Representing the Effect of Crystallographic Texture on the Anisotropic Performance Behavior of Rolled Aluminum Plate

[+] Author and Article Information
M. P. Miller, N. R. Barton

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853

J. Eng. Mater. Technol 122(1), 10-17 (Jun 15, 1999) (8 pages) doi:10.1115/1.482759 History: Received February 22, 1999; Revised June 15, 1999
Copyright © 2000 by ASME
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Juul Jensen,  D., and Hansen,  N., 1990, “Flow Stress Anisotropy in Aluminum,” Acta Metall. Mater., 38, No. 8, pp. 1369–1380.
Hansen,  N., and Juul Jensen,  J., 1992, “Flow Stress Anisotropy Caused by Geometrically Necessary Boundaries,” Acta Metall. Mater., 40, pp. 3265–3275.
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.
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.
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.
Hatch, J. E. (ed.), 1984, Aluminum: Properties and Physical Metallurgy, American Society for Metals, Metals Park, pp. 376–377.
Hill,  R., 1948, “A Theory of the Yield and Plastic Flow of Anisotropic Metals,” Proc. R. Soc. London, Ser. A, 193, pp. 281–297.
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.
Harvey, S. J., 1985, “The Use of Anisotropic Yield Surfaces in Cyclic Plasticity,” Multiaxial Fatigue, ASTM STP 853, ASTM, Philadelphia, PA, pp. 49–53.
Barlat,  F., 1987, “Crystallographic Texture, Anisotropic Yield Surfaces and Forming Limits of Sheet Metals,” Mater. Sci. Eng., 91, pp. 55–72.
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.
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.
Sachs,  G., 1928, “Zur Ableitung Einer Fliessbedingung,” A. Ver. dt. Ing., 12, pp. 134–136.
Taylor,  G. I., 1938, “Plastic Strain in Metals,” J. Inst. Met., 62, pp. 307–324.
Iwakuma,  T., and Nemat-Nasser,  S., 1984, “Finite Elastic-Plastic Deformation of Polycrystalline Metals,” Proc. R. Soc. London, Ser. A, 394, pp. 87–119.
Asaro,  R. J., and Needleman,  A., 1985, “Texture Development and Strain Hardening in Rate Dependent Polycrystals,” Acta Metall., 33, pp. 923–953.
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.
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.
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.
Lipinski,  P., and Berveiller,  M., 1989, “Elastoplasticity of Micro-Inhomogeneous Metals at Large Strain,” Int. J. Plast., 5, pp. 149–172.
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.
Cailletaud,  G., 1992, “a Micromechanical Approach to Inelastic Behavior of Metals,” Int. J. Plast., 8, pp. 55–73.
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.
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.
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.
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.
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.
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.
Havliček,  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.
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.
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.
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.
Mika,  D. P., and Dawson,  P. R., 1998, “Effects of Grain Interaction on Deformation in Polycrystals,” Mater. Sci. Eng., A, 257, pp. 62–76.
Mika, D. P., and Dawson, P. R., 1999, “Polycrystal Plasticity Modeling of Intracrystalline Boundary Textures,” Acta Mater (in press).
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.
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.
Hutchinson,  J. W., 1964, “Plastic Deformation of BCC Polycrystals,” J. Mech. Phys. Solids, 12, pp. 25–33.
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.
Kallend,  J. S., Kocks,  U. F., Rollett,  A. D., and Wend,  H., 1991, “Operational Texture Analysis,” Mater. Sci. Eng., A, 132, pp. 1–11.
Frank,  F. C., 1988, “Orientation Mapping,” Metall. Trans. A, 19A, pp. 403–408.
Becker,  S., and Panchanadeeswaran,  S., 1989, “Crystal Rotations Represented as Rodriguez Vectors,” Textures Microstruct., 10, pp. 167–194.
Mitchell, M. R., 1978, “Fundamentals of Modern Fatigue Analysis for Design,” Fatigue Microstructure, pp. 385–438.
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.
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.
Kocks, U. F., Tome, C. N., and Wenk, H.-R., 1998, Texture and Anisotropy. Cambridge University Press, Cambridge, p. 365 ff.
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.
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.
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.
Miller, M. P., and Turner, T. J., 1999, “Quantification and Representation of Crystallographic Texture Fields in Processed Alloys,” Int. J. Plast. (accepted).


Grahic Jump Location
The slopes of the stress-strain curve, Θ, predicted by the finite element model employing cubic elements. Also shown are the RD, TD and ϕ=45° data.
Grahic Jump Location
The slopes of the stress-strain curve, ϴ, predicted by the lower bound model. Also shown are the RD, TD and ϕ=45° data.
Grahic Jump Location
The slopes of the stress-strain curve, ϴ, predicted by the upper bound model. Also shown are the RD, TD and ϕ=45° data.
Grahic Jump Location
The finite element simulations of the RD and TD experiments employing initial element aspect ratios of RD:TD:ND=1:1:1 (cube) and RD:TD:ND=16:4:1
Grahic Jump Location
The simulations of the tensile experiments using the finite element formulation. Also depicted are the RD, TD, and ϕ=45° data along with the simulation of the TD experiment with slip system hardening neglected (ġ=0 in Eq. (3)).
Grahic Jump Location
The simulations of the tensile experiments using the lower bound linking assumption. Also depicted are the RD, TD, and ϕ=45° data, along with the simulation of the TD experiment with slip system hardening neglected (ġ=0 in Eq. (3)).
Grahic Jump Location
The simulations of the tensile experiments using the upper bound linking assumption. Also depicted are the HD, TD, and ϕ=45° data, along with a simulation of the TD experiment with the slip system hardening neglected (ġ=0 in Eq. (3)).
Grahic Jump Location
The stress amplitude, σa versus the strain amplitude, εa, for the cyclic experiments conducted on the 7075 plate
Grahic Jump Location
The hysteresis loops for the first 5 cycles of the fully reversed cyclic experiment conducted on the 7075 plate in the rolling direction at a εa=0.01
Grahic Jump Location
The slopes of the stress-strain data, ϴ, in the transition region
Grahic Jump Location
(a) The stress strain data from the tensile tests conducted on the 7075 plate. The angle, ϕ, is the angle between the specimen axis and the rolling direction. (b) A close-up of data focusing on the elastic/elastic-plastic transition.
Grahic Jump Location
The ODF at the 12 plane of the 7075 plate depicted on slices through the fundamental region of orientation space parameterized with the Rodrigues vector defined in Eq. (1). The slices were taken normal to the plate normal direction. An ODF value of 2.42 corresponds to a random texture.



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