Electro-elastic analysis of bonded piezoelectric finite wedges with two collinear interface cracks under anti-plane deformation

Abstract

This paper studies two collinear impermeable interface cracks in bonded piezoelectric finite wedges. The radial edges are subjected to anti-plane concentrated forces and in-plane electric surface charges. The circular boundary is considered as traction free and electrically insulated. The finite complex transform developed in the literature for elastic wedges is extended to electro-elasticity for piezoelectric wedges. Based on the finite Mellin transforms and series expansions, the crack surface conditions are expressed analytically in the form of a set of simultaneous standard singular integral equations, which can be solved numerically by the Lobatto–Chebyshev method. The Normalized Intensity Factors (NIFs) around crack tips are obtained for the elastic and electric field in explicit forms. Dependence of the NIFs on the crack length and crack interval, as well as the wedge angle, is discussed in detail. Crack interaction is graphically demonstrated and analyzed. Results show that extension of one crack length generally enhances the NIFs for both tips of the other crack. Crack interval significantly affects the NIFs of the inner crack tips of the collinear cracks. The formulation and results in this paper include, as special cases, some wedge problems presented in the literature. These analyses are expected to provide some guidance for the design of piezoelectric composite wedges.