8 Turcotte (2003) ; Rundle et al. (2003); Carpinteri et al. (2008) ). Therefore, by determining the bvalue it becomes possible to identify the energy release modalities in a structural element during the AE monitoring process. The extreme cases envisaged are D = 3.0, which corresponds to b=1.5, a critical condition in which the energy release takes place through small defects evenly distributed throughout the volume, and D=2.0, which corresponds to b = 1.0, when energy release takes place on a fracture surface. In the former case diffused damage is observed, whereas in the latter case two dimensional cracks are formed leading to the separation of the structural element. Moreover, in seismology, the energy released during an earthquake can be linked with seismogram amplitude thanks to the classical expression proposed by Ritcher (1958), Es ∝ Ac, where: A is the earthquake amplitude, and c=[1.5, 2] is an exponent obtained experimentally from earthquakes measurements. Another expression appearing in a seismological context, in Chakrabarti and Benguigui (1997), is N(>=Es) ∝ Es -d, where N is the cumulative distribution of released energy and d=[0.8,1.1] is an exponent obtained from earthquakes observations. 2 RELATIONSHIP BETWEEN SIGNAL AMPLITUDE AND THE NUMBER OF AE EVENTS Magnitude (m) is a geophysical log-scale quantity which is often used to measure the amplitude of an electrical signal generated by an AE event. Magnitude is related to amplitude (A), expressed in volts (V), by the following equation: m = Log A. (1) The widely accepted Gutenberg–Richter (GR) law, initially proposed for seismic events, describes the statistical distribution of AE signal amplitudes : N(≥A) = ζ Α−b, (2) where ζ and exponent b are coefficients that characterize the behavior of the model. We shall focus our attention on coefficient b. By rewriting Eq. (2.2) as a logarithmic equation: Log( N≥A) = Log ζ −bm, (3) where N is the number of AE peaks with magnitude greater than m, and coefficient b, referred to as ‘‘b-value”, is the negative slope of the Log N vs. m diagram. Microcracks release low-amplitude AEs, while macrocracks release high-amplitude AEs. This intuitive relationship is confirmed by the experimental observation that the area of crack growth is proportional to the amplitude of the relative AE signal Pollock (1973). From Eq. (2.3) we find that a regime of microcracking generates weak AEs, and therefore leads to relatively high b-values (raising the threshold m, gives rise to a fast decline in the number of surviving signals). When macrocracks start to appear, instead, lower b-values are observed. Therefore the analysis of the b-value, which changes systematically with the different stages of fracture growth has been recognized as a useful tool for damage level assessment. In general terms, the fracture process moves from micro to macrocracking as the material approaches impending failure and the b-value decreases. While testing the materials undergoing brittle failure, the b-value is found to be around 1.5 in the initial stages. It then decreases with increasing stress level to ≈1.0 and even less as the material approaches failure:
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