This paper deals with localized necking in stretched metal sheets using the initial imperfection approach. The first objective is to study the effect of kinematic hardening on the formability of a freestanding metal layer. To this end, the behavior of the metal layer is assumed to follow the rigid-plastic rate-independent flow theory. The isotropic (respectively, kinematic) hardening of this metal is modeled by the Hollomon (respectively, Prager) law. A parametric study is carried out in order to investigate the effect of kinematic hardening on the formability limits. It is shown that the effect of kinematic hardening on the ductility limit is noticeably different depending on the strain path considered. The second aim of this paper is to analyze the effect of an elastomer substrate, perfectly bonded to the metal layer, on the formability of the whole bilayer. It is found that the addition of an elastomer layer substantially enhances the formability of the bilayer, in agreement with earlier studies.

References

References
1.
Keeler
,
S. P.
, and
Backofen
,
W. A.
,
1963
, “
Plastic Instability and Fracture in Sheets Stretched Over Rigid Punches
,”
Trans. Am. Soc. Met.
,
56
(
1
), pp.
25
48
.
2.
Goodwin
,
G. M.
,
1968
, “
Application of Strain Analysis to Sheet Metal Forming Problems in the Press Shop
,”
Metall. Ital.
,
60
, pp.
764
774
.
3.
Abed-Meraim
,
F.
,
Balan
,
T.
, and
Altmeyer
,
G.
,
2014
, “
Investigation and Comparative Analysis of Plastic Instability Criteria: Application to Forming Limit Diagrams
,”
Int. J. Adv. Manuf. Technol.
,
71
(
5
), pp.
1247
1262
.
4.
Jaamialahmadi
,
A.
, and
Kadkhodayan
,
M.
,
2011
, “
An Investigation Into the Prediction of Forming Limit Diagrams for Normal Anisotropic Material Based on Bifurcation Analysis
,”
ASME J. Appl. Mech.
,
78
(
3
), p.
031006
.
5.
Jaamialahmadi
,
A.
, and
Kadkhodayan
,
M.
,
2012
, “
A Modified Storen-Rice Bifurcation Analysis of Sheet Metal Forming Limit Diagrams
,”
ASME J. Appl. Mech.
,
79
(
6
), p.
061004
.
6.
Chow
,
C. L.
,
Yang
,
J.
, and
Chu
,
E.
,
2002
, “
Prediction of Forming Limit Diagram Based on Damage Coupled Kinematic-Isotropic Hardening Model Under Nonproportional Loading
,”
ASME J. Eng. Mater. Technol.
,
124
(
2
), pp.
259
265
.
7.
Jalali Aghchai
,
A.
,
Shakeri
,
M.
, and
Mollaei Dariani
,
B.
,
2013
, “
Influences of Material Properties of Components on Formability of Two-Layer Metallic Sheets
,”
Int. J. Adv. Manuf. Technol.
,
66
(
5
), pp.
809
823
.
8.
Hutchinson
,
J. W.
, and
Neale
,
K. W.
,
1978
,
Sheet Necking-II, Time-Independent Behavior, Mechanics of Sheet Metal Forming
,
D. P.
Koistinen
and
N. M.
Wang
, eds.,
Plenum
,
New York
, pp.
127
153
.
9.
Ghosh
,
A.
,
1977
, “
A Tensile Instability and Necking in Materials With Strain Hardening and Strain-Rate Hardening
,”
Acta Metall.
,
25
(
12
), pp.
1413
1424
.
10.
Hutchinson
,
J. W.
, and
Neale
,
K. W.
,
1978
,
Sheet Necking-III. Strain-Rate Effects
,
D. P.
Koistinen
and
N. M.
Wang
, eds.,
Plenum
,
New York
, pp.
269
285
.
11.
Neale
,
K. W.
, and
Chater
,
E.
,
1980
, “
Limit Strain Predictions for Strain-Rate Sensitive Anisotropic Sheets
,”
Int. J. Mech. Sci.
,
22
(
9
), pp.
563
574
.
12.
Cao
,
J.
,
Yao
,
H.
,
Karafillis
,
A.
, and
Boyce
,
M. C.
,
2000
, “
Prediction of Localized Thinning in Sheet Metal Using a General Anisotropic Yield Criterion
,”
Int. J. Plast.
,
16
(
9
), pp.
1105
1129
.
13.
Kuroda
,
M.
, and
Tvergaard
,
V.
,
2000
, “
Forming Limit Diagrams for Anisotropic Metal Sheets With Different Yield Criteria
,”
Int. J. Solids Struct.
,
37
(
37
), pp.
5037
5059
.
14.
Haddag
,
B.
,
Abed-Meraim
,
F.
, and
Balan
,
T.
,
2009
, “
Strain Localization Analysis Using a Large Deformation Anisotropic Elastic–Plastic Model Coupled With Damage
,”
Int. J. Plast.
,
25
(
10
), pp.
1970
1995
.
15.
Mansouri
,
L. Z.
,
Chalal
,
H.
, and
Abed-Meraim
,
F.
,
2014
, “
Ductility Limit Prediction Using a GTN Damage Model Coupled With Localization Bifurcation Analysis
,”
Mech. Mater.
,
76
, pp.
64
92
.
16.
Tvergaard
,
V.
,
1978
, “
Effect of Kinematic Hardening on Localized Necking in Biaxially Stretched Sheets
,”
Int. J. Mech. Sci.
,
20
(
9
), pp.
651
658
.
17.
He
,
J.
,
Cedric Xia
,
Z.
,
Zhu
,
X.
,
Zeng
,
D.
, and
Li
,
S.
,
2013
, “
Sheet Metal Forming Limits Under Stretch-Bending With Anisotropic Hardening
,”
Int. J. Mech. Sci.
,
75
, pp.
244
256
.
18.
He
,
J.
,
Zeng
,
D.
,
Zhu
,
X.
,
Cedric Xia
,
Z.
, and
Li
,
S.
,
2014
, “
Effect of Nonlinear Strain Paths on Forming Limits Under Isotropic and Anisotropic Hardening
,”
Int. J. Solids Struct.
,
51
(
2
), pp.
402
415
.
19.
Hommel
,
M.
, and
Kraft
,
O.
,
2001
, “
Deformation Behavior of Thin Copper Films on Deformable Substrates
,”
Acta Mater.
,
49
(
19
), pp.
3935
3947
.
20.
Huang
,
H. B.
, and
Spaepen
,
F.
,
2000
, “
Tensile Testing of Free-Standing Cu, Ag and Al Thin Films and Ag/Cu Multilayers
,”
Acta Mater.
,
48
(
12
), pp.
3261
3269
.
21.
Lu
,
N.
,
Wang
,
X.
,
Suo
,
Z.
, and
VIassak
,
J.
,
2007
, “
Metal Films on Polymer Substrates Stretched Beyond 50%
,”
Appl. Phys. Lett.
,
91
(
22
), p.
221909
.
22.
Morales
,
S. A.
,
Albrecht
,
A. B.
,
Zhang
,
H.
,
Liechti
,
K. M.
, and
Ravi-Chandar
,
K.
,
2011
, “
On the Dynamics of Localization and Fragmentation—V: Response of Polymer Coated Al 6061-O Tubes
,”
Int. J. Fract.
,
172
(
2
), pp.
161
185
.
23.
Guduru
,
P. R.
,
Bharathi
,
M. S.
, and
Freund
,
L. B.
,
2006
, “
The Influence of a Surface Coating on the High-Rate Fragmentation of a Ductile Material
,”
Int. J. Fract.
,
137
(
1
), pp.
89
108
.
24.
Jia
,
Z.
, and
Li
,
T.
,
2013
, “
Necking Limit of Substrate-Supported Metal Layers Under Biaxial In-Plane Loading
,”
Int. J. Plast.
,
51
, pp.
65
79
.
25.
Stören
,
S.
, and
Rice
,
J. R.
,
1975
, “
Localized Necking in Thin Sheets
,”
J. Mech. Phys. Solids
,
23
(
6
), pp.
421
441
.
26.
Ben Bettaieb
,
M.
, and
Abed-Meraim
,
F.
,
2015
, “
Investigation of Localized Necking in Substrate-Supported Metal Layers: Comparison of Bifurcation and Imperfection Analyses
,”
Int. J. Plast.
,
65
, pp.
168
190
.
27.
Marciniak
,
Z.
, and
Kuczynski
,
K.
,
1967
, “
Limit Strains in the Processes of Stretch-Forming Sheet Metal
,”
Int. J. Mech. Sci.
,
9
(
9
), pp.
609
620
.
28.
Hollomon
,
J. H.
,
1945
, “
Tensile Deformation
,”
Trans. AIME
,
162
(
444
), pp.
268
290
.
29.
Prager
,
W.
,
1955
, “
The Theory of Plasticity—A Survey of Recent Achievements
,”
Proc. Inst. Mech. Eng.
,
169
(
1955
), pp.
41
57
.
30.
Hunter
,
S. C.
,
1979
, “
Some Exact Solutions in the Theory of Finite Elasticity for Incompressible NHeo-Hookean Materials
,”
Int. J. Mech. Sci.
,
21
(
4
), pp.
203
211
.
31.
Amirkhizi
,
A. V.
,
Isaacs
,
J.
,
McGee
,
J.
, and
Nemat-Nasser
,
S.
,
2006
, “
An Experimentally-Based Viscoelastic Constitutive Model for Polyurea Including Pressure and Temperature Effects
,”
Philos. Mag.
,
86
(
36
), pp.
5847
5866
.
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