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

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 E 3 along the poling direction. Results show that under low electric fields, the elastic coefficients [Formula: see text], [Formula: see text] and all internal frictions decrease linearly with E 3 , whereas [Formula: see text] increases linearly with E 3 . 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 [Formula: see text] and [Formula: see text], among which [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] 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 [Formula: see text] and [Formula: see text] and butterfly curves for [Formula: see text]. 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.