Studies On Elastic-Electro Fields And Effective Properties Of Piezoelectric Composites

Due to the mechanical-electric coupling behaviors, piezoelectric materials have been widely applied inengineering applications. However, the brittleness of piezoelectric materials has limited their sizes.One way to solve this problem is to embed the piezoelectric materials into the elastic matrix and makeup piezoelectric composites. The physical discontinuity in the composites will lead to local stressconcentration along the interface, causing the separation of the fibers from the matrix and finallyfailures. One way to improve the interface strength is to add an appropriate interphase between thepiezoelectric fibers and the matrix. In addition, the reasonable array type of piezoelectric fibers canalso effectively reduce the stress concentration near the interphase.Based on the complex variable theory and the generalized self-consistent method with interphase, inthe paper we study the local mechanical-electric fields and the effective properties of the piezoelectriccomposites. The effect of array type of fibers and interphase on the mechanical-electric fields andeffective properties are analyzed, respectively. This paper consists of seven chapters and the maincontents are as follows:In the first Chapter, a brief introduction to piezoelectric composites is given and the problems neededto be solved are outlined.In the second Chapter, the basic equations in this paper are obtained. Based on the Stroh theory, thebasic equations of the anti-plane problem for the piezoelectric materials are firstly derived when thepolar direction is assumed to be along the x₃axis. Then according to the complex variable theory andlinear elastic piezoelectric equations, the mechanic-electric equations of the plane problems for thepiezoelectric composites are also derived when the polar direction of piezoelectric fiber is assumed tobe along the x₃axis.In the third Chapter, the mechanical-electric field under anti-plane and plane deformation for thepiezoelectric fiber with a functionally graded interphase embedded into the matrix is studied,respectively. The functionally graded interphase is divided into be uniform, and the complex potentialsof matrix, the after-homogenization of interphase and piezoelectric fiber are set to power series with undetermined coefficients. Then according to the corresponding boundary conditions, themechanical-electric fields of the composites are obtained under different kinds of known remote loads.In the fourth Capter, studied is an anti-plane problem for mechanical-electric field of the multiplepiezoelectric fibers with an interphase in the matrix. Based on the complex variable theory and theStroh formalism, the elastic equilibrium of the multiply-connected problem in the complex potential issolved and the analytical solutions for all the constituents of the piezoelectric composites are derived.Then numerical results are presented to discuss the influences of interphase properties, interphasethickness and distances on the mechanical-electric fields of the piezoelectric composites.In the fifth Chapter, addressed is a plane problem for mechanical-electric field of the multiplepiezoelectric fibers with interphase randomly-distributed in the elastic matrix under remote in-planemechanical load and electric load along the piezoelectric fiber. Numerical solutions are made toexplore the influence of different interphase on the mechanical-local field of the piezoelectriccomposites.In the sixth Chapter, investigated is the effective properties problem for a variety of an interphaseembedded into the piezoelectric composites' models. According to the generalized self-consistentmethod with interphase and the solutions obtained from the last three Chapters, the effectiveproperties of piezoelectric composites under statistics homogeneity are derived by different kinds ofmodels. Numerical results are presented to discuss the influence of interphase on the effectiveproperties of piezoelectric composites.Finally, in the last Chapter, the present work is summarized and some future works are proposed onthe topic.