Vol. 1, No. 3, 2006

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ISSN: 1559-3959
Microcrack initiation at the tip of a finite rigid conducting line in piezoelectric media

Zhongmin Xiao, Hongxia Zhang and Bingjin Chen

Vol. 1 (2006), No. 3, 559–579
Abstract

In this paper is proposed a dislocation emission mechanism for microcrack initiation at the tip of a finite rigid conducting line in a piezoelectric solid. When a finite rigid conducting line is embedded in a piezoelectric matrix, because of the highly concentrated stress and electric displacement fields at its tips, dislocations of one sign are driven away from the tip, while the stationary dislocations of the opposite sign are left behind. As a result, a micro Zener–Stroh crack is initiated at each tip for the in-plane case, and two microcracks at each tip for the anti-plane case. We obtain analytical solutions of both in-plane and anti-plane extension forces for microcracks initiated at the tip of a finite rigid conducting line. By obtaining the stress and electric displacement fields at the tip under nonzero net Burgers vectors, we observe two critical crack lengths. We find that the in-plane and anti-plane critical extension forces for a finite rigid conducting line are related to those for a conventional crack in the same piezoelectric materials.

Keywords
Zener–Stroh crack, rigid line, mechanical strain energy release rate, stress and electric displacement (SED) intensity factors, piezoelectric material
Milestones
Received: 8 December 2005
Accepted: 5 March 2006
Published: 1 July 2006
Authors
Zhongmin Xiao
School of Mechanical & Aerospace Engineering
Nanyang Technological University
Nanyang Avenue
Singapore 639798
Hongxia Zhang
School of Mechanical & Aerospace Engineering
Nanyang Technological University
Nanyang Avenue
Singapore 639798
Bingjin Chen
School of Mechanical & Aerospace Engineering
Nanyang Technological University
Nanyang Avenue
Singapore 639798