Using Gsc Theory for Effective Thermal Expansion and Pyroelectric Coefficients of Cracked Piezoelectric Solids

Many brittle materials, such as concrete, piezoelectricity, have a large number of preexisting microcracks, The determination of their effective material properties has been the focus of considerable research. Current research into the development of effective material properties has mostly concentrated on the Taylor's method[l], the self-consistent method[2], the differential theory[3], the Mori-Tanaka method[4] and generalized selfconsistent(GSC) method[5]. For the themmelectroelastic problems, the first theoretical study appears to be that of Nemflmm and co-workers which is applicable to two phase thermopiezoelectric laminates that are connected in series or parallel[6]. After that, Dunn [7] evaluated the effective properties of two phase composites using dilute, self-consistent, Mori-Tanaka and differential micromechanical models. Benveniste[8] and Dunn[9] showed that the effective thermal-stress constants and p)qoelectric coefficients are related to the corresponding isothermal electroelastic moduli in two-phase media. Chen[10] further obtained some simple algebraic formulae tbr the prediction of overall thermoelectroelastic moduli of multiphase fibrous composites with the self-consistent and Mori-Tanaka methods. He indicated that when the phases have equal transverse shear rigidities, the overall moduli estimated by both methods are identical with exact solutions given by Chen[1 IJ for composites with arbitrary transverse geometry. More recently, Yu and his colleagues[12-14] obtained some new results of cracked thermopiezoelectric materials, additional references to work in this area can be found therein. This paper constitutes a continuation of analysis completed by the authors of those paper[12-14] on cracked thermopiezoelectric materials. In contrast to our previous studies, the present work focus on developing a GSC them T for efli:ctive thermal expansion and p3aoelectric coefficients of piezoelectric medium containing microcracks with given length and same orientation, The derivation is based on the extended Stroh formalism and a recently developed explicit solution of thermal-, electricand elastic fields for a cracked in an infinite piezoelectric solid. In the analysis, a representative area element is adopted, which contains a microcrack surrounded by an elliptic matrix in a solid x~dth effective properties. Numerical results are given tbr a piezoelectric ceramic BatiO3.