Dynamic Antiplane Behaviors On Piezoelectric Materials With Various Interfacial Defects

As a kind of new intelligent materials, the piezoelectric material, which has been widely used in national defense construction, industrial production and many areas which closely relates to the people's lives, attracts extensive attention of many researchers due to its properties of electromechanical coupling. And more attention is paid to the investigation of the fracture behaviors on piezoelectric materials with various kinds of defects. Dynamic antiplane problems of the piezoelectric medium, piezoelectric bimaterials and quarter-infinite piezoelectric medium which contain circular cavity, crack, inclusion and composite defects are investigated in this article using the linear piezoelectric theory. Some useful conclusions are obtained.The main work in present paper can be summarized into three parts as follows:In part one, dynamic antiplane behaviors of the radial cracks at the edge of the circular cavity are solved in piezoelectric medium and piezoelectric bimaterials. Firstly, the Green's functions which satisfy the boundary conditions of this problem are given. The total displacement field and the total electric potential field are also obtained in piezoelectric medium without any cracks. Secondly, the problems are reduced to a set of the first kind of Fredholm integral equations by the conjunction method and the crack-division technique. And the integral equations are solved by the direct numerical integration method. Finally, the numerical results reveal the effects of the length of the crack, the circular cavity radius, the incident wave frequency and the material parameters on dynamic stress intensity factors of the crack-tip. It can be concluded that the values of radial crack-tip DSIFs on a circular cavity aren't invariably less then those on a reduced straight crack with an effective length at the dynamic situation. The oscillating phenomenon can be seen around the straight crack DSIFs.Then, dynamic antiplane behaviors of one cavity and two cavities near the interface are investigated in piezoelectric bimaterials. And the dynamic interaction between a circular cavity and a interface crack is also analyzed in the present paper. Based on the Green's functions which are agreed with the boundary conditions, a pair of the first kind of Fredholm integral equations for solutions of the unknown stresses and the unknown electric fields at the interface can be established according to the conjunction method. The values of the additional stress and electric fields on the discrete points are obtained to solve the integral equations by the direct numerical integration method. And the expressions of dynamic stress concentration and electric intensity concentration at the edge of the circular cavity are also given. The interface crack problem is also reduced to solve a set of the first kind of Fredholm integral equations by the conjunction method and the crack-division technique. Dynamic stress intensity factors of the crack-tip can be contained in the integral equations by a substitution. As a numerical example, the effects of the circular cavity radius, the distance between the hole and the interface, the incident wave frequency, the material parameters and the length of the crack on dynamic stress concentration, electric field intensity concentration at the edge of the circular cavity and dynamic stress intensity factors at the crack-tip are given.Dynamic antiplane problems in the quarter-infinite piezoelectric medium with a single cylindrical defect are studied in part three. Firstly, the displacement field and the electric potential field, which satisfy the governing equations and the boundary conditions at the two free surfaces, are structured by the image method. Secondly, the scattering fields of displacement and electric potential are constructed by the complex variable function method, multi-polar coordinate transformation and the superposition theorem. And the scattering fields satisfy all the boundary conditions. Finally, the expressions of displacement field and electric potential field in the defect are given. And the unknown coefficients in the expressions can be solved according to the boundary conditions at the edge of the defect. The analytical expressions of the stress concentration and the electric field intensity concentration at the edge of the defect are achieved. The effects of the defect radius, the distances between the defect and the two free surfaces, material parameters and the incident wave frequency on the distributions of stress and electric field at the edge of the defect are drawn.It is expected that the investigations on dynamic antiplane behaviors of piezoelectric material with various kinds of defects can provide some references for the project designing, manufacture and application of piezoelectric material.