Analysis of Surface Stress Influence on the Effective Properties of Nanoporous Piezocomposites

Abstract

The present paper considers the homogenization problems for mixed piezoelectric composite materials with stochastic distributions of inclusions or pores and with taking into account the mechanical imperfect interphase boundaries. The accepted interface statements correspond to the Gurtin - Murdoch model and give a significant contribution only for nanostructured composites. To determine the effective properties, an integrated approach was used, based on the theory of effective moduli, on the modelling of representative element volumes and on the finite element method. An aggregate of boundary value problems was described, which allow one to find a complete set of effective stiffness moduli, piezomoduli, and dielectric constants for a piezocomposite of arbitrary anisotropy class. The numerical solution of homogenization problems was carried out in the ANSYS finite-element package, which was used both for modelling of representative element volumes and for computation of the effective properties of composite material. The representative volume consisted of a regular cubic array of piezoelectric finite elements with the material properties of the two phases. The contact boundaries between materials of different phases were covered with elastic membrane elements that simulated interface surface stresses. Specific implementation was performed for nanoporous piezoceramic composites, for which both the initial phases and the homogeneous material were materials of the hexagonal symmetry class, and the pores were considered as piezoelectric material with negligibly small stiffness moduli and piezomoduli. For this composite the membrane elements inherited the anisotropy structure of volume elements on their common edges. As an example, the results of calculations of effective moduli for porous ferroelectric soft piezoceramics PZT-5H were presented. It was noted that the surface stresses on the boundaries of the pores can significantly increase the values of the effective stiffness moduli. However, they had a weak influence on the values of the effective piezomoduli and dielectric constants.