In finite element analysis of sheet metal forming the use of combined isotropic-kinematic hardening models is advisable to improve stamping simulation and springback prediction. This choice becomes compulsory to model recent materials such as high strength steels. Cyclic tests are strictly required to evaluate the parameters of these constitutive models. However, for sheet metal specimens, in case of simple axial tension-compression tests, buckling occurrence during compression represents a serious drawback. This is the reason why alternative set-ups have been devised. In this paper, two experimental arrangements (a cyclic laterally constrained tension-compression test and a three-point fully reversed bending test) are compared so as to point out the advantages and the disadvantages of their application in tuning the well-known Chaboche’s hardening model. In particular, for tension-compression tests, a new clamping device was specifically designed to inhibit compressive instability. Four high strength steel grades were tested: two dual phases (DP), one transformation induced plasticity (TRIP) and one high strength low alloy material (HSLA). Then, the Chaboche’s model was calibrated through inverse identification methods or by means of analytical expressions when possible. The proposed testing procedure proved to be successful in all investigated materials. The achieved constitutive parameters, obtained independently from the two experimental techniques, were found to be consistent. Their accuracy was also been assessed by applying the parameter set obtained from one test to simulate the other one, and vice versa. Clues on what method provides the better transferability are given.

References

References
1.
Hansen
,
S.
,
1982
, “
The Formability of Dual-Phase Steels
,”
Journal of Applied Metalworking, Springer
,
2
(
2
), pp.
107
118
.10.1007/BF02834208
2.
Besdo
,
D.
,
2000
, “
On Numerical Problems With the Simulation of the Spring Back Phase of Sheet Metal Forming Process
,”
Plastic and Viscoplastic Response of Materials and Metal Forming: Proceedings of Plasticity ’00, the Eighth International Symposium on Plasticity and its Current Applications, Whistler, Canada July 16–20
,
A. S.
Khan
,
H.
Zhang
, and
Y.
Yuan
, eds.,
NEAT Press
,
Fulton, MD
, pp.
17
19
.
3.
Shi
,
M. F.
,
Thomas
,
G. H.
,
Chen
,
X. M.
, and
Fekete
,
J. R.
,
2001
, “
Formability Performance Comparison Between Dual Phase and HSLA Steels
,”
43rd Mechanical Working and Steel Processing Conference Proceedings
, Vol.
39
, October 28–31,
Charlotte, NC, Iron and Steel Society/AIME
,
Warrendale, PA
, pp.
165
174
.
4.
Uemori
,
T.
,
Okada
,
T.
, and
Yoshida
,
F.
,
1998
, “
Simulation of Springback in V-Bending Process by Elasto-Plastic Finite Element Method With Consideration of Bauschinger Effect
,”
Met. Mater
.,
4
(
3
), pp.
311
314
.10.1007/BF03187783
5.
Uemori
,
T.
,
Okada
,
T.
, and
Yoshida
,
F.
,
2000
, “
FE Analysis of Springback in Hat-Bending With Consideration of Initial Anisotropy and the Bauschinger Effect
,”
Key Eng. Mater.
,
177–180
, pp.
497
502
.10.4028/www.scientific.net/KEM.177-180.497
6.
Zhao
,
K.
,
Chun
,
B.
, and
Lee
,
J.
,
2000
, “
Numerical Modeling Technique for Tailor Welded Blanks
,”
SAE
Technical Paper 2000-01-0410.10.4271/2000-01-0410
7.
Li
,
K. P.
,
Carden
,
W. P.
, and
Wagoner
,
R. H.
,
2002
, “
Simulation of Springback
,”
Int. J. Mech. Sci.
,
44
(
1
), pp.
103
122
.10.1016/S0020-7403(01)00083-2
8.
Drucker
,
D. C.
, and
Palgen
,
L.
,
1981
, “
On Stress-Strain Relations Suitable for Cyclic and Other Loadings
,”
J. Appl. Mech.
,
48
(
3
), pp.
479
485
.10.1115/1.3157660
9.
Weinmann
,
K. J.
,
Rosenberger
,
A. H.
,
Sanchez
,
L. R.
, and
von Turkovich
,
B. F.
,
1988
, “
The Bauschinger Effect of Sheet Metal Under Cyclic Reverse Pure Bending
,”
CIRP Ann. – Manuf. Technol.
,
37
(
1
), pp.
289
293
.10.1016/S0007-8506(07)61638-2
10.
Yoshida
,
F.
,
Uemori
,
T.
, and
Fujiwara
,
K.
,
2002
, “
Elastic-Plastic Behavior of Steel Sheets Under In-Plane Cyclic Tension-Compression at Large Strain
,”
Int. J. Plast.
,
18
(
5–6
), pp.
633
659
.10.1016/S0749-6419(01)00049-3
11.
Yoshida
,
F.
, and
Uemori
,
T.
,
2002
, “
A Model of Large-Strain Cyclic Plasticity Describing the Bauschinger Effect and Workhardening Stagnation
,”
Int. J. Plast.
,
18
, pp.
661
686
.10.1016/S0749-6419(01)00050-X
12.
Zaiqian
H.
,
Rauch
E. F.
, and
Teodosiu
,
C.
,
1992
, “
Work-Hardening Behavior of Mild Steel Under Stress Reversal at Large Strains
,”
Int. J. Plast.
,
8
(
7
), pp.
839
856
.10.1016/0749-6419(92)90006-X
13.
Haddag
,
B.
,
Balan
,
T.
, and
Abed-Meraim
,
F.
,
2007
, “
Investigation of Advanced Strain-Path Dependent Material Models for Sheet Metal Forming Simulations
,”
Int. J. Plast.
,
23
(
6
), pp.
951
979
.10.1016/j.ijplas.2006.10.004
14.
Eggertsen
,
P. A.
, and
Mattiasson
,
K.
,
2009
, “
On the Modeling of the Bending-Unbending Behavior for Accurate Springback Predictions
,”
Int. J. Mech. Sci.
,
51
(
7
), pp.
547
563
.10.1016/j.ijmecsci.2009.05.007
15.
Chun
,
B. K.
,
Jinn
,
J. T.
, and
Lee
,
J. K.
,
2002
, “
Modeling the Bauschinger Effect for Sheet Metals, Part I: Theory
,”
Int. J. Plast.
,
18
(
5–6
), pp.
571
595
.10.1016/S0749-6419(01)00046-8
16.
Prager
,
W.
,
1956
, “
A New Method of Analyzing Stresses and Strains in Work-Hardening Plastic Solids
,”
ASME J. App. Mech.
,
23
, pp.
493
496
.
17.
Ziegler
,
H.
,
1959
, “
A Modification of Prager’s Hardening Rule
,”
Q. Appl. Mech.
,
17
, pp.
55
65
.
18.
Armstrong
,
P. J.
, and
Frederick
,
C. O.
,
1966
, “
A Mathematical Representation of the Multiaxial Bauschinger Effect
,” G.E.G.B Report No. RD/B/N 731.
19.
Chaboche
,
J. L.
,
1986
, “
Time-Independent Constitutive Theories for Cyclic Plasticity
,”
Int. J. Plast.
,
2
(
2
), pp.
149
188
.10.1016/0749-6419(86)90010-0
20.
Chaboche
,
J. L.
,
1989
, “
Constitutive Equations for Cyclic Plasticty and Cyclic Viscoplasticity
,”
Int. J. Plast.
,
5
, pp.
247
302
.10.1016/0749-6419(89)90015-6
21.
Mroz
,
Z.
,
1967
, “
On the Description of Anisotropic Work Hardening
,”
J. Mech. Phys. Solids
,
15
, pp.
163
175
.10.1016/0022-5096(67)90030-0
22.
Mroz
,
Z.
,
1981
, “
On Generalized Kinematic Hardening Rule With Memory of Maximal Prestress
,”
J. Mec. Appl.
,
5
, pp.
241
259
.
23.
Dafalias
,
Y. F.
, and
Popov
,
E. P.
,
1975
, “
A Model for Nonlinearly Hardening Materials for Complex Loading
,”
Acta Mech.
,
21
(
3
), pp.
173
192
.10.1007/BF01181053
24.
Tseng
,
N. T.
, and
Lee
,
G. C.
,
1983
, “
Simple Plasticity Model of Two Surface Type
,”
ASCE J. Eng. Mech.
, 109, pp.
795
810
.10.1061/(ASCE)0733-9399(1983)109:3(795)
25.
McDowell
,
D. L.
,
1985
, “
A Two Surface Model for Transient Nonproportional Cyclic Plasticity—Part I: Development of Appropriate Equations
,”
ASME J. Appl. Mech.
,
52
, p.
298
.10.1115/1.3169044
26.
McDowell
,
D. L.
,
1985
, “
A Two Surface Model for Transient Nonproportional Cyclic Plasticity—Part II: Comparison of Theory With Experiments
,”
ASME J. Appl. Mech.
,
52
, p.
303
.10.1115/1.3169045
27.
McDowell
,
D. L.
,
1989
, “
Evaluation of Intersection Conditions for Two Surface Plasticity Theory
.”
Int. J. Plast.
,
5
, pp.
29
50
.10.1016/0749-6419(89)90018-1
28.
Geng
,
L
, and
Wagoner
,
R. H.
,
2000
, “
Springback Analysis With a Modified Hardening Model
,”
SAE
Technical Paper 2000-01-0768.10.4271/2000-01-0768
29.
Chun
,
B. K.
,
Kim
,
H. Y.
, and
Lee
,
J. K.
,
2002
, “
Modeling the Bauschinger Effect for Sheet Metals, Part II: Applications
,”
Int. J. Plast.
,
18
(
5–6
), pp.
597
616
.10.1016/S0749-6419(01)00047-X
30.
Yoshida
,
F.
, and
Uemori
,
T.
,
2003
, “
A Model of Large-Strain Cyclic Plasticity and Its Application to Springback Simulation
,”
Int. J. Mech. Sci.
,
45
, pp.
1687
1702
.10.1016/j.ijmecsci.2003.10.013
31.
Boger
,
R. K.
,
Wagoner
,
R. H.
,
Barlat
,
F.
,
Lee
,
F.
, and
Chung
,
K.
,
2005
, “
Continuous Large Strain, Tension/Compression Testing of Sheet Material
,”
Int. J. Plast.
,
21
(
12
), pp.
2319
2343
.10.1016/j.ijplas.2004.12.002
32.
Omerspahic
,
E.
,
Mattiasson
, and
Enquist
,
K. B.
,
2006
, “
Identification of Material Hardening Parameters by Three-Point Bending of Metal Sheets
,”
Int. J. Mech. Sci.
,
48
(
12
), pp.
1525
1532
.10.1016/j.ijmecsci.2006.05.009
33.
Zhao
,
K. M.
, and
Lee
,
J. K.
,
2002
, “
Finite Element Analysis of the Three-Point Bending of Sheet Metals
,”
J. Mater. Process. Technol.
,
122
, pp.
6
11
.10.1016/S0924-0136(01)01064-0
34.
Eggertsen
,
P.-A.
, and
Mattiasson
,
K.
,
2010
, “
An Efficient Inverse Approach for Material Hardening Parameter Identification From a Three-Point Bending Test
,”
Eng. Comput.
,
26
(
2
), pp.
159
170
.10.1007/s00366-009-0149-y
35.
Cortese
,
L.
,
2006
, “
Cold Plastic Formability of Metals: FEM Modelling and Optimization of Material Models
,”
Ph.D. dissertation in Theoretical and Applied Mechanics, University of Rome
La Sapienza
,”
Rome
.
36.
Lee
,
M. G.
,
Kim
,
D.
,
Kim
,
C.
,
Wenner
,
M.
, and
Chung
,
K.
,
2005
, “
Spring-Back Evaluation of Automotive Sheets Based on Isotropic-Kinematic Hardening Laws and Non-Quadratic Anisotropic Yield Functions, Part III: Applications
,”
Int. J. Plast.
,
21
(
5
), pp.
915
953
.10.1016/j.ijplas.2004.05.014
37.
Campana
,
F.
,
Cortese
,
L.
, and
Placidi
,
F.
,
2006
, “
Finite Element Analysis of High Strength Steel Stamping Process Adopting a Combined Isotropic-Kinematic Hardening Model: Experimental Investigation of the Improvements Achieved in Springback Prevision
,”
IDDRG 06, International Deep Drawing Research Group, Proceedings of the 2006 Conference
,
Porto, Portugal
,
June
19
21
.
38.
Hu
,
Z.
,
1994
, “
Work-Hardening Behavior of Mild Steel Under Cyclic Deformation at Finite Strains
,”
Acta Metall. Mater.
,
42
(
10
), pp.
3481
3491
.10.1016/0956-7151(94)90480-4
39.
Broggiato
,
G. B.
,
Campana
,
F.
, and
Cortese
,
L.
,
2008
, “
The Chaboche Nonlinear Kinematic Hardening Model: Calibration Methodology and Validation
,”
Meccanica
,
43
, pp.
115
124
.10.1007/s11012-008-9115-9
40.
Marya
,
M.
,
Wang
,
K.
,
Hector
,
L. G.
, Jr.
, and
Gayden
,
X. Q.
,
2006
, “
Tensile-Shear Forces and Fracture Modes in Single and Multiple Weld Specimens in Dual-Phase Steels
,”
ASME J. Manuf. Sci. Eng.
,
128
, pp.
287
298
.10.1115/1.2137751
41.
Savic
,
V.
,
Hector
,
L. G.
, Jr.
,
Snavely
,
K. S.
, and
Coryell
,
J. J.
,
2010
, “
Tensile Deformation and Fracture of TRIP590 Steel From Digital Image Correlation
,”
SAE
Paper No. 2010-01-0444.10.4271/2010-01-0444
42.
Rizzo
,
L.
,
Cavallo
, P.
,
Brun
, R.
,
Melander
,
A.
,
Bleck
,
W.
,
Troive
,
L.
, and
Eggers
, U.
, “
An Efficient and Effective Methodology and Simulation Tools for Die Design and Springback Compensation for HSS and UHSS, ‘SPRINCOM
,’”
Midterm Report March 2010, Research Program of the Research Fund for Coal and Steel
, Contract No. RFCS-CT-2008-00029.
43.
Khan
,
A. S.
, and
Huang
,
S.
,
1995
,
Continuum Theory of Plasticity
,
John Wiley & Sons, Inc
.
44.
Campana
,
F.
,
Cortese
,
L.
, and
Placidi
,
F.
,
2005
, “
FEM Evaluation of Springback After Sheet Metal Forming: Application to High Strength Steels of a Combined Isotropic-Kinematic Hardening Model
,”
1st International Conference on Super High Strength Steels
,
Nov
.
2–4
,
Rome
,
Italy
.
45.
Toropov
,
V. V.
, and
Var der Giessen
,
E.
,
1992
, “
Parameter Identification for No Linear Costitutive Models: Finite Element Simulation, Optimization, Nontrivial Experiments
,”
Proceedings of the IUTAM SYMPOSIUM on Optimal Design with Advanced Materials
,
Aug
.
18–20
,
Lyngby, Denmark
,
Pauli
Pedersen
, ed.,
Elsevier, Amsterdam
, pp.
113
130
.
You do not currently have access to this content.