TY - JOUR
T1 - A rate-dependent three-dimensional free energy model for ferroelectric single crystals
AU - Kim, Sang Joo
AU - Seelecke, Stefan
PY - 2007/2
Y1 - 2007/2
N2 - The one-dimensional free energy model for ferroelectric materials developed by Smith et al. [Smith, R.C., Seelecke, S., Ounaies, Z., 2002. A free energy model for piezoceramic materials. In: 9th SPIE Conference on Smart Structures and Materials, San Diego, USA, pp. 17-22; Smith, R.C., Seelecke, S., Ounaies, Z., Smith, J., 2003. A free energy model for hysteresis in ferroelectric materials. J. Intell. Mater. Syst. Struct. 14, 719-739; Smith, R.C., Seelecke, S., Dapino, M.J., Ounaies, Z., 2005. A unified framework for modeling hysteresis in ferroic materials. J. Mech. Phys. Solids 54, 46-85] is generalized to three space dimensions including both polarization and strain. In the resulting nine-dimensional energy function, six free energy potentials representing the six distinct types of tetragonal variants of perovskite lattice structures are given as quadratic functions of polarization vector and strain tensor. Energy barrier expressions as functions of thermodynamic driving forces are obtained through a generalization of the one-dimensional equations derived from the model of Smith et al. This approach presents an alternative to the cumbersome determination of higher-dimensional saddle points and is attractive for a computationally efficient implementation. The energy barrier expressions are combined with evolution equations for the variant fractions based on the theory of thermally activated processes and thus allow for a natural treatment of rate-dependent effects. The predictions of the model are compared with recent measurements on BaTiO3 single crystals by Burcsu et al. [Burcsu, E., Ravichandran, G., Bhattacharya, K., 2004. Large electrostrictive actuation of barium titanate single crystals. J. Mech. Phys. 52, 823-846]. The effects of applied stress and 90°- and 180°-switching processes are discussed in detail.
AB - The one-dimensional free energy model for ferroelectric materials developed by Smith et al. [Smith, R.C., Seelecke, S., Ounaies, Z., 2002. A free energy model for piezoceramic materials. In: 9th SPIE Conference on Smart Structures and Materials, San Diego, USA, pp. 17-22; Smith, R.C., Seelecke, S., Ounaies, Z., Smith, J., 2003. A free energy model for hysteresis in ferroelectric materials. J. Intell. Mater. Syst. Struct. 14, 719-739; Smith, R.C., Seelecke, S., Dapino, M.J., Ounaies, Z., 2005. A unified framework for modeling hysteresis in ferroic materials. J. Mech. Phys. Solids 54, 46-85] is generalized to three space dimensions including both polarization and strain. In the resulting nine-dimensional energy function, six free energy potentials representing the six distinct types of tetragonal variants of perovskite lattice structures are given as quadratic functions of polarization vector and strain tensor. Energy barrier expressions as functions of thermodynamic driving forces are obtained through a generalization of the one-dimensional equations derived from the model of Smith et al. This approach presents an alternative to the cumbersome determination of higher-dimensional saddle points and is attractive for a computationally efficient implementation. The energy barrier expressions are combined with evolution equations for the variant fractions based on the theory of thermally activated processes and thus allow for a natural treatment of rate-dependent effects. The predictions of the model are compared with recent measurements on BaTiO3 single crystals by Burcsu et al. [Burcsu, E., Ravichandran, G., Bhattacharya, K., 2004. Large electrostrictive actuation of barium titanate single crystals. J. Mech. Phys. 52, 823-846]. The effects of applied stress and 90°- and 180°-switching processes are discussed in detail.
KW - Ferroelectric
KW - Free energy
KW - Rate-dependent
KW - Single crystal
KW - Thermal activation
KW - Three-dimensional
UR - http://www.scopus.com/inward/record.url?scp=33751002344&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2006.06.007
DO - 10.1016/j.ijsolstr.2006.06.007
M3 - Article
AN - SCOPUS:33751002344
SN - 0020-7683
VL - 44
SP - 1196
EP - 1209
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
IS - 3-4
ER -