DEVELOPMENT OF FINITE ELEMENTS FOR ANALYSIS OF FERROELECTRIC CERAMIC MATERIALS WITH CRACKS Ai Kah Soh1 and Daining Fang2 1Department of Mechanical Engineering, University of Hong Kong, Hong Kong 2Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R.China ABSTRACT Formulation of the electro-mechanically coupled finite element analysis for ferroelectric materials with defects has been described in this paper. Various crack surface electric boundary conditions for ferroelectric ceramics are implemented in the finite element procedure developed. Thus, the existing finite element method is extended to account for the impermeable, permeable and conducting cracks, by considering that the crack gap is filled with homogenous dielectric media. As an example, the crack propagation of a double edge notched specimen of a PZT-5H ferroelectric ceramic with exact electric boundary conditions on the crack surfaces is analyzed. Introduction The concerns of structural reliability of various electromechanical devices call for a better understanding of the mechanisms of piezoelectric fracture in ferroelectric materials. Theoretical studies of fracture in piezoelectric solids have been made by many researchers [1-4]. However, for these materials, due to the unexplained discrepancies between the theory and experiments, even the basic criterion of fracture remains a point of controversy [4]. As the electromechanical devices developed become more complex in geometry, analysis of such devices is even more complicated due to the electro-mechanical coupling effect of the ferroelectric materials. Thus, there is a necessity to formulate numerical methods capable of analyzing the macroscopic coupling response of the system, and simulating the failure behavior (e.g. fracture, fatigue) of the materials and structures. To-date, some attempts have already been made by researchers in the aforementioned area of interest [5]. Another problem that is of great interest to researchers is the crack surface electrical boundary conditions (hereafter called CSEBCs) [2,6]. These CSEBCs increase the complications and difficulties in the fracture analysis of ferroelectric materials. Although some theoretical work has been carried out by researchers to investigate the effect of CSEBCs on piezoelectric fracture, the use of numerical tools to study such fracture has rarely been reported. The purpose of this paper is to present an electro-mechanically coupled finite element approach for analyzing deformation and fracture of ferroelectric ceramic materials with defects. GOVERNING EQUATIONS FOR STATIC ELECTROMECHANICS Ferroelectric materials are approximately linear when an applied electric field or stress is small compared to the depoling field. Thus, the stress σ, strain ε, electric displacement D, and electric field E obey the following linear constitutive relations:
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