Polycrystal plasticity models are commonly developed with a narrow focus on the grain as the fundamental unit of crystallographic orientation and anisotropic behavior. However, deformation and strengthening mechanisms occur simultaneously at multiple length scales and may lead to bulk deformation behavior of metals that is substantially different from that predicted by simple forms of polycrystal plasticity. The development of dislocation substructure occurs at subgrain scales while, at the same time, geometrically necessary dislocation boundaries (GNBs) are generated that extend over several grain diameters. A framework is presented here for the efficient treatment of multiple, simultaneously evolving strengthening mechanisms. The theory focuses on a macroscale hardening surface representation of the strengthening due to GNB formation. Crystallographic shear flow resistance is determined via a mapping procedure of the macroscale hardening surface to the length scale of grains. Predicted stress-strain curves based on the hardening surface formulation are compared to experimental data and polycrystal plasticity predictions for OFHC Cu. It is demonstrated that the hardening surface model of GNB strengthening mechanisms can provide improved predictive capability of nonproportional loading behavior of Cu compared to conventional slip system hardening laws commonly used in polycrystal plasticity applications.
Issue Section:
Technical Papers
Topics:
Plasticity,
Hardening,
Deformation,
Dislocations,
Anisotropy,
Metals,
Shear flow,
Stress-strain curves
1.
Anand
L.
Kothari
M.
1996
, “A Computational Procedure for Rate-Independent Crystal Plasticity
,” J. Mech. Phys. Solids
, Vol. 44
, No. 4
, pp. 525
–558
.2.
Armstrong, P. J., and Frederick, C.O., 1966, “A Mathematical Representation of the Multiaxial Bauschinger Effect,” G.E.G.B. Report RD/B/N, p. 731.
3.
Asaro
R. J.
Rice
R.
1977
, “Strain Localization in Ductile Single Crystals
,” J. Mech. Phys. Solids
, Vol. 25
, p. 309
309
.4.
Asaro, R. J., 1983, “Micromechanics of Crystals and Polycrystals,” Advances in Applied Mechanics, Vol. 23, Academic Press, San Diego.
5.
Asaro
R. J.
Needleman
A.
1985
, “Texture Development and Strain Hardening in Rate Dependent Polycrystals
,” Acta Metall.
, Vol. 33
, No. 6
, pp. 923
–953
.6.
Bassani
J. L.
Wu
T. Y.
1991
, “Latent Hardening in Single Crystals II, Analytical Characterization and Predictions
,” Proc. R. Soc., London
, Vol. A435
, p. 21
21
.7.
Bay
B.
Hansen
N.
Hughes
D. A.
Kuhlmann-Wilsdorf
D.
1992
, “Evolution of FCC Deformation Structures in Polyslip
,” Acta Met. Mater.
, Vol. 40
, No. 2
, pp. 205
–219
.8.
Bronkhorst
C. A.
Kalidindi
S. R.
Anand
L.
1992
, “Polycrystalline Plasticity and the Evolution of Crystallographic Texture in FCC Metals
,” Phil. Trans. R. Soc.
, London, Series A, Vol. 341
, pp. 443
–477
.9.
Butler
G. C.
Graham
S.
McDowell
D. L.
Stock
S. R.
Ferney
V. C.
1998
, “Application of the Taylor Polycrystal Plasticity Model to Complex Deformation Experiments
,” ASME JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY
, Vol. 120
, No. 3
, pp. 197
–205
.10.
Butler
G. C.
McDowell
D. L.
1998
, “Polycrystal Constraint and Grain Subdivision
,” Int. J. Plasticity
, Vol. 14
, No. 8
, pp. 703
–717
.11.
Chang
Y. W.
Asaro
R. J.
1981
, “An Experimental Study of Shear Localization in Aluminum-Copper Single Crystals
,” Acta Metall.
, Vol. 29
, pp. 241
–257
.12.
Cuitin˜o
A. M.
Ortiz
M.
1992
, “Computational Modeling of Single Crystals
,” Modelling Simul. Mater. Sci. Eng.
, Vol. 1
, pp. 225
–263
.13.
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, Proc. 15th Riso Symposium On Materials Science, Anderson, S. I., Bilde-Sorensen, J. B., Lorentzen, T., Pedersen, O. B., and Sorenson, N. J., eds., Riso National Lab, Roskilde, Denmark, pp. 33–44.
14.
Graham, S., 1995, “The Stress State Dependence of Finite Inelastic Deformation Behavior of FCC Polycrystalline Materials,” Master’s thesis, Georgia Institute of Technology.
15.
Hansen
N.
Juul Jensen
D. J.
1992
, “Flow Stress Anisotropy Caused by Geometrically Necessary Boundaries
,” Acta Met.
, Vol. 40
, No. 12
, pp. 3265
–3275
.16.
Havner, K. S., 1992, Finite Plastic Deformation of Crystalline Solids, Cambridge University Press, New York, NY.
17.
Hill
R.
1965
, “A Self-Consistent Mechanics of Composite Materials
,” J. Mech. Phys. Solids
, Vol. 13
, pp. 213
213
.18.
Hughes
D. A.
Hansen
N.
1991
, “Microstructural Evolution in Nickel During Rolling and Torsion
,” Mater. Sci. Tech.
, Vol. 7
, No. 6
, pp. 544
–553
.19.
Hughes, D. A., 1996, “The Development of High Angle Deformation Boundaries and Local Orientations in Aluminum,” Aluminum Alloys for Packaging II, J. G. Morris, S. K. Das and H. S. Goodrich, eds., The Minerals, Metals and Materials Society, pp. 129–144.
20.
Hughes
D. A.
Liu
Q.
Chrzan
D. C.
Hansen
N.
1997
, “Scaling of Microstructural Parameters and Misorientations of Deformation Induced Boundaries
,” Acta. Mater.
, Vol. 45
, No. 1
, pp. 105
–112
.21.
Hutchinson
J. W.
1976
, “Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials
,” Proc. R. Soc., London
, Vol. A348
, pp. 101
–127
.22.
Jonas, J. J., Canova, G. R., Shrivistava, S. C., and Christodoulou, N., 1981, “Sources of the Discrepancy Between the Flow Curves Determined in Torsion and in Axisymmetric Tension and Compression Testing,” Proceedings of The Workshop on Plasticity of Metals at Finite Strain: Theory, Experiment and Computation, Division of Applied Mechanics, Stanford University, Stanford, CA, pp. 206–222.
23.
Kalidindi
S. R.
Bronkhorst
C. A.
Anand
L.
1992
, “Crystallographic Texture Evolution in Bulk Deformation Processing of FCC Metals
,” J. Mech. Phys. Solids
, Vol. 40
, No. 3
, pp. 537
–569
.24.
Kocks
U. F.
Stout
M. G.
Rollett
A. D.
1988
, “The Influence of Texture on Strain Hardening
,” Strength of Metals and Alloys
, Vol. 1
, pp. 25
–34
.25.
Kocks, U. F., Kallend, J. S., Wank, H. R., Roller, A. D., and Wright, S. I., 1994, popLA, Preferred Orientation Package-Los Alamos, LANL LA-CC-89-18.
26.
Kroner, E., 1958, “Kontinuumstheorie der Versetzungen und Eigenspannungen,” Springer-Verlag, Berlin.
27.
Miller
M.
Dawson
P.
1997
, “Influence of Slip System Hardening Assumptions on Modeling Stress Dependence of Work Hardening
,” J. Mech. Phys. Solids
, Vol. 45
, No. 11/12
, pp. 1781
–1804
.28.
Molinari
A.
Canova
G.
Ahzi
S.
1987
, “A Self-Consistent Approach of the Large Deformation Polycrystal Plasticity
,” Acta Met.
, Vol. 35
, p. 2983
2983
.29.
Nemat-Nasser, S., Mehrabadi, M. M., and Iwakuma, T., 1981, “On Certain Macroscopic and Microscopic Aspects of Plastic Flow of Ductile Materials,” Three-Dimensional Constitutive Relations and Ductile Fracture, S. Nemat-Nasser, ed., North-Holland Publ., pp. 147–172.
30.
Nemat-Nasser
S.
Obata
M.
1986
, “Rate Dependent, Finite Elasto-Plastic Deformation of Polycrystals
,” Proc. R. Soc., London
, Vol. A407
, p. 45
45
.31.
Peirce
D.
Asaro
R. J.
Needleman
A.
1983
, “An Analysis of Non-uniform and Localized Deformation in Ductile Single Crystals
,” Acta Metall.
, Vol. 31
, p. 1951
1951
.32.
Rashid
M. M.
Nemat-Nasser
S.
1990
, “A Constitutive Algorithm for Rate Dependent Crystal Plasticity
,” Computer Methods in Applied Mechanics and Engineering
, Vol. 94
, pp. 201
–228
.33.
Rollet, A. D., Juul Jensen, D., and Stout, M. G., 1992, “Modelling the Effect of Microstructure on Yield Anisotropy,” Proc. 13th Ris0 Int. Symp. On Materials Science, S. I. Andersen et al., eds., Ris0 National Laboratory, Roskilde, Denmark, pp. 93–109.
34.
Schro¨der
J.
Miehe
C.
1997
, “Aspects of Computational Rate-Independent Crystal Plasticity
,” Computational Materials Science
, Vol. 9
, pp. 168
–176
.35.
Stout, M. G., Kallend, J. S., Kocks, U. F., Przystupa, M. A., and Rollett, A. D., 1988, “Material Dependence of Deformation Texture Development in Various Deformation Modes,” Proc. 8th Int. Conf. On Textures of Materials (ICOTOM 8), J. S. Kallend and G. Gottstein, eds., the Metallurgical Society.
36.
Taylor
G. I.
Elam
C. F.
1925
, “The Plastic Extension and Fracture of Aluminum Crystals
,” Proc. Royal Soc., London
, Vol. A108
, p. 28
28
.37.
Taylor
G. I.
1938
, “Plastic Strain in Metals
,” J. Inst. Metals
, Vol. 62
, p. 307
307
.38.
Teodosiu, C., 1991, Anisotropy and Localization of Plastic Deformation, J. P. Boehler and A. S. Khan, eds., pp. 179–182.
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