Time Dependent Polarization and Strain Evolution Around a Circular Hole in Ferroelectrics

The simulation of inhomogeneous creep around a circular hole in the center of ferroelectric plate is presented aiming for understanding the birefringence measurements around the hole. The time dependent fields of strain and polarization around the hole in response to its concentrated electric field effect can be determined using the finite element method. It was found that the electric field concentration factor by a hole can achieve 6 times of the applied loads and shows slightly time dependence; the creep of polarization and strains process is controlled by the local electric field magnitude, which governs the saturation of remnant polarization and strain. The result of geometric principal strain difference contours around the hole agrees with that of birefringence observation. The remnant polarization increased in a power-law relation with electric field magnitude, while the principal strain difference developed quadratically with the total electric displacement. Both experimental and numerical results suggest that the strain distributes around the hole and changes with time, which is controlled by both the local electric field magnitude and the saturation process. Although the inhomogeneities enhance fields locally, the saturated values of strain and polarization decrease with an increase in the defect volume.