During the past several years, the Materials Science Division and the Mechanical and Environmental Sciences Division of the Army Research Office have been supporting projects focusing on basic resaserch in the area of smart materials and structures. The major emphasis of the ARO Structures and Dynamics Program has been on the theoretical, computational, and experimental analysis of smart structures and structural dynamics, damping, active control, and health monitoring as applied to rotor craft, electromagnetic antenna structures, missiles, land vehicles, and weapon systems. The research projects supported by the program have been primarily directed towards improving the ability to predict, control, and optimize the dynamic response of complex, multi-body deformable structures. The projects in the field of smart materials and structures have included multi-disciplinary research conducted by teams of several faculty members as well as research performed by individual investigators.

An embedded active fiber composite tape was investigated for use as a sensor for structural health monitoring. The material has unidirectional piezoceramic fibers with interdigital electrodes on the top and bottom surfaces and is poled in the fiber direction. A long active fiber composite tape with segmented electrodes was modeled as a sensor to measure longitudinal stress waves in a uniform cantilever bar. Only plane longitudinal standing and traveling waves in the bar are modeled. The sensor was connected to an electrical tuning circuit to filter out undesirable noise due to ambient vibrations. The elastic response of the bar was compute in closed form at small time steps, and the coupled piezoceramic constitutive equations and the electrical circuit equations were solved by numerical integration using the Newmark-Beta method. Strain vibration and wave propagation responses were computed in the simulations. The simulations indicate that such a sensor will be capable of detecting damage to the bar from the change sin the wave propagation responses. Further, the sensor has adequate sensitivity to detect fiber breaks in the composite bar. An active fiber composite patch was also tested to measure vibration and simulated acoustic emissions.

This paper presents the governing equations for small deformation electroelastic continua with electric conduction, consistently derived from the general continuum physics theory for electromagnetics and thermomechanics of deformable continua. The resulting small deformation equations are exactly the classical piezoelectric equations with additional electric body force and electric conduction terms. Furthermore, the paper presents weak forms of the small deformation equations and a corresponding finite element formulation suitable for nonlinear material constitutive equations. The response of highly electrically insulating devices can be dominated by the cumulative effects of weak electric conduction currents. Much of the engineering analysis literature is concerned with perfect electrically insulating deformable bodies, but the perfect insulator approximation is only accurate provided the time scales of loading are sufficiently fast compared to the time scales of electric conduction currents. Device designs based on perfect insulator analysis are likely to fail when subjected to sufficiently slow time scale loadings. A finite element example is presented for the transient response of a nonlinear repolarizable piezoelectric material embedded in an epoxy matrix, subject to an electric voltage step loading.

This article presents an overview of the necessary conditions for the formation of Shape Memory Alloys (SMAs) and how these must overlap with the occurrence of ferromagnetism so that FerroMagnetic Shape Memory Alloys (MSMAs) may be formed. The electronic, elastic and geometric conditions permit an understanding of the occurrence of Cu and Fe based SMAs as well as NiMnGa Heusler MSMAs except that the naively determined critical electron concentration for the latter, 7.3, disagrees with the values of 1.5 and 8.6 accepted for the Hume-Rothery Phases and certain Fe- based systems.

One of the primary factors limiting the performance of high speed and precision computer controlled machinery such as robotic systems is the dynamic response limitation of their actuation mechanisms. This is particularly the case when revolute joints are used in the construction of a machine, thereby resulting in systems with highly nonlinear dynamics. In such systems, even if the joint motion trajectories were synthesized with low harmonic contents, the actuating torques required for accurate tracking of the synthesized motions would contain high harmonic components. The higher harmonic components are generated to the nonlinearity in the dynamics and kinematics of the system. As the operating sped of such machines is increased, the high harmonic component of the required actuating torques become more significant and at some point move beyond the dynamic response limitations of the main drives. The performance of the system would therefore start to degrade and vibration and control begins to become problematic. In this paper, a method is presented for minimizing the high harmonic components of the required actuating torques using smart materials based actuators. The effective dynamic response of the system drives is thereby enhanced. In this paper, the development of the general methodology is presented. The method is then applied to a plane 2R robot manipulator. The effectiveness of the proposed approach in reducing the higher harmonic components of the primary drives and thereby enhancing the performance of the system is illustrated by computer simulation.

This paper is concerned with design, manufacturing and performance test of lightweight THUNDER using a top fiber composite layer with near-zero CTE, a PZT ceramic wafer and a bottom glass/epoxy layer with high CTE. The main point of this design is to replace the heavy metal layers of THUNDER by the lightweight fiber reinforced plastic layers without losing capabilities to generate high force and displacement. It is possible to save weight up to about 30 percent if we replace the metallic backing materials by the light fiber composite layer. We can also have design flexibility by selecting the fiber direction and the size of prepreg layers. In addition to the lightweight advantage and design flexibility, the proposed device can be manufactured without adhesive layers when we use epoxy resin prepreg system. Glass/epoxy prepregs, a ceramic wafer with electrode surfaces, and a graphite/epoxy prepreg were simply stacked and cured at an elevated temperature by following autoclave bagging process. It was found that the manufactured composite laminate device had a sufficient curvature after detaching form a flat mold. From experimental actuation tests, it was observed that the developed actuator could generate larger actuation displacement than THUNDER.

Active long-fiber composites based on a hollow fiber topology have advantages over solid fiber composites in that they require lower voltages for activation and are not limited to electrically non-conductive matrix materials. One critical issue for hollow fiber composites is the fiber aspect ratio. To investigate this at the individual fiber level, analytical and finite element models which include electric field variations, were developed to determine the 'effective d₃₁' of a hollow fiber. By using the effective fiber properties in this way, it was possible to derive a single-row lamina strain/electric field model form classical composite theory. The models were validated with a series of deflection/voltage experiments conducted utilizing hollow fibers fabricated y microfabrication by coextrusion (MFCX) techniques. To determine the feasibility of MFCX hollow fiber composites, the models and experimental results were employed to study the effect of the fiber aspect ratio on a variety of fiber/composite design issues: fiber/lamina performance, fiber strength, matrix material, and electric field effects.

The field induced strain has been measured for a broad variety of piezoelectric and electrostrictive actuator materials. These measurements have been made under AC drive conditions with variations in DC bias, peak to peak voltage, and prestress. Data for three types of PMN-PT electrostrictors, hard and soft piezoelectric ceramics, and PZN-PT single crystal have been collected. For smart structures applications fine grain Type II ceramic and PZN- PT single crystals were found to have the best combination of moderate to high strain, low to moderate hysteresis, and resistance to stress depoling. Electrostrictive ceramics used for high frequency transducers were found to exhibit some stress induced domain reorientation effects that depended on drive conditions and operating temperature. These effects became more pronounced for electrostrictors with high lead titanate content. Epoxy bonded stacks have been constructed form some of the materials to determine the merits of materials properties for actuator performance. This work has shown that fine grain Type II ceramics have many advantages for high authority stack actuators including high strain energy density and lifetimes > 10⁹ cycles at 100 percent rated peak-to-peak voltage.

The dielectric loss factor tan (delta) is a critical parameter in transducer design and performance prediction, as it is directly related to the electrical energy lost to Joule heating. A method for calculating the equivalent loss factor of 'quasi linear' materials from a measured major polarization vs. field loop by extending the standard definition of tan (delta) for a linear lossy capacitor to nonlinear materials is presented. To extract effective loss tangents for minor loops from the major loops, an area correction algorithm was implemented. This algorithm proves to be nearly exact for all bias and drive levels in the case of an ideal linear capacitor. In most cases, the effective tan (delta) calculated from a major loop agrees fairly well with that calculated from a directly measured minor loop. Finally, the behavior of the loss tangent as a function of the dc bias field, ac drive field, prestress level and temperature will be examined. It shall be shown that, in general, the effective loss factor of lead magnesium niobate-lead titanate decreases with increasing temperature, consistent with its transition from a piezoelectric to an electrostrictive material, but increases with prestress. At a fixed temperature and prestress level, the loss factor increases as the bias or drive levels decrease. However, at certain bias levels, the loss tangent is practically the same, regardless of the drive level.

Piezoelectric transducers are often used under compressive stress in smart structure and other applications and it is therefore important to know properties of these materials as a function of applied stress. We have developed an experiment that allows us to find the piezoelectric charge coefficient as a function of uniaxial stress in the poled direction . Both dynamic and static measurements were carried out and the corresponding values of the charge coefficient d₃₃ were obtained as a function of applied stress. These coefficients differ from each other because of the different proportions of reversible and irreversible domain changes that contribute to them and each coefficient can be important in specific applications. Results on a range of PZT ceramics manufactured by EDO Corporation are presented; in general, they show a non- linear behavior with an initial increase in d₃₃ as the stress increases followed by a significant decrease. The time dependence of the measurement has also been investigated.

This paper examines the compressive depolarization of commercial lead zirconate titanate PZT-5A piezoelectric ceramics by evaluating the actuation strain at different electric fields, compressive stresses and stress durations. Varying the combination of these parameters allows further understanding of the coupling effects among them. The experimental results showed a remarkable difference between the under-load actuation and the residual actuation, determined at zero stress after exposure to compressive stress. Under-load actuation was reduced relatively low at high compressive stress either at low or high electric excitation levels and was found to be relatively independent of stress duration, while high electric drive residual actuation was found to be strongly dependent upon stress duration and maintained its initial actuation for short compression duration. The data also indicates that the compressive stress combined with high negative electric field can expedite the depolarization of material.

This paper addresses the modeling of certain rate-dependent mechanisms which contribute to hysteresis inherent to piezoelectric materials operating at low frequencies. While quasistatic models are suitable for initial materials characterization in some applications, the reduction in coercive field and polarization values which occur as frequencies increase must be accommodated to attain the full capabilities of the materials. The model employed here quantifies the hysteresis in two steps. In the first, anhysteretic polarization switching is modeled through the application of Boltzmann principles to balance the electrostatic and thermal energy. Hysteresis is then incorporated through the quantification of energy required to translate and bend domain walls pinned at inclusions inherent to the materials. The performance of the model is illustrated through a fit to low frequency data from a PZT5A wafer.

Several methods have been applied to obtain the crystals with regular domain structures. The most common ins the use of patterned electric field poling, but the quality of resultant periodically poled material can depend on a number of factors and periodicities below approximately 3 micrometers are difficult to produce however, particularly with simultaneously large aspect ratios. Here we present an alterative method for production of periodically patterned domain structures due to optical periodic poling, a technique involving the simultaneous applications of combined electrical and optical fields: the electric field is applied via planar electrodes, while light is used to define those regions where domain inversion should occur. The optical poling route therefore offers a potentially simpler method, effectively eliminating the photolithographic patterning steps. Using interferometric methods, the periodicity of optically induced domain structures is a function of laser wavelength, and intersection angle of the two interfering beams, and hence is easily changed. We present also the investigations of the mechanisms of optical control of domain structures in ferroelectrics, in particularly the roles of the various internal field components, their origins and dynamic behavior following domain reversal.

We present detail investigation of the domain evolution in lithium niobate and lithium tantalate during backswitched electric field poling which allowed to produce micro- and nanoscale domain patterns by applications of voltage to lithographically defined strip electrodes. In situ optical observation of the domain kinetics during poling and high- resolution visualization by SEM and SFM of the static domain patterns on polar surfaces and cross-sections have been used. We separated and studied the main stages of domain evolution. The important role of backswitching as a powerful tool for high-fidelity domain patterning in thick wafers and for production of quasi-periodic nanoscale domain patterns has been demonstrated. We have proposed several variants of domain manipulation during backswitched poling: the frequency multiplication of the domain patterns, domain 'erasing' and 'splitting', formation of oriented arrays of nanoscale domains. We have demonstrated the production of lamellar domain patterns with period down to 2.6 microns in 0.5-mm-thick wafers and strictly oriented quasi-periodic domain arrays consisting of the individual nanodomains with diameter down to 30 nm and density up to 100 per square micron.

Previous measurements of the fracture toughness of PZT have relied on Vicker's indentations, bend specimens, and compact tension specimens. Vicker's indentations are qualitative and are not suitable for toughness measurements. Recent work has clearly shown that non-linear material behavior induces a non-linear stress gradient through other specimen geometries that must be accounted for to accurately determine the fracture toughness. This work describes the development of a measurement technique for the R-curve behavior of unpoled ferroelastic ceramics using 4-point bend specimens with semi-elliptical surface cracks. The model material is a soft, transparent composition of 8/65/35 lead lanthanum zirconate titanate. The aspect ratio is measured during crack growth. The non-linear stress gradient through the cross section calculated from strain gage data. A parametric study based on the analysis of Newman and Raju is used to elucidate the restrictions on application of this technique.

Cofired multilayer piezoceramic actuators as extremely fast valve driving elements will lead to a significant progress in the field of fuel injection systems. A careful adaptation of the component performance to the system demands, an extraordinary high reliability, and competitive low production costs are prerequisites for this large-scale industrial application. With proper material selection as basis, conventional multilayer technology has to be substantially extended in order to achieve large stack volumes, to avoid degradation effects during cofiring and nevertheless to meet the target costs. Under large-signal driving conditions, the static and dynamic behavior of the component is essentially influenced by driving pulse shape, clamping force, and stiffness of the load. Linear FE methods are employed to calculate the performance criteria of different actuator designs. Moreover, a FE-implementation using a micromechanical domain switching model was developed in order to describe the strongly nonlinear material behavior. Together with a quantitative estimation of crack initiation and propagation by means of fracture mechanics, these methods can give valuable hits for controlling the effects of fatigue and deterioration which may limit the operating life time. In order to optimize the interaction of the electrical and mechanical parts in the injection system, dynamic models of piezoelectric components must be provided. A nonlinear model of the stack actuator has been developed for the analysis software MATLAB/SIMULINK. Special attention has been paid to the hysteresis properties.

The energy release rates for dielectric, piezoelectric and ferroelectric strips are analyzed. Energy minimization is used to determine the electromechanical fields in the strip. Once these fields are computed conservation of energy is used to determine the energy release rate. Three different sets of assumptions are used to treat the void space and solid material. First, an impermeable void space assumption is analyzed with small deformation assumed to be valid in the solid. Next, the void space is assumed to have finite dielectric permittivity and aside form changes in the position of its boundary the solid is treated with small deformation theory. Finally, a large deformation formulation is used for the solid along with a permeable void space. By minimizing the energy of the system we are able to show that mechanical tractions act on the crack surfaces as a result of the finite dielectric permittivity of free space. Lastly, a piezoelectric strip with remanent polarization is analyzed and it is shown that the energy release rate for a poled piezoelectric is not equal to that of a material with identical elastic, dielectric and piezoelectric properties but no remanent polarization.

One of the most essential problems with ferroelectric ceramics is the low strength and durability of the brittle material, which prevents many most promising technical applications in mechatronics and adaptronics. In order to supply knowledge about design features and strength criteria and to improve the safety of components with smart ceramics, a more fundamental understanding about the process of fracture under combined mechanical and electrical loading is required. Therefore, numerical tools are developed permitting the stress analysis of arbitrarily shaped smart ceramics with a given crack under combined electromechanical loading boundary conditions. To solve the coupled electromechanical field problem, the FEM is used taking account of linear constitutive equations for an anisotropic piezoelectric continuum. Stress intensity factors and energy release rates are subsequently calculated inserting near tip nose values for mechanical displacements and forces as well as electrical potentials and charges. In connection with experiments on the cracking of Double Cantilever Beam specimens, the influence of electrical and mechanical loading conditions on the crack propagation is investigated. On the basis of calculated energy release rates and intensity factors as functions of the crack length, possible fracture criteria are discussed.

Strength measurements were carried out in different poling states under several eternally applied electrical fields perpendicular to the specimen length axis and with different test procedures. The main results were: (a) polarization parallel to the specimen length axis reduces the strength significantly, polarization in thickness direction showed small strength reduction only, (b) an electrical field directed normally to the length axis yields a significantly lower tensile strength compared with unpoled material, and (c) strength in bending and tensile tests exhibits strongly different results. The differences caused by the poling state and externally applied electric field are discussed in terms of orientation of domains ahead of natural cracks.

The electric fatigue behavior of commercial lead zirconate titanate (PZT) was investigated by optical microscopy and instrumented Hertzian microindentation. Macroscopic delamination cracks were found near the electrodes after large numbers of electrical cycles. Additionally, macroscopics edge cracks were found to orientate from the boundary between electroded and unelectroded material. Instrumented Hertzian microindentation measurements on specimen cross sections show larger indentation depths just beneath the electrodes than in the center of the sample. This behavior may result form a higher microcrack density near the electrodes. The role of micro- and macrocracks in the electrical fatigue behavior of ferroelectric ceramics is discussed and compared to macroscopic material parameters and acoustic emissions.

This paper presents result on electro-thermo-mechanical behavior of piezoelectric materials for use in actuator applications with an emphasis on durability performance. The objective of this study was to compare the performance of different commercially available actuator systems and to determine the properties necessary for design of such actuator systems. Basic piezoelectric properties of five stack actuators were determined as a function of mechanical preload and temperature. Changes in these properties during ferroelectric fatigue up to 10⁷ cycles were determined from strain-field relations after specified number of fatigue cycles. Experimental results indicate strong dependence of piezoelectric properties and power requirements on mechanical loading conditions. Results indicate that the optimum operating conditions can be determined that will improve actuation capabilities of piezoelectric stack actuators. That is, strain output was found to increase by 60 percent for some actuators upon the application of certain compressive prestress. Results of fatigue tests indicate negligible degradation in strain output for some stack actuators even when operated under mechanical preload that cause large displacements through domain wall motion. Similar trends in strain output and current degradation curves suggest that material degradation can be indirectly inferred from simply measuring the current being dissipated by the material. Finally, temperature rise of PZT stacks due to self-heating into account when designing actuator systems, since temperature changes were found to significantly influence both strain output and power required to drive piezoelectric stack actuators.

We examine the stability of polarization switching in polycrystalline ferroelectric/ferroelastic materials subject to continuous electromechanical loading. In case of unstable switching, a finite change of remanent polarization or strain result from an infinitesimally small increment of the applied load. A micromechanical switching model is studied as well as a simple macroscopic boundary value problem in combination with a phenomenological switching law. The micromechanical model of a ferroelastic layered composite is based on an energy switching criterion. Stable response is promoted by (i) homogeneity of mechanical stress, (ii) proximity of local load conditions to mechanical strain control. For the macroscopic boundary value problem of a ferroelectric ring, switching stability depends on the applied load conditions as follows: Charge control result in stable response; voltage control may initiate unstable switching. For voltage control, the mathematical instability disappears if a small amount of ferroelectric 'hardening' is postulated. Nevertheless, an enhanced switching activity is predicted near the former instability.

Multiaxial ferroelectric/ferroelastic constitutive laws governing the behavior of ceramic lead zirconate titanate (PZT) are needed for numerical calculations of stress and electric field in the vicinity of field concentrators such as cracks, inhomogeneities, and partial electrodes. Such constitutive laws are under development and are in need of experimental verification. Multiaxial constitutive behavior has been measured using tubular specimens, both poled and unpoled. The results were used to map out a yield surface. The composition used, 8/65/35 PLZT, was found to obey a Tresca yield criterion when in the unpoled state. The yield surface was found to be a function of the polarization state. Kinematic and isotropic hardening appear to be good candidates for describing subsequent yield surfaces. The multiaxial measurements are also being used to verify and calibrate a multiaxial micromechanics based constitutive model. This constitutive model has been implemented in a finite element code written by the authors. Some of the capabilities of this code are presented and discussed. This proceedings article gives an overview of our recent research in this area.

A simple macroscopic constitutive law for ferroelectric and ferroelastic hysteresis effects of piezoceramics is presented. After summarizing the uniaxial formulation, it is generalized to a 3D tensorial formulation. This constitutive model has been implement in the public domain finite element code PSU of Stuttgart University. The fully coupled electro- mechanical boundary value problem for our hysteresis model is solved by incrementation of the loading history. In order to verify the capabilities of our tool, a multilayer like actuator geometry is analyzed. It is shown that the remanent polarization remaining after poling gives rise to a non- vanishing distribution of the electric potential even if the voltage is reduced to zero at all electrodes. Concerning the residual stresses present after poling, a tensile stress field perpendicular to the direction of the electrodes. Concerning the residual stresses present after poling, a tensile stress field perpendicular to the direction of the electrodes can be found in the passive region of the actuator where so-called poling cracks are known to occur. It is the key feature of our finite element tool that it allows to consider in structural mechanical analyses such phenomena as they are induced by the remanent hysteresis properties of piezoceramic.

This paper addresses the development of a temperature- dependent constitutive model for relaxor ferroelectrics which is based on the assumption that the material is comprised of an aggregate of micropolar regions having a range of Curie temperatures. The diffuse transition behavior of the material is due to its chemical heterogeneity, and thermodynamic models for the microregions are developed by considering near neighbor interactions for varying cation ratios.. The result in micropolar model can be used to predict the saturation polarization and distribution of regions as a function of temperature. Hysteresis below the freezing point is incorporated through the quantification of energy required to bend and translate domain walls pinned at inclusions inherent to the material. The resulting ODE model quantities the constitutive non linearities and hysteresis exhibited by the materials through a wide range of temperatures and input drive levels. The predictive capabilities of the model are illustrated through a comparison with PMN-PT-BT data collected at temperatures ranging from 263 degrees K to 313 degrees K.

Effective elastic, dielectric, and piezoelectric properties of piezoceramics are calculated with the finite element method using a representative volume element. A polycrystal is considered which consists of single-domain crystals defined by a 2D random Voronoi tessellation. The random orientations of the domains in the unpoled state are described by an isotropic orientation distribution. To model poled stats, simple switching criteria are applied, so that e.g. the polarization direction of the individual grains fall within a cone of a specific angle about the poling direction. Homogeneous boundary conditions are imposed and the volume averages of the local mechanical and electrical fields are calculated. The effective material properties can then be calculated as a function of the single crystal moduli and the poling degree. The main advantages of this procedure are the more realistic random geometry and the fact that interactions among the grains are taken into account. Interest is focused on basic questions such as the influence of the boundary conditions, the necessary size of the representative volume element, and the variation of the effective moduli due to the stochastic model, in particular due to the orientation distribution. The numerical results are compared to those of analytical models.

The use of ferroelectrics in increasingly demanding roles as sensors and actuators motivates study of their fundamental constitutive behavior. This paper gives a preliminary report on measurements of the behavior of PZT-5H under multiaxial loading paths, and comparison with model predictions. The loading paths considered are loading of poled material with electric field at various angles (theta) to the poling direction, and loading with uniaxial compressive stress rotated through various angles (theta) to the poling direction. In each case the material response is measured by tracking electric displacement in the form of surface charge. Model predictions are made using a self-consistent crystal plasticity approach. The model is able to predict well the response to multiaxial electric field loading. There is good qualitative agreement in the case of mechanical loading.

The complex arrangement of domains observed in ferroelectric crystals is a consequence of multiple energy minima of the crystal free energy density. Since the total energy is a sum of the free energy, and electrical and mechanical work, switching between the different energetically equivalent domain states can be achieved by both electrical and mechanical means. For many ferroelectric materials, this result in an electrostrictive phenomenon resulting from domain switching. In the current study, the electrostrictive behavior of single crystal ferroelectric perovskites has been investigated experimentally. Experiments have been performed in which a crystal of barium titanate is exposed to a constant compressive stress and an oscillating electric field and global deformation is measured. The combined electromechanical loading result in a cycle of stress and electric field induced 90 degree domain switching. The domain switching cycle result in a measurable strain response theoretically limited by the crystallographic unit cell dimensions. Induced strains of more than 0.8 percent have been measured in barium titanate. Larger strains of up to 5 percent are predicted for other materials of the same class.

An anodic bond is modeled as a moving nonmaterial line forming the intersection of three material surfaces representing the unbonded conductor, the unbonded insulator, and the bonded interface. The component mass balance equations, Gauss' law, and the linear momentum equations are placed in a finite element formulation, which is used to predict the evolution of the sodium ion concentration, electric potential, and stress during anodic bonding of Pyrex glass and silicon.

Piezoelectric materials exhibit nonlinear behavior when subjected to large electric or mechanical loads. This strong nonlinear material behavior is induced by localized polarization switching at the domain level. In this paper, a finite element code in conjunction with a polarization switching criterion is described to model the nonlinear behavior in piezoceramics. Each element represents a single domain with a tetragonal structure. The nonlinearity is introduced in the behavior of each element by allowing it to undergo 180 degrees and 90 degrees polarization switchings. In order to simulate the real piezoceramic, which possesses a polycrystalline nature, material is modeled as a mixture of crystallites each oriented in some random direction. The mode is used to generate the dielectric and strain response of the material, i.e. hysteresis and butterfly loop. The model output is compared with experimental dat, and reasonable agreement is achieved. Behavior of the material under compressive stress, which does not cause full polarization switching, is studied to investigate the influence of compressive stress on the strain output. It is observed that strain output. It is observed that strain output of a preloaded block of piezoceramic increases for moderate electric fields but decreases for small and large electric fields.

We study the viscoelectroelastic behavior of heterogeneous piezoelectric solids, focusing on the connection between heterogeneity and coupled mechanical and electrical relaxations. Our approach is based on the existence of a correspondence between quasistatic viscoelectroelasticity and static piezoelectricity when linear constitutive response exists. We couple this correspondence principle with micromechanics models to predict the overall behavior of heterogeneous piezoelectric solids in terms of microstructural details. We devote specific attention to a class of two-phase materials consisting of a lossless piezoelectric phase embedded in a lossy matrix and obtain closed form expressions for the effective complex electroelastic moduli. Numerical results are presented and discussed, and reasonable agreement with experiment is observed.

The absence of explicit Green's functions for piezoelectric media has hindered progress in the modeling of material properties of piezoelectric materials for a long time. Due to the importance of piezoelectrics in smart structures, the construction of explicit Green's functions for such materials is highly desirable. We introduce here a method of integral transformation to construct the electroelastic Green's function for a piezoelectric hexagonal infinitely extended medium in explicit compact form. This Green's function gives the elastic displacements and electric potentials caused by a unit point force and a unit point charge, respectively. This explicit form of the Green's function is convenient for many applications due to its natural representation in a tensor basis of hexagonal symmetry. For vanishing piezoelectric coupling the derived Green's function coincides with two well known results: Kroner's expression for the elastic Green's functional tensor is reproduced and the electric part then coincides with the electric potential caused by a unit point charge. For spheroidal inclusions having the same electroelastic characteristics and orientation as the hexagonal matrix the constructed Green's function is used to obtain the electroelastic analogue of Eshelby tensor in explicitly form.

A constitutive model for the nonlinear effective behavior of ferroelectric ceramics is presented. The model is developed on the basis of the effective medium approximation which describes the interaction of the crystallites in a statistical way. Additionally, a particular simplified domain configuration within the crystallites and the possibility of domain wall motion are taken into account. In connection with a thermodynamic criterion for the domain wall displacement the volume fractions of domains can be calculated dependent on the crystallite orientation and the applied load in a self-consistent manner. This mechanism leads to an extrinsic contribution to the effective behavior. If the domain wall displacement is associated with energy dissipation the macroscopic behavior is nonlinear and hysteretic.

Rainbow and Thunder actuators constitute a family of 'stress-biased' devices that display enhanced strain and load-bearing capabilities in comparison to traditional flextensional devices. For both of these actuators, doming occurs during the cooling phase of the fabrication process to relieve thermal expansion mismatch between the metallic and piezoelectric layers. Accompanying dome formation is the development of a tensile stress within the surface region of the piezoelectric layer that can approach 400 MPa. This tensile stress affects the ferroelectric domain configuration and improves the 90 percent domain wall movement within the surface region of the piezoelectric under an applied electric field. It has been reported that this effect is responsible for the enhanced electromechanical performance of these devices. The results of the presented study, however, suggest that in addition to stress, other mechanical and mass loading effects may also play a role in the enhanced performance of these devices. Equivalent circuit and finite element modeling studies of these stress-biased actuators are reported, and in particular, the effects of specimen geometry on internal stress in the piezoelectric layer are discussed. Finite element analysis shows that in the surface region of the piezoelectric, the highest tensile stresses are, in fact, predicted for those devices that display the greatest displacement performance, i.e., devices that have a piezoelectric layer that is approximately twice as thick as the 'metallic' layer. However, equivalent circuit studies show that the highest predicted strains should also be observed for samples with similar geometries yet this approach does not include stress effects. This implies that not only stress, but also mass loading and other mechanical effects must also be considered in predicting optimum design geometries.

A new type of piezoelectric actuator has been developed by combining two piezoelectric Functionally Gradient Material (FGM) composite laminates into a bimorph to produce an actuator with large out of plane displacements while having reduced mid-plane stresses. This combination of high displacement with reduced stress keeps the benefit of the bimorph while reducing one of its drawbacks. These properties are varied symmetrically about the mid-plane of the actuator with the entire actuator being poled in one direction through the thickness of the device. These deices are produced by stacking individual layers of piezoelectric fibers in a modified epoxy matrix with varying fiber volume fraction form layer to layer thereby leading to varying material properties through the thickness of the composite. The focus of this work has been to use the finite element method to first predict the material properties for individual piezoelectric fiber based layers using a symmetrical unit cell model, which allowed the inter-layer and intra-layer volume fractions to be varied independently reflecting the rectangular packing of fibers present in the actual devices. And, then to predict the behavior of the actual composite devices using these predicted properties.

An apparatus has been fabricated to measure the admittance of a PZT bar in rotation. The rotation sensitivity of admittance of soft PZT and hard PZT bars has been detected at the rate of several thousand revolutions per minute, using an Impedance Analyzer. It has also been confirmed that the hard PZT bar has higher rotation sensitivity of the admittance than the soft PZT bar. The authors note that their experimental results suggest the possibility of developing a gyroscope based on rotation sensitivity of admittance of PZT ceramics.

A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced switching and stress induced switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, bu different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate are modeled well below the Curie temperature.

As SMAs gain popularity for use as large force actuators, one constitutive parameter that becomes particularly important is the thermomechanical fatigue life, in addition to maximum transformation strain and stability of actuation cycles. Even though the effect of thermal transformation cycles on the transformation characteristics of SMAs has been studied both experimentally and analytically, these studies have not been extended to high cycle levels related to the fatigue life. In this paper, a novel test frame and testing protocol are discussed to establish the transformation fatigue characteristics of SMAs under various loading conditions. Results are presented for the thermomechanical transformation fatigue life of SMA wire actuators under different applied stress levels and for different annealing conditions.

There have been very few research results available for high cycle fatigue properties of SMAs. In many of the devices designed to exploit the effect of fatigue loadings, the specimen is subjected to only several thousand thermal or loading cycles. Therefore, the stability of the alloy under applied loading with high cycle fatigue becomes an important issue. Moreover, there has not been any fatigue testing in compression for SMAs. The behavior of SMAs under tension and compression may be different, which is very important for many special applications of SMAs. The behavior of SMAs under tension and compression may be different, which is very important for many special applications of SMAs. The present study focus on the high cycle fatigue to SMAs under compression. A new surface monitoring technique for micro- deformation and micro-strain analysis, called IIMT, is introduced. IIMT is used for monitoring the performance of SMAs under high cycle stress loading in compression. The stress-strain curves and shape memory strain output at various loading cycles were obtained, which provide valuable information for design and applications of SMAs.

Ausforming treatment can improve the shape memory effect of Fe-Mn-Si based shape memory alloys, however, the mechanism of this improvement is not so clear. In this paper, the influence of ausforming treatment on stress-induced martensitic transformation and its reverse transformation in an Fe-28Mn-6Si-5Cr shape memory alloy has been studied using atomic force microscope and TEM aiming to clarify the origin of this improvement. It was found that the ausforming treatment at 970K by 9 percent pre-straining, which is the optimum condition for improving shape memory recovery, can introduce many uniformly distributed stacking faults on the same slip plane in austenite. When an external stress is applied to such an ausformed specimen for shape change, uniformly distributed martensite bands with the same variant are produced in a grain due to the assistance of those preexisted stacking faults. When being heated over Af, these martensite bands are nearly completely reverse-transformed to parent phase through the same atomic pass as for the forward transformation, so a nearly perfect shape memory effect is obtained.

Active composite materials with fibers and players of SMA are investigated. The behavior of the SMA composites is studied under thermomechanical loading that provides a complete cycle of the phase transformation in SMA active elements. The models of the descriptions of SMA deformation are developed. The refined theories of the beams and plates are proposed for the strain-stress-state investigation of the SMA composites. The method of solution is developed which is based on the Laplas transformation in view of the phase process parameter. The algorithm of the account of damage accumulations, connected with matrix damages, and also their influence on the active composite's behavior is suggested. The influence of the viscoelastic matrix' properties and damage accumulations on the deformation of the active composite, the capability of an implementation of the two-way shape memory effect and the change of the hysteresis loop should be taken into account at a deformation of an active composite in the compete cycle of the phase transformations.

Introducing the phase interaction energy between austenite and detwinned martensite, the presented authors studied pseudoelastic transformations of shape memory alloys and have analytically shown that the transformation is a thermomechanical process along a stable equilibrium path, as observed in experiments. To further exploit the phase interaction energy, here we present a unified approach for treating both shape memory effect and pseudoelasticity, taking into account another state of phase, i.e., twinned martensite. Analytical models formulated using experimental data will be compared with experimental constitutive relationships. A god curve-fitting to complicated experimental stress-strain curves is also presented through a higher-order polynomial representation of the interaction energy function.

Most current applications of shape memory alloys (SMAs) make use of static properties. However, the hysteresis in the load-deformation behavior also constitutes a very efficient damping mechanism in vibrational applications. The paper studies the SDOF vibration of a rigid mass suspended by a thin-walled SMA tube under torsional loading. The behavior is analyzed for the cases of quasiplasticity and pseudoelasticity on the basis of an improved version of the Mueller-Achenbach model. To illustrate the damping capacity and the nonlinear vibration characteristics, both, free and forced vibration cases are considered.

The paper presents a mathematical description of shape memory alloys within the framework of continuum mechanics, where the spatially multidimensional case is considered. A new simple model is introduced, which correctly describes not only all well-studied shape memory effects but also the more complex behavior. The key idea is a new set of internal state variables, which are averaged values for a representative volume element of the polycrystalline material. A tensor-valued variable describes the state of orientation of martensite. The relative volume fraction of stress induced martensite is defined by taking a certain tensor norm of this internal variable. A free energy is chosen and thermodynamical forces are derived. These forces are sufficient to define the onset of the phase transitions, so that we do not need to introduce transition surfaces explicitly within the evolution equations. Finite element discretizations for the approximation of the field variables and finite difference approximations for the time integration of local variables are explained.

Shape memory alloys (SMAs) have emerged as a class of materials with unique thermal and mechanical properties that have found numerous applications in various engineering areas. While the shape memory and pseudoelasticity effects have been extensively studied, only a few studies have been done on the high capacity of energy dissipation of SMAs. Because of this property, SMAs hold the promise of making high-efficiency damping devices that are superior to those made of conventional materials. In addition to the energy absorption capability of the dense SMA material, porous SMAs offer the possibility of higher specific damping capacity under dynamic loading conditions, du to scattering of waves. Porous SMAs also offer the possibility of impedance matching by grading the porosity at connecting joints with other structural materials. As a first step, the focus of this work, is on establishing the static properties of porous SMA material. To accomplish this, a micromechanics-based analysis of the overall behavior of porous SMA is carried out. The porous SMA is modeled as a composite with SMA matrix, which is modeled using an incremental formulation, and pores as inhomogeneities of zero stiffness. The macroscopic constitutive behavior of the effective medium is established using the incremental More-Tanaka averaging method for a random distribution of pores, and a FEM analysis of a unit cell for a periodic arrangement of pores. Results form both analyses are compared under various loading conditions.

Vibration control in structures often requires the addition of viscoelastic constrained layer damping treatments. In critical applications, however, the low strength of the viscoelastic material and the threat of delamination prevent the use of these treatments. In this paper we present a means of how to overcome these difficulties by using high strength shape NiTi fibers to increase the damping of aluminum structures. Specifically, we show that the introduction of high strength, shape memory alloy fibers into an aluminum beam can result in a significant increase in the passive damping response of the beam. The objective of our research is to develop passive and active structural materials that can be sued in applications that demand high loss factors, strength, and high reliability. The development of the NiTi fiber reinforced aluminum matrix composite beam is a first important step towards achieving this objective.

A simplified multivariant model for SMA single crystals is developed. Although the new model is a simplified version, removing explicit interaction energy calculations, it considers certain aspects of martensite transformation much better. Most significantly, martensite variants tend to rapidly form large plates most of which have an invariant plane interface with the austenite and/or reach the grain boundary. Hence the formulation of the previous Multivariant model in which every variant group is embedded in the austenite phase together with numerous other inclusions is inaccurate. In the simplified model, the energy contributed by the incompatibility of inclusion to the matrix is neglected. The prediction by the new model for different uniaxial tension directions on a single CuAlNi crystal agrees excellently with the experimental results. Furthermore, the counter-intuitive results for a polycrystalline CuZnAl SMA under triaxial loading are also well captured by the simplified model. Experimental result considering in situ loading in the MTS loading frame and SEM are shown illustrating the invariant plane in a single (gamma) '₁ CuAlNi crystal under uniaxial loading. These results also necessitate further microstructure mapping for phase transition and detwinning and/or reorientation of correspondence variants in SMA with an internal twinned structures.

The issue of phase transformations in shape memory alloys is revisited in the 1D context. We focus on problems where there is a sharp interface between the two phase of austenite and martensite. Apart from the usual conservations equations, it is proposed that an extra equation be used to render the system of equations complete, when a first-order transition is considered. Seen within this context, the following two approaches can be derived as special cases: (i) Leo et al approach where the phase boundary temperature is taken to be linearly related to the stress, (ii) Abeyaratne and Knowles approach where a kinetic relation is assumed. Certain other implications of the new approach are discussed in light of these special cases.

In this paper a thermomechanical material model for shape memory alloys is proposed. The model can depict the shape memory effect, the pseudo elasticity and pseudo plasticity as well as the transition region between pseudo elasticity and -plasticity. Moreover, the geometric non linearities are considered in the constitutive equations. For all thermomechanical processes, the CLAUSIUS-DUHEM inequality is fulfilled. Besides the phenomenological modeling, the finite element implementation of the constitutive equations at finite strains is developed. For simplification and in order to construct an efficient stress algorithm, only small elastic but finite inelastic strains are considered.

Detwinning of thermally formed martensite twins in shape memory alloys leads to a macroscopic stress-plateau in the stress-strain curves. The response of twinned domains under stresses plays a critical role in the anisotropy of both the mechanical and the thermomechanical behavior of especially textured shape memory alloys. A recent result has shown that the relation between the shear direction of certainly distributed martensite twins and the loading direction is the key to understand both the microscopic and the macroscopic deformation processes. Based on this result, the present research has systematically analyzed the orientation-dependence of the detwinning process from a crystallographic approach and using mechanics of heterogeneous materials. The results are found to be well coherent with the experimental observations without superstitiously imposed conditions. For a NiTi sheet with given textures, the predicted response of two types of martensite twins, namely, type II and compound twins as a function of loading direction, agrees well with the experimental observations.

Energy absorption properties of polymer matrix Terfenol-D particulate composites have been experimentally measured. In this work two volume fractions of Terfenol-D were investigated and both exhibited peak energy absorption of up to 25 percent per cycle. The tests include mechanical loading in both axial and shear combined with applied axial magnetic fields. The results show that the energy absorbed in a cycle of loading is a strong function of stress amplitude. The peak energy absorption for the zero magnetic field case in both axial and shear loading occurs near zero amplitude and decreases with increasing stress amplitude. The maximum energy absorption near zero stress amplitude has been observed previously in monolithic Terfenol-D and is a result of the low magnetic anisotorpy of Terfenol-D. Combined magnetic-mechanical loading demonstrated the influence of magnetic field on energy absorption properties. The energy absorption is decreased as the static magnetic field is increased if the cyclic stress amplitude is held constant. If however, we hold a constant magnetic field and vary the cyclic stress amplitude is held constant. If however, we hold a constant magnetic field and vary the cyclic mechanical loading amplitude, it has been observed that the peak energy absorption curve is shifted to higher stress values. This suggests stress tunable dampers are possible.

We report cyclic strain measurements form an experimental Terfenol-D actuated polymer matrix composite. Basic material constitutive response are identified as functions of frequency. Anhysteric theory is used to quantitatively model the behavior of the composite. Insight provided by the analysis is used to suggest material design changes leading to improved composite performance.

TRIP steels have been used as sensors for smart solid-state damage assessment systems. TRIP steels are materials which change state from austenitic, nonmagnetic to a martensitic, ferromagnetic phase as the material undergoes straining. There is a direct correspondence of the peak strain level experienced in the material with the percentage of ferromagnetism, hence monitoring the relative among of the ferromagnetic content will indicate the level of strain. The phase transition that accompanies the straining is irreversible so the monitor material indicates the peak strain until that value is subsequently exceeded. Materials research discussed will cover the selection of compositions with a suitable ferromagnetic response and the development of thermomechanical treatments to achieve high tensile strength required for this application. Tensile properties and related phase changes are described.

A dynamic simulation model of magnetostrictive actuators and transducers has been used to study the performance and thermal balance of an ultrasonic magnetostrictive power transducer. Electrically resistive, eddy current, mechanically resistive and hysteresis losses have been deduced when the transducer works against a purely mechanically resistive load of r a moderate driving current of 10 A and a frequency of 21 kHz. The eddy current losses can be reduced significantly by laminating the active material. However the hysteresis losses are the main source for heating the transducers. The power losses obtained from the dynamic simulations have been used as thermal sources in electro-thermal finite element calculations. The calculations show that free air convection is not enough to cool the actuator. Water cooling of the actuator with a flow of 6.8 l/min will decrease the active materials temperature to around 80 degrees C. This has been obtained by estimating the heat transfer and use the heat flow as sinks in the finite element calculations. The design of a magnetostrictive ultrasonic transducer must therefore comprise an optimal working point regarding magnetic biasing and mechanical pre-stress to minimize the hysteresis.

On the base of method of structural-analytical theory of physical mesomechanics there are formulated the determining equations for forecast of complex deformations properties in materials with thermoelastic martensite transformations. There is a developed method of construction of coherent system of integral-differential relations for describing processes of structural evolutions and mass transfer on micro-meso and macroscale levels.

Recently, high-performance piezoelectric actuators with larger force and displacement output are being studied by many researchers due to their prospective application in smart material and structural systems, especially for vibration and noise control. The improvement of performance is achieved by the improvement on material composite, sintering process, and actuator structures. On the other hand, studies have also been carried out on the application of microwave sintering process in the sintering of structural ceramic materials. In this study, the application of. 28GHz microwave sintering process in the sintering of PZT materials was tried and sintering conditions were intensively investigated. Microwave sintering offers advantages over conventional technologies, such as repression of grain growth due to rapid heating, and improvement of microstructure due to internal heating. As a result, the sintering time of PZT materials using 28GHz microwave was reduced to 1/10 of the time needed for the conventional sintering process, with improvements on the properties such as electromechanical coupling factor, and piezoelectric constants. Furthermore the performances of the actuators fabricated with the microwave sintering process were evaluated in a vibration test and compared with the performances of the actuator fabricated with the traditional sintering process, and the performance superiority was confirmed.

The next generation of shape memory alloy constitutive models must explicitly or implicitly account for the physics of deformation. Such thermodynamic based micro-mechanical or internal state variable models yield a class of constitutive models with predictive capabilities extending past traditional phenomenological models. Unfortunately, a lack of quantitative understanding of pertinent deformation mechanisms in polycrystalline NiTi shape memory alloys has hampered the advancement of the aforementioned state-of-the- art constitutive modeling approaches. With a goal to improve our fundamental quantitative understandings of the deformation of polycrystalline NiTi shape memory alloys, the circumvent modeling roadblocks, the present talk outlines recent experimental results on single crystal NiTi. Particular attention is paid to macroscopic phenomenon which have recently been elucidated based on the mechanical testing of NiTi single crystals such as texture effects, tension-compression asymmetry, coupled detwinning and transformation stains, and cyclic loading effects. Ultimately, the aim of the talk is to present an overview of our recent findings while concurrently outlining the needs for state-of-the-art constitutive modeling efforts to address some longstanding issues. Throughout the paper, we will also outline future experiments on single crystal NiTi necessary to strengthen our fundamental understandings.

The dynamic behavior of Terfenol-D actuators with laminated magnetostrictive materials for ultrasonic applications has been modeled using a new technique developed on the Simulink platform. The nonlinear simulation model is based on the finite difference method and lumped-circuit approaches with modified constitutive equations, which can simultaneously handle the non-linearities, eddy currents, hysteresis effects, and the electrical, magnetic and mechanical system interactions. Because the power losses are so considerable at ultrasonic frequencies, a thermal lumped circuit approach of the electro-thermal performance has been incorporated in the model and the thermal balance of the actuators with possible cooling system thus can be taken into account in the whole system design. The nonlinear properties of Terfenol-D, obtained from static material characterizations, were used as numerical input to the simulation models. The model integration and some application examples including the numerical estimation of the effects of frequency, number of lamination, magnetostrictive rod dimensions, and eddy currents were presented. The preliminary result indicate that the new design and simulation package is very straightforward and the dynamic behavior of the laminated magnetostrictive actuators at high frequencies can be predicted and estimated fairly well from the simulation model.