Determination of reversible and irreversible contributions to the polarization and strain response of soft PZT using the partial unloading method

Experimental work is aimed at systematically investigating the non-linear ferroelectric and ferroelastic behavior of a commercially available soft lead zirconate titanate (PZT) material. The fast partial unloading method is used to measure the material properties of unpoled soft PZT under pure electric field and of initially pre-poled soft PZT under compressive stress loading. In the first experiment using unpoled PZT, the evolution of piezoelectric constants and dielectric permittivity is determined as a function of electric field. It is found that the piezoelectric constants and dielectric permittivity depend on the electric field history. The results are used to separate the reversible strain and polarization from the irreversible ones caused by domain switching. In the second experiment using initially pre-poled PZT, it is found that the strain response is significantly dependent on the stress loading rate. The elastic moduli and piezoelectric coefficients are evaluated with respect to the compressive stress history. The measured longitudinal and transverse irreversible strains change significantly during both loading and unloading processes. An attempt is made to discuss the use of irreversible strain and irreversible polarization as internal variables for constitutive modeling. This investigation provides valuable information for modeling to predict the performance and for improving the reliability of piezoelectric devices.