Journal of Intelligent Material Systems and Structures

A new experimental technique for accelerated fatigue testing has recently been developed (Du, T.B., Liu, M., Seghi, S., Hsia, K.J., Economy, J. and Shang, J.K. 2001. “Piezoelectric Actuation of Crack Growth along Polymer-Metal Interfaces in Adhesive Bonds,’’ Journal of Material Research, 16(10):2885-2892). Using a piezoelectric actuator, cyclic loading can be applied at frequencies up to 20 kHz, several orders of magnitude higher than that achieved by a conventional mechanical cyclic loading technique. Moreover, the new technique using piezoelectric actuators directly addresses the debonding problem in piezoelectric multilayered smart structures. However, the threshold energy release rate for interfacial crack propagation, evaluated based on plane strain and linear piezoelectricity assumptions in (Du, T.B. 2001. “Durability of Polymer/Metal Interfaces under Cyclic Loading,” PhD Thesis, University of Illinois at Urbana-Champaign, Urbana, IL, May), seems to be almost an order of magnitude lower than that measured by the conventional mechanical cyclic loading. In this article, we investigate the origin of such discrepancies, and find that the driving force provided by piezoelectric actuator is intrinsically three-dimensional in nature. To account for this effect, we develop both a plane strain model and a modified plane strain analytical model that takes into account the effects in the third dimension to evaluate the energy release rate. The results show that the plane strain solution underestimates the driving force. We also study the effect of nonlinear piezoelectricity on crack driving forces by performing detailed finite element simulations. The results show that the nonlinear piezoelectric effect is another important factor that contributes to the discrepancy between the results from the piezoelectric loading and that from the conventional mechanical loading.

It is interesting to know how thermal effects influence the fracture behaviors of piezoelectric materials. Experimental observations have found that the fracture toughness of piezoelectric solids under electric loading may be significantly different from that under mechanical loading, and that a pronounced rise of temperature may be caused by either mechanical or electrical loading. There are many factors that change the temperature distribution and energy dissipation at a crack tip, for instance, concentration of electroelastic fields, coupling of mechanical and electrical fields, and nonlinear behaviors of materials. In the present paper, two kinds of thermal effects are investigated under electric saturation and electromechanical impact loading. The temperature fields are derived under the assumption of decoupling between thermal and electromechanical fields.

This paper develops a theoretical electroelastic fracture mechanics for piezoelectric layered composites. A piezoelectric layer bonded between two elastic or piezoelectric materials containing a crack normal to the interfaces is considered. The ends of the crack are situated at equal distances away from the interfaces. Both analytical and simulation methods are formulated to determine the effects of applied electric field and polarization switching on the fracture mechanics parameters such as stress intensity factor, energy release rate, and energy density factor. The results for the exact (permeable) and approximate (impermeable) boundary conditions are presented in graphical form.

Mechanical depolarization is an important cause of failure in piezoelectric actuators and sensors. In this paper, the effects of one-dimensional lateral pressure on the linear and nonlinear behavior of PZT ceramics were experimentally studied. The experimental results show that the lateral pressure can change the crystal symmetry of the ceramic from 1mm to mm2. A domain-switching model dividing each 180 switching to two successive 90 switching is proposed to explain the experimental results. Finally, based on the experimental results, a simple design is proposed to prevent piezoelectric sensors from mechanical depolarization. Meanwhile, the simple design is apt to increase the hydrostatic piezoelectric constant of the piezoelectric marine sensors, thus enhancing their sensitivity.

In this article, the model and the algorithm developed in our previous work are used to investigate the thickness effect and the length effect of the piezoelectric patch and the influence of the substrate material properties on the responses of the piezoelectric-elastic structure. For an actuator-substrate structure, a thicker piezoelectric patch may be preferable in decreasing the stress concentration. Longer the piezoelectric patch, lower the interfacial normal stress. The interfacial stresses will go up with the increase of the stiffness of the host materials. For a sensor system, the strain transfer from substrate to sensor will decrease with the increase of the thickness of the piezoelectric sensor patch. The output voltage of the piezoelectric sensor rises with the increase of both the thickness and the length. A harder host material can make higher output voltage under the same strain.

All the existing works on the mechanics and physics of magnetoelectroelastic solids are based on the only available set of constitutive equations in which the stress, electric displacement, and magnetic induction are expressed in terms of the strain, electric field, and magnetic field. In this paper, we provide other forms of the constitutive equations and the thermodynamic potential corresponding to each form. The mathematical properties of the thermodynamic potentials and the relations between the material constants are discussed.

A multiscale modeling scheme of electromechanical coupling of ferroelectric ceramic composites is proposed, which is effective for quantitatively analyzing the relationships among variables of micro/meso/macroscopic and structural (sensor or actuator) scales. This is done by developing effective constitutive equations of material at an intermediate scale, which can be used to connect the mechanical and electric variables between the smaller and larger scales. The methodology is exemplified through investigating the behavior of ferroelectric ceramics of PLZT. The key for connection of variables at different scales is through the remnant polarization and strain at the mesocell. This study deals with the connection of macroscopic variables of ceramics with those of polymer layers for developing constitutive equations for the layered composites of sensors. The numerical results agree with the well-known nonlinear butterfly curve of strain versus electrical field. The influence of volume fraction of the ceramic layers and the relative Young’s modulus on the behavior of the composites are discussed here.

Two-dimensional equations for multilayered shells of piezoelectric semiconductors are derived. The equations are used to analyze the propagation of torsional waves in a single-layered circular cylindrical shell of a piezoelectric semiconductor, and in a multilayered shell of nonconducting piezoelectrics and nonpiezoelectric semiconductors. Dispersion and dissipation due to semiconduction as well as wave amplification by a biasing DC electric field are discussed.

Surface acoustic waves (Rayleigh waves) are analyzed for semi-infinite anisotropic solids only for essential propagation characteristics like the velocity and decaying parameters, which are important in engineering applications. The limitations of these results are obvious because devices are usually built on a finite piezoelectric substrate with propagation properties different from the analytical model with which the parameters are derived. For an accurate analysis of the dominant mode of surface acoustic wave propagation in plate-like finite piezoelectric solids, a two-dimensional theory has been developed based on the exponential expansion of displacements and electrical potential in the thickness direction, effectively creating a theory similar to popular plate theories of Mindlin, Lee, and others.

Thermoelectroelastic analysis of piezoelectric circular cylinders under extension, torsion, bending, pressuring, shearing, and temperature changes is presented. Referring to the cylindrical coordinates, the material is radially inhomogeneous and cylindrically anisotropic. Exact solutions are obtained for generalized plane problems of the piezoelastic cylinder with power-law radial inhomogeneity. For arbitrary radial inhomogeneity, two viable solution schemes are suggested. The analysis is useful for studying the responses of cylindrically anisotropic bodies of functionally graded materials subjected to thermoelectromechanical loading.

This paper presents an exact analysis of a functionally graded piezothermo-electric rectangular plate that is simply supported, electrically grounded and isothermal on its four lateral edges. The governing equations are established for an orthotropic functionally graded piezothermoelectric plate under an assumption that the mechanical, electrical, and thermal properties of the material have the same exponential dependence on the thickness-coordinate. An exact three-dimensional general solution in the form of double Fourier series is derived for arbitrary distributions of combined mechanical, electrical, and thermal loadings at the top and bottom surfaces of the plate. Numerical results are presented for three special cases of uniformly distributed loads at the top and bottom surfaces of the plate, and the effect of truncation of the series on the accuracy of the solution is discussed.

The chain formation process of ferromagnetic particles under an applied magnetic field is simulated. Three main forces - magnetic force, viscous force, and repelling force, are considered. A model to simulate the motion of particles is proposed based on the analysis of the dynamics of the particles, and a corresponding numerical approach is developed. The formation of particle chains in magnetorheological (MR) fluids under an applied magnetic field is simulated, and the result agrees well with the experimental observation. The developed method is significant for the analysis of the overall behavior of MR fluids and their microscopic mechanisms as well as the effects of the influencing factors, which may be helpful for the design of new MR fluids.

The hysteresis phenomena of ferroelectric-ferroelastic materials in polarization procedure are investigated. Some assumptions are presented based on published experimental data. The electrical yielding criterion, mechanical yielding criterion, and isotropic hardening model are established. The flow theory in incremental forms in polarization procedure is presented. The nonlinear constitutive law for electrical-mechanical coupling is proposed phenomenologically. Finally, the nonlinear constitutive law expressed in the form of matrices and vectors, which is immediately associated with finite element analysis, is formulated. The finite element calculation and computational results of example problems will be given later.

The current understanding on fracture behaviors of ferroelectric/piezoelectric materials are reviewed in this article. Two main obstacles in understanding such fracture behaviors are discussed: (i) the selection of electric boundary condition on crack faces and (ii) the near-tip domain switching or nonlinear zone. Some previous controversial results in theoretical studies and experimental observations are also discussed here; particularly, the inherent load-dependence of the variable tendencies of the crack tip energy release rate against the applied electric field, on the applied mechanical loading level found recently, which reveals that the applied mechanical loading does significantly influence the role played by the applied electric field in piezoelectric fracture.