Measurement of Young's Moduli for Lead Zirconate Titanate (PZT) Ceramics

Abstract

Knowledge of the Young's moduli is necessary for piezoelectric ceramics in order to separate the total deformation into an elastic and a plastic contribution. The methods for the determination of the Young's moduli, well known from conventional ceramics, are much more complicated due to the special electrical boundary conditions. The main aim of the report is to discuss the question in which mechanical tests the conditions of a constant electrical field are fulfilled and in which type of test constant dielectric displacements occur. It will be illustrated that the results from tests with homogeneous stress states are much more trustworthy than results from bending tests.

Depolarization field effect on elasticity of unpoled piezoelectric ceramics

“…Eq. ( 30) is in the same form as it was derived in our previous work [22] . The motional admittance part of Eq.…”

“…From the inequality relationship above, we can conclude that elastic compliance and elastic loss of unpoled piezoelectric ceramic is not simply a statistical average of s D 33 and s D 11 , but "intermediate" between intensive-ness and extensive-ness; the electrical constraint condition of unpoled piezoceramic is not purely D -constant. Relationship 1 was proposed by Fett et al [22] , whereas relationship 2 has not been so widely discussed as long as the authors' knowledge. Only the very recent study [23] demonstrated measurement of elastic loss of unpoled piezoelectric ceramic, but proper discussion was missed.…”

“…For obtaining elastic constants (either compliance or stiffness, and their corresponding elastic losses) of unpoled piezoelectric ceramics, conventional Voigh-Reuss-Hill method [ 15 , 16 ] causes laborious task, because all tensor elements are required, yet its accuracy is quite low [17] . There have been several attempts to obtain elastic compliance of unpoled piezoelectric ceramic; these attempts include finite element analysis (FEA) simulation [18][19][20] , empirical approach [21] , modified 4-bending test and ultrasound pulse-echo method [22] . However, little attention has been paid on elastic loss of unpoled piezoelectric ceramics and phenomenological explanations of determined elastic parameters.…”

“…However, little attention has been paid on elastic loss of unpoled piezoelectric ceramics and phenomenological explanations of determined elastic parameters. For example, several studies [20][21][22] proposed methods to obtain elastic compliance of unpoled piezoelectric ceramic, yet the methods neglected elastic loss. Recently, Xie et al .…”

Multiaxial Electromechanical Couple Behavior of Ferroelectric Ceramic PZT53

“…The existing literature on the electro-mechanical performance of PZT ceramics was mainly investigated under uniaxial loading, predominantly in compression tests, for the basic design of transducers [1]- [10]. The nonlinear nonsymmetrical deformation behavior in tension and compression was also investigated [11]- [12].…”