The Fracture Analysis of Collinear Periodic Cracks in an Infinite Piezoelectric Plate

Abstract

The fracture problem of collinear periodic cracks in an infinite transversely isotropic piezoelectric plate subjected to the anti-plane shear stress and the in-plane electric load at infinity is studied. Using the complex function method, the mechanical problem is turned into the boundary value problem of partial differential equations. The solutions of the boundary value problem of partial differential equation are obtained by undetermined coefficients method. Then, considering the periodicity of cracks, the stress intensity factors and the electric displacement intensity factors for mode III near the right tip of every crack are defined, the expressions of the stress fields, electric displacement fields, displacement fields, electric potential fields and the mechanical strain energy release rate around the crack tip are obtained with the assumption that the surface of the crack is electrically impermeable. Finally, interference effect and scale effect of collinear periodic cracks and the mechanical strain energy release rate are discussed by analysis of examples. It can be seen interference effect of collinear periodic cracks is strong when 1 < b / a < 2. The scale effect of the singularity of the stress intensity factors and electric displacement intensity factors in crack tip is obvious. Stress always promotes extension of the cracks, the mechanical strain energy release rate is related to the size and direction of the electric field, the positive electric field can promote the expansion of the cracks, the negative electric field can inhibit the extension of cracks.