Abstract
The double singularities including singular stress field and singular electric displacement field, in the tips of piezoelectric composite junctions, are analyzed by the interpolation matrix method (IMM). The double singularity analysis problem of piezoelectric composite junctions is converted into eigenvalue solution problem of ordinary differential equations with variable coefficients under corresponding boundary conditions. In numerical examples, the first couple of singularity orders and the corresponding characteristic angular functions of displacement and electric potential for the electromechanical coupling field are obtained and comparisons are presented to validate the accuracy of the proposed method. The singularity of the electromechanical coupling field at the tip of piezoelectric composite material junctions is closely related to the bonding angle and fiber direction. According to the numerical results, the best scheme can be configured for the combination of dissimilar materials.
Highlights
Piezoelectric devices such as brakes and sensors are composed of piezoelectric materials, conductors, and composite materials. e problem of material and geometric discontinuities is common at the junctions and interface edge of piezoelectric materials, conductors, and composite materials, which leads to the singularity of stress and electric displacement. e singular field at the tips of piezoelectric composite junctions directly affects the safety and engineering structures [1, 2]. erefore, it is of great significance to study the singularity of the notch to ensure the reliability and safety of the structure in service
Since Williams [3] first gave the classical solution of stress field of interface crack in isotropic bimaterials, many research studies have been performed on the singularity in piezoelectric composite material wedges. e failure behavior and failure criteria of deep notch of piezoelectric ceramics were experimentally analyzed by Zhang et al [4]
E developed interpolation matrix method (IMM) program [20,21,22,23] was used to solve the formed characteristic ordinary differential equations, which can calculate each singularity order and the corresponding characteristic angular function of displacement and electric potential for piezoelectric composite material junctions at one time. e present method has the characteristic of strong adaptability, high accuracy, and small calculation
Summary
Piezoelectric devices such as brakes and sensors are composed of piezoelectric materials, conductors, and composite materials. e problem of material and geometric discontinuities is common at the junctions and interface edge of piezoelectric materials, conductors, and composite materials, which leads to the singularity of stress and electric displacement. e singular field at the tips of piezoelectric composite junctions directly affects the safety and engineering structures [1, 2]. erefore, it is of great significance to study the singularity of the notch to ensure the reliability and safety of the structure in service. Xu and Rajapakse [14] used the complex potential function method to investigate the singular electroelastic field at the tip of junctions of conductors, composite materials, and piezoelectric materials under plane deformation, and the influencing parameters including material properties, binding angle, and polarization angle were considered. E displacement field at the tip of piezoelectric composite material junctions was firstly asymptotically expanded by power series, so that the electromechanical boundary/interface conditions of junctions were transformed into a combination expression of singularity-order characteristic equation. E developed IMM program [20,21,22,23] was used to solve the formed characteristic ordinary differential equations, which can calculate each singularity order and the corresponding characteristic angular function of displacement and electric potential for piezoelectric composite material junctions at one time. E developed IMM program [20,21,22,23] was used to solve the formed characteristic ordinary differential equations, which can calculate each singularity order and the corresponding characteristic angular function of displacement and electric potential for piezoelectric composite material junctions at one time. e present method has the characteristic of strong adaptability, high accuracy, and small calculation
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