The field-dependent Young's modulus shows a promising application in the design and miniaturization of phononic crystals, tunable mechanical resonators, interdigital transducers, etc. With the multifield bulge-test instrument developed by our group, the electric field-tunable elastic modulus of ferroelectric films has been studied experimentally. A butterfly change in the Young's modulus of lead titanate zirconate (PZT) film under biaxial tensile stress state with electric field has been discovered for the first time. Based on the phase field model, an electromechanical coupling model is constructed, and a case of PZT ferroelectric film subjected to a vertical electric field and horizontal tensile strains is simulated. The numerical results show that the change in the Young's modulus is proportional to the variation of volume fraction of 90-deg domain switching under a pure tensile strain. It is the constraint of 90-deg domain switching by the electric field that contributes to the butterfly change in the elastic modulus.
Issue Section:
Research Papers
References
1.
Zhou
, X.
, and Chattopadhyay
, A.
, 2001
, “Hysteresis Behavior and Modeling of Piezoceramic Actuators
,” ASME J. Appl. Mech.
, 68
(2
), pp. 270
–277
.2.
Chicharro
, J. M.
, Bayon
, A.
, and Salazar
, F.
, 1999
, “Measurement of Field-Dependence Elastic Modulus and Magnetomechanical Coupling Factor by Optical Heterodyne Interferometry
,” J. Magn. Magn. Mater.
, 202
(2–3
), pp. 465
–472
.3.
Savage
, H.
, Clark
, A.
, and Powers
, J.
, 1975
, “Magnetomechanical Coupling and ΔE Effect in Highly Magnetostrictive Rare Earth—Fe2 Compounds
,” IEEE Trans. Magn.
, 11
(5
), pp. 1355
–1357
.4.
Cao
, H. C.
, and Evans
, A. G.
, 1993
, “Nonlinear Deformation of Ferroelectric Ceramics
,” J. Am. Ceram. Soc.
, 76
(4
), pp. 890
–896
.5.
Lu
, W.
, Fang
, D. N.
, Li
, C. Q.
, and Hwang
, K.-C.
, 1999
, “Nonlinear Electric-Mechanical Behavior and Micromechanics Modelling of Ferroelectric Domain Evolution
,” Acta Mater.
, 47
(10
), pp. 2913
–2926
.6.
Fang
, D. N.
, and Li
, C. Q.
, 1999
, “Nonlinear Electric-Mechanical Behavior of a Soft PZT-51 Ferroelectric Ceramic
,” J. Mater. Sci.
, 34
(16
), pp. 4001
–4010
.7.
Zhou
, D. Y.
, Wang
, R. Y.
, and Kamlah
, M.
, 2010
, “Determination of Reversible and Irreversible Contributions to the Polarization and Strain Response of Soft PZT Using the Partial Unloading Method
,” J. Eur. Ceram. Soc.
, 30
(12
), pp. 2603
–2615
.8.
Marsilius
, M.
, Webber
, K. G.
, Aulbach
, E.
, and Granzow
, T.
, 2010
, “Comparison of the Temperature-Dependent Ferroelastic Behavior of Hard and Soft Lead Zirconate Titanate Ceramics
,” J. Am. Ceram. Soc.
, 93
(9
), pp. 2850
–2856
.9.
Liu
, Q. D.
, and Huber
, J. E.
, 2007
, “State Dependent Linear Moduli in Ferroelectrics
,” Int. J. Solids Struct.
, 44
(17
), pp. 5635
–5650
.10.
Zhao
, P.
, and Li
, J.
, 2008
, “Orientation Dependence on Electromechanical Coupling Behavior of Ferroelectrics Under Compression
,” J. Appl. Phys.
, 103
(10
), p. 104104
.11.
Li
, F. X.
, and Fang
, D. N.
, 2005
, “Effects of Electrical Boundary Conditions and Poling Approaches on the Mechanical Depolarization Behavior of PZT Ceramics
,” Acta Mater.
, 53
(9
), pp. 2665
–2673
.12.
Schaufele
, A. B.
, and Hardtl
, K. H.
, 1996
, “Ferroelastic Properties of Lead Zirconate Titanate Ceramics
,” J. Am. Ceram. Soc.
, 79
(10
), pp. 2637
–2640
.13.
Zhou
, D. Y.
, Kamlah
, M.
, and Munz
, D.
, 2005
, “Effects of Bias Electric Fields on the Non-Linear Ferroelastic Behavior of Soft Lead Zirconate Titanate Piezoceramics
,” J. Am. Ceram. Soc.
, 88
(4
), pp. 867
–874
.14.
Chaplya
, P. M.
, and Carman
, G. P.
, 2002
, “Compression of Piezoelectric Ceramic at Constant Electric Field: Energy Absorption Through Non-180 Degrees Domain-Wall Motion
,” J. Appl. Phys.
, 92
(3
), pp. 1504
–1510
.15.
Amin
, A.
, Ewart
, L.
, Mclaughlin
, E.
, and Robinson
, H.
, 2006
, “Transitions in Morphotropic PMN-PT Single Crystals
,” Ferroelectrics
, 331
(1
), pp. 29
–33
.16.
Li
, Y. W.
, Ren
, X. B.
, Li
, F. X.
, Luo
, H. S.
, and Fang
, D. N.
, 2013
, “Large and Electric Field Tunable Superelasticity in BaTiO3 Crystals Predicted by an Incremental Domain Switching Criterion
,” Appl. Phys. Lett.
, 102
(9
), p. 092905
.17.
Yu
, Z. J.
, Mao
, W. G.
, Li
, F. X.
, Feng
, X.
, Pei
, Y. M.
, and Fang
, D. N.
, 2014
, “Magnetic and Electric Bulge-Test Instrument for the Determination of Coupling Mechanical Properties of Functional Free-Standing Films and Flexible Electronics
,” Rev. Sci. Instrum.
, 85
(6
), p. 065117
.18.
Ruud
, J. A.
, Josell
, D.
, Spaepen
, F.
, and Greer
, A.
, 1993
, “A New Method for Tensile Testing of Thin-Films
,” J. Mater. Res.
, 8
(1
), pp. 112
–117
.19.
Weihs
, T. P.
, Hong
, S.
, Bravman
, J. C.
, and Nix
, W. D.
, 1999
, “Mechanical Deflection of Cantilever Microbeams: A New Technique for Testing the Mechanical Properties of Thin Films
,” J. Mater. Res.
, 3
(5
), pp. 931
–942
.20.
Oliver
, W. C.
, and Pharr
, G. M.
, 1992
, “An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments
,” J. Mater. Res.
, 7
(6
), pp. 1564
–1583
.21.
Vlassak
, J. J.
, and Nix
, W. D.
, 1992
, “A New Bulge Test Technique for the Determination of Young's Modulus and Poisson's Ratio of Thin Films
,” J. Mater. Res.
, 7
(12
), pp. 3242
–3249
.22.
Beams
, J.
, 1959
, The Structure and Properties of Thin Film
, Wiley
, New York
.23.
Li
, Y. L.
, Hu
, S. Y.
, Liu
, Z. K.
, and Chen
, L. Q.
, 2002
, “Effect of Substrate Constraint on the Stability and Evolution of Ferroelectric Domain Structures in Thin Films
,” Acta Mater.
, 50
(2
), pp. 395
–411
.24.
Gu
, Y. J.
, Hong
, Z. J.
, Britson
, J.
, and Chen
, L. Q.
, 2015
, “Nanoscale Mechanical Switching of Ferroelectric Polarization Via Flexoelectricity
,” Appl. Phys. Lett.
, 106
(2
), p. 022904
.25.
Su
, Y.
, and Landis
, C. M.
, 2007
, “Continuum Thermodynamics of Ferroelectric Domain Evolution: Theory, Finite Element Implementation, and Application to Domain Wall Pinning
,” J. Mech. Phys. Solids.
, 55
(2
), pp. 280
–305
.26.
Zhang
, H. L.
, Zhang
, X. Y.
, and Pei
, Y. M.
, 2016
, “A Finite Element Based Real-Space Phase Field Model for Domain Evolution of Ferromagnetic Materials
,” Comput. Mater. Sci.
, 118
, pp. 214
–223
.27.
Wang
, J.
, and Zhang
, J. W.
, 2013
, “A Real-Space Phase Field Model for the Domain Evolution of Ferromagnetic Materials
,” Int. J. Solids Struct.
, 50
(22–23
), pp. 3597
–3609
.28.
Qiu
, Q. Y.
, Mahjoub
, R.
, Alpay
, S. P.
, and Nagarajan
, V.
, 2010
, “Misfit Strain–Film Thickness Phase Diagrams and Related Electromechanical Properties of Epitaxial Ultra-Thin Lead Zirconate Titanate Films
,” Acta Mater.
, 58
(3
), pp. 823
–835
.29.
Melro
, A. R.
, Camanho
, P. P.
, Andrade Pires
, F. M.
, and Pinho
, S. T.
, 2013
, “Micromechanical Analysis of Polymer Composites Reinforced by Unidirectional Fibres—Part II: Micromechanical Analyses
,” Int. J. Solids Struct.
, 50
(11–12
), pp. 1906
–1915
.30.
Li
, S.
, and Zou
, Z.
, 2011
, “The Use of Central Reflection in the Formulation of Unit Cells for Micromechanical FEA
,” Mech. Mater.
, 43
(12
), pp. 824
–834
.31.
Arlt
, G.
, 1990
, “Twinning in Ferroelectric and Ferroelastic Ceramics—Stress Relief
,” J. Mater. Sci.
, 25
(6
), pp. 2655
–2666
.32.
Wang
, J.
, Shi
, S. Q.
, Chen
, L. Q.
, Li
, Y. L.
, and Zhang
, T. Y.
, 2004
, “Phase-Field Simulations of Ferroelectric/Ferroelastic Polarization Switching
,” Acta Mater.
, 53
(3
), pp. 749
–764
.33.
Su
, Y.
, Liu
, N.
, and Weng
, G. J.
, 2015
, “A Phase Field Study of Frequency Dependence and Grain-Size Effects in Nanocrystalline Ferroelectric Polycrystals
,” Acta Mater.
, 87
, pp. 293
–308
.34.
Kontsos
, A.
, and Landis
, C. M.
, 2010
, “Phase-Field Modeling of Domain Structure Energetics and Evolution in Ferroelectric Thin Films
,” ASME J. Appl. Mech.
, 77
(4
), p. 041014
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