Effective properties of a transversely isotropic piezocomposite with cylindrical inclusions

Abstract

Based on the hypothesis of equivalent homogeneity, a calculation has been carried out of effective dielectric, piezoelectric and elastic properties of a piezocomposite consisting of a transversely isotropic matrix reinforced with anisotropic fibers randomly distributed in the isotropy plane. Approximation of this composite using the model of coaxial cylinders made up of a binding material and cylindrical inclusions with the parallel principal axes of symmetry has permitted the electroelastic problem of equilibrium of a composite cylinder to be calculated. As a result, the distribution of electrical and mechanical fields in nonhomogeneous medium has been found and, on this basis, effective electrophysical properties of the piezocomposite have been calculated depending on the properties of the components and their concentration. Variational estimates have shown that the results obtained are, in terms of the model selected, exact, corresponding to the self-consistent calculational scheme. Complete set of effective tensors of electrophysical properties of such a piezocomposite allows one to derive various figures of merit of a given piezomaterial for different component pairs. The distinctive features of the results obtained, namely, the unchanged value of the piezomodulus d*₃₃ as the concentration of the piezoactive component PZT-5 is decreased, the maximum of d* _v and the anomaly of g* _v all stem from considerable redistribution of the electrical and mechanical fields in nonhomogeneous piezotexture. Depending on the type of matrix (polymer or piezoceramic), the formulas obtained may describe a composite of either the type 1–3 or 3–1. The results may be used to assess the accuracy of statistical models as well as for target-oriented search and optimization of the properties of piezocomposites.