Research Papers

Butterfly Change in Electric Field-Dependent Young's Modulus: Bulge Test and Phase Field Model

[+] Author and Article Information
Honglong Zhang

College of Civil Engineering and Transportation,
South China University of Technology,
Guangzhou 510640, China

Zejun Yu

State Key Laboratory for Turbulence
and Complex Systems,
College of Engineering,
Peking University,
Beijing 100871, China

Yongmao Pei

State Key Laboratory for Turbulence
and Complex Systems,
College of Engineering,
Peking University,
Beijing 100871, China
e-mail: peiym@pku.edu.cn

Daining Fang

Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China
e-mail: fangdn@pku.edu.cn

1Corresponding authors.

Manuscript received January 18, 2017; final manuscript received March 15, 2017; published online April 5, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(5), 051009 (Apr 05, 2017) (6 pages) Paper No: JAM-17-1040; doi: 10.1115/1.4036298 History: Received January 18, 2017; Revised March 15, 2017

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.

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Grahic Jump Location
Fig. 1

(a) Pressure–deflection curves and (b) stress–strain curves under various positive electric fields, (c) stress–strain curves under various negative electric fields of PZT film with initial upward polarization

Grahic Jump Location
Fig. 2

The change in ΔM/M0 under a cycling electric-loading

Grahic Jump Location
Fig. 3

Schematic illustration of the simulated ferroelectric PZT

Grahic Jump Location
Fig. 4

(a) The hysteresis loop and (b) strain–electric field curve under zero strain in the x1 direction

Grahic Jump Location
Fig. 5

(a) Stress–strain curves under different electric fields and (b) Comparison of electric field-dependent modulus between experimental and numerical results

Grahic Jump Location
Fig. 6

(a) The change in variation of volume fraction of 90-deg domain switching with electric field and (b) the relation between ΔM/M0 and Δf



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