This dissertation presents a comprehensive theoretical study of the plane strain problem of cracked piezoelectric materials. Existing studies indicate that the commonly used electrically impermeable and permeable crack models may be inadequate in evaluating the fracture behaviour of piezoelectric materials in some cases. This is due to the difficulties in describing the electric boundary condition along crack surfaces. In this project, a dielectric crack model based on the ’real’ electric boundary condition is proposed to study the nonlinear fracture properties and electromechanical coupling of cracked piezoelectric materials. The electric boundary condition along the crack surfaces is governed by the opening displacement of the crack, which is deformation-dependent and thus nonlinear.

In the current work, the crack is modelled by continuously distributed dislocations involving both displacement and electric potential jumps. The formulation of this nonlinear problem is based on the use of Fourier transform technique and solving the resulting nonlinear singular integral equations. Numerical simulation is conducted to describe the complicated nonlinear fracture behaviour of piezoelectric materials under different electromechanical loads.

The effect of this nonlinear electric boundary condition upon the fracture behaviour of cracked piezoelectric materials is investigated systematically. Multiple deformation modes are observed and discussed, which are governed by geometric and loading conditions. The results obtained from this dielectric crack model demonstrate how the transition between electrically impermeable and permeable crack surface conditions occurs with the change of the crack opening displacement in response to the applied electromechanical loading. The asymptotic behaviour of cracked piezoelectric media is provided when two limiting cases, permeable and impermeable conditions, are reached. Unlike the results predicted by the traditional crack models, the fracture behaviour and the effective electroelastic property of cracked piezoelectric media are found to be nonlinear and sensitive to loading conditions. Based on theoretical analyses and existing experimental results, a new fracture parameter, crack opening displacement intensity factor K_COD, is introduced to predict the effect of applied electric field upon the crack propagation. This work contributes in understanding the nonlinear nature of piezoelectric materials and improving the design and application of this kind of materials in smart structures.