Experimental Evidence for Critical Dynamics in Microfracturing Processes

Abstract

We performed the statistical analysis of acoustic emission time series in the ultrasonic frequency range, obtained experimentally from laboratory samples subjected to external uniaxial elastic stress. We found a power law scaling behavior in both the acoustic emission amplitude distribution and time correlation function, with exponents very close to those found in fracturing processes occurring at different time and space scales. These facts strongly suggest the existence of a critical dynamics underlying the process, which might be related to the idea of a self-organized critical state based on the energy dissipation through all the length scales.PACS numbers: 62.20.Mk, 05.40.+j, 91.60.Lj Power law behavior in physical phenomena is usually the fingerprint of temporal and spatial critical fluctuations of which well known examples are Ising-like systems, fractal growth phenomena, turbulence, etc. Unlike the usual second order phase transitions, some of the previous examples exhibit a critical behavior without the need to fine tune any control parameter; i.e., the critical state is an attractor of the dynamics. A few years ago Bak, Tang, and Wiesenfeld [1] termed this kind of situation "self-organized criticality" (SOC) and introduced a simple model of a dynamically driven system, inspired by the dynamics of sandpiles, that evolves spontaneously to a stationary critical state. This model is an example of SOC phenomenon in which a system with short range coupling self-stabilizes in a stationary state characterized by avalanches (activity) with power law distribution functions. Hence, the system has no characteristic length (and is therefore self-similar) and is in this sense critical. The SOC concept has been proposed also as a possible mechanism for the generation of the so-called 1/ f noise; however, it has been shown successively [2,3] that the spatialtemporal scaling in the SOC state does not necessarily manifest itself in nontrivial exponents for the power spectrum.Because of the importance of the SOC concept as a possible unifying framework for a wide range of physical phenomena, a lot of work has been devoted to studying these systems through computer simulations, theoretical approaches, and experimental findings [4]. In particular, the SOC framework has been proposed as a possible interpretation for the empirical observation of the energy release in earthquakes [5]. In fact, existence of statistical self-similarity in seismic processes is a well established fact, which has its strongest evidence in the power law behavior of the well known Gutenberg'S [6] and Omori's [7] empirical laws. Power law behavior was observed by Mogi [8] in the distribution of the maximum trace amplitude of audio signals emitted from samples subjected to various forms of stress, in analogy with the Ishimoto Iida 0031-9007/94/73(25)/3423(4)$06.00 empirical relation [9]. Hirata [10] observed self-similarity in the time frequency distribution of aftershock signals due to fracturation of basalt under constant stress. More recently, ...

General framework for acoustic emission during plastic deformation

“…A good example from the geological scale is the acoustic emission (AE) during volcanic activity [1]. Varied laboratory scale examples such as AE from crack nucleation and propagation in fracture of solids [2][3][4], thermal cycling of martensites [5][6][7], peeling of an adhesive tape [8][9][10][11] and collective dislocation motion can be cited [12][13][14]. Clearly, while the sources that lead to AE signals in such widely different situations are necessarily different, they are generally attributed to the release of stored elastic energy in the system.…”

Sliding susceptibility of a rough cylinder on a rough inclined perturbed surface

“…If energy is continuously injected into nonequilibrium systems, a complex sequential response characterized by time series of events of all sizes is often observed. Besides sliding blocks on inclines, other important examples of systems and phenomena associated with a similar type of temporal response include piles of sand and other granular materials [8,9]; acoustic emission from volcanic rocks and microfracturing processes in general [10,11]; interface depinning in magnetic systems [12]; stick-slip motion in lubricated systems [13], and turbulence [14], among others.…”

Statistical analysis of dislocation dynamics during viscoplastic deformation from acoustic emission

“…The so-called steady state viscoplastic deformation is, in fact, shown to occur in bursts of relaxation following a power law distribution of energy and time separation. Such power law behavior is suggestive of a critical dynamics of dislocations, similar to those argued for microfracturing [Petri et al, 1994;Guarino et al, 1998]. …”

“…In the present paper, we propose to embed these earlier results in the more general framework of critical systems. Such a critical framework has been recently proposed to describe brittle fracturing [e.g.,Hermann and Roux, 1990;Andersen et al, 1997], fromthe laboratory sample scale [Petri et al, 1994;Guarino et al, 1998] to the earth crust scale [Main, 1996].…”