Linear and nonlinear electro-elastic/electro-damping effect in ferroelectric ceramics

Abstract

The linear piezoelectric and nonlinear hysteresis behaviors of ferroelectrics are well-known and have been extensively studied. However, less attention has been paid to the variations of their mechanical properties under electric loading. In this work, using tube and cylinder specimens, three independent elastic coefficients and related internal frictions of PZT-5H ferroelectric ceramics are measured using our proposed modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT) under an electric field E3 along the poling direction. Results show that under low electric fields, the elastic coefficients s11E, s66E and all internal frictions decrease linearly with E3, whereas s44E increases linearly with E3. Based on these linear results, two fifth-order tensors are defined, i.e., linear electro-elastic and linear electro-damping tensor with the reduced symbol of pikl and qikl, among which p311, p366, p344 and q311, q366, q344 are obtained in this work. When the applied electric field exceeds the coercive field (∼500 V/mm), nonlinear electro-elastic/electro-damping effect dominates, resulting in reversed butterfly curves for s11E and s66E and butterfly curves for s44E. As to the internal frictions under large bipolar fields, they seem to be a superposition of the reversed butterfly curves and a peak or valley at the coercive field. The linear electro-elastic effect in ferroelectric ceramics is caused by the reversible domain wall motions while the nonlinear electro-elastic effect is caused by non-180° domain switching and is well reproduced by a statistical model. The linear and nonlinear electro-elastic/electro-damping results obtained in this work offer new insight into the electromechanical coupling behavior of ferroelectric materials.