digimatum09 rhodia good practices to build robust digimat constitutive models polyamide matrixes
TRANSCRIPT
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
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
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18 PRODUCTION
sites
1 566EMPLOYEES
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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
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
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