Modeling the complexity of acoustic emission during intermittent plastic deformation: Power laws and multifractal spectra

Abstract

Scale invariant power law distributions for acoustic emission signals are ubiquitous to several plastically deforming materials. However, power law distributions for the acoustic emission energies are reported in distinctly different plastically deforming situations such as hcp and, fcc single and polycrystalline samples exhibiting smooth stress-strain curves, and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there has been no models that predict the power law statistics for the discontinuous flow. Furthermore, the statistics of the acoustic emission signals in jerky flow is even more complex requiring multifractal measures for a proper characterization. There has been no model that explains the complex statistics either. Here, we address the problem of statistical characterization of the acoustic emission signals associated with the three types of the Portevin-Le Chatelier bands. Following our recently proposed general framework for calculating acoustic emission, we set-up a wave equation for the elastic degrees of freedom with plastic strain rate as a source term. The energy dissipated during acoustic emission is represented by the Rayleigh-dissipation function. Using the plastic strain rate obtained from the Ananthakrishna model for the Portevin-Le Chatelier effect, we compute the acoustic emission signals associated the three Portevin-Le Chatelier bands and the Lüders like band. The so calculated acoustic emission signals are used for further statistical characterization. Our results show that the model predicts power law statistics for all the acoustic emission signals associated with the three types of Portevin-Le Chatelier bands with the exponent values increasing with increasing strain rate. The calculated multifractal spectra corresponding to the acoustic emission signals associated with the three band types has a maximum spread for the type C decreasing with type B and A. We further show that the acoustic emission signals associated with Lüders like band also exhibits power law distribution and multifractality.

Crossover in the scale-free statistics of acoustic emission associated with the Portevin-Le Chatelier instability

“…Only scale-free statistics was found on the mesoscopic scale relevant to acoustic emission (AE) accompanying plastic deformation in the conditions of the PLC effect [11][12][13]. This persistence of avalanche-like behavior qualitatively agrees with the predictions of the dynamical model [14][15][16] developing a unique framework to explain both the PLC serrations and the concomitant AE. Moreover, such a scale invariance was observed for numerous materials in the absence of the PLC effect [17][18], albeit the PLC effect displays a larger range of experimental values of the power-law exponent.…”

Features of Acoustic Emission in Tensile Testing of Dissimilar Welded Joints of Pearlitic and Austenitic Steels

“…The distribution function of time intervals is used as an indicator of the destruction process by a few authors [35]. The correspondence of the function of time intervals to the exponential distribution in [36], as well as in this paper, is a sign of scattered accumulation.…”

Dynamics of deformation band formation investigated by high-speed techniques during creep in an AlMg alloy

“…The suggested composite nature of the measured AE signal makes the quantitative analysis of its source quite sophisticated. A possible way to predict the AE in this case may be a physically based numerical modeling like that implemented for the PLC effect [40,59]. Nevertheless, taking into account the mechanism of the occurrence of stress drops which represent the elastic response of the machine-specimen system to the strain bursts, it may be noted that the proportionality observed between the amplitudes of the AE and stress drop rate signals (Fig.…”