Towards a Quantitative Analysis of Crackling Noise by Strain Drop Measurements

Abstract

The method of measuring strain drops with a Dynamic Mechanical Analyzer (DMA) at slowly varying stress has a considerable potential to become an interesting complementary tool for the study of mechanical failure and earthquake dynamics in micron-sized materials. Evidence for this claim is provided by measurements of the $\mathrm {SiO_2}$-based porous materials Vycor and Gelsil under slow uniaxial compression at constant force rates of $10^{-4}{-}10^{-3}\,\mathrm{N s}^{-1}$ using a Diamond DMA (Dynamical Mechanical Analyzer, Perkin Elmer). The jerky evolution of the sample’s height with time is analyzed in order to determine the corresponding power-law exponents for the maximum velocity distribution, the squared maximum velocity distribution as well as the aftershock activity in the region before macroscopic failure. A comparison with recent results from acoustic emission (AE) data on the same materials (J. Baró, Á. Corral, X. Illa, A. Planes, E. K. H. Salje, W. Schranz, D. E. Soto-Parra, and E. Vives, Phys. Rev. Lett. 110, 088702 (2013)) shows similitude in the statistics, although the two methods operate on different spatial and temporal scales. Moreover, the obtained power-law exponents are in reasonable agreement with theoretical mean-field values (M. LeBlanc, L. Angheluta, K. Dahmen, N. Goldenfeld, Phys. Rev. B 87, 022126 (2013)). The results indicate that the failure dynamics of materials can be well studied by measuring strain drops under slow compression, which opens the possibility to study earthquake dynamics in the laboratory also at non-ambient conditions, i.e. at high temperatures or under confining liquid pore pressure.