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TECHNICAL PAPERS

Modeling the Rotation of Orthotropic Axes of Sheet Metals Subjected to Off-Axis Uniaxial Tension

[+] Author and Article Information
Wei Tong, Hong Tao, Xiquan Jiang

Department of Mechanical Engineering, Yale University, 219 Becton Center, New Haven, CT 06520-8284

J. Appl. Mech 71(4), 521-531 (Sep 07, 2004) (11 pages) doi:10.1115/1.1755694 History: Received February 28, 2003; Revised September 03, 2003; Online September 07, 2004
Copyright © 2004 by ASME
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References

Hill, R., 1950, The Mathematical Theory of Plasticity, Clarendon Press, Oxford, UK.
Prager,  W., 1955, “The Theory of Plasticity: A Survey of Recent Achievements,” Proc. Inst. Electr. Eng., 169, pp. 41–57.
Eisenberg,  M. A., and Yen,  C. F., 1981, “A Theory of Multiaxial Anisotropic Viscoplasticity,” ASME J. Appl. Mech., 48, pp. 276–284.
McDowell,  D. L., 1987, “An Evaluation of Recent Developments in Hardening and Flow Rules for Rate-Independent, Non-Proportional Cyclic Plasticity,” ASME J. Appl. Mech., 54(2), pp. 323–334.
Hill,  R., 1948, “A Theory of the Yielding and Plastic Flow of Anisotropic Metals,” Proc. R. Soc. London, Ser. A, 193, pp. 281–297.
Hill,  R., 1979, “Theoretical Plasticity of Textured Aggregates,” Math. Proc. Cambridge Philos. Soc., 85, pp. 179–191.
Karafillis,  A. P., and Boyce,  M. C., 1993, “A General Anisotropic Yield Criterion Using Bounds and a Transformation Weighting Tensor,” J. Mech. Phys. Solids, 41, pp. 1859–1886.
Wu,  H. C., Hong,  H. K., and Shiao,  Y. P., 1999, “Anisotropic Plasticity With Application to Sheet Metals,” Int. J. Mech. Sci., 41, pp. 703–724.
Dawson,  P., and Marin,  E. B., 1998, “Computational Mechanics for Metal Deformation Process Using Polycrystal Plasticity,” Adv. Appl. Mech., 34, pp. 77–169.
Boehler, J. P., and Koss, S., 1991, “Evolution of Anisotropy in Sheet-Steels Subjected to Off-Axes Large Deformation,” Advances in Continuum Mechanics, O. Bruller, V. Mannl, and J. Najar, eds., Springer, Berlin, pp. 143–158.
Kim,  K. H., and Yin,  J. J., 1997, “Evolution of Anisotropy Under Plane Stress,” J. Mech. Phys. Solids, 45(5), pp. 841–851.
Bunge,  H. J., and Nielsen,  I., 1997, “Experimental Determination of Plastic Spin in Polycrystalline Materials,” Int. J. Plast., 13(5), pp. 435–446.
Mandel, J., 1974, “Thermodynamics and Plasticity,” Foundations of Continuum Thermodynamics. J. J. Delgado et al., eds., MacMillan, New York.
Loret,  B., 1983, “On the Effects of Plastic Rotation in the Finite Deformation of Anisotropic Elastoplastic Materials,” Mech. Mater., 2, pp. 287–304.
Dafalias,  Y. F., 1984, “The Plastic Spin Concept and a Simple Illustration of Its Role in Finite Plastic Transformations,” Mech. Mater., 3, pp. 223–233.
Onat, E. T., 1984, “Shear Flow of Kinematically Hardening Rigid-Plastic Materials,” Mechanics of Material Behavior, G. J. Dvorak and R. T. Shield, eds., Elsevier, New York, pp. 311–324.
Dafalias,  Y. F., 1985, “The Plastic Spin,” ASME J. Appl. Mech., 52, pp. 865–871.
Dafalias,  Y. F., and Rashid,  M. M., 1989, “The Effect of Plastic Spin on Anisotropic Material Behavior,” Int. J. Plast., 5, pp. 227–246.
Dafalias,  Y. F., and Aifantis,  E. C., 1990, “On the Microscopic Origin of the Plastic Spin,” Acta Mech., 82, pp. 31–48.
Aravas,  E. C., and Aifantis,  E. C., 1991, “On the Geometry of Slip and Spin in Finite Plastic Deformation,” Int. J. Plast., 7, pp. 141–160.
van der Giessen,  E., 1992, “A 2D Analytical Multiple Slip Model for Continuum Texture Development and Plastic Spin,” Mech. Mater., 13, pp. 93–115.
Prantil,  V. C., Jenkins,  J. T., and Dawson,  P. R., 1993, “An Analysis of Texture and Plastic Spin for Planar Polycrystals,” J. Mech. Phys. Solids, 41(8), pp. 1357–1382.
Dafalias,  Y. F., 1993, “On Multiple Spins and Texture Development. Case Study: Kinematic and Orthotropic Hardening,” Acta Mech., 100, pp. 171–194.
Lubarda,  V. A., and Shih,  C. F., 1994, “Plastic Spin and Related Issues in Phenomenological Plasticity,” ASME J. Appl. Mech., 61, pp. 524–529.
Schieck,  B., and Stumpf,  H., 1995, “The Appropriate Corotational Rate, Exact Formula for the Plastic Spin and Constitutive Model for Finite Elastoplasticity,” Int. J. Solids Struct., 32(24), pp. 3643–3667.
Kuroda,  M., 1997, “Interpretation of the Behavior of Metals Under Large Plastic Shear Deformations: A Macroscopic Approach,” Int. J. Plast., 13, pp. 359–383.
Levitas,  V. I., 1998, “A New Look at the Problem of Plastic Spin Based on Stability Analysis,” J. Mech. Phys. Solids, 46(3), pp. 557–590.
Dafalias,  Y. F., 2000, “Orientational Evolution of Plastic Orthotropy in Sheet Metals,” J. Mech. Phys. Solids, 48, pp. 2231–2255.
Sidoroff,  F., and Dogui,  A., 2001, “Some Issues About Anisotropic Elastic-Plastic Models at Finite Strain,” Int. J. Solids Struct., 38, pp. 9569–9578.
Kuroda,  M., and Tvergaard,  V., 2001, “Plastic Spin Associated With a Non-Normality Theory of Plasticity,” Eur. J. Mech. A/Solids, 20, pp. 893–905.
Lee,  E. H., 1969, “Elastic-Plastic Deformations at Finite Strains,” ASME J. Appl. Mech., 36, pp. 1–6.
Rice,  J. R., 1970, “On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals,” ASME J. Appl. Mech., 37, pp. 728–737.
Rice,  J. R., 1971, “Inelastic Constitutive Relations for Solids: An Internal-Variable Theory and Its Application to Metal Plasticity,” J. Mech. Phys. Solids, 19, pp. 433–455.
Rogers, T. G., 1990, “Yield Criteria, Flow Rules, and Hardening in Anisotropic Plasticity,” Yielding, Damage, and Failure of Anisotropic Solids, J. P. Boehler, ed., Mechanical Engineering Publications Limited, London, pp. 53–79.
Tong,  W., 2002, “A Planar Plastic Flow Theory of Orthotropic Sheets and the Experimental Procedure for Its Evaluations,” Proc. R. Soc. London, Ser. A, submitted for publication.
Tong,  W., 2002, “A Plane Stress Anisotropic Plastic Flow Theory for Orthotropic Aluminum Sheet Metals,” Int. J. Plast., accepted for publication.
Tong,  W., 2003, “A Planar Plastic Flow Theory for Monoclinic Sheet Metals,” Int. J. Mech. Sci., submitted for publication.
Tong, W., Zhang, N., and Xie, C., 2003, “Modeling of the Anisotropic Plastic Flows of Automotive Sheet Metals,” Aluminum 2003, S. K. Das, ed., The Minerals, Metals & Materials Society, to appear.
Tong,  W., Xie,  C., and Zhang,  N., 2003, “Micromechanical and Macroscopic Modeling of Anisotropic Plastic Flows of Textured Polycrystalline Sheets,” Modell. Simul. Mater. Sci. Eng., submitted for publication.
Tong,  W., Xie,  C., and Zhang,  N., 2003, “Modeling the Anisotropic Plastic Flow of Textured Polycrystalline Sheets Using the Generalized Hill’s 1979 Non-Quadratic Flow Potential,” Int. J. Plast., submitted for publication.
Hill,  R., 1980, “Basic Stress Analysis of Hyperbolic Regimes in Plastic Media,” Math. Proc. Cambridge Philos. Soc., 88, pp. 359–369.
Hill,  R., 1990, “Constitutive Modeling of Orthotropic Plasticity in Sheet Metals,” J. Mech. Phys. Solids, 38, pp. 405–417.
Truong Qui,  H. P., and Lippmann,  H., 2001, “Plastic Spin and Evolution of an Anisotropic Yield Condition,” Int. J. Mech. Sci., 43, pp. 1969–1983.
Truong Qui,  H. P., and Lippmann,  H., 2001, “On the Impact of Local Rotation on the Evolution of an Anisotropic Plastic Yield Condition,” J. Mech. Phys. Solids, 49, pp. 2577–2591.
Losilla,  G., Boehler,  J. P., and Zheng,  Q. S., 2000, “A Generally Anisotropic Hardening Model for Big Offset-Strain Yield Stresses,” Acta Mech., 144, pp. 169–183.
McDowell, D. L., Miller, M. P., and Bammann, D. J., 1993, “Some Additional Considerations for Coupling of Material and Geometric Nonlinearities for Polycrystalline Metals,” Large Plastic Deformations: Fundamental Aspects and Applications to Metal Forming (MECAMAT’91), C. Teodosiu, J. L. Raphanel, and F. Sidoroff, eds., Balkema, Rotterdam, pp. 319–327.
Stoughton,  T. B., 2002, “A Non-Associated Flow Rule for Sheet Metal Forming,” Int. J. Plast., 18, pp. 687–714.
Dafalias,  Y. F., 1998, “The Plastic Spin: Necessity or Redundancy?” Int. J. Plast., 14, pp. 909–931.
Asaro,  R. J., 1983, “Micromechanics of Crystals and Polycrystals,” Advances in Mechanics,23, p. 1.
Bassani,  J. L., 1994, “Plastic Flow of Crystals,” Advances in Appl. Mech.,30, pp. 191–258.
Hutchinson,  J. W., 1976, “Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials,” Proc. R. Soc. London, Ser. A, 348, pp. 101–127.
Asaro,  R. J., and Needleman,  A., 1985, “Texture Development and Strain Hardening in Rate-Dependent Polycrystals,” Acta Metall., 33(6), pp. 923–953.
Gambin,  W., 1992, “Refined Analysis of Elastic-Plastic Crystals,” Int. J. Solids Struct., 29(16), pp. 2013–2021.
Darrieulat,  M., and Piot,  D., 1996, “A Method of Generating Analytical Yield Surfaces of Polycrystalline Materials,” Int. J. Plast., 12(5), pp. 575–610.

Figures

Grahic Jump Location
Definitions of the three Cartesian coordinate systems for a monoclinic sheet metal: (a) the principal axes of stress (σ123); (b) the principal axes of the current material texture frame XYZ; and (c) the sheet material coordinate system X0Y0Z0. The principal axis of σ3 always coincides with Z0-axis and Z-axis to ensure the planar plastic flow of the sheet metal. The in-plane axes X and Y of the texture frame are defined to be the principal straining directions of the sheet metal under equal biaxial tension (σ123=0). The material coordinate system X0Y0Z0 undergoes the same rigid body rotation as the sheet metal itself and it may be chosen to coincide with the initial texture frame of the sheet metal (the initial texture frame of an orthotropic sheet metal is defined by its rolling (RD), transverse (TD), and normal (ND) directions). The loading orientation angle θ is defined as the angle between the principal axis of σ1 and the X-axis of the material texture frame. The relative rotation ω12 of the texture frame with respect to the material coordinate system of the sheet metal is due to the macroscopic plastic spin ω̇12,28.
Grahic Jump Location
The amount of rotation ω12 of the material texture frame due to plastic spin at a fixed uniaxial plastic strain ε1 of 20% as a function of the initial loading orientation angle θ0 with three different k values according to Eq. (13b) (D=1 is used for all data points)
Grahic Jump Location
The current loading orientation angle θ and the amount of rotation ω12 of the material texture frame due to plastic spin as a function of uniaxial plastic strain ε1 with three different initial loading orientation angles θ0 and three different k values according to Eq. (13) (kD=10 is used for all data points)
Grahic Jump Location
Comparison of the model description (solid and dashed lines) and the experimental data (filled symbols) of a steel sheet reported by Boehler and Koss 10 and Losilla et al. 45 on the rotation ω12 of the material texture frame due to plastic spin as a function of uniaxial plastic strain ε1 with different initial loading orientation angles θ0=30deg, 45 deg, and 60 deg. The solid lines are given by Eq. (14) with d1=7,d2=10 and d3=−3 (all other coefficients are zero). The dashed lines are given by Eq. (13b) with k=2 and D=9 (the initial loading orientation angles of 30 deg, 46 deg, and 60 deg were used).
Grahic Jump Location
Comparison of the model description (solid and dashed lines) and the experimental data (filled symbols) of a steel sheet reported by Kim and Yin 11 on the rotation ω12 of the material texture frame due to plastic spin as a function of uniaxial plastic strain ε1 with different initial loading orientation angles θ0=30deg, 45 deg, and 60 deg. The solid lines are given by Eq. (14) with d1=−8,d2=17 and d3=3 (all other coefficients are zero). The dashed lines are given by Eq. (13b) with k=2 and D=12.5 (the initial loading orientation angles of 30 deg, 46 deg, and 60 deg were used).
Grahic Jump Location
Comparison of the model description (solid and dashed lines) and the experimental data (filled symbols) of an aluminum sheet reported by Bunge and Nielsen 12 on the amount of rotation ω12 of the material texture frame due to plastic spin at a fixed uniaxial plastic strain ε1 of 20% with 11 different initial loading orientation angles θ0. The solid line is given by Eq. (13b) with k=2 and D=0.45.

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