Temperature-dependent model for ferroelectrics embedded into two-dimensional polygonal finite element framework

Abstract

A two-dimensional constitutive model, which is based on micromechanical rotation of domains, is presented in this work to demonstrate the non-linear behavior of ferroelectric materials under different loading conditions. A temperature-dependent combined material model that incorporates both phases i.e., tetragonal and rhombohedral phases is embedded into two-dimensional polygonal finite element framework. The developed material model which has easily overcome shortcomings related to tetragonal model and rhombohedral model alone. This model is developed on the morphotropic phase boundary which has produced desired behavior based on macroscopic material parameters. Temperature effects on behavior of combined material model are obtained in the work. Furthermore, polarization rotation test and temperature effects on polarization rotation are also studied in present work. There are numerous studies conducted on ferroelectric materials. All of them incorporate behavior of ferroelectric material confined to specific conditions. Either tetragonal model or rhombohedral model has been used extensively to get the desired behavior based on macroscopic material parameters. This model has some limitations in either satisfying one or another condition related to experiments conducted to study the behavior of ferroelectric materials. The tetragonal material model is capable of producing results with microscopic material properties but in case of macroscopic material parameters the tetragonal model is insufficient to produce the desired behavior for PZT ceramics. The rhombohedral material model is sufficient to produce results based on macroscopic material parameters. Therefore, model is extended by rhombohedral phase, allowing a mixture of both phases with varying quantities inside the grain. Though, rhombohedral model is also not used to that extent. We have developed material model that gives desired behavior and overcomes the hurdles in the existing model.