Asymmetric Damage Avalanche Shape in Quasibrittle Materials and Subavalanche (Aftershock) Clusters

Acoustic emissions from spin crossover complexes

Acoustic emission from the compounds [Fe(HB(tz)3)2] and [Fe(Htrz)(trz)2]BF4 was detected during the thermally induced spin transition and is correlated with simultaneously recorded calorimetric signals. We ascribe this phenomenon to elastic waves produced by microstructural and volume changes accompanying the spin transition. Despite the perfect reversibility of the spin state switching (seen by the calorimeter), the acoustic emission activity decreases for successive thermal cycles, revealing thus irreversible microstructural evolution of the samples. The acoustic emission signal amplitude and energy probability distribution functions followed power-law behavior and the characteristic exponents were found to be similar for the two samples both on heating and cooling, indicating the universal character, which is further substantiated by the well scaled average temporal shapes of the avalanches.

Scaling of Average Avalanche Shapes for Acoustic Emission during Jerky Motion of Single Twin Boundary in Single-Crystalline Ni2MnGa

Temporal average shapes of crackling noise avalanches, U(t) (U is the detected parameter proportional to the interface velocity), have self-similar behavior, and it is expected that by appropriate normalization, they can be scaled together according to a universal scaling function. There are also universal scaling relations between the avalanche parameters (amplitude, A, energy, E, size (area), S, and duration, T), which in the mean field theory (MFT) have the form E∝A3, S∝A2, S∝T2. Recently, it turned out that normalizing the theoretically predicted average U(t) function at a fixed size, U(t)=atexp-bt2 (a and b are non-universal, material-dependent constants) by A and the rising time, R, a universal function can be obtained for acoustic emission (AE) avalanches emitted during interface motions in martensitic transformations, using the relation R~A1-φ too, where φ is a mechanism-dependent constant. It was shown that φ also appears in the scaling relations E~A3-φ and S~A2-φ, in accordance with the enigma for AE, that the above exponents are close to 2 and 1, respectively (in the MFT limit, i.e., with φ= 0, they are 3 and 2, respectively). In this paper, we analyze these properties for acoustic emission measurements carried out during the jerky motion of a single twin boundary in a Ni₅₀Mn_28.5Ga_21.5 single crystal during slow compression. We show that calculating from the above-mentioned relations and normalizing the time axis of the average avalanche shapes with A1-φ, and the voltage axis with A, the averaged avalanche shapes for the fixed area are well scaled together for different size ranges. These have similar universal shapes as those obtained for the intermittent motion of austenite/martensite interfaces in two different shape memory alloys. The averaged shapes for a fixed duration, although they could be acceptably scaled together, showed a strong positive asymmetry (the avalanches decelerate much slower than they accelerate) and thus did not show a shape reminiscent of an inverted parabola, predicted by the MFT. For comparison, the above scaling exponents were also calculated from simultaneously measured magnetic emission data. It was obtained that the φ values are in accordance with theoretical predictions going beyond the MFT, but the AE results for φ are characteristically different from these, supporting that the well-known enigma for AE is related to this deviation.

Clustering Characterization of Acoustic Emission Signals Belonging to Twinning and Dislocation Slip during Plastic Deformation of Polycrystalline Sn

Results of acoustic emission (AE) measurements, carried out during plastic deformation of polycrystalline Sn samples, are analyzed by the adaptive sequential k-means method. The acoustic avalanches, originating from different sources, are separated on the basis of their spectral properties, that is, sorted into clusters, presented both on the so-called feature space (energy-median frequency plot) and on the power spectral density (PSD) curves. We found that one cluster in every measurement belongs to background vibrations, while the remaining ones are clearly attributed to twinning as well as dislocation slips at −30 °C and 25 °C, respectively. Interestingly, fingerprints of the well-known “ringing” of AE signals are present in different weights on the PSD curves. The energy and size distributions of the avalanches, corresponding to twinning and dislocation slips, show a bit different power-law exponents from those obtained earlier by fitting all AE signals without cluster separation. The maximum-likelihood estimation of the avalanche energy (ε) and size (τ) exponents provide ε=1.57±0.05 (at −30 °C) and ε=1.35±0.1 (at 25 °C), as well as τ=1.92±0.05 (at −30 °C) and τ= 1.55±0.1 (at 25 °C). The clustering analysis provides not only a manner to eliminate the background noise, but the characteristic avalanche shapes are also different for the two mechanisms, as it is visible on the PSD curves. Thus, we have illustrated that this clustering analysis is very useful in discriminating between different AE sources and can provide more realistic estimates, for example, for the characteristic exponents as compared to the classical hit-based approach where the exponents reflect an average value, containing hits from the low-frequency mechanical vibrations of the test machine, too.

Denouement of the Energy-Amplitude and Size-Amplitude Enigma for Acoustic-Emission Investigations of Materials

There are many systems producing crackling noise (avalanches) in materials. Temporal shapes of avalanches, U(t) (U is the detected voltage signal, t is the time), have self-similar behaviour and the normalized U(t) function (e.g., dividing both the values of U and t by S^1/2, where S is the avalanche area), averaged for fixed S, should be the same, independently of the type of materials or avalanche mechanisms. However, there are experimental evidences that the temporal shapes of avalanches do not scale completely in a universal way. The self-similarity also leads to universal power-law-scaling relations, e.g., between the energy, E, and the peak amplitude, A_m, or between S and A_m. There are well-known enigmas, where the above exponents in acoustic emission measurements are rather close to 2 and 1, respectively, instead of E~Am3 and S~Am2, obtained from the mean field theory, MFT. We show, using a theoretically predicted averaged function for the fixed avalanche area, U(t)=atexp(−bt2) (where a and b are non-universal, material-dependent constants), that the scaling exponents can be different from the MFT values. Normalizing U by A_m and t by t_m (the time belonging to the A_m: rise time), we obtain tm~Am1−φ (the MFT values can be obtained only if φ would be zero). Here, φ is expected to be material-independent and to be the same for the same mechanism. Using experimental results on martensitic transformations in two different shape-memory single-crystals, φ = 0.8 ± 0.1 was obtained (φ is the same for both alloys). Thus, dividing U by A_m as well as t by Am1−φ (~t_m) leads to the same common, normalized temporal shape for different, fixed values of S. This normalization can also be used in general for other experimental results (not only for acoustic emission), which provide information about jerky noises in materials.

Dislocation avalanches are like earthquakes on the micron scale

Compression experiments on micron-scale specimens and acoustic emission (AE) measurements on bulk samples revealed that the dislocation motion resembles a stick-slip process - a series of unpredictable local strain bursts with a scale-free size distribution. Here we present a unique experimental set-up, which detects weak AE waves of dislocation slip during the compression of Zn micropillars. Profound correlation is observed between the energies of deformation events and the emitted AE signals that, as we conclude, are induced by the collective dissipative motion of dislocations. The AE data also reveal a two-level structure of plastic events, which otherwise appear as a single stress drop. Hence, our experiments and simulations unravel the missing relationship between the properties of acoustic signals and the corresponding local deformation events. We further show by statistical analyses that despite fundamental differences in deformation mechanism and involved length- and time-scales, dislocation avalanches and earthquakes are essentially alike.

Change of Acoustic Emission Characteristics during Temperature Induced Transition from Twinning to Dislocation Slip under Compression in Polycrystalline Sn

In this study, acoustic emission (AE) measurements on polycrystalline tin as a function of temperature at different driving rates under compression were carried out. It is shown that there is a definite difference between the acoustic emission characteristics belonging to twinning (low temperatures) as well as to dislocation slip (high temperatures). The stress averaged values of the exponents of the energy probability density functions decreased from ε = 1.45 ± 0.05 (-60 °C) to ε = 1.20 ± 0.15 (50 °C) at a driving rate of ε=0.15 s-1, and the total acoustic energy decreased by three orders of magnitude with increasing temperature. In addition, the exponent γ in the scaling relation S_AE~D_AE^γ (S_AE is the area and D_AE is the duration) also shows similar temperature dependence (changing from γ = 1.78 ± 0.08 to γ = 1.35 ± 0.05), illustrating that the avalanche statistics belong to two different microscopic deformation mechanisms. The power law scaling relations were also analyzed, taking into account that the detected signal is always the convolution of the source signal and the transfer function of the system. It was obtained that approximate values of the power exponents can be obtained from the parts of the above functions, belonging to large values of parameters. At short duration times, the attenuation effect of the AE detection system dominates the time dependence, from which the characteristic attenuation time, τ_a, was determined as τ_a ≅ 70 μs.

Thermally activated intermittent dynamics of creeping crack fronts along disordered interfaces

We present a subcritical fracture growth model, coupled with the elastic redistribution of the acting mechanical stress along rugous rupture fronts. We show the ability of this model to quantitatively reproduce the intermittent dynamics of cracks propagating along weak disordered interfaces. To this end, we assume that the fracture energy of such interfaces (in the sense of a critical energy release rate) follows a spatially correlated normal distribution. We compare various statistical features from the obtained fracture dynamics to that from cracks propagating in sintered polymethylmethacrylate (PMMA) interfaces. In previous works, it has been demonstrated that such an approach could reproduce the mean advance of fractures and their local front velocity distribution. Here, we go further by showing that the proposed model also quantitatively accounts for the complex self-affine scaling morphology of crack fronts and their temporal evolution, for the spatial and temporal correlations of the local velocity fields and for the avalanches size distribution of the intermittent growth dynamics. We thus provide new evidence that an Arrhenius-like subcritical growth is particularly suitable for the description of creeping cracks.

Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media

The behavior of granular media under quasistatic loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regime traditionally linked to a self-organized critical state. This, together with the nonuniqueness and the nonmonotony of macroscopic deformation curves, suggests that the statistical avalanche properties and the susceptibilities of the system cannot be reduced to a function of the macromechanical state. The associated scaling exponents are nonuniversal and depend on the interactions between particles. For stiffer particles (or samples at low confining pressure) we find distributions of avalanche properties compatible with the predictions of mean-field theory. The scaling exponents decrease below the mean-field values for softer interactions between particles. These lower exponents are consistent with observations for amorphous solids at their critical point. We specifically discuss the relationship between microscopic and macroscopic variables, including the relation between the external stress drop and the internal potential energy released during kinetic avalanches.

The duration-energy-size enigma for acoustic emission

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 ~ A_max^x and A_max ~ D^χ 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 A_max as predicted by MFT but scales linearly S ~ A_max. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal.