The stress singularities at the apex of composite piezoelectric junctions

Abstract

The stress singularities at the apex of a piezoelectric-conductor, -composite, or -piezoelectric junction are investigated under generalized plane deformation in this paper. The influencing parameters on the stress singularity order are the wedge angles, material properties, graphite fiber orientation, and piezoelectric poling direction. The singularities of decoupled inplane and antiplane electromechanical field s are investigated when piezoelectric materials are polarized in the (x-y)-plane or along the z-axis. From the numerical results, the conditions of strongest and weakest singularity orders can be determined. IntroductionDue to their electromechanical coupling behavior, piezoelectric materials, such as PZT-4, PZT-5, etc, are widely used in smart structures and electronic devices. Because the materials are brittle, cracking may start at the apex of these junctions where stresses are unbounded.It is known that three-dimensional piezoelectric problems can be decoupled into inplane and antiplane electro-elastic fields when the poling direction of the material is in the (x-y)-plane or along the z-axis. An extention of Stroh's formalism, [2], to an eight-dimensional framework was presented in [1] and the problem of piezoelectric insulators under a line charge and a straight dislocation was solved. Paper [3] extended the Lekhnitskii formalism [4] in anisotropic elasticity to derive a general solution to the plane strain piezoelectric problem in terms of complex potentials, assuming that the piezoelectric material is polarized along the x-or y-axis. The same approach was used in [5] to solve piezoelectric problems under generalized plane deformations. Exact correspondences have been indicated between plane piezoelectricity and generalized plane strain in elasticity.Piezoelectric wedge problems have not been yet addressed extensively. Papers [6-7] employed Stroh's formalism to solve the problems of a homogeneous anisotropic piezoelectric wedge and an angularly inhomogeneous piezoelectric wedge subjected to a line force, line charge and line dislocation applied at the apex. Paper [8] studied the singular behavior of the inplane electro-elastic field near the apex of piezoelectric wedges and junctions, with the polarization orientation of the piezoelectric medium arbitrary in the (x-y)-plane. Paper [9] applied the Mellin transform to the antiplane electric-mechanical field of a piezoelectric bonded wedge subjected to a pair of concentrate shear forces and free charges. In this study, the generalized stress, strain and electrical displacement intensity factors were derived analytically as well as the singularity orders and angular functions expressed in the electro-mechanical field. The formulation of piezoelectric elasticity under generalized plane deformation was derived in [10] and applied to wedge problems, while four decoupled cases were discussed in detail. Later, in paper [11] explicit forms were derived for eigen-equations, which govern the antiplane stress singularities of a bi-material piezoelectric wedge.T...

Electromechanical fracture analysis for corners and cracks in piezoelectric materials

“…Although the singular orders in composite piezoelectric wedges and junctions have been presented in the literature such as (Xu and Rajapakse, 2000;Weng and Chue, 2004), their results leave the solutions to a system of simultaneous algebraic equations whose details are usually ignored due to complexity. Here, the solutions are explicitly expressed by the multiplication of the key matrix as those shown in (3.4).…”

“…However, relatively few discussions have been devoted into corners in piezoelectric materials (Chung and Ting, 1995;Xu and Rajapakse, 2000;Weng and Chue, 2004) and the connections between cracks and corners. Recently, a unified definition of stress intensity factor was proposed (Hwu and Kuo, 2007) to build a bridge connecting the failure prediction among the interface corners, interface cracks and cracks in homogeneous materials.…”