solidification criteria and rheology during solidification giuseppe titomanlio university of salerno...
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Solidification criteria and
rheology during solidification
Giuseppe TitomanlioUniversity of Salerno Italy
PIAM Winter School, January 15-19, 2007 Aussois, France
What do we mean by solidification criteria?
Non flow Non flow temperature, Ttemperature, Tnf nf :: Solidification Solidification temperature, Ttemperature, Ts s ::
The two temperatures in principle can be very different
ViscosityViscosity is is one or two one or two orders of magnitude orders of magnitude largerlarger than every where than every where else in the same cross else in the same cross sectonsecton
Relaxation timeRelaxation time is much is much largerlarger than the cooling than the cooling timetime
They are often regarded as a single temperature
and . . . . they can also be very close
About non flow and solidification criterion
Amorphous polymers Amorphous polymers
Tg: WLF Tg: WLF Semicrystalline polymersSemicrystalline polymers
Tg changes with
Pressure and cooling rate
Both non flow and Both non flow and solidification conditions are solidification conditions are determined by crystallinity, determined by crystallinity, XXnfnf and and XXss
and thus by and thus by crystallizationcrystallization temperature and temperature and kineticskinetics
CTT
TTA
TTAD g
; exp2
110
Amorphous polymers, aPS
reported by Zoetelief. Solidification temperature was chosen reported by Zoetelief. Solidification temperature was chosen as indicated by Zoetelief asas indicated by Zoetelief asTs(P)=100°C+0.051K/barTs(P)=100°C+0.051K/bar 8.68.6
As mentioned above, a solidification temperature should As mentioned above, a solidification temperature should depend also on cooling rate. If indeed this approach is depend also on cooling rate. If indeed this approach is followed, the following expression is obtained for Tsol:followed, the following expression is obtained for Tsol:
8.78.7where both the reference temperature and the constant where both the reference temperature and the constant describing the effect of describing the effect of
Tsol 81C 2logqsol
1Cs 1
0.051
Cbar
P
•Dependence upon cooling rate q: 2log (q/1°C/s)
•Dependence upon pressure P: P *0.05 °C/bar
Often non flow and solidification temperatures are
regarded as a single temperature,
for amorphous polymers
T, [ºC]
85
90
95
100
105
110
115
120
125
130
135
0 200 400 600 800 1000
1 ºC/s100 ºC/s10000 ºC/s
P, bar
Tg (P, T’)Tg (P, T’)
• DOW PS 678E
Outline
2.2. Observations and modelling of rheology Observations and modelling of rheology evolution during crystallization evolution during crystallization
3.3. Role of non flow criterion in the simulation of Role of non flow criterion in the simulation of injection moulding and identification of the injection moulding and identification of the proper crystallization kinetic modelsproper crystallization kinetic models
4.4. Solidification Criterion and its relevance on Solidification Criterion and its relevance on internal stresses and warpageinternal stresses and warpage
1.1. Non flow and solidification temperaturesNon flow and solidification temperatures
Solidification ProcessSolidification Process amorphous vs Crystalline behaviouramorphous vs Crystalline behaviour
Amorphous Polymer Viscosity
Model Extrapolation
Measurements
SolidificationTemperature
Melt Temperature
MoldTemperature
Depend on the Solidification Conditions
Vis
cosi
ty
Semicrystalline Polymer Viscosity
Viscosity increase with crystallinity is always sharp
iPP T30GiPP T30G
An example of quiescentcrystallization
Sferulites are seen when they are already big
RheologyRheology vs crystallinity , suspension vs crystallinity , suspension viewview
1. Small molecules: solid particles suspension
Rheology changes with time because particles grow, with very small interactions.
Interactions became relevant only at the end
NUCLEI ACT AS PHYSICAL CROSSLINKS NUCLEI ACT AS PHYSICAL CROSSLINKS
3. A different, melt structure-based view
The small crystalline nuclei ACT AS physical crosslinks which produce an apparent molecular
weigth increase with a parallel fast viscosity change.
A nucleus
Crystallization determines a network?Crystallization determines a network?
physical
Gel Point Gel Point [Winter et al.1986][Winter et al.1986]
Suspension vs Crosslinks based views? Suspension vs Crosslinks based views?
Suspension-like microstructure for low melt connectivity:
Low molecular weightLow nuclei density
Crosslinks for high melt connectivity:
High molecular weightHigh nuclei density
Eterogeneous nucleation tTTEtTE m exp
Nuclei density depends upon temperature
Nuclei density changes with temperature and cooling rate
E(T)decreasing crystallization temperature or increasing cooling increasing cooling raterate produces an increase of the number of nuclei and a decrease of particle dimensions
, s
iPP T30G
123°C121°C
tTTEtTE m exp0
Crystallization takes place at the temperature where crystallization time equals cooling time
Eterogeneous nucleation: density =
thus, connettivity depends also upon cooling rate
SEMSEM
0.02 K/s
50 K/s90 K/s
.
T
.
T
2 K/s
Morphology vs cooling rates, Morphology vs cooling rates, iPP T30GiPP T30G
AVERAGE DIAMETER OF AVERAGE DIAMETER OF SPHERULITESSPHERULITES iPP iPP T30GT30G
0.1
1
10
100
1000
0.01 0.1 1 10 100- (dT/dt) at 343K [K/s]
Dia
mete
r of
sp
heru
lite
s [
m]
Experimental - SEM
1 phase model - (Optical and Calorimetric Measurements)
2 phases model - (Full Data Set)
Diametro(T) Diametro(T)
34
3
aNR
calorimetry
iPP T30G
Quenching esperiments
time (s)
0 2000 4000
(P
a s
)
0
4e+6
8e+6
T (
°C)
80
100
120
140
160
180
annealing at 160°C to erase any crystalline memory
time (s)
0 2000 4000
(P
a s
)
0
4e+6
8e+6
T (
°C)
80
100
120
140
160
180
rapid cooling to 98°C
time (s)
0 2000 4000
(P
a s
)
0
4e+6
8e+6
T (
°C)
80
100
120
140
160
180
constant stress is applied, polymer viscosity is monitored
time (s)
0 2000 4000
(P
a s
)
0
4e+6
8e+6
T (
°C)
80
100
120
140
160
180
crystallization determines a
viscosity upturn
PB200
RHEOLOGICAL RHEOLOGICAL EVIDENCEEVIDENCE of crystallization of crystallization
T
Effect of flowEffect of flowPB200
T=105°C
time [s]
0 2000 4000 6000 8000
0
2
4
6
8
10
4500 Pa10000 Pa18000 Pa
Flow enhances
crystallization rate
Polipropilene T30GPolipropilene T30G
Viscosity upturn during crystallization
Crystallinity increases during calorimetric measurements
Crossing both informations at the same temperature and time, the evolution of viscosity with crystallization is obtained
o
Only total crystallinity?
ViscosityViscosity Models and relationshipsModels and relationshipsEquation Author derivation parameters
/0=1+a0 a Katayama 85 Suspensions a=99
/0= (1- /a0)-2 Metzner 85 also Tanner 2002 Suspensions a=0.68 for smooth spheres
/0=1+(/a1)a2/(1-/a1)
a2 Tanner 2002 Empical, based on suspensions
a1=0.44 for compact
a1=0.68 for spherical
crystallites
/0= exp(a1 a2) Shimizu 85; also Zuidema 2001, and Hieber 2002
Empirical
/0=1/(-c)a0 Ziabicki 88 Empirical c=0.1
/0=1+a1 exp(-a2/ a3) Titomanlio 97; also Guo 2001, and Hieber 2002
Empirical
/0= exp(a1 + a2 2) Han , 97 Empirical
/0= 1+a1 +a22 Tanner 2003 Empirical a1=0.54 , a2=4, <0.4
Only total crystallinity is considered ! !
Shapes reproduced by equations of the Shapes reproduced by equations of the ModelsModels
1
10
100
1000
0.0% 2.5% 5.0% 7.5% 10.0% 12.5% 15.0%
Relative Crystallinty
Vis
co
sit
y [
Eta
(Xc
)/E
ta(0
)]
Eta(Xc)/Eta(0) Katayama
Eta(Xc)/Eta(0) Ziabicki
Eta(Xc)/Eta(0) Titomanlio
Eta(Xc)/Eta(0) Shimizu
All equations were adopted with a factor of about 20 at crystallinity sligtly above 5%
1,E+02
1,E+03
1,E+04
1,E+05
1,E+06
1,E+07
0,001 0,01 0,1 1 10 100 1000 10000
Shear rate [s-1]
[P
a*s]
Exp. 431K Exp. 453K Exp. 473KExp. 503K Model 431K Model 453KModel 473K Model 503K 500 bar, 431K
Effect of pressure and temperature on viscosityEffect of pressure and temperature on viscosity
iPP T30G
Viscosity and relaxation time increase with pressure
When the viscosity increases the curve shifts also on the left
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
0.1 1 10 100
Xc= 0% Xc= 0.1%Xc= 0.3% Xc= 0.4%Xc= 0.6% Xc= 1.1%Model Xc= 0% Model Xc= 0.1%Model Xc= 0.3% Model Xc= 0.4%Model Xc= 0.6% Model Xc= 1.1%
', [s-1]
, [Pa s]
T30G: effect of cristallinity on viscosity
m
ffh
21 exp 1 )(
22
32110 exp
DTA
PDDTAD
n
xPTC
xPTxPT
1.
0
0.
,,1
,,,,,
).(h
The viscosity curve becomes higher and shifts on the left
Non flow and solidification conditions
For crystalline polymers:
are determined by crystallinity, Xnf Xs
For amorphous polymers:Tg(P, cooling rate)
for both conditions, most commercial codes adopt a single constant temperature :
Ts=Tnf=const.
Outline
1.1. Non flow and solidification temperatures Non flow and solidification temperatures
2.2. Observations and modelling of rheology Observations and modelling of rheology evolution during crystallization evolution during crystallization . . . 24: suspensions or . . . . physical crosslinks
3.3. Role of Role of non flownon flow criterion in the simulation of criterion in the simulation of injection moulding and identification of the injection moulding and identification of the proper crystallization Kinetic modelsproper crystallization Kinetic models
4.4. Solidification Criterion and its relevance on Solidification Criterion and its relevance on internal stresses an warpageinternal stresses an warpage
Pressure evolution during injection moulding, BA238G
GATE:thickness: 1.5mm or 0.5mm
P2
P3
P4
P1
SPRUE:initial diam: 4.7mmfinal diam: 7mmlength: 80mm
8mm
9mm
68mm
6mm
120mm
15mm
60mm
105mm
30mm
CAVITYthickness: 2mm
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20
P0
P1
P2
P3
P4
t, s
P, bar
Thick gate
experimental
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20
P0
P1
P2
P3
P4
t, s
P, bar experimental
Thin gate
1,E-05
1,E-04
1,E-03
1,E-02
1,E-01
1,E+00
1,E+01
1,E+02
0 2 4 6 8t, s
Flo
w R
ate
, cc
/s
P4
P2
Thermomechanical history changes with position
Termomechanical history (dT/dt, pressure, flowdT/dt, pressure, flow) is a strong function of position, in injection moulding
P3P2 P4
z
y
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
0 0.2 0.4 0.6 0.8 1
0
50
100
150
200
250
-T'@100ºC
P@100ºC
y, mm
-T', [ºC/s] P, [bar]
Cooling rate and pressure at 100°C; Simulated
Morphology changes mainly with the distance from mould wall and also along the flow path
“Standard” sample
P2 P3 P4
Micrographs taken in a polarized optical microscope of “Standard” sample along flow direction.
Morphology distribution in inj. moulded samplesMorphology distribution in inj. moulded samples
P3P2 P4
x
y
iPP T30G
Morphology changes with the distance from the skin and slowly along the flow direction
Sferulite dimensions increase with the distance from the skin
DIAMETER OF SPHERULITESDIAMETER OF SPHERULITES
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1Distance from the skin [mm]
Dia
mete
r of
sph
eru
lite
s [ m
]
SEM
Model prediction
End of dark zone
FastFast
0
5
10
15
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1
Distance from sample skin [mm]
Dia
mete
r of
spheru
lite
s [
m] SEM
Model prediction
End of dark zone
Both non flow and solidification conditions
For crystalline polymers:
are determined by crystallinity For amorphous polymers:Tg(P, cooling rate)
In order to calculate Xnf and Xs, the crystallization kinetics has
to be defined and implemented in the codes
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
10 100 1000 10000t [sec]
410K
413K
416K
418K
0102030405060708090
0 500 1000 1500 2000 2500 3000t [sec]
410K
413K
416K
418K
410K
413K
416K
418K
Calorimetric isotherms, BA238G :
Calorimetric and PVT cooling scans, BA238G
1.00E-03
1.05E-03
1.10E-03
1.15E-03
1.20E-03
1.25E-03
1.30E-03
1.35E-03
1.40E-03
273 323 373 423 473T [K]
iPP; C-Mold data baseHigh temperature fit: amorphous phaseCrystal phaseLow temperature fit
Room pressure
1.00E-03
1.05E-03
1.10E-03
1.15E-03
1.20E-03
1.25E-03
1.30E-03
1.35E-03
1.40E-03
273 323 373 423 473T [K]
iPP; C-Mold data baseHigh temperature fit: amorphous phaseCrystal phaseLow temperature fit
P=50MPa
0
5
10
15
20
340360380400420T [K]
1.33K/sec
1.00K/sec
0.83K/sec
0.33K/sec
0.16K/sec
0.10K/sec
0.02K/sec
cooling rate, q
0%
10%20%
30%
40%50%
60%
70%
80%90%
100%
340360380400420T [K]
cooling rate, q
BA230g-Comparison between expermental and simulated pressure curves with Xnf = 5%
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20
P0
P1
P2
P3
P4
t, s
P, bar
Thick gate
experimentalThermomechanical model with Kinetics calibrated by calorimetric and PVT experiments
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25
Trsd 1
Trsd 2
Trsd 4
Trsd 5
Trsd 6
t, s
P, barsimulated
Poorcomparison !
WHAY ?
BA238g; non-flow temperatures and final crystallinities obtained by simulation with Xnf 5%
Crystallization kinetics was identifies by calorimetric tests (low cooling rate)
Kinetics needs to account of behaviour at high cooling rates
20
30
40
50
60
70
80
90
100
0 0.2 0 .4 0 .6 0 .8 1
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
T so lXc
Xc, [ - ]T , [ º C ]
y, [m m ]
Thick gate
Non
-flo
w te
mpe
ratu
re
Distance from the skin
Characterised Quenching experiments
1.100E-03
1.105E-03
1.110E-03
1.115E-03
1.120E-03
1.125E-03
1.130E-03
1.135E-03
1.140E-03
0.01 0.1 1 10 100 1000 10000
cooling rate at 343K [K/sec]
0.01
0.1
1
10
100
1000
10000
250 300 350 400 450 500T [K]
47
61 68
19
2DSC1.7
DSC0.1
DSC0.51
C1000
250
300
350
400
450
500
0.1 1 10 100 1000 10000time [sec]
47
6168
19
2
DSC1.7
DSC0.5DSC0.1
1C1000
nozz le
spray
sample
Coolant outlet
thermocoup le
Copper sample holder
Sliding rod
Electical heater
Oven
Bath
Final crystallinity in quenched samples: comparison
1.110E-03
1.120E-03
1.130E-03
1.140E-03
1.150E-03
1.160E-03
1.170E-03
1.180E-03
0.01 0.1 1 10 100 1000 10000
cooling rate at 343K [K/sec]
Meas. at298K
Pred.: Fulldata set
Pred: onlyDSC data
0%
10%
20%
30%
40%
50%
60%
70%
0.01 0.1 1 10 100 1000 10000
cooling rate at 343K [K/sec]
Meas. at 298KMeas. at 318KMeas. At 298KPred: full data setPred: only DSC data
….. model 1: Calorimetry
___ model 2: full data set
models obtained by calorimetry usually give poor results at high cooling rates
and should not be adopted for injection moulding
Calorimetric and PVT results: comparison
1.00E-031.05E-03
1.10E-031.15E-031.20E-031.25E-03
1.30E-031.35E-031.40E-03
300 350 400 450 500T [K]
Equilibrium
1E-3 K/sec
1K/sec
500 K/sec
Room Pressure
1.00E-031.05E-03
1.10E-031.15E-031.20E-031.25E-03
1.30E-031.35E-031.40E-03
300 350 400 450 500T [K]
Equilibrium
1E-3 K/sec
1K/sec
500 K/sec
P=50MPa
330340350360370380390400410420430
0.01 0.1 1 10Cooling rate [K/sec]
peak from DSC cooling rampsPredictions: Full data setPredictions: only DSC data
Model 1: Calorimetric
Model 2: full data set
Results of Simulation with full data crystalliztion kinetics
0
20
40
60
80
100
120
140
160
0 0.2 0.4 0.6 0.8 1
0
50
100
150
200
250
300
350
T(t sol)
P(t sol)
y, mm
T, [ºC] P, [bar]
Sol
idifi
catio
n t
empe
ratu
re
Distance from the sample skin
Sol
idifi
catio
n p
ress
ure
BA238G, solidification temperatures and pressures
0
1
2
3
4
5
6
7
0 0.2 0 .4 0 .6 0 .8 1
0
50
100
150
200
250
300
350
t so lP( t so l)
y, m m
t, [ s ] P, [ bar]
Distance from the sample skin
So
lidifi
catio
n t
ime
accounting of the full data setfull data set in the
crystallization Kinetics was required In
order to acheive non-flow temperature
on the wholeon the whole cross section, in the
simulation0
20
40
60
80
100
120
140
160
0 0.2 0.4 0.6 0.8 1
Dsc
Dsc&Quenches
y, mm
T, [ºC]
Non-flow temperatures
Xnf=5%
BA230G - Comparison between expermental and simulated pressure curves with Xnf = 5%
Kinetics from full data set (quenches included)
0
20
40
60
80
100
120
140
160
0 0.2 0.4 0.6 0.8 1
Dsc
Dsc&Quenches
y, mm
T, [ºC]
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25
Trsd 1
Trsd 2
Trsd 4
Trsd 5
Trsd 6
t, s
P, bar
Kinetics: full data set
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25
Trsd 1
Trsd 2
Trsd 4
Trsd 5
Trsd 6
t, s
P, bar
Kinetics: DSC
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20
P0
P1
P2
P3
P4
t, s
P, bar
Thick gate
experimental
Crystallization kinetics calibrated by calorimetric & PVT experiments usually is not adequate to describy injection moulding
Comparison for final crystallinity in position P3, BA238g
0%
10%
20%
30%
40%
50%
60%
70%
0 0.2 0.4 0.6 0.8 1
DSC&QuenchDSC
y, mm
Xc, [-]
Cystallinity distribution is essentially constant on the cross section consistently with experimental risults
50%
52%
54%
56%
58%
60%
62%
0 0.2 0.4 0.6 0.8 1
DSC&QuenchExperimental
y, mm
Xc, [-]
Dettailed comparison
BA230G -Comparison between expermental and simulated pressure curves with Xnf = 5%
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20
P0
P1
P2
P3
P4
t, s
P, bar
Thin gate
Experimental
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25
Trsd 1
Trsd 2
Trsd 3
Trsd 4
Trsd 5
P, bar
DSC Kinetics
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25
Trsd 1
Trsd 2
Trsd 3
Trsd 4
Trsd 5
t, s
P, bar
Kinetics: full data set(Quenches)
Crystallization kinetics calibrated by calorimetric & PVT experiments usually is not adequate to describy injection moulding
Outline
1.1. Non flow and solidification temperatures Non flow and solidification temperatures
2.2. Observations and modelling of rheology Observations and modelling of rheology evolution during crystallization evolution during crystallization . . . 24: suspensions or . . . . physical crosslinks
3.3. Role of non flow criterion in the simulation of Role of non flow criterion in the simulation of injection moulding and identification of the injection moulding and identification of the proper crystallization Kinetic modelsproper crystallization Kinetic models
4.4. Solidification Criterion and its relevance on Solidification Criterion and its relevance on internal stresses an warpageinternal stresses an warpage
The solidification cristallinityThe solidification cristallinity1. consider a layer which goes under stress during the
cooling of the object
2. as long as relaxation time is small with rspect to cooling time, stresses relaxe and the solid will have the new geometry as reference configuration
This is a simplification, which replaces a dettailed knowledge of the evolution of rheology with crystallization
3. If, viceversa, relaxation time is long with respect to cooling time, relaxation will be negligible and the final solid will keep its initial reference configuration (under stress)
4. at crystallinities higher than that which gives rise to condition 2 the material behaves as a solid, this identies Xs
5. a simplified model for cooling stresses build up would consider the polymer as a melt at crystallinities lower than Xs and as a solid at higher crystallinities
Solidification criterion: How big is Xs?
0
10
20
30
40
50
60
70
80
90
100
1000000
10000000
100000000
1000000000
10000000000
0 50 100 150 200
T [°C]
X/Xeq
E''
E'
A slight melting may reduce the moduli by orders of magnitude
Xs is probably close to Xeq
BA230G
Schematic of cooling stesses build up and thus of warpage
distributions of solidification temperature and Xs are relevant to cooling stresses distribution and to warpage
If they are constant over the whole section trey contribute only on shrinkage
.Pressure free configuration
Also contraction due to cooling and crystallization
Small points to remember
1. Viscosity has been related only to total crystallinity
2. Non-flow condition is different from solidification condition, which is determined by the value of the relaxation time compared to cooling time
3. A low value of Xnf (5%) was often found adequate to describe experimental viscosity increase, Xs is larger than Xnf
4. Crystallization kinetics calibrated by calorimetric & PVT experiments usually is not adequate to describe injection moulding (crystallization, flow, pressure evolution, orientation, morphology)
5. Experiments performed at high cooling rates (100-1000k/s) need to be considered
6. Solidification pressure, temperature and crystallinity are relevent to shrinkage, treir distribution are relevance to internal stresses and warpage
I would be happy to discuss any comment
Thank You