Material Models in Simulation- Part 3 - New viscosity models
Transcript of Material Models in Simulation- Part 3 - New viscosity models
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Material Models in Simulation-
Part 3 - New viscosity models
Hubert Lobo
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Evaluation Parameters
material property based parameters
evaluate effects seen in the process
understand and interpret simulation results
compare materials
develop criteria for selection based on desired
processability
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Properties of Evaluation
Parameters
easily available
measures or estimates of actual effects
must be considered along with other relevant
parameters
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Shear sensitivity of viscosity
10
100
1000
10 100 1000 10000 100000
Shear Rate 1/s
Vis
co
sit
y P
a∙s
.
200 °C
230 °C
260 °C
Newtonian
Shear-
thinning
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Plastics may have large shear
thinning regions
10
100
1000
10000
10 100 1000 10000 100000
Shear Rate 1/s
Vis
co
sity
Pa
·s .
180 °C
190 °C
200 °C
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Temperature sensitivity of
viscosity
1
10
100
1000
150 170 190 210 230 250 270Temperature (°C)
Vis
co
sity
(Pa
•s)
100 s-1
1000 s-1
10000 s-1
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Evaluation Parameters -
2nd Order
nature of the 2nd order matrix
– temperatures
» Tmelt
» Tmelt+20
» Tmelt-20
– shear rates
» 100
» 1000
» 10000
T
Tmelt-20 1000
Tmelt 100
Tmelt 1000
Tmelt 10000
Tmelt+20 100 Tmelt+20 1000
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Evaluation Parameters -
2nd Order
temperature sensitivity of viscosity
– TVL= ( ln- ln ) / 20
– TVH = ( ln- ln ) / 20 T
Tmelt-20 1000
Tmelt 100
Tmelt 1000
Tmelt 10000
Tmelt+20 100 Tmelt+20 1000
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Evaluation Parameters -
2nd Order rules
– if TV is large, material is highly sensitive
– TVL > TVH
– semi-crystalline
» TVL == TVH
– amorphous
» TVL >> TVH
PP
ABS
PS
PC
PPA
0 10 20 30 40 50 60
TV* 1E+03
PP
ABS
PS
PC
PPA
Resin
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Evaluation Parameters -
2nd Order
shear sensitivity of viscosity
– defining a limited power-law index.
» SHB= ( ln- ln ) / 2.303
T
Tmelt-20 1000
Tmelt 100
Tmelt 1000
Tmelt 10000
Tmelt+20 100 Tmelt+20 1000
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Evaluation Parameters -
2nd Order rules
– 0<SHB < 1
– large SHB = shear sensitive
– important exception:
» broad newtonian (eg.
PC)
10
100
1000
10000
10 100 1000 10000 100000
Shear Rate (s-1
)
Vis
co
sity
(Pa
•s)
180 °C
200 °C
220 °C
240 °C
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New models used in Moldflow
viscosity:
Cross Model
NΒ
P
T
Pa
PT
TB b
N
, , , , :Unknowns
Pa Pressure
C eTemperatur
sec RateShear
sec.Viscosity
expexp
1
*
b
1-
0
1
*
0
0
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Evaluation Parameters -
Cross Model B -no direct relevance
measures o when taken with Tb
“zero shear viscosity normalized for temperature”
T
TB bexp0
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Evaluation Parameters -
Cross Model
Tb -measures temperature sensitivity of viscosity
rules
– if Tb is large, material is highly sensitive
– semi-crystalline
» Tb is small and relatively constant
– amorphous
» Tb is larger and increases with temperature
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Evaluation Parameters -
Cross Model
* -critical transition stress for shear-thinning behavior
rules
– if * is large, wide Newtonian region
– if * is small, narrow Newtonian region
– * is small for simple linear polymers
» eg HDPE, LDPE, PP
– * is large for polymers with large side chains
» eg. PC
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Evaluation Parameters -
Cross Model N - measures shear thinning behavior
– inverse of the power-law index
rules for N
– 0 < N < 1
– small N = shear sensitive
– important exception:
» fails if shear thinning region is not defined
10
100
1000
10000
10 100 1000 10000 100000
Shear Rate (s-1
)
Vis
co
sity
(Pa
•s)
180 °C
200 °C
220 °C
240 °C
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Assessment of the Cross Model
easy model
– terms have direct physical relevance
– easy to assess and evaluate
temperature sensitivity of viscosity is constant
– cannot model temperature sensitivity for
amorphous materials
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New models used in Moldflow
viscosity:
Cross-WLF
NAADDD
P
T
Pa
PDDT
TTA
TTAD
N
:Unknowns
Pa Pressure
C eTemperatur
sec RateShear
sec.Viscosity
exp
1
*
21321
1-
32
*
*
2
*
110
1
*
0
0
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Evaluation Parameters -
Cross-WLF Model
D1 -no direct relevance
similar to B
measures o when taken with WLF equation
“zero shear viscosity normalized for temperature”
*
2
*
110 exp
TTA
TTAD
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Evaluation Parameters -
Cross-WLF Model
D2 - a reference temperature
theoretically, the temperature where goes to
typically D2=Tg, and = 109 Pa.s
D3 defines the pressure sensitivity of D2
PDDT 32
*
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Evaluation Parameters -
Cross-WLF Model
A1 & A2 - WLF parameters
A1 defines the temperature sensitivity of viscosity
A2 defines change in temperature sensitivity with
temperature
classical WLF parameters are
– A1 = 40.1, A2 = 51.6; if D2 = Tg
– not always so for plastics
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New models used in Moldflow
viscosity:
Carreau Model
NTB
T
Pa
PT
TB
b
b
N
, , , , :Unknowns
Pa Pressure P
C eTemperatur
sec RateShear
sec.Viscosity
expexp
1
*
1-
0
2
12
*
0
0
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Evaluation Parameters -
Carreau Model similar to Cross model
terms have similar relevance
Carreau Model will give sharper transitions from
Newtonian to shear thinning region
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If the data follows the model
Cross 2nd Order
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100
1000
10 100 1000 10000 100000
Shear Rate 1/s
Vis
co
sit
y P
a∙s
.
260 °C
270 °C
280 °C
290 °C
10
100
1000
10 100 1000 10000 100000
Shear Rate 1/s
Vis
co
sit
y P
a∙s
.
260 °C
270 °C
280 °C
290 °C
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If the data does not follow the
model
10
100
1000
10000
10 100 1000 10000 100000
Shear Rate 1/s
Vis
co
sit
y P
a∙s
.
60 °C
75 °C
90 °C
10
100
1000
10000
10 100 1000 10000 100000
Shear Rate 1/s
Vis
co
sit
y P
a∙s
.
60 °C
75 °C
90 °C
Cross 2nd Order
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Issues in data fitting
rheological data may not be complete
complete data should contain Newtonian & shear
thinning regions
data must show the right temperature sensitivity
trends
if not, model coefficients are indeterminate
extrapolation will be dangerous
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New models are constrained
models
not generalized; designed for polymers
predict the expected trends for polymers
incorporate both Newtonian and shear-thinning
behavior
do not work well if polymer does not follow expected
trend (rare cases)
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Benefits of constrained models
predict a particular kind of behavior
prevent inaccuracies in measured data from affecting
the model
safer to use
model coefficients have useful interpretations
are adaptable to master-curves
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Conclusions
we have a wider range of models for simulation
each has its own benefits
with new Moldflow formats, we can select the best
model.
model coefficients contain vital information
– if properly understood, they will save you time and
money
see previous presentations (MUG ‘96 & MUG’97) for
details on how to use evaluation parameters.