Internal Friction Measurements Research Articles

Thermo-kinetic modelling of the giant Snoek effect in carbon-supersaturated iron

Snoek relaxation in interstitial bcc solid solutions is the origin of the Snoek peak in frequency-dependent and temperature-dependent internal friction measurements. When applied to low-carbon steels, the internal friction profiles show a linear dependence of the peak height with carbon content. However, recent Monte Carlo simulations of frequency-dependent internal friction exhibited a non-linear giant peak height at high carbon contents. To investigate this effect in temperature-dependent internal friction, we developed a thermo-kinetic mean-field theory of the Snoek relaxation phenomenon. By taking into account the collective behaviour of the interstitial atoms, our theory predicts (i) a non-linear dependence of the peak height with composition when approaching the order–disorder transition of the alloy; (ii) a shift in the temperature of the peak; (iii) a composition-dependent activation enthalpy of the relaxation time. The theory is exemplified by the case of carbon-supersaturated iron.

Influence of Nb on Ti diffusion in γ-TiAl intermetallics studied by mechanical spectroscopy

The development of intermetallic titanium aluminides has been driven by the aeronautic and aerospace industries because of the excellent mechanical properties and low density of γ-TiAl based alloys. Up to now, several generations of γ-TiAl based alloys were developed with increasing complexity of the alloy systems. Nb is one of the most important alloying elements in γ-TiAl alloys and although it is considered as a slow diffuser, its influence has not been fully quantified yet. In this work we demonstrate, through mechanical spectroscopy measurements conducted on several γ-TiAl based alloys with different Nb content, that Nb impedes the diffusion of Ti atoms in the α2-Ti3Al phase. Internal friction measurements show a relaxation peak P(α2), which is associated with short distance diffusion of Ti atoms in the α2 phase, involving stress-induced rotation of dipoles Al-VTi-Al, whose activation energy is dependent on the Nb content. The increase of the activation energy is quantified as ΔEa(Ti)= 0.037 eV × at% Nb, being attributed to the next-neighbor interaction of Nb atoms with the local configuration of Ti-VTi. This mechanism also produces a further broadening of the relaxation peak, which is attributed to the near-next-neighbor interactions for high Nb contents. Finally, an atomic model for the mechanism responsible for this relaxation is proposed allowing to explain the observed experimental behavior.

Long-term thermal stability, β relaxation, and mechanical behavior of a LaCe-based bulk metallic glass

In this work, the long-term thermal stability, dynamic relaxation behavior, and mechanical performance of (La60Ce40)60Al15Co25 bulk metallic glass (BMG) were studied using differential scanning calorimetry, internal friction measurement, and compression testing, respectively. The long-term stability of the LaCe-based BMG was realized by constructing a continuous heating transformation diagram on the basis of the kinetic characteristics of the crystallization behavior. The internal friction analysis of the LaCe-based BMG showed the emergence of prominent slow β relaxation before the glass transition temperature. The β relaxation had a close relationship with the heterogeneous distribution and the good mobility of the constituting elements. The compression testing results in different temperature ranges near and far from the activation temperature of the β relaxation showed that the plastic deformation could proceed continuously as the deformation temperature reached the activation temperature of the β relaxation.

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.

Measurement of internal friction of Zr–1%Nb alloy after oxidation and nitriding

This paper presents results of research of the Zr–1% Nb alloy using internal friction on sheet samples after oxidation due to leakage of air into the measurement facility, as well as after nitriding in an atmosphere of technical nitrogen. The measured temperature dependences of internal friction have been separated into partial maxima with the calculation of the effective activation energy according to the Wert-Marx formula. The purpose of the work is to detect the maxima of the internal friction of interstitial impurities in the alloy. It has been established that the oxygen maximum in successive measurements has activation energy 225, 222, 204 kJ/mol, and the nitrogen maximum has 234–236 kJ/mol. After lengthy high-temperature measurements, a carbon maximum appeared with activation energy 165 kJ/mol. For the grainboundary maximum activation energy from 197 to 203 kJ/mol was obtained for different samples, while the maximum height monotonously decreased with oxidation. These results for the Zr–1% Nb alloy were obtained for the first time and can be useful in corrosion tests of zirconium alloys.

Ni–Ti-Hf high-temperature shape memory alloy: Measure of the Clausius-Clapeyron coefficient through mechanical spectroscopy

The martensitic transformation of Ni49.5Ti35.5Hf15 high temperature shape memory alloy is characterized by internal friction measurements. The temperatures for the reversible B2 ↔ B19’ transformation appear in the range 410–479 K on cooling and 447–526 K on heating. In addition, a strong anomalous pre-martensitic softening of the dynamic modulus is reported in the high-temperature phase, between 850 K and 550 K, evidencing the thermoelastic character of this family of alloys. Based on the analysis of the internal friction spectra, a theoretical and experimental methodology is proposed to measure the Clausius-Clapeyron coefficient through mechanical spectroscopy. This new non-destructive method could be extremely useful for the development of advanced prototypes of shape memory alloys.

Influence of Cyclic Loading on the Internal Friction Measured on Magnesium Alloys AZ31, AZ61 and AZ91

The article is aimed on the analysis of the influence of cyclic loading on the internal friction measured on magnesium alloys, especially AZ31, AZ61 and AZ91, after homogenization annealing. Microplastic processe and dissipation of energy within the alloys are evaluated and investigated by internal friction measurements. In experimental measurements resonance method was used, which is based on continuous excitation of oscillations of specimens. Measurements were performed at final excitation voltages of 5 V, 6 V and 7 V.

Impulse excitation technique and its application for identification of material damping: an overview

The recent work presents an overview of the papers devoted to the application of Impulse Excitation Technique (IET) for the measurement of internal friction in different materials. IET is an advanced method to measure such materials’ characteristics as Dynamic Young’s and Share Moduli, Dynamic Poisson’s Ratio, Damping, to investigate the deformation behavior, softening phenomena and relaxation mechanisms and phase transformations in different materials. The experimental studies can be performed at both, room and high temperatures. Due to its simplicity, low cost, high accuracy and reproducibility it may take the leading position among the other non-destructive testing methods and techniques.

Internal friction measurements of low energy excitations in amorphous germanium thin films

Motivated to create a germanium analog to nearly two-level-tunneling-system (TLS)-free amorphous silicon, six germanium films, all about 350 nm thick, were deposited by molecular beam epitaxy onto substrates held at temperatures between room temperature and 280∘C. The internal friction and speed of sound of the films was measured between 375 mK and 300 K. Although the intent was to study amorphous thin films, those grown at 200∘C and higher were shown to be at least partially crystalline. The tunneling strength C, a measure of the interaction between phonons and two-level tunneling systems, decreased monotonically with increasing substrate growth temperature, and for films grown on substrates at temperatures above room temperature, C was below the glassy range. The lowest value for an amorphous film, for the 160∘C-grown film, was C=1.9×10−5.

Comparing amorphous silicon prepared by electron-beam evaporation and sputtering toward eliminating atomic tunneling states

It has previously been shown that amorphous silicon (a-Si) thin films can be produced free of tunneling two-level systems (TLS) by e-beam evaporation onto substrates held at elevated temperatures, and there appears to be a strong anticorrelation between the atomic density of these films and the number density of TLS. We have prepared a-Si films with higher atomic density using magnetron sputtering at substrate temperatures comparable to those used in the e-beam studies. We compare the atomic densities measured using Rutherford backscattering and the shear moduli, the speeds of sound, and the densities of TLS calculated using internal friction measurements at cryogenic temperatures of sputtered a-Si films to those of the e-beam films. Our results show that despite their higher atomic densities, sputtered a-Si films prepared at elevated substrate temperatures have lower speeds of sound and higher densities of TLS, which we attribute to the different film growth mechanism from that of e-beam evaporation. We conclude that a collaborative improvement of both local structure and network connectivity, determined by atomic density and speed of sound, respectively, to approach their crystalline values is required to eliminate atomic tunneling states.

High-temperature phenomena in an advanced intermetallic nano-lamellar γ-TiAl-based alloy. Part I: Internal friction and atomic relaxation processes

Intermetallic γ-TiAl based alloys have found applications in the low-pressure turbine of aircraft engines as well as in the turbocharger unit of automotive engines. However, these light-weight alloys must still be improved, through micro-alloying and tailoring the microstructure, to increase their creep resistance and consequently their maximum working temperature. In this work, a fully nano-lamellar advanced γ-TiAl based alloy doped with small amounts of C and Si is investigated in order to gain a deeper understanding of the atomic mobility mechanisms taking place at high temperature, thus controlling the creep properties. The study was approached through internal friction measurements up to 1223 K. We demonstrate that C has a notable influence on Ti diffusion in α2 phase, leading to an increase of the activation energy for Ti diffusion, which is assessed at ΔETi(α2)=0.32 eV per at% C. An atomic model for the relaxation process is proposed capable to explain this phenomenon. An additional internal friction peak, which, up to now, remained hidden by the high temperature background, was observed in this nano-lamellar TiAl alloy and analyzed through a careful de-convolution of the internal friction spectra. This new relaxation process, with activation energy of 3.70 eV, is attributed to the short distance diffusion of Al atoms in the γ-TiAl lattice. A novel concept of stress-induced cell-lattice reorientation is proposed to explain this relaxation. Finally, a new experimental method to analyze the high temperature internal friction background, which is closely related to the creep behavior, was developed to study the fully nano-lamellar microstructure, whose high temperature background exhibits the highest activation energy ever measured in a γ-TiAl based alloy.

Strengthening mechanism of Nb addition in Fe–13Cr–4.5Al–2Mo alloys assessed by internal friction measurement

The Fe–13Cr–4.5Al–2Mo (FeCrAlMo) alloys, one of the most promising candidates for the accident tolerant fuel cladding in the light-water reactors, were strengthened with Nb addition and the strengthening mechanism were assessed by an internal friction (IF) measurement method combined with microstructure characterization. The FeCrAlMo alloy with 1.0 wt% Nb addition exhibited the highest ultimate tensile strength (UTS) and an acceptable ductility at each tested temperature (room temperature, 300 °C or 700 °C). For example at 700 °C, the UTS of FeCrAlMo −1 wt%Nb was about 215 MPa, which was 53.5% higher than that of Nb-free FeCrAlMo alloy. For Nb-free FeCrAlMo alloy, a high IF peak P2 appeared at about 680 °C was related to the recovery and recrystallization process during the first heating cycle, which was characterized by an internal friction measurement method. Another small IF peak P1 corresponding to Zener relaxation process and a predominant IF peak P3 corresponding to the grain boundary relaxation process were observed at 560 °C and 720 °C, respectively, during the second heating cycle. However none of IF peaks was detected for the Nb containing FeCrAlMo alloys up to 800 °C. Based on the IF theory, the disappearance of P1 (Zener peak), P2 (recrystallization peak) and P3 (grain boundary peak) in the first and second heating cycles was owing to the pinning of dislocations and grain boundaries by high density Fe2Nb nanoscale particles dispersed in the FeCrAlMo matrix, which enhanced the tensile strength of the Nb containing FeCrAlMo alloys.

Effects of solute oxygen on kinetics of diffusionless isothermal ω transformation in β-titanium alloys

We have investigated the effects of solute oxygen on the kinetics of diffusionless isothermal omega (DI-ω) transformation in β-titanium vanadium alloys. This transformation constitutes a third category of ω transformation beside the athermal and isothermal modes. Thermal analysis, hardness and internal friction measurements were conducted after quenching oxygen-containing and near-oxygen-free alloys with ~ 21 at%V from the β-stable temperature. At this level of vanadium concentration, the athermal ω transformation is not expected. It is found that the DI-ω transformation more rapidly progresses in the low oxygen alloy and the relaxation strength of the elementary process of {111}β collapse is significantly reduced.

Giant Snoek peak in ferrite due to carbon-carbon strain interactions

Internal friction measurements are commonly used to quantify solute carbon in body-centered iron via the Snoek relaxation effect. For low-carbon steels, the height of the Snoek peak is proportional to the carbon content in solid solution. Our simulations show that highly carbon-supersaturated ferrite violates this linear relationship and exhibits a giant Snoek peak around a specific temperature-dependent carbon content. This effect is related to the carbon-carbon strain interaction, also responsible for the Zener order-disorder transition. We provide analytic formulae allowing the quantitative analysis of experimental results of mechanical spectroscopy on supersaturated ferrite. Our conclusions rely on Monte Carlo simulations carried out at the atomic scale and on the mean-field elastochemical model, using no adjustable parameter.

Quick and repeatable shear modulus measurement based on torsional resonance using a piezoelectric torsional transducer

Shear modulus is one of the fundamental mechanical properties of materials, while its quick and accurate measurement is still a challenge. Here we proposed a method for shear modulus measurement based on torsional resonance using a piezoelectric torsional transducer bonded on a cylindrical specimen. Firstly, the torsional transducer was introduced which consists of two thickness poled, thickness shear (d15) piezoelectric half-rings. Secondly, the equivalent circuit of the transducer-cylindrical specimen system is derived and the shear modulus can be explicitly obtained using the torsional resonance frequency. The internal friction can also be obtained, which is calculated by using an approximate formula. Then, shear modulus and internal friction measurement on four materials including 1045 steel, 6061 aluminum, quartz glass and PMMA were conducted. Results indicate that all the measured shear moduli are consistent with the reference values in literatures. The repeatable error in shear modulus measurement is within 0.2%, which is very desirable. Finally, shear modulus measurement scheme under high (or low) temperature is proposed using a frequency-match quartz glass bar as the thermal insulator. Measurement results on the 6061 aluminum indicates that from room temperature to 500 °C, the shear modulus decreases from 26.8 GPa to 16.6GPa. The proposed method is very reliable and quite convenient, which can be widely used in near future.

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.

Internal friction in Ti29.7Ni50.3Hf20 alloy with high temperature shape memory effect

Martensitic transformation of Ti29.7Ni50.3Hf20 high temperature shape memory alloy was investigated by subresonance internal friction measurements using forced bending vibrations with frequency from 0.1 to 3 Hz. The transformation peak corresponding to reversible B2 ↔ B19′ transformation appears in temperature range of 230–270 °C upon heating and 170–220 °C upon cooling. The height of internal friction martensitic peak is Q−1 ≈ 80.015 and 0.023 at heating and cooling under 1 Hz, respectively. The reason for the low internal friction peak value of Ti29.7Ni50.3Hf20 alloy in comparison with binary TiNi can be attributed to different twinning modes of invariant shear upon martensitic transformation.

Analysis of β relaxation using internal friction measurement and mechanical testing for a LaCe-based bulk metallic glass

The β relaxation in bulk metallic glasses (BMGs) is reversible and dynamic and is directly related to local atomic cooperative motions. In this study, the effects of thermal cycle and crystallization friction on the reversibility of β relaxation of a LaCe-based BMG are studied by measuring internal friction and by using thermal cycle to certain characteristic temperatures single or repeatedly. Experimental results show that unstable structural units are released after heating to the end temperature of the β relaxation, and partial crystallization does not impede the reversibility but postpones the appearance of the β relaxation. By investigating the atomic mobility and the β relaxation, compression testing at the temperature range that corresponds to the activation of the β relaxation shows a large plastic deformation behavior.

Cluster compounds formation in metal alloys crystals

The formation and physical origin of the pre-cluster complexes and pre-phase (cluster) compounds have been studied on cast magnesium alloys (in the liquid and solid states) as well as other primary solutions enriched with excess (non-intrinsic, structural) vacancies. The results produced by DSC, TEM observation, Auger-electron, UV-and X-ray photoelectron spectroscopy techniques were combined with positron annihilation, electroresistance, and internal friction measurements to evaluate different stages of the cluster compounds formation and to examine the strength of their chemical bonding in terms of a detailed analysis of electron-sensitive properties. The thermally activated deviations from classical (Arrhenius) behaviour in hydrogen-charged hcp and fcc metal crystals are found to be caused by the nucleation of the solute/excess vacancy complexes. Additional support for this short-range self-supported mechanism comes from data obtained by mechanical spectroscopy and positron annihilation. These pre-cluster separations are assumed to act as nuclei for the synthesis of the cluster compounds such as Mg16Ba2 and Al18Ba9 with own electronic (hybridized) structure in hcp magnesium- and fcc aluminium alloy crystals, respectively. A unified concept of the liquid/solid conversion for condensed cluster-forming alloys is considered. This approach is particularly useful for the development of chemically combined cluster compounds with own electronic configurations as functional materials for high-current electronics.

Confirmation of Dynamically Recrystallized Grains in Hexagonal Zirconium through Local Internal Friction Measurements

Fully recrystallized hexagonal Zirconium was subjected to controlled hot compression tests. Deformation above 723 K showed both flow saturation, characteristic of dynamic recovery, and also the presence of fine equiaxed grains, indicating dynamic recrystallization (DRx). Though data from relative work hardening were inconclusive, a combination of transmission Kikuchi diffraction plus transmission electron microscopy clearly confirmed the presence of DRx grains. A separation between the deformed and the DRx grains was not possible with microtexture or nano-indentation data. Local internal friction measurements (or tanδ values), however, clearly distinguished the DRx grains from both statically recrystallized (SRex) and the hot deformed grains.