Field distributions in piezoelectric composites with semi-infinite cracks

Abstract

A method is offered for the prediction of the electromechanical field in periodic piezoelectric composites with embedded semi-infinite cracks. It is based on the knowledge of the K-field in piezoelectric materials in which the material constants are replaced by the effective moduli of the piezoelectric composite. In addition to the existing semi-infinite crack, the proposed method can analyze localized inhomogeneities near the crack tip. The established effective K-field is applied at the boundaries of a rectangular domain that should be sufficiently far away from the crack tip and the other inhomogeneities. The proposed approach is based on the combined utilization of a micromechanical analysis, the representative cell method and the higher-order theory. The micromechanical analysis establishes the effective electromechanical constants of the piezoelectric composite, and the representative cell method reduces the periodic composite that is discretized into numerous identical cells to a single cell problem in the Fourier transform domain. The governing equations and constitutive relations that are formulated in this single cell are solved by employing the higher-order theory where discretization into subcells is employed. The inverse of the Fourier transform provides the electromechanical field at any point in the composite. The proposed approach is verified for crack fronts that are parallel and perpendicular to the poling direction (axis of symmetry). Applications are given for a cracked porous piezoelectric material, cracks that have been arrested by cavities and for a periodically bilayered composite with a semi-infinite crack.