Leszek B. Magalas

Theoretical basis and general applicability of the coupling model to relaxations in coupled systems

Abstract The coupling model proposed more than a decade ago for the description of relaxations in complex correlated systems by one of us (KLN) have been shown repeatedly to be applicable to amorphous polymers, viscous liquids, the glassy state, metallic glasses, glassy ionic conductors and etc. In these examples, the relaxing species are dense packed and mutually interacting. As a consequence, the constraints between them have a strong influence on the relaxation dynamics. Very recent quasielastic neutron scattering experimental data as well as molecular dynamics simulation results which provide dramatic proof of the validity of the coupling model will be discussed. The applicability of the coupling model to some relaxations in metals including precipitates and the Snoek—Koster relaxation is less obvious but has recently been proposed, justified and demonstrated to be relevant by one of us (YNW). The applicability of the coupling model to these and other problems of immediate interest to participants of ICIFUAS-10 will be summarized and discussed. For Snoek—Koster relaxation, additional experimental data in ultra-high purity iron containing low concentration of carbon obtained by one of us (LBM) show characteristics that cannot be explained by Seegers model of thermally activated formation of kink pairs on screw dislocations in the presence of foreign interstitial atoms, but are consistent with the coupling model.

DFT-based Estimation of Damped Oscillation Parameters in Low-Frequency Mechanical Spectroscopy

In this paper, we analyze and compare the properties of different well-known and also new nonparametric discrete Fourier transform (DFT)-based methods for resonant frequency and logarithmic decrement estimation in application to mechanical spectroscopy. We derive a new DFT interpolation algorithm for a signal analyzed with Rife-Vincent class-I windows and also propose new formulas that extend Bertocco and Yoshida methods. We study errors of the resonant frequency and logarithmic decrement estimation in realistic conditions that include measurement noise and a zero-point drift. We also investigate the systematic errors of the estimation methods of interest. A nonlinear least squares time-domain parametric signal fitting is used to determine the boundaries of statistical efficiency in all tests.

Effect of Substitutional Ordering on the Carbon Snoek Relaxation in Fe–Al–C Alloys

It is shown that the alloying of iron by Al (0 to 30 at%) shifts the carbon Snoek peak to a higher temperature and broadens it in the disordered state (quenched samples). Ageing of quenched samples with 19.6 at% Al shifts the peak to lower temperatures and makes it more narrow due to substitutional ordering of the DO 3 -type. The explanation of concentration dependence of internal friction and influence of ordering is done on the basis of computer simulation of energy distribution for carbon atoms in solid solution due to its interaction with Al atoms and changing of this distribution due to Al ordering. The model of the long-range strain-induced (elastic) C-Al interaction supplemented by the short-range chemical interaction is successfully used. The change of the calculated peak temperature and its width is in good agreement with experimental data. It is shown that the main factor which determines the effect of Al on the carbon Snoek peak in iron is the long-range elastic interaction.

Mechanical Spectroscopy and other Relaxation Spectroscopies

Mechanical spectroscopy is a powerful technique in investigations of the molecular mobility, atomic interactions, and more particularly the structural defects in matter. In crystalline materials, the problem is mainly dealing with point defects, dislocations, and their interactions. As a general rule, large frequency and temperature ranges are required in order to capture the characteristics of these defects at a microscopic level, namely the dynamics and the concentration. In the case of non-crystalline solids, the low temperature relaxation processes obey the Arrhenius law (i.e. the atomic or molecular motions are individual). If the temperature is not far below the liquid glass transition, the internal degrees of freedom are no more independent and thus enter a cooperative regime. The wide band mechanical spectroscopy appears to be necessary for the complete analysis of the complex dynamics of such systems. In addition, complementary relaxation spectroscopies (e.g. dielectric spectroscopy, NMR), in combination with non elastic radiation scattering are shown to provide a clear understanding of the dynamics and structure at a microscopic level.

Application of the wavelet transform in mechanical spectroscopy and in Barkhausen noise analysis

Abstract In this work, the wavelet transform and the Fast Fourier Transform FFT are introduced to analyze the quality of the strain response signal in order to improve the accuracy of computation of both the logarithmic decrement and the mechanical loss angle. The wavelet transform of the strain response signal yields a three-dimensional representation (the time-scale joint representation), i.e. space (time), frequency (scale) and amplitude. To emphasize that not only time but also frequency content of the strain response signal collected from a mechanical spectrometer is identified, the author suggests that the time-scale joint representation of the strain response signal should be called ‘Identified Strain Response Signal — ISRS’. The wavelet transform was shown to be an excellent tool to test the quality of the strain and/or of the stress signal in a mechanical spectrometer working in a resonant or subresonant mode. A new approach to the non-stationary Barkhausen noise (BN) signal based on the wavelet transform is also presented. The BN level is usually expressed with the magnetoelastic parameter MP which is a relative number proportional to the root mean square level of the BN. It was found that the MP value is not a reliable parameter for the identification of stress concentrations in ferromagnetic materials. Indeed, a stress concentration resulting from internal stresses can be successfully revealed by the time-scale joint representation of the BN signal. The author suggests that the wavelet transform of the non-stationary RN signal should be called the ‘Identified Barkhausen Noise — IBN’. This approach produces a physically reliable relationship between the IBN and either the level of internal stresses or fine variations in the microstructure.

Measurement Techniques of the Logarithmic Decrement

A comparison of eight algorithms used in computations of the logar ithmic decrement and three algorithms used for measurements of the resonant frequency of free decaying oscillations is reported. Basic definitions and measuring principles of the logarithm ic decrement and error analysis for tested algorithms are briefly described. It is demonstrated that it is possible to tailor high quality mechanical loss spectra for a number of various experimental situa tions by appropriate selection of the numerical algorithms and optimization of several parameters used in signal acquisition of exponentially damped harmonic oscillations. The described strategy c an be applied in mechanical spectroscopy, internal friction measurements, and mechanical damping measur ements in general. Introduction The purpose of this paper is to review briefly the basic concept of t he logarithmic decrement δ and to discuss the algorithms used in measuring δ and the resonant frequency o f . The logarithmic decrement of free decaying oscillations can be measured either from discrete values of decaying amplitudes or from the entire data set of digitized strain respons e signal via integral transform techniques such as the Fourier and Hilbert transform [1]. Resonant fr equency can be measured using one of three different techniques, as described below. In this paper we show that the choice of the algorithm and optimization of a number of parameters used in signa l acquisition can substantially reduce computation error and therefore increase the qu ality of measured mechanical loss spectra. Error analysis for both the logarithmic decreme nt and the resonant frequency of decaying oscillations is discussed. The contents of this paper were presented at the Second International School on Mechanical Spectroscopy MS-2 in December 2000 as an oral presentation and introduct ion to a round table discussion. Indeed, it was originally planned to only discuss this topic during the round table discussion in lieu of publication. The interest shown by participants to measuring techniques was overwhelming. We were therefore encouraged to write this paper and to provide a number of practical suggestions on how to improve precision in mechanical loss me a urements. Indeed, precision in measurements of the logarithmic decrement can be r eadily improved without substantial investment in equipment, while the quality of mechanical loss spectra can also be easily tailored by a mechanical spectroscopist if an appropriate strat egy in measuring the logarithmic decrement is used, as described in this paper. It is critically important to recognize that different algorithms generate different degrees of error in computation of the logarithmic decrement. We will also demonstrate that different strategies for logarithmic dec rement measurements should be employed to measure mechanical loss peaks of different shape and hei ght at a high level of precision. The scope of this paper does not cover a description of the computing techniques of the mechanical loss angle φ . This problem is a subject for a separate paper. Solid State Phenomena Online: 2003-02-13 ISSN: 1662-9779, Vol. 89, pp 247-260 doi:10.4028/www.scientific.net/SSP.89.247

Determination of the Logarithmic Decrement in Mechanical Spectroscopy

The comparison between the classical methods and a new algorithm OMI used to compute the logarithmic decrement is reported. The OMI algorithm is tested in the computation of the logarithmic decrement from exponentially damped harmonic oscillations. The OMI algorithm yields high precision in the computation of the logarithmic decrement and the resonant frequency, and the smallest dispersion of experimental points.

Mechanical Spectroscopy – Fundamentals

Mechanical spectroscopy is described as a member of the fami ly of spectroscopic techniques. It is shown that mechanical spectroscopy investigates t he mechanical energy absorbed by a physical object subjected to an external time-dependent pertur bation field, that is, an impulsed, quasi-static, or harmonic mechanical field over the entire range of attainable frequencies (from 10 Hz to 10 Hz). The modulus of compliance and modulus of elasticity is discussed in t rms of generalized susceptibility within the framework of linear respons e theory. The relationship of the response and relaxation functions to generalized susceptibility is gi ven via the Fourier-Laplace transformation of the relaxation or response function. This approach des ribes linear mechanical responses to time-dependent mechanical perturbation and enables calcula tion of mechanical loss in solids. Debye and non-Debye relaxations are briefly described and illustrated. A record of discussions which took place during the Second International School on Mechani cal Spectroscopy MS-2 and author’s answers to questions raised after the lecture are included. Definition of Mechanical Spectroscopy Spectroscopy is the science which consists in the investigation of the energy absorbed or emitted by a physical object subjected to an interacting (perturbation) fie ld. Mechanical spectroscopy can be defined in the framework of an interacting system in which the ext rnal perturbing field F, used for probing the response R of the physical object, is mechanical in nature, that is, stres s σ and strain ε [1]. In general, mechanical spectroscopy consists in the investigat ion of the time-dependence of macroscopic response R(t) under the perturbation of a time-dependent m echanical field F(t); a single direct mechanical perturbation is depicted in Fig. 1.1 while coupled perturbation with mechanical probing field is illustrated in Fig. 1.2. In both cases the macroscopic response comes ultimately from the microscopic motions of relaxing entities.

Recent Advances in Determination of the Logarithmic Decrement and the Resonant Frequency in Low-Frequency Mechanical Spectroscopy

The advantages of the OMI algorithm to compute the logarithmic decrement and the resonant frequency from free decaying oscillations is reported. The OMI algorithm is proved to be the best solution in the computation of the logarithmic decrement and the resonant frequency for high damping levels.

Selected Applications of the Wavelet Transform

The wavelet transform is used to analyze: (1) the strain respons e signal in a resonant mechanical spectrometer, (2) the signal from a magnetic inspec tion of wire ropes, and (3) the Barkhausen noise signal. The wavelet transform of the analyzed signal yields a three-dimensional representation (the time-scale joint representation), that is, s pace (time), frequency (scale), and amplitude. The time-dependent strain signals measured by a mecha nical spectrometer, represented in the time-scale joint representation, are called “Identifie d Strain Response Signal” (ISRS) to emphasize that not only frequency content of the strain response signal but lso time is clearly revealed. The wavelet transform is applied to on-line analysis of the strain signal during mechanical loss measurements. The wavelet transform of the strain response s ig al can also be used to identify fine irregularities in a very low frequency strain response sig nal and to denoise this signal in order to obtain better signal to noise ratio of the strain signal recor d d in a subresonant mechanical spectrometer. For these reasons the wavelet analysis has proved t o b a useful tool to analyze the strain and the stress signals and thereby to improve the quali ty of oscillations in both a resonant and a subresonant mechanical spectrometer. It is concluded that the wave let transform can be successfully used in spectroscopic techniques. Nonstationary Barkhausen noi (BN) signals and signals obtained during magnetic inspection of twisted and lay ropes are also investigated by the wavelet analysis. The wavelet transform is used in the magnet ic i spection of wire ropes and in the decomposition of signals from induction sensors, that is, in non-destructive testing (NDT) techniques of wire ropes. Appropriate levels of signal decomposition provi de both reliable detection of various forms of rope wear and supplementary information about wear-of f forms in twisted and lay ropes. The wavelet transform of nonstationary magnetic signal is a promising and powerful tool for wire rope inspection and investigation of ferromagnetic materials. Introduction This paper reports results on the application of wavelet analysis: (1) to nearly stationary harmonic signals recorded in a mechanical spectrometer, (2) to nonstationary signals obtained in the investigation of the magnetic Barkhausen noise (BN), and (3) to nonstationa ry signals obtained in the non-destructive magnetic inspection of wire ropes. Solid State Phenomena Online: 2003-02-13 ISSN: 1662-9779, Vol. 89, pp 355-0 doi:10.4028/www.scientific.net/SSP.89.355