Anti-plane Shear Crack Normal To And Terminating At The Interface Of Bi-piezoelectric Materials

Piezoelectric material is a kind of functional material with force-electric coupling characteristic.It is widely used in aerospace,automatic control,micro-mechanical system,precision sensor and so on.It has become a research hotspot both at home and abroad.However,the piezoelectric material itself is a brittle material,in the force field and the role of the electric field often lead to premature failure of the materia l,especially with such as cracks and other defects.Therefore,it is of great theoretical and practical significance to study the crack behavior based on fracture mechanics of piezoelectric materials.In this paper,the anti-plane problem of the interface crack in the bi-piezoelectric material is studied by Fourier transform and singular integral equation theory.The main results are as follows:1.The anti-plane problem of two kinds of vertical crack with two semi-infinite piezoelectric materials in a single direction is studied.After solving the singularity equation,the relevant parameters of crack tip and crack surface are obtained.The stress intensity factor and the energy release rate of the crack at the interface are obtained.Assuming the change o f the stress intensity factor and the energy release rate at the crack tip by changing the single material constant(elastic constant,piezoelectric constant,dielectric constant)under the premise that the material properties are arbitrarily variable,the results show that by changing the material properties and polarization directions of the bi-piezoelectric will change the singularity at the tip of the crack perpendicular to the interface,and will significantly affect the interfacial stress intensity factor and the energy release rate,which can affect the behavior of the crack tip.2.The piezoelectric materials with finite thickness and semi-infinite piezoelectric base are analyzed.The model considers the influence of the conduction and non-conduction crack boundary conditions on the crack behavior.The boundary conditions are used to solve the singularity equation,and the stress intensity factor at the crack tip and the singularity index at the interface are obtained.By changing the material parameters and the size of the model between the two piezoelectric materials,the relationship between the stress intensity factor and the material parameters and the model parameters of the crack tip is obtained.The results show that the boundary condition of the crack surface affects the crack tip Stress intensity factor;changes in material properties will affect the interface of the singularity index,thus affecting the displacement of the entire crack surface.3.The numerical model is used to analyze the theoretical model by finite element software.The correctness of the theoretical model is verified by fitting the numerical results and the theoretical model results.