Theoretical Analysis Of Fracture Mechanics In Piezoelectric Functional Materials

Fracture behaviors of piezoelectric functional ceramics have received much attention due to their extensive application in modern high technoligical industry. Theoretical analysis of fracture mechanics in piezoelectric materials are performed by using the Stroh complex potential theory. A semi-permeable interface crack between two dissimilar piezoelectric materials and in elastic dielectric/piezoelectric composites are analyzed, respectively. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and the crack tip energy release rate (ERR). It is concluded that the previous investigations under the impermeable crack model overestimates the effect of the electric field on the ERR very much. Whereas the previous investigations under the permeable crack model underestimates the effect of the electric field but may be accepted in a tolerant way especially when it is full with more permeable medium of Silicon oil. Compared to the impermeable crack and the permeable crack, the semi-permeable crack represents a more realistic and general model for fracture mechanics in piezoelectric functional materials.Following the two essential results that the crack may be thought of as a low-capacitance medium carrying a potential drop and charge separation in the materials and discharges within the crack may occur during fracture, according to Coulomb's Law, the Coulombic traction can be generated due to the existence of electric charges on the crack surfaces. We propose a non-zero traction crack model considering such an electrostrictive effect. The roles played by the coulombic traction for an interface crack in piezoelectric functional composites and for a penny shaped crack in 3D piezoelectric body are clarified, respectively. It is found that the low-capacitance medium (air or vacuum) inside the crack gap yields some large Coulombic traction as compared to the applied mechanical loading. Unlike the traction-free crack condition, the applied electric field does change the Mode I stress intensity factor and energy release rate and in this way may significantly influence on the Mode I fracture duo to the existence of the Coulombic traction.This thesis deals with the invariant integrals in piezoelectric materials with a permeable crack and with a number of arbitrary oriented and distributed defects, respectively. Some inherent relations exist between the Bueckner integral and the Jk-integral or M- integral whatever the detailed configurations of the defect is. Finally, the surface effect and size dependence on the M-integral representing the energy release rate due to a nano-defect expansion in plane elasticity are concluded to be significant, whereas it is mainly induced from the residual surface stress?0 rather than from the surface Lam? constants?s and?s.This thesis may provide a better understanding of the failure mechanism or crack growth in piezoelectric ceramics or pirzoelectric composites when the electrical and mechanical loadings are preferred. Only after sucessfully solving the fracture problems, piezoelectric functional materias can be better used in smart structures of high-tech industry such as electronics, laser, supersonics, infranics, navigation, biology et al.