An exact solution of crack problems in piezoelectric materials

An assumption that the normal component of the electric displacement on cra ck faces is thought of as being zero is widely used in analyzing the fractu re mechanics of piezoelectric materials. However, it is shown from the avai lable experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material wit h a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions wh en the material is subjected to uniform loads at infinity. It is shown from these solutions that: (i) the stress intensify factor is the same as that of isotropic material, while the intensity factor of the electric displacem ent depends on both material properties and the mechanical loads, but not o n the electric load. (ii) the energy release rate in a piezoelectric materi al is larger than that in a pure elastic-anisotropic material, i.e., it is always positive, and independent of the electric loads. (iii) the field sol utions in a piezoelectric material are not related to the dielectric consta nt of air or vacuum inside the crack.