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

Abstract

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 S1/2, 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, Am, or between S and Am. 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 Am and t by tm (the time belonging to the Am: 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 Am as well as t by Am1−φ (~tm) 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.

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

“…It was shown in Ref. [ 34 ], that it appears also in the scaling relations and . We can observe in Figure 3 , that the exponent of the power law relation between the energy and the amplitude has the value of 2.2 for Clusters 2 and 3 (and for Cluster 1 at higher amplitudes), which is in the acceptable range, proposed by Ref.…”

“…Clusters 2 and 3 are very similar, the only difference is that Cluster 3 has high-frequency components around 350 kHz, while Cluster 2 has negligible contribution in this range. This behavior is related to the transfer function of the sample-sensor system: one can observe the so-called ringing effect on a certain part, or on the whole avalanche, when the transfer function has a high influence on the detected signal [ 12 , 34 ]. For longer avalanches, the effect of ringing on the slope of the versus plot is usually negligible [ 34 ].…”

“…This behavior is related to the transfer function of the sample-sensor system: one can observe the so-called ringing effect on a certain part, or on the whole avalanche, when the transfer function has a high influence on the detected signal [ 12 , 34 ]. For longer avalanches, the effect of ringing on the slope of the versus plot is usually negligible [ 34 ]. Thus, Clusters 2 and 3 probably have the same origin, the only difference is the duration of the avalanches.…”

“…The number of avalanches in Cluster 1 is very high compared to the others, but the energy and amplitude values of these avalanches are low and the deviation of points on the first part of the plot in Figure 3 is most probably due to the threshold effects and distortion effects of ringing [ 12 , 34 ]. Thus, this cluster can also be identified as belonging to the real deformation mechanism (similar to Clusters 2 and 3).…”

“…Recently, it turned out [ 34 ] that in the theoretically predicted averaged temporal shape of avalanches at a fixed area, , and are not universal constants [ 35 , 36 ], rather they can be given as and , where is the rising time and is a mechanism-dependent constant, . It was shown in Ref.…”