Dislocation avalanche correlations

doi:10.1016/j.msea.2004.01.101

Materials Science and Engineering: A

Volumes 387–389, 15 December 2004, Pages 292-296

https://doi.org/10.1016/j.msea.2004.01.101 Get rights and content

Abstract

Recently, mechanical tests on ice as well as dislocation dynamics simulations have revealed that plastic flow in materials exhibiting a largely dominating slip system displays a scale-free intermittent dynamics characterized by dislocation avalanches with a power law distribution of amplitudes. To further explore the complexity of dislocation dynamics during plastic flow, we present a statistical analysis of dislocation avalanche correlations and avalanche triggering. It is shown that the rate of avalanche triggering immediately after any avalanche is larger than the background activity due to uncorrelated events. This self-induced triggering increases in intensity, and remains over the background rate for longer times, as the amplitude of the mainshock increases. This analysis suggests that stress redistributions and the associated collective dislocation rearrangements may be responsible for aftershock triggering in the complex process of plastic deformation.

Introduction

Acoustic emission (AE) measurements performed during the creep of ice single crystals as well as dislocation dynamics simulations of a single slip system have shown that dislocations can move in a scale-free intermittent manner characterized by dislocation avalanches with power law distributions of amplitudes, P(A) ∼ A^−τ [1]. This suggests a close-to-critical state for the dislocation ensemble during plastic deformation. Other deformation induced processes, such as fracture, display similar complexity. At geophysical scales, in addition to power law distributions of earthquake amplitudes, complexity of fracture and faulting is expressed by complex time patterning and interactions. Earthquakes trigger aftershocks with a rate that decays in time as a power law, n(t) = K(t + c)^−p, where n(t) is the rate of aftershock triggering after a given mainshock, p a characteristic exponent close to 1, and K and c the constants (see e.g. [2]). Whereas the value of p is independent of the amplitude of the mainshock, large earthquakes trigger many more aftershocks than smaller ones, a fairly intuitive result. Thus the constant K is proposed to scale with the earthquake amplitude A as A^α or, equivalently, after introducing the earthquake magnitude M = log(A), as K ∼ 10^αM, where α ≈ 1 [2], [3]. This slow and scale-free decay, which has been tentatively ascribed to mechanisms such as sub-critical cracking or fatigue [4], is rather unusual, since many physical systems relax instabilities through an exponential decay, n(t) = K exp(−t/t₀). At much smaller scales, aftershock triggering in the microfracturing of rocks has been documented by means of acoustic emission experiments [5], [6], though the data were not very conclusive about the most appropriate decay law (power law or exponential) in this case.

Previous work has revealed a time clustering of dislocation avalanches [7], as well as a complex space/time coupling that can be interpreted as the result of a cascade process where avalanches increase the occurrence probability of subsequent avalanches in their vicinity [8]. Here, we investigate in more detail these avalanche correlations by performing an analysis of triggered events (aftershocks) for two types of datasets: (i) acoustic emission measurements performed during the creep of ice single crystals, and (ii) model data obtained from 2D simulations of collective dislocation dynamics.

Section snippets

Methods and results

As detailed elsewhere [9], fast and collective motions of dislocations (dislocation avalanches) generate acoustic waves whose properties can be recorded by a piezoelectric transducer in an acoustic emission experimental setup. In particular, the occurrence time of an avalanche can be determined to a high resolution (0.1 μs for the present work), as well as the amplitude of the acoustic wave A, which is proportional to the total area browsed by the dislocations during the avalanche. In our

Discussion and conclusions

As shown previously [1], plastic deformation in materials exhibiting a largely dominating slip system is the result of a scale-free, intermittent, collective dislocation dynamics that suggests that the flow process may be happening in the vicinity of a critical state. The present analysis shows that this non-equilibrium dynamics is also characterized by the presence of dislocation avalanche correlations and self-induced avalanche triggering in the course of time. The enhancement of collective

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Dislocation avalanche correlations

Abstract

Introduction

Section snippets

Methods and results

Discussion and conclusions

Mater. Sci. Eng. A

Mater. Sci. Eng. A

Nature

J. Phys. Earth

J. Geophys. Res