| In this review we highlight a micromechanics-based homogenization scheme that has wide applicability for calculations of the overall rate-independent plasticity, time-dependent creep, strain-rate sensitivity, effect of porosity, and void growth for nanocrystalline materials. Based on the morphology disclosed in molecular dynamic simulation, we establish a composite model to represent the grain interior and the grain-boundary zone (GB zone). The nonlinear rate-independent plasticity is formulated in terms of the secant moduli of the constituent phases, whereas the rate-dependent viscoplasticity is formulated in terms of their secant viscosity. In both cases the heterogeneous stress and strain fields of the constituent phases are analytically determined. Through two related field fluctuation approaches, the effective stresses of the grain interior and the GB zone are derived through the variation of the overall secant moduli and the overall secant viscosity with respect to the constituent property. The overall behavior then can be calculated from the effective secant moduli or effective secant viscosity. We demonstrate how this approach provides the overall stress-strain relation as the grain size decreases from the coarse grain to the nano-meter range, and how the slope of the Hall-Petch plot continues to decrease and eventually turns into negative below certain critical grain size. This critical grain size also gives rice to the maximum yield strength, and is an important factor in material design. We also show how the creep resistance increases with decreasing grain size and then decline, how the strain-rate sensitivity of the nanocrystalline materials is affected by grain size, and how porosity and grain size compete with each other under a constant strain rate loading. We conclude by the study of void growth during viscoplastic deformation of nanocrystalline materials. |
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