Abstract
In this work, a model to describe the vertical deflection of ferroelectric bending tongues with a load at their free end is proposed. The model is based on the ferroelectric switching criterion developed by Hwang et al. [“Ferroelectric/ferroelastic interactions and a polarization switching model,” Acta Metall. Mater. 43, 2073–2084 (1995)] and the Euler-Bernoulli beam theory. It notably takes into account the geometry of the bending tongue, the mechanical and piezoelectric material properties, the applied electrical field, the crystallographic state of the ferroelectric thin film and its built-in strain. Hwang’s model is improved by incorporating strain saturation at high field, as expected for the butterfly loop. This allows accurate estimates of the vertical deflection for ferroelectric bending tongue based applications.
Highlights
With the need for miniaturization of devices and components as actuators, sensors or energy harvesters, the use of bending tongues based on piezoelectric ceramics is increasing
EeYff − νe2ff where νeff corresponds to the Poisson’s ratio of the substrate as per the equivalent cross-section obtained from Eq 1. Due to both loads and strains acting simultaneously on the bending tongue, the equation describing its vertical deflection, Z, along the z-axis, is complex
From Eq 6 and 8, the equation of vertical deflection due to the bending tongue’s own weight and the load applied at its free end can be obtained: Z = 1 − νe2ff 24EeYff Ieff qWx4 + qL < x − m >4 + 4(−qWl − qL(l − m))x3
Summary
With the need for miniaturization of devices and components as actuators, sensors or energy harvesters, the use of bending tongues (cantilevers or wider beams) based on piezoelectric ceramics is increasing. Due to its large piezoelectric coefficient, PbZr0.52Ti0.48O3 (PZT) is the most commonly used material, but it is ferroelectric (i.e. the polarization direction can be switched between discrete crystallographically allowed orientations by an external electric field) This particularity should be taken into account when modelling the vertical deflection of bending tongues.. The model described, based on Hwang’s switching criterion, aims to bridge the gap between the mechanical and ferroelectric approaches by describing the vertical deflection of a bending tongue fixed at one end and loaded at its free end while taking into account ferroelectric switching at the grain scale. The proposed model includes the impact of the crystallographic state of the ferroelectric (polycrystalline, textured or epitaxial) on the vertical deflection It increases the accuracy of Hwang’s model by taking macroscopic polarization saturation into account. By analyzing in details the different contributions to the vertical deflection, the proposed model allows optimization of the bending tongue’s geometry for various applications
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
