Effects of the piezoelectric phase’s geometric properties on effective coefficients of 1–3 piezoelectric composites

The present paper reports the electromechanical coupling coefficients of piezoelectric composite material (PCM) are affected by different geometric properties of piezoelectric phase for 1–3 periodic composites that is made of piezoceramic fibers embedded in a soft non-piezoelectric matrix. Three-dimensional finite element model has been developed to study the three types of geometric models of piezoelectric phase with different volume fraction. Geometric models with circular cylinder, square column and circular cylinder alternated with square column are used to predict the coefficients of the validity via asymptotic homogenization method (AHM) and the numerical approach the finite element method (FEM). Three types of geometric model are built via the finite element software ABAQUS, and the elastic, piezoelectric and dielectric coefficients are evaluated via AHM both FEM. The results indicate that the validity parameters of PCM have the direct relationship with the volume fraction, and geometric shape is essential factor for distribution of Von-Misses when device working. The present work may improve application of 1–3 type PCM and offer useful guidelines to the design of PCM devices.     

Determination of the reduced matrix of the piezoelectric, dielectric, and elastic material constants for a piezoelectric material with C∞ symmetry

We present a procedure for determining the reduced piezoelectric, dielectric, and elastic coefficients for a C(∞) material, including losses, from a single disk sample. Measurements have been made on a Navy III lead zirconate titanate (PZT) ceramic sample and the reduced matrix of coefficients for this material is presented. In addition, we present the transform equations, in reduced matrix form, to other consistent material constant sets. We discuss the propagation of errors in going from one material data set to another and look at the limitations inherent in direct calculations of other useful coefficients from the data.     

Crack deflection at an interface between dissimilar piezoelectric materials

The problem of crack deflection in bimaterial systems is considered in this paper. The material combinations may be of piezoelectric-piezoelectric, or one is piezoelectric and the other is not. Based on the Stroh formulation for anisotropic material, Green's functions for various bimaterial combinations are presented within the framework of two-dimensional electroelasticity, allowing the crack problem to be expressed in terms of coupled singular integral equations. A crack impinging on an interface joining two dissimilar materials may arrest or may advance be either penetrating the interface or deflecting into the interface. The competition between deflection and penetration is investigated using the maximum energy release rate criterion. Numerical results are presented to study the role of remote electroelastic loads on the path selection of crack extension. Key words: Crack, piezoelectric material, interface, Green's function, singular integral equation.     

Lamb wave propagation in the functionally graded piezoelectric–piezomagnetic material plate

The propagation behaviour of Lamb waves in the functionally graded piezoelectric–piezomagnetic material plate with material parameters varying continuously along the thickness direction is investigated in this paper. The power series technique is employed to solve these variable coefficient ordinary differential equations. Dispersion equations are given for different boundary conditions. In numerical examples, the influence of the variation of each parameter on dispersion curves and cut-off frequency in electrically and magnetically open cases is discussed in detail. Results show that the elastic parameters and density varying along the thickness direction obviously influence the variation of phase velocity. Some variations in electric and magnetic parameters also affect the phase velocity but the influence is too small, while others almost cannot affect the dispersion curves. Cut-off frequency is closely related to two elastic parameters and to density, whereas other parameters almost cannot influence it. All the results can provide theoretical guidance not only for the analysis and design of a magnetoelectric transducer using functionally graded materials, but also for ultrasonic nondestructive evaluation.     

Modeling and fabrication of a piezoelectric vibration‐induced micro power generator

Abstract

In this paper, theoretical and experimental study on a piezoelectric vibration‐induced micro power generator that can convert mechanical vibration energy into electrical energy is presented. The mechanical‐electrical energy conversion mechanism is a voltage between two capacitors, which belong to the mechanical and the piezoelectric equivalent circuits, respectively. To verify the theoretical analysis, two clusters of transducer structures are fabricated. Piezoelectric lead zirconate titanate (PZT) material is chosen to make the energy conversion transducer. The desired shape of the piezoelectric generator with its resonance frequency in accordance with the ambient vibration source is designed by finite element analysis (FEA).

Experimental results show that the maximum output voltages are generated at the first mode resonance frequencies of the structure. The overall conversion efficiency is measured to be 33%. The experimental results coincide with the theoretical analysis.     

Dielectric and piezoelectric characterization of PSZT–BT ceramics for capacitor applications

The ceramic compositions (1 − x)Pb_0.9875Sr_0.0125(Zr_0.53Ti_0.47)O₃ –xBaTiO₃ where x = 0.2, 0.4, 0.6 and 0.8, fabricated through solid state reaction method were investigated for phase formation, microstructure, density, dielectric and piezoelectric properties. The X-ray diffraction patterns indicated that introduction of BaTiO₃ in isovalent donor Sr modified PZT lattice, diminished the tetragonality. All the specimens were homogenous in nature due to the coarse grains of BaTiO₃, which had undergone inter-granular growth and were homogeneously distributed within the PSZT–BT lattice. Introduction of BaTiO₃ in PSZT perovskite lattice resulted in enhanced grain growth till x = 0.6 (2.03 μm). Dielectric properties (ε_RT, Tanδ and T _c) were influenced by both BaTiO₃ and Sr. The maximum ε_RT = 1588 and ε_Tc = 10478 were found in 0.2PSZT–0.8BT ceramic system. The optimum dielectric permittivity at room temperature with a low Curie transition temperature was found in 0.2PSZT–0.8BT composition. Piezoelectric properties are very sensitive to isovalent substitutions, where isovalent donor Sr modification and BT concentrations in PZT, affected the piezoelectric properties (k _p and d ₃₃) in the ceramic system. Thus, the series PSZT–BT compositions could be ideal candidates for capacitors and suitable sensor applications.     

Green’s functions of a half-infinite piezoelectric body: Exact solutions

Summary. Greens functions of a half-infinite piezoelectric space play an important role in electroelastic analyses of piezoelectric media. However, almost all works available on the topic are based on the assumption that the normal component of the electric displacement is zero on the surface of the piezoelectric solid, neglecting the effect of polarized surface charge. In the present work, we develop an exact solution for the Greens functions of a half-infinite piezoelectric solid by means of the Stroh formalism. The solution is based on using the exact electric boundary conditions at the interface between the solid and the air medium. First, Greens function for an arbitrary line load in the solid is derived taking into account the effect of polarized charge at the interface, and then the surface Greens function for a surface load is obtained as a special example. Finally, by using the superposition principle, a general expression for the polarized charge distribution on the surface of the piezoelectric solid is presented when an arbitrarily distributed force is exerted on the boundary. It is shown that the normal component of the electric displacement on the solid surface is not zero and it is dependent on the applied loads and the electro-elastic constants of the piezoelectric material and air.     

A theoretical study of nonlinear magnetoelectric effect in magnetostrictive–piezoelectric trilayer

A novel nonlinear theoretical model is established for magnetoelectric (ME) effect in trilayer of magnetostrictive and piezoelectric phases, in which the nonlinear magnetic–mechanical coupling behavior for the magnetostrictive phase is firstly taken into account. In this theoretical model, the interface coupling parameter k is used for characterizing actual bonding conditions at the interface. The coupled magnetic–mechanical–electric effect involving linear and nonlinear coupling interactions in the ME laminated composites is numerically simulated using this nonlinear model. The numerical results predict giant ME effect for Terfenol-D based ME laminated composites. The quantitative dependences of the giant ME effect on the applied magnetic field, the piezoelectric property of piezoelectric phase, the volume fraction of magnetostrictive phase and the interface coupling parameter k are discussed in details. All of these dependences indicate that the nonlinear theoretical model established in this article can accurately capture nonlinear magnetic–mechanical–electric coupling behavior for Terfenol-D based ME laminated composites. The giant ME effect predicted for the Terfenol-D/PMN-PT/Terfenol-D composites is in excellent agreement with recent experimental data available. It confirms the validity and reliability of the obtained nonlinear theoretical model, and demonstrates the significance and necessity of considering the nonlinear magnetic–mechanical coupling behavior of Terfenol-D.     

Structure,ferroelectric and piezoelectric properties of Bi0.5(Na0.8K0.2)0.5TiO3 modified BiFeO3–BaTiO3 lead-free piezoelectric ceramics

A new lead-free solid solution of (0.75 ? x)BiFeO₃–0.25BaTiO₃–xBi_0.5(Na_0.8K_0.2)_0.5TiO₃ + 1 mol% MnO₂ has been prepared by a conventional ceramic technique and the effects of Bi_0.5(Na_0.8K_0.2)_0.5TiO₃ and sintering temperature on the structure, ferroelectric and piezoelectric properties of the material have been studied. The ceramics sintered at 960 °C for 2 h possess a pure perovskite structure and no second phases can be detected. After the addition of Bi_0.5(Na_0.8K_0.2)_0.5TiO₃, a morphotropic phase boundary of rhombohedral and orthorhombic phases is formed at x = 0.01. The addition of a small amount of Bi_0.5(Na_0.8K_0.2)_0.5TiO₃ can promote the grain growth, while excess Bi_0.5(Na_0.8K_0.2)_0.5TiO₃ causes an inhibition of grain growth. Sintering temperature has an important influence on the structure and electrical properties of the ceramics. The sintering temperature of 960 °C is a critical temperature to obtain the ceramics with good piezoelectric properties. For the ceramic with x = 0.01 sintered at/above 960 °C located at the morphotropic phase boundary, large grains, good densification, high resistivity and enhanced electrical properties are obtained.     

Ferroelectric and piezoelectric properties of [(Ba1−3x/2Bix)0.85Ca0.15](Ti0.90Zr0.10)O3 lead-free piezoelectric ceramics

Bismuth-modified barium calcium zirconate titanate ceramics [(Ba_1?3x/2Bi_x)_0.85Ca_0.15](Ti_0.90Zr_0.10)O₃ (BBCTZ) have been prepared by the conventional solid-state reaction method, and effects of Bi content on the electrical properties of BBCTZ ceramics were systematically investigated. BBCTZ ceramics endure a phase transition from the coexistence of rhombohedral and tetragonal phases, a tetragonal phase, to a cubic phase with increasing Bi content. The Curie temperature, the remanent polarization, and the dielectric loss of BBCTZ ceramics gradually decrease with increasing the Bi content. The BBCTZ ceramic with x = 0.0075 exhibits an optimum electrical behavior: d₃₃ ～ 361 pC/N and k_p ～ 40.2%.     

Singularity parametersε andκ for interface cracks in transversely isotropic piezoelectric bimaterials

Two parameters, and (Suo et al., 1992), are of key importance in fracture mechanics of piezoelectric material interfaces. In this paper, it is shown, for any transversely isotropic piezoelectric (TIP) bimaterial, that one of the two parameters and always vanishes but the other one remains non-zero. Physically, it means that the non-oscillating crack-tip generalized stress field singularity exists for some TIP bimaterials (with vanishing ). Consequently, TIP bimaterials can be classified into two classes: one with vanishing performed crack tip generalized stress field oscillating singularity and the other one with vanishing is independent from the oscillating singularity. Some numerical results for and are given too.     

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.     

Thermo-electro-mechanical response of 1–3–2 piezoelectric composites: effect of fiber orientations

A micromechanics-based analytical model is developed to evaluate the performance of 1–3–2 piezoelectric composite where both matrix and fiber materials are piezoelectrically active. A parametric study is conducted to investigate the effects of variations in the poling characteristics of the fiber phase on the overall thermo-electro-mechanical behavior of a 1–3–2 piezocomposite. The performance of the 1–3–2 composite as a transducer for underwater and biomedical imaging applications is analyzed. The proposed model is capable of predicting the effective properties of the composite subjected to thermo-electro-mechanical loading conditions. The predicted variations in the effective elastic, piezoelectric and dielectric material constants with fiber volume fraction are nonlinear in nature. It is observed that the influence of thermal effects on effective properties of the composite also induces polarization in the composite. The analytical results show that an appropriate selection of the poling characteristics of the individual fiber and matrix phases could lead to the development of a piezocomposite with significant effective properties.     

Crack-tip amplification and shielding by micro-cracks in piezoelectric solids – Part I: Static case

Analysis of the crack-tip amplification and shielding by micro-cracks in an unbounded two-dimensional piezoelectric solid is presented in this paper. A boundary element method (BEM) based on the hypersingular traction boundary integral equations (BIEs) is developed for this purpose. Integrals with hypersingular kernels are analytically transformed into weakly singular and regular integrals. A collocation method is applied for the spatial discretization. Quadratic quarter-point elements are implemented at all crack-tips. The amplification ratios of the field intensity factors and mechanical strain or electrical energy release rate are defined to show the crack-tip amplification and shielding. Numerical results are compared with the analytical results for isotropic materials to verify the present BEM. The influences of various loading conditions, the location and orientation angles of micro-cracks on the amplification ratios are investigated. The contours of the amplification ratios for an arbitrarily located micro-crack are also presented to show the crack-tip amplification and shielding effects.     

Swift heavy ion induced ordering and piezoelectric β-phase in poly(vinylidene fluoride)

Ion flux dependent swift heavy ions (SHI) induced structural changes have been reported for pristine poly(vinylidene fluoride) (PVDF). Ordering phenomena has been observed first followed by its transformation from α to β-form (polar metastable piezoelectric phase). The ordering of (020) plane become prominent at higher ion flux SHI irradiation and its further increase induces structural change from α to β phase as revealed by XRD and FTIR analyses. Structural changes are also supported by morphological evidence and thermal studies before and after SHI irradiation.     

Active constrained layer damping of smart laminated composite sandwich plates using 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of sandwich plate with laminated composite faces. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1?C3 piezoelectric composites. Several honeycomb core materials like HEREX honeycomb and honeycomb with foam fill separated by different facing materials have been studied and a three-dimensional finite element model has been developed considering first order shear deformation theory individually for each layer of the sandwich plate. The effect of the ratio between the face sheet thickness and the core thickness of the sandwich plate on the frequency response has been studied. Particular emphasis has been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD treatment.     

Investigation on the fabrication and properties of Ce-doped PMN–PT translucent piezoelectric ceramics

Journal of Materials Science: Materials in Electronics - Relaxor ferroelectric ceramics (1–x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 (PMN–PT) at the morphotropic phase boundary exhibit high...     

Shear horizontal (SH) waves propagating in piezoelectric–piezomagnetic bilayer system with an imperfect interface

This work considers the propagation of shear horizontal (SH) waves in a bilayer system consisting of a piezoelectric (PE) layer and a piezomagnetic (PM) substrate. The interface between the PE layer and the PM substrate is imperfectly bonded. The surfaces of the bilayer system are free of traction, electrically shorted or open and magnetically open or shorted. The exact dispersion equations are derived. The numerical examples are given to illustrate the effects of the electromagnetic boundary conditions, the imperfect interface, the different PE layers and the thickness ratio on the dispersion behaviors. It is found that (a) the electrical boundary conditions dominate the propagation characteristics of SH waves; (b) the imperfect bonding lowers the phase velocities; (c) the thickness ratio and the properties of PE layers have a significant effect on the dispersion behaviors. The obtained results provide a predictable and theoretical basis for applications of PE–PM composites to acoustic wave devices.     

Smart damping of geometrically nonlinear vibrations of functionally graded sandwich plates using 1–3 piezoelectric composites

Geometrically nonlinear dynamic analysis of smart functionally graded (FG) sandwich plates integrated with the patches of active constrained layer damping (ACLD) treatment has been carried out by the finite element method. The constraining layer of the ACLD treatment is considered to be made of vertically/obliquely reinforced 1–3 piezoelectric composite while the constrained layer is made of a viscoelastic material, which is modeled using the Golla–Hughes–McTavish method in the time domain. The top and bottom faces of the substrate sandwich plate are composed of the FG isotropic material whose mechanical properties are assumed to vary according to a standard power-law distribution in terms of the volume fractions of the constituents while the core layer may be either a soft honeycomb material or a hard ceramic material. Several FG sandwich plates with different core configurations are studied to evaluate the numerical results. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the FG sandwich plates for suppressing their geometrically nonlinear vibrations. Effects of metal- or ceramic-rich top and bottom surfaces, the variation of power-law index on the control authority of the ACLD patches have been investigated. Emphasis has also been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD patches.