Fracture Analysis Of Cracks Terminating At The Interface Of Elastic-piezoelectric Bimaterials

With the development of science and technology,multi-field coupling composite materials have been widely used in the manufacture of smart devices such as transducers,sensors and actuators.Among them,piezoelectric composite materials are a kind of multi-field coupling materials with good mechanical-electrical coupling characteristics.But in the engineering application,cracks are inevitable at the interface due to mismatch in the interface of different materials.Therefore,an understanding of the fracture behavior of interface cracks is of great importance to the evaluation of composite structures.The existing interface crack research focuses on cracks propagating along the crack surface.The research on cracks terminating at the interface is very limited,and only applicable to infinite models,which cannot solve the problem of finite-size structures in the engineering application.Then there is a great demand to propose an analytical method for crack terminating at the interface in composite structures with limited size.In this paper,a symplectic approach is applied to investigate the fracture behaviors of a composite with cracks terminating at the interface.In the Hamiltonian system,the governing equations in the Hamiltonian form is derived by the Hamiltonian variational principle and a total unknown vector consisted of generalized displacements and stresses.The interface fracture problem is reduced into a symplectic eigenproblem which can be directly solved by the method of separation of variables.Thus,the total unknown vector is expanded in terms of symplectic eigenfunctions.The unknown coefficients of the symplectic series can be determined from the continuity conditions at the interface and outer boundary conditions.Consequently,exact solutions for the singular fields and explicit expression of fracture parameters are obtained simultaneously.Results indicate that the singularities and fracture parameters only depend on the first few terms of symplectic eigenfunctions with non-zero eigenvalues.Numerical examples are presented to show the effects of key influencing factors on the singularity orders and fracture parameters of such cracks.Some new results are given also.