A concept for a high authority shape morphing plate is described and demonstrated. The design incorporates an active back-plane comprising a Kagome truss, capable of changing the shape of a solid face, connected to the back-plane by means of a tetrahedral truss core. The two shape deformations to be demonstrated consist of hinging and twisting. The design is performed by a combination of analytic estimation and numerical simulation, guided by previous assessments of the Kagome configuration. It is shown that, while the structure is capable of sustaining large passive loads at low weight, the demonstrable authority is actuator-limited. The full potential of the system can only be realized by developing and incorporating superior actuators.
A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced switching and stress induced switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, bu different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate are modeled well below the Curie temperature.
The energy release rates for dielectric, piezoelectric and ferroelectric strips are analyzed. Energy minimization is used to determine the electromechanical fields in the strip. Once these fields are computed conservation of energy is used to determine the energy release rate. Three different sets of assumptions are used to treat the void space and solid material. First, an impermeable void space assumption is analyzed with small deformation assumed to be valid in the solid. Next, the void space is assumed to have finite dielectric permittivity and aside form changes in the position of its boundary the solid is treated with small deformation theory. Finally, a large deformation formulation is used for the solid along with a permeable void space. By minimizing the energy of the system we are able to show that mechanical tractions act on the crack surfaces as a result of the finite dielectric permittivity of free space. Lastly, a piezoelectric strip with remanent polarization is analyzed and it is shown that the energy release rate for a poled piezoelectric is not equal to that of a material with identical elastic, dielectric and piezoelectric properties but no remanent polarization.
In this paper a self-consistent model for the switching of a ferroelectric polycrystal will be presented. We will assume that the polycrystal is made up of spherical grains or crystallites. Each crystallite is made up of two domain types separated by 180 degree domain walls. The linear dielectric properties of the domains are assumed to be isotropic. When the electric field in the crystallite reaches a critical level the domain walls are allowed to sweep through the crystallite. This gradual domain wall motion causes the tangential dielectric permittivity of the crystallite to be transversely isotropic. Each spherical crystallite is given a distinct orientation and embedded in a matrix material. The tangential dielectric permittivity of the matrix is taken to be consistent with the overall averaged incremental response of the crystallites taking into account the constraint or depolarization fields imposed by the matrix. Hysteresis loops and switching surfaces are presented for the polycrystal.
Ferroelectric and ferroelastic switching cause ferroelectric ceramics to depolarize and deform when subjected to excessive electric field or stress. Switching is the source of the classic butterfly shaped strain vs. electric field hysteresis loops and the corresponding electric displacement vs. electric field loops. It is also the source of a stress-strain curve with linear elastic behavior at low stress, non-linear switching strain at intermediate stress, and linear elastic behavior at high stress. In this work, a series of experiments on lead lanthanum zirconate titanate are modeled with a computer simulation of the ceramic microstructure. The polarization and strain for an individual grain are predicted from the imposed electric field and stress through a Preisach hysteresis model. The response of the bulk ceramic to applied loads is predicted by averaging the response of individual grains that are considered to be statistically random in orientation. The random orientation yields essential non-linear behavior of the observed strain and electric displacement hysteresis loops and the non-linear stress- strain curve for the polycrystalline ceramic. The linear piezoelectric effect opens up a butterfly shape to the strain vs. electric field hysteresis loop but the model fails to predict the observed effect of 90 degree(s) switching. The grain to grain residual stress and residual polarization are estimated from inclusion calculations. These are both a function of the remanent strain and remanent polarization of the ceramic. This constraint opposed switching but has little effect on the butterfly shape in the strain vs. electric field hysteresis loop.
Several degradation mechanisms in ferroelectric ceramics are analyzed in this article. A ferroelectric crystal under cyclic electric field fatigues by forming a-domain bands. An energy based model is proposed, indicating that these bands are retarded by the electric field, but driven by the shear stress resolved onto the bands. The stress has been attributed to the misfit strain near the 180 degree(s) domain wall and the edge of the electrodes. A second problem is related to fracture of piezoelectric ceramics. A double-cantilever beam subjected to combined electrical and mechanical loadings is analyzed using finite elements. Also analyzed is electrode debonding, which is shown to decrease capacitance.
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