Edward Balizer

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...

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...

Calculation of B/A for n-alkane liquids using the Tait equation

The B/A parameter of acoustic nonlinearity was calculated for a series of n-alkane liquids using the Tait PVT equation of state supplemented with specific heat data. The calculations of sound speed, sound speed derivatives, the two components of B/A, and the value of B/A itself were compared with experimental data taken from the literature and with earlier calculations using a different equation of state. In addition, a comparison of the results with Ballous rule (linear relation of B/A and reciprocal sound speed) was made. It is concluded that B/A can be calculated from the Tait equation of state with about the same accuracy as direct measurements of sound speed versus pressure and temperature, though the the temperature derivatives of the sound speed are calculated with much lower accuracy than pressure derivatives. The calculations made using the Tait equation are about the same accuracy as calculations made using our equation of state. Also, Ballous rule does not hold for these liquids.

Investigation of microstructural changes in impacted polyurea coatings using small angle X-ray scattering (SAXS)

Three polyureas with decreasing soft segment molecular weights of 1000, 650, and a 250/1000 blend were molded onto circular steel plates and then impacted with a high speed (275 m/s) conical-shaped steel cylinder. The polyurea layer of the post mortem bilayers was characterized on a molecular level by small angle synchrotron X-ray scattering (SAXS) at the Advanced Photon Source at the Argonne National Laboratory. Analysis revealed that the hard domains of the polyureas with lower molecular weight soft segments reformed and oriented over a greater area of the coating, thus increasing the polymer strain hardening and resulting in visibly less out of plane bilayer deformation. This agrees with the hypothesis that polymer strain hardening is a mechanism that retards necking failure of the metal plate.

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...

8 – Modeling and Simulations, Applications in Ballistic and Blast

Three polyureas of decreasing soft segment molecular weights of 1000, 650, and a 250/1000 blend, with increasing modulus and hysteresis, were molded onto circular steel plates and then impacted with a high-speed (275 m/s) pointed projectile. The polyurea layer of the post mortem bilayers was characterized on a molecular level by small angle synchrotron X-ray scattering (SAXS) at the Advanced Photon Source at Argonne National Laboratory. Analysis revealed that hard domains of the polyureas of the lower molecular weight soft segment reformed over a greater area of the coating that resulted in less out-of-plane bilayer deformation. This supports the hypothesis that polymer strain hardening is a mechanism that retards necking failure of the metal plate. The mechanical behavior of elastomeric copolymer polyureas at extreme loading conditions is further discussed in this chapter. Here the Taylor impact behavior of the exemplar polyureas (PU1000 and PU650), where extreme deformation and deformation rates are incurred, is elucidated in experiments and numerical simulations using the constitutive modeling framework of the two polyurea copolymers detailed in Chapter 4. The hybrid glassy and rubber nature of the elastomeric copolymers is addressed by examining the extreme deformation of “model” glassy and rubbery polymers, for which the constitutive laws have been partially selected from the original polyurea models. Then the extreme behavior of copolymeric polyureas is rationalized in the Taylor impact experiments and simulations, revealing how the elastomeric copolymer polyurea can take advantages from both glassy and rubbery polymeric features in terms of resilience, shape recovery and energy dissipation under such extreme deformation conditions. Polyurea is of particular interest to armor systems designers due to its unique physical behavior, low density, and favorable manufacturing and application techniques. Inherent rate and pressure dependencies exhibited by polyurea allow this otherwise soft material to exert large resistive forces and dissipate large amounts of energy under ballistic impact conditions. The design and evaluation of armor systems using complex materials such as polyurea may be enhanced with improved analytical material models implemented within appropriate computational tools. This work details a modified temperature and pressure dependent viscoelastic constitutive model for polyurea under ballistic impact conditions. The constitutive model is implemented and demonstrated within the shock physics hydrocode CTH. Demonstration of the models performance is first given through comparison with high-rate confined compression and pressure–shear plate impact test data. Second, model performance and design optimization considerations are demonstrated through comparison with various experimentally studied polyurea coated armor configurations.

Acoustic nonlinearity calculations using the Tait equation of state

Beyer’s B/A parameter of acoustic nonlinearity was calculated using the Tait equation of state supplemented with specific heat results, in the same manner as done earlier with our equation of state [J. Acoust. Soc. Am. 82, 614 (1987)]. Calculations were made of sound speed, sound‐speed temperature and pressure derivatives, the two components of B/A, and the value of B/A for a series of six n‐alkane liquids as well as the limiting case of molten polyethylene. All these results were compared with experimental data from the literature. In addition, a comparison of the results with Ballou’s rule (linear relation of B/A versus reciprocal sound speed) was made. Overall, values calculated using the Tait equation are found to agree with experiment about as well as our equation of state, though the pressure derivatives of the sound speed and the final value of B/A are generally not as accurate using the Tait equation. [Work supported by the Naval Surface Warfare Center’s In‐house Laboratory Independent Research Pr...

Beyer’s B/A parameter and the equation of state.

Beyer’s B/A parameter for liquids can be calculated using an analytical PVT equation of state supplemented with specific heat data. Results for two equations will be investigated: the Tait equation and our own. The calculations of sound speed, sound speed derivatives, and the two components of B/A will be compared with experimental data for a series of normal alkane liquids. A comparison of these results with the prediction of Ballou’s rule (linear relation of B/A vs 1/c) will be presented. Tentative conclusions about the relative utility of the two equations will be presented as well as the outlook for the approach using any PVT equation of state. [Work supported by Naval Surface Warfare Center’s in‐house Laboratory Independent Research Program sponsored by the Office of Naval Research.]

A fiber optic dual‐beam laser Doppler vibrometer for measurement of electrostrictive and piezoactive response of thin films

A two‐beam laser Doppler vibrometer (LDV) is described, designed to measure the d33 electromechanical coupling coefficient for electrostrictive and piezoactive thin films. Optical fiber couplers are used to split the light into multiple beams and optical fibers are used to simultaneously illuminate the same spot on both sides of the film. The LDV measures the normal displacement on each side and the change in thickness of the film is determined from the algebraic sum of the two LDV signals. It is found that large bending motion of the film can lead to a significant error in the measured d33 coefficient. This is illustrated with data for PVF2 films and sources of this error are identified. The application of the LDV system to measure the large electrostrictive effect in polyurethane films is discussed. [Work supported by the Office of Naval Research.]