Obstacles and sources in dislocation dynamics: Strengthening and statistics of abrupt plastic events in nanopillar compression

TL;DR

This paper presents a minimal dislocation dynamics model explaining size-dependent strengthening and stochastic plastic events in nanopillars, unifying behaviors across scales and conditions.

Contribution

It introduces a realistic model that captures the transition from nanopillar to bulk-like plasticity and clarifies the link between obstacles, dislocation sources, and size effects.

Findings

Strengthening and stochasticity depend on obstacle strength and dislocation sources.

Behavior transitions from nanopillar to bulk-like as sample size increases.

Universal avalanche dynamics occur when dislocation sources are comparable to obstacles.

Abstract

Mechanical deformation of nanopillars displays features that are distinctly different from the bulk behavior of single crystals: Yield strength increases with decreasing size and plastic deformation comes together with strain bursts or/and stress drops (depending on loading conditions) with a very strong sensitivity of the stochasticity character on material preparation and conditions. The character of the phenomenon is standing as a paradox: While these bursts resemble the universal, widely independent of material conditions, noise heard in bulk crystals using acoustic emission (AE) techniques, they strongly emerge primarily with decreasing size and increasing strength in nanopillars. In this paper, we present a realistic but minimal discrete dislocation plasticity model for the elasto-plastic deformation of nanopillars that is consistent with the main experimental observations of nano pillar compression experiments and provides a clear insight to this paradox. With increasing sample size, the model naturally transitions between the typical progressive behavior of nanopillars to a behavior that resembles evidence for bulk mesoscale plasticity. The combination of consistent strengthening, large flow stress fluctuations and critical avalanches is only observed in the {\it depinning regime} where obstacles are much stronger than dislocation sources; in contrast, when dislocation source strength becomes comparable to obstacle barriers, then yield strength size effects are absent but plasticity avalanche dynamics is strongly universal, across sample width and aspect-ratio scales. Finally, we elucidate the mechanism that leads to the connection between depinning and size effects in our model dislocation dynamics. In this way, our model builds a way towards unifying statistical aspects of mechanical deformation across scales.