A parametric study of the electromechanical response of ionic polymer transducers is presented. This study is designed to investigate the impacts of loading condition, solvent type and counter-ion on the macroscopic response of the ionic polymer and how this translates to the internal mechanisms that govern the charge-to-strain sensitivity observed in these materials. In this study three separate loading conditions are considered focusing on the material response to imposed bending, elongation and applied pressure. These tests are conducted to illustrate the difference between the mechanisms involved in sensing and actuation. The study is then expanded to include a range of solvents and their influence on the material sensitivity. Solvent types are selected to provide a range of dielectric constants (5.1-78.4) as well as viscosities in an effort to study their impact on ion transport and the actuation response. Each of the measurements is repeated for a number of counter-ion species. Varying the size and valence of the cation, material sensitivity is again measured and related to the known size and concentration of the counter-ion. These results are then compiled and compared in order to draw conclusions about specific material properties and parameters, specifically on the cross coupling terms that relate the sensing and actuation responses of the ionic polymer transducer. A discussion of the impact of these findings is also presented, along with a discussion of how these findings may be used later for empirical and analytical modeling efforts.

Recent advances in manufacturing of multifunctional materials that respond to multi-field excitation have motivated the design and prototyping of sensing and actuating devices for various applications aiming to improve functionality and decrease overall cost. Computer aided design is one of the techniques utilized for achieving these goals. However, it requires the development and integration of behavioral evolution models for the respective materials. This paper addresses the initiation of an effort to develop a computational implementation of a theoretical methodology for describing such systems in a way that allows accurate prediction of their behavior within their state space. Continuum mechanics, irreversible thermodynamics, and electrodynamics are utilized to derive the general four dimensional multiphysics field equations of materials used for artificial muscle applications along with the appropriate constitutive theories. The generalized nonlinear Von-Karman equations expressing the behavior of multi-field artificial muscle-based materials are derived as a special case of electric multi-hygrothermoelasticity developed as the closest theory for modeling the behavior electro-hygro-thermo-elasto-active materials. Numerical solution examples of these equations are presented for the case of an ionic polymeric material structure.

Heat-activated self-healing is a desirable property of multi-functional composite materials, particularly if the components of the material itself can be used as a heating element. The heating capabilities and resultant temperature changes of such a composite are investigated in this paper, using finite element modeling and then experimental testing. The composite to be tested consists of thin-wire copper fibers, chosen for particular electromagnetic properties, and an epoxy matrix, which will later be replaced by a self-healing polymer matrix. Direct electrical current is passed through the wires and causes heat dissipation throughout the composite, a process known as resistive heating. For this particular composite, a temperature of 80°C is desired, because at this temperature the polymer can heal within a reasonable amount of time. Using finite element simulations and testing of an actual sample, it was found that resistive heating can achieve the desired temperature using electrical power inputs as low as 0.1 W per square cm of composite panel. The temperature results from the experiments agree with the results from the finite element simulations.

Single wall carbon nanotube (SWNT)-polymer composites aligned by an AC electric field were characterized using Raman spectroscopy and electrical conductivity measurements to assess the resulting alignment. The Polarized Raman spectra was recorded at several angles between the SWNT axis and the incident polarization ranging from 0° to 180°. Inspection of the spectra revealed that maximum intensity is obtained when the polarization of incident radiation is parallel to the SWNT axis (0° and 180°), while the smallest intensity is obtained when the polarization of incident radiation is perpendicular to the SWNT axis (90°). The electrical measurements were made in three directions; parallel to the aligned SWNTs and perpendicular to the aligned SWNTs. Based on the electrical conductivity and polarized Raman spectroscopy measurements, it can be concluded that the SWNTs in the polymer matrix were preferentially aligned by applying an AC electric field of 43.5 V/mm at a frequency of 1 Hz, 10 Hz, 10 KHz and 100 KHz.

While exhibiting powerful characteristics, monolithic piezoelectric sensors and actuators suffer from many drawbacks due to inherent material properties and implementation issues. As a result of their stiff structure and primary operating principle, monolithic piezoelectric wafers perform poorly in a variety of important engineering applications. Piezoelectric Fiber Composites (PFCs) offer one possible solution to these limitations. Mechanically flexible and functioning on the basis of the d33 effect, these actuators enable and improve many piezoelectric applications. The NASA-Langley Research Center recently developed the Macro-Fiber Composite (MFC) actuator to address several shortcomings in the operational characteristics of competing PFC packages. While the construction of this actuator results in many advantages over comparable PFCs, potential exists for improvement in the design of the MFC. Thus, the single-crystal MFC is proposed. Single-crystal PMN, a specific piezoceramic compound, comprises the piezoceramic fibers of the proposed device, contributing larger piezoelectric coupling, higher bandwidth and higher stiffness to the MFC configuration. Development of this new actuator necessitates extensive characterization of its electromechanical properties. This paper describes the development and computational results of a short-circuit stiffness model that produces the four independent mechanical properties which describe the single-crystal MFC. Modeling results are compared to those of the standard MFC.

Layered composites have attracted attention for their high specific stiffness, high specific strength, and application specific tailoring of their properties. It is also recognized that layered composites are prone to delamination failure in addition to other failure modes. Consideration of transverse shear on the deformation behavior of the composites is an important aspect in the study of delamination mode failure of such plates. In this paper, we consider the effects of including the transverse shear deformation on the vibration characteristics of layered piezoelectric composites. The formulation is based on the Raleigh-Ritz method using the beam characteristic functions. MATLAB based symbollic math tool box is used in evaluating th eintegrals resulting from the Raleigh Ritz approach. Various commonly occuring boundary conditions are discussed. Results are provided showing the effects of the shear deformation on the dynamics of layered laminated composites. The effects of laminate thickness, fiber orientation, and the plate aspect ratios on the free vibration characteristics of the composite laminates are given to demonstrate the methodology described.

A major issue yet to be resolved for embedding sensors, actuators and microelectromechanical systems (MEMS) in 'smart' structures is that of providing power. Work is ongoing in the field with examples of micro battery technology, use of solar power and micro fuel cells. The work presented here considers a technology to enable the development of integrated power generation and actuation. Magnetic fibre reinforced composite material has been developed which utilises hollow glass fibres filled with active magnetic material. The resulting material maintains structural integrity as well as providing a possible means of electrical power generation from a dynamically loaded structure. The hollow glass fibres were manufactured in-house using a bespoke fibre drawing facility. Hard magnetic powder materials were introduced into the hollow fibre cores to provide an active electromagnetic function. This paper will discuss the manufacture, characterization and optimisation of active magnetic fibre reinforced composite materials.

A -1200 ppm forced volume magnetostriction has been obtained in a [0-3], resin-bonded, Gd₅Si₂Ge₂ particulate composite. The strain is a result of a magnetically induced phase transformation from a high volume (high temperature, low magnetic field) monoclinic phase to a low volume (low temperature, high magnetic field) orthorhombic phase. The particles used in the composite were ball-milled from a bulk sample and sieved to obtain a size distribution of ≤600 mm. Bulk Gd₅Si₂Ge₂ was manufactured via arc melting and subsequently annealed at 1300°C for 1 hour to produce a homogenous, polycrystalline sample. The transformation temperatures of the bulk sample, as measured using a Differential Scanning Calorimeter (DSC), were Ms = -9.3°C, Mf = -14.6°C, As = -4.4°C, and Af = -1.2°C. The composite and the bulk samples were magnetically characterized using a SQUID magnetometer, and found to undergo a paramagnetic to ferromagnetic transition during the phase transformation, consistent with published results. The bulk sample was also found to possess a maximum linear magnetostriction of -2500 ppm.

We study the magnetomechanical behavior of two-phase composites containing randomly dispersed ferromagnetic particles and nonmagnetic matrix. Starting from Green's functions we investigate the magnetic and elastic fields for two particles embedded in the infinite domain and define pair-wise interaction between particles. Macroscopically, we derive the averaged stress and strain fields over the composite and two phases. We then present effective magnetostriction and elasticity of composites and simulate the magnetomechanical coupling behavior during combined magnetomechanical loading conditions. Simulations are compared with other methods and experimental data to demonstrate the capability of the proposed method.

In this study, we identify and survey energy harvesting technologies for small electrically powered unmanned systems designed for long-term (>1 day) time-on-station missions. An environmental energy harvesting scheme will provide long-term, energy additions to the on-board energy source. We have identified four technologies that cover a broad array of available energy sources: solar, kinetic (wind) flow, autophagous structure-power (both combustible and metal air-battery systems) and electromagnetic (EM) energy scavenging. We present existing conceptual designs, critical system components, performance, constraints and state-of-readiness for each technology. We have concluded that the solar and autophagous technologies are relatively matured for small-scale applications and are capable of moderate power output levels (>1 W). We have identified key components and possible multifunctionalities in each technology. The kinetic flow and EM energy scavenging technologies will require more in-depth study before they can be considered for implementation. We have also realized that all of the harvesting systems require design and integration of various electrical, mechanical and chemical components, which will require modeling and optimization using hybrid mechatronics-circuit simulation tools. This study provides a starting point for detailed investigation into the proposed technologies for unmanned system applications under current development.

Novel autophagous (self-consuming) systems combining structure and power functionalities are under development for improved material utilization and performance enhancement in electric unmanned air vehicles (UAV's). Much of the mass of typical aircraft is devoted separately to the functions of structure and fuel-energy. Several methods are proposed to extract structure function from materials that can also serve as fuel for combustion or as a source of hydrogen. Combustion heat is converted to electrical energy by thermoelectric generation, and hydrogen gas is used in fuel cells to provide electrical energy. The development and implementation of these structure-fuels are discussed in the context of three specific designs of autophagous wing spars. The designs are analyzed with respect to mechanical performance and energy storage. Results indicate a high potential for these systems to provide enhanced performance in electric UAV's.

Two micromechanisms including a microactuator of a shape memory alloy (SMA) and a retaining system are presented, which are implemented in a microvalve to maintain a closed condition while no power is supplied. In one design, the retaining system is realized by a pseudoelastic SMA microspring coupled to the SMA microactuator. Alternatively, a pressure compensation mechanism is developed based on two mechanically coupled membranes, which are located above and below the SMA microactuator. The mechanical, electrical and thermal behaviors of the SMA microactuator are simulated by a coupled finite element program. Based on force-displacement characteristics of microspring and microactuator, a design of the two micromechanisms is developed. The investigation reveals several advantages of the pressure-compensation mechanism. In particular, pressure compensation allows a maximum controllable pressure difference of more than 500 kPa compared to 100 kPa for the microspring mechanism. Furthermore, a larger actuation stroke close to the maximum possible design value is achieved. Dynamic flow measurements reveal similar time constants for both mechanisms of 15 and 55 ms for opening and closing, respectively.

This paper reports experimental results of an airfoil-based flap actuator that is actuated using high temperature Nickel-Titanium (NiTi) polycrystal and Copper-Aluminium-Nickel (CuAlNi) single crystal wires with a nominal diameter of 1.5 mm. The stress-free transformation temperatures of the commercially available NiTi wires are Mf = 53°C, Ms = 70°C , As = 95°C , Af = 110°C whereas those for the CuAlNi wires are Mf = 80°C ,Ms = 100.5°C, As = 104.5°C , Af = 117°C. Due to a significantly low electrical resistivity of the CuAlNi, the commonly used joule heating approach for thermal actuation is shelved for a heating coil approach. Uniaxial stress measurements, trailing edge flap deflections and temperature measurements are recorded during a typical heating and cooling cycle using a load cell in line with the SMA wire, a LVDT at the trailing edge tip and a thermocouple on the wire (outside the heating coil). It is seen that actuation by the CuAlNi (with a prestrain = 5.5%) leads to about a 50% higher tip deflection and about a 67% lower cooling time after actuation as compared to the corresponding values for NiTi (with a prestrain = 5.6%). The larger tip deflection is attributed to a higher strain recovery for the CuAlNi as compared to the NiTi during phase transformation whereas the lower actuation time is attributed, in part, to the narrow hysteresis in the stress-free transformation temperatures of the CuAlNi (~ 37°C) as compared to the NiTi (~ 57°C).

Performing mechanical testing experiments in all the different martensitic phases of Ni-Mn-Ga under the constant magnetic field applied perpendicular to the load direction we show that such a magnetic field can dramatically modify standard zero field strain stress relationships of MSMA's like Ni-Mn-Ga. In a particular case of 5M and 7M martensites we observe a so-called pseudo-elastic or rubber-like behavior during the standard compression-decompression cycling under the field at about 1T. This effect is finally discussed from the point of the general thermodynamic background and some particular modeling concepts.

Polycrystalline Ni-Mn-Ga in bulk, pulsed laser deposition (PLD) thin film, and radio frequency (RF) sputtered thin film are studied. A thin film of direct current (DC) magnetron sputter deposited NiTi was also used in the study. A polycrystalline Ni-Mn-Ga bulk sample was measured to have a tan δ = 0.4925 and a maximum elastic modulus E = 7.3 GPa. Material characterization studies were performed on polycrystalline Ni-Mn-Ga thin films deposited by PLD onto single crystal (100) Si and (100) MgO substrates at substrate temperatures ranging from 550°C to 650°C. Damping measurements on RF sputter deposition of 1 μm Ni-Mn-Ga and 10 μm of NiTi both on copper substrates were performed in cantilever beam ring down tests. Results show 1 μm RF sputter deposited Ni-Mn-Ga thin film on a 54 μm copper substrate improves damping properties.

A thermodynamically consistent phenomenological model is presented which captures the ferromagnetic shape memory effect, i. e. the large macroscopically observable shape change of magnetic shape memory materials under the application of external magnetic fields. In its most general form the model includes the influence of the microstructure for both the volume fraction of different martensitic variants and magnetic domains on the described macroscopic constitutive behavior. A phase diagram based approach is taken to postulate functions governing the onset and termination of the reorientation process. A numerical example is given for an experiment on a NiMnGa single crystal specimen reported in the literature, for which the model is reduced to a two-dimensional case of an assumed magnetic domain structure.

The magnetic shape memory (MSM) effect occurs in some ferromagnetic martensitic alloys at temperatures below the martensite finish temperature and involves the re-orientation of martensite variants by twin boundary motion, in response to an applied stress and/or magnetic field. The driving force for twin boundary motion is the magnetic anisotropy. In this study, magnetization measurements as a function of magnetic field were made on several oriented single crystals of Ni-Mn-Ga alloys using a vibrating sample magnetometer. The magnetization versus magnetic field curves were characteristic of magnetically soft materials with magnetic anisotropy consistent with literature estimates for the different martensite structures observed in Ni-Mn-Ga alloys. Differences in the slope of the curves were due to the martensite structure, the relative proportion of martensite variants present, and their respective easy and hard axis orientations. Thermo-magneto-mechanical training was applied in an attempt to transform multi-variant specimens to single variant martensite. Training of the orthorhombic 7M martensites was sufficient to produce a near single variant of martensite, while the tetragonal 5M martensite responded well to training and produced a single-variant state. The strength of the uniaxial magnetic anisotropy constant for single-variant tetragonal 5M martensite, Ni_52.9Mn_27.3Ga_19.8, was calculated to be K_u=1.8 x 10⁵ J/m3, consistent with literature values. To obtain single-variant martensites, heat-treatment of the specimens prior to thermo-magneto-mechanical training is necessary.

In a certain temperature range, NiTi and other shape memory alloys show the so-called pseudoelastic effect. In the present study, the pseudoelasticity of NiTi is experimentally investigated in tension tests on thin-walled tubes. The observed phenomena are modeled within the framework of continuum thermomechanics regarding a geometric linear theory. The model is based on a free energy function in order to represent the occurring energy storage and release effects. Additionally, evolution equations for internal variables, like the inelastic strain tensor and the fraction of martensite, are introduced. The proposed system of constitutive equations represents the observed history-dependent material behavior. To identify the material parameters, the theory of neural networks is applied.

Shape Memory Alloys are now well recognized as potential materials for structural control. Even if some applications already exist, the dynamic behaviour of SMAs has not been clearly explained. This paper focuses on the study of a martensitic Cu Al Be beam under dynamical loading. A simplification of the thermomechanical model is necessary to build a Finite Element formulation able to perform dynamic simulations. In a first part, we study a classical tensile test in order to choose the way the model should be simplified. In a second part, dynamic test on the cantilever beam are presented and discussed. Wavelet techniques are also used to underline non linear behavior of this material in showing the dependence of the non linear natural frequency on the vibration magnitude.

The buckling behavior of TiNi Shape Memory Alloy (SMA) plates is evaluated numerically and experimentally with aim of using TiNi as an Energy Absorption (EA) material. To this end, we performed FEM analysis for TiNi plates of several thickness and length. The present analytical study shows promising result of using TiNi as an EA material. This is confirmed by the experiment work. The post-buckling shape and the load-displacement relationship are quite different from those of conventional materials such as aluminum and steel. Post-buckling strength of the conventional materials decreases gradually with increase in applied loading (or deformation). This reduction in the load bearing capacity at higher loads is attributed to the localized high strain in deformed specimen under compression while the majority of the specimen volume deform at modest strain. If this localized high strain is avoided and high straining can be made more uniformly in the entire specimen under compression load, then such a plate is expected to exhibit large energy absorption, i.e. a new EA material. The present study reveals that the energy absorption in TiNi plate under compression is 3 times larger than that of aluminum plate for the same level of compression loading.

We present an analysis on a complicated combined process of martenistic transformation and two-way shape memory effect due to cyclic loadings of stress and heat in order to further develop the constitutive model of an SMA wire which is based on the phase interaction energy function proposed in our previous studies. Stress-induced martenistic transformation is modeled by introducing residual martensite in the transformation process between austenite and detwinned martensite. As for heat-induced two-way shape memory effect, it is assumed that a mixed-state of austenite and residual detweinned martensite changes into another mixed-state of twinned and detwinned martensites during colling of the alloy, whereas a reversal change between the mixed-states occurs during heating. To examine the effectiveness of this analytical model based on the phase interaction energy function, an experiment is performed using a uniform SMA wire. Numerical analysis is carried out to compare with experimental data on the stress-induced martensitic transformation and the heat-induced two-way shape memory effect, which reveal very complicated training effect.

Understanding thermoelastic martensitic transformations is a fundamental component in the study of shape memory alloys. These transformations involve a hysteretic change in stability of the crystal lattice between an austenite (high symmetry) phase and a martensite (low symmetry) phase within a small temperature range. In previous work, a continuum energy density W(U;θ) (as a function of the right stretch tensor U and temperature θ) for a perfect bi-atomic crystal was derived based on temperature-dependent atomic pair-potentials. For this model, only high symmetry cubic configurations were found to be stable (local energy minimizers). The present work derives an energy density W(U,P(1),P(2),...;θ) that explicitly accounts for a set of internal atomic shifts P(i). In addition, the model permits the calculation of the crystal's dispersion relations which determine the stability of the crystal with respect to bounded perturbations of all wavelengths (Bloch-waves). Using a specific model of a bi-atomic crystal with the temperature serving as the loading parameter, a stress-free bifurcation diagram is generated. Stable equilibrium branches corresponding to the B2 (cubic) and B19 (orthorhombic) crystal structures are found to exist and overlap for certain temperatures. The group-subgroup relationship between these two crystal structures is necessary for the shape memory effect. Thus, our results are consistent with the transformations that occur in shape memory alloys such as AuCd and NiTi.

This work aims to connect atomistic model with continuum theory of phase transformations in Shape memory alloys(SMA). A formulation of the Helmholtz free energy potential based on the Lennard-Jones potential has been developed. Lennard-Jones potential was used to describe the inter-atomic interactions in bi-atomic crystal of NiTi. The microscopic expressions of the instantaneous mechanical (continuum) variables of mass, momentum, internal energy and temperature have been derived in terms of the atomic variables. The developed Helmholtz thermodynamic potential is used in the context of the sharp phase front-based continuum framework proposed by Stoilov et. el.(Acta Mat. 2002) to study the micro-macro transition during the thermomechanical response of NiTi crystals. The developed model has been successfully used to predict the response of 1D single crystal system.

Copper-Aluminum-Nickel (Cu-Al-Ni) single crystal shape memory alloy (SMA) wires show great potential in actuator applications due to their high stress-free transformation temperatures and superior mechanical stability compared to common Nickel-Titanium SMAs. In this paper, Cu-13.3%Al-4%Ni (wt %) single crystal wires with stress-free transformation temperatures in the range of 80° C to 120° C were subjected to stress cycling tests at ambient temperatures up to 100° C at low deformation rates. Stress/strain curves up to 9% and 3% strain in the range of the transformation temperatures point to the possibility of phase transformation by detwinning. However, the residual overall strain after unloading decreased significantly at 60° C for both 3% and 9% strains. Accumulation of plastic deformation was observed for subsequent cycles.

Wires of nickel-titanium have been tensile tested to evaluate their elastic constants, super-elastic characteristics and strength. These data are compared with the response of the same material to (hot stage) indentation testing, using both nano-indentation and micro-indentation equipment, and both a Berkovich and a spherical indenter. Indentation characteristics indicative of super-elastic behaviour are identified. In particular, the observation of enhanced indentation strain recovery when tested above the Af temperature, compared with tests performed at lower temperature, is recorded here and appears to represent a reliable indicator of super-elastic behaviour. Wires have also been joined together by liquid phase sintering, after a copper electroplating treatment, and by solid state diffusion bonding. Microstructural studies of these joints revealed the expected phases. Preliminary mechanical studies have given an indication that it may be possible to produce strong, highly porous super-elastic material in this way.

One way Shape Memory Effect (SME) is not suitable mechanism for application to the repeated actuation of an Shape Memory Alloy(SMA) wire because the host structure does not return to its initial shape after it cools down. In the present study, the two-way SME under residual stress is considered. A structure using the two-way effect returns to its initial shape by increasing or decreasing temperature under an initially given residual stress. A thermo-mechanical constitutive equation of SMA proposed by Lagoudas et al. was employed in the present study. Laminated composite beams and plates are considered as simple morphing structural components. The modeling of beams and plates are based on first-order shear deformable laminated composite beam and plate theories with large deflections. Numerical results of fully coupled SMA-composite structures are presented. The proposed actuation mechanism based on the two-way SMA effect and a simulation algorithm can be used as a powerful morphing mechanism and simulation tool for structures.

A complex modulus approach typical of viscoelastic materials is used to linearize the equation of motions of a combined beam-rod SMA pseudoelastic element and use a Spectral Finite Element formulation to study the dynamic behavior in the frequency domain. The complex modulus approach allows using viscoelastic SFE formulations presented in literature and adapt them to Ni-Ti alloy elements with different tensile pre-strain levels. The dispersion relations of Love rod and Euler-Bernoulli beams are discussed in view of the use of the experimental available complex modulus curves of the materials. As a demonstration of the use of the SFE technique, a cantilever beam loaded with a tip force is then modeled with a single Spectral Element, with increased accuracy of lower number of linear FE elements per unit wavelength.

Recently our group has succeeded, by producing very small particles of NbC carbides in austenite, in improvement of shape memory effect (SME) of the low-cost conventional Fe-Mn-Si based SMAs to such an extent that the so-called "training" treatment is no longer necessary. It was also found that the shape memory properties of the Fe-Mn-Si based SMAs were further improved by pre-rolling at 870K. The present paper describes similar improvement of shape memory properties of an Fe-15Mn-5Si-9Cr-5Ni-0.5NbC (mass %) by more convenient way of pre-extension at room temperature. This alloy is high corrosion-resistant (equivalent to SUS430) as well as low cost material, which is also one of the important requisites for industry application in various fields. A nearly perfect shape recover (90%) of an initial 4% strain was achieved when the alloy was pre-extended 12% at room temperature and then aged at 1070K for 10min. The origin of this improvement of SME has been studied by atomic force microscopy (AFM) and trasmission electron microscopy (TEM). It is concluded that uniform distribution of fine martensite plates with the same variant on the primary system is the key factor to obtain a perfect shape memory recovery.

The details and results of an analysis of two-dimensional (plane-stress), transversely isotropic, linear ferroelectro-magnetic continua are provided. An effective coupling coefficient for determining the ability of a ferroelectro-magnetic material to convert and store input energies for purposes such as active damping or energy harvesting is also presented.

A phase field model based on the work of Hu and Chen has been computationally implemented. The approach uses a minimization of global free energy to simulate the evolution of domain structures through the time dependent Ginzburg-Landau equation. The work focuses on the assumptions made when setting up the free energy function and the effect of these assumptions on the behavior of the model. Polarization is used as the independent variable. A fourth order polynomial is used to create four energy minima that represent the tetragonal phase in the two-dimension simulations. Linear superposition is used to modify the energy to account for the effects of sterss, electric field, and polarization gradients. This approach neglects field concentrations associated with material anisotropy and local geometric features. Considerable work will be required to incorporate these effects.

Nonlinear fracture mechanics concepts for ferroelastic materials are presented. A phenomenological constitutive law for ferroelastic domain switching is implemented within a steady state finite element formulation to determine the stress and strain fields near growing cracks in ferroelastic materials. Hutchinson's I-integral is applied to determine the relationship between the far field applied energy release rate and the local crack tip energy release rate. Computations are performed on both unpoled and "mechanically poled" materials with and without T-stress to quantitatively determine the toughening due to domain switching in these situations. Results are discussed in comparison to "transformations toughening" type analytical models.

A non-linear bimorph device is proposed, in which the strain accompanying ferroelectric switching is used to drive curvature of a bilayer of ferroelectric material. An analysis of the proposed device suggests that a curvature about an order of magnitude greater than that readily obtained by conventional piezoelectric bimorphs is possible, whilst the peak tensile stresses in the device are comparable with those in conventional devices. The curvature achieved by the device upon poling is calculated approximately by using an analytical approach with idealized material behaviour. Two potential designs for the poling electrodes are suggested, and numerical calculations are used to optimize these designs.

This paper examines the switching process occuring in ferroelectric and ferroelastic single crystals under electro-mechanical loadings. Ferroelectrics undergoing a cubic to tetragonal phase transition are considered. The single crystal energy has three origins: elastic, electric and the incompatibilities of the spontaneous strain and electric displacement fieds between domains. The stress and electric fields fluctuate and present jumps at the domain walls. As a consequence, they induce electro-elastic interaction energy. Thus, it involves dissipation that the present work aims to capture through a micromechanical approach.

The role of oxygen vacancies in fatigue and dielectric breakdown has been a topic of intense research in ferroelectric perovskites like BaTiO₃. This paper presents a comprehensive model that treats the ferroelectrics as polarizable wide band-gap semiconductors where the oxygen vacancies act as donors. First, a fully coupled nonlinear model is developed with space charges, polarization, electric potential and elastic displacements as variables without making any a priori assumptions on the space charge distribution and the polarization. Second, a Pt/BaTiO₃/Pt structure is considered. Full-field coupled numerical simulations are used to investigate the structure of 180° and 90° domain walls in both perfect and defected crystals. The interactions of oxygen vacancies with domain walls are explored. Numerical results show that there is pronounced charge trapping near 90° domain walls, giving rise to possible domain wall pinning and dielectric breakdown. Third, a simple analytical solution of the potential profile for a metal/ferroelectric semiconductor interface is obtained and the depletion layer width is estimated. These analytical estimates agree with our numerical results and provide a useful tool to discuss the implications of our results.

In this paper, we present an energy-minimization theory of ferroelectrics to characterize the domain engineered ferroelectric crystals. The energy-minimizing domain configuration is constructed, and the effective piezoelectricity is predicted.

A cohesive fatigue-crack nucleation and growth model for ferroelectric materials under electro-mechanical loading is presented. The central feature of the model is a hysteretic cohesive law which couples the mechanical and electrical fields. This law can be used in conjunction with general constitutive relations of bulk behavior, possibly including domain switching, in order to predict fatigue crack growth under arbitrary loading conditions. Another appealing feature of the model is its ability to predict fatigue-crack nucleation. Despite the scarcity and uncertainty of the experimental data, comparisons with PZT fatigue-life data are encouraging.

In this article, an experimental investigation to study the effect of residual stresses on the nonlinear behavior of ferroelectric ceramic material is reported. The effect of residual stresses on the behavior at low electric field and mechanical stress is demonstrated first by showing the large difference in the linear properties measured from strain behavior under mechanical and electrical loading, and resonance method. This is followed by an investigation on the mechanism of polarization reversal due to cyclic electric field. Based on the observed large magnitude of strain and the comparison of the magnitude of the sum of transverse strains with the magnitude of strain in the poling direction it is concluded that polarization reversal due to cyclic electric field in the ferroelectric material at morphotropic phase boundary is the result of two successive 90o domain switchings. Finally, two types of combined loading experiments were conducted to investigate the residual stress and electric field effect on the mechanism of domain switching. The behavior under combined loading showed many new interesting characteristics, and possible mechanisms for such behavior is discussed. While most of the characteristics of the ferroelectric behavior observed in the present experimental study could be explained based on the residual stress state, the understanding of others need further studies.

In the present paper a constitutive model for piezoceramics under multiaxial electromechanical loadings is developed for the engineering reliability analysis of piezoceramic components designed for so-called "smart" electromechanical sensor and actuator applications. At first a constitutive framework capable of representing general thermo-electromechnical processes is presented. This framework is established by using internal variables and is thermodynamically consistent with the Clasius-Duhem inequality for all admissible processes. Then, two scalar and two unit vector internal variables are introduced. One of the vectorial internal variables indicates the overall alignment direction of the c-axes of domains and the other variable represents the direction of the macroscopic irreversible polarization. The two scalar internal variables represent the fraction of domains whose c-axis is oriented in the alignment direction and the relative irreversible polarization, respectively. We indicate the microscopic foundation of the scalar internal variables in terms of an approximate orientation distribution function. A domain switching function is formulated in the driving force space to indicate the onset of the domain switching. The evolution equations of the internal variables are derived from the switching function by using the normality flow rule. Remanent strain and polarization are calculated as functions of the internal variables.In order to verify the underlying assumptions and to examine the ability of the model indescribing the material responses to electromechanical loadings, we demonstrate the simulation of various uniaxial and multiaxial loading processes.

Piezoelectric materials exhibit nonlinear behavior when subjected to large electric or mechanical loads. This strong nonlinear behavior is induced by localized polarization switching at the domain level. In this work, certain piezoelectric materials having tetragonal perovskite type microstructure characteristics are simulated using micromechanical approach in which linear constitutive and nonlinear switching models are done in each and every grain of the material. Uniaxial loading is applied in the simulation. The effect of different domain switchings (90° or 180° domain switching for tetragonal perovskite structure) due to energy differences, different probability functions, different statistical random generators and material parameters are analysed. The response of the bulk ceramics is predicted by averaging the response of individual grains that are considered to be statistically random in orientation. The observed strain and electric displacement hysteresis loops for the piezoelectric and ferroelectric materials are compared with previous experimental works described in the literature.

The current NASA Decadal mission planning effort has identified Venus as a significant scientific target for a surface in-situ sampling mission. The Venus environment represents several extremes including high temperature (460°C), high pressure (~9 MPa.), and potentially corrosive (condensed sulfuric acid droplets that adhere to surfaces during entry) environments. This technology challenge requires new actuator and sensor designs that can withstand these extreme conditions. In addition a variety of industrial applications could benefit from an extended operating temperature range of actuators and sensors. Piezoelectric materials can potentially operate over a wide temperature range reaching as low as -270°C to as high as +650°C. Single crystals, like LiNbO₃, have a Curie temperature that is higher than +1000°C. In order to investigate the feasibility of producing actuators/sensors that can operate under these conditions we have initiated a study of the properties of a variety of piezoelectric materials in the temperature range 250C to 5000C. These piezoelectric materials were chosen because they are solid state and can be designed as actuators to provide high torque, stroke, and speed. However the feasibility of this critical actuation capability has never been demonstrated under the extreme conditions mentioned above. We will present the results of our measurements on a variety of piezoelectric materials that can be operated at temperatures above 460°C. The data for small signal resonance analysis (ring, radial and thickness extensional modes) of disk and ring samples made of BST-PT and BMT-PT (TRS Technologies Inc.) and Bismuth Titanate BT (Ferroperm Piezoceramics A/S, Sinoceramics) as a function of the temperature will be presented.

The material properties of different piezoelectric ceramics were studied at elevated temperatures using the resonance method. Specifically the behavior of the longitudinal and transverse charge coefficients, dielectric constant, compliance coefficient and coupling coefficient were investigated. The modes studied were the length expander modes with the field both parallel and perpendicular to the strain and the materials under investigation were PZT (Navy II), Lead Metaniobate and Bismuth Titanate. All the samples studied were from the same manufacturing batch. The measured values of the charge coefficient at room temperature were compared with those obtained through direct methods (d33 meter and laser interferometer) and were found to compare well. Each material is affected differently by temperature changes, though all show a general increase in the charge coefficient with an increase in temperature. The increase in values of the charge coefficient is seen to be mainly due to the increase in the dielectric constant with very little influence from the mechanical coupling and compliance, except close to the Curie temperature where the coupling coefficient goes to zero. Bismuth Titanate has the widest temperature range however, based on a temperature scale normalized by the Curie Temperature PZT Navy II and Lead Metaniobate show the more stable material properties.

Pre-stressed curved actuators typically consist of a piezoelectric ceramic (lead zirconate titanate or PZT) laminated between various layered materials. In one configuration, THUNDER, the bottom layer is stainless steel and the top layer is aluminum; the metallic layers are attached to the PZT ceramic using a polymeric adhesive. In another configuration, Lipca-C2, the layers comprise a glass/epoxy composite and a carbon/epoxy composite. Experimental and numerical results of displacement performance under unloaded conditions have been investigated in the past. The results show that the Lipca-C2 devices produced more displacement than the THUNDER devices when clamped and unloaded. The present study includes a comparative performance of both devices under load to evaluate their lifting capability. Both out-of-plane and in-plane displacements are assessed as a function of load and voltage at low frequency. A non-contact laser was used for the out-of-plane measurements simultaneously with an optic fiber for in-plane displacement at 0 to 5N load values. The load is attached to one end of the actuators, and to avoid possible damage to the actuators, it is moved through a mechanism that utilizes a frictionless linear bearing and a pulley.

The present paper presents cyclic strain amplitude and longitudinal strain measurements of longitudinally compressed Terfenol-D particle samples subjected to magneto-strain cycling. A comparison is made of the responses of material strain cycle tested at temperatures near the matrix glass transition start temperature, and material strain cycle tested at a temperature near the matrix glass transition finish temperature. The cyclic strain amplitude of the material was significantly larger when tested at a temperature near the matrix glass transition finish temperature. A useful range of longitudinal applied stress exists where the composite suffers little apparent degradation. Beyond this range the composite exhibits steadily decreasing cyclic strain amplitude with increases in longitudinal compressive stress magnitude.

The Zone Melt Crystal Growth Method (FSZM) has been used to produce polycrystalline Galfenol specimens, Fe_81.6Ga_18.4, with preferred {100} orientation. This crystal growth technique has advantages over conventional Bridgman methods in that zone rates used were at least an order of magnitude greater; 350 mm/hr versus 2-4 mm/hr. This material had measured magnetostrictions ranging from 168 ppm to 220 ppm compared to 290 ppm for a single crystal with a similar composition. It was discovered that upon machining a large increase in magnetostriction occurred, ~15%. Using Orientation Imaging Microscopy (OIM) techniques it was shown that the magnetostriction increase is due to the removal of off-axis grains located on the circumference of the FSZM samples. The room temperature mechanical properties were measured to be 72.4 GPa-86.3 GPa modulus of elasticity, 348 MPa-370 MPa ultimate strength, and elongation values of 0.81% - 1.2% depending upon zoning conditions.

This investigation focused on dynamic characterization of a laminated polycrystalline sample of Fe_81.6Ga_18.4 alloy grown by the FSZM process. Previous studies using static characterization methods have shown unique properties of the alloy for use in transducers and active structures. Static characterization values were verified and material properties were contrasted with the "giant" magnetostrictive material Terfenol-D. Common test methods were used for dynamic characterization to calculate Young's modulus, coupling coefficient, magnetostrictive coefficient, and permeability. In addition, mechanical Q and potential efficiency were calculated. Comparison with static testing of single crystal samples showed that modulus, permeability, and magnetostrictive coefficient were very close to static values, with any differences being attributed to test fixture effects and material differences. Coupling coefficient appeared to be quite low, but no correction was applied for the test fixture losses and magnetic circuit effects. Comparisons with Terfenol-D show that with significantly less magnetic field, iron-gallium alloys can be used in high Q systems to achieve large acceleration and force output. The unique structural and magnetic properties of gallium-iron alloys enable applications that would be difficult or impossible with Terfenol-D.

The addition of Al and Ga to b.c.c. α-Fe increases the magnetostriction of Fe in the [100] direction (a factor of 12 for Fe₈₁Ga₁₉). Fe-based magnetostrictive materials are machineable, mechanically tough and relatively inexpensive. They can be used with tensile loading and saturate in fields of only a few hundred Oe, even under compressive loads up to -100 MPa. The effects of annealing single crystal Fe_86.9Ga_4.1Al_9.0 and Fe_86.9Ga_8.7Al_4.4 and polycrystalline Fe_81.6Ga_18.4 rods under stress were examined. Stress annealing allows the material to achieve most of its strain without applying a prestress, simplifying device design. Most importantly, it allows the materials to operate magnetostrictively under a tensile load. Annealing was performed in a vacuum furnace with a -100 MPa stress for 10 minutes. The Fe-Ga-Al samples were annealed at 700°C and the Fe-Ga samples at 625°C. The magnetostriction was determined before and after stress annealing using compressive stresses of -0.7 MPa to -28 MPa for the Fe-Ga-Al samples and from ~0 to -97 MPa for the Fe-Ga samples. One of the stress annealed Fe_81.6Ga_18.4 samples was measured under tensile stresses up to 34 MPa. After annealing, all samples showed full performance at near-zero stresses and tensile stress up to +20 MPa.

Tension testing is used to identify Galfenol material properties under low level DC magnetic bias fields. Dog bone shaped specimens of single crystal Fe_100-xGa_x, where 17≤x≤33, underwent tensile testing along two crystalographic axis orientations, [110] and [100]. The material properties being investigated and calculated from measured quantities are: Young's modulus and Poisson's ratio. Data are presented that demonstrate the dependence of these material properties on applied magnetic field levels and provide a preliminary assessment of the trends in material properties for performance under varied operating conditions. The elastic properties of Fe-Ga alloys were observed to be increasingly anisotropic with rising Ga content for the stoichiometries examined. The largest elastic anisotropies were manifested in [110] Poisson's ratios of as low as -0.63 in one specimen. This negative Poisson's ratio creates a significant in-plane auxetic behavior that could be exploited in applications that capitalize on unique area effects produced under uniaxial loading.

Iron-Gallium alloys demonstrate moderate magnetostriction (~350 ppm) and saturation material induction (~1 T) under low magnetic fields (~400 Oe) as well as high tensile strength (~500 MPa) and limited dependence of magnetomechanical properties on temperatures between -20°C and 80°C, making them promising materials for sensing and actuation applications. However, the mechanical and magnetic properties of these materials vary significantly with the percentage of gallium, which motivates this study on the effect of stoichiometry on the behavior of Fe-Ga alloys. Major loop compressive tests (loading to 110 MPa and unloading, at magnetic fields ranging from 0 to 891 Oe) were performed on single crystal 19% Ga and 24% Ga samples with longitudinal axis in the [100] direction. The effect of % Ga on Young's modulus, saturation magnetization (M_sat), ΔE-effect and d*₃₃ are discussed and explained. Furthermore, it was found that the magnetic field (H) through the sample changed with applied stress. A simple magnetic circuit analysis is developed in the latter part of the paper to model this effect. The ramification of both stoichiometry effects and variation in field on the design of Fe-Ga sensors is discussed.

In this paper, we present an energy-minimization theory of ferromagnetic particles to characterize the magnetization reversal and hysteresis loop of ferromagnetic polycrystals, with the inter-granular magneto-static interactions accounted for through the effective medium approximation. The energy-minimizing magnetization distribution is determined, and the remanence and coercivity are predicted.

The primary objective of this study is to estimate the parameters of a constitutive model characterizing the rheological properties of a ferrous nanoparticle-based magnetorheological fluid. Constant shear rate rheometer measurements were carried out using suspensions of nanometer sized iron particles in hydraulic oil. These measurements provided shear stress vs. shear rate as a function of applied magnetic field. The MR fluid was characterized using both a Bingham-Plastic constitutive model and a Herschel-Bulkley constitutive model. Both these models have two regimes: a rigid pre-yield behavior for shear stress less than a field-dependant yield stress, and viscous behavior for higher shear rates. While the Bingham-Plastic model assumes linear post-yield behavior, the Herschel-Bulkley model uses a power law dependent on the dynamic yield shear stress, a consistency parameter and a flow behavior index. Determination of the model parameters is a complex problem due to the non-linearity of the model and the large amount of scatter in the experimentally observed data. Usual gradient-based numerical methods are not sufficient to determine the characteristic values. In order to estimate the rheological parameters, we have used a genetic algorithm and carried out global optimization. The obtained results provide a good fit to the data and support the choice of the Herschel-Bulkley fluid model.

Alloys of iron and non-magnetic gallium (of the form Fe1-xGax where x ranges from 13 to 30) exhibit large magnetostrictions of over 300 ppm at room temperature that are produced by saturation magnetic fields of approximately 600 Oe. While not producing magnetostrictions of the degree achievable with giant magnetostrictives, large magnetostrictive alloys of iron and gallium, called Galfenol, have much more desirable mechanical characteristics, such as non-brittleness and in-plane auxetic behavior. Additionally, Galfenol requires a much smaller saturation magnetic field than the giant magnetostrictives Terfenol and Terfenol-D (alloys of Iron and non-metallic Terbium and Dysprosium). Beginning from the body of knowledge gained from Terfenol and Terfenol-D dynamic research transducer designs is a good starting point for designing a Galfenol dynamic research transducer. However, several modifications are being made to adapt the transducer to some of Galfenol's unique properties. Any measured value uncertainty will quickly propagate through the calculated material properties. While not completely successful at addressing all the unique aspects Galfenol in this transducer design, the data presented will assist in future design attempts.

Pre-existing cracks introduced by a Vickers diamond hardness indenter in PMN-0.3PT, which displays piezoelectric properties, increase in length under the action of low frequency cyclic electric fields applied normal to the crack. A minimum applied field of 1.1 x Ec is required to cause crack growth. In applied fields of 1.85-5.70 x Ec cracks grow to a common limiting length which is approximately 0.8 times the separation between the electrodes. New cracks are not generated at the corners of a Vickers diamond indent by applied fields up to 5.70 x Ec.

Mechanical testing of a bulk, single-crystal sample of Ni₅₀Mn₂₉Ga₂₁ produced large hysteresis loops indicating the potential for the material to be used as a damper. Damping capacity was measured as a function of energy absorbed by the material relative to the mechanical energy input to the system. Tan delta, the tangent of the phase lag between stress and strain, was calculated and shown to increase as a function of maximum strain level. Five strain levels were evaluated (1%, 2%, 3%, 3.5%, and 3.7%) with tan delta values increasing from 0.6 at 1% strain level to 1.1 at 3.7% strain level. The secant modulus of these curves was also evaluated at each strain level to characterize the sample in terms of both damping and stiffness. The maximum secant modulus of 285 MPa occurred at the 1% strain level and decreased to 56 MPa at 3.7% strain. Examining the stress and strain values in the time domain reveals a varying time lag and thus the reported values for tan d are considered an average measure of the material's damping capacity.

Ferromagnetic shape memory nickel-manganese-gallium (Ni-Mn-Ga) has shown tremendous promise as an actuator material due to its large strain and high bandwidth. However, current Ni-Mn-Ga devices are electromagnet based as this configuration allows for an externally applied force perpendicular to the applied field, and are therefore bulky, energy inefficient, and narrowband. We investigate the dynamic response of Ni-Mn-Ga driven by a solenoid transducer in which the magnetic field is aligned collinearly with the loading stress. The work focusses on the quasistatic and dynamic testing of a Ni₅₀Mn_28.7Ga_21.3 sample which is believed to have an internal stress field which plays the role of the restoring force necessary for reversible strains. This sample is shown to exhibit reversible compressive strains of -0.41% with no external forces applied. Several experimental apparatus are used in order to verify these results. The measurements demonstrate a 231% change in stiffness with applied dc magnetic fields.

A quasi-static model for NiMnGa magnetic shape memory alloy (MSMA) is formulated on the basis of NiTi SMA constitutive models such as the Brinson model, because of the similarities that exist in the behavior of both materials. NiMnGa shows a magnetically induced shape memory effect as well as a pseudoelastic behavior. Quasi-static tests at constant applied magnetic field and stress were conducted to identify the model parameters. The material parameters include free strain, Young's modulus, critical threshold fields and stress-influence coefficients. The Young's moduli of the material in its field preferred and stress preferred states were determined to be 450 MPa and 820 MPa respectively. Critical threshold fields as a function of stress were determined from constant stress testing. These test data were used to assemble a critical stress-temperature profile that is useful in predicting the various states of the material for a wide range of magnetic or mechanical loading conditions. Although the constant applied field and constant stress data have yet to be fully correlated, the model parameters identified from the experiments were used to implement an initial version of the quasi-static model. The model shows good correlation with test data and captures both the magnetic shape memory effect and pseudoelasticity. This introductory model provides a sound basis for further refinements of a quasi-static NiMnGa model.

In the current work, repeated mechanical and magnetic forces have been applied to Ni-Mn-Ga samples with different compositions and different thermomechanical histories in order to determine the combined effects of these parameters on the magnetic shape memory effects, especially the magneto-mechanical properties, of these alloys. The results demonstrate that prior history has strong influence on the twinning start stress and twinning strain. In addition, heat treatment of the materials seems to increase the amount of strain that can be obtained (up to the theoretical limit). Moreover, there is indication that prior heat treatment may also affect the martensite crystal structure that is formed during cooling. In addition, the dependence of martensitic transformation on composition and prior thermomechanical treatments was also studied by differential scanning calorimetry (DSC) analysis.

The experimental results of a preliminary study on stress-strain behavior of Cu-13.3% Al- 4% Ni (by wt.) single crystal shape memory alloy grown along the [001] direction at high temperatures are given. An Instron testing machine with a high temperature environmental chamber has been used to study the quasi-static stress-strain response of 1.5 mm diameter Cu-Al-Ni single crystal wires at different ambient temperatures in the range 100 - 160°C. Local strain measurements using a highly sensitive extensometer are compared with overall strain measurements computed from the net displacements between grips. The effect of stress cycles on overall strain on full loading, after unloading and after heating in between stress cycles has been discussed.

In order to understand the solidification behavior of Ni-Mn-Ga alloys, ingots with different compositions were prepared by arc melting. Two series of compositions were investigated: Ni_100-2xMn_xGa_x (15≤x ≤30) and Ni₅₀Mn_50-yGa_y (0≤y≤50). The microstructures obtained were observed and the compositions of the phases occurring in the ingots were identified by energy dispersive spectroscopy in the scanning electron microscope. Based on these observations, three solidification paths were identified: direct solidification of γ-Ni from the liquid, direct solidification of β-NiMnGa from the liquid, and solidification of β-NiMnGa phase via a peritectic reaction. It was found that the γ-Ni liquidus surface covers a large area of the ternary phase diagram. The γ-Ni liquidus boundary is located between Ni₅₀Mn₂₅Ga₂₅ and Ni₄₅Mn_27.5Ga_27.5 in the equal Mn and Ga alloy series, and between Ni₅₀Mn₅Ga₄₅ and Ni₅₀Mn₁₀Ga₄₀ in the 50 at.% Ni alloy series. The alloys with compositions close to the stoichiometric Ni2MnGa composition that show the magnetic shape memory effect are all covered by the γ-Ni liquidus surface. The β-NiMnGa liquidus surface covers the remaining alloy compositions.

This work illustrates the design, manufacturing and tensile testing of a novel concept of honeycomb structure made of shape memory alloy (SMA) core material. The honeycomb is manufactured using SMA Nitinol ribbons inserted in a special dye and using cyanoacrilate to bond the longitudinal strips of the unit cells. Analytical and Numerical FE models of the ribbons are developed to predict the homogenized properties and the overall tensile test behavior of the honeycomb sample. Good agreement is observed between numerical nonlinear simulations and experimental results carried out at room temperature (martensite phase).