The Pennsylvania State University. The Graduate School. Mechanical and Nuclear Engineering

Transcription

1 The Pennsylvania State University The Graduate School Mechanical and Nuclear Engineering SYSTEMATIC CHARACTERIZATION OF PZT 5A FIBERS WITH PARALLEL AND INTERDIGITATED ELECTRODES A Thesis in Mechanical Engineering by Nicholas Wyckoff 2016 Nicholas Wyckoff Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2016

2 ii The thesis of Nicholas Wyckoff was reviewed and approved* by the following: Zoubeida Ounaies Professor of Mechanical Engineering Thesis Advisor Aman Haque Professor of Mechanical Engineering Karen Thole Professor of Mechanical Engineering Head of the Department of Department or Graduate Program *Signatures are on file in the Graduate School

3 iii ABSTRACT Lead zirconate titanate (PZT) fibers are mainly used in active fiber composites (AFC) where they are embedded in a polymer matrix. The PZT fibers provide the electromechanical actuation and sensing capabilities derived from the inherent piezoelectricity of PZT. The role of the epoxy matrix is to transfer the external loads amongst the fibers while also serving as protection to enable more flexibility in the AFC device as a whole. Interdigitated electrodes (IDE) placed on the planar surfaces of the AFC are along the direction of the fibers, hereby exploiting the d 33 coefficient of PZT, which is twice that of the d 31 coefficient. Despite this clever strategy, the AFC electromechanical response is lower than that of bulk PZT. Although the polymer matrix has been widely studied, the PZT fibers have not. By directly characterizing the behavior of PZT fibers, recommendations to redesign of the AFC with the goal of improving its performance can be proposed. Therefore, it is important to characterize the electrical and electromechanical behavior of these fibers ex-situ using the IDE configuration to assess the impact of fiber configuration and non-uniform electric field on the piezoelectric response. For this reason, the broad goal of this thesis is to characterize the impact of IDE electrodes on the electrical and electromechanical behavior of PZT fibers, which is necessary for their successful implementation in devices like AFC. As mentioned above, limited research has been conducted on characterizing the behavior of PZT fibers, and no electrical characterization of individual PZT fibers has been done to the best of our knowledge. Therefore, to accomplish the broad goal of this study, the following research tasks are planned: 1.) To characterize PZT fibers with parallel electrodes; the parallel electrode testing will determine baseline properties that will be compared to the IDE results and will also allow for quantification of the fiber geometry s impact on the bulk PZT properties. 2.) To characterize PZT fibers using IDE configuration; the

4 iv characterization of PZT fibers ex-situ with the IDE configuration will convey the PZT fiber behavior in the AFC to assist in improving the AFC design. 3.) To experimentally determine Young s modulus, coercive field, remnant polarization, dielectric permittivity and both d 33 and e 33 piezoelectric coefficients of PZT fibers. To the best of our knowledge, these results will be the first dielectric permittivity, d 33 and e 33 values determined with direct measurement of PZT fibers using both parallel electrode and IDE configurations. These results will allow for direct comparison of bulk PZT and PZT fiber properties as well as the impact of the nonuniform electric filed generated by the IDE. The PZT fiber mechanical properties and dielectric permittivity measured with parallel electrodes were found to be approximately 65% of the bulk PZT fibers. The fiber s Young s modulus was determined to be 33 GPa and the dielectric permittivity determined to be The PZT fiber IDE remnant polarization, dielectric permittivity, and e 33 results were found to be within the range of 50%-75% of the results found for parallel electrode configuration. The combined reduction found in the PZT fiber properties compared to bulk PZT leads to the conclusion that implementing the fiber properties into AFC models will result in a substantially different response.

5 v TABLE OF CONTENTS List of Figures... vii List of Tables... xi Acknowledgements... xii Chapter 1 Introduction Problem Statement Piezoelectricity Background Constitutive Equations Literature Review AFC Development and Characterization PZT Fiber Characterization Scope of Thesis Goal and Related Tasks Organization of Thesis Chapter 2 Experimental Methods for Characterization of PZT Fibers Introduction IDE Assembly Design Mechanical and Electrical Characterization of Unpoled PZT Mechanical Behavior Electrical Behavior Mechanical Loading Effect DC Poling Effect Dielectric Testing Simultaneous Mechanical and Electrical Loading Parallel Electrode Method IDE Method Chapter 3 Mechanical Testing Results Unloaded PZT Fiber Results Mechanical Response Electrical Response Mechanically Loaded PZT Fiber Results Mechanical Response Electrical Behavior Results Chapter 4 Electrical and Electromechanical Testing Results DC Poled PZT Fiber Results Mechanical Behavior Results... 77

6 vi Electrical Response Dielectric Testing Results Electromechanical Testing Results Parallel Electrode Configuration Results IDE Configuration Results Chapter 5 Modeling and Verification Model Descriptions Parallel Electrode Model for PZT Fibers IDE Model for PZT Fibers Verification of Dielectric Results Parallel Electrode Configuration IDE Configuration Simultaneous Mechanical and Electrical Loading Verification Parallel Electrode Configuration IDE Configuration Chapter 6 Conclusions and Recommendations Summary of Results Conclusions Recommendations for Future Work References Appendices Appendix A IDE Screen Print Process Appendix B PZT IDE Assembly Manufacturing Process Appendix C Material Properties Used for ABAQUS Models PZT Properties IDE Assembly Component Properties

7 vii LIST OF FIGURES Figure 1-1: AFC composition schematic [10]... 2 Figure 1-2: Electric field line schematic for (A) parallel electrodes and (B) IDE Figure 1-3: Cubic unit cell structure of PZT (left) compared to tetragonal unit cell structure (right) when below T c [22]... 5 Figure 1-4: Poling of a piezoelectric material: (A) random orientation of domains, (B) polarization of domains in direction of DC electric field and (C) remnant polarization in direction of DC field after field is removed... 6 Figure 1-5: Example ferroelectric polarization hysteresis loop... 7 Figure 1-6: PZT phase diagram [22]... 8 Figure 1-7: Comparison of conventional (top figure) parallel electrode and IDE (bottom figure) of piezoelectric actuators [24] Figure 1-8: Manufacturing method for IDE fiber composite [14] Figure 1-9: Comparison of experimental piezoelectric d 33 with modeled value [14] Figure 1-10: Configuration of injection molded piezofiber preform utilized in enhanced performance AFCs [12] Figure 1-11: AFC's dielectric constant for different values of the matrix dielectric constant [13] Figure 1-12: d 33 as a function of (a) electrode gap and (b) electrode width [13] Figure 1-13: Geometrical parameters measured using optical microscope [6] Figure 1-14: Schematic view of the AFC and symmetry to form the RVE [6] Figure 1-15: Fixture for fiber permittivity and polarization measurements [15] Figure 1-16: Schematic representation of a 1-3 piezocomposite comprising active piezoelectric ceramic fibers and a passive polymer matrix [19] Figure 1-17: Experimental fiber results property comparison between manufacturing process and bulk properties [19] Figure 2-1: PZT 5A fibers from Advanced Cerametrics Figure 2-2: PZT IDE assembly illustrating components Figure 2-3: AFC IDE (A) size comparison to (B) IDE assembly... 37

8 viii Figure 2-4: PZT fiber installed in DMA grips for tensile testing Figure 2-5: Modified Sawyer-Tower circuit for ferroelectric hysteresis [30] Figure 2-6: Polarization and strain test fixture (left) showing LVDT and micrometer for pressure control (right) Figure 2-7: PZT fiber installed in PE fixture (left) and spring mechanism shown (right) Figure 2-8: Visual representation of load/unload cycles Figure 2-9: DMA environmental chamber with fiber installed for mechanical loading Figure 2-10: Schematic of DC poling with IDE assembly Figure 2-11: Parallel electrode test fixture set-up for dielectric permittivity measurements Figure 2-12: Cascade probe station setup with PZT fiber samples installed Figure 2-13: Cascade probe test conducted using parallel electroded fibers (left) and magnified view of probe in contact with silver paint electrode (right) Figure 2-14: Cascade probe test conducted using IDE assembly (left) and magnified view of probe contact with copper wire (right) Figure 2-15: Parallel electrode configuration installed in DMA with PZT 5A fiber Figure 2-16: Schematic of electromechanical testing setup utilizing IDE assembly Figure 2-17: IDE assembly installed in DMA for electromechanical testing Figure 3-1: Stress-strain behavior of unpoled PZT fibers Figure 3-2: Ferroelectric PE loops developing for increasing electric field in parallel electrodes Figure 3-3: PE loop of unloaded PZT fibers with 2.5 MV/m applied electric field Figure 3-4: IDE dipole orientation for (A) random orientation before poling, (B) alignment of the dipoles with nonuniform electric field and (C) remnant polarization after electric field is removed Figure 3-5: SE butterfly loops developing for increasing electric field in parallel electrodes Figure 3-6: Strain rate of mm/s resulting in stress limit overshoot Figure 3-7: Room temperature loading cycle effect on Young's Modulus Figure 3-8: Temperature effect on cyclic loading behavior of 5MPa load limit... 71

9 ix Figure 3-9: Temperature effect on cyclic loading behavior of 20MPa load limit Figure 3-10: Combined loaded PZT fiber PE loops for 25 o C testing Figure 3-11: Combined loaded PZT fiber SE butterfly loops for 25 o C testing Figure 4-1: Unpoled vs poled PZT fiber stress-strain comparison Figure 4-2: Comparison of Young's modulus for poled and unpoled PZT fibers in linear elastic regime Figure 4-3: Poled vs unpoled PZT fiber PE loops at 2 MV/m with IDE exposed to air Figure 4-4: Poled PZT fiber SE loop at 0.2 Hz with 0.1 MV/m AC electric field Figure 4-5: PZT fiber d 33 as a function of electric field Figure 4-6: Experimental dielectric permittivity measured with QuadTech LCR meter Figure 4-7: Parallel electrode 2 MV/m DC poling of PZT fiber Figure 4-8: Dipole alignment under electric field (A) with no external load and (B) with external load in opposite direction of poling Figure 4-9: Pre-stress determination for optimized piezoelectric output for 0.3 MV/m electric field at 100 mhz Figure 4-10: PZT fiber induced stress for 1.0 MV/m electric field at 100 mhz Figure 4-11: Piezoelectric e 33 behavior of PZT fiber in parallel electrode tested with DMA as a function of electric field Figure 4-12: IDE PZT fiber sample stress-electric field loops at 1Hz Figure 4-13: Piezoelectric e 33 behavior of PZT fiber in IDE tested with Instron 5866 as a function of electric field Figure 4-14: Fiber grips used in IDE Instron electromechanical testing Figure 4-15: Stress-strain comparison of DMA and Instron results illustrating error in Instron due to compliancy of grips Figure 4-16: Image of fiber grip (left) before tensile test and (right) during tensile test before fracture highlighting bending of the grip Figure 4-17: Piezoelectric e 33 behavior of PZT fiber in IDE tested with Instron 5866 as a function of electric field Figure 5-1: PZT parallel electrode model

10 x Figure 5-2: Flattened fiber cross section to improve contact with electrodes Figure 5-3: PZT assembly model partition breakdown Figure 5-4: IDE model electric potential schematic Figure 5-5: IDE model mechanical boundary constraints and loads Figure 5-6: IDE screen print quality on acrylic (left) and Mylar (right) Figure 5-7: Electric field lines of PZT fiber in (A) parallel electrode configuration and (B) IDE configuration Figure A-1: Presco Thick Film Screen Printer Figure A-2: IDE screen from UTZ Technologies Figure A-3: Proper ink placement for screen printing Figure A-4: Screen print process activated by foot pedal Figure A-5: Aligned IDE patterns for IDE assembly fabrication Figure A-6: IDE acrylic plate with double sided scotch tape applied and excess tape removed Figure A-7: IDE screen patterns placed onto first acrylic plate Figure A-8: Both acrylic plates aligned and adhered to IDE screen printed patterns Figure A-9: Full pattern screen printed IDEs assembled to acrylic plates

11 xi LIST OF TABLES Table 1: Rules for matrix notation [23] Table 2: Data taken at 500 V/mm for wafers with conventional and IDE configurations [24] Table 3: Ultimate tensile strength of AFC [11] Table 4: Summary of PZT 5A fibers tested [19] Table 5: Bulk PZT 5A reported values [26] Table 6: Loaded PZT fiber electrical testing results Table 7: Dielectric permittivity comparison Table 8: PZT bulk vs fiber dielectric permittivity comparison Table 9: Comparison of predicted dielectric permittivity for PZT fibers in parallel and IDE configuration models Table 10: Simulation predicted electromechanical results for varying applied plate pressured Table 11: IDE assembly component properties used in ABAQUS model

12 xii ACKNOWLEDGEMENTS I would like to thank Dr. Zoubeida Ounaies for her great help, assistance, and guidance during this work as well as during my collegiate career at Penn State University. I would also like to thank Dr. Hassene Ben Atitallah for his guidance and assistance with my experiments and thesis. I thank you both for introducing me to this work with great knowledge and passion for the material. I would like to offer my gratitude to Dr. Aman Haque for serving as my faculty reader and thank him for his time and patience. I would also like to thank my fellow colleagues in the Electroactive Material Characterization Lab at Penn state for their support during my time with the lab. I have enjoyed our time working together and wish you all the best. Finally and most importantly, I would like to thank my family for their love and support they have provided me throughout my collegiate career at Penn State. I thank my parents for providing me with the opportunity to attend Penn State University and my grandfather for inspiring me to pursue a career in mechanical engineering. I would like to dedicate this thesis in loving memory of my cousin, Colin.

13 1 Chapter 1 Introduction 1.1 Problem Statement Active fiber composites, or AFCs, are composed of lead zirconate titanate (PZT) fibers embedded in an epoxy matrix. PZT is a piezoelectric ceramic. The piezoelectric effect is an ability the material possesses that can generate a voltage when a mechanical strain is applied or generate a mechanical deformation when a voltage is applied. The generation of a voltage from a mechanical stress or strain is referred to as the direct piezoelectric effect. The generation of a mechanical deformation from an applied voltage is referred to as the converse piezoelectric effect. The direct piezoelectric effect is analogous to the material acting as a sensor while the converse piezoelectric effect is analogous to the material acting as an actuator. Therefore, AFCs can function as both actuator and sensor due to presence of PZT fibers, thus allowing AFCs to be utilized for various applications. Applications for AFCs as sensors include structural health monitoring and damage detection [1-4]. In these applications, the AFCs are adhered to a structure; if the structure experiences a deformation then the deformation will generate a voltage from the AFC. The value of the voltage generated is used to monitor the deformation of the structure and can provide indication whether the structure is approaching it structural limitations. Actuation applications have also been studied for vibration control [4-7] as well as flapping wings [8]. In the actuation applications the AFC utilizes the converse piezoelectric effect of the PZT. Applications for vibration control have been investigated for use in helicopter rotor blades [9]; vibrations

14 2 experienced in the helicopter rotor blades are sensed by the AFC. An equivalent but inverted signal is used to actuate the AFCs, thus canceling out the unwanted vibrations AFCs are composed of a piezoelectric fiber in the form of PZT embedded in an epoxy matrix between two layers of interdigitated electrodes (IDE). A schematic of a typical AFC composition is shown in Figure 1-1. The PZT fibers are generally 250 µm in diameter with length varying from 25 mm to 200 mm depending on the limitations of the application and environment for use. The epoxy matrix is highly flexible and functions to secure the fibers in place and mechanically protect them. The IDE design follows alternating electrode fingers through the length of the fibers. The alternating pattern of positive to negative electrodes allows the electric field to flow along the length of the fibers. The IDE for the AFC depicted in the schematic was screen printed onto a Kapton sheet. The Kapton sheet is used as the substrate for screen-printing due to its low thickness and electrical insulating nature. Figure 1-1: AFC composition schematic [10] AFCs have been studied through both experimental and modeling means [6, 11-14]. The focus of these studies has been to optimize the AFC design to generate the highest piezoelectric

15 3 capabilities. The designs consider the epoxy matrix material properties, PZT fiber thickness, and IDE dimensions for optimization. While these studies assist in improving the design of AFCs, the PZT fiber behavior was assumed to be the same as that of bulk, which remains a weakness in these particular studies. By not characterizing the PZT behavior for fibers the models have to rely on bulk properties of PZT, which can be very different from the bulk properties, resulting in inaccurate predictions and validations of the AFC performance and capabilities. PZT fibers are difficult to characterize owing to their size and their brittle nature. The most covered topics for PZT fibers are determination of their mechanical properties [15-18] where individual PZT fibers were considered. Although bulk PZT has been studied heavily for its dielectric and piezoelectric properties, the amount of research focused on PZT fibers is scarce [19-21]. The majority of the studies with PZT fibers do not consider an individual fiber but rather infer its properties based on the effective performance of the fiber while embedded in an epoxy [19, 21]. The properties of the fibers are then determined through analytical models that take into account the properties of the matrix itself to provide estimates of the fiber properties. Similarly, studies in the determination of piezoelectric coefficients for PZT fibers do not explicitly measure the property of the fiber but rather conduct the testing while the fiber is in the AFC composite [19, 21]. An exception to this was found with explicit fiber testing done by Guillot et al., however, the testing utilized hollow PZT fibers rather than solid fibers which were then electroded on the inside and outside of the tubular fiber [20]. While the testing was done without the addition of an epoxy, the results cannot be directly compared to AFCs due to the substantial difference in electrode configuration and fiber structure. In addition, applications utilizing PZT fibers in AFCs generally use IDEs, which give rise to electric field lines different from those in parallel electrodes (see Figure 1-2). As seen in Figure 1-2 (A) the parallel

16 4 electrodes result in a uniform electric field between electrodes. Figure 1-2 (B) illustrates the nonuniform electric field lines from the IDEs, which result a net electric field between electrodes that is at a lower magnitude than in the case of the parallel electrodes, due to the nonlinear path the electric field flows between the electrodes. It is therefore of importance to not only characterize PZT in fiber form, but also with IDE configurations. To the best of our knowledge, research in the determination of dielectric and piezoelectric properties of single PZT fibers using IDE as electrode configuration is not available in the literature. Figure 1-2: Electric field line schematic for (A) parallel electrodes and (B) IDE. In this work, experimental characterization of the mechanical, electrical and piezoelectric behavior of individual PZT fibers was conducted. The PZT fibers are tested to gather properties with parallel electrodes to allow for direct comparison of PZT fiber and PZT bulk behavior. The fibers are then tested with IDE configuration to examine the effect of the nonuniform electric field effect on the fiber behavior. The IDE configuration is the same used in the AFCs, which allows us to test the fibers in the same environment that is experienced in AFCs. Characterizing the behavior of PZT fibers for parallel electrode and IDE configurations not only will improve the modeling of AFCs but can also be used as a basis to improve AFC performance.

17 5 1.2 Piezoelectricity Background Piezoelectricity is the ability of a material to convert mechanical energy into electrical energy and vice versa. For PZT, the piezoelectric behavior is due to the noncentrosymmetric nature of its unit cell. PZT crystallizes in the Perovskite structure. The Perovskite structure follows the general formulation of ABO 3. When a Perovskite is above Curie temperature, T c, the unit cell structure is cubic, this is the paraelectric phase. In the cubic structure, the large A cations are located in the corners of the cubic, the smaller B cations are in the body center and oxygen anions are in the center of the faces. Below T c, there is a distortion that occurs in the unit cell structure that results in the central cation and the oxygen atoms moving in opposite directions away from the center plane. The offset results in a permanent dipole, which leads to an inherent nonzero spontaneous polarization in the material. The change from cubic structure to tetragonal for PZT is shown in Figure 1-3. Figure 1-3: Cubic unit cell structure of PZT (left) compared to tetragonal unit cell structure (right) when below T c [22]

18 6 Adjacent dipoles with the same orientation form ferroelectric domains. In the PZT material, the dipoles are randomly oriented and will cause the net polarization of the ferroelectric domains to cancel out. To align the dipoles in the same direction, a DC electric field with large enough magnitude is applied for an extended period of time. The application of the electric field will cause the dipoles to reorient and align in the direction of the electric field. Given a high enough electric field and sufficient time, when the field is removed the dipoles will experience some relaxation but overall will still be aligned in the direction of the field and result in an overall remnant polarization as seen in Figure 1-4. The degree of poling is influenced by the applied electric field, time the field is applied and the temperature at which the poling process is conducted. Figure 1-4: Poling of a piezoelectric material: (A) random orientation of domains, (B) polarization of domains in direction of DC electric field and (C) remnant polarization in direction of DC field after field is removed The maximum polarization the material can reach while the electric field is applied is referred to as the saturation polarization (P s ), represented by the schematic in Figure 1-4 (B). As the electric field is removed, the remaining polarization from the sum of the dipoles aligned is the remnant polarization (P r ) and can be described by Figure 1-4 (C). When an electric field with high enough magnitude is applied in the opposite direction as the poling process the dipoles can rotate to align with the new electric field. The net polarization of the material can be brought back

19 7 to zero when an electric field known as the coercive field (E c ) is applied. The coercive field is the minimum field necessary to switch the orientation of the dipoles. As the electric field increases in the opposite direction the material can now be reach a saturation polarization in the opposite direction from the initial poling. The full ferroelectric polarization behavior, also known as ferroelectric hysteresis loop, as a function of electric field can be seen in Figure 1-5. Figure 1-5: Example ferroelectric polarization hysteresis loop Polarization enhances the electromechanical coupling of piezoelectric materials and the material composition can affect the susceptibility of the material to polarize. For PZT there are two possible unit cell configurations for the ferroelectric phase below the Curie temperature. One, as previously mentioned, is the tetragonal unit cell structure. The second is the rhombohedral unit cell structure. The structure the PZT takes is dependent on the composition of the PZT. The phase diagram of PZT is provided in Figure 1-6. For lower mol % of lead titanate (PbTiO 3 ), the PZT transforms into the rhombohedral configuration when under T c. For higher mol % PbTiO 3 the

20 8 PZT transforms into the tetragonal tetragonal. As observed in the phase diagram, there is a boundary between the rhombohedral and tetragonal phases called the morphotropic phase boundary [22]. Compositions of PZT at the morphotropic phase boundary benefit from the combination of possible poling directions. There are 8 possible poling directions in the rhombohedral and 6 directions in the tetragonal which leads to 14 possible poling directions at the morphotropic phase boundary. Because the morphotropic phase boundary has the most possible poling directions it is the most desired composition for use. Figure 1-6: PZT phase diagram [22]

21 9 1.3 Constitutive Equations This section will provide background on the most common constitutive equations for piezoelectric materials. The mechanical behavior for linear elastic materials is described by Hooke s Law provided in equation (1.1). T is the second-rank stress tensor (N/m 2 ), S is the second-rank strain tensor (m/m), and s is the fourth-rank compliance tensor (m 2 /N). S ij = s ijkl T kl (1.1) The dielectric behavior of a material is typically characterized by its dielectric permittivity ε. The dielectric permittivity is derived from the relationship between the dielectric displacement D (C/m 2 ) and the electric field E (V/m). The dielectric displacement is given by the expression in equation (1.2). D i = P i + ε 0 E i (1.2) In equation (1.2), ε o is the dielectric permittivity of free space in vacuum (8.85 x F/m) and P is the induced polarization given by equation (1.3). P i = χ ij E j (1.3) Χ is the second rank dielectric susceptibility tensor (F/m). From equations (1.2) and (1.3) the dielectric displacement can be expressed as equation (1.4). D i = χ ij E j + ε 0 E i = χ ij E j + ε 0 δ ij E j = (ε 0 δ ij + χ ij )E j = ε ij E j (1.4)

22 10 In equation (1.4), ε ij is the dielectric permittivity of the material and δ ij is Kronecker s symbol (δ ij = 1 for i = j, δ ij = 0 for i j) [22]. The relative dielectric permittivity, ε r, of a material, also referred to as the dielectric constant, is provided in equation (1.5). ε r = ε ij /ε 0 (1.5) The piezoelectric effect of a piezoelectric material can be classified as either the direct effect or converse effect. As mentioned in an earlier section, the direct effect is when a mechanical stress T is applied to a piezoelectric material resulting in an induced charge density D (also known as dielectric displacement). For low electric fields, this relationship is linear and characterized by a piezoelectric constant d (C/N or V/m). The direct effect is described in equation (1.6). The constant d ijk is a third rank tensor of piezoelectric coefficients. D i = d ijk T jk (1.6) The converse piezoelectric effect is when an electric field E is applied to a piezoelectric material resulting in an induced mechanical strain S. Like the direct effect, for low electric fields this is a linear relationship also characterized by the d constant. The converse effect is provided in equation (1.7). It was determined that d direct = d converse. t S ij = d kij E k = d ijk E k (1.7)

23 Piezoelectric materials exhibit a coupling between mechanical and dielectric behaviors. The coupling is fully described by equations (1.8) and (1.9). 11 D i = d ijk T jk + ε ij E j (1.8) S ij = s ijkl T kl + d ijk E k (1.9) Due to symmetry of the tensor, the tensors can be simplified; following the Voight convention (shown in Table 1) the tensors can be written in matrix form. The simplified tensor notation is provided in equation (1.10) and the matrix form is provided in equation (1.11). D i = d ik T k + ε ij E j S i = s ij T j + d ik E k (1.10) { D S } = [ ε d t d s ] { E T } (1.11) Table 1: Rules for matrix notation [23]

24 Literature Review AFC Development and Characterization AFCs have been studied through experimentation and modeling to optimize their design and achieve the largest actuating and sensing functionalities. The various studies available focus on different elements of the AFC design; these include the dimensions of the IDE pattern, thickness of the composite and varying the composite materials such as the epoxy matrix used. A visual representation of the components and dimensions are provided in Figure 1-1. Two of the leading researchers in the study of AFCs are Bent and Hagood. A study by Hagood et. al. examined the implementation of IDEs on bulk wafers to compare the response to that of conventional parallel electroded bulk wafer [24]. This paper highlights the benefits of the IDE by showing improved sensing and actuation compared to the parallel electrode configuration due to the use of the d 33 and e 33 piezoelectric coefficients. Given to the poling direction for the parallel electrode is through the thickness, the produced strain in the planar direction is coupled through the d 31 and e 31 piezoelectric coefficients (see Figure 1-7). For PZT the d 33 is typically twice as large as the d 31 and e 33 four times larger than e 31. For that reason, the IDE configuration, by exploiting the 33-mode is potentially more beneficial. The study incorporates models using the finite element method and Rayleigh-Ritz method to predict the actuator behavior.

25 13 Figure 1-7: Comparison of conventional (top figure) parallel electrode and IDE (bottom figure) of piezoelectric actuators [24] The wafers are then fabricated with the IDE pattern for experimental testing to verify the model predictions. The experimental results for strain in the X and Y directions (as defined in Figure 1-7) are determined for both the conventional parallel electrode and IDE configurations. The results are also compared to the predicted model response. The results are shown in Table 2. It was found that the IDE configuration did result in larger strain production than the parallel electrode configuration. The ratio of the d 33 from the IDE to d 31 of the parallel electrode was found to be Although the ratio was not doubled as expected, this is due to the presence of the nonuniform electric field produced from the IDE. Nonetheless, the result illustrates the benefit of the IDE configuration for the PZT, where the geometric benefit dominates other disadvantages such as nonuniform electric fields.

26 14 Table 2: Data taken at 500 V/mm for wafers with conventional and IDE configurations [24] In a study conducted by Bent and Hagood [14], the implementation of the IDE for PZT fiber composites was examined. The study investigates improving PZT composites by combining the previous studies on fiber composites with the benefit of the IDE configuration found by Hagood [24]. Piezoelectric ceramics have been utilized for many transducer and controlled structural applications as they are effective active materials. The high stiffness of piezoceramics provides them with a high actuation authority and they are easily controlled through applied voltages. However, newer applications that can utilize the sensing and actuating capabilities require design and arrangement that cannot be provided by monolithic piezoceramic wafers due to their lack of flexibility. The brittleness of the PZT limits the possible geometries of the bulk material resulting in discrete placement of the actuator/sensor. Utilizing PZT fibers composites can allow for distributed actuation/sensing capabilities. Piezoelectric fiber composites were introduced as a means to improve upon reliability and conformability of bulk piezoceramics. The piezoceramic fibers supply the composite with stiffness, strength and piezoelectric capabilities while the passive material, generally an epoxy matrix, serves to protect the fibers and transfer the load of the composite amongst the fibers. The goal set by Bent and Hagood [14] was to create an AFC that allows for implementation into more

27 15 applications due to its conformability while also maintaining the piezoelectric capabilities of bulk PZT. The task was undertaken through prediction of the AFC behavior with two methods of modeling. The first method of modeling was accomplished through the uniform fields model. The second method of modeling was accomplished through the finite element method. The model results for the two methods were compared and found to have very good agreement. Experimental verification was then conducted after fabrication of the PZT fiber composite. The fabrication of AFC was performed and an overview schematic is provided in Figure 1-8. PZT 5H fibers with lengths of 82.5 mm and diameters of 130 µm were utilized. The matrix was a two-phase hybrid material composed of Epo-Tek 301 epoxy and fine high dielectric particulate in the form of PZT 5H powder. Full details are provided in the literature [14]. The IDE electrodes were created from etching a Kapton thin film using a photomask. Locator pins were used to align the top and bottom electrode patterns. The assembly procedure utilized an aluminum cure plate and vacuum fixtures depicted in Figure 1-8. Figure 1-8: Manufacturing method for IDE fiber composite [14]

28 16 The experimental results for the composite were found to deviate from the predicted values for both models. The d 33 predicted by the model and experimental results are shown in a plot as a function of fiber content in Figure 1-9. The deviations in the experimental behavior from the model are due to multiple unknown parameters incorporated into the model such as the specimen thickness, range of fiber piezoelectric constants (estimated 75%-100% bulk value) and range of fiber stiffness (estimated 50%-100% bulk value). The values for either case are found to be lower than the bulk PZT values. Further work aims towards better characterization of the composite constituents and improvements to the model to account for material behavior in the thickness direction. Figure 1-9: Comparison of experimental piezoelectric d 33 with modeled value [14] As the initial results from the previous study were found to be lower than the bulk PZT properties, investigations into improving AFC performance focused on bringing the performance

29 17 closer to that of bulk PZT. Bent, Hagood and Rodgers examined the effects of different materials used in AFCs [11]. In their study, AFCs were tested for high electrical and mechanical loading scenarios to determine the peak response of the composite. The AFCs used in the study consisted of PZT 5H fibers embedded in an epoxy based matrix. This study examined the impact of including high modulus S-glass filaments to reinforce the stiffness of the epoxy matrix. The intent of the S-glass filaments was to improve the load transfer mechanism in the composite actuator with the hypothesis that it would improve the toughness and damage tolerance of the composite. An alternate configuration examined involved E-glass fabric plies to laminate the AFC and create a symmetric three ply composite also with the intent of improved toughness and damage tolerance. The AFCs were tested under passive and active loading conditions. The passive tests determined the mechanical properties of the composite to determine the stiffness and long term mechanical fatigue. The active tests determined the electromechanical coupling properties of the AFCs. The passive tests results showed similar stiffness for the three cases but the ultimate tensile stress was greatly increased with the addition of the S-glass filaments and E-glass laminate. The baseline AFC had an ultimate tensile strength corresponding to that of the PZT 5H. A table of the ultimate tensile strengths is provided in Table 3. Table 3: Ultimate tensile strength of AFC [11]

30 18 While the mechanical properties of the composite were increased with the glass reinforced filaments, the electrical properties saw a decrease. The inclusion of the glass filaments led to a reduced effective capacitance in the hybrid matrix thus reducing the electric field concentration in the fibers. A similar effect is shown in determination of the d 33 coefficient with the laminate having a value of 59 pm/v which is substantially lower value than the baseline value of 116 pm/v. This study illustrates the research conducted in attempt to improve the composite performance by changing the composition through the addition of glass substituents. The results from the study showed that the addition of substituents did not lead to conclusive improvement of the composite and other parameters must be investigated for improving the composite response. Another study by Gentilman, McNeal and Schmidt examined changing the PZT from individual fibers to injection molded free standing piezofiber modules [12]. Using the injection molded piezofiber modules is done in hopes to improve fiber geometry and property consistency. The influence of fiber geometry is also examined as the circular cross section with a rectangular cross section. An image of the injection molded preform is shown in Figure The advantage of the injection molded preforms is the ability to tailor the cross section of the modules to maximize the piezoelectric material in the composite matrix. The injection molding of the modules also results in excellent uniformity in material in both geometry and microstructure. The fibers in the array are attached to a common strip at one end which allows the entire array of fibers to be handled as a single unit.

31 19 Figure 1-10: Configuration of injection molded piezofiber preform utilized in enhanced performance AFCs [12] The resulting properties of the preform show an increase in the produced strain compared to conventional AFC design. In terms of the piezoelectric d 33 constant, the value for the injection molded preforms was 195 pm/v, which is larger than the reported 150 pm/v for conventional AFCs utilizing individual circular cross section fibers. This study provided insight into piezoelectric response behavior when changing the cross section design of the conventional circular cross section fibers and increasing the fiber uniformity. The increase in piezoelectric production can be contributed to both the fiber uniformity of the injection molding process and the increased cross sectional area of the fiber modules from the rectangular geometry. Other studies by Ben Atitallah et al. and Belloli et al. have focused on the impact of the IDE electrode dimensions [6, 13] and matrix properties [13]. The study by Ben Atitallah examined the impact of varying the electrode width and gap of the IDE as well as examining different epoxy matrices on the AFC response using simulation in ABAQUS [25]. In the simulations conducted in the study, the permittivity ε and piezoelectric d 33 constant were determined for various electrode widths and gaps and for various epoxy matrices. The

32 20 permittivity of the epoxy matrix was found to have a significant effect on the overall composite permittivity as seen in Figure As observed in the plot, the effective permittivity of the composite drastically increases when an epoxy matrix with higher permittivity is used with the PZT. The full benefit of this plot cannot be exploited as most epoxies do not have high permittivity and those that do may have poor interfacial behavior with the fiber due to material behavior differences. Figure 1-11: AFC's dielectric constant for different values of the matrix dielectric constant [13] Similarly, the d 33 also dramatically increased as the permittivity of the matrix increased. The d 33 was also examined in relation to electrode width and gap with respect to the fiber geometry. The d 33 exhibited a linear increase with increased electrode gap. Increasing the electrode width also increased the d 33 but not in a linearly relationship as was experienced with the electrode gap. Plots illustrating the behavior are shown in Figure The electrode gap

33 21 however is limited by the voltage that can be applied to the sample. As the gap increases the voltage necessary to provide a similar electric field also increases. Figure 1-12: d 33 as a function of (a) electrode gap and (b) electrode width [13] As modeling parameters such as the IDE geometry and epoxy matrix selection becomes narrowed down to a small selection corresponding to optimal predicted AFC response, the remaining components to improve upon is accurate depiction of the constituent behavior. The study by Belloli et al. [6] offered an additional element into their AFC simulation which used ANSYS. When examining Figure 1-13, a contact angle is observed between the PZT fiber and IDE electrode. This contact angle was included as an additional parameter in the simulations conducted on the AFC. With the contact angle, there is more surface area of the electrode in contact with the fibers than in the case of a fiber being tangent to the electrode. The contact angle of the fiber and electrode were found to have a substantial effect on the AFC response. Increasing the contact angle reduces the amount of space between the electrode and fiber resulting in effective field distribution that is more efficient as the electric field experiences fewer losses from having the epoxy matrix between the electrodes and fibers.

34 22 Figure 1-13: Geometrical parameters measured using optical microscope [6] A finite element (FE) model is used to predict the response of the AFC. Using symmetry of the model to reduce computing requirements the model can be simplified into a representative volume element (RVE). The RVE, from symmetry, can be defined as the octant of a single PZT fiber in the AFC. Representation of the RVE is provided in Figure The magnitude of the electric field generated and actuated strain are observed in the simulations. The contact angle leads to a generated electric field of four times larger than the area of the fiber not in direct contact with the electrode. The strain results were corroborated with previous studies that illustrate enhanced actuation performance for increasing electrode spacing to fiber diameter ratios.

35 23 Figure 1-14: Schematic view of the AFC and symmetry to form the RVE [6] From these studies, AFC design has become standardized in terms of composite geometry such as IDE dimensions, fiber geometry and composite thickness as well as the epoxy matrix used in the composite. As the design predicted by the models is standardized for the optimal result, it can be concluded that the AFC is at its best response design. However, the experimental results are not following the behavior predicted by the models. The discrepancy between the model and experimental results may be attributed to the properties utilized by the models for the PZT fibers. The studies rely on using bulk PZT properties because PZT fiber properties are not readily available. This leads to some error in the predicted responses of AFCs from the models as one would expect to see variation in the properties of PZT from bulk to fiber. Therefore, it is becoming vital to characterize PZT in fiber form.

36 PZT Fiber Characterization While PZT bulk ceramic has been studied thoroughly with properties widely available, studies focused on PZT fibers are rather scarce [15, 18-21]. Of the studies that have been conducted, the mechanical properties are the most reported due to the easier nature of the experiments [15, 18]. As the fibers are generally on the order of 250 µm in diameter, equipment used to test the electromechanical properties becomes more challenging. In fact, references [19, 21], although focused on electrical and electromechanical properties, did not measure individual fibers directly but rather indirectly by embedding them in an epoxy matrix. The mechanical stress-strain response of single PZT fibers was examined by Kornmann and Huber [18]. Three different manufacturing process fibers were used in the experiment, all with a diameter of approximately 250 µm. The first fibers were manufactured through an extrusion process. The second fibers were manufactured through a spinning process followed by coagulation in water. The third fibers were manufactured via a viscous-suspension-spinning process (VSSP). Tensile testing was then performed on the unpoled fibers. The tests were conducted for fiber lengths of 100 mm at strain rates of 0.4 mm/min and 0.3 mm/min. The elastic moduli for all three processed fiber techniques were roughly 40 GPa. This puts the elastic modulus for PZT fibers at approximately 75% of that reported for bulk, i.e. 53 GPa [26]. Mechanical testing was also performed in a study conducted by Yoshikawa et al. [15]. The mechanical testing was performed on pure Perovskite PZT and Nb-PZT fibers with different heat treatments of either 750 o C or 1250 o C. The fibers used ranged between 26 and 36 µm in diameter and were cut to lengths of 1 to 2 cm. The fibers were glued to carbon fiber and standard tensile testing was performed. The tensile strength of the pure Perovskite PZT fibers was found to

37 25 be 36 MPa and 40 MPa per the respective heat treatment. The Nb-PZT experienced a higher tensile strength of approximately 55 MPa. Similar to the elastic modulus in the testing by Kornmann and Huber [18], the tensile strength was found to be lower than bulk PZT. The pure Perovskite PZT was roughly 52 % of bulk value while the Nb-PZT was roughly 72 % of bulk value. Electrical testing was also conducted on PZT fibers in the study by Yoshikawa [15]. Fibers of diameter ranging between 20 and 30 µm were installed in a micrometer controlled electrode fixture with fibers of 3 mm in length. A schematic of the fixture is shown in Figure Polarization testing of the fibers was performed in the fixture where an electric field is applied to the fiber and current density is measured to graph PE loops. The dielectric constant was also investigated through experimentally determining the PZT fiber capacitance with the same fixture. The capacitance testing was conducted with fibers cut to lengths of 1 to 2 cm in length and the parallel plate capacitance was measured through connection to a LCR meter. Figure 1-15: Fixture for fiber permittivity and polarization measurements [15]

38 26 The polarization testing yielded results much more comparable to that of bulk. The remnant polarization was found to be 0.37 C/m 2 which is near the expected bulk value that typically falls around 0.3 C/m 2. The coercive field for the PZT fibers was found to be a little higher than bulk at an E c of 1.9MV/m, compared to E c = 1.2 MV/m for bulk. The dielectric constant was calculated from the capacitance testing. The dielectric results from the testing report a range of 500 to 1250 ± 15% for dielectric constant. The lower range of was found for the pure PZT while the Nb-PZT fibers resulted in the higher range of for dielectric constant. As observed the fiber properties are below the bulk dielectric constant of approximately This study was the only study found with direct dielectric measurements of PZT fibers with parallel electrodes. However, as the study was performed in 1995 and PZT processing has been improved, these results may no longer be representative of current available PZT fibers. A study by Zhang et al. examined the crystalline behavior and microstructure of PZT fibers prepared through a sol-gel process [21]. The majority of the study was on the examination of the FTIR and C-NMR analysis of the fibers. The dielectric permittivity of the fibers was also examined. Because of the fiber s geometry and brittleness, conventional permittivity testing conducted on single fibers was very challenging or deemed impossible. Therefore, to detect the permittivity of the fibers, the fibers were tested using a modified atomic force microscope (AFM). The AFM observation was carried at a 16 V peak to peak signal applied to the composite. The AC signal induces a converse piezoelectric response and this oscillation is detected by the AFM photodiodes. The resulting signal is detected by a lock-in amplifier. The permittivity was measured at 10 khz frequency and determined to be 544 for the PZT fibers. The low permittivity was attributed to the presence of pores left in the fiber due to the loss of organics from heat treatment.

39 27 Piezoelectric analysis of PZT fibers was conducted in a study by Lagoudas et al. [19]. In this study, fibers from four different distributers, outlined in Table 4, were tested for determination of the piezoelectric d constant, dielectric permittivity ε, mechanical compliance s and electromechanical coupling coefficient k. For the experimental procedures the fibers were cut to lengths of 5 mm and fabricated into 1-3 composites using an epoxy resin (Struers Specifix-40) due to the challenge of testing individual fibers. A schematic of the 1-3 composite is shown Figure The 1-3 composite properties were compared to analytical equations to extract the properties of the PZT fibers. Table 4: Summary of PZT 5A fibers tested [19] Figure 1-16: Schematic representation of a 1-3 piezocomposite comprising active piezoelectric ceramic fibers and a passive polymer matrix [19]

40 28 The dielectric permittivity measurements were done at 1 khz using a parallel-plate dielectric test fixture in connection to a LCR meter. Using an impedance analyzer, the impedance was measured over a frequency range of 150 khz to 500 khz with excitation voltage of 500 mv. D The impedance results were used to determine the k 33, d 33, s 33 and s E 33 of the composites. The experimental results were then compared to analytical models to determine the fiber properties. The analytical models and assumptions used in the study were derived from the study by Smith [27]. An excerpt from the study illustrating the calculated fiber properties and bulk comparison is shown in Figure The overall fiber property trends show a general reduction in piezoelectric capability compared to the bulk values. Similar comments can be made for the permittivity and compliance of the fibers. It is noted that the exact PZT composition for the fibers is not known and the piezoelectric and permittivity behavior is heavily dependent on the composition due to the morphotropic phase boundary between the rhombohedral and tetragonal phases of PZT. Therefore, a possible cause of the deviations in properties between the fibers may be due to deviations in PZT composition. The reduction in fiber properties from bulk value is attributed to smaller grain size and increased porosity. It was also found that the properties varied depending upon the processing method which is due to the different methods resulting in different grain sizes (see Figure 1-17) and porosity.

41 29 Figure 1-17: Experimental fiber results property comparison between manufacturing process and bulk properties [19] The study also speculates on source of other errors that may have caused the experimental properties deviating from the true fiber properties may be from the frequency dependence of the polymer matrix mechanical properties and the strength of the fiber-matrix interface. The testing frequency will change the behavior of the matrix mechanical properties as at higher frequencies the polymer matrix becomes increasingly stiffer. The volume fraction of the fiber content will also affect the composite behavior as a composite with higher fiber volume content become less sensitive to the polymer matrix and therefore less dependent on frequency. While the 1-3 fiber composite allows the fiber properties to be calculated from analytical models, idealization of the fiber and fiber-matrix interface behavior leads to an overestimation of the true

42 30 fiber properties. Therefore, for characterization of true fiber behavior, explicit testing of single PZT fibers is needed. As mentioned, explicit testing of PZT fibers is very challenging due to the small scale diameter of the fibers as well as the brittleness of the fibers. The geometry makes it difficult to apply electrodes to the fibers for testing while the brittleness makes the use of conventional equipment difficult due to the load sensitivity of the fiber. A study by Guillot et al. investigated testing of a hollow PZT fiber that was then electroded on the inner and outer surfaces [20]. The focus of the study was to characterize the energy harvesting ability of an individual electrode hollow fiber for applications to be woven into fabrics for energy harvesting. The permittivity of the fibers was calculated from the measured capacitance using an impedance analyzer over the frequency range of 100 Hz 5 khz. The permittivity of the fiber was found to be 40% of that reported for bulk. The d 31 piezoelectric constant was determined from analyzing the tip displacement using a laser vibrometer while applying an AC voltage. The experiment yielded a d 31 of -105x10-12 m/v, a value approximately 55% of that reported for bulk PZT. The fiber properties are expected to fall between 65%-75% of the bulk material. This range was provided by Smart Materials Corporation, the supplier of the fibers used in the study conducted by Guillot. While the study characterizes the behavior of single PZT fibers, the electrode configuration and geometry orientation make it difficult to compare the properties directly to that of bulk PZT and responses of AFCs utilizing IDEs. As a result, research examining the behavior of PZT must not only be characterized for single PZT fibers with parallel electrode configuration, but also with an IDE configuration to better understand the PZT fibers in the AFC environment.

43 Scope of Thesis Goal and Related Tasks The goal of this thesis focuses on experimental characterization of single PZT fibers using two electrode configurations. Replicating the environment of the AFC is challenging but will ultimately be rewarding: The characterization of the fibers will result in better understanding of the fibers that will assist in improving the designs of AFCs and will also positively impact the development of better models. By determining the fiber behavior in replicated AFC environments the polymer matrix can be selected to better match the fiber. A systematic approach will be utilized to methodically characterize the PZT fibers in a manner that will account for different loading conditions that the fiber would experience in the AFC. The specific tasks of this research are: Characterization of mechanical and electrical behavior of PZT fibers Determination of PZT fiber permittivity for parallel and IDE electrodes Electromechanical characterization of PZT in parallel and IDE electrode configurations Verification of experimental results for parallel and IDE electrodes using FEA Organization of Thesis Chapter 1 of this thesis provides background into past and current research studies on the improvement of AFCs and the determination of PZT fiber behavior. Chapter 1 highlights the lack of explicit determination of PZT behavior in the fiber form and defines the goals to accomplish this task throughout this work. Chapter 2 of the thesis outlines the systematic experimentation

44 32 conducted to achieve the set goals of the thesis. The experimentation begins with mechanical and electrical characterization of unpoled and unloaded fibers to form a control data set. Cyclic mechanical loading is then investigated to resemble the repeated actuation the fiber may experience in the AFC. The loading effect is examined for both mechanical and electrical properties. The PZT fibers are then poled for examination of the effect of dipole alignment for both mechanical and electrical behavior. The second task of determination of PZT fiber permittivity is then addressed. The experimental procedure is conducted for both parallel and IDE electrodes. It is noted that direct dielectric permittivity with IDE configuration has never been performed for single PZT fibers before. The third task of determining the electromechanical behavior of PZT fibers is addressed next. The task is conducted for the determination of the piezoelectric e 33 in particular. It is noted that direct e 33 determination of single PZT fibers has never been performed before for parallel electrode or IDE configurations. Chapter 3 of the thesis reports and discusses the results from the control and mechanical loading experiments. Chapter 4 reports and discusses the results from the poled fiber, permittivity and electromechanical testing results. As results for the permittivity with IDEs and e 33 for both parallel and IDE electrodes have not been previously published for individual PZT fibers, verification of these results through modeling is needed. Chapter 5 details the construction of the models and conditions used for the simulations with the attempt of validating the experimental results as defined in task 4. Chapter 6 provides of a summary of the findings of the thesis, conclusions that can be made based on the results, and recommendations for future work.

45 33 Chapter 2 Experimental Methods for Characterization of PZT Fibers 2.1 Introduction This chapter details the equipment utilized for the experimental characterization of the PZT fibers. The detailed procedures conducted for each experiment are also provided. The first experiments conducted are done to determine of the performance of unloaded PZT fibers that will be used as control in subsequent experiments. The PZT 5A fibers used for testing are supplied by Advanced Cerametrics (Lambertville, NJ) (Figure 2-1). The fibers have a diameter of 250 µm with a length of 200 mm. The 5A in PZT refers to the composition and classification of the material. Commercially available PZT compositions usually have added dopants to tailor the properties for specific applications; the type of doping used leads to PZT being classified as either hard or soft PZT. Hard PZT is obtained by acceptor doping either by replacing Pb with monovalent cations such as K +1 or by replacing (Zr, Ti) with acceptors such as Fe +3. Soft PZT is formed when donor dopants such as La +3 is used in place of Pb or Nb +5 in place of (Zr, Ti). Soft PZT exhibit high dielectric loss, low electrical conductivity, low coercive field, and is easy to pole/depole while possessing high piezoelectric coefficients. PZT 5A is classified under soft PZT and differs from other soft PZT such as PZT 5H in terms of composition and dopants used [22].

46 34 Figure 2-1: PZT 5A fibers from Advanced Cerametrics The experimental testing utilizes two electrode configurations for testing of the PZT fibers: parallel and IDE. The assembly used to test the fibers using IDEs is detailed in section 2.2. The experimentally determined properties of PZT fibers will be compared to the bulk PZT values provided in Table 5. A reduction in the bulk PZT values reported in Table 5 is expected for the PZT fibers due to the increased porosity and smaller grain size of the fibers. The values for the electromechanical properties of PZT fibers is estimated to range from 65%-75% of the bulk PZT values [20]. In previous studies, the density of bulk PZT was found to reduce by less than 5% during the sintering process due to the organic components evaporating during the sintering process resulting in bulk porosity of approximately 5%. The porosity has differing effects as the elastic properties can vary as much as 5%, piezoelectric properties as much as 10% and dielectric properties as much as 20% [28]. The porosity found in fibers was found to be approximately 20% [18]. With the porosity of PZT fibers approximately four times larger the effects on the mechanical, piezoelectric and dielectric properties will be substantial. The experimental results will be compared to the estimated 65%-75% of bulk range values.

47 35 Table 5: Bulk PZT 5A reported values [26] Bulk PZT 5A Dielectric Constant, ε r 1700 Young's Modulus, Y (GPa) 53 Induced Strain, d 33 (pm/v) 374 Induced Stress, e 33 (C/m 2 ) 15.8 Coercive Field, E c (MV/m) 1.2 Remnant Polarization, P r (C/m 2 ) IDE Assembly Design To reproduce the PZT fibers behavior in the AFC with interdigitated electrodes, an IDE assembly was created, shown in Figure 2-2, to place the fibers between electrodes but without the presence of the epoxy matrix. The assembly is composed of laser cut acrylic plates with M2 plastic bolts and nuts to maintain contact between the fiber and the two plates. On the inner faces of the acrylic plates, Mylar sheets with screen-printed IDEs are secured with adhesive. The screen-printed electrodes are fabricated using screens ordered from UTZ Technologies with a polycarbonate bus ink. The screen-printing procedure is provided in Appendix A. Adhesion of the Mylar sheets to each other is done carefully to assure proper alignment of the IDE of the top and bottom acrylic plates. Very fine gage copper wires (0.125 mm diameter) are attached to the end terminals of the interdigitated electrodes patterns to allow for voltage to be applied establishing an electric field on the PZT fibers.

48 36 Figure 2-2: PZT IDE assembly illustrating components Figure 2-3 illustrates the dimensions of the full scale AFC IDE design and smaller IDE used for testing single PZT fibers. The IDE pattern used for the assembly is a scaled down version of the IDE pattern utilized in the AFCs as a means to test a single PZT fiber. The distance between electrode fingers of the IDE pattern was increased from 500 µm in the AFC design to 750 µm to reduce arcing between electrodes. The overall width of the IDE was reduced from the 15 mm AFC design to 7.5 mm for the single fiber assembly. Similarly, the length was reduced from 140 mm to 36 mm. These dimension reductions were taken to reduce the weight that is added from the laser cut acrylic plates. As only a single fiber will be tested in the assembly it is vital to reduce the impact the assembly will have on the fiber due to the component s weight acting on the fiber. The screen printed electrode pattern maintains the 500 µm electrode width from the AFC pattern.

49 37 Figure 2-3: AFC IDE (A) size comparison to (B) IDE assembly The end terminals were also redesigned into a T-shaped pattern to maximize the effective electrode area of the tested PZT fiber as well as providing distance between the copper wire connections and the testing equipment to prevent electrical damage to the testing equipment. The copper wires are secured on the electrode terminals using Kapton tape. A step by step procedure of fabricating the IDE assembly is supplied in Appendix B. 2.3 Mechanical and Electrical Characterization of Unpoled PZT Mechanical Behavior Tensile testing was conducted on PZT fibers to gather control properties that will be used to compare the effect of various treatments of the fibers. The PZT fibers supplied by Advanced

50 38 Cerametrics were cut from their shipped length of 200 mm to lengths of 50 mm to allow for easier installation between grips. A RSA-G2 Dynamic Mechanical Analysis (DMA) from TA Instruments is used in conjunction with Trios software to collect the tensile test data. The DMA was chosen for testing for testing due to of its versatile test configurations. The DMA has different grips that can be installed for tensile, compression, three point bending and shear testing. The DMA in conjunction with the Trios software allows for highly customizable procedures as well. An environmental chamber is also available in the DMA and is used in the mechanical loading experiments in section 2.4. The DMA tensile grips designed for thin films are used with the PZT fibers (Figure 2-4). The fibers are secured in the grips in place though bolts that lock the grips closed. The fiber is installed carefully in the top grip first and bolts tightened manually as to not apply too much pressure from the grips that may damage the fibers. The grips themselves contain threaded grooves that assist in proper alignment of the fibers, see inset of Figure 2-4. With the bottom grip open, the fiber is slowly lowered while making sure the fiber is on track to enter the grip opening. Before tightening of the bottom grip, the DMA force is tared so any force measured by the DMA is from tension on the fibers from the grips. Upon locking of the bottom grip, the load of the fiber is brought to 2 MPa to apply an initial pre-stress on the fiber prior to testing. The pre-stress is to ensure fiber is in tension and will minimize test errors such as slack of the fiber. An image of a fiber loaded in the DMA is provided Figure 2-4.

51 39 Figure 2-4: PZT fiber installed in DMA grips for tensile testing The tensile tests were conducted at room temperature 25 o C. The strain rate selected for the test was initially 0.005mm/s to match the strain rate used by Kornmann et al. [18] but was later reduced to 0.001mm/s. The reasoning for the change was due to DMA performance for the mechanical loading discussed in section 2.4. The loading conditions in the Trios procedure outlined step termination limits for set stress levels. At the mm/s strain rate the DMA would overshoot the set stress limit. This became problematic at higher stress limits as the larger stress that was imposed on the sample would cause premature failure in the middle of the 15 load/unload cycles. Lowering the strain rate to mm/s minimized this overshoot and increased the success rate of samples undergoing all 15 load/unload cycles. The tensile test was revisited for the mm/s strain for mechanical property determination consistency. For the tensile test the fibers are subjected to the strain rate until fracture. From the test the stress and strain are recorded. The Young s modulus and tensile strength of the fibers are determined. The Young s modulus is taken as the slope of the stress

52 40 strain curve for strain below 0.01%. This correlates to the linear elastic regime of the stress-strain curve for PZT. The tensile strength is taken as the fracture strength as is the convention for brittle materials Electrical Behavior Polarization tests were conducted on the supplied fibers to measure the electrical displacement D given by equation (2.1). The polarization P is given by equation (2.2). Because the permittivity for PZT is on the order of 1700 times larger than the permittivity of free space, ε o = 8.85 x F/m, the polarization can be taken as equivalent to the electrical displacement; i.e. ε r (ε r 1). The polarization tests were conducted for both parallel electrode and IDE configurations. The equipment for the testing was the same for both electrode types with only the fixtures being different. The polarization equipment consists of a Trek Model 609A-3 high voltage amplifier and a Stanford Research Systems Model SR830 DSP Lock-In Amplifier. D = ε r ε o E (2.1) P = ε o (ε r 1)E (2.2) The test connections are made using coaxial cables from the high voltage amplifier and lock-in amplifier to a parallel electrode setup through a modified Sawyer-Tower circuit. The Sawyer-Tower circuit is used to observe the polarization switching of a piezoelectric material with an external electric field [29]. A schematic of a Sawyer-Tower circuit is provided in Figure 2-5. In the circuit, the linear capacitor, C, stores the charge developed in the ferroelectric sample,

53 41 C x. The potential difference on C is measured with the lock-in amplifier to determine the electrical polarization of the material as a function of the applied electric field [29]. The parallel electrode setup features two spherical copper electrodes with a spring on the top electrode that could be used to control pressure on the sample. A shaft extends from the top electrode through the spring mechanism where it is attached to a LVDT used to measure the strain on the sample. The strain is observed in the lock-in amplifier and the force on the sample was controlled through micrometer connected to the shaft of the top electrode. The polarization test fixture for parallel electrodes is shown in Figure 2-6 as well as an image of the LVDT and micrometer locations. Figure 2-5: Modified Sawyer-Tower circuit for ferroelectric hysteresis [30]

54 42 Figure 2-6: Polarization and strain test fixture (left) showing LVDT and micrometer for pressure control (right) Figure 2-7: PZT fiber installed in PE fixture (left) and spring mechanism shown (right) PZT fibers are cut to lengths of 2mm and then installed vertically between the two spherical copper electrodes as shown in Figure 2-7. The spring mechanism, also shown in Figure 2-7, on the parallel electrode setup is locked into a position with a bolt so it does not apply any

55 43 additional force on the sample other than the weight of the copper electrode itself. The weight of the electrode is then removed from the sample by changing the top electrode position by turning the micrometer at the top of the fixture. The parallel setup is then placed in a container of Galden oil so that the fiber and both electrodes are submerged to prevent arcing from the close proximity of the spheres. Once submerged in the oil, a range of uniform AC electric fields from 0.1 MV/m to 3 MV/m is applied at a frequency of 1Hz. For the IDE setup, the fibers are cut to a longer length of 45mm so that the fiber is in contact with the full electrode pattern (see Figure 2-2). Unlike the parallel electrode setup that utilized a LVDT to measure the strain of the sample, the IDE assembly does not have a component to measure the strain so only the polarization and electric field from the test are recorded. When calculating the polarization with the IDE, the effective area used is the cross sectional area of the fiber multiplied by the number of electrode gaps. The number of electrode gaps is 24 as observed in the IDE Figure 2-3. This is done to effectively sum the electric field contribution for each electrode gap. The IDEs were submerged in Galden oil for comparison to the parallel electrode results as well as tested without being submerged in oil. The IDE was tested without submersion in oil to quantify any change in behavior when the IDE is exposed to air. This was done as when the IDE is used for electromechanical tests it will not be submerged in oil but exposed to air. For both electrode setups, the samples were tested for five AC electric field cycles at 1Hz. The value of the electric field ranged from 0.1MV/m to 3MV/m.

56 Mechanical Loading Effect While in the AFC device, the PZT fibers may undergo cyclic or periodic stress. It is therefore important to understand how the PZT fibers behave after experiencing multiple loading cycles. To determine the cyclic loading effect on the PZT fibers, the DMA is utilized. The Trios software allows for a test method to define multiple steps to be performed on a sample. Using the step functionality in the Trios software, loading and unloading cycles were created by alternating a tensile stress step and a relaxation compressive stress step. The tensile stress is controlled to maintain a maximum predetermined value for the entirety of the respective test. This is controlled by defining a step termination condition in the Trios software for a step based on the current applied stress on the sample. A visual representation of the load/unload cycle is provided in Figure 2-8. In the schematic a PZT fiber is loaded between the tensile grips of the DMA. The initial position represents the state of the fiber before any load has been applied other than a small pre-stress of 2 MPa. The second image represents the tensile loading step and shows the fiber being stretched. Below the schematic is an illustration of the stress (T) strain (S) curve showing the fiber being loaded to a predetermined maximum stress. The third image shows the fiber being relaxed back to zero stress. It should be noted that this value does not correspond to zero strain as there will be unrecoverable strain due to irreversible motion of domain walls. It should also be noted that the stress does not follow the previous step s tensile stress curve due to the ferroelastic behavior of PZT which results in a hysteresis loop of the stress and strain (analogous to the ferroelectric hysteresis PE loop discussed in section 1.2).

57 45 Figure 2-8: Visual representation of load/unload cycles For a single test, the PZT fiber will experience 15 complete load/unload cycles. A range of maximum stresses as well as three different temperature settings are used to test the fibers. Depending on the application, the AFC will experience different loading conditions so it is important to understand the behavior of the fibers for a wide range of stresses. The stress levels investigated in this work include 5, 10, 15, 20 and 25 MPa. The maximum stress of 25 MPa is the highest stress that could be conducted for successful testing of all 15 load/unload cycles. The three temperatures that the mechanical loading tests were conducted at were 25 o C, 50 o C and 75 o C. The temperatures were applied to the PZT fibers while in the DMA grips using the DMA s environmental chamber seen in Figure 2-9. To prevent the temperature from causing premature failure due the thermal expansion of the fiber, an initial step is added to the test procedure. The initial step performs a temperature ramp from room temperature to the desired testing temperature at a rate of 3 o C/min. Once the desired temperature is reached, the sample is held at temperature for 5 minutes before undergoing the loading and unloading cycles.

58 46 Figure 2-9: DMA environmental chamber with fiber installed for mechanical loading 2.5 DC Poling Effect DC poling of PZT fibers is performed to reorient and align the dipoles in the PZT. The orientation of dipoles is known to improve the piezoelectric capabilities of bulk PZT and is thus a factor that is considered in the characterization of PZT fibers. Poling of the PZT fibers is a difficult task with parallel electrodes as positioning the fibers between the electrodes without breaking the fibers due to their brittle nature is very challenging. By implementing the IDE assembly the challenge of poling became simpler. PZT fibers are cut to a length of 45 mm and inserted into the IDE assembly between the screen-printed electrodes. The fibers are then secured into the assembly by tightening the plastic bolts and nuts. Once secured, the wires attached to the end terminals of the IDE are then connected to the Trek high voltage amplifier which is connected with the HP function generator as seen in Figure 2-10.

59 47 The high voltage amplifier is turned on and the function generator is configured for DC output and slowly ramped up in voltage until reaching the voltage corresponding to 2 MV/m. An electric field of 2 MV/m is used since it is greater than the coercive field necessary for dipole reorientation as was discussed in section 1.2. In the polarization testing results in section 3.1.2, the coercive field was found to be approximately 1.5 MV/m for PZT fibers. Once at 2 MV/m the sample is maintained at the electric field for a minimum of 5 minutes to provide sufficient time for the dipoles to reorient and align in the poling direction. The 5 minutes time frame was determined through comparison with poling at longer time frames of 10 minutes and 15 minutes. The values determined for remnant polarization remained identical for the three times, thus 5 minutes was used to optimize time efficiency of the experiments and allow for testing of more samples. Figure 2-10: Schematic of DC poling with IDE assembly After poling the PZT fiber, the effect on the mechanical and electrical behavior was determined. For the electrical testing, the PZT fiber was kept in the IDE assembly and connected

60 48 to the polarization testing equipment described in section The fiber is then placed under the same testing conditions applied to the unpoled samples. For the mechanical testing, the poled PZT fiber is carefully removed from the IDE assembly and installed into the DMA with a gage length of 20 mm. It is noted that the gage length of the fiber is concentrated on the portion of the PZT fiber that was under the effective electrode area of the IDE. The fiber is then subjected to a strain rate of mm/s for a standard tensile test as was done during the mechanical characterization of the PZT fibers in section Dielectric Testing Two methods are utilized in the determination of the dielectric constant for PZT fibers using parallel and interdigitated electrode configurations. The first method is conducted utilizing a QuadTech 7600 Plus Precision LCR meter. The tests for the two electrode configurations are conducted in a similar manner with the same test parameters. For dielectric testing with the IDE assembly, the PZT fiber is loaded into the IDE assembly with the bolts and nuts tightened. The LCR meter is calibrated for the IDE assembly before testing. The calibration is performed for both open and short circuit terminal conditions. For parallel electrode setup additional steps are taken to improve the connection. A preliminary step of cutting PZT fibers between 1 and 3 mm in length is performed. Once the PZT fibers are cut, the individual pieces are measured and placed on a grid with the corresponding length recorded. Before testing, the cut fibers are dipped at both ends into a thin pool of silver paint to improve the electrical connection between the parallel electrodes and the ends of the fibers. Once the dimensions of the fibers are properly recorded, the LCR meter calibration can be

61 49 done. As with the IDE setup, the calibration consists of open and short circuit conditions. After calibration, the fibers are carefully place in the parallel electrode setup, which is analogous to a parallel plate capacitor but utilizes spherical electrodes instead of plates. A schematic of the parallel electrode setup is shown in Figure Figure 2-11: Parallel electrode test fixture set-up for dielectric permittivity measurements Upon completion of calibration, the dielectric test with the LCR meter for the two electrode configurations follows the same procedure. The testing is done for a frequency range of 100 Hz to 1 MHz. The test was performed with a voltage of 5 V, which is the limit of the LCR meter. The capacitance and the dielectric loss factor are recorded by the LCR meter and stored in a USB. The capacitance is used to calculate the dielectric constant, ε r, as shown in equation (2.3). In equation (2.3), C p is the capacitance, d is the electrode gap, A is the cross sectional area of the fiber and ε o is the permittivity of free space (ε o = 8.85 x F/m). When calculating the permittivity for the IDE, the effective area used in the calculations is the cross sectional area of

62 the fiber multiplied by the number of electrode gaps as was done in the polarization calculations discussed in section ε r = C pd ε o A (2.3) A second method of dielectric testing was conducted using a Cascade Microtech Probe Station connected to a HP 4980 Precision LCR Meter. The Cascade Probe Station has interchangeable probes varying in probe tip size from 5 µm to 20 µm. The tips of the probes are made of copper and are used to measure the capacitance and loss of the specimen under the test. The probe with a 5 µm tip size is used for easier placement onto the samples. A microscope is featured with interchangeable magnifications lenses of 2x, 5x and 10x. The microscope allows the user to have a magnified view of the specimen to ensure proper placement of the probes. The Cascade Probe Station is shown in Figure Figure 2-12: Cascade probe station setup with PZT fiber samples installed

63 51 The parallel electrode test is performed the following manner: the PZT fibers are cut to lengths of 2 mm and their exact lengths are measured with a digital caliper and recorded for determination of dielectric permittivity after testing. The fibers are then dipped at both ends into conductive silver paint. After allowing a few hours for the silver paint to dry, the fibers are tested with the Cascade Probe Station where the dried silver paint will act as the electrodes. The electrode fibers are placed on doubled sided scotch tape adhered to a glass slide to secure the fibers in place while the probes are lowered to make contact. The parallel electrode setup is and magnified view showing probe contact with silver paint electrode is provided in Figure Figure 2-13: Cascade probe test conducted using parallel electroded fibers (left) and magnified view of probe in contact with silver paint electrode (right) The Cascade Probe Station is also used with the PZT fibers using the IDE assembly. The testing is performed with the probes contacting the copper wires of the IDE assembly. Similar to the parallel electrode testing with the probe station, a glass slide with double sided scotch tape is used to secure the connections. The probes are carefully placed in contact with the copper wires in connection with the IDE terminals. The IDE assembly installed in the Cascade Probe Station with magnified view of probe connection is show in Figure 2-14.

64 52 Figure 2-14: Cascade probe test conducted using IDE assembly (left) and magnified view of probe contact with copper wire (right) 2.7 Simultaneous Mechanical and Electrical Loading For AFCs, the composite will be subjected to both mechanical and electrical loading simultaneously. If the AFC is acting as an actuator, then an electric field will be applied resulting in a mechanical strain. On the other hand, if the AFC is acting as a sensor then a mechanical deformation will be applied resulting in an induced electric potential. Therefore, both functions are important in the characterization of a PZT fiber. The initial challenge in determining the PZT behavior for both electrical and mechanical loading conditions was how to apply and measure the electric potential to an individual fiber without the presence of an epoxy matrix. The solution was to create a small assembly that would encase the fiber with IDEs and provide the needed support without breaking the brittle fiber. The PZT fibers are then tested under two conditions: 1) while applying an AC electric field under pre-stress and measuring the resulting change in stress, and 2) applying a sinusoidal mechanical load to the fiber with constant applied electric field bias and measuring the resulting change in voltage.

65 53 In addition to stress-strain behavior under electric loading and electric field-charge behavior under mechanical pre-stress, the effective piezoelectric coefficient e 33 is also calculated from these sets of measurements. The piezoelectric coefficient e 33 is defined in the S-E form of the constitutive equations below in equations (2.4) and (2.5) [31]. Details on the constitutive equations, the meaning of the indices and common forms of the piezoelectric coefficients can be found in section 1.3. T 3 = c 3 E S 3 e 33 E 3 (2.4) D 3 = e 33 S 3 + ε 3 S E 3 (2.5) It is noted that e 33 is considered here because it is the coefficient that is the more straightforward to obtain when using FEA modeling, allowing us to compare measured and predicted results later in the thesis (see Chapter 5). In equation (2.4) the term c is defined as the material stiffness. The electromechanical testing conducted will utilize equation (2.4) with the additional boundary condition that the strain will be held constant at 0. Thus the e 33 will be directly determined as the stress produced divided by the electric field applied Parallel Electrode Method There is no off-the-shelf equipment that can test the piezoelectric response of fibers while under mechanical loading. For that reason, great effort was expanded in order to design a set-up that is appropriate for the sample of interest as well as the experimental conditions required. Here

66 54 too the goal was to characterize the fibers using two electrode configurations: parallel and IDE. For the parallel electrode setup, the designed procedure included a Dynamic Mechanical Analysis (DMA) TA Instruments RSA-G2, a HP 33120A function generator and a Trek model 609D-6 high voltage amplifier. The parallel electrodes were fabricated using brass ball bearings that were machined and connected to 3D printed fixtures to electrically insulate the DMA tensile fiber/film grips. The electrodes were also given a small indent on the fiber interface to allow for easier fiber installation between electrodes. The electrodes are connected to the high voltage amplifier through insulated wires with terminal connections to the electrodes. The electrode configuration and the DMA grip connections are shown in Figure Figure 2-15: Parallel electrode configuration installed in DMA with PZT 5A fiber The PZT fibers are cut to approximately 2 mm in length and are then measured with digital calipers for exact length. The fibers are cut to 2 mm to maximize the range of electric fields that can be produced given the limitations of the high voltage amplifier. The exact length is reduced by 0.10 mm to account for the small indents on the electrodes, and is used as the gap distanced entered into the Trios software. The fiber is carefully held while aligned between the

67 55 electrodes and the electrode gap desired is set in the DMA. Once the DMA secures the fiber in place a compressive pre-stress is applied. The pre-stress was varied from 2 MPa to 40 MPa with electric field at 0.3 MV/m to determine which pre-stress would result in the highest peak-to-peak stress output. This was done to determine a pre-stress that would allow the PZT fibers to achieve their optimal piezoelectric capabilities. A range between 10 MPa and 20 MPa was found to produce the maximum peak-to-peak stress and was used going forward. The pre-stress evaluation is discussed in more detail in section The samples are loaded in the electrodes at the 10 MPa pre-stress and placed under a 2 MV/m DC electric field for poling. The samples are held at the DC field for a minimum of 5 minutes. After poling, the samples are tested at AC electric fields from 0.1 MV/m to 1.0 MV/m with a DC offset of the same electric field. The electric fields are tested at three frequencies: 0.1 Hz, 0.5 Hz, and 1.0 Hz. The frequencies chosen were due to the sampling rate limitations of the equipment used for the IDE testing. The force is recorded from the Trios software working in conjunction with the DMA. From the force, the stress is calculated using the cross sectional area of the fiber. The resulting sinusoidal behavior of the generated stress as a function of the applied electric field is obtained. In addition, the piezoelectric coefficient e 33 is calculated from the maximum peak to peak value of the stress divided by the corresponding peak to peak applied electric field using equation (2.4) and the boundary condition of S = IDE Method To test the PZT fiber under simultaneous electrical and mechanical loading with IDEs, an Instron 5866 load frame, HP 33120A function generator and Trek model 609D-6 high voltage

68 56 amplifier were utilized concurrently. The synchronized voltage and stress data from the tests are recorded in the Bluehill software used with the Instron. The PZT fibers were cut to lengths of 75 mm and installed into the IDE assembly before placement in grips designed for testing fibers. The length was chosen as initial installation of shorter fiber lengths were very difficult to install into the spring loaded fiber grips without breaking the fibers. The longer length allows for more space between the acrylic plates and grips, which decreased the risk of the fiber breaking during installation. When installing the PZT fibers into the IDE assembly, the plastic nuts and bolts were tightened to the point where the fiber was in contact with the screen printed IDE pattern but no too tight as to restrict motion of the fiber from the acrylic plates. Exact measurement of the torque applied on the bolts could not be determined as the value was below the range of torque screwdriver that can measure values as low as 15 cn/m. The fiber is carefully loaded into the fiber grips with the IDE assembly preinstalled with the T-shape design pointing down (Figure 2-16). Placing the IDE assembly with the T-shape at the top fixture adds more weight at the top grip and because the top grip contains a pin connector it can cause bending of the fiber. Extra care is taken due to the brittle nature of the PZT fibers. Once in the grips, the leads from the high voltage amplifier are carefully connected to the wires of the IDE assembly while avoiding pulling on the wires, which could exert a force on the fiber. A schematic of the experimental setup is shown in Figure The PZT fiber is then gradually strained to apply a constant pre-stress to the fiber. For the testing a constant stress of 5 MPa was applied so that the fiber is solely in tension throughout testing. The PZT fiber is given sufficient time to reach a stabilized value of the 5 MPa pre-stress as the fiber will experience stress relaxation when first installed in the grips.

69 57 Figure 2-16: Schematic of electromechanical testing setup utilizing IDE assembly Upon reaching equilibrium, the fiber is to undergo DC poling through a 2 MV/m electric field applied through the IDE. The field is applied for a minimum of 5 minutes to provide sufficient time for dipole reorientation. After the electric field is removed, the pre-stress is adjusted back to the 5 MPa value. The fiber is then ready for the application of the AC electric fields from 0.1 MV/m to 1.0 MV/m. The AC electric fields are applied for frequencies of 0.1 Hz, 0.5 Hz and 1.0 Hz at each respective electric field. The stress and voltage applied to the sample are recorded simultaneously through the Bluehill software. The electric field is calculated from the voltage using the fiber cross sectional area and the electrode gap and number of gaps from the IDE geometry. The single sinusoidal cycle of stress is then plotted as a function of the

70 58 corresponding electric field. For each field, a linear trendline is added and the slope of the trendline is taken as the e 33 for that respective electric field. The calculations are performed for every electric field and frequency. From examining the results, the calculated e 33 for the IDE were found to be well below what was initially expected. Upon examining the experimental setup, it was observed that the stress values recorded were affected by the compliance of the fiber grips. The fiber grips are composed of a small steel base connected to a spring-loaded grip which was made of plastic. Along with the composition, the top fiber grip was connected through a pin connector that allows the grip to swivel around an origin at the connection. The combination of this lead to some of the stress become absorbed by the grips and reduced values being output in the software. To attempt to gather more accurate stress data the DMA was used for further IDE testing. For the IDE DMA testing, the high voltage amplifier and function generator used for the parallel electrode setup is utilized. The differences from the parallel electrode setup are the grips and electrode configuration used for the IDE testing. The IDE testing utilized the tensile grips of the DMA without any additional fabricated component; the PZT fibers were installed into the IDE assembly and then placed in the tensile grips of the DMA. The fibers were cut to lengths of 75 mm with the gage length of the DMA set for 50 mm. The length of the acrylic plates is only 38 mm but the extra space between the grips and the IDE assembly is needed to ensure no electrical current can travel and damage the DMA. Electrical tape was placed on the faces of the grips closest to the IDE assembly to apply electrical insulation from the fine gage copper wires. The IDE assembly installed in the DMA is shown in Figure 2-17.

71 59 Figure 2-17: IDE assembly installed in DMA for electromechanical testing The DMA test run is identical to the Instron procedure. The PZT fiber with IDE assembly preinstalled is carefully loaded into the grips of the DMA. Once in the grips, the leads from the high voltage amplifier are carefully connected to the copper wires of the IDE assembly while avoiding pulling of the wires that may exert force on the fiber. The PZT fiber is gradually pre-stressed to 10 MPa and given sufficient time to reach equilibrium from stress relaxation before applying the voltage to the IDE. Upon reaching equilibrium, the fiber is to undergo DC poling through a 2 MV/m electric field for 5 minutes. After the electric field is removed, the prestress is adjusted back to the 10 MPa. The fiber is then ready for the application of the AC electric fields from 0.1 MV/m to 1.0 MV/m. The AC electric fields are applied for frequencies of 0.1 Hz, 0.5 Hz and 1.0 Hz at each respective electric field. The force is recorded from the Trios software working in conjunction with the DMA. From the force, the stress is calculated using the cross sectional area of the fiber and the resulting sinusoidal behavior of the stress from the electric field is observed. The maximum peak-to-peak

72 60 value of the stress response for a single cycle at a respective electric field and frequency is recorded. The value of the peak-to-peak stress is then divided by the maximum peak-to-peak amplitude of the electric field to report the e 33 constant. It is noted that the calculation of the e 33 for testing with the DMA may include some small errors because the voltage signal and the force cannot be recorded simultaneously in the Trios software.

73 61 Chapter 3 Mechanical Testing Results 3.1 Unloaded PZT Fiber Results Mechanical Response The Young s modulus for unpoled PZT fibers was found to be 33GPa. A total of 15 samples were tested for the tensile tests. A standard deviation for 95% confidence (2 sigma) resulted in a value of approximately 3 GPa. Therefore, the experimental value with standard deviation included is reported as 33 ± 3 GPa. The stress-strain plot for the linear behavior below 0.1% strain is shown in Figure 3-1. The solid line in the plot represents the average experimental Young s modulus with the dashed lines representing the upper and lower limits with the standard deviation. The value is lower than the modulus found by Kornmann et al. of approximately 40 GPa [18]. The discrepancy can be explained by the difference in strain rate. Initially the same strain rate of mm/s was used but due to the problem that developed for the mechanical loading the strain rate was lowered to mm/s. Generally, a faster strain rate correlates to an increase in modulus. The value for the Young s modulus of bulk PZT reported by Bent is 53GPa [9]. Based upon the reported bulk value and the determined Young s modulus, the average value of the fiber is found to be 62% of that of the bulk. This percentage is found to be just outside of the expected 65%-75% range [20]. With the inclusion of the standard deviation to a 95% confidence level value of the Young s modulus falls within the 65%-75% range.

74 Stress (MPa) Strain (%) Figure 3-1: Stress-strain behavior of unpoled PZT fibers Some source of error in the experimental value is due to the fact that some of the fibers experienced initial lag in the stress strain curve that results from slight fiber misalignment in the grips. This effect is minimized by an applied pre-stress but twisting of the fiber may still be present. Another source of error in the Young s modulus is the nonlinear nature of the stressstrain curve. Due to this nonlinearity, it becomes difficult to determine the linear elastic region of the curve. For the values determined in the experiments, the Young s modulus was determined as the slope of the stress-strain curve for the range of strain between zero strain to 0.01%. This region corresponds to stress levels below 5 MPa. The data used in these cases maintained an R 2 value of or higher and therefore led to the conclusion that the 0.01% strain limit was appropriate.

75 63 Other mechanical properties of interest such as the ultimate tensile strength, fracture strength and fracture strain were unable to be determined to a conclusive value. For the tensile tests conducted, the values for ultimate tensile strength, fracture strength and fracture strain were too inconsistent to report a value range with a reasonable standard deviation. Sample values for fracture stress ranged from 18MPa to 55MPa with a non-gaussian distribution. Possible causes of this large range are surface imperfections of the PZT fibers that act as stress concentrators and weakened areas of the fibers due possible overtightening of the grips Electrical Response The electrical testing conducted was to determine the coercive field and remnant polarization of the unloaded PZT fibers. The coercive field and remnant polarization was defined in section 1.2. The voltage was applied for 5 cycles for every test and the resulting polarizationelectric field (PE) loops were recorded as described in section Some with the parallel electrode configuration tests resulted in poor results with large deviation between cycles. These deviations are likely owing to the difficulty in aligning the fiber between the parallel electrodes and possible slipping in during the tests. The results with these deviations were discarded and not considered further in the analysis. The coercive field, remnant polarization and strain are calculated from a code run in MATLAB that examines the intercepts of the PE loops and magnitude of the strain in the butterfly SE loops. The resulting coercive field and remnant polarization for the unloaded fibers at 2.5 MV/m were found to be 1.49 MV/m and C/m 2 respectively for the parallel electrode configuration. The reported values for bulk PZT coercive field and remnant polarization are 1.2

76 Polarization (C/m 2 ) 64 MV/m [26] and 0.3 C/m 2 [32] respectively. The values found for the fibers are very comparable to that reported for bulk PZT with the coercive field within 20% and remnant polarization within 8% respectively. The PE loops for the electric fields progressing to the fully developed ferroelectric loop is provided in Figure 3-2. As observed, the PE loop starts without the defined saturation polarization described in section 1.2 because the applied electric field is below the coercive field value. As the electric field increases above coercive field the saturation polarization becomes more defined. This pattern continues for higher electric fields until the fiber experiences dielectric breakdown MV/m 1.5 MV/m MV/m 2.5 MV/m Electric Field (V/m) x 10 6 Figure 3-2: Ferroelectric PE loops developing for increasing electric field in parallel electrodes The coercive field and remnant polarization for the IDE submerged in Galden oil were found to be 1.57 MV/m and 0.16 C/m 2 respectively. The IDE exposed to air was not able receive electric fields higher than 2 MV/m as multiple sparks could be seen most likely due to the breakdown of air which damaged the IDE patterns and fibers. The coercive field and remnant

77 Polarization (C/m 2 ) 65 polarization of the dry samples remained comparable to the parallel and submerged IDE results with a coercive field of 1.6 MV/m but slightly lower remnant polarization of 0.11 C/m 2. The lower remnant polarization is due to the lower field possible with the IDE exposed to air compared to the Galden oil. A plot of the PE loop for unloaded fibers tested with both electrode configurations while submerged in Galden oil is shown in Figure PE Comparison Parallel vs IDE Parallel IDE Electric Field (V/m) x 10 6 Figure 3-3: PE loop of unloaded PZT fibers with 2.5 MV/m applied electric field The coercive field for the parallel electrode and IDE configurations is comparable but a noticeable drop in remnant polarization is observed for the IDE. The drop is a result of the nonuniform electric field applied on the fiber by the IDE (see Figure 1-2 for electric field schematic). The middle of the PZT fiber experiences a localized uniform electric field between the electrode fingers. However, directly under the electrode fingers the localized field is angled between the direction of poling and through the fiber thickness. An approximation of the resulting

78 66 dipole alignment with IDE for a DC poling field is shown in Figure 3-4. As observed, the case for dipole alignment under the DC field doesn t result in the dipoles as pointing in the direction of the electric field as is the case for parallel electrodes shown in Figure 1-4.The sum of the electrode widths makes up roughly 67% of the entire effective electrode area of the fiber. Considering that the surface of the fiber in between electrode gaps also do not experience a localized uniform field, then it is reasonable to receive roughly 50% of the polarization with the IDE in comparison to the parallel electrode which has a 100% uniform electric field. Figure 3-4: IDE dipole orientation for (A) random orientation before poling, (B) alignment of the dipoles with nonuniform electric field and (C) remnant polarization after electric field is removed The strain on the PZT fibers is recorded using the LVDT discussed in section The strain reported is the difference between the maximum and minimum values of the SE butterfly loop for a single cycle. The average value determined for unloaded PZT fibers in parallel electrodes was found to be 0.072% strain at a 2.5 MV/m electric field. The strain-electric field (SE) butterfly loops for increasing electric field are shown in Figure 3-5. Substantial increase in strain is observed as the electric field is increased. After reaching 2.0 MV/m, the change in increasing electric field is less pronounced as the PZT is now above the coercive field and now experiencing ferroelectric behavior describe in section 1.2. The coercive field remains identical for the 2.0 MV/m and 2.5 MV/m electric fields since ferroelectric behavior has been reached. The

79 Strain (%) 67 strain is still able to increase due to the saturation polarization still increasing at higher fields until dielectric breakdown is reached. No strain was recorded for the IDE electrode configuration during the polarization experiments due the IDE assembly MV/m MV/m 2.0 MV/m 2.5 MV/m Electric Field (V/m) x 10 6 Figure 3-5: SE butterfly loops developing for increasing electric field in parallel electrodes 3.2 Mechanically Loaded PZT Fiber Results Mechanical Response The PZT fibers are tested under cyclic loading using a DMA at set load limits discussed in section 2.4. As mentioned in section the strain rate had to be lowered due to stress limit overshoot being experienced at the mm/s strain. A plot illustrating the stress exceeding the 10 MPa limit for the mm/s strain rate is provided in Figure 3-6. The overshoot was still

80 68 found in the lower mm/s strain rate but the magnitude of overshoot was minimized to approximately 1 MPa. Figure 3-6: Strain rate of mm/s resulting in stress limit overshoot The Young s modulus (Y) of the samples is calculated for the 15 loading and unloading cycles of the experiment. The values are normalized by dividing the Young s modulus for each cycle by the overall average of the respective sample for all 15 cycles. The normalized modulus is plotted against the corresponding loading cycle. From the results, an initial increase in the normalized modulus is observed illustrating a strain hardening effect where the Young s Modulus of the fiber increases upon loading cycles. After initial increase the normalized values begin to exhibit less increase in values and plateau. A plot of the loading cycle effect for room temperature testing is shown in Figure 3-7.

81 Y/Y avg MPa 10MPa 15MPa 20MPa 25MPa Load Cycle # Figure 3-7: Room temperature loading cycle effect on Young's Modulus The initial increase observed in Young s modulus is due to dipole alignment as a result of mechanical loading. This is termed mechanical poling where the dipoles are reoriented creating a net dipole moment in the direction of the elongation and is due to the ferroelastic behavior of PZT. The limit of dipole alignment by mechanical means is illustrated by the plateau that occurs in the loading cycle plots. Quality of poling will be examined later in the electrical behavior of the mechanically loaded samples in section The stress level set for the cyclic loading affects how many cycles are necessary for the fiber to reach its mechanical poling limit. The higher loading limits, such as 20 MPa and 25 MPa, reach the plateau after the second loading cycle whereas the lower loading limits, such as the 5 MPa, stabilize at the plateau after the fifth loading cycle as observed in Figure 3-7.

82 70 As mentioned in the experimental procedure for mechanical loading, the loading cycles are representative of what the PZT fibers will experience in the AFC due to repeated use. The cyclic loading is therefore also tested at higher temperatures; since the fibers are surrounded by epoxy in the AFCs, there is evidence that the fibers may experience temperature increase due to the energy dissipation in the form of dielectric loss in the composite [33]. With the fibers, electrodes and epoxy matric encapsulated in a Kapton substrate layer, the energy dissipated in the form of thermal energy from the dielectric loss of the PZT cannot escape from the composite. The trapped thermal causes the composite to heats up. For the experimental testing, the elevated temperatures used were 50 o C and 75 o C. These temperatures did not seem to affect the higher loading limits but the lower loading limits saw a change in behavior. For the 5 MPa loading limit, the 50 o C temperature tests showed a slower increase in the loading cycle effect on the modulus. The 75 o C testing environment showed a drastic change as the modulus actual decreases with more loading cycles. The environmental effect on the 5 MPa testing is shown in Figure 3-8.

83 Y/Y avg C 50C 75C Load Cycle # Figure 3-8: Temperature effect on cyclic loading behavior of 5MPa load limit The decrease due to the elevated temperatures observed could result from a combination of the thermal expansion and dielectric loss overcoming the 5 MPa loading limit. At 50 o C higher than room temperature testing the thermal expansion contribution is no longer negligible. For the 75 o C testing temperature, it appears as though the 5 MPa load is not high enough to overcome the thermal expansion and dielectric loss of the fiber and bring the dipoles to a thermodynamically stable orientation and thus the dipoles do not align. As discussed the initial strain range of zero to 0.01% was used to calculate the modulus due to the resulting trendline being linear. This range of strain correlating to stress levels up to 5 MPa. Therefore, there is minimal strain that is unrecoverable due to the linear elastic behavior of the ferroelastic hysteresis loop at low stress and strains.

84 72 As the sample is in the compression step the strain returns relatively close back to zero. Therefore the length of the fiber has very minimal change in length before the next loading step and minimal irreversible domain wall motion occurs. This can allow the thermal expansion to repeatedly influence the fiber before each loading step. With the dipoles unable to stay aligned in a thermodynamically stable state the strain hardening like effect is no longer observed as the fibers return to the initial random dipole orientation. However, at the higher load limits the loads can overcome the thermal expansion as the higher stresses result in strain that cannot be recovered due to plastic deformation. The plastic deformation then prevents the dipoles from returning to their random orientation allows the dipoles to reach alignment under a thermodynamically stable condition. The plot for the 20 MPa loading limit is shown in Figure 3-9. As observed in the plot, the Young s modulus shows the same increasing behavior for all three tested temperatures. The decrease in behavior that exists for the 5 MPa limit is not observed for 20 MPa at elevated temperatures as the higher stresses produce irreversible domain wall motions that limit the effect of thermal expansion.

85 73 20 MPa Y/Y avg C 50C 75C Loading Cycle # Figure 3-9: Temperature effect on cyclic loading behavior of 20MPa load limit Electrical Behavior Results After undergoing cyclic loading in the DMA, the PZT fibers are tested with the polarization equipment as discussed in section The mechanically loaded fibers are tested to determine their coercive field, remnant polarization and strain at a 2.5 MV/m electric field. The experimental values for the loaded as well as the unloaded fibers are reported in Table 6. The coercive field and remnant polarization both exhibit a gradual increase in value with increased cyclic load limit. The strain shows the most substantial change as the strain increases consistently with increased cyclic load limit. The increases in the measured quantities seem to support the conclusion that the fibers were poled mechanically.

86 74 Table 6: Loaded PZT fiber electrical testing results E c (MV/m) P r (C/m 2 ) Strain (%) 0 MPa 1.49 ± ± ± MPa 1.51 ± ± ± MPa 1.49 ± ± ± MPa 1.56 ± ± ± MPa 1.54 ± ± ± MPa 1.52 ± ± ± In examination of the coercive field and remnant polarization, the loaded samples show a slight increase in value compared to the control unloaded fiber. The increase in the coercive field and remnant polarization may be due to the strain hardening like effect that was observed in the cyclic mechanical loading of the fibers that resulted in an increase in the modulus value. As the fibers are mechanically loaded, each load/unload cycle adds unrecoverable domain wall motions to the fiber as the stress exceeds the linear elastic regime. This mechanically aligns the dipoles through the elongation of the fiber. As more irreversible domain wall motions occur, the fiber length increases to new final length and by Poisson s ratio the fiber would experience a decrease in the diameter. These mechanical deformations and irreversible domain wall motions align the dipoles through the length of the fiber. The aligning of the dipoles means the fiber was poled effectively through mechanical loading. With the dipole alignment caused from the ferroelastic behavior of PZT orienting the domains and creating irreversible domain walls, the task of depoling the fiber becomes more challenging. This could explain the increase in the coercive field as a higher field is required to force the domains and dipoles to depole and become randomly orientated. This could also explain

87 Polarization (C/m 2 ) 75 the increase in remnant polarization as the change from polarization saturation to zero polarization is now occurring over a wider range of electric field. The wider PE loops for the mechanically loaded fibers can be seen in Figure The increased strain can be explained by the mechanical poling of the fibers that leads to higher piezoelectric strain output since the fibers are poled. The larger strains can be seen in Figure MPa 5 MPa 10 MPa 15 MPa MPa 25 MPa Electric Field (V/m) x 10 6 Figure 3-10: Combined loaded PZT fiber PE loops for 25 o C testing

88 Strain (%) MPa 5 MPa 10 MPa 15 MPa MPa 25 MPa Electric Field (V/m) x 10 6 Figure 3-11: Combined loaded PZT fiber SE butterfly loops for 25 o C testing

89 77 Chapter 4 Electrical and Electromechanical Testing Results 4.1 DC Poled PZT Fiber Results Mechanical Behavior Results PZT fibers are installed in the IDE assembly and poled through the application of a 2 MV/m DC electric field using a function generator and high voltage amplifier as discussed in section 2.5. Poled PZT fibers from the IDE assembly are carefully removed and installed into the grips of the DMA for tensile testing as was performed on unpoled fibers detailed in section The hypothesis is that DC poling will align the dipoles of the PZT fiber and the alignment of the dipoles will improve the mechanical properties. This theory is based on boundary conditions and the material stiffness. The boundary conditions of question will be zero electric field (short circuit) and zero dielectric displacement (open circuit). When applying these conditions to both equations supplied in equation (1.10) the resulting relationship in terms of material compliance is shown in equation (4.1). By implementing the relationship that the compliance is equal to the inverse of stiffness and rearranging, the equation (4.1) becomes equation (4.2). The stiffness c E represents the stiffness when the electric field is zero and c D represents the stiffness under electric field. From equation (4.2) it can be concluded that under an electric field the material stiffness increases (c D > c E ). Therefore, when under poling (application of an electric field) the material stiffness increases. Due to remnant polarization it is expected that the material will maintain some of the increased stiffness. This outcome would then result in an increase in Young s modulus due to higher stiffness and the stiffness and Young s modulus are proportional.

90 78 s D = s E (1 κ 2 ) (4.1) c E = c D (1 κ 2 ) (4.2) The tensile test results do exhibit an increased Young modulus for the poled sample as the new modulus is 36 GPa but this was not as great as an increase as expected. The increase in modulus is approximately 7% from the unpoled modulus of 33 GPa. The full stress-strain curves for the unpoled and poled fibers are shown in Figure 4-1 with a focused look at the linear elastic region (strain less than 0.1%) provided in Figure 4-2. While the modulus was increased in the poled fibers the fracture strain was reduced. This could result from the dipoles having preliminary alignment in the poled samples due to remnant polarization while the unpoled fibers have no preliminary alignment and utilize the tensile load to mechanically orient the fibers. However, conclusive behavior of the fracture strain could not be determined as the variation in fracture stress and strain was too large to have a consistent tensile strength and fracture strain. This was the case with the tensile testing results for the unpoled samples as well (section 3.1.1). Therefore, the only aspect mechanical aspect that can be reported is the Young s modulus behavior.

91 Stress (MPa) Stress (MPa) Unpoled Poled Strain (%) Figure 4-1: Unpoled vs poled PZT fiber stress-strain comparison Unpoled Poled Strain (%) Figure 4-2: Comparison of Young's modulus for poled and unpoled PZT fibers in linear elastic regime

92 80 A possible explanation of the smaller impact of poling on the Young s modulus could be due to a few factors that were observed during electrical characterization of unloaded fibers in section From the polarization results, the IDE was found to have a remnant polarization of approximately half that of the remnant polarization found when using parallel electrodes. As was discussed in section 3.1.2, the drop in remnant polarization is due to the nonuniform electric field produced by the IDE, as shown in Figure 1-4 and Figure 3-4. As discussed in section 2.5, IDEs were used for the poling of the fibers for the tensile test because the effective electrode area of the IDE provides a poled region of fiber over 20 mm which can be used as the gage length of the fiber for tensile testing. An effective method that is also simple to allow for quick poling of long (20 mm or larger) PZT fibers has not been determined for parallel electrodes. If such a method was available, then results from tensile testing poled PZT fibers from parallel electrodes would be expected to produce a more noticeable increase in the Young s modulus compared to the unpoled case Electrical Response The electrical testing was conducted on poled fibers to confirm poling in the PZT fibers and determine the d 33 coefficient of the fibers. The poling was conducted with the IDE assembly exposed to air. The poling is confirmed by conducting polarization testing on the poled fiber and observing the PE plot. The PE loop for an unpoled and poled PZT fiber at a 2 MV/m electric field is shown in Figure 4-3. The starting polarization has a magnitude of C/m 2. As the electric field is applied to the fiber the 2 MV/m DC field depoles the fiber and reduces the remnant polarization to 0.16 C/m 2. The starting polarization having a 25% increase in magnitude demonstrated the fiber is indeed poled. The reduced remnant polarization after depoling shows an increase in value compared to the remnant polarization found when testing unpoled fibers

93 Polarization (C/m 2 ) 81 (starting polarization = 0) with the IDE resulting in a remnant polarization of 0.11 C/m 2. The poled fiber shows an effective increase of 45% in remnant polarization compared to the unpoled case Unpoled Poled Electric Field (V/m) x 10 6 Figure 4-3: Poled vs unpoled PZT fiber PE loops at 2 MV/m with IDE exposed to air The piezoelectric d 33 is calculated from the strain measurement captured by the LVDT of the parallel electrode configuration polarization equipment. The strain in measured for poled fibers at electric fields below coercive field at frequencies of 0.2 Hz, 1 Hz and 5 Hz. The strain loops for poled samples at electric fields below coercive field do not exhibit behavior corresponding to butterfly loops as scene is section Since the fibers are not applied an electric field above coercive field, the dipoles remain oriented from the DC poling. Rather the loops appear more like the PE loops at low electric fields. A plot of the SE loop is shown in Figure 4-4 for a poled fiber tested at 1 Hz with a 0.5 MV/m AC electric field.

94 Strain (%) Electric Field (MV/m) Figure 4-4: Poled PZT fiber SE loop at 0.2 Hz with 0.1 MV/m AC electric field From the SE plots, a linear trendline is fitted and the slope of the trendline is taken as the d 33 coefficient. The calculated d 33 as a function of electric field for the three frequencies is displayed in Figure 4-5. The behavior illustrates an increasing in value of d 33 with increasing electric field. The increasing trend is due to irreversible displacements of domain walls as is explained by the Rayleigh law [34]. The Rayleigh law, originally implemented for ferromagnetic behavior, is able to model the nonlinear behavior of ferroelectric materials at low electric fields.

95 d 33 (pm/v) Hz 1.0 Hz 5.0 Hz Electric Field (MV/m) Figure 4-5: PZT fiber d 33 as a function of electric field d 33 = d 33,initial + αe 3 (4.3) The Rayleigh predicts the d 33 as the d 33 at zero electric field plus the applied electric field multiplied by the Rayleigh coefficient α as shown in equation (4.3). Equation (4.3) holds for free strain conditions (T = 0) applied to equation (1.9). Therefore, the slope of the trendline for the d 33 as a function of electric field in Figure 4-5 corresponds to the Rayleigh coefficient α and the y- intercept corresponds to d 33,initial. The d 33,initial is the value that will be used for the d 33 comparison to the reported bulk PZT value. The values were found to be 516 pm/v, 477 pm/v and 432 pm/v for the respective frequencies of 0.2 Hz, 1 Hz and 5 Hz. All three predicted values are observed to be larger than the reported d 33 for bulk of 374 pm/v [26]. This is the opposite of what was expected from inspection of the decrease in bulk material properties found in all other tests of

96 84 PZT fibers. The source of error is more than likely due to true free strain not being experience during testing by the fiber. This would result from the electrode applying a load on the fiber resulting in some stress which would then invalidate equation (4.3). 4.2 Dielectric Testing Results The reported dielectric constant for bulk PZT 5A is ε 33 = 1750 [35] from PI Ceramic at a frequency of 1 khz. Bulk PZT 5A wafers supplied by PI Ceramic were used for experimental determination of the dielectric permittivity with the LCR meter. The experimental was found to be 1780 at 1 khz which is slightly larger than the reported value but within 2% which is acceptable. The results of the dielectric testing using the QuadTech LCR meter, the dielectric constant for the parallel electrode was found to be ε 33 = 3000 at 1kHz and ε 33 = 800 at 1kHz for the interdigitated electrode. A plot comparing the experimental dielectric permittivity for the bulk PZT wafer, PZT fiber in parallel electrodes and PZT fiber in IDE electrodes is shown in Figure 4-6. The experimental dielectric permittivity values corresponding to 1 khz are indicated for each of the three experimental cases.

97 Dielectric Constant E+02 1.E+03 1.E+04 1.E+05 1.E+06 Frequency (Hz) PZT Fiber (Parallel) PZT Fiber (IDE) Bulk PZT Parallel 1 khz IDE 1 khz Bulk 1 khz Figure 4-6: Experimental dielectric permittivity measured with QuadTech LCR meter In comparison to bulk PZT, PZT fibers are estimated to have electromechanical properties in the range of 65-75% of bulk values [20]. The decrease in value is a result of increased porosity of the fibers and smaller grain size compared to bulk as well as any imperfections in the fiber that will inhibit dipole motion such as micro voids and cracks. There is an additional expectation for decrease in electromechanical properties when comparing parallel electrode to interdigitated electrodes. This further reduction from bulk values is caused by the non-uniform electric field produced by the IDE as well as the added losses from imperfections that may exist in the multiple electrode fingers in the IDE from the screen printing process. The reduction is found in the experimental result for the IDE electrode configuration; however, the exact degree of reduction has not been previously published. Therefore, whether the experimental value is accurate or not still needs to be determined. The IDE result is investigated

98 86 further with the second permittivity measurement method using the Cascade Probe Station later in this section. The validity of both methods is determined through modeling techniques in Chapter 5. The parallel electrode result was found to be well out of the expected range and even greater than the bulk material dielectric constant. The fixture was investigated for possible flaws in wiring that may result in an inflated value but none could be found to explain the increased value reported. A possible explanation for some of the error in the parallel electrode is the orientation of the fiber when placed between two spherical electrodes. Because the electrodes do not have flat contact with the fiber, it becomes difficult to achieve a perfectly vertical fiber alignment in between electrodes. Another source of error is from the cutting of the fibers. When the fibers are cut with a razor blade, the cut doesn t result in a consistent perpendicular cut surface. While these factors lead to some error, it would not account for much larger error found between expected and reported results. The conclusion from the permittivity testing of PZT fibers in parallel electrodes is the use of conventional parallel electrodes is very challenging and thus other means of testing should be investigated. This other means was conducted using the Cascade dielectric probe measurement technique. For the second testing setup utilizing the Cascade probe, the experimentally determined permittivity values as well as reported literature values are provided in Table 7. Bulk PZT 5A in the form of PZT wafers supplied from PI Ceramic were tested for comparison of reported value with experimental using the Cascade probe. The experimental value of 1780 was found to be in acceptable range of the permittivity reported by PI Ceramic. The experimental permittivity for AFCs was determined to be 420. This value is close to the reported value in literature. The reported value from Gentilman et al. [12] for AFCs is 495. The discrepancy between the

99 87 experimental and reported values may result from broken fibers in the tested AFCs. Broken fibers will reduce the number of complete PZT fibers contributing to the composite. With less PZT contributing to the permittivity of the composite the epoxy matrix will increase its contribution. Since the epoxy has a lower permittivity than PZT it will reduce the overall composite s dielectric permittivity. Table 7: Dielectric permittivity comparison Sample Experimental ε Literature Bulk PZT 5A 1780 ± [35] AFC 420 ± [12] Single PZT Fiber (Parallel Electrode) 1115 ± [19] Single PZT Fiber (IDE) 830 ±100 N/A The experimental dielectric permittivity for the parallel electrode configuration of the PZT fibers was found to be 1115 which is within a reasonable range of the values reported in literature of 1330 [19]. The reported value from the study by Lagoudas et. al provided in Table 7 was also conducted using PZT fibers supplied by Advanced Cerametrics. However, as mentioned in the section 1.4.2, available studies in dielectric testing of PZT fibers are done so with the fibers embedded in an epoxy matrix and permittivity determined through analytical models removing the impact of the matrix. Therefore, there is some error in the analytical models since assumptions are made in the calculations that idealize the fibers may not completely depict their behavior. This leads to the analytical models overestimating the true value of the PZT fibers. As the experimental result has approximately a 15% difference from the analytical model results

100 88 from the literature, the difference can be contributed to the overestimation of the models. In contrast to the parallel electrodes, reported values of dielectric permittivity for single PZT fibers using interdigitated electrodes could not be found in the literature. Thus, both experimental determination and verification will be done through modeling (Chapter 5). The experimental dielectric permittivity for the IDE electrode configuration was determined to be 830. This result matches well with the dielectric permittivity result from the QuadTech LCR meter used in the first experimental method. For PZT fibers in parallel electrodes, both the reported and calculated dielectric permittivity values are observed to be noticeably below the reported bulk material value. In comparison of bulk PZT to fiber form, it is estimated that the electromechanical properties of the fiber will be 65-75% of that of the bulk [20]. Reduction in bulk value is contributed to increased porosity of the fibers compared to bulk as well as any imperfections in the fiber that will inhibit dipole motion such as micro voids and cracks. Possible flaws in the silver painted electrodes such as uneven electrode thickness may also contribute some error in the experimental values. The predicted value for fibers lies at the upper limit of the range with 75%-78% depending on the source of the bulk PZT 5A value (PI Ceramic lists 1750 [35], Morgan Electro Ceramics lists 1700 [26]). The experimental PZT fiber value from the parallel electrode configuration lies within the lower limit of 64%-66% depending on the source value. With the inclusion of the standard deviation added to the experimental value the dielectric permittivity falls within 66%-70% of the bulk value. As the value falls within the expected range, the experimental value is believed to be an accurate depiction of the dielectric permittivity for PZT fibers. Therefore, the dielectric permittivity determined experimentally for PZT fibers in parallel electrodes will be used in the PZT fiber models in Chapter 5.

101 89 There is an additional expectation for decrease in electromechanical properties when comparing parallel electrode to interdigitated electrodes. This decrease is caused by the nonuniform electric field produced by the IDE as well as the added losses from imperfections that may exist in the multiple electrode fingers in the IDE from the screen printing process. Upon examination of the experimental results in Table 7, a reduction for parallel to IDE is observed. The IDE value is found to be approximately 75% of the parallel electrode determined value for PZT fibers. This follows a similar result that was found in the polarization testing (section 3.1.2) where the remnant polarization for IDEs was found to be approximately 50% of the value found for parallel electrodes. A higher drop is reasonable for the polarization results considering much higher electric fields were applied to both electrode configurations as there will likely be higher dielectric loss. The IDE comparison of single fibers ad AFCs demonstrates the reduction in dielectric permittivity due to the influence of the epoxy matrix in the composite. With an IDE result for single fibers, an estimation of the direct influence of the epoxy can be made whereas previously assumptions had to be made to distinguish the reduction in dielectric permittivity from the contribution of the IDE on the PZT and the epoxy on the PZT. However, due to lack of studies for single fiber testing in IDEs, an alternative method must be used to attempt to verify the experimental result which is done through modeling in Chapter Electromechanical Testing Results Parallel Electrode Configuration Results Electromechanical testing was conducted on PZT fibers with parallel electrodes. As described in section 2.7.1, a mechanical pre-stress is applied to poled PZT fibers and AC electric

102 90 fields are applied. The resulting induced stress from the applied electric field is recorded and used to determine the e 33 piezoelectric coefficient. The e 33 is then compared to bulk PZT to quantify the error that is introduced when bulk PZT properties are used instead of fiber properties for AFC models. The electromechanical results using parallel electrode help quantify the piezoelectric property difference between bulk PZT and fibers. The electromechanical testing was performed on PZT fibers that were poled while installed in the DMA. The poling was recorded and an induced stress was observed indicating the dipoles were aligned during poling. After the electric field is removed the stress on the sample reduces but not to the initial applied pre-stress. The elevated final stress compared to the initial pre-stress is indicative of remnant polarization in the fibers. A plot of the DC poling for a PZT fiber in the parallel electrode configuration illustrating the remnant polarization is shown in Figure 4-7. The amount of stress maintained by the remnant polarization is lower than expected. The polarization testing results in section showed a remnant polarization of approximately 75% of the saturated polarization value. The stress from the remnant polarization only corresponds to roughly 35% of the stress the fiber produces while undergoing poling with the 2 MV/m DC field.

103 Stress (MPa) Time (s) Figure 4-7: Parallel electrode 2 MV/m DC poling of PZT fiber The cause of the drop in remnant polarization is due to the pre-stress applied to the fiber and blocked stress conditions. While in between the electrodes in the DMA the PZT fiber is placed under a compressive pre-stress that accomplished two things. The first is to secure the fiber in between the electrodes ensuring good connection of the fiber and electrode. The second is from the investigation that was conducted into varying pre-stress and recording the piezoelectric capabilities. This was done to determine the pre-stress that would lead to the highest piezoelectric output (discussed next). While the pre-stress adds these benefits, it also fights the dipole alignment during poling. A schematic illustrating the effect of an external force opposing the dipole alignment is shown in Figure 4-8.When the poling field is applied to the fibers the fibers want to extend and align dipoles in the direction of the field. However, the applied pre-stress prevents the dipoles from achieving the full effect of polarization. The restricted motion of the grips further prevents the fiber from extending which increases the difficulty of dipole

104 reorientation. Therefore, the dipoles are not able to fully align with the applied field and remnant polarization is reduced. 92 Figure 4-8: Dipole alignment under electric field (A) with no external load and (B) with external load in opposite direction of poling As mentioned in section 2.7.1, an optimal pre-stress is investigated to examine which prestress will result in the highest piezoelectric production of the fibers. To determine the optimal pre-stress to apply to the PZT fiber a range of pre-stresses were tested at identical electric fields and frequencies. The pre-stresses examined were 2 MPa, 10 MPa, 20 MPa, 30 MPa and 40 MPa. These pre-stresses were investigated as the lower pre-stresses correspond to regime where irreversible domain wall motion is less pertinent while higher stress correspond to a regime where irreversible domain wall motion is more significant. From the mechanical loading results (section 3.2.1) it was observed that stresses applied to the fibers can mechanical pole the fibers. The higher stresses were able to mechanical pole the fibers in less load/unload cycles than lower stresses. However, stresses too high can damage the fibers and lead to premature failure. Since brittle materials can withstand more load in compression than in tension, these pre-stresses correspond the range before damage of the fibers typically takes place.

105 93 The tests for determination of the optimal pre-stress were conducted at a frequency of 100 mhz with a 0.3 MV/m AC electric field. The frequency of 100 mhz allows for easily identifiable sinusoidal behavior of the induced stress. An electric field of 0.3 MV/m was chosen as it is a low requires lower applied voltages and a high enough field that noise found in 0.1 MV/m and 0.2 MV/m is no longer observable. The e 33 was calculated of each respective prestress case by dividing the peak to peak stress produced by a single electric field cycle by the peak to peak electric field (as described in section 2.7.1) and plotted as a function of the applied pre-stress as shown in Figure 4-9. The results show an initial increase in e 33 production for increasing pre-stress up to a plateau followed by a decreasing effect. It was found that a pre-stress between 10 MPa and 20 MPa leads to the largest piezoelectric output. 10 MPa was used as the pre-stress for all parallel electrode electromechanical testing. A DC offset was implemented to the applied AC electric field to place the induced stresses between the limits of the 10 MPa and 20 MPa stress range. Loads larger than 20 MPa were avoided as much as possible as the pre-stress optimization plot shows a decrease after the 20 MPa load.

106 e 33 (C/m 2 ) Pre-stress (MPa) Figure 4-9: Pre-stress determination for optimized piezoelectric output for 0.3 MV/m electric field at 100 mhz With the optimal pre-stress determined the testing of poled PZT fiber samples for electric fields from 0.1 MV/m to 1.0 MV/m at a frequency of 100 mhz. The force is recorded with the DMA and converted to stress using the cross sectional area of the fiber. A plot of the induced stress for a single AC electric field cycle as a function of time for a PZT fiber sample at a 1.0 MV/m electric field with 100 mhz frequency is provided in Figure The stress is shown without the pre-stress offset for an easier observation of the balance of positive and negative stress experienced by the fiber during application of the electric field. As observed, the positive and negative stress is relatively well balanced.

107 Stress (MPa) Time (seconds) Figure 4-10: PZT fiber induced stress for 1.0 MV/m electric field at 100 mhz Since the recorded voltage was not synchronized with the force measurement, the e 33 is estimated using the peak to peak stress and electric field for a single cycle. The e 33 is directly related to the induced stress and applied electric field due to the zero strain boundary condition detailed in section in conjunction with equation (2.4). The e 33 is calculated for each electric field and plotted against the corresponding electric field in Figure A total of 6 fibers were tested for the results in Figure The e 33 was determined range from 3 ± 0.3 C/m 2 at an electric field of 0.1 MV/m to 5.7 ± 0.8 C/m 2 at an electric field of 1.0 MV/m.

108 e 33 (C/m 2 ) Electric Field (MV/m) Figure 4-11: Piezoelectric e 33 behavior of PZT fiber in parallel electrode tested with DMA as a function of electric field The plot of e 33 as a function of electric field illustrates an increasing trend as the electric field is increase. This behavior was observed in the d 33 results in section As discussed in section 4.1.2, the nonlinear behavior for ferroelectric materials can be modeled with the Rayleigh law. In section 4.1.2, this led to equation (4.3) being utilized for determination of the d 33 piezoelectric coefficient. Similarly, an equation can be defined for the e 33 coefficient using the Rayleigh law. The e 33 can be defined as the e 33,initial at zero electric field plus the product of the applied electric field and a Rayleigh coefficient which will be defined as β to distinguish it from the Rayleigh coefficient for d 33 in equation (4.3). The e 33 equation for Rayleigh is applicable for blocked force testing condition (S = 0) applied to equation (2.4) and is provided in equation (4.4). e 33 = e 33,initial + βe 3 (4.4)

109 97 From the plot of e 33 as a function of electric field in conjunction with the use of equation (4.4), a linear trendline is applied. The slope of the resulting trendline corresponds to the Rayleigh coefficient β and the y-intercept corresponds to e 33,initial. For comparison to bulk PZT, the e 33 of the fibers for the parallel electrode configuration is taken as e 33,initial. The value of e 33 for the fibers is determined to be 2.8 C/m 2. This value is well below the 15.8 C/m 2 e 33 value reported for bulk PZT [26]. A drop in the bulk material is expected but the fiber property is less than 20% of the bulk value. As discussed earlier in this section the remnant polarization o the PZT fiber is reduced due to the pre-stress preventing full dipole alignment under the poling field. Since the remnant polarization is half of what the remnant polarization was determined for electric field only, the piezoelectric capability is reduced. If the fiber was poled in an electric field without the compressive load and restricted grip motion and then installed into the DMA it could result in the fiber maintaining its higher remnant polarization. Improving the remnant polarization from 35% to its original 75% would increase the e 33 for a PZT fiber in parallel electrode configuration to ideally 5.6 C/m 2. However, due to the size limitations of the fibers for testing (2 mm), poling before installing the fiber in the DMA would become very time consuming as it is not guaranteed the poled fiber will be successfully installed in the DMA. The installing process was very challenging and typically required multiple attempts before successful installation of a fiber. The experimental e 33 determined for the parallel electrode configuration will be compared to a PZT fiber model predicted value for validation in Chapter 5.

110 IDE Configuration Results Electromechanical testing was conducted on PZT fibers with IDE configuration on an Instron 5866 load frame. As described in section 2.7.2, a mechanical pre-stress is applied to poled PZT fibers and AC electric fields are applied. The resulting induced stress from the applied field is recorded and used to determine the e 33 piezoelectric coefficient. The e 33 is then compared to the e 33 determined for the PZT fibers in the parallel electrode configuration. The comparison of the parallel and IDE electrode configuration will quantify the influence the nonuniform electric field produced by the IDE compared to the uniform electric field produced by the parallel electrodes. The induced stress and applied voltage were recorded by the Instron in the Bluehill software. By plotting the induced stress by the PZT fiber as a function of the applied electric field the e 33 piezoelectric coefficient can be determined. The strain is held at zero during the test by restricting grip motion to enable blocked force conditions as detailed in section With the mechanical strain held at zero during the testing, the e 33 is directly related to the stress and electric field as shown in section 2.7 by equation (2.4). The induced stress in plotted against the applied electric field. The e 33 is calculated by taking the slope of the stress-electric field loop produced by one complete cycle of the AC electric field. The stress-electric field loops for one recorded sample for each electric field tested at frequency of 1Hz is shown in Figure The stress-electric field loops demonstrate the ferroelastic behavior of the PZT as the loops resemble hysteresis loops.

111 Stress (MPa) Electric Field (MV/m) 0.1MV/m 0.2MV/m 0.3MV/m 0.4MV/m 0.5MV/m 0.6MV/m 0.7MV/m 0.8MV/m 0.9MV/m 1.0MV/m Figure 4-12: IDE PZT fiber sample stress-electric field loops at 1Hz The slope for each respective electric field was determined and recorded. The effect of the electric field on the e 33 coefficient is illustrated in Figure The reported value in literature is taken at low electric fields. When inspecting Figure 4-13, it is observed that at the lowest tested electric field of 0.1 MV/m, the average e 33 from all recorded samples was determined to be 0.23 C/m 2. This value is found to be much lower than the reported value of 15.8 C/m 2 found in literature for bulk PZT and lower than values that were expected. A drop in value is expected due to the combination of the PZT being in fiber form (see section 4.3.1), the non-uniform electric field produced by the IDE and impurities in the fiber and IDE. However, a difference this large was not expected.

112 e 33 (C/m 2 ) Electric Field (V/m) Figure 4-13: Piezoelectric e 33 behavior of PZT fiber in IDE tested with Instron 5866 as a function of electric field When examining the equipment used, the root of the error is found to be from the grips used with the Instron (Figure 4-14). The grips themselves were found to be very compliant and actually bend during testing. This was due to the grips being composed of a thin steel shaft base and gripping mechanism being made of plastic. The top grip is also secured through a small pin connector that does not constrain the grip from rotating. The combination of these factors led to the grips effectively absorbing the stress from the fiber and output only a small margin of the stress induced by the electric field. A tensile test was performed on PZT fibers using the fiber grips in the Instron to compare to the tensile test results found in the DMA. As observed in the stress-strain curve comparison in Figure 4-15, the Instron is reporting much higher strains required to provide equivalent stresses found in testing with the DMA. This provides evidence of the error resulting from the compliancy of the Instron fiber grips. The bending of the grips was not visible with normal visual inspection but with zoomed in pictures taken at the start and end of

113 101 the tensile test before fracture slight bending can be seen (Figure 4-16). From the image comparison, a slight displacement can be seen at the end of the grip during the test compared to its initial position before the stress is applied. As the strains observed for fibers are on the scale of micrometers (10-6 m) this displacement is significant. The stress-electric field hysteresis loop and nonlinear behavior of the e 33 with respect to the electric field determined with the Instron is believed to be an accurate depiction of the fiber behavior but the values are largely off due to the incorrect stress being recorded. Figure 4-14: Fiber grips used in IDE Instron electromechanical testing

114 Stress (MPa) Instron DMA Strain (%) Figure 4-15: Stress-strain comparison of DMA and Instron results illustrating error in Instron due to compliancy of grips Figure 4-16: Image of fiber grip (left) before tensile test and (right) during tensile test before fracture highlighting bending of the grip

115 103 The PZT fibers were then tested with the IDE assembly in the DMA to determine the e 33. The grips of the DMA are composed of hardened steel and secured in the DMA with no rotation of the grips possible. Therefore, the DMA will have accurate stress measurements. The flaw with using the DMA is that the voltage signal cannot be recorded with the DMA in the same software as the force. This was the reason the Instron was first used as the force and voltage responses could be recorded simultaneously and synchronized. However, due to the stress problem that was found in the Instron results, the simultaneous measurement is willing to be sacrificed for accurate stress measurements. The e 33 can still be estimated using the peak to peak stress and electric field, as was done with the parallel electrode, within a reasonable range of the true value. The test procedure remains the same as the parallel electrode DMA configuration only the fiber is now pre-stressed in tensile stress as opposed to compression. The force was recorded for the electric fields range of 0.1 MV/m to 1.0 MV/m. The e 33 was calculated from the peak to peak induced stress and applied electric field for a single cycle. The results were found to be an order of magnitude higher than the Instron and much more reasonable. The plot of e 33 as a function of the electric field for the IDE DMA results is shown in Figure The trend observed in the e 33 behavior is similar to that found in the parallel electrode configuration in section Likewise, the Rayleigh expressed in equation (4.4) for e 33 will be utilized again for determination of the IDE e 33 piezoelectric coefficient.

116 e 33 (C/m 2 ) Electric Field (MV/m) Figure 4-17: Piezoelectric e 33 behavior of PZT fiber in IDE tested with Instron 5866 as a function of electric field A linear trendline is applied to the e 33 as a function of electric field plot in Figure 4-17 to define the Rayleigh coefficient and e 33,initial. The Rayleigh coefficient is taken as the slope and the y-intercept as the e 33,initial value. For comparison of e 33, the e 33,initial is taken as the e 33 piezoelectric coefficient for PZT fiber with IDE configuration. The e 33 was determined to be approximately 1.5 C/m 2. Compared to the parallel electrode determined value of 2.8 C/m 2, the IDE e 33 is approximately 55% of the parallel electrode value. This follows suit in property comparison for the two electrode configuration as the remnant polarization for IDE was determined to be approximately 50% of the parallel electrode value (section 3.1.2). In comparison to bulk, like the parallel electrode result, the IDE value seems rather low. As discussed in section for the parallel electrode configuration, the remnant polarization of the fiber was 50% of that when poled in the DMA due to the pre-stress preventing full dipole

117 105 alignment. The same is experienced for the IDE. During poling of the PZT in the IDE installed in the DMA, a pre-stress was applied before application of the electric field and DMA grips are held stationary during testing. This prevents full polarization of the fiber with the IDE configuration the same as what was observed in the parallel electrode configuration. Applying the factor of poling in only an electric field compared to with pre-stress and blocked stress conditions, then ideally the e 33 for the IDE configuration would be 3 C/m 2. The experimental value of the IDE configuration for e 33 will be compared to an IDE model predicted value in Chapter 5.

118 106 Chapter 5 Modeling and Verification 5.1 Model Descriptions Parallel Electrode Model for PZT Fibers The experimental dielectric permittivity for PZT fibers in parallel electrodes was compared to reported values in PZT fiber studies that were determined through testing of PZT fibers indirectly in 1-3 composites; only one study was found with direct measurement of the dielectric permittivity for PZT fibers and the dielectric permittivity was found to fall between 500 and 800 [15]. However, the results from the study were never validated with models or other experimental means. As the experimental results done in this study as well as the studies using the 1-3 composites result in dielectric permittivity between 1100 and 1400, it would seem the study from 1995 cannot be used for comparison. For the studies utilizing 1-3 composites, the composites were tested for dielectric permittivity instead of single PZT fibers. The composite experimental results were then used in combination with analytical models to estimate the dielectric permittivity of the PZT fibers. The dielectric permittivity values found with this method (ε = 1330 [19]) are comparable to the results in this study (ε = 1115 ± 55) after taking into account the overestimation of the analytical models. Since no recent studies have been performed with direct PZT fiber measurements, the experimental results determined in this study need to be verified and will be done so with modeling. A PZT fiber for parallel electrode configuration will be simulated for dielectric permittivity testing. As no studies could be found that performed electromechanical testing for the

119 determination of the piezoelectric e 33 coefficient on single PZT fibers, simulations must also be conducted to represent this testing. 107 The model for a single PZT fiber with parallel electrodes is composed of PZT fiber geometry and accounts for the parallel electrodes through electric potential boundary conditions on the fiber ends. As the tests are conducted on a single fiber, the only parameters necessary are the material properties of the PZT fiber and boundary conditions. The PZT fiber in the model is made to a length of 2 mm as this was the size used for the fibers in all of the parallel electrode configuration experiments. There were two types of boundary conditions applied to the fiber in the model (electrical and mechanical) for both dielectric permittivity and electromechanical verification. For the dielectric permittivity simulations, one fiber end face is given an electric boundary condition in the form of an electric potential of 5 V (voltage used in experimental tests, section 4.2). The other end face is given an electric potential of 0 V to resemble a ground connection. The electrical boundary conditions act as the parallel electrodes. Two sets of mechanical boundary conditions were examined. For the free strain condition of dielectric permittivity the stress T is zero. Therefore, no mechanical constraints are applied to provide the fiber with zero stress. The dielectric permittivity found for these conditions is reported as ε T where the superscript T denotes the stress is zero for testing. The second set of mechanical boundary conditions used for blocked stress testing which results in the strain being held at zero. Therefore, mechanical constraints are applied to the end faces of the fiber preventing any motion effectively removing the strain in the direction of poling. The dielectric permittivity found for these conditions is reported as ε S where the superscript S denotes the strain is zero for testing. For the dielectric permittivity simulations, the reactive charge of the end face with the 5 V potential is

120 108 recorded. The reactive charge is converted to dielectric displacement D by dividing the reactive charge by the cross sectional area of the fiber. Then, the dielectric displacement is divided by the electric field E to determine the dielectric permittivity using equation (1.4). For the electromechanical simulations, the electric boundary conditions are the same except the value of the electric potential is changed from 5 V in the dielectric permittivity simulations to 200 V, which is the corresponding voltage to create a 0.1 MV/m electric field for a 2 mm fiber. The simulations of the electromechanical testing are performed only for blocked stress conditions. This corresponds to both end faces of the fiber being mechanically constrained in the z-direction. The reactive force of the end face of the fiber from the simulations is used to calculate the induced stress from the applied electric field. The induced stress is calculated as the sum of the reactive force for the nodes of the fiber end face divided by the cross sectional area of the fiber. The e 33 piezoelectric coefficient is calculated as the induced stress divided by the applied electric field (equation (2.4)). An illustration of the parallel electrode model is shown in Figure 5-1. Figure 5-1: PZT parallel electrode model

121 109 The PZT fiber properties were taken from the experimental characterization results from this study (Chapters 3 and 4). The experiments performed did not include determination of full property matrices but rather focus on the properties in the direction of poling. Therefore, to estimate the full matrix the bulk material matrices were multiplied by the reduction ratios found for properties that were determined experimentally for the fibers (e.g. [d fiber ] = [d bulk ] * (d 33,fiber /d 33,bulk ). The properties necessary for input in ABAQUS include the stiffness matrix, d piezoelectric coefficient matrix and dielectric permittivity matrix. The values used in the model are provided in Appendix C. While this estimation is an oversimplification of the bulk to fiber comparison, it is deemed reasonable for the modeling purposes because, like the experiments, the model will focus on predicting the PZT behavior in the direction of poling. As the model is focusing on the direction of poling and with the inclusion of boundary conditions, the contribution from the non-poling direction properties will be negligible. The mesh elements used for the parallel electrode configuration simulations were of tetrahedral geometry. The element type is switched from the default to piezoelectric elements. The element size used corresponds to a seed size of 2 x From variation of the seed size it was determined that a smaller seed size (smaller element size) did not lead to a change in the convergence results. Therefore, a 2 x 10-5 seed size was used to minimize computation time. These details of mesh element type and size as well as fiber properties are the same for both parallel electrode and IDE configuration models.

122 IDE Model for PZT Fibers It is necessary to verify the experimental results for both dielectric permittivity and e 33 for the PZT fibers with IDE electrode configuration as there was no published literature that could be found for testing single PZT fibers with IDEs. The model created resembles the PZT fiber installed in the IDE assembly (for IDE assembly, see Figure 2-2). For the model, the acrylic plate, scotch tape and Mylar sheet are combined into one component as their respective properties are similar and the overall focus of the model will be on the interdigitated electrodes and PZT fiber. For the fiber electrode interface, the fiber will be in direct contact with the electrodes as it is in the experimental setup. However, due to the software not being able to mesh a contact surface between the tangent of a circular cross section with a flat surface, the cross section of the fiber had to be manipulated. To achieve a surface contact that could be meshed by the software the cross section of the fiber was redefined to have a flat surface at the contact interface of the fiber and electrode. The newly formed cross section resembles a square with filleted corners. The cross section is shown in Figure 5-2. The flattened surface of the fiber corresponds to approximately one-fourth of the fiber diameter. Figure 5-2: Flattened fiber cross section to improve contact with electrodes

123 111 The representative volume element (RVE) is a section of the overall IDE assembly that is focused at the effective electrode area of the IDE and contact with the fiber. The number of electrodes featured in the model is reduced using symmetry and features two characteristic regions. The first region is designed to resemble the positive poling direction of the fiber with the electric field flowing from electrode with positive potential to an electrode with zero potential. The second region features the inverse of this which is due to the alternating electrode fingers from positive potential to zero potential and negative poling direction for the fiber. The two regions are shown in the first quadrant of Figure 5-3. The rest of the components of the PZT IDE assembly model are broken down in the remaining quadrants in Figure 5-3. Figure 5-3: PZT assembly model partition breakdown The boundary conditions for the model consists of mechanical constraints in the x, y and z directions. The simulations conducted for dielectric permittivity testing for free strain has no mechanically boundary conditions enforced on the model. The simulations conducted for dielectric permittivity testing for blocked stress on the other hand has the model constrained mechanically in all directions (fully constrained). Electrical boundary conditions in the form of

124 112 electric potentials are applied to the IDE electrodes. A positive 5 V electric potential is applied to the positive voltage electrodes while a 0V potential is applied to the ground electrodes. A visual representation of the electrodes with corresponding potentials is shown in Figure 5-4. As with the parallel electrode model, the permittivity is calculate using the reactive charge discussed in section The reactive charge is summed for all non-zero potential electrodes only. Figure 5-4: IDE model electric potential schematic For the electromechanical test simulations a pressure is applied on the top acrylic plate to replicate the tightening of the bolts of the IDE assembly. The value of the pressure was varied to estimate the pressure applied to the assembly by the bolts because the magnitude of the torque applied to the bolts was too small for a calibrated torque screwdriver to measure. The mechanical boundary conditions applied to the model for the electromechanical testing included an x constraint on the outer side surface of the acrylic plates and electrodes. A y constraint was applied to the bottom surface of the acrylic plate opposite to that of the applied pressure. A z constraint was applied to the end faces of the fiber as well as the end surfaces of the acrylic plates and electrodes. A schematic of the mechanical constraints and loading can be seen in Figure 5-5.

125 113 Figure 5-5: IDE model mechanical boundary constraints and loads The mechanical boundary conditions applied are to replicate blocked stress conditions for the fiber and monitor the reaction forces to determine the stress induced by the applied electric field. The electric field is applied to the model in a similar manner as the permittivity testing only the electric potential boundary condition is changed from a value of 5 V to 75 V to create a 0.1 MV/m electric field on the fiber. The simulation is run for both a positive 0.1 MV/m and a negative 0.1 MV/m electric field. The reactive forces are summed for the fiber end and divided by the cross section to determine the induced stress by the electric field. The peak to peak stress is recorded by examining the results for the positive and negative 0.1 MV/m results. The test is repeated for a range of plate pressures from 100 Pa to 10 MPa. The e 33 is calculated from equation (2.4) as discussed for the parallel electrode configuration in section

126 Verification of Dielectric Results Parallel Electrode Configuration The parallel electrode model was examined for the dielectric permittivity in free strain and blocked stress conditions. As described in section 5.1.1, a 5 V electric potential was applied as the boundary condition for one end face and ground (0 V) was applied to the other. The simulation was also conducted for both free strain (T = 0, ε = ε T ) and blocked stress (S = 0, ε = ε S ) conditions. The permittivity entered in the model was that found experimentally in section 4.2 as it represents the permittivity of PZT in fiber form (ABAQUS fiber properties used in Appendix C). The experimental dielectric permittivity determined was 1115 ± 5. The free strain dielectric permittivity was predicted to be 1350 by the parallel electrode configuration model. This value is very close to the predicted dielectric permittivity of 1330 from literature when the 1-3 composite is used in conjunction with an analytical model [19]. This makes sense since the PZT fiber model used in the simulation, like the analytical model used in the literature, assumes idealized fiber behavior and geometry. The blocked stress dielectric permittivity was predicted to be This is very close to the average experimental value found in the experiments. It makes sense that the experimental value would be closer to the blocked force predicted value due to the experimental setup. In the setup, the fibers are adhered to a glass slide substrate using double sided scotch tape. The scotch tape as well as the contact from the dielectric probes will restrain the fiber from strain. There is still expected to be some strain produced by the fiber which would correspond to the upper range of the experimental value with standard deviation included. Therefore, the experimental value lying between the predicted free strain and blocked stress values is understandable. As the experimental dielectric permittivity entered into the model

127 (ε r = 1115) is essentially identical to the predicted blocked stress condition result (ε S = 1110), the model and boundary conditions used for the model are verified. 115 The free strain and blocked stress dielectric permittivity values are related through the coupling coefficient κ. The equation for the relationship is provided in equation (5.1). The bulk PZT values and predicted model PZT fiber values are reported in Table 8. As observed the resulting coupling coefficient predicted for the PZT fibers is approximately 60% of the bulk value. The reduction in value follows the experimental trends that have been determined in this thesis for Young s modulus and experimental dielectric permittivity. ε S = ε T (1 κ 2 ) (5.1) Table 8: PZT bulk vs fiber dielectric permittivity comparison Bulk PZT [26] PZT Fiber ε T ε S κ IDE Configuration The resulting dielectric permittivity from the dielectric testing was determined to be 830 ± 100. The free strain dielectric permittivity predicted by the IDE model was The prediction for the blocked stress result was 930. The experimental dielectric permittivity with inclusion of the standard deviation matches the predicted blocked stress dielectric permittivity.

128 116 The predicted free strain dielectric permittivity is noticeably larger than the experimental dielectric permittivity. From the comparison, it can be concluded that the bolts used in the IDE assembly are restricting the fibers and minimizing the strain produced by the voltage in the experimental testing. This explains why the experimental permittivity is much more comparable to the one under blocked stress conditions (S = 0). However, it is still noted the majority of the experimental range results are lower than that of the predicted blocked stress value. The experimental average being a lower value than the predicted value is reasonable since the model assumes perfect fiber and electrode geometry. The PZT fibers will have some degree of deviation in the cross sectional area throughout its length due to the manufacturing process. Additionally, defects such as micro-voids and cracks may be present in the fibers due to the fibers increased porosity compared to bulk PZT. The fiber cross section in the model having flattened surfaces for meshing will cause some additional error as well. The error found due to the slight change in cross sectional area was less than 10%. The IDEs will have some defects from the screen printing process as well. The designed electrode widths and gaps will have some margin of deviation from limitations of quality for the screen printing equipment as well as some electrode shrinkage that may occur during the ink drying process. The deviation in electrode widths and gaps will also affect the electric field produced by the IDE as the aligned electrodes may differ in size which will limit the electric field to the area of the smaller electrode. The electrode gap sizes and electrode widths were measured under optical microscope and it was found that the average electrode width was smaller than the designed width. The average width was found to be approximately 478 µm which results in a 4.5% error of the designed 500 µm width. The electrode width itself also has a standard deviation of 5.8 µm. Therefore, we can conclude that the discrepancy in measured dielectric permittivity

129 from the predicted dielectric permittivity in the model results from the compounded deviations in screen printed electrode width sizes. 117 A factor that was investigated for the screen print quality is the substrate utilized for the IDE to be screen printed on. Initially, the IDE patterns were screen printed directed onto the acrylic plates. However, the print quality observed was rather low and inconsistent throughout a printed IDE pattern. The electrodes contained very jagged edges and large deviations in electrode widths and gaps from the designed dimensions. Mylar was then used as the substrate and the print quality was observed to be much superior. The consistency of the electrode measurements and smoother edges led to Mylar being utilized as the substrate. The average electrode width of 485 µm reported previously is from the IDE patterns screen printed on Mylar. An image demonstrating the print quality comparison of acrylic and Mylar is shown in Figure 5-6. Figure 5-6: IDE screen print quality on acrylic (left) and Mylar (right) The dielectric permittivity results for varying pressure applied to the acrylic plates showed reasonable behavior. At the lower pressure of 100 Pa the permittivity was found to be slightly higher than fully constrained condition at a value of 984, less than 6% increase from the 930 value. The increased value can be from strains produced in the lateral directions as the fiber

130 118 is now only constrained at its end faces in the z direction. As the pressure is increased, the permittivity decreases as the strains in the lateral direction become restricted by the plate pressure. At a plate pressure of 100 kpa the determined permittivity is actually equivalent to the fully constrained condition with a permittivity of 930. At higher pressures there is a significant reduction in permittivity possibly due to the structural integrity of the fiber becoming diminished due to the large pressures. A pressure of 1 MPa results in a permittivity of 445. The predicted dielectric permittivity values for both the parallel electrode configuration and IDE configuration models are presented in Table 9.As observed there is a decrease in value for IDE in comparison to parallel. This is due to the nonuniform electric field produced by the IDE compared to the uniform electric field produced by the parallel electrodes. The electric field lines for both electrode configuration models are provided in Figure 5-7. The decrease is less pronounced than the experimentally determined value comparison. This is because the idealization of perfect linear behavior of the models whereas the experimental values have deviations due to defects in the fibers and electrode geometries. The coupling coefficient for the IDE exhibits a similar reduction as the predicted permittivity reduction (IDE 80% parallel). This is due to the decrease for ε T from parallel to IDE approximately equivalent to the ε S decrease (approximately 20% reduction).

131 119 Table 9: Comparison of predicted dielectric permittivity for PZT fibers in parallel and IDE configuration models Parallel IDE ε T ε S κ Figure 5-7: Electric field lines of PZT fiber in (A) parallel electrode configuration and (B) IDE configuration

132 Simultaneous Mechanical and Electrical Loading Verification Parallel Electrode Configuration The electromechanical simulations were run for the parallel electrode model to verify the experimental results found. The model was simulated for blocked stress conditions with the application of a 0.1 MV/m electric field on the PZT fiber for parallel electrode configuration. The e 33 predicted by the model for an electric field of 0.1 MV/m was found to have a value of 6 C/m 2. This value is over 2 times larger than the experimental e 33 for a 0.1 MV/m electric field of 2.8C/m 2. It is important to note the PZT behavior is treated as linear (i.e. constant e 33 ) in the model because the electric field used in the model was well below coercive field and very close to zero electric field. The experimental results did not demonstrate a linear behavior at the lower electric fields (i.e. e 33 increased with increased electric field). This behavior has been studied by applying the Rayleigh law for ferromagnetic behavior to ferroelectric behavior of piezoelectric ceramics as was discussed in section [34]. From the Rayleigh law formulations, the e 33 of the PZT would correspond to the value found at zero electric field with any value taken with an electric field experiencing contributions from the irreversible displacements of domain walls. The e 33 determined experimentally with the Rayleigh was 2.8 C/m 2 for the parallel electrode configuration. As mentioned, this value is approximately half that of the model predicted value. Deviations in the fiber geometry, material defects and porosity can all account for the discrepancy found between the predicted model value and experimentally determined value. The surface of the cut fiber end can also lead to a loss of piezoelectric ability due to the rough surface interaction between the fiber and electrodes. The rough edge arises from difficulty in a clean cut due to the brittleness of PZT. Fiber alignment between the parallel electrodes in the

133 121 DMA was also very challenging. The fibers typically had some angle deviation from perfect alignment. The angle will affect the polarization of the fiber and lead to reduced remnant polarization after poling. This will then lead to reduced piezoelectric capabilities compared to a perfectly aligned fiber that is simulated in the model. The largest source of discrepancy between the experimental and predicted value is from the pre-stress and blocked stress conditions. The pre-stress and blocked stress conditions prevent the dipoles form aligning properly under the influence of the electric field (discussed in section 4.3.2). Due to the prevention of proper dipole alignment, the remnant polarization was estimated to be reduced by approximately 50%. If the fibers were poled under zero stress conditions and dipoles allowed to properly aligned, then an assumption for the ideal case would be the fiber s piezoelectric response would improve by twice the experimental value determined for the prestress and blocked stress conditions. Therefore, the true experimental value would be closer to 5.6 C/m 2 for the parallel electrode configuration and be very comparable to the predicted 6 C/m 2. The noticeable drop in value from reported bulk PZT value of 15.8 C/m 2 and the predicted model e 33 value arises from a few causes. The first cause is from the material behavior change due to the geometry of bulk to fiber. When the PZT is in fiber form the PZT experiences increased porosity compared to bulk as well as lower stiffness due to the aspect ratio of fiber length to diameter. The expected decrease in electromechanical output was reported to be 65% to 75%. The percentage of bulk value predicted by the model is lower than this range of approximately 40% of the bulk value. This drop is caused from the material properties determined and utilized in the model. The e 33 is a function of the stiffness, c 33, and the piezoelectric d 33 constant. As mentioned PZT in fiber form has lower stiffness than that of bulk

134 which will lower the e 33. The d 33 was also determined to be lower than that of bulk which can also lower the e IDE Configuration The electromechanical simulations are conducted to determine a predicted piezoelectric e 33 constant for PZT fibers. For the simulations, mechanical constraints were placed to enforce blocked stress conditions with the application of a 0.1 MV/m electric field. The IDE model had the additional factor of a plate pressure applied to resemble the tightening of the bolts of the IDE assembly. The induced stress from the 0.1 MV/m applied electric field were recorded for determination of the e 33 piezoelectric coefficient. The e 33 was estimated as the peak to peak induced stress divided by the peak to peak electric field. It was found that the peak to peak induced stress did not change as the plate pressure was increased which led to the e 33 not changing either. The e 33 determined by the simulations was a value of 4 C/m 2. The value is comparable but higher than the experimental value of 1.6 C/m 2. The lower value can again be partially contributed to the nonlinear behavior found in the experimental results as the model behavior is treated as linear. The Rayleigh law was implemented (section 4.3) to determine the zero electric field e 33 of 1.5 C/m 2. Another possible source of error in the form of the applied pressure from the acrylic plate limiting piezoelectric output was inspected. Initially, it was expected that the applied pressure would reduce the peak to peak induced stress due to increasing the friction on the fiber from the acrylic plates and electrodes and transfer some of the stress to the plates and electrodes. Instead, it appears as though the applied pressure would contribute to the stress and act similar to an offset stress. As the pressure is applied, the compressive stress examined at the fiber end from the

135 123 mechanical constraint is increased from zero to a nominal value when no electric field is applied. The peak to peak induced stress remains the same when the electric field is applied but the values produced from the positive 0.1 MV/m and negative 0.1 MV/m are shifted to more compressive stresses due to the applied pressure. A brief overview of the results can be seen in Table 10. Table 10: Simulation predicted electromechanical results for varying applied plate pressured Induced Stress (Pa) Applied Pressure 0 Pa 100 Pa 1 kpa 10 kpa 100 kpa 1 MPa 10 MPa 0.1MV/m -4.31E E E E E E E+07 Neg 0.1MV/m 4.31E E E E E E E+07 Peak to Peak -8.63E E E E E E E+05 e 33 (C/m 2 ) Possible explanations for the discrepancy between the experimental and predicted e 33 values from the model can be explained similar to the permittivity discrepancy. The quality of the screen printed electrodes is not perfect as in the ideal case scenario of the model. The deviations of the electrode dimensions will influence the accuracy of the experimental values and result in some experimental error. The deviations in screen-print quality of the IDEs is concluded to reasonably account for the discrepancy in the experimental and predicted permittivity values. However, the print quality is not enough to cover the discrepancy found in e 33. The fiber length used for testing could also reduce some of the piezoelectric output. The full gage length of the fiber is not under the influence of the effective electrode area of the IDE. The effective electrode area accounts for 30 mm of the 50 mm gage length used for testing in the DMA. That leaves 20 mm of fiber that will not be poled using the IDE. Therefore, up to 40% of the fiber will contain the properties of an unpoled PZT fiber which exhibits lower stiffness and piezoelectric capabilities. As discussed for the parallel electrode setup in the previous section, the largest source of error is due to the pre-stress and blocked stress conditions applied during poling. The

136 124 conditions lead to approximately a 50% reduction in remnant polarization which can be assumed to lead to a 50% reduction in piezoelectric capability in the ideal case. This assumption could result in the true experimental value of e 33 for the IDE configuration having a value of 3 C/m 2 which is much more comparable to the predicted 4 C/m 2 by the model. An additional source of error is most likely from the stiffness matrix and piezoelectric d matrix used for the PZT in the model. The model uses experimentally determined properties of the PZT fibers instead of the reported bulk PZT properties. These properties include the permittivity vector, the piezoelectric d matrix and the stiffness matrix. Due to the geometry and brittle nature of the PZT fibers, the determination of full property matrices could not be determined. Instead this research focuses on determination of the properties in the 3-direction. As the ABAQUS software requires the input of the full matrices and vectors of the properties estimated values were used. The estimates were done by examining the reduction ratio of bulk to fiber properties for the experimentally determined values and applying the same ratio to full reported bulk matrices and vectors. Considering the simulations, like the experiments, focus on results in the direction of poling the contribution of the properties corresponding to the other directions will be minimized.

137 125 Chapter 6 Conclusions and Recommendations 6.1 Summary of Results Active fiber composites have a wide array of applications due to the piezoelectric ability of the PZT fibers embedded in the composite. PZT fibers of dimensions of approximately 250 µm in diameter and of varying lengths (depending on application limitations) are embedded in an epoxy matrix at with volume content generally below 45% when fabricating AFCs. Studies have been performed on AFCs attempting to optimize the AFC design effectively standardizing the IDE geometries; however, for these studies, although the epoxy polymer matrix was characterized mechanically, dielectrically and thermally, to the best of our knowledge, the individual PZT fiber was not directly tested. The rationale is that fully characterizing the PZT fiber outside of the AFC may clarify whether the AFC s performance can be improved further or whether current AFCs have reached a limitation in performance. Therefore, the focus of this study was the characterization of PZT fibers for parallel and interdigitated electrodes. Initial testing was done to characterize the mechanical and electrical properties of unpoled PZT fibers to function as a control for comparison to fibers that will be poled and mechanically loaded. Tensile testing was performed to determine the Young s modulus of the fibers and polarization testing to determine the remnant polarization, coercive field and strain. The tensile test results and polarization tests conducted with parallel electrodes were able to be compared to previous studies by polarization with IDE configuration could not as it has not previously been performed. The influence of mechanical loading on the fiber s properties was examined next through cyclic loading at set load limits. This cycling loading was performed to

138 126 examine the effect of repeated actuation of the PZT fibers in the AFC. The mechanical loading effect was examined for its influence on the Young s modulus and influence on the electrical behavior through polarization testing of the mechanically loaded fibers. The effect of poling the fibers was also investigated mechanically through tensile testing and electrical behavior through polarization testing. Next, the permittivity of the fibers was determined for both parallel and interdigitated electrodes. The IDE was applied to the fibers using screen-printed IDE patterns, which would be attached to laser cut acrylic plates that would secure the fiber in place using plastic bolts. The permittivity testing was conducted through two experimental setups, LCR meter and Cascade Probes. The most challenging behavior determination proved to be the electromechanical behavior of the PZT fibers. Fixtures had to be created specifically for the purpose of testing the fibers for both mechanical and electrical loads. The electromechanical testing was performed using a DMA with electrodes connected to a function generator and high voltage amplifier. Finally, models were created for both parallel and IDE electrode configurations. The models were designed to run simulations of the PZT fibers for both permittivity and electromechanical testing to verify the experimental results as no results could be found in the literature. 6.2 Conclusions From the control property determination, noticeable reduction in properties from reported bulk PZT was found as expected; specifically the Young s modulus, dielectric permittivity and e 33 piezoelectric coefficient. The results found for PZT fibers are comparable to other results for characterization of PZT fibers found in literature, i.e. the Young s modulus, coercive field and remnant polarization. The coercive field and remnant polarization found for PZT fibers with

139 127 parallel electrodes compared well with previous studies. The results from the polarization study with IDE configuration was never performed before so comparison to previous studies was not possible. The remnant polarization for the IDE configuration was found to be approximately 50% of the parallel value. This is attributed to the nonuniform electric field produced by the IDE and the 50% reduction was found to be consistent with the reduction found from parallel to IDE in the other experiments. When cyclic mechanical loading was applied to the PZT fibers changes in the behavior were observed due to mechanical poling and the ferroelastic behavior of PZT; the cyclic loading led to an initial increase in the Young s modulus for the first few cycles before reaching a plateau. The rate at which the fiber reached this plateau is dependent on the set load limit. For higher load limits the fiber requires fewer cycles to reach the plateau; for example, when the set load limit was 25 MPa the modulus reached the plateau after 1 cycle whereas when the set load limit was 5 MPa the modulus reached the plateau after approximately 5 cycles. Temperature effect was also examined for the cyclic loading and had its greatest impact on the lower set load limits. The increasing Young s modulus for increasing cycle numbers was attributed to mechanically aligning the dipoles effectively poling the fibers through mechanical loading. At the higher test temperature of 75 o C for a set load limit of 5 MPa, the modulus behavior as a function of load cycles actually decreased and was attributed to the thermal expansion and dielectric loss now overcoming the dipole alignment as the lower stress level results in fewer irreversible domain wall motions. The electrical characterization of the mechanically loaded fibers revealed some evidence of dipole re-orientation, which led to mechanical poling of the fibers. Increases in coercive field, remnant polarization and strain were observed for all the loaded fibers compared to the unloaded

140 128 control fibers. The increase is due to the mechanical loads aligning the dipoles and irreversible domain wall motion preventing the domains from returning to their original random orientation. Polarization testing was also conducted to quantify the level of impact that poling the fibers presents on the PZT fiber properties. It was found that fibers that were poled experienced a 45% increase in remnant polarization compared to fibers that were tested unpoled. The piezoelectric d 33 coefficient was investigated but the values determined were higher than bulk and attributed to boundary condition errors. The calculations assume free strain conditions but were not fully achieved due to the weight of the electrode preventing zero stress conditions. As the force on the fiber from the electrode could not be measured an accurate and conclusive d 33 for PZT fibers could not be determined. The permittivity results for PZT fibers in parallel electrodes were found to be comparable to literature but due to the values from the literature resulting from testing 1-3 composites in conjunction with analytical models further verification was conducted. This experimental value found is lower than that in the literature due to the reported values being determined through composite testing and analytical models to back out the permittivity of the PZT fiber. The analytical models used have assumptions that idealize the PZT fiber geometry and interfacial behavior with the epoxy matrix. These assumptions will lead to an overestimation of the fiber permittivity. Therefore, the experimentally determined permittivity of 1115 ± 55 can be deemed reasonable when compared to the literature analytical results of approximately The permittivity for PZT fibers with IDE were found to be lower than that of parallel electrodes with a value of 830 ± 100 which was expected due to the nonuniform electric field created by the IDE. As discussed, the nonuniform electric field on the PZT fiber from the IDE results in localized electric fields in the fiber with different directions and magnitudes. These localized electric fields result in the net electric field in the direction of poling being lower than the electric field applied.

141 129 As no studies could be found on individual PZT fiber testing with either parallel or IDE configurations, verification of the experimental results needed to be performed through the use of models in ABAQUS. The models contain perfect fiber geometry consistency as well as electrode geometry consistency; therefore the results from the models can be expected to overestimate the permittivity. This was found to be the case as the experimental permittivity for the parallel electrode configuration fell into the bottom of the range predicted by the model for blocked stress (low value) and free strain (high value) conditions. The IDE experimental dielectric permittivity was also found in the bottom of its model s predicted range of for blocked stress and free strain conditions. The experimental value for the parallel electrode configuration lies in the lower predicted range due to the scotch tape in the experimental setup restricting strain production from the applied voltage as well as overestimation of the model due to idealized geometry and behavior. The IDE experimental value was similarly low due restriction of strain but as a result of the pressure applied by the bolts on the IDE assembly. Deviations in IDE geometry also lowers the experimental value as discussed in section The electromechanical characterization of the PZT fibers was determined in both parallel electrode and IDE configurations. The parallel electrode configuration yielded a piezoelectric e 33 constant ranging between C/m 2 for electric fields from MV/m. The IDE configuration yielded a piezoelectric e 33 constant ranging between C/m 2 for electric fields from MV/m. The nonlinear behavior that both electrode configurations exhibited is attributed to irreversible displacements of domains as explained by studies utilizing the Rayleigh law to model the behavior. The remnant polarization was found to be half for the fibers poled in the DMA compared to fibers poled outside with only an electric field applied. This reduction was due to the fibers being given a pre-stress and restricted movement of the grips creating blocked

142 130 stress conditions as the conditions prevent proper dipole alignment during poling. This could result in the fiber piezoelectric production reduced by half (ratio of remnant polarization in electric field only to that measured in DMA) due to the lower polarization. The determination of the e 33 for parallel electrode and IDE configurations for single PZT fibers has never been performed prior to this study. Therefore, models of the testing configuration were created to predict the behavior and verify the experimental results. For the parallel electrode configuration, the model predicted an e 33 of 6 C/m 2 which is comparable to the range of values determined experimentally. The idealization of the fiber geometry and alignment is expected to result in overestimation of the e 33 and appears to be the case. The IDE configuration model predicted an e 33 of 4 C/m 2 which is slightly higher than the experimental range, but, similar to the parallel electrode model, the idealization of the model assuming perfect geometries the predicted value can be assumed to be an overestimation. The experimental results for the parallel electrode will have additional error attributed to angle in the PZT fiber alignment between electrodes and rough fiber ends due to cutting the fibers as opposed to the flat ends assumed in the model. The IDE experimental results will have errors due to electrode alignment deviations and well as defects in the electrodes and fibers. The lower remnant polarization may have also reduced the true piezoelectric capabilities of the fibers in both electrode configurations. The true e 33 of the fibers may actually be closer to 5.6 C/m 2 and 3 C/m 2 for the parallel electrode and IDE configurations respectively. Further testing of the PZT fibers with the poling performed without the mechanical constraints will be performed to verify this hypothesis.

143 131 The reduction is value from bulk to fiber was found to be consistent for the Young s modulus and dielectric permittivity as the fiber values were found to be approximately 65% of the bulk values. A larger reduction was observed in the piezoelectric e 33 coefficient as the fiber value was found to be 40% of the bulk when using the predicted e 33 from the parallel electrode PZT fiber model. This lower value can be attributed the varying effect the porosity has on the different properties along with the increased porosity of the fiber. The drop in value from parallel to IDE is also fairly consistent as determined from the experiments performed. The results for the IDE were found to be within the range of 50% - 70% of the parallel electrode determined values for remnant polarization, permittivity and e 33. This leads to the conclusion that the average electric field produced by the IDE falls within the range of 50% - 70% of the value of the electric field produced by a parallel electrode configuration due to the nonuniformity of the IDE electric field. From the experimental characterization results of PZT fibers, the impact of using PZT fiber properties in AFC models will be substantial. The fiber-bulk property comparison shows that not only will large reductions in property values occur, but the reduction itself is not a single ratio. The mechanical and dielectric properties of the fiber were found to be 65% of the respective bulk values when the properties were determined individually. However, during the electromechanical testing the fiber e 33 value was found to be approximately 40% of the bulk due to electrical-mechanical coupling compounding the individual property reductions. With the fiber properties utilized in the AFC models, the hope is to achieve predicted AFC behavior that closely resembles the actual experimental AFC behavior. It is presumed that the implementation of the fiber properties into the AFC models will likely lead to a new optimized design of the AFC corresponding to the PZT fiber behavior. The optimized design for the AFC with PZT fiber properties may result in changes to the IDE dimensions and a different epoxy matrix used in the composite.

144 Recommendations for Future Work For future work in characterization of the PZT fibers, determination of other piezoelectric constants can be investigated. The e 33 constant was determined in this work for monitoring the induced stress from an applied electric field; however synchronized force and voltage data could not be obtained in the tests. Determination of a method to record the force and voltage can be investigated to provide a more accurate experimental e 33 piezoelectric coefficient. The pre-stress and blocked force conditions were also found to reduce the remnant polarization of the fibers poled while installed in the DMA. Poling the fibers and verification of P r before DMA installation should be investigated. The direct piezoelectric effect can be investigated as well for induced electric field from applied stress in the form of the piezoelectric g 33. Other testing can examine the electromechanical testing at elevated temperatures. The elevated temperatures will replicate the internal temperatures that the fibers may experience in the AFC. Other recommendations would be for improving the experimental determination of the d 33 piezoelectric coefficient. The accuracy may be improved by utilizing a fiber optic sensor instead of the LVDT method used. The fiber optic sensor could also allow for the strain of the fiber while in the IDE assembly to be measure. Improvements to the ABAQUS models can be done by including the nonlinear behavior that is found in PZT with implementation of the Rayleigh law. The model used in this study contained linear treatment of the PZT because the simulations were conducted for low electric fields (0.1 MV/m). The behavior at 0.1 MV/m will be very similar to the zero field piezoelectric effect but implementing the Rayleigh can better predict the value and for a wider range of electric fields.

145 133 References 1. Melnykowycz, M., et al., Performance of integrated active fiber composites in fiber reinforced epoxy laminates. Smart materials and structures, (1): p Schulz, M.J., et al. Active fiber composites for structural health monitoring. in SPIE's 7th Annual International Symposium on Smart Structures and Materials International Society for Optics and Photonics. 3. Sodano, H.A., G. Park, and D.J. Inman, An investigation into the performance of macrofiber composites for sensing and structural vibration applications. Mechanical Systems and Signal Processing, (3): p Brunner, A.J., et al., Piezoelectric fiber composites as sensor elements for structural health monitoring and adaptive material systems. Journal of Intelligent Material Systems and Structures, Barbezat, M., et al., Integrated active fiber composite elements: characterization for acoustic emission and acousto-ultrasonics. Journal of intelligent material systems and structures, Belloli, A., et al., Structural vibration control via RL shunted active fiber composites. Journal of intelligent material systems and structures, (3): p Williams, R.B., et al., An overview of composite actuators with piezoceramic fibers. Proceeding of IMAC XX, 2002: p Shen, X., Y. Liu, and J. Zhang. Study of piezoelectric fiber composite actuators applied in the flapping wing. in Applications of Ferroelectrics, ISAF th IEEE International Symposium on the IEEE. 9. Bent, A.A., Active Fiber Composites for Structural Actuation, in Department of Aeronautics and Astronautics. 1997, Massechusetts Institute of Technology. 10. Atitallah, H.B., Z. Ounaies, and A. Muliana, Temperature and time dependence of the electro-mechanical properties of flexible active fiber composites. Smart Materials and Structures, (4): p Rodgers, J.P., A.A. Bent, and N.W. Hagood. Characterization of interdigitated electrode piezoelectric fiber composites under high electrical and mechanical loading. in 1996 Symposium on Smart Structures and Materials International Society for Optics and Photonics. 12. Gentilman, R.L., et al. Enhanced-performance active fiber composites. in Smart Structures and Materials International Society for Optics and Photonics. 13. Atitallah, H.B., Z. Ounaies, and A. Muliana, A parametric study on flexible electro-active composites: Importance of geometry and matrix properties. Journal of Intelligent Material Systems and Structures, (17): p Bent, A.A. and N.W. Hagood. Improved performance in piezoelectric fiber composites using interdigitated electrodes Yoshikawa, S., et al., PZT Fibers - Fabrication and Measurement Methods. Journal of Intelligent Material Systems and Structures, Cain, M. and M. Stewart, The measurement of blocking force. NPL report MATC (A), Fett, T. and G. Thun, Determination of room-temperature tensile creep of PZT. Journal of Materials Science Letters, (22): p Kornmann, X. and C. Huber, Microstructure and mechanical properties of PZT fibres. Journal of the European Ceramic Society, (7): p

146 19. Nelson, L., et al., Modeling and measurement of piezoelectric fibers and interdigitaded electrodes for the optimization of piezofibre composites : p Guillot, F.M., H.W. Beckham, and J. Leisen, Hollow Piezoelecric Ceramic Fibers for Energy Harvesting Fabrics. Journal of Engineered Fibers and Fabrics, (1): p Zhang, M., et al., Preparation and ferroelectric properties of PZT fibers. Ceramics International, (2): p Damjanovic, D., Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics. Reports on Progress in Physics, (9): p Nye, J.F., Physical properties of crystals: their representation by tensors and matrices. 1985: Oxford university press. 24. Hagood, N.W., et al. Improving transverse actuation of piezoceramics using interdigitated surface electrodes ABAQUS. Computer software. Vers DS. 26. Berlincourt, D. and H.H.A. Krueger. Technical Publication TP-226 Properties of Piezoelectric Ceramics. Available from: Smith, W.A., Modeling 1-3 composite piezoelectrics: hydrostatic response. Ultrasonics, Ferroelectrics, and Frequency Control, IEEE Transactions on, (1): p Measurement of Properties of Piezoelectric Ceramics. Sensor Technology Limited, BM91-309, Manufacturer Handbook, Ogihara, H., STRUCTURE-PROPERTY-COMPOSITIONAL RELATIONSHIPS IN THE BaTiO3 BiScO3 CERAMIC SYSTEM. 2008, The Pennsylvania State University. 30. Sinha, J., Modified Sawyer and Tower circuit for the investigation of ferroelectric samples. Journal of Scientific Instruments, (9): p IEEE Standard on Piezoelectricity. ANSI/IEEE Std , 1988: p. 0_ Bystricky, P. Ceramic piezoelectric fibers: correlating single-fiber properties with active fiber composite performance Khan, K.A., et al., Time-dependent and Energy Dissipation Effects on the Electro- Mechanical Response of PZTs Manuscript submitted for publication. 34. Damjanovic, D. and M. Demartin, The Rayleigh law in piezoelectric ceramics. Journal of Physics D: Applied Physics, (7): p PI Ceramics Piezoelectric Ceramic Products: Fundamentals, Characteristics and Applications, P. Ceramics, Editor

147 135 Appendices Appendix A IDE Screen Print Process The IDE screen printing process is accomplished using a Presco Thick Film Screen Printer, IDE pattern screen ordered from UTZ Technologies, polycarbonate polybus ink and 0.1 mm thick Mylar sheets. The Presco Screen Printer is shown in Figure A-1. The screen printer is run through compressed air that controls a vacuum suction in top of the sample stage to hold the sample in place, the sliding of the sample stage under the printer, the motion of the printer to press the ink through the screen and retrieving the sample stage from under the printer. Figure A-1: Presco Thick Film Screen Printer Step 1: The first step is two install the screen into the printing through bolts that are screwed in through the screen frame (Figure A-2). With the screen installed the height between the bottom of the screen and top of the sample stage has to be configured to the thickness of the

148 136 substrate being utilized. For the 0.1mm thick Mylar sheet being used the gap is set to approximately 0.3 mm. Figure A-2: IDE screen from UTZ Technologies Step 2: After the screen has been installed and height configured, the ink used for screen printing can be placed on the screen. The ink is carefully placed between the squeegee of the printer and screen pattern (Figure A-3). The ink only needs to cover the width of the pattern. The ink should be thoroughly mixed before use. Figure A-3: Proper ink placement for screen printing

149 137 Step 3: The substrate can now be placed on the sample stage. A foot pedal is pressed to turn on the vacuum suction of the stage from the compressed air to secure the substrate in place during the printing process. A second foot pedal is pressed and activates the printing procedure where the sample stage slides under the printer, squeegee pushes the ink over the pattern and sample stage returns to initial position (Figure A-4). The pressure of the squeegee may need adjustment through turning the micrometer on top of the printer. The micrometer is only turned a little at a time until the full pattern with consistent print quality is achieved. Too much pressure from the squeegee may damage the screen and lower print quality. Once the proper pressure is found, more prints of the pattern can be conducted. After the desired amount is reached, the ink is cleaned from the printer and screen. The process can now be repeated for the second IDE pattern. Figure A-4: Screen print process activated by foot pedal

150 138 Appendix B PZT IDE Assembly Manufacturing Process Step 1: The process of creating the IDE assemblies starts with screen printing the IDE patterns on Mylar sheets using silver ink to make the conductive electrodes. Two patterns are created that when placed on top of each other overlap and all electrode paths align. For a single IDE assembly, one of each pattern are carefully aligned and secured using scotch tape on the Mylar with some buffer room in between the tape and the ends of the electrode pattern. A photo of the aligned and taped patterns is shown in Figure A-5 below. Figure A-5: Aligned IDE patterns for IDE assembly fabrication Step 2: The next step is to prepare the laser cut acrylic plates that the Mylar sheets will be adhered to using double sided scotch tape. The negative of the acrylic pattern is kept from the laser cutting process. The IDE acrylic plate is placed in the negative and the double sided tape is applied over the entirety of the plate. The negative acts as a stencil to guide a razor blade to cut

151 139 and remove the excess double sided scotch tape. A photo showing the finished step is shown below in Figure A-6. Figure A-6: IDE acrylic plate with double sided scotch tape applied and excess tape removed Step 3: After the double sided scotch tape is applied, the acrylic plate is left in the negative. The aligned patterns from step 1 are carefully placed onto the acrylic plate and scotch tape. The patterns are placed carefully into the center of the IDE acrylic plate. Firm pressure is applied on the screens to assure solid adhesion to the double side scotch tape. It is important to apply force directly on top of screens and to avoid sliding fingers up and down the patterns as it will create friction and may scratch the electrode breaking the connection. A photo showing proper screen placement onto the acrylic plate is shown in Figure A-7.

152 140 Figure A-7: IDE screen patterns placed onto first acrylic plate Step 4: The first IDE acrylic plate with adhered IDE screens are carefully removed and placed to the side. A second acrylic plate is placed into the negative and step 2 is repeated. Step 3 is then repeated for the other side of the screen printed IDE. The first acrylic plate is used for alignment with the second acrylic plate. Firm pressure is applied to assure adhesion of the second acrylic plate to the IDE printed screens. The attached components are then removed from the negative and placed on an aluminum plate for the next step. See Figure A-8.

153 141 Figure A-8: Both acrylic plates aligned and adhered to IDE screen printed patterns Step 5: With the adhered components on an aluminum plate, the excess Mylar is carefully removed by tracing the acrylic plates with a razor blade. It is important to apply firm pressure directly to acrylic plates while cutting with razor. It is also important to avoiding sliding the acrylic plates across each other as it may damage the screen printed electrodes. Once the acrylic plates have been traced with a razor blade, the plates are carefully separated and excess Mylar removed. See Figure A-9.

154 Figure A-9: Full pattern screen printed IDEs assembled to acrylic plates 142