In this study, it was assumed that the plate's width is infinitely long along the y-axis. A totla of 36 elements are assigned in the z-axis, the thickness of the plate is discretized into elements, and each element is 0.097 mm. In this multilayered CFRP plate, each ply is assigned two elements. Each ply had a thickness of 0.194 mm, and the thickness of 18 plies of CFRP plate was 3.5 mm.
The purpose of the SAFE method was to determine the phase velocity, , and group velocity, , at various frequencies. The dispersion curves obtained for the CFRP plate under investigation are presented in Figure 3a,b. Based on the dispersion curves, it can be observed that at a frequency of 150 kHz, the A0 mode phase and group velocities are 1450 m/s and 1623 m/s, respectively. The S0 mode phase and group velocities are 7664 m/s and 7616 m/s, respectively.
The maximum amplitude of each mode varies depending on the excitation frequency. At higher frequencies, the guided wave modes exhibit higher-order modes with smaller wavelengths. However, this results in complex signal interpretation because of dispersion, as multiple modes are superimposed on each other. By selecting the frequency range of 150 kHz, only fundamental modes were exhibited, and higher-order modes should not be present.

Guided Wave Frequency Tuning Curves
In GW inspection, fundamental or higher-order modes can be selected for the inspection according to dispersion curves. The dispersion curves obtained give only velocity and frequency, but the sensitive mode cannot be selected. For this purpose, GW tuning curves are important to select sensitive mode and optimal frequency for the inspection.
To obtain the frequency tuning curves, the simulation was carried out in COMSOL with a contact transducer having similar properties to those of the transducer used in the experiments. Figure 4 shows the schematic diagram of the inspection setup. GW excited with an excitation frequency range from 10 to 300 kHz on a 3.5 mm CFRP plate. The maximum displacements of both S0 and A0 were calculated for each 10 kHz frequency step. The maximum displacements of the GW modes are presented in Figure 5. Frequency tuning curves are used to select the optimal GW mode for the inspection.  The A0 mode is sensitive to delamination-type defects and is also sensitive to the length of the delamination. The displacements of the A0 mode are higher than those of the S0 mode at 150 kHz frequency and are dominant. Therefore, the A0 mode is selected for inspection.

Reconstruction of GW Modes
The working procedure of the combined phase spectrum and analytical model is presented in Figure 6. The proposed analytical model is divided into two steps: one is pre-processing, whereas B-scan data refer to baseline data obtained prior to installing the sensors to reconstruct the phase velocity of GW modes. Another is post-processing, whereas GW mode was reconstructed to measure the defect location. The first step in this method is to perform 2D FFT on B-scan data obtained from the inspection. A 2D FFT-based spatial filtering was used to filter the GW modes from the B-scan data. To separate the mode of interest, a frequency-dependent bandpass filter with cosine-tapered window was used to eliminate the S mode in the frequency wavenumber domain. Then, the A mode was extracted for further analysis. In this analysis, the zero-crossing technique was used to calculate the ToF along the 200 mm scanning length with a 1 mm step. The threshold level is assigned to define the zero crossing points to calculate the ToF of A mode. The first and second half period of the signal which exceeds the defined threshold value can be expressed by the following equation [57]: (2) where, is the threshold value, n is the number of periods and, is the signal. The phase velocity of the A mode is calculated by the following equation: where dx = is the distance, dt = is the ToF, is the phase velocity. Once the phase velocity of A mode is obtained, and the analytical signal was generated to reconstruct possible GW modes. The excitation signal used in the analytical model is presented in Figure 7. The excitation signal is generated in the form of the Hanning window function by the following equation [58]: where A is the amplitude of the excitation signal, 2 is the angular frequency, t is the time, and N is the number of cycles.

Numerical Simulation of Guided Waves
Numerous mock-up trials are necessary for the experimental evaluation of each GW propagation scenario for various inspection setups, different types of flaws, loading, and environmental conditions. Numerical simulation of guided waves is an effective method to understand the propagation of GW and the interaction of various modes with delamination in composite materials.
In this 2D model, the x-axis represents the length of the plate, the y-axis represents the thickness of the plate, and the z-axis is infinitely long. The velocity of the guided wave varies due to anisotropic properties and ply direction. Numerical simulation using a 3D model could model guided wave propagation in all directions. However, 20 elements per wavelength criterion in 3D modeling of ultrasonic GW propagation would consume a significant amount of time and computational resources.
Therefore, in this research, a numerical simulation of GW propagation was performed using the 2D plane strain model. The simulation involved 3750 time steps, with each step lasting 0.08 s. The duration of the propagation of the GW in the simulation was 300 μs. In the finite element method (FEM), the mesh size and shape are key features. The simulation was performed using CPE4R-type elements, which are quadrilateral elements specifically designed for plain-strain models. These elements offer faster hourglass control and faster integration, resulting in reduced mesh deformation and a finer mesh.
The accuracy of the GW simulation depends on the mesh size. A finer mesh gives accurate results but increases computation time. Twenty elements per wavelength (λ) criterion was selected to maintain the balance between accuracy and computation time. Therefore, the mesh size was 0.6 mm.
By applying normal force to the excitation zone, the fundamental asymmetrical A mode was excited. The input signal was a three-cycle sine wave with a driving frequency of 150 kHz. The selected frequency provides an optimal balance between dispersion, attenuation, and mode complexity. To extract the A mode, signals were recorded on the plate surface at every 0.6 mm, and the corresponding B-scan data were obtained. The Bscan data were then subjected to a 2D fast Fourier transform to determine the phase velocity at each frequency, as shown in Figure 8. The dispersion characteristics of the guided waves in the CFRP plate were obtained using a 2D fast Fourier transform. The propagation of guided waves along the plate is represented by u(x,t) in terms of distance and time and was transformed into the wavenumber, k, at each frequency using the 2D FFT method [59]: where x is the distance, t is the time, ω is the angular frequency, and k is the wavenumber.

Guided Wave Interaction with Delamination
For reference, the defect-free signal is required to be compared with the signal in case of delamination. Then, the reference location of delamination is estimated by calculating the ToF between and as shown in Figure 9. The low amplitude reflected and overlapped converted modes can be reconstructed by considering the estimated reference location using the defect-free signal and phase velocity from the phase spectrum approach. Using the analytical model, targeted modes can be reconstructed at any distance with an accurate time of flight. By comparing the analytical signal with the numerical or experimental signal, the defect location can be estimated.
After interaction with delamination, guided waves are reflected, transmitted, and converted to other modes, as shown in Figure 10. Part of excited A mode is reflected at the leading edge of the delamination, i.e., A mode, and another part of the excited A is converted into S mode. i.e., S mode. In this study, the A0 mode is dominant, and the S0 mode has a lower amplitude. Therefore, the out-of-plane displacement component of guided waves is extracted for analysis, as shown in Figure 11. In the case of defect-free, both S0 and A0 modes are reflected from the leading and trailing edge of the plate. In the case of delamination, the A0 mode is reverberated multiple times within the delamination due to the displacement profile of the A0 mode being perpendicular to the delamination. The reflection coefficient of the S0 mode is lower compared to the A0 mode because the displacement profile of the S0 mode is parallel to the delamination.

Localization of Delamination Using an Analytical Model
The interaction of guided waves with the delamination located at 250 mm was analyzed. To determine the position of the delamination (Xd), two different receiver positions were used. The GW signals were received (Xr) at 20 mm and 10 mm from the leading edge of the delamination. In this specific scenario, the A0 mode, which is reflected from the leading edge of the delamination, was analyzed for the purpose of localizing the delamination.
During the analysis of the reflected A0 mode from the delamination, the A0 mode that is initially excited and propagates directly to the receiver is referred to as the direct A0 mode (t1). Similarly, the reflection from the leading edge of the delamination is denoted as t2. Taking into account the time of flight (ToF) between t1 and t2, it is possible to determine the location of the delamination.
During guided wave inspection, the reflection coefficients of the excited A mode change based on the delamination position within the specimen thickness. As a result, the reflection obtained from the leading edge of the delamination tends to have a lower amplitude. Delamination estimation using these lower amplitude modes is complex. For this reason, an analytical model was developed to match the lower amplitude A mode, and then the ToF of the reflected mode (t2) is estimated. Figure 12 shows the Hilbert envelope of the asymmetrical mode of guided wave signals received at various receiver positions. The envelope of the guided wave signal, represented by H(t), is obtained using the Hilbert transform and can be expressed using the following equation [45]: |Hilbert | (6) Figure 12. GW signal received in case the delamination is located further than the receiver.
By calculating the time of flight (ToF) between and , the delamination location can be estimated based on the time difference between direct and reflected A mode.
where is the group velocity and ∆ is the time difference between direct and reflected A mode.
The distance from the receiver to delamination estimated using an analytical model is presented in Table 3. In this case, the location of the delamination was estimated by taking into account the reflection from the leading edge of the delamination. The absolute error to estimate the delamination location was calculated by considering the difference between the actual and measured value by the following Equation: where is the absolute error, and Da and Dm are the actual and measured values, respectively. In the case where the delamination is between the excitation source and the receiver, GW signals were received at distances of 280 mm, 290 mm, and 300 mm from the leading edge of the CFRP plate. The distance between the delamination and the receiver (Xdr) was measured as 10 mm, 20 mm, and 30 mm. In this case, when the A mode propagates above and below the delamination, part of it is transmitted A and part of it is converted into S mode. The converted S mode is received at the receiver as the first wave packet (t1), while the transmitted A mode continues to propagate within the delamination and is received as the second wave packet (t2), as shown in Figure 13.
Analyzing the guided wave (GW) signals becomes challenging due to the differing velocities of the converted S0 modes combined with the transmitted A0 mode or other modes. Estimation of delamination location in case of overlapped modes is complex. For this reason, an analytical model was developed to match the overlapped modes, and then the ToF of the converted S0 mode (t2) can be estimated. The delamination location (Xd) can be estimated by calculating the ToF between the converted S0 mode and the transmitted A0 mode. The estimated distance from the delamination to the receiver and the absolute error of the estimated delamination position are presented in Table 4.

Experimental Investigation
The experimental inspection focused on a multilayer CFRP plate with dimensions of 540 mm in length, 450 mm in width, and 3.5 mm in thickness. The unknown characteristics of the CFRP material were intentionally selected to verify the developed phase spectrum approach and analytical model. A 60 × 20 mm rectangular Teflon tape was inserted between 9 and 10 plies of the CFRP plate, i.e., 1.7 mm in the through-thickness of the plate. GW inspection was performed using a contact transmitter and receiver inspection setup, as shown in Figure 14. The phase velocity dispersion of the A0 mode obtained using the two-dimensional fast Fourier transform and phase spectrum approach is presented in Figure 15.

Experimental Analysis Using Contact Transducers
The contact transducer setup (a pair of transmitter-receivers) developed by Ultrasound Institute; Kaunas University of Technology was used to analyze the CFRP plate with 20 mm delamination in a contact manner. The schematic experimental setup is presented in Figure 13. −6 dB bandwidth and wideband contact piezo ceramic transducers with a conical protection layer of 0.2 mm diameter were used to excite and receive the GW signals.
Glycerol was used to have good contact between the transducers and the test object. The transducer was excited with 200 V, and signals were recorded at each 1 mm along the scanning length of 200 mm. The initial distance between the transmitter and receiver was 80 mm. The scanning was performed in both the defect-free and defective regions on the CFRP plate. The B-scan images of guided wave propagation along the length of the plate with respect to time for both defect-free and defective regions are presented in Figure 16. In case the delamination is positioned after both the transmitter and the receiver; the GW signals are reflected from the leading edge of the delamination. In this specific case, the A mode, which was reflected from the leading edge of the delamination, was analyzed to determine the delamination position.
While analyzing the reflected A mode obtained from the delamination is initially excited and propagates directly to the receiver, which is referred to as the direct A mode (t1). The guided wave reflected from the leading edge of the delamination is denoted as t2. The time of flight (ToF) between t1 and t2 and the location of the delamination can be determined.
In the GW inspection, reflection coefficients of excited A mode depends on the location of the delamination in the thickness direction of the specimen. Consequently, the reflection acquired from the leading edge of the delamination has a lower amplitude and, in addition, is superimposed with other modes reflected from the edges of the sample. Delamination estimation using lower amplitude and overlapped modes is complex. Thus, an analytical model was developed to identify the lower amplitude and overlapped modes, and then the ToF of the reflected mode (t2) can be estimated. The guided wave signals transmitted A and reflected A are presented in Figure 17. The measured distance from the receiver to the delamination is presented in Table 5. The absolute error of the delamination location was calculated by considering the difference between the actual and the measured values. In the case when the delamination is located between the excitation source and the receiver, GW signals were received at distances of 280 mm, 290 mm, and 300 mm from the leading edge of the CFRP plate. In this case, the excited A mode propagates within the delamination, further divided into converted S and transmitted A modes. The converted S mode is received at the receiver as the first wave packet (t1), while the transmitted A mode is received as the second wave packet (t2), as shown in Figure 18.
The complexity in signal interpretation arises from the varying velocities of the converted S0 modes when combined with the transmitted A0 mode or other modes. Estimation of delamination location using such type of overlapped modes is complex. For this reason, an analytical model was used to match the overlapped modes, and then the ToF of the converted S0 mode (t2) was estimated. The delamination location (Xd) was estimated by calculating ToF between converted S0 mode and transmitted A0 mode. The estimated distance from delamination to the receiver and the absolute error of the estimated delamination position are presented in Table  6.

Conclusions
In this article, an effective GW inspection setup was proposed to locate the delamination in the multilayered CFRP material. This method has the advantage of locating the delamination either in between the excitation and receiver positions or even between the receiver and the boundary of the sample. The guided waves are excited with a single excitation source, and several receiver positions are used to locate the delamination in the longitudinal direction. Thus, the proposed inspection setup has the advantage of locating the delamination with the minimum number of sensors.
The A0 mode was selected for the inspection by analyzing dispersion curves and frequency tuning curves. GW mode selection based on dispersion curves provides only the velocity of a particular mode at different frequencies. Therefore, the selection of GW modes following dispersion curves is not accurate and is limited. The use of frequency tuning curves has the advantage of selecting dominant modes and optimal frequencies for the inspection. Thus, the A0 mode was selected for the inspection because it has a dominant amplitude compared to the S0 mode and is sensitive to a delamination-type defect.
Phase velocity is one of the important features in detecting and locating the delamination. Phase velocity estimation of GW modes in composite materials with unknown properties is difficult. For this reason, a phase spectrum approach was developed to estimate the phase velocity of GW modes. The estimated phase velocity of the A0 mode is further used in the developed analytical model.
The excited GW is reflected, converted, and overlapped with other modes when it encounters delamination. Analysis of GW modes in the presence of low amplitude, converted, and overlapped modes is difficult. For this reason, a novel analytical model was developed to locate the delamination in the presence of low amplitude and overlapped modes.
The analytical model developed was verified with five different scenarios using numerical and experimental investigations. In the case of numerical results, the delamination position was estimated with an average absolute error of 2.8 mm from the actual position of delamination. In the case of experimental results, the delamination position was estimated with an average absolute error of 2.6 mm from the actual position of delamination.

Conflicts of Interest:
The authors declare no conflict of interest.