The nature of stress and electric-displacement concentrations around a strongly oblate cavity in a transversely isotropic piezoelectric material

In this paper we explore the nature of stress and electric-displacement concentrations around a strongly oblate spheroidal cavity that possesses a finite dielectric permittivity. We start out from Eshelby's general inclusion method but give specific account on the important class of piezoelectric ceramics whose structure is represented by the 6mm symmetry. It is found that under axial electromechanical loading these concentrations are governed by a dimensionless parameter eta, defined as (k(0)/k(33))/(c/a), that involves the ratio of the dielectric permittivity of the medium inside the cavity k(0), to that of the transversely isotropic piezoelectric ceramic k(33), and the aspect ratio of the cavity c/a. When the medium inside the cavity is an impermeable one it is found that both the axial stress and axial electric displacement can have direct contribution to the concentration factors, but when the medium is a conducting one only the applied stress has an effect on it. Our analysis further indicates that it is the parameter eta - not k(0)/k(33) or c/a alone - that plays the key role here; when eta < 0.01, the cavity can be effectively treated as an impermeable one, while for eta > 100 it can be treated as a conducting case. Numerical results for several PZT ceramics suggest that under a pure tensile stress the ceramic tends to fracture on the equatorial plane, but under a pure electrostatic load it tends to develop radial cracks normal to the edge of the cavity.