Buckling delamination of the PZT/Metal/PZT sandwich circular plate-disc with penny-shaped interface cracks

The axisymmetric buckling delamination of the Piezoelectric/Metal/Piezoelectric (PZT/Metal/PZT) sandwich circular plate with interface penny-shaped cracks is investigated. The case is considered where open-circuit conditions with respect to the electrical displacement on the upper and lower surfaces, and short-circuit conditions with respect to the electrical potential on the lateral surface of the face layers are satisfied. It is assumed that the edge surfaces of the cracks have an infinitesimal rotationally symmetric initial imperfection and the development of this imperfection with rotationally symmetric compressive forces acting on the lateral surface of the plate is studied by employing the exact geometrically non-linear field equations and relations of electro-elasticity for piezoelectric materials. The sought values are presented in the power series form with respect to the small parameter which characterizes the degree of the initial imperfection. The zeroth and first approximations are used for investigation of stability loss and buckling delamination problems. It is established that the equations and relations related to the first approximation coincide with the corresponding ones of the three-dimensional linearized theory of stability of electro-elasticity for piezoelectric materials. The quantities related to the zeroth approximation are determined analytically, however the quantities related to the first approximation are determined numerically by employing Finite Element Method (FEM). Numerical results on the critical radial stresses acting in the layers of the plate are presented and discussed. In particular, it is established that the piezoelectricity of the face layer material causes an increase (a decrease) in the values of the critical compressive stress acting in the face (core) layer.