The Analytical Method Of Doubly Periodic Piezoelectric Fiber Composites With Multiple Interface Layer Under Antiplane Shear

Interfaces of piezoelectric composite materials, which transmit electrical and mechanical load from the matrix to the reinforcemrnt phase of composites, act as a linking bridge of the reinforcement phase and the matrix, the change of interface phase properties(such as thickness, properiteis, the order of the coating) have a significant impact on local electro-elastic field and macroscopic effective properities. Therefore, the study of the interface layer has a very important significance. This paper dedicate to the resrearch on the internal relations between macroscopic properties and microstructure paremeters of piezoelectric composites with doubly periodic multiple coated piezoelectric fibers under far-field uniform anti-plane shear stress and inplane electric displacement .By use of the concept of Eshelby's equivalent inclusion, a problem of doubly-periodic eigenstains and eigen-electric-fields for piezoelectric materials, which is equivalent to an originally heterogeneous materials problem (doubly periodic piezoelectric fiber composites), is constructed by the introduction of non-uniform eigenstrain and non-uniform eigen-electric-field for piezoelectric materials in the doubly-periodic cylindrical regions of a uniform solid whose properties are the same as the matrix properties of originally heterogeneous materials problem, equivalent equations are established between non-homogeneous piezoelectric composite material and homogeneous piezoelectric composite materials with eigenstrains and eigen-electric-fields. By using Laurent series, Taylor series expansion, and the results of doubly quasi-periodic Riemann boundary value problem, combined with compatibility conditions of displacement and electric potential, and continuity conditions of stress and electric displacement at contact interface of different phases, the electro-elastic field is obtained in series form. The solutions can be used to analyze the electro-elastic field within unit cell, and predict the effective electro-elastic modulus of the piezoelectric composite materials. Programming by using Mathematica symbolic computation software, stress concentration factor and the effective electro-elastic modulus are calculated. Numerical analysis show that interface microstructure of composite material have a significant impact on local electro-elastic field and macroscopic effective properties. Conclusions obtained from this paper are useful complements to the study of the relevance between macroscopic properties and microstructure of such materials. By dividing the interface into enough sub-layer ( the property of each sub-layer is uniform), the present method can also be applied to researching interface which the properity is gradual.