doi:10.1016/j.physme.2011.04.006
Physical elastoplastic analysis of deformation of fcc metals
P.V. Trusov*, V.N. Ashikhmin and A.I. Shveykin
Perm State Technical University, Perm, 614990, Russia
The paper considers a model of elastoplastic deformation of single crystals that takes into account elastic and plastic anisotropy,
intragranular dislocation glide, geometric nonlinearity, and rotation of a crystal lattice. An alternate solution for the problem of non-
uniqueness in the choice of active slip systems is proposed. Available models in which lattice rotation is associated with quasirigid motion
are analyzed. An algorithm of model realization for uniaxial tension and compression of single crystals is described and data of corresponding
model calculations are analyzed.
Keywords: anisotropy of properties, quasirigid motion, constitutive relations, physical theories of plasticity
Copyright © 2011 ISPMS, Siberian Branch of the RAS. Published by Elsevier BV. All rights reserved.
* Corresponding author
Prof. Peter V. Trusov, e-mail: tpv@matmod.pstu.ac.ru
1. Introduction
The properties of polycrystalline materials depend in
large measure on their internal structural state; in particu-
lar, the nonuniform distribution function of grain lattice
orientations in a representative volume of a polycrystal (tex-
ture) generates anisotropy of its elastic and plastic proper-
ties and determines the functional properties of an part made
thereof. In certain of material treatment modes, e.g., in equal-
channel angular pressing, grain fragmentation and refine-
ment also adds much to the process resulting in submicro-
crystalline materials with increased strength properties.
Therefore, one of the most urgent problems to date in solid
state mechanics is the simulation of the structural evolution
of polycrystals under deformation and primarily in metal
forming.
Recent models of meso- and microstructural evolution
of deformed polycrystals have increasingly used explicit
introduction of constitutive relations and formulation of evo-
lution (kinetic) equations for meso- and microstructural pa-
rameters as internal state variables and carriers of loading
history [17]. Part of the internal variables is directly en-
tered into a system of constitutive relations of a given scale
level; these variables can be termed explicit internal vari-
ables. The other group of internal variables is latent or im-
plicit variables referred in most cases to deeper scale levels
and used to complete the system of equations.
In the context of the foregoing approach, inelastic defor-
mation of a polycrystal representative volume is normally
described by direct or statistical models derived from physi-
cal theories of plasticity.
Direct models, as a rule, use the finite element method
[8, 9] and allow more accurate determination of the stress
and strain distribution in a region taking into account short-
and long-range interactions of grains. However in the ma-
jority of available works, direct models are limited to the
two-dimensional statement, because calculations of bound-
ary problems in their three-dimensional statement, which
is appropriate to actual technological treatments of metals,
are very time-consuming even with high-performance com-
puter clusters.
In computation terms, statistical models are more effi-
cient and are widely used for simulation of elastoplastic
deformation of real materials [1012]. These models, as a
rule, consider one mechanism of plastic deformation
intragranular glide of edge dislocations according to the
Schmidt law. Most of models of this class go back to the
pioneering Taylor work or to the Lin model [7, 13, 14].
A statistical sample element in these models is typically
a grain. Thus, the description of the behavior of crystal-
lites-grains is fundamental for any physical theory of plasti-
P.V. Trusov, V.N. Ashikhmin and A.I. Shveykin / Physical Mesomechanics 14 12 (2011) 4048
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