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 stresses in grain-boundary surroundings; (d) multislip is activated in the grain-boundary regions, whereas grain interiors are initially dominated by single slip, if properly oriented. As a result, the regions adjoining grain boundaries harden at a rate much higher than grain interiors. A phenomenological constitutive equation predicting the effect of grain size on the yield stress of metals is discussed and extended to the nanocrystalline regime. At large grain sizes, it has the Hall–Petch form, and in the nanocrystalline domain the slope gradually decreases until it asymptotically approaches the flow stress of the grain boundaries. The material is envisaged as a composite, comprised of the grain interior, with flow stress sfG, and grain boundary work-hardened layer, with flow stress sfGB. The predictions of this model are compared with experimental measurements over the mono, micro, and nanocrystalline domains. Computational predictions are made of plastic flow as a function of grain size incorporating differences of dislocation accumulation rate in grainboundary regions and grain interiors. The material is modeled as a monocrystalline core surrounded by a mantle (grain-boundary region) with a high work hardening rate response. This is the first computational plasticity calculation that accounts for grain size effects in a physically-based manner. A discussion of statistically stored and geometrically necessary dislocations in the framework of strain-gradient plasticity is introduced to describe these effects. Grain-boundary sliding in the nanocrystalline regime is predicted from calculations using the Raj–Ashby model and incorporated into the computations; it is shown to predispose the material to shear localization.  2001 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.