A continuum theory of stress gradient plasticity based on the dislocation pile-up model

A unified treatment of dislocation pile-ups experiencing various stress situations is given by using the Tricomi method. The complete fields for a double dislocation pile-up are derived for non-uniform stress cases. The analysis of a dislocation pile-up under a linear stress gradient predicts an increase in the yielding stress with increasing obstacle spacing, which is competitive with the classical Hall-Petch relation. A continuum theory of stress-gradient plasticity incorporating both grain and specimen sizes is established. The size effects in wire torsion and film bending are interpreted in the light of the new theory. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.