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Active SHM for composite pipes using piezoelectric sensors
Materials Today: Proceedings xxx (xxxx) xxx
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Active SHM for composite pipes using piezoelectric sensors S. Carrino, A. Maffezzoli, G. Scarselli University of Salento, Department of Engineering for Innovation, Via per Monteroni, 73100 Lecce, Italy
a r t i c l e
i n f o
Article history: Received 2 September 2019 Accepted 5 December 2019 Available online xxxx Keywords: Structural health monitoring Ultrasonic waves Composite pipes PZT sensors Nonlinearities
a b s t r a c t Composite materials, in addition to the high specific mechanical properties, have properties enabling their applications in high-pressure, high-temperature (HPHT) and corrosive environment as occurs in deep water. Their use for manufacturing pipelines and offshore risers can provide relevant performance advantages over steel such as lower weight, improved fatigue capacity, corrosion resistance and higher strain limits. However, composite materials are more complex to use in design than metallic materials due to their anisotropic properties and lack of accurate failure prediction models. Thus, a continuous in-situ and in real-time Structural Health Monitoring (SHM) of composite components would be necessary and useful to promote their use in a wider range of operational conditions. In this work, an FRP pipe sample was instrumented with Piezoelectric Wafer Active Sensors (PWAS) used either as passive receivers or as transmitters of guided waves for active health monitoring in pitch-catch configuration. The propagation properties of guided waves in glass fibres reinforced composites were studied by developing MATLAB scripts, running FE simulation and experiments. The numerical and experimental signals were post-processed in MATLAB by Short Time Fourier Transform (STFT) in order to evaluate their frequency and time-frequency content. Furthermore, the guided waves were used to detect artificial defects imposed on the structure identifying their location. Several testcases were studied to find out the limitations and the most suitable conditions of using guided waves for defects monitoring in a composite pipe. The work proposes effective methods for pipe structural health evaluation by non-destructive techniques and ultrasonic guided waves. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 12th International Conference on Composite Science and Technology.
1. Introduction The need to enhance performances of civil and military structures constantly drives the development of improved highperformance structural materials. Composite materials are a class of materials that, having many attractive physics and mechanical properties, play an important role in current and future aerospace, automotive and marine components. They are particularly attractive because of their exceptional strength and stiffness-to-density ratios, superior physical properties and, in the last years, they have been recognized as enabling technology for deep-water HPHT and corrosive applications [1]. Furthermore, cylindrical and spherical pressure vessels are widely used for commercial, aerospace and under water vehicles applications. Their performances, such as payload, speed and operating range, depend upon the weight. In the pressure vessels field, the use of composite materials improves the performance and allows significant amount of material savings
[2]. However, composites still have some limits to enter in relation to metals due to limited specific field experience, assurance of performance and lack of failure predictions. In addition to several problematics related to manufacturing procedures, composites are susceptible to delaminations also during the assembly and in service [3]. During fabrication, undesired materials such as prepeg backing paper can be left in the lay-up. Mechanical machining, improper part handling or incorrectly installed fasteners can cause delaminations. During the operational service, low-velocity impacts (due to the dropping of tools for a plant pipes) can cause damages that may appear as only a small indentation on the surface but they can propagate though the laminates grow under fatigue loading. The Structural Health Monitoring (SHM) allows constant health monitoring of composites in real-time and insitu in order to assess actively the structural state at any time of service life changing the classical maintenance paradigms. SHM is an area of great technical and scientific interests that can allevi-
https://doi.org/10.1016/j.matpr.2019.12.048 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 12th International Conference on Composite Science and Technology.
Please cite this article as: S. Carrino, A. Maffezzoli and G. Scarselli, Active SHM for composite pipes using piezoelectric sensors, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.048
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ate the cost of scheduled maintenance and repairs replacing them with as-needed maintenance (Condition Based Maintenance – CBM). Active SHM is aimed to directly assessing the state of structural health by trying to detect the presence and extent of structural damage. SHM through guided-wave NDE has gained extensive attraction [4–7]. Guided waves, such as Lamb and SH waves, are elastic perturbation that can propagate for long distance in thin-wall structures with little amplitude loss. They can be generated by Piezoelectric Wafer Active Sensor (PWAS) bonded onto the structural surface, mounted inside built-up structures or embedded between the structural and non-structural layers of a complete structure. In [8] the capability of embedded PWAS to perform in-situ NonDestructive Evaluation (NDE) was proved by carrying out experiments on transmission and reception, pulse-echo and pitch-catch of Lamb waves. In [9] it was demonstrated the capability of PWAS to excite Lamb wave and to be used in a phased array technique (such as Embedded Ultrasonic Structural Radar EUSR) for Time Reversal Process (TRP) useful to obtain damage detection. The position of PZTs is usually defined by avoiding the overlap of the direct wave packet with reflections due to the boundaries. Genetic algorithms (as in [10]) can be used to design an optimal sensor positioning. In engineering practice, fatigue cracks in metallic structures or micro-delaminations in composites have been difficult to predict especially by using only linear elastic waves. However, the sensitivity of the linear Lamb waves to a damage is dependent on the wavelength so, when used to detect or to locate damages much smaller than the wavelength of the excited wave, linear features may become less sensitive. Lamb waves based on nonlinear methods gives better results on the location and detection of micro-damages by using frequency spectral information of the received signals. Li et al in [11] investigated the ultrasonic linear and nonlinear parameters for evaluating the thermal damage in aluminium pipe demonstrating that nonlinear methods [12] are a promising candidate for the prediction of micro-damages. In [13] experimental and numerical studies were performed to validate the cumulative generation of second harmonic S0 mode due to various fatigue damages on Al7075 aluminium alloy specimen produced by the continuous low cycle fatigue tests. In this study, a nonlinear Lamb wave method to assess the structural state of a composite pipe is presented. This method allows to locate a ‘‘breathing” (opening and closing) damage by using spectral as well as temporal data obtained from postprocessed signals of PZTs bonded on the structure. In Section 2 the physical and mechanical properties of used materials and methodology are discussed. In Section 3 the method for dispersion curves calculation is presented. Numerical models of Lamb wave propagation in composite pipes are reported in Section 4. The experimental validation is proposed in Section 5. The analytical, numerical and experimental results are presented in Section 6. Conclusion, innovation and research potentials are discussed in Section 7.
2. Materials and methods The proposed nonlinear method is aimed to detect and locate a ‘‘breathing” damage present on composite pipe by using a PZT array and a geometric algorithm. The studied composite pipe had a mean radius Rm of 75.7 mm, it was 800 mm long with a total thickness h of 3.6 mm (see Fig. 1). The composite was manufactured by filament winding technique: the lay-up order obtained by wounding pre-preg glass fibres is reported in Fig. 2 where thicknesses are also reported. The composite pipe consisted of four layers [90°/±55°/±55°/90°] covered by a resin layer applied after filament winding process.
Fig. 1. Composite pipe.
Fig. 2. Ply sequence (drawing not in scale).
The pipe had an outer and inner radius of 77.5 mm and 73.9 mm respectively. The layers with fibres along z-axis had a thickness of 0.523 mm, while the layers with a deposition angle of ±55° had a thickness of 1.046 mm. The outer layer of resin was 0.462 mm thick. The estimated physical and mechanical properties of materials are reported in Table 1.
Table 1 Physical and mechanical materials properties. Material
Density [kg/m3]
Elastic properties [GPa]
Poisson’s Ratio
Resin Glass Fibre Pre-preg
q = 1162 q = 1982
E = 3.24 Ex = 42.4 Ey = Ez = 11.1 Gyz = 3.81 Gxy = Gxz = 3.79
m = 0.38 mxy = mxz = 0.27 myz = 0.45
Please cite this article as: S. Carrino, A. Maffezzoli and G. Scarselli, Active SHM for composite pipes using piezoelectric sensors, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.048
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Five PZT sensors were bonded on the external surface pipe in order to excite and receive in pitch-catch configuration. PZT sensors by Physik Instrumente (PIC255 see [14]) were used: they have a resonance frequency of 10 MHz (along thickness vibrational mode) and 200 kHz (radial vibrational mode), and they are made of piezoelectric ceramic material. These sensors have large charge coefficient, moderate permittivity and high coupling factor. The electrical contacting is allowed by the wrapped-around electrode so avoiding to affect the adhesion on inspected surface. The position of five PZT sensors is showed in Fig. 3 where the transmitter sensor was labelled with T1 and the others four receiver sensors with R1, R2, R3 and R4. The receivers were 300 mm far from transmitter sensor and they were circumferentially equidistant (60° as shown in Fig. 3). The structure was a multi-layered cylindrical composite pipe, the layers were not quasi-isotropic lay-ups of composite laminae and so it was not possible to consider a homogeneous velocity propagation in any direction. Thus, the first part of the study was related to the characterization of the Lamb wave propagation velocities in any direction by carrying out pitch-catch measurements between T1 and receiver sensors. Zero-Lamb modes was excited by imposing voltage toneburst on T1 that, acting unsymmetrically respect to the midplane, generated both S0 and A0 wave packets picked by receiver sensors. Group and phase velocities were numerically and experimentally calculated by evaluating the Time-of-Flight (ToF) and the helical path of the wave packets that reached the receiver sensors. The length of helical path travelled by wave packets was calculated in cylindrical coordinate system (see Fig. 4) placed in a plane containing T1 with the z-axis coincident with the pipe axis. In order to study the propagation properties on 90° propagation angle, pitch-catch measurements were also carried out on R1 R3 sensors pair using R1 as transmitter and R3 as receiver. The propagation angles reported in Tables 2 and 3 were calculated respect to reference fibre axis that usually in filament winding corresponds to z-axis as showed in Fig. 4. Group velocities cg were numerically and experimentally estimated by the ToF/helical path length ratio (1) and then compared to the dispersion curves analytically obtained for each propagation angle.
cg ¼
LH ½m=s ToF
ð1Þ
The purpose of this work is not only to characterise the Lamb waves behaviour in composite pipes but also to prove the capability of a proposed nonlinear method to detect and to locate superficial defects such as delaminations by mean of a preliminary study. In order to simulate damage on the pipe surface, a oneeuro cent coin was partially bonded on the surface (Fig. 5) with a thermoplastic adhesive (as in [1]). The partially adhesion was
3
Fig. 4. Cylindrical coordinate system and propagation angle.
exploited to simulate breathing damage. The contact between the coin and the pipe surface caused nonlinearities in the Lamb waves propagation behaviour that led to the generation of superharmonic wave packets at multiples of excitation frequency. These higher harmonics travelled in all directions from the damage reaching the receiver sensors. In this study, the second harmonic A0 wave packet was chose to inspect the structure since it, inducing out-of-plane motions, promoted much higher nonlinearities than those caused by S0 mode. The temporal data of the second harmonic wave packet was used to locate the coin presence. Furthermore, the dispersion behaviour of A0 mode enhanced the distinction between direct and harmonic wave packets. Nonlinear ultrasonic techniques usually use toneburst ultrasonic waves with a narrow bandwidth by which a separation between fundamental frequency component and second-order harmonic component can be obtained. In order to highlight the harmonic content of ultrasonic signals, the Pulse Inversion (PI) method was applied allowing to extract only even or odd harmonics by superposing or subtracting two wave signals obtained from 180° out-of-phase inputs [15].
Fig. 3. Position of PZT sensors.
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Table 2 Calculation of wave path length and propagation angle for wave packets generated by T1. Sensor
Cylindrical coordinates x [mm]
y [°]
z [mm]
T1 R1 R2 R3 R4
775 775 775 775 775
0 0 60 120 180
0 300 300 300 300
Helical path length LH [m]
Propagation angle [°]
– 0.300 0.310 0.339 0.383
– 0.0 14.8 27.8 38.4
Helical path length LH [m]
Propagation angle [°]
– 0.158
– 90.0
Table 3 Calculation of wave path length and propagation angle for wave packets generated by R1. Sensor
R1 R3
Cylindrical coordinates x [mm]
y [°]
z [mm]
775 775
0 120
300 300
monic wave packet is more intense among all the higher harmonics [16]. PI technique was used to filter second harmonics in the received signals. These harmonic packets contained frequency and time information about the presence of coin. The ToF of second harmonic packets received by R1, R2, R3 and R4 are denoted with tR1, tR2, tR3 and tR4 respectively. It can be written that, defining with N the number of receivers, the following relation yields:
tRi ¼ t T 1 d þ t dRi i ¼ 1; ; N
ð2Þ
with tdRi the time taken by the harmonic packet to reach the receiver sensors. For each pair of sensors, it can be also written by using (2):
Dtij ¼ tRi t Rj ¼ t dRi t dRj i ¼ 1; ; N i < j N
ð3Þ
where D tij is the difference of arrival times of the second harmonics from the surface discontinuity to the sensors Ri and Rj respectively. The group velocity of the fundamental and second harmonic packet are defined with cgf = cg(f) and cg2f = cg(2f). The helical path lengths between the bonded coin and receivers are defined as rdR1, rdR2, rdR3 and rdR4, they can be calculated by the following equations:
rT 1 d ¼ cg f t T 1 d r dRi ¼ cg2f tdRi
i ¼ 1; ; N
ð4Þ
The helical path length can be calculated by knowing the cylindrical coordinates of each PZT sensor and by geometric considerations: Fig. 5. Artificially damaged composite pipe.
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 T 1x T 1y dy þ ðT 1z dz Þ i ¼ 1; ; N qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ Rix Riy dy þ ðRiz dz Þ
rT 1 d ¼ The five PZT sensors bonded on the structure have coordinates (in cylindrical coordinate system showed in Figs. 4 and 5) (T1x,T1y, T1z), (R1x,R1y,R1z), (R2x,R2y,R2z), (R3x,R3y,R3z) and (R4x,R4y,R4z). The one-euro cent coin was placed on point of coordinates (dx,dy,dz). The transmitter T1 actuated both S0 and A0 Lamb wave modes while other four sensors acted as receivers. S0 and A0 wave packets could be easily distinguishable for the high difference of their group velocities and dispersion behaviour. During the propagation, Lamb waves strike the breathing discontinuity (bonded coin) at time tT1d and nonlinear wave damage interaction takes place producing higher harmonics due to contact nonlinearity. These higher harmonics propagate in all directions from the coin. In this way, the signals received by R1, R2, R3 and R4 contain the direct wave packet generated by T1, a group of higher harmonics produced by the contact nonlinearity and the reflections due to the pipe boundaries. Several previous studies have demonstrated that second har-
rdRi
ð5Þ
It can be written by using (3):
Drij ¼ r dRi r dRj ¼ cg2f ðtdRi tdRj Þ i ¼ 1; ; N Drij ¼ cg2f Dtij i
ð6Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 Rix Riy dy þ ðRiz dz Þ þ Rjz dz Rjx Rjy dy ¼ cg2f Dt ij
i ¼ 1; ; N i
In (7) D tij can be evaluated by the (3), cg2f is function of physical and mechanical material properties, and the only unknowns are dx, dy and dz. At each point of the pipe corresponds a specific vector (dx,dy,dz) that can satisfy or not the (7): the inspected region on
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the pipe was managed by a geometrical algorithm. A Gaussian distribution with variance r2 and mean l = cg2f D tij was used to obtain a probability density function Pij = Pij (dx,dy,dz) and to map the space of points satisfying the (7): 2
ðDrij cg Dtij Þ 2f 1 2r2 Pij ¼ pffiffiffiffiffiffiffiffiffiffiffiffi e 2 2pr
i ¼ 1; ; N i
ð8Þ
The total probability density function PDF was evaluated according to the following equation:
P¼
N N 1 Y Y i¼1
P ij i ¼ 1; ; Ni < j N
ð9Þ
j>i
The Eq. (9) gives an estimation of discontinuity locations as those points where the values P = P (dx,dy,dz) get close to 1. The method is baseline free since it is not based on data from the pristine composite pipe. 3. Analytical model For the low excitation frequencies used in this work, only the basic symmetric and antisymmetric Lamb-wave modes (S0 and A0) existed. In [17] it was studied the influence of the ratio between inner radius Rin and the thickness h (g = Rin/h) on the Lamb wave dispersion curves in anisotropic materials. It was proved that for high values of g (g > 10) the dispersion curves of curved plate approach to those of flat plates. The composite pipe studied in this work has g 21 and so the dispersion curves were calculated for composite flat plate. In the case of an isotropic material, the dispersion curves can be derived from the solution of the Rayleigh-Lamb equation. For composite materials it is not possible to find a closed form solution of the dispersion curves and thus the Transfer Matrix Method (TMM) was used to characterize the Lamb waves [18]. This method has the advantage that it condenses the multi-layered system into six equations relating the boundary conditions at the upper and lower surfaces.
½ u1
u2
u3
5
and layered configuration. The Lamb wave packets were excited by imposing displacements or forces equivalent to the PZT transmitter action. S0 wave packets were generated imposing the equivalent PZT loads in a plane tangent to the pipe, while A0 wave packets were excited by imposing out-of-tangential plane (radial) loads (as in Fig. 6). The received signals were obtained by monitoring in-plane (for S0) and out-of-plane (for A0) displacements of nodes placed on the receiver position. The Lamb wave propagation was simulated in a transient analysis: the timestep and element size was set respectively equal to 1/ (40fe) and ke/40 where fe and ke are the excitation frequency and the wavelength of the generated wave packets. The bonded coin was modelled with SOLID186 element and its partially adhesion was simulated by the definition of Multi-Point-Constraint (MPC) contact. The interaction between coin and surface was taken into account by a nonlinear frictionless contact and solved in nonlinear transient analysis. The characterization of the Lamb wave propagation properties (phase and group wave velocities) were carried out for frequencies of 50 kHz, 100 kHz, 150 kHz and 200 kHz. The location of partially bonded coin was investigated by exciting the transmitter PZT with a 30 kHz 5-peaks toneburst.
r33 r13 r23 U ¼ ½T ½ u1 u2 u3 r33 r13 r23 L ð10Þ
In (10) the subscript U and L indicates the displacements and the stresses on the upper and lower surfaces respectively, while T is the transfer matrix. The free stress boundary conditions for Lamb waves on these surfaces are:
½ r33
r13 r23 U ¼ ½ r33 r13 r23 L ¼ 0
Fig. 6. Numerical simulation, Lamb waves excitation.
ð11Þ
The equation (11) leads to the characteristic equation:
T 41 T 51 T 61
T 42 T 52 T 62
T 43 T 53 ¼ 0 T 63
ð12Þ
The Eq. (12) was resolved iteratively in MATLAB obtaining the phase and group dispersion curves for each wave propagation angle in the studied composite pipe. 4. Numerical simulations The propagation of Lamb waves in composite pipe was simulated by Finite Element Method (FEM) in ANSYS (related mesh is reported in Fig. 7). The finite element simulation is based on the calculation of stress-strain relationships in a specimen volume governed by the structural mechanics constitutive equation. The partial differential equations for equilibrium conditions were solved for external stimulation. The stack sequence of composite pipe was specified in the FE model by using SHELL181 element
Fig. 7. Mesh of the partially bonded coin.
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Fig. 8. Direct received signal in numerical analyses (30 kHz).
T1 with 75 Vpp 5 peaks-toneburst. An oscilloscope (Series 3000 PicoScope) allowed real-time acquisition at receiver PZT sensors of the propagating waves to a PC. During the experimental tests, free-free conditions were achieved using vibration-absorbing sponges. The propagation velocities were estimated for frequencies of 50 kHz, 75 kHz, 100 kHz, 125 kHz, 150 kHz, 175 kHz and 200 kHz. The one-euro cent coin was bonded on the position of coordinates dx = 77.5 mm, dy = p/4 and dz = 100 mm referred to the cylindrical system of Fig. 4. Like in numerical analyses, the composite pipe was inspected by generating two 180°-delayed tonebursts. The received signals reported in Fig. 11 were filtered by PI technique as reported in Fig. 12 in order to highlight nonlinearities due to partially bonded contact and then they were post-processed in MATLAB by Short Time Fourier Transform (STFT).
Fig. 9. Filtered received signal in numerical analyses (60 kHz).
In Fig. 8 an example of direct received signal obtained by numerical analyses was reported. A0 mode was excited by imposing an out-of-plane displacement to the node representing the transmitter T1. The spectrogram of Fig. 8 shows the frequencytime content of signal received at receiver R1 (propagation angle equal to 0°). The first lobe represents the direct wave packet, while the others are due to the reflections of pipe boundaries. This signal was filtered by PI technique in order to evaluate the harmonic packet at 60 kHz generated by the partially bonded coin. The first harmonic lobe in Fig. 9 preceded the direct packet because of its higher group velocity.
Fig. 11. Direct received signal in experiments (30 kHz).
5. Experiments In Fig. 10 the experimental set-up is reported: a signal generator fed a power amplifier (input 50) exciting the PZT transmitter
Fig. 12. Filtered received signal in experiments (60 kHz).
Fig. 10. Experimental set-up (R4 on the pipe opposite side).
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6. Results In Fig. 13 the phase velocity dispersion curves calculated by TMM are reported. For the used sensor configuration, the propagation directions to reach R1, R2, R3 and R4 from T1 correspond respectively to angles of 0.0°, 14.8°, 27.8° and 38.4°. The dispersion curves related to 90.0° were obtained by using R1 as transmitter and R3 as receiver. As showed in the following graphs, only S0
7
and SH0 exhibited a low dispersion behaviour to the left of cut-off frequency that was estimated at about 300 kHz (for each propagation direction) in this study. A0 mode was much more dispersive and it approached to the asymptote Rayleigh (2000 m/s) only after it reached 500 kHz. S0 phase velocity was strongly influenced by the global elastic modulus and thus by the propagation angle. The glass fibres were mainly wound at angles of ± 55.0° and 90.0°. Thus, the S0 velocity at low frequencies varied
Fig. 13. Phase velocity dispersion curves for each sensor (or propagation direction).
Fig. 14. Group velocity dispersion curves for each sensor (or propagation direction).
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from a minimum value of 2743 m/s along 0.0° direction to a maximum value of 3981 m/s along 90.0° direction. For low frequencies SH0 mode approached to a velocity around 2000 m/s in any propagation direction. In Fig. 14 the S0, A0 and SH0 group velocity dispersion curves are reported. The velocities evaluated numerically and experimentally are compared in the same graphs. It was not possible to measure the SH0 velocity in the experiments because the used transducers did not allow to excite shear waves in the structure. However, these velocities were estimated numerically in order to match analytical and numerical results. The high dispersive behaviour of A0 mode is also highlighted in Fig. 14, while S0 and SH0 velocities are almost constant up to the higher used inspection frequency of 200 kHz. The numerical and experimental results were in a good agreement with the analytical predictions. The maximum percent error was around 15% and it was essentially ascribed to the velocity S0 at 50 kHz excitation frequency. This can be justified with the big length of S0 5-peaks-50 kHz wave packet that, causing the overlap of the direct and the reflected packets, made the ToF estimation difficult both in simulations and experiments. The percent error of other estimated velocities was below 10%. In the following figures, the analytical, numerical and experimental mapping of nonlinear sources are showed. The colour maps represent the total probability function of nonlinearity origins obtained by studying the time-frequency content of signals received at the sensor locations R1, R2, R3 and R4. The proposed geometrical algorithm was based on the ToF of second harmonic to map the nonlinearity. The working space confined by the transducers was discretised by quadrangular mesh with 180,000 nodes on
Fig. 17. Experimental mapping of nonlinearity.
which the probability density function was evaluated. The red zone in Figs. 15–17 consisted of nodes where the functions Pij appearing in (8) were computed and the total probability density P given by the (9) approaches to values close to 1. This zone indicates the location of nonlinear source on the inspected structure. 7. Conclusion In this work, a method based on the interaction between Lamb waves and nonlinear sources is proposed. It is based on the time– frequency content of the Lamb waves in order to detect the presence of nonlinearities and to locate them in the inspected areas. In this study, the subject of the investigation was a typical pipe made of glass fibres composite. A ‘‘breathing” damage was artificially created by partially bonding a metallic coin on the structure surface. The coin, inducing nonlinearity in the structure response, caused higher harmonics that allowed the damage detection. The proposed method was proved to be effective in locating the source of nonlinearity with a good degree of reliability and without the need of defining a baseline. References
Fig. 15. Analytical mapping of nonlinearity.
Fig. 16. Numerical mapping of nonlinearity.
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material degradation in plates, Int. J. Precis. Eng. Manuf. 20 (2019) 549–558, https://doi.org/10.1007/s12541-019-00093-1. [16] N.P. Yelve, M. Mitra, P.M. Mujumdar, Spectral damage index for estimation of breathing crack depth in an aluminum plate using nonlinear Lamb wave, Struct. Control Heal. Monit. 21 (2014) 833–846, https://doi.org/10.1002/ stc.1604. [17] Y. Jiangong, W. Bin, H. Cunfu, Characteristics of guided waves in graded spherical curved plates, Int. J. Solids Struct. 44 (2007) 3627–3637, https://doi. org/10.1016/j.ijsolstr.2006.10.006. [18] V. Giurgiutiu, Structural Health Monitoring With Piezoelectric Wafer Active Sensors, Elsevier/Academic Press, 2008, doi: 10.2514/1.26141.
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Active SHM for composite pipes using piezoelectric sensors S. Carrino, A. Maffezzoli, G. Scarselli University of Salento, Department of Engineering for Innovation, Via per Monteroni, 73100 Lecce, Italy
a r t i c l e
i n f o
Article history: Received 2 September 2019 Accepted 5 December 2019 Available online xxxx Keywords: Structural health monitoring Ultrasonic waves Composite pipes PZT sensors Nonlinearities
a b s t r a c t Composite materials, in addition to the high specific mechanical properties, have properties enabling their applications in high-pressure, high-temperature (HPHT) and corrosive environment as occurs in deep water. Their use for manufacturing pipelines and offshore risers can provide relevant performance advantages over steel such as lower weight, improved fatigue capacity, corrosion resistance and higher strain limits. However, composite materials are more complex to use in design than metallic materials due to their anisotropic properties and lack of accurate failure prediction models. Thus, a continuous in-situ and in real-time Structural Health Monitoring (SHM) of composite components would be necessary and useful to promote their use in a wider range of operational conditions. In this work, an FRP pipe sample was instrumented with Piezoelectric Wafer Active Sensors (PWAS) used either as passive receivers or as transmitters of guided waves for active health monitoring in pitch-catch configuration. The propagation properties of guided waves in glass fibres reinforced composites were studied by developing MATLAB scripts, running FE simulation and experiments. The numerical and experimental signals were post-processed in MATLAB by Short Time Fourier Transform (STFT) in order to evaluate their frequency and time-frequency content. Furthermore, the guided waves were used to detect artificial defects imposed on the structure identifying their location. Several testcases were studied to find out the limitations and the most suitable conditions of using guided waves for defects monitoring in a composite pipe. The work proposes effective methods for pipe structural health evaluation by non-destructive techniques and ultrasonic guided waves. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 12th International Conference on Composite Science and Technology.
1. Introduction The need to enhance performances of civil and military structures constantly drives the development of improved highperformance structural materials. Composite materials are a class of materials that, having many attractive physics and mechanical properties, play an important role in current and future aerospace, automotive and marine components. They are particularly attractive because of their exceptional strength and stiffness-to-density ratios, superior physical properties and, in the last years, they have been recognized as enabling technology for deep-water HPHT and corrosive applications [1]. Furthermore, cylindrical and spherical pressure vessels are widely used for commercial, aerospace and under water vehicles applications. Their performances, such as payload, speed and operating range, depend upon the weight. In the pressure vessels field, the use of composite materials improves the performance and allows significant amount of material savings
[2]. However, composites still have some limits to enter in relation to metals due to limited specific field experience, assurance of performance and lack of failure predictions. In addition to several problematics related to manufacturing procedures, composites are susceptible to delaminations also during the assembly and in service [3]. During fabrication, undesired materials such as prepeg backing paper can be left in the lay-up. Mechanical machining, improper part handling or incorrectly installed fasteners can cause delaminations. During the operational service, low-velocity impacts (due to the dropping of tools for a plant pipes) can cause damages that may appear as only a small indentation on the surface but they can propagate though the laminates grow under fatigue loading. The Structural Health Monitoring (SHM) allows constant health monitoring of composites in real-time and insitu in order to assess actively the structural state at any time of service life changing the classical maintenance paradigms. SHM is an area of great technical and scientific interests that can allevi-
https://doi.org/10.1016/j.matpr.2019.12.048 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 12th International Conference on Composite Science and Technology.
Please cite this article as: S. Carrino, A. Maffezzoli and G. Scarselli, Active SHM for composite pipes using piezoelectric sensors, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.048
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ate the cost of scheduled maintenance and repairs replacing them with as-needed maintenance (Condition Based Maintenance – CBM). Active SHM is aimed to directly assessing the state of structural health by trying to detect the presence and extent of structural damage. SHM through guided-wave NDE has gained extensive attraction [4–7]. Guided waves, such as Lamb and SH waves, are elastic perturbation that can propagate for long distance in thin-wall structures with little amplitude loss. They can be generated by Piezoelectric Wafer Active Sensor (PWAS) bonded onto the structural surface, mounted inside built-up structures or embedded between the structural and non-structural layers of a complete structure. In [8] the capability of embedded PWAS to perform in-situ NonDestructive Evaluation (NDE) was proved by carrying out experiments on transmission and reception, pulse-echo and pitch-catch of Lamb waves. In [9] it was demonstrated the capability of PWAS to excite Lamb wave and to be used in a phased array technique (such as Embedded Ultrasonic Structural Radar EUSR) for Time Reversal Process (TRP) useful to obtain damage detection. The position of PZTs is usually defined by avoiding the overlap of the direct wave packet with reflections due to the boundaries. Genetic algorithms (as in [10]) can be used to design an optimal sensor positioning. In engineering practice, fatigue cracks in metallic structures or micro-delaminations in composites have been difficult to predict especially by using only linear elastic waves. However, the sensitivity of the linear Lamb waves to a damage is dependent on the wavelength so, when used to detect or to locate damages much smaller than the wavelength of the excited wave, linear features may become less sensitive. Lamb waves based on nonlinear methods gives better results on the location and detection of micro-damages by using frequency spectral information of the received signals. Li et al in [11] investigated the ultrasonic linear and nonlinear parameters for evaluating the thermal damage in aluminium pipe demonstrating that nonlinear methods [12] are a promising candidate for the prediction of micro-damages. In [13] experimental and numerical studies were performed to validate the cumulative generation of second harmonic S0 mode due to various fatigue damages on Al7075 aluminium alloy specimen produced by the continuous low cycle fatigue tests. In this study, a nonlinear Lamb wave method to assess the structural state of a composite pipe is presented. This method allows to locate a ‘‘breathing” (opening and closing) damage by using spectral as well as temporal data obtained from postprocessed signals of PZTs bonded on the structure. In Section 2 the physical and mechanical properties of used materials and methodology are discussed. In Section 3 the method for dispersion curves calculation is presented. Numerical models of Lamb wave propagation in composite pipes are reported in Section 4. The experimental validation is proposed in Section 5. The analytical, numerical and experimental results are presented in Section 6. Conclusion, innovation and research potentials are discussed in Section 7.
2. Materials and methods The proposed nonlinear method is aimed to detect and locate a ‘‘breathing” damage present on composite pipe by using a PZT array and a geometric algorithm. The studied composite pipe had a mean radius Rm of 75.7 mm, it was 800 mm long with a total thickness h of 3.6 mm (see Fig. 1). The composite was manufactured by filament winding technique: the lay-up order obtained by wounding pre-preg glass fibres is reported in Fig. 2 where thicknesses are also reported. The composite pipe consisted of four layers [90°/±55°/±55°/90°] covered by a resin layer applied after filament winding process.
Fig. 1. Composite pipe.
Fig. 2. Ply sequence (drawing not in scale).
The pipe had an outer and inner radius of 77.5 mm and 73.9 mm respectively. The layers with fibres along z-axis had a thickness of 0.523 mm, while the layers with a deposition angle of ±55° had a thickness of 1.046 mm. The outer layer of resin was 0.462 mm thick. The estimated physical and mechanical properties of materials are reported in Table 1.
Table 1 Physical and mechanical materials properties. Material
Density [kg/m3]
Elastic properties [GPa]
Poisson’s Ratio
Resin Glass Fibre Pre-preg
q = 1162 q = 1982
E = 3.24 Ex = 42.4 Ey = Ez = 11.1 Gyz = 3.81 Gxy = Gxz = 3.79
m = 0.38 mxy = mxz = 0.27 myz = 0.45
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Five PZT sensors were bonded on the external surface pipe in order to excite and receive in pitch-catch configuration. PZT sensors by Physik Instrumente (PIC255 see [14]) were used: they have a resonance frequency of 10 MHz (along thickness vibrational mode) and 200 kHz (radial vibrational mode), and they are made of piezoelectric ceramic material. These sensors have large charge coefficient, moderate permittivity and high coupling factor. The electrical contacting is allowed by the wrapped-around electrode so avoiding to affect the adhesion on inspected surface. The position of five PZT sensors is showed in Fig. 3 where the transmitter sensor was labelled with T1 and the others four receiver sensors with R1, R2, R3 and R4. The receivers were 300 mm far from transmitter sensor and they were circumferentially equidistant (60° as shown in Fig. 3). The structure was a multi-layered cylindrical composite pipe, the layers were not quasi-isotropic lay-ups of composite laminae and so it was not possible to consider a homogeneous velocity propagation in any direction. Thus, the first part of the study was related to the characterization of the Lamb wave propagation velocities in any direction by carrying out pitch-catch measurements between T1 and receiver sensors. Zero-Lamb modes was excited by imposing voltage toneburst on T1 that, acting unsymmetrically respect to the midplane, generated both S0 and A0 wave packets picked by receiver sensors. Group and phase velocities were numerically and experimentally calculated by evaluating the Time-of-Flight (ToF) and the helical path of the wave packets that reached the receiver sensors. The length of helical path travelled by wave packets was calculated in cylindrical coordinate system (see Fig. 4) placed in a plane containing T1 with the z-axis coincident with the pipe axis. In order to study the propagation properties on 90° propagation angle, pitch-catch measurements were also carried out on R1 R3 sensors pair using R1 as transmitter and R3 as receiver. The propagation angles reported in Tables 2 and 3 were calculated respect to reference fibre axis that usually in filament winding corresponds to z-axis as showed in Fig. 4. Group velocities cg were numerically and experimentally estimated by the ToF/helical path length ratio (1) and then compared to the dispersion curves analytically obtained for each propagation angle.
cg ¼
LH ½m=s ToF
ð1Þ
The purpose of this work is not only to characterise the Lamb waves behaviour in composite pipes but also to prove the capability of a proposed nonlinear method to detect and to locate superficial defects such as delaminations by mean of a preliminary study. In order to simulate damage on the pipe surface, a oneeuro cent coin was partially bonded on the surface (Fig. 5) with a thermoplastic adhesive (as in [1]). The partially adhesion was
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Fig. 4. Cylindrical coordinate system and propagation angle.
exploited to simulate breathing damage. The contact between the coin and the pipe surface caused nonlinearities in the Lamb waves propagation behaviour that led to the generation of superharmonic wave packets at multiples of excitation frequency. These higher harmonics travelled in all directions from the damage reaching the receiver sensors. In this study, the second harmonic A0 wave packet was chose to inspect the structure since it, inducing out-of-plane motions, promoted much higher nonlinearities than those caused by S0 mode. The temporal data of the second harmonic wave packet was used to locate the coin presence. Furthermore, the dispersion behaviour of A0 mode enhanced the distinction between direct and harmonic wave packets. Nonlinear ultrasonic techniques usually use toneburst ultrasonic waves with a narrow bandwidth by which a separation between fundamental frequency component and second-order harmonic component can be obtained. In order to highlight the harmonic content of ultrasonic signals, the Pulse Inversion (PI) method was applied allowing to extract only even or odd harmonics by superposing or subtracting two wave signals obtained from 180° out-of-phase inputs [15].
Fig. 3. Position of PZT sensors.
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Table 2 Calculation of wave path length and propagation angle for wave packets generated by T1. Sensor
Cylindrical coordinates x [mm]
y [°]
z [mm]
T1 R1 R2 R3 R4
775 775 775 775 775
0 0 60 120 180
0 300 300 300 300
Helical path length LH [m]
Propagation angle [°]
– 0.300 0.310 0.339 0.383
– 0.0 14.8 27.8 38.4
Helical path length LH [m]
Propagation angle [°]
– 0.158
– 90.0
Table 3 Calculation of wave path length and propagation angle for wave packets generated by R1. Sensor
R1 R3
Cylindrical coordinates x [mm]
y [°]
z [mm]
775 775
0 120
300 300
monic wave packet is more intense among all the higher harmonics [16]. PI technique was used to filter second harmonics in the received signals. These harmonic packets contained frequency and time information about the presence of coin. The ToF of second harmonic packets received by R1, R2, R3 and R4 are denoted with tR1, tR2, tR3 and tR4 respectively. It can be written that, defining with N the number of receivers, the following relation yields:
tRi ¼ t T 1 d þ t dRi i ¼ 1; ; N
ð2Þ
with tdRi the time taken by the harmonic packet to reach the receiver sensors. For each pair of sensors, it can be also written by using (2):
Dtij ¼ tRi t Rj ¼ t dRi t dRj i ¼ 1; ; N i < j N
ð3Þ
where D tij is the difference of arrival times of the second harmonics from the surface discontinuity to the sensors Ri and Rj respectively. The group velocity of the fundamental and second harmonic packet are defined with cgf = cg(f) and cg2f = cg(2f). The helical path lengths between the bonded coin and receivers are defined as rdR1, rdR2, rdR3 and rdR4, they can be calculated by the following equations:
rT 1 d ¼ cg f t T 1 d r dRi ¼ cg2f tdRi
i ¼ 1; ; N
ð4Þ
The helical path length can be calculated by knowing the cylindrical coordinates of each PZT sensor and by geometric considerations: Fig. 5. Artificially damaged composite pipe.
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 T 1x T 1y dy þ ðT 1z dz Þ i ¼ 1; ; N qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ Rix Riy dy þ ðRiz dz Þ
rT 1 d ¼ The five PZT sensors bonded on the structure have coordinates (in cylindrical coordinate system showed in Figs. 4 and 5) (T1x,T1y, T1z), (R1x,R1y,R1z), (R2x,R2y,R2z), (R3x,R3y,R3z) and (R4x,R4y,R4z). The one-euro cent coin was placed on point of coordinates (dx,dy,dz). The transmitter T1 actuated both S0 and A0 Lamb wave modes while other four sensors acted as receivers. S0 and A0 wave packets could be easily distinguishable for the high difference of their group velocities and dispersion behaviour. During the propagation, Lamb waves strike the breathing discontinuity (bonded coin) at time tT1d and nonlinear wave damage interaction takes place producing higher harmonics due to contact nonlinearity. These higher harmonics propagate in all directions from the coin. In this way, the signals received by R1, R2, R3 and R4 contain the direct wave packet generated by T1, a group of higher harmonics produced by the contact nonlinearity and the reflections due to the pipe boundaries. Several previous studies have demonstrated that second har-
rdRi
ð5Þ
It can be written by using (3):
Drij ¼ r dRi r dRj ¼ cg2f ðtdRi tdRj Þ i ¼ 1; ; N Drij ¼ cg2f Dtij i
ð6Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 Rix Riy dy þ ðRiz dz Þ þ Rjz dz Rjx Rjy dy ¼ cg2f Dt ij
i ¼ 1; ; N i
In (7) D tij can be evaluated by the (3), cg2f is function of physical and mechanical material properties, and the only unknowns are dx, dy and dz. At each point of the pipe corresponds a specific vector (dx,dy,dz) that can satisfy or not the (7): the inspected region on
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the pipe was managed by a geometrical algorithm. A Gaussian distribution with variance r2 and mean l = cg2f D tij was used to obtain a probability density function Pij = Pij (dx,dy,dz) and to map the space of points satisfying the (7): 2
ðDrij cg Dtij Þ 2f 1 2r2 Pij ¼ pffiffiffiffiffiffiffiffiffiffiffiffi e 2 2pr
i ¼ 1; ; N i
ð8Þ
The total probability density function PDF was evaluated according to the following equation:
P¼
N N 1 Y Y i¼1
P ij i ¼ 1; ; Ni < j N
ð9Þ
j>i
The Eq. (9) gives an estimation of discontinuity locations as those points where the values P = P (dx,dy,dz) get close to 1. The method is baseline free since it is not based on data from the pristine composite pipe. 3. Analytical model For the low excitation frequencies used in this work, only the basic symmetric and antisymmetric Lamb-wave modes (S0 and A0) existed. In [17] it was studied the influence of the ratio between inner radius Rin and the thickness h (g = Rin/h) on the Lamb wave dispersion curves in anisotropic materials. It was proved that for high values of g (g > 10) the dispersion curves of curved plate approach to those of flat plates. The composite pipe studied in this work has g 21 and so the dispersion curves were calculated for composite flat plate. In the case of an isotropic material, the dispersion curves can be derived from the solution of the Rayleigh-Lamb equation. For composite materials it is not possible to find a closed form solution of the dispersion curves and thus the Transfer Matrix Method (TMM) was used to characterize the Lamb waves [18]. This method has the advantage that it condenses the multi-layered system into six equations relating the boundary conditions at the upper and lower surfaces.
½ u1
u2
u3
5
and layered configuration. The Lamb wave packets were excited by imposing displacements or forces equivalent to the PZT transmitter action. S0 wave packets were generated imposing the equivalent PZT loads in a plane tangent to the pipe, while A0 wave packets were excited by imposing out-of-tangential plane (radial) loads (as in Fig. 6). The received signals were obtained by monitoring in-plane (for S0) and out-of-plane (for A0) displacements of nodes placed on the receiver position. The Lamb wave propagation was simulated in a transient analysis: the timestep and element size was set respectively equal to 1/ (40fe) and ke/40 where fe and ke are the excitation frequency and the wavelength of the generated wave packets. The bonded coin was modelled with SOLID186 element and its partially adhesion was simulated by the definition of Multi-Point-Constraint (MPC) contact. The interaction between coin and surface was taken into account by a nonlinear frictionless contact and solved in nonlinear transient analysis. The characterization of the Lamb wave propagation properties (phase and group wave velocities) were carried out for frequencies of 50 kHz, 100 kHz, 150 kHz and 200 kHz. The location of partially bonded coin was investigated by exciting the transmitter PZT with a 30 kHz 5-peaks toneburst.
r33 r13 r23 U ¼ ½T ½ u1 u2 u3 r33 r13 r23 L ð10Þ
In (10) the subscript U and L indicates the displacements and the stresses on the upper and lower surfaces respectively, while T is the transfer matrix. The free stress boundary conditions for Lamb waves on these surfaces are:
½ r33
r13 r23 U ¼ ½ r33 r13 r23 L ¼ 0
Fig. 6. Numerical simulation, Lamb waves excitation.
ð11Þ
The equation (11) leads to the characteristic equation:
T 41 T 51 T 61
T 42 T 52 T 62
T 43 T 53 ¼ 0 T 63
ð12Þ
The Eq. (12) was resolved iteratively in MATLAB obtaining the phase and group dispersion curves for each wave propagation angle in the studied composite pipe. 4. Numerical simulations The propagation of Lamb waves in composite pipe was simulated by Finite Element Method (FEM) in ANSYS (related mesh is reported in Fig. 7). The finite element simulation is based on the calculation of stress-strain relationships in a specimen volume governed by the structural mechanics constitutive equation. The partial differential equations for equilibrium conditions were solved for external stimulation. The stack sequence of composite pipe was specified in the FE model by using SHELL181 element
Fig. 7. Mesh of the partially bonded coin.
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Fig. 8. Direct received signal in numerical analyses (30 kHz).
T1 with 75 Vpp 5 peaks-toneburst. An oscilloscope (Series 3000 PicoScope) allowed real-time acquisition at receiver PZT sensors of the propagating waves to a PC. During the experimental tests, free-free conditions were achieved using vibration-absorbing sponges. The propagation velocities were estimated for frequencies of 50 kHz, 75 kHz, 100 kHz, 125 kHz, 150 kHz, 175 kHz and 200 kHz. The one-euro cent coin was bonded on the position of coordinates dx = 77.5 mm, dy = p/4 and dz = 100 mm referred to the cylindrical system of Fig. 4. Like in numerical analyses, the composite pipe was inspected by generating two 180°-delayed tonebursts. The received signals reported in Fig. 11 were filtered by PI technique as reported in Fig. 12 in order to highlight nonlinearities due to partially bonded contact and then they were post-processed in MATLAB by Short Time Fourier Transform (STFT).
Fig. 9. Filtered received signal in numerical analyses (60 kHz).
In Fig. 8 an example of direct received signal obtained by numerical analyses was reported. A0 mode was excited by imposing an out-of-plane displacement to the node representing the transmitter T1. The spectrogram of Fig. 8 shows the frequencytime content of signal received at receiver R1 (propagation angle equal to 0°). The first lobe represents the direct wave packet, while the others are due to the reflections of pipe boundaries. This signal was filtered by PI technique in order to evaluate the harmonic packet at 60 kHz generated by the partially bonded coin. The first harmonic lobe in Fig. 9 preceded the direct packet because of its higher group velocity.
Fig. 11. Direct received signal in experiments (30 kHz).
5. Experiments In Fig. 10 the experimental set-up is reported: a signal generator fed a power amplifier (input 50) exciting the PZT transmitter
Fig. 12. Filtered received signal in experiments (60 kHz).
Fig. 10. Experimental set-up (R4 on the pipe opposite side).
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6. Results In Fig. 13 the phase velocity dispersion curves calculated by TMM are reported. For the used sensor configuration, the propagation directions to reach R1, R2, R3 and R4 from T1 correspond respectively to angles of 0.0°, 14.8°, 27.8° and 38.4°. The dispersion curves related to 90.0° were obtained by using R1 as transmitter and R3 as receiver. As showed in the following graphs, only S0
7
and SH0 exhibited a low dispersion behaviour to the left of cut-off frequency that was estimated at about 300 kHz (for each propagation direction) in this study. A0 mode was much more dispersive and it approached to the asymptote Rayleigh (2000 m/s) only after it reached 500 kHz. S0 phase velocity was strongly influenced by the global elastic modulus and thus by the propagation angle. The glass fibres were mainly wound at angles of ± 55.0° and 90.0°. Thus, the S0 velocity at low frequencies varied
Fig. 13. Phase velocity dispersion curves for each sensor (or propagation direction).
Fig. 14. Group velocity dispersion curves for each sensor (or propagation direction).
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from a minimum value of 2743 m/s along 0.0° direction to a maximum value of 3981 m/s along 90.0° direction. For low frequencies SH0 mode approached to a velocity around 2000 m/s in any propagation direction. In Fig. 14 the S0, A0 and SH0 group velocity dispersion curves are reported. The velocities evaluated numerically and experimentally are compared in the same graphs. It was not possible to measure the SH0 velocity in the experiments because the used transducers did not allow to excite shear waves in the structure. However, these velocities were estimated numerically in order to match analytical and numerical results. The high dispersive behaviour of A0 mode is also highlighted in Fig. 14, while S0 and SH0 velocities are almost constant up to the higher used inspection frequency of 200 kHz. The numerical and experimental results were in a good agreement with the analytical predictions. The maximum percent error was around 15% and it was essentially ascribed to the velocity S0 at 50 kHz excitation frequency. This can be justified with the big length of S0 5-peaks-50 kHz wave packet that, causing the overlap of the direct and the reflected packets, made the ToF estimation difficult both in simulations and experiments. The percent error of other estimated velocities was below 10%. In the following figures, the analytical, numerical and experimental mapping of nonlinear sources are showed. The colour maps represent the total probability function of nonlinearity origins obtained by studying the time-frequency content of signals received at the sensor locations R1, R2, R3 and R4. The proposed geometrical algorithm was based on the ToF of second harmonic to map the nonlinearity. The working space confined by the transducers was discretised by quadrangular mesh with 180,000 nodes on
Fig. 17. Experimental mapping of nonlinearity.
which the probability density function was evaluated. The red zone in Figs. 15–17 consisted of nodes where the functions Pij appearing in (8) were computed and the total probability density P given by the (9) approaches to values close to 1. This zone indicates the location of nonlinear source on the inspected structure. 7. Conclusion In this work, a method based on the interaction between Lamb waves and nonlinear sources is proposed. It is based on the time– frequency content of the Lamb waves in order to detect the presence of nonlinearities and to locate them in the inspected areas. In this study, the subject of the investigation was a typical pipe made of glass fibres composite. A ‘‘breathing” damage was artificially created by partially bonding a metallic coin on the structure surface. The coin, inducing nonlinearity in the structure response, caused higher harmonics that allowed the damage detection. The proposed method was proved to be effective in locating the source of nonlinearity with a good degree of reliability and without the need of defining a baseline. References
Fig. 15. Analytical mapping of nonlinearity.
Fig. 16. Numerical mapping of nonlinearity.
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Please cite this article as: S. Carrino, A. Maffezzoli and G. Scarselli, Active SHM for composite pipes using piezoelectric sensors, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.12.048