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Research Papers

Application of the VPSC Model to the Description of the Stress–Strain Response and Texture Evolution in AZ31 Mg for Various Strain Paths

[+] Author and Article Information
Nitin Chandola

Department of Mechanical and
Aerospace Engineering,
REEF,
University of Florida,
1350 North Poquito Road,
Shalimar, FL 32579

Raja K. Mishra

General Motors Research and
Development Center,
30500 Mound Road,
Warren, MI 40890-9055

Oana Cazacu

Department of Mechanical and
Aerospace Engineering,
REEF,
University of Florida,
1350 North Poquito Road,
Shalimar, FL 32579
e-mail: cazacu@reef.ufl.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received August 8, 2014; final manuscript received June 30, 2015; published online August 6, 2015. Assoc. Editor: Said Ahzi.

J. Eng. Mater. Technol 137(4), 041007 (Aug 06, 2015) (10 pages) Paper No: MATS-14-1161; doi: 10.1115/1.4030999 History: Received August 08, 2014

Accurate description of the mechanical response of AZ31 Mg requires consideration of its strong anisotropy both at the single crystal and polycrystal levels, and its evolution with accumulated plastic deformation. In this paper, a self-consistent mean field crystal plasticity model, viscoplastic self-consistent (VPSC), is used for modeling the room-temperature deformation of AZ31 Mg. A step-by-step procedure to calibrate the material parameters based on simple tensile and compressive mechanical test data is outlined. It is shown that the model predicts with great accuracy both the macroscopic stress–strain response and the evolving texture for these strain paths used for calibration. The stress–strain response and texture evolution for loading paths that were not used for calibration, including off-axis uniaxial loadings and simple shear, are also well described. In particular, VPSC model predicts that for uniaxial tension along the through-thickness direction, the stress–strain curve should have a sigmoidal shape.

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References

Flynn, P. W. , Mote, D. J. , and Dorn, J. E. , 1961, “On the Thermally Activated Mechanism of Prismatic Slip in Magnesium Single Crystals,” Trans. Metall. Soc. AIME, 221(6), pp. 1148–1154.
Reed-Hill, R. E. , and Robertson, W. D. , 1957, “Additional Modes of Deformation Twinning in Magnesium,” Acta Metall., 5(12), pp. 717–727. [CrossRef]
Agnew, S. R. , and Duygulu, O. , 2005, “Plastic Anisotropy and the Role of Non-Basal Slip in Magnesium Alloy AZ31B,” Int. J. Plast., 21(6), pp. 1161–1193. [CrossRef]
Lebensohn, R. A. , and Tomé, C. N. , 1993, “A Self-Consistent Anisotropic Approach for the Simulation of Plastic Deformation and Texture Development of Polycrystals: Application to Zirconium Alloys,” Acta Metall. Mater., 41(9), pp. 2611–2624. [CrossRef]
Jain, A. , and Agnew, S. R. , 2007, “Modeling the Temperature Dependent Effect of Twinning on the Behavior of Magnesium Alloy AZ31B Sheet,” Mater. Sci. Eng.: A, 462(1–2), pp. 29–36. [CrossRef]
Khan, A. , Pandey, A. , Gnaupel-Herold, T. , and Mishra, R. K. , 2011, “Mechanical Response and Texture Evolution of AZ31 Alloy at Large Strains for Different Strain Rates and Temperatures,” Int. J. Plast., 27(5), pp. 688–706. [CrossRef]
Lou, X. Y. , Li, M. , Boger, R. K. , Agnew, S. R. , and Wagoner, R. H. , 2007, “Hardening Evolution of AZ31B Mg Sheet,” Int. J. Plast., 23(1), pp. 44–86. [CrossRef]
Knezevic, M. , Levinson, A. , Harris, R. , Mishra, R. K. , Doherty, R. D. , and Kalidindi, S. R. , 2010, “Deformation Twinning in AZ31: Influence on Strain Hardening and Texture Evolution,” Acta Mater., 58(19), pp. 6230–6242. [CrossRef]
Van Houtte, P. , 1978, “Simulation of the Rolling and Shear Texture of Brass by the Taylor Theory Adapted for Mechanical Twinning,” Acta Metall., 26(4), pp. 591–604. [CrossRef]
Tomé, C. N. , Lebensohn, R. , and Kocks, U. F. , 1991, “A Model for Texture Development Dominated by Deformation Twinning: Application to Zirconium Alloys,” Acta Metall. Mater., 39(11), pp. 2667–2680. [CrossRef]
Proust, G. , Tomé, C. N. , Jain, A. , and Agnew, S. R. , 2009, “Modeling the Effect of Twinning and Detwinning During Strain-Path Changes of Magnesium Alloy AZ31,” Int. J. Plast., 25(5), pp. 861–880. [CrossRef]
Wang, H. , Wu, P. D. , Wang, J. , and Tomé, C. N. , 2013, “A Crystal Plasticity Model for Hexagonal Close Packed (HCP) Crystals Including Twinning and De-Twinning Mechanisms,” Int. J. Plast., 49, pp. 36–52. [CrossRef]
Taylor, G. I. , 1938, “Plastic Strain in Metals,” J. Inst. Met., 62, pp. 307–324.
Taylor, G. I. , 1938, “Analysis of Plastic Strain in a Cubic Crystal,” Stephen Timoshenko 60th Anniversary Volume, Macmillan, New York, pp. 218–224.
Wang, H. , Wu, P. D. , Tomé, C. N. , and Huang, Y. , 2010, “A Finite Strain Elastic–Viscoplastic Self-Consistent Model for Polycrystalline Materials,” J. Mech. Phys. Solids, 58(4), pp. 594–612. [CrossRef]
Walde, T. , and Riedel, H. , 2007, “Simulation of Earing During Deep Drawing of Magnesium Alloy AZ31,” Acta Mater., 55(3), pp. 867–874. [CrossRef]
Choi, S. H. , Kim, D. H. , and Seong, B. S. , 2009, “Simulation of Strain-Softening Behaviors in an AZ31 Mg Alloy Showing Distinct Twin-Induced Reorientation Before a Peak Stress,” Met. Mater. Int., 15(2), pp. 239–248. [CrossRef]
Wang, H. , Raeisinia, B. , Wu, P. D. , Agnew, S. R. , and Tomé, C. N. , 2010, “Evaluation of Self-Consistent Polycrystal Plasticity Models for Magnesium Alloy AZ31B Sheet,” Int. J. Solids Struct., 47(21), pp. 2905–2917. [CrossRef]
Tomé, C. N. , and Lebensohn, R. A. , 2009, “Manual for Code Visco-Plastic Self-Consistent,” Ver. 7c, Los Alamos National Laboratory, Los Alamos, NM,
Beyerlein, I. J. , and Tomé, C. N. , 2008, “A Dislocation-Based Constitutive Law for Pure Zr Including Temperature Effects,” Int. J. Plast., 24(5), pp. 867–896. [CrossRef]
Guo, X. Q. , Wu, W. , Wu, P. D. , Qiao, H. , An, K. , and Liaw, P. K. , 2013, “On the Swift Effect and Twinning in a Rolled Magnesium Alloy Under Free-End Torsion,” Scr. Mater., 69(4), pp. 319–322. [CrossRef]
Barlat, F. , Yoon, J. W. , and Cazacu, O. , 2007, “On Linear Transformations of Stress Tensors for the Description of Plastic Anisotropy,” Int. J. Plast., 23(5), pp. 876–896. [CrossRef]
Cazacu, O. , Plunkett, B. , and Barlat, F. , 2006, “Orthotropic Yield Criterion for Hexagonal Closed Packed Metals,” Int. J. Plast., 22(7), pp. 1171–1194. [CrossRef]
Hill, R. , 1950, The Mathematical Theory of Plasticity, Oxford University Press, Oxford, UK.
Nixon, M. E. , Cazacu, O. , and Lebensohn, R. A. , 2010, “Anisotropic Response of High-Purity α-Titanium: Experimental Characterization and Constitutive Modeling,” Int. J. Plast., 26(4), pp. 510–532. [CrossRef]
Agnew, S. R. , Mehrotra, P. , Lillo, T. M. , Stoica, G. M. , and Liaw, P. K. , 2005, “Texture Evolution of Five Wrought Magnesium Alloys During Route A Equal Channel Angular Extrusion: Experiments and Simulations,” Acta Mater., 53(11), pp. 3135–3146. [CrossRef]
Beausir, B. , Toth, L. S. , Qods, F. , and Neale, K. W. , 2009, “Texture and Mechanical Behavior of Magnesium During Free-End Torsion,” ASME J. Eng. Mater. Technol., 131(1), p. 011108.

Figures

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Fig. 1

Pole figures showing initial texture of AZ31 Mg sheet (a) reported by Khan et al. [6] and (b) measured from a large EBSD scan and used as input in the polycrystal model

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Fig. 2

Comparison between the measured texture and predicted texture: (a) uniaxial tension along RD at 13% strain (∼ failure); (b) uniaxial compression along RD at 8% strain; and (c) ND compression (no measured texture available)

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Fig. 3

Deformation response in RD tension: (a) stress–strain response and evolution of the microstructure according to calibrated VPSC model (line) in comparison with mechanical test data (symbol) and (b) relative activities of each deformation mode

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Fig. 4

Deformation response in RD compression: (a) stress–strain response and evolution of the microstructure according to calibrated VPSC model (line) in comparison with mechanical test data (symbol); (b) relative activities of each deformation mode; and (c) predicted twin volume fraction evolution

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Fig. 5

Deformation response in ND compression: (a) evolution of microstructure according to the calibrated VPSC (line) model and (b) relative activities of each deformation mode

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Fig. 6

Deformation response in TD tension: (a) stress–strain response and evolution of the microstructure according to the VPSC model (line) in comparison with mechanical test data (symbol) and (b) relative activities of each deformation mode

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Fig. 7

Deformation response in TD compression: (a) stress–strain response and evolution of the microstructure according to calibrated VPSC model (line) in comparison with mechanical test data (symbol), (b) relative activities of each deformation mode, and (c) predicted twin volume fraction evolution

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Fig. 8

Deformation response in DD tension: (a) stress–strain response and evolution of the microstructure according to the VPSC model (line) in comparison with mechanical test data (symbol) and (b) relative activities of each deformation mode

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Fig. 9

Deformation response in DD compression: (a) stress–strain response and evolution of the microstructure according to the VPSC model (line) in comparison with mechanical test data (symbol), (b) relative activities of each deformation mode, and (c) predicted twin volume fraction evolution

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Fig. 10

Deformation response in ND tension: (a) evolution of microstructure predicted by the VPSC model (line), (b) predicted relative activities of each deformation mode, and (c) predicted twin volume fraction evolution

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Fig. 11

Element subjected to a simple shear deformation γ in the plane (x–y), x being along RD and y along TD

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Fig. 12

Deformation response in RD shear: (a) stress–strain response and evolution of the microstructure according to the VPSC model (line) in comparison with mechanical test data (symbol), (b) relative activities of each deformation mode, and (c) predicted twin volume fraction evolution and experimentally observed value (x)

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Fig. 13

Pole figures in RD shear test at a von Mises equivalent strain γ/√3 = 20% (a) measured by Khan et al. [6] and (b) obtained with VPSC model

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