Frequency damage indicators for piezoelectric composites

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1 Frequency damage indicators or piezoelectric composites *Ayech Benjeddou ), Mohsen Hamdi ) and Samir Ghanmi ) ) Structures, SUPMECA, Saint Ouen 900, France ) benjeddou@supmeca.r,) Technology department, IPEIN, Nabeul 8000, Tunisia ABSTRACT The present contribution ocuses on vibration-based damage detection o laminated composite beams using integrated piezoceramic patches and requency indicators. The latter are assessed via three-dimensional ully coupled piezoelectric inite element parametric analyses on the damage key parameters under dierent mechanical and electrical conditions, and or all types o vibration modes. It is ound that squared requency change actors perormances are much better, as damage indicators, than simple requency change ones; moreover, open-circuit requency based damage indicators perormances are ound to be similar to short-circuit ones. The obtained results can be urther used, or example, or training artiicial neural networks or the quantiication o the analyzed damage types (crack and delamination).. INTRODUCTION Vibration-based damage detection (VBDD) or structural health monitoring (SHM) is a well-established technique or passive (Sinou 009) and active (Huang et al. 00) structures. However, except ew works (Jian et al. 997, Penn et al. 999, Tan and Tong 00, Yam et al. 00, Benjeddou 006, Benjeddou et al. 006, Qiao et al. 007, Al-Ajmi and Benjeddou 008), the use o piezoceramic transducers as sensors or/and actuators was mainly limited to Lamb waves (see or example Ihn et al. 008)- and impedance (see or example Giurgiutiu et al. 0) based high requency approaches. It is then the objective o the present contribution to ocus on low-requency VBDD or piezoelectric laminated composite beams. Hence, requency damage indicators, other than the classical simple requency change (Tan and Tong 00), are here explored via parametric analyses on the damage key parameters (position, length, depth) and on various mechanical (clamped-ree, CF; clamped supported, CS; clamped-clamped, CC; supported supported, SS) and electrical (short circuit, SC; open circuit, OC) ) Full Proessor ) PhD Student ) Assistant Proessor 050

2 conditions. For this purpose, three-dimensional (D) piezoelectric ully coupled inite element (FE) analyses are used or assessing the eects o these parameters and conditions on the proposed VBDD indicators perormance or all types o vibration modes (bending, membrane and torsion). The damage is modeled as a removal o material (RM), simulating a crack (Qiao et al. 007), and as inclusion o a sot layer (ISL) o Telon material, simulating a delamination (Yam et al. 00). The added values o the present work to the authors earlier ones and to the current state o the art o VBDD o composite structures with piezoelectric patches are: (i) use o D ully coupled piezoelectric FE models instead o one-dimensional (D) models that do not model explicitly the beam width; (ii) considering all mode types (bending, membrane and torsion) instead o transverse bending ones only as previously retained; (iii) considering most mechanical boundary conditions (BC) and not only the popular CF or SS ones; (iv) investigation o a new OC requency-based damage indicator; Hence, hereater, requency damage indicators are irst discussed; then, simple and squared requency-change actor (FCF) indicators are analyzed irst under ixed RM and ISL damage characteristics; next, they are assessed through FE parametric analyses under RM and ISL varied damage characteristics o hybrid carbon/graphite iber reinorced polymer (CFRP/GFRP) composite laminated beams with symmetrically integrated pair o piezoceramic (PZT-5A) patches under our (CF, CS, CC, SS) mechanical and two (SC, OC) electrical conditions. Finally, conclusions and perspectives are given as a closure.. FREQUENCY-BASED DAMAGE INDICATORS A qualitative way to track damage presence in a structure is to compare tabulated damage requencies ( d ) to healthy ones ( h ) o the vibrating structure as considered in Penn et al. (999) or controlled delaminated (created by placing inter-ply Telon polyimide release ilm pieces) unidirectional (UD) GFRP cantilever plates using piezoelectric polymer (PVDF) sensors. A quantitative detection was considered earlier, in Jian et al. (997), through graphical representations, versus mode number, o this requencies ratio (FR) indicator FR d () h It s worthy to notice that in these experimental analyses (Jian et al. 997, Penn et al. 999) no indication was given on the electric conditions (SC or OC) applied to the electrodes o piezoelectric sensors bonded to the vibrating composite plates. Later, in Tan and Tong (00), the ollowing percent requencies change (FC) was used or delamination detection o composite beams using piezoceramic (PZT) sensors FC d h d (%) ( ) () h h Here (Tan and Tong 00) also, no indication was given on the electric conditions applied to the electrodes strips made on the piezoelectric sensors suraces. 05

3 First consideration o the electric conditions applied on the electrodes o the piezoelectric actuators or sensors was proposed by Benjeddou et al. (006), or piezoelectric hybrid CFRP/GFRP laminated composite cantilever beams, through this percent requency change actor (FCF) that uses damaged and healthy requencies under SC patches electrodes FCF sc ( sc ) h ( sc ) d (%) ( FRsc) () ( ) sc h Notice in eq. () the opposite sign to Eq. (); it is motivated by the act that the damage generally reduces the requencies (Yam et al., 00); hence this deinition is expected to provide mostly positive values o the damage presence indicator. A new OC FCF damage indicator is here proposed in order to investigate the piezoelectric eect (present under OC conditions) inluence on the simple FCF FCF oc ( oc ) h ( oc ) d (%) ( FRoc ) () ( ) oc h This indicator is to be compared to above SC FCF one, as given in Eq. (), that inherently does not show the piezoelectric eect. Later, in Al-Ajmi and Benjeddou (008), new indicators using squared requencies under SC and OC patches electrodes were proposed as ollows, respectively FCF FCF ( sc ) h ( sc ) d sc FR sc ( sc ) h (%) ( ) (5) ( oc ) h ( oc ) d oc FR oc ( oc ) h (%) ( ) (6) The last our VBDD indicators, as deined in Eq. () Eq. (6), will be assessed on the same piezoelectric hybrid laminated composite beam benchmark, but under various mechanical and electrical BC. Also, all mode types will be considered thanks to the use o a D ully coupled piezoelectric FE model with the help o ANSYS commercial code.. DAMAGE INFLUENCE ON MODAL PROPERTIES AND INDICATORS The benchmark used or the assessment o above requency-based damage indicators is that proposed in Benjeddou et al. (006); it consists o a -ply symmetric laminated composite beam with dimensions L B H = 00 0 mm and symmetric stacking sequence o [0 /90 8 /0 ] S, where bold plies are made o GFRP, while the others are in CFRP. Two piezoceramic (PZT-5A) patches, polarized along their thickness and o dimensions L a B H a = mm, are placed in replacement o bottom and top our 90 -plies at the length position o X a =.5 mm rom the beam let end. The sketched geometrical model shown in Fig. is meshed using D quadratic (0 nodes) elastic (displacement) SOLID9 and ully coupled piezoelectric SOLID6 05

4 (displacement-potential) FE or composite and piezoelectric layers, respectively, according to the subdivisions summarized in Table ; this leads to a FE mesh o 80 elements and 879 nodes. Materials data are given in Appendix A. The geometric and FE model are shown in Fig.. z H x L L a L X a Fig. Smart hybrid laminated beam sketch (red: PZT-5A, green: GFRP, gray: CFRP) Table D FE discretization o the smart hybrid healthy laminate composite beam Healthy beam Geometric parameter Dimension (mm) Number o elements Size o elements (mm) Host composite L 0.5 L a L B H PZT L a B a Hp Fig. Smart hybrid laminated composite beam (a) geometric and (b) FE D models Two types o damages are considered; the irst simulates a notch or crack, and is modeled by the removal o corresponding material, while the second simulates a 05

5 delamination and is modeled by an inclusion o a sot layer made o a thin Telon ilm. The corresponding geometrical sketches are shown in Fig., while their FE mesh details are provided in Table, leading to elements and 77 nodes or the RM model, and 80 elements and 879 nodes or the ISL one; they are shown in Fig.. Ld z Hd H x X L Xa La Xd L L (a) Notched (RM: [X d L d H d ] = [80 5.5] mm) beam Ld z Hd Hd H x L Xa La Xd L L L (b) Delaminated (ISL: [X d L d H d ] = [80 5 ] mm) beam Fig. Damaged hybrid composite beam (red: PZT-5A, green: GFRP, gray: CFRP) Table D FE discretization o the damaged smart hybrid composite beam Damaged beam Geometric parameter Dimension (mm) Number o elements Size o elements (mm) Host composite L 0.5 L a L L B H 0.5, PZT L a B a Hp Notched (RM) damage Delamination (ISL) damage L d 5.5 B d H d L d 5.5 B d H d

6 (a) RM D geometric model (b) RM D FE model (c) ISL D geometric model (d) ISL D FE model Fig. Damaged hybrid composite beam (a,c) geometric and (b,d) FE D models The FE simulations have been conducted or the healthy and damage (RM and ISL) smart hybrid laminated composite beam under our mechanical BC (CF, CS, CC, SS) and two electric conditions (SC, OC). The obtained results are shown in Table, where bold values indicate electromechanically uncoupled modes since there is no dierence between SC and OC values (tenth or hundredth Hz dierences are only numerical). Worthy to mention that clamping is obtained by ixing the FE three displacements (translations) degrees o reedom (DOF) to zero values, while simply-supported condition is modeled here by letting ree only the axial displacement (translation) DOF. From the results, it can be observed that (i) only the RM damage changes the modes types or only the CF BC; (ii) the modes electromechanical coupling is not aected by the damage since the healthy uncoupled x-y in-plane bending and torsion modes remain uncoupled or the damaged (RM and ISL) beams; hence, only the transverse () bending modes are coupled and aected by the damage; (iii) in contrary to the RM damage model, the ISL one does not aect the mode order and type; care should be then taken when using RM model or the damage simulation under CF BC since it aects the modes types and order (see modes,, 7, 8 o this case); (iv) the CS, CC and SS BC have dierent modes types than the CF one; besides, the SS BC case has dierent rd and th modes types than CS and CC BC which have the same modes types; hence, it appears clearly that the popular numerical CF and analytical SS BC are not the best ones or studying theoretically (numerically or analytically) the VBDD perormance in D modeling which is the realistic way o simulating actual damaged structures which have intrinsically a D response; the best BC rom this point o view are then CS and CC, with a preerence to the latter due to its practical interest. 055

7 Table First 8 requencies (Hz) o healthy and damaged smart hybrid composite beams Mode Healthy requencies (Hz) RM requencies (Hz) ISL requencies (Hz) BC order Type SC OC Type SC OC Type SC OC CF xy xy t t xy CS t xy t xy t t xy t xy t t t CC t xy t t SS xy t t xy t t xy t t t t t t t xy t xy t t t xy t t xy t t t Processing SC and OC requency results o Table provides SC and OC FCF (Eqs. and ) and squared FCF (Eqs. 5 and 6) ones given in Table. The latter indicates or FCF indicators that: (i) due to the more structural degradation, RM indicators have much higher values than ISL ones, although both o them remain low (less than 5%); (ii) RM indicators are mostly positive, while ISL ones are mostly negative, indicating that in contrary to the RM damage which decreases the healthy requencies (see Eq. ), the ISL damage increases the healthy requencies (Eq. ); (iii) OC and SC indicators 056

8 highest values (in bold) are obtained or transverse bending modes under all BC or RM damage, but or the irst membrane mode or the ISL damage under all BC, except the SS case; (iv) SC and OC FCF maximum values can be dierent or the RM damage model but are the same or the ISL one. Table First 8 modes FCF damage indicators (%) o the smart hybrid composite beams Damage model RM ISL Mode FCF (%) Squared FCF (%) FCF (%) Squared FCF (%) BC type SC OC SC OC SC OC SC OC CF xy t t xy CS t xy t t CC t xy t t SS xy t t t For the squared FCF, it is ound that these indicators are much more perormant (having much higher values) or indicating both RM and ISL damages than the FCF 057

9 ones; they are then retained or the subsequent parametric analyses; thereore, since SC and OC values are ound to be close to each other, ocus is made mainly on SC squared FCF in order to get reerence with earlier D results (Benjeddou et al. 006).. DAMAGE DETECTION INDICATORS PARAMETRIC ASSESMENT In order to check the validity o above obtained results or ixed MR and ISL damage characteristics o [X d L d H d ] = [80 5.5] mm and [80 5 ] mm, respectively, these parameters are varied according to the values summarized in Table 5. Table 5 Damage characteristics variations or the parametric analysis o damaged smart hybrid composite beams Model parameters X d (mm) L d (mm) H d (mm) case X d /L L d /L H d /H RM ISL 60 (ixed) (ixed) The D simulations are then conducted under the previously investigated our mechanical BC o the damaged hybrid composite beams and two electric conditions on the patches electrodes. It s worth noticing that, or the ISL damage model, the number and thickness o Telon layers vary in terms o the damage geometric characteristics. Due to the space limitation, only the irst mode CF BC related SC squared FCF results, or normalized damages characteristics (X d /L, L d /L, H d /H), are shown or the RM and ISL in Fig. 5. The latter indicates that: (i) or all parametric analysis cases, RM damage is much more inluential on the SC FCF indicator than does the ISL one; (ii) or a ixed damage position (case ), SC FCF indicator increases or both damages when increasing the latters length and height, but more rapidly or the ormer than or the latter; (iii) or ixed damage length (case ) and thickness (case ), SC FCF indicator behaves oppositely or RM and ISL damages when varying the damages positions; it is higher or RM at the beam root, while it is lower or ISL at this position. Maximum reached squared FCF values or both damages models, our BC and two electric conditions are summarized in Table 6. It can be noticed that: (i) RM induced squared FCF is much higher than ISL one; (ii) maximum values are obtained or the CF BC or both damage models but with dierent values and or dierent modes and damages characteristics; SC and OC squared FCF reach the same maximum values and or the same modes, except or ISL under CF. 058

10 Case Case Case Fig. 5 SC squared FCF parametric analysis or mode o CF hybrid composite beams Table 6 Damage characteristics o maximum reached squared FCF indicators Damage Indicator Characteristics CF CS CC SS RM SC [X d, L d, H d ] [0 0.5] [00 0.5] [00 0.5] [00 0.5] (%, mode) (.0; 6) (9.08; 6) (0.6; 6) (0.07; 6) OC [X d, L d, H d ] [0 0.5] [00 0.5] [00 0.5] [00 0.5] (%, mode) (.0; 6) (9.08; 6) (0.6; 6) (0.07; 6) ISL SC [X d, L d, H d ] [60 0 ] [0 0 ] [00 0 ] [00 0 ] (%, mode) (-7.0; ) (-6.6; ) (-6.58; ) (-5.8; ) OC [X d, L d, H d ] [60 0 ] [0 0 ] [00 0 ] [00 0 ] (%, mode) (-6.5; ) (-6.7; ) (-6.58; ) (-5.8; ) 059

11 . CONCLUSIONS This contribution presented short-circuit (SC) and open-circuit (OC) simple and squared requency change actors (FCF) or the damage detection in hybrid laminated composite beams using piezoceramic patches integrated in a symmetrical coniguration. The structural damage was modeled using removal o material (RM), simulating a notch or crack, and inclusion o sot layer (ISL), simulation a delamination The proposed damage indicators perormance analysis was investigated using three-dimensional ully coupled piezoelectric inite elements (FE) under our mechanical boundary conditions and or varying damage geometric characteristics (position, length and height). It was ound that the squared FCF are much more perormant than the classical simple ones; also, both damage indicators were ound to be much more inluenced by varying the RM model characteristics than the ISL ones; besides, it was shown that the popular numerical cantilever and analytical simple support boundary conditions (BC) are not suitable or investigating theoretically requency-based RM damage detection since in these cases, changes o modes order and type occur, rendering the obtained results speciic and not generalizable to other BC; it is then recommended or numerical analysis, to preer clamped-clamped BC or these and or practical reasons. As an extension o the present work, modal energy-based damage indicators have been explored; or space limitation, corresponding results will be presented separately. ACKNOWLEDGMENTS Support o the irst author rom the Comet-K Austrian Centre o Competence in Mechatronics (ACCM) at Linz (Austria) is grateully acknowledged. REFERENCES Al-Ajmi, M.A. and Benjeddou, A. (008), Damage indication in smart structures using modal eective electromechanical coupling coeicients. Smart Mater. Struct., 7(), art. n 050 (5 pages). Benjeddou, A. (006), First use o the shear piezoceramics and eective electromechanical coupling coeicient or damage detection and characterization, Proceedings o rd European Workshop on Structural Health Monitoring, Granada. Benjeddou, A., Vijayakumar, S. and Tawiq, I. (006), A new damage identiication and quantiication indicator or piezoelectric advanced composites, Proceedings o the rd ECCM on Solids. Structures and Coupled Problems in Engineering, Lisbon. Giurgiutiu, V., Lin, B., Santonni-Bottai, G. and Cuc, A. (0), Space application o piezoelectric waer sensors or structural health monitoring, J. Intell. Mater. Syst. Struct., (8), Huang, G., Song, F. and Wang, X. (00), Quantitative modeling o coupled piezoelasto-dynamic behavior o piezoelectric actuators bonded to an elastic medium or structural health monitoring: a review, Sensors, 0, Ihn, J.B. and Chang, F.K. (008), Pitch-catch active sensing methods in structural health monitoring or aircrat structures, Struct. Health Monit., 7(),

12 Jian, X.H., Tzou, H.S., Lissenden, C.J. and Penn, L.S. (997), Damage detection by piezoelectric patches in a ree vibration method, J. Compos. Mater., (), Penn, L.S., Jump, J.R. and Geenield, M.J. (999), Use o ree vibration spectrum to detect delamination in thick composites, J. Compos. Mater., (), 5-7. Qian. P., Lestari. W., Shah, M.G. and Wang, J. (007), Dynamics-based damage detection o composite laminated beams using contact and non-contact measurement systems, J. Compos. Mater., (0), 7-5. Sinou, J.J. (009), A review o damage detection and health monitoring o mechanical systems rom changes in the measurements o linear and nonlinear vibrations, In Sapri R.C, (Ed.), Mechanical vibrations: measurement, eects and control, Nova Sci. Pub., Chap., Tan, P. and Tong, L. (00), Delamination detection o composite beams using piezoelectric sensors with evenly distributed electrode strips, J. Compos. Mater., 8(), -5. Yam, L.H., Wei, Z. and Cheng, L. (00), Nondestructive detection o internal delamination by vibration-based method or composite plates, J. Compos. Mater., 8(), APPENDIX A Table 7 Materials properties Elastic E (GPa) E (GPa) E (GPa) G (GPa) G (GPa) G (GPa) CFRP (M55J/9) GFRP (G87/9) Telon PZT-5A Piezoelectric e (C/m ) e (C/m ) e (C/m ) e 5 (C/m ) e (C/m ) s s s 0 (pf/m) PZT-5A

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