Grain-size dependence of the flow stress of Cu from millimeters to nanometers

Data in the literature on the effect of grain size (d) from millimeters to nanometers on the flow stress of Cu are evaluated. Three grain-size regimes are identified: regime I, d>∼10−6 m; regime II, d ≈10−8 to 10−6 m; and regime III, d<∼10−8 m. Grain-size hardening occurs in regimes I and II; grain-size softening occurs in regime III. The deformation structure in regime I consists of dislocation cells; in regime II, the dislocations are mostly restricted to their slip planes; in regime III, computer simulations indicate that dislocations are absent and that deformation occurs by the shearing of grain-boundary atoms. The transition from regime I to II occurs when the dislocation cell size becomes larger than the grain size, and the transition from regime II to III occurs when the dislocation spacing due to elastic interactions becomes larger than the grain size. The rate-controlling mechanism in regime I is concluded to be the intersection of dislocations; in regime II, it is proposed to be grain-boundary shear promoted by the pileup of dislocations; in regime III, it appears to be grain-boundary shear by the applied stress alone.