Size effects under plastic deformation of microcrystals and nanocrystals

A theoretical analysis of size effects in plastically deformed crystals with transverse sizes in micro and nanometer ranges has been performed in the framework of the dislocation-kinetic approach. The analysis is based on the evolution equation of the dislocation density in these crystals and takes into account the generation of dislocations from surface dislocation sources and the escape of dislocations from the crystal through the crystal surface. It has been established that the generation of dislocations from the sources leads to a strong strain hardening of the crystal and that the escape of dislocations through the crystal surface results in a fast equilibration of these two kinetic processes. As a result, there occurs a strong “exhaustion” of strain hardening of thin crystals at the early stage of their plastic deformation in accordance with experiments. According to the theory, the flow stresses σ and transverse sizes D of microcrystals and nanocrystals are related by the expressions σ ∼ D ⁻ⁿ (n = 0.625–1.0), which are in agreement with the experiment.