- Email: [email protected]
The electric field, dc bias voltage and frequency dependence of actuation performance of piezoelectric fiber composites
Sensors and Actuators A 203 (2013) 304–309
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
The electric field, dc bias voltage and frequency dependence of actuation performance of piezoelectric fiber composites Xiujuan Lin, Kechao Zhou, Song Zhu, Ziqi Chen, Dou Zhang ∗ State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, PR China
a r t i c l e
i n f o
Article history: Received 15 May 2013 Received in revised form 14 September 2013 Accepted 14 September 2013 Available online 25 September 2013 Keywords: Piezoelectric fiber composites Actuation d33 Coefficient Voltage amplitude dc Bias voltage Frequency
a b s t r a c t The free strain performance of piezoelectric fiber composites (PFCs) and the PFCs’ capability of actuating a cantilever exhibited strong dependence on the excitation voltage, e.g., the voltage amplitude, dc bias voltage and frequency. The enhanced free strain performance was observed when a large voltage amplitude and low dc bias voltage were applied, owning to the increase of d33 piezoelectric coefficient. The PFCs showed better free strain performance under the quasi-static condition than dynamic conditions due to the frequency dependence of d33 piezoelectric coefficient. The influence of voltage amplitude and dc bias voltage on the actuation capability was similar to that on the free strain performance. However, for the customized cantilever structure, the first bending resonance existed definitely at around 25 Hz, which indicated that the mechanical effect was the key factor influencing the actuation performance at measured frequency range of 0.1–35 Hz. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Over the past few decades, development of smart materials and structures is a rapidly emerging field [1]. Piezoceramics received great interests in a wide range of smart applications due to their high actuation capability and sensing ability [2]. However, the inherent brittle nature and additional mass limited their application, particularly in areas such as curved or irregularly shaped surfaces and flexible or lightweight structures [3]. These limitations have motivated novel design and new types of piezoelectric materials for wider applications. Since the development of piezoelectric fiber composites (PFCs) with interdigitated electrodes (IDEs), the unique advantages of PFCs have attracted widespread attention. PFCs have layered structures comprising of unidirectional piezoceramic fibers, which have either circular or rectangular cross section and are embedded in the epoxy matrix [4,5]. The advantages of the thin nature of the fibers and the flexibility of the epoxy matrix provide the PFCs improved strength, conformability and toughness compared with monolithic piezoceramic wafers. An in-plane electric field can be applied via the interdigitated electrodes in PFCs to unidirectional, in-plane piezoceramic fibers, thus exploiting the d33 piezoelectric effect
∗ Corresponding author. Tel.: +86 731 88877196; fax: +86 731 88877196. E-mail address: [email protected] (D. Zhang). 0924-4247/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sna.2013.09.014
which is stronger than the d31 piezoelectric effect used by traditional piezoceramic actuators with through-the-thickness poling [6,7]. The unique structures ensure that PFCs are not only light weight and flexibile but also exhibit high actuation strain energy density. These benefits have provided PFCs a wide variety of applications, e.g., structural health monitoring systems, actuation, energy harvesting and active/passive vibration damping systems [8–12]. Recently an increasing number of investigations have been conducted on aspects of the piezoelectric and mechanical behavior of the PFCs. A finite element homogenization method was proposed for characterizing d15 coefficient of a shear actuated PFCs and evaluating the effective material properties [13]. The electroelastic properties of PFCs were evaluated using the asymptotic expansion approach [14]. The tensile and shear modulus, thermoelastic properties as a function of temperature and nonlinear actuation behaviors under a variety of mechanical load levels were provided in details for PFCs [15–17]. Though the properties of PFCs were given through either analytical or experimental researches, information about the actuation performance of PFCs under different electric field conditions is still limited. The aim of the present work is to study the free strain and actuation performances of PFCs with the variation of excitation voltage amplitude, dc bias field and frequency. The influence of these factors on the effective piezoelectric coefficient d33 of PFCs derived from free strain was also investigated.
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309
305
Fig. 1. (a) Schematic diagram of the experimental setup for actuation measurement; (b) PFCs used in the experiment (active area of 28 mm × 8 mm).
2. Setup of experiments The experimental arrangement of the system was schematically shown in Fig. 1(a). The system was controlled by a computer using NI-LabView interfaces. A sine-wave voltage generated by a function generator (National Instruments) was amplified by a voltage amplifier (Smart Material Corp.), and then applied to the PFCs. The displacement was measured by a laser sensor (Micro-Epsilon Messtechnik GmbH). Monitoring of the laser probe data and control of the amplifier voltage were made using an acquisition card and LabView software. The LabView interfaces were designed to allow for the required voltage pattern, the maximum and minimum applied voltages, excitation frequencies. The standard electrical resistance foils strain gages (Jinan Sigmar Tech Co., Ltd., China) were bonded to the center of the top and bottom of mechanically unconstrained PFCs to obtain both longitudinal and transverse strains simultaneously. These data were used to characterize the free strain performance under unloaded operating conditions. In order to characterize the actuation capabilities, the substrate material was chosen as a flexible Mylar (DuPont Teijin Films) beam of 0.125 mm thickness, 25 mm width and 75 mm length. Young’s modulus and the mass density of Mylar substrate were taken as 3.5 GPa and 1.39 g/cm3 [18], respectively. The PFCs was bonded to the substrate in a region of 18–46 mm from the fixed end. The laser sensor was placed 68 mm from the fixed end to measure the tip displacement of the customized cantilever. The actuation experiments were conducted at seven different excitation voltage levels with three different dc bias voltages at frequencies from 0.1 to 50 Hz. For example, given that the PFCs had a typical voltage input range of −500 V to +1500 V, the maximum excitation voltage amplitude was 2000 V with a +500 V dc bias voltage. The excitation voltage amplitudes were between 500 V and 2000 V in 250 V increments. And the average value of thirty stable cycles were obtained and used for further evaluation. The PFCs with an active area of 28 mm × 8 mm and an electrode spacing of 0.5 mm were fabricated by viscous polymer processing [19], as shown in Fig. 1(b). The piezoceramic material used for the fabrication of PFCs was soft PZT-51.
Fig. 2. The free strain performance of PFCs under −500 V to +1500 V at 0.1 Hz.
of PFCs reached 1900 microstrain in the longitudinal direction and about 930 microstrain in the transversal direction, respectively. Fig. 3 shows the peak-to-peak free strain of PFCs in the longitudinal direction at 0.1 Hz as a function of excitation voltage amplitudes and dc bias voltages. The free strain performance showed strong dependency on the applied voltage conditions, and increased in a nonlinear manner significantly with the increase of excitation voltage amplitude. When the smallest voltage range of 0 to +500 V was applied, the free strain retained about 162 microstrain, which demonstrated that PFCs still had relative good actuation performance even under low electric field. As the voltage amplitude
3. Results and discussion Fig. 2 shows the free strain performance under excitation voltage range of −500 V to +1500 V at 0.1 Hz. The results demonstrated a nonlinear hysteretic behavior between the actuation strain of the PFCs and the applied voltage, which was typically observed in piezoceramic actuators. PFCs actuators with high levels of free strain capability and actuation anisotropy also demonstrated great suitability to the design of tailored smart structures. The free strain
Fig. 3. The free strain performances of PFCs under different voltage amplitudes and dc bias voltages at 0.1 Hz.
306
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309
Fig. 5. Vertical section of PFCs with IDEs, qualitatively illustrating the distribution of the electric field lines.
piezoelectric coefficient and its associated hysteresis loop across a wide range of applied loads. d33 = d0 + ˛1 F0 + ˇ1 F02 Fig. 4. The d33 coefficients of PFCs under different voltage amplitudes and dc bias voltages at 0.1 Hz.
increased to 2000 V, the free strain increased sharply to 1900 microstrain. Additionally, significant changes in free strain performance were observed along with variation of the dc bias voltage. The values of peak-to-peak free strain were consistently higher for 0 V dc bias voltage than those for 250 V and 500 V dc bias voltages, indicating that smaller dc bias voltages were in favor of significantly enhancing the free strain performance. For instance, the free strain at 1000 V voltage amplitudes showed a marked decrease of around 27.8%, i.e. from 690 to 540 microstrain, with the increase of dc bias voltage from 0 to 500 V, respectively. The longitudinal strain response to the electric field related to the piezoelectric coefficient, which was the most important factor inducing the significant diversification in the free strain performance [20]. The piezoelectric coefficient d33 was typically used to characterize the actuation performance of PFCs. Using Eq. (1) [3], d33 was calculated for each of the applied voltage under the free strain condition, where s3 was the mechanical strain in the longitudinal direction, E3 was the electric field amplitude. d33 =
s3 E3
(1)
The d33 coefficients of PFCs as a function of the applied voltage amplitude with 0 V, 250 V and 500 V dc bias voltages were shown in Fig. 4. Similar to the trend of free strain performances, d33 coefficients were also highly dependent on applied voltage conditions. The d33 coefficient under high electric field was almost three times the magnitude of that under low electric field. As the applied voltage amplitude increased, a significant nonlinear increase in d33 coefficient was observed. The second order polynomials (2) were used to fit the experimental data and to represent the nonlinear relationship.
(3)
where F0 was the field amplitude. And this nonlinear relationship could be explained by the following two factors. Firstly, soft PZT-51 was characterized by a high piezoelectric coefficient and mobile domain boundaries. Larger electric field enhanced the domain switching, which led to the increase of d33 coefficients [23]. Secondly, the unique electrode structure led to the unique electric field profile, as depicted in Fig. 5. The electric field strength in PFCs was distinctly inhomogeneous. The zone between each pair of electrode fingers could be subdivided to three different regions: an active zone between the electrodes with homogeneous electric field, an ineffective zone in the range beneath the fingers with vanishing electric fields which was also called “dead zone” and a transition zone in the range between the active zone and the ineffective zone [24]. For the strain being induced by the electric field, the transition zone contributed much less actuation strain of PFCs due to the weak electric filed strength in the longitudinal direction, while the dead zone did not contribute to the actuation strain. Therefore, the effective electric field in PZT fiber for actuating PFCs was smaller than the actual applied electric field. And this relationship became more significant in the case of lower electric field since the existence of a thin interlayer between IDE finger and PZT fiber weakened the electric field strength to some extent [19]. Besides the voltage amplitude, the dc bias voltage also had a great influence on d33 coefficients. As suggested by Masys et al. [23], the clamping of domain wall motion with the application of dc bias voltages reduced the piezoelectric response of the material, thus leading to the decrease of d33 coefficients.
d33 = −112.9 + 0.88U − 4.18E−4 U2 (500 v ≤ U ≤ 1000 v) d33 = 24.4 + 0.39 U − 7.5E−5 U2 (500 v ≤ U ≤ 1500 v) −5
d33 = 78.0 + 0.16U + 1.80E
(2)
2
U (500 v ≤ U ≤ 2000 v)
The yielded R2 values during the nonlinear fitting procedure were 0.999, 0.972 and 0.994 for three different applied voltages, respectively. Eq. (2) demonstrated that the nonlinearities between the applied voltage amplitude and the d33 coefficient were in good agreement with what were predicted by Eq. (3) according to the Preisach approach [21,22], which had been widely used to describe the observed quadratic field dependence of the direct longitudinal
Fig. 6. Free strain actuation performances of PFCs under different frequency with 500 V dc bias voltage.
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309
307
Fig. 7. (a) The free strain performances and (b) d33 coefficients of PFCs at 750 V with different frequencies.
Fig. 6 shows the variation of free strain performance of PFCs as a function of the frequency at different voltage amplitudes with 500 V dc bias voltages. As discussed previously, free strain performance changed dramatically with the variation of voltage amplitude. Moreover, the most defining feature of results was the frequency dependence of free strain performances. The free strain values decreased dramatically in the frequency range of ≤5 Hz, for frequency above this limit a slight decrease was observed, especially under larger electric field. The results showed that when the voltages of −500 V to +1500 V were applied to PFCs, the free strain decreased from 1900 to 1565 microstrain, i.e. a decrease of 17.6% with the increase of the frequency from 0.01 Hz to 5 Hz, while the free strain further decreased to 1406 microstrain at 50 Hz, corresponding to a total decrease of 26.0%. However, the free strain decreased by only about 12.5% from 0.01 Hz to 50 Hz when +250 V to +750 V was applied. These comparative results obviously indicated that the frequency dependence of free strain performance was enhanced significantly under high electric field. In order to further characterize the influence of both frequency and dc bias voltage on the free strain performance, the voltage amplitude of 750 V with dc bias voltages of 0 V, 250 V and 500 V was applied, respectively. Besides considering the influence of frequency and bias voltage separately, the combined influences of the two factors on the free strain performances and d33 were shown in Fig. 7. As the frequency increased from 0.01 Hz to 50 Hz, the free strain decreased by 37.6% under 0 V dc bias voltage, from 466 microstrain to 291 microstrain, whereas the free strain decreased by 17.1% under 500 V dc bias voltages, from 314 microstrain to 260
microstrain. Therefore, the free strain performance showed more significant dependency on the frequency under smaller dc bias voltage. Fig. 7(b) shows that the effective piezoelectric coefficient d33 decreased monotonically with the logarithm of the frequency and could be well represented with the linear equation: d33 = d0 + ˛2 × ln (w)
(4)
where w was the frequency, d0 and ˛2 were −263.6, 247.9, 200.4 and −42.3, −36.0, −13.6 for 0 V, 250 V and 500 V dc bias voltages, respectively. The linear fitting procedure took into consideration the error at each data point and the yielded R2 were 0.987, 0.996 and 0.942 for 0 V, 250 V and 500 V dc bias voltages, respectively. The frequency dispersion of the d33 coefficients can be explained by considering the time dependence of the extrinsic response of PZT. As discussed by Seshadri et al. [25] and Masys et al. [23], the non-180◦ domain changes took a finite time to occur. Masys et al. revealed that at any frequency, following up the changing electric field was a contribution criteria of the domain wall motion toward the strain [25]. Therefore fewer domains had time to realign at higher frequency, which induced smaller piezoelectric response [23,25]. Fig. 8 shows the influence of the input voltage conditions, e.g. the voltage amplitude, dc bias voltage and frequency on the actuation performance of a cantilever bonded with the PFCs. With an applied input voltage, the PFCs started to expand on top of the cantilever and a bending strain was induced. The tip displacement value of the cantilever increased significantly at 0.1 Hz with the increase of the voltage amplitude and the decrease of the dc bias voltage,
Fig. 8. The tip displacement of a cantilever actuated by the PFCs (a) at 0.1 Hz under different voltage amplitudes and dc bias voltages, (b) at different frequencies.
308
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309
Acknowledgments This work was financially supported by the Natural Science Foundation of China (No. 51072235), Hunan Provincial Natural Science Foundation of China (No. 11JJ1008), Ph.D. Programs Foundation of Ministry of Education of China (No. 20110162110044) and Hunan Provincial Innovation Foundation for Postgraduate (No. CX2012B041).
References
Fig. 9. The modeling result of the first bending mode for the customized cantilever.
as shown in Fig. 8(a). Similar results were obtained at frequencies below 10 Hz. These results showed that the trend of actuation performances with the voltage amplitude and bias voltage was the same as the free strain. In views of free strain performance, it can be concluded that at low frequency, especially under the quasi-static condition, the piezoelectric effect is the most important factor influencing the actuation performance. However, the influence of frequency on the actuation performance was definitely different from that on the free strain, as shown in Fig. 8(b). The tip displacement of the cantilever enhanced dramatically at around 25 Hz regardless of the input voltage amplitude and dc bias voltage. In order to explain this phenomenon, the first vibration mode of this cantilever was modeled using ANSYS. The result showed that 22.1 Hz was the first bending mode of the cantilever, as shown in Fig. 9. The small discrepancy between the experimental result and modeling result was due to the negligence of the assembling polymer membranes, i.e. 0.1 mm thick polyimide film in our PFCs samples, in the modeling. The thin polymer membrane could affect the stiffness of the PFCs, and the cantilever. Different from the piezoelectric effect on the free strain performance, the mechanical effect of cantilever played more important role than the piezoelectric effect in influencing the actuation performance, especially at frequencies above 10 Hz.
4. Conclusion The free strain value and tip displacement of the cantilever were used to demonstrate the influences of input voltage conditions, e.g., voltage amplitude, dc bias voltage and frequency on the free strain performance of PFCs and the capability of actuating the cantilever, respectively. The increases of domain switching of soft PZT and effective electric field in the PZT fibers under larger electric fields enhanced the d33 piezoelectric coefficient, which induced higher free strain performance and actuation capability. The decrease of d33 coefficient due to the clamping of domain wall motion caused by large dc bias voltage weakened the free strain performance and actuation capability. Due to the time dependence of domain wall motion of soft PZT, the free strain performance decreased with the increase of frequency. However, bending resonance of the customized cantilever existed definitely at 25.0 Hz, which was verified by FEM modeling indicating that the mechanical effect was the key factor influencing the actuation performance at relatively low frequency range of 0.1–35 Hz.
[1] M. Karpelson, G.Y. Wei, R.J. Wood, Driving high voltage piezoelectric actuators in microrobotic applications, Sensors and Actuators A: Physical 176 (2012) 78–89. [2] S.C. Shen, P.C. Tsai, Y.J. Wang, H.J. Huang, A new type of multi-degreeof-freedom miniaturization actuator using symmetric piezoelectric pusher element for a pocket sun-tracking system, Sensors and Actuators A: Physical 182 (2012) 114–121. [3] A.A. Bent, Active Fiber Composite for Structural Actuation, Massachusetts Institute of Technology, Cambridge, 1997, pp. 19–25. [4] V.K. Wickramasinghe, N.W. Hagood, Durability characterization of active fiber composite actuators for helicopter rotor blade applications, Journal of Aircraft 41 (2004) 931–937. [5] M. Melnykowycz, X. Kornmann, C. Huber, M. Barbezat, A.J. Brunner, Performance of integrated active fiber composites in fiber reinforced epoxy laminates, Smart Materials and Structures 15 (2006) 204–212. [6] N. Hagood, R. Kindel, K. Ghandi, P. Gaudenzi, Improving transverse actuation of piezoceramics using interdigitated surface electrodes, in: Smart Structures and Materials, Smart Structures and Intelligent Systems, 1993, pp. 341–352. [7] A.A. Bent, N.W. Hagood, J.P. Rodgers, Anisotropic actuation with piezoelectric fiber composites, Journal of Intelligent Material Systems and Structures 6 (1995) 338–349. [8] A. Belloli, D. Niederberger, S. Pietrzko, M. Morari, P. Ermanni, Structural vibration control via R-L shunted active fiber composites, Journal of Intelligent Material Systems and Structures 18 (2007) 275–287. [9] P.A. Tarazaga, D.J. Inman, W.K. Wilkie, Control of a space rigidizable inflatable boom using macro-fiber composite actuators, Journal of Vibration and Control 13 (2007) 935–950. [10] A.J. Brunner, M. Birchmeier, M.M. Melnykowycz, M. Barbezat, Piezoelectric fiber composites as sensor elements for structural health monitoring and adaptive material systems, Journal of Intelligent Material Systems and Structures 20 (2009) 1045–1055. [11] H.J. Song, Y.T. Choi, N.M. Wereley, A.S. Purekar, Energy harvesting devices using macro-fiber composite materials, Journal of Intelligent Material Systems and Structures 21 (2010) 647–658. [12] H.P. Konka, M.A. Wahab, K. Lian, Piezoelectric fiber composite transducers for health monitoring in composite structures, Sensors and Actuators A: Physical 194 (2013) 84–94. [13] M.A. Trindade, A. Benjeddou, Finite element homogenization technique for the characterization of d15 shear piezoelectric macro-fibre composites, Smart Materials and Structures 20 (2011) 1–17. [14] F. Biscani, H. Nasser, S. Belouettar, E. Carrera, Equivalent electro-elastic properties of Macro Fiber Composite (MFC) transducers using asymptotic expansion approach, Composites Part B: Engineering 42 (2011) 444–455. [15] R.B. Williams, D.J. Inman, W.K. Wilkie, Nonlinear response of the macro fiber composite actuator to monotonically increasing excitation voltage, Journal of Intelligent Material Systems and Structures 17 (2006) 601–608. [16] R.B. Williams, D.J. Inman, W.K. Wilkie, Temperature-dependent thermoelastic properties for macro fiber composite actuators, Journal of Thermal Stresses 27 (2004) 903–915. [17] R.B. Williams, D.J. Inman, M.R. Schultz, M.W. Hyer, W.K. Wilkie, Nonlinear tensile and shear behavior of macro fiber composite actuators, Journal of Composite Materials 38 (2004) 855–869. [18] http://usa.dupontteijinfilms.com/informationcenter/downloads/Physical And Thermal Properties.pdf [19] X.J. Lin, K.C. Zhou, T.W. Button, D. Zhang, Fabrication, characterization and modeling of piezoelectric fiber composites, Journal of Applied Physics 114 (2013) 0270151–270156. [20] R.B. Williams, D.J. Inman, W.K. Wilkie, Nonlinear actuation properties of Macro Fiber Composite actuators, in: ASME International Mechanical Engineering Congress, 2003, pp. 11–18. [21] G. Robert, D. Damjanovic, N. Setter, Preisach modeling of piezoelectric nonlinearity in ferroelectric ceramics, Journal of applied physics 89 (2001) 5067–5074. [22] G. Robert, D. Damjanovic, N. Setter, Preisach distribution function approach to piezoelectric nonlinearity and hysteresis, Journal of applied physics 90 (2001) 2459–2464. [23] A.J. Masys, W. Ren, G. Yang, B.K. Mukherjee, Piezoelectric strain in lead zirconate titante ceramics as a function of electric field, frequency, and dc bias, Journal of Applied Physics 94 (2003) 1155–1162.
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309 [24] C.R. Bowen, A. Bowles, S. Drake, N. Johnson, S. Mahon, Fabrication and finite element modeling of interdigitated electrodes, Ferroelectrics 228 (1999) 257–269. [25] S.B. Seshadri, A.D. Prewitt, A.J. Studer, D. Damjanovic, J.L. Jones, An in situ diffraction study of domain wall motion contributions to the frequency dispersion of the piezoelectric coefficient in lead zirconate titanate, Applied Physics Letters 102 (2013) 0429111–0429114.
Biographies Xiujuan Lin received the BE degree from Qingdao University of Science and Technology in 2008. She is currently pursuing her PhD in Materials Science in Central South University. Her current research interests are fabrication, characterization and applications of piezoelectric composites as actuators. Kechao Zhou received the PhD from Central South University in 1997. In 1998, he became a Professor in Central South University. His major research interests involve
309
the development of advanced materials for a range of industrial applications. He is currently serving as the Vice-President of Central South University and a member of the council of the Chinese Materials Research Society. Song Zhu received the BE degrees from Central South University in 2012. He is currently a postgraduate student in Central South University and works on numerical evaluation of piezoelectric ceramic and composites. Ziqi Chen received the BE degrees from Central South University in 2012. He is currently a postgraduate student in Central South University and works on the processing and characterization of piezoelectric composites. Dou Zhang received the BE and ME degrees from the Wuhan University of Technology, China in 1992 and 1995, respectively, and PhD degree from the University of Birmingham, U.K., in 2006. In 2004, he became a Research Associate and, in 2006, a Research Fellow in School of Metallurgy and Materials, University of Birmingham. In 2009, he joined Central South University, China, and was appointed as the Professor in 2010. His current research interests involve the fabrication and characterization of ferroelectric and piezoelectric ceramics, films, composites, and devices.
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
The electric field, dc bias voltage and frequency dependence of actuation performance of piezoelectric fiber composites Xiujuan Lin, Kechao Zhou, Song Zhu, Ziqi Chen, Dou Zhang ∗ State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, PR China
a r t i c l e
i n f o
Article history: Received 15 May 2013 Received in revised form 14 September 2013 Accepted 14 September 2013 Available online 25 September 2013 Keywords: Piezoelectric fiber composites Actuation d33 Coefficient Voltage amplitude dc Bias voltage Frequency
a b s t r a c t The free strain performance of piezoelectric fiber composites (PFCs) and the PFCs’ capability of actuating a cantilever exhibited strong dependence on the excitation voltage, e.g., the voltage amplitude, dc bias voltage and frequency. The enhanced free strain performance was observed when a large voltage amplitude and low dc bias voltage were applied, owning to the increase of d33 piezoelectric coefficient. The PFCs showed better free strain performance under the quasi-static condition than dynamic conditions due to the frequency dependence of d33 piezoelectric coefficient. The influence of voltage amplitude and dc bias voltage on the actuation capability was similar to that on the free strain performance. However, for the customized cantilever structure, the first bending resonance existed definitely at around 25 Hz, which indicated that the mechanical effect was the key factor influencing the actuation performance at measured frequency range of 0.1–35 Hz. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Over the past few decades, development of smart materials and structures is a rapidly emerging field [1]. Piezoceramics received great interests in a wide range of smart applications due to their high actuation capability and sensing ability [2]. However, the inherent brittle nature and additional mass limited their application, particularly in areas such as curved or irregularly shaped surfaces and flexible or lightweight structures [3]. These limitations have motivated novel design and new types of piezoelectric materials for wider applications. Since the development of piezoelectric fiber composites (PFCs) with interdigitated electrodes (IDEs), the unique advantages of PFCs have attracted widespread attention. PFCs have layered structures comprising of unidirectional piezoceramic fibers, which have either circular or rectangular cross section and are embedded in the epoxy matrix [4,5]. The advantages of the thin nature of the fibers and the flexibility of the epoxy matrix provide the PFCs improved strength, conformability and toughness compared with monolithic piezoceramic wafers. An in-plane electric field can be applied via the interdigitated electrodes in PFCs to unidirectional, in-plane piezoceramic fibers, thus exploiting the d33 piezoelectric effect
∗ Corresponding author. Tel.: +86 731 88877196; fax: +86 731 88877196. E-mail address: [email protected] (D. Zhang). 0924-4247/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sna.2013.09.014
which is stronger than the d31 piezoelectric effect used by traditional piezoceramic actuators with through-the-thickness poling [6,7]. The unique structures ensure that PFCs are not only light weight and flexibile but also exhibit high actuation strain energy density. These benefits have provided PFCs a wide variety of applications, e.g., structural health monitoring systems, actuation, energy harvesting and active/passive vibration damping systems [8–12]. Recently an increasing number of investigations have been conducted on aspects of the piezoelectric and mechanical behavior of the PFCs. A finite element homogenization method was proposed for characterizing d15 coefficient of a shear actuated PFCs and evaluating the effective material properties [13]. The electroelastic properties of PFCs were evaluated using the asymptotic expansion approach [14]. The tensile and shear modulus, thermoelastic properties as a function of temperature and nonlinear actuation behaviors under a variety of mechanical load levels were provided in details for PFCs [15–17]. Though the properties of PFCs were given through either analytical or experimental researches, information about the actuation performance of PFCs under different electric field conditions is still limited. The aim of the present work is to study the free strain and actuation performances of PFCs with the variation of excitation voltage amplitude, dc bias field and frequency. The influence of these factors on the effective piezoelectric coefficient d33 of PFCs derived from free strain was also investigated.
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309
305
Fig. 1. (a) Schematic diagram of the experimental setup for actuation measurement; (b) PFCs used in the experiment (active area of 28 mm × 8 mm).
2. Setup of experiments The experimental arrangement of the system was schematically shown in Fig. 1(a). The system was controlled by a computer using NI-LabView interfaces. A sine-wave voltage generated by a function generator (National Instruments) was amplified by a voltage amplifier (Smart Material Corp.), and then applied to the PFCs. The displacement was measured by a laser sensor (Micro-Epsilon Messtechnik GmbH). Monitoring of the laser probe data and control of the amplifier voltage were made using an acquisition card and LabView software. The LabView interfaces were designed to allow for the required voltage pattern, the maximum and minimum applied voltages, excitation frequencies. The standard electrical resistance foils strain gages (Jinan Sigmar Tech Co., Ltd., China) were bonded to the center of the top and bottom of mechanically unconstrained PFCs to obtain both longitudinal and transverse strains simultaneously. These data were used to characterize the free strain performance under unloaded operating conditions. In order to characterize the actuation capabilities, the substrate material was chosen as a flexible Mylar (DuPont Teijin Films) beam of 0.125 mm thickness, 25 mm width and 75 mm length. Young’s modulus and the mass density of Mylar substrate were taken as 3.5 GPa and 1.39 g/cm3 [18], respectively. The PFCs was bonded to the substrate in a region of 18–46 mm from the fixed end. The laser sensor was placed 68 mm from the fixed end to measure the tip displacement of the customized cantilever. The actuation experiments were conducted at seven different excitation voltage levels with three different dc bias voltages at frequencies from 0.1 to 50 Hz. For example, given that the PFCs had a typical voltage input range of −500 V to +1500 V, the maximum excitation voltage amplitude was 2000 V with a +500 V dc bias voltage. The excitation voltage amplitudes were between 500 V and 2000 V in 250 V increments. And the average value of thirty stable cycles were obtained and used for further evaluation. The PFCs with an active area of 28 mm × 8 mm and an electrode spacing of 0.5 mm were fabricated by viscous polymer processing [19], as shown in Fig. 1(b). The piezoceramic material used for the fabrication of PFCs was soft PZT-51.
Fig. 2. The free strain performance of PFCs under −500 V to +1500 V at 0.1 Hz.
of PFCs reached 1900 microstrain in the longitudinal direction and about 930 microstrain in the transversal direction, respectively. Fig. 3 shows the peak-to-peak free strain of PFCs in the longitudinal direction at 0.1 Hz as a function of excitation voltage amplitudes and dc bias voltages. The free strain performance showed strong dependency on the applied voltage conditions, and increased in a nonlinear manner significantly with the increase of excitation voltage amplitude. When the smallest voltage range of 0 to +500 V was applied, the free strain retained about 162 microstrain, which demonstrated that PFCs still had relative good actuation performance even under low electric field. As the voltage amplitude
3. Results and discussion Fig. 2 shows the free strain performance under excitation voltage range of −500 V to +1500 V at 0.1 Hz. The results demonstrated a nonlinear hysteretic behavior between the actuation strain of the PFCs and the applied voltage, which was typically observed in piezoceramic actuators. PFCs actuators with high levels of free strain capability and actuation anisotropy also demonstrated great suitability to the design of tailored smart structures. The free strain
Fig. 3. The free strain performances of PFCs under different voltage amplitudes and dc bias voltages at 0.1 Hz.
306
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309
Fig. 5. Vertical section of PFCs with IDEs, qualitatively illustrating the distribution of the electric field lines.
piezoelectric coefficient and its associated hysteresis loop across a wide range of applied loads. d33 = d0 + ˛1 F0 + ˇ1 F02 Fig. 4. The d33 coefficients of PFCs under different voltage amplitudes and dc bias voltages at 0.1 Hz.
increased to 2000 V, the free strain increased sharply to 1900 microstrain. Additionally, significant changes in free strain performance were observed along with variation of the dc bias voltage. The values of peak-to-peak free strain were consistently higher for 0 V dc bias voltage than those for 250 V and 500 V dc bias voltages, indicating that smaller dc bias voltages were in favor of significantly enhancing the free strain performance. For instance, the free strain at 1000 V voltage amplitudes showed a marked decrease of around 27.8%, i.e. from 690 to 540 microstrain, with the increase of dc bias voltage from 0 to 500 V, respectively. The longitudinal strain response to the electric field related to the piezoelectric coefficient, which was the most important factor inducing the significant diversification in the free strain performance [20]. The piezoelectric coefficient d33 was typically used to characterize the actuation performance of PFCs. Using Eq. (1) [3], d33 was calculated for each of the applied voltage under the free strain condition, where s3 was the mechanical strain in the longitudinal direction, E3 was the electric field amplitude. d33 =
s3 E3
(1)
The d33 coefficients of PFCs as a function of the applied voltage amplitude with 0 V, 250 V and 500 V dc bias voltages were shown in Fig. 4. Similar to the trend of free strain performances, d33 coefficients were also highly dependent on applied voltage conditions. The d33 coefficient under high electric field was almost three times the magnitude of that under low electric field. As the applied voltage amplitude increased, a significant nonlinear increase in d33 coefficient was observed. The second order polynomials (2) were used to fit the experimental data and to represent the nonlinear relationship.
(3)
where F0 was the field amplitude. And this nonlinear relationship could be explained by the following two factors. Firstly, soft PZT-51 was characterized by a high piezoelectric coefficient and mobile domain boundaries. Larger electric field enhanced the domain switching, which led to the increase of d33 coefficients [23]. Secondly, the unique electrode structure led to the unique electric field profile, as depicted in Fig. 5. The electric field strength in PFCs was distinctly inhomogeneous. The zone between each pair of electrode fingers could be subdivided to three different regions: an active zone between the electrodes with homogeneous electric field, an ineffective zone in the range beneath the fingers with vanishing electric fields which was also called “dead zone” and a transition zone in the range between the active zone and the ineffective zone [24]. For the strain being induced by the electric field, the transition zone contributed much less actuation strain of PFCs due to the weak electric filed strength in the longitudinal direction, while the dead zone did not contribute to the actuation strain. Therefore, the effective electric field in PZT fiber for actuating PFCs was smaller than the actual applied electric field. And this relationship became more significant in the case of lower electric field since the existence of a thin interlayer between IDE finger and PZT fiber weakened the electric field strength to some extent [19]. Besides the voltage amplitude, the dc bias voltage also had a great influence on d33 coefficients. As suggested by Masys et al. [23], the clamping of domain wall motion with the application of dc bias voltages reduced the piezoelectric response of the material, thus leading to the decrease of d33 coefficients.
d33 = −112.9 + 0.88U − 4.18E−4 U2 (500 v ≤ U ≤ 1000 v) d33 = 24.4 + 0.39 U − 7.5E−5 U2 (500 v ≤ U ≤ 1500 v) −5
d33 = 78.0 + 0.16U + 1.80E
(2)
2
U (500 v ≤ U ≤ 2000 v)
The yielded R2 values during the nonlinear fitting procedure were 0.999, 0.972 and 0.994 for three different applied voltages, respectively. Eq. (2) demonstrated that the nonlinearities between the applied voltage amplitude and the d33 coefficient were in good agreement with what were predicted by Eq. (3) according to the Preisach approach [21,22], which had been widely used to describe the observed quadratic field dependence of the direct longitudinal
Fig. 6. Free strain actuation performances of PFCs under different frequency with 500 V dc bias voltage.
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309
307
Fig. 7. (a) The free strain performances and (b) d33 coefficients of PFCs at 750 V with different frequencies.
Fig. 6 shows the variation of free strain performance of PFCs as a function of the frequency at different voltage amplitudes with 500 V dc bias voltages. As discussed previously, free strain performance changed dramatically with the variation of voltage amplitude. Moreover, the most defining feature of results was the frequency dependence of free strain performances. The free strain values decreased dramatically in the frequency range of ≤5 Hz, for frequency above this limit a slight decrease was observed, especially under larger electric field. The results showed that when the voltages of −500 V to +1500 V were applied to PFCs, the free strain decreased from 1900 to 1565 microstrain, i.e. a decrease of 17.6% with the increase of the frequency from 0.01 Hz to 5 Hz, while the free strain further decreased to 1406 microstrain at 50 Hz, corresponding to a total decrease of 26.0%. However, the free strain decreased by only about 12.5% from 0.01 Hz to 50 Hz when +250 V to +750 V was applied. These comparative results obviously indicated that the frequency dependence of free strain performance was enhanced significantly under high electric field. In order to further characterize the influence of both frequency and dc bias voltage on the free strain performance, the voltage amplitude of 750 V with dc bias voltages of 0 V, 250 V and 500 V was applied, respectively. Besides considering the influence of frequency and bias voltage separately, the combined influences of the two factors on the free strain performances and d33 were shown in Fig. 7. As the frequency increased from 0.01 Hz to 50 Hz, the free strain decreased by 37.6% under 0 V dc bias voltage, from 466 microstrain to 291 microstrain, whereas the free strain decreased by 17.1% under 500 V dc bias voltages, from 314 microstrain to 260
microstrain. Therefore, the free strain performance showed more significant dependency on the frequency under smaller dc bias voltage. Fig. 7(b) shows that the effective piezoelectric coefficient d33 decreased monotonically with the logarithm of the frequency and could be well represented with the linear equation: d33 = d0 + ˛2 × ln (w)
(4)
where w was the frequency, d0 and ˛2 were −263.6, 247.9, 200.4 and −42.3, −36.0, −13.6 for 0 V, 250 V and 500 V dc bias voltages, respectively. The linear fitting procedure took into consideration the error at each data point and the yielded R2 were 0.987, 0.996 and 0.942 for 0 V, 250 V and 500 V dc bias voltages, respectively. The frequency dispersion of the d33 coefficients can be explained by considering the time dependence of the extrinsic response of PZT. As discussed by Seshadri et al. [25] and Masys et al. [23], the non-180◦ domain changes took a finite time to occur. Masys et al. revealed that at any frequency, following up the changing electric field was a contribution criteria of the domain wall motion toward the strain [25]. Therefore fewer domains had time to realign at higher frequency, which induced smaller piezoelectric response [23,25]. Fig. 8 shows the influence of the input voltage conditions, e.g. the voltage amplitude, dc bias voltage and frequency on the actuation performance of a cantilever bonded with the PFCs. With an applied input voltage, the PFCs started to expand on top of the cantilever and a bending strain was induced. The tip displacement value of the cantilever increased significantly at 0.1 Hz with the increase of the voltage amplitude and the decrease of the dc bias voltage,
Fig. 8. The tip displacement of a cantilever actuated by the PFCs (a) at 0.1 Hz under different voltage amplitudes and dc bias voltages, (b) at different frequencies.
308
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309
Acknowledgments This work was financially supported by the Natural Science Foundation of China (No. 51072235), Hunan Provincial Natural Science Foundation of China (No. 11JJ1008), Ph.D. Programs Foundation of Ministry of Education of China (No. 20110162110044) and Hunan Provincial Innovation Foundation for Postgraduate (No. CX2012B041).
References
Fig. 9. The modeling result of the first bending mode for the customized cantilever.
as shown in Fig. 8(a). Similar results were obtained at frequencies below 10 Hz. These results showed that the trend of actuation performances with the voltage amplitude and bias voltage was the same as the free strain. In views of free strain performance, it can be concluded that at low frequency, especially under the quasi-static condition, the piezoelectric effect is the most important factor influencing the actuation performance. However, the influence of frequency on the actuation performance was definitely different from that on the free strain, as shown in Fig. 8(b). The tip displacement of the cantilever enhanced dramatically at around 25 Hz regardless of the input voltage amplitude and dc bias voltage. In order to explain this phenomenon, the first vibration mode of this cantilever was modeled using ANSYS. The result showed that 22.1 Hz was the first bending mode of the cantilever, as shown in Fig. 9. The small discrepancy between the experimental result and modeling result was due to the negligence of the assembling polymer membranes, i.e. 0.1 mm thick polyimide film in our PFCs samples, in the modeling. The thin polymer membrane could affect the stiffness of the PFCs, and the cantilever. Different from the piezoelectric effect on the free strain performance, the mechanical effect of cantilever played more important role than the piezoelectric effect in influencing the actuation performance, especially at frequencies above 10 Hz.
4. Conclusion The free strain value and tip displacement of the cantilever were used to demonstrate the influences of input voltage conditions, e.g., voltage amplitude, dc bias voltage and frequency on the free strain performance of PFCs and the capability of actuating the cantilever, respectively. The increases of domain switching of soft PZT and effective electric field in the PZT fibers under larger electric fields enhanced the d33 piezoelectric coefficient, which induced higher free strain performance and actuation capability. The decrease of d33 coefficient due to the clamping of domain wall motion caused by large dc bias voltage weakened the free strain performance and actuation capability. Due to the time dependence of domain wall motion of soft PZT, the free strain performance decreased with the increase of frequency. However, bending resonance of the customized cantilever existed definitely at 25.0 Hz, which was verified by FEM modeling indicating that the mechanical effect was the key factor influencing the actuation performance at relatively low frequency range of 0.1–35 Hz.
[1] M. Karpelson, G.Y. Wei, R.J. Wood, Driving high voltage piezoelectric actuators in microrobotic applications, Sensors and Actuators A: Physical 176 (2012) 78–89. [2] S.C. Shen, P.C. Tsai, Y.J. Wang, H.J. Huang, A new type of multi-degreeof-freedom miniaturization actuator using symmetric piezoelectric pusher element for a pocket sun-tracking system, Sensors and Actuators A: Physical 182 (2012) 114–121. [3] A.A. Bent, Active Fiber Composite for Structural Actuation, Massachusetts Institute of Technology, Cambridge, 1997, pp. 19–25. [4] V.K. Wickramasinghe, N.W. Hagood, Durability characterization of active fiber composite actuators for helicopter rotor blade applications, Journal of Aircraft 41 (2004) 931–937. [5] M. Melnykowycz, X. Kornmann, C. Huber, M. Barbezat, A.J. Brunner, Performance of integrated active fiber composites in fiber reinforced epoxy laminates, Smart Materials and Structures 15 (2006) 204–212. [6] N. Hagood, R. Kindel, K. Ghandi, P. Gaudenzi, Improving transverse actuation of piezoceramics using interdigitated surface electrodes, in: Smart Structures and Materials, Smart Structures and Intelligent Systems, 1993, pp. 341–352. [7] A.A. Bent, N.W. Hagood, J.P. Rodgers, Anisotropic actuation with piezoelectric fiber composites, Journal of Intelligent Material Systems and Structures 6 (1995) 338–349. [8] A. Belloli, D. Niederberger, S. Pietrzko, M. Morari, P. Ermanni, Structural vibration control via R-L shunted active fiber composites, Journal of Intelligent Material Systems and Structures 18 (2007) 275–287. [9] P.A. Tarazaga, D.J. Inman, W.K. Wilkie, Control of a space rigidizable inflatable boom using macro-fiber composite actuators, Journal of Vibration and Control 13 (2007) 935–950. [10] A.J. Brunner, M. Birchmeier, M.M. Melnykowycz, M. Barbezat, Piezoelectric fiber composites as sensor elements for structural health monitoring and adaptive material systems, Journal of Intelligent Material Systems and Structures 20 (2009) 1045–1055. [11] H.J. Song, Y.T. Choi, N.M. Wereley, A.S. Purekar, Energy harvesting devices using macro-fiber composite materials, Journal of Intelligent Material Systems and Structures 21 (2010) 647–658. [12] H.P. Konka, M.A. Wahab, K. Lian, Piezoelectric fiber composite transducers for health monitoring in composite structures, Sensors and Actuators A: Physical 194 (2013) 84–94. [13] M.A. Trindade, A. Benjeddou, Finite element homogenization technique for the characterization of d15 shear piezoelectric macro-fibre composites, Smart Materials and Structures 20 (2011) 1–17. [14] F. Biscani, H. Nasser, S. Belouettar, E. Carrera, Equivalent electro-elastic properties of Macro Fiber Composite (MFC) transducers using asymptotic expansion approach, Composites Part B: Engineering 42 (2011) 444–455. [15] R.B. Williams, D.J. Inman, W.K. Wilkie, Nonlinear response of the macro fiber composite actuator to monotonically increasing excitation voltage, Journal of Intelligent Material Systems and Structures 17 (2006) 601–608. [16] R.B. Williams, D.J. Inman, W.K. Wilkie, Temperature-dependent thermoelastic properties for macro fiber composite actuators, Journal of Thermal Stresses 27 (2004) 903–915. [17] R.B. Williams, D.J. Inman, M.R. Schultz, M.W. Hyer, W.K. Wilkie, Nonlinear tensile and shear behavior of macro fiber composite actuators, Journal of Composite Materials 38 (2004) 855–869. [18] http://usa.dupontteijinfilms.com/informationcenter/downloads/Physical And Thermal Properties.pdf [19] X.J. Lin, K.C. Zhou, T.W. Button, D. Zhang, Fabrication, characterization and modeling of piezoelectric fiber composites, Journal of Applied Physics 114 (2013) 0270151–270156. [20] R.B. Williams, D.J. Inman, W.K. Wilkie, Nonlinear actuation properties of Macro Fiber Composite actuators, in: ASME International Mechanical Engineering Congress, 2003, pp. 11–18. [21] G. Robert, D. Damjanovic, N. Setter, Preisach modeling of piezoelectric nonlinearity in ferroelectric ceramics, Journal of applied physics 89 (2001) 5067–5074. [22] G. Robert, D. Damjanovic, N. Setter, Preisach distribution function approach to piezoelectric nonlinearity and hysteresis, Journal of applied physics 90 (2001) 2459–2464. [23] A.J. Masys, W. Ren, G. Yang, B.K. Mukherjee, Piezoelectric strain in lead zirconate titante ceramics as a function of electric field, frequency, and dc bias, Journal of Applied Physics 94 (2003) 1155–1162.
X. Lin et al. / Sensors and Actuators A 203 (2013) 304–309 [24] C.R. Bowen, A. Bowles, S. Drake, N. Johnson, S. Mahon, Fabrication and finite element modeling of interdigitated electrodes, Ferroelectrics 228 (1999) 257–269. [25] S.B. Seshadri, A.D. Prewitt, A.J. Studer, D. Damjanovic, J.L. Jones, An in situ diffraction study of domain wall motion contributions to the frequency dispersion of the piezoelectric coefficient in lead zirconate titanate, Applied Physics Letters 102 (2013) 0429111–0429114.
Biographies Xiujuan Lin received the BE degree from Qingdao University of Science and Technology in 2008. She is currently pursuing her PhD in Materials Science in Central South University. Her current research interests are fabrication, characterization and applications of piezoelectric composites as actuators. Kechao Zhou received the PhD from Central South University in 1997. In 1998, he became a Professor in Central South University. His major research interests involve
309
the development of advanced materials for a range of industrial applications. He is currently serving as the Vice-President of Central South University and a member of the council of the Chinese Materials Research Society. Song Zhu received the BE degrees from Central South University in 2012. He is currently a postgraduate student in Central South University and works on numerical evaluation of piezoelectric ceramic and composites. Ziqi Chen received the BE degrees from Central South University in 2012. He is currently a postgraduate student in Central South University and works on the processing and characterization of piezoelectric composites. Dou Zhang received the BE and ME degrees from the Wuhan University of Technology, China in 1992 and 1995, respectively, and PhD degree from the University of Birmingham, U.K., in 2006. In 2004, he became a Research Associate and, in 2006, a Research Fellow in School of Metallurgy and Materials, University of Birmingham. In 2009, he joined Central South University, China, and was appointed as the Professor in 2010. His current research interests involve the fabrication and characterization of ferroelectric and piezoelectric ceramics, films, composites, and devices.