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Micro‐mechanical Modelling of a Bi‐crystal Lamellar Composite's Behaviour at Large strain: A Double Scaled Transition Method
Author(s) -
Krummeich R.,
Sabar H.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.20000801488
Subject(s) - materials science , lamellar structure , crystal plasticity , mesoscale meteorology , multiscale modeling , plasticity , micromechanics , hardening (computing) , continuum mechanics , constitutive equation , composite number , formalism (music) , finite element method , composite material , mechanics , thermodynamics , physics , chemistry , computational chemistry , art , musical , visual arts , layer (electronics) , meteorology
Nanoscaled lamellar structures involve complex deformation behaviour at finite strain due to the preserve of a large number of interfaces. The aim of the work is to develop a micromechanical approach based on interfacial operators in the context of statistical continuum mechanics. Using Hill's formalism, constitutive equations at mesoscale (1 μm) are derived from Nemat‐Nasser's finite elastic‐plastic deformation model ]3,5[ and solved numerically by a self‐consistent method ]1[. At micro‐scale (O.1 μm), a thermodynamical process may be defined to describe intrinsic hardening mechanism found to be linearly dependent with the interlamellar spacing's inverse ]4[. Specific crystal plasticity of both phases may then be introduced in the micromechanical approach to obtain a double scale model describing global and local behaviour of a pearlitic ilot under an imposed loading.