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.

References

1.
Kelley
,
E. W.
, and
Hosford
,
W. F.
,
1968
, “
The Deformation Characteristics of Textured Magnesium
,”
Trans. Metall. Soc. AIME
,
242
(
4
), pp.
654
661
.
2.
Roberts
,
C. S.
,
1960
,
Magnesium and Its Alloys
,
Wiley
,
New York
.
3.
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
.10.1016/j.actamat.2007.03.006
4.
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
.10.1016/j.msea.2006.12.037
5.
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
.10.1016/j.msea.2007.02.109
6.
Lou
,
X. Y.
,
Li
,
M.
,
Boger
,
R. K.
,
Agnew
,
S. R.
, and
Wagoner
,
R. H.
,
2007
, “
Hardening Evolution of AZ31B Mg Sheet
,”
Int. J. Plasticity
23
(
1
), pp.
44
86
.10.1016/j.ijplas.2006.03.005
7.
Agnew
,
S. R.
,
2002
, “
Plastic Anisotropy of Magnesium Alloy AZ31B Sheet
,”
Magnesium Technology
,
H. I.
Kaplan
, ed., TMS, Warrendale, PA, pp.
169
174
.
8.
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
.10.1016/S1359-6462(02)00591-2
9.
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
.10.1016/S0749-6419(03)00039-1
10.
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
.10.1016/j.scriptamat.2004.01.010
11.
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
.10.1016/j.msea.2007.09.058
12.
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
.10.1016/j.ijplas.2008.05.005
13.
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
.10.1016/j.msea.2006.03.160
14.
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
.10.1016/j.ijplas.2010.08.009
15.
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
.10.1016/j.ijplas.2010.09.004
16.
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
.10.1016/j.ijplas.2007.07.009
17.
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
.10.1016/0956-7151(93)90130-K
18.
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
.10.1016/j.ijplas.2009.05.001
19.
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
.10.1016/j.ijplas.2008.05.003
20.
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
.10.1016/j.jmps.2010.01.004
21.
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
.10.1016/j.ijsolstr.2010.06.016
22.
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
.10.1016/j.ijsolstr.2004.08.019
23.
Dorum
,
C.
,
Dispinar
,
D.
,
Hopperstad
,
O. S.
, and
Berstad
T.
,
2009
, “
Numerical Modelling of Magnesium Die-Castings Using Stochastic Fracture Parameters
,”
Eng. Fract. Mech.
,
76
(
14
), pp.
2232
2248
.10.1016/j.engfracmech.2009.07.001
24.
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
.10.1016/j.ijplas.2003.11.021
25.
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
.10.1016/j.ijplas.2007.05.004
26.
Dafalias
,
Y. F.
, and
Popov
,
E. P.
,
1976
, “
Plastic Internal Variables Formalism of Cyclic Plasticity
,”
J. Appl. Mech.
,
43
(
4
), pp.
645
651
.10.1115/1.3423948
27.
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
.10.1016/j.ijplas.2007.12.003
28.
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
.10.1016/j.ijplas.2009.11.001
29.
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
.10.1007/s11340-007-9053-9
30.
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
.10.1016/j.actamat.2010.12.040
31.
Chaboche
,
J. L.
,
2008
, “
A Review of Some Plasticity and Viscoplasticity Constitutive Theories
,”
Int. J. Plasticity
,
24
(
10
), pp.
1642
1693
.10.1016/j.ijplas.2008.03.009
You do not currently have access to this content.