Digimatum09 Rhodia Good Practices to Build Robust Digimat Constitutive Models Polyamide Matrixes
Transcript of 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
Gilles ROBERT
Rhodia : Who are we ?
Rhodia Polyamide
Engineering plastics
Rhodia group
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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
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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
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Rhodia Polyamide
Engineering plastics
Rhodia group
Rhodia
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Rhodia Polyamide
Performance Materials
Intermediates & Polymers
N°2 worldwide in
Polyamide 6.6
EngineeringPlastics
N°3 worldwide
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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
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Rhodia Polyamide
Engineering plastics
Rhodia group
Rhodia
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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
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
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
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
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
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
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
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
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.
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
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
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!
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
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
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
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°
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
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
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
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
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
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
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
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
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)
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!
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
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 ?
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
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
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 !
.
Gilles ROBERT
Thank you for your attention