Research Papers

Deformation Behavior of Magnesium Extrusions With Strong Basal Texture: Experiments and Modeling

[+] Author and Article Information
Marc-Antoine Chevin

Solid Mechanics Laboratory (CNRS-UMR 7649),
Department of Mechanics, École Polytechnique,
Palaiseau, France;
Impact and Crashworthiness Laboratory,
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139

Lars Greve

Volkswagen AG,
Group Research,
Wolfsburg 38436, Germany

Manuscript received February 6, 2012; final manuscript received January 26, 2013; accepted manuscript posted March 6, 2013; published online August 19, 2013. Assoc. Editor: Vikram Deshpande.

J. Appl. Mech 80(6), 061002 (Aug 19, 2013) (14 pages) Paper No: JAM-12-1053; doi: 10.1115/1.4023958 History: Received February 06, 2012; Revised January 26, 2013; Accepted March 06, 2013

Reverse tension-compression and compression-tension experiments are performed on an extruded AZ31B magnesium sheets using a newly-developed antibuckling device. In addition, combined tension and shear experiments are performed to investigate the material response to multiaxial loading. A constitutive model is proposed which makes use of a single crystal approach to describe the dominant twinning and detwinning response, while a quadratic anisotropic yield function is employed to model the slip-dominated material response. The model accounts for the characteristic tension-compression asymmetry in the hardening mechanisms. Both the convex-up shaped stress-strain response under twinning and concave-down shaped response for slip-dominated behavior are predicted accurately. Furthermore, the effect of latent hardening among slip and twinning systems is taken into account. Due to strong simplifications regarding the kinematics of twinning, the model is computationally efficient and suitable for large scale structural computations.

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Kelley, E. W., and Hosford, W. F., 1968, “The Deformation Characteristics of Textured Magnesium,” Trans. Metall. Soc. AIME, 242(4), pp. 654–661.
Roberts, C. S., 1960, Magnesium and Its Alloys, Wiley, New York.
Jiang, L., Jonas, J. J., Mishra, R. K., Luo, A. A., Sachdev, A. K., and Godet, S., 2007, “Twinning and Texture Development in Two Mg Alloys Subjected to Loading Along Three Different Strain Paths,” Acta Mater., 55(11), pp. 3899–3910. [CrossRef]
Barnett, M. R., 2007a, “Twinning and the Ductility of Magnesium Alloys: Part I: “Tension” Twins,” Mater. Sci. Eng. A, 464(1–2), pp. 1–7. [CrossRef]
Barnett, M. R., 2007b, “Twinning and the Ductility of Magnesium Alloys: Part II. “Contraction” Twins,” Mater. Sci. Eng. A, 464(1–2), pp. 8–16. [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. Plasticity23(1), pp. 44–86. [CrossRef]
Agnew, S. R., 2002, “Plastic Anisotropy of Magnesium Alloy AZ31B Sheet,” Magnesium Technology, H. I.Kaplan, ed., TMS, Warrendale, PA, pp. 169–174.
Agnew, S. R., Tome, C. N., Brown, D. W., Holden, T. M., and Vogel, S. C., 2003, “Study of Slip Mechanisms in a Magnesium Alloy by Neutron Diffraction and Modeling,” Scr. Mater., 48(8), pp. 1003–1008. [CrossRef]
Staroselsky, A., and Anand, L., 2003, “A Constitutive Model for hcp Materials Deforming by Slip and Twinning: Application to Magnesium Alloy AZ31B,” Int. J. Plasticity, 19(10), pp. 1843–1864. [CrossRef]
Styczynski, A., Hartig, C., Bohlen, J., and Letzig, D., 2004, “Cold Rolling Textures in AZ31 Wrought Magnesium Alloy,” Scr. Mater., 50(7), pp. 943–947. [CrossRef]
Chino, Y., Kimura, K., and Mabuchi, M., 2008, “Twinning Behavior and Deformation Mechanisms of Extruded AZ31 Mg Alloy,” Mater. Sci. Eng. A, 486(1–2), pp. 481–488. [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. Plasticity, 25, pp. 861–880. [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. S., 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. Plasticity, 27(5), pp. 688–706. [CrossRef]
Zhang, J. X., Yu, Q., Jiang, Y. Y., and Li, Q., 2011, “An Experimental Study of Cyclic Deformation of Extruded AZ61A Magnesium Alloy,” Int. J. Plasticity, 27(5), pp. 768–787. [CrossRef]
Graff, S., Brocks, W., and Steglich, D., 2007, “Yielding of Magnesium: From Single Crystal to Polycrystalline Aggregates,” Int. J. Plasticity, 23(12), pp. 1957–1978. [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]
Levesque, J., Inal, K., Neale, K. W., and Mishra, R. K., 2010, “Numerical Modeling of Formability of Extruded Magnesium Alloy Tubes,” Int. J. Plasticity, 26(1), pp. 65–83. [CrossRef]
Neil, C. J., and Agnew, S. R., 2009, “Crystal Plasticity-Based Forming Limit Prediction for Non-Cubic Metals: Application to Mg Alloy AZ31B,” Int. J. Plasticity, 25(3), pp. 379–398. [CrossRef]
Wang, H., Wu, P. D., Tome, C. N., and Huang, Y., 2010a, “A Finite Strain Elastic-Viscoplastic Self-Consistent Model for Polycrystalline Materials,” J. Mech. Phys. Solids, 58(4), pp. 594–612. [CrossRef]
Wang, H., Raeisinia, B., Wu, P. D., Agnew, S. R., and Tome, C. N., 2010b, “Evaluation of Self-Consistent Polycrystal Plasticity Models for Magnesium Alloy AZ31B Sheet,” Int. J. Solids Struct., 47(21), pp. 2905–2917. [CrossRef]
Dorum, C., Hopperstad, O. S., Lademo, O. G., and Langseth, M., 2005, “Numerical Modelling of the Structural Behaviour of Thin-Walled Cast Magnesium Components,” Int. J. Solids Struct., 42(7), pp. 2129–2144. [CrossRef]
Dorum, C., Dispinar, D., Hopperstad, O. S., and BerstadT., 2009, “Numerical Modelling of Magnesium Die-Castings Using Stochastic Fracture Parameters,” Eng. Fract. Mech., 76(14), pp. 2232–2248. [CrossRef]
Cazacu, O., and Barlat, F., 2004, “A Criterion for Description of Anisotropy and Yield Differential Effects in Pressure-Insensitive Metals,” Int. J. Plasticity, 20(11), pp. 2027–2045. [CrossRef]
Lee, M. G., Wagoner, R. H., Lee, J. K., Chung, K., and Kim, H. Y., 2008, “Constitutive Modeling for Anisotropic/Asymmetric Hardening Behavior of Magnesium Alloy Sheets,” Int. J. Plasticity, 24(4), pp. 545–582. [CrossRef]
Dafalias, Y. F., and Popov, E. P., 1976, “Plastic Internal Variables Formalism of Cyclic Plasticity,” J. Appl. Mech., 43(4), pp. 645–651. [CrossRef]
Lee, M. G., Kim, S. J., Wagoner, R. H., Chung, K., and Kim, H. Y., 2009, “Constitutive Modeling for Anisotropic/Asymmetric Hardening Behavior of Magnesium Alloy Sheets: Application to Sheet Springback,” Int. J. Plasticity, 25(1), pp. 70–104. [CrossRef]
Li, M., Lou, X. Y., Kim, J. H., and Wagoner, R. H., 2010, “An Efficient Constitutive Model for Room-Temperature, Low-Rate Plasticity of Annealed Mg AZ31B Sheet,” Int. J. Plasticity, 26(6), pp. 820–858. [CrossRef]
Mohr, D., and Oswald, M., 2008, “A New Experimental Technique for the Multi-Axial Testing of Advanced High Strength Steel Sheets,” Exp. Mech., 48(1), pp. 65–77. [CrossRef]
Beese, A. M., and Mohr, D., 2011, “Effect of Stress Triaxiality and Lode Angle on the Kinetics of Strain-Induced Austenite-to-Martensite Transformation,” Acta Mater., 59(7), pp. 2589–2600. [CrossRef]
Chaboche, J. L., 2008, “A Review of Some Plasticity and Viscoplasticity Constitutive Theories,” Int. J. Plasticity, 24(10), pp. 1642–1693. [CrossRef]


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Fig. 4

Results from combined tension and shear experiments: (a) normal and (b) shear stress-strain curves for tensile loading along the extrusion direction (α = 0 deg), (c) normal and (d) shear stress-strain curves for tensile loading along the transverse direction (α = 90 deg)

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Fig. 3

Uniaxial stress-strain curves measured throughout monotonic loading (dashed lines) and reverse loading (solid lines) experiments; this figure must be viewed in color

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Fig. 2

Stress-strain curves for uniaxial tension and uniaxial compression along the extrusion direction (ED) and transverse direction (TD)

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Fig. 1

Selected EBSD pole figures of the polycrystalline Mg AZ31B extrusion (ED = extrusion direction, TD = transverse direction, ND = normal direction)

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Fig. 5

Twinning of a magnesium crystal: (a) regions of different c-axis orientation after twinning, (b) crystal rotation, and (c) shear deformation along twinning plane

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Fig. 6

Visualization of the six twinning conditions in stress space

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Fig. 7

Yield envelopes for a plastic work density of 2 mJ/mm3. The solid dots correspond to experimental data while the solid lines show the corresponding model

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Fig. 8

Visualization of the parameterized functions for (a) the direct twinning resistance sd(γi), (b) the twinning penalty sp(χI), and (c) the latent hardening modulus Ht→s(γtw)

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Fig. 9

Comparison of model predictions (solid black curves) with experiments (dashed blue lines) for uniaxial loading along the extrusion direction

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Fig. 11

Comparison of model predictions (solid black curves) with experiments (dashed blue lines) for combined tension and shear loading for α=0 deg (a)–(b) and for α = 90 deg (c)–(d)

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Fig. 10

Comparison of model predictions (solid black curves) with experiments (dashed blue lines) for uniaxial loading along the transverse direction

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Fig. 12

Evolution of the yield and twinning surfaces for compression followed by tension along (a) the extrusion direction, and (b) the transverse direction



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