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a
gloaguen@lamm.univnantes.fr,
b
jamal.fajoui@univnantes.fr,
c
bruno.courant@univnantes.fr,
d
ronald.guillen@univnantes.fr
1 4
Abstract. A twolevel homogenisation approach is applied to the micromechanical modelling of
the elastoplasticity of polycrystalline materials during various strainpath changes. The model is
tested by simulating the development of intragranular strains during different complex loads.
Mechanical tests measurements are used as a reference in order to validate the model. The
anisotropy of plastic deformation in relation to the evolution of the dislocation structure is analysed.
The results demonstrate the relevance of this approach for FCC polycrystals.
Introduction
This study is devoted to complex path loads. It aims the numerical study of the influence of
intragranular stresses on the evolution of the mechanical behaviour. Based on the work of Muller et
al. [1], a micromechanical description of a single crystal is developed through a micromeso
transition based on the Kröner’s model. The grain is considered as a twophase material
(dislocation walls and cells). Dislocation densities on each slip system are considered as internal
variables and a hardening matrix taking into account the different dislocations interactions is
proposed. Next, a mesomacro transition using the elastoplastic selfconsistent method (EPSC) is
applied to deduce the macroscopic response of the aggregate. Different numerical results
concerning macroscopic behaviour as well as microscopic features are given.
Model description
Based on the works of Mughrabi [2], the crystallite containing a heterogeneous dislocation
distribution is considered as a twophase composite, consisting of hard dislocationrich and soft
dislocationpoor regions. The phases have the behaviour described by the
shear modulus and Poisson’s ratio ν. The grain undergoes a deformation ε (with a stress σ)
composed of an elastic deformation ε
e
and a plastic part ε
p
. Describing by ε
pc
and ε
pw
the mean
plastic strain in the dislocations cells (c) and walls (w) respectively, one can write:
ε = (1 f)ε
w
+fε
c
and σ
σ
σ = (1 ) σ
σ
σ
+ σ
σ
σ
(1.a)
and with an isotropic elastic behaviour: ε
ε
ε
= (1 )ε
ε
ε
+ ε
ε
ε
(1.b)
where f (respectively 1f) is the volume fraction of cell interiors (respectively cell walls) in a grain.
The stress tensor σ
α
in the phase α is:
σ
α
= σ + α
T
.c
α
..(I s
esh
)..(ε
p
ε
pα
) (2)
A..B denotes the double scalar product A
ijkl
B
klmn
. c
α
is the elastic constant tensor for the phase α.
s
esh
is the Eshelby tensor and I is the fourth order identity tensor. σ is the stress tensor induced in
the grain. α
T
is a plastic accommodation factor. In the remainder of the paper and for more clarity,
the factor α
T
is omitted. Taking into account the relations (1.a) and (2), the mean stress tensors σ
c
and σ
w
within the cells and the walls can be written as:
σ
c
= σ + (1 – f)c
c
..(I s
esh
)..(ε
pw
ε
pc
) and σ
w
= σ fc
w
..(I s
esh
)..(ε
pw
ε
pc
) (3)
Materials Science Forum Vols. 524-525 (2006) pp. 511-516
online at http://www.scientific.net
© (2006) Trans Tech Publications, Switzerland
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the
written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net . (ID: 193.52.108.46-21/09/06,08:49:51)