Amplitude-dependent Internal Friction Research Articles

Low-temperature relaxation in faulted Cu-based martensites

An extensive investigation of elastic and anelastic properties, at an ultrasonic frequency of around 100 kHz, of a variety of binary and ternary Cu-based alloys forming faulted martensites evidences the existence of a strong anelastic relaxation over a wide temperature range propagating down to lowest temperatures achieved in experiments of around 10 K. The anelastic phenomenon observed is the most pronounced for low oscillatory strain amplitudes (approximately from 10 −7 to 10 −6) and results in a rapid decrease of Young's modulus (measured at low strain amplitudes) with increasing temperatures from the lowest values of around 10 K. The relaxation of Young's modulus is accompanied by a linear increase of the low-amplitude internal friction with increasing temperature. The low-temperature relaxational behaviour is strongly dependent on concentration of quenched-in vacancies: the relaxation is enhanced by β-phase ageing and is strongly suppressed by direct quenching of ternary Cu–Al–Ni, Cu–Zn–Al and Cu–Al–Be alloys. The anelastic effect observed exhibits an unusual property: the amplitude-independent internal friction background emerging as a result of this relaxation is non-additive with the amplitude-dependent internal friction. We suggest that this low-temperature relaxation is associated with a reversible transition from a cooperative to an individual mode of motion of the system of partial dislocations.

Damping caused by fatigue in porous 316L steel

An analysis of the effect of microcracks in porous metals on amplitude-dependent internal friction (ADIF) is carried out. A mathematical model is developed, which takes into account an initial distribution of microcracks lengths defining subsequent crack growth during cycling. Using the Dugdale model, the linear density of microplastic zones at the tips of the microcracks is obtained as a function of applied stress and porosity. Resulting simulations of internal friction are compared with corresponding experimental data.

Effect of Deformation and Heat Treatment on the Damping Constant and Shear Modulus of a Bulk Zr–Cu–Ni–Al–Ti Metallic Glass

The effect of deformation by rolling or quenching from temperatures close to the glass transition temperature on the damping constant and the shear modulus of preliminarily annealed bulk samples of a Zr52.5Ti5Cu17.9Ni14.6Al10 metallic glass was studied. These treatments are found to result in recovery of the “irreversible” contributions to the damping constant and the shear modulus, and the deformation treatment is shown to lead to an increase in the amplitude-dependent internal friction.

Experimental study of the effects of amplitude-dependent internal friction in a sandstone bar resonator

Results of an experimental study of the effects of amplitude-dependent internal friction (nonlinear loss, resonance frequency shift, and sound-by-sound damping) in an acoustic bar resonator made of sandstone are presented. The measurements were carried out for the first five longitudinal modes of the resonator. The analytical description of the observed effects is performed within the framework of the phenomenological equations of state that include hysteretic and dissipative components of nonlinearity. The parameters of the hysteretic and dissipative components of sandstone nonlinearity are obtained from a comparison of the experimental data with analytical dependences describing the nonlinear effects.

Simultaneous breakaway of a dislocation from several pinning points

The amplitude-dependent internal friction (ADIF) of very pure aluminum (99.9999%) and Al dilute alloys (20–100 ppm) has been measured at temperatures between 2 and 240 K. Two universal properties have been found in the temperature dependence of the required stress amplitude for a constant decrement. At relatively low temperatures (or high stress amplitude), the decrease of the stress with increasing temperature is proportional to T 2/3 down to 65% of the stress for 0 K, and then deviates from the T 2/3 dependence. It is explained that the elementary process is due to unpinning of a dislocation from a single solute atom. The interaction potential has been determined successfully from this region (above 40% of the stress at 0 K). At relatively high temperatures (or stress less than 40% of that for 0 K), we find for the first time that the stress changes as proportional to T −1 for all dilute Al alloys but for a pure Al crystal. It is explained that the elementary process is due to simultaneous unpinning of a dislocation from several solute atoms for dilute alloys.

Amplitude-dependent internal friction in copper thin films on silicon substrates

Abstract Internal friction in copper thin films 0.2–1.5 μm thick on silicon substrates has been measured between 180 and 340 K as a function of strain amplitude. Analysis of the amplitude-dependent internal friction in the copper films shows the relation between the plastic strain of the order of 10−9 and the effective stress on dislocation motion. The stress–strain curves thus obtained for the copper films tend to shift to a higher stress with decreasing film thickness and also with decreasing temperature, both indicating a suppression of microplastic flow. It is concluded that the microflow stress at a constant level of the plastic strain varies inversely with the film thickness at all temperatures examined. The film thickness effect in the microplastic range can be explained on the basis of a dislocation-bowing model.

Hydrogen-induced internal friction of Zr-based bulk glassy alloys in a rod shape above 90 K

Hydrogen-induced internal friction of Zr 65Al 7.5Ni 10Cu 17.5 bulk glassy alloys in a short rod shape (1.5 mm in diameter, 44 mm in length) have been investigated above 90 K using a vibrating reed technique. A quite broad and asymmetric peak is observed around 240 K ( H=2.21 at.%) in the temperature dependence of internal friction. Strain amplitude dependence of internal friction of Zr 63.57Al 7.32Ni 9.79Cu 17.11H 2.21 have been also measured at about the peak temperature and room temperature. It is found that the internal frictions at both temperatures are independent of the strain amplitude. Effects of hydrogen concentration ( H=0.24–2.21 at.%) on the temperature dependence of internal friction have been also clarified. The peak temperature decreases with increasing hydrogen concentration and the peak internal friction increases almost linearly. These results are compared with the reported results of Zr–Al–Ni–Cu–Pd bulk glassy alloys and discussed from the viewpoints of local structure of the Zr-based glassy alloys.

Amplitude-Dependent Internal Friction of Dislocation Interactions in Dual-Phase Steel

Abstract Dislocation interactions in the ferrite matrix of a dual-phase steel have been studied as a function of martensite volume fraction (11–25%) and tensile straining (0–5%) by strain-induced amplitude-dependent (strain amplitude varying from 10−7 to 10−4) internal friction measurements at room temperature, using a high-frequency composite oscillator (40 kHz). Results showed that a higher volume fraction of martensite increases the internal stress in the softer ferrite matrix and restricted the dislocation motions, giving rise to a lower amplitude-dependent internal friction. Application of tensile straining further shortened the effective mobile dislocation length which was revealed by the internal friction measurements and this resulted in a high initial strain hardening rate of the high-martensite samples. Reduction in the martensite volume fraction and the mobile dislocations in the ferrite matrix through process control resulted in an increase in the amplitude-dependent internal friction, indicat...

Amplitude-Dependent Internal Friction in SrTiO 3 in a Vicinity of the Ferroelastic Phase Transition

Amplitude dependences of the low-frequency internal friction and shear modulus in the ferroelastic as well as in the paraelastic phases of SrTiO 3 crystal have been studied using a torsion pendulum. Experimental data are discussed in terms of models of dislocation hysteresis and ferroelastic domain boundary dynamics.

FCC-HCP Transformation-Related Internal Friction in Fe–Mn Alloys

Abstract The e  reversible transformation has been studied in Fe-14 wt.% Mn and Fe-21 wt.% Mn alloys which are known to exhibit a weak shape memory effect. The internal friction changes and the associated elastic modulus changes were measured using the high frequency (40 kHz) composite oscillator technique in the temperature range 20–350°C in which the e  transformation occurs. The strain-induced amplitude dependent internal friction was measured in order to evaluate changes in the dislocation structure that occur during the transformations and to identify the transformation mechanism involved. The study revealed that the propagation of the e/γ interface boundary during the e  γ transformation is a thermally activated relaxation process obeying the Debye relaxation equation. The internal friction data were used to determine the activation energy of the process responsible for the martensitic transformation. The damping peak is observed at temperatures where both phases coexist and is due to the motion ...

Effect of nitrogen on damping, mechanical and corrosive properties of Fe–Mn alloys

The influence of alloying by nitrogen on the damping capacity of Fe–14Mn and Fe–16.5Mn wt.% alloys was studied by means of the amplitude-dependent internal friction technique. Also, the effect of nitrogen on phase constitution, mechanical properties and resistance to immersion corrosion was investigated. It was found that the Fe–14Mn alloy possesses a much higher level of damping capacity than the Fe–16.5Mn alloy. The addition of approximately 0.1 wt.% of nitrogen slightly affects the damping capacity of the Fe–14Mn alloy and increases it in the Fe–16.5Mn alloy. At the same time the ultimate tensile strength of the Fe–16.5Mn alloy is increased from 455 to 655 MPa, and the uniform elongation increased from 3.3 to 12.4%. The ultimate tensile strength of the Fe–14Mn alloy is increased from 480 to 660 MPa due to nitrogen alloying, while the uniform elongation is slightly lowered from 5.1 to 4.1%. The corrosion resistance in 1 N sulphuric acid solution is improved by more than two times in both alloys due to nitrogen alloying.

Elasticity and inelasticity of silicon nitride/boron nitride fibrous monoliths

A study is reported on the effect of temperature and elastic vibration amplitude on Young’s modulus E and internal friction in Si3N4 and BN ceramic samples and Si3N4/BN monoliths obtained by hot pressing of BN-coated Si3N4 fibers. The fibers were arranged along, across, or both along and across the specimen axis. The E measurements were carried out under thermal cycling within the 20–600°C range. It was found that high-modulus silicon-nitride specimens possess a high thermal stability; the E(T) dependences obtained under heating and cooling coincide well with one another. The low-modulus BN ceramic exhibits a considerable hysteresis, thus indicating evolution of the defect structure under the action of thermoelastic (internal) stresses. Monoliths demonstrate a qualitatively similar behavior (with hysteresis). This behavior of the elastic modulus is possible under microplastic deformation initiated by internal stresses. The presence of microplastic shear in all the materials studied is supported by the character of the amplitude dependences of internal friction and the Young’s modulus. The experimental data obtained are discussed in terms of a model in which the temperature dependences of the elastic modulus and their features are accounted for by both microplastic deformation and nonlinear lattice-atom vibrations, which depend on internal stresses.

Microplasticity of copper thin films on silicon substrates

Internal friction in polycrystalline copper films 0.2-1.5 w m thick on silicon substrates has been measured as a function of strain amplitude. The internal friction in the films increases with increasing strain amplitude but at a value of the strain amplitude that is at least two orders of magnitude greater than the similar increase in bulk copper. Analysis of the amplitude-dependent internal friction provides the plastic strain of the order of 10 -9 as a function of effective stress on dislocation motion. Since the grain size is larger than the film thickness, the microflow stress at a constant level of plastic strain varies inversely with the film thickness. The film thickness effect in the microplastic range can be explained on the basis of a dislocation-bowing model.

Transformation temperatures, elastic and anelastic properties of Cu-Al-Ni crystals subjected to impact loading

Experimental investigations of the influence of impact loading on properties of Cu-Al-Ni single crystals have been performed. Crystals in the β 1 phase were impacted with pulses of a uniaxial plane strain wave with a duration of about 2×10 -6 s. A normal component of stress in the direction of the pulse propagation ranged from 0.5 to 5.4 GPa. For as-quenched and impacted crystals martensitic transformation temperatures were determined, the Young's modulus (YM), strain amplitude-independent and strain amplitude-dependent internal friction were measured at a frequency of about 100 kHz over the temperature range of 300-90 K for strain amplitudes of 10 -7 -2×10 -4 , Experimental results indicate that β 1 →γ 1 ' martensitic transformation (MT) and plastic deformation of the martensite are induced by the impact. The impact loading generates a « structure memory effects: the YM in the austenite is not sensitive to the impact, but the consequent temperature-induced MT reveals a dramatic influence of the impact on the YM of the γ 1 ' martensite. The conclusion is drawn that the observed effect is fundamentally similar to the two-way memory effect, but is extremely sensitive to the impact stress. The origin of this phenomenon is attributed to the internal stresses, created by impact, which control the nucleation of preferentially oriented anisotropic martensitic variants during temperature-induced MT in impacted crystals. No influence of the impact loading on the transformation temperatures was detected for β 1 →γ 1 ' MT, in contrast to elastic properties of the martensitic phase, indicating that structural changes due to the high-velocity impact do not affect appreciably the thermoelastic equilibrium and hysteretic motion of parent- martensite boundaries during the MT.

Structural and transient internal friction due to thermal expansion mismatch between matrix and reinforcement in Al–SiC particulate composite

Microyield phenomena during thermocycling of Al 7075 alloy/15 vol.% SiC metal-matrix composite due to mismatch of the thermal expansion coefficients of the matrix and the SiC particles are studied over the temperature range from ∼50 to 300 K by means of internal friction techniques. The transient component of the internal friction is measured in the infrasonic frequency range, whereas the structural strain amplitude-independent and strain amplitude-dependent internal friction is investigated at ultrasonic frequencies. Combining the two techniques enables us to follow the variation of the defect structure during thermocycling as well as to evaluate basic contributions to the microyield phenomenon. The following conclusions are drawn: (1) thermal stresses are responsible for creation of fresh, i.e. mobile dislocations, whose density does not differ significantly, for the same temperature, during heating and cooling or in consecutive thermocycles; (2) yielding is much more pronounced during the first cooling from a stress-free state than in the consecutive thermocycles; this pronounced yielding is due to long-range motion of approximately the same amount of fresh dislocations as in consecutive thermocycles; and (3) during thermocycling, the matrix undergoes dynamic strain ageing; its intensity depends strongly on temperature and therefore varies continuously in a thermocycle.

Temperature dependence of amplitude-dependent internal friction due to simultaneous breakaway of a dislocation from several pinning points

The amplitude-dependent internal friction of very pure aluminum (99.9999%) and Al dilute alloys (20–100 ppm) has been measured at temperatures between 2 and 250 K. Two universal properties have been found in the temperature dependence of the required stress amplitude for a constant decrement. At relatively low temperatures (or high stress amplitude), the decrease of the stress with increasing temperature is proportional to T 2/3 down to 65% of the stress for 0 K, and then deviates from the T 2/3 dependence. It is explained that the elementary process is due to unpinning of a dislocation from a single solute atom. The interaction potential has been determined successfully from this region. At relatively high temperatures (or stress less than 40% of that for 0 K), we find for the first time that the stress changes as proportional to T −1 for all dilute Al alloys but for a pure Al crystal. It is explained that the elementary process is due to simultaneous unpinning of a dislocation from several solute atoms for dilute alloys.

Amplitude dependent internal friction during plastic deformation of KCl doped with KBr, KI, or SrCl2

Flow stress decreases by superimposition of ultrasonic oscillatory stress during plastic deformation. The amplitude dependent internal friction is investigated together with the stress decrement due to the superimposition of oscillation during the plastic deformation of KCl single crystals doped with KBr, KI or SrCl2. The relation between the amplitude dependent internal friction and the stress decrement is divided into three regions for KCI doped with KBr or KI. The internal friction is proportional to the stress decrement in the first region up to the first bending point at the lower stress amplitude. The stress decrement at the first bending point is proportional to the square root of KBr or KI concentration. The internal friction of KCl–SrCl2has the amplitude independent part. The stress decrement at the onset of increasing of internal friction is independent of SrCl2concentration. The amplitude dependent internal friction of KCl–KBr and KCl–KI consists of the part due to the impurity and that due to forest dislocation. The amplitude dependent internal friction of KCl–SrCl2is only due to the forest dislocation.

Evaluation of Microplastic Flow Stress in Copper Alloys from Amplitude-Dependent Internal Friction

Stress-strain relations are evaluated from amplitude-dependent internal friction in polycrystalline solid solution copper alloys. The flow stress in microplastic strain range much below the yield point is examined for eight kinds of specimens, prepared by alloying commercial-grade pure copper with 0.3 at% solute atoms (aluminum, silicon, nickel, gallium, germanium, indium, tin and gold). Internal friction is measured at room temperature under atmospheric pressure using the free-decay method of flexural resonant vibration with both free ends around 600 Hz, The flow stress of Cu-Sn alloys required to cause the plastic strain of I x 10 -9 is about 440 times larger than that of pure Cu, while that of Cu-Ni alloys only 6 times larger. Thus the flow stress evaluated from amplitude-dependent internal friction reflects sensitively the change of solute elements. The flow stress is examined in terms of the misfit parameters between solute and solvent atoms proposed by Fleischer, and it is shown that the flow stress in microplastic strain range is controlled by the elastic interactions between screw dislocations and solute atoms in solid solution copper alloys.

高減衰能金属における内部摩擦の振幅依存性の評価

高減衰能金属における内部摩擦の振幅依存性の評価

Dislocation-defect interactions in nuclear reactor pressure-vessel steels investigated by means of internal friction

A study of pressure-vessel steel embrittlement mechanisms by means of temperature-dependent and amplitude-dependent internal friction has been carried out within the framework of commercial surveillance of nuclear reactor components. An inverted torsion pendulum operating at ∼1 Hz has been employed to study a wide variety of pressure-vessel steels and an IAEA reference material in various conditions. This contribution will discuss the results for the JRQ reference material only and serve as a basis on which to interpret the data from real pressure-vessel steels. The temperature-dependent experiments evidence a reduction in the dislocation mobility as a result of neutron irradiation and prove that the technique is sensitive to thermal ageing involving changes in the dislocation mobility and type of dislocation-defect interaction. Amplitude-dependent internal friction provides a means to determine the yield strength of the material. The importance of the influence of dislocation dragging on the yield stress is highlighted.