Electromechanically Coupled Materials

AIN Artificial muscle materials Electrets Electroactive materials Electromechanically coupled materials Lead zirconate titanate PZT Quartz Zinc oxide... 

The resonance and antiresonance states are described by the following intuitive model. In a high electromechanical coupling material with k almost equal to 1, the resonance or antiresonance states appear for tan( >L/2v) = 00 or 0 [i.e. (oL 2v = (m — 1/2)7T or mjT (m integer)], respectively. The strain amplitude Xi distribution for each state (calculated using Eq. 28) is illustrated in... 

To satisfy this statement, the expression in parentheses describing the potential energy is required to assume a stationary value. Furthermore, it can be shown that this extremum has to be the minimum of the potential energy, see Sokolnikoff [167] or Knothe and Wessels [113]. Thus, Dirichlet s principle of minimum potential energy can be extended to electromechanically coupled materials ... 

For sensor applications, use is made of the direct piezoelectric effect and thus the piezoelectric cube described above now has to be subjected to mechanical fields. Strains and stresses are applied via associated surfaces either by prescribed displacements in a clamped configuration or by applied forces in a free configuration. Besides the intended sensor application, this, of corrse, is also relevant to the case of solely passive transmission of loads. Consequently, the subsequent examinations are also important for the general application of electromechanically coupled materials in adaptive structures. For mechanical fields operating opposed or transverse to the polarization direction, the field levels are limited by the risk of repolarization similar to the actuation case. 

Uncoupled solutions for current and electric field give simple and explicit descriptions of the response of piezoelectric solids to shock compression, but the neglect of the influence of the electric field on mechanical behavior (i.e., the electromechanical coupling effects) is a troublesome inconsistency. A first step toward an improved solution is a weak-coupling approximation in which it is recognized that the effects of coupling may be relatively small in certain materials and it is assumed that electromechanical effects can be treated as a perturbation on the uncoupled solution. 

The contribution to the stress from electromechanical coupling is readily estimated from the constitutive relation [Eq. (4.2)]. Under conditions of uniaxial strain and field, and for an open circuit, we find that the elastic stiffness is increased by the multiplying factor (1 -i- K ) where the square of the electromechanical coupling factor for uniaxial strain, is a measure of the stiffening effect of the electric field. Values of for various materials are for x-cut quartz, 0.0008, for z-cut lithium niobate, 0.055 for y-cut lithium niobate, 0.074 for barium titanate ceramic, 0.5 and for PZT-5H ceramic, 0.75. These examples show that electromechanical coupling effects can be expected to vary from barely detectable to quite substantial. 

Probably the best measure of the effectiveness of a piezoelectric material is its electromechanical coupling constant, k, defined as... 

The electromechanical coupling coefficient (k) is a measure of the ability of a piezoelectric material to transform mechanical energy into electrical energy, and vice versa. It is defined [5] by... 

Selected classes of asymmetric crystal structures exhibit the property of piezoelectricity. With the application of a mechanical strain, piezoelectric materials develop an electrical potential difference across them conversely, when a potential difference is applied to these materials, a displacement occurs. The efficiency of the conversion between mechanical energy and electrical energy is described by the electromechanical coupling constant, which practically ranges to values as high as 0.7 a value of 1 would imply complete conversion between mechanical and electrical energy. 

These materials have shown piezoelectric responses after appropriate poling [18]. Their piezoelectric actuation properties are typically worse than ceramic piezoelectric crystals however, they have the advantages of being lightweight, flexible, easily formed, and not brittle. Additionally, while ceramics are limited to strains on the order of 0.1%, ferroelectric polymers are capable of strains of 10% [91] and very high electromechanical coupling efficiencies [93]. 

Kofod used advanced materials models in an attempt to elucidate the effects that prestrain have on the actuation performance of a simple cuboid DE actuator [183]. The results are purely phenomenological however, they indicate that in the special case of a purely isotropic amorphous material, prestrain does not affect the electromechanical coupling directly. The enhancement in actuation strain due to prestrain occurs through the alteration of the geometrical dimensions of the acmator. Kofod also determined that the presence of an optimum load is related to the plateau region in the force-stretch curve and that prestrain is not able to affect the location of this region. 

While progress is being made, fully modeled systems that include the fiiU range of electromechanical coupling effects and environmental sensitivities do not yet exist. Further, the necessary software tools to model or solve for the material behavior, nonlinear electrical effects, and complex interactions with the environment are not available. 

Relaxor-type electrostrictive materials, such as those from the lead magnesium niobate-lead titanate, Pb(Mgp 3Nb2/3)03-PbTi03 (or PMN-PT), solid solution are highly suitable for actuator applications. This relaxor ferroelectric also exhibits an induced piezoelectric effect. That is, the electromechanical coupling factor kt varies with the applied DC bias field. As the DC bias field increases, the coupling increases and saturates. Since this behavior is reproducible, these materials can be applied as ultrasonic transducers which are tunable by the bias field [12]. 

The electromechanical coupling factor ksi is calculated from the v value and the antiresonance frequency /a through Eq. 34. Especially in low-coupling piezoelectric materials, the following approximate equation is available ... 

The second category of actuators is based on electrostriction as exhibited by PMN [Pb(Mg 3Nb2/3)03] based ceramics. Although it is a second-order phenomenon of electromechanical coupling (x = ME, where M is called the electrostrictive coefficient), the induced strain can be extraordinarily large (more than 0.1%) [33], An attractive feature of these materials is the near absence of hysteresis (Fig. 4.1.19b). The superiority of PMN to PZT was demonstrated in a scanning tunneling microscope (STM) [34]. The STM probe was... 

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