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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.

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