Nonlinear Internal Friction Research Articles

Theory of Nonlinear Anelastic Internal Friction Peaks. I. The Migration of Solute Atoms in Dislocation Core

Based on the kink model, the diffusion mode of the solute atoms situated at the kink and at the extremities of the kink was analyzed. The probability density or the distribution function of a solute atom at the position (x, y) on a kink chain was formulated. This distribution function changes atom at the position (x, y) on a kink chain was formulated. This distribution function changes when the kink chain moves under an applied stress. The change of the total energy of the kink chain was calculated and thus the transverse and the longitudinal forces acted upon the solute atom. The equations of the longitudinal and transverse core diffusion of the solute atom were formulated accordingly.

Nonlinear Anelastic Internal Friction Associated with the Diffusion of Solute Atoms in Dislocation Cores

Recently, the activation energy associated with the anomalous internal friction peaks appearing in cold-worked Al-Cu and Al-Mg specimens around room temperature was found to be close to that associated to the pipe diffusion along dislocations. Consequently these internal friction peaks were attributed to the diffusion of Cu or Mg atoms in the dislocation core in aluminium and a physical model was suggested in terms of the dislocation kink model. The manifestations of these anomalous internal friction peaks conform to those predicted through a detailed mathematical analysis of the dislocation core diffusion by Winkler-Gniewek et al., in terms of the string model. This confirms further that the nonlinear anomalous internal friction peaks observed originate from dislocation core diffusion. In this paper, discussions are made on similarities and diversities of the string model and the kink model concerning this problem.

NONLINEAR ANELASTIC INTERNAL FRICTION PEAKS ASSOCIATED WITH DISLOCATION CORE DIFFUSION

Early since 1950, a systematic study was made on the anomalous internal friction peaks appeared in cold-worked Al-Cu and Al-Mg specimens around room temperature. The activation energy associated with these internal friction peaks was found to be close to that associated with the pipe diffusion along dislocations. Consequently the internal friction peaks were attributed to the diffusion of Cu or Mg atoms in the dislocation core in aluminium. A physical model of these internal friction peaks was suggested in terms of the dislocation kink concept. The manifestation of these anomalous internal friction peaks was found to be similar to that predicted through a detailed mathematical analysis of the dislocation core diffusion by Winkler-Gneiwek et al. according to the string model. In this paper, a critical comparison has been made between the string model and the kink model concerning this problem and it is shown that the predictions derived from the string model can be adequately applied to the case of the kink model. This confirms further that the nonlinear anelastic internal friction peaks we observed are originated from dislocation core diffusion.

Non-linear internal friction and resonance in manganese-copper alloys

Internal friction and modulus at different amplitudes and frequencies were measured for as-cast Mn60Cu40 alloy. Strong non-linear internal friction and resonance were observed. It was proposed that the sources of these were derived from different factors. A parameter, P, which can be used to weigh up non-linear resonance of materials, is proposed. A high damping mechanism is discussed for manganese-copper alloy.

Elastic Modulus Effect Related with Nonlinear Internal Friction

The behavior of elastic modulus related with strain amplitude is studied. It was found that modulus behaves softening when internal friction exhibits normal amplitude-dependent effects, while increases slightly with the appearance of anomalously amplitude-dependent effect. With the decrease of frequency of measurement, the variation of modulus with amplitude becomes small. A trial for obtaining information from amplitude internal friction peak was made on the basis of Debye equations.

Activation Energy Associated with the Nonlinear Internal Friction Peak around Room Temperature in Cold-Worked Al-0.1 wt% Cu

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Anelastic relaxation and internal strain in lead magnesium niobate relaxors

Abstract Non-linear internal friction measurements have been carried out on lead magnesium niobate with 10 at.% lead titanate. The purpose of these measurements was to investigate the field dependence of the elastic and anelastic responses, and to determine how the response depends on the amplitude of an applied stress. The linear elastic response was found to stiffen at all bias levels with the maximum electroelastic coupling occurring near the Vogel—Fulcher freezing temperature. A strong frequency dependence of the kinetics of the anelastic relaxation was found at low measurement frequencies. These data are compared with recent high-frequency results. The existence of an inhomogeneous internal strain has been found from the line broadening of the (220) and (321) diffraction peaks. On application of an electrical field the internal strain is relieved by the development of a macrostrain which is shown to be the electrostrictive strain. It is proposed that the local electrostrictive strains are dynamic in nature and are at the origin of the anelastic relaxation. Strong elastic non-linearities, both an elastic softening and hardening under stress, have also been observed. These results are interpreted as a stress activation of the internal deformation process.

Internal strain relaxation and the glassy behavior of La-modified lead zirconate titanate relaxors

Nonlinear internal friction measurements have been carried out on La-modified lead zirconate titanate relaxors with a Zr/Ti ratio of 65/35. Measurements have been made as a function of La content and dc bias. The elastic softening is believed to have a ferroelastic contribution due to the tilting of the oxygen octahedra, in addition to the expected electrostrictive effects. The temperatures of the maximum softening form a plausible extension to the rhombohedral-rhombohedral phase boundary [Proc. IEEE 61, 959 (1973)]. A frequency dependence of the softening has also been found which was interpreted as the existence of fluctuations in the orientations of the tilts. These fluctuations are proposed to arise in an attempt to partially relieve an inhomogeneity in the electrostrictive strains associated with the polarization fluctuations. The results are discussed in context with previously reported transmission electron microscopy work [C. Randall, Ph. D. dissertation, University of Essex (1987)]. Dielectric measurements have also been done as a function of La content and bias, and the freezing temperature of the polarization fluctuations determined as a function of composition. A revised phase diagram has been proposed using this data base which shows different phase fields having various combinations of freezing mechanisms.

Activation Energy Associated with Nonlinear Internal Friction Peaks (P1′ and P1″ Peaks) in Cold-Worked and Partially Annealed AlMg Solid Solutions

L'ordre de grandeur de l'energie d'activation a un processus de relaxation est hautement instrumental dans la revelation du mecanisme de ce processus. On determine l'energie d'activation associee aux pics P1' et P1'' qui presentent un effet prononce dependant de l'amplitude

NON-LINEAR INTERNAL FRICTION FROM FLEXURE PENDULUM MEASUREMENTS

In many applications a flexure pendulum is more stable and better suited to available sample geometries than the more popular torsion pendulum. Examples of flexure pendulum measurements of non-linear internal friction, using free decay, constant amplitude drive and distortions of the resonance curve are compared.

Parametrically excited oscillations of viscoelastic rods with a nonlinear elasticity relation and nonlinear internal friction

Parametrically excited oscillations of viscoelastic rods with a nonlinear elasticity relation and nonlinear internal friction

Vibrations of a system with memory, non-linear elasticity, friction and relaxation

The solution of a third-order non-linear differential equation with slowly varying coefficients and small time lag is found. This equation governs processes with significant damping, and an application is made to a mechanical vibrating system with non-linear elasticity, internal friction and relaxation.