Theoretical model for crack branching in magnetoelectroelastic solids

Article type: Research Article

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

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

Correspondence: [*] Corresponding author. E-mail: rajapakse@mech.ubc.ca

Abstract: A mathematical model is presented to determine the fracture parameters of a finite impermeable crack with one or more branches in a magnetoelectroelastic plane subjected to the remote mechanical, electrical and magnetic loading. An integral equation approach based on the fundamental solution for a generalized dislocation is used to formulate the problem. The problem is reduced to a set of singular integral equations with the dislocation densities along the crack line as the unknown variables. The integral equation system is solved by using numerical quadrature. Selected numerical results are presented to demonstrate the dependence of crack tip field intensity factors on branch length, branch orientation, poling orientation of the medium and type of loading. Numerical results imply that a branch crack cannot propagate in a self-similar manner. Solutions for a crack with double branches show that simultaneous propagation of branches is not possible.

Keywords: Branched crack, fracture mechanics, impermeable crack, magnetoelectroelastic materials, piezoelectricity, stress intensity factors

DOI: 10.3233/JAE-2008-932

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 27, no. 1-2, pp. 53-74, 2008