Characterisation of carbon fibre-reinforced polymer composites through complex Radon-transform analysis of eddy-current data

Characterisation of carbon fibre-reinforced polymer composites through comple x Radon-transform analysis of eddy-current data R.R. Hughes 1, , B.W . Drinkwater 1 and R.A. Smith 1 1 Department of Mechanical Engineering, Queens Building , University W alk, University of Bristol, BS8 1TR, UK Abstract Maintaining the correct fibre orientations and stacking sequence in carbon-fibre reinforced polymers (CFRP) during manufacture is essential for achieving the required mechanical properties of a component. This paper presents and ev aluates a method for the rapid characterisation of the fibre orientations present in CFRP structures, and the di ff eren- tiation of di ff erent stacking sequences, through the Radon-transform analysis of complex-v alued eddy-current testing (ECT) inspection data. A high-frequency (20 MHz) eddy-current inspection system was used to obtain 2D scans of a range of CFRP samples of di ff ering ply stacking sequences. The complex electrical impedance scan data was analysed using Radon-transform techniques to quickly and simply determine the dominant fibre orientations present in the structure. This method is compared to 2D-f ast F ourier transform (2D-FFT) analysis of the same data and shown to gi ve superior quantitati ve results with comparati vely fewer computational steps and corrections. Further analysis is presented demonstrating and examining a method for preserving the complex information inherent within the eddy- current scan data during Radon-transform analysis. This inv estigation shows that the real and imaginary components of the ECT data encode information about the sacking sequence allo wing the distinction between composites with di ff erent stacking structures. This ne w analysis technique could be used for in-process analysis of CFRP structures as a more accurate characterisation method, reducing the chance of costly manufacturing errors. K e ywor ds: Directional orientation, Carbon fibre, Non-destructi v e testing, Lay-up, stacking sequence, CFRP, Radon, Data analysis 1. Introduction Carbon-fibre reinforced polymer (CFRP) is used in increasingly sophisticated industrial applications [1]. High strength-to-weight ratio, tolerance to f atigue damage and the ability to form complex geometries mak e it an attracti ve material for use in many industries including aerospace and automotiv e. CFRP components get their strength from the order and alignment of fibres along specific axes [2] and as such their structural integrity is dependent on reliable manufacturing processes. Misalignments and stacking errors can easily occur during the layup process of comple x geometries and may lead to in-plane fibre waviness, out-of-plane ply wrinkling and ply-bridging in the finished com- ponent, introducing structural weaknesses [2, 3, 4, 5]. Costly manufacturing errors such as these are easily corrected if found during the layup process. As such, new reliable non-destructi v e testing (NDT) techniques are required for quality-control on these parts during the layup process. The introduction of foreign contaminants in the manufacturing process must be minimised to prevent defects in the finished component. This presents a problem for many traditionally e ff ective NDT methods such as ultrasonic testing (UT) as they require contact with the test material through a coupling medium or for the sample to be submerged in water . Potential in-line non-destructi ve testing techniques include optical sensing with image processing methods to measure fibre alignment [6, 7, 8, 9]. Such approaches are fast and low cost but cannot measure orientation in I Email addr ess: robert.hughes@bristol.ac.uk (R.R. Hughes) Pr eprint submitted to arxiv .or g J anuary 31, 2018 sub-surface plies. Ho wev er, an alternati ve lies in eddy-current testing (ECT), a non-contact inductive sensing NDT technique that can penetrate below the surf ace. ECT measures the local electrical properties of a sample’ s surface and near surface. The technique works by measuring the complex electrical impedance ( Z = R + iX ) of an electromagnetic coil when excited with a sinusoidal signal. R is the real, or resistive, component and X is the imaginary , or reactive, component of impedance. The measured impedance depends on the induced current density , J ( z ), within the material which decays with depth, z , into an isotropic material as [10], J = J 0 e x p − z δ sd (1 + i ) ! . (1) The depth at which the magnitude of the current density has fallen to 1 / e f its surface v alue is know as the depth of penetration, δ sd , and is dependent on the electrical conductivity , σ and magnetic permeability , µ , of the test sample, as well as the excitation frequency , ω , and the geometry of the e xcitation coil which is a distribution of spatial frequencies represented by the ’e ff ectiv e’ spatial-frequency term, κ , as given belo w [11], δ sd = 1 p κ 2 + µσω . (2) Smaller ECT coils and higher frequencies will therefore result in a faster rate of decay in a gi ven material. In this way the depth over which an ECT measurement is made can be controlled. Although traditionally carried out on high-conductivity metallic materials, ECT techniques ha ve been sho wn to be capable of detecting multiple stacked ply orientations in CFRP structures due to the electrical anisotropy of carbon-fibre plies [12, 13, 14]. 1.1. Ply Orientation Lange and Mook [14] recognised that a non-axially symmetric ECT probe could be rotated and used to determine ply orientations in a sample by deconv olving the angular measurements via a F ourier-transform. This was later ex- panded for use on 2D raster-scan ECT data by performing 2D fast Fourier transforms (2D-FFTs) [15]. This analysis approach has been widely adopted for automated in-process monitoring of fibre alignment [16, 17, 18, 19, 20]. How- ev er, 2D-FFT analysis is an inherently Cartesian transform making the accurate extraction of angular information an inelegant secondary process requiring careful correction to remain uni versally v alid. A potential alternati ve to the 2D-FFT method is Radon-transform (R T) analysis, which has been used in a wide range of image processing applications for extracting or reconstructing angular information [21, 22, 23, 24, 25, 26]. A Radon transform performs line integrals in the plane of a 2D image function, A ( x , y ), mapping line-integrals at position s , and angle θ , into ( s , θ )-space (Figure 1). The resulting transform image, R ( s , θ ), contains information on the angular structure of an image function A ( x , y ). The Radon transform image can be straightforwardly analysed to determine which angles exhibit strong structural information with fewer processing steps compared to 2D-FFT techniques [27]. 1.2. Ply Structur e A desirable output from quality-control inspections of CFRP structures is the stacking sequence. Pre vious authors using ECT typically perform the standard 2D-FFT analysis on either the magnitude, | Z | , or the phase, ψ , of the ECT data, | Z | = √ R 2 + X 2 ψ = tan − 1  X R  , (3) and use the signal strength at particular orientations to infer stacking sequences making the assumption that weaker orientation signals are deeper in the material [28, 16]. This approach overlooks the full information encoded into the complex v alues and could misrepresent the structure of more complex stacking sequences. 2 x y a)  2D  Image  Data,  A( x,y) c)  R adon  Image,  R (s, 𝜃 ) P osition,  s b)  Angular  Pr ojections  𝜃 =  -4 5 o P osition,  s Ang le,  o P osition,  s 𝜃 =  4 5 o Figure 1: Schematic diagram sho wing the principle of Radon transform analysis of a structured 2D image dataset (a), via pixel summation along di ff erent projection angles. c) shows the full angular radon image, demonstrating image structure at − 45 ◦ . Eddy-current sensors measure the superposition of magnetic field contrib utions from all depths, arising from the flow of current within the material. The complex current density , J ( z ), decays in magnitude and phase with depth such that each layer of a material will contribute di ff erently to the real and imaginary parts of the overall magnetic- field measured and thus the ECT coil impedance. The electrical anisotropy of CFRP plies leads to a non-uniform distribution of current density within cross-ply CFRP materials, as sho wn by Cheng et al. [19] through finite-element modelling. The simulated results in Cheng et al. [19] predict that the current density is a local maximum at the inter- face between cross-ply layers, where contact is made between orthogonal fibres. It is predicted that the complex phase of the current density will also vary irregularly with depth and exhibit transitions at the ply interfaces. The di ff erence in beha viour of the current density in di ff erent CFRP stacking sequences will therefore lead to measurable di ff erences in the complex contrib utions measured by the ECT sensor . In this study , R T analysis is e valuated as an alternativ e to 2D-FFT analysis for the non-destructiv e characterisation of fibre orientations in CFRP structures. This R T method is then used to carry out the analysis on the full complex ECT data from v arious di ff erent samples to e xplore the e ff ect of stacking sequence of ECT measurements and e xploit these e ff ects to distinguish between di ff erent CFRP structures. 2. Materials and Methods CFRP samples, with di ff erent stacking sequences, were manufactured and tested using a high-frequency eddy- current inspection system. The complex coil-impedance data w as analysed using 2D-FFT & R T analysis to e xplore the e ff ects of ply orientations and lay-up structure. 2.1. T est Specimens Three IM7 / 8552 CFRP specimens were manufactured in-house with specific ply structures - unidirectional, cross- ply and complex - sho wn in T able 1. T able 1: T est specimen ply lay-up structures Sample No. Plies lay-up structure 001 32 [90 o ] 32 002 32 [0 o / 90 o ] 16 003 32 [90 o / 45 o / 90 o / 135 o ] 8 3 Samples were manufactured manually from pre-preg plies and cured, as per the manufacturer’ s instructions [29], under vacuum and sandwiched between aluminium plates. The resulting samples were 4 mm thick. 2.2. Experimental Setup A Zurich Instruments HFLI2 Lock-in Amplifier was used to operate and measure the electrical impedance of the ECT coil at 20 MHz. A Howland current source 1 was used to conv ert the input v oltage into an equi valent current to the sensor coil [30], and mounted immediately behind the sensor coil to eliminate the detrimental high-frequency impedance e ff ects of connecting cables. A low inductance, 25 turn, 1 mm external diameter coil was constructed in-house around a 0 . 75 mm diameter ferrite rod core 2 . A schematic diagram of the experimental set-up is sho wn in Figure 2. T wo-dimensional raster scans were performed on test samples using tw o high-accuracy linear stages controlled via PC. Scan data consisted of complex coil-impedance measurements taken at X and Y positions in 0 . 2 mm increments ov er a 20 × 20 mm area. The ECT probe was used in an absolute (reflection) mode [31] and T eflon tape used to protect the probe head during scanning, providing a constant lift-o ff of 0 . 1 mm from the surface, maintained by the pressure of a spring-loaded probe mount. Initial in vestigations rev ealed that single-frequency e xcitation at 20 MHz produced the highest image contrast for the test samples and so was used throughout the study although the frequency dependence of the response will be in vestigated in future studies. L ock-in Ampli fi er - <5 0MHz Coil V out V in Cur r ent Sour ce I out V in V out USB 2.0 USB 2.0 PC/M atlab T est Sample XY Stage Figure 2: Schematic diagram of the experimental set-up for eddy-current measurements. 2.3. ECT Data The eddy-current scans produce 2D M × N complex matrices, ˜ A ( x , y ). Prior to analysing the fibre orientations, a 41 × 41 pixel (8 . 2 × 8 . 2 mm) hamming-window high-pass filter was applied to the scan data to remove low spatial- frequency variations. The unfiltered complex data is shown in the complex plane in Figure 3.a, alongside magnitude (b) and phase (c) images. Figure 3.a shows the complex-plane impedance ( Z ) data for the full 2D data-sets for each sample. W e hypothesis that the data distribution in complex-space provides information about the structure of each material. The images shown in Figure 3.b & c clearly sho w the fibre orientations within the three test samples b ut not the depth of plies. Reliable automated analysis is therefore required to quantify the orientations present, their dominance in the data and, if possible, their stacking sequence. 1 Designed and manufactured by SonEMA T (Coventry , UK) 2 Grade 61 from Fair -Rite (New-Y ork, US) 4 b) Magn itude, O hms. c) Phase, o a) Complex Plane, O hms 001 - [0 o ] 002 - [0 o /90 o ] 003 - [90 o /45 o /90 o /135 o ] Figure 3: Raw 20 MHz ECT scan data of test samples (left to right) 001, 002, 003 showing the data in the complex plane (a), and in 2D images of the magnitude (b) and phase (c). 3. Ply Orientation Radon-transform analysis was ev aluated against the current literature standard, 2D-FFT , as a method for auto- matically detecting and quantifying the dominant ply orientations present in test samples. For this comparison, the magnitude of the complex ECT was used for both analysis techniques and angular-distrib ution plots obtained from each processing method. Figure 4 shows the steps in v olved in the R T (a-c) and 2D-FFT (a & i-iii) analysis processes. 3.1. 2D-FFT Analysis 2D-FFT analysis was performed on the ECT magnitude scan data, | ˜ A ( x , y ) | , (Figure 4.a) of each test sample (see T able 1) to giv e the 2D-FFT image, F ( u , v ), (Figure 4.i). The 2D-FFT of an M × N image A ( x , y ) is, F ( u , v ) = 1 M N M X x = 0 N X y = 0 A ( x , y ) exp  − i 2 π  u x M + vy N  . (4) The center pix el is remov ed from the F ( u , v ) image and the image re-sampled in polar coordinates using cubic interpolation at radial increments of 0.2 mm and angular increments of 0 . 1 ◦ to give the polar 2D-FFT , F ( u 0 , θ ), (Fig- ure 4.ii) [32]. Angular distributions, α ( θ ), were calculated by summing along the radial axis, u 0 , for each angle, θ , as performed by Bardl et al. [16]. The 2D-FFT images are shown in Figure 5.b and the resulting angular-distributions, α ( θ ) F F T , are shown in Figure 5.d, sho wing peaks for the dominant fibre orientations within each sample. 5 , arb. s, px . R(s, 𝜃 ) b) Y, mm 0 5 10 15 20 X, mm 0 5 10 15 20 A(x,y) a) -2 0 2 -2 0 2 0 45 90 135 180 u', m m -1 -2 0 2 0 45 90 135 180 2D-FFT cart R T Orientation 𝜃 ,  o 0 45 90 135 180 F(u,v) i) F(u', 𝜃 ) ii) R T anaysis steps 2D-FF T anaysis steps 2D-FFT polar iii) FFT c) R T ECT  D ata v , mm -1 u, mm -1 Figure 4: Comparison between Radon transform (R T) and 2D-FFT analysis steps of ECT data (a) for quantitati ve characterisation of ply orienta- tions. The R T process (a-c) inv olves performing an R T to giv e the R T image (b) follo wed by the calculation of the angular-distrib ution (c). The 2D-FFT process (a, i-iii) in volv es transforming (a) into its 2D-FFT image (i), re-sampling in polar co-ordinates (ii) and generation of angular- distribution (iii). 3.2. Radon T ransform Analysis Radon transform analysis w as performed on the ECT magnitude scan data (Figure 4.a-c) and compared against the 2D-FFT analysis method. The Radon transform is gi ven as, R ( s , θ ) = M − 1 X x = 0 N − 1 X y = 0 A ( x , y ) δ ( x cos θ + y sin θ − s ) . (5) In equation 5, δ , is a Dirac delta function [21] allowing for the summation of values along the orientation, θ , direction. The angular distribution, α ( θ ) RT , was calculated from the R T image (Figure 4.b) by the mean absolute gradient along the s -axis at each orientation angle, θ . α ( θ ) RT = 1 N N X n = 1      ∂ R ∂ s      n , (6) where N is the number of points in the position axis s . The resulting angular distribution, α ( θ ), sho ws the orienta- tion and dominance of certain ply orientations in the original image data, A ( x , y ), (see Figure 4.c). 3.3. T echnique Comparison Figure 5 directly compares the results of the two analysis methods and plots their angular distributions in the same plot, normalised to their peak magnitude α ma x . In this way the angular distributions are normalised to the dominant (surface) ply orientation. The features of peaks at specific angles provide information as to the structure and alignment reliability of the lay-up process. The peak features for each analysis technique are compared in T able 2. 6 T able 2: Angular distribution peak features. Comparison between 2D-FFT and Radon transform (R T) analysis results. Orientation, θ ± 0 . 1 ◦ Relative Magnitude FWHM ± 0 . 2 ◦ Sample 2D-FFT R T 2D-FFT R T 2D-FFT R T 001 [90] 89.7 89.6 1.00 1.00 17.5 11.6 002 [0] -0.7 -0.6 0.76 1.00 26.3 7.6 [90] 89.5 89.5 1.00 0.76 21.9 8.7 003 [45] 44.8 44.7 0.74 0.63 25.7 6.1 [90] 89.6 89.6 1.00 1.00 20.9 8.4 [135] 133.3 133.7 0.49 0.59 48.2 10.5 The results shown in Figure 5 and T able 2 compare the R T analysis method to 2D-FFT analysis. From Figure 5 there is good general qualitativ e agreement between both techniques in measuring the dominant orientations present in the ECT data. Cross-correlation coe ffi cients, χ , were calculated between the normalised 2D-FFT and R T angular- distributions and displayed in Figure 5.d to quantify the agreement between the techniques. The major di ff erences between the two analysis techniques are in the relati ve amplitudes and angular spread of peaks in α ( θ ). The angular peak spread, characterised by the full-width-half-maximum (FWHM) in T able 2, is a measure of the alignment accurac y of di ff erent ply layers with the same orientations within the samples. Figure 5.d shows that R T analysis generates sharper orientation peaks compared to 2D-FFT . This is likely a result of the polar re-sampling of the 2D-FFT image (see Figure 4.i) where the low-frequenc y peaks near the origin contribute to a wide range of orientations, resulting in a greater peak spread. This issue, which could obscure smaller peaks resulting from ply misalignments, is not observed in the R T analysis method. The FWHM will scale inv ersely with the number of pixels in the analysed data as demonstrated by Bardl et al. [16], tending to wards a minimum limit that will depend on the diameter of the inspection coil. 3.4. Stacking-Sequence Di ff er entiation: Magnitude In this section two ne w test samples, manufactured using the same material and process as detailed in section 2.1, were inspected. Both samples contain the same number of plies but with di ff erent stacking-sequences. Samples A and B have stacking sequences [45 ◦ / 90 ◦ / 135 ◦ / 0 ◦ ] re peat ed and [0 ◦ / 45 ◦ / 90 ◦ / 135 ◦ / 0 ◦ ] re f lected respectiv ely . The specimens were inspected at 19.5 MHz using the experimental set-up in section 2.2 and 2D-FFT and R T angular distribution analysis performed on the magnitude of the complex ECT data. Figure 6.a) shows the ECT magnitude images and b) compares the normalised angular-distrib utions obtained via 2D-FFT and R T . 2D-FFT analysis (Figure 6.b .i) fails to detect the presence of plies at 135 ◦ in both samples whereas R T analysis (Figure 6.b.ii) picks up all ply-orientations. R T analysis also produces strong 45 ◦ ply peaks for both samples. This could be accounted for in sample A due to the top ply having an orientation of 45 ◦ . Howe ver , the reason behind the same 45 ◦ strength in sample B is unclear . Cross-correlation coe ffi cients, χ , were obtained to compare the angular- distributions between samples A & B, and sho w strong correlation (less than 3% di ff erence) between the two samples for both 2D-FFT and R T analysis methods. It is therefore reasonable to conclude that it very di ffi cult to automatically di ff erentiate between these two samples based on analysis of ECT magnitude data alone. 4. Complex-Component Angular Distributions A truly univ ersal quantitativ e ev aluation system must be capable of independently validating the stacking sequence without prior kno wledge. The follo wing section explores ho w R T analysis can be used to better di ff erentiate between two similar test samples via the analysis of complex information inherent in ECT measurements. As discussed in section 1, ECT measurements produce complex values with depth information encoded into the relationship between real and imaginary components. The following study e xploits this inherent property of ECT measurements to produce an angular distribution that reflects the relati ve changes in the complex data with depth. 7 ii) iii ) i) 2D-FFT R T | A(x,y) | a) F(u,v) b) R(s,  ) c) d) / max , arb. u, mm -1 u, mm -1 u, mm -1 v , mm -1 v , mm -1 v , mm -1 ~ / max , arb. / max , arb. 𝜒 =99 .2% 𝜒 =92 .6% 𝜒 =96 .5% Figure 5: Image-processing results of ECT scan data sho wing a) absolute magnitude, | ˜ A ( x , y ) | , of the scan data, b) the 2D F ourier transform (2D- FFT) image, F ( u , v ), c) the Radon transform (R T) image, R ( s , θ ), and d) the normalised angular-distributions obtained from 2D-FFT and R T images. Cross-correlation coe ffi cients, χ , between the two angular distrib utions are displayed next to each angular-distrib ution plot. Results for three test samples are shown i) 001 - [90 ◦ ], ii) 002 - [0 ◦ / 90 ◦ ] and iii) 003 - [90 ◦ / 45 ◦ / 90 ◦ / 135 ◦ ]. Equation 5, in section 3.2, was used to produce the comple x Radon image, ˜ R ( s , θ ), (see Figure 4.b). The Radon image is proportional to the mean complex v alue along each line at orientation angle, θ . In order to preserve the com- plex information the angular distribution calculation (equation 6) is performed on both real and imaginary components of ˜ R separately , α < ( θ ) = 1 N N X n = 1       ∂ <{ ˜ R } ∂ s       n , α = ( θ ) = 1 N N X n = 1       ∂ ={ ˜ R } ∂ s       n , (7) where N is the number of points along the position axis s . The resulting angular distributions, α < ( θ ) & α = ( θ ), reflect the relati ve variations in the real and imaginary components of the ra w complex data as a result of the material structure (i.e. fibres) at a gi ven orientation angle, θ . Figure 7 plots α < ( θ ) & α = ( θ ) relativ e to one another in a 3D plot. The relativ e contribution angle (RCA), φ θ , is defined as the angle a peak makes with the real axis, α < ( θ ), in the relativ e contribution plane (blue projection in Figure 7) as demonstrated in Figure 8.a. φ θ provides complementary 8 i)  2D-F FT ii)  R T a)  ECT  Images i)  A ii)  B b)  Angular  distributions / max , arb. / max , arb. 𝜒 =98 .9% 𝜒 =97 .3% Figure 6: Distinguishing between similar layup structures - Comparing 2D-FFT and R T magnitude analysis of sample A - [45 ◦ / 90 ◦ / 135 ◦ / 0 ◦ ] re peated (blue dotted) and sample B - [0 ◦ / 45 ◦ / 90 ◦ / 135 ◦ / 0 ◦ ] re f lected (red solid). Showing a) ECT magnitude images and b) normalised angular-distrib utions, α ( θ ), with cross-correlation coe ffi cients, χ , between angular-distributions of the tw o samples from i) 2D-FFT and ii) R T analysis. 3 Imag. Gradient, arb. Real Gradient, arb. Orientation , o , arb. , arb. Figure 7: Example three-dimensional representation of a complex angular distribution of sample 003, obtained via Radon transform analysis. Showing the relati ve Real (green), Imaginary (red) and relativ e contribution (blue) plane projections. information to the relativ e contribution magnitude (RCM), A θ , as to the stacking sequence of the CFRP materials. A θ = p { α < } 2 + { α = } 2 φ θ = tan − 1 α = α < ! (8) The resulting relativ e real-imaginary plots in Figure 8 demonstrate the di ff erence in φ θ between orientation peaks in the complex-contrib ution space for samples 001, 002 & 003. The RCA separation between di ff erent ply orientations in Figure 8 is a result of fibres in plies at di ff erent depths contrib uting di ff erently to the relati ve real and imaginary components in the ECT measurements. The RCA provides new information about the stacking sequence of the material as demonstrated by the changes in RCA of the same ply orientations across multiple samples (see T able 3). In the following section 4.1, this analysis technique is used to distinguish between samples A & B from section 3.4. 4.1. Stacking-Sequence Di ff er entiation: Comple x Figure 9 compares the relativ e real-imaginary angular-distrib ution plots of samples A & B exposing the di ff erences between the two samples that were hidden in the magnitude-only analysis of section 3.4. The results are displayed in 9 a ) c ) b) Orientation , o , arb. , arb. , arb. , arb. , arb. , arb. A 90 Figure 8: Experimental real-imaginary angular distributions of three test samples a) [90 o ] b) [0 o / 90 o ] and c) [90 o / 45 o / 90 o / 135 o ] from Radon transform analysis of 20 MHz ECT inspection. The color-bar represents the orientation angle, θ , in degrees, φ θ is the phase angle and A θ is the relativ e magnitude. two forms; the first (Figure 9.a) sho ws the full normalised angular distribution of each sample in the real-imaginary plot, and the second figure (Figure 9.b) compares the RCAs of the dominant peaks for the tw o samples, sho wing them in descending order of peak magnitude to demonstrate the correlation between ply depth, peak angular-distribution (dominance) and RCA. Figure 9 shows that the greatest di ff erences in RCA occur for the more dominant ply-orientations in spite of having the same ply orientations and v ery similar peak amplitudes (see Figure 6). It is the di ff erence between these dominant orientations that allo w the stacking sequences to be di ff erentiated between. Samples A & B exhibit strong di ff erences in RCA for their two most dominant orientations (0 ◦ and 45 ◦ ) of 21 ± 2 ◦ and 3 ± 1 ◦ respectiv ely (see Figure 9 and T able 3). This is an indication of the di ff erence in the structure of samples A & B. RCA analysis of complex ECT data could be used as a fingerprinting technique to determine the stacking sequence of CFRP structures. It is also important to note the trend in RCA as a function of ply dominance, where the most dominant peaks exhibiting the lowest RCAs with the second most dominant exhibiting the highest RCAs. This is likely linked to the fact that the current density is real at the surface of a test material and decays in amplitude and phase with depth (see equation 1) such that the top layer will contribute more to the real component of the ECT measurement. Properly characterised, this analysis technique could be used to identify unknown layup structures and could be incorporated into in-process inspections to independently , and accurately check stacking sequence and alignment accuracy of multiple plies at a time. T able 3: Features of real-imaginary angular -distribution plots. A verages from 36 separate analysis calculations made of 91 × 91 pixel windo ws of each data set. Errors defined as 3 standard deviations about the mean. Sample θ, ± 0 . 1 ◦ A θ , arb . φ θ , ◦ 001 [90] 89.6 2 . 2 ± 0 . 1 51 ± 1 002 [0] -0.5 5 . 9 ± 0 . 1 73 . 1 ± 0 . 5 [90] 89.5 4 . 1 ± 0 . 2 61 ± 1 003 [45] 44.7 2 . 3 ± 0 . 1 73 ± 1 [90] 89.6 4 . 0 ± 0 . 2 50 ± 1 [135] 133.7 2 . 1 ± 0 . 1 65 . 7 ± 0 . 6 A [0] -0.4 6 . 0 ± 0 . 2 39 ± 2 [45] 45.5 4 . 6 ± 0 . 1 79 ± 1 [90] 90.5 3 . 1 ± 0 . 1 77 ± 1 [135] 134.2 1 . 22 ± 0 . 02 90 ± 2 B [0] 0.6 7 . 4 ± 0 . 3 60 ± 2 [45] 44.5 5 . 8 ± 0 . 2 82 ± 1 [90] 90.3 3 . 1 ± 0 . 1 77 ± 1 [135] 136.9 0 . 8 ± 0 . 03 64 ± 2 10 Orientation , o / A max , arb. / A max , arb. / A max , arb. / A max , arb. A B a) b) Figure 9: Real-imaginary R T analysis results for two CFRP samples: A - [45 ◦ / 90 ◦ / 135 ◦ / 0 ◦ ] re peated and B - [0 ◦ / 45 ◦ / 90 ◦ / 135 ◦ / 0 ◦ ] re f lected . Showing a) the full, normalised R T angular distributions in real-imaginary space, and b) the relati ve contribution angles (RCAs) of the dominant peaks in all test samples samples A & B. 5. Conclusion High frequenc y eddy-current testing inspections of CRFP were used to produce high resolution images of the ma- terial structure. W e demonstrated a Radon-transform analysis method applied to the complex inspection measurement data of an ECT scan to determine the dominant ply orientations and their distribution about this angle. The Radon- transform analysis method was shown to produce superior results compared to the commonly used 2D-fast Fourier transform analysis technique, and has the added advantage of eliminating a number of computational steps to quickly and quantitati vely determine the ply orientations present in a structure. This analysis technique could be incorporated into automatic quality-control ECT inspections of pre-preg CFRP after lay-up to confirm the correct alignment and stacking sequence has been achiev ed. This study outlined a method for analysing the complex behaviour of ECT inspection data using the Radon- transform. This technique conclusi vely demonstrated that more structural information is retrie vable from full analysis of the complex data than merely the magnitude-only analysis methods commonly used. The method generated sepa- rate real and imaginary angular -distributions and plotted them on a relati ve real-imaginary angular-distrib ution plot, representing the relati ve changes in the original complex scan data. It was sho wn that di ff erent ply-orientations are distinguishable in the relativ e contribution angle in real-imaginary space, providing additional information about the sample-structure. Through the inspection and analysis of multiple CFRP structures, we hav e shown that this angular information is dependent on the stacking sequence of the CFRP structure, making it possible to distinguish between samples that are otherwise indistinguishable using magnitude-only analysis methods, but have di ff erent stacking se- quences. 11 This work could lead to more accurate inspection techniques for composites at the pre-cure stage of the manu- facturing process. Such a technique would allo w re-work and guard against manufacturing errors that could result in unnecessary material losses or mechanical failure of critical components. Acknowledgements The authors would like to thank Dr Luke Nelson and Ms Christina Fraij of the Univ ersity of Bristol for their help with data analysis and sample manufacture respectiv ely . 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