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.

References

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
.
You do not currently have access to this content.