Study On Anti-plane Crack Problem Of Orthotropic Piezoelectric Materials

Piezoelectric material has a good electromechanical coupling and is an essential material in engineering applications.In practical applications,piezoelectric materials are usually brittle materials,and mechanical loads and electrical loads are more complex,which are easy to cause cracks in piezoelectric materials.And there exists a interface between the two piezoelectric materials.The process defects at the interface will also form interface cracks under the action of mechanical and electrical loads,which greatly affects the reliability and service life of piezoelectric elements in normal operation.Therefore,the research on the crack problem of piezoelectric materials is of great theoretical significance for its application in engineering.The main research workers in this paper as follows:(1)The anti-plane central crack problem of orthotropic piezoelectric materials under mechanical and in-plane electrical loads at infinity of antiplane is studied by means of composite fracture complex method and undetermined coefficient method.Firstly,according to the boundary conditions,the anti-plane crack tip fracture problem of piezoelectric materials is transformed to solve the boundary value problem of partial differential equations.Secondly,the stress intensity factor and the electric displacement intensity factor are defined near the crack tip.Thus,the theoretical expressions of stress intensity factor,electric displacement intensity factor,stress field and electric displacement field are obtained.The results show that the larger the crack length is,the larger the crack length is.The larger the electromechanical load is,the greater the strain release rate of mechanical energy is.The positive electric field promotes the crack propagation,while the negative electric field inhibits the crack propagation.(2)The anti-plane interface crack problem of piezoelectric bimaterial is studied.The theoretical expressions of stress intensity factor,electric displacement intensity factor,stress field and electric displacement field are obtained.The results show that the larger the crack length and the greater the mechanical load,the greater the mechanical energy strain release rate,the stressalways promotes the crack propagation,the positive electric field promotes the crack propagation,and the negative electric field inhibits the crack propagation.The mechanical energy strain release rate of different materials is different.(3)The anti-plane crack interface problem of piezoelectric bimaterials is studied.The theoretical solutions of stress intensity factor and electric displacement intensity factor are obtained.The factors affecting stress intensity factor and electric displacement intensity factor are analyzed by numerical examples.The results show that the stress intensity factor and the electric displacement intensity factor depend on the polar coordinate radius.The growth rate of different materials is different.