Nonlinear modeling of piezoceramics.

摘要

Piezoelectric materials exhibit nonlinear behavior when subjected to large electric or mechanical loads. This strong nonlinear material behavior is induced by localized polarization switching at the domain level. In this thesis a finite element code in conjunction with a polarization switching criterion is described to model the nonlinear behavior in piezoceramics. Each element represents a single domain with a tetragonal structure. The nonlinearity is introduced in the behavior of each element by allowing it to undergo 180° and 90° polarization switchings.; As an initial step, the finite element code is used to analyze stress concentrations near a circular void in an infinite piezoelectric media when no polarization switching takes place. Parametric studies indicate that for certain combinations of piezoelectric coefficients, called optimal properties, electrically induced stresses can be reduced to zero. Parametric studies of a hole in a finite plate show that optimal properties are independent of the interactions between neighboring holes.; To verify the nonlinear material model for a single domain material, the averaged dielectric and strain response is compared with the experimental data. Further, the analytical results are pointwise compared with experimental data obtained using a Moire interferometer. Comparison of experimental data and theoretical results indicates reasonable agreement. Next, stress concentrations near both holes and cracks in the presence of an electric field are calculated. When domain wall motion occurs, the hole and the crack have stress intensity factors of similar magnitude. It is determined that for a material undergoing full polarization switching compressive stress along the polarization direction reduces internal stresses and extends fatigue life. If the applied electric field value is below the coercive field limit, however, the compressive preload can increase the stresses and thus reduce the fatigue life.; Finally, the material is modeled as a polycrystalline. Basic material response is simulated and a relatively good agreement with experimental data is obtained, suggesting that the correct physics is included in the model. The results indicate that the polycrystalline model is more representative of the test data than the single-domain model.