The annular crack in piezoelectric material

The problem of electroelasticity for piezoelectric materials containing an annular crack is considered. For axially symmetric states three potentials are utilized, which determine the displacements, the electric potential, the stresses, the components of the electric field vector and the electric displacements in piezoelectric body. Two cases of boundary-value problems are considered, namely the electrically permeable and impermeable crack boundary conditions. The three-part mixed boundary conditions are reduced into an equivalent system of simultaneous algebraic equations. By means of the coefficients, which are obtained from this system, the electrical and mechanical fields in the plane where the annular crack appears are obtained. The main results are the intensity factors for stress and electric displacement.