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Multiscale Modeling of Nanocrystalline Materials: A Variational Approach
Author(s) -
El Sayed Tamer,
Gürses Ercan
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110247
Subject(s) - nanocrystalline material , homogenization (climate) , materials science , isotropy , plasticity , grain size , dislocation , phase transition , grain boundary , grain boundary strengthening , multiscale modeling , inverse , thermodynamics , condensed matter physics , mechanics , composite material , mathematics , geometry , microstructure , physics , nanotechnology , chemistry , biodiversity , ecology , computational chemistry , quantum mechanics , biology
This paper presents a variational multi‐scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc‐material is modeled as a two‐phase material consisting of a grain interior (GI) phase and a grain boundary (GB) phase. A rate‐independent isotropic porous plasticity model is employed to describe the GB phase, whereas a crystal‐plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the GI phase. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor‐type homogenization. It is shown that the proposed model is able to capture the inverse Hall‐Petch effect. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)