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A Stress-Dependent Hysteresis Model for PZT

Published online by Cambridge University Press:  01 February 2011

Brian L. Ball
Affiliation:
Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC 27695, blball@unity.ncsu.edu, rsmith@eos.ncsu.edu
Ralph C. Smith
Affiliation:
Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University, Raleigh, NC 27695, blball@unity.ncsu.edu, rsmith@eos.ncsu.edu
Sang-Joo Kim
Affiliation:
Mechanical and Information Engineering, University of Seoul, 130-743 Korea, sjk@uos.ac.kr
Stefan Seelecke
Affiliation:
Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695, stefan seelecke@ncsu.edu
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Abstract

This paper addresses the development of an energy-based characterization framework which quantifies stress-induced dipole switching in ferroelectric materials. Helmholtz and Gibbs energy relations that accommodate 90° and 180° dipole orientations as equilibrium states are constructed at the lattice level. For regimes in which thermal relaxation mech- anisms are negligible, minimization of the Gibbs relations provides local polarization and strain relations. Alternatively, behavior such as creep or thermal relaxation can be incorpo- rated by balancing Gibbs and relative thermal energies through Boltzmann principles. In the nal step of the development, stochastic homogenization techniques based on the assump- tion that parameters such as coercive and induced elds are manifestations of underlying distributions are employed to construct macroscopic models suitable for nonhomogeneous polycrystalline compounds. Attributes and limitations of the model are illustrated through comparison with experimental PLZT data.

Type
Research Article
Copyright
Copyright © Materials Research Society 2005

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References

[1] Kim, S.J., Seelecke, S., Ball, B.L., and Smith, R.C., Continuum Mechanics and Thermo-dynamics, submitted.Google Scholar
[2] Lynch, C.S., Acta Materialia, 44, 4137 (1996).CrossRefGoogle Scholar
[3] Massad, J.E. and Smith, R.C., International Journal on the Science and Technology of Condensed Matter Films, to appear.Google Scholar
[4] Nambu, S. and Sagala, D. A., Physical Review B, 50, 5838 (1994).CrossRefGoogle Scholar
[5] Seelecke, S. and Müller, I., ASME Applied Mechanics Reviews, 57, 23 (2004).CrossRefGoogle Scholar
[6] Smith, R.C., Smart Material Systems: Model Development, SIAM, Philadelphia, PA, 2005.CrossRefGoogle Scholar
[7] Smith, R.C., Seelecke, S., Dapino, M.J. and Ounaies, Z., model for hysteresis in ferroic materials,” Proceedings of the SPIE, Volume 5049, 88 (2003).Google Scholar
[8] Smith, R.C., Seelecke, S., Ounaies, Z. and Smith, J., Journal of Intelligent Material Systems and Structures, 14, 719 (2003).CrossRefGoogle Scholar

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