We present in this paper a minimal macroscopic theory leading to the hysteresis loop and the butterfly loop in ferroelectricity. This theory is based on the notion that as domains switch under the action of an external electric field the number of dipoles aligned in the direction of the field also alters and it obeys a rate law which depends non-linearly on the field. In addition, we specify the siimplest constitutive relations of the stress and the electric displacement which together with the rate law are sufficient to yield the hysteresis loop and the butterfly loop. Comparison with experimental data is exhibited for the case corresponding to the hysteresis loop.
The dynamic behavior of a tungsten carbide filled epoxy composite is studied under planar loading conditions. Planar impact experiments were conducted to determine the shock and wave propagation characteristics of the material. Its stress-strain response is very close to a similar alumina filled epoxy studied previously, suggesting that the response of the composite is dominated by the compliant matrix material. Wave propagation characteristics are also similar for the two materials. Magnetically driven ramp loading experiments were conducted to obtain a continuous loading response which is similar to that obtained under shock loading. Spatially resolved interferometry was fielded on one experiment to provide a quantitative measure of the variability inherent in the response of this heterogeneous material. Complementing the experiments, a two-dimensional mesoscale model in which the individual constituents of the composite are resolved was used to simulate its behavior. Agreement of the predicted shock and release wave velocities with experiments is excellent, and the model is qualitatively correct on most other aspects of behavior.
Some time ago we presented evidence that, under nonhydrostatic loading, the of a randomly-oriented polycrystal to completion. In this paper, we present results from uniaxial compression experiments that confirm both of these predictions. We then revisit our earlier results from constant-shear-stress experiments on poled and unpoled PNZT. We show that the the hypothesis can quantitatively explain the effect of shear stress on the mean stress for onset of the transformation of unpoled ceramic, and can qualitatively reconcile the results for poled ceramic with those for unpoled material.
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