Reinforced Crack Propagation in a Prestressed and Prepolarized Piezoelectric Material

In this paper the problem of an antiplane reinforced crack in prestressed and prepolarized piezoelectric materials is considered. Using the boundary conditions of the reinforced crack we get the homogeneous and a nonhomogeneous Riemann-Hilbert problems. Nonhomogeneous linear complex differential equations having the unknown complex potentials are obtained. For a constant value of the applied incremental forces can be obtained the complex potentials, incremental displacement and stress fields corresponding to the third mode of the classical fracture. Extending Sih’s strain energy density failure criterion for prestressed and prepolarized piezoelectric materials we study the antiplane reinforced crack propagation in a PZT type piezoelectric material. Using numerical results and the graphical representation of incremental strain energy density, the direction of antiplane reinforced crack initiation can be predicted versus different values of stiffness constant and for different small values of initial mechanical and electrical fields.