The piezoelectric transducers (PZT) are bonded to smart structures by means of an intermediate adhesive layer, with the main objectives of applying methodologie s of structural health monitoring, nondestructive evaluation, nondestructive inspection and structural control to the structures. However, the application of these methodologies depends on the health of the adhesive joint that couples mechanically the PZT with the structure. This research shows an experimental technique based on the segmentation of electrodes of a PZT patch in sheet form. One electrode is segmented in thre e equal parts (end left, middle and end right) to obtain three electrical signatures o f a PZT. The electrical signatures (voltage) of the end electrodes are related to the middle electrode voltage. Three experiments were carried out in this study: two static cases and one dynamic case. For the static case, the left end (first case) and the right end (first case) were debonded. In the dynamic case, only one side was debonded. The results show that the voltage relations present linear behavior and the chang ing in the slope of the voltage ratio allow s identifying which electrode is debonded. Th is technique showed to be effective in the three studied cases of debonding and it could be used to identify debonding in real time. KEYWORDS: Debonding detection, piezoelectric transducers, segmented electrode, structural health monitoring. HECTOR A. T INOCO Mechanical Engineer , M.Sc. Universidad Autónoma de Manizales -UAM, C olombia htinoco @autonoma.edu.co ALBERTO L . SERPA Mechanical Engineer , Ph.D. Professor University of Campinas UNICAMP -Brazil serpa @fem.unicamp.br 1. INTRODUCTIO N Piezoelect ric transducers of Lead Zirconate Titanate (PZT) are used in structural engineering to apply monitoring methodologies in different types of structures, such as civil structures [ 1], aerospace structures [ 2], and among others [ 3]. Some methodologies applied are structural he alth monitoring ( SHM ) and nondestructive evaluation (NDE ) and these depend on the health of piezoelectric transducers to apply the monitoring task s. Usually , the piezoelectric transducers used for SHM and NDE are bonded wit h an adhesive layer to the host structure that will be either monitored or evaluated . Adhesive layer applied provide s the mechanical coupling in order to transfer the mechanical forces through it. Adhesive layer is considered an interfacial layer of finite thickness which is applied between the piezoelectric element and host structure (see Fig. 1) . Some techniques that use PZT in structures for detection, identification, quantification and damage localization are: EMI technique [ 4, 5-6], Lamb -wave - based techniques in S HM methodologies [ 7] and others. The application and reliability of the different techniques depend on the health of sensors and actuators , due to that the electrical signatures emitted by transducers can be influenced either by the properties of mechanica l coupling (geometric and physical properties of the adhesive layer) or by the debonding of the piezoelectric transducers . Despite that the geometrical properties of the adhesive layer influence the electrical signatures and it produces mechanical effects in the set (host structure, adhesive and P ZT) these have been studied to show that its effects can be controlled in the design (see [ 8]). Therefore, major attention has been paid in the last few years on the debonding of piezoelectric transducers . A study carried out by [9] shows that the control of smart structures can be affected by the occurrence of debonding. An analytical and experimental investigation was carried out to identify the effects of delamination on smart beams with bonded piezoelectric actu ators [10], and the results of this study showed that edge delaminations origin a decreasing in the natural frequency , however the interior delaminations do not produce d change . The study carried out by [11] also show ed that debonding effects influence th e electrical impedance of the piezoelectric sensor s. These authors established an algorithm for detecting debonding using optimization and these results can be applied in the EMI technique. In addition, [ 12] showed, by means of simulation that when active control is applied to smart beams, the effects of debonding of an actuator can significantly affect the passive and hybrid control. Recently, [ 13] provided a comprehensive theoretical study of the effect s of the debonding on the dynamic behavior of piezoel ectric actuators. Results showed that debonding defects modify the electromechanical coupling between the host structure and the piezoelectric actuator. In advance, a numerical study was carried out to show that the electrical performanc e of partially First International Conference on Advance d Mechatronics, Design , and Manufacturing Technology - AMDM 2012. 2 debonded sensors is diminished cause by the debonding [8]. Further , [14] show ed how the electrical performance of a piezoelectric sensor can be related to the debonding by means of the electrical power consumption of an electric circuit coupled to the set h ost structure, adhesiv e and piezoelectric sensor. This study analyzes how the power consumption can indicate debonding and how a piezoelectric sensor can be monitored by its electrical performance. Another method of debonding detection was proposed by [ 15], where a modified electro - mechanical impedance model of PZT actuator -sensor was proposed. The results of a modified model showed that if the bonding quality is reduced , the natural frequencies are modified and the frequency response augments its amplitude , as well as the EMI spectrum was perturbed with noise. A numerical example demonstrated the feasibility to use the modified model for debonding detec tion of piezoelectric patches. Recently, [ 16] shows a new method to monitor debonding of piezoelectric s ensors , which consists of segmenting the electrode of a piezoelectric sheet in three parts. Voltage relations between the segmented electrodes show a linear behavior and these relations correspond to force relations in electrodes , respectively . The results show ed that if debonding happens , the force relations in electrodes are influenced and the voltage relations vary. The technique was explained analytically. This r esearch shows a n experimental study that verifies if the voltage relations are linear in ele ctrodes. Further, voltage relations can help to identify edge delaminations as it was proposed by [16]. This study shows that the changing in the slope of linear relations indicates that one end of the electrode presents debonding. The proposed technique by [16] could be used for monitoring the bonding of piezoelectric sheets bonded to structures in an operational state. 2. THEORETICAL PRINCIPLES [16] 2.1 Equilibrium E quations The set shown in Fig. 1 is composed of a p iezoelectric sensor bonded to a host structure by means of an adhesive layer , which is submitted to external forces. Figur e 1. (a) Set structure, adhesive layer and piezoelectric - sensor. (b) Infin itesimal element dx of the set structure, adhesive layer and piezoelectric sensor [16]. The lengths of the piezoelectric senso r pl and the structure sl are finite along x axis and these are assumed to be equal . The width of the set is denoted by w (along y axis) and the thickness by h (along z axis). Subscripts , sp and a indicate structure, piezoelectric sensor and adhesive layer , respectively . The notation of subscripts is applied to all geometric and physical parameters defined . From Fig . 1 the equilibrium equations for the set are obtained , such that 2 2 2 2()( ) ( ), ()( ) ( ),s a a sp a s s a s s p aa ps a p p a p pd u x G Gu x u xh E h h E h dx d u x GGu x u xh E h h E h dx    (1) where ()pux and ()sux are the displacements, pE and sE are the elasticity modulus of the sensor and the structure . Equilibrium equations of Eq. ( 1) were solved by [16]. 2.1 Voltage Relations The electro -mechanical coupling of piezoelectric materials is express ed by constitutive laws (see [ 17]) of the following form , ,E p pq q kp k i ik k ik ksd D d e       (2) Where 2/iD C m is electric displacement, p is the strain vector (dimensionless), /kVm is the applied electric field vector, 2/kNm is the mechanical stress vector , /ike F m is the e lectric permittivity to constant stress, /kpd C N and /ikd C N are piezoelectric strain coefficients, and 2/E pqs m N is the elastic compliant to constant elect ric field. The piezoelectric sensor showed in Fig. 2 has the segmented electrode in the top part. The electrode is divided in three equal parts. In order to obtain voltages in each electrode ( 1,Le 1e and 1Re ), according to [18], the electric potential is determined for each electrode ( 12, VV and 3V) considering that each electrode acts as a capacitor , so we have that 1 2 1 3 210 2 3( ( ) ( )) , ( ( ) ( )) , ( ( ) ( )) ,lxx sp lxx spl lxx splV x x dx V x x dx V x x dx             (3) First International Conference on Advance d Mechatronics, Design , and Manufacturing Technology - AMDM 2012 . 3 where 15 a p p apd G w h hC , ()x sx and ()x px are strains . Figure 2. Equivalent system o f springs for the set structure, adhesive layer and piezoelectric sensor [16]. Figure 2 shows a set in which the piezoelectric patch has divided its electrode in three equal parts. In each segmented electrode we consider that there is two springs coupled in series of stiffness sK (structure) and pK (piezoelectric). The spring system presents linear behavior and it is established to approximate the displacements of each electrode and of each section of the structure. Therefore, it is assumed that each section 1,Le 1e and 1Re can be represented by 1 1 1 2 1 2 2 3 2 31 1 1 2 2 2 3 3 3, , .p pl s sl p pl l s sl l p pl l s sl lF K U K U F K U K U F K U K U     (4) It is important to point out that if the lengths of the electrodes are the same, we can assume that 1 2 3s s s sK K K K   and 1 2 3 .p p p pK K K K   Then , Eq. ( 4) is introduced in Eq. ( 3) and the following relations are obtained 13 1 2 3 2 221 1 1 1 , . 1 1 1 1s p s p s p s pFFK K K K V V V V FFK K K K                            (5) Reorganizing Eq. (5), we determine that 1 1 2 3 3 2 , , V V V V (6) where 1 1 2 /FF and 3 3 2 /FF are the force relations in electrodes. Those relations are directly proportional to the voltage of the middle electrode. Equation ( 6) shows that the el ectric potentials of the electrodes of the extremity are linear functions. Their slopes are the force relations in electrodes. 3. EXPERIMENTAL TEST In these experimental test s are evaluated the voltage relations in three cases, two static cases and one dynamic case. For both cases (static and dynamic) the applied forces are random, due to that the theory expose d by [16] demonstrates that the voltage relation s do not depend on external forces. The following material s are used for the experimental tests: 1. Adhesive: Epoxi resin . 2. Structure: Aluminium . 3. Data acquisition card (dSPACE) . 4. Piezoelectric transducer (PZT -5H). 5. Software: MATLAB. For the static test the forces applied are provided by a device called press. The segmentation of electrodes was carried on the top electrode that covers one side of the piezoelectric patch. Simply, the segmentation is a created discontinuity in the electrode. The top electrode was segmented in three equal parts , for the three specimens. Other works have used the segmentation of electrodes for energy harvesting, which are [ 19-20]. 3.1 Static Test for Specimens 1 and 2 Figure 3 shows the configuration for the specimens used in the static test. The specimen number 1 presents debonding in the left edge (see Table 1) and the specimen number 2 presents it in the right edge (see Table 2). Figur e 3. Characteristics of the specimen s. The applied forces to the specimens are random, since [16] explain that the voltage relations do not depend on external forces. Then, the principal aim is to identify that the side is debonded in the specimens using the voltage relations between electrodes. Table 1. Dimensions in mm of the specimen 1: static case (see Fig.3) . First International Conference on Advance d Mechatronics, Design , and Manufacturing Technology - AMDM 2012. 4 Table 2 . Dimensions in mm of the specimen 2: static case (see Fig.3) . Figur e 4 shows the results obtained for the voltage relation s in electrodes when applied random external forces in the specimen number 1 . The results for the slopes V1 and V3 indicate that the force relations for 1Le and 1Re are 12.46 and 23.36 times the force of the middle electrode (see Eq. ( 6)). The slope indicates the for ce relation in electrodes as described by [ 16]. This test confirm s that the voltage relation in elect rodes h ave a linear behavior (see Eq. ( 6)). Further, it is possible to identify which electrode is debonded, as explained by [16], where the voltage relation (slope) that is smaller will indicate debonded. This is due to the fact that initially the voltag e relations are equal and when the electrode is debonded the adhesive coupling lose s stiffness (see Eq. (4)). Therefore, in this case we can identify that the left electrode is debonded ( 12 ). For this test the induced debonding is 5 mm. The slopes were obtained using linear approximation s with correlation coefficients of 0.992 and 0.996 for V1 and V3. Figure 4. Characteristics of the specimen s. The same procedures that for the specimen number 1 were carried out f or the specimen number 2 . The results obtained from the voltage relation s in electrodes are shown in Fig. 5. The slopes V1 and V3 indicate that the force relations for 1Le and 1Re are 10.598 and 20.432 times th e force of the middle electrod e. Similar to the test number 1, the voltage relations are linear. Hence, we can identify that the electrode 1Re is debonded, since it presents a smaller slope than the electrode 1Le. Then, it is possible conclude that 21 . The correlation coefficients for the linear approximations are 0.999 and 0.999 for V1 and V3. The length of debonding induced was of 3 mm. Figure 5. Characteris tics of the specimen s. In both cases the prediction provided by voltage ratio was correct. In each case , the electrode that pre sented smaller voltage ratio was debonded. In piezoelectric patches the probability that th e debonding occurs in the ends is due to that the shear stresses are bigger there than along the patches , as explained by [ 8]. 3.2 Dynamic Test: Especimen 3 In this experimental test was used a data acquisition card USB 6211 National Instruments, the information was obtained by means of an algo rithm made in MATLAB . Figure 6. Characteristics of the specimen . Two piezoelectric patches with the segmented electrode were bonded to host structure as shown in Fig. 6. However, one patch presents debonding in the electrode number 3 and another patch is fully bonded. Between both patches, a n actuator is located for exciting the structure and so, to get measures of voltage in each First International Conference on Advance d Mechatronics, Design , and Manufacturing Technology - AMDM 2012 . 5 sensor. The voltage function applied to the actuator was chosen as ( ) 8sin( )V t t  [V]. (7) For Eq . (7)  is the frequency and t the time. Table 3 show s the geometric properties of the specimen used in this test . Table 3 . Dimensions in mm of the specimen 3 : dynamic cas e (see Fig.6) . For the sensor 1 (sensor fully bonded) the values of force relations obtained are 10.97 , 20.98 and these were approximated from voltages obtained of the sensor 1 (voltages in each electrode) . Those values were calculated using a linear regression . The voltage ratio functions are shown in Fig. 7. The values 1 and 2 determine that the slopes are parallel; this means that voltage relations are approximat ely equal. Figure 7. Voltage ratios obtained from the sensor 1, sensor fully bonded. Figure 7 demonstrates that if voltage ratios are equal, the mechanical coupling means fully bonded. In the contrary case , we can identify some changes in the mechanic al coupling when the debonding take place. For the sensor 2 (sensor partially bonded) the values of force relations obtained are 11.15 , 20.1426 and those were approximated from voltages obtained of the sensor 2 (vol tages in each electrode). A linear regression was applied for determining the voltage ratio functions shown in Fig. 8. The values 1 and 2 determine that electrode is debonded, such that 2 < 1. Therefore , we can conclude that the electrode 3 of the sensor 2 presents partial debonded, but it is not possible to quantify the value on it. In this case is evidenced that the methodology proposed by [ 16] works in the dynamic case, and this methodology helps to identify existence of debonding in the edges of piezoelectric patches. Figure 8. Voltage ratios obtained from the sensor 2, sensor partially bonded. 4. CONCLUSION S In this research the segmentation of elect rodes of piezoelectric patches was proposed to detect the debonding of it. However, the detection is limited only to the debonding of edges. Further, this study showed that volta ge ratio in electrodes presents a linear behavior. In three proposed cases fo r the experimental tests performed , the technique of segmentation of electrodes in three parts show to be effective to identify which electrode was debonded. Therefor e, it is possible that this technique c an be used in operational state, since the results were similar for the dynamic and static cases. Also, some effect s should be studied and understood , such as effects on the lateral debonding and which are the effects of the ratio in the length and the width of the patches to apply the proposed technique. 6.