Vol. 11, No. 4, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 3, 249–351
Issue 2, 147–247
Issue 1, 1–146

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
Cover
Editorial Board
Research Statement
Scientific Advantage
Submission Guidelines
Submission Form
Subscriptions
Author Index
To Appear
 
ISSN: 1559-3959
An anisotropic piezoelectric half-plane containing an elliptical hole or crack subjected to uniform in-plane electromechanical loading

Ming Dai, Peter Schiavone and Cun-Fa Gao

Vol. 11 (2016), No. 4, 433–448
DOI: 10.2140/jomms.2016.11.433
Abstract

We derive a series solution for the electro-elastic field inside an anisotropic piezoelectric half-plane containing an elliptical hole or a crack when the half-plane is subjected to in-plane mechanical and electric loadings. Our solution is based on a specific type of conformal map which allows for the mapping of a complete half-plane (without a hole) onto the interior of the unit circle in the imaginary plane. We illustrate our solution with several examples. We show that with decreasing distance between the hole and the edge of the half-plane, the maximum hoop stress around the hole increases rapidly under mechanical loading but slowly in the presence of electric loading. In particular, for a crack with particular orientation in a piezoelectric half-plane subjected to pure shear, we find that the mode-II stress intensity factor at the crack tip farthest from the edge of the half-plane may decrease as the crack approaches the edge. Moreover, if the distance between the crack or the elliptical hole and the edge of the half-plane exceeds four times the size of the hole or semi-length of the crack, the half-plane can be treated essentially as a whole plane without inducing significant errors in the stress concentration around the hole or in the stress and electric displacement intensity factors at the crack tips.

Keywords
elliptical hole, crack, piezoelectric material, half-plane
Milestones
Received: 3 December 2015
Revised: 21 January 2016
Accepted: 9 March 2016
Published: 4 August 2016
Authors
Ming Dai
State Key Laboratory of Mechanics and Control of Mechanical Structures
Nanjing University of Aeronautics and Astronautics
Nanjing, 210016
China
Department of Mechanical Engineering
University of Alberta
Edmonton, Alberta T6G 2G8
Canada
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
Edmonton, Alberta T6G 2G8
Canada
Cun-Fa Gao
State Key Laboratory of Mechanics and Control of Mechanical Structures
Nanjing University of Aeronautics and Astronautics
Nanjing, 210016
China