An Analytic Modeling Of Spring Back For Bending Bimetallic Sheet Material Considering Change in Young Modulus

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Volume 3, Issue 5, 2016

187 Available online at www.ijiere.com

International Journal of Innovative and Emerging

Research in Engineering

e-ISSN: 2394 – 3343 p-ISSN: 2394 – 5494

An Analytic Modeling of Spring Back For Bending Bimetallic

Sheet Material Considering Change in Young Modulus

Abhishek M. Purohit, Deepali Bharti, Patel Divyeshkumar Amulbhai

1_{Mechanical Department, C.K.Pithawala Collage of engineering technology, Surat, India}

GUJARAT TECHNOLOGICAL UNIVERSITY

Abstract

Spring back prediction is an important issue for sheet metal forming industry. Most sheet metal elements undergo a complicated cyclical deformation history during the forming process. For an accurate prediction of spring back the young modulus in change effect must be considered to determine accurately the internal stress distribution within the sheet metal deformation. Mathematical modeling of spring back predication has done in this report. There are swift’s model law for elastic region and power rule for modeling is used to estimate predication Keywords —spring back ,swift’s model, isotropic hardening, power rule

I.Introduction

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.[1]

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[12]

0

(

0

)[1 exp(

)]

chord s p

E



E



E



E





where E0, Es and ξ are material parameters which are calculated from the loading-unloading curves during the uniaxialtension test.

II. 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[1]

1. Plane sectionremains plane.

2. Sheet is nearly flat and not pre stressed 3. Plane stressconditionsapply.

4. Bausch Inger effect is neglected.

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188 Fig .1Geometry of the multi layered sheet [1]

Fig.2Location of elastic zone for the layer under consideration [1]

(

) ...(

)

(

)...(

)

(

) ...(

)

m

y y y

y y

m

y y y

H

E

H



 









 



_

_{ }

_{ }











  









_

_{ }

_







,

_y y

where

E







b

P _zdz

a





 

0

[

1

( , )

2

( ,

)

3

( . )]

P

E t I

a c

I

c d

I

d b







1 0

1 ( , )

[

(

) ]

c m

y y z

a

I a c

H

dz

E t













 

1 1 0 0 0

!(

)

1 [

(

)

!

(

1 )!

m j i K z y y i j

m

I

c a

HR

E t

i

m

j

 





     





 





 



 





_



_



_



_



 



_

_





 



2 2 0 2 2 0

2 ( ) ( , ) ( )

2

d

c

ER d c

I c d d c

E t R R



     _   _  



1 3 0 0 0

( 1) !( )

1

( , ) ( )

! ( 1 )!

j m j

i K z y y i j m

I d b b d HR

E t i m j

                        _  _ _ _{ } ___  _ _ _ _ ____ 

 

 ' '

0 2

( , )

2

( , )

P

 

P

E t I



_

a b



I a b



_

' 2 '

0 4

( , )

5

( , )

6

( , )

5

( , )

5

( , )

b z a

(3)

189

III. CALCULATION FOR SINGLE LAYER MATERIAL Case 1: 430SS material properties for evaluation of spring back

Material E (GPa)

₍

₎

y

MPa



H (MPa) m H(mm)

430SS 200 300 707 0.095 5

Case 2: AL100 material properties for evaluation of spring back

Material E (GPa)

₍

₎

y

MPa



H(MPa) m H(mm)

Al100 70 35 115 0.2 5

Case 3:AL110/450SS bimetal material properties for evaluation of spring back

Material E (GPa)

₍

₎

y

MPa



H(MPa) M H(mm)

Al110 70 35 115 0.2 3

430SS 200 300 707 0.095 2

y R

R

f

t

E







 



_{ }

_

_

 



'

0 0 '

1

2

a

t

R

E













_





_







'

3

1 0...

2

1 1 3

4 ...

2

R

R R R

f

R

f



_





 





_{ }

_



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190

Sr.no Case 1 Case 2 Case 3

R0 R0’ R0 R0’ R0 R0’

1.1 ₃ ₂ ₀ ₁ ₀ ₁

1.2

20 21.49 20 27.34 20 19.83

1.3 ₄₀ _43.58 ₄₀ _34.27 ₄₀ _39.9

1.4 ₆₀ _68.26 ₆₀ _54.76 ₆₀ _59.88

1.5 ₈₀ _89.49 ₈₀ _73.11 ₈₀ _79.48

1.6 ₁₀₀ _113.3 ₁₀₀ _92.8 ₁₀₀ _99.35

1.7 ₁₂₀ _143.35 ₁₂₀ _111.8 ₁₂₀ _119.2

Case 3

Case 2

Case 1

0 50 100 150 200 250 300

1 2 3 4 5 6 7

R0'

R0

0 20 40 60 80 100 120 140

1 2 3 4 5 6

R0

R0'

0 20 40 60 80 100 120 140

1 2 3 4 5 6

R0

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191

SIMPLE MODEL FOR CHANGE OF YOUNG ‘S MODULUS

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. [yoshida]

' 3 '

1 0

2 [

]

(

)

3

ep

E I





R E

' * 3 3 * 3 4 '

2 0

2

0.32

0.32 [

]

((

)

(

) )

((

)

(

) )

3

0.21

ep ep m

0.28

_m ep m

E I

y

R

y

R

E

R





_

_





_

_



_



_









3

' * 3 '

3 0

1.68 [

]

(

)

3

8 s

E I





_



y



_

E





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.

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

Acknowledgment

I take this opportunity to express my profound gratitude and deep regards to my guide Prof. Chintan K. Patel for his exemplary guidance, monitoring and constant encouragement throughout the course of this seminar. The blessing, help and guidance given by him time to time shall carry me a long way in the journey of life on which I am about to embark.

References

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