Electro-mechanical analysis of a layered sphere with functionally graded piezoelectric material

Nowadays, piezoelectric materials are widely used in sensor technology. Amongst variety of types, piezoceramics have been demonstrated as efficient tools for sensing applications. Piezoelectric ceramics are more versatile so that their physical, chemical, and piezoelectric characteristics can be tailored to specific purposes. Typical applications include undersea sonar systems, high-resolution ultrasonic imaging, non-destructive testing, materials evaluation, medical diagnostic analyses and measurements, and therapeutic treatments [1]. Functionally Graded Materials (FGMs), that have been recently explored in coating technology, are generally nonhomogenous composites with continuous variation of the constituents from one surface of the material to the other. In such material, the composition and structure gradually change over volume, resulting in corresponding changes in the properties of the material. This gradual change in composition eliminates the mismatch of material properties between the base structure and coating layer, which is the main reason for cracking, debonding, and in some cases eventual failure of the structure [2]. The efficiency of FG coating within a spherical pressure vessel has been recently studied by authors in which the role of graded coating in enhancement of through-the-thickness stress distribution is investigated [3]. In the present study, a layered spherical sensor is electro-mechanically studied within the context of elasticity theory. The sensor has been considered as a sphere with two layers: an outer layer composed of a homogeneous material and an inner layer made of piezoceramic. It is also assumed that the piezoelectric layer has graded composition resulting in graded electro-mechanical properties. The gradation is realized along the radial direction and based on a power function. Results including through-the-thickness stress components and electrical potential are presented for different gradation parameters. Also, results are compared with those of a layered sensor with non-graded piezoelectric layer. At the end, the role of gradation in piezoelectric layer and its effect on the overall behavior of the sensor is discussed.