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Research Papers

Linking Internal Dissipation Mechanisms to the Effective Complex Viscoelastic Moduli of Ferroelectrics

[+] Author and Article Information
Charles S. Wojnar

Department of Mechanical and
Aerospace Engineering,
Missouri University of Science and Technology,
400 West 13th Street,
Rolla, MO 65409
e-mail: wojnarc@mst.edu

Dennis M. Kochmann

Graduate Aerospace Laboratories,
California Institute of Technology,
1200 East California Boulevard,
Pasadena, CA 91125
e-mail: kochmann@caltech.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 25, 2016; final manuscript received October 17, 2016; published online November 17, 2016. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 84(2), 021006 (Nov 17, 2016) (14 pages) Paper No: JAM-16-1473; doi: 10.1115/1.4035033 History: Received September 25, 2016; Revised October 17, 2016

Microstructural mechanisms such as domain switching in ferroelectric ceramics dissipate energy, the nature, and extent of which are of significant interest for two reasons. First, dissipative internal processes lead to hysteretic behavior at the macroscale (e.g., the hysteresis of polarization versus electric field in ferroelectrics). Second, mechanisms of internal friction determine the viscoelastic behavior of the material under small-amplitude vibrations. Although experimental techniques and constitutive models exist for both phenomena, there is a strong disconnect and, in particular, no advantageous strategy to link both for improved physics-based kinetic models for multifunctional rheological materials. Here, we present a theoretical approach that relates inelastic constitutive models to frequency-dependent viscoelastic parameters by linearizing the kinetic relations for the internal variables. This enables us to gain qualitative and quantitative experimental validation of the kinetics of internal processes for both quasistatic microstructure evolution and high-frequency damping. We first present the simple example of the generalized Maxwell model and then proceed to the case of ferroelectric ceramics for which we predict the viscoelastic response during domain switching and compare to experimental data. This strategy identifies the relations between microstructural kinetics and viscoelastic properties. The approach is general in that it can be applied to other rheological materials with microstructure evolution.

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References

Figures

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Fig. 1

A schematic of the one-dimensional generalized Maxwell model consisting of n linear springs with stiffnesses Ek in series with dashpots with strain εkr and damping parameter ηk (k = 1,…, n). The spring-dashpot systems are arranged in parallel with a linear spring of stiffness E0. The entire system is subjected to an applied stress σ causing a total strain of ε.

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Fig. 2

Maxwell model results for (a) the dynamic stiffness |E*| and (b) loss tangent tan δ versus frequency for the parameters of Table 1

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Fig. 3

An electric field e is applied to a PZT patch (resulting in an overall polarization p) through the thickness in the three-direction. If such a patch is attached to a vibrating structure, it will be subjected to a harmonic stress, σ, perpendicular (a) or parallel (b) to the electric field direction.

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Fig. 4

Graph showing the maximum loss tangent, tan δmax, versus the parameter ξ according to Eq. (37)

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Fig. 7

Simulated (a) electric displacement, (b) strain, (c) dynamic stiffness, and (d) loss tangent of PZT versus electric field with a transverse compression of 20 MPa

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Fig. 6

Simulated (a) electric displacement, (b) strain, (c) dynamic stiffness, and (d) loss tangent of PZT versus electric field with a transverse tension of 20 MPa

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Fig. 5

Simulated (solid line) and experimentally measured (connected dots) (a) electric displacement, (b) strain, (c) dynamic stiffness, and (d) loss tangent of PZT versus electric field. Experimental data were obtained from BES in Ref. [17]. Simultaneous experimental data on strain were not available.

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