Controlling Strain Bursts and Avalanches at the Nano- to Micrometer Scale

We demonstrate, through three-dimensional discrete dislocation dynamics simulations, that the complex dynamical response of nano- and microcrystals to external constraints can be tuned. Under load rate control, strain bursts are shown to exhibit scale-free avalanche statistics, similar to critical phenomena in many physical systems. For the other extreme of displacement rate control, strain burst response transitions to quasiperiodic oscillations, similar to stick-slip earthquakes. External load mode control is shown to enable a qualitative transition in the complex collective dynamics of dislocations from self-organized criticality to quasiperiodic oscillations.

Figure 1

Simplified sketch of pillar compression. (a) Experimental setup with an open-loop (directly applying a force $F_0$) and a closed-loop control (to realize displacement control). (b) Simulation setup, a proportional dominated closed-loop control is considered here with $F_f=K_p(U_0-U)$, which is simplified as a spring with a finite machine stiffness $K_p$. The external stress rate ${\dot{\sigma }}_0={\dot{F}}_0/A$, the target strain rate ${\dot{ϵ}}_0={\dot{U}}_0/H$, and the actual strain rate $\dot{ϵ}=\dot{U}/H$, where $A$ and $H$ are the cross section area and the height of the pillar, respectively. One typical dislocation configuration in a pillar with $d=3000b$ is shown as an example.

Figure 2

(a) Statistical properties of burst displacement under pure strain and stress control modes for pillar with diameters $d=1000b$ and $3000b$. (b),(c) Typical evolution of plastic strain rate and its averaged value in $0.24\mu \mathrm{s}$ windows, showing (b) quasiperiodic strain bursts under pure strain control, and (c) a depinning transition dislocation avalanche under pure stress control.

Figure 3

Typical simulation results under different loading modes for a pillar with $d=1000b$. (a) Stress-strain curves. (b)–(d) Snapshots of dislocation configurations (from the top view) at a strain value of 0.4%. Arrows indicate the bowing out directions of activated sources.

Figure 4

(a) Schematic showing the random branching dislocation source generation and activation process. $n_a$ is the number of newly generated dislocation sources, and the green filled circles indicate that a new source is activated. Only an activated source may trigger a further branching process. (b)–(d) Typical predicted results for a pillar with $d=1000b$. (b) Stress-strain curve. (c) Comparison of the activated source number during each burst under pure strain control. (d) Probability density function of burst displacement for different machine stiffness. (e) Probability density function of burst displacement for different sample sizes.