When external stresses in a system—physical, social or virtual—are relieved through impulsive events, it is natural to focus on the attributes of these avalanches1, 2. However, during the quiescent periods between them3, stresses may be relieved through competing processes, such as slowly flowing water between earthquakes4 or thermally activated dislocation flow5 between plastic bursts in crystals6, 7, 8. Such smooth responses can in turn have marked effects on the avalanche properties9. Here we report an experimental investigation of slowly compressed nickel microcrystals, covering three orders of magnitude in nominal strain rate, in which we observe unconventional quasi-periodic avalanche bursts and higher critical exponents as the strain rate is decreased. Our experiments are faithfully reproduced by analytic and computational dislocation avalanche modelling10, 11 that we have extended to incorporate dislocation relaxation, revealing the emergence of the self-organized avalanche oscillator: a novel critical state exhibiting oscillatory approaches towards a depinning critical point12. This theory suggests that whenever avalanches compete with slow relaxation—in settings ranging from crystal microplasticity to earthquakes—dynamical quasi-periodic scale invariance ought to emerge.
At a glance
- Collective transport in random media: from superconductors to earthquakes. Phys. Rep. 301, 113–150 (1998)
- Crackling noise. Nature 410, 242–250 (2001) , &
- Driven particle in a random landscape: disorder correlator, avalanche distribution, and extreme value statistics of records. Phys. Rev. E 79, 051105 (2009) &
- Collective behavior of earthquakes and faults: continuum-discrete transitions, progressive evolutionary changes and different dynamic regimes. Rev. Geophys. 46, RG4006 (2008)
- Cottrell, A. H. Dislocations and Plastic Flow in Metals (Clarendon, 1953)
- Intermittent dislocation flow in viscoplastic deformation. Nature 410, 667–671 (2001) , , , &
- Scale-free intermittent flow in crystal plasticity. Science 312, 1188–1190 (2006) , , &
- Scale invariance in plastic flow of crystalline solids. Adv. Phys. 55, 185–245 (2006)
- Realistic spatial and temporal earthquake distributions in a modified Olami-Feder-Christensen model. Phys. Rev. E 81, 046117 (2010)
- Fluctuation phenomena in crystal plasticity—a continuum model. J. Stat. Mech. 2005, P08004 (2005) &
- Avalanches and scaling in plastic deformation. Phys. Rev. Lett. 93, 125502 (2004) , &
- Nonequilibrium dynamics of interfaces and lines. Phys. Rep. 301, 85–112 (1998)
- Uber sprunghafte Dehnung von Zinkkristallen. Z. Phys. 79, 566–572 (1932) &
- Evidence for universal intermittent crystal plasticity from acoustic emission and high-resolution extensometry experiments. Phys. Rev. B 76, 224110 (2007) et al.
- Plasticity of micrometer-scale single crystals in compression. Annu. Rev. Mater. Res. 39, 361–386 (2009) , &
- Overview of experiments on microcrystal plasticity in FCC-derivative materials: selected challenges for modelling and simulation of plasticity. Model. Simul. Mater. Sci. Eng. 15, 135–146 (2007) , , , &
- Spatio-temporal dynamics of the Portevin–Le Chatelier effect: experiment and modelling. Acta Mater. 48, 2529–2541 (2000) , , , &
- 103–188 (North Holland, 2002) et al. in Dislocations in Solids (eds & ) Ch. 57
- The hidden order behind jerky flow. Acta Mater. 50, 2813–2824 (2002) , , , &
- On the similarity of plastic flow processes during smooth and jerky flow: statistical analysis. Acta Mater. 60, 3729–3740 (2012) et al.
- Statistics of earthquakes in simple models of heterogeneous faults. Phys. Rev. Lett. 78, 4885–4888 (1997) , , &
- Universality beyond power laws and the average avalanche shape. Nature Phys. 7, 316–320 (2011) et al.
- 2004) & Fundamentals of Creep in Metals and Alloys (Elsevier,
- Activated states for cross-slip at screw dislocation intersections in face-centered cubic nickel and copper via atomistic simulation. Acta Mater. 58, 5547–5557 (2010) et al.
- Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale. Science 318, 251–254 (2007) , , , &
- Slip avalanches in crystal plasticity: scaling of the avalanche cut-off. J. Stat. Mech. 2007, P04013 (2007) &
- Noise-induced mixed-mode oscillations in a relaxation oscillator near the onset of a limit cycle. Chaos 18, 015111 (2008) &
- Episodic tremor and slip on the Cascadia subduction zone: the chatter of silent slip. Science 300, 1942–1943 (2003) &
- Avalanches in strained amorphous solids: does inertia destroy critical behavior? Preprint at http://arxiv.org/abs/1204.5965 (2012) , &
- A simple analytic theory for the statistics of avalanches in sheared granular materials. Nature Phys. 7, 554–557 (2011) , &
- Asymptotic uniqueness of the sliding state for charge-density waves. Phys. Rev. Lett. 68, 670–673 (1992)
- Point-occurrence self-similarity in crackling-noise systems and in other complex systems. J. Stat. Mech. 2009, P01022 (2009)
- Model and theoretical seismicity. Bull. Seismol. Soc. Am. 57, 341–371 (1967) &
- Dynamics of earthquake faults. Rev. Mod. Phys. 66, 657–671 (1994) , &
- Large earthquake cycles and intermittent criticality on heterogeneous faults due to evolving stress and seismicity. J. Geophys. Res. 108, 2307–2328 (2003) , &
- Disorder-induced critical phenomena in hysteresis: numerical scaling in three and higher dimensions. Phys. Rev. B 59, 6106–6119 (1999) , &
- 1986) , , & Numerical Recipes (Cambridge Univ. Press,
- Supplementary Information (858K)
This file contains Supplementary Text and Data and Supplementary Figures 1-13.