Micromechanical modelling of switching phenomena in polycrystalline piezoceramics: application of a polygonal finite element approach

Abstract

A micromechanically motivated model is proposed to capture nonlinear effects and switching phenomena present in ferroelectric polycrystalline materials. The changing remnant state of the ferroelectric crystal is accounted for by means of so-called back fields-such as back stressesto resist or assist further switching processes in the crystal depending on the local loading history. To model intergranular effects present in ferroelectric polycrystals, the computational model elaborated is embedded into a mixed polygonal finite element approach, whereby an individual ferroelectric grain is represented by one single irregular polygonal finite element. This computationally efficient coupled simulation framework is shown to reproduce the specific characteristics of the responses of ferroelectric polycrystals under complex electromechanical loading conditions in good agreement with experimental observations.

Tailoring of unipolar strain in lead-free piezoelectrics using the ceramic/ceramic composite approach

“…Bintachitt et al 36 has reported that in PZT thin films, nonlinear response of piezoelectricity is not homogeneous throughout a compositionally uniform sample, i.e., piezoelectric nonlinear response shows local deviation from the average due to difference in domain wall pinning. A local deviation in electric field distribution, polarisation, and strain response has been shown by Jayabal et al 37,38 for bulk materials by micromechanical modelling. This local deviation has been attributed to the domain The variation in (200) shoulder peak intensity in as-prepared (E 0 ), at 6 kV/mm (E max ) field and after removal of electric field (E rem ) for all compositions (bottom).…”

Electromechanical Response of Polycrystalline Barium Titanate Resolved at the Grain Scale

“…(b) showing the distributions of neighbor misorientations for grains A (dark) and B (light), clearly demonstrate that in reality an individual grain sees a local neighborhood that is significantly different from the statistical average, as also indicated by the mean and spread of the two distributions given in Table . So, while the bulk macroscopic properties and response are predictable, at the grain‐scale the material behavior is far more localized in nature, as has been predicted from multigrain models and simulations …”

“…The first 3D simulation of faceted grains of variable size (made by Voronoi tessellation from a random texture) represents an important step toward modeling real structures . In some cases, real 3D microstructures measured by serial sectioning and EBSD have been used as input, however, it is most often the case that microstructural input relies on simulation and extrapolation of selected grain morphology and orientation measurements …”

“…So, while the bulk macroscopic properties and response are predictable, at the grain-scale the material behavior is far more localized in nature, as has been predicted from multigrain models and simulations. 51,52 Figure 6 also indicates that it is not only grain A that has a larger strain response than B, but so does its immediate neighborhood as a whole. A reason could be that grains in the neighborhood of grain A are generally more favorably aligned relative to the field vector.…”

“…56 In some cases, real 3D microstructures measured by serial sectioning and EBSD have been used as input, 17 however, it is most often the case that microstructural input relies on simulation and extrapolation of selected grain morphology and orientation measurements. 12,28,46,51,52,[55][56][57] Macroscopic measurements such as hysteresis loops and piezoelectric constants are often used for validation. While these are useful measures, it has been shown that such macroscopic measurements can agree without the model capturing the local interactions that are life limiting for the component.…”