Crack branch in piezoelectric bimaterial system.pdfVIP

Crack branch in piezoelectric bimaterial system Qing-Hua Qin *, Yiu-Wing Mai Centre for Advanced Materials Technology, Department of Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW 2006, Australia Received 17 February 1999; accepted 12 May 1999 Abstract A solution is presented for a class of two-dimensional electroelastic branched crack problems in various bimaterial combinations. The combinations may be piezoelectric±piezoelectric, or one is piezoelectric and the other is not. Explicit Green?s function for an interface crack subject to an edge dislocation is developed within the framework of two-dimensional electroelasticity, allowing the branched crack problem to be expressed in terms of coupled singular integral equations. The integral equations are obtained by the method that models a kink as a continuous distribution of edge dislocations, and the unknown dislocation density functions are de?ned on the line of branch crack only. Competition between crack extension along the interface and kinking into the substrate is investigated using the integral equations and the maximum energy release rate criterion. Numerical results are presented to study the e?ect of electric ?eld on the path of crack extension. ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Crack branching and bifurcation; Energy release rate; Piezoelectric material 1. Introduction Due to the intrinsic coupling e?ect between electrical and mechanical ?elds, piezoelectric ma- terials have been widely used as electromechanical devices in which interfaces between materials are ubiquitous. As such the interfacial failure mechanism has caused researchers to devote a great deal of attention to study the selection of crack path. Generally fracture along and adjacent to bima- terial interfaces has several morphological manifestations. In some cases the fracture occurs at the interface, while in others fracture occurs in the more brittle constituent [6]. Various hypotheses h