The $Λ$-invariant and topological pathways to influence sub-micron strength and crystal plasticity

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 paper, we study the effect of sample dimensions with a full control on 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 appear virtually independent from sample dimensions, either by biased-random dislocation loop deposition or by sequential mechanical loads of compression and torsion.

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