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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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Figures

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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. 2

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

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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. 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. 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. 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. 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. 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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