Mathematical Analysis of Piezoelectric Sandwich Torsion Transducers Based on the d36-Effect

In the present article, we analyze a d₃₆-effect piezoelectric torsion transducer following the Saint-Venant torsion theory taking the electrical field into account. A representation of the stress function, the electric potential, and the warping function are derived and solved with finite differences. Then, the one-dimensional governing equations at the structural beam level, including the constitutive relations as well as the balance equations for the dynamics of the transducer, are presented. The axial moment and the total charge are computed as functions of the rate of twist and the applied potential difference. As an example, a cantilevered transducer is studied.     

Functional composites for sensors,actuators and transducers

Following the trend in structural applications, composite structures are being used more commonly in transducer applications to improve acoustic, mechanical and electrical performance of piezoelectric devices. Functional composite transducers for actuators and sensors generally consist of an active ceramic phase incorporated with a passive polymer phase, each of which has a phase transition associated with it. In this paper, several polymer–piezoelectric ceramic composite transducers, mostly designed for sensing hydrostatic waves, are discussed based on the connectivity of the constituent phases. Also discussed are some recent examples of metal–ceramic composites, and single element ceramic transducers with modified shapes for improved performance. A comparison of these designs is given based on their hydrophone figure of merit (d_h·g_h).     

Numerical and experimental characterizations of longitudinally polarized piezoelectric d 15 shear macro-fiber composites

This contribution presents original numerical and experimental characterizations for prototyped longitudinally polarized piezoelectric d ₁₅ shear macro-fiber composites (MFC). The numerical characterization consists of a finite element (FE) simulation based on a representative volume element. It implements an enthalpy-based homogenization method (EBHM), recently proposed by the authors, as an extension of the so-called strain energy method to orthotropic piezoelectric fiber-reinforced composites. The numerical validation is carried out on a previously assumed layout of shear MFC. Later on, the EBHM is used to get the effective electromechanical material parameters of the shear MFC actual layout. These parameters are further validated experimentally through their use in the FE simulation of an original actuation benchmark that is proposed for the manufactured shear MFC experimental characterization. The latter is based on low-frequency (quasi-static) displacement measurements where the shear MFC serves as a voltage-driven actuator. Due to the small overall dislocation, a laser vibrometer is used for the measurements. The comparison of experimental and numerical results shows a reasonably good agreement and a nonlinear actuation response is observed. This work’s major outcomes are the experimental validation of the EBHM and the actuation functional operability of the manufactured longitudinally polarized piezoelectric d ₁₅ shear MFC. This opens the possibility for their application as actuator and sensor of shear-induced bending and torsion for vibration, shape and health control, or as a transducer for energy harvesting.     

Efficient finite element with physical and electric nodes for transient analysis of smart piezoelectric sandwich plates

This paper presents an assessment of a recently developed quadrilateral element with four physical nodes and one electrical node, based on a coupled improved zigzag theory, for the transient response of smart sandwich plates with electroded piezoelectric sensors and actuators. The novel features of the element include the use of electric nodes to model the equipotential condition of the electroded surface of sensors and actuators, and the inclusion of the d ₃₃-effect on transverse deflection. The assessment is done for a skew plate in comparison with a converged three-dimensional finite element solution obtained using ABAQUS. The accuracy as well as the computational efficiency of the present element is highlighted.     

Finite element characterization and parametric analysis of the nonlinear behaviour of an actual d 15 shear MFC

Nonlinear dependence between mechanical deformation and applied voltage has been experimentally observed on a recently manufactured lengthwise poled piezoelectric d ₁₅ shear macro-fibre composite (MFC) transducer. This work proposes a methodology to model this phenomenon by combining the nonlinear behaviour of the constituent piezoceramic fibre (electric field dependence of material properties) with a finite element homogenization technique to evaluate the resulting nonlinearity of the effective properties of the d ₁₅ MFC. Results show that the experimentally observed nonlinear behaviour of d ₁₅ MFC is reasonably well predicted by the proposed methodology indicating that this behaviour could be explained by an electric field dependence of the piezoceramic fibre material properties. Results also show that d ₁₅ and ${\epsilon_{11}^T}$ coefficients of the d ₁₅ MFC are not significantly reduced by the MFC packaging, while e ₁₅ and G ₁₃ coefficients are reduced by 90 %, compared to the piezoceramic fibre ones. A conducted parametric analysis indicates that the actuation performance of the d ₁₅ MFC transducer could be improved by increasing the active layer thickness.     

Dielectric and piezoelectric properties and electrical conductivity of LiNbO<Subscript>3</Subscript>:ZnO crystals in a wide range of dopant concentrations

The dielectric and piezoelectric properties and electrical conductivity of initially multidomain LiNbO₃:ZnO crystals have been studied in a wide range of dopant concentrations with the aim of determining the composition range of the anomalous increase in unipolarity. The results demonstrate that the development of spontaneous unipolarity during high-temperature annealing takes place only in LiNbO₃:ZnO crystals grown from melts in a “near-threshold” composition range (~5.4 < C_m ≤ 6.76 mol % ZnO). The effect is accompanied by a considerable and reproducible increase in the static piezoelectric modulus d₃₃₃. The increase in the piezoelectric modulus, Δd₃₃₃, rises linearly with increasing jump in electrical conductivity, Δσ, near a temperature T* ≈ 800 K.     

A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids

This paper presents a single-domain boundary element method (BEM) analysis of fracture mechanics in 2D anisotropic piezoelectric solids. In this analysis, the extended displacement (elastic displacement and electrical potential) and extended traction (elastic traction and electrical displacement) integral equations are collocated on the outside boundary (no-crack boundary) of the problem and on one side of the crack surface, respectively. The Green's functions for the anisotropic piezoelectric solids in an infinite plane, a half plane, and two joined dissimilar half-planes are also derived using the complex variable function method. The extrapolation of the extended relative crack displacement is employed to calculate the extended `stress intensity factors' (SIFs), i.e., K_I, K_II, K_III and K_IV. For a finite crack in an infinite anisotropic piezoelectric solid, the extended SIFs obtained with the current numerical formulation were found to be very close to the exact solutions. For a central and inclined crack in a finite and anisotropic piezoelectric solid, we found that both the coupled and uncoupled (i.e., the piezoelectric coefficient e_ijk=0) cases predict very similar stress intensity factors K_I and K_II when a uniform tension σ_yy is applied, and very similar electric displacement intensity factor K_IV when a uniform electrical displacement D_y is applied. However, the relative crack displacement and electrical potential along the crack surface are quite different for the coupled and uncoupled cases. Furthermore, for a inclined crack within a finite domain, we found that while a uniform σ_yy (=1 N m⁻²) induces only a very small electrical displacement intensity factor (in the unit of Cm^−3/2), a uniform D_y (=1 C m⁻²) can produce very large stress intensity factors (in the unit of Nm^−3/2).     

Morphology and structure of hexagonal MoO<Subscript>3</Subscript> nanorods

We have prepared h-MoO₃ nanocrystals in the form of well-faceted straight hexagonal rods with an aspect ratio of l/d ? 60. The nanocrystals have been characterized by x-ray diffraction, scanning and transmission electron microscopy, and IR/Raman spectroscopy. Their phase composition has been determined, and their morphology and spectroscopic properties have been studied in detail.     

Microstructure and electrical properties of K<Subscript>0.5</Subscript>Na<Subscript>0.5</Subscript>NbO<Subscript>3</Subscript> lead-free piezoelectric ceramics sintered in low pO<Subscript>2</Subscript> atmosphere

Pure K_0.5Na_0.5NbO₃ lead-free piezoelectric ceramics without any dopants/additives were sintered at various temperatures (950–1125 °C) in low pO₂ atmosphere (pO₂?~?10^?6 atm). All ceramics exhibit high relative densities (>?94%) and low weight loss (<?0.6%). Compared to the ceramics sintered in air, the ceramics sintered in low pO₂ exhibit improved electrical properties. The piezoelectric constant d₃₃ and converse piezoelectric constant d₃₃* are 112 pC/N and 119 pm/V, respectively. The ceramics show typical ferroelectric behavior with the remnant polarization of 21.6 µC/cm² and coercive field of 15.5 kV/cm under measurement electric field of 70 kV/cm. The good electrical properties of the present samples are related to the suppression of volatility of the alkali cations during the sintering process in low pO₂ atmosphere.     

Simplified fabrication of PZT/polymer composites

Skinner, et al. prepared PZT/polymer composites using the coral replamine process. The composites were found to have, for certain applications, greatly improved electromechanical and physical properties over those of conventional piezoelectric materials. However, the coral replamine process requires natural coral from the ocean as the starting replica material, making this process industrially unfavorable.This paper discussed PZT/polymer composites electromechanically and physically comparable to the Skinner replamine composites. Fabrication is simplified by the use of a compacted mixture of volatilizable plastic spheres and PZT powder, which when sintered yields a piezoelectric with a density of less than 2.9 g/cm³, a permittivity of ～120 and a d₃₃ of 180×10^?12 C/N. The improved connectivity increases d_h (hydrostatic) from ～35×10^?12 C/N (solid PZT) to 100×10^?12 C/N.     

Characterisation of barium titanate-silver composites part II: Electrical properties

Barium titanate-silver composites were manufactured with silver contents ranging from 0 wt.% to 30 wt.%. The electrical properties were systematically characterised in terms of relative permittivity, conductivity, piezoelectric properties (d₃₃, d₃₁ and coupling coefficient), polarisation-field measurements and electrical breakdown strength. The electrical properties are strongly influenced by the conducting phase, with an increase in relative permittivity, conductivity, coercive field and remnant polarisation measured. A decrease in breakdown strength and piezoelectric coefficients were observed.     

Piezoelectric tubes and tubular composites for actuator and sensor applications

Piezoelectric actuators and sensors made with a tubular structure can provide a great agility of effective response in the radial direction. For a radially poled piezoelectric tube, the effective piezoelectric constant in that direction can be tuned to be positive, zero or negative by varying the ratio of the outer radius (R _o) to the inner radius (r _o) of the tube. For a suitable ratio of R _o/r _o, this effective constant can also be changed in sign or set to zero by adjusting the d.c. bias field level for tubes made of electrostrictive materials. Therefore, one can make a piezoelectric transducer with all the effective piezoelectric tensile constants having the same sign. End-capped thin-walled tubes also exhibit an exceptionally high hydrostatic response, and the small size of the tubular structure makes it very suitable for integration into a 1–3 composite which possesses low acoustic impedance and high hydrostatic response.     

Measurements of LiNbO<Subscript>3</Subscript> Properties by Multi-parameter Inversion Based on Acoustic Microcopy

This paper expands on a theoretical model between the mechanical and electrical properties with acoustic characteristics to obtain the theoretical dispersion curve for Y-cut LiNbO₃ piezoelectric plate. The experimental dispersion curve of the LiNbO₃ plate is extracted via V(f,z) analysis through defocusing measurements based on an acoustic microscopy and a lens-less line focusing transducer. The objective function of the inversion depends on the experimental dispersion curve. The inversion method adopts a hybrid particle-swarm-based simulated-annealing (PS-B-SA) optimization, which is used for joint inversion of the mechanical and electrical parameters of LiNbO₃. The theoretical dispersion curve will approach the experimental dispersion curve by constantly modifying the mechanical and electrical parameters in the theoretical model: the elastic constants (C₁₁, C₁₂, C₂₂, C₂₃, C₂₅, C₅₅), piezoelectric constants (e₁₁, e₁₂, e₂₆, e₃₃), and dielectric constants (ε₁₁, ε₂₂). The inversed series of constants are those who make the theoretical dispersion curve most fit the experimental ones. The results show that the inversed mechanical and electrical parameters agree well with the reported values, and the stability and accuracy of the inversion is acceptable. This research provides a useful tool to characterize the mechanical and electrical properties of piezoelectric materials simultaneously.     

Effect of Zr/Ti ratio on the dielectric and piezoelectric properties of Mn-doped Ba(Zr,Ti)O3 ceramics

Lead-free piezoelectric Ba(Zr _y Ti_1?y )O₃:0.5 mol%Mn (abbreviated as BZTM-100y, y = 0.04, 0.045, 0.05, and 0.055) ceramics were prepared via the conventional solid-state reaction method. The cubic to tetragonal phase transition temperature (T _c ) shifts to lower temperature with increasing Zr concentration, and the transition temperature from tetragonal to orthorhombic (T _o?t ) which is a shift to higher temperature from 26 to 47 °C with increasing y value from 0.04 to 0.055. And a small amount of Mn can improve effectively the electrical properties, especially the piezoelectric properties of the BZT ceramics. Compared to the pure BZT ceramics, the Mn-doped BZTM ceramic shows an excellent piezoelectric coefficient d ₃₃ as 213 pC/N.     

Influence of the connectivity pattern,the nature of the piezoelectric material,and rod thickness on the properties of 50 vol % PZT/50 vol % NiCo0.02Cu0.02Mn0.1Fe1.8O4 − δ magnetoelectric composites

We have studied the influence of the connectivity pattern, the nature of the piezoelectric material, and rod thickness on the properties of magnetoelectric composites with the composition 50 vol % PZT/50 vol % NiCo_0.02Cu_0.02Mn_0.1Fe_1.8O_{4 ? δ} (where PZT stands for various commercially available lead zirconate titanate based piezoelectric materials). The results indicate that the magnetoelectric conversion efficiency of the rod composites with any connectivity pattern (1-1, 1-3, or 3-1) is 10–20% higher than that of laminate composites. The largest magnetoelectric conversion coefficient ΔE/ΔH is offered by the 1-1 connectivity composites. The ΔE/ΔH of the composites correlates with both their piezoelectric sensitivity g ₃₃ and the piezoelectric sensitivity of the corresponding piezoelectric materials. ΔE/ΔH is shown to be inversely proportional to the thickness of the piezoelectric and ferrite rods. The highest ΔE/ΔH at a frequency of 1 kHz, 450 mV/(cm Oe), has been reached in the PZT-36 based composites with 1-1 connectivity and 0.3-mm-thick rods.     

Effects of CuO doping on the electrical properties of 0.98K0.5Na0.5NbO3-0.02BiScO3 lead-free piezoelectric ceramics

CuO-doped 0.98K_0.5Na_0.5NbO₃-0.02BiScO₃ (0.98KNN-0.02BS-xCu) lead-free piezoelectric ceramics have been fabricated by ordinary sintering technique. The effects of CuO doping on the dielectric, piezoelectric, and ferroelectric properties of the ceramics were mainly investigated. X-ray diffraction reveals that the samples at doping levels of x ≤ 0.01 possess a pure tetragonal perovskite structure. The specimen doped with 1 mol% CuO exhibits enhanced electrical properties (d₃₃ ~ 207 pC/N, k_p ~ 0.421, and k_t = 0.424) and relatively high mechanical quality factor (Q_m = 288). These results indicate that the 0.98KNN-0.02BS-0.01Cu ceramic is a promising candidate for lead-free piezoelectric ceramics for applications such as piezoelectric actuators, harmonic oscillator and so on.     

Effects of Co doping on microstructure and properties of (K0.5Na0.5)NbO3–LiSbO3–BiFe(1−x)Co x O3 lead-free piezoelectric ceramics

0.998 [(0.95(K_0.5Na_0.5)NbO₃–0.05LiSbO₃]–0.002BiFe_(1?x)Co _x O₃ (KNN–LS–BF_(1?x)C _x ) lead-free piezoelectric ceramics were prepared by conventional solid-state reaction method. The influences of Co content on the phase structure, microstructure, density and related electrical properties were investigated. The results reveal that the substitution of Co significantly improves the sinterability and the electrical properties of KNN–LS–BF_(1?x)C _x ceramics, sintered at a lower temperature of 1,030 °C, compared with that of KNN–LS–BF ceramics. With increasing x from 0 to 0.8, all samples show a pure perovskite structure, but the grain size increases continuously,and the porosity level reaches it’s lowest value at x = 0.2. The density ρ, piezoelectric constant d ₃₃, coupling factor k _p and dielectric constant ε _r increase with x up to 0.2, and then decrease with further increase in x value, but the variation of dielectric loss tan δ is opposite. The density and electrical properties achieve optimal value of ρ = 4.287 g/cm³, d ₃₃ = 276 pC/N, k _p  = 48 %, ε _r  = 1,284 and tan δ = 1.95 %, when x = 0.2. And Tc ≈ 340 °C at all the variation range of Co content.     

Structural, ferroelectric and piezoelectric properties of Mn-modified BiFeO3–BaTiO3 high-temperature ceramics

Mn modified BiFeO₃–BaTiO₃ (abbreviated as BFBT-Mnx%, x = 0.1, 0.3, 0.6, 0.9, 1.2) high-temperature lead-free ceramics were prepared by conventional oxide-mixed method and the effect of Mn doping on microstructure and electrical properties was investigated. The solid solutions show a single phase perovskite structure, and the content of Mn has a significant effect on the microstructure of ceramics. The addition of Mn can induce combinatory “hard” and “soft” piezoelectric characteristics due to aliovalent substitutions. In particular, x = 0.6 BFBT-Mnx% ceramic, with a Curie temperature, T _c, of ~463 °C, shows optimum piezoelectric properties of d ₃₃ = 131pC/N, k _p = 0.298. The simultaneous existence of good piezoelectric properties and high T _c makes these ceramics suitable for elevated temperature piezoelectric devices.