The duration-energy-size enigma for acoustic emission

Abstract

Acoustic emission (AE) measurements of avalanches in different systems, such as domain movements in ferroics or the collapse of voids in porous materials, cannot be compared with model predictions without a detailed analysis of the AE process. In particular, most AE experiments scale the avalanche energy E, maximum amplitude Amax and duration D as E ~ Amaxx and Amax ~ Dχ with x = 2 and a poorly defined power law distribution for the duration. In contrast, simple mean field theory (MFT) predicts that x = 3 and χ = 2. The disagreement is due to details of the AE measurements: the initial acoustic strain signal of an avalanche is modified by the propagation of the acoustic wave, which is then measured by the detector. We demonstrate, by simple model simulations, that typical avalanches follow the observed AE results with x = 2 and ‘half-moon’ shapes for the cross-correlation. Furthermore, the size S of an avalanche does not always scale as the square of the maximum AE avalanche amplitude Amax as predicted by MFT but scales linearly S ~ Amax. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal.

Crackling noise and avalanches in minerals

“…8). All other avalanche parameters have been evaluated by Salje et al (2019) and were confirmed by optical microscopy by Casals et al (2021a).…”

“…This is not true for long and smooth A(t) functions. Various scalings E ~ A X with 2 < x < 3 are discussed in literature (Casals et al 2019(Casals et al , 2020(Casals et al , 2021aMcFaul et al 2020).…”

“…As an example, if the movement relates to low-dimensional dynamical patterns, the relationship is linear S ~ A while in magnetic systems with high fractal dimensions we find S ~ A 2 . This already highlights that model calculations are often required to determine this S(A) scaling and that scaling depends sensitively on the fractal dimension of the domain patterns (Casals et al 2019(Casals et al , 2021aNataf et al 2020;Xu et al 2020).…”

“…The measured AE profile A AE (t) is the convolution of the source function with the transfer function. (Modified from Casals et al 2021a, b).…”

“…The avalanche duration is not easily determined while the rise time R during the incubation period often correctly represents the avalanche formation and propagation much better. It is close to the atomic rise time and is less polluted by the effect of the transfer function (Salje et al 2017a;Casals et al 2021a, b).…”