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All rights reserved by www.ijaresm.net ISSN : 2394-1766 1
AN ANALYTIC MODELING OF SPRING BACK FOR
BENDING BIMETALLIC SHEET MATERIAL
CONSIDERING CHANGE IN YOUNG MODULUS Divyeshkumar Amulbhai Patel
1, Chintan K Patel
2
Student of .Mechanical Dept. , CKPCET , Surat, Gujarat, India 1
Assistant Professor, of Mechanical Dept., CKPCET , Surat, Gujarat, India2
Abstract: Spring back predication is an important issue for sheet metal forming industry.
Most sheet metal elements undergo a complicated cyclical history during the metal forming
process. In present study development of analytical model for predication of spring back
done with considering of change in young modulus. Isotropic hardening and kinematic
hardening multi surface model plane strain assumption and experimental observation a
new incremental method and hardening model is proposed in analytically.
Keywords: Spring back, material model, bending, isotropic hardening and kinematic
hardening.
INTRODUCTION
The Advanced high strength steels (AHSS) usually undergo inaccurate
dimension after stamping due to spring back. The final spring back is controlled by
increasing tension, for instance with an increase of the blank holding force. Points out
that many researchers have tried to predict this phenomenon by the application of
advanced finite element techniques and the use of accurate material constitutive models.
The internal state of stress and moment at the end of the forming process defines
the amount of subsequent spring back after unloading. Therefore, the strain path, i.e.,
the stress– strain dependency on the forming history, should to be taken into account
especially when the material undergoes bending unbending behavior. It has been
reported that Young’s modulus is not constant but usually decreases when the uniaxial
plastic strain increases. Therefore, the variation in elastic modulus for AHSS with high
strength-to-modulus ratio as a function of the plastic strain has to be considered for a
better modeling of spring back. The chord modulus is calculated from the stress–strain
curve as the slope of the straight line that connects the point before unloading to that of
the stress-free state. The chord modulus may be represented as a function of the plastic
strain (εp) at reversal.
0 0( )[1 exp( )]chord s pE E E E
Objective of the present work
Based on the finding from the literature it is observed that spring back in bending
is critical issue. Little work has been done for considering the variation young modulus. That
work is Bending Bimetallic Sheet Material. An Analytic Modeling for considering the
change the young modulus for following assumption.
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1. Plane section remains plane.
2. Sheet is nearly flat and not pre stressed
3. Plane stress conditions apply.
4. Bauschinger effect is neglected.
Young modulus remain constants during deformation
The stress-strain relation of each layer is expressed by constitutive equation reported by
Woo and Mars
Fig .1 Geometry of the multilayered sheet
Fig .2 Location of elastic zone for the layer under consideration
( ) ......................( )
( )...........................................( )
( ) .........................( )
m
y y y
y y
m
y y y
H
E
H
,y
ywhereE
b
P dzz
a
0 1 2 3[ ( , ) ( , ) ( . )]P E t I a c I c d I d b CALCULATION FOR SINGLE LAYER MATERIAL
Case 1: Al100 material properties for evaluation of spring back
Material E (GPa)
H (MPa) m H(mm)
Al100 200 300 707 0.095 5
R0 R’0
3 2
20 21.49
40 43.58
60 68.26
80 89.49
100 113.3
120 143.35
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A. Case 2 AL100 material properties for evaluation of spring back.
Material E (GPa)
H(MPa) m H(mm)
Al100 70 35 115 0.2 5
3
3
'
3 8
'
'
' '
0
'
0
21.35 35
5 70 10
0.0021
1 3(0.0021) 4(0.0021)
21.351 (6.3 10 ) (3.70 10 )
21.48
/ exp(0.19)
25.97
y
R
R
R
Rf
t E
f
f
R
R
R
R
R R
R
'
0 0 '
'
0
1
2
0.194
at t
R R E
R0 R0'
0 1
20 27.34
60 54.76
80 73.11
100 92.8
120 111.8
B. CASE 3 AL110/450SS bimetal material properties for evaluation of spring back.
Material E (GPa)
H(MPa) M H(mm)
Al110 70 35 115 0.2 3
430SS 200 300 707 0.095 2
R0 R0'
0 1
20 19.83
40 39.9
60 59.88
80 79.48
100 99.35
120 119.2
SIMPLE MODEL FOR CHANGE OF YOUNG ‘S MODULUS
( )y MPa
( )y MPa
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The author will include the use of other model for the change in young modulus
the bending moment will be extended simple model for the elastic plastic recovery.
The overall objective of this study is to develop a new analytical model to predict the
spring back in air bending of bimetallic. The young modulus variation and a suitable model to
describe material property of bimetallic will be considered in new approach. The analytical
model will be updated based on the new method.
0 0( )[1 ]aE E E E e
2 2
0 0 02 2
0
( )[1 ] 2 ( )( , ) ( )
2
aE E E e d cI c d d c
E t R R
Al 1000
R0 R0'
20 20.1
40 40.25
60 60.48
70 70.66
80 80.62
90 90.5
100 100.3
120 120.6
For 430SS
R0 R0'
20 27.5
40 48.6
60 66.7
70 76.6
80 88.8
90 97.98
100 107.2
120 120.78
CONCLUSION
The overall objective of this study is to develop a new analytical model to predict the
spring back in air bending of bimetallic.
The young modulus variation and a suitable model to describe material property of
bimetallic will be considered in new approach,
The analytical model will be updated based on the new method.
In previous section it was derived considering young’s modulus but if it is accurate
prediction you must considering change in young’s modulus [yoshida]
It is the function of the strain.
In metal forming process is young modulus’s decrease.
Parameter
Yilamu et al.
Yuen
Constant
in young
modulus
Change
in young
modulus Exp.
Sim.
(YUModel)
Sim.
(IHModel)
hAl(initial) 1.05 1.05 1.05 1.05 1.05 1.05
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hSS(initial) 0.51 0.51 0.51 0.51 0.51 0.51
ttotal(initial) (mm) 1.56 1.56 1.56 1.56 1.56 1.56
R0 (mm) 3.418 3.62 3.57 3.4188 3.4188 3.4188
R0’(mm) 3.62 3.86 3.91 3.4218 3.4908 3.4908
hAl(mm) 0.86 0.86 0.86 1.05 0.894 0.894
hSS(mm) 0.51 0.52 0.52 0.517 0.517 0.517
t total (mm) 1.37 1.37 1.38 1.38 1.56 1.411
γ(ss/al) = R0’/ R0 1.05 1.066 1.095 1.01 1.02 1.02
δ(ss/al) 0 1.523 4.304 3.809 2.85 2.85
Alin/ SSout
hAl(initial) 1.05 1.05 1.05 1.05 1.05 1.05
hSS(initial) 0.51 0.51 0.51 0.51 0.51 0.51
ttotal(initial) (mm) 1.56 1.56 1.56 1.56 1.56 1.56
R0 (mm) 5.231 5.48 5.39 5.231 5.231 5.231
R0’(mm) 5.483 5.29 5.81 5.39 5.231 5.231
hAl(mm) 1.16 1.18 1.16 1.05 1.117 1.117
hSS(mm) 0.5 0.5 0.5 0.51 0.51 0.499
t total (mm) 1.16 1.68 1.68 1.66 1.56 1.677
γ(al/ss) = R0’/ R0 1.04 1.08 1.077 1.035 1.028 1.028
δ(al/ss) 0 3.846 3.556 0.98 1.15 1.17
ACKNOWLEDGMENT
The author wishes to thanks Mr. Chintan K Patel for providing the use ful
knowledge of spring back and metal forming process and the management of the IJARESM
for permission to publish the paper.
REFERENCES
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