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 similar to A(m)(3) and S similar to A(m)(2), obtained from the mean field theory, MFT. We show, using a theoretically predicted averaged function for the fixed avalanche area, U(t)= at exp(-bt(2)) (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 similar to A(m)(1-phi) (the MFT values can be obtained only if phi would be zero). Here, phi 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, phi = 0.8 +/- 0.1 was obtained (phi is the same for both alloys). Thus, dividing U by A(m) as well as t by A(m)(1-phi) (similar to 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.