  Dislocations are the carriers of plasticity in crystalline materials. Their
collective interaction behavior is dependent on the strain rate and sample
size. In small specimens, details of the nucleation process are of particular
importance. In the present work, discrete dislocation dynamics (DDD)
simulations are performed to investigate the dominant yielding mechanisms in
single crystalline copper pillars with diameters ranging from 100 to 800 nm.
Based on our simulations with different strain rates and sample size, we
observe a transition of the relevant nucleation mechanism from "dislocation
multiplication" to "surface nucleation". Two physics-based analytical models
are established to quantitatively predict this transition, showing a good
agreement for different strain rates with our DDD simulation data and with
available experimental data. Therefore, the proposed analytical models help to
understand the interplay between different physical parameters and nucleation
mechanisms and are well suitable to estimate the material strength for
different material properties and under given loading conditions.
