Analytical and computational description of effect of grain size on yield stress of metals

Four principal factors contribute to grain-boundary strengthening: (a) the grain boundaries act as barriers to plastic flow; (b) the grain boundaries act as dislocation sources; (c) elastic anisotropy causes additional stress es in gain-boundary surroundings; (d) multislip is activated in the grain-b oundary regions, whereas grain interiors are initially dominated by single slip, if properly oriented. As a result, the regions adjoining grain bounda ries harden at a rate much higher than grain interiors. A phenomenological constitutive equation predicting the effect of grain size on the yield stre ss of metals is discussed and extended to the nanocrystalline regime. At la rge grain sizes, it has the Hall-Petch form, and in the nanocrystalline dom ain the slope gradually decreases until it asymptotically approaches the fl ow stress of the grain boundaries. The material is envisaged as a composite , comprised of the grain interior, with flow stress sigma (fG) and grain bo undary work-hardened layer, with flow stress sigma (fGB). The predictions o f this model are compared with experimental measurements over the mono, mic ro, and nanocrystalline domains. Computational predictions are made of plas tic flow as a function of grain size incorporating differences of dislocati on accumulation rate in grain-boundary regions and grain interiors. The mat erial is modeled as a monocrystalline core surrounded by a mantle (grain-bo undary region) with a high work hardening rate response. This is the first computational plasticity calculation that accounts for grain size effects i n a physically-based manner. A discussion of statistically stored and geome trically necessary dislocations in the framework of strain-gradient plastic ity is introduced to describe these effects. Grain-boundary sliding in the nanocrystalline regime is predicted from calculations using the Raj-Ashby m odel and incorporated into the computations; it is shown to predispose the material to shear localization. (C) 2001 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.