A continuum model is proposed to characterize the macroscopic behavior of ferroelectric materials undergoing an electrically-induced phase transformation. Within the framework of electromechanics, the author has investigated the feasibility of adjusting stresses within a ferroelectric device by applying an electric field to induce the paraelectric-ferroelectric transformation. The present analysis shows that the rate at which the stress can be adjusted is governed by a nonlinear ordinary differential equation which resulted from the kinetic relation that controls the evolution of the electrically-induced phase transformation. The present model, implemented with a numerical scheme, is able to predict the relation between the stress rate and the rate at which the electric field is applied. Some numerical results are included for illustration.
Get full access to this article
View all access options for this article.
References
1.
Abeyaratne, R. and J. K. Knowles. 1988. "On the Dissipative Response Due to Continuous Strains in Bars of Unstable Elastic Material", International Journal of Solids and Structures, 24:1021-1042.
2.
Abeyaratne, R. and J. K. Knowles. 1992. "A Continuum Model of a Thermoelastic Solid Capable of Undergoing Phase Transitions", Journal of Mechanics and Physics in Solids, 41:541-571.
3.
Billesbach, D. P. , F. G. Ullman and J. R. Hardy. 1985. "Effect of Uniaxial Stress on the 130K and 93K Phase Transformations in K2A504", Japanese Journal of Applied Physics, 24:775-777.
4.
Buerger, M. J.1971. Introduction to Crystal Geometry. New York: McGraw-Hill.
5.
Collins, C. and M. Luskin. 1989. "The Computation of the Austenitic Martensitic Phase Transition", Partial Differential Equations and Continuum Models of Phase Transitions, M. Rascle, D. Serre and M. Slemrod, eds., Springer Lecture Notes in Physics 344, Springer-Verlag: pp. 34-50.
6.
Cross, L. E. 1989. "Piezoelectric and Electrostrictive Sensors and Actuators for Adaptive Structures and Smart Materials", Proceedings of AME 110th Annual Meeting, San Francisco, California.
7.
de Quervain, M.1944. "Rontgenometrische Untersuchungen an Kaliumphosphat bei Tiefen Temperaturen", Helvetica Physica Acta, 17:509-552.
8.
Forsbergh, P. W.1954. "Effect of a Two-Dimensional Pressure on the Curie Point of Barium Titanate", Physical Review, 93:686-692.
9.
Jiang, Q. 1989. "A Continuum Model for Phase Transformation in Thermo Elastic Solids", Technical Report No. 9, U.S. Office of Naval Research Contract N00014-87-K-0117, California Institute of Technology.
10.
Jiang, Q.1992a. "On Phase Transformations and Intelligent Behavior of Ferroelectric Crystals", Journal of Smart Materials and Structures, 1: 258-268.
11.
Jiang, Q.1992b. "Thermomechanical and Electric Effect on the Ferroelectric-Paraelectric Phase Transition", Micromechanical Systems, D. Cho et al., eds., Vol. 40, pp. 199-209, ASME Dynamic Systems and Control Division, and Advanced Energy Systems Division.
12.
Jiang, Q.1993a. "On the Driving Traction Acting on a Surface of Discontinuity within a Continuum in the Presence of Electromagnetic Fields", Journal of Elasticity, 34:1-21.
13.
Jiang, Q.1993b. "Macroscopic Behavior of a Bar Undergoing the Paraelectric-Ferroelectric Phase Transformation", Journal of Mechanics and Physics in Solids, 41:1599-1635.
14.
Jiang, Q.1993c. "On Modeling of Thermo-Mechanical Phase Transformations in Solids", Journal of Elasticity, 32:61-91.
15.
Jona, F. and G. Shirane. 1962. Ferroelectric Crystals. New York: Pergamon Press Inc.
16.
Li, D. Y. , X. F Wu and T. Ko.1991. "The Effect of Stress on Soft Modes for the Phase Transformation in a Ti-Ni Alloy", Philosophical Magazine A-Physics of Condensed Matter, Defects and Mechanical Properties, 63:585-601.
17.
Liang, C. and C. A. Rogers. 1990. "A One-Dimensional Thermomechanical Constitutive Relation of Shape Memory Materials", Journal of Intelligent Materials Systems and Structures, 1:207-234.
18.
Little, E. A.1955. "Dynamic Behavior of Domain Walls in Barium Titanate", Physical Review, 98:978-984.
19.
Merz, W. J.1950. "The Effect of Hydrostatic Pressure on the Curie Point of Barium Titanate Single Crystals", Physical Review, 77:52-54.
20.
Merz, W. J.1953. "Double Hysteresis Loop of BaTiO3 at the Curie Point", Physical Review, 91:513-517.
21.
Merz, W. J.1954. "Domain Formation and Domain Wall Motions in Ferroelectric BaTiO3 Single Crystals", Physical Review, 95:690-698.
22.
Muller, I. and H. Xu.1991. "On the Pseudo-Elastic Hysteresis", Acta Metallurgica, 39:263-271.
23.
Newnham, R. E. , Q. C. Xu, S. Kumar and L. E. Cross. 1990. "Smart Ceramics", Ferroelectrics, 102:77-89.
24.
Silling, S. A.1988a. "Numerical Studies of Loss of Ellipticity near Singularities in an Elastic Material", Journal of Elasticity, 19:213-239.
25.
Silling, S. A.1988b. "Consequences of the Maxwell Relation for Anti Plane Shear Deformations of an Elastic Solid", Journal of Elasticity, 19:241-284.
26.
Swart, P. J. and P. J. Holmes. 1992. "Energy Minimization and the Formation of Microstructure in Dynamic Anti-Plane Shear", Research Report No. 92-NA-025, Center for Nonlinear Analysis.
27.
Turchi, P. E. A.1990. "Electronic Structure and Phase Stability: Effect of a Bain Transformation on the Thermodynamic Properties of Substitutional Alloys", Materials Science and Engineering, A127:145-153.
