Electromagnetic emission under uniaxial compression of ice: III. Dynamics and statistics of dislocation avalanches and c
- PDF / 193,220 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 116 Downloads / 226 Views
ICAL PROPERTIES OF CRYSTALS
Electromagnetic Emission under Uniaxial Compression of Ice: III. Dynamics and Statistics of Dislocation Avalanches and Cracks A. A. Shibkov and A. A. Kazakov Tambov State University, ul. Internatsional’naya 33, Tambov, 392000 Russia e-mail: [email protected] Received February 14, 2008
Abstract—Statistical analysis of the plastic deformation steps and fracture of polycrystalline ice has been performed. It is established that an increase in deformation leads to gradual evolution of the statistics of amplitudes of mesoscopic deformation jumps from random (with a Poisson distribution of dislocation avalanche amplitudes) to “critical” (with a power-law distribution), which indicates occurrence of long-range correlations of the dislocation mesodynamics of deformed polycrystalline ice. The state of self-organized criticality at subcritical ice fracture has been revealed from the power-law statistics of the amplitudes of electric pulses and pauses between them, flicker-noise structure, and almost monofractal character of signals. PACS numbers: 05.65+b, 62.20.F-, 64.60.Av DOI: 10.1134/S1063774509020205
INTRODUCTION It was shown in the previous parts (I, II) of this study [1, 2] that measurement of electromagnetic emission (EME) signals is a map of the formation of a structure of mesoscopic defects in a deformed ice crystal on a time series (i.e., on one of the degrees of freedom). This procedure, involving formation of an EME map album [1] and its analysis [2], allows one to control (on the basis of identified EME signals) the evolution of the populations of defects of certain type (slip bands, conservative dislocation pile-ups, and micro- and macrocracks) directly during deformation. The purpose of this study was to perform EME investigation of the statistical regularities of the collective processes of structural relaxation in polycrystalline ice, which involve many dislocation avalanches and cracks.
an type-I EME pulse, ϕ m is the mean amplitude, and N is the statistical ensemble size. Figures 1 and 2 present typical distribution functions of the amplitudes of type-I EME pulses in different deformation stages with a constant initial stress growth rate σ˙ 0 = const (5 kPa/s). At relatively small strains (ε < 2%), a bell-shaped distribution function is generally observed, similar in shape to the Poisson disD 0.8 0.6
RESULTS
0.4
Statistics of Dislocation Avalanches EME signals of type I can be used in statistical treatment of dislocation mesodynamics because they contain information about the unstable dynamics of formation of the ice dislocation structure at the mesoscopic level [1]. To study the statistical regularities of dislocation avalanches, we calculated the normalized statistical distribution function of signal amplitudes D(s)= N–1δN/δs, where δN is the number of events (type-I EME pulses) falling in the range from s – δs to s + δs, where s = ϕm / ϕ m is the normalized amplitude of 299
0.2 0
0.5
1.0
1.5
2.0 s
Fig. 1. Distribution D(s) of normalized pulse amplitudes, reflecting
Data Loading...
