Phononic Crystal Sensing Devices for Enhanced Nonlinear Ultrasonic Inspection

Transcription

1 Pononic Crystal Sensing Devices for Enanced Nonlinear Ultrasonic Inspection More info about tis article: ttp:// 1 Francesco Ciampa and 2 Andrea Marini 1 Material and Structures Centre (MAST), Department of Mecanical Engineering, University of Bat, Claverton Down, BA2 7AY, Bat, UK 2 Department of Pysics and Cemical Sciences, University of L'Aquila, Via Vetoio, Edificio Coppito I, 67100, L'Aquila, Italy. Abstract Nonlinear ultrasonic metods ave proven to be far more sensitive tan conventional linear ultrasounds to early detection of damage suc as micro- or partially closed cracks, by measuring small nonlinear ultrasonic waves generated by te defect. However, te efficiency of nonlinear ultrasonic testing and teir large-scale use in industrial applications is still limited by undesired instrumentation effects caused by ig-power ultrasonic signal transmission, wic may mask nonlinear ultrasonic waves and prevent damage detection. Tis paper aims to overcome te callenge of accurate detection of nonlinear ultrasonic signals by designing and developing new portable and compact pononic crystal (PC) waveguide transducers, wic enance te performance of nonlinear ultrasonic metods by acieving unprecedented sensitivity and reliability. Tese innovative PC sensing devices are material-based tunable filters tat allow natural propagation of nonlinear ultrasonic waves and suppression of undesired instrumentation effects. PC waveguide transducers can be integrated directly on te monitored component and are easily fabricated using additive manufacturing (3D printing) processes. Teir design and optimisation is driven by a pioneering teoretical model based on perturbative couple-mode teory of guided wave propagation in structures wit periodic corrugated surface profiles. Experimental nonlinear ultrasonic tests confirmed tese teoretical predictions and indicated tat PC sensing device are able to enance te sensitivity of nonlinear ultrasonic inspection for various materials and components.

2 1 Introduction Nonlinear ultrasonic tecniques measure material nonlinear effects suc as armonics (multiples), sub-armonics (sub-multiples) and sidebands (modulation) of one or more excitation frequencies, wic ave proven to be more sensitive to material micro-cracks tan linear ultrasonic indicators suc as wave attenuation and wave scattering from damage [1], [2], [3]. Tese nonlinear material effects are caused by te interaction of ultrasonic guided Lamb waves (GLWs) wit micro- or partially closed cracks, wic produces frictional contact at damage interfaces (referred to as kissing bonds or clapping ) [4], [5], [6], [7]. Te intensity of armonics is generally very low and nonlinear ultrasonic testing require ig amplification of transmitted signals (typical input voltages range between 50 V and 150 V) in order to igligt material nonlinear effects from te measured signal noise. However, ig voltage excitation may create additional armonic frequencies caused by te ultrasonic equipment, wic are difficult to discern from tose generated by te crack. Traditional digital Butterwort filters and advanced signal processing tools ave been developed to filter out undesired armonic signals [8], [9], [10], but tey involve signal manipulation and calibration processes tat may alter te measured waveforms and prevent damage detection. Hence, tere is a need for efficient and reliable ultrasonic signal filters. Pononic crystals (PCs) wit periodic structures are te mecanical analogous of well-known potonic crystals in optics and ave been studied since te pioneering work of Lord Rayleig in 1887 [11]. However, only recently tey ave received widespread interest in te ultrasonic scientific community because of ig computing performance of modern calculators and innovative additive manufacturing processes, wic provide unprecedented accuracy for te design and fabrication of intricate parts. PC structures can be designed to inibit te propagation of ultrasonic guided waves in specific frequency ranges (also known as frequency band gaps or stop bands). Outside tese band gaps, GLWs can propagate in any direction, so tat PCs can be considered as natural signal filters. Depending on teir geometry and constituents, PCs include: (a) structures made of materials wit different mecanical properties in a periodic repetition, (b) structures wit enclosed periodic units suc as oles containing fluids and (c) waveguide structures caracterised by periodic surface profiles [12]. Wilst PCs of type (a) and (b) ave been widely used for applications suc as noise filters and acoustic diodes, tey are impractical for large-scale industrial applications as tey require substantial modification of test components suc as oles and inclusions to exibit frequency band gaps, tus affecting te structural integrity [13]. Tis paper presents an innovative material-based solution to te problem of filtering out undesired frequencies witout modifying te geometry of te ost structure and te measured signals, troug te design of te first PC waveguide tunable filter of type (c) for nonlinear ultrasound. It is ere provided teoretical and experimental evidence of its functionality. 2 Teoretical Model of PC Waveguide Transducers PC waveguide transducers are material-based filters caracterised by frequency band gaps in wic te propagation of ultrasonic Lamb waves is proibited. Tey consist of traditional piezo-electric (PZT) transducers bonded on circular plates wit corrugated surface profiles (Figure 1) [14]. Te material used for te fabrication of PC corrugated structures is acrylonitrile butadiene styrene (ABS) termoplastic polymer, as it satisfies te two following conditions: (i) it can be used as te print material in additive manufacturing processes and (ii) it as low wave (pase) velocities to induce Lamb waves 2

3 at te interface between te PC waveguide and te ost sample, in accordance wit te Snell s Law [15]. Figure 1. ABS PC waveguide transducer wit corrugation wavelengt = 2.1 mm and diameter D = 45.6 mm. Band gaps are pysically induced by te well-known Bragg scattering (or Bragg resonance) effect, i.e. by te destructive interference of bot incident and reflected waves in specific stop bands, wic are excited resonantly wen te guided wave-vector matces 2/, wit te corrugation wavelengt of te PC periodic structure [16]. Suc a wavelengt can be arbitrarily cosen to acieve stop bands in te desired frequency range. PC sensing devices were designed to naturally filter te undesired second armonic frequency, 2f0, caused by te ultrasonic instrumentation. Hence, a perturbative coupledmode teory based on GLW propagation was developed to identify tose stop bands on te edges of te first Brillouin zone (± ) tat matced te second armonic frequency. Tese frequency bands were defined as function of material properties of te PC structure (i.e. Young s Modulus, E, Poisson s ratio,, and density, ), te corrugation dept, corrugation period, average plate tickness 2 and corrugation distance D (see Figure 2). Figure 2. Illustration of te geometrical parameters used to design te adiabatic model for PC waveguides. Te most common approac for solving te GLW problem in a bounded isotropic medium of tickness 2 derives from te potentials metod (also known as Helmoltz decomposition) applied to te following invariant form of Navier s equation in absence of corrugation (i.e. = ) and body forces [17] 2 2 = (1) were = =, is te two-dimensional displacement vector in a Cartesian reference frame, =, is te coordinates vector and and are te Lame parameters, wic are a combination of E and of te isotropic PC material. By setting traction-free boundary conditions of te normal and sear stresses perpendicular to te axis of elastic wave propagation (x-axis) and assuming armonic waves bounded by 3

4 planes ± = ±, te two-well known independent algebraic equations for bot symmetric and anti-symmetric modes can be obtained: an k2 ( 2 2 ) 2 = an, (2) an = (2 2 ) 2 an k 2 were =, =, = /, = /, = + / is te longitudinal wave speed, = / is te sear wave speed and k is te wave number. Figure 3 sows te dispersion relations obtained from Eq. (2) of te lowest symmetric and antisymmetric modes k S,A and te non-dispersive longitudinal and sear k l,t modes of an un-corrugated plate of tickness 2 = 10 mm made of ABS polymer. Figure 3. ABS PC waveguide transducer wit corrugation wavelengt = 2.1 mm and diameter D = 45.6 mm. In te presence of corrugation, it is assumed tat te unperturbed lowest symmetric S0 and antisymmetric A0 modes follow adiabatically te corrugated plate profile suc tat teir displacement vector mode profiles are ±,, were = cos / and te signs + and denote forward and backward GLWs [18]. Under te assumption tat, te corrugation can be treated as a perturbation and te general solution, of te GLW problem induced by te corrugation can be set as te superposition of bot forward and backward propagating waves as follows:, = (3) were ±, represent te scalar amplitudes of symmetric and antisymmetric modes of te corrugated plate. In order to study penomenologically te effect of te corrugation, Eq. (3) is substituted in Eq. (1) and te resulting system of differential equations is expanded in multiple scales at te first order in te parameter /. Te solvability condition of te te vectorial system of equations is obtained by taking te scalar product wit te symmetric and antisymmetric forward and backward unperturbed modes. It can be found tat te coupling between forward and backward modes of identical symmetry vanises, wilst te coupling between forward and backward modes of opposite symmetries remains finite. Tis leads to te following system of coupled differential equations for te mode amplitudes 4

5 + + = = + = [2 + ] 2 [ + ] 2 [ + ], (4) = + [2 + ] were coefficient C S,A are functions of te material and geometrical features of te PC waveguide and are given by = /, = /, wit = [ + ] ( ) = [ + ( ) ] ( ) = [ + ( ) + ], ( ) = [ + ( ) + ] = [ + ] ( ) = [ + ( ) ] were te sign (*) denotes te complex conjugate operation. Te propagation of forward and backward modes accounted by Eq. (4) can be uncoupled into two second-order dispersion equations for te forward propagating modes 2 + = [ 2 + ] + +, (5) 2 + = [ 2 + ] wic provide te solutions + = + and + = +, were te corrugation-induced wavenumber sift is: = [ + ] + [ + ], (6) + and te amplitudes, are constant. In order to obtain stop band in te desired armonic frequency range, bot wavenumbers, from te unperturbed GLW problem [Eq. (2)] are set equal to, and te corrugation period to = /[ + ]. Band gaps are analytically calculated by analysing te wave extinction dependency over te frequency troug te imaginary part of = + as in Eq. (6). Figure 4 sows te analytical results of bot real and imaginary parts of in ABS PC waveguides for two spatial periods, = 2.1 mm (2f0 = 200 khz) and = 1.4 mm (2f0 = 300 khz), by setting 2 = 10 mm and = mm. + 5

6 (a) (b) Figure 4. Analytical results of real (blue lines) and imaginary (red lines) parts of te corrugation-induced wavevector sift for PC waveguides wit 2 = 10 mm and = mm. ABS PC plate wit = 2.1 mm (2f 0 = 200 khz) (a) and ABS PC plate wit = 1.4 mm (2f 0 = 300 khz) (b). As it can be seen from Figure 4, te ABS corrugated structure displays two stop band regions for eac wavelengt. For = 2.1 mm, stop bands are obtained at frequencies f < 80 khz and f > 150 khz [igligted in green in Figure 4(a)], wereas for = 1.4 mm, stop bands are acieved at f < 80 khz and f > 180 khz [igligted in green in Figure 4(b)]. Te real part of te corrugation-induced wavenumber sift vanises at te second armonic frequency, were te imaginary part is maximum, tus suppressing propagation into evanescent waves in suc a frequency range. Anoter key parameter to be considered for te design of PC structures is te corrugation distance =, wit p an integer number. In particular, te transmission coefficient T, defined as = [ ] = [ ], (7) provides te required distance for te travelling Lamb wave to be attenuated. Suc information is necessary to evaluate te number of corrugations upon wic te stop band region becomes effective. As sown in Figure 5, only p = 2 periods are sufficient for bot ABS PCs wit =2.1 mm and =1.4 mm to attenuate nearly 100% of te elastic energy at te stop band. 2 Figure 5. Analytical results of te transducer transmission coefficient T for te ABS PC waveguides wit = 2.1 mm (green continuous line) and =1.4 mm (blue dased line). 3 Experimental Set-up ABS PC structures wit sinusoidal corrugations were fabricated using conventional fused deposition modelling (FDM) 3D printing based on te analytical model reported in Section 2. Teir geometrical properties are reported in Table 1. 6

7 Table 1. Geometrical parameters of fabricated PC waveguide transducers. ABS PC Waveguide Fundamental frequency, f0 [khz] Second armonic frequency, 2f0 [khz] Tickness, 2 [mm] Corrugation dept, [mm] 3 3 Wavelengt at 2f0, [mm] Corrugation Distance, P [mm] 18.8 (8) 11.2 (8) Diameter, D [mm] For te nonlinear ultrasonic experiments reported in te following Section, twenty cycles long sine wave bursts = sin enclosed in a Hanning window, wit Q0 being te input amplitude, were transmitted at frequencies f0 ranging between 0 and 400 khz by te piezoelectric transducer (from AmericanPiezo, wit central frequency of 330 khz, radius of 3 mm and tickness of 1 mm), wic was surface bonded on te PC waveguide. Suc a sensor was driven by an arbitrary waveform signal generator (TTI 50MHz Pulse Generator T6501) connected to an amplifier (Falco Systems DC 5MHz Hig Voltage WMA-300). Te receiver transducer was glued directly on te aluminium plate (wit dimensions of mm) and it was linked to an oscilloscope (Pico Tecnology oscilloscope 100V max input, Model 4424) and a personal computer in order to display te recorded waveforms (Figure 6). Figure 6. Illustration of te experimental set-up for te nonlinear ultrasonic experiments. Signals received by te piezoelectric sensor were sampled at 2 MHz wit an acquisition window τ = 5 ms and processed using MATLAB software. Time istories were averaged 20 times for eac input frequency in order to improve te signal-to-noise ratio of measured signals. Additionally, te ost aluminium sample was positioned along te edges on four foam pieces in order to reduce environmental noise effects. 4 Nonlinear Ultrasonic Results wit PC Waveguide Transducers As reported in te Introduction section of te paper, te input voltage in nonlinear ultrasonic experiments usually ranges between 50 V and 150 V. Tis is generally due to te material attenuation of te transmitted signal and te quadratic dependence of te amplitude of te second armonic frequency over te fundamental one. Te maximum input amplitude of current signal generators is typically 5-10 V peak-to-peak, tus preamplification systems are necessary. No pre-amplification of te transmitted signal would inevitably result in a low amplitude fundamental frequency wit te associated second armonic frequency idden into te noise. As an example, Figure 7 illustrates te material response measured by te receiver transducer in te absence of pre-amplification system and wit no PC waveguide using an input voltage of 2.5 V. 7

8 Figure 7. Experimental ultrasonic response measured in te absence of PC structure and amplification at te input voltage of 2.5 V. From Figure 7, it can be seen tat at te input voltage of 2.5 V, te amplitude of te fundamental frequency f0 = 100 khz is 7.8 dbv, wereas, as expected, te second armonic amplitude at 2f0 = 200 khz is very low and idden into te noise. Nonlinear ultrasonic experiments were performed to validate te adiabatic model of Section 2 and to analyse te caracteristics of propagating GLWs. As reported in Section 3, single toneburst periodic signals in te < < khz frequency range were transmitted from te piezoelectric transducer surface bonded on te ABS PC waveguide tat, in turn, was glued on a omogeneous aluminium plate. Suc a frequency range of interest was specifically cosen in order to generate fundamental Lamb modes S0 and A0 in te PC structure, so to activate te periodicity effect of band gaps induced by destructive interference only among tese two waves. In order to measure te nonlinear second armonic elastic response generated by te amplification system, a receiver piezoelectric transducer was located at direct contact wit te aluminium plate ~150 mm far away from te input elastic source (see Figure 6). Te same experiments were also performed in te absence of corrugated waveguides in order to compare te strengt of te recorded signals and evaluate te extinction efficiency of te proposed PC transducers. Figure 8 sow te ultrasonic results for f0 equal to 100 khz and 150 khz, respectively, at te input voltage of 125 V. (a) (b) Figure 8. Experimental material response measured by te receiver sensor wit (black continuous line) and witout PC structure (blue dased line) using an amplified input voltage of 125 V and a driving frequency f 0 = 100 khz (a) and f 0 = 150 khz (b). In comparison wit te case of te transmitter transducer directly in contact wit te ost aluminium plate, te elastic wave energy of received signals was attenuated in te 8

9 PC sensing device, wit an amplitude loss of ~25 dbv [Figure 8(b)] at f0 = 100 khz and ~16 dbv at f0 = 150 khz [Figure 8(c)]. However, te amplification system wit no PC waveguides was not subject to any filtering and created undesired second armonics at bot driving frequencies (see dased blue lines in Figure 8). Te same frequencies were, instead, successfully filtered out wit te ABS PC waveguide (see dased red and continuous black lines). In order to furter investigate te band-gaps of PC waveguides, te peak amplitudes of bot fundamental and second armonic frequencies were experimentally recorded at two input voltages of 75 V and 125 V. Te results are sown in Figure 9 for te four sensing devices reported in Table 1. (a) (b) (c) (d) Figure 9. Experimental maximum amplitudes at te input voltage of 75V and 125V. Peak amplitude at te fundamental frequency using = 2.1 mm (a) and = 1.4 mm (b). Peak amplitude at te second armonic frequency using = 2.1 mm (c) and = 1.4 mm (d). Figures 9(a) and 9(b) report te maximum amplitudes of fundamental frequencies using bot aluminium and ABS PC waveguide transducers, wilst Figures 9(c) and 9(d) sow te measured second armonic peak amplitudes. As envisaged by te analytical model presented in Section 2, wilst PC transducers do not alter fundamental and second armonic frequencies outside te stop band region, te lowest voltages are acieved at 200 khz and 300 khz for bot fundamental and second armonic amplitudes, wit values respectively of approximately 6 dbv and 50 dbv. Moreover, in agreement wit te adiabatic coupled-mode teory, te elastic wave extinction produces two stop bands below ~78 khz and above ~147 khz [Figures 9(a) and 9(b)], and below ~78 khz and above ~182 khz [Figures 9(c) and 9(d)]. Suc experimental results are all consistent wit te predicted energy band-gaps illustrated in Figure 4. 9

10 5 Conclusions Tis paper proposed and demonstrated te development of ABS termoplastic polymer ultrasonic pononic crystal waveguide transducers tat exibit multiple frequency stop-bands filtering out fictitious second armonic frequencies. Tese sensing devices were easily fabricated using additive manufacturing processes and integrated on te surface of te test structure witout altering its mecanical and geometrical properties. Te design of te pononic crystal structure was supported by a perturbative couple mode teory of guided Lamb waves predicting te frequency band-gaps of periodic plates wit sinusoidal corrugation. Te analytical model revealed tat te corrugation wavelengt is inversely proportional to te sum of te lowest symmetric and antisymmetric Lamb wavenumbers. By analysing te frequency dispersion of te corrugationinduced wavevector sift β, dual stop bands were generated by simply canging te geometrical features of te pononic crystal material. Tese teoretical findings were found in excellent agreement wit nonlinear ultrasonic experimental testing, tus revealing tat te proposed pononic crystal waveguide transducer successfully attenuates second armonics caused by te ultrasonic equipment, tus demonstrating its wide range of potential applications for acousto/ultrasonic material damage inspection. 6 References [1] Ostrovsky, L. & Jonson, P. Dynamic nonlinear elasticity in geomaterials. Rivista del nuovo cimento 24(7), 1 46, [2] Ginzburg, D., Ciampa, F., Scarselli, G., Meo, M. SHM of Single Lap Adesive Joints using Subarmonic Frequencies. Smart Materials and Structures, 26, , [3] Scarselli, G., Nicassio, F., Ciampa, F., Meo, M. Non-linear metods based on ultrasonic waves to analyse disbonds in single lap joints, Proceedings of te Institution of Mecanical Engineers, Part C: Journal of Mecanical Engineering Science, , [4] Delsanto, P. P. Universality of nonclassical nonlinearity. Springer, Berlin, [5] Ciampa, F., Scarselli, G., Pickering, S., Meo, M. Nonlinear elastic wave tomograpy for te imaging of corrosion damage. Ultrasonics, 62, , [6] Malfense Fierro, G.-P, Ciampa, F., Ginzburg, D., Onder, E., Meo, M. Nonlinear ultrasound modelling and validation of fatigue damage. Journal of Sound and Vibration, 343, , [7] Ciampa, F., Barbieri, E., Meo, M. Modelling of Multiscale Nonlinear Interaction of Elastic Waves wit Tree Dimensional Cracks. Journal of Acoustical Society of America, 135 (4), [8] Ciampa, F., Meo, Nonlinear imaging metod using second order pase symmetry analysis and inverse filtering. Journal of Nondestructive Evaluation, 34(2), 1-6, [9] Ciampa, F., Meo, M. Nonlinear elastic imaging using reciprocal time reversal and pase symmetry analysis. Journal of Acoustical Society of America, 130(6), pp , [10] Bruno, C. L. E., Gliozzi, A. S., Scalerandi, M. & Antonaci, P. Analysis of elastic nonlinearity using te scaling subtraction metod. Pysical Review B 79(6), , [11] Rayleig, L. On te maintenance of vibrations by forces of double frequency, and on te propagation of waves troug a medium endowed wit a periodic structure. Pilos. Mag. 24(147), ,

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