Injection Molding Process
Jae Wook Lee Chemical Engineering Department Sogang University http://pollab.sogang.ac.kr
Plastics Injection Molding Process ... Mass Production, Complex Geometry, High Precision
Decaying slope Peak cavity pressure
Average holding pressure Smoothness of holding pressure
Slope of compression
Fill-up point
Gate freeze off time Stability point
Cavity pressure during cooling stage
Slope of filling pressure Start of injection
Induction time
Melt front reaches tranducers
Residual cavity pressure
Fig. Parameters used for characterization of a standard cavity pressure curve
Filling Completeness, reproduction of mold surface, flashing, damage to mold
Nature of surface layer
Packing along flow path Voids, sink sports, weight shrinkage, distortion, degree of crystallinity interior orientation, demolding difficulties
Appearance, orientation, crystallization
Strain on melt (thermal, mechanical) D A B C Filling Holding pressure Packing
E
Fig. The cavity pressure pattern dominantly affects quality features
High injection speed Late switch-over High holding pressure High holding pressure High injection speed Low melt temperature High injection speed Low melt temperature Low mold temperature
Injection speed
Thick part
High mold temperature High melt Temperature High hold pressure
Low hold pressure Thin part Strong cooling Low mold temperature Low melt temperature
Fig. Cavity pressure patterns and molding conditions
Holding Pressure
Melt temperature
Mold temperature
Injection speed
Shot size
Switch over point
Holding time
Mold clamping
Cushion size
Short holding time
Premature transfer
Low hold pressure
Standard Curve
High peak cavity pressure
Mold breathing
Cushion runs out
Low injection speed
Small shot size
Fig. Conversion of abnormal patterns into a standard curve
• Governing Equations ui ,i 0 ui u j ui , j ) P,i ij , j S i t ij ( I 2 )( ui , j u j ,i )
(
• Continuity equation. • Momentum equation. • Constitutive equation.
• Boundary Conditions on Free Surface n ( n) 0 t ( n) 0 P
• Normal Component • Tangential Component
Hele-Shaw Approximation • Length/Thickness > 50 P P ( S ) ( S • Governing Equation x x y y ) 0
Discretization of Governing Equation • 2D – – – –
Classical Galerkin finite element formulation. 9-noded rectangular elements in 2D case. Biquadratic interpolation of velocities. Bilinear interpolation of pressure
• 3D – Penalty Formulation. – Trilinear interpolation of velocities.
SUPPLIER/file name
PC
: GEUSA
LEXAN 141
Conductivity Specific Heat Melt Density Ejection Temperature No Flow Temperature
GE USA 0.280000 W/m/degC 2232.000000 J/kg/degC 1017.000000 kg/cu.m 160.000000 deg.C 180.000000 deg.C
Viscosity Temperature deg.C 300.000 320.000 320.000 320.000 340.000 340.000
Shear Rate 1/s 1000.000 100.000 1000.000 10000.000 100.000 1000.000
Viscosity Pa.s 294.500000 225.600006 185.500000 65.099998 132.500000 116.900002
PVT Specific Volume Temperature deg.C 25.000 141.000 25.000 194.600 142.400 196.600 147.400 240.000 201.600 240.000
Pressure MPa 0.000 0.000 160.000 160.000 0.000 160.000 0.000 0.000 160.000 160.000
Specific Volume cu.cm/g 0.834459 0.852009 0.808354 0.827074 0.853920 0.827368 0.856604 0.906335 0.828974 0.841328
Processing Conditions: Melt Temperature Maximum 340.00 deg.C Melt Temperature Suggested 320.00 deg.C Generic Mold Temperature Minimum 80.00 deg.C Melt Temperature Absolute Maximum 360.00 deg.C Generic Maximum Shear Stress 0.50 MPa Generic Maximum Shear Rate 40000.00 1/s Molding Conditions ================== Mold temperature : 100.00 deg.C Melt temperature : 320.00 deg.C Injection time : 2.00 sec Total Volume : 173.29 cu.cm Flow rate : 86.65 cu.cm/s
Numerical Scheme for Free Surface
Lagrangian Scheme
Eulerian Scheme
( 2 D ) 0 3 M a r 1 9 9 8 2 D N O N - N E W T O N F L U ID S I M U L A T I O N
1.9
4
9
1.84
44 1.
1 .0 4
1.6
0 .1 6 0 .0 8
24 1.
0. 8 0 .6 44 0 .4 0 .2 4 8
Results of Numerical Simulation ( Newtonian Case) 6
5
FF 0.9375 0.875 0.8125 0.75 0.6875 0.625 0.5625 0.5 0.4375 0.375 0.3125 0.25 0.1875 0.125 0.0625
4
3
2
14788.2 13666.4 12544.6 11422.8 10300.9 9179.13 8057.31 6935.5 5813.69 4691.88 3570.06 2448.25 1326.44 204.625 -917.188
0.010959 0.010228 0.009497 0.008766 0.008035 0.007305 0.006574 0.005843 0.005112 0.004381 0.003650 0.002920 0.002189 0.001458 0.000727
0.084375 0.07875 0.073125 0.0675 0.061875 0.05625 0.050625 0.045 0.039375 0.03375 0.028125 0.0225 0.016875 0.01125 0.005625
1
0 0
0.5
1
F
1.5
0
0.5
1
Uz
1.5
0
0.5
1
Ur
1.5
0
0.5
1
P
1.5
MF/FLOW3D Fill Pattern Prediction
Filling Pattern Prediction Actual
Predicted
Click to play
(Glass Model)
Actual
Predicted
Packing Pressure Prediction
Predicted vs. actual packing pressure
Mold filling
Mold filling(different gate position)
Weld Line
Minimizing weld lines 1. Locate weld lines closer to a gate to make them strong. 2. It is important to have enough pressure to get good packing. 3. P rovide venting at the weld line. 4. Increase part thickness at the weld line 5. Increase melt temperature more flow. 6. Increase injection pressure and speed.
Shrinkage causes the post mold dimensions of plastic parts to differ from the mold cavity dimensions
Warpage causes the post mold shape of plastic parts to differ from the mold cavity shape - results from nonuniform shrinkage
w=hpart or w=dpart
Shrinkage is not a material property! It depends on... Material properties --- PVT data, Thermal properties, etc. Part geometry --- Thickness, mold constraints, etc. Manufacturing --- Temperature, pressure, flow, etc.
Shrinkage is a system property! A good predictor of shrinkage must consider all three factors.
Prediction of shrinkage
Nonuniform shrinkage due to pressure gradient
The Application of Artificial Neural Network for the Prediction of Mechanical Property in Injection Molding Process
Jung Gon Kim, Hern Jin Park* ,Jae Wook Lee
Department of Chemical Engineering Sogang University, Seoul, Korea *SKI Inc. , Suwon, Korea Sogang University
ntroduction Engineering Properties
Processing Parameters 1. Injection rate 2. Mold Tmep. 3. Injection Pres. 4. Holding Pres. Etc.
1. Impact Strength 2. Yield Strength 3. Modulus 4. Tensile Strength Etc.
Injection Machine
Neural Network
Thermomechanical History 1. Pressure 2. Temperature 3. Vol.shrinkage 4. Shear stress Etc.
Test Geometry MOLDFLOW
Thermomechanical History
Another Geometry
Traditional method Predicted Engineering Properties
Method to train Method to predict
1. Pressure 2. Temperature 3. Vol.shrinkage 4. Shear stress Etc.
1. Impact Strength 2. Yield Strength 3. Modulus 4. Tensile Strength Etc.
Sogang University
input neurons
design variables
hidden neurons
output neurons
1
1
1
i
j
k
L
M
N
1
1
responses
threshold neurons
Fig. Structure of an Artificial Neural Network. Sogang University
Rule
i
At t, Wij(t)
neuron
j
- Least Mean Squared Error
neuron
Ep (opj tpj)2 j
W ij ( t 1) Wij ( t ) Wij x pi (o pj t pj )
pj o pj t pj
E Ep p
- Chain Rule
Learning parameter (0 , 1) o pj Objective value t pj Output value
E p Wij
E p o pj pj x pi o pj Wij
Sogang University
Method to avoid Local Minimum - Momentum Parameter () y value
W ij ( t 1) pj o pj Wij ( t ) B A
- Noise Factor (NF) old o new pj o pj (1 NF Rndf ) x value
A : Global Minimum B : Local Minimum
Sogang University
1.25
Calculation of the output value 1.00
net pi Wij o pj i
Output
.75
i
o pi f i ( net pi )
.50 = 0.5 = 1.0 = 2.0 = 4.0
.25 0.00 -.25 -15
-10
-5
0
5
10
- Squashing Function
fi 15
1 1 exp( net pi )
Input
Fig. Plot of Sigmoid Function
Sogang University
Material - Poly styrene (PS) < GPPS-25sp supplied by LG-Chem. In Korea> Tg = 97.11oC
MI = 3.3g/10min
1.05g/cm3
- Pre-drying Condition At 80oC for 24 hours in Convection oven
Mechanical Test - Impact Strength < CEAST Impact Tester> Tested 5 samples at least
- Shear Modulus < TA Instrument DMA 983> Heating rate = 2oC/min from 10 to 70oC , Frequency = 1Hz
Sogang University
Mechanical Test 1 1
2
3
2 3 4 5
6
5
4
6 7 8
(a) Location of Impact Strength
(a) Location of Shear Modulus
Fig. Schematic representation of the methodology used to predict the mechanical properties of injection molded parts Sogang University
Apparatus - Injection Molding Machine < Allrounder 220M 250-75 ARBURG> 25 ton clamping force, 2.08oz capacity, 25mm screw with 20 L/D mold temperature controller (RG-150, Regloplas Co.)
- Mold Geometry Two 100mm x 50mm x 3mm plates
Table Injection Molding Condition Condition Injection Temperature (oC) Injection Pressure (MPa) Mold Temperature (oC) Packing Pressure (MPa) Packing Time (sec) Cooling Time (sec) Filling Time (sec) Clamp Opening Time (sec)
Value 220 – 280 90 – 100 60 80 10 30 0.8 – 1.4 2
Sogang University
Computer Simulation - MOLDFLOW < Used MF/VIEW, MF/FLOW, MF/COOL> Work Station = Indogo 2, Impact
Thermomechanical History Calculated from the Results of Injection Molding Simulation. Node Value Pressure (MPa) Temperature (oC) Instant Temperature (oC)
Element Value
Vol. Shrinkage (%) Max. Shear Stress (MPa) Apparent Density (kg/m3) Top Temperature (oC) Bottom Temperature (oC) Different Temperature (oC)
Sogang University
Plot of Cavity and Mold Cooling-Line at MOLDFLOW Simulation
(a) Mesh of Cavity
(b) Geometry of Mold
Sogang University
MOLDFLOW Simulation for Node Value
(a) Pressure
(b) Temperature
(c) Instant Temperature
Sogang University
MOLDFLOW Simulation for Element Value(1)
(b) Max Stress
(a) Volume Shrinkage
(c) Apparent Density
Sogang University
MOLDFLOW Simulation for Element Value(2)
(d) Top Temperature
(e) Bottom Temperature
(f) Different Temperature
Sogang University
Results 5
5
3
4
Pattern error
Pattern error
4
2
3
2
1
1
0
0
0
25
50
500
Iteration number
(a) Shear Modulus
1000
0
25
50
500
1000
Iteration number
(b) Impact Strength
Fig. Plot of Simulated Pattern Error Curve for Learning Parameter Sogang University
Results 2.5
2.5
1.5
1.0
1.5
1.0
.5
.5
0.0
0.0 0
25
50
500
Iteration number
(a) Shear Modulus
2.0
Pattern error
Pattern error
2.0
1000
0
25
50
500
1000
Iteration number
(b) Impact Strength
Fig. Plot of Simulated Pattern Error Curve for Momentum Parameter Sogang University
Results 5
5 NF = 0 NF = 0.1 NF = 0.2 NF = 0.4
4
Pattern error
Pattern error
4
NF = 0 NF = 0.1 NF = 0.2 NF = 0.4
3
2
3
2
1
1
0
0
0
25
50
500
Iteration number
(a) Shear Modulus
1000
0
25
50
500
1000
Iteration number
(b) Impact Strength
Fig. Plot of Simulated Pattern Error Curve for Noise Factor Sogang University
950
20.0
900
17.5
Impact strength [J/m]
Shear modulus [MPa]
Results
850
Real data (set=7) 3-layer (72-36-8) 4-layer (72-50-20-8) 5-layer (72-60-40-15-8)
800
750
15.0
Real data (set=5) 3-layer (54-27-6) 4-layer (54-34-17-6) 5-layer (54-40-20-10-6)
12.5
10.0 1
2
3
4
5
6
Sample location
7
8
1
2
3
4
5
6
Sample location
Fig. Predictions of Shear Modulus and Impact Strength of Injection molded parts on layer number of ANN Sogang University
950
950
900
900
850
Real data (set=7) = 0, = 0.02, NF = 0 = 0.1, = 0.001, NF = 0.1
800
750
Shear modulus [ MPa ]
Shear modulus [ MPa ]
Results
850
Real data (set=12) = 0, = 0.02, NF = 0 = 0.1, = 0.001, NF = 0.1
800
750 1
2
3
4
5
6
Sample location
7
8
1
2
3
4
5
6
7
8
Sample location
Fig. Predictions of Shear Modulus of Injection molded parts
Sogang University
Results 20.0
22.5
15.0
Real data (set=5) = 0, = 0.02, NF = 0 = 0.1, = 0.001, NF = 0.1
12.5
10.0
Impact strength [ J/m ]
Impact strength [ J/m ]
20.0 17.5
17.5
15.0 Real data (set=10) = 0, = 0.02, NF = 0 = 0.1, = 0.001, NF = 0.1
12.5
10.0 1
2
3
4
Sample location
5
6
1
2
3
4
5
6
Sample location
Fig. Predictions of Impact Strength of Injection molded parts
Sogang University
Conclusions 1. The Impact strength and Shear modulus within a part is more dependent of the thermomechnical histories than the others are. 2. The accuracy of predicted results doesn’t get any better even though the number of hidden layer increases. 3.In order to guarantee the global minimum and to approach to the minimum as soon as possible, in the neural network, not only learning parameter but also momentum parameter and noise factor should be applied. 4. In case of impact strength, except 9 thermomechanical histories, another history seems to be influenced.
Sogang University
Parts Weight Prediction Using On-Line Variables
In Ho Shin, Jung Gon Kim, Jae Wook Lee Department of Chemical Engineering
Introduction Injection Molding Process Mass Production In a Discontinuous Manner Quality Consistency is a Crucial Issue
Mold T Holding P, t Injection P, T Material
Cavity P, T
Parts Quality
Theory Factorial Design (FD)
y f(x)
Linear
y bo b1 x1 b2 x2 residual
Interaction y bo b1 x1 b2 x2 b12 x1 x2 residual Quadratic Exp. No.
22
1 2 3 4
y bo b1 x1 b2 x2 b11 x12 b22 x22 b12 x1 x2 residual
Factor
Response
x1
x2
1 +1 1 +1
1 1 +1 +1
x1 x2 +1 1 1 +1
A B C D
Theory Modified Factorial Design (mFD)
h f(g)
g1
Mean of P/T from a Shot
g2
Peak of P/T from a Shot
g3
Integrated Area of P/T from a Shot
(+)
h (–) (–)
g
(+)
Theory Modified Factorial Design (mFD) R e sp o n se ( )
(+ )
F a cto r 1
a
e
F a cto r 2
b
f
F a cto r 3
c
g
F a cto r 4
d
h
Factor 1
Factor 2
Factor 3
Factor 4
Response
Case 1
0.25(a+b+c+d)
Case 2
+
0.25(e+b+c+d)
Case 3
+
0.25(a+f+c+d)
Case 15
+
+
+
0.25(a+f+g+h)
Case 16
+
+
+
+
0.25(e+f+g+h)
Theory Artificial Neural Network (ANN)
input value
W
ij
output value
xi
factors
input neurons
hidden neurons
output neurons
1
1
1
i
j
k
L
M
N
1
1
threshold neurons
responses
Experiments Material Polypropylene by Honam Petrochemical Corp. (SFR 170-G) Injection Molding Machine Arburg Allrounder 220M 75 (25-ton clamping, 25mm screw) Regloplas RG-150
Machine Settings Nozzle Temperature (oC, 200/220, x1) Mold Temperature (oC, 50/70, x 2 ) Holding Pressure (bar, 550/850, x 3 ) Injection Speed (ccm/s, 45/55, x 4 )
}
24 = 16 16 + 1 = 17
Experiments Cavity Transducers Two Pressure Transducers (Kistler 6157BB, 9221A) One Pressure-Temperature Transducer (Kistler 6190A)
P1-T1
50mm
P2
100mm 40mm
P3 (indirect) 10mm
Experiments Data Acquisition GPIB (National Instruments AT-MIO-16X) Sampling Rate of 20/sec Three LVDT Signals (Nozzle, Screw, Mold)
• Mean • Peak • Integrated Area
Results Temperature Profiles
Peak and Average of T1
Integrated Area of T1
85
640
620 80
Integrated Temperature [oC sec]
600
Temperature [oC]
75
70
65
4 mean 10 mean 17 mean 4 paek 10 peak 17 peak
60
580
560
540
520
case 4 case 10 case17
500
480
55
460 10
20
30
Part Number
40
50
10
20
30
Part Number
40
50
Results Variational Noise Shot-By-Shot Variation of Parts Weight C a s e 17
W e i g h t [g]
10.0
9.9 0
25
50
75 100 125 Part Number
150
175
200
Results Developed Response Model of FD y 9.9400 0.0520x1 1.9870e 3 x2 6.2510e 4 x3 6.9990e 4 x4 4.0750e3 x1x2 2.6180e4 x1x3 2.0620e3 x1x4 1.4630e3 x2 x3 9.3720e4 x2 x4 1.4500e3 x3x4
Results Four Factors Having the Highest R2 of mFD
0.9248
0.9337
10.10
10.10
10.05
10.05
Weight [g]
Weight [g]
10.15
10.00 9.95
10.00 9.95 9.90
9.90 9.85
9.85 9.80
1
2
Peak Points at P3
2
3
Peak Points at P2
Results Four Factors Having the Highest R2 of mFD
0.9009
0.8775
10.15
10.10
10.10
Weight [g]
Weight [g]
10.05 10.00 9.95 9.90
10.05 10.00 9.95 9.90
9.85
9.85
9.80
9.80 1
2
Peak Points at P1
1
2
3
4
5
6
7
Intrgrated Areas of P2
8
9
Results Developed Response Model of mFD h 9.9870 0.0310g1 0.0310g 2 0.0320g 3 0.0360g 4 6.2150e7 g1g 2 8.1250e7 g1g 3 2.9780e 6 g 1g 4 5.4400e 6 g 2 g 3 2.8890e 6 g 2 g 4 3.0240e 6 g 3 g 4
Results ANN Training • standard feed-forward back-propagation network • 4 input neurons / 4 hidden neurons / 1 output neuron • 700 training data sets and 150 testing data sets • learning rate was 0.5 • momentum factor was 0.8 • trained for half and an hour (100000 iterations) • final sum squared error was 0.0011
Results
Case 4
Case 10
10.08
10.08
measured FD mFD ANN
10.04
Weight [g]
Weight [g]
10.04
measured FD mFD ANN
10.00
9.96
10.00
9.96
20
30
Part Number
30
40
Part Number
Results
Case 16
Case 12 10.12
measured FD mFD ANN
10.04
10.04
Weight [g]
Weight [g]
10.08
10.00
measured FD mFD ANN
10.00
9.96 9.96
9.92 40
50
Part Number
20
Part Number
Results
Case 12
Case 4 10.08
10.08
measured FD mFD ANN ANN2
10.04
Weight [g]
Weight [g]
10.04
measured FD mFD ANN ANN2
10.00
10.00
9.96 9.96
20
30
Part Number
40
50
Part Number
Conclusions Conventional factorial design is not capable of monitoring shot-by-shot variation of the process at all. On the contrary, modified factorial design, which does utilize on-line variables, successfully traces constantly varying parts weight. Meanwhile, artificial neural network, which is based on non-linear function inside each neuron, yields the most reliable predictions. Adjustment of training parameters, such as learning rate, noise and momentum factor, will affect the performance of ANN. Two-stage-strategy is believed to be of practical value for the optimization of injection molding process.
Rheo-Kinetic Analysis of Shear Induced Crystallization of Semicrystalline Polymers
Jung Gon Kim, Hyun Seog Kim and Jae Wook Lee
Department of Chemical Engineering Sogang University, Seoul, Korea
Sogang University
Introduction Stress b
Injection Molding Non-isothermal, Semi-Batch Process
Gate
Temperature
a
c d
a wide variety of Thermal and Deformation Histories Tmelt
Structural Gradient in the injection molded parts
Tmold Time a
Time b
Time c
Time d
Sogang University
Effects on Crystallization Behavior Thermal History
Deformation History
• Temperature • Heating / Cooling Rate • Heating / Cooling Time
• Shear Rate • Shear Stress • Shearing Time
Combined Analysis
Rheo-Kinetic Analysis Sogang University
Material Polymer Resins - Poly buthylene terephthalate (PBT) < SKYTON 1100A supplied by SKI in Korea > Tg = 36 oC
Tmo = 227 oC
- Poly propylene (PP) < SJ-170 supplied by Honam Petrochemical in Korea > Tg = -10 oC
Tmo = 165 oC
- Pre-drying Condition PBT ; at 120 oC for 2 hours, PP ; at 80 oC for 4 hours Sogang University
Experimental Rheological Measurement of Shear-Induced Crystallization Behavior Rheometrics RMS 800 < with 2Kg-force transducer & plate-plate attachment > After melting at 250 oC for 10 minutes, Quenching to crystallizing temperature and then shearing. Monitoring the shear stress due to shear-induced crystallization
True shear rate was obtained by single-point correction method
Preparation of Sheared Polymer Samples Taking the sheared samples at true shear rate region (at rs* = 0.75) Sogang University
Single-Point Correction Method 1.0
M.M.Cross and A.Kaye, Polymer, 28, 435 (1987). M.S.Carvalho, M.Padmanabhan and C. Macosko, J. Rheology, 38, 1925 (1994).
rR
0.8
0.6
Power-law fluid
rsorsrs*oR rsrs* R
Newtonian fluid
0.4
rs* = rs/R = [4/(3+n)]1/(n-1)
0.2
rs* 0.0 0.0
0.2
0.4
0.6
0.8
1.0
rs* = 0.75 - 0.785 for n from 0 to 1.2
r/R
Sogang University
Memory effects in the crystallization A.Ziabiki and G.C.Alfonso, Colloid & Polym. Sci., 272, 1027 (1994) The memory of previous structures manifests itself in the distribution of atomic clusters which determines the initial number of crystal nuclei and the initial rate of thermal nucleation. Crystallization rate depends on original structure of the sample and its thermo-mechanical histories.
Measurements of Crystallinity Dupont 9900 DSC system Heating rate 10 oC/min from 30 oC to 250 oC Sogang University
Crystallization Kinetics Dupont 9900 DSC system < with Mechanical Cooling Accessory >
- Isothermal Kinetics After melting at 250 oC for 10minites, Quenching to crystallizing temperature
- Non-Isothermal Kinetics After melting at 250 oC for 10minites, Cooling rate 2, 5, 10, 15 oC/min from 250 oC to 30 oC.
Sogang University
Analysis Kinetic Experiment (Unsheared & Sheared Samples)
Isothermal Kinetics (JMA equation)
k(T) vs. , t1/2
Non-Isothermal Kinetics (Kamal & Nakamura equation)
k(T,)
Half-time Analysis (Hoffman-Laurizen equation)
Sogang University
- Isothermal Kinetics Johnson-Mehl-Avrami equation Xr = 1 - exp( - k t n )
Here, Xr : relative crystallinity k : rate constant n : JMA constant
Sogang University
- Half-time Analysis Hoffman-Laurizen equation (1/t1/2) = (1/t1/2)oexp(-U*/R(T-Too ))exp(-C3/TTf) Here, R : gas constant T : Tmo - T f : 2T/(T+Tmo) T oo : Tg - 30K U* : universal constant C3 : folding constant of polymer chain Sogang University
- Non-Isothermal Kinetics Nakamura equation
T
Xr = 1 - exp[ - ( K(T) dT/R)n], K(T) = k(T)1/n To
Kamal equation
T
Xr = 1 - exp[ - k(T) n ((To - T)/R)n-1 dT/R] To
Sogang University
Time dependent shear stress of PP at various temperatures. 8000 . -1 = 1.0s
Shear stress [Pa]
6000
o 130 C
The shear stress of PP is steeply increased with time after showing oscillatory fluctuation at the early state.
o 140 C o 150 C
4000
The reason may be that the cluster is repeatedly formed and destroyed at the early shearing state before the formation of clusters above the critical size.
2000
0 0
400
800
1200
1600
2000
Time [sec]
Sogang University
Time dependent shear stress of PP at various shear rates. 8000 T = 140oC
The increasing behavior of shear stress of PP is pronounced with the increase in shear rate at constant crystallizing temperature.
Shear stress [Pa]
6000 2.0 s
-1 1.0 s
-1
4000
0.5 s
2000
The induction time for crystallization occurs at an earlier point in time for higher shear rate and lower temperature.
-1
0 0
200
400
600
800
1000
1200
Time [sec]
Sogang University
Time dependent shear stress of PBT at various temperatures and shear rates 10000
10000
T = 215oC
210oC
1000 215oC 220oC
225oC
Shear stress [Pa]
Shear stress [Pa]
. = 1.0s-1
4.0 s-1
1000
2.0 s-1
1.0 s-1
230oC
100 0
200 400 600 800 1000 1200 1400
Time [sec]
100 0
200
400
600
800
1000
Time [sec] Sogang University
DSC melting area and shear stress for sheared PBT sample 600
500
T = 215oC . = 1 s-1
52
450 50
400 350
48
300 250
46
200
Melting area [J/g]
Shear stress [Pa]
550
54
The melting area of sheared PBT sample significantly increases with the shearing time, and it shows similar trend to shear stress data. The increase of shear stress is due to the formation of crystal.
150 0
200
400
600
800
1000
Time [sec] Sogang University
DSC thermogram at isothermal temperatures 0.8
0.7
0.6
0.6
187oC
Heat flux [W/g]
Heat flux [W/g]
0.5
0.4
0.2
0.0
0.4 191oC
0.3
193oC 195oC 197oC 199oC
0.2
-0.2
-0.4 10
0.1
tc
201oC
0.0
11
12
13 Time [min]
14
15
16
0
2
4
6
8
10
12
14
Time [min]
Sogang University
JMA analysis of isothermal crystallinity data for PBT 1 424.57Pa
The isothermal JMA analysis of PBT samples is carried out in the range of relative crystallinity between 20 and 80%.
ln(-ln(1-Xr))
3382.60Pa
0
-1
The results show that as the shear stress increases, the rate constant increases.
unsheared 1445.10Pa
-2 -1
0
1
2
ln t Sogang University
JMA constants and rate constants of sheared PBT as a function of the applied shear stress 2.7
0
2.5 -1 ln k
JMA constant
2.6
2.4
-2 2.3 -3
2.2
2.1
-4 0
2000 4000 6000 8000 10000 12000
Shear stress [Pa]
0
2000 4000 6000 8000 10000 12000
Shear stress [Pa]
Sogang University
Linear regression of unsheared PBT isothermal kinetics for Half-time analysis 1
U* = 6066.8 J/mol
ln(1/t1/2)+U*/R(T-Too)
0
(1/t1/2)o = 23.3164 min-1 -1
C3 = 65090.3325 K2.
-2
The half-times can be extrapolated to lower temperatures and rate constant can be calculated using k = ln2/(t 1/2)n
-3
-4 4e-5
6e-5
8e-5
1e-4
o
1/T(Tm -T)f
Sogang University
Half-time of isothermal kinetics for sheared PBT samples 3
From the isothermal kinetics, the half-time of sheared PBT sample with different histories lies on a single line as a function of shear stress.
207oC
log(t1/2) [sec]
199oC
2 193oC
Half time is strongly dependent on the applied shear stress rather than the shear rate, the shearing time and the crystallization temperature.
. T=215 C, =1s-1 . T=215oC, =2s-1 . T=215oC, =4s-1 . T=210oC, =1s-1 . T=210oC, =2s-1 . T=210oC, =4s-1 o
1
0 2
3
4
log(shear stress) [Pa] Sogang University
(1/t1/2)o and C3 of sheared PBT samples with different histories 7.0
6.5 4
C3 x 10-4
ln(t1/2)o [sec]
5
. T = 215oC, =1s-1 . T = 215oC, =2s-1 . T = 215oC, =4s-1 . T = 210oC, =1s-1 . T = 210oC, =2s-1 . T = 210oC, =4s-1
3
6
7
8
9
ln(shear stress) [Pa]
. -1 T=215oC, =1s . o T=215 C, =2s-1 . T=215oC, =4s-1 . T=210oC, =1s-1 . T=210oC, =2s-1 . T=210oC, =4s-1
5.5
2 5
6.0
10
5.0 5
6
7
8
9
10
ln(shear stress) [Pa] Sogang University
Comparison of extrapolated reciprocal half-times of PBT with experimental results 0.08 0.07
3382.60Pa
The results of half-time analysis are in good agreement with the experimental data.
0.06 1/t1/2 [sec-1]
0.05
1445.10Pa
0.04
The shear stress increases both the crystallization kinetics and the onset of crystal melting temperature.
0.03
424.57Pa 0.02 0.01
unsheared
0.00 250
300
350
400
450
500
550
Temperature [K]
Sogang University
Envelope of time-temperature-transition of PBT 500
Temperature [K]
475 unsheared 424.57Pa 921.88Pa 1445.10Pa 2099.36Pa 5249.80Pa 10175.60Pa
450 425 400
The half-time of high shear stress is shorter than that of low shear stress. As the shear stress increases, the TTT envelope broadens.
375 350 10
100
1000
t1/2 [sec] Sogang University
Determination of crystallization rate constant of PBT 14 1091.46Pa 2099.36Pa 5249.80Pa 10175.60Pa unsheared
12 10
k(T)
8 6 4
The results are obtained from Hoffman-Laurizen equation and the isothermal kinetics data at different shear stresses. As the shear stress increases, the crystallization rate constant significantly increases.
2 0 450
475
500
Temperature [ K ] Sogang University
Prediction of the extent of non-isothermal crystallization using Nakamura equation Unsheared
Sheared [5249.8Pa]
1.0
0.5
0.0
450
475
500
525
Temperature [ K ]
550
Relative crytallinity
Relative crystallinity
o
2 C/min (Exp.) o 5 C/min o 10 C/min 15oC/min 2oC/min (Pred.) o 5 C/min o 10 C/min o 15 C/min
2oC/min (Exp.) 5oC/min 10oC/min 15oC/min o 2 C/min (Pred.) 5oC/min 10oC/min 15oC/min
1.0
0.5
0.0
450
475
500
525
550
Temperature [ K ] Sogang University
Prediction of the extent of non-isothermal crystallization using Kamal equation Sheared [5249.8Pa]
2oC/min (Exp.) 5oC/min 10oC/min 15oC/min 2oC/min (Pred.) 5oC/min 10oC/min 15oC/min
1.0
0.5
0.0
450
475
500
Temperature [ K ]
525
Relative crytallinity
Relative crystallinity
Unsheared
2oC/min (Exp.) 5oC/min 10oC/min 15oC/min 2oC/min (pred.) 5oC/min 10oC/min 15oC/min
1.0
0.5
0.0
450
475
500
525
Temperature [ K ] Sogang University
Summary The increase of melting area shows a similar trend to shear stress data. From this result, we can deduce that the increase of shear stress is due to the formation of crystal. When shear stress is applied to a polymer melt, crystal is formed at a higher temperature and at a shorter time than a quiescent one. The shear stress of PP is increased with time showing oscillatory fluctuation, but in the case of PBT the oscillatory fluctuation is not significant. This phenomenon might be expected that the cluster is repeatedly formed and destoryed in the shearing field before it grows up to the critical cluster size. The induction time of crystallization reduces as shear rate increases and also temperature decreases. Sogang University
The shear stress can reduce the dimension of the crystal growth from 3 dimensional spherulite to 2 dimensional lamellar morphology in case of PBT. The half-time of sheared samples is strongly dependent on the applied shear stress rather than the shear rate, the shearing time and the crystallization temperature. The results of non-isothermal kinetics of unsheared and sheared PBT accord with Kamal equation rather than Nakamura equation.
Sogang University
Time dependent shear stress of PBT at various shear rates 10000
o T = 210 C
Shear stress [Pa]
4.0 s-1
2.0 s
-1
1000
1.0 s
-1
100 0
100
200
300
400
500
Time [sec]
Sogang University
8
9
7
8
6
7 Peak time [min]
Peak time [min]
Dependence of the isothermal crystallization peak time on melt annealing temperature and time
5 4 3
o
T1 = 180 C o T1 = 200 C o T1 = 220 C T1 = 240oC T1 = 260oC
o
PP2, Tc = 127 C
3
o
1 0 420
5 4
PP1, Tc = 124oC
2
6
PP3, Tc = 126 C
2 440
460
480
500
Melt temperature [K]
520
540
0
100
200
300
400
500
Isothermal time [min]
Sogang University
