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.