Delamination imaging in composites using cross-correlation method by non-contact air-coupled Lamb waves

This paper presents a cross-correlation damage detection technique using damage scattered waves of all directions cross-correlate with the incident waves for delamination imaging in carbon fiber reinforced polymer (CFRP) composite plate. The presented imaging can not only detect the delamination but also precisely quantify the damage with locations and sizes. First, a CFRP composite sample with interlaminar delamination by inserting the Teflon layer is designed and manufactured in house using the hot-press machine. And a three-dimensional model of composite sample is simulated using the finite element method. Next, the cross-correlation imaging algorithm is introduced in detail, and the cross-correlation imaging proof-of-concept study is conducted with the simulated Lamb waves in the composite sample. Finally, a fully non-contact air-coupled transducer and scanning laser Doppler vibrometer system with a single-mode Lamb wave method is established to actuate and sense the interrogating Lamb waves in the structure. The imaging method is experimentally implemented for the one delamination and two delaminations imaging and quantification.


Introduction
Composite materials have received extensive attention and have been widely used in various industries due to their superior strength-to-weight ratio, corrosion resistance, and design flexibility. However, unexpected damage can occur in composites due to impact events or due to stressing of the material during off-nominal loading events. Delamination is the * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. most common and dangerous failure mode for composite structures, because it occurs and grows in the absence of any visible surface damage, making it difficult to detect by visual inspection [1]. Such hidden delamination damage must be detected and evaluated before it becomes critical [2][3][4]. Developments of reliable and quantitative techniques to detect delamination damage in laminated composites are imperative for safe and functional optimally designed next-generation composite structures.
Among various nondestructive evaluation (NDE) methods, ultrasonic Lamb waves have been proven effective for damage detection in plate-like structures due to their ability to inspect a large area while maintaining sensitivity to small defects in the structure [5][6][7][8][9][10][11][12]. Lamb waves propagate in-between the upper and lower surfaces of plate-like structures and interact with structural discontinuity in the propagation path. Such features allow for Lamb waves NDE, in contrast to point by point excitation and sensing pairs over the entire area of interest, to have excitation just at a single location. Advances in Lamb wavebased NDE technologies over the last decade have demonstrated the feasibility of detecting and locating damage in composite structural components using various Lamb wave detection algorithms [13][14][15][16][17][18]. However, compared to Lamb waves in isotropic materials and the complex damage scenarios, wave propagation in composite structures presents additional complexity for efficient damage identification [19][20][21].
Lamb wave excitation and sensing are critical for Lambwave damage detection in structural health monitoring (SHM)/NDE. Non-contact transducers have attracted many interests in recent years since they do not need to use liquid or solid couplant. This feature makes it relatively convenient for installation while avoid introducing issues such as contamination of host structure and bonding layer degradation [22]. Several non-contact Lamb wave excitation methods including electromagnetic acoustic transducer [23][24][25], pulsed laser [26,27], and air-coupled transducer (ACT) [28][29][30][31][32][33][34][35], as well as sensing method using laser Doppler vibrometer [30,36] or laser interferometers [37] have been reported. Among them, ACTs have emerged as a promising non-contact method for Lamb waves SHM/NDE [22]. Piezoelectric ACT works on the piezoelectric principle and uses air as the couplant to transduce the waves into solids with a certain stand-off distance to the structure surface [38]. It actuates Lamb waves based on Snell's law and can be controlled to achieve single-mode excitation or sensing [22,30]. Castaings et al [39] conducted ACT generation and reception of pure A 0 mode for single side inspection of the delamination defects in composite materials. Zhang et al used ACT and laser vibrometer for delamination detection using wavenumber based analysis and imaging methods [40]. Kažys et al [41] studied the pure A 0 mode inspection of the impact type damages theoretically and experimentally, both B-scan and C-scan results were obtained with the damage was successfully detected. In addition, detailed pure A 0 mode Lamb wave interactions with damage have been studied.
However, challenges are associated with ACT Lamb waves for SHM/NDE in composite structures. One is the high loss of ultrasound energy at the air and structure interface due to the impedance mismatch [42]. If both ACT actuation and sensing are used, the loss could be significant and affect the application efficiency [30][31][32]. A solution is to replace either the actuation or sensing with a different type such as a scanning laser Doppler vibrometer (SLDV). The SLDV remotely measures surface velocity or displacement over a spatially dense grid and provides high-resolution imaging sequences of wave propagation based on the Doppler's effect [36]. For composites, the general anisotropic behavior and complicated Lamb wave features have posed challenges for Lamb waves SHM/NDE techniques. In composites, Lamb waves propagate at various velocities in different directions. Besides, Lamb wave attenuation due to material damping is strong and anisotropic [10].
Moreover, signal processing and damage imaging techniques are of great importance in establishing Lamb wavebased damage inspection [43]. Different approaches have been developed based on the measurement of wave interactions with damage [44][45][46][47][48][49][50][51][52][53]. The cross-correlation imaging method uses back-scattered waves and incident waves to generate the images. The imaging condition was defined based on the concept that if both source waves and the receiver waves were extracted separately, these two wavefields would be kinematically coincident at the discontinuities [30], and the magnitude of the cross-correlation values at the discontinuities would be much larger than that of the remaining locations where it would be small or near zero. Zhu et al [43] developed a fastreal-time imaging method of multiple damage sites by crosscorrelating the back-scattered waves and incident waves in the frequency domain. Yu and Giurgiutiu [54] developed a zerolag cross-correlation (ZLCC) imaging technique, using forward waves and the back-scattered waves to image structural damage in composites quantitatively. This ZLCC method utilizes all the input frequencies and the dispersion effect was compensated automatically. Later, an enhanced imaging condition for composite damage imaging was developed which can provide enhanced imaging for multi-site damage as compared to the ZLCC method [55]. The authors have explored cross-correlation using the full scattered wave method but only have applied it to metallic plates for crack detection [56,57].
In this paper, a cross-correlation based imaging method is developed for delamination defect NDE and quantification in laminated composites. Compared to previous work reported in literature, this cross-correlation imaging uses the scattered waves in all directions in the algorithms for Lamb waves in composite structures. Experimentally, a fully non-contact Lamb wave system is established by judiciously combining an ACT for actuation and a SLDV for sensing to use single A0 mode for inspection. The paper is organized into five sections including this one (section 1). Section 2 presents the preparation of the quasi-isotropic carbon fiber-reinforced polymer (CFRP) composite sample with single and two delamination cases. To provide guidance for the imaging algorithm development in this sample, Lamb wave modeling is conducted using finite element (FE) method. Sections 3 introduces the scattered waves cross-correlation imaging algorithm, and the simulation Lamb waves are adopted for the preliminary validation of the imaging algorithm. The experimental application of the delamination detection is performed in section 4. Non-contact ACT-SLDV Lamb wave system is used to generate single-mode Lamb waves for the delamination imaging and detection. Section 5 summarizes the findings in the paper and outlines areas envisioned for future work.

Preparation of quasi-isotropic CFRP plates with delamination
To investigate the subject study in composite structures, two 3 mm thick quasi-isotropic CFRP composite plates with a  stacking sequence of [−45/90/45/0] 3s were manufactured in house using the hot-press machine at the authors' institution with IM7 12K/CYCOM 5320-1 prepreg. The delamination was created by inserting circular Teflon films during the ply layup process. The thickness of the Teflon film was 50 µm. Two cases of delamination were created independently in these two samples. Case 1 is a single delamination (25 mm diameter) between plies 20 and 21 (figure 1(a)), and case 2 is two overlapping delamination of different diameters placed at different pliers. One delamination (25 mm diameter) is added between plies 20 and 21 and the other one (20 mm diameter) between plies 16 and 17 ( figure 1(b)). The manufacturing setup and curing cycle used for creating the specimens are given in figures 1(c) and (d).
After manufacturing, ultrasonic C-scan inspection was conducted to image and verify the creation of simulated delaminations by Teflon inserts in the composite plates [4]. A 10 MHz, 25.4 mm focused transducer was utilized for the inspection. The ultrasonic C-scan results of case 1 and case 2 plates are shown in figure 2. From the C-scan images, both the size and shape of the delaminations can be observed. In the Cscan of case 1 (figure 2(a)), one 25 mm delamination image is observed clearly. For case 2 (figure 2(b)), a solar eclipse type image is observed with 20 mm insert shadowing over the image of the 25 mm one, as it blocks the ultrasonic wave to penetrate and to arrive at the 25 mm insert. The results confirmed the simulated delaminations at a single or multilayer locations have been successfully manufactured for further usage.

FE modeling of composite samples with delamination
Three-dimensional (3D) multi-physics FE models using ANSYS software were utilized to simulate Lamb wave propagation and interaction with the delaminations in the subject CFRP composite plates in order to understand the wavedelamination interaction mechanism. The lamina was created and meshed with the SOLID185 structural solid elements. The delaminations were modeled by detaching the nodes at the adjacent layers where the nodes at both layers have the same coordinates but are not being merged. Non-reflective boundaries (NRBs) were implemented around the 3D FE CFRP plates which eliminate boundary reflections and thus allow for the simulation of guided wave propagation in an infinite medium [4]. COMBIN14 spring-damper elements were utilized to construct the NRB. The excitation source in the modeled plate is set as the origin of a defined Cartesian coordinate. The delamination center is located at x = 70 mm at each composite plate for each case.
To actuate the waves in the model, a circular strain field [4] is used to generate an omnidirectional Lamb wave propagation as shown in figure 3. The stain field is implemented by applying an excitation signal of three-count Hanning window modulated tone burst with a center frequency of 120 kHz. The out-of-plane velocity of Lamb wave propagation is then extracted on the surfaces and the obtained time-space wavefields are given in figures 4(a)-(c) for pristine, case 1, and case 2 delaminations, respectively. It is noted that there are only incident waves in the pristine wavefield (figure 4(a)). However, in the delaminated plate (case 1 and case 2) wavefield, there are scattered waves that are introduced by the delamination damage. No significant difference in the scattered waves can be noted between case 1 and case 2. To image and quantify the delaminations, the cross-correlation imaging algorithm will be implemented.

Cross-correlation imaging algorithm
For Lamb wave propagation, when the incident waves interact with damage or defect, these waves will be partially reflected and refracted due to the geometric discontinuity and generate scattered waves [32-35, 37, 38]. In such a scenario, the damage acts as a new wave source and propagates scattered waves outward in all directions [24][25][26][27][28][29][30][31][32], including those directly back to the source (a.k.a. back-scattered waves). Cross-correlation imaging is a method that defined based on the concept that if both incident waves and the damage scattered waves are extracted separately, these two wavefields kinematically coincident at the discontinuities, and the magnitude of the crosscorrelation values at the discontinuities will be much larger than that of the remaining locations where it will be small or near zero [55][56][57][58]. In literature, most of the reported cross-correlation imaging work used incident waves to crosscorrelate with the back-scattered waves only for damage detection. It depended solely on the back-scattered wave for damage imaging, thus might reduce its effectiveness when the backscattered wave was insignificant. Rather, scattered waves in all-direction (including back-scattered) contain more information of the interaction with the damage and usually are stronger than back-scattered wave only. If used, there can be the potential of improved image likelihood, enhanced resolution as well as more inference of the damage.
In this paper, a 2D cross-correlation imaging method that uses scattered waves of all directions to correlate with the incident waves is developed for delamination imaging for laminated composites. The imaging algorithm is expressed as where v incident (x, y, t) is the incident wave wavefield w.r.t. time variable t, and spatial variables x and y, and v scattered (x, y, t) is the scattered wave wavefield. I (x, y) is the cross-correlation value at the point (x, y). With the cross-correlation of all data points (x, y) calculated, an image of the structure being inspected could then be generated by plotting the cross-correlation values that are taken as the image's pixel values at all data points. As seen in equation (1), to implement the imaging method, the essential step is to obtain the incident waves and the scattered waves. The frequency wavenumber filtering technique has been reported and used as a promising method to separate and extract various wave modes, as well as scattered waves for damage detection [30,36,38]. It is adopted in this work to extract the desired incident and scattered wavefields. For this purpose, the original Lamb wave wavefield in the time-space domain is first converted to the frequencywavenumber domain, through a 3D Fourier transform (3DFT) method: where V ( f, k x , k y ) is the transformed frequency wavenumber spectra w.r.t. frequency f and wavenumbers k x and k y for x and y. Next, the incident waves and scattered waves filtering process in the wavenumber spectrum is performed and expressed as the product between the frequency wavenumber spectrum V ( f, k x , k y ) and the filter function F ( f, k x , k y ), as described in [24]:  where V F ( f, k x , k y ) is the filtered frequency-wavenumber component. Finally, inverse 3DFT is applied to convert the filtered spectrum back to the time-space domain resulting in the cross-correlated wavefield v (x, y, t). Details of the frequencywavenumber filtering process can be found in [54].

Delamination imaging using simulated Lamb waves
The simulated Lamb waves acquired with the FE method for all pristine and delaminated cases presented in section 2.2 are processed as a proof-of-concept imaging study. The resulted wavenumber spectra at the excitation frequency of 120 kHz obtained by applying the 3DFT given in equation (2) on the time-space wavefield are presented in figures 5(a), (b), and (c) for the pristine, case 1 and case 2, respectively. Theoretical dispersion curves of A 0 Lamb wave mode at the 120 kHz are also plotted for mode identification. Figure 5(a) shows that in the pristine plate, the wavenumber components match well with the A 0 mode and are the only mode present in the waves.
However, in the spectra for case 1 and case 2 delaminations, there are additional higher wavenumbers in addition to the A 0 mode wavenumbers. These higher wavenumbers are introduced by the presence of the delaminations. To obtain the incident waves and the scattered waves for cross-correlation imaging, filters that keep desired associated wavenumbers while eliminating the rest shall be designed. In this study, a bandpass filter has been designed for acquiring the incident A 0 waves by retaining the positive A 0 wavenumbers. The filter at 120 kHz is shown in figure 5(a) with the bandpass filter along the 0 direction is given in the callout, with the wavenumbers passband being centered about the theoretical A 0 wavenumber. When incident wave excited, it propagates forward in the positive x direction, therefore, the bandpass filter is applied along the positive x-axis direction. For the scattered waves which are associated with higher wavenumbers beyond the A 0 , a highpass filter has been designed as shown in figure 5(b). At 120 kHz, the highpass filter along the 0 direction at k y = 0 within the range of  0 rad mm −1 ⩽ k x ⩽ 1.5 rad mm −1 is given in the callout in figure 5(b). When waves interact with the delamination, the scattered waves will propagate in any random direction, therefore, the highpass filter is applied in all directions.
With the designed filters, incident and scattered wavenumber spectrum are obtained. At 120 kHz, they are presented in figures 6(a) and (b), respectively. The filtered spectra are then converted to the time-space domain using inverse 3DFT to obtain the corresponding wavefield data. The time-space wavefields at 60 µs during the propagation are presented in figures 6(d) and (e), respectively, with the original unfiltered wavefield presented in figure 6(c) for comparison. The results demonstrate that both the incident waves and the scattered waves are successfully separated and obtained from the original wavefield.
The cross-correlation imaging algorithm is applied for the case 1 delamination inspection using the filtered wavefields. The result is presented in figure 7(a). It shows that the delamination imaging matches very well with the simulated delamination damage. The cross-correlation image of case 2 the two modeled overlapping delaminations (of 20 mm and 25 mm diameters, respectively) are plotted in figure 7(b). It is noted that the contour of the 25 mm delamination is precisely imaged and similar to the single case given in figure 7(a). However figure 7(b) presents extra orange and yellow pixels at the area where the 20 mm delamination is arranged to overlapping with the 25 mm one. The extra pixels indicate stronger scattered waves that are caused by the additional 20 mm delamination compared to case 1. Overall results of both cases show that cross correlation imaging can be used for delamination evaluation in laminated composites with Lamb wave inspection and has the potential to evaluate the severity of delaminations (doubled overlapped delamination in this study).

Non-contact single-mode ACT-SLDV Lamb wave in composite
The noncontact ACT-SLDV NDE system was adopted using an ACT for Lamb wave actuation and SLDV for sensing [56]. The ACT-SLDV schematic setup is shown in figure 8(a).  An x-y-z Cartesian coordinate system was defined in the plate with the ACT actuation point on the plate defined as the origin O. The ACT used in this study is a resonant type spherical focusing ACT with a nominal resonant frequency of 120 kHz and a focal length (d) approximately 25 mm. It actuates singlemode Lamb wave at a specific incident angle θ (w.r.t to the normal direction of the plate surface) based on Snell's law [57]. On the sensing side, the laser head of the SLDV system was placed normally to the plate surface for out-of-plane velocity measurements of the wave propagation. A point-bypoint rectangular scanning grid with 0.5 mm spatial resolution is used for the SLDV multi-dimensional Lamb wave scanning. The laboratory experimental setup of the system is given in figure 8(b).
ACT incident angle θ can be controlled so to excite or sense a certain single-mode Lamb wave based on Snell's law and the Lamb wave phase velocity [22,30]. In the composite, the theoretical incident angles of the fundamental A 0 and S 0 modes in all directions at the 120 kHz ACT resonant frequency are calculated with the phase velocities and they are plotted in figure 9(a). For S 0 mode, it is noted that the incident angles of all directions are always smaller than 5 • . For A 0 mode, the incident angles of different directions are different. In 0 • direction, the incident angle is about 15 • . In our study, A 0 mode is selected for delamination detection for the reasons of configurable incident angle setup and dominant out of plane motion around 120 kHz. To obtain the optimal excitation of the desired A 0 Lamb wave in the 0 • direction in the composite plate with maximum strength, we experimentally obtained and evaluated the ACT actuated Lamb waves at incident angle from 10 • to 20 • with 1 • interval. The signal strength is represented by the peak-to-peak values of the signals. The signal strengths of all incident angles are extracted and plotted in figure 9(b). The ACT Lamb waves are found to achieve a maximum peak-to-peak value at 15 • incident angle, which is consistent with the theoretically calculated incident angle. Therefore, the incident angle for A 0 mode Lamb wave is experimentally tuned at 15 • .
Using the configured ACT-SLDV system, the 1D timespace Lamb wave wavefield in the pristine area of the composite specimen along a line of propagation is first collected and shown in figure 10(a). It is seen that the Lamb waves are actuated in the plate by the non-contact ACT. To further analyze the characteristics of the waves in composite,  its frequency-wavenumber spectrum is obtained by the 2DFT method as given in figure 10(d), plotted with the theoretical wavenumber spectrum. Through comparison, singlemode A 0 Lamb waves actuation in the composite specimen is verified.
The time-space wavefield of ACT actuated Lamb waves in the composites of single delamination case and double delamination case are also collected by the SLDV scanning as given in figures 10(b) and (c), respectively. Wavedelamination interactions are readily noted in the wavefields for both cases. Their frequency-wavenumber spectra are presented in figure 10(e) and plotted with theoretical dispersion curves of the composite specimen. Wave reflections, represented by negative wavenumbers, are also observed in delaminated cases. Additional theoretical dispersion curve of A 0 wave mode for 0.5 mm thick composite plates is also plotted which matches well with part of the new wavenumber components for the delaminated cases. Moreover, for the case of two delaminations, it is seen that new wavenumbers of additional 1 mm sub-laminates are also present.

Delamination imaging and detection
To detect possible damage in the composite plate, the crosscorrelation imaging is applied. To use cross-correlation imaging, 2D time-space wavefields are needed and obtained by measuring the Lamb waves over a rectangular grid with a spatial resolution of 1 mm using the SLDV. The resulted 2D wavefield of the single delamination and double delaminations plates are given in figures 11(a) and (b), respectively. Strong scattered waves in the delamination regions can be observed for both delamination cases. This is consistent with previous studies which show that the multiple reflections occur within the delamination area resulting a considerable amount of ultrasonic energy being trapped in the delaminated region [4]. However, it is difficult to estimate the size of the delamination  in composites solely with the wavefield images. Moreover, the cases of the single delamination and double delaminations are hard to distinguish by directly comparing the Lamb wavefield.
To implement the cross-correlation imaging, the incident waves and the scattered waves shall be filtered using the wavenumber filtering method introduced earlier in section 3.2. With the bandpass filter and the highpass filter, the incident wavenumber and scattered wavenumber are first obtained, then the filtered spectra are converted to the time-space domain using inverse 3DFT to obtain the corresponding wavefield data. For the single delamination, the filtered incident wavefield and scattered wavefield of 60 µs are given in figures 12(a) and (b), respectively.
Through comparing to the original unfiltered wavefield presented in figure 11(a), the filtered wavefields demonstrate that both the incident waves and the scattered waves are successfully separated and obtained from the original wavefield. Finally, by cross correlating the filtered incident waves with the scattered waves, the imaging of the single delamination is generated as shown in figure 12(c). It is observed that the delamination is imaged with its size and location match very well with that of the actual delamination.
The cross-correlation imaging method was further applied to the inspection of double delamination experimental data. Same to the single delamination imaging process, the incident wavefield and the scattered waves are firstly filtered (as shown in figures 13(a) and (b)) and then correlated to generate the image as shown in figure 13(c). A good agreement of size and location between the imaged and actual delamination is observed. Besides, by comparing the pixel values to those of the single delaminations, it is noted that in the image of double delaminations (figure 13(c)), the intensity at the overlapping area is stronger compared to the intensity for the single delamination case ( figure 12(c)). This is consistent with the result presented in section 3.2, demonstrating the cross-correlation imaging potential to evaluate the severity of the delaminations caused by overlapping additional delaminations.

Conclusions
This paper presented a cross-correlation imaging method for delamination inspection and quantification using a noncontact ACT-SLDV Lamb wave system with a single-mode Lamb wave method. The method is based on the features of guided Lamb waves' propagation ability in-between the upper and lower surfaces of plate-like structures and their interactions with structural discontinuity in the propagation path. Such features allow for Lamb waves NDE, in contrast to point by point excitation and sensing pairs over the entire area of interest, to have excitation just at a single location as shown in the presented work. A cross-correlation imaging method using the incident waves and scattered waves was introduced.
To capture more information about the overall dimension of the damage, the scattered waves of all directions were adopted for imaging implementation. Compared to the work published previously in metallic plates for crack detection, the work in this paper is focused on detecting and evaluating delamination defects in composite laminates. The anisotropic property of composites and the resulted anisotropic wave propagation in combination with directional air couple Lamb waves actuation presented a new paradigm for the effectiveness of the cross-correlation imaging method. Hence, by simulation and by experiments we explored the cross-correlation imaging method in composite plates with a single delamination and with two overlapping delamination, respectively. Through both simulation and experimental explorations, the understanding of wave propagation and interactions with single or overlapping delamination cases is obtained.
Lamb waves interact with the delamination and cause wave scattering in all directions. Based on multidimensional Fourier transform, a frequency wavenumber filtering method tailored to separate the incident waves and scattered waves was applied. A bandpass filter with positive wavenumber k x was proposed to filter incident waves only, while a highpass filter of all directions was proposed to filter the scattered waves of all directions. Thus, the damage overall dimension could be retained. The method was first applied and tested with simulation data, followed with laboratory experimental testing. A 3 mm thick in-house quasi-isotropic CFRP composite plate with a stacking sequence of [−45/90/45/0] 3s was manufactured with the IM7 12K/CYCOM 5320-1 prepreg. One single delamination (25 mm) and one double delamination (25 mm and 20 mm) were generated by inserting Teflon films during the ply layup process. With the non-contact ACT-SLDV Lamb wave system and the cross-correlation imaging algorithm, both cases of single delamination and double overlapping delamination have been precisely localized and evaluated, demonstrating that the proposed method has been successfully implemented for delamination inspection. The work shows that the method can be potentially used as an alternative method for composite NDE for delamination defects and possibly the intensity evaluation.
The imaging method presented here relied on the correlation between the incident waves and the scattered waves induced by the defect, as well as the successful acquisition of these waves. It is believed the damage had a good chance to be detected as long as there were sufficient scattered waves caused by the damage and they could be extracted, regardless of the structural material or the defect shape. The inspection ability applies to defects sitting in between the top ply and the midplane as explored previously in [59]. For practical applications, the previous study recommended performing the inspection on both surfaces. Additionally, the future work would, therefore, be focused on extending its application to more complex defects with highly irregular profiles, such as the real impact damage in the composite.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).