A micro-continuum model for the creep behavior of complex nanocrystalline materials

A nanocrystalline material which has an average grain size of less than 100 nm is characterized with a significant portion of atoms residing in the grain boundaries or in the grain-boundary affected zone (GBAZ), while nanocrystalline materials with a more complex structure may contain additional strengthening nanoparticles or nano pores. In this article we develop a micro-continuum model to capture the creep response of such a complex nanocrystalline system. We make use of the concept of a three-phase composite with the GBAZ serving as the matrix, and grain interiors and dispresed particles (or voids) as two distinct types of inclusions. Both the grain interior and the GB zone are capable of undergoing the rate-dependent plastic deformation, but the strengthening nanoparticles or pores are taken to deform only elastically. During deformation the porosity will continue to evolve: its evolution is also addressed. In addition, the effect of temperature on the overall creep response is also accounted for. Several important features of creep characteristics in light of grain size, and nanoparticle and nanopore concentrations, are illustrated, and it is also demonstrated that the calculated results are in reasonable agreement with available experimental data. (C) 2010 Elsevier Ltd. All rights reserved.