Nonlinear Internal Friction Research Articles

Effect of Acoustic Oscillations on Non-Equilibrium State of Magnetic Domain Structure in Cubic Ni2MnGa Single Crystal.

Magnetic hysteresis is a manifestation of non-equilibrium state of magnetic domain walls trapped in local energy minima. Using two types of experiments we show that, after application of a magnetic field to a ferromagnet, acoustic oscillations excited in the latter can "equilibrate" metastable magnetic domain structure by triggering the motion of domain walls into more stable configurations. Single crystals of archetypal Ni2MnGa magnetic shape memory alloy in the cubic phase were used in the experiments. The magnetomechanical absorption of ultrasound versus strain amplitude was studied after step-like changes of a polarizing magnetic field. One-time hysteresis was observed in strain amplitude dependences of magnetomechanical internal friction after step-like variations of a polarizing field. We distinguish two ingredients of the strain amplitude hysteresis that are found in the ranges of linear and non-linear internal friction and show qualitatively different behavior for increasing and decreasing applied polarizing fields. The uncovered effect is interpreted in terms of three canonical magnetomechanical internal friction terms (microeddy, macroeddy and hysteretic) and attributed to "triggering" by acoustic oscillations of the irreversible motion of domain walls trapped in the metastable states. To confirm the suggested interpretation we determine the coercive field of magnetization hysteresis through the measurements of the reversible Villari effect. We show that the width of the hysteresis loops decreases when acoustic oscillations in the non-linear range of domain wall motion are excited in the crystal. The observed "equilibration" of the magnetic domain structure by acoustic oscillations is attributed to the periodic stress anisotropy field induced by oscillatory mechanical stress.

The Influence of Thermal Treatment on Elastic and Anelastic Properties of Ni55Fe18Ga27 Alloy Single Crystals

We have studied the influence of thermal treatment on the dynamic Young’s modulus, linear and nonlinear internal friction, and Young’s modulus defect of Ni55Fe18Ga27 alloy single crystals. Strong variations of all these parameters were observed and explained by changes in the concentration of vacancies in the crystal lattice. It is concluded that vacancies form atmospheres near twin boundaries, the density of which (but not their extension) strongly depend on the concentration of vacancies.

Влияние термической обработки на упругие и неупругие свойства монокристаллов сплава Ni-=SUB=-55-=/SUB=-Fe-=SUB=-18-=/SUB=-Ga-=SUB=-27-=/SUB=-

AbstractWe have studied the influence of thermal treatment on the dynamic Young’s modulus, linear and nonlinear internal friction, and Young’s modulus defect of Ni_55Fe_18Ga_27 alloy single crystals. Strong variations of all these parameters were observed and explained by changes in the concentration of vacancies in the crystal lattice. It is concluded that vacancies form atmospheres near twin boundaries, the density of which (but not their extension) strongly depend on the concentration of vacancies.

Mechanical interpretation and generalization of the Cole-Cole model in viscoelasticity

The mechanical basis of the popular Cole-Cole rheological model in viscoelasticity is investigated by using Lagrangian mechanics with nonlinear energy dissipation. The Cole-Cole model is usually viewed as a convenient way to fit the observed frequency-dependent attenuation and velocity-dispersion spectra, but its time-domain and numerical formulations are complex and contradict standard physical principles. For example, time-domain modeling of Cole-Cole media requires special mathematical tools such as fractional derivatives, convolutional integrals, and/or memory variables. Nevertheless, we find that Cole-Cole spectra naturally arise from conventional mechanics with nonlinear internal friction (non-Newtonian viscosity). The Lagrangian mechanical formulation is applied to a finite body (a rock sample in a laboratory experiment) and a wave-propagating medium, in both cases providing rigorous differential equations of motion and revealing the time- and frequency-independent material properties. The model also leads to a generalized Cole-Cole (GCC) model with multiple internal variables (relaxation mechanisms), similar to the generalized standard linear solid (GSLS). As a practical application, the GSLS and GCC models are compared on interpretations of recent P-wave attenuation and dispersion measurements on bitumen-sand samples in the laboratory. The GSLS and GCC models can be used to predict the observed strain/stress ratios with adequate accuracy. However, each of these models offers certain advantages, which are the linearity (for GSLS) and potentially smaller number of dynamic variables and broader peaks in attenuation spectra (for GCC). Therefore, additional experiments focusing on linearity of internal friction are required to establish which of these models may be preferable for rock. The Lagrangian approach provides a simple and physically meaningful way for comparing all types of observations, formulating numerical modeling schemes, and predicting the propagation of waves and behavior of other deformations of earth media.

Effect of Hydrogen on the Elastic and Anelastic Properties of the R Phase in Ti50Ni46.1Fe3.9 Alloy

The linear and non-linear internal friction, effective Young’s modulus, and amplitude-dependent modulus defect of a Ti50Ni46.1Fe3.9 alloy have been studied after different heat treatments, affecting hydrogen content, at temperatures of 13–300 K, and frequencies near 90 kHz. It has been shown that the contamination of the alloy by hydrogen gives rise to an internal friction maximum in the R martensitic phase and a complicated pinning stage in the temperature dependence of the effective Young’s modulus at temperatures corresponding to the high-temperature side of the maximum. Dehydrogenation of the H-contaminated alloy transforms the internal friction maximum into a plateau and minimizes the pinning stage. The internal friction maximum is associated with a competition of two different temperature-dependent processes affecting the hydrogen concentration in the core regions of twin boundaries. The amplitude-dependent anelasticity of the R phase is also very sensitive to hydrogen content, its temperature dependence reflects the evolution of extended hydrogen atmospheres near twin boundaries.

On the Effect of Hydrogen on the Low-Temperature Elastic and Anelastic Properties of Ni-Ti-Based Alloys.

Linear and non-linear internal friction and the effective Young’s modulus of a Ni50.8Ti49.2 alloy have been studied after different heat treatments, affecting hydrogen content, over wide ranges of temperatures (13–300 K) and strain amplitudes (10−7–10−4) at frequencies near 90 kHz. It has been shown that the contamination of the alloy by hydrogen strongly affects the internal friction and Young’s modulus of the martensitic phase. Presence of hydrogen gives rise to a non-relaxation internal friction maximum due to a competition of two different temperature-dependent processes. The temperature position and height of the maximum depend strongly on the hydrogen content. We conclude that many of the internal friction peaks, reported earlier for differently treated Ni-Ti-based alloys, had the same origin as the present maximum.

Twinning in Ni–Fe–Ga–Co shape memory alloy: Temperature scaling beyond the Seeger model

The temperature dependence of the macroscopic de-twining stress in Ni–Fe–Ga–Co shape memory alloy is proportional to the temperature dependence of the micro-yield stress. This proportionality holds for all values of the reversible anelastic strain derived from non-linear internal friction experiments and contradicts predictions of the Seeger model for the temperature dependence of the yield stress. The Seeger model requires two length scales which leads to the independence of two yield stress components. Instead, we find the self-affine behaviour of anelastic strain, which excludes all separations of lengthscales.

Stability analysis of rotor whirl under nonlinear internal friction by a general averaging approach

The two main sources of internal friction in a rotor-shaft system are the shaft structural hysteresis and the possible shrink-fit release of the assembly. The internal friction tends to destabilize the over-critical rotor running, but a remedy against this effect may be provided by a proper combination of some external damping in the supports and an anisotropic arrangement of the support stiffness, or at most by the support damping alone, depending on the system geometry. The present analysis reported here considers a general asymmetric rotor-shaft system, where the rotor is perfectly rigid and is constrained by viscous–flexible supports having different stiffnesses on two orthogonal planes. The internal friction is modelled by nonlinear Coulombian forces, which counteract the translational motion of the rotor relative to a frame rotating with the shaft ends. The nonlinear equations of motion are dealt with using an averaging approach based on the Krylov-Bogoliubov method with some adaptation to address the multi-degree-of-freedom nature of the problem. Stable limit cycles may be attained by the overcritical whirling motions, whose amplitudes are inversely proportional to the external dissipation applied by the supports. A noteworthy result is that the stiffness anisotropy of the supports is recognized as beneficial in reducing the natural whirl amplitudes, albeit mainly in the symmetric configuration of the rotor at the mid span and, to a rather lesser extent, in the asymmetric configuration, which then requires a stronger damping action in the supports.

A modeling approach for robotic catheters: effects of nonlinear internal device friction

Recently, robotic surgery systems using passive flexible catheters have been developed for minimally invasive surgical applications – such as in the treatment of atrial fibrillation – where catheter control in the open chamber of the heart is required. The soft, atraumatic construction of these devices help reduce injury to delicate cardiac structures while providing a means of tool placement and control. To provide kinematic and control relationships, various models of continuous catheters have been developed. However, these approaches cannot explain the nonlinear behavior of the catheter when the effect of internal friction is considered. In this paper, we describe a lumped-parameter modeling approach which directly accounts for the effects of internal device friction. The nonlinear model is validated against experimental results from a prototype robotic catheter and is shown to correctly predict the variations in curvature and path-dependent instantaneous behavior observed. Finally, the validated model is used to investigate and describe a set of non-ideal catheter motions observed in practice.

Mechanical Spectroscopy of Hyperstabilized Martensites

The internal friction of the hyperstabilized martensite demonstrates very low values, both above and below the nominal martensitic transformation temperature, due to a pronounced pinning effect. Over a wide temperature range it is comparable with the level of damping in the parent phase. A study of the temperature dependence of the non-linear ultrasonic internal friction and its strain amplitude hysteresis indicates that the diffusion, assisted by dislocations/interfaces, is quite pronounced and in Ni-Fe-Ga and Cu-Al-Be alloys it operates at temperatures around 20 K. The renucleation of the lamellar parent phase during the reverse martensitic transformation close to 600 K is accompanied by an internal friction peak which demonstrates a substantial transitory contribution. After renucleation of the parent phase the samples recover a conventional martensitic transformation with the internal friction level in the martensite comparable to the one in non-stabilized samples. Observations of a relaxation peak in the parent phase of different alloys for temperatures just below the renucleation stage of the reverse transformation point to the essential role of diffusion in the nucleation of the parent phase in hyperstabilized martensites.

Theory of the nonlinear internal friction associated with bulk diffusion of solute atoms around dislocations in Al–Mg alloys

In this paper the nonlinear (amplitude-dependent) internal friction (P 3 peak) in cold-worked Al–Mg alloys is theoretically studied by solving the bulk diffusion equations of the solute atoms (Mg atoms) under the action of dislocation drag. The results in the case of a constant external stress show that the bow-out distance of the dislocation has an exponential relation with time, which can be well described by an exponential creep function with a Gaussian distribution in τ. With the increasing strain amplitude, the relaxation strength Δ and relaxation time τ decrease, while the distribution parameter increases. Both activation energy H and pre-exponential factor τ 0 deduced from τ through Arrhenius relation are dependent on strain amplitude.

Experimental study of the nonlinear internal friction peaks in Al–Mg solid solutions

Nonlinear internal friction peaks associated with the interaction between dislocations and point defects are experimentally studied in cold-worked Al–Mg solid solutions. It is found that the appearance of these peaks is very sensitive to the cold-work methods among which the stretching method in the strain range of several percent is effective for reproducing the peaks. A maximum of the internal friction vs. strain amplitude at a given temperature around the peak is observed. With the forced vibration method and by using a nonlinear fitting program to subtract the background, the activation energies are measured to be 1.3, 1.1 and 0.7 eV, respectively, for the three peaks ( P L1, P 1′, P 1″) in the order of ascending temperature.

Theory of dislocation-solute atom interactions in solid solutions and related nonlinear anelasticity

A theory for dislocation-solute atom interactions in solid solutions has been developed which allows one to calculate the nonlinear dislocation strain-amplitude-dependent internal friction. The suggested model accounts for different modes of dislocation-solute atom interactions: (i) Solute atoms distributed in the dislocation glide plane interact with the dislocation core and represent short-range obstacles for the dislocation motion; (ii) Solute atoms situated away from the dislocation glide plane create relatively weak long-range elastic stress fields, also impeding dislocation motion. We assume that dislocations move in a two-component system of obstacles which differ with respect to the thermodynamics of dislocation--point-defect interactions. Namely, dislocations overcome short-range obstacles under the combined action of applied stress and thermal energy, whereas relatively weak long-range obstacles are surmounted athermally. The model predicts a complicated multistage behavior of the nonlinear internal friction in the strain amplitude--temperature--solute concentration domain, which is in excellent agreement with recent experimental data.

Theory of Low-Frequency Nonlinear Anelastic Internal Friction Peaks around Room Temperature

Since a low-frequency internal friction phenomenon exhibiting anomalous amplitude effect was observed in an Al-Cu alloy [1], a series of similar internal friction peaks versus temperature were observed in cold-worked and partially annealed Al-Mg and Al-Cu dilute alloys [2]. These internal friction peaks exhibit the common features of relaxation characteristics and anomalous amplitude effects giving rise to internal friction peaks versus strain amplitude in the temperature range of the internal friction peaks versus temperature. This series of nonlinear anelastic internal friction peaks were considered to be originated from the dislocation slip or kink drift, rate-controlled by different diffusion processes of different point defects interacting with dislocations or kinks. The amplitude effect can be ascribed to the dependence of the mobility of the dislocations or kinks on the amplitude because of the escaping of point defects from the stress fields of the moving dislocations or kinks. An attempt is made to establish a simple interaction model between kinks and point defects using a low-frequency approximation and to demonstrate at least semiquantitatively how the interaction between dislocations and mobile point defects can give rise to anelastic relaxation peaks with anomalous amplitude effect. The theoretical results obtained correspond satisfactorily with the experimentally observed internal friction phenomena (e.g. P 1 peak) around room temperature in Al-Mg and Al-Cu alloys. This P 1 peak was considered to be related to the transverse core diffusion (TCD) of the solute atoms within the dislocation core.

Nonlinear Internal Friction Character of Foamed Aluminum

An experiment has been carried out to investigate the damping behavior of foamed aluminum. It was found that foamed aluminum has a significant nonlinear internal friction character, i.e., its damping capacity is amplitude-dependent, and this character tends to be more pronounced with decreasing the density and pore size.

Internal friction and dislocation collective pinning in disordered quenched solid solutions

We introduce the collective pinning of dislocations in disordered quenched solid solutions and calculate the macroscopic mechanical response to a small dc or ac applied stress. This work is a generalization of the Granato–Lücke string model, able to describe self-consistently short and long range dislocation motion. Under dc applied stress the long distance dislocation creep has at the microscopic level avalanche features, which result in a macroscopic nonlinear “glassy” velocity-stress characteristic. Under ac conditions the model predicts, in addition to the anelastic internal friction relaxation in the high frequency regime, a linear internal friction background which remains amplitude-independent down to a crossover frequency to a strongly nonlinear internal friction regime.

Nonlinear internal friction character of foamed aluminum

Nonlinear internal friction character of foamed aluminum

A New Experimental Method to Develop the Nonlinear Anelastic Internal Friction Peaks Appearing around Room Temperature

A New experimental procedure to definitely develop the nonlinear anelastic internal friction peaks (P' 1 and P 1 peaks) appearing around room temperature, called medium cold work method, is suggested. This method consists in stretching and then twisting the thoroughly annealed specimen at room temperature by a medium amount. The experimental results indicate that the tensile deformation plays a decisive role and no peaks appear in the case of pure twisting deformation. The temperature internal friction peaks in Al-Mg alloys are studied with this method.

Theoretical treatment of the nonlinear anelastic internal friction peaks appearing in the cold-worked Al-based solid solutions

The longitudinal and transverse diffusion equations of solute atoms along the dislocation core formulated based on the dislocation kink model are solved with the numerical difference method. The theoretical internal friction and modulus defect curves versus temperature and strain amplitude were calculated for the nonlinear anelastic internal friction peaks (${P}_{0},$ ${P}_{1}^{\ensuremath{'}},$ and ${P}_{1}^{\ensuremath{''}}$ peaks). The manifestations of these curves are compared with the experimental results previously obtained in cold-worked Al-Mg and Al-Cu solid solutions around room temperature.

Theoretical Study of the Nonlinear Anelastic Internal Friction Peaks Associated with Diffusion of Solute Atoms in Dislocation Core

Based on the dislocation kink atmosphere model, the longitudinal and transverse core diffusion equation of solute atoms was formulated. The relaxation time and the relaxation strength associated with the diffusion processes under quasi-static stress were computed by solving the diffusion equation analytically, and were found to be nonlinear with respect to the applied stress. The theoretical internal friction curves versus temperature and strain amplitude were calculated by solving the diffusion equations with numerical method and manifestation of these curves conform to the experimental results previously obtained.