In this paper, intermediate modeling of polycrystalline plasticity is proposed for rigid viscoplatic large deformations. This approach is based on the use of a bicrystal as the elementary local element representing the polycrystal. The local homogenization is obtained by considering the bicrystal volume-averaging and the jump conditions at the assumed planar interface between the two crystals. Two interaction laws based on Taylor and Sachs type assumptions are proposed. These bicrystal-based averaging schemes are different from the classical Taylor and Sachs models since they allow for stresses and strains to vary from one single crystal to the other. We simulate uniaxial tension and compression as well as plane strain compression tests. Results in terms of stress-strain curves are shown in comparison to those of the pure Taylor and Sachs models. We also show results for texture evolution and discuss their comparison with the experimental measurements.

1.
Taylor
,
G. I.
,
1938
, “
Plastic strain in metals
,”
J. Inst. Met.
,
62
, p.
307
307
.
2.
Hutchinson
,
J. W.
,
1976
, “
Bounds and self-consistent estimates for creep of polycrystalline materials
,”
Proc. R. Soc. London, Ser. A
,
348
, p.
101
101
.
3.
Kocks
,
U. F.
,
1970
, “
The relation between polycrystalline deformation and single-crystal deformation
,”
Metall. Trans.
,
1
, p.
1121
1121
.
4.
Asaro
,
R. J.
, and
Needleman
,
A.
,
1985
, “
Texture development and strain hardening in rate dependent polycrystals
,”
Acta Metall.
,
33
, p.
923
923
.
5.
Kalidindi
,
S. R.
,
Bronkhorst
,
C. A.
, and
Anand
,
L.
,
1992
, “
Crystallographic texture evolution in bulk deformation processing of FCC metals
,”
J. Mech. Phys. Solids
,
40
, p.
537
537
.
6.
Sachs
,
G.
,
1928
, “
Plasticity problems in metals
,”
Z. VD1
,
72
, p.
734
734
.
7.
Leffers
,
T.
, and
van Houtte
,
P.
,
1989
, “
Calculation and experimental orientation distributions of two lamellae in rolled brass
,”
Acta Metall.
,
37
, p.
1191
1191
.
8.
Leffers
,
T.
,
1968
, “
Computer simulation of the plastic deformation in faced centered cubic polycrystals and the rolling texture derived
” Riso Report No. 184 (ICOTOM 1),
1
33
9.
Leffers
,
T.
,
1993
, “
Lattice rotations during plastic deformation with grain subdivision
,”
Mater. Sci. Forum
,
157-162
, pp.
1815
1820
.
10.
Leffers, T., 1998, “Aspects of Grain Subdivision,” Plasticity 98, A. Khan, ed., pp. 165–168.
11.
Leffers
,
T.
,
2001
, “
A model for rolling deformation with grain subdivision. Part I: the initial stage
,”
Int. J. Plast.
17
, pp.
469
489
.
12.
van Houte P., Delannay L., and Samajdar I., 1998, “Prediction of cold rolling textures and strain heterogeneity of steel sheets by means of the lamel model,” Plasticity 98, A. Khan, ed., pp. 149–152.
13.
van Houte
,
P.
,
Delannay
,
L.
, and
Samajdar
,
I.
,
1999
, “
Prediction of cold rolling textures and strain heterogeneity of steel sheets by means of the lamel model
,”
Textures Microstruct.
,
31
, p.
109
109
.
14.
Kocks, U. F., and Canova, G. R., 1981, “How many slip systems and which?,” Deformation of Polycrystals, Riso National Laboratory, Hansen et al., eds., pp. 35–44.
15.
Molinari
,
A.
,
Canova
,
G. R.
, and
Ahzi
,
S.
,
1987
, “
A self-consistent approach of the large deformation polycrystal Viscoplasticity
,”
Acta Metall.
,
35
, p.
2983
2983
.
16.
Parks
,
D. M.
, and
Ahzi
,
S.
,
1990
, “
Polycrystalline plastic deformation and texture evolution for crystal lacking five independent slip systems
,”
J. Mech. Phys. Solids
,
38
, p.
701
701
.
17.
Ahzi, S., Parks, D. M., and Argon, A. S., 1990, “Modeling of plastic deformation and evolution of anisotropy in semi-crystalline polymers,” Computer Modeling and Simulation of Manufacturing Processes, B. Singh et al., eds, ASME, MD-20, p. 287.
18.
Schoenfeld
,
S. E.
,
Ahzi
,
S.
, and
Asaro
,
R. J.
,
1995
,
J. Mech. Phys. Solids
,
43
, p.
415
415
.
19.
Lee
,
B. J.
,
Ahzi
,
S.
, and
Asaro
,
R. J.
,
1995
,
Mech. Mater.
,
20
, p.
1
1
.
20.
Dahoun
,
A.
,
Canova
,
G. R.
,
Molinari
,
A.
,
Phillipe
,
M. J.
, and
G’Sell
,
C.
,
1991
,
Textures Microstruct.
,
14-18
, p.
347
347
.
21.
G’Sell
,
C.
,
Dahoun
,
A.
,
Royer
,
F. X.
, and
Phillipe
,
M. J.
,
1999
,
Modelling Simul. Sci. Eng.
,
7
, pp.
817
828
.
22.
Ahzi
,
S.
,
Asaro
,
R. J.
, and
Parks
,
D. M.
,
1993
, “
Application of crystal plasticity to mechanically processed BSCCO superconductors
,”
Mech. Mater.
,
15
, p.
201
201
.
23.
Lee
,
B. J.
,
Parks
,
D. M.
, and
Ahzi
,
S.
,
1993
, “
Micromechanical modeling of large plastic deformation and texture evolution in semi-crystalline polymers
,”
J. Mech. Phys. Solids
,
41
, p.
1651
1651
.
24.
Lee
,
B. J.
,
Ahzi
,
S.
,
Kad
,
B.
, and
Asaro
,
R. J.
,
1993
,
Scr. Metall.
,
29
, pp.
823
828
.
25.
Hines
,
J.
,
Vecchio
,
K. S.
, and
Ahzi
,
S.
,
1998
, “
Modeling of microstructure evolution in adiabatic shear bands
,”
Metall. Mater. Trans. A
,
29
, p.
191
191
.
26.
Lee
,
B. J.
,
Vecchio
,
K. S.
,
Ahzi
,
S.
, and
Schoenfeld
,
S.
,
1997
, “
Modeling the mechanical behavior of tantalum
,”
Metall. Mater. Trans. A
,
28
, p.
113
113
.
27.
Molinari
,
A.
, and
Toth
,
L.
,
1994
,
Acta Metall. Mater.
,
42
, p.
2453
2453
.
28.
Lebensohn
,
R. A.
, and
Tome´
,
C. N.
,
1993
,
Acta Metall. Mater.
,
41
, p.
2611
2611
.
29.
Bronkhorst
,
C. A.
,
Kalidindi
,
S. R.
, and
Anand
,
L.
,
1992
, “
Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals
,”
Philos. Trans. R. Soc. London, Ser. A
,
341
, p.
443
443
.
30.
Leffers
,
T.
,
2001
, “
A model for rolling deformation with grain subdivision. Part II: the subsequent stage
,”
Int. J. Plast.
17
, pp.
491
511
.
31.
Garmestani
,
H.
,
Lin
,
S.
,
Adams
,
B. L.
, and
Ahzi
,
S.
,
2001
,
J. Mech. Phys. Solids
,
49
, pp.
589
607
.
32.
Asaro
,
R. J.
, and
Rice
,
J. R.
,
1977
, “
Strain localization in ductile single crystals
,”
J. Mech. Phys. Solids
,
25
, p.
309
309
.
33.
Lee, B. J., Ahzi, S., and Parks D. M., 1998, “Intermediate modeling of polycrystal deformation,” Plasticity 98, A. Khan, ed., pp. 377–380.
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