In this paper, a finite element model is developed for 3000 series clad aluminum alloy brazing sheet to account for temperature and strain rate dependency, as well as plastic anisotropy. The current work considers a novel implementation of the Barlat YLD2000 yield surface in conjunction with the Bergstrom hardening model to accurately model aluminum alloy sheet during warm forming. The Barlat YLD2000 yield criterion is used to capture the anisotropy while the Bergstrom hardening rule predicts the temperature and strain rate dependency. The results are compared with those obtained from experiments. The measured stress–strain curves of the AA3003 aluminum alloy sheet at elevated temperatures and different strain rates are used to fit the Bergstrom parameters and measured R-values and directional yield stresses are used to fit the yield function parameters. Isothermal uniaxial tensile tests and nonisothermal deep drawing experiments are performed and the predicted response using the new constitutive model is compared with measured data. In simulations of tensile tests, the material behavior is predicted accurately by the numerical models. Also, the nonisothermal deep drawing simulations are able to predict the load–displacement response and strain distributions accurately.

References

1.
Kaya
,
S.
,
Spampinato
,
G.
, and
Altan
,
T.
,
2008
, “
An Experimental Study on Non-Isothermal Deep Drawing Process Using Aluminum and Magnesium Alloys
,”
ASME J. Manuf. Sci. Eng.
,
130
, p.
061001
.10.1115/1.2975228
2.
Tebbe
,
P. A.
, and
Kridli
,
G. T.
,
2004
, “
Warm Forming of Aluminum Alloys: An Overview and Future Directions
,”
Int. J. Mater. Prod. Technol.
,
21
, pp.
24
40
.10.1504/IJMPT.2004.004737
3.
Shehata
,
F.
,
Painter
,
M. J.
, and
Pearce
,
R.
,
1978
, “
Warm Forming of Aluminum/Magnesium Alloy Sheet
,”
J. Mech. Work. Technol.
,
2
, pp.
279
291
.10.1016/0378-3804(78)90023-2
4.
Wilson
,
D. V.
,
1988
, “
Aluminum Versus Steel in the Family Car-The Formability Factor
,”
J. Mech. Work. Technol.
,
16
, pp.
257
277
.10.1016/0378-3804(88)90055-1
5.
Schmoeckel
,
D.
,
Liebler
,
B. C.
, and
Speck
,
F. D.
,
1995
, “
Grundlagen und modellversuche-temperaturgefu hrterstofffluß beim tiefziehen von Al-blech-realversuche
,”
Bander Bleche Rohre
,
36
, spp.
14
21
.
6.
Li
,
D.
, and
Ghosh
,
A.
,
2003
, “
Tensile Deformation Behavior of Aluminum Alloys at Warm Forming Temperatures
,”
Mater. Sci. Eng., A
,
352
, pp.
279
286
.10.1016/S0921-5093(02)00915-2
7.
Van den Boogaard
,
A. H.
, and
Huetink
,
J.
,
2006
, “
Simulation of Aluminum Sheet Forming at Elevated Temperatures
,”
Comput. Methods Appl. Mech. Eng.
,
195
, pp.
6691
6709
.10.1016/j.cma.2005.05.054
8.
Mckinley
,
J.
,
Abedrabbo
,
N.
,
Worswick
,
M. J.
, and
Kozards
,
M.
,
2008
, “
Effect of Independent Die and Punch Temperature Control on the Formability of 3003 Aluminum Alloy in Warm Deep Drawing
,”
Proceedings of the 7th International Conference
, Numisheet, Interlaken, Switzerland.
9.
Kim
,
H. S.
,
Koç
,
M.
,
Ni
,
J.
, and
Ghosh
,
A.
,
2006
, “
Finite Element Modeling and Analysis of Warm Forming of Aluminum Alloys-Validation Through Comparisons With Experiments and Determination of a Failure Criterion
,”
ASME J. Manuf. Sci. Eng.
,
128
, pp.
613
621
.10.1115/1.2194065
10.
Tugcu
,
P.
,
Wu
,
P. D.
, and
Neale
,
K. W.
,
2002
, “
On the Predictive Capabilities of Anisotropic Yield Criteria for Metals Undergoing Shearing Deformations
,”
Int. J. Plast.
,
18
, pp.
1219
1236
.10.1016/S0749-6419(01)00068-7
11.
Paquet
,
D.
,
Dondeti
,
P.
, and
Gosh
,
S.
,
2011
, “
Dual-Stage Nested Homogenization for Rate-Dependant Anisotropic Elasto-Plasticity Model of Dendritic Cast Aluminum Alloys
,”
Int. J. Plast.
,
27
, pp.
1677
1701
.10.1016/j.ijplas.2011.02.002
12.
Desmorat
,
R.
, and
Marukk
,
R.
,
2011
, “
Non-Quadratic Kelvin Modes Based Plasticity for Anisotropic Materials
,”
Int. J. Plast.
,
27
, pp.
328
351
.10.1016/j.ijplas.2010.06.003
13.
Thomson
,
W. K.
, (Lord Kelvin),
1856
, “
Elements of a Mathematical Theory of Elasticity
,”
Philos. Trans. R. Soc. London
,
166
, pp.
481
498
.
14.
Segurado
,
J.
,
Lebensohn
,
R. A.
,
Lorca
,
J.
, and
Tome
,
C. N.
,
2012
, “
Multiscale Modeling of Plasticity Based on Embedding the Viscoplastic Self-Consistent Formulation in Implicit Finite Elements
,”
Int. J. Plast.
,
28
, pp.
124
140
.10.1016/j.ijplas.2011.07.002
15.
Fourmeau
,
M.
,
Borvki
,
T.
,
Benallal
,
A.
,
Lademo
,
O. G.
, and
Hopperstad
,
O. S.
,
2011
, “
On the Plastic Anisotropy of an Aluminum Alloy and Its Influence on Constrained Multiaxial Flow
,”
Int. J. Plast.
,
27
, pp.
2005
2025
.10.1016/j.ijplas.2011.05.017
16.
Barlat
,
F.
,
Aretz
,
H.
,
Yoon
,
J. W.
,
Karabin
,
M. E.
,
Brem
,
J. C.
, and
Dick
,
R. E.
,
2005
, “
Linear Transformation-Based Anisotropic Yield Functions
,”
Int. J. Plast.
,
21
, pp.
1009
1039
.10.1016/j.ijplas.2004.06.004
17.
Yoon
,
J. W.
,
Dick
,
R. E.
, and
Barlat
,
F.
,
2011
, “
A New Analytical Theory for Earing Generated From Anisotropic Plasticity
,”
Int. J. Plast.
,
27
, pp.
1165
1184
.10.1016/j.ijplas.2011.01.002
18.
Bagheriasl
,
R.
,
Ghavam
,
K.
, and
Worswick
,
M.
,
2011
, “
Formability Analysis of Aluminum Alloy Sheets at Elevated Temperatures With Numerical Simulation Based on the M-K Method
,”
Proceedings of ESAFORM
, Belfast, Ireland.
19.
Farrokh
,
B.
, and
Khan
,
A. S.
,
2009
, “
Grain Size, Strain Rate, and Temperature Dependence of Flow Stress in Ultra-Fine Grained and Nanocrystalline Cu and Al: Synthesis, Experiment, and Constitutive Modeling
,”
Int. J. Plast.
,
25
, pp.
715
732
.10.1016/j.ijplas.2008.08.001
20.
Ghavam
,
K.
, and
Naghdabadi
,
R.
,
2011
, “
Constitutive Modeling of Temperature and Strain Rate Dependent Elastoplastic Hardening Materials Using a Corotational Rate Associated With the Plastic Deformation
,”
Int. J. Plast.
,
27
, pp.
1445
1455
.10.1016/j.ijplas.2011.04.004
21.
Mahabunphachai
,
S.
,
Koc
,
M.
, and
Carsley
,
J. E.
,
2011
, “
Investigations on Deformation Behavior of AA5754 Sheet Alloy Under Warm Hydroforming Conditions
,”
ASME J. Manuf. Sci. Eng.
,
133
, p.
051007
.10.1115/1.4004924
22.
Khan
,
A. S.
, and
Baig
,
M.
,
2011
, “
Anisotropic Response, Constitutive Modeling and the Effect of Strain-Rate and Temperature on the Formability of an Aluminum Alloy
,”
Int. J. Plast.
,
27
, pp.
522
538
.10.1016/j.ijplas.2010.08.001
23.
Khan
,
A. S.
, and
Liang
,
R.
,
1999
, “
Behavior of Three BCC Metal Over a Wide Range of Strain Rates and Temperatures
,”
Int. J. Plast.
,
15
, pp.
1089
1109
.10.1016/S0749-6419(99)00030-3
24.
Bergstrom
,
Y.
, and
Hallen
,
H.
,
1982
, “
An Improved Dislocation Model for the Stress-Strain Behavior of Polycrystalline α-Fe
,”
Mater. Sci. Eng.
,
55
, pp.
49
61
.10.1016/0025-5416(82)90083-0
25.
Nes
,
E.
,
1998
, “
Modeling of Work Hardening and Stress Saturation in FCC Metals
,”
Prog. Mater. Sci.
,
145
, pp.
129
193
.
26.
Kurukuri
,
S.
,
van den Boogaard
,
A. H.
,
Mirox
,
A.
, and
Holmedal
,
B.
,
2009
, “
Warm Forming Simulation of Al-Mg Sheet
,”
J. Mat. Process. Technol.
,
209
(
15–16
), pp.
5636
5645
.10.1016/j.jmatprotec.2009.05.024
27.
Lee
,
M. G.
,
Kim
,
C.
,
Pavlina
,
E. J.
, and
Barlat
,
F.
,
2011
, “
Advances in Sheet Forming-Materials Modeling, Numerical Simulation, and Press Technologies
,”
ASME J. Manuf. Sci. Eng.
,
133
, p.
061001
.10.1115/1.4005117
28.
Barlat
,
F.
,
Brem
,
J. C.
,
Yoon
,
J. W.
,
Chung
,
K.
, and
Dick
,
R. E.
,
2003
, “
Plane Stress Yield Function for Aluminum Alloy Sheets—Part 1: Theory
,”
Int. J. Plast.
,
19
, pp.
1297
1319
.10.1016/S0749-6419(02)00019-0
29.
Abedrabbo
,
N.
,
Pourboghrat
,
F.
, and
Carsley
,
J.
,
2007
, “
Forming of AA5182-O and AA5754-O at Elevated Temperatures Using Coupled Thermo-Mechanical Finite Element Models
,”
Int. J. Plast.
,
23
(
5
), pp.
841
875
.10.1016/j.ijplas.2006.10.005
30.
Simo
,
J. C.
, and
Hughes
,
T. J. R.
,
1998
,
Computational Inelasticity
,
Springer
,
New York
, pp.
143
149
.
31.
McKinley
,
J.
,
2010
, “
Warm Forming of Aluminum Brazing Sheet
,” M.Sc. thesis, University of Waterloo, Waterloo, Ontario, Canada.
32.
Yoon
,
J.
,
Barlat
,
F.
,
Dick
,
R. E.
,
Chung
,
K.
, and
Kang
,
T. J.
,
2004
, “
Plane Stress Yield Function for Aluminum Alloy Sheets-Part II: FE Formulation and Its Implementation
,”
Int. J. Plast.
,
20
(
3
), pp.
495
522
.10.1016/S0749-6419(03)00099-8
33.
Abedrabbo
,
N.
,
Pourboghrat
,
F.
, and
Carsley
,
J.
,
2006
, “
Forming of Aluminum Alloys at Elevated Temperatures—Part 1: Material Characterization
,”
Int. J. Plast.
,
22
(
2
), pp.
314
341
.10.1016/j.ijplas.2005.03.005
34.
Belytschko
,
T.
, and
Tsay
,
C. S.
,
1981
, “
Explicit Algorithms for Nonlinear Dynamics of Shells
,”
AMD
, ASME,
48
, pp.
209
231
.
35.
Takuda
,
H.
,
Mori
,
K.
,
Masuda
,
I.
,
Abe
,
Y.
, and
Matsuo
,
M.
,
2002
, “
Finite Element Simulation of Warm Deep Drawing of Aluminum Alloy Sheet When Accounting for Heat Conduction
,”
J. Mater. Process. Technol.
,
120
, pp.
412
418
.10.1016/S0924-0136(01)01180-3
You do not currently have access to this content.