Excitability of guided waves in composites with PWAS transducers

Transcription

1 Excitability of guided waves in coposites with PWAS transducers Yanfeng Shen and Victor Giurgiutiu Citation: AIP Conference Proceedings 65, 658 (25); doi:.63/ View online: View Table of Contents: Published by the AIP Publishing Articles you ay be interested in Ultrasonic guided wave sensing perforance of a agnetostrictive transducer using Galfenol flakes-polyer coposite patches J. Appl. Phys. 7, 7A96 (25);.63/.4968 Efficient excitation of guided acoustic waves in seiconductor nanorods through external etallic acoustic transducer Appl. Phys. Lett. 5, 243 (24);.63/ Frequency dependent directivity of guided waves excited by circular transducers in anisotropic coposite plates J. Acoust. Soc. A. 32, EL9 (22);.2/ FE SIMULATION OF GUIDED WAVES IN COMPOSITE MATERIALS GENERATED AND DETECTED BY AIR COUPLED TRANSDUCERS AIP Conf. Proc. 96, 94 (29);.63/ Ultrasonic Guided Wave Iaging of a Coposite Plate with Air Coupled Transducers AIP Conf. Proc. 894, 7 (27);.63/.27877

2 Excitability of Guided Waves in Coposites with PWAS Transducers Yanfeng Shen a) and Victor Giurgiutiu b) Departent of Mechanical Engineering, University of South Carolina, Colubia, South Carolina, United States a) b) Abstract. Piezoelectric Wafer Active Sensors (PWAS) are convenient enablers for generating and receiving ultrasonic guided waves. The wide application of coposite structures has put new challenges for the Structural Health Monitoring (SHM) and Nondestructive Evaluation (NDE) counity due to the general anisotropic behaviors and coplicated guided wave features in coposites. The excitability of guided waves in coposite structures directly influences the ipleentation of active sensing systes to achieve the best interrogation of certain sensing directions. This paper presents a hybrid odeling technique for studying the excitably of guided waves in coposite structures with PWAS transducers. This hybrid technique coprehensively covers local finite eleent odel (FEM), sei-analytical finite eleent (SAFE) ethod, and analytical guided wave solutions. Haronic analysis of a sall-size local FEM with non-reflective boundaries (NRB) was carried out for obtaining guided wave generation features in plate structures. The PWAS transducers were odeled with coupled filed eleents. Thus, the FEM can fully capture the geoetry and aterial property effects of PWAS transducers and their influence on the guided wave excitation. SAFE ethod was used to obtain the coplicated guided wave features in coposites such as dispersion curves and odeshapes. The SAFE procedure was coded into MATLAB Graphical User Interface (GUI), and the software SAFE-DISPERSION was developed. To study the excitability of each wave ode, we considered all the possible wave odes being generated siultaneously and propagating independently. The analytical wave expressions based on the exact guided wave solution with Hankel functions were used to join the SAFE ethod and the local FEM. Forulated in frequency doain, the hybrid odel is highly efficient, providing an over deterined equation syste for the calculation of ode participation factors. Case studies were carried out: () the Lab wave excitability in an aluinu plate was investigated and copared with classical pin force odels to show the feasibility of the hybrid technique; (2) the guided wave excitability in a woven glass fiber coposite (GFRP) plate was studied with circular and square PWAS transducers. The paper finishes with suary, conclusions, and suggestions for future work. INTRODUCTION Piezoelectric wafer active sensors (PWAS) are widely explored in structural health onitoring (SHM) and nondestructive evaluation (NDE) procedures for generating and receiving guided waves []. Their advantages over conventional ultrasonic transducers are found in their sall size and light weight characteristics, aking the ore suitable for the purpose of peranent installation and real tie onitoring. Besides, PWAS transducers work in the in-plane ode and generate long propagating Lab waves in plates, enabling the to interrogate large areas of structures, while conventional ultrasonic transducers can only perfor thickness direction point inspections. The increasing use of coposite coponents in structures brought new challenges to the SHM and NDE counity, because coposite aterials usually have anisotropic properties and exhibit directional echanical behaviors. The iportance of studying guided wave excitability in coposite structures can be seen in two aspects: () to optiize directional sensing capability of SHM/NDE syste; (2) to reduce sensing signal coplexity for ease of signal interpretation. Due to the general anisotropic aterial properties of coposites, guided waves excited by the transducers will be strong in certain directions and week in soe others. This effect needs to be fully understood to excite strong interrogating field in the direction of interest. Besides, the nature of guided waves in coposites is ultiodal and dispersive. This will introduce coplicated wave packets in the sensing signals. By choosing the 4st Annual Review of Progress in Quantitative Nondestructive Evaluation AIP Conf. Proc. 65, (25); doi:.63/ AIP Publishing LLC /$. 658

3 appropriate PWAS size and excitation frequency, one can diinish the participation of other wave odes, achieving a single wave packet in the interrogating field. This will considerably reduce the sensing signal coplexity. The excitability of guided waves in etallic structures has been explored with analytical approach and experiental verifications [2, 3]. But this topic becoes ore challenging in the case of coposites. Analytical approaches have been proposed using the pin-force odel and 3-D Green s function ethod [4, 5]. But in these odels, the distribution of traction field between the PWAS and the plate is hard to be deterined and is usually assued to be pin-forces around PWAS edges. This estiation is accurate when the PWAS thickness is sall copared with plate thickness and when the adhesive layer is thin enough to be considered as ideal bonding. In other words, the analytical odels cannot capture the local dynaics of the PWAS transducer and the adhesive layer, while these local dynaics ay exert considerable influence on the excitability of guided waves. In addition to the analytical ethods, nuerical odeling techniques provide an alternative way to study this topic. Nuerical ethods, such as spectral eleent ethod (SEM), local interaction siulation approach (LISA), and FEM have been investigated to study the guided wave generation by PWAS transducers [6, 7, 8]. They have shown the capability of capturing the local dynaics of PWAS and adhesive. The first two techniques have not reached their ature stage, while the FEM has been widely exained by experients for reliable results. However, full scale transient odeling is coputational expensive and ay becoe prohibitive for high frequency, short wavelength, long propagating waves in lainate coposites. This paper presents a hybrid odeling technique, cobining local FEM, SAFE ethod, and global analytical expression together, to solve the excitability of guided waves in coposite structures. GUIDED WAVES IN COMPOSITE PLATES AND SAFE-DISPERSION In this study, the sei-analytical finite eleent (SAFE) ethod was adopted to obtain the dispersion curves and odeshapes of coposite plates. The SAFE ethod has been intensively explored as a powerful ethod to copute the nuerical solution of waves in waveguides with arbitrary cross-sections and coposite structures [9, ]. The SAFE ethod uses finite eleents to discretize the cross-section of the waveguide, while the wave propagation direction is expressed with analytically. This sei-analytical forulation finally reaches a stable eigenvalue proble. The eigenvalues are the wavenubers; the eigenvectors are the corresponding odeshapes. The SAFE procedure was coded using MATLAB Graphical User Interface (GUI), and the predict tool SAFE-DISPERSION was developed to obtain the guided wave solutions for plate structures. Figure shows the aterial properties input panel and the ain interface of SAFE-DISPERSION. FIGURE. SAFE-DISPERSION GUI: aterial properties input panel; ain interface. 659

4 The coposite aterial in this study is woven glass fiber reinforced polyer (GFRP) which is widely used in naval applications. The aterial stiffness atrix CGFRP is given in Eq. (). The density GFRP is 9 kg/ 3.The lainate coposite is - thick, constructed with 6 woven GFRP plies with the sae stacking orientation. CGFRP GPa () Figure 2a shows the SAFE solution of phase velocity dispersion curves in degree direction with respect to fiber orientation. It can be noticed that the solution can capture the syetric odes, anti-syetric odes, and shear horizontal odes. The wave velocity varies with propagation direction due to the anisotropic aterial properties of the woven GFRP plate. The directivity plot of phase velocity at 2 khz is shown in Fig. 2b as an illustrative exaple. It can be observed that the velocities of syetric and antisyetric odes reach axiu along the /9 fiber direction and iniu in 45 degree directions, while the shear horizontal ode has highest velocity in 45 degree directions and lowest velocity in /9 fiber directions. Phase Velocity (k/s) FIGURE 2. Dispersion curves in degree direction; (2) Phase velocity directivity plot at 2 khz. SMALL-SIZE FEM WITH NON-REFLECTIVE BOUNDARY A sall-size FEM with non-reflective boundary (NRB) was used to odel the guided wave excitation procedure. Figure 3a shows the scheatic of the FEM. The size of the FEM was iniized by adopting NRB and syetric conditions. Frequency doain haronic analysis was carried out, so that we can get the solution for all the frequencies of interest with only one run the FEM. The NRB akes it possible to siulate continuous propagating waves rather than standing waves with the sall-size FEM. The NRB was constructed using COMBIN4 spring daper eleents available in ANSYS. The daping paraeter distribution is shown in Fig. 3b. For detailed description of the NRB construction, readers are referred to Ref []. The sensing boundary picks up the outward propagating waves arriving at the sensing nodes. PWAS was odeled using the coupled field eleents which couple the electrical and echanical behavior through piezoelectric constitutive equations. Thus, the sall-size FEM can capture the coplex PWAS diension and the local dynaics of PWAS and adhesive layer. The odel is highly efficient due to its sall-size and frequency doain solving schee. 6

5 Non-reflective boundary Syetric boundary Sensing boundary PWAS Coupled filed eleents NRB constructed with COMBIN4 Syetric boundary FIGURE 3. Sall-size FEM with NRB; NRB constructed with COMBIN4 spring-daper eleents. EXTRACTION OF EXCITABILITY INFORMATION FROM SMALL-SIZE FEM The difficulty of extracting excitability inforation fro the sall-size FEM is that the wave otion is no longer uncoupled aong the wave odes in coposites. For instance, the odeshape of SH ode shows not only the priary u displaceent coponent, but also the ur coponent. S ode shows the priary ur displaceent coponent, the u coponent, and also uz coponent as well. FIGURE 4. Extraction of excitability inforation fro the sall-size FEM. To extract the excitability inforation, we assued that the guided wave odes are generated by PWAS and propagate into the structure siultaneously as shown in Fig. 4. The outward propagating 2-D wave field has been shown to follow Hankel function pattern [, 2]. The total displaceent coponents picked up at the sensing boundary FEM are the superposition of displaceents fro all the wave odes. For exaple, Ur z represents the ur displaceent coponent fro FEM solution at a thickness location z and consists of the superposition of ur coponents contributed by S, A, and SH ode. At discretized thickness-wise locations, this relationship can be expressed as shown in Eq. (2) below, i.e., M FEM ar zh r Ur z M FEM ar z2h r Ur z2 M FEM ar znh r Ur zn (2) 66

6 where r n is the ur coponent of the th wave odeshape at location z n ; H is Hankel function of the first kind and order one describing an outward propagating 2-D wave field; is the wavenuber of the th wave ode; r is the distance between the PWAS center and the sensing boundary. Siilar relationship can be obtained for u and uz displaceent coponents. These relationships are described using the analytical expressions. The odeshapes and wavenubers can be calculated using the SAFE ethod. The U z are calculated fro the sall-size FEM. Thus, we arrive at a series of linear equations with a is the ode participation factor of the th wave ode; z FEM r the ode participation factors as the only unknown quantities. Since the nuber of equations is greater than the nuber of unknowns and increases as we further discretize the thickness direction in the sall-size FEM, we finally obtain an over-deterined equation syste, which is solved with least square ethod using MATLAB. The equation syste is expressed in atrix for as FEM H A U (3) where is the odeshape atrix; H is the 2-D wave propagation atrix; A is the unknown ode participation FEM factor vector to be solved; U is the FEM solution vector. These atrices and vectors are given as follows. H H z z z r 2 r r r z z z z z z 2 r n r n r n 2 zn zn zn z z z 2 2 z z z z z z 2 z n z n z n 2 r H H r (4) (5) T A a a2 a (6) FEM FEM FEM FEM FEM FEM FEM U Ur z Ur zn U z U zn Uz z Uz z n (7) The displaceent aplitude for the th wave ode can be calculated using the calculated ode participation factor and the corresponding odeshape. ; ; u a z u a z u a z (8) r r z z T 662

7 CASE STUDIES Three groups of cases studies will be shown based on the hybrid ethod described in the previous sections: () excitability of guided waves by a circular PWAS on a - thick aluinu plate verified with analytical solution; (2) excitability of guided waves by a circular PWAS on a - thick woven GFRP plate; (3) excitability of guided waves by a rectangular PWAS on a - thick woven GFRP plate. Circular PWAS on a - Thick Aluinu Plate In this case study, five situations are considered: () pin force excitation; (2).2 thick PWAS with ideal bonding condition; (3).2 thick PWAS with adhesive layer; (4).2 thick PWAS with adhesive layer; (5).5 thick PWAS with adhesive layer. The pin force excitation odel is used to copare with the analytical solution given in Eq. (9). For ore details of the derivation, readers are referred to Ref []. The PWAS and the adhesive layer thickness changes ai at deonstrating the capability of the hybrid odel to capture the local dynaics of the transducer and bonding agent. The density, Young s odulus, and Poisson s ratio of the bonding layer were taken as 7 kg/ 3, E 5 GPa, and.4 as suggested by Ref [3]. 2 S S 2 A A a a J( a) NS( ) () S it a a J( a) NA( ) () A it r () ( ) ( ) zd S A 2 S D ( ) 2 A S DA ( ) (9) u r i H re i H re Noralized Aplitude Analytical solution vs hybrid odel (UX) Analytical A Analytical S Hybrid odel A Hybrid odel S A Rejection 252 khz Noralized Aplitude Effects fro PWAS and adhesive (UX) S Aplitude Increase A Rejection Point Shift S pinforce A pinforce S.2PWAS A.2PWAS S.2PWAS+uAD A.2PWAS+uAD S.2PWAS+uAD A.2PWAS+uAD S.5PWAS+uAD A.5PWAS+uAD FIGURE 5. Tuning curves of case studies: analytical solution vs hybrid odel; effects fro PWAS and adhesive. Figure 5a shows the coparison between the hybrid odel with the analytical solution for the in-plane displaceent. It should be noted only four eleents (five FEM nodal solutions) were used across the thickness for this case study. It can be observed that the hybrid odel copared well with the analytical solution especially for A ode. For high frequency range, the hybrid odel deviates fro the analytical solution, because ore eleents are needed to accurately depict the odeshape across the plate thickness. However, it can be noticed that the tuning behavior and the rejecting point (at 252 khz) copared well. Figure 5b shows different cases with various PWAS and adhesive layer thickness. It can be seen that the hybrid odel is capable of capturing the local dynaics of PWAS and adhesive. When the PWAS and adhesive layer effects are considered, the A rejecting point shifts toward higher frequencies, and the rejecting effect becoes weaker. This rejecting point shift effect agrees with the observation in Ref [4]. At lower frequency range, the thicker PWAS/adhesive will reduce the excitability for both S and A odes, but the excitability of S becoes stronger at higher frequency range ( khz- khz) due to the local dynaical effects. It should be noted that the dynaics of PWAS and adhesive cannot be fully captured by conventional pin force odels. On the other hand, our hybrid odel uses a sall-size ulti-physics FEM to handle this coplex transducer structure interactions. 663

8 Circular PWAS on a - Thick Woven GFRP Plate Figure 6a shows the setup of the coposite case study, which investigates the excitability of guided waves by a circular PWAS (7- diaeter and.5 thick) bonded on a - thick woven GFRP plate. It also shows the and degree directions. Figure 6b and Fig. 6c show the ode participation factor of S, A, and SH odes in the and degree directions respectively. It can be noticed that along degree direction, only S and A wave odes are excited, while SH ode cannot be excited. In the degree direction, not only S and A wave odes are excited, but also SH wave ode as well. Aplitude Mode participation factor ( degree) 7.5 x -7.5 No SH 2 4 FIGURE 6. Circular PWAS on the woven CFRP plate (arrows showing and degree directions); ode participation factor for degree direction; (c) ode participation factor for degree direction. A SH S Aplitude Mode participation factor ( degree).5 x -7.5 SH A SH S 2 4 (c) 5 S ode Mode A ode Mode SH Mode ode 9.5e-8 9 8e-8 9 6e-9 e-8 6e-8 4e-9 5 4e-8 5 5e-9 2e-8 2e-9 khz khz 9 4e-8 9 3e-8 9.5e-8 3e-8 2e-8 e-8 5 2e e-8 e-8 5e FIGURE 7. Directivity plots of ode participation factors for S, A, and SH odes excited by circular PWAS. 664

9 Figure 7 shows directivity plots of ode participation factors for S, A, and SH odes excited by the circular PWAS at khz and 2 khz. It can be observed that strong S and A wave odes are excited along and 9 directions, while no SH waves are excited in, 45, and 9 directions. The aplitude of S and A waves are weak in 45 degree directions. Rectangular PWAS on a - Thick Woven GFRP Plate Figure 8a shows the setup of the coposite case study, which investigates the excitability of guided waves by a rectangular PWAS (7 by 8 and.5 thick) bonded on a - thick GFRP plate. Mode Participation Factor ( Degree) -7 Aplitude x -7 No SH A SH S Aplitude Mode Participation Factor ( Degree) x -7 SH A SH S (c) FIGURE 8. Rectangular PWAS on the woven CFRP plate (arrows showing and degree directions); ode participation factor for degree direction; (c) ode participation factor for degree direction. 665

10 5 S Mode ode A ode Mode SH Mode ode 9 4e-8 9.5e-7 9 2e-8 3e-8 e-7.5e-8 2e e-8 e-8 5e-8 5e-9 khz e-8 6e-8 4e-8 2e e-7 e-7 5e e-8 2e-8 e-8 2 khz FIGURE 9. Directivity plots of ode participation factors for S, A, and SH odes excited by rectangular PWAS. Figure 8b and Fig. 8c show the ode participation factor of S, A, and SH odes in the and degree directions respectively for the rectangular PWAS case. It can be noticed that along degree direction, only S and A wave odes are excited, while SH ode cannot be excited. In the degree direction, not only S and A wave odes are excited, but also SH wave ode as well. Figure 9 shows the directivity plots of S, A, and SH wave odes excited by the rectangular PWAS at khz and 2 khz. Since the PWAS shape is rectangular with two different sizes in and 9 directions, the tuning effects are different along these two directions. Such behavior is very obvious for the case of A wave ode. At khz, the strongest A waves are excited in 9 degree direction. However, at 2 khz, the strongest A waves are excited in degree direction. Strong S waves are excited along and 9 degree directions, but the aplitudes in these two directions differ fro each other. SH wave odes cannot be excited in and 9 degree directions. CONCLUSIONS AND FUTURE WORK The sall-size FEM with NRB can be used to extract guided wave excitation inforation in a highly efficient anner. The hybrid odel coprehensive cobines the FEM, SAFE ethod, and analytical solution. The hybrid odel result copares well with analytical solution for the aluinu plate. This ethod can capture the dynaics of PWAS transducers and the adhesive layer. Only S and A waves can be excited by the extensional PWAS transducers in the aluinu plate. However, SH ode can be excited by the extensional PWAS in the woven GFRP coposite plate. The case studies deonstrated the capability of this hybrid ethod to investigate the excitability of guided waves by coplex diension PWAS transducers on coposite structures. For future work, study of the influences on coputational accuracy should be carried out. Experiental validation with pitch-catch and laser vibroetry should be perfored. This work should be extended to cobine with global analytical solution to for hybrid global local odels for wave generation and propagation in coposites. 666

11 ACKNOWLEDGMENTS Support fro Office of Naval Research # N4---27, Dr. Ignacio Perez, Technical Representative; Air Force Office of Scientific Research #FA , Dr. David Stargel, Progra Manager; SPARC fellowship at University of South Carolina; are thankfully acknowledged. REFERENCES. V. Giurgiutiu, Structural Health Monitoring with Piezoelectric Wafer Active Sensors, 2nd Edition,, Elsevier Acadeic Press, V. Giurgiutiu, "Tuned Lab-Wave Excitation and Detection with Piezoelectric Wafer Active Sensors for Structural Health Monitoring," Journal of Intelligent Material Systes and Structures, vol. 6, no. 4, pp. 29-6, A. Raghavan and C. Cesnik, "Fintie-diensional piezoelectric transducer odeling for guided wave based structural health onitoring," Sart Materials and Structures, vol. 4, pp , A. Raghavan and C. Cesnik, "3-D Elasticity-based Modeling of Anisotropic Piezocoposite Transducers for Guided Wave Structural Health Monitoring," in 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynaics, and Materials Conference, Newport, A. Velichko and P. Wilcox, "Modeling the excitatino of guided waves in generally anisotropic ulti-layered edia," The Journal of the Acoustical Society of Aerica, vol. 2 (), R. Schulte and C. Fritzen, "Siulation of wave propagation in daped coposite structures with piezoelectric coupling," Journal of Theoretical and Applied Mechanics, vol. 49, pp , K. Nadella and C. Cesnik, "Effect of piezoelectric actuator odeling for wave generation in LISA," in SPIE conference proceeding, vol. 964, doi:.7/ , M. Gresil and V. Giurgiutiu, "Prediction of attenuated guided waves propagation in carbon fiber coposites using Rayleigh daping odel," Journal of Intelligent Material Systes and Structures, doi:.77/45389x454987, L. Gavric, "Coputation of propagative waves in free rail using a fintie eleent technique," Journal of Sound and Vibration, vol. 85, pp , I. Bartoli, A. Marzani, F. Lanza de Scalea and E. Viala, "Modeling wave propagation in daped waveguides of arbitrary cross-section," Journal of Sound and Vibration, vol. 295, pp , 26.. Y. Shen, Structural health onitoring using linear and nonlinear ultrasonic guided waves, PhD dissertation University of South Carolina, E. Glushkov, N. Glushkova, R. Laering, A. Erein and M. Neuann, "Lab wave excitation and propagation in elastic plates with surface obstacles: proper choice of central frequencies," Sart Material and Structures, doi:.88/ /2//52, C. Ong, Y. Yang and Y. Wong, "The effects of adhesive on the electro-echanical response of a piezoceraic transducer coupled sart syste," in Proceeding of SPIE 562:24-247, G. Bottai and V. Giurgiutiu, "Exact shear-lag solution for guided waves tuning with piezoelectric wafter active sensors," AIAA Journal, vol. 5, pp ,