Amplitude-dependent Internal Friction Research Articles

Temperature and strain amplitude dependence of internal friction measured with an automatic pendulum

The influence of the variations in the oscillation frequency with temperature on the calibration constant of an automatic internal friction pendulum is discussed. A method to obtain the intrinsic damping and modulus defect, as a function of temperature, from data obtained either in torsion or in flexure is suggested. The method does not involve measurements of the damping against the applied strain for different temperatures.

INFLUENCE OF PLASTIC DEFORMATION ON MAGNETOMECHANICAL DAMPING OF Co-Pt ALLOY

Amplitude dependent internal friction of a disordered Co-Pt alloy was measured as function of a torsional plastic deformation up to 1.2 %. Magnetomechanical damping was quantitatively discussed using the Smith and Birchak model. The correlation between internal stress and dislocation density was estimated.

Internal friction due to hysteretic dislocation motion in solid solution crystals

In analogy to Rayleigh’s law in magnetism a Rayleigh law of plastic deformation is defined to explain the amplitude dependent internal friction and the modulus defect in materials with high solute concentrations. The forces opposing dislocation motion in a solid solution crystal with high solute concentrations are described with the help of random functions. Using this statistical treatment it is possible to calculate the parameters of Rayleigh’s law of plastic deformation and explain quantitatively the amplitude and concentration dependence of the internal friction and modulus defect in alpha brass.

Internal friction study of AISI 410 stainless steel

From this study of the internal friction at low stresses of AISI 410 stainless steel in four different conditions of heat treatment the following conclusions are made: 1. 1. Young's modulus of the material is influenced by heat treatment and varies in the range 211 to 218 GPa. 2. 2. The internal friction is amplitude dependent and varies in the range 2 to 8 × 10 −4 for the different heat treatments and range of strain amplitudes investigated. 3. 3. The break away strain amplitude of the internal friction depends on the heat treatment of the specimen and varies in the range 10 −6 to 3 × 10 −5. Moreover, the trend of the break away strain amplitude with heat treatment is the inverse of that for the trend of Young's modulus. 4. 4. When the internal friction data for 10 −5 ε −1 < 1 are analyzed in terms of the Granato-Lücke (GL) theory of dislocation damping, values of the minor loop length L c of the vibrating dislocation line and of the mobile dislocation density Λ could be extracted for the specimens. 5. 5. The values of L c (13 to 46 nm) and of Λ (10 10 to 10 12 m −2) obtained from the analysis are acceptable when interpreted in terms of TEM observations on carbide precipitates and dislocations in turbine blade materials similar to the material used in this study. 6. 6. The mobile dislocation density under conditions of amplitude dependent internal friction is less than the estimated total dislocation density. 7. 7. The internal friction results suggest that the value of K (the variable in the GL theory which depends on crystallographic orientation and specimen material) for the specimens used should be near 0.5, and that the value of L N (the major dislocation loop length) should be near 10 −7m.

Low Frequency Internal Friction Due to Dislocations Oscillating in the Lattice

The amplitude-dependent internal friction which is due to dislocations oscillating in the lattice is described in terms of dislocation mobility, under the condition that the motion of dislocation is limited by tension forces, as will be the case at low frequencies. It is shown that the friction increases as the frequency increases and that it decreases as the amplitude increases. These results are in contrast to those obtained before for the internal friction at high frequencies, where the internal friction increases with the amplitude and has an inverse frequency dependence. Comparison with available data of low frequency internal friction on copper and α-brass shows that the line-tension limited motion accounts for the observed results.

Modulus Change Associated with Amplitude-Dependent Internal Friction in Crystals

The ratio of amplitude-dependent internal friction to the associated modulus change is discussed for the case where the both quantities are due to dislocations oscillating in the lattice. It is shown that the ratio lies between π and 4, when the motion of dislocation is limited by frictional forces. The ratio has a smaller value, when the motion is prevented by the obstacles such as subboundaries, or when it is limited by tension forces. Comparison of the above results with available data on copper, copper alloys and lead shows that the experimental values of the ratio can be explained by assuming that the internal friction is due to dislocations oscillating in the lattice, where impurities are randomly distributed.

The photodamping of dislocations in KCl single crystals

The effect of F-light ( λ = 550 nm) on the dislocation amplitude-dependent internal friction (dislocation photodamping) and dislocation charge in KCl crystals of different purity containing F-centers has been investigated. The photodamping process in all the crystals under study has been found to be due to the optical generation of new pinning points. The conditions of photopinner formation are found to depend on the magnitude of dislocation charge, the manner of the F-center introduction (γ-irradiation, additive coloration), and crystal purity. A model of photopinner formation has been proposed. The results obtained are used to analyse the binary systems in which the effect of dislocation photodamping is likely to occur.

The Static and Dynamic Hysteresis Responsible for the Dislocational Amplitude Dependent Internal Friction. I. Theory

A dynamic theory of the amplitude dependent dislocation hysteresis is developed, emphasising the importance of the quasi-particle–dislocation interaction for the non-linear response of the real crystal to the high-frequency ultrasonic wave propagation. A strong frequency dependence of the sound attenuation rate is predicted, with a characteristic maximum near the transition from the dynamic to the static hysteresis. In the latter case the transition to the limit gives the basic results of the Granato-Lucke and Rogers theories describing the amplitude dependent internal friction due to underdamped dislocation loops. The dynamic theory of the dislocation hysteresis provides an explanation to the anomaly shown by the high-frequency, amplitude dependent internal friction of metals at the N–S transition. As is seen from the analysis, it is directly related to the decrease in the S-state of the electron drag to dislocation. Eine dynamische Theorie der amplitudenabhangigen Versetzungshysteresis wird entwickelt und auf die Bedeutung der Quasiteilchen–Versetzungs-Wechselwirkung fur die nichtlineare Response des Realkristalls auf eine hochfrequente Ultraschallausbreitung hingewiesen. Eine strenge Frequenzabhangigkeit der Schalldampfungsrate wird vorausgesagt mit einem charakteristischen Maximum in der Nahe des Ubergangs von der dynamischen zur statischen Hysteresis. Im letzteren Falle ergibt der Grenzubergang die grundlegenden Ergebnisse der Granato-Lucke- und Rogers-Theorien, die die amplitudenabhangige innere Reibung infolge von unterdampften Versetzungsschleifen beschreiben. Die dynamische Theorie der Versetzungshysteresis liefert eine Erklarung der Anomalie, die sich in der hochfrequenten, amplitudenabhangigen inneren Reibung der Metalle zum N–S-Ubergang zeigt. Aus der Analyse ist ersichtlich, das sie direkt mit dem Abfall des S. Zustands des Elektronendrags zu Versetzungen verbunden ist.

The Amplitude Dependence of Internal Friction and the Young's Modulus Defect in Solids Due to Anharmonism of Dislocation Motion at Low Vibration Amplitudes

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Corrections due to inhomogeneous strains to the internal friction measured in free decay

The theoretical models for amplitude-dependent damping are worked out for hypothetical samples under homogeneous strains. This is called the intrinsic damping. Experimentally, however, a strain distribution is imposed onto the sample and the measured data must be corrected, for a comparison with the theoretical models. This problem has been treated in the internal friction literature, for the case where the spatial strain distribution in the specimens remains constant during each experiment, i.e., when the internal friction is measured at constant maximum strain amplitude. The situation is more complicated when the internal friction is amplitudedependent and the data are obtained in free decay, so that, in addition to a spatial strain distribution, the maximum strain amplitude is changing during each vibration period. This problem has not been considered in the literature or the correction due to the strain distribution has been wrongly applied to internal friction data, obtained during free decay, by taking into account only the distribution in space and ignoring the fact that the strain amplitude is also time dependent. Since several amplitude-dependent internal friction data, taken during free decay, are reported in the literature, and several dislocation parameters are obtained from these results, it is important to evaluatemore » the influence of variable strains (in space and time) on the shape of the intrinsic damping versus strain curves.« less

Comments on corrections due to inhomogeneous strains to the internal friction measured in free decay

Povolo's argument that amplitude-dependent internal friction curves of the form anti ..delta.. (A) vs A measured in free decay can be grossly distorted is valid. It is essentially a restatement of the fact that any derivative curve obtained by numerical differences from a raw data set is grossly distorted if an inappropriately large difference interval is chosen. Such is not the case for data obtained and treated in the manner outlined.

Peculiarities of High-Amplitude Dislocation Internal Friction in Molybdenum Single Crystals of High Purity in the Temperature Range 5.9 to 300 K

Amplitude dependences of internal friction in molybdenum single crystals of the orientations 〈100〉, 〈110〉, 〈111〉, 〈941〉 are studied. The residual resistance ratio of the samples is (1 to 2) × 105. The measurements are carried out at the frequency of 88 kHz in the temperature range 5.9 to 300 K. At low temperatures (≦ 90 K) a maximum is found in the decrement amplitude dependences the height of which decreases rapidly with decreasing temperature. In this case the maximum position in the amplitude deformation axis does not change. In the same amplitude range a saturation region appears in the modulus defect amplitude dependences the magnitude of which also decreases rapidly with decreasing temperature. The observed behaviour of amplitude-dependent internal friction testifies to the fact that while decreasing temperature the losses connected with dislocation unpinning from the pinning centres decrease sharply. In molybdenum single crystals of lower purity or deformed at room temperature a maximum in the decrement amplitude dependences measured in the same amplitude range is absent. The peculiarities described cannot be explained in the framework of the theories presented. [Russian Text Ignored.]

Acoustic technique application in determining structure and dislocation-point defect force interaction parameters

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Amplitude-dependent internal friction calculations for dislocations in alloys

The amplitude-dependent internal friction produced by the dissipative motion of dislocations in alloys has been calculated. The dislocations were modeled in terms of a known string analogy and the alloy was represented by a random planar distribution of weak obstacles of finite interaction range. The equation of motion describing the dislocation behavior (including inertial and viscous forces) was integrated using a numerical method recently developed by Labusch and Schwarz. The results show that the flow stress and other important alloy properties can be derived from the general shape and asymptotic behavior of the decrement vs stress-amplitude curves, without the need to subject them to detailed analytical study. The present calculations were found to be in good agreement with measurements in freshly deformed crystals in which solute atoms had not been able to segregate to dislocations. On the other hand, when these crystals were annealed, the measurements were better described by the Granato-Lücke theory (based on a linear distribution of obstacles). The calculations also showed good agreement with previous measurements in superconducting materials, in which the viscous drag is low and the dislocations exhibit inertial effects.

POINT DEFECT - DISLOCATION INTERACTION IN MgO

Amplitude Dependent Internal Friction has been measured from 77 K to 593 K in MgO single crystals plastically deformed at room temperature. Experimental results have been tested with several theoretical models of dislocation breakaway. A reliable value of interaction energy (0.5 eV) is deduced from the model of Teutonico, Granato and Lucke, but only a partial agreement between experimental results and the model is obtained. For that reason, a numerical analysis of thermomechanical breakaway has been undertaken.

Ａｌ‐Ｃｕ共晶合金の超塑性変形と室温内部摩擦

Interrelation between superplastic deformation and internal friction was investigated using an Al-Cu eutectic alloy. The increment of internal friction at room temperature due to deformation, ΔQ-1, increased with the amount of strain under non-superplastic deformation conditions, while under superplastic conditions the change in ΔQ-1 was relatively small. Strain amplitude dependence was observed in ΔQ-1 of specimens deformed at lower temperatures or higher strains. An analysis of the strain amplitude dependent internal friction was carried out by using Granato-Lücke theory. It was found that ΔQ-1 was proportional to the dislocation density ∧. It was also found that the strain rate sensitivity of flow stress m (σ=kεm, σ: flow stress, ε: strain rate, k: constant) was proportional to the negative value of ΔQ-1 or ∧. Changing characteristics of ΔQ-1 for various strains and deformation conditions showed a good correspondence to the results of the direct observation of dislocation structures.These results are consistent with the superplastic deformation mechanism proposed previously, which involves the grain boundary sliding compensated by the diffusional process predominantly and the dislocation motion acting to decrease the m value.

DISLOCATION RELAXATION IN A RANDOM ARRAY OF SOLUTES

An amplitude-dependent internal friction peak occurs at ≈ 475 K in well-annealed, pure α-Zr after slight deformation. Qualitatively, the results agree with a model for the motion of zig-zag dislocations in an array of obstacles. Comparison of theoretical and experimental results yields estimates of the effective activation enthalpy and activation volume of the process involved.

Dislocation Velocities in Al Obtained from Amplitude-Dependent Internal Friction

A method is presented to obtain dislocation velocities in crystals from measurements of the amplitude-dependent internal friction, which is due to the dislocations oscillating in the lattice. The velocities calculated from the experimental data of the internal friction of an Al crystal are consistent with the data obtained by direct observation.

Internal-friction measurements of dislocation inertial effects in dilute alloys of lead

The temperature dependence of the yield stress of pure lead and lead containing 3000 ppm of tin was measured using amplitude-dependent internal-friction measurements. The results are used to distinguish between models for the effect. It is shown that the temperature dependence of the stress drop is not consistent with existing rate theories, but is as expected from the inertial model. However, the low-temperature dependence of the yield stress is characteristic of a thermally-activated rate process and indicates that a mechanism combining thermal activation and inertial effects is required. It is concluded that the effect is initiated by the thermal overcoming of obstacles by dislocations, followed by inertial overcoming of subsequent obstacles.

Amplitude dependent modulus effect in copper

Copper single crystals with a high initial dislocation density or with an orientation near and on symmetry lines show an amplitude dependent modulus effect and internal friction. This effect occurs at lower strains than the effect predicted by the Granato-Lücke theory. Moreover the effect is strongly temperature dependent and in some cases almost 3 times as large as the normal effect. The extra-effect seems to be a result of intersecting dislocations.