B.L. Wang

Crack tip field in piezoelectric/piezomagnetic media

This paper considers the magnetoelectroelastic problem of a crack in a medium possessing coupled piezoelectric, piezomagnetic and magnetoelectric effects. Based on the extended Stroh formalism, the general two-dimensional solutions to the magnetoelectroelastic problem are obtained, involving five analytic functions of different variables. The magnetoelectroelastic field around the crack tip is given. It contains five modes of square root singularities. Expressions of the stresses, electric displacements and magnetic inductions in the vicinity of the crack tip are derived and the field intensity factors are provided. The path-independent conservative integral is derived. The energy release rate is written in terms of those field intensity factors. The explicit algebraic results are given for a special case of an anti-plane crack in a magnetoelectroelastic medium.

Thermally induced fracture of a smart functionally graded composite structure

Discussed is the fracture behavior of a cracked smart actuator on a substrate under thermal load. The actuator is made of piezoelectric material with functionally graded material (FGM) properties. Integral transform method is used to reduce the problem to the solution of a set of singular integral equations and is solved numerically. This paper is completed by including graphical plots of the thermal flow, stress and electric displacement intensity factors around the crack for different crack positions and material gradients. Directions of crack initiation are also predicted by using the energy density criterion.

Impermeable Crack and Permeable Crack Assumptions, Which One is More Realistic?

This paper investigates the applicability and effect of the crack-free electrical boundary conditions in piezoelectric fracture. By treating flaws in a medium as notches with a finite width, the results from different electrical boundary condition assumptions on the crack faces are compared. It is found that the electrically impermeable boundary is a reasonable one for engineering problems. Unless the flaw interior is filled with conductive media, the permeable crack assumption may not be directly applied to the fracture of piezoelectric materials in engineering applications.

A mode III crack in functionally graded piezoelectric materials

Abstract This paper considers the mode III crack problem in functionally graded piezoelectric materials. The mechanical and the electrical properties of the medium are considered for a class of functional forms for which the equilibrium equations have an analytical solution. The problem is solved by means of singular integral equation technique. Both a single crack and a series of collinear cracks are investigated. The results are plotted to show the effect of the material inhomogeneity on the stress and the electric displacement intensity factors.

On the electrical boundary conditions on the crack surfaces in piezoelectric ceramics

Abstract This paper investigates a cracked piezoelectric ceramic under remote electro-mechanical loads. The ideal crack boundary conditions for electrically impermeable and permeable crack assumptions, and the deformed crack with a yet-to-be-determined crack shape are considered. The last is referred to as the “natural boundary condition (NBC)”. Closed-form solutions to the crack-tip field intensity factors are obtained. The analysis shows that traditional approaches to the electric boundary conditions on the crack faces, that is, either the impermeable crack assumption or the permeable crack assumption, produce significantly different results for the crack-tip quantities such as electric displacement intensity factor, energy release rate and crack opening displacement. There are also considerable differences between the results obtained from traditional impermeable and permeable crack analyses and those obtained from the proposed NBC. The difference increases with applied electric loads.

Cracks problem for non-homogeneous composite material subjected to dynamic loading

Abstract In this paper, we present a method to analyse the dynamic and steady response of non-homogeneous composite materials. Differing from the existing works reported in literature, the present method can be used for arbitrarily varying material properties through thickness direction and the crack number can be larger than one. It is assumed that the composite material is orthotropic and all the material properties depend only on the coordinates y (along the thickness direction). The material non-homogeneity is simulated by dividing the plate into a number of layers, each layer is assigned slightly different material properties. The method is based upon the Fourier and Laplace transforms to reduce the boundary value problem to a system of generalized singularity integral equations in the Laplace transform domain. The singular integral equations for the problem are derived and numerically solved by weighted residual value methods. By utilized numerical Laplace inversion the time-dependent full field solutions are obtained. As the numerical illustrates, three different cracked specimens, a functionally graded material, a metal-ceramic joint with functionally graded interlayer, and a metal substrate/functionally graded film structure are presented for various material non-homogeneity parameters and/or functionally graded layer thickness. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of composite materials with properties varying in the thickness direction.

Vibrational modes of Timoshenko beams at small scales

This letter presents a theoretical treatment of Timoshenko [S. Timoshenko, Philos. Mag. 41, 744 (1921)] beams, in which the influences of shear deformation, rotary inertia, and scale coefficient are taken into account. Based on the nonlocal elasticity theory, coupled equations for transverse deflection and rotation of cross section are derived. Free vibration of several typical beams is analyzed. Explicit expressions for modal shapes of vibration are presented. Natural frequencies are evaluated for free vibration of simply supported beams, clamped beams, cantilever beams, and clamped-hinged beams. The effects of the nonlocal parameter on natural frequencies and modal shapes are discussed in detail.

DESIGN OF A SMART FUNCTIONALLY GRADED THERMOPIEZOELECTRIC COMPOSITE STRUCTURE

In this paper, a smart functionally graded piezoelectric structure is analyzed. The smart structure consists of three layers: one layer of metal, one layer of piezoelectric material (PZT) used as an actuator, and a graded metal/PZT layer between the metal layer and the PZT layer. A finite element code is developed in the programming environment MATLAB and FORTRAN, with each finite element having varied material properties through space coordinates. The results reveal that both the stress discontinuity and thermal deformation of the structure can be controlled. By introducing a functionally graded layer between the PZT actuator layer and the metal beam layer, both stress discontinuity and the edge local stresses can be essentially reduced. The proposed method is expected to be useful for functionally graded thermopiezoelectric composite structures under operating environments where the thermal and piezoelectic effects are important.

Fracture Mechanics Analysis Model for Functionally Graded Materials with Arbitrarily Distributed Properties

Functionally Graded Materials (FGMs) have been developed as super-resistant materials for propulsion systems and airframe of space-planes in order to decrease thermal stresses and to increase the effect of protection from heat. It has been experimentally observed that surface cracking in FGMs is the most common failure mode of a metal-ceramic FGM when it is subjected to a thermal shock. Therefore, it is very important to consider the thermally induced fracture behaviors of FGMs. In this paper, a functionally graded material strip containing an embedded or a surface crack perpendicular to its boundaries is considered. The graded region is treated as a large number of single layers, with each layer being homogeneous material. The problem is reduced to an integral equation and is solved numerically. Unlike most of the existing researches, which considered only certain assumed material distributions, the method developed in this paper can be used to investigate functionally graded materials with arbitrarily varied material properties.

The electromechanical coupling behavior of piezoelectric nanowires: Surface and small-scale effects

The influence of the surface and small-scale effects on electromechanical coupling behavior of a piezoelectric nanowire is studied by using the beam bending model. An explicit formula for the electromechanical coupling (EMC) coefficient of the piezoelectric nanowire is obtained based on the nonlocal electroelasticity theory. It is found that the inclusion of the nonlocal effect in the model produces a significant difference from the past model which ignores the nonlocal effect in the prediction of the EMC coefficient and the electric field in the nanowire, confirming the significance of including the surface and small-scale effects in the analysis of piezoelectric nanowires. In particular, the influence of surface effects on the electric field is dominant for smaller nonlocal parameters. If the nanowire is subjected to an applied concentrated load and without surface effect, the nonlocal effect has no effect on its bending and electric field. This study might be helpful for understanding the size-dependent electromechanical properties of piezoelectric nanowires and design of piezoelectric-beam–based nanogenerators.