Effects of electric field and pressure on the shrinkage behaviors of cylindrical pore in piezoelectric materials

Abstract

This paper presents an analytical method to describe the effect of electric field on the shrinkage rate and healing history of a cylindrical pore in piezoelectric grain under hydrostatic pressure. Based on the thermal dynamic potential theory of piezoelectric elastic solid, the coupled influence of the surface energy of pore, the interface energy of piezoelectric grain, and the elastic energy and electric potential stored in the piezoelectric grain dominates the shrinkage rate and healing history of the pore. Utilizing the excess chemical potential in an axisymmetric piezoelectric grain with a cylindrical pore, the govern equation of thermodynamic for the piezoelectric grain with a cylindrical pore is established. Then, an analytical expression for the govern equation is given to predict the shrinkage rate and healing time of a cylindrical pore in piezoelectric grain. Results show that the effect of electric field on the shrinkage rate and healing history of a pore in piezoelectric grain is obviously different from the effect of hydrostatic pressure applied on the interface of the piezoelectric grain, and the finally shrinkage size of pore in piezoelectric grain is larger than that of the pore in non-piezoelectric grain when other calculation parameters are fixed.