Numerical analysis of the effective properties of inhomogeneously polarized porous piezoelectric ceramics with Ni-doped pore walls taking into account the influence of volume fractions of metal and pores

The paper considers a porous piezoelectric composite with metal layers deposited on the interface between the piezoelectric and vacuum phases. Such metal layers can be added technologically to improve the mechanical and electromechanical properties of the composite. To find the effective moduli, we designed a simple representative cubic volume of a unit cell consisting of a piezoelectric matrix with a compound spherical pore in its center. In turn, the compound pore includes the pore itself and a hollow metal sphere on its surface. The composite's three phases were all modeled as piezoelectric materials. The conducting interface layer was modeled as a piezoelectric material with very high dielectric constants, small piezoelectric moduli, and elastic properties of the employed metal, while the vacuum pore was modeled as a piezoelectric material with marginal moduli. The mathematical formulation of boundary value homogenization problems with full contact conditions on the interface boundaries, based on the Hill energy criterion, was described. By solving nine boundary value problems of electroelasticity with different boundary conditions for displacements and electric potential by the finite element method, a complete set of effective moduli of the piezoelectric composite is determined. The importance of considering the inhomogeneous polarization due to the presence of pores and metallic inclusions was discussed. An approximate method was proposed for determining the inhomogeneous polarization field in a piezoceramic matrix, based on a preliminary solution of the electrostatic problem for dielectrics and locating the element coordinate systems rotated along the polarization vector. The paper describes the results of computational experiments for a piezocomposite consisting of PZT-5H piezoceramic matrix, pores, and nickel layers on the pore surfaces. Comparisons between the effective properties of this composite with different volume fractions of metal and the conventional porous piezocomposite were provided, depending on the porosity and taking into account the inhomogeneous polarization. Significant differences were observed for some piezomoduli and dielectric constants, which are promising for various practical applications of the considered composites in piezoactuators using the phenomenon of the transverse piezoelectric effect.