Marc Lethiecq

A matrix method for modeling electroelastic moduli of 0-3 piezo-composites

A model is proposed to predict the electroelastic moduli of 0-3 connectivity piezo-composites from which parameters such as longitudinal wave velocity and thickness mode coupling factor can be deduced. The composite, a polymer loaded with ceramic particles, is represented by a unit cell, and a matrix manipulation is shown to be a practical way to perform a generalization of the series and parallel analysis used for 2-2 connectivity composites. The anisotropy of the ceramic phase is taken into account, and its effect on the properties of the composite is shown. The model is then used to optimize composite performance and to choose the two constituents through comparison of results obtained using several commercial polymers and ceramics.

High-frequency transducers based on integrated piezoelectric thick films for medical imaging

A screen-printed PZT thick film with a final thickness of about 40 mum was deposited on a porous PZT substrate to obtain an integrated structure for ultrasonic transducer applications. This process makes it possible to decrease the number of steps in the fabrication of high-frequency, single-element transducers. The porous PZT substrates allow high acoustic impedance and attenuation to be obtained, satisfying transducer backing requirements for medical imaging. The piezoelectric thick films deliver high electromechanical performance, comparable to that of standard bulk ceramics (thickness coupling factor over 45%). Based on these structures, high-frequency transducers with a center frequency of about 25 MHz were produced and characterized. As a result, good sensitivity and axial resolution were obtained in comparison with similar transducers integrating a lead titanate (PT) disk as active material. The two transducers were integrated into a high-frequency imaging system, and comparative skin images are shown

Preparation and electromechanical properties of PZT/PGO thick films on alumina substrate

PZT thick films with lead germanate as low temperature sintering aid were prepared on alumina substrates. The thickness of films after sintering procedures reached 50 μm. Chemical compatibility and microstructure of layers was studied by EDS/SEM analysis. A fit between theoretical and experimental electrical impedance of several samples as a function of frequency is used to determine the elastic, dielectric and piezoelectric properties in thickness mode of the ceramic layers. Results for different poling fields (3 and 12 kV/mm) and sintering temperatures are obtained. Finally, the KLM equivalent circuit is used to obtain simulations of transducers integrating these thick films and their performance for medical imaging applications is evaluated.

Comparison of several methods to characterise the high frequency behaviour of piezoelectric ceramics for transducer applications

Thickness mode resonances in commercial piezoelectric ceramics have been characterised as a function of frequency by two methods. The first is based on a fit on the electrical impedance for the fundamental and the overtones. This method has been applied to a large number of PZT ceramic samples and frequency dependence for all the parameters is investigated, in particular for the piezoelectric coefficient e33. The second is based on the measurement of the mechanical displacement at the centre of the surface of a PZT ceramic disk. With a modified KLM scheme, this displacement is modelled. The dielectric, elastic and piezoelectric parameters are extracted and compared for the fundamental and the third overtone. The results are found to be in good agreement.

Theoretical and experimental study of the influence of the particle size distribution on acoustic wave properties of strongly inhomogeneous media

The ultrasonic method is particularly suitable to characterize diffusive media, as acoustic properties (velocity and attenuation) are related to the properties and concentrations of the homogeneous phase and scatterers. Thus, ultrasonic characterization can be useful in the study of sedimentation or flocculation processes, in concentration measurements, and granulometry evaluation. Many models have been developed for media where particles are very small compared to the incident wavelength. When the diameter of the particles is close to the wavelength, multiple-scattering theories have to be used to describe the propagation of waves. In this paper, the case where the ratio of wavelength to scatterer size is around unity is studied. First, the particle size distribution is taken into account in two types of multiple-scattering theories based on the effective field approximation or on the quasicrystalline approximation and theoretical results are produced. The T-matrix formalism has been used to calculate the amplitude of the wave scattered by a single sphere. The calculation of the complex wave number in the effective medium has been implemented, using in particular the Percus-Yevick equation as a spatial pair-correlation function between scatterers, and a normal particle-size distribution. The influence of these parameters is discussed. Finally, attenuation and phase velocity measurements are performed in moving suspensions of acrylic spheres in ethylene glycol, at various concentrations and for different particle-size distributions. A good agreement between the theoretical results and the measurements is found for both velocity and attenuation. These results show that the size distribution is a critical parameter to understand velocity and attenuation behavior as function of frequency and volume fraction.

Experimental verification of the theory of elastic properties using scattering approximations in (0-3) connectivity composite materials

New methods of estimating effective macroscopic elastic constants for inhomogeneous materials have recently been proposed using elastic-wave scattering theory. However, there are few experimental measurements which allow the validation of these models. The purpose of this paper is to verify if the scattering approximation theories allow prediction of the acoustic properties of epoxy composites containing tungsten powder for various particle sizes and various volume fractions of filler. The theoretical predictions are compared with the experimental results and the different models are discussed.

Modeling of piezoelectric transducers with combined pseudospectral and finite-difference methods.

A new hybrid finite-difference (FD) and pseudospectral (PS) method adapted to the modeling of piezoelectric transducers (PZTs) is presented. The time-dependent equations of propagation are solved using the PS method while the electric field induced in the piezoelectric material is determined through a FD representation. The purpose of this combination is to keep the advantages of both methods in one model: the adaptability of FD representation to model piezoelectric elements with various geometries and materials, and the low number of nodes per wavelength required by the PS method. This approach is implemented to obtain an accurate algorithm to simulate the propagation of acoustic waves over large distances, directly coupled to the calculation of the electric field created inside the piezoelectric material, which is difficult with classical algorithms. These operations are computed using variables located on spatially and temporally staggered grids, which attenuate Gibbs phenomenon and increase the algorithms accuracy. The two-dimensional modeling of a PZT plate excited by a 50 MHz sinusoidal electrical signal is performed. The results are successfully compared to those obtained using the finite-element (FE) algorithm of ATILA software with configurations spatially and temporally adapted to the FE requirements. The cost efficiency of the FD-PS time-domain method is quantified and verified.

Modeling of the influence of a prestress gradient on guided wave propagation in piezoelectric structures

The objective of this study is to model the propagation of guided waves in piezoelectric structures subjected to a prestress gradient. The constitutive equations for a piezoelectric bulk material are first modified to take into account a uniform prestress on a given cross section. Then, these modified constitutive equations are used to derive a formalism for the propagation of guided waves in piezoelectric structures under a prestress gradient. In particular, we modify the recursive stiffness matrix method to introduce a gradient of stress in a piezoelectric structure. Numerical studies are then led for a bending and for an exponential stress profile. For a piezoelectric plate, the Lamb and shear horizontal modes are found to be sensitive to the prestress gradient. In particular, some key features of dispersion curves appearing in the presence of a gradient of properties are highlighted. In the last part, these results are extended to a piezoelectric film laid down on a substrate in order to model the imp...

Experimental investigation of cross-coupling and its influence on the elementary radiation pattern in 1D ultrasound arrays

Cross-coupling mechanisms in ultrasound arrays have deep influences on their performances. Here, to investigate them, the surface displacement of a 1D linear array is measured in water with a laser interferometer. Displacement data are then analyzed in both Time-Space and in Time frequency-Spatial frequency domains. Radiation pattern is then simulated from this data and compared to the radiation pattern of a plane piston and to hydrophone measurements. Cross-coupling influence on the 1D array element behavior is finally compared and discussed. Laser interferometry is shown to be a useful tool for ultrasound array optimization as it allows the identification of vibration modes, the determination of the elementary effective aperture and the radiation pattern of elements.

Effect of radial displacement of lens on response of focused ultrasonic transducer

A lens-focused single-element transducer designed for high-resolution medical imaging requires a high ratio of radius of curvature to source radius. Therefore, classical models neglecting the radial contribution may not be accurate. The objective of this study is to evaluate the contribution of radial displacement to the pressure response of the transducer, both in terms of focal spot and pulse response characteristics. To achieve this objective, two finite element method calculations (FEM) were performed (commercial atila® software), namely those for free and clamped radial displacements. A propagation code adapted to an axisymmetric transducer geometry was implemented to compare the radiated fields, and FEM results for the transducer surface were used as inputs to obtain the radiated fields. Subsequently, the differences between the results of the two calculations results were determined. However, it was demonstrated that the radial displacements slightly affect the propagated field and can therefore be neglected in realistic transducer designs. Moreover, the effects of lens acoustic properties were studied for realistic configurations in terms of resolution and sensitivity to obtain an optimal ultrasound image quality.