Abstract
Based on the theory of damage mechanics, an anisotropic damage coupled mixed isotropic-kinematic hardening plastic model for the prediction of forming limit diagram (FLD) is developed. The model includes the formulation of nonlinear anisotropic kinematic hardening. For the prediction of limit strains under nonproportional loading, a damage criterion for localized necking of sheet metals subjected to complex strain history is proposed. The model is employed to predict the FLDs of AL6111-T4 alloy. The predicted results agree well with those determined experimentally.
Issue Section:
Technical Papers
1.
Sing
, W.
M.
, and
Rao
, K.
P.
, 1997
,
“Study of Sheet Metal Failure Mechanisms Based on
Stress-state Conditions
,” J. Mater. Process.
Technol.
, 67
, pp.
201
–206
.2.
Arrieux
,
R.
,
1995
, “Determination and Use of the Forming
Limit Stress Diagrams
,” J. Mater. Process.
Technol.
, 53
, pp.
47
–56
.3.
Takuda
,
H.
,
Mori
,
K.
,
Takakura
,
N.
, and
Yamaguchi
,
K.
,
2000
, “Finite Element Analysis of Limit Strains
in Biaxial Stretching of Sheet Metals Allowing for Ductile
Fracture
,” Int. J. Mech. Sci.
,
42
, pp.
785
–798
.4.
Laukonis
, J.
V.
, and
Ghosh
, A.
K.
, 1978
,
“Effect of Strain Path Changes on the Formability of Sheet
Metals
,” Metall. Trans. A
,
9A
, pp.
1849
–1856
.5.
Graf
, A.
F.
, and
Hosford
,
W.
,
1993
, “Calculation of Forming Limit Diagrams for
Changing Strain Paths
,” Metall. Trans. A
,
24A
, pp.
2497
–2501
.6.
Graf
, A.
F.
, and
Hosford
,
W.
,
1994
, “The Influence of Strain-Path Changes on
Forming Limit Diagram of AL 6111-T4
,” Int. J. Mech.
Sci.
, 36
, pp.
897
–910
.7.
Barata da Rocha
,
A.
,
Barlat
,
F.
, and
Jalinier
, J.
M.
, 1984
,
“Prediction of the Forming Limit Diagram of Anisotropic
Sheets in Linear and Nonlinear Loading
,” Mater. Sci.
Eng.
, 68
, pp.
151
–164
.8.
Wang
,
J.
, and
Chow
, C.
L.
, 1989
,
“Hysteretic Effects of Damage and Stress on Ductile Fracture
Characterization
,” Eng. Fract. Mech.
,
34
, pp.
209
–220
.9.
Chow
, C.
L.
, Yu
,
L. G.
, and
Demeri
, M.
Y.
, 1997
,
“A Unified Damage Approach for Predicting Forming Limit
Diagrams
,” ASME J. Eng. Mater. Technol.
,
119
, pp.
346
–353
.10.
Hayakawa
,
K.
, and
Murakami
,
S.
,
1997
, “Thermodynamical Modeling of
Elastic-Plastic Damage and Experimental Validation of Damage
Potential
,” Int. J. Damage Mech.
,
6
, pp.
333
–363
.11.
Chaboche
, J.
L.
, 1992
,
“Damage Induced Anisotropy: On the Difficulties Associated
with the Active/Passive Unilateral Condition
,” Int.
J. Damage Mech.
, 1
, pp.
148
–171
.12.
Ju
, J.
W.
, 1990
,
“Isotropic and Anisotropic Damage Variable in Continuum
Damage Mechanics
,” J. Eng. Mech.
,
116
, pp.
2764
–2770
.13.
Demeri, M. Y., Chow, C. L., and Tai, W. H., 1998, “Predication and
Experimental Validation of Path-dependent Forming Limit Diagram of VDIF Steel,”
Developments in Sheet Metal Stamping, SAE SP-1322, pp.
53–58.
14.
Chow
, C.
L.
, and
Tai
, W.
H.
, 2000
,
“Damage Based Formability Analysis of Sheet Metal with
LS-DYNA
,” Int. J. Damage Mech.
,
9
, No. 3
, pp.
241
–254
.15.
Chow, C. L., Yang, X. J., and Chu, E., 2000, “Viscoplastic
Constitutive Modelling of Anisotropic Damage under Nonproportional Loading,”
International Mechanical Engineering Congress and Exposition, Proceedings of the
ASME Manufacturing Engineering Division, MED- Vol. 11, pp.
705–711.
16.
Chow
, C.
L.
, and
Yang
, X.
J.
, 2001
,
“Prediction of Forming Limit Diagram Based on Damage
Criterion under Nonproportional Loading
,” J. Mech.
Eng. Sci.
, 215
,
405
–414
.17.
Hill
,
R.
,
1948
, “A Theory of Yield and Plastic Flow of
Anisotropic Metals
,” Proc. R. Soc. London, Ser.
A
, A193
, pp.
281
–297
.18.
Prager
,
W.
,
1955
, “The Theory of Plasticity: a Survey of
Recent Achievements
,” Proc. Inst. Mech.
Eng.
, 169
, pp.
41
–57
.19.
Chaboche
, J.
L.
, and
Jung
,
O.
,
1998
, “Application of a Kinematic Hardening
Viscoplasticity Model with Thresholds to the Residual Stress
Relaxation
,” Int. J. Plast.
,
13
, pp.
785
–807
.20.
Moosbrugger
, J.
C.
, 2000
,
“Anisotropic Nonlinear Hardening Rule Parameters from
Reversed Proportional Axial-torsional Cycling
,” ASME
J. Eng. Mater. Technol.
, 122
, pp.
18
–28
.21.
Wu
, H.
C.
,
Hong
, H.
K.
, and
Shiao
, Y.
P.
, 1999
,
“Anisotropic Plasticity with Application to Sheet
Metals
,” Int. J. Mech. Sci.
,
41
, 703
–724
.22.
Chaboche
, I.
L.
, 1993
,
“Cyclic Viscoplastic Constitutive Equations, Part I: A
Thermodynamically Consistent Formulation
,” ASME J.
Appl. Mech.
, 60
, pp.
813
–820
.23.
Mroz
,
Z.
,
1967
, “On the Description of Anisotropic Work
Hardening
,” J. Mech. Phys. Solids
,
15
, pp.
163
–175
.24.
Dafalias
, Y.
F.
, and
Popov
, E.
P.
, 1976
,
“Plastic Internal Variables Formalism of Cyclic
Plasticity
,” ASME J. Appl. Mech.
,
98
, pp.
645
–651
.25.
McDowell
, D.
L.
, 1985
,
“An Experimental Study of the Structure of Constitutive
Equations for Nonproportional Cyclic Plasticity
,”
ASME J. Eng. Mater. Technol.
, 107
, pp.
307
–315
.26.
Geng, L., and Wagoner, R. H., 2000, “Springback Analysis with a
Modified Hardening Model,” Sheet Metal Forming: Sing Tang 65th Anniversary
Volume, SAE SP-1536, pp. 21–31.
27.
Armstrong, P. J., and Frederick, C. O.1966, “A Mathematical
Representation of the Multiaxial Bauschinger Effect,” CEGB Report RD/B/N73 1,
Central Electricity Generating Board.
28.
Chow
, C.
L.
, and
Yang
, X.
J.
, 2001
,
“Effect of Principal Damage Plane Rotation on Anisotropic
Damage Plastic Model
,” Int. J. Damage
Mech.
, 10
, No. 1
, pp.
43
–55
.29.
Chow
, C.
L.
, and
Chen
, X.
F.
, 1992
,
“An Anisotropic Model of Damage Mechanics Based on
Endochronic Theory of Plasticity
,” Int. J.
Fract.
, 55
, pp.
115
–130
.30.
Chow
, C.
L.
, and
Wang
,
J.
,
1988
, “Ductile Fracture Characterization with an
Anisotropic Continuum Damage Theory
,” Eng. Fract.
Mech.
, 30
, pp.
547
–563
.31.
Chow, C. L., Yu, L. G., and Demeri, M. Y., 1996, “Prediction of
Forming Limit Diagram with Damage Analysis,” SAE Technical Paper Series 960598,
pp. 73–80.
Copyright © 2002
by ASME
You do not currently have access to this content.