Half Plane Piezoelectric Materials Line Crack Stress Analysis

With the progress of science and technology, all kinds of new composite materials apply in engineering which is becoming more common. Especially, the piezoelectric materials is a new kind of material which is widely used in making high precision sensor, brake and electronics, and so on. Because of the piezoelectric material brittleness which is presented itself. The fracture mechanics of piezoelectric materials analysis has become the focus of academic circles.This article is in piezoelectric materials under the theory of fracture mechanics, In view of the half plane problems on line crack in piezoelectric materials, the numerical solution are obtained by using the Fourier transform method and separation function method. The main contents are as follows:The first chapter of this paper is the introduction part, which is introduced the research background of fracture mechanics, the produce and application of piezoelectric materials, and. the research status of piezoelectric materials and the research methods.The second chapter is introduced the piezoelectric effect of piezoelectric materials, the piezoelectric fracture mechanics of the three basic equation and boundary condition, which is in order to establish model laid a certain foundation.The third chapter, we establish the half plane line crack model of piezoelectric materials, which is based on the actual engineering and gives the corresponding boundary conditions. With the help of a potential function method the problem will simplify its constitutive equation, and using split half an inverse method construct the function, which is get into a simple two relatively independent system of equations and a powerful electric coupling equation, the isolated contain electric equation. It makes electrical properties more clear.The fourth chapter, we use comprehensive methods to solve partial differential equations, and using the boundary conditions get the special solution,. A closed form solution are obtained.The fifth chapter takes an examination of PZT-4, refer to the corresponding literature find corresponding parameters of piezoelectric materials, and simulation using MATLAB to get the solution. Draw on the tip of crack stress function of the image and the crack in the whole half plane stress function and the change tendency of the distance between the half plane boundaries, and to draw the graphics and comparison, the results of the analysis.The six chapter is summarized that the image reflects the mechanical characteri-stics, and the development of this subject are prospected.