François M. Guillot

Measurement of electrostrictive coefficients of polymer films

A new technique to experimentally determine the electrostrictive coefficients of thin polymer films is presented. This technique is a second-order extension of the first-order quasistatic method for the measurement of piezoelectric coefficients previously introduced by Guillot and Jarzynski [J. Acoust. Soc. Am. 108, 600–607 (2000)]. In the present method, electrically induced strains are measured optically on a rubber-encapsulated sample. These strains are used in a Rayleigh–Ritz procedure that minimizes the total energy of the sample and whose output is a set of three tensile electrostrictive coefficients. The total energy of the sample includes elastic contributions from the polymer and the encapsulating rubber as well as two quadratic electromechanical terms corresponding to Maxwell stress and to electrostriction. Therefore, the external electrostatic effects can be separated from the intrinsic electrostrictive behavior, and the measured coefficients are true material properties. Data obtained on two t...

A dynamic Young’s modulus measurement system for highly compliant polymers

A new system to determine experimentally the complex Youngs modulus of highly compliant elastomers at elevated hydrostatic pressures and as a function of temperature is presented. A sample cut in the shape of a bar is adhered to a piezoelectric ceramic shaker and mounted vertically inside a pressure vessel equipped with glass windows. Two independent measurement methods are then used: a resonant technique, to obtain low-frequency data, and a wave propagation technique, to obtain higher-frequency data. Both techniques are implemented utilizing laser Doppler vibrometers. One vibrometer detects sample resonances through a window located at the bottom of the pressure vessel, and a set of two separate vibrometers monitors the speed of longitudinal waves propagating in the sample, through windows located on the sides of the vessel. The apparatus is contained inside an environmental chamber for temperature control. Using this approach, Youngs modulus data can be obtained at frequencies typically ranging from 100 Hz to 5 kHz, under hydrostatic pressures ranging from 0 to 2.07 MPa (300 psi), and at temperatures between -2 degrees C and 50 degrees C. Experimental results obtained on two commercial materials, Rubatex R451N and Goodrich Thorodin AQ21, are presented. The effects of lateral inertia, resulting in dispersive wave propagation, are discussed and their impacts on Youngs modulus measurements are examined.

Electromechanical response of polymer films by laser Doppler vibrometry

A two-sided laser Doppler vibrometer (LDV) was designed to measure the d33 electromechanical coupling coefficient of piezoelectric and electrostrictive thin films. Optical fibers and optical fiber couplers were used to split the light into multiple beams and to simultaneously illuminate the same spot on both sides of the film. This probe measured the normal displacement on each side of the sample and allowed computation of the change in thickness by summing the two LDV signals. Data for PVDF films are presented to illustrate problems associated with this type of measurement. A large bending motion of the sample occurred which was responsible for a significant error in the measured thickness change. Reducing the amplitude of this motion by stacking films was an efficient way to increase the accuracy of the data. An error analysis was carried out to qualitatively explain these experimental observations. It was also discovered that the measurement accuracy improved when the ac driving voltage frequency was l...

A new method for the absolute measurement of piezoelectric coefficients on thin polymer films

A new quasistatic method to measure piezoelectric coefficients on thin polymer films is presented. This method is based on a combined experimental/analytical approach, where small polymer samples (6 mm x 3 mm x 110 microm) are encapsulated in a soft silicone rubber and an electric field is applied across their thickness (3-direction). Strains are measured optically along three perpendicular directions using a laser Doppler vibrometer, and the experimental measurements are used in a Rayleigh-Ritz energy minimization procedure implemented symbolically in MATHCAD, which yields the absolute piezoelectric coefficients d(3ii). These measured coefficients are material properties of the polymer and do not depend on the specific boundary conditions of the problem. The validity of the method is established using the ATILA finite element code. Experimental values of d(311), d(322), and d(333) obtained for polyvinylidene fluoride (PVDF) at room temperature, in the frequency range 500-2000 Hz, are presented and compared with existing data; excellent agreement is found. The extension of the method to the determination of electrostrictive coefficients on soft polyurethane materials is introduced.

Piezoelectric fibers for energy harvesting.

Most energy harvesting devices rely on traditional piezoelectric materials integrated in structures subjected to mechanical vibrations. A new kind of commercially available composite sensors consists of several PZT fibers embedded in a passive polymer matrix with interdigitated electrodes deposited on the polymer. The main advantage of these sensors is that they combine the large transduction capabilities of PZT with the mechanical flexibility of polymers. The present study evaluates the performance of single PZT fibers, with electrodes directly deposited onto the ceramic and with individual polymer jackets. This approach should optimize the amount of electrical energy available from the material by placing the electrodes on its surface and by maximizing the active piezoelectric volume. Fibers with tubular and “crimped” cross‐sections were electroded, poled, and glued to a vibrating cantilever beam equipped with a strain gauge. The performance of the fibers was compared to that of the composite sensors, a...

Development of a dynamic Young’s modulus measurement system for compliant polymers

A new system to experimentally determine the complex Young’s modulus of elastomers at elevated hydrostatic pressures and as a function of temperature is presented. A sample cut in the shape of a rod is glued to a piezoelectric ceramic shaker and mounted vertically inside a pressure vessel equipped with glass windows. Two independent measurement methods are then used: a resonant technique, to obtain low frequency data, and a wave propagation technique, to obtain higher frequency data. Both techniques are implemented utilizing laser Doppler vibrometers; one vibrometer detects sample resonances through a window located at the bottom of the pressure vessel, and a set of two separate vibrometers monitors the speed of longitudinal waves propagating in the sample (by measuring symmetric lateral displacements), through windows located on the sides of the vessel. The apparatus is contained inside an environmental chamber for temperature control. Using this approach, Young’s modulus data can be obtained at frequenc...

Electrostriction in polyurethanes as measured by laser Doppler vibrometry

The electrostriction of polyurethanes of two widely different morphologies were measured by laser Doppler vibrometry (LDV). The typical morphology of a polyurethane is that of two separated phases, one of hard regions embedded in the second of a soft elastic matrix. In contrast to this is a polyurethane of a single homogenous phase (i.e., phase mixed). A postulated mechanism for electrostriction is the relaxation, under electric field, of the elastic matrix which is strained in the phase separated system and not in the phase mixed system. To test this hypothesis, both of these systems were synthesized and their d33 coupling coefficient was determined from measurements of the out‐of‐plane displacement. The measured electrostriction coefficient at 250 Hz, for bilayers, for the phase separated system is 0.20 A/V (514 V/mil bias) and for the phase mixed system is 0.55 A/V (316 V/mil bias). The larger value for the phase mixed system is in accord with its modulus being less than that of the phase separated sys...

Experimental determination of the complex Poisson’s ratio of viscoelastic materials.

An empirical procedure to determine the dynamic, complex Poisson’s ratio of viscoelastic materials as a function of temperature and hydrostatic pressure is presented. In this procedure, the Young’s modulus and the bulk modulus of the material are measured, and the complex values of these moduli are combined to compute Poisson’s ratio. The two independent measurement systems used to obtain these data are described. The Young’s modulus system requires a sample cut in the shape of a bar and relies on traditional resonance measurements for low‐frequency data as well as on wave speed measurements for higher‐frequency data; measurements are performed in air. The bulk modulus system measures the dynamic compressibility of a sample of arbitrary shape immersed in Castor oil. Data can be obtained at frequencies typically ranging from 50 Hz to 5 kHz, at temperatures comprised between ‐2 and 50° C and under hydrostatic pressures ranging from 0 to 2 MPa (Young’s) or 6.5 MPa (bulk). The two moduli can also be combined ...

Underwater tensor sensors based on optical fiber bragg gratings

This paper deals with the development a new type of low‐noise underwater tensor sensor aimed at improving the performance and the design of directional arrays. The transducer can be configured either as a particle velocity sensor (dipole) or as fluid shear sensor (quadrupole). The sensing principle of the device relies on the interference signal from two Bragg gratings written on the same fiber, and illuminated by a tunable, narrowband light source. The gratings are a few centimeters apart, and they each reflect a portion of the incident light. The fiber is epoxied to two spacers separated by a small gap situated between the gratings. This assembly is then adhered to two plates connected by a hinge, which is located below the gap. One plate is held rigidly and the tip of the other (free) plate experiences transverse vibrations, when ensonified. These vibrations produce periodic gap length changes, which modulate the interference signal from the two gratings. The modulation is related to the amplitude of t...

A new optical‐fiber‐based underwater sensor

A new type of underwater sensor based on optical fiber Bragg gratings is presented. This transducer can be used in a dipole or a quadrupole (shear sensor) configuration. The sensing principle of the device relies on the interference signal from two Bragg gratings written on the same fiber and illuminated by a tunable, narrow‐band light source. The gratings are 5 cm apart, and they each reflect a portion of the incident light. The fiber is epoxied to two spacers separated by a 1‐mm gap situated between the gratings. This assembly is then adhered to two plates connected by a hinge, which is located below the gap. One plate is held rigidly and the tip of the other (free) plate experiences transverse vibrations, when ensonified. These vibrations produce periodic gap length changes, which modulate the interference signal from the two gratings. The modulation is related to the amplitude of the sound wave and is monitored with a photodetector. Design optimization to increase the sensitivity and to reduce the noi...