Λ-Invariant and Topological Pathways to Influence the Strength of Submicron Crystals.

In small volumes, sample dimensions are known to strongly influence mechanical behavior: especially strength and crystal plasticity. This correlation fades away at the so-called "mesoscale," loosely defined at several micrometers in both experiments and simulations. However, this picture depends on the "entanglement" of the initial defect configuration. In this Letter, we study the effect of dislocation topology through the use of a novel observable for dislocation ensembles (the Λ invariant) that depends only on mutual dislocation linking: It is built on the natural vortex character of dislocations, and it has a continuum-discrete correspondence that may assist multiscale modeling descriptions. We investigate arbitrarily complex initial dislocation microstructures in sub-micron-sized pillars using three-dimensional discrete dislocation dynamics simulations for finite volumes. We demonstrate how to engineer nanoscale dislocation ensembles that are independent from sample dimensions, either by biased-random dislocation loop deposition or by sequential mechanical loads of compression and torsion.

Size-Tuned Plastic Flow Localization in Irradiated Materials at the Submicron Scale.

Three-dimensional discrete dislocation dynamics (3D-DDD) simulations reveal that, with reduction of sample size in the submicron regime, the mechanism of plastic flow localization in irradiated materials transitions from irradiation-controlled to an intrinsic dislocation source controlled. Furthermore, the spatial correlation of plastic deformation decreases due to weaker dislocation interactions and less frequent cross slip as the system size decreases, thus manifesting itself in thinner dislocation channels. A simple model of discrete dislocation source activation coupled with cross slip channel widening is developed to reproduce and physically explain this transition. In order to quantify the phenomenon of plastic flow localization, we introduce a "deformation localization index," with implications to the design of radiation-resistant materials.

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.