Analysis of a Crack in a Finite Thermopiezoelectric Plate under Heat Flux

Abstract

The mechanical and electric fields in a finite thermopiezoelectric plate containing an isolated crack are formulated by applications of the Stroh’s formulism and conformal transformation. The general form of the solution is constructed consisting of a holomorphic part in terms of Laurent series of each mapping planes, and a nonholomorphic part in integral form due to the crack. The approximate solution is obtained by least square method for a rectangular plate in which supplementary functions are introduced concerning its four corners for the purpose of accelerating the convergency of the Laurent series. The coefficients of the Laurent series of the solution, both for thermal field and electro-mechanical field, are exhibited for a crack problem, and the accuracy of the approximation is explored subsequently. The stress and electric displacement (SED) intensity factors are given for varying the plate size and the crack site. For specified crack length, considerable enhancement of SED intensity factors may be attained as the plate size increases owing to the mechanical and electric fields formed under uniform heat flow.