Piezoelectric Ultrasonic Composite Oscillator Technique Research Articles

Linear and nonlinear electro-elastic/electro-damping effect in ferroelectric ceramics

The linear piezoelectric and nonlinear hysteresis behaviors of ferroelectrics are well-known and have been extensively studied. However, less attention has been paid to the variations of their mechanical properties under electric loading. In this work, using tube and cylinder specimens, three independent elastic coefficients and related internal frictions of PZT-5H ferroelectric ceramics are measured using our proposed modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT) under an electric field E3 along the poling direction. Results show that under low electric fields, the elastic coefficients s11E, s66E and all internal frictions decrease linearly with E3, whereas s44E increases linearly with E3. Based on these linear results, two fifth-order tensors are defined, i.e., linear electro-elastic and linear electro-damping tensor with the reduced symbol of pikl and qikl, among which p311, p366, p344 and q311, q366, q344 are obtained in this work. When the applied electric field exceeds the coercive field (∼500 V/mm), nonlinear electro-elastic/electro-damping effect dominates, resulting in reversed butterfly curves for s11E and s66E and butterfly curves for s44E. As to the internal frictions under large bipolar fields, they seem to be a superposition of the reversed butterfly curves and a peak or valley at the coercive field. The linear electro-elastic effect in ferroelectric ceramics is caused by the reversible domain wall motions while the nonlinear electro-elastic effect is caused by non-180° domain switching and is well reproduced by a statistical model. The linear and nonlinear electro-elastic/electro-damping results obtained in this work offer new insight into the electromechanical coupling behavior of ferroelectric materials.

Anomalies in the ultrahigh-temperature elastic moduli and internal frictions of Ti-6Al-4V alloys revealed by M-PUCOT

Although titanium alloys can be operative at high temperatures up to 700 ∘C, their mechanical properties at ultrahigh temperatures are not well studied. In this work, an automatic testing system is designed for the modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT) to measure the elastic moduli and internal frictions of two different Ti-6Al-4V alloys from room temperature to 1200 ∘C. The results show that for the as-received Ti-6Al-4V (with standard heat treatment), which contains an equiaxed α phase and a small amount of the β phase, a large internal friction peak due to the phase transition (α+β→β) is observed for the first time. However, for the Ti-6Al-4V annealed at 1200 ∘C, no phase transition peak is observed; instead, a weak Debye-type peak is observed. Moreover, the elastic moduli and hardness are significantly enhanced, which is attributed to the increase in interstitial oxygen atoms and the complete formation of the Widmanstätten α structure.

High-frequency K[formula omitted] internal friction peaks in polycrystalline aluminum and magnesium near the melting points at longitudinal and torsional resonance

By using a modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT), the temperature dependence of Young’s modulus, shear modulus and related internal frictions of 4 N polycrystalline aluminum and magnesium were measured from room temperature to 900 K at longitudinal and torsional resonance under several tens of kilohertz. The grain boundary internal friction peaks (Keˆ peaks) accompanied by large moduli relaxations were observed near the melting point (~0.86 Tm and 0.78 Tm for Al and Mg respectively) in both vibration modes. The activation energy of grain boundary relaxation is almost the same for the two vibration modes, which is 31.2 kcal/mol for aluminum and 36 kcal/mol for magnesium. The peak values of grain boundary internal frictions are significantly dependent on the vibration mode, and for both materials, the torsional peak is about 1.5 times higher than that of longitudinal peak. Finally, the experimental results were evaluated by using existing grain boundary slipping models (including 3D and 2D Zener’s model, Budiansky and O’Connell’s model and Ghahremani’s model). Results show that the periodic hexagonal grains sliding model (Ghahremani’s model) can reproduce the experiments best.

High-frequency elastic moduli and internal frictions of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass during glass transition and crystallization

Temperature dependent Young's modulus, shear modulus and the related internal frictions of Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit-1) bulk metallic glass (BMG) were measured by using the modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT) at longitudinal and torsional resonance under several tens of kilohertz, respectively. An irreversible internal friction peak accompanied by a very small modulus relaxation (about 10%) are observed near the onset crystallization temperatures Tx in each resonance mode, and the peak values in these two modes are almost the same, indicating that the supercooled liquid region (SLR) is far from liquid state under high frequency vibration with micro strain (~10−7) amplitude. What is more, the internal friction peak value decreases obviously after a preheating process to SLR (~410 °C) and the final values of moduli are proportional to the crystallinity. All these interesting phenomena during the glass transition and crystallization can well be interpreted through a three-parameter anelastic solid phenomenological model.

Review of the measurement methods for elastic moduli and internal frictions of solids

Elastic moduli and internal frictions are fundamental properties of solid materials and their measurement accuracy and convenience are of great significance to industrial production and scientific research. This paper reviews the measurement methods of elastic moduli and internal frictions of solid materials in the past 100 years, which can be divided into four types: quasi-static method, low frequency method, resonance method and wave propagation method. Firstly, the measurement principle of each type method is introduced and evaluated. Then the resonance methods, including free-free beam method, impulse excitation technique, resonant ultrasound spectrum and piezoelectric ultrasonic composite oscillator technique (PUCOT) are presented and discussed in detail. After that, a new method called modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT), proposed by the current authors, are introduced. This new method is based on the principle of electromechanical impedance, and can measure the Young’s modulus/shear modulus and the related internal frictions simultaneously, accurately and quickly. Finally, the significance and prospective of this new method are discussed.

New method enables multifunctional measurement of elastic moduli and internal frictions

Elastic moduli and internal frictions are fundamental properties of solid materials, and they are usually fairly sensitive to temperature, microstructure, deformation, and external fields. Measurement of elastic moduli and internal frictions is very important and useful in both academics and engineering. In this work, we first briefly reviewed the measurement methods of elastic moduli and internal frictions over the past 100 years and the related applications. Next, a promising measurement method called modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT) was presented which can measure Young's modulus, shear modulus, and the related internal frictions accurately and quickly. Then, some typical measurement results using M-PUCOT on metals and phase transition materials were presented from room temperature up to 500 °C. The M-PUCOT measurement on rocks after different levels of compression was also conducted to predict the damage before fracture. The perspective and challenge of the M-PUCOT method as the indicator of heat treatment, mechanical fatigue, and early damage of metals and ceramics were further presented and discussed. It is expected that, in the near future, the measurement of elastic moduli and internal friction will be as convenient as that of electric conductivity, permittivity, etc. and can turn to be a multi-functional tool for many advanced applications.

Anomalies in Young's modulus behavior after annealing in polycrystalline SmS

In this paper, the dependencies of Young's modulus and attenuation decrement on samarium sulfide polycrystals (SmS) under various annealing temperatures are studied by the piezoelectric ultrasonic composite oscillator technique at a frequency of 100 kHz in the temperature range of 80–300 K. A decrease in Young's modulus with an increase of the annealing temperature due to the texturing of the material was revealed. At the same time, attenuation peaks were observed at temperatures about 90 and 125 K, presumably due to Niblett-Wilks and Bordoni relaxations.

Measurement of elastic moduli and internal frictions using modified piezoelectric ultrasonic composite oscillator technique with large frequency mismatch

In this Note, first, the calculation errors of elastic moduli and internal frictions using the explicit formulas in the traditional and modified piezoelectric ultrasonic composite oscillator technique (PUCOT and M-PUCOT) are comparatively studied when the frequency match condition is not satisfied. Then, new implicit formulas free of frequency match are proposed for the three-component M-PUCOT. Finally, the measurement results on a lead zirconate titanate ferroelectric ceramic from room temperature to 500 °C by using the pervious explicit formulas and the new implicit formulas are compared. The results show that when the frequency mismatch is within 15%, the induced error by using the explicit formulas is less than 0.5% and 2.5% for moduli and internal frictions, respectively. When the frequency mismatch is over 15%, the implicit formulas are suggested to improve the accuracy of M-PUCOT.

Anomalous elastic moduli and internal frictions in unpoled and poled lead titanate zirconate ceramics near the Curie temperature

Phase transitions in ferroelectric materials are always accompanied by mechanical property variations; thus, besides the dielectric measurement, the measurement of mechanical properties can also be used to study the phase transition process in ferroelectrics. In this work, the temperature-dependent Young’s modulus, shear modulus, and the related internal frictions of unpoled and poled lead titanate zirconate (PZT) ceramics (including soft PZT-5H and hard PZT-4) were comparatively measured at tens of kilohertz by using a modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT). It is found that for the unpoled and poled PZT ceramics at Curie temperature (190 °C for PZT-5H and 330 °C for PZT-4), both moduli reach their local minima and both internal frictions exhibit peaks. Below the Curie temperature, the Young’s modulus of the poled PZT is larger than that of the unpoled one, while the tendency of the shear modulus is just the opposite. Above the Curie temperature, both moduli increase quickly and both internal frictions drop quickly, and all the four mechanical parameters of poled PZT coincide with those of the unpoled PZT; they stabilize at about 400 °C for PZT-5H and at about 480 °C for PZT-4. In addition, it is found from the mechanical measurement that poled PZT-5H can be partially depolarized even at 180 °C, slightly below the Curie temperature of 190 °C. The results in this work are very helpful to deeply understand ferroelectric phase transitions, and the M-PUCOT is strongly suggested to measure the temperature-dependent mechanical properties of ferroelectrics.

A modified piezoelectric ultrasonic composite oscillator technique for simultaneous measurement of elastic moduli and internal frictions at varied temperature.

In this work, a modified piezoelectric ultrasonic composite oscillator technique (M-PUCOT) is developed for measuring a material's elastic moduli and internal frictions, as a function of temperature. Different from the traditional PUCOT that employs two quartz bars as the drive and gauge, here, a single small piezoelectric transducer (PZT) ring is used to drive and sense longitudinal or torsional vibration in a cylinder specimen. Because of the strong piezoelectric effect and relatively large bandwidth of the PZTs compared to their quartz counterpart, the frequency match condition between the transducer and the specimen is not required in this M-PUCOT. For high temperature measurement, a fused quartz spacer, whose resonance frequency matches the specimen's, is bonded between the transducer and the specimen to provide thermal insulation. First, the united equivalent circuit of the transducer- (spacer) -specimen composite system was derived. Then, Young's modulus, longitudinal friction, shear modulus, and torsional friction were explicitly obtained by measuring the resonance frequency and antiresonance frequency of the 2- or 3-component system's electrical susceptance curve using an impedance analyzer. The accuracy of this method was validated both by measuring the system's amplitude-frequency curves using a laser vibrometer and through finite element simulations. The repeatability error of the M-PUCOT is only ∼0.2% for moduli measurement and ∼2.5% for internal friction measurement, which is very promising for studying the moduli and internal friction variations during damage, fatigue, and phase transitions. Finally, the M-PUCOT was employed to measure the variations in moduli and internal frictions of an Fe64Ni36 Invar alloy from room temperature to 500 °C. Results show that above the ferromagnetic phase transition temperature Tc, both moduli reach their maxima, and both internal frictions reach their minima. The proposed M-PUCOT is expected to be widely used in the near future for its quick measurement, high repeatability, and low cost.

A review of mechanomagnetic spectroscopy. Case study: Dy polycrystals

The current state and capabilities of mechanomagnetic spectroscopy (MMS) are reviewed. Such technique, based on the Piezoelectric Ultrasonic Composite Oscillator Technique (PUCOT) has been developed to study the magnetoelastic coupling through the reversible inverse magnetostriction (reversible Villari effect, RVE) over wide ranges of periodic stress, temperature and polarizing magnetic field H. The technique allows one to study also elastic and anelastic properties simultaneously with RVE. Measurements of RVE can be performed as a function of cyclic applied field H(t)=H0sinωt at constant temperature or as a function of temperature at fixed H. In contrast to other macroscopic techniques, MMS is not based on the measurement of the strain or length of the sample with and without applied field. This important advantage allows us to study very weak magnetoelastic coupling, like in the antiferromagnetic phase of Dy for magnetic fields as low as the Earth's one, which requires an extremely high sensitivity. Based on the Maxwell relation, an algorithm was developed to estimate the direct longitudinal magnetostriction versus H from the RVE.

Mechanomagnetic spectroscopy of ferromagnetic shape memory alloys

We have used a recently designed mechanomagnetic spectroscopy technique to study the inverse magnetoelastic effect (stress-induced magnetization) in ferromagnetic materials simultaneously with their elastic and anelastic properties. Special attention has been paid to ferromagnetic shape memory alloys. Application of mechanomagnetic spectroscopy technique allows one to study the stress-induced motion of elastic (by means of the anelasticity measurements) and magnetic domain boundaries (through the detection of the stress-induced magnetization). The experimental technique is based on the piezoelectric ultrasonic composite oscillator technique with an additional magnetic channel, enabling to register the induction, produced by the strain of a ferromagnetic sample, down to 10 −10 T. Examples of application of this new technique are given, which include observation of a temperature–magnetic field domain wherein magnetoelastic coupling demonstrates variations of sign and analysis of magnetic domain wall dynamics in polycrystalline ferromagnetic martensites.

Automated apparatus for dynamic mechanical analysis using the piezoelectric ultrasonic composite oscillator technique

Computer-controlled apparatus for the measurements of dynamic Young's modulus and internal friction as functions of temperature, using the piezoelectric ultrasonic composite oscillator technique (PUCOT), has been designed and demonstrated. The versatility of the apparatus and its resonance tracking techniques have been proven by detecting subtle structural phase transformations within the Ca1−xSrxTiO3 perovskite system as well as dramatic changes accompanying the martensitic transformation in a Au–Cd shape-memory alloy. The simplicity of the PUCOT technique allows a system such as this to be constructed easily and with low cost.

A new design of automated piezoelectric composite oscillator technique

We describe the latest design of the automated piezoelectric ultrasonic composite oscillator technique, which has traditionally been used for the measurements of elastic and anelastic properties of solids at frequencies of 70–140 kHz in a continuous positive feedback mode. The new equipment features several substantial advantages, as compared to previous constructions, owing to the application of up-to-date data acquisition units and microelectronics components.

Dynamic Shear Modulus and Damping in Iron-Copper and Steel-Based Metal Matrix Composites

Abstract Measurements were made of the density, dynamic shear modulus, damping, strain amplitude, and resistivity in iron-copper and steel-based metal matrix composites. The density was determined using the Archimedes method and was found to be in the range of 7463 to 8257 kg/m3. The shear modulus, damping, and strain amplitude were determined using the piezoelectric ultrasonic composite oscillator technique (PUCOT). The shear modulus was in the range of 73 to 81 GPa. Electrical resistivity measurements were performed to assess the change in the conductivity of the composites by adding copper. Metallographic studies and microhardness testing were performed to assess the distribution and hardness of the fibers in the composites. The variation of shear modulus and electrical conductivity with respect to the percentage of copper in some of the composites followed the rule of mixtures. The damping in the specimens was near 3 × 10-3 and independent of strain amplitude.

Experimental Investigation of the Dynamic Elastic Modulus and Vibration Damping in MoSi<SUB>2</SUB>-30%Si<SUB>3</SUB>N<SUB>4</SUB> as a Function of Temperature

The dynamic elastic modulus, E, and vibration damping of molybdenum disilicide (MoSi2) with 30% volume addition of silicon nitride (Si3N4) were measured at varying temperatures using the piezoelectric ultrasonic composite oscillator technique (PUCOT). The value of the elastic modulus of the composite was observed to decrease as temperature, T, was increased. The value of dE/dT of MoSi2 was determined to be −0.03 GPa/K. The vibration damping of MoSi2-30%Si3N4 increased as temperature was increased, with an effective activation energy of 0.076 eV/atom. This was an average over the entire temperature range, but two distinct slopes were observed in the plot of damping versus inverse temperature.

Temperature dependence of dynamic Young's modulus and mechanical damping in SCS-6/Beta-21S titanium metal matrix composites

Titanium-metal matrix composites (Ti-MMCs) are useful in applications that require high temperature performance, high specific strength, specific stiffness, creep resistance, and fracture strength. They are particularly useful in applications such as aerospace and engine components when conventional metals and ceramics are inadequate. The SCS-6/Beta-21S Ti-MMC gains its strength and stiffness from a network of silicon carbide fibers embedded in a titanium alloy matrix. This paper discusses an investigation into the temperature dependence of dynamic Young’s modulus and mechanical damping. The Piezoelectric Ultrasonic Composite Oscillator Technique (PUCOT) was used to determine the modulus and damping. The experimental data, together with findings from metallography, were applied to the Granato-Lucke theory of mechanical damping due to dislocations to give estimates of the dislocation density. The material was fabricated by hot-pressing alternating layers of matrix foils (Ti-15Mo-2.7Nb-3Al-0.2Si0.15O2) and continuous SiC (Textron SCS-6) fibers in a quasi-isotropic [0/±45/90]s orientation. The volume percent of the fibers was approximately 35% [1]. Strips 3 mm wide and approximately 30 mm in length were cut from the as-received sections with a low speed diamond saw. The PUCOT is a popular method of measuring the dynamic Young’s modulus, mechanical damping, and strain amplitude. Two α-quartz crystals (a drive crystal and a gauge crystal), a fused quartz spacer rod, and the specimen were glued together and excited by alternating voltages so that they experience resonant longitudinal stress waves. The gauge voltage is proportional to the strain amplitude. Values for the drive and gauge voltages, the resonant period of the system, and the density of the specimen were required for the PUCOT analysis, which returns the values of Young’s modulus, mechanical damping, and strain amplitude. The density was determined using Archimedes’ method. More information on the PUCOT theory is available elsewhere [2, 3]. For PUCOT tests at elevated temperatures, the specimen was glued onto the end of a fused quartz rod and inserted into a furnace. The spacer rod allowed the piezoelectric crystals to remain near room temperature while the specimen was brought to an elevated temperature within the furnace. A different length of rod was required for each test temperature to transmit longitudinal vibrations from the transducers to the specimen at the resonant frequency of the system. The damping that occurred within the rod is accounted for in the PUCOT analysis. PUCOT tests were conducted at test temperatures of 220, 350, 530, 680 and 850◦C. At each test temperature, the strain amplitude of the specimen was varied by modifying the gauge voltage, and hence the magnitude of the longitudinal vibrations, while holding the temperature constant. The strain amplitude was varied between a background level of approximately 3× 10−7 and a peak value of approximately 3× 10−4. Mechanical damping was measured at each strain amplitude. Micrographs were taken of two samples from the same specimen: a room temperature sample that did not experience elevated temperatures, and a sample that was held near 500◦C for 0.5 h, which was the duration of a typical PUCOT test. The samples were prepared by cutting the composite specimen with a diamond blade in a direction perpendicular to most of the fibers. The metallography facilitated investigation into the occurrence of oxidation and estimation of network length for application of the Granato-Lucke theory of dislocation damping. Table I summarizes the results of measurements of Young’s modulus, damping and density at room temperature for the quasi-isotropic [0/±45/90]s orientation. Figs 1 through 6 show micrographs of the etched specimens. The cross-sectional shapes of the fibers in Figs 1 and 2 reflect the fiber orientations. Two adjacent layers of fibers angled at 90◦ to the cut appear as perfect circles on the outside edge, followed by two layers at 45◦ that appear as ovals, and two layers angled at 0◦ that appear longitudinally in the center of the specimen. The micrographs in Figs 3 and 4 reveal the layered microstructure of the SiC fibers: a carbon core, a pyrolytic coating, the SiC region, a carbon-rich coating, and the reaction zone between the fiber and matrix [4]. Metallographic results showed little differences between the heated and unheated specimens. The

Dynamic Elastic Modulus and Vibrational Damping in Nicalon SiCxOy Fiber/Borosilicate Glass Composites: Effects of Thermal Cycling

Measurements of dynamic elastic modulus and vibrational damping were made at room temperature for DURAN (a borosilicate glass) and SiCxOy Nicalon™/DURAN (a glass matrix composite). Both sets of materials had been thermal cycled to 500 and 700°C which are below and above the glass transition temperature (Tg = 530°C), respectively. The piezoelectric ultrasonic composite oscillator technique (PUCOT) was used to determine the values of the Young’s modulus and damping. Archimedes’ method was used to find the density of the specimens, and the impulse excitation technique was used to find the flexural modulus. Microstructural examinations were made on selected specimens. The experimental results showed that thermal cycling of the composites below Tg had no distinguishable effect on the density, dynamic Young’s modulus or flexural modulus values; however, an increase in damping of 56% was observed. For thermal cycling above Tg, the density decreased by about 0.5%, the Young’s modulus decreased by 8%, the flexural modulus decreased by 15% and the damping increased by 608%. The simultaneous decrease of elastic modulus and density, and increase of damping in the composites with increasing thermal cycling temperature were analyzed in terms of microstructural degradation due to thermal effects on the matrix, fibers and interfaces.

Dynamic elastic modulus and vibration damping behavior of porous silicon carbide ceramics at elevated temperatures

The piezoelectric ultrasonic composite oscillator technique (PUCOT) has been used to measure the Young's modulus, E, the mechanical damping, Q{sup {minus}1}, and the strain amplitude, {epsilon}, of a sintered silicon carbide containing pores (Hexoloy-SP). The silicon carbide material used in this study had at least 14 vol% porosity. Young's modulus was found to have a linear temperature dependence from room temperature to 740 C. The damping was near 10{sup {minus}4} and was independent of strain amplitude above room temperature.

Measurement of Young’s modulus and damping for hexoloy SG silicon carbide

Stiffness and damping are important design parameters for the potential applications of silicon carbide in the aerospace industry. Thus, Young`s modulus values are needed for calculations of stress and strain, and mechanical damping determines the rate at which vibrations are dissipated in the material. In this paper, the measurements of Young`s modulus and mechanical damping of Hexoloy SG silicon carbide at high temperatures are discussed and compared with published values. These measurements were made using the Piezoelectric Ultrasonic Composite Oscillator Technique (PUCOT). The modulus values are important for calculations involving stress and strain for design purposes. The mechanical damping determines the rate at which vibrations are dissipated in the material. The relationship of the mechanical damping to the strain amplitude is discussed. Microstructural analysis and microhardness tests are discussed as well.