Amplitude-dependent Internal Friction Research Articles

Structural anelasticity of NiTi during two-stage martensitic transformation

The two-staged thermoelastic martensitic transformation (TMT) B2→R→B19′ in polycrystalline equiatomic NiTi has been studied by means of measurements of strain amplitude-independent and amplitude-dependent internal friction (ADIF), Young’s modulus and amplitude-dependent modulus defects. The internal friction measurements were performed at a frequency of about 100 kHz, rendering negligible the transient internal friction component and allowing one to investigate the structural internal friction, much less dependent on the external parameters such as the heating/cooling rate or the frequency of vibrations. Attention is focussed on the amplitude-dependent anelasticity. Based on the data obtained, the anelasticity is associated with the dislocations inside the martensitic variants, not with the interfaces or interface dislocations, as is traditionally done. The ADIF and anelastic strain in the R phase have been found to be an order of magnitude higher than in the B19′ martensitic phase. This observation is explained by a much higher density of the dislocations inside the variants of the R phase as compared with that of the B19′ phase.

Towards understanding anelasticity of the β 1′ martensitic phase of Cu–Al–Ni

The present work continues the series of experimental investigations undertaken in order to elucidate the mechanisms controlling elastic and anelastic properties of the β 1′ martensitic phase of Cu-based shape memory alloys. The paper reports an attempt to distinguish between ‘dislocation’ and ‘interface’ mechanisms of the internal friction in the β 1′ martensitic phase of Cu–Al–Ni single crystals. Two types of experiments have been performed. First, the ultrasonic strain amplitude-independent and amplitude-dependent internal friction (ADIF) of a monovariant specimen for temperatures 90–300 K is carefully re-examined. Second, in situ measurements of the ADIF and of the influence of ultrasonic oscillations on the plastic deformation (acoustoplastic effect) were carried out during quasistatic deformation of a quenched polyvariant specimen. Experimental results support a dislocation rather than an interface mechanism of anelasticity, at least at ultrasonic frequencies and moderate strain amplitudes.

Effect of dislocation density on the low temperature aging behavior of an ultra low carbon bake hardening steel

Strain aging was studied in an ultra low carbon (ULC) steel with a total carbon content of 20 ppm (wt.%) in order to identify the process stages and mechanism of bake hardening in this type of steel. The effects of dislocation density, varied by means of uniaxial tensile prestraining (1–10%) on the aging kinetics were investigated within an aging temperature range of 50–170°C. The aging was evaluated by means of strength measurements and the determination of interstitial carbon content after aging using a piezoelectric composite oscillator operating at 40 kHz. The interaction between interstitial carbon and dislocations was examined through amplitude dependent internal friction measurements. The influence of dislocation density on the aging behavior have been discussed with reference to the kinetics and mechanism of the aging process.

Internal friction and loss tangent of nonlinear viscoelastic materials: different concepts, different results

This paper aims to give some insight into measurements of the nonlinear processes involved in the dynamical response of viscoelastic materials. The main goal is to point out that these nonlinear effects can be observed with forced oscillating torsion pendulums, but by measuring the complete hysteretic loop, instead of just looking at the phase lag angle. The response of a nonlinear rheological model constructed with a standard anelastic element in series with a nonlinear dashpot is considered. The characteristic parameters of this model are according to previous empirical results reported in the literature. This system is dynamically driven as if it were in a forced torsion pendulum, which is almost the optimal device for the analysis of amplitude dependent internal friction at low frequencies. The intrinsic internal friction is calculated from the ratio between the dissipated energy per cycle and the maximum stored energy for the nonlinear rheological model. The simulation of the internal friction that could be measured with a torsion pendulum for the rheological model is then determined from the intrinsic internal friction after considering the non-homogeneous strain distribution. The intrinsic internal friction and the simulated internal friction data are compared with the tangent of the phase angle by which the strain lags behind the stress in order to show that the differences are important enough to be measured. In summary, the nonlinear response could potentially be measured with commercial equipment, but usually is not, because only the phase lag angle is considered. Automatic measurements of both the temporal evolution of stress and strain in a cycle will lead to the determination of the real value of the internal friction of nonlinear systems from the hysteretic σ– ε loop.

Amplitude-dependent internal friction and similarity of temperature dependences of microflow and macroflow stresses of a crystal

A dislocation-kinetic mechanism is discussed of amplitude-dependent internal friction and of the similar temperature dependences of the microflow and yield stresses of a crystal. The similarity of these dependences is shown to be due to the similarity of strain-(dislocation-) strengthening curves of the crystal in the microplastic-and macroplastic-strain ranges, respectively.

Motion of dislocations and interfaces during deformation of martensitic Cu–Al–Ni crystals

Investigations of the ultrasonic strain amplitude-dependent internal friction (ADIF) and of the influence of ultrasonic vibrations on the macroplastic strain (the acoustoplastic effect) have been performed in situ during deformation of quenched Cu–Al–Ni single crystals in the β′ 1 martensitic phase. The effect of the macroscopic plastic strain rate on the ADIF and acoustoplastic effect as well as the kinetics of the acoustoplastic effect has been studied. The results of in situ ADIF measurements are compared with data on the ADIF temperature dependence. Observed regularities are attributed to differences in the mechanisms of the macroplastic deformation of the martensitic phase, related to the motion of intervariant interfaces, and of the reversible anelastic strain, which, at ultrasonic frequencies and moderate strain amplitudes, is largely due to the oscillatory motion of the partial dislocations. The conclusion has been drawn that the dynamics of partial dislocations at temperatures of 210–300 K is to a great extent determined by their interaction with atmospheres of mobile pinners with saturated density. Simultaneous measurements of the ADIF and acoustoplastic effect allows the conclusion that, for high oscillatory strain amplitudes, the breakthrough of partial dislocations beyond the mobile atmospheres of pinners initiates the step-like accumulation of the macroplastic strain due to the motion of intervariant boundaries.

Amplitude Dependence of Internal Friction in Zinc

Amplitude Dependence of Internal Friction in Zinc

Determination of the yield strength of nuclear reactor pressure vessel steels by means of amplitude-dependent internal friction

Amplitude-dependent internal friction measurements allow the determination of a critical amplitude which corresponds to the onset of plastic behaviour and is related to the yield stress (YS) in torsion. The results compare well with the YS obtained from static tensile tests on three different pressure vessel steels and can be fitted with a two- or three-component model comprising long- and short-range dislocation-defect interactions and grain-boundary effects. The effect of thermal aging is to emphasize the presence of dragging contributions to the yield strength, while neutron-irradiation results in an athermal increase in the YS related to irradiation-induced clustering.

Theory of amplitude-dependent internal friction and acoustoplastic effect in shape memory alloys

Mechanisms of amplitude-dependent internal friction and the acoustoplastic effect in shape memory alloys are discussed in terms of the previously developed theory of diffuse thermoelastic martensitic transformations. The amplitude dependences of these effects are found for different temperatures and applied stresses.

3111 金属の振動疲労における非線形変形に伴う高調波の発生(OS.10 故障診断・予知・メンテナンス・安全性)

The resonant vibration tests were carried out on type 304 stainless steel to develop the non-destructive method for evaluating fatigue damage. The authors have studied the critical strain amplitude of fatigue above which dislocation multiplication begins to occur. The critical strain amplitude was determined from the stain amplitude dependence of internal friction which is due to dislocation motion of breakaway from pinning points and multiplication. Such dislocation motion gives the nonlinear stress-strain relationship of resonant vibration. The non-linear stress-strain relationship yields higher harmonics on vibration. In this study, the dynamic displacement of resonant vibration was measured using a non-contact laser displacement meter. The 3rd harmonics was strongly dependent on the strain amplitude over the region above the critical strain amplitude, though hardly be identified below that strain. As a consequence, detecting higher harmonics could be used to determining the critical amplitude of vibrating structures such as small bore piping systems with branch joints.

Interaction of Nitrogen with Dislocations Studied by Means of Amplitude-Dependent Internal Friction

Interaction of Nitrogen with Dislocations Studied by Means of Amplitude-Dependent Internal Friction

Mechanical properties of thin-film materials evaluated from amplitude-dependent internal friction

A method is presented to evaluate the mechanical properties of thin-film materials from measurements of the amplitude-dependent internal friction. According to the constitutive equation, the internal friction in the film can be determined separately from measured damping of the film/substrate composite. The internal friction in aluminum films is dependent on the strain amplitude that is approximately two orders of magnitude higher than that for bulk aluminum. On the basis of the microplasticity theory, the amplitude-dependent internal friction in the film can be converted into the plastic strain as a function of effective stress on dislocation motion. The mechanical responses thus obtained for aluminum films show that the plastic strain of the order of 10−9 increases nonlinearly with increasing stress. These curves tend to shift to a higher stress with decreasing film thickness and also with decreasing temperature, both indicating a suppression of microplastic flow. The microflow stress at a constant level of the plastic strain varies inversely with the film thickness, provided the grain size is larger than the film thickness. The film thickness effect in the microplastic range can be well explained by the bowing of a dislocation segment whose ends are pinned at the film surface and at the film/substrate interface.

Solid solution hardening evaluated from amplitude-dependent internal friction in polycrystalline copper alloys

In the present study, the authors evaluated plastic strain as a function of stress from data of the amplitude-dependent internal friction in polycrystalline Cu alloys under the condition that the flow stress is controlled only by the mobility of dislocations. The polycrystalline alloys were employed as specimens in the measurements, because the amplitude dependence of internal friction is too structure-sensitive to show reproducible results in highly pure monocrystals. In addition, the application of the present evaluation of plastic strain to engineering materials is expected as a new non-destructive strength test. The solute elements were restricted within IVb group and the concentration was fixed at 0.3% in order to examine the dependence of flow stress on the size misfit between solute and solvent atoms.

Strain amplitude-dependent anelasticity in Cu–Ni solid solution due to thermally activated and athermal dislocation–point obstacle interactions

Experimental investigations of the internal friction and the Young’s modulus defect in single crystals of Cu-(1.3–7.6) at. % Ni have been performed for 7–300 K over a wide range of oscillatory strain amplitudes. Extensive data have been obtained at a frequency of vibrations around 100 kHz and compared with the results obtained for the same crystals at a frequency of ∼1 kHz. The strain amplitude dependence of the anelastic strain amplitude and the average friction stress acting on a dislocation due to solute atoms are also analyzed. Several stages in the strain amplitude dependence of the internal friction and the Young’s modulus defect are revealed for all of the alloy compositions, at different temperatures and in different frequency ranges. For the 100 kHz frequency, low temperatures and low strain amplitudes (∼10−7–10−5), the amplitude-dependent internal friction and the Young’s modulus defect are essentially temperature independent, and are ascribed to a purely hysteretic internal friction component. At higher strain amplitudes, a transition stage and a steep strain amplitude dependence of the internal friction and the Young’s modulus defect are observed, followed by saturation at the highest strain amplitudes employed. These stages are temperature and frequency dependent and are assumed to be due to thermally activated motion of dislocations. We suggest that the observed regularities in the entire strain amplitude, temperature and frequency ranges correspond to a motion of dislocations in a two-component system of obstacles: weak but long-range ones, due to the elastic interaction of dislocations with solute atoms distributed in the bulk of the crystal; and strong short-range ones, due to the interaction of dislocations with solute atoms distributed close to dislocation glide planes. Based on these assumptions, a qualitative explanation is given for the variety of experimental observations.

Dislocation Tunneling in Plastically Deformed Aluminum

ABSTRACTWe have measured the amplitude dependent internal friction (ADIF) and sound velocity down to 0.065 K of a 99.9999% (6N) aluminum that was plastically deformed by 1%. The strain amplitude was varied from ε = 1 × 10−8 to ε = 6 × 10−7, a factor of 60. It is observed that with increasing strain amplitude, both the internal friction and the sound velocity become temperature independent over an increasingly wider temperature range. ADIF measurements show a flattening of the temperature dependence of the strain amplitude at low temperatures which is taken to be strong evidence for dislocation tunneling.

Influence of temperature and strain on the amplitude-dependent internal friction of high-purity aluminum

The dislocation amplitude-dependent friction (ADIF) of high-purity (99.999%) polycrystalline aluminum is investigated in the temperature range 7–300K at vibrational strain amplitudes of 10−7–10−4 for samples in the annealed and deformed (by quasistatic, shock, and ultrasonic loading) states. The ADIF is a multistage effect in the indicated temperature and vibration amplitude ranges. Analysis of the amplitude-temperature spectra of the ADIF permits separation of components attributable to: interaction between dislocations, the interaction of dislocations with pinning points, and pure dislocation relaxation (the interaction of dislocations with the Peierls relief). ADIF is observed to depend nonmonotonically on the initial quasistatic strain determined by strain hardening and recovery processes.

Low-temperature anomalies in Young's modulus and internal friction of Cu–Al–Ni single crystals

Elastic and anelastic properties of Cu–Al–Ni single crystals ( M s∼370 K) in the β ′ 1 martensitic phase have been studied in the temperature range 7–300 K at a frequency of about 100 kHz. Crystals, quenched below M f or aged in the β-phase were investigated. For quenched crystals, the Young's modulus exhibits a pronounced anomalous increase in the range 70–230 K, simultaneously with a significant decrease of the amplitude-independent and amplitude-dependent internal friction. This anomalous behaviour is attributed to a large contribution of dislocations to the measured Young's modulus and internal friction, due to the existence of an ordered network of partial dislocations in the β ′ 1 martensitic phase. Anomalies in the temperature dependence of Young's modulus and amplitude-dependent internal friction are explained by depinning of dislocations from atmospheres of point obstacles under the action of thermal stresses induced within martensitic variants. Ageing in the β-phase leads to a drastic (up to 30%) decrease of the Young's modulus and an increase of the internal friction in the martensitic phase at room temperature. Only traces of the anomalies are revealed in aged crystals, due to the much smaller concentration of mobile obstacles.

Influence of impurity content on the acoustoplastic effect, internal friction, and Young's modulus defect during deformation of Cu-Ni single crystals

Abstract Oscillatory stress amplitude dependences of the acoustoplastic effect, absorption of ultrasonic vibrations (frequency of about 100 kHz) causing this effect, and Young's modulus defect were simulataneously measured in situ during quasistatic deformation of Cu-1·3–7·6 at.% Ni single crystals. The time dependences of the magnitude of the acoustoplastic effect at constant oscillatory stress amplitudes were also obtained. The amplitude-dependent internal friction and Young's modulus defect diminish drastically with increasing Ni content. The dependence of the magnitude of the acoustoplastic effect on the Ni concentration is much less pronounced and is reversed with increase in oscillatory stress amplitude. Data on the kinetics of the acoustoplastic effect revealed ‘instant’ (time-independent) and ‘relaxational’ (time-dependent) components. Both components show a similar dependence on Ni concentration, thus indicating their common origin. It is concluded that, while the amplitude—dependent internal friction is largely due to dislocation—point-defect interactions, the acoustoplastic effect originates mainly from dislocation—dislocation interactions.

Influence of impurity content on the acoustoplastic effect, internal friction, and Young's modulus defect during deformation of Cu-Ni single crystals

Abstract Oscillatory stress amplitude dependences of the acoustoplastic effect, absorption of ultrasonic vibrations (frequency of about 100 kHz) causing this effect, and Young's modulus defect were simulataneously measured in situ during quasistatic deformation of Cu-1·3–7·6 at.% Ni single crystals. The time dependences of the magnitude of the acoustoplastic effect at constant oscillatory stress amplitudes were also obtained. The amplitude-dependent internal friction and Young's modulus defect diminish drastically with increasing Ni content. The dependence of the magnitude of the acoustoplastic effect on the Ni concentration is much less pronounced and is reversed with increase in oscillatory stress amplitude. Data on the kinetics of the acoustoplastic effect revealed ‘instant’ (time-independent) and ‘relaxational’ (time-dependent) components. Both components show a similar dependence on Ni concentration, thus indicating their common origin. It is concluded that, while the amplitude—dependent internal friction is largely due to dislocation—point-defect interactions, the acoustoplastic effect originates mainly from dislocation—dislocation interactions.

Effect of temperature on the amplitude dependences of the acoustoplastic effect and internal friction during deformation of crystals

Abstract Oscillatory strain amplitude dependences of the acoustoplastic effect and absorption of ultrasonic vibrations (frequency of about 100 kHz) causing this effect were measured in a wide temperature range in situ during quasistatic deformation of NaCl and Al single crystals. An increase in efficiency of the ultrasonic effect on the plastic deformation process has been found with an increase in temperature. The data obtained provide evidence for the distinction in basic mechanisms of the acoustoplastic effect and amplitude-dependent internal friction. The absorbtion of ultrasound is largely due to dislocation-point-defect interactions under reversible movement of mobile dislocations. Mechanical activation of irreversible movement of the same mobile dislocations through long-range internal stress fields of other dislocations and dislocation pileups is suggested as the basic mechanism of the acoustoplastic effect. Mechanisms are discussed determining the temperature dependences of the acoustoplastic eff...