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

Abstract

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 avalanches^1,2. 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 crystals^6,7,8. 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 modelling^10,11 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.