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Average yielding and weakest link statistics in micron-scale plasticity

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.