J Nondestruct Eval DOI 10.1007/s10921-013-0211-y
Damage Localization in Plates Using Mode Conversion Characteristics of Ultrasonic Guided Waves S.M.H. Hosseini · S. Duczek · U. Gabbert
Received: 23 April 2013 / Accepted: 12 November 2013 © Springer Science+Business Media New York 2013
Abstract The present study provides a concise description of wave propagation in cellular sandwich panels. A novel approach of damage detection based on mode conversion is proposed which can be useful for detecting relatively small damages in cellular sandwich structures using high frequency guided waves. The new methodology applies the continuous wavelet transform (CWT) and the cosine formula to extract the damage location from the time signal of displacements. Experiments conducted on a honeycomb and a metallic hollow sphere sandwich plate highlight the feasibility of the novel technique. Keywords Non-destructive testing · Cellular sandwich plates · Guided waves · Mode conversion · Continuous wavelet transformation · Laser vibrometry
1 Introduction Guided wave (GW) propagation has already been used for structural health monitoring (SHM) applications in composite structures in several studies [6, 37, 40]. A network of piezoelectric actuators and sensors is used to generate and receive the GWs [14]. The advantages of GW based SHM
S.M.H. Hosseini (B) · S. Duczek · U. Gabbert Institute of Numerical Mechanics, Department of Mechanical Engineering, Otto-von-Guericke-University Magdeburg, 39106 Magdeburg, Germany e-mail:
[email protected] S. Duczek e-mail:
[email protected] U. Gabbert e-mail:
[email protected]
are its high sensitivity towards structural damages, the possibility of implementing an online monitoring and the low costs of the required equipment [37]. In this context, different approaches based on either a forward or an inverse algorithm can be used to localize possible damages within the structure. A forward analysis normally yields a unique result. On the other hand, the solution of an inverse problem is not always unique [48]. In the following paragraphs recent approaches based on forward analysis are reviewed and discussed. The time-of-flight (ToF) is used in forward algorithms to locate the damage. In this approach each piezoelectric transducer acts both as actuator and sensor (pulse-echo system). This methodology was used by Mustapha et al. in [26] to locate damages in a sandwich carbon fiber/epoxy composite structure with a honeycomb core. They used the fundamental anti-symmetric Lamb mode (A0 ) at a low frequency range of 6.5 kHz. Modern lightweight structures are typically made of carbon fiber reinforced plastic, glass fiber reinforced plastic or sandwich panels. In order to detect damages in such materials the shape of the wave front has to be known, as the propagation velocity differs depending on the angle (wave propagation direction in the medium). Ungethüm et al. proposed to use an optimization model based on migration strategies [40]. Thus, they could locate damages in orthotropic plates using a forward algorithm based on the ToF measurement. The method has been verified experimentally on a carbon fiber reinforced plastic plate. In another approach sparse arrays are used, where the actuators and sensors are applied in different locations. In this case, scatter signals are more useful compared to incident wave signals to locate damages [47]. In this triangulation approach, three sensors are required in order to locate the damage. Special care has to be taken when the damage oc-
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curs on the line of sight between two sensors. In this case, a fourth sensor is required to ensure the feasibility of the approach [47]. One disadvantage of the mentioned approaches is the limitation to single mode analysis. In addition, neglecting the mode conversion phenomenon can cause further difficulties to separate the converted modes from the reflected modes in further signal processing procedures. Contemplating the S0 mode [47], the limitation to detect damages can be further increased. In Ref. [5] it is illustrated that deeper flaws, damages and/or perturbations result in a notably lower energy transmission when the S0 mode is taken into consideration. Therefore, it is possible that these damages are not registered. To overcome drawback of a mono-mode damage detection, a system based on mode conversion has been proposed in [21]. It has been successfully applied to carbon fiber reinforced plastic plates. However, the assumption of wave propagation in every direction with different velocity is not considered in this study. Furthermore, accuracy of ±10 mm has been reported for the proposed damage detection system. In another study, a multi-modal approach based on mode conversion is used to size strip-like defects [33]. However, it was assumed that the locations of the damages are known a priori. In another study an automated and integrated Lamb wave-based active SHM system was developed employing the definition of different damage indexes using various signal analysis approaches [38]. A schematic representation of the proposed system is shown in Fig. 1. Several steps are considered to determine the damage location. In each step one piezoelectric element acts as an actuator and the remaining piezoelectric elements work as sensors. For every step the damage index is calculated for the signals which are received at the sensors. A dashed line between the active actuator and the sensor with the highest damage index is drawn, see Fig. 1. The location, where most of the dashed lines are crossing, is considered to be the damage location. The disadvantage of this method is its limitations to locate the exact position of the damage. The damage location can only be estimated in the area between the piezoelectric wafers, as indicated in Fig. 1 by the rectangle. Thus, the accuracy depends on the spacing of the transducer network. Outlier analysis is another algorithm for SHM. This approach uses statistical methods to indicate whether the structure is in a healthy condition or not. However, it cannot provide much information about the damage quality and its location is impossible [27]. In a different study also deploying statistical methods, the formulation of a maximum-likelihood damage estimation has been described [11]. Promising results have been obtained using only a sparse array of piezoelectric transducers. However, it has to be mentioned that this process is rather time consuming.
Fig. 1 Automated and integrated Lamb wave-based active SHM system developed in [38]. Dashed lines indicate the highest damage index
Sohn et al. [35] used image processing techniques to detect damages in multi-layer composites. The GWs are excited by piezoelectric wafers being attached to the surface of a composite plate and a scanning laser Doppler vibrometer (LDV) was used to obtain wave-field images. Afterwards, image processing techniques were used to highlight the defect in the scanned area. In addition, frequency-wavenumber domain filtering was used in [24, 31] to improve the damage detection process based on full wave field measurements. However, the disadvantage of these approaches is their dependency on the image resolution (number of nodes scanned by the LDV) to detect small damages within the scanned field. In the current paper a new methodology based on the mode conversion phenomenon is proposed for damage detection. The geometrical locations of the damages are determined by the cosine formula and the ToF which is calculated using signal processing based on a scattered continuous wavelet transform (CWT). In regard to detection and localization of small debondings (comparable to the wavelength of the propagating waves), the new approach has some advantages. No dependency on a single mode propagation is observed and only a low spatial resolution of the wave field images is needed from LDV. The application of the proposed approach is extended for SHM of cellular composite structures. Cellular structures are defined as materials with high porosity that are divided by solid walls into separate cells where the internal regions are air cavities [10]. Nowadays, the industrial standard for sandwich cores are honeycomb structures which exhibit a high stiffness to density ratio. However, the processing of honeycomb structures, especially as a core between curved face sheets, is complex and therefore increases the manufacturing costs [32, 45, 46]. Metallic hollow sphere structure (MHSS) is a relatively new approach in the design of cellular lightweight structures made of metal. The geometry of the core structure of an MHSS plate can be easily reproduced with respect to consistent mechanical and physical properties [15]. A similar be-
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havior compared to open-cell metallic foams was observed for these materials [22]. The article at hand presents the application of the proposed SHM methodology to detect damages in a honeycomb and a MHSS sandwich panels. In the course of the following section a brief introduction to GW propagation in cellular structures and mode conversion phenomena is given. Afterwards, the proposed damage detection method is presented in detail. Finally, the experimental results are discussed.
2 Guided Wave Propagation in Elastic Medium For isotropic materials, the Rayleigh-Lamb waves propagate along the medium with different dispersive modes including the symmetric (Si ) and the anti-symmetric (Ai ) mode shapes respectively [1, 12, 13]. The out-of-plane displacements are symmetrical with respect to the mid-plane of the thin-walled structures for the Si mode, while for the Ai mode propagation the out-of-plane displacements are anti-symmetrical. 2.1 Mode Conversion The interaction of the Si and Ai modes with geometrical changes has been addressed in several studies. It has been mentioned that depending on the geometrical perturbations, reflections of the waves and changes in the shape of the propagating wave field can be observed [4]. The interaction of symmetric and anti-symmetric obstacles with Lamb waves are studied in [2, 5, 8]. It has been reported that at symmetric obstacles with respect to the mid-plane of the plate, no mode conversion of the GWs occurs [3, 9]. However, it has been reported that when GWs encounter an unsymmetrical obstacle the different modes are converted into each other. The influence of the dimensions and the shape of unsymmetrical obstacles in plates on the wave scattering has been addressed in these Refs. [5, 7, 33]. Another important phenomenon that has been first observed and studied by Willberg et al. [42, 43] is the so called continuous mode conversion which is a material induced mode conversion. It is the result of the interaction of the GWs with the interior structure of multi-layer carbon fiber reinforced plastic composites. Numerical and experimental techniques have been used in [42, 43] to investigate this phenomenon in plain and twill fabric plates. 2.2 Guided Wave Propagation and Mode Conversion in Cellular Composite Structures To apply GWs for SHM in cellular structures, the interaction of the GWs with the macro- and micro-structure has to be well understood. The description of the interaction of GWs traveling from the cover plates to the core structure
and vice versa is necessary to understand how GWs propagate through cellular structures. As an example, the mechanisms of ultrasonic GW propagation in a foam core sandwich structure have been studied in [6]. It has been shown that by exciting the S0 mode on a high density foam structure an additional mode appears after the arrival of the S0 mode. The second mode is attributed to a reflection from the bottom surface. However, to gain a better understanding of the wave propagation in such structures more detailed investigations are needed. In some recent parametric studies [14, 17, 41] it has been reported that for the low frequency range, where the wavelength (λ) is bigger than the complete sandwich plate thickness (tp ), the energy of the GWs travelling on the top surface (where the wave is excited) and the energy of the propagating waves in the bottom surface are comparable. While in the higher frequency range, where the wavelength is smaller than the plate thickness, the energy of the GWs on the top surface is higher than that of the waves propagating along the bottom surface. Meaning, less energy is transmitted through the core of the structure. Accordingly, in the current work the propagation of guided elastic waves in cellular structures is studied in detail for a wide range of frequencies. Low Frequency Range (λ > tp ) In the remainder of this section the S0 mode is neglected and all discussions are focused on the A0 mode. Only a single LDV is deployed to measure the out-of-plane displacements of the fundamental symmetric wave mode. Since the primary displacement components of the symmetric mode are in in-plane direction, it is hardly registered. The low energy transmission through the thickness of the plate of the S0 mode compared to the A0 mode makes its measurement even more difficult [26]. Therefore, only the fundamental anti-symmetric mode A0 is studied in detail. The A0 mode is essentially a flexural wave [26]. To illustrate the behavior of the A0 mode in a cellular structure in a low frequency regime the simulation results for a central frequency of 10 kHz are shown in Fig. 2. As an example the wave propagation in a lattice block structure (two cover plates connected by thin walls) is studied. The lattice block structures are used to illustrate general features of GW propagation in a cellular structure. The main advantage of such a material is an easy visualization of the propagating waves and their interaction with the core layer. It is shown that in the low frequency range the whole structure acts as a single unit and therefore the energy transmission from the top surface to the bottom surface is comparable to the results reported in [14, 17, 41]. Because there is no interaction between GWs and the micro-structure in the low frequency range, one can neglect the geometrical details of the core structure to model wave propagation in cellular structures. Therefore, simplified models in which the core
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Fig. 2 Simulation of the low frequency range GW propagation in an aluminum lattice block structure with 10 kHz central frequency. The snapshot of the displacement field is taken with 0.11 e−4 s delay after
the signal is excited and the scale factor of 2 e5 is used to visualize the out-of-plane displacements. The cover plate is 0.5 mm thick, the core height is 15 mm and the core cells thicknesses are 0.1 mm
structure is replaced by an orthotropic homogenized layer can be used [14, 17, 41]. The homogenized material properties can be obtained based on a representative volume element (RVE) approach [14, 41] or on evaluating experimental data [17]. However, one can also use an analytical formulation to obtain the properties of GWs (e.g. wavelength) propagating in cellular structures in the low frequency range [39]. A comparison of the wavelength values obtained with the analytical formulation presented in [39] to values calculated by finite element method (FEM) modeling presented in [14] shows a good agreement with about 6 % error. In the low frequency range the A0 mode is not influenced by the core layer due to a mismatch between the wavelength and the dimensions of the cellular core structure. Thus, it can be concluded that GWs are able to interact with damages that are introduced in the whole thickness of the sandwich structure, but they cannot register small damages in the micro-structure of the core layer.
Figure 3 presents the results of FEM simulations of high frequency range wave propagation with a central frequency of (a) 200 kHz and (b) 350 kHz in a lattice block cellular structures. The GWs are excited using a piezoelectric element attached to the top surface. The interaction of the waves traveling from the cover plate to the core structure is obvious for high frequency range signals, cf. Fig. 3(a). Due to the small wavelength, the waves interact with the core structure which can be thought of as geometrical perturbations. As mentioned before, both Si and Ai modes are reflected and transmitted from such anti-symmetrical geometrical changes, therefore, one may expect propagation of both modes in the top and bottom surface at any time. For a better identification of the Si mode (which cannot be easily identified in Fig. 3(a) due to the lower out-of-plane displacements), the propagation of both modes on the cover plates are highlighted in Fig. 3(b). Here the in-plane displacements are shown and lattice block structure with thicker cover plates is deployed. However, as reported in parametric studies and as shown in Fig. 3, less energy is transmitted to the bottom surface due to the energy “lost” in the conversion process. In addition, a delay in the ToF is seen caused by the through-thickness propagation of the wave modes. Due to the interaction of GWs with the core structure in the high frequency range, damages which are located in the regions of the connection between the core structure and the cover plate, i.e. small debondings, can be recognized. However, small damages inside the core structures are much harder to detect. The interacting with damages can be masked by multiple reflections and/or mode conversion in the cover plates and in the core layer. To execute the simulations, the commercial FEM software ANSYS® 11.0 has been used. For the simulation of GW propagation in solid structures a spatial resolution of 10 elements per wavelength and a time step size which is given by the minimum element size divided by the maximum group velocity are considered. Further modeling details and convergence studies are provided in [14, 17].
High Frequency Range (λ < tp ) As mentioned earlier in this section, previous parametric studies have revealed that in the high frequency range more energy is contained in the wave packet propagating in the cover plate, where the actuator is located (top surface) in comparison to the cover plate on the other side of the sandwich structure (bottom surface). The main reason for this behavior is attributed to the shorter wavelength. It has been shown that the relative density of the core structure and core geometry are important parameters for the prediction of the energy transmission from the top surface to the bottom surface [14, 17, 41]. In the high frequency range the GWs interact with the core structure due to their shorter wavelength. Real core layers can be regarded as being geometrically unsymmetrical with respect to the cover plates. Therefore, mode conversion occurs when the wave propagates through the thickness of the plate. As the wave enters the core structure, the wave energy is divided. The wave is partially reflected and partially transmitted into the core structure and converted into a different wave mode.
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Fig. 3 Simulation of GW propagation in aluminum lattice block structures excited in the high frequency range; (a) 200 kHz and (b) 350 kHz. In part (a) the cover plate is 0.5 mm thick and the core height is 15 mm, the snapshot of the displacement field is taken with 3.0 e−5 s delay after the signal is excited and the scale factor of 4 e5 is used to visualize the
out-of-plane displacements. In part (b) the cover plate is 2 mm and the core height is 5.6 mm, the snapshot of the displacement field is taken with 2.9 e−5 s delay after the signal is excited. The core cell thickness is 0.1 mm in both parts
Fig. 4 Contour plot of the high frequency range wave propagation field (fc = 150 kHz) on the top surface of the CELLITE silver standard 69 honeycomb sandwich plate measured with the LDV. Interaction of
the honeycomb core with the propagating symmetric mode is highlighted. Schematic representation of reading B-scan nodes (see Fig. 5) are shown along the wave propagation direction
Experimental Examples In the present paragraph the focus is on experimental investigations of the interaction of GWs with sandwich panels. Special interest is taken in honeycomb plates. A CELLITE silver standard 69 honeycomb sandwich plate (Axson GmbH) made of aluminum is used for the experimental tests. The honeycomb cell height is 12.7 mm, the cover plate is 0.6 mm thick, the honeycomb cell size is 6.4 mm and the honeycomb wall thickness is 0.0635 mm. The tests are performed with a scanning LDV from Polytec (PSV 400 3D) [29, 34, 42]. To design a free surface
boundary condition, the plate has been placed on a foam material. Paraffin is used to attach the actuator (piezoelectric transducer made of PIC-181) at the top surface of the cover plate. The surfaces are coated by a retro-reflective layer to enhance the signal to noise ratio of the LDV measurements. The high frequency range wave propagation field on the top surface of the CELLITE silver standard 69 honeycomb sandwich plate measured with the LDV is presented in Fig. 4. Interaction of the GWs with the core structure, i.e. mode conversion from the S0 to the A0 mode, is eas-
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Fig. 5 B-scan of the GW propagation on the top surface of the aluminum honeycomb sandwich plate with a excitation frequency fc of (a) 50 kHz and (b) 150 kHz. One can see the interaction of high frequency GWs with core structure in part (b). The reading points are
schematically shown in Fig. 4 where X is considered to be in the wave propagation direction. The B-scan figures are plotted using a filled twodimensional contour plot (contourf) in MATLAB®
ily observed (due to the higher out-of-plane displacement components of the A0 mode) and highlighted with a pentagonal shape which corresponds to a cell in the core. However, more studies similar to [42, 43] can be performed to characterize this phenomenon as continuous mode conversion in cellular composite structures. In order to illustrate the interaction of the waves (both in a high and low frequency regime) with the core layer of a honeycomb sandwich panel B-scan are taken. The results are plotted for different central frequencies, cf. Fig. 5. The B-scan diagram includes the displacements of the nodes along the wave propagation direction in the time domain. The reading points are schematically shown in Fig. 4 . They are taken every 1 mm and the first measurement point is also the origin of the coordinate system, i.e. x = 0. The slope of the black solid lines shown in Fig. 5, indicate the phase velocity of each mode [19]. Figure 5(a) highlights the fact that that for an excitation frequency of 50 kHz (i.e. low frequency range) the GWs do not interact with the honeycomb structure due to the longer wavelength. According to the results in this figure no change in the phase velocity is observed. Whereas, Fig. 5(b) demonstrates the mode conversion phenomenon (appearance of an A0 mode where only the existence of a S0 mode is expected) in the honeycomb structure . Reflections of the A0 mode (phase velocity is given be the slope of the solid black line) can be observed
as well. These reflections can be attributed to the geometry of the core structure in a frequency excitation regime (fc = 150 kHz). Because of the different phase velocities the two fundamental wave modes can be easily distinguished in Fig. 5. The mode conversion phenomenon (due to the interaction with the core layer) can be identified by a change in phase velocity. It has to be mentioned that the mode conversion from S0 to A0 , as shown in Figs. 4 and 5(b) (where the whole structure is made of aluminum), has not been reported in [14] for honeycomb plates where the core materials are more compliant than the cover plate (i.e. smaller Young’s modulus).
3 Damage Detection Using Mode Conversion Characteristics A novel approach of damage localization based on mode conversion is proposed in this section. The conversion of the S0 mode to the A0 mode, caused by defects, is used to reach this goal. The converted A0 mode has higher out-of-plane displacements (in comparison to the reflections and transmissions of the incident S0 mode) which can be utilized to identify the damage location in the wave field. In the current study we focus on damages between the core layer and the cover plate (i.e. small debondings) which often occur during
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Fig. 6 Schematic representation of actuator, sensor and damage locations
service or after accidents. As described in the previous section, GWs in the high frequency range are more suitable to detect such damages in cellular structures. The distance between the damage and the actuator (xDA ) and that between the damage and the sensor (xDS ) can be obtained by solving Eqs. (1) and (2) as shown in Fig. 6. 2 2 2 xDS + xAS − 2xDS xAS cos α = xDA .
(1)
The distance between actuator and sensor (xAS ) is fixed and known. Furthermore, Eq. (2) is used to define xDA based on ToF. The GWs propagate with the group velocity of the S0 mode (Gsym ) along xDA and with the group velocity of the A0 mode (Ganti−sym ) along xDS . The change in propagation velocity is due to the mode conversion at the damage. Therefore, the ToF is the sum of the ToFs from the actuator to the damage and from the damage to the sensor. Hence, xDA can be expressed as xDS . (2) xDA = Gsym T oF − Ganti−sym When the ToF flight is known the cosine formula described in Eq. (1), can be used to determine xDS for a given value of α in a medium where the absolute group velocity of different modes is independent of wave propagation direction (e.g. a honeycomb plate with isotropic cover plates made of aluminum). Assuming the sensor location (xs , ys ) is a priori known and the xDS has been computed as detailed above the damage location can be estimated. Using four sensors the exact damage location can be calculated as proposed in [47]. It has to be mentioned, however, that one has to take time delays, caused by the through-thickness propagation of the waves, into account when only data measured at the bottom surface is available. Therefore, the ToF has to be adjusted. Determination of ToF As the GWs propagate along the structure and interact with damages, the scatter signals can be used to estimate the ToF of the converted mode [47].
However, despite the approach described in Refs. [26, 47], using the converted modes in the high frequency range to determine the location of small damages (comparable to the wavelength) based on low resolution scatter signals is difficult because of the high similarity of the “damaged” signal to the baseline measurements. In a numerical example GWs excited with 200 kHz central frequency, encounter a small damage (4 mm long, 1 mm wide and 2 mm deep; approximately 5 times smaller than the S0 wavelength) in an aluminum plate with thickness of 3 mm. In order to characterize the differences in the time domain signals, the cross-correlation function (CCF) is used [44]. Cross correlation samples of the damaged and baseline signals obtained from a node at the boundary of damage show that the highest CCF value occurs in Lag = −1. Considering that the Lag = 0 shows the complete correspondence of two signals and therefore, a small absolute value of Lag = −1 (only 1 step) shows high similarity of two signals. It is worth noting that high similarity of damaged and baseline signals from the selected node (which is located directly next to the damaged area) indicates how bad the situation can be for other nodes located farther away from damage location. However, using B-scan diagrams is a reliable method to determine the ToF in this case. In order to plot these diagrams several signals from different nodes have to be determined, which is a time consuming process. In addition, high resolution information is required to make sure that the damage position is resolved. As the aim is to reduce the measuring nodes, appropriate signal processing steps based on the time-frequency analysis are needed to calculate the ToF of the converted mode [36]. Various methods are used in different studies each having its own advantages and limitations [28]. In the present study, the wavelet transform is used as it offers several advantages. The data are recorded both in the time and in the frequency domain with the capability to provide quantitative information about the signal behavior [18, 20, 23, 30]. The Daubechies wavelet D10 is used as the wavelet function in several studies to determine the ToF and generally a good agreement with analytical solutions has been reported [14, 36, 40]. In order to determine ToF for the converted mode, the changes in the signal are recognized using scattered CWT coefficients. Both baseline and the damaged signals are transformed using CWT and then the CWT coefficients are subtracted. Because of the high resolution of CWT, the determination of changes in the signal is possible even for very small changes that occur in the case of mode conversion in the high frequency range. From the characterization of the changes in the signal the ToF for the converted modes can be calculated. Different wave packets appear in the scattered CWT diagram belonging to different modes [21], see Fig. 9 for an illustration. The different modes (including incident
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and converted modes, respectively) can be distinguished by means of the group velocity and the ToF (traveling time form actuator to the measuring point). As a definition, the ToF for each group of the waves (e.g. converted modes) corresponds to the time when the maximum value of the CWT coefficients for this group is reached [36]. The application of the proposed approach to experimental data is demonstrated in the next section. The CWT coefficients are calculated using the commercial software MATLAB® .
4 Experimental Examples In the present study a LDV system with sampling frequency of 512 kHz is used to measure the out-of-plane nodal velocities on the cover plate. A square shaped piezoelectric actuator with 10 mm length and a thickness of 0.5 mm made of PIC-181 is used to excite a three cycle narrow band tone burst [37] with central frequency of 150 kHz.
Fig. 7 Interaction of the S0 mode with a damage in a honeycomb sandwich plate. (a) Schematic representation of the damage type on the cover plate; (b) out-of-plane displacement wave field from the experimental test. The central loading frequency is 150 kHz
4.1 Honeycomb Sandwich Plate In the first example, the general idea of the proposed SHM system based on mode conversion is presented and an arbitrary set of nodes is used to detect a known damage in a CELLITE silver standard 69 honeycomb sandwich plate. A small damage (6 mm long, approximately 1 mm wide), as shown in Fig. 7(a), is introduced to the top surface of the honeycomb sandwich plate. A small rod entered to the structure from the opposite side and generated small impact damage at the top surface. The impact is generated from inside to make sure that the retro reflective layer is still fully attached to the surface. The out-of-plane nodal velocity field and the conversion of the S0 to the A0 mode caused by the damage (highlighted in a white rectangle) are shown in Fig. 7(b) with a resolution of 100 × 100 scanning nodes. The prove for the mode conversion assumption is provided by a B-scan diagram presented in Fig. 8. The reading points are schematically shown in Fig. 9(a). They are taken near the damaged region with an increment of 0.5 mm where the beginning point is considered as the origin, i.e. x = 0. For a better presentation, the nodes are chosen within the area which covers one cell of the honeycomb core to illustrate only the interactions of the waves with the damage and to avoid showing the interactions caused by the core structure. The description of the experimental setup and the chosen nodes are given in Fig. 9(a). Four reading nodes are selected on the top, bottom, right and left hand side of the damage in approximately distance of 0.015 m from center of the damage. The scattered CWT coefficients of the damaged and the baseline signals are obtained from the top node shown in Fig. 9(b). Different wave packages are recognized. These groups can be identified according to the estimated ToF for
Fig. 8 B-scan diagram for the reading nodes crossing damaged region shown in Fig. 9 is presented in order to visualize the mode conversion. The figure is plotted using a filled two-dimensional contour plot (contourf) in MATLAB®
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Fig. 9 (a) Position of the piezoelectric actuator and a small damage on the surface of the honeycomb plate and reading points; (b) Scattered CWT coefficients of the damaged and baseline signals; (c) Determination of damage using cosine formula
each mode as well as changes in the local extremes of the CWT coefficients. The ToF from the piezoelectric actuator to the damaged location (0.11 m) for the S0 and A0 modes are experimentally evaluated in this study which are approximately 0.025 ms and 0.096 ms, respectively. The estimated ToF for both S0 and A0 modes are highlighted in Fig. 9(b) with solid lines. However, one can recognize a wave packet occurring before the expected first arrival of the A0 mode which is also slower than the S0 mode. As described earlier, in the high frequency range the GWs propagate from the cover plate to the core structure. According to the dispersion curves for aluminum [2], the propagation of the fundamental modes (S0 and A0 ) is expected in the cover plate (with thickness of 0.6 mm) and the core walls (with the thickness of 0.0635 mm) at 150 kHz. Therefore, these wave packets are considered to be a mode conversion product (a S0 mode is converted into an A0 mode). Using the ToF of the converted mode, calculated for each reading point, and applying the cosine formula, described in Eq. (1), the damage location is determined as shown in Fig. 9(c). The damage location is in-
Fig. 10 MHSS sandwich plate
dicated by a star. The location of this star agrees nicely with the real location of the damage (with 2 mm error). 4.2 Metallic Hollow Sphere Sandwich Plate In the second example, the GW propagation in a MHSS (1 m × 320 mm × 20 mm) made of steel is studied, in which the cover plate thickness, the average hollow sphere wall thickness and the average hollow sphere outer diameter are equal to 0.60 mm, 0.15 and 3.00 mm respectively,
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Fig. 11 (a) The out-of-plane velocity component of the GW propagation on the bottom surface of HSS sandwich plate, measured by 1D laser vibrometry. The mode conversion locations are highlighted with
the white circles The scanning points are shown by black squares. (b), (c), (d) and (e) The estimated damage locations are presented. The central excitation frequency is 150 kHz
see Fig. 10. The single hollow spheres are partially glued together with epoxy to create the core structure [16]. Because of the random distribution of the single hollow spheres in the adhesive matrix, gaps inside the sandwich plate are expected. Both the top and the bottom surface of the structure are scanned. It is observed that in some regions the S0 mode is converted to the A0 mode. Illustrations of these regions on the bottom surface are highlighted with white circles in Fig. 11(a). The correctness of the mode conversion assumption in these regions is demonstrated using B-scan diagrams. In Fig. 12 a B-scan derived from nodes located at the bottom surface is shown. The measurement points are located on a line defined by the center of region C and the projection of the actuator position on the bottom surface. The location of the reading points is schematically indicated in Fig. 11(a) with a dashed line. The measurements are taken for every 1 mm and the beginning point is considered as the origin,
i.e. x = 0. It has to be mentioned that the reflected S0 mode and the reflected converted A0 mode (reflections and conversion form S0 to A0 which propagate in opposite direction of incident waves) are not visible in this figure which can be explained due to the low energy transmission of this mode to the bottom surface of the sandwich plate [41]. A CT image of region “B” in Fig. 13 shows a gap in the structure of the size of a single hollow sphere where Δs = 0.6 mm. This figure shows a cross section of the plate. The rectangle in the upper image represents the position of the beginning of the region “B”. The lower small figures are taken from the following cross section CT images (inside the white rectangle). The solid materials are shown by white color while the black areas indicate debondings or epoxy. Several black areas between the core material and the cover can be seen in Fig. 13 which are not continued to the next frames. Only the continued debonding region causes a mode
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Fig. 12 B-scan diagram for the reading nodes crossing region “C” shown in Fig. 11 is presented in order to visualize the mode conversion. The figure is plotted using filled two-dimensional contour plot (contourf) in MATLAB®
Fig. 13 CT images of mode conversion region “B”, see Fig. 11
conversion as shown in Fig. 13. The regions without continued debonding are too small and do not interact with the S0 mode. Similar CT images have been obtained for regions “A” and “C”. The wave field image given in Fig. 11(a) is obtained with a resolution of 100 × 100 scanning nodes which takes approximately 45 minutes to be scanned. In order to reduce the measurement time, only 9 nodes are chosen in a regular arrangement as presented in 11(a). The scattered CWT coefficient of each node is obtained to calculate the ToF of the converted modes. Figure 14 shows an example of scattered CWT coefficient for reading point number 4. The ToF from the piezoelectric actuator (on the top surface) to the reading point number 4 (on the bottom surface) for the S0 and A0 modes, measured by LDV in this study, are 0.046 and 0.16 ms, respectively. The ToF of the wave packet depicted in Fig. 14 neither corresponds to the S0 mode nor the A0 mode. However, because of the thickness of the cover plate and the hollow spheres and considering the excitation
frequency, only S0 and A0 modes are expected in the structure. Therefore, the wave packet shown in Fig. 14 can only be the product of mode conversion from the S0 to A0 mode. No effect caused by the reflected S0 can be seen in this figure. This can be explained by the relatively far distance of the reading point number 4 from the damage location which causes the reflected S0 mode to be damped. Furthermore, Fig. 11 parts (b), (c), (d) and (e) present the damage localization based on the calculated ToF and the cosine formula described in Eq. (1) (with maximum error of 2 mm for Fig. 11(d)). In this example, the manufacturing defects are detected. In order to obtain the baseline signal different parts of the structure are scanned and a part with no failure is chosen as the baseline. The computed damage locations are marked by stars, cf. Fig. 11(b). The intersection of multiple damage estimations is recognized as a damage. One possible damage location is marked by a question mark, however. This shows that a false alarm has been indicated (according to the wave field
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Fig. 15 Geometrical place of detected damages in different arrangements. The figure indicates one of the limitations of the proposed approach in which the sensors are blinded with specific sets of damages
Fig. 14 Scattered CWT coefficient in node 4 shown in Fig. 11(a)
images and the CT data there is no debonding in this region) and points towards a certain limitation of the proposed approach. Therefore, the important factors and limitations when designing an efficient SHM system based on the proposed approach should be considered. 4.3 System Design Concerns To design an optimal SHM system based on the proposed method one should consider some options. First, the appropriate number and distance of scanning nodes must be chosen depending on the size of the expected damages. Very small damages may cause weak influence on the mode conversion of GWs, therefore a finer mesh is needed to detect them. Bigger damages cause a higher energy transmission to the converted A0 mode [5], therefore the converted mode can be sensed easily even after propagating long distances. However, the damping properties of the subjected structure must be known to choose an appropriate number and orientation of nodes for SHM applications. In some cases, i.e. multiple damages in the structure, the system may indicate false alarms. The question mark in Fig. 11(c) indicates such a wrong damage location predicted by the proposed approach. In this case, several geometrical locations are estimated for several neighboring damages with different sensors. Intersections of these geometrical locations would be considered as damages. However, it is possible that the estimated geometrical locations for different damages intersect each other in another point in addition to the damage location. Repeating the process, by choosing new sensing points near the areas which are determined as damage to achieve reproducible results, will grantee the accuracy of the process. Only the estimated damage locations which are contained in every measurement can be consid-
ered as the location of real damages. However, more studies are required to design a reliable iterative algorithm. In addition, in a low resolution scanning field the damage detection based on the proposed approach may fail to locate the exact position of the damage. Figure 15 illustrates two damage arrangements that show this limitation. In this case the geometrical locations of detected damages estimated by sensors (shown by schematic circles) do not have any intersection. Nevertheless, the system would alarm for existence of damages in the structure without being able to determine the exact location. One can say each sensor is blinded with a big size damage or a set of nearby damages. In both cases (shown in Figs. 11(c) and 15) a second try choosing new set of reading nodes in these regions is needed for providing a clear image of the structure situation. In addition, applying filters as suggested in [25] for the signal processing approach can reduce the effects of noise and unwanted reflections, e.g. from borders. Finally, it has to be mentioned that using the high frequency range GWs provides the advantage of detecting small damages. But in case of thick cellular structures, where some small damages are located inside the core structure (not near the surface), the converted modes are hard to be seen on the surface (because of several mode conversions from the core structure to the surface).
5 Summary and Conclusion Different SHM systems based on the ToF of the reflected waves from the damaged regions in structures are discussed. The disadvantages of each technique, such as being limited to the low frequency range, dependency on mono-modal propagation and dependency on the resolution of the scanning field are discussed. Within this study a new SHM approach based on the mode conversion phenomenon is presented. The ToF of the converted mode is calculated using scattered CWT coefficients. The geometrical location of possible damages around a sensor can be determined by solving the cosine formula in consideration of the ToF of the converted mode and the group velocity of the propagating modes in the structure. Intersections of estimated geometrical locations of damage by
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different sensors can identify the real position. Using this approach one can deploy high frequency range GWs to detect small damages (in the same order as the wavelength) with low resolution information of the wave field. Therefore, relatively fast scanning of large areas to detect small damages with a LDV system is possible. In order to extent the application of the proposed method to SHM in cellular structures, the wave propagation in such structures is described in the low and the high frequency ranges. It has been shown that due to flexural behavior of GWs in the low frequency range the waves do not interact with the core structure and therefore cannot detect small damages such as small debondings. By increasing the frequency range the waves interact with the core structure which causes mode conversion. However, the waves are capable to detect small damages between the core and the cover plate in this frequency range. The proposed methodology is employed to experimentally detect damages in a honeycomb sandwich panel and in a MHSS. A maximum error of 2 mm is obtained to predict the damage location in these examples. This can be improved using noise reducing techniques in signal analysis to evaluate ToF. However, future statistical studies are required to indicate the accuracy of the proposed approach. Finally, the important factors which have to be considered to design an efficient SHM applications based on the proposed method are discussed. It has been mentioned that in some cases the estimated geometrical locations around sensors for neighboring damages can intersect in a random point rather than a damage location which causes false alarms by the system. In addition, certain orientations of the damages and the sensors (e.g. where each sensor is located near a damage) bring the system to its limitations. Therefore, an iterative process is needed to overcome these limitations. Further studies are required to design an automatized and optimal SHM system based on the proposed method for isotropic and nonisotropic medias in future applications. Acknowledgements By means of this, the authors acknowledge the German Research Foundation for the financial support (GA 480/13-3). We would also like to thank Dr.-Ing. C. Willberg and Dr.-Ing. S. Ringwelski for their invaluable help in the execution of the experimental tests and Hollomet GmbH is also highly appreciated for providing the hollow sphere sandwich panel.
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