ECO-FRIENDLY LAMINATES: FROM THE INDENTATION TO NONDESTRUCTIVE EVALUATION BY OPTICAL AND INFRARED MONITORING TECHNIQUES

Short Title: A NDT approach for hybrid composites

Sfarra S.1(*), Ibarra-Castanedo C.2, Santulli C.3, Sarasini F.3, Ambrosini D.1, Paoletti D.1, Maldague X.2

1Department of Industrial and Information Engineering and Economics (DIIIE), Las.E.R. Laboratory, University of L’Aquila, L’Aquila, Italy

2Department of Electrical and computer Engineering, Computer Vision and Systems Laboratory (CVSL), Laval University, Québec city, Canada

3Department of Chemical Engineering Materials Environment (DCEME), University of Roma Sapienza, Rome, Italy

(*) corresponding author: Stefano Sfarra, Piazzale E. Pontieri no. 1, I-67100, Monteluco di Roio, L’Aquila (AQ), work telephone number : +39 0862 434362, work fax number : +39 0862 431233, e-mail: stefano.sfarra@univaq.it

ABSTRACT

In this work, the combined effect of indentation damage and of manufacturing defects of a hybrid laminate including jute hessian cloth (plain weave) and hemp fibres in an epoxy matrix has been investigated. With this aim, various non-destructive evaluation (NDE) techniques have been employed, such as near-infrared (NIR) reflectography, infrared thermography (IRT), holographic interferometry (HI) and digital speckle photography (DSP). In particular, two different methods of heating were applied during IRT data collection: pulse thermography (PT) and square pulse thermography (SPT). The first one using a mid-wave infrared (IR) camera, while the second one by a long-wave IR camera. In the same way, two different cameras working into the near- and short-wave IR spectra were used, in order to compare different results from ~ 0.74 μm to ~ 14 μm. Data were processed applying principal component thermography (PCT), correlation and the robust second order blind identification (SOBI-RO) algorithms. The latter is used for the first time to our knowledge in this work. The defects found were enhanced by image subtraction between the reflectogram and the transmittogram, distance transform, and image fusion. In particular, data fusion from IRT and DPS images allowed clearly defining the extension of the indentation damage.

Keywords: digital speckle photography; holographic interferometry; hybrid material; image processing; infrared thermography.

INTRODUCTION

Defining the effects of damage on composite material’s stiffness, strength, and durability has long been a subject of investigation in the composites community. Indeed, ASTM Committees D-30 and E-7, individually and jointly sponsored several symposia on the subjects since the early 1980s. Our knowledge of composites has advanced significantly in recent years. Structural design and non-destructive techniques have evolved as increased emphasis has been placed on durability and

damage tolerance. The materials have likewise improved. Tough thermoplastic and thermoset resins have been developed to improve impact and delamination resistance. Ceramic and metal matrix systems have also evolved to address high-temperature applications [1]. Currently, plenty of research material is being generated on the potential of cellulose based fibres as reinforcement for plastics [2]. Researchers working in the area of natural fibers composites suggested that the application of these renewable [3], abundantly available materials have several drawbacks: poor wettability, high moisture absorption and incompatibility of the fibres with oil-derived polymeric matrices [4]. This incompatibility can affect fibre-matrix adhesion, reducing the effectiveness of the matrix in transferring the load to the fibres through shear stresses at the interface. This process requires a good bond between the polymeric matrix and the fibres. Poor adhesion at the interface means that the full capabilities of the composite cannot be exploited and leaves it vulnerable to environmental attacks that may weaken it, thus reducing its life span [5]. As a consequence, insufficient adhesion between hydrophobic polymers and hydrophilic fibres results in poor mechanical properties of the natural fibre reinforced polymer composites.

The above mentioned problem has restricted the full potential of composites in terms of their response to impact loading. Low-velocity impacts, such as those caused by dropped tools during maintenance, are of primary concern since these impacts can cause barely visible impact damage (BVID) that is difficult to detect during routine inspections. BVID can result in internal damage such as delamination and back face splitting, which can reduce the residual strength by as much as 60% [6-7]. To address this problem, current design criteria limit the allowable strain to a very low levels (e.g. 0.3%) so that much of the weight-saving potential is lost [8]. Usually, the most common impactor shape used by researchers is hemispherical, useful for impact damage modeling, although obviously a dropped tool on a composite panel during maintenance does not always impact the panel with a relatively blunt shape such as a hemisphere. Research works that considered the effect of impactor shape has predominantly been in the high-velocity impact field where, for instance, the impact resistance of armour has led to research into the ballistic limit of projectile shapes. However, it is known that specimens react differently to high-velocity impacts, where there is a localized response compared to low-velocity impacts, where a global response may predominate. Different impactor shapes will produce different damage mechanisms and areas in composite laminates; hence the residual properties of the material will change according to the impactor shape [8].

Three relevant publications in the BVID field and linked to infrared thermography were published in the last fifteen years [9-11]. In Avdelidis et al. [9] the effectiveness of pulsed thermography (PT) to assess various defects and/or features on representative aerospace materials was studied. The success of this technique is highly dependent on defect depth and size, which restricts its application to near-surface defect imaging. Instead, in Ball and Almond [10], the results have shown that transient thermography (TT) is a potentially viable method for detecting impact damage in thick CFRP laminates. Later on, Polimeno et al. [11] investigated BVID using a second harmonic imaging technique (SEHIT). The results accurately identified and quantified damage, and were validated by pulsed thermography and thermosonics.

Trying to broaden the field of application of composite materials reinforced with natural fibers, more stringent mechanical and impact resistance criteria are required [12]. In spite of the growing interest for these materials, fiber selection is still based on economical factors and local availability rather than on materials properties. However, difficult damage evaluation on plant fiber composites

may require the use of NDT for post-impact monitoring of mechanical degradation. In the last decades, several types of full-field techniques have been proposed and used in composite material characterization. The nature of the measurements can be displacement, strain or temperature. Displacements are measured with various techniques [13], for instance speckle [14], speckle interferometry [15], geometric moiré [16], moiré interferometry [17], holographic interferometry [18], image correlation [19] or grid method [20]. Strain can be obtained by numerical differentiation of the above displacement fields with suitable algorithms [21] or directly, for instance with shearography [22-23], speckle shearing photography [24] or by moiré fringes shifting [25]. These techniques can be classified according to various criteria based on the nature of the physical phenomenon involved. For instance, interferometric (digital speckle interferometry or photography: DSP, holographic interferometry: HI) are subsequently discussed [26].

An integrated approach between infrared thermography (IRT), DSP and HI, proved to be an interesting possibility when applied to glass and basalt fibre composite materials, in order to study their behaviour as a result of low velocity impacts [27]. In the present work, these techniques are assessed through the application of two different heating stimulation, named pulse (linked with mid- wave IRT, for this particular study) and square pulse (linked with long- wave IRT, for this particular study) [28]. This method, combined with others IR equipments, such as near- and short- wave IR reflectography and transmittography and/or advanced signal processing, used together for the first time to our knowledge on a natural fibre reinforced composites, allows predicting the initiation and development of the phenomena leading to laminate failure and offers comparative evaluation of the different damage modes of hybrid laminates.

In addition, an advanced signal processing is used [robust SOBI (SOBI-RO) algorithm]; it combines robust whitening and time-delayed decorrelation. It was applied using the same number of frames as for the PCT algorithm for reference, and the comparison between the results obtained is described in the experimental section. This algorithm, introduced in [29], improves the classical SOBI method [30] by integrating robust whitening [29, 31-32] instead of simple whitening, the main objective being the reduction of the influence of the white noise. Finally, the use of the distance transform is innovative in order to visualize on a final image the areas of the sample with a lower concentration of fibers [33], as well as the use of correlation algorithm, from which a single image is derived for comparison with the previous results obtained. In the infrared context, the correlation coefficient refers to the strength and direction of the linear relationship between a given temperature evolution reference and all the temperature evolution of the pixels over the specimen under inspection [34].

NONDESTRUCTIVE TESTING (NDT) METHODS

From now on, the paper is divided into two main parts. The first one is devoted to provide the reader with relevant theoretical background about the NDT methods used along with the experimental set-ups, while the second one summarizes the main findings.

Digital Speckle Photography (DSP) – Theoretical background

In digital speckle photography, the object is illuminated with a laser beam under an angle θ and the scattered light is imaged onto a CCD sensor (Figure 1). The lens of the recording system is determined by the required magnification. The speckle size must be bigger than the pixel dimensions. The purpose of this technique is the comparison of two different speckle patterns, corresponding to two object states. The first one is considered as the reference state, and is recorded before the object modification process starts, while the second one is recorded after the surface has been modified. In our case, the surface was modified heating the sample in transmission mode by a soldering iron. As it is a digital recording, each speckle image is a matrix of intensity values, I(r), associated with the intensity of the interference at each point of the image. The characteristics of the CCD camera determine the intensity level range and the matrix dimensions. Due to the random nature of the speckle fields, changes in the object surface cannot be inferred from each individual speckle. The information has to be extracted through an averaging process. Correlation functions are used to quantify the variation between the intensity fields in two speckle images.

The normalized 2D cross correlation function has been used. It is defined as:

CC I1 I2(∆ r⃗ )=

⟨ I 1 ( r⃗ ) I 2 ( r⃗+∆ r⃗ ) ⟩− ⟨ I 1 ( r⃗ ) I 2 ( r⃗ ) ⟩

[ ( ⟨ I12 ( r⃗ ) ⟩− ⟨ I 1 ( r⃗ ) ⟩2)( ⟨ I 2

2 ( r⃗ ) ⟩− ⟨ I 2 ( r⃗ ) ⟩2 ) ]12

(1)

where I1(r) and I2(r) are the intensity field of the first and second speckle images, respectively. This function has a different value for each Δr = (Δx, Δy), and has a maximum at a certain value. The peak position is proportional to the in-plane sample displacement and its height is related to the surface modifications.

Both contributions can be analyzed separately. The peak value, also known as the correlation coefficient, changes from 1, when the surface remains unchanged, to zero that corresponds to a total decorrelation. The calculation of the 2D cross correlation function using Eq. (1) is a time consuming process, it is a numerically implemented with Fast Fourier Transform algorithms [35]. Then:

⟨ I 1 ( r⃗ ) I2 ( r⃗+∆ r⃗ ) ⟩=[ζ−1 [ ζ [I 1 ] ζ [I 2 ] ] ] (2)

where ζ means Fourier transform. The correlation coefficient can be calculated over the full image or using correlation windows of Nx x Ny pixels. In the first case, the evolution of the correlation coefficient gives a global value of surface changes. As the value at each interrogation area indicates the local changes, the second procedure allows obtaining a 2D correlation map, with information on where the surface modification process has taken place. The size of the sub-regions has to be big enough for the statistical analysis to be feasible but as small as the size of the defects to be identified [36].

Fig.1 Experimental setup for Digital Speckle Photography (DSP)

A very simple way to perform data processing by the cross-correlation approach is given by the possibility of using existing Particle Image Velocimetry (PIV) software with only minor modifications. In the following, pattern displacements are evaluated using correlation algorithms based on the toolbox MatPIV 1.6.1. This package has the distinctive feature of being free, Open Source and of being compatible with MATLAB environment, thus sharing its capabilities of technical calculations and data visualizations.

The interrogated images are divided into smaller regions, also known as sub-windows, interrogation-windows or interrogation-regions. Each sub-window in the first image is compared with the corresponding sub-window in the second image. For every possible overlap of the sub-windows, the sum of the squared difference between them is calculated looking for the position where the sub-windows are the “least unlike”. Expanding the squared difference, it can be considered that only one term, the so-called cross-correlation, actually deals with both images. Cross-correlation is traditionally used in PIV and is the basis of many of the different algorithms performed in MatPIV since it can be calculated using Fast Fourier transforms (FFTs) and therefore can be executed faster.

The following options are available in MatPIV: - single, which calculates the displacement with a single iteration through the images, using cross-correlation; - multi, that, using cross-correlation, performs three iterations through the images. This will start off using whatever window size specified, but the final iteration is performed using half this size; - multin, which is an extension of multi and makes the calculations with n iterations through the images. In this case the size of the sub-window for each iteration should be inserted manually; - mqd, which calculates the displacement in a single pass using the more general form; - norm, which is very similar to single but uses a normalized equation [37]. Results coming from MATPIV 1.6.1 were compared with the results obtained by 2D-PIV ver. 3.001-1.11 [38]. This PIV software, which calculates the 2D-2C (two dimensional - two components) velocity field, demanding in input images of the light scattered by seeding particles immersed into the flow field [39-41], can be used with minor modifications also in the present case.

Holographic Interferometry (HI) – Double-Exposure (DE) – Theoretical background

When a hologram storing more than one wave is illuminated with coherent light, the reconstructed wave fronts interfere with each other or with any other phase-related wave front derived from the illuminating source. This multiple wave front comparison is called holographic interferometry (HI), and one application is called holographic non-destructive testing (HNDT). HI, or non-destructive testing, is concerned with the formation and interpretation of the fringe patterns which appear when a wave generated at some earlier time and stored in a hologram is later reconstructed and caused to interfere with a comparison wave. It is this storage or time delay aspect which gives the holographic method a unique advantage over conventional optical interferometry. Holography permits diffusively reflecting or scattering surfaces, which are subjected to stress to be interferometrically compared with their non-stressed state, without requiring the preparation of test object surface, which is necessary for the conventional interferometer.

Fig.2 Experimental setup for Double-Exposure (DE) Holographic Interferometry (HI)

Continuous comparison of surface displacement relative to an initial state may in certain cases supply more information than necessary. Whenever it is sufficient to form a permanent record of the relative surface displacement occurring after a fixed interval of time, a method obviating the experimental difficulties of real-time interferometry [42] may be employed. Two exposures of the hologram, once to the initial state of the surface and once to its strained state, are superimposed prior to processing. Each exposure is made with the identical reference wave. With this double-exposure, or time-lapse method, the problems of registering a reconstructed wave with an original one are eliminated. After the exposure of the hologram is completed, the subject and the optical components used to illuminate it are no longer of concern. Both the comparison wave, characteristics of the surface in its initial state, and the wave representing a subsequent, altered state of the surface are reconstructed in register by illuminating the hologram with a wave similar to the original reference wave.

No more care in illumination is necessary than is taken in illuminating any pictorial hologram. Distortion due to emulsion shrinkage is identical for both reconstructed waves and is, therefore, not

a factor in determining the spacing of the fringes formed by the interference of the two waves. However, limitations on the change of subject surface microstructure apply here as in the real-time method. Illumination of the doubly exposed hologram not only effects the simultaneous reconstruction of two waves which had been scattered from the subject at different times but causes them to interfere under ideal conditions. The waves can share the diffraction efficiency of the hologram equally. Thus, their intensities are equal and the interference fringes they produce can have high visibility or contrast. For analysis purpose, the two virtual images of the subject surface generated by the reconstructed waves may be considered to be two slightly different physical surfaces. One can image these initial-state and final-state surfaces to be simultaneously illuminated with the coherent light originally illuminating the subject. One difference in the interference resulting from the double-exposure method as compared to that obtained from the real-time technique may be observed when initial and final states of the subject surface are identical. Each reconstructed wave is negative with respect to the original subject wave; and, consequently, when the initial and final states are identical, the reconstructed waves add to give a bright image of the subject [43].

Pulsed Thermography (PT) and Square Pulse Thermography (SPT) – Principal Component Thermography (PCT) – Theoretical background

The term SPT follows the survey by Vavilov and Burleigh [44-45] of the most important heating types in active thermography: instantaneous pulse, step function, square pulse and periodic function. According to this classification, pulsed (PT) and pulsed phase thermography (PPT) can easily assigned to instantaneous or just “pulse” heating, step heating thermography to step heating and lock-in thermography to periodic heating. It can be easily seen, that the thermography concept is most frequently defined by its type of heating [46].

In PT a high energetic heat pulse is applied to the specimen and the surface temperature cooling is monitored and analyzed with an IR camera.

Fig.3 Experimental setup for Square Pulse Thermography

Information about delaminations and near surface voids is gathered by the temperature differences at the surface of disturbed and undisturbed areas [47]. Especially by applying an adequate degree of energy and time to the thermography measurements PT is quite useful for NDT of composite materials [48-49]. The special form of PT with long heating pulses (square pulse heating) and

observation times may be called square pulse thermography (SPT) in time domain [50]. Other quite similar forms of PT are the long square pulse and slow thermal wave techniques by Vavilov, Kauppinnen and Grinzato [51]. This is according to the thermography concepts of pulse and step heating thermography, which are named also after their most important characteristic: the type of the heating used. In order to facilitate the processing of the infrared image sequences generated using PT and SPT applied on jute/hemp fibre hybrid laminates and to enhance the contrast between the defect and non-defect areas, we used the statistical analysis tool Singular Value Decomposition (SVD) [52]. The Fourier Transform provides a valuable tool to decompose signal in the temperature-time space to a phase-frequency space. SVD is an alternative tool to extract spatial and temporal data from a matrix in a compact or simplified manner. Instead of relying on a basis function, SVD is an eigenvector-based transform forming an orthonormal space. Assuming that data are represented as a MxN matrix A (M>N), then the SVD allows writing [53]:

A = URVT (3)

With R being a diagonal NxN matrix (with singular values of A present in the diagonal), U is a MxN matrix, VT is the transpose of an NxN matrix (characteristic time). A singular value decomposition is available in MATLAB®. The column of U represents a set of orthogonal statistical modes known as empirical orthogonal functions (EOF) describing spatial variations of data [53]. On the other hand, the principal components (PCs), representing the time variations, are arranged row-wise in matrix VT. These characteristics of the SVD approach are very useful for pulse thermography applications. Principal component thermography (PCT) [54-55] uses SVD to extract the spatial (EOFs) and temporal (PCs) information from a thermogram matrix.

The thermographic 3D matrix needs to be rearranged as a 2D matrix with time along the columns and space as illustrated in Figure 4. After applying the SVD to the 2D matrix, the resulting U matrix, providing the spatial information, can be rearranged as a 3D sequence as illustrated in the same Figure.

Fig.4 Thermographic data rearrangement from a 3D sequence to a 2D A matrix in order to apply SVD, and rearrangement of 2D U matrix into a 3D matrix containing the EOFs [56]

Near-Infrared (NIR) Reflectography and distance transform (DT) – Theoretical background

NIR gives possibility to reveal fibres distribution, voids and porosity and subsurface defects due to impacts and therefore this method provides information about the nature, and present state of semi-transparent composite materials made by natural fibres. Taking into consideration the fact that the

fibers are covered by other layers like resin or different layers of fibers (hybrid materials), it is important to underline that this method could be applied in reflection or transmission (transmittography) modes. Infrared reflectography utilises near infrared light in the band 0.8 - 2 μm. The NIR and SWIR parts of the radiation, which contain practically no thermal emissions, can penetrate thin layers of sample before being reflected back to the surface from a non-absorbing media, whilst this same radiation will be absorbed by other elements such as thermosetting or thermoplastic resin.

For the reflectance R of a uniform layer of resin with defined thickness x can be derived the following expression [57]:

R=1−R s (a−b ∙coth (bSx ) )

a−R s+b ∙coth (bSx )(4)

where a = [(S+K)/S], b = √(a2 – 1).

and S is scattering coefficient of the resin layer; K is absorption coefficient of the resin layer and RS

is reflectance of the fiber layer. In the case in which under a resin layer there is a subsurface defect, similar equation can be derived:

R=1−RU ( a−b ∙ coth (bSx ) )

a−R s+b ∙coth (bSx )(5)

where RU is reflectance of the resin.

From equations (4) and (5) follows that infrared light reflected from a sample carries information about the resin. Optical contrast of resin image will increase if:

• thickness x of resin layer decreases;

• scattering and absorption coefficients S and K of resin layer decreases;

• difference between reflectance of fiber layer RS and resin RU increases.

Basic configuration of an IR reflectographic system consists of a source of infrared radiation, camera, IR filter, frame-grabber and personal computer. Composite material samples under test are uniformly irradiated by a source of IR radiation (tungsten or LED lamps) and radiation reflected from sample is detected by the near infrared camera coupled with frame-grabber and personal computer. The optimal sensitivity band of the camera for IR reflectography is up to wavelength around 2000 nm. NIR cameras are in most cases based on PbS, InGaAs or PtSi image sensors (CCD, CMOS or vidicon). Many resins have absorption coefficient small enough also in the band 800-1300 nm and therefore silicon CCD camera with 800 nm short-wavelength cut filter (Schott UG8) was used. A filter was also used to suppress sensitivity of detector in visible band. The main advantage of such solution is, besides the relatively low price of such equipment, the high spatial resolution of contemporary silicon CCD arrays (more than 7 millions of pixels). The camera signal is digitized by a frame-grabber and the image is then digitally processed with a personal computer and after that can be stored and printed or presented on a computer screen. Comparing to classical IR photography, the digital IR system has several advantages [58]:

• real-time information about presence of subsurface defects;

• better quality of IR images due to digital image processing;

• possibility to digitally compare infrared and visible images.

The distance transform (DT) was applied to reflectographic and transmittographic images in order to enhance the areas of the sample with low fibers’ distribution. DT maps each image pixel into its smallest distance to regions of interest [59]. It is a fundamental geometrical operator with great applicability in computer vision and graphics, shape analysis, pattern recognition, and computational geometry. DT methods are useful propagation schemes that efficiently construct a solution to the eikonal differential equation [60] in the integer lattice. This in turn, is related to many other important entities such as medial axes, Voronoi diagrams, shortest-path computation, and image segmentation.

The DT can be defined in terms of arbitrary metrics. The Euclidean distance is often necessary in many applications, as it is the adequate model to numerous geometrical facts of the human-scale world. However, as in pure mathematics, some non-Euclidean metrics are much easier to manipulate and to compute. For this reason, efficient non-Euclidean DT algorithms have been reported since 1966, while fast algorithms for the exact Euclidean DT (EDT) started to appear only in the 1990s. Many others have recently been proposed [61]. It is still uncertain what the best exact EDT algorithm is, or even whether the recently proposed ones are correct or not. Moreover, validation of EDT methods is scarce and incomplete. In the majority of cases, such as ours, comparative evaluation is published in the manuscript where an algorithm being judged is also being proposed. This survey is targeted to a novel method, with test cases that tend to emphasize its assets and overlook liabilities. Comprehensive validation and comparison of methodologies is still incipient in image analysis, mainly because the algorithms are complicated, and because this type of activity tends to be disregarded [62]. In the case of EDTs, thorough evaluation faces a series of particular difficulties. To begin with, interesting EDT methods are numerous, recent, and relatively obscure both in theory and implementation. In addition, performance depends on the contents of the input image, not only on its size. Therefore it is not trivial to predict the behavior of an EDT algorithm on a given input. Another difficulty is that there exist a number of factors that can be used to compare the algorithm, such as temporal and spatial performance, accuracy, and ease of implementation [63]. In our work, the Saito’s algorithm was used and its performance is discussed next. It is extremely efficient for images of the size studied herein [64].

Second order blind identification (SOBI)

Second-order statistics (SOS) are the basis for modern subspace methods of spectrum analysis and array processing and are often used in a pre-processing stage in order to improve convergence properties of adaptive systems, to eliminate redundancy or to reduce noise [65]. The simplest SOS algorithm is spatial decorrelation or whitening, which is often considered a necessary condition for stronger stochastic independence criteria. In fact, whitening (or data sphering) is an important pre-processing step in a variety of blind source separation (BSS) methods, i.e. the separation of a set of signals form a mixed data set, without having or using the information of the source signals. After

whitening, the BSS or independent component analysis (ICA) tasks usually become more straightforward easier and well-posed, because the subsequent separating (unmixing) system is described by an orthogonal matrix for real-valued signals and a unitary matrix for complex-valued signals and weights. Based on the same second-order statistic, for non-stationary signals one can compute different whitening transformations. Using these different transforms, one can obtain spatio-temporal and time-delayed decorrelation, which can be used to identify the mixing matrix and to perform blind source separation of coloured sources [30-31]. On the other hand, conventional whitening exploits the equal-time correlation matrix of the data x, so that the effect of additive noise cannot be removed. More robust whitening lies in utilizing time-delayed correlation matrices that are not sensitive to the white noise [31-32, 65]. In a second order statistics framework, source signals s are assumed to be mutually uncorrelated and temporally correlated (instead of independents). Computing a separating matrix on this model can be difficult because of the noise, which influences the correlation between the signals. Contrary to the sources, no assumptions are made on the distribution or the spatial correlation properties of the noise vector n, which is nevertheless considered as white noise (individual components of the vector are not autocorrelated). Hence, its covariance matrix at lag 0 Rn(0) = E[n(k)n(k)T], can be a full matrix which is generally unknown, while any time delayed correlation matrix Rn(i) = E[n(k)n(k-i)T] will be null. Given the above assumptions, the correlation matrices of the observation have the following structure [29, 31]:

Rx(0) = E[x(k)x(k)T] = ARs(0)AT + Rn (6)

Rx(i) = E[x(k)x(k-i)T] = ARs(i)AT ۷ i (7)

The robust SOBI (SOBI-RO) algorithm combines robust whitening and time-delayed decorrelation. This algorithm, introduced in [29], improves the classical SOBI method [30] by integrating robust whitening [29, 31-32] instead of simple whitening, the main objective being the elimination of the influence of the white noise. The first step (robust whitening) consists, in the general case, in finding a matrix Q that decorrelates the signals in x for several (small) time lags. This method is described in detail in [29, 31-32]. In our case, we have utilized the ICALAB [66] implementation. The matrix Rx(1) is diagonalized by an eigen-decomposition:

Rx(1) = Uc diag [λ12… λN2] UcT (8)

The whitening matrix Q will be obtained from the eigen-vectors matrix Uc and the diagonal eigen-values matrix:

Q = diag [λ1… λn] UcT (9)

Using this Q matrix, one can compute whitened signal z(k-i) = Qx(k-i) for different time lags (the default option under ICALAB is 100 time lags). The second step of SOBI-RO is the same as in classical SOBI, namely an appropriate joint diagonalization of the different Rz(i) matrices, computed according to equation 7. This approximate diagonalization aims to minimize the sum of the squared off-diagonal elements of these matrices [30, 32]. The result of this operation will be an orthonormal matrix V, and the final estimation for the demixing matrix W will be:

W = VTQ (10)

EXPERIMENTAL

The laminates tested in this work have been manufactured using jute hessian cloth (plain weave) of areal weight 250 g/m2, obtained locally (Italy), and hemp fibres, supplied by AMCO (Egypt), decorticated and bleached using sodium chlorite in optimised conditions, impregnated with I-SX10 LEGNO epoxy resin by Mates Italiana with SX10 LEGNO 33% general purpose hardener, again by Mates Italiana. The lay-up of the indented laminates includes six inner layers of jute plain weave disposed at 0°/0°/45°/-45°/0°/0° sandwiched between two non-woven hemp mats. The composite includes approximately 30 wt. % of jute fibre and 20 wt. % of hemp fibre. They were produced using a hand lay-up procedure in a closed matching mould of dimensions 220x250x3.7 (± 0.2) mm by applying a slight pressure in the order of 0.02 MPa. Static indentation test was performed using a hemispherical nose of 12.7 mm diameter according to ASTM D6264-98 standard on simply supported, 110 mm side laminates. Four laminates have been tested to failure. Loading has been applied in displacement control with 1 mm/minute cross-head speed using an Instron 5584 universal testing machine. One of these laminates was considered for NDT analysis. Optical and infrared NDT techniques, according to the set-ups exposed above, have subsequently monitored the presence of damage due to loading on the whole surface of the sample.

COMPARATIVE RESULTS

Typical loading curves measured during indentation test are reported in Figure 5. Linear stiffness, which measures the elastic energy dissipated through impact or indentation in the laminate [67-68], is calculated by considering the “quasi-elastic” part of the curve, fitting all the points between 20 and 80% of the displacement corresponding to the maximum load. The value obtained is then normalised by the laminates average thickness (3.7 mm). The standard deviation represented the oscillation of the slope of the curve between the measurement points. The specific values obtained for the plates examined by NDT techniques are reported in Table 1.

Fig.5 Indentation curves

Table 1 Result of indentation test on the laminates

Plate number

Max load (N)

Displacement at maximum load (mm)

Final displacement (mm)

Normalised linear stiffness (N/mm)/mm

1 1843 3.18 5.15 212 ± 43

2 2168 3.03 5.31 248 ± 43

3 2141 3.73 5.14 217 ± 35

4 2339 3.88 5.25 189 ± 18

In general, it can be noticed that the values of the normalized linear stiffness are higher than what reported in [69] for hemp loose quasi-unidirectional fibre (LU)/epoxy laminates (around 110±20 (N/mm)/mm). This may suggest that the combination of the two reinforcements (i.e., loose hemp fibres and jute hessian cloth) reduces the dispersion of mechanical values. Also, in terms of indentation damage, the external presence of hemp fibres does not result in the extensive tearing of the laminates along the impact loading diameter line, which is a characteristic of impact damage on jute fibre reinforced laminates [70-71]. This assumption is also confirmed by comparing the NDT experimental results obtained from the laminate object of our study which is shown in Figure 6a.

(a) (b)

Fig. 6 a) Picture of the sample n. 1 (back face), b) DE result of the sample n. 1

During the HI inspection the interferogram was acquired using a laser product (G4plus250 laser by ELFORLIGHT Ltd.), with a fundamental wavelength of 532 nm, vertical polarization and a specific power of 250 mW. Double-Exposure measurement (distance tip of the soldering iron-sample: 25 mm) was performed in transmission mode using a soldering iron station made by The Cooper group WELLER®, WECP-20 type (Pmax = 50 W at 24 V). In this version, analogue temperature regulation is carried out using a potentiometer, able to set the temperature continuously in a range of 50 °C to 450 °C. A green LED indicates the status of the regulation. An heat conveyor mounted between the soldering tip and the back face of the sample was manufactured. Because of its extreme sensitivity to surface deformation, HI is well suited to inspect composite materials made by natural fibres, since very small thermal stress are involved. In our case, a surface temperature increase up to 3 °C was used.

P1P1

Back face

D

The interferogram reported in Figure 6b was obtained with the first exposure (texp = 2 s) 10 s after switching off the soldering iron and a second exposure (texp = 2 s) 2 min after the first exposure and a heating time of 3 min. The stressing method is usually selected empirically with guidance provided by an analysis of anticipated deformation and by previous results obtained from programmed models. Most surface damage, as it can be observed in Figure 6a (red dotted line), is related to the insufficient control of fibre orientation: spalling i.e., loss of material at rear, though a frequent occurrence in plant fiber composites, usually is not easily detected visually. In our case, this anomaly does not produce detectable perturbations in the surface deformation [72] as shown in the holographic result (Figure 6b), although important delaminations are correlated with the impact (defect D - yellow dashed line).

In order to study the P1 indented area (Figure 6), to explore the MatPIV 1.6.1 software and 2D-PIV software ver. 3.001-1.11, and to confirm the presence of the defect D (comparing the DSP results and trying to understand the shape of the damage provoked by the impact), we used the configuration reported in Figure 1 which provided the experimental results shown in Figures 7a and 7b. The result shown in Figure 7a comes from MatPIV 1.6.1 software, after having applied SNR 1.5 filter and NANINTERP with “single” interpolation and “linear” iteration, while the result shown in Figure 7b comes from 2D-PIV software ver. 3.001-1.11 using the simplifiedprocess.cfg function. Defect D after having applied the appropriate filter, is slightly visible in Figure 7a; moreover the shape that the fringes have below the impact (P1 - Fig. 6b) was confirmed by both software but especially using MatPIV 1.6.1 software (Figure 7a – red dashed line).

(a) (b)

Fig. 7 a) MatPIV 1.6.1 software - QUIVER result, b) 2D-PIV software ver. 3.001-1.11 - QUIVER result. In both cases, the first and second images after switching off the soldering iron were processed

Subsequently the sample was analyzed by SPT, for which Figure 8 shows the experimental setup for data acquisition. The sample was heated for 4 minutes using one 500 kW lamp positioned in reflection mode, and the surface cooling down was recorded by an IR camera (FLIR Systems – ThermaCAM S65 HS). One thermogram every second was acquired and the acquisition lasted for 780 s (i.e. 13 minutes), providing 780 thermograms.

D

Fig. 8 SPT experimental setup for data acquisition

The same configuration of the impact (Fig. 7a) was found by PCT-EOF12 result (Fig. 9b).

(a) (b) (c)

Fig. 9 Selected PCT results by SPT of the sample n. 1 a) EOF3, b) EOF12; c) NIR result in transmission mode

IRT (PCT-EOF12 result in Figure 9b) has detected also a rectangular area underlined by yellow arrows, probably due to an epoxy resin rich area. In this case, the fringes configuration (Figure 6b) does not permit to discover this sub-surface anomaly. For this reason, NIR technique in transmission mode (Figure 9c) was applied in order to confirm the result detected by IRT [73-74]. It was surprising to detect lack of homogeneity in another area, marked by red arrows in Figure 9c, which is located above the former one and is likely to be the consequence of local lower fibers concentration. Readers can see the same result but with greater contrast between the areas at high and low fibers distribution in Figure 10a.

T = Infrared camera

S = Sample

L = Lamp

AB = 47 cm

CB = 30 cm

(a) (b)

Fig. 10 (a) Image subtraction between reflectogram and transmittogram, (b) distance transform applied on (a)

Figure 10a, which summarizes the anomalies inherent in a resin rich area (Figure 9b) and in an area at low fibers distribution (Figure 9c), derives from the images’ subtraction carried out in Matlab©

environment between the reflectogram and the transmittogram. This method reveals that the two non-woven hemp mats are not equally distributed in terms of fibers on the two sides. This statement is evident seeing the dark zone highlighted by a red dashed rectangle. A CMOS camera (Canon 40DH 22.2 x 14.8 mm – 10 megapixel 0.38-1.0 μm), with a visible cut-off filter to limit the spectrum to 0.7 to 0.9 μm was used. The radiation source, consisted of one halogen lamp (OSRAM SICCATHERM – 250 W IR), which provided a wide spectrum radiation including the NIR band (Figure 11).

Fig. 11 Blue line: relative spectral distribution of OSRAM SICCATHERM® lamps [75]

The NIR result shown in Fig. 9c was useful to identify the non-woven hemp mat also detected by PCT (EOF3, see Figure 9a) using the SPT configuration, but more as a base for applying the distance transform operator (Figure 10b). In fact, this operator proved to be very useful for the identification of areas at low concentration of hemp fibers, if applied as in our case, on the image subtraction between reflectogram and transmittogram (Figure 10a). It is based on the Saito’s algorithm [64]. The 1D DT is first constructed for each row (or column) independently; then this intermediate result is used in a second phase to construct the full 2D DT. The first stage is common to all Eucledian DTs based on independent scanning: given an input image F, the first transformation (transformation 1) of independent scan generates an image G is defined by:

G (i, j) = miny {(j - y)2 | F(i, y) = 0} (11)

This corresponds to computing, for each pixel (i, j), its (squared) distance to the closest black pixel in the same line. This transformation is efficiently implemented by performing a forward scan (left to right) followed by a backward scan in each line of the image. Then, Saito and Toriwaki devised an algorithm to produce the EDT of a k-dimensional image using K transformations, one for each coordinate direction. For 2D images, distance values are first computed along each row (1st

transformation). These values are then used for computing minimal distances along each column (2nd transformation). Using Eq. 11: starting from G (of transformation 1) the 2nd transformation of Saito generates an image H, which is the distance map of F:

H (i, j) = minx {G(x, j) + (i - x)2} (12)

Figure 12 illustrates transformation 2.

Fig.12 Example of transformation 2 at a pixel (i, j) [63]

Note that the square Eucledian distance between two pixels is defined as the squared vertical distance plus the squared horizontal distance. After transformation 1, every pixel (x, j) of column j has the value G(x, j), which is the squared distance between (x, j) and the nearest black pixel in the same row. Adding to G(x, j) the vertical distance between (i, j) and (x, j), (i – x)2, one finds the 2D distance between (i, j) and the nearest pixel to (x, j) in row x. Taking the minimum of the results for all lines x, H(i, j) will be the distance from (i, j) to the nearest seed pixel. Saito and Toriwaki implement transformation 2 using a downward scan followed by an upward scan in each column of G. During the downward scan, for each pixel (i, j) one applied a test to restrict the number of pixels ahead over which distance minimization is performed. The upward scan proceeds in a similar fashion [63].

(a) (b)

Fig.13 (a) Fusion of images: 6a, 7a and 9b, (b) SOBI-RO result. A magnification of the defect D contrasted (gray scale), is also reported.

DD

D

By this operator the critical white areas (Figure 10b) were linked with the impact shape. The hemispherical impactor produced permanent indentation causing fibers breakage (Figure 6a). The superimposition between the visible image, the DSP-QUIVER result and the PCT-EOF12 result (Figure 13a), shows that the small white round area detected by EOF12 (Figure 9b – red arrow), due to a zone poor of fibres and resin after the impact (Figure 6a), was detected also by DSP - MatPIV 1.6.1 software (Figure 7a – red arrow) but with lesser contrast.

This integrated approach determines the various internal damage mechanisms present within the sample. This is of importance since the compressive and tensile residual strengths are influenced by the type of damage present in the laminate [8]. Interestingly to note that the impacted area (Figure 13a) does not fall in the white area previously discussed (Figure 10b). The use of the SOBI-RO algorithm (Figure 13 b) applied on the same SPT image sequence for reference (Figure 9 a-b), permits to confirm the D defect (delamination) also by IRT. In addition, the small white round area previously described (Figure 6a) and detected (Figure 13a) marked by one red arrow appears very clear in Figure 13b. Finally, a part of the subsurface anomaly due to an epoxy resin rich area (marked by yellow arrows) already highlighted in Figures 9 b, 10 a, and the edge zone (Figs. 9 c, 10 a) due to a lower fibers concentration (marked by red arrows) better described subsequently, are shown in the SOBI-RO result. Very surprising is the detection, by the latter method, of a strange configuration highlighted by white arrows. Because this defect, not visible to the naked eye (Figure 6a), was also revealed during the PT inspection by PCT (Fig. 14 a, d) both in EOF2 and EOF7, taking into account its position (from the impact’s point up to the top side having two defects), the physic connection between EOFs and the depth of the sample [76], we can assume that it is a subsurface crack. Note that it is the only linear configuration between EOF2 and EOF7 confirmed in the latter. The color change from dark to white is explained in [77].

(a) (b)

(c) (d)

Fig.14 Selected PCT results by PT of the sample n. 1 a) EOF2, b) EOF3, c) EOF4, d) EOF7

PCT results obtained by SPT configuration were compared with PCT results coming from an integrated flash thermography (PT configuration) by employing a MWIR system (Figure 14). In this way, the resin rich area (Figure 14c – yellow arrows) and the area at low fibers distribution (Figure 14 a-b – red arrows) are confirmed. A new area on the opposite side of that highlighted by yellow arrows (Figure 14 b, c – violet arrows) at low fibers distribution was discovered by PT. These areas could be due to the cutting machine (end-mill) operating at the end of the manufacture. In fact, cutting temperature increases with cutting speed. The cutting temperature in steel can rise to 800 °C or higher. On the other hand, the melting points of the components of cellulose, hemicelluloses, and lignin are about 240, 180, and 420°C, respectively. Taking into account these considerations, probably the cutting temperature was more than 180°C [78]. The impact zone is evident only in the Figure 14 c, d, while in Figure 14 b, d, appears a curious anomaly not discovered in the previous NDT analysis (probably a detachment between inner layers). At this point, an NDT inspection in transmission mode by a SWIR camera (Goodrich SU640SDWH-1.7 RT 640x512 pixels, InGaAs, 900-1700 nm) was conducted in order to cover the non-thermal and thermal infrared vision (Figure 15 a-e).

(a) (b)

(c) (d)

(e) (f)

Fig.15 SWIR results in transmission mode of the sample n. 1 (back face) a) 940 nm, b) 1050 nm, c) 1300 nm, d) 1430 nm, e) 1650 nm, f) correlation result applying PT

In order to compare the result obtained in these Figs. with another method that summarizes all the information contained in a sequence into a single image, the IR correlation operator was applied (Figure 15f) [34]. This technique was selected taking into account the hybrid nature of the sample material being tested. In fact, the correlation coefficient image is mostly sensitive to material changes, being much less sensitive to temperature non-uniformities or initial heat absorption as these are temperature offsets in terms of temperature evolution. The effects of the offsets are cancelled in correlation computation as they do not affect the linear relationship between two variables.

In the SWIR inspection, different filters at 1050 nm, 1300 nm, 1430 nm and 1650 nm were mounted, while the result at 940 nm (Figure 15a) was acquired using a LED lamp. Light emitting diodes (LED) are an example of a very interesting illumination source since they provide a narrow spectrum at specific narrow wavelengths, from UV to VLWIR including NIR/SWIR [79]. The contrast between the dark and white zones grows from 940 nm to 1650 nm (for example, note the zone marked by red arrows), as well as the impact’s shape is more evident here than in Figure 9c. It reflects and confirms the third and fourth alignment of the jute layers.

The subsurface anomaly highlighted by a white dashed oval in Figure 14 b, d, is also confirmed by the latter inspection working with the 1300, 1430, 1650 nm (Fig. 15 c, d, e) filters mounted on the camera. This is a useful marker for the future SWIR inspections on the same target. The correlation result proposed in Figure 15f reveals the second edge at lower fibers distribution already detected in Figure 14 b, c and marked by violet arrows. In this case, no further indications can be drawn about

the impact zone, if we exclude the zone poor of fibers and resin after the impact, marked by a red arrow also in Figure 13.

CONCLUSIONS

In this study, a jute/hemp fibre hybrid laminate after indentation was investigated by optical, NIR/SWIR and thermographic NDT inspections under laboratory conditions. Different signal analysis operators (distance transform, PCT, SOBI-RO, IR correlation, image subtraction, superimposition by image fusion) were applied to investigate the extension of the subsurface defects, different in nature and position. The processing of the SPT data by PCT can provide results concerning the shape of the impact, while the same operator applied on the PT data, gives information about different defects’ typology, like cracks and due to cutting, or suspected resin rich areas and detachments to be verified by chemical analysis and in a destructive manner, respectively. The use of NIR/SWIR proved useful to visualize the non-woven hemp mat with higher image resolution and to detect anomalies like resin rich areas, which were also highlighted through image subtraction between reflectogram and transmittogram. The shape of the subsurface damage produced by indentation was better characterized by data fusion from EOF12 and DSP. In addition, PCT improved the quality and the visibility of the square pulse thermographic signal, while holographic interferometry provided supplementary information on internal delaminations. The use of different filters working in the SWIR spectrum confirmed the presence of different subsurface defects, while applying distance transform on the NIR data acquired in transmission and reflection mode with mutual image subtraction, resulted in a clear and complete map of the zones with low impact resistance, due to a uneven distribution of the hemp fibers. The combination of these NDT techniques can offer a diagnostic tool for damage assessment on natural fiber composites, in that it provides a huge amount of information concerning the subsurface conditions after static indentation. Finally, also dent depth measurement of composites after impact damage is an interesting point to be analysed in the present field: this will be discussed in future testing - experiments in order to complete the study.

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CAPTION FOR FIGURES

Fig. 1 Experimental setup for Digital Speckle Photography (DSP)

Fig. 2 Experimental setup for Double-Exposure (DE) Holographic Interferometry (HI)

Fig. 3 Experimental setup for Square Pulse Thermography

Fig. 4 Thermographic data rearrangement from a 3D sequence to a 2D A matrix in order to

apply SVD and rearrangement of 2D U matrix into a 3D matrix containing the EOFs [56]

Fig. 5 Indentation curves

Fig. 6 a) Picture of the sample n. 1 (back face), b) DE result of the sample n. 1

Fig. 7 a) MatPIV 1.6.1 software - QUIVER result, b) 2D-PIV software ver. 3.001-1.11 -

QUIVER result. In both cases, the first and second images after switching off the

soldering iron were processed

Fig. 8 SPT experimental setup for data acquisition

Fig. 9 Selected PCT results by SPT of the sample n. 1 a) EOF3, b) EOF12; c) NIR result in

transmission mode

Fig. 10 (a) Image subtraction between reflectogram and transmittogram, (b) distance transform

applied on (a)

Fig. 11 Blue line: relative spectral distribution of OSRAM SICCATHERM® lamps [75]

Fig. 12 Example of transformation 2 at a pixel (i, j) [63]

Fig. 13 (a) Fusion of images: 6a, 7a and 9b, (b) SOBI-RO result. A magnification of the defect D

contrasted (gray scale), is also reported.

Fig. 14 Selected PCT results by PT of the sample n. 1 a) EOF2, b) EOF3, c) EOF4, d) EOF7

Fig. 15 SWIR results in transmission mode of the sample n. 1 (back face) a) 940 nm, b) 1050

nm, c) 1300 nm, d) 1430 nm, e) 1650 nm, f) correlation result applying PT