Electric Dipole Model and Computer Simulation of the Fracture Behavior of a Conductive Crack in a Dielectric Material
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Electric Dipole Model and Computer Simulation of the Fracture Behavior of a Conductive Crack in a Dielectric Material Tianhong Wang and Xiaosheng Gao Department of Mechanical Engineering, The University of Akron Akron, OH 44325, U.S.A. ABSTRACT Fracture tests on poled and depoled lead zirconate titanate (PZT) ceramics indicate that purely electric fields are able to propagate the conductive cracks (notches) and fracture the samples. To understand the fracture behavior of conducting cracks in ferroelectric ceramics, an electric dipole model is proposed, in which a discrete electric dipole is used to represent the local spontaneous polarization and the force couples are used to represent the local strains. The electric dipole model provides basic solutions for microstructural modeling. The microstructural modeling is based on a domain switching mechanism. The domain structure is simulated with a grid of points where polarizations and strains vary with the applied loads. As a first step study, the microstructural modeling is conducted for a dielectric material with a conductive crack. The simulation result explains why the electric fracture toughness is much higher than the mechanical fracture toughness. INTRODUCTION Internal electrodes are widely adopted in electronic and electromechanical devices made of ferroelectric ceramics. These embedded electrodes may function as conductive pre-cracks or notches, which can lead to failure of these devices under combined electrical and mechanical loads [1, 2]. This calls for a thorough investigation and comprehensive understanding the fracture behavior of piezoelectric materials. A significant body of work has developed on fracture mechanics of linear piezoelectric materials, see [3] for an extensive review. However, the linear fracture mechanics can not give a satisfactory explanation to the effect of electrical loading on the fracture behavior of piezoelectric materials [4, 5]. Piezoelectric ceramics are mechanical brittle, but their electrical response is highly nonlinear. The coupling effects between mechanical and electrical responses further complicate the problem. In recent years various models have been proposed to explain the nonlinear fracture behavior of piezoelectric materials. In this work, we conduct microstructural simulation based on the domain switching model. Fulton and Gao [6] developed a methodology for microstructural modeling and studied insulating cracks in piezoelectric ceramics, where the spontaneous polarization and local strains are represented by a discrete electric dipole and force couples. Following this idea we derive the analytical solution of the electric dipole model for conductive cracks in piezoelectric materials and use it to formulate the microstructural simulation. As a simple case application, computer simulations are conducted for a conductive edge crack in a dielectric plate and the hysteresis curves are reproduced. Using a fracture criterion based on local energy release rate, our results demonstrate that this domain switching
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