Theoretical modelling of a conducting crack in a magnetoelectroelastic solid

Article type: Research Article

Authors: Tian, W.-Y.^a | Rajapakse, R.K.N.D.^{a; *}

Affiliations: [a] Department of Mechanical Engineering, The University of British Columbia, Vancouver V6T 1Z4, Canada

Correspondence: [*] Corresponding author. Fax: +1 604 822 0944; E-mail: rajapakse@mech.ubc.ca

Abstract: A theoretical study of a magnetoelectroelastic composite plane with a single conducting crack is presented. Crack is assumed to be arbitrarily oriented with respect to the poling direction of the medium. General solutions for fully coupled magnetoelectroelasticity expressed in term of complex potential functions are used to formulate the problem. The formulation of a conducting crack is reduced to a classical Riemann-Hilbert problem and explicit analytical solutions are derived for the field intensity factors, total and mechanical energy release rates and crack tip hoop stress. The formulation is then extended to obtain common fracture parameters of an arbitrarily oriented permeable crack. Selected numerical results are presented for a conducting and a permeable crack in magnetoelectroelastic composite BaTiO_{3}-CoFe_{2}O_{4}. It is found that crack orientation, volume fraction of piezoelectric phase and magnitude of electro-magnetic and mechanical loading have a significant influence on fracture parameters.

Keywords: Conducting cracks, energy release rates, fracture mechanics, magnetoelectroelastic materials, permeable cracks, piezoelectricity

DOI: 10.3233/JAE-2005-698

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 22, no. 3-4, pp. 141-158, 2005