A composite model of nanocrystalline materials

Inspired by the morphology revealed in molecular dynamic simulations, we develop a composite model to study the viscoplastic behavior of nanocrystalline materials. The composite consists of the plastically harder grain interiors serving as inclusions and the plastically softer grain boundaries (or grain-boundary affected zone) serving as the matrix, with the possibility of additional interfacial grain-boundary sliding. The constitutive equations of both phases are represented by a set of power-law, unified theory whereas that of GB sliding is taken to be Newtonian. To address this nonlinear, strain and strain-rate dependent heterogeneous problem, we introduce the methods of secant viscosity and field-fluctuation to build a homogenization scheme, so that the overall stress-strain relations of the nanocrystalline material can be calculated from those of the constituent phases. The conditions without and with grain-boundary sliding are applied to Ni and Cu, respectively, to examine how their stress-strain relations, strain-rate sensitivity, and activation volume change as a function of grain size. The results show that, as the grain size decreases from micrometers all the way down to a few nanometers, both flow stress and strain-rate sensitivity increase and then decrease, whereas the activation volume decreases and then increases. These general trends are found to be consistent with the dislocation theories of Armstrong and Rodriguez29,30 and the test results of Trelewicz and Schuh.²⁰.