ESI Korea Forum 2012.09.13_NGUYEN.pdf

7/29/2019 ESI Korea Forum 2012.09.13_NGUYEN.pdf

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Constitutive modeling and springback

prediction of lightweight alloy sheet

September 13, 2012

Copyright ESI Group, 2012 All rights reserved.Copyright ESI Group, 2012. All rights reserved.

NGOC-TRUNG NGUYEN

[email protected]

Contents

Constitutive modeling and springback prediction of

lightweight alloy sheet

2. - 1. Background

3.

Copyright ESI Group, 2012 All rights reserved. 2

4. 5. Conclusion


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1 Background


prediction of lightweight alloy sheetNGOC-TRUNG NGUYEN et al.

2. - 1. Background

3. 4.


5. Conclusion

Weight reduction(*) while maintaining functional

requirements:

Lightweight materialsWhy?

,

materials, energy, and costs are saved

environmental damage is reduced.

Superiorproperties:thermal/electrical properties,

dam in ca acit

(*) Weight reduction can also be achieved by using thinner sheets ofhigh strength steelsand forming them using advanced forming processes.

FCX[ issue ]

21C

/ recycling /


fatigue properties,

dimensional stability, and

easy machinability

911GT3

E-class

BMW E

WPM (World Premier Materials) project.: super-light vehicle


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Vehicle components

shallow parts in automobile

bod anels and chassis

Lightweight materialsApplications

Camera case

Bonnet

Notebook case

Engine block

applications

seat frame (35% weight

reduction), panel plenum (45%

weight reduction), door inner

and outer

Consumer products

Mobile Phone Case


Trunk lid

Side outer

Door

Dash panel

Hood

Loop

Center pillar

Floor

Fender

( + )

Mg Al Ti Zn Steel

1.8

2.7

4.5

7.1

7.8

Specificgravity(g/cm

3)

Forming process:

low formability at ambient temperature.

Lightweight materialsChallenges (1)

against pressure (sheet hydroforming)

and at elevated temperatures (warm

forming).5xxx series and 6xxx series Al alloys

show increased formability at the range

of 250oC to 300oC

formability of AZ31B Mg alloy is improved


significantly above 200oC

FLD of AZ31B magnesium alloy sheet at

different temperatures.

Suitable material model to capture the temperature dependent formability is needed.


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Material behavior:

Yielding behavior:

stron anisotro ic stren th differential

Lightweight materialsChallenges (2)

AZ31B

effect)

Hardening response:

asymmetric

abnormal

large springback (to be discussed later)

Material flow:

0 45 90 R

AZ31B


fracture characteristics (Mg alloy sheet)Evolution of the elastic modulus

Constitutive model

Yield function:

Isotro : von Mises

Lightweight materialsConstitutive model (1)

Anisotropy: Hill (48, 90), Barlat (89, 2000), Gotoh, Vegter, etc.

Material card: input data from tests

045

90


The contours of Yld2000-2D yield function.


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Constitutive model

Hardening rule:

Isotro ic hardenin Kru kowski ower law tabular data etc


, , , .

Kinematic hardening (linear, nonlinear, Yoshida-Uemori)

Mixed kinematic hardening (Chaboche)


Constitutive model

Cyclic stress-strain behavior

Sheet metal formin : low number of c cles


Features:

Symmetry in yield stress

tension = compression

Symmetry in hardening

concave-down shape

Anisotropy

Bauschinger effect

p

Copyright ESI Group, 2012 All rights reserved.

Transient behavior

Permanent softening

Hardening rule:

Obtain an accurate stress prediction

10


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Lightweight materialsSpringback prediction (1)

Springback phenomenon

Elastic recovery of a portion ofthe deformation roduced durinforming.

Stress driven

Proportional to the ratio between

residual stresses and Youngs

modulus

Forlightweight materials (with

low Youngs modulus) and HSS


becomes more serious concerns.Springback results in a difference inshape between the part and thetooling.

Lightweight materialsSpringback prediction (2)

Springback prediction:

Hardening rule:

Accurate stress rediction

Reverse loading behavior

Advanced hardening rules

Y-U modelHardening model for Mg alloy sheet

Evolution of the elastic modulus


Source: Mazda Motor Corporation, Japan


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1 Background



2. - 1. Background

3. 4.


5. Conclusion

Design requirements:

Horizontal typeAuto-ali nment s stem

Heating

systemLoading dir.

Holding force

control

Strain

measurement

OSU Yes Vertical Hydraulic Indirect

Cyclic loading testerRequirements

Specimen thickness:0.5~5.0 mm

Max. stroke:Tension 140 mm

Compression 20 mm

Anti-buckling system

Heating system

Tokyo

UniversityNo Horizontal Hydraulic Direct

KNU Yes HorizontalHydraulic /

Dead weightIndirect


Uniform temp. distribution in the gage area

Cyclic loadingExperimental methods for applying

continuous stress reversals to a sheet

specimen.

Indirect strain measuring system


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Side force system Jig systemLoading dir. Horizontal type

Capacity 30 kN

Tem erature RT~400oC

Cyclic loading testerDesign and specification

side force

Side force

-

align

Heating system Jig movement

Speed 0.001~1,000 mm/min

Strain measurement Laser extensometer

Side force 10 kN


Heat cartridge

( 2, 3)

/

align

Uniaxial tension test:

Reference test data:

Cyclic loading testerValidation

Crosshead speed 2 mm/min, gauge length 50 mm

Room temperature

Temperature measurement:

Heat cartridge installation:upper die (2EA), lower die (3EA)


temperature: 400oC

K-type thermal sensor

Sheet thickness: 2 mm

Result:uniform distribution of temperature in the gage area


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Upper die 1 Upper die 2 Specimen

FC fs FTfs

Friction effect:

Significant

Cyclic loading testerCalibration

FT FN=FL-Friction

FN=FL-2Fv

FC FN=FL+Friction

FN=FL+2Fv

FT=Tension force

FC=Compression force

FN=Net force

FL=Load

Fv=Vertical force

=Friction coefficient

Lower die 1 Lower die 2

fs fs

Die-to-die

Die-to-specimen

Thermal expansion

Biaxial stress state effect

Insi nificant


1 Background



2. - 1. Background

3. 4.


5. Conclusion


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Aluminum alloy sheetYoshida-Uemori model (1)

Framework:

The yield surface moves kinematically

.

The bounding surface can translate

and extend in the stress space.The yield surface: f = ( - ) Y= 0The bounding surface:F= ( - ) (B + R) = 0

Hardening behavioris characterized by

the relative motion of the two surfaces.


Hardening rules are applied for each surfaceA so-called non-isotropic hardening surface describes the

workhardening stagnation effect.

TheYoungs modulus is a function of plastic strain.


Non-IH of bounding surfaceWorkhardening stagnation


IH and non-IH hardening case of bounding surface

: backstress (center of the yield surface)

: center of the bounding surface

B : initial size of the bounding surface

R : isotropic hardening component


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Plastic strain dependency of Youngs modulus

0 0( )[1 exp( )]apE E E E

Seven(*) material parameters (Y , C , B , Rsat , b , m , h )

- Y : Inner surface size


Parameters:

Initial yield surface: the initial backstress components

The relative motion law:

Isotropic hardening of the bounding surface:

Kinematic hardening of the bounding surface:

*

* **

paC

a

Y

a RB Y

( )satpRRR m

2 p p

- C : Inner surface

- B : Bounding surface

- Rsat : Bounding surface

(Isotropic hardening)

-b : Bounding surface

- m : Bounding surface


The non-isotropic hardening (non-IH) surface:

3m

23( , , ) ( ) : ( ) 0

2g r r q q q

( ) q q 3( ) :

02

0 0

r when Rr

r wh

h

en R

q

(Isotropic & Kinematic hardening)

- h : Stagnation

(*) Additional parameter(s) can be found in the PAM-STAMP version.

Parameter Test + Procedure(*)

Plastic strain dependency of Youngs modulus:


PAM-STAMP inputs:

Xi, Younga Cyclic loading test (T-C-T or C-T-C)

Initial yield surface:

X11, X22, X12 Cyclic loading test (T-C-T or C-T-C)

The relative motion law:

Xsati =B Y

Cx1; Cx2; EpRef = pref

Uniaxial tension test

Cyclic loading test (T-C-T or C-T-C)

Kinematic hardening of the yield surface:

Rsatx =RsatAM = m


Cyclic loading test (T-C-T or C- -C)

X11, X22, X12

- Yield locus at origin point ( yield point

: 0, 0, 0=)

Xsat


Kinematic hardening of the bounding surface:

Bsat = bsat Uniaxial tension test


The non-isotropic hardening (non-IH) surface:

Hnih= h

Rnih0 = r0



(*) Using the optimization technique

- = -

Xi

- Stagnation

Younga

- Stagnation

EpRef, Rnih0

- default


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Procedure:

A computer code was developed

Aluminum alloy sheetParameter identification

simplex method1

(PAM-OPT can be used alternatively)

Input data:stress - plastic strain curve

cyclic loading test data

various prestrain cases


Y (MPa) C B (MPa) Rsat b (MPa) m h

Value 186.01 561.64 202.20 109.49 33.33 10.20 0.31

Values:

[1] Nelder, J.A., Mead, R. A simplex method for function minimization (1965) Computer Journal, 7, pp. 308-313

NUMISHEET 93 Benchmark model

U-draw bending test

Aluminum alloy sheetSpringback prediction (1)

35

Blank

350

RD

Material: Al5052

Shape: width: 35 mm, length: 350 mm

Punch speed: 0.3 mm/s

Stroke: 70 mm

Blank holding force: 1.3 kN


Unit: mm

Die set and dimensions


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General property

2.6E-6 kg/mm3

Elastic property


FE model and inputs:

Boundary condition

PUNCH

HOLDER

Stroke: 70mm

BLANK

BHF: 1.3kN

E 70 GPa

0.3

Plastic property

Krupkowsky's law: =K(0+P))n

K 398.294

n 0.162

0 0.014


DIE

Fixed

x

z

y

175 mm

17.5 mm

Results




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1 Background



2. - 1. Background

3. 4.


5. Conclusion

Magnesium alloy sheetIntroduction (1)

Characteristics:

Lowest density of all metallic materials

Mg alloy ~170

Al alloy ~120

Steel ~50Excellent welding capability

Good corrosion resistance

High thermal-electric conductivity

Increasing demands

Expanding applicable areas

(Automotive and electronics)


Excellent EMI shielding


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Comparative Material Performance IndexWith same thickness, Mg AZ31B is 77.5% lighter than steel

With same stiffness, Mg AZ31B is 62.8% lighter than steel


Room tem erature 5


Basal plane

Pyramidal planePrismatic plane

Over about 200

HCP structure0

1

2

3

4

0 100 200 300 400()

(kgfmm)

Low formability

Twinning effect

Anisotropy

No twinning effect

Asymmetry is less

(Tension Compression)

0 45 90 R


Asymmetry

Bauschinger effect Good formability

Good formability

Low Bauschinger effect

Low anisotropy

Hurdles: Lower formability at RT and large springback

Cost, high oxidation and low corrosion resistance


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Magnesium alloy sheetCharacterization

Comparative Material Performance

Index

hardening model

Bauschinger effect,

Transient behavior

But always exponential behavior

New hardening rule:Anisotropic/asymmetric yielding

Flow as mmetr durin c clic loadin


Accurate modeling of reverse loading behaviorLarge springback

Correlation between measured stress-strainresponses and calculated ones

Magnesium alloy sheetHardening behavior (2)

@RT 150oC


@RT 150oC


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Yielding asymmetry + unusual hardening behavior:

Magnesium alloy sheetNew constitutive model (1)

Cazacu model Phenomenological yield

surfaces

Cazacu and Barlat, 2004; Cazacu et al.,

2006; Kelley and Hosford, 1968).

Co-existence of

phenomenological yield surfaces

for different deformation modes.


Yield surface ofslip modeYield surface of

twin mode

slip mode

twin mode

Yield surface of

slip modeYield surface ofactivated pyramidal slip mode

slip mode

slip mode

Yield function:

Co-existence of phenomenological yield surfaces


Untwining

021 pp

Consider the history of

deformation: untwining occurs

only after twining

rule is active, others should be inactive.

The criterion on deformation modes decides which yield surface is active.

Criterion on deformation modes: Yield surface ofslip modeYield surface of

twin mode


021 pp

Occurs when the deformation

does not satisfy either twining or

untwining.

slip mode

twin mode

021 pp


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Isotropic hardening rule:

- -


Hardening rule

0iso plocal R

a *1lo c l

local*0

1

1 exp

p

p

baQ

de

R e

sigmoid (S-shape) function


Kinematic hardening rule:

iso

p pd d dC

Chaboche-type model

Types of sigmoid function

Parameter identification:

Using a computer codes

.tens .comp .re tens


Levenberg-Marquardt algorithm

(PAM-OPT is also applicable)

Input data:stress - plastic strain curve

cyclic loading test data: separate the cyclic loading test data into 3 curves:

tension from undeformed state (slip)

Stres

Plastic strain

SLIP TWIN UNTWIN

p

pU

pT

pS


compress on o owng ens on w n

tension following compression (untwin)

various prestrain cases

Output: material card


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User-defined material (UDM):

Input data:



User-defined material (UDM):

Input data:-




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User defined material (UDM):

Input data:


(to appear soon)


Room temperature 150oC


Verification

estress(MPa)

estress(MPa)


True strain True strain

Tr

Tr


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Magnesium alloy sheetSpringback prediction (1)

Results

Room temperature 150oC


Magnesium alloy sheetSpringback prediction (2)

Discussion

The built-in isotropic hardening model in PAM-STAMP fails to

.

The proposed constitutive model can improve much the ability

of springback prediction.

Discrepancies are due to:Calibration was done only with small prestrain.

Correct measurement of BHF.

Friction coefficient.


Youngs modulus.

Degradation of Youngs modulus is an vital factor:Different rules of evolution in tension and compression should be used

simultaneously to improve the result.


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1 Background



2. - 1. Background

3. 4.


5. Conclusion

Conclusion

Lightweight materials (Al and Mg sheets) show complex

behaviors which require more specific material model and/or

technique to simulate.

Characterization the cyclic hardening behavior was

conducted using the newly developed cyclic testing machine.

A procedure was developed to obtain the parameters of the

Y-U hardening model from test data.

The practical new constitutive model for Mg alloy sheet was

implemented as the user defined material (MAT184) in PAM-


STAMP.

Springback prediction using the new model is quite

promising.

Accuracy of the model can be improved by including more

effects.


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.

Q & A



prediction of lightweight alloy sheet

September 13, 2012

Copyright ESI Group, 2012 All rights reserved.Copyright ESI Group, 2012. All rights reserved.

NGOC-TRUNG NGUYEN

[email protected]

ESI Korea Forum 2012.09.13_NGUYEN.pdf

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