Theoretical modelling of a conducting crack in a magnetoelectroelastic solid

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.