Fracture analysis of cracks terminating at the interface of elastic-piezoelectric bimaterials

Abstract

In this paper, the fracture behaviors of a piezoelectric-elastic bimaterial with cracks terminating at the interface are investigated by a symplectic approach. In the Hamiltonian system, the Hamiltonian forms of governing equations 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 electro-elastic fields and explicit expression of electric/elastic intensity factors are obtained simultaneously. Results indicate that the electro-elastic singularities and intensity factors 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 intensity factors of such interface cracks. Some new results are given also.