Fracture parameters of a penny-shaped crack at the interface of a piezoelectric bi-material system

Abstract

A penny-shaped crack at the interface of a piezoelectric bi-material system is considered. Analytical general solutions based on Hankel integral transforms are used to formulate the mixed-boundary value problem corresponding to an interfacial crack and the problem is reduced to a system of singular integral equations. The integral equations are further reduced to two systems of algebraic equations with the aid of Jacobi polynomials and Chebyshev polynomials. Thereafter, the exact expressions for the stress intensity factors and the electric displacement intensity factor at the tip of a crack are obtained. Selected numerical results are presented for various bi-material systems to portray the significant features of crack tip fracture parameters and their dependence on material properties, poling orientation and electric loading.

Analysis of a Griffith crack at the interface of two piezoelectric materials under anti-plane loading

“…So, many studies to grasp and describe the fracture behavior of piezoelectric materials under electro-mechanical loading have been done. In most studies, the research orientation carried in general is on the mode of cracking; mode I as in [19,21,38], mode II as in [12] (for a composite laminates material), mode III as in [3][4][5]17,30,36], mixed mode as in [29], or on the model; Griffith model as in [14,21,42], Dugdale-Barenblatt model as in [8,15], or in the position of the crack in the structure; infinite plane as in [19,25], semi-infinite plane as in [8] (for a non-piezoelectric material) or still on the composition of the structure; only one material as in [25], bi-material as in [22,39].…”

“…To et al [40] examined the propagation of a mode III interfacial crack along a conductive interface between two piezoelectric materials. Tian and Rajapakse [39] analyzed the axisymmetric problem of an interfacial penny-shaped crack in a piezoelectric bi-material system. The weak-discontinuous interface fracture in a non-homogeneous piezoelectric bi-material structure is considered in [20].…”

The transient analysis of a conducting crack in magneto-electro-elastic half-space under anti-plane mechanical and in-plane electric and magnetic impacts

“…Ueda [1], Nishioka et al [2], Jin et al [3], Li and Tang [4], He [5], Ricci et al [6], Chen and Worswick [7], Wang and Mai [8] and Li [9] have analyzed fracture problems, which are limited to insulating crack. Several earlier works on magnetoelectro-elastic and piezo-electric solids with cracks: Tian and Rajapakse [10,11] are worth mentioning. In the first paper, the solutions for plane static problem of impermeable cracks have been formulated in terms of set of singular integral equations using Stroh formalism [12] and which are solved by a numerical integration technique.…”

On contact zone models for an electrically limited permeable interface crack in a piezoelectric bimaterial

“…For a bimaterial the situation is more complicated and the calculation of fracture parameters is far from obvious. Main contributions to the investigation of cracks between two dissimilar piezoelectric materials has been made by the works of Suo et al (1992), Beom and Atluri (1996), Gao and Wang (2000), Ma and Chen (2001), Beom (2003), Scherzer and Kuna (2004), Tian and Rajapakse (2006) and others. However, it should be noted that the above cited studies were restricted to the idealized impermeable or permeable interface crack assumptions.…”