on the development, verification and validation of a semi...

1ADMOS 2005 Barcelona / 09-2005 / Haufe et al.

A. Haufe₤, M. KöstersҰ, P. DuBois¥, M. Feucht‡, S. Kolling‡ ₤ DYNAmore GmbH, Stuttgart, Germany

Ұ North Eastern University, USA¥ Consultant, Offenbach, Germany

‡ DaimlerChrysler AG, Sindelfingen, Germany

On the Development, Verification and Validation of a semi-analytical Model for Polymers

subjected to dynamic Loading


Introduction and motivation Overview on an extended V&V process Details of a new material model Verification of implementation Calibration by simple tests Validation of constitutive model Outlook

For inquiries please contact Dynamore GmbHDr. Andre HaufeIndustriestraße 2

70565 Stuttgarthttp://www.dynamore.de

Overview


More and more structural parts are made from plastics. At present important crashworthiness applications are:

Pedestrian protection (bumper, fascia, hood, adhesives) Passenger protection (cockpit, internal structures)

Their mechanical behaviour is strongly dependent on Underlaying chemical structure and production process Temperature, strain rate etc.

Many thousand different blends are available today!!

Motivation


V&V processes for complete FE models

V&V process of each individual part of the numerical model necessary:

In engineering practise the numerical model shall correlate to experimental data close enough, to allow sound predictions in a predefined range of model variations.

Element formulation, type & size

Global solution strategy

Constitutive model

… more …

Discretisation depth & modeling techniques


V&V processes for complete FE models


Extended V&V process for material model dev.

Validationof verified and calibrated

model by experiments

[Schwer 2002]

Calibrationof verified model to gain

material parameters

Verificationof implemented

constitutive model

Identificationof characteristic material behaviour with respect to

the application

Implementationinto a suitable comp. mech.

code.


Plastics is a group name comprising many different materialsMechanical response at room temperature may be glassy or rubbery,

brittle or viscous

Fiber reinforcement may cause anisotropic response Rib reinforcements represent an important modeling effort

stre

ss

1 2

34

5

strain

ε& Z

T Z

1 glasslike behaviour2 plastic or viscous flow3 low ductility

Identification challenge: Structures made of plastics

4 high ductility5 rubbery

amorphous thermoplasticcrystalline thermoplastic

thermoset plastic (Duroplast) elastomerthermoplastic


Identification:Requirements for a model targeting polymers

Plastic incompressibility is not a realistic assumption for the most polymers Hence a pressure dependency must be considered in the yield surface and the plastic potential

i. e. the plastic flow Initial isotropy – on a macroscopic level - will be disturbed eventually by straining:

Molecule chains will be stretched leading to induced anisotropic behaviour Different behaviour in tension, compression and shear direction

Homogeneousinitial state

Shear loading

Tension loading

Compression loading

Von Mises strain [-]

Vo

n M

ise

s st

ress

[M

Pa

]


Identification:Requirements for a model targeting polymers

True strain

Tru

e St

ress

In addition crazing and the development of shear bands have to be taken into account

Young’s modulus and failure strain show a strong dependency on the strain rate Sometimes even viscose effects can be observed in the elastic region Investigation on the unloading behaviour show damage effects (strain rate dependent)

[Junginger 2002]

Crazing effect Shear band development

Weak connectionTension connection Weak connection

Interlaminar defect

Amorphous region

Crystallized domainfillervoid

Separatedalien phase

End of chain


Identified yield loci for different plastics

Polycarbonate

[Vogler 2005]

Polypropylene (PP)

Polyvinylchloride (PVC) Epoxy resin CY232 (EP)


Classification of polymers (from a structural point of view) according to their mechanical behaviour

elastomers elastic foams

crushable foams Plastics/polymers

Which of the observed mechanical effects are important to consider for the targeted application of the constitutive model?

Hyperelastic/viscous behaviour

Visco-hyperelastic-visco-plastic behaviour

Identification summary: Structures made of plastics

Polymer blends show a wide range in their characteristic behaviour!


SAMP-1: Semi-Analytical Model for Polymerswith C1-continuous yield surface

vmg pσ α= −2 2

Plastic potential:

( , , )plvm vmf p A A p A pσ ε σ= − − −2 2

0 1 2 0

Yield surface:

p

f = 0

3

1

0

q

To achieve a fast and easy calibration process, test results from tension, compression and shear tests can be fed directly into SAMP-1 via table definitions:

compressiontension

shear

22 2

0 1 2

33 9 9c t c t s

s sc t c t

A A Aσ σ σ σ σσ σσ σ σ σ

− −= = =

Tension test data

tε

tσ

Compression test data

cε

cσ

Shear test data

sε

sσ

Therefore the yield surface coefficients A0,1,2 are calculated directly from stresses gained from a table lookup:


SAMP-1: Damage and failure

( ) [0,1[plχ ε =

cd

Damaging of the stresses by scalar curve definition (plastic damage)

( )( )pleff pl χ ε= −σ σ 1

0,00 0,01 0,02 0,03 0,04 0,05

0

0

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

6

6

6

6

7

7

7

7

8

8

8

8

9

9

9

9

10

10

10

10

11

11

11

11

12

12

12

12

13

13

13

13

14

14

14

14

15

15

15

15

16

16

16

16

17

17

17

17

18

18

18

18

19

Spalte B Spalte B Spalte B

wahre Dehnung [-]

wah

re S

pann

ung

[MP

a] E0Eeff1 Eeff2

Tru

e St

ress

True strain

TestApproximated effective modulus of elasticity

Failure onset defined by the parameter , further fading of the element defined by

d

ε p

ε∆ prupt

cd

1.0

pruptε∆


Verification and calibration

Verification of the implemented model was done by means of simple, strain driven one-element tests. Clearly, the input as curve definitions should be given by the model directly as output for the corresponding load cases.

Limiting cases (e. g. standard von Mises plasticity) have been checked against available constitutive models in the software package LS-DYNA.

Robustness and stability - not efficiency – were checked during the whole V&V process and was steadily improved.

Verification

The calibration process is somewhat simplified for a semi-analytical model, since test results despite being gained through small structural tests, are fed to the constitutive model directly.

Calibration


-200

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30

force

[N]

displacement [mm]

PP_EPDM tensile tests

experiment quasi staticexperiment slowly

experiment middle experiment high

simulation quasi staticsimulation slowly

simulation middlesimulation high

Calibration PP_EPDM -1-

Tensile test

48.6

mm

8x20 mmF

orce

Displacement

F

F

Tensile test conducted by Ernst-Mach-Institute/Freiburg/Germany

- for different strain rates Quasi static ≈ 1e-04 [mm/ms] Low ≈ 7e-03 [mm/ms] Medium ≈ 0.5 [mm/ms] High ≈ 8.75 [mm/ms]

- with unloading Material model calibrated for 2mm shell elements (BT, 1 point integ.)


0

50

100

150

200

250

300

350

400

450

500

0 0.5 1 1.5 2

force

[N]

displacement [mm]

tensile tests with unloading

experiment unloadingsimulation with damage

simulation no damage


Tensile test

48.6

mm

8x20 mmF

orce

Displacement

Unloading at 125% yield stress

F

F





0

50

100

150

200

250

300

350

400

450

500

0 5 10 15 20 25 30

force

[N]

displacement [mm]

tensile tests with unloading

experiment unloadingsimulation with damage

simulation no damage


Tensile test

48.6

mm

8x20 mmF

orce

Displacement

Unloading at 80% rupture strain

F

F





0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14 16

force

[N]

displacement [mm]

DKI PP_EPDM compression tests : 2.5mm mesh

experimentsimulation


Compression test

To achieve this fit from tension test data, the shear

curve had to be multiplied by a factor of 2.0!

40x60 mm

F

F

For

ce

Displacement

Compression test conducted at DKI/Germany Quasi static loading Thickness = 4.0 mm Straining measured additionally by optical analysis (GOM) Specimen was fixed at top/bottom and hold sideways to prevent

buckling The tabulated input data had to be transformed into true stress/true

equivalent plastic strain curves Material model calibrated for 2.5 mm shell elements (BT, 1 point integ.)



Shear test Shear test conducted at DKI/Germany Quasi static loading Thickness = 4.0 mm Straining measured additionally by optical analysis (GOM) Specimen was fixed at top and bottom Material model calibrated for 1.0 mm shell elements (BT, 1 point integ.)

F

F

0

50

100

150

200

250

300

350

400

450

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

force

N

displacement mm

PP_EPDM - Shear Test

experimentsimulation

For

ce

Displacement

Artificially increased stiffness and strength due to enforced

convexity of yield surface.


Validation PP_EPDM

Three point bending test

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8 10 12 14 16

force

[N]

displacement [mm]

Bending test : PP_EPDM : 2mm shells

experimentsimulation SAMP1

vonMises

For

ce

Displacement

SAMP-1 compared to tension test-validated von Mises input

parameters!

F

Specimen size 10 x 133 x 3.8 mm Downward prescribed displacement (quasi static) Solid elements, 1mm mesh size

Overall we see good agreement with the results of small bending validation tests so far. However, tests on component basis (bumper, fascia etc.) are still to be done.


Most critical issues have been addressed with SAMP-1 Damage and strain rate dependence Failure and unloading Load direction dependent behaviour Pressure dependent plastic potential

Features still missing: Crazing Transition to anisotropic behaviour

Future work: Further testing of material model Calibration and validation of more polymers Simulation of more component tests

LS-DYNA Forum 2005, October 21&22, Bamberg, Germany

Roadmap for public release: SAMP-1 should be available in the next release of LS-DYNA (971)

Conclusions and outlook


Thank you for your attention.


Stress update algorithms

( )( )( )

( )

1 1 1

1

1

1

1

1

1

1

1 1

1 1 11

:

:

: : :

: :

:

:

p pn n n n

p pn n n

p pn n n

pn n

n

trial pn

n

n

n

n

n

trialn n n

C

C

C C C

C C

C

C r

σ ε ε ε

ε ε ε ε

ε ε ε ε

σ ε εσ ε

σ

σ

σ

σσ

λσ

+ + +

+

+

+

+ +

+

+

+

+

+

+ + +

= − − ∆

= + ∆ − − ∆

= − + ∆ − ∆

= + ∆ − ∆

= − ∆

= − ∆

nσ

1trialnσ +

sII

sIsIII

1nσ +


Stress update algorithms:NEWTON-iteration

nσ

1trialnσ +

sII

sIsIII

1nσ +

Backward Euler return mapping or general closest-point-projection or radial return

linearization around the elastic trail state :

1 11 1

11 1 1 1

( ) 0

( )

k k kn n

kk k k k n

ff f d

fd

f

λλ

λ λ λ λ

λ

− −+ +

−− − − +

= + ∆ =∆

∆ = ∆ + ∆ = ∆ −

∆

fully implicit algorithm


Stress update algorithms:cutting plane

explicit algorithm

1 11 1

11 1 1 1

( ) 0

( )

k k kn n

kk k k k n

ff f d

fd

f

λλ

λ λ λ λ

λ

− −+ +

−− − − +

= + ∆ =∆

∆ = ∆ + ∆ = ∆ −

∆

nσ

1trialnσ +

sII

sIsIII

linearization around the elastic trail state :


Validation by three point bending test with PP-EPDM

0,00E+00 1,00E+01 2,00E+01 3,00E+01 4,00E+01 5,00E+010

2,5

5

7,5

10

12,5

15

17,5

20

22,5

25

27,5

30

32,5

Spalte C

Spalte D

SAMP-0: experimental results (tension and compression test) have been used directly as input data for this three point bending test.

Specimen size 10 x 133 x 3.8 mm Downward prescribed displacement (quasi static) 3 integration points across thickness direction

Tensile TestCompression Test


Three point bending test with PP-EPDM

on the development, verification and validation of a semi...

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