ABSTRACT
E-mail: weng@jove.rutgers.eduInspired 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 Mechanical Properties of Nanocrystalline Materials Edited by James C. M. Li Copyright © 2011 Pan Stanford Publishing Pte. Ltd. www.panstanford.com
The influence of grain size on the yield strength and hardness of polycrystalline materials has long been described by the Hall-Petch relation.1,2 This equation, given by sy = s0 + kyd-1/2, (4.1) states that the yield strength increases linearly with the inverse of the
square root of grain size, d. Such a linear dependence has been explained from the standpoint of dislocation pile-ups of Eshelby et al.3 by Hall and Petch, and by Armstrong et al.4 It can also be explained from the mechanism suggested by Li5 that grain boundaries serve as dislocation sources, and from the dislocation density models of Conrad6 and Ashby.7 This relation holds sufficiently well in the traditional coarse grain range, but it apparently cannot continue to hold as the grain size approaches zero, for the yield strength would approach infinity. This was not an issue until 1984, when it became possible to process nanocrystalline materials by inert gas condensation.8 Since then many new processing routes have been developed and many experimental and theoretical studies have been carried out to investigate the influence of grain size all the way down to the very fine grained range, even below 10 nm.
