Rolled aluminum alloys are known to be anisotropic due to their processing histories. This paper focuses on measuring and modeling monotonic and cyclic strength anisotropies as well as the associated anisotropy of the elastic/elastic-plastic transition of a commercially-available rolled plate product. Monotonic tension tests were conducted on specimens in the rolling plane of 25.4 mm thick AA 7075-T6 plate taken at various angles to the rolling direction (RD). Fully-reversed tension/compression cyclic experiments were also conducted. As expected, we found significant anisotropy in the back-extrapolated yield strength. We also found that the character of the elastic/elastic-plastic transition (knee of the curve) to be dependent on the orientation of the loading axis. The tests performed in RD and TD (transverse direction) had relatively sharp transitions compared to the test data from other orientations. We found the cyclic response of the material to reflect the monotonic anisotropy. The material response reached cyclic stability in 10 cycles or less with very little cyclic hardening or softening observed. For this reason, we focused our modeling effort on predicting the monotonic response. Reckoning that the primary source of anisotropy in the rolled plate is the processing-induced crystallographic texture, we employed the experimentally-measured texture of the undeformed plate material in continuum slip polycrystal plasticity model simulations of the monotonic experiments. Three types of simulations were conducted, upper and lower bound analyses and a finite element calculation that associates an element with each crystal in the aggregate. We found that all three analyses predicted anisotropy of the back-extrapolated yield strength and post-yield behavior with varying degrees of success in correlating the experimental data. In general, the upper and lower bound models predicted larger and smaller differences in the back-extrapolated yield strength, respectively, than was observed in the data. The finite element results resembled those of the upper bound when initially cubic elements were employed. We found that by employing an element shape that was more consistent with typical rolling microstructure, we were able to improve the finite element prediction significantly. The anisotropy of the elastic/elastic-plastic transition predicted by each model was also different in character. The lower bound predicted sharper transitions than the upper bound model, capturing the shape of the knee for the RD and TD data but failing to capture the other orientations. In contrast, the upper bound model predicted relatively long transitions for all orientations. As with the upper bound, the FEM calculation predicted gentle transitions with less transition anisotropy predicted than that of the upper bound. [S0094-4289(00)00201-2]

1.
Juul Jensen
,
D.
, and
Hansen
,
N.
,
1990
, “
Flow Stress Anisotropy in Aluminum
,”
Acta Metall. Mater.
,
38
, No.
8
, pp.
1369
1380
.
2.
Hansen
,
N.
, and
Juul Jensen
,
J.
,
1992
, “
Flow Stress Anisotropy Caused by Geometrically Necessary Boundaries
,”
Acta Metall. Mater.
,
40
, pp.
3265
3275
.
3.
Hostord
,
W. F.
, and
Zeisloft
,
R. H.
,
1972
, “
The Anisotropy of Age-Hardened Al-4 Pct Cu Single Crystals During Plain-Strain Compression
,”
Metall. Trans.
,
3
, pp.
113
147
.
4.
Bate
,
P.
,
Roberts
,
W. T.
, and
Wilson
,
D. V.
,
1981
, “
The Plastic Anisotropy of Two-Phase Aluminum Alloys-I. Anisotropy in Unidirectional Deformation
,”
Acta Metall.
,
29
, pp.
1797
1814
.
5.
Barlat
,
F.
,
Liu
,
J.
, and
Weiland
,
H.
,
1996
, “
On Precipitate-Induced Anisotropy Modeling in Binary Al-Cu Alloys
,”
Mater. Sci. Forum
,
217–222
, pp.
635
640
.
6.
Hatch, J. E. (ed.), 1984, Aluminum: Properties and Physical Metallurgy, American Society for Metals, Metals Park, pp. 376–377.
7.
Hill
,
R.
,
1948
, “
A Theory of the Yield and Plastic Flow of Anisotropic Metals
,”
Proc. R. Soc. London, Ser. A
,
193
, pp.
281
297
.
8.
Stout
,
M. G.
,
Hecker
,
S. S.
, and
Bourcier
,
R.
,
1983
, “
An Evaluation of Anisotropic Effective Stress-Strain Criteria for the Yield and Flow of 2024, Aluminum Tubes
,”
ASME J. Eng. Mater. Technol.
,
105
, pp.
242
249
.
9.
Harvey, S. J., 1985, “The Use of Anisotropic Yield Surfaces in Cyclic Plasticity,” Multiaxial Fatigue, ASTM STP 853, ASTM, Philadelphia, PA, pp. 49–53.
10.
Barlat
,
F.
,
1987
, “
Crystallographic Texture, Anisotropic Yield Surfaces and Forming Limits of Sheet Metals
,”
Mater. Sci. Eng.
,
91
, pp.
55
72
.
11.
Lin, H., and Nayeb-Hashemi, H., 1993, “Effects of Material Anisotropy on Cyclic Deformation and Biaxial Fatigue Behavior of Al-6061 T6,” Advances in Multiaxial Fatigue, ASTM STP 191, McDowell and Ellis, eds., ASTM, Philadelphia, pp. 151–182.
12.
Karafillis
,
A. P.
, and
Boyce
,
M. C.
,
1993
, “
General Anisotropic Yield Criterion Using Bounds and a Transformation Weighting Tensor
,”
J. Mech. Phys. Solids
,
41
, No.
12
, pp.
1859
1886
.
13.
Sachs
,
G.
,
1928
, “
Zur Ableitung Einer Fliessbedingung
,”
A. Ver. dt. Ing.
,
12
, pp.
134
136
.
14.
Taylor
,
G. I.
,
1938
, “
Plastic Strain in Metals
,”
J. Inst. Met.
,
62
, pp.
307
324
.
15.
Iwakuma
,
T.
, and
Nemat-Nasser
,
S.
,
1984
, “
Finite Elastic-Plastic Deformation of Polycrystalline Metals
,”
Proc. R. Soc. London, Ser. A
,
394
, pp.
87
119
.
16.
Asaro
,
R. J.
, and
Needleman
,
A.
,
1985
, “
Texture Development and Strain Hardening in Rate Dependent Polycrystals
,”
Acta Metall.
,
33
, pp.
923
953
.
17.
Kocks, U. F., 1987, “Constitutive Behavior Based on Crystal Plasticity,” Unified Constitutive Equations for Plastic Deformation and Creep of Engineering Alloys, A. K. Miller, ed., Elsevier, New York, pp. 1–88.
18.
Molinari
,
A.
,
Canova
,
G. R.
, and
Ahzi
,
S.
,
1987
, “
A Self Consistent Approach of the Large Deformation Polycrystal Viscoplasticity
,”
Acta Metall.
,
35
, No.
123
, pp.
2983
2994
.
19.
Mathur
,
K. K.
, and
Dawson
,
P. R.
,
1989
, “
On Modeling the Development of Crystallographic Texture in Bulk Forming Processes
,”
Int. J. Plast.
,
5
, pp.
67
94
.
20.
Lipinski
,
P.
, and
Berveiller
,
M.
,
1989
, “
Elastoplasticity of Micro-Inhomogeneous Metals at Large Strain
,”
Int. J. Plast.
,
5
, pp.
149
172
.
21.
Mathur
,
K. K.
,
Dawson
,
P. R.
, and
Kocks
,
U. F.
,
1990
, “
On Modeling Anisotropy in Deformation Processes, Involving Polycrystals with Distorted Grain Shapes
,”
Mech. Mater.
,
10
, pp.
183
202
.
22.
Cailletaud
,
G.
,
1992
, “
a Micromechanical Approach to Inelastic Behavior of Metals
,”
Int. J. Plast.
,
8
, pp.
55
73
.
23.
Lebensohn
,
R. A.
, and
Tome
,
C. N.
,
1994
, “
A Self-Consistent Viscoplastic Model: Prediction of Rolling Textures of Anisotropic Polycrystals
,”
Mater. Sci. Eng., A
,
175
, pp.
71
82
.
24.
Zouhal
,
N.
,
Molinari
,
A.
, and
Toth
,
L. S.
,
1996
, “
Elastic-Plastic Effects During Cyclic Loading as Predicted by the Taylor-Lin Model of Polycrystal Viscoplasticity
,”
Int. J. Plast.
,
12
, No.
3
, pp.
343
360
.
25.
Feyel
,
F.
,
Calloch
,
S.
,
Marquis
,
D.
, and
Cailletaud
,
G.
,
1997
, “
F. E. Computation of a Triaxial Specimen Using a Polycrystalline Model
,”
Comput. Mater. Sci.
,
9
, pp.
141
157
.
26.
Molinari
,
A.
,
Ahzi
,
S.
, and
Kouddane
,
R.
,
1997
, “
On the Self-Consistent Modeling of Elastic-Plastic Behavior of Polycrystals
,”
Mech. Mater.
,
26
, pp.
43
62
.
27.
Harren
,
S. V.
, and
Asaro
,
R. J.
,
1989
, “
Nonuniform Deformations in Polycrystals and Aspects of the Validity of the Taylor Theory
,”
J. Mech. Phys. Solids
,
37
, pp.
191
232
.
28.
McHugh
,
P. E.
,
Varias
,
A. G.
,
Asaro
,
R. J.
, and
Shih
,
C. F.
,
1989
, “
Computational Modeling of Microstructures
,”
Future Gen. Comp. Sys.
,
5
, pp.
295
318
.
29.
Havlicˇek
,
F.
,
Tokuda
,
M.
,
Hino
,
S.
, and
Kratochvil
,
J.
,
1992
, “
Finite Element Method Analysis of Micro-Macro Transition in Polycrystalline Plasticity
,”
Int. J. Plast.
,
8
, pp.
477
499
.
30.
Dawson, P. R., Beaudoin, A. J., and Mathur, K. K., 1994, “Finite Element Modeling of Polycrystalline Solids,” Numerical Predictions of Deformation Processes and the Behavior of Real Materials, Anderson et al., eds., Riso National Laboratory, Roskilde, Denmark, pp. 33–43.
31.
Beaudoin
,
A. J.
,
Dawson
,
P. R.
,
Mathur
,
K. K.
, and
Kocks
,
U. F.
,
1995
, “
A Hybrid Finite Element Formulation for Polycrystal Plasticity with Consideration of Macrostructural and Microstructural Linking
,”
Int. J. Plast.
,
11
, pp.
501
521
.
32.
Beaudoin, A. J., Mecking, H., and Kocks, U. F., 1995, “Development of Local Shear Bands and Orientation Gradients.” Simulation of Materials Processing: Theory, Methods, and Applications, Shen and Dawson, eds., Balkema, Rotterdam, pp. 225–230.
33.
Mika
,
D. P.
, and
Dawson
,
P. R.
,
1998
, “
Effects of Grain Interaction on Deformation in Polycrystals
,”
Mater. Sci. Eng., A
,
257
, pp.
62
76
.
34.
Mika, D. P., and Dawson, P. R., 1999, “Polycrystal Plasticity Modeling of Intracrystalline Boundary Textures,” Acta Mater (in press).
35.
Czyzak
,
S. J.
,
Bow
,
N.
, and
Payne
,
H.
,
1961
, “
On the Tensile Stress-Strain Relation and the Bauschinger Effect for Polycrystalline Materials From Taylor’s Model
,”
J. Mech. Phys. Solids
,
9
, pp.
63
66
.
36.
Hutchinson
,
J. W.
,
1964
, “
Plastic Stress-Strain Relations of FCC Polycrystalline Metals Hardening According to Taylor’s Rule
,”
J. Mech. Phys. Solids
,
12
, pp.
11
24
.
37.
Hutchinson
,
J. W.
,
1964
, “
Plastic Deformation of BCC Polycrystals
,”
J. Mech. Phys. Solids
,
12
, pp.
25
33
.
38.
Barton
,
N.
,
Dawson
,
P. R.
, and
Miller
,
M. P.
,
1999
, “
Yield Strength Asymmetry Predictions from Polycrystal Elastoplasticity
,”
ASME J. Eng. Mater. Technol.
,
121
, pp.
230
239
.
39.
Kallend
,
J. S.
,
Kocks
,
U. F.
,
Rollett
,
A. D.
, and
Wend
,
H.
,
1991
, “
Operational Texture Analysis
,”
Mater. Sci. Eng., A
,
132
, pp.
1
11
.
40.
Frank
,
F. C.
,
1988
, “
Orientation Mapping
,”
Metall. Trans. A
,
19A
, pp.
403
408
.
41.
Becker
,
S.
, and
Panchanadeeswaran
,
S.
,
1989
, “
Crystal Rotations Represented as Rodriguez Vectors
,”
Textures Microstruct.
,
10
, pp.
167
194
.
42.
Mitchell, M. R., 1978, “Fundamentals of Modern Fatigue Analysis for Design,” Fatigue Microstructure, pp. 385–438.
43.
Marin
,
E. B.
, and
Dawson
,
P. R.
,
1998
, “
On Modeling the Elasto-Viscoplastic Response of Metals Using Polycrystal Plasticity
,”
Comput. Methods Appl. Mech. Eng.
,
165
, pp.
1
21
.
44.
Miller
,
M. P.
, and
Dawson
,
P. R.
,
1997
, “
Influence of Slip System Hardening Assumptions on Modeling Stress Dependence of Work Hardening
,”
J. Mech. Phys. Solids
,
45
, pp.
1781
1804
.
45.
Kocks, U. F., Tome, C. N., and Wenk, H.-R., 1998, Texture and Anisotropy. Cambridge University Press, Cambridge, p. 365 ff.
46.
Wright
,
S. I.
, and
Adams
,
B. L.
,
1990
, “
An Evaluation of the Single Orientation Method for Texture Determination in Materials of Moderate Texture Strength
,”
Textures Microstruct.
,
12
, pp.
65
76
.
47.
Baudin
,
T.
, and
Penelle
,
1993
, “
Determination of the Total Texture Function from Individual Orientation Measurements by Electron Backscattering Pattern
,”
Metall. Trans. A
,
24A
, pp.
2299
2311
.
48.
Wright, S. I., and Kocks, U. F., 1996, “A Comparison of Different Texture Analysis Techniques,” Proceedings of the Eleventh International Conference on Textures of Materials, Liang, Zuo, and Chu, eds., The Metallurgical Society, pp. 53–62.
49.
Miller, M. P., and Turner, T. J., 1999, “Quantification and Representation of Crystallographic Texture Fields in Processed Alloys,” Int. J. Plast. (accepted).
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