A secant-viscosity composite model for the strain-rate sensitivity of nanocrystalline materials

In order to address the strain-rate sensitivity of nanocrystalline solids, a secant-viscosity composite model is developed in this article. The microgeometry of the composite is taken to consist of the grain-interior phase and the grain-boundary affected zone (GBAZ) as suggested by Schwaiger et al. [Schwaiger, R., Moser, B., Dao, M., Chollacoop, N., Suresh, S., 2003. Some critical experiments on the strain-rate sensitivity of nanocrystalline nickel. Acta Mater. 51, 5159-5172), while the constituent properties are modeled by a unified viscoplastic constitutive law. The drag stress of the grain interior is assumed to follow the Hall-Petch relation, but that of the GBAZ is independent of grain size, d. Then in terms of the secant viscosity of the constituent phases, the strain-rate sensitivity of the nanocrystalline solid is determined with the help of a linear viscous comparison composite and a field-fluctuation approach. To test the applicability of the developed model, it is applied to predict the strain-rate effect of a nanocrystalline Ni, and the grain-size dependence of its stress-strain relations. Our theoretical calculations indicate that the tensile strength of a nanocrystalline Ni with d = 40 nm is about five times that of a microcrystalline one with d = 10 mu m under the same strain rate of = 3 x 10(-4) s(-1), and that the nanocrystalline Ni exhibits a much stronger strain-rate effect. These predictions are found to be consistent with the experimental data of Schwaiger et al. Possible grain-size softening with further grain-size reduction such as reported in molecular dynamic simulations is also demonstrated. (C) 2007 Elsevier Ltd. All rights reserved.