Investigation On Interface And Fracture Problem Of Piezoelectric Materials

In view of the intrinsic coupling effects that take place between electric fields and mechanical deformation, piezoelectric materials have been extensively used in intelligent and adaptive structure systems as sensors and actuators. The disadvantage of these materials, such as brittleness, has been recognized. A wealth of theoretical studies has been performed on fracture mechanics of piezoelectric materials. However, for they are used in more and more complex conditions, there is an urgent need for more comprehensive researches for mechanical reliability of piezoelectric materials in engineering practice.Firstly, considering the fact of that thermopiezoelectric materials have been used increasingly in engineering practice, the thermo-electric-mechanical coupling problem in thermopiezoelectric media with holes, cracks or inclusions has been studided. An analysis is performed on an elliptical anisotropic piezoelectric inclusion embedded in an infinite anisotropic piezoelectric matrix subjected to arbitrary far-field uniform loadings by employing the Stroh formalism, the method of analytical continuation, the technique of conformal mapping, and the principle of superposition. Solutions of the temperature and stress functions either in the matrix or in the inclusion are obtained in terms of complex matrix notation. It shows that the mechanic and electric loading leads to the appearance of the constant stress fields in the inclusion and the heat flux leads to that of the linear stress fields.Secondly, considering the fact of that Green's functions reflect the analytical nature of the boundary element method considered being a good alternative for studying the complicated problems in applications, an analysis is performed on the Green's functions problem of a two-dimensional infinite anisotropic magneto- electroelastic solid containing an elliptic hole subjected to a generalized force on the hole surface. The solutions are obtained by employing the Stroh formalism, the method of analytical continuation, the technique of conformal mapping, the principle of superposition, and the exact electromagnetic boundary conditions. Then, the two-dimensional Green's functions problem of an elliptic inclusion embedded into an anisotropic magnetoelectroelastic solid is studied. The general solutions for the stress and deformations in the entire domain are obtained when a generalized line force and a generalized line dislocation are located at a point outside, inside, or on the interface of an elliptical inclusion. Comparisons with some related solutions show that the present solutions are valid.Lastly, considering the nonlinear electroelasticity at crack tip, the stress field near the crack tip in an infinite piezoelectric media subjected to a far-field uniform loading is studied by means of an electrical strip saturation model and the complex variable method. The solutions show that the normalized stress components on an arbitrarily point near the crack tip are determined by the angle of the point alone and independent of the distance between the point to the origin. The distributions of in-plane stress components near the crack tip are analyzed based on numerical results for PZT-5H. Then, using the same model, the anti-plane problem of an interfacial crack between two semi-infinite anisotropic piezoelectricity subjected to a far-field uniform loading is solved. Solutions of stress and electric displacement are obtained. The explicit closed form expressions for the stress components and the stress intensity factor at the crack tip are given. Finally, the anti-plane problem of a circular-arc interfacial crack between a circular piezoelectric inhomogeneity and an infinite piezoelectric matrix subjected to a far-field uniform loading is investigated by means of an electrical strip saturation model, the complex variable method and the method of analytical continuation. The explicit closed form expressions for the complex potentials in both the matrix and the inclusion and for the stress intensity factor at the crack tip are presented. Comparisons with some related solutions based on linear electroelastic theory show that the present solutions are valid.