Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator



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.

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Figure 1: Dislocation motion and several slow relaxation processes during the waiting intervals between avalanches.
Figure 2: Comparison between microplasticity experiments and theoretical modelling.
Figure 3: The avalanche oscillator mechanism and stochastic modelling of the slip susceptibility.


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We thank J. Guckenheimer, C. L. Henley, E. A. Jagla, E. Nadgorny, C. O’Hern, R. Thorne, D. Trinkle, E. van der Giessen and V. Vitelli for discussions. We acknowledge support from DTRA 1-10-1-0021 (S.P.), DOE-BES DE-FG02-07ER-46393 (S.P., W.C. and J.P.S.), the Air Force Office of Scientific Research (D. Stargel) and the Materials and Manufacturing Directorate (D.M.D., C.F.W. and M.D.U.) and the ComplexityNet pilot project LOCAT (S.Z.).

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D.M.D., M.D.U. and C.F.W. designed and performed the experiments. S.P., D.M.D. and C.F.W. performed the experimental data analysis. S.P., W.C., J.P.S. and S.Z. developed the theoretical modelling, performed the numerical simulations and carried out the data analysis. S.P. wrote the first draft of the manuscript and then all authors contributed equally to improve the manuscript.

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Correspondence to Stefanos Papanikolaou.

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The authors declare no competing financial interests.

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Papanikolaou, S., Dimiduk, D., Choi, W. et al. Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator. Nature 490, 517–521 (2012). https://doi.org/10.1038/nature11568

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