Dynamic performance for piezoelectric bi-materials with an interfacial crack near an eccentric elliptical hole under anti-plane shearing

Abstract

The purpose of this paper is to evaluate the stress concentration at the tip of a permeable interfacial crack near an eccentric elliptical hole in piezoelectric bi-materials under anti-plane shearing. Fracture analysis is performed by Green’s function method and the conformal mapping method, which are used to solve the boundary conditions problem. The mechanical model of the interfacial crack is constructed by interface-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack-tips can be derived. The validity of the present method is verified by comparing with a crack emerging from the edge of a circular hole as a reference. Numerical cases reveal parametric dependence of DSIFs on the geometry of eccentric elliptical holes and interfacial cracks, the characteristics of the incident wave, the equivalent piezoelectric elastic modulus and piezoelectric parameters. The results illustrate that the eccentric distance has a great effect on the stress concentration at the crack tip, which may be harmful to the normal service of piezoelectric devices and materials. In addition, the method proposed in this paper can also deal with non-eccentric problems and has wider applicability.

Magnetoacoustic Wave Scattering and Dynamic Stress Concentration around the Elliptical Opening in Exponential-Gradient Piezomagnetic Materials

“…In addition, the material parameters vary exponentially along the polar axis. The constitutive equations of the exponential-gradient piezomagnetic materials can be written as [5]: 1 1…”

“…where τ rz and τ θz are the shear stress components, ρ is the density, w is the displacement in the z-direction, and B r and B θ are the magnetic displacement components. The constitutive equations of the exponential-gradient piezomagnetic materials can be written as [5]:…”

“…It is assumed that all the material properties of the exponential-gradient piezomagnetic materials have the same exponential function distribution along the polar axis, and the material properties are given as [9]: c 44 = c 440 e 2βr cos θ , ρ = ρ 0 e 2βr cos θ , h 15 = h 150 e 2βr cos θ , µ 11 = µ 110 e 2βr cos θ (5) where c 440 is the initial Young's modulus, ρ 0 is the initial density, h 150 and µ 110 are the initial piezomagnetic constant and the initial magnetic permeability, respectively, and β is the inhomogeneity coefficient of the exponential distribution along the polar axis. Substituting Equation (2) into Equation ( 1), the expressions are given as: where…”

“…In recent years, in order to study the structural strength and stability of materials, many scholars have carried out a lot of experimental research and theoretical analysis on the propagation of coupled elastic waves in functional materials, and provided theoretical results at the same time [3][4][5][6][7][8][9]. Hei et al [3], based on complex function theory, investigated an analytical solution for the dynamic stress concentration due to an arbitrary cylindrical cavity in an infinite inhomogeneous medium.…”

“…They calculated the dynamic stress concentration factor around the edge of a semicylindrical salient, and discussed the influences of incident wave number, incident angle, effect of interface and different combinations of material parameters, etc., on the dynamic stress concentration factor. An et al [5] evaluated the stress concentration at the tip of a permeable interfacial crack near an eccentric elliptical hole in piezoelectric bimaterials under antiplane shearing. Green's function method and the conformal mapping method, which are used to solve the boundary conditions problem, are used to analyze fracture.…”