Average yielding and weakest link statistics in micron-scale plasticity

TL;DR

This study investigates the stochastic nature of micron-scale plasticity in single crystalline materials, revealing a characteristic average yield stress and Weibull-distributed stress values indicative of a weakest-link phenomenon.

Contribution

It introduces a combined approach of simulations and experiments to identify universal statistical features of micron-scale plasticity, emphasizing the weakest-link behavior.

Findings

Yield stress can be defined in an average sense for specimen ensembles.

Stress at a given strain follows a Weibull distribution.

Plastic yielding exhibits a weakest-link statistical characteristic.

Abstract

Micron-scale single crystalline materials deform plastically via large intermittent strain bursts that make the deformation process unpredictable. Here we investigate this stochastic phenomenon by analysing the plastic response of an ensemble of specimens differing only in the initial arrangement of dislocations. We apply discrete dislocation dynamics simulations and microcompression tests on identically fabricated Cu single crystalline micropillars. We find that a characteristic yield stress can be defined in the average sense for a given specimen ensemble, where the average and the variance of the plastic strain start to increase considerably. In addition, in all studied cases the stress values at a given strain follow a Weibull distribution with similar Weibull exponents, which suggests that dislocation-mediated plastic yielding is characterized by an underlying weakest-link phenomenon. These results are found not to depend on fine details of the actual set-up, rather, they represent general features of micron-scale plasticity.