Jin H. Huang

The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions

A unified method based on the inclusion formulation is proposed to determine the magnetic, electric, and elastic fields in a composite with piezoelectric and piezomagnetic phases. The composite reinforcements are treated as ellipsoidal inclusions that enable the reinforcement geometries ranging from thin flakes to continuous fibers. Utilizing the proposed method, the magneto-electro-elastic tensors analogous to Eshelby tensors for elastic ellipsoidal inclusions are obtained. With these tensors, the magnetic, electric, and elastic fields around the inclusion as well as concentration factors are determined. Furthermore, based upon the Mori–Tanaka mean-field theory [Acta Metall. 21, 571 (1973)] to account for the interaction between inclusions and matrix, the effective magneto-electro-elastic constants (elastic moduli, piezoelectric coefficients, dielectric constants, piezomagnetic coefficients, magnetoelectric, and magnetic permeability) of the composites are expressed explicitly in terms of phase propertie...

Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases

Abstract This paper presents an analytical method to investigate the magnetoelectric coupling effect that is a new product property of piezoelectric–piezomagnetic intelligent composites since it is not present in each constituent. Based on the eigenstrain formulation and the Mori–Tanaka theory, the magneto–electro–elastic Eshelby tensors and the effective material properties of the composite are obtained explicitly. Particularly when both the matrix and the inclusions of the composite are transversely isotropic with different magneto–electro–elastic moduli, and shapes of inclusions are of elliptical cylinder, circular cylinder, disk, and ribbon, simple and closed-form solutions for the magnetoelectric coupling coefficients are acquired. The solutions are a function of the shape of inclusion, phase properties, and volume fraction of inclusions. Moreover, the derived simple expressions also show that the magnetoelectric coupling coefficients vanish as the volume fraction of inclusions tends to zero or one. This verifies that the magnetoelectric coupling coefficients are absent in each phase of the composite.

Detection of cracks using neural networks and computational mechanics

An inverse analysis method is proposed to simulate the A-scan ultrasonic nondestructive testing by means of back-propagation neural networks and computational mechanics. Both direct problem and inverse problem are considered in this study. In the direct problem, the frequency responses of a cracked medium subjected to an impact loading are calculated by the computational mechanics combining the finite element method with the boundary integral equation. The transient responses are obtained using fast Fourier transform. In the inverse problem, the back-propagation neural networks are trained by the characteristic parameters extracted from the various surface responses obtained from the direct problem. These surface responses carry a great deal of information about the structure of the medium with or without cracks. The trained neural networks are then utilized for the classification and identification of the crack in the medium to determine the type, location, and length of the crack.

Magneto-electro-elastic Eshelby tensors for a piezoelectric-piezomagnetic composite reinforced by ellipsoidal inclusions

The magneto-electro-elastic Eshelby tensors that represent the stress, electric displacement, and magnetic induction in an inclusion resulting from the constraint of the surrounding matrix of piezomagnetic-piezoelectric composites are presented. The tensors provide the basis for analysis of the magneto-electro-elastic response of the composites and have numerous applications such as to the study of defects, overall properties of multiphase composites, and fracture mechanics, etc. For a three-dimensional transversely isotropic piezoelectric/piezomagnetic composite containing spheriodal inclusions, the number of nonzero Eshelby tensors is 41 while among them only 17 are independent. These independent tensors can be divided into three categories. The first category consists of those tensors related to the elastic response, the second involves those related to the piezomagnetic response, while the third includes elastic and magnetic interactive terms. Moreover, the magneto-electro-elastic Eshelby tensors are ...

The optimized fiber volume fraction for magnetoelectric coupling effect in piezoelectric–piezomagnetic continuous fiber reinforced composites

Abstract Explicit formulae are presented to assess the optimized fiber volume fraction for maximum magnetoelectric coupling effect exhibiting in the composite with piezomagnetic matrix reinforced by piezoelectric continuous fibers. The formulae consist of the analytical expressions for the effective properties of the composite and the magneto-electro-elastic Eshelby tensors. With these expressions, the closed-form solution for the magnetoelectric coupling effect, which is a new property existing in the piezoelectric–piezomagnetic composite even though neither of the individual phases exhibits such a property, is acquired. Furthermore, by taking the derivative of the close form for magnetoelectric coupling effect with respect to the fiber volume fraction as zero yields the optimized volume fraction of fibers analytically. The optimized fiber volume fraction shows that it is a function of the elastic properties of constituents, but not a function of the magnetic and electric properties.

Analysis of hybrid multilayered piezoelectric plates

A first-order shear deformation theory is presented for studying the fully coupled response characteristics of hybrid composite and piezoelectric plates. The plates consist of a combination of fiber-reinforced composite laminates and piezoelectric layers and the response quantities of the plates are coupled by the mechanical field and the electric field. The theory, based on the three-dimensional linear piezoelectricity, assumes that the fundamental unknowns such as the displacement components and the electric potential can be expanded through the plate thickness coordinate. The governing equations are obtained in terms of the displacement and electric potential coefficients. Numerical studies of single piezoelectric layer plate and a nine-layered hybrid plate show that the proposed method is accurate to predict the response quantities for both mechanical and electric loading cases.

Micromechanics determination of the effective properties of piezoelectric composites containing spatially oriented short fibers

Abstract This article presents an analytical unified method for determining the effective electroelastic properties of piezoelectric composites containing spatially oriented short fibers, which are treated as spheroidal inclusions. Both the matrix and inclusions are assumed to be linearly piezoelastic and transversely isotropic. The electroelastic tensors analogous to Eshelby tensors for elastic ellipsoidal inclusions have been obtained and also evaluated numerically for finite fiber aspect ratios. Utilizing these tensors and applying the Mori-Tanaka mean field theory to account for the interaction between inclusions and matrix, the effective electroelastic properties of the composites are expressed analytically in terms of phase properties, orientation angles, volume fraction and inhomogeneity shape. It is indicated that the proposed methods yield identical results when either a traction-electric displacement or an elastic displacement-electric field is prescribed on the compsite boundary. Finally, numerical examples are given for a BaTiO 3 PZT -5 H composite. The results show that the longitudinal and in-plane shear moduli increase with fiber length, while the other moduli, piezoelectric and dielectric constants decrease.

Overview no. 126 Stress relaxation by plastic flow, interfacial sliding and diffusion in an inclusion bearing material

Stress relaxation, a decrease of energy by plastic flow, interfacial sliding, local diffusion and bulk diffusion, has been studied for an inclusion bearing material. The complete relaxed state is found by minimizing the total energy, using a variational method. A relaxation process or the combination of two processes imposes a subsidiary condition that matches the physics of the process. The complete relaxation occurs when total stresses are uniformly hydrostatic in a plastic region. In interface-related phenomena, the complete relaxed state is as follows: tangential traction vanishes for interfacial sliding; normal traction is constant for local diffusion; and total traction is constant and normal to the interface for the combination of interfacial sliding and diffusion. When bulk diffusion is allowed, normal traction vanishes. If sliding is further allowed, an inclusion becomes stress free. By examining subsidiary conditions, the effectiveness of two processes can be compared.

A fracture criterion of a penny-shaped crack in transversely isotropic piezoelectric media

Abstract By utilizing the eigenstrain formulation and Cauchys residue theorem, a unified explicit expression for the electroelastic fields inside a flat ellipsoidal crack embedded in an infinite piezoelectric solid subjected to electromechanical loads is presented. In particular, an explicit expression is obtained for a penny-shaped crack in a transversely isotropic piezoelectric medium. Three loading cases, a simple tension, a pure shear, and an electric displacement, have been considered to examine the behavior of penny-shaped cracking. The results show that the applied shear stress does not couple with the electric displacement, unlike the simple tension case. Furthermore, the change of potential energy due to the presence of the crack is evaluated. With this result and based on the Griffith theory, the fracture stresses and critical electric displacement are presented in closed forms. Explicit expressions for stress and electric displacement intensity factors are also given. It is verified that the resulting fracture stresses and stress intensity factors can be reduced to those for uncoupled linear elastic fracture mechanics when piezoelectric coupling is absent and the material is isotropic.

Kinetics of stress relaxation caused by the combination of interfacial sliding and diffusion: Two-dimensional analysis

Abstract The kinetics of stress relaxation due to the combined action of sliding and diffusion on the matrix–inclusion interface has been examined in a material containing inclusions. The interaction between the inclusions is taken into account by the average field method. The sliding rate is connected to a tangential traction, and the normal displacement jump rate due to the diffusion is written in terms of the distribution of a normal traction. These tractions are also determined by the amount of sliding and diffusion. The strain due to the relaxation consists of two parts, each having the form of a first-order reaction. The relaxation strength and time of both terms depend on the interfacial viscosity and diffusivity, i.e. the sliding and diffusion are coupled. This is because the sliding induces the normal traction and the diffusion the tangential traction. The Coble creep is examined as an extreme case of the inclusion volume fraction approaching unity. The role of boundary sliding is emphasized in the Coble creep.