Electro-elastic stress analysis for a Zener–Stroh crack at the metal/piezoelectric bi-material interface

Abstract

A Zener–Stroh crack may nucleate at the interface of metal/piezoelectric bi-materials, when piled-up dislocations along a slip plane in metal material are stopped by the interface which works as an obstacle. As a kind of microcrack, Zener–Stroh crack controls the initial phase of crack nucleation. In the first step of our current research, the stress and electric displacement fields for a single interfacial dislocation in general piezoelectric/metal bimaterials are obtained in an explicit close form. With this solution as the Green function, the interfacial Zener–Stroh crack problem is formulated into a set of singular integral equations with distributed dislocation technique. These singular integral equations are then solved by numerical method based on the singularity nature at the crack tips. To deal with the oscillation behaviors near the interfacial crack tips, both open crack tip model and contact zone model are considered and compared each other in the paper. Solutions on the stress field, stress and electric displacement intensity factors and contact zone length are obtained. A numerical example of a Zener–Stroh crack at the Pt/PZT-5H bimaterial interface is given. Some useful electro-elastic characteristics related to the crack are found and discussed.