Time dependent behavior of ferroelectric materials undergoing changes in their material properties with electric field and temperature

• Published in: International journal of solids and structures Vol. 48; no. 19; pp. 2718 - 2731
• Main Author: Muliana, Anastasia
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 15.09.2011; Elsevier
• Subjects: Constitutive relationships; Electric fields; Exact sciences and technology; Ferroelectric; Ferroelectric materials; Fundamental areas of phenomenology (including applications); Hysteresis; Lead zirconate titanates; Mathematical models; Nonlinear; Nonlinearity; Physics; Piezoelectricity; Polarization; Polarization switching; Solid mechanics; Static elasticity (thermoelasticity...); Strain; Structural and continuum mechanics; Temperature; Viscoelastic; Ferroelectric; Nonlinear; Temperature; Polarization switching; Viscoelastic; Hysteresis; Constitutive equation; Viscoelasticity; Electrical properties; Temperature effect; Mechanical properties; PZT; Electrostriction; Experimental study; Modeling; Piezoelectric ceramics; Ferroelectricity; Ferroelectric switching; Piezoelectric constant; Electric field effect; Non linear effect; Room temperature; Internal clock; Electromechanical properties
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2011.05.021

This paper presents a time dependent polarization constitutive model suitable for predicting nonlinear polarization and electro-mechanical strain responses of ferroelectric materials subject to various histories of electric fields. The constitutive model is derived based on a single integral form with nonlinear (electric field and temperature dependent) integrand. The total polarization consists of the time-dependent and residual components. The residual component of the polarization is due to polarization switching in the ferroelectric materials. We use an ‘internal clock’ concept to incorporate the effect of electric field on the rate of polarization. The corresponding strain response is determined through the use of third order piezoelectric constant and/or fourth order electrostrictive constant that vary with polarization stage. It is assumed that in absence of polarization, both piezoelectric and electrostrictive constants are zero. To incorporate the effect of temperature on the overall polarization behavior all material parameters in the constitutive model are allowed to change with the ambient temperature. We present numerical studies on the effect of time, temperature, and electric field on the response of ferroelectric material followed by verification of the constitutive model. Experimental data on lead zirconate titanate (PZT) materials available in the literature are used to verify the model.