Universality Class of Nanocrystal Plasticity: Localization and Self-Organization in Discrete Dislocation Dynamics.

The universality class of the avalanche behavior in plastically deforming crystalline and amorphous systems has been commonly discussed, despite the fact that the microscopic defect character in each of these systems is different. In contrast to amorphous systems, crystalline flow stress increases dramatically at high strains and/or loading rates. We perform simulations of a two-dimensional discrete dislocation dynamics model that minimally captures the phenomenology of nanocrystalline deformation. In the context of this model, we demonstrate that a classic rate dependence of dislocation plasticity at large rates (>10^{3}/s) fundamentally controls the system's statistical character as it competes with dislocation nucleation: At large rates, the behavior is statistically dominated by long-range correlations of "dragged" mobile dislocations. At small rates, plasticity localization dominates in small volumes and a spatial integration of avalanche behavior takes place.

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 avalanches. However, during the quiescent periods between them, stresses may be relieved through competing processes, such as slowly flowing water between earthquakes or thermally activated dislocation flow between plastic bursts in crystals. Such smooth responses can in turn have marked effects on the avalanche properties. 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 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 point. 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.

Scale-free intermittent flow in crystal plasticity.

Under stress, crystals irreversibly deform through complex dislocation processes that intermittently change the microscopic material shape through isolated slip events. These underlying processes can be revealed in the statistics of the discrete changes. Through ultraprecise nanoscale measurements on nickel microcrystals, we directly determined the size of discrete slip events. The sizes ranged over nearly three orders of magnitude and exhibited a shock-and-aftershock, earthquake-like behavior over time. Analysis of the events reveals power-law scaling between the number of events and their magnitude, or scale-free flow. We show that dislocated crystals are a model system for studying scale-free behavior as observed in many macroscopic systems. In analogy to plate tectonics, smooth macroscopic-scale crystalline glide arises from the spatial and time averages of disruptive earthquake-like events at the nanometer scale.

Sample dimensions influence strength and crystal plasticity.

When a crystal deforms plastically, phenomena such as dislocation storage, multiplication, motion, pinning, and nucleation occur over the submicron-to-nanometer scale. Here we report measurements of plastic yielding for single crystals of micrometer-sized dimensions for three different types of metals. We find that within the tests, the overall sample dimensions artificially limit the length scales available for plastic processes. The results show dramatic size effects at surprisingly large sample dimensions. These results emphasize that at the micrometer scale, one must define both the external geometry and internal structure to characterize the strength of a material.