Mechanical Prestress Research Articles

Modeling and numerical study of the electroacoustic behavior in integrated piezoelectric structures under external mechanical stress

The purpose of this study is to model and understand the role of an applied mechanical stress in piezoelectric materials as far as electroacoustic parameters are concerned.In the field of thick or thin film technology, understanding and predicting the behavior of integrated structures when submitted to external or internal mechanical stress is of primary importance. Thus, we propose a modified KLM electroacoustic model of transducer that enables to take into account the effect of a mechanical pre-stress. Then, a numerical study of the electroacoustic parameters for lithium niobate piezoelectric material(coupling coefficient, velocities, associated polarizations,and electrical input impedance) is conducted with regard to the azimuthal and elevation angles, as well as initial pre-stress values. Finally, we study the pulse-echo response of a complete piezoelectric transducer consisting of a piezoelectric film laid down upon a backing material and matching layers, with and without an initial stress, to highlight some benefits of a prestress load.

Measurements investigating the embedding procedure of the Wendelstein 7-X non-planar coils

One manufacturing step of the Wendelstein 7-X non-planar coils is intended to generate a mechanical prestress between winding pack and casing. To document this “embedding” procedure, we performed several temperature and electric resistivity measurements and geometric surveys before, during and after the embedding. We also investigated the behaviour of quartz sand, used to fill the gap between winding pack and casing, under pressure. The results of the whole body of investigations are consistent with the assumption that the achieved prestress is significantly lower than initially intended.

Plectin contributes to mechanical properties of living cells.

Plectin is a 500-kDa cross-linking protein that plays important roles in a number of cell functions including migration and wound healing. We set out to characterize the role of plectin in mechanical properties of living cells. Plectin(-/-) cells were less stiff than plectin(+/+) cells, but the slopes of the two power laws in response to loading frequencies (0.002-1,000 Hz) were similar. Plectin(-/-) cells lost the capacity to propagate mechanical stresses to long distances in the cytoplasm; traction forces in plectin(-/-) cells were only half of those in plectin(+/+) cells, suggesting that plectin deficiency compromised prestress generation, which, in turn, resulted in the inhibition of long distance stress propagation. Both plectin(+/+) and plectin(-/-) cells exhibited nonlinear stress-strain relationships. However, plectin(+/+) cells, but not plectin(-/-) cells, further stiffened in response to lysophosphatidic acid (LPA). Dynamic fluorescence resonance energy transfer analysis revealed that RhoA GTPase proteins were activated in plectin(+/+) cells but not in plectin(-/-) cells after treatment with LPA. Expression in plectin(-/-) cells of constitutively active RhoA (RhoA-V14) but not a dominant negative mutant of RhoA (RhoA-N19) or an empty vector restored the long distance force propagation behavior, suggesting that plectin is important in normal functions of RhoA. Our findings underscore the importance of plectin for mechanical properties, stress propagation, and prestress of living cells, thereby influencing their biological functions.

Power-law creep behavior of a semiflexible chain.

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Contributions of the Active and Passive Components of the Cytoskeletal Prestress to Stiffening of Airway Smooth Muscle Cells

Airway smooth muscle cells exhibit stiffening during contractile activation. This stiffening may be interpreted as a result of the stabilizing influence of the mechanical prestress stored within the cytoskeleton (CSK). However, in vivo, airway smooth muscle cells contract while simultaneously experiencing breathing-induced stretching. Excessive stretching of cells could cause actin-myosin crosslinks, and possibly other cytoskeletal filaments, to break, thereby leading to dissipation of the prestress and inhibition of further cell stiffening. The aim of this study is to investigate the stiffening behavior of individual human airway smooth muscle (HASM) cells exposed to a combination of substrate stretching, contractile activation and relaxation. We treated cultured HASM cells with either contractile (histamine) or relaxing (DBcAMP) pharmacological agonists and used magnetic cytometry technique to investigate the stiffening behavior of these cells during uniform substrate stretching (0-30%). Cells that were not treated, as well as those treated with histamine, exhibited increasing stiffening during stretching up to 20% of substrate strain, with additional stiffening becoming inhibited for substrate strains of 20-30%. In contrast, in cells treated with DBcAMP, stretching produced moderate but continuous stiffening with increasing substrate strain. These results indicate that both active and passive components of the prestress contribute to cell stiffening. We also observed that cells permeabilized with saponin exhibited stiffening at low levels (<10%) of substrate stretching, similar to non-permeabilized cells, but not at high levels (10-30%) of stretching, where stiffening was inhibited. These data suggest that at low levels of substrate strains the relative contributions of ion channel activation as well as actin and focal adhesion remodeling are less important for stiffening than passive distension of the CSK. Taken together, our results suggest that both the active and passive components of the cytoskeletal prestress contribute to the stiffening behavior of HASM cells under physiological conditions, but that at high levels of cellular distensions there is a possible tradeoff between these two components with the contribution from the passive component becoming increasingly more important.

A magnetostrictive mini actuator for long-stroke positioning with nanometer resolution

Giant magnetostrictive material can generate about 1600 ppm strain, and with the solid-state deformation principle it has the potential to render high force and precise displacement with a small volume, which makes it suitable to realize efficient miniature actuators. We have developed an inchworm linear motion mini actuator (50 × 30 × 30 mm) which is required to position an object over a range of some millimeters with nanometer resolution. An analytical model has been established for step displacement in quasi-static conditions, depending nonlinearly on both the magnetic excitation and the mechanical prestress exerted on the rod. Tests with the actuator prototype show that it can move on a flat surface with a velocity of 97.2 µm s−1 and a positioning resolution of up to 4 nm.

Design of a terfenol-D based fiber-optic current transducer

The authors have developed and tested a prototype magnetostriction-based, passive optical current sensing device for high-voltage applications. The sensor contains a ferromagnetic yoke, a modulator of magnetostrictive Terfenol-D that responds to the magnetic field, and a fiber Bragg grating that converts this response into a wavelength-modulated optical signal and transmits it via an optical fiber to ground-level electronics. To linearize the output, the modulator material was subjected to both mechanical and magnetic biases. The prototype CT was found to have a useable linear range of 100-1000 A with a measured phase shift of around 30/spl deg/ for a steady-state 60-Hz excitation. Both the gain and the phase response have been found to be dependent on mechanical prestress and magnetic bias. The authors also report on materials characterization and modeling that support the actual design process.

Single-crystal ferroelectrics for sonar devices

Single-crystal ferroelectrics or piezocrystals were recently introduced into the electroactive materials community. The 33-mode electromechanical coupling factor of piezocrystals is typically greater than 0.90, which is significantly larger than typical values for piezoelectric ceramics (0.62–0.74). For sonar projector applications this large, k33 has been responsible for more than doubling the bandwidth of active sonar arrays over what is currently achievable with ceramics. More recently, a crystal grower produced a cut of lead magnesium niobate-lead titanate (PMN-PT) single crystal with piezoelectric shear coefficient values of 7000 pm/V and shear coupling factors of 0.97. (For PZT5H, d15 is 730 pm/V.) This piezocrystal d15 coefficient implies significantly improved sensitivity and signal-to-noise ratio for accelerometers and hydrophones, while the high coupling promises bandwidth increases greater than those realized in 33-mode projectors using piezocrystals. The 31-mode is also being investigated. By measuring the response of the materials to high- and low-level electrical bias and excitation fields, mechanical prestresses, over temperature, the material’s effective material properties as a function of these operational variables have been determined. [This work sponsored by ONR and NUWC ILIR.]

Stress-Dependent Behavior of d33 and Y in Navy Types III and VI Ceramics E 33

The stress dependence of hard and soft active ceramic properties is important because many submarine sonar transducers are subject to compressive mechanical prestress as well as dynamic stress variations caused by ac electrical excitation. The level of prestress to which a ceramic in a transducer is subjected also depends in part on operational factors, such as the level of ac activation and depth of the submersible. This investigation builds upon prior work (Yang, G., Liu, S-F., Ren, W. and Mukherjee, B.K. 2000. “Uniaxial Stress Dependence of the Piezoelectric Properties of Lead Zirconate Titanate Ceramics,” Smart Structures and Materials 2000: Active Materials: Behavior and Mechanics, Proceedings of SPIE, Vol. 3992, pp. 103-113.) by examining the time dependence and the uniaxial stress dependence of the average, differential and dynamic d33 and YE33 of Navy Type III (PZT8) and Navy Type VI (PZT5H) lead zirconate titanate ceramics. This research incorporates higher levels of prestress and various mid-level ac stress cycles. Under short-circuit conditions, large and small compressive stresses are applied while measuring dielectric displacement and strain. The piezoelectric coefficient, d33, is evaluated using the direct method as a function of time, prestress level, and ac stress magnitude. The constant-field modulus is calculated from the slope of the corresponding stress-strain curves. Intrinsic and extrinsic contributions to these properties are discussed.

The influence of the thickness of non-piezoelectric pieces on pre-stressed piezotransducers

The mechanical pre-stress applied in piezotransducers used to generate high power ultrasound is needed to avoid ceramics fracture on traction cycle. Pre-stress levels inferior to 50 MPa can yield resonance shifting due to effectiveness of acoustic coupling between transducer pieces. Symmetrical transducers with different thickness of passive parts were submitted to axial mechanical pre-stress up to 50 MPa and their resonances were measured. The experimental results show the increasing of the resonances frequencies with the level of applied pre-stress. Similar effect is verified in simulations by using a model based on Mason’s equivalent electric circuit. Due to the similarity of these effects, a relation between applied pre-stress and pieces coupling was proposed for the transducer assembled. In addition, the dependence of the thickness of non-piezoelectric pieces on the coupling effectiveness between them is discussed. The results show that transducers with small thickness present more expressive shifting resonance ratio.

Stress Relaxation in Prestressed Composite Laminates

Viscoelastic deformation caused in symmetric laminated plates by release of fiber prestress and by uniform thermomechanical loads is analyzed on the constituent, ply and overall laminate scales with the Transformation Field Analysis (TFA) method (G. J. Dvorak, Proc. R. Soc. Lond., 1992, A437, pp. 311–327). Fiber prestress is applied in individual plies prior to matrix cure and released after matrix consolidation. Linear or nonlinear viscoelastic constitutive relations are used to evaluate the inelastic deformation rates in terms of current constituent stress averages. The TFA method regards both thermal and inelastic strains as piecewise uniform eigenstrains acting in superposition with mechanical loads and fiber prestress release on an elastic laminate. Interactions between the eigenstrains at the three different size scales are described by certain influence functions derived from micromechanical analysis of the plies and laminates. Applications describe stress relaxation in two carbon/epoxy laminates after cooling from the curing temperature and release of optimized fiber prestress, that allows maximum tensile load application while keeping both interior and free-edge stresses within prescribed strength limits. Subsequent viscoelastic deformation under constant rate loading, and stress relaxation caused by a sustained application of an elevated temperature to a laminate without prestress are also analyzed. Results are presented in the form of initial failure maps that identify overall stress states which may or may not initiate a specific damage mode in the laminate.

Design, production and testing of PMN–PT electrostrictive transducers

Lead magnesium niobate ceramics (PMN) are promising materials for application in the field of high power transducers. The advantage of PMN materials are the large strains generated under moderate electric field and the low hysteresis. The electrostrictive effect is non-linear, the corresponding physical constants depend on temperature and frequency and a DC electrical bias is required. These difficulties must be considered at the design stage. A finite element model has been developed and validated in the ATILA code for non-linear static and time-domain analyses. These numerical modelings are used to design and test two Langevin-type electrostrictive transducers. The first transducer is made of PMN–PT–La (90–10–1%) ceramics (TRS Ceramics), the second one of ESC1 ceramics (Morgan Matroc). For given static mechanical prestresses, resonance frequencies and effective coupling coefficients are measured at different DC electric fields and temperatures.

Characterization of piezoelectric single crystals for sonar and actuator applications

Piezoelectric single crystals show great promise for sonar and actuator applications due to their very high piezoelectric constant and electromechanical coupling factor. However, in order to accurately assess their potential, the effect of operating conditions (i.e., applied electric field, mechanical loading, and temperature) on their material properties must be determined. Furthermore, the mechanical strength of these materials in compression and tension must be known to avoid mechanical failure in transducers. A brief overview of the various methods used to characterize these crystals will be presented. In particular, material properties obtained using the NUWC Newports Stress Dependent Electromechanical Characterization System (SDECS) will be detailed. The variability of these properties under applied mechanical prestress, high electric fields, and varying temperatures shall be examined. An enhancement of the piezoelectric response with the application of prestress in certain crystals will be shown. In addition, results from compression strength testing conducted at NUWC will be presented. It shall be demonstrated that these crystals are much stronger than was assumed previously. Finally, future challenges in the measurement and analysis of these materials will be identified, including the identification of material flaws and quantification of the processes that lead to cracking in piezocrystals. [Work sponsored by DARPA.]

Nonlinear output control in hysteretic, saturating materials

The problem of determining the drive waveform that produces a desired output from a hysteretic, saturating material is considered both theoretically and experimentally. The specific problem of interest is the production of a high-amplitude, but monofrequency, sinusoidal polarization response. (The techniques presented could also be used to control other physical variables, such as the strain, if desired.) Two sample materials were considered, one of which is characterized by relatively low hysteresis (tan δ≈0.03) and tested using mechanical prestresses of 20.7 MPa (3 kpsi) and 41.4 MPa (6 kpsi), and the other of which is characterized by relatively high hysteresis (tan δ≈0.11), and tested without a prestress. Both samples were fabricated from the electrostrictive material lead magnesium niobate (PMN), although a magnetostrictive material (such as Terfenol-D) could have been tested instead. The samples were subjected to a bias voltage and prestress in order to simulate conditions that might arise in a full transducer. By analytically inverting a theory of hysteresis [J. C. Piquette and S. E. Forsythe, J. Acoust. Soc. Am. 106, 3317–3327 (1999) and J. Acoust Soc. Am. 106, 3328–3334 (1999)], the required (predistorted) drive waveform was determined. Both semi-major and minor hysteresis loops, in both polarization and strain, were measured and the parameters of the theory determined by least-squares fitting. The measurements were obtained under quasi-static conditions, with drive frequencies at or below 10 Hz. The observed fits of theory to data are of high quality. The theory was then inverted analytically to determine the drive required to produce the desired monofrequency polarization response, having a peak polarization value approximately equal to that achieved using a biased sinusoid of AC amplitude equal to the bias. The total harmonic distortion (THD) in the output polarization resulting from the inverting drive, computed using 10 harmonics, was experimentally observed to be about an order of magnitude less than that resulting from a biased sinusoid in all cases. It is shown that the hysteresis loop arising when using the distortion-reducing drive is of smaller area than that obtained when driving with a sinusoid to achieve the same polarization amplitude. Thus, the distortion-reducing drive results in a smaller loss per cycle than is obtained with a sinusoidal drive.

Formation of tangential pre-stress as a residual stress and its influence on the tribological performance of nodular cast irons

Since any state of residual stress influences the service behavior of a material, it is of particular interest for engineers and designers to know its benefits to machine parts, and where it can be utilized successfully. From this point of view, mechanical tangential pre-stress as circumferential compressive residual stress has been investigated for wear performance. For this purpose, a thick walled cylinder specimen model was established as a tribo-element, and the force, which will form the desired tangential pre-stress representing residual stress, has been calculated by the rules of elasticity theory. In order to compare the effect of residual stress on the wear performance under dry and lubricated conditions, 0.8 R e (R e: unidirectional yield strength) were applied to the nodular cast iron (DDK-40, DDK-60) specimens. Wear test results have been evaluated in terms of two different stress levels, 0 R e and 0.8 R e, formed on the specimen.

Comparison of minor to major loop properties in PMN-PT ceramics

The electromechanical properties of lead magnesium niobate-lead titanate (PMN-PT) ceramics are of great interest to transducer designers. Typically, the strain versus electric field and polarization versus electric field curves used to obtain those properties are measured over a major loop, i.e., one with a large dc bias and large ac signal. However, many devices are designed to operate at lower fields that fall entirely within the major loop, i.e., in a minor loop. Since the electromechanical properties of PMN-PT are strong functions of the bias and drive levels, it is crucial to understand how well properties derived from the major loop measurement correspond to the actual minor loop properties. In this study, electromechanical measurements on PMN-PT corresponding to minor loops at varying dc bias, ac drive, mechanical prestress, and temperature levels were made. The equivalent piezoelectric constant, dielectric constant, and dielectric loss factor for these minor loops will be compared to the corresponding major loop parameters. It will be shown that, in many cases, the parameters derived from the major loop agree quite well with the directly measured minor loops. An attempt to establish the lower limit for extracting minor loop properties from major loop data will be made.

Large-signal characterization of prestressed PMN-PT-Ba and PMN-PT-Sr at various temperatures

Quasistatic (10-Hz) electromechanical measurements were made of two relaxor ferroelectrics, PMN–PT–Ba (90 mol% lead-magnesium-niobate, 10 mol% lead-titanate, doped with 3% barium) and PMN–PT–Sr (88 mol% lead-magnesium-niobate, 10 mol% lead-titanate, 2 mol% strontium, w/2500 ppm iron oxide) under high electric fields (0–1.5 MV/m) and high mechanical prestresses (0–41.4 MPa) over a temperature range (−5–40 °C). The measured quantities—the piezoelectric constant, d33, the permittivity, ε33T the Young’s modulus, Y33E the electromechanical coupling factor, k33, and the energy density, U—are found for both small and large ac signal conditions. These measurement conditions and material properties are of great interest for applications in high-power Navy sonar transducers to material manufacturers. Material property trends with increasing prestress, temperature, and electric field are identifieid. The PMN–PT–Sr is shown to have better properties for sonar transducers than the PMN–PT–Ba. Compared to Navy type-III PZT piezoelectric ceramic, the energy density of PMN–PT–Sr at 5°C and 41.4 MPa is nearly 11 dB higher and the coupling 23% lower.

Characterization of PMN-PT-La for use in high-power electrostrictive projectors

There is increasing interest in relaxor ferroelectrics such as PMN-PT-La,Ba (lead magnesium niobate-lead titanate doped with lanthanum or barium) for use as high-power transducer driver materials in lightweight projector arrays. These electrostrictive materials have been shown to have induced strains an order of magnitude greater than PZT at modest electric fields. The drawback, however, is that the response of the material is dependent on frequency, prestress, temperature, and ac drive and dc bias fields. To date no measurements have been made of all these relationships for 33-mode vibration applications. In this study, using various mechanical prestresses, quasistatic room temperature measurements were made of the piezoelectric constant, d33, of the relative permittivity, ε33T/ε0, and of the short-circuit Young’s modulus, Y33E for PMN-PT-La (TRS Ceramics, Inc., 0.90 / 0.10 /1%, 31 March 1995). Electric fields of up to 2 MV/m were applied to samples (2×2×10 mm that were prestressed from 0 to 12 ksi (83 MPa). The material was found to have energy density values comparable to Terfenol-D, but its lower electromechanical coupling may compromise the useful bandwidth. [Work sponsored by the Office of Naval Research.]

Two-dimensional modeling and characterization of PMN electrostrictive materials using the finite-element code ATILA

New electrostrictive lead magnesium niobate ceramics (PMN) are promising materials for applications in the field of actuators, transducers, and motors. These materials have strains roughly an order of magnitude larger than those of the lead zirconate–titanate (PZT) ceramics. However, the use of these electrostrictive materials for practical applications presents some difficulties: highly nonlinear properties, temperature dependence of dielectric permittivity near the dielectric maximum, dc bias field needed. To improve the use of these electrostrictive materials, a better knowledge of the physical tensors of PMN and the development of a numerical tool are necessary. In this study, the development of a two-dimensional electrostrictive element in the ATILA code for nonlinear static analysis and time-domain analysis is presented. Two different models are tested including or not the effect of polarization saturation. The validity of both models is demonstrated by comparing computed strain and charge density with analytical solutions and measured results for a PMN bar at various electric dc fields and mechanical prestresses. Measurements are realized to obtain the complete physical tensor of PMN. Finally, the model is applied to a Janus transducer to describe the application of prestress and the electrical dc polarization.

Calculation of quasi-static electromechanical coupling coefficients for electrostrictive ceramic materials

The quasi-static coupling coefficients, k/sub 13/ and k/sub 33/, for electrostrictive ceramics are computed analytically. The calculation is based on a three-dimensional constitutive relation that models both electrostriction and nonlinear dielectric behaviors. The results show that the coupling factors depend on the amplitudes of the applied ac field and the dc bias, as well as the mechanical prestress. For an actuator without bias voltage or prestress, the coupling coefficients approach an asymptotic value with increasing electric field. The primary coefficients, k/sub 13/ and k/sub 33/, for a lead magnesium niobate, Pb(Mg/sub 1/3/Nb/sub 2/3/)O/sub 3/-PbTiO/sub 3/BaTiO/sub 3/(PMN-PT-BT), based relaxor ferroelectric are computed as an example. The results show that the coupling coefficients for PMN-PT-BT materials are roughly comparable with those of existing piezoelectrics. These coefficients are important parameters for material section and power source design for transducer devices.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>