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Some Good Practices to Build Robust DIGIMAT Constitutive Models on Polyamide Matrixes Gilles ROBERT/Olivier MOULINJEUNE

Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

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Page 1: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Some Good Practices to Build Robust DIGIMAT Constitutive Models on Polyamide Matrixes

Gilles ROBERT/Olivier MOULINJEUNE

Page 2: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Rhodia : Who are we ?

Rhodia Polyamide

Engineering plastics

Rhodia group

Page 3: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Organics& Services

2007 net sales : €5 billion

PerformanceMaterials

FunctionalChemicals

NovecarePolyamide Eco Services Organics

Energy ServicesSilceaAcetow

Rhodia in 2009:

an undisputed leader in its core businesses

80 percent of sales generated in markets where the Group is number 1, 2 or 3 worldwide

36 percent of sales generated in fast-growing regions: Asia Pacific and Latin America

Page 4: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

18 PRODUCTION

sites

1 566EMPLOYEES

17% OF SALES

Rhodia in 2009: a global presence

20 PRODUCTION

sites

3 210EMPLOYEES

20% OF SALES

7 PRODUCTION

sites

3 063EMPLOYEES

16% OF SALES

24 PRODUCTION

sites

8 085EMPLOYEES

47% OF SALES

Page 5: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Rhodia Polyamide

Engineering plastics

Rhodia group

Rhodia

Page 6: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Rhodia Polyamide

Performance Materials

Intermediates & Polymers

N°2 worldwide in

Polyamide 6.6

EngineeringPlastics

N°3 worldwide

Page 7: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Industrial sites

14 plants worldwide

N°2 in Polyamide 6.6

N°3 in Engineering Plastics

Polyamide: A sustainable pillar of Rhodia

40% Group Net Sales 41% Group Recurring EBITDA

Net Sales

€ 1,975 million

Employees

4,000

2007 data

Page 8: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Rhodia Polyamide

Engineering plastics

Rhodia group

Rhodia

Page 9: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Leveraging our mastery of the PA 6.6 chain:

from intermediates to polymers and compounds

• Polymers and compounds

with improved ageing

and high temperature

performances

• Cost effective polymers

and compounds with improved

"Flowability" and surface aspects

• Compounds with higher dimensional

stability

• Application development

• Design support

Page 10: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Summary

Data used for matrix behaviour identification

Impact of data quality on modeling : some examples

Building an elastoplastic model : impact of input data

What should be taken into account in the constitutive

model

Page 11: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Summary

Data used for matrix behaviour identification

Impact of data quality on modeling : some examples

Building an elastoplastic model : impact of input data

What should be taken into account in the constitutive

model

Page 12: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Matrix identification with Digimat : input data

• The material : Polyamide 6.6 filled with glass fibres

• The target : identify PA66 matrix mechanical properties

• Glass properties necessary :

• Modulus, density, Poisson’s ratio

• No specific difficulty

• Glass fibres properties :

• Weight fraction

• Measured after burning away the polymer

• Simple and accurate, weak fluctuations

• Aspect ratio

• Measured by image processing

• Accuracy can be sometimes be questioned

• Orientation

• Modelled

• Or measured

• Accuracy must be questioned

Page 13: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Quantification of orientation

• Injection molding of short glass fibres

reinforced polymer generates orientation

• Orientation of a fiber is described with

• θ,φ Euler angles

• Many ways to represent orientation of a

population :

• Ψ (θ, φ) distribution function

• No information loss

• Orientation tensors

• Hand (’62)

• Tensors and orientation functions represent

only a part of total information available in Ψ

(θ, φ)

x

y

z

f

q

q

fq

fq

cos

sinsin

cossin

3

2

1

p

p

p

Page 14: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Orientation tensor a2

• a2 is the most common representation of fiber orientation

• Used by Folgar and Tucker model

• Essential in injection Molding

• Used by Moldflow, Moldex, REM3D…

• a2 must be used simultaneously with a4

• a4 expressed as a function of a2 thanks to closure approximations

qfqqfqq

fqqfqffq

fqqffqfq

2

222

222

cossincossincoscossin

sincossinsinsincossinsin

coscossincossinsincossin

00

01

10

00

5,00

05,0

Page 15: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Summary

Data used for matrix behaviour identification

Impact of data quality on modeling : some examples

Building an elastoplastic model : impact of input data

What should be taken into account in the constitutive

model

Page 16: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Summary

Data used for matrix behaviour identification

Impact of data quality on modeling : some examples

Building an elastoplastic model : impact of input data

What should be taken into account in the constitutive

model

Page 17: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Approach followed

• How to identify the impact of input data on matrix elastic modulus identification ?

• Input mechanical data : modulus of a dumbbell

• Study of changes

• In orientation tensor used

• … on the matrix modulus identified

• Then comparison with modulus measured for several orientations and those

modelled.

Page 18: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Impact of orientation tensors on identifications

• Three tensors :

• Measured

• Modelled with Moldflow Mid Plane

• Automatic choice of parameters

• Modelled with Moldflow MidPlane,

• Optimised parameters

• Constant aspect ratio

• Same composite modulus for

identification

• Mistake quite important

360

100

50

100

2

Thickness=2,1mm

100

1gate

0

0,2

0,4

0,6

0,8

1

1,2

0 500 1000 1500 2000

Position in thickness (µm)

ori

en

tati

on

a1

1

Expérimental

Auto

Optimum

a2 Moldflow auto Ematrix=2715 MPa

a2 Moldflow opt. Ematrix=3460 MPa

a2 µtomo Ematrix=3250 MPa

Page 19: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Impact of mistakes : general case

• Use of Moldflow mid plane requires

precautions

• With optimised parameters : good

predictions

• Though not perfect

• Auto modelling : 25% max. mistake

• Best choice for identification :

measured tensors

4000

5000

6000

7000

8000

9000

10000

11000

0 20 40 60 80 100

Angle between fibres and strain applied (°)

Mo

du

lus

(MP

a)

Experimental values

Modelled values_a2_Moldflow_auto

Modelled values_a2_Moldflow_optim

Modelled values_a2_µtomo

Page 20: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

First conclusions

• First good practises :

• Be careful with Moldflow mid plane

• Optimised parameters are compulsory for good data fitting

• And experimental measurements of orientation are even better

• Sensitivity to aspect ratio is lower, but only in the linear range!

Page 21: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Summary

Data used for matrix behaviour identification

Impact of data quality on modeling : some examples

Building an elastoplastic model : impact of input data

What should be taken into account in the constitutive

model

Page 22: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Summary

Data used for matrix behaviour identification

Impact of data quality on modeling : some examples

Building an elastoplastic model : impact of input data

What should be taken into account in the constitutive

model

Page 23: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

0

50

100

150

200

250

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5

Engineering Strain (%)

En

gin

ee

rin

g S

tre

ss (

MP

a)

0

50

100

150

200

250

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5

Engineering Strain (%)

En

gin

ee

rin

g S

tre

ss (

MP

a)

Bottom line

• Minimal values necessary for matrix

identification :

• Tensile curve “ISO 527” as found in

Campus

• Moldflow modelling of the dumbbell

• Aspect ratio (nicely given in Moldflow)

• Identification of elastoplastic behaviour of

the matrix

• Modulus

• Re

• R∞

• m

• Use of spectral method for

homogenisation

Ematrix 3020 MPa

RE 14,1 MPa

R∞ 34,8 MPa

m 258,8

∑( RE+ R∞) 48,9 MPa

Page 24: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Bottom line : comparison with tensile trials at several

angles

• Constitutive model applied to tensile

specimens cut in plaques

• Same aspect ratio

• Structure modelled with MF

• 23°C, dry, 10-3s-1

• Results are rather good

• However

• Between 5% and 25% mistake on

elastic modulus

• Between 5% and 20% mistake on

stresses

Lines : experimentsDots : Digimat

0

50

100

150

200

0,00 0,02 0,04 0,06 0,08 0,10

True strain

Tru

e s

tre

ss (

MP

a)

fibres0°

15°

30°

45°

60°90°

Page 25: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

How to go further ? (1)

• Always with a single tensile curve

• Use optimised parameters in Moldflow

• Use measured aspect ratios

• Re quite sensitive to aspect ratio

• Or use direct measured orientation tensors

• Laws quite dissimilar. Which one is best ?

AR literaturea2 MF auto

Measured ARa2 MF auto

Measured ARa2 MF optim

Measured ARMeasured a2

Ematrix3017 3080 2715 3406

RE14,1 15,2 20,3 20,7

R∞34,8 36,2 27,5 36,7

m 258,8 270,9 234,6 248,3

∑( RE+ R∞) 48,9 51,4 47,8 57,4

Page 26: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

How to go further ? (2)

• The only way to discriminate the

models :

• Use at least 2 tensile curves.

• With measured input data,

transverse behaviour is better

predicted

• Which improvement to expect ?

0

50

100

0,00 0,02 0,04 0,06 0,08 0,10

True strain

Tru

e s

tre

ss (

MP

a)

fibres

90° exp

90° "bottom line"

90° one curve, measured structure

Page 27: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Matrix behaviour identification with two tensile curves

• Choice of an identification based on two tension curves with varying angles

• 0 and 30°

• 0 and 45°

• 0 and 90°

• Experimental conditions

• Room temperature

• Strain rate 10-3s-1

• Material : dry polyamide 66 filled with 30w% glass fibers

Page 28: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Results

• Identifications quite OK

• 0-45° fits slightly better

0°-30°

0°-45°

0°-90°

0

20

40

60

80

100

120

140

160

180

200

0,00 0,02 0,04 0,06 0,08

Strain

Str

ess

(MP

a)

Trac_Digi_0 (0°-45°)

Trac_Digi_45 (0°-45°)

Trac_exp_0

Trac_exp_45

0

20

40

60

80

100

120

140

160

180

200

0,00 0,01 0,02 0,03 0,04 0,05 0,06

Strain

Str

ess

(MP

a)

Trac_Digi_0 (0°-90°)

Trac_Digi_90 (0°-90°)

Trac_exp_0

Trac_exp_90

0

20

40

60

80

100

120

140

160

180

200

0,00 0,01 0,02 0,03 0,04 0,05 0,06

Strain

Str

ess

(MP

a)

Trac_Digi_0 (0°-30°)

Trac_Digi_30 (0°-30°)

Trac_exp_0

Trac_exp_30

Page 29: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Conclusions

• Accuracy only slightly improved

• 0°-90° is not the best choice to build a matrix constitutive model

• Main change : RE is much higher when two tensile curves are used

• Matrix plasticization changes much, while tensile behaviour is quite constant

• Optimal method to identify a constitutive model still not found

Identification

0°-30°

Identification

0°-45°

Identification

0°-90°

Ematrix 3050 3050 3050

RE (MPa) 36,8 39,5 39,8

R∞ (MPa) 12 14,8 22,9

m 241,2 96,8 54,6

∑(RE+R∞) (MPa) 48,8 54,3 62,7

Page 30: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Matrix identification with six tensile curves

• For some specific conditions

• W% fibres

• Temperature

• Water content

• Strain rate

• Six different orientations have been

tested.

• Optimal fit is performing

• Except at 30°

• And 90°

• If two curves only are used : best

choice 0° and 45°

• Constitutive models for 6 curves or

2 curves, 0° and 45° are close

Page 31: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

• Use of modified spectral

• Modulus and Poisson’ ratio fixed

• RE

• R∞

• m

• 3/4 possible parameters

• free variables

• Residual mistake on stresses reduced

from 8% to 4,5%

• Situation worse at 0°

• But much better on all other angles

Change of isotropisation method

0

20

40

60

80

100

120

140

160

180

200

0 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08

True strain

Tru

e s

tre

ss

(MP

a)

0°_exp15°_exp30°_exp45°_exp60°_exp90°_exp0° Digi15°_Digi30°_Digi45°_Digi60°_Digi90°_Digi

0

20

40

60

80

100

120

140

160

180

200

0 0,02 0,04 0,06 0,08

True strain

Tru

e s

tre

ss (

MP

a) 0°_exp

15°_exp30°_exp45°_exp60°_exp90°_exp0° Digi15°_Digi30°_Digi45°_Digi60°_Digi90°_Digi

Page 32: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Extension of constitutive models

• Constitutive model of the matrix determined for

• Several w% fibres

• Several w% water

• Several temperatures and strain rates

• For many sets of parameters : three tensile curves measured

• Main conclusions :

• Parameters of modified spectral isotropisation methods are constant• 18 sets of three tensile curves

• Each time identification converges towards similar values

• Aspect ratio and orientation have a big impact• Especially on RE

87,572,662,351,9∑(RE+R∞) (MPa)

120,6174,7118,896,2m (MPa)

52,137,126,414,1R∞ (MPa)

36,435,535,937,8RE (MPa)

3240305032403050Ematrix (MPa)

6 curvesseveral w% fibresoptimal modified

spectral

6 curves1w% fibres

optimal modified spectral

6 curvesseveral w%

fibresspectral

6 curves1w% fibres

spectral

87,572,662,351,9∑(RE+R∞) (MPa)

120,6174,7118,896,2m (MPa)

52,137,126,414,1R∞ (MPa)

36,435,535,937,8RE (MPa)

3240305032403050Ematrix (MPa)

6 curvesseveral w% fibresoptimal modified

spectral

6 curves1w% fibres

optimal modified spectral

6 curvesseveral w%

fibresspectral

6 curves1w% fibres

spectral

Page 33: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Extension of constitutive models (2)

• Comparison between experimental

matrix and real matrix

• With spectral modified method, both

curves are very close

• But of course, you have to choose

the right values for the four

parameters….

0

10

20

30

40

50

60

70

80

90

100

0,00 0,05 0,10 0,15 0,20

Déformation

Co

ntr

ain

te (

MP

a)

10-4s-110-3s-110-2s-110-3s-1 exp10-4s-1 exp

Strain

Str

es

s (

MP

a)

Page 34: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Conclusions

• To develop good constitutive models :

• Be careful about orientation modelling

• Except if optimised parameters are available

• Use at least two tensile curves

• Or the yield won’t be determined accurately

• Choose the right angles

• Avoid transverse tensile tests

• Be very careful about the microstructure

• Preferred measured characteristics

• If you really want accuracy :

• Work on isotropisation method

• And take carefully into account the polymer behaviour!

Page 35: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Summary

Data used for matrix behaviour identification

Impact of data quality on modeling : some examples

Building an elastoplastic model : impact of input data

What should be taken into account in the constitutive

model

Page 36: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Summary

Data used for matrix behaviour identification

Impact of data quality on modeling : some examples

Building an elastoplastic model : impact of input data

What should be taken into account in the

constitutive model ?

Page 37: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Extension of constitutive models : what’s next ?

• Polyamide behaviour is not equal

in tension and compression.

• Difference between both

solicitations depends on :

• Temperature

• W% of fibres

• Constitutive models used should

be pressure sensitive.

• Drücker-Präger ?0

50

100

150

200

250

0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16

True strain

Tru

e s

tre

ss (

MP

a)

0°_tensile

15°_tensile

45°_tensile

60°_tensile

0°_compression

15°_compression

45°_compression

60°_compression

Page 38: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

• Polymers close to glass transition are

not elastoviscoplastic

• They are also viscoelastic

• Models developed on purpose are a

necessity

Extension of constitutive models : what’s next ?

Frequency(Hz)

Mo

du

lus (

MP

a)

23°C

0

20

40

60

80

100

120

140

160

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

Strain

Str

ess

(M

Pa

)

100s-1

10-4

s-1

Page 39: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

DIGIMAT-MX release : Rhodia offer

• Based on the identification work presented here …

• Accurate aspect ratio distribution measurement

• µTomography for experimental fiber orientation tensors

• Large experimental database in tension, compression and high speed

• At various speed, temperature and humidity content

• Accurate retro fitting of matrix properties

• Global model identified : F ( T , W% , , Moisture ) to generate a coherent database

• RHODIA Polyamide offers two levels of availability for all TECHNYL PA66 grades from

15% to 50% :

• Direct access to :

• all elastic models, in temperature and humidity

• elasto-plastic models, at 23° and 60°C dry and conditioned

• On demand access to :

• all temperature elasto-plastic models

• all temperature elasto-visco plastic models

• Thermo-elastic and dilatation models

• All data are directly usable in Digimat as .mat file !

.

Page 40: Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes

Gilles ROBERT

Thank you for your attention