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Blow Molding Modeling: Pressure Rise and Die Swell
PredictionsEdición Única
Title
Blow Molding Modeling: Pressure Rise and Die Swell
PredictionsEdición Única
Authors
Juan José Aguirre González
Affiliation
Campus Monterrey
Issue Date
20000501
Item type
Tesis
Rights
Open Access
Downloaded
19Jan2017 06:47:56
INSTITUTO TECNOLÓGICO Y DE ESTUDIOS
SUPERIORES DE MONTERREY
CAMPUS MONTERREY
DIVISION DE INGENIERÍA Y ARQUITECTURA
PROGRAMA DE GRADUADOS EN INGENIERÍA
TECNOLÓGICO
DE MONTERREY
BLOW MOLDING MODELING: PRESSURE RISE AND
DIE SWELL PREDICTIONS
THESIS
SUBMITTED TO THE OFFICE OF GRADUATE
STUDIES OF I.T.E.S.M. UNIVERSITY
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS OF TOE DEGREE OF
MASTER OF SCIENCE
MAJOR SUBJECT: CHEMICAL ENGINEERING
BY:
JUAN JOSE AGUIRRE GONZALEZ
A Thesis
by
JUAN JOSÉ A G U I R R E G O N Z Á L E Z
Submitted to the Office of Graduate Studies of I.T.E.S.M. University
in partial fulfillment of the requirements of the degree of
M A S T E R OF SCIENCE
May 2000
A Thesis
by
J U A N JOSÉ A G U I R R E G O N Z Á L E Z
Submitted to the Office o f Graduate Studies o f
I.T.E.S.M. University
in partial fulfillment o f the requirements o f the degree of
M A S T E R OF SCIENCE
Approved as to style and content by:
Jaime Bonilla Ríos (Chair o f Committee)
Miguel Angel Romero (Member)
Michel Daumerie (Member)
Federico Viramontes (Head o f Department)
M a y 2 0 0 0
ABSTRACT
Blow Molding Modeling: Pressure Rise and Die Swell. (May 2000)
Juan José Aguirre González, B.S., ITESM, Monterrey, Mexico;
Chairs of Advisory Committee: Dr. Jaime BonillaRios
In the present study a rheological analysis of the polymer melt history inside a concentric annular die of
an extrusion blowmolding machine was studied using momentum and continuity balances for six high
density polyethylene (HDPE) resins to determine the pressure rise and thickness swell. It also tried to
develop a laboratory technique to predict die swell during blow molding.
The rheological measurements included oscillatory behavior, relaxation modulus, steady state behavior,
and capillary flow. They were used to generate material functions that were compared to predictions from
the Wagner constitutive model and to blow molding processability data.
A modified damping function was developed and used in the prediction of steady state elongational
D E D I C A T I O N
T o m y parents Juan Jose Aguirre and Irma González for all their love, patience, and wisdom. Thank you
for helping m e in m y early days, and for filling me with confidence from kindergarten through graduate
school. You are always giving me positive examples and good familiar principles. You have taught me to
challenge new opportunities in m y life and become a better human being.
To m y fiancee Martha A. Sanchez for all her love, understanding and patience. You have been with me all
the weeks I spent to accomplish this goal in m y life. Thank you for your support and your beautiful smile.
To m y sister Ericka and m y brother Alejandro, your are m y best friends.
T o m y uncle Sergio Gonzalez, he will always b e a motivation to m e in the Engineering field.
To my friends Carlos Vazquez, Raúl Vallejo, Eugenio Soltero, Virgilio Gómez, N o e Gutierrez and Arturo
A C K N O W L E D G M E N T S
I want to thank God who gives me new opportunities each day and helped m e to achieve this goal in m y
life.
To Dr. Jaime BonillaRíos.
Thank you for the privilege of being your student, for directing me to be consistent and for offering me
your knowledge and experience in the countless hours you spent with me during this study. Also for
introduced m e to most of the other people who were major contributors to this work.
To Dr. Michel Daumarie.
Thank you for the support and time you provided to me throughout this study and for help me to put in
practice all the theoretical concepts for the research and technology industry.
To Dr. Miguel Angel Romero.
Thank you for your teachings and helpful comments.
To M y Professors at I.T.E.S.M. University.
Thank you for your teachings and knowledge shared with me.
I would thank some of the people who made it possible, apologizing for leaving out many extraordinary
people:
at Fina Oil and Chemical Co.
Tim Coffy, Greg Dekunder and Gerhard Guenther for their support, interest, knowledge, attentions and
time gave during all the stages of this study.
Jeff Nairn and Theresa Lewis for their help in the testing laboratory.
Marc Mayhall and Ben Hicks for their work in blow molding.
at I.T.E.S.M. Unviersity
Dr. Bonilla for proofreading this document.
Martha Sanchez, Fernando Pacheco, Arturo Gérez, Pedro Cortes and Rodolfo Mier, w h o collaboration
Instituto Tecnológico y de Estudios Superiores de Monterrey
(I.T.E.S.M., Mexico)
T A B L E O F C O N T E N T S
C H A P T E R Page
I. I N T R O D U C T I O N 1
A. Statement of the problem 1
B . Objectives 3
C. Expected benefits 3
D. General procedure 3
E. Organization 4
II. B A C K G R O U N D 6
A. Production of H D P E resins 6
B. Blow molding process 11
C. Modeling of the blow molding process 18
D. Constitutive models 21
E. Rheological measurements and interpretations 27
III. L A B O R A T O R Y A N D P R O C E S S I N G M E T H O D S 30
A. General aspects for rheological characterization 30
B . Oscillatory response 30
C. Creep and recovery compliance 32
D. Steady shear testing 33
E. Shear viscosity by capillary rheometry 34
F. Transient stress using the capillary rheometry 37
G. Elongational viscosity b y capillary rheometry 37
H. Melt flow indexer 38
I. Density 38
J. Gel Permeation Chromatography (GPC) 39
K. Operating conditions in the Uniloy 250 R l extrusion blow molding machine 39
L. Models and mathematical techniques 41
IV. B L O W M O L D I N G M A C H I N E PROCESSABILITY D A T A 42
A. Typical quality control data 42
B. Molecular weight data 42
C. Pressure rise data at the Uniloy 250 R l 44
D . Thickness profile data at the Uniloy 250 R l 44
C H A P T E R Page
V. R H E O L O G I C A L M E A S U R E M E N T S 49
A. Oscillatory response 49
B. Relaxation spectra and the Relaxation moduli 56
C. Steady shear viscosity 58
D. Elongational viscosity 65
E. Transient data 66
VI. W A G N E R M O D E L 70
A. Wagner model 70
B. Stress and first normal stress response to step shear rate 71
C. Stress response to uniaxial deformation at constant extension rate 87
VII. M A T H E M A T I C A L M O D E L I N G OF A L A M I N A R N O N N E W T O N I A N F L O W IN
A N N U L A R DIE F O R A N EXTRUSION B L O W M O L D I N G M A C H I N E 103
A. Pressure rise using continuity and momentum equations with the power law
model 103
B. Pressure rise using continuity and momentum equations with the Wagner m o d e l . . . . 136
C. Swell phenomenon 138
VIII. C O N C L U S I O N A N D R E C O M M E N D A T I O N S 160
A. Rheological properties 161
B. Prediction of rheological properties 162
C. Prediction of pressure rise 163
D. Prediction of die swell 164
E. Recommendations 165
R E F E R E N C E S 167
A P P E N D I X A U N I L O Y 250R1 B L O W M O L D I N G RUN SHEET 171
A P P E N D I X B R H E O L O G I C A L D A T A FOR THE SIX H D P E 189
A P P E N D I X C STRESS A N D FIRST N O R M A L STRESS D I F F E R E N C E R E S P O N S E T O
STEP SHEAR R A T E 192
A P P E N D I X D W A G N E R M O D E L : U N I A X I A L E L O N G A T I O N U N D E R C O N S T A N T
STRAIN R A T E 194
A P P E N D I X E E Q U A T I O N S O F C O N T I N U I T Y A N D M O M E N T U M FOR THE S T E A D Y
S T A T E A X I A L F L O W O F A N I N C O M P R E S I B L E N O N N E W T O N I A N
F L U I D IN A N A N N U L A R DIE 198
A P P E N D I X F F O R T R A N C O D E F O R S U B R O U T I N E D Q D A G S F R O M IMSL L I B R A R Y . 202
A P P E N D I X G F O R T R A N C O D E F O R P R E S S U R E RISE: U S I N G CONTINUITY A N D
A P P E N D I X H A U T O L I S P P R O G R A M M I N G L A N G U A G E C O D E 223
A P P E N D I X I DIE S W E L L P R E D I C T I O N U S I N G E G G E N M O D E L 224
A P P E N D I X J A R E A S W E L L U S I N G THE MODIFIED E G G E N M O D E L 236
A P P E N D I X K F O R T R A N C O D E T O C A L C U L A T E THE A X I A L V E L O C I T Y U S I N G T H E
LIST OF F I G U R E S
Page
Figure 1 . 1 . Symbols used to define swell ratios 2
Figure 2. 1. Schematic representation of the structures of various types of polyethylenes... 6
Figure 2. 2. Highdensity polyethylene (HDPE) U.S. major markets in 1999. (Modern
Plastics, 2000) 8
Figure 2. 3. High density polyethylene (HDPE) Japan major markets in 1999. (Modern
Plastics, 2000) 9
Figure 2. 4. High density polyethylene (HDPE) Western Europe major markets in 1999.
(Modern Plastics, 2000) 9
Figure 2. 5. ReciprocatingScrew Extrusion Blow Molding Machine Uniloy 250 R l 12
Figure 2. 6. Variables affecting diameter and thickness distribution of the parison shape... 13
Figure 2. 7. Variables affecting parison inflation 16
Figure 2. 8. Variables affecting the parison cooling 17
Figure 3. 1. Typical creep and recovery compliance curves and their main parameters 33
Figure 3. 2. Capillary rheometer like the one used in the steady and transient shear
viscosity analysis 34
Figure 3. 3. Differences between the entrance angles (90° and 180°) for two dies with
constant L/D ratios 35
Figure 3. 4. Tinius Olsen Plastometer like the one used in the determination of the melt
flow index analysis 38
Figure 3. 5. Schematic diagram of the extrusion blow molding process 39
Figure 3. 6. Converging annular die used in the Uniloy 250 R l extrusion blowmolding
machine 40
Figure 3. 7. The five spots indicate where the thickness was measured 40
Figure 4. 1. Molecular weight distribution curves as obtained from G P C measurements
for the H D P E resins 43
Figure 4. 2. Pressure rise data at different die gap flat profiles in the Uniloy 250 R l 44
Figure 4. 3. Thickness distributions for the six resins with a flat profile (9 % die gap),
measured with a magnetic pen 45
Figure 4. 4. Thickness distributions for the six resins with a flat profile (11 % die gap),
measured with a magnetic pen 45
Figure 4. 5. Thickness distributions for the six resins with a flat profile (13 % die gap),
measured with a magnetic pen 46
Figure 4. 6. Total parison weight at different flat profiles 46
Figure 4. 8. Parison swell for the six HDPE resins at three different die gaps (9 %, 11 %,
and 13 %) using a flat profile 48
Figure 4. 9. Parison swell and thickness swell (at the 3rd point) ratio at several die gaps
( 9 % , 1 1 % , and 13%) versus the thickness swell at 9 % of die gap 48
Figure 5 . 1 . Storage modulus for the H D P E resins. Data from the Rheometrics RAA 49
Figure 5. 2. Loss modulus for the H D P E resins. Data from the Rheometrics R A A 49
Figure 5. 3. Complex viscosity for the H D P E resins. Data from the Rheometrics R A 50
Figure 5. 4. Loss tangent vs. frequency data at different temperatures (Resin C) 53
Figure 5. 5. Loss tangent vs. complex modulus data at different temperatures (Resin
C) 53
Figure 5. 6. Shifted data at 190 °C of loss tangent vs. frequency, showing superposition
(Resin C) 54
Figure 5. 7. Natural logarithm shift factor versus inverse temperature to determine the
activation energy. The slope of the curve is the activation energy for the
Resin C 55
Figure 5. 8. Relaxation spectra for the H D P E resins. Estimation made by using the
R H I O S software 56
Figure 5. 9. Relaxation moduli for the H D P E resins. Estimation made b y using the
R H I O S software from the relaxation spectra 57
Figure 5. 10. Fitting of the relaxation modulus for the Resin C with an eight exponentials
function (equation 5.13) 57
Figure 5 . 1 1 . Steady shear viscosity curves for the H D P E resins at 190 °C 58
Figure 5. 12. Corrected viscosity curves for the H D P E resins at 180° entrance angle,
obtained from the Instron capillary rheometer 59
Figure 5. 13. Corrected viscosity curves for the H D P E resins at 90° entrance angle,
obtained from the Instron capillary rheometer 59
Figure 5. 14. Corrected viscosity curve for the Resin C, obtained using two different die
entrance angle (90° and 180°) from the Instron capillary rheometer 60
Figure 5. 15. Viscosity curves from different sources for the Resin C. Filled triangles:
steady shear viscosity from cone and plate test in Rheometrics RAA; filled
diamonds: complex viscosity from cone and plate test in Rheometrics RAA ;
open diamonds: capillary viscosity (Instron) 61
Figure 5. 16. Viscosity vs. shear rate shape related to the CarreauYasuda model
parameters 62
Figure 5. 17. CarreauYasuda model fit for viscosities of the Resin D and Resin
C 63
E 63
Figure 5. 19. CarreauYasuda model fit for viscosities of the Resin B and Resin A 64
Figure 5. 20. Elongational viscosity versus elongational rate for the six H D P E resins, using
a die with 90° entrance effect 65
Figure 5 . 2 1 . Elongational viscosity versus elongational rate for the six H D P E resins, using
a die with 180° entrance effect 65
Figure 5. 22. Elongational stress versus elongational rate for the six H D P E resins, using a
die with 90°entrance effect 66
Figure 5. 2 3 . Load versus time at a piston velocities of 0.0667 in/min =apparent shear rate
of 9.88 s1 67
Figure 5. 24. Load versus time at a piston velocities of 0.67 in/min = apparent shear rate of
99.3 s1 67
Figure 5. 25. Load versus time at a piston velocities of 3.33 in/min = apparent shear rate of
493.5 s1 68
Figure 5. 26. Load versus time at a piston velocities of 6.7 in/min = apparent shear rate of
993 s 1 68
Figure 5. 27. Viscosity versus time for the six H D P E resins, at 190 °C for a 0.1 s1 shear
rate 69
Figure 5. 28. Viscosity versus time for the six H D P E resins, at 190 °C for a 1.0 s1 shear
rate 69
Figure 6. 1. Flow diagram showing the procedure followed to obtain the memory and
damping functions (Bonilla 1996) 73
Figure 6. 2. Fitting of the relaxation modulus for the Resin F with an eight exponentials
function (6.16) as mentioned in step 6 in the flow diagram of Figure 6.
1 75
Figure 6. 3. M e m o r y function for the Resin F obtained as mentioned in step 6 in the flow
diagram of Figure 6. 1 (equation 6.17) 75
Figure 6 . 4 . Fitting of the shear viscosity for the Resin F, using a single (dotted line) and a
double exponential damping function (continuos line) as mentioned in step 7
in the flow diagram of Figure 6. 1 76
Figure 6. 5. Information used b y Otsuki to estimate the steady shear viscosity and first
normal stress difference for a 530 B H D P E resin at 190°C, where " a " = n l
and " n " = n 2 . (Otsuki et al. 1997) 77
Figure 6. 6. Values of shear viscosity versus shear rate were read and put at the right side
for 530 B H D P E resin 78
Figure 6. 7. Shear viscosity versus shear rate for the 530 B H D P E resin, using the P S M ' s
b y Otuski et al. (1997) 78
Figure 6. 8. Fitting of the shear viscosity for the Resin F, using the P S M ' s and modified
P S M ' s damping function as mentioned in step 7 in the flow diagram of
Figure 6 . 1 79
Figure 6. 9. Estimation of the shear viscosity (equation 6.11) versus time for the Resin F,
using the modifiedPSM's damping function (equation 6.6) and the memory
function (equation 6.17) as mentioned in step 8, Figure 6. 1 80
Figure 6 . 1 0 . Estimation of the first normal stress difference (equation 6.15) versus time
for the Resin F, using the modifiedPSM's damping function (equation 6.6)
and the memory function (equation 6.17) as mentioned in step 9 and 10,
Figure 6 . 1 80
Figure 6. 11. Relaxation moduli for the H D P E resins, as obtained from 6.16. Symbols are
used for identification (they are not measured values) 81
Figure 6. 12. Memory functions for the H D P E resins, as obtained from equation 6.17.
Symbols are used for identification (they are not measured values) 82
Figure 6. 13. Predicted shear viscosity versus time at the constant shear rate of 1 s1, for
the H D P E resins. Symbols are used for identification (they are not measured
values) 83
Figure 6. 14. Predicted shear viscosity versus time at the constant shear rate of 500 s1, for
the H D P E resins. Symbols are used for identification (they are not measured
values) 83
Figure 6 . 1 5 . First normal stress difference for the H D P E resins as calculated from
equation 6.15 as time goes to infinite. Symbols are used for identification
(they are not measured values) 84
Figure 6. 16. Shear viscosity versus shear rate for the strain sensitivity parameters n l =
1000 and n2 = 0, and n l and n2 = 1. Experimental viscosity fitted when n l =
16 and n2 = 1.1 (thick line) 85
Figure 6. 17. Shear viscosity versus shear rate for the different magnitudes for the strain
sensitivity parameters n l and n2 . Experimental viscosity fitted when n l =
16 and n2 = 1.1 (thick line) 85
Figure 6. 18. First normal stress difference ( N l ) versus shear rate for strain sensitivity
parameters n l = 1000 and n2 = 0, and n l and n 2 = l . N l fitted when n l = 16
and n2 = 1.1 (thick line) 86
Figure 6 . 1 9 . First normal stress difference ( N l ) versus shear rate for different magnitudes
for the strain sensitivity parameters n l and n2. N l fitted when n l = 16 and
n 2 = 1.1 (thick line) 87
elongational viscosity for 530 B H D P E resin at 190°C, with ε = 0.31 s"
1 91
Figure 6. 2 1 . Values of transient elongational viscosity vs. time were read and put at the
left side for 530 B H D P E resin 92
Figure 6. 22. Unsteady elongational viscosity versus time for the 530 B H D P E resin, using
the modifiedPSM's damping function with the fitting parameters reported by
Otuski (1997) 92
Figure 6. 23. Calculated elongational viscosity versus time, at different elongational rates
for the Resin F, applying the Lodge and the Wagner
model 93
Figure 6. 24. Elongational and shear viscosity versus elongational and shear rate for the
Resin F. Experimental data presented for comparison 94
Figure 6. 25. Calculated elongational viscosity versus time for the Resin F at several
elongational fates. Lodge predictions included for comparison 95
Figure 6. 26. Elongational and shear viscosity versus elongational and shear rate for the
Resin F. Predicted data using the damping function 6.41 96
Figure 6. 27. Elongational viscosity versus time with =100 s1 for the different magnitudes
for the strain sensitivity parameter " a " . Symbols are used for identification
(they are not measured values) 97
Figure 6. 28. Elongational viscosity versus time with =100 s1 for the different magnitudes
for the strain sensitivity parameter "|3". Symbols are used for identification
(they are not measured values) 97
Figure 6. 29. Elongational viscosity versus elongational rate for the different magnitudes
for the strain sensitivity parameter s " a " and "(3". Symbols with the lines are
used for identification (they are not measured values) 98
Figure 6 . 3 0 . Elongational viscosity versus elongational rate. The fitting was made
adjusting the " a " parameter to the experimental elongational viscosity 98
Figure 6. 3 1 . Relation between " a " parameter and the elongational rate for the Resin F.
The power law equation is showed 99
Figure 6. 32. Modeled elongational viscosity versus elongational rate for the Resin F.
Modeling performed using the modified Papanastasiou's damping function
proposed b y the authors of this study (see equation 6.42) 99
Figure 6. 33. Calculated elongational viscosity versus time for the Resin F at several
elongational rates. Lodge predictions included for comparison. Using
modifieddamping function (see equations 6.42, and 6.43) 100
Figure 6. 34. Relation between parameter " b l " and molecular weight peak 102
2.475 in 104
Figure 7. 2. Shear stress and velocity distribution for axial annular flow 104
Figure 7. 3. Schematic representation of coordinates describing axial annular and conical
sections of the die configuration 105
Figure 7. 4. Conical sections of the die 105
Figure 7. 5. Function F(S,K) needed to obtain the volumetric flow rate through an annulus
for a powerlaw fluid. (The highest number (10) corresponds to the highest
curve, the last number (0) corresponds to the last onestraight line) 109
Figure 7 . 6 . F(S,K) tabulated data for power law flow through an annulus (from
Fredickson et al. 1958) 109
Figure 7. 7. Flow diagram showing the procedure to obtain the pressure rise 112
Figure 7 . 8 . Die and Mandrel geometries at different positions in 3D image 119
Figure 7. 9. A schematic representation of the program used in A u t o C A D R14 and the
input parameters 120
Figure 7. 10. Shows the die and mandrel radii result from A u t o C A D R14 121
Figure 7 . 1 1 . Schematic picture that shows were to write " m o v e " command 121
Figure 7. 12. Schematic picture that shows the selected geometry "mandrel". The yellow
box indicates the base point or displacement selected to move the mandrel 122
Figure 7 . 1 3 . Schematic picture that shows the selected geometry "mandrel" displaced to
the left side 123
Figure 7. 14. Schematic picture that shows the "mandrel" displaced to the left side in 0.1
inches 123
Figure 7. 15. Shear stress (Pa) versus shear rate (s1) at 190°C for a H D P E resin blow
molding grade (Parnaby et al. (1974)) 124
Figure 7. 16. Detail drawing of the diemandrel configuration used to study its effect on
pressure drop. Converging annular die. All dimensions are in m m . (Parnaby
e t a l . (1974) 124
Figure 7. 17. Converging annular die used to obtain the pressure rise and shear rate
calculation...: 125
Figure 7. 18. Pressure rise (psia) due to shear viscous effect versus distance (in.) 125
Figure 7. 19. Shear rate (s1) calculated vs. distance (in.) 126
Figure 7. 20. Die gap (mm.) versus stroke (mm.) using the die and mandrel configuration
in A u t o C A D 128
Figure 7. 2 1 . Die gap (in.) versus stroke (in.) using AutoCAD. Several approaches ( G l , Figure 7. 1. Diemandrel configuration employed in extrusion blow molding experiments
to study its effect on pressure rise and parison swelling for six H D P E resins.
G2 and G3) are displayed to see their positions and differences among die
gaps 130
Figure 7. 22. Diverging annular die with converging flow used in the Uniloy blowmolding
machine 131
Figure 7. 2 3 . Axial velocity versus distance for the three different gaps in the Uniloy blow
molding machine 131
Figure 7. 24. Elongational rate versus distance at three different gaps in the Uniloy blow
molding machine 132
Figure 7. 25. Residence time versus distance for three different gaps in the Uniloy blow
molding machine 132
Figure 7. 26. Shear pressure rise versus distance for the three different gaps in the Uniloy
blowmolding machine 133
Figure 7. 27. Conceptual m a p with several approaches tested and n e w methods proposed to
predict the thickness swell in this study. * See page 151 (equivalent diameter
approach) 138
Figure 7. 28. a) Final thickness distribution around the bottle circumference: comparison
between (line): numerical predictions; (shaded): experimental measurements
from Debbaut et al. (1998). b) Thickness measurement locations on the
molded parts 139
Figure 7. 29. Area swell versus die gap (%) using the "reverse technique" at the center of
the parison 141
Figure 7. 30. Thickness swell versus die gap (%) using the "reverse technique" at the
center of the parison 141
Figure 7 . 3 1 . Outer diameter swell versus die gap (%) using the "reverse technique" at the
center of the parison 142
Figure 7. 32. Diameter swell versus shear rate for the six H D P E resins using Tanner's
equation 143
Figure 7. 33. Diameter swell versus shear rate for the six H D P E resins using Han's
equation with L/D = 1 0 144
Figure 7. 34. Diameter swell versus shear rate for the six HDPE resins using Gottfert's
equation with L/D = 1 0 144
Figure 7. 35. Diameter swell versus shear rate using Tanner, Han and Gottfert equations
for the Resin A 145
Figure 7. 36. Recoverable shear calculated using Laun empirical equation as a function of
shear rate 146
Figure 7. 37. Laboratory technique proposed to predict blow molding die swell using
Figure 7. 38. Diameter swell versus shear rate for the six HDPE resins using Eggen's
equation with L/D = 10 149
Figure 7. 39. Diameter swell versus shear rate for different land lengths L/D and entry
angles a as indicated in the legends for Resin E 149
Figure 7 . 4 0 . " K " values versus the steadystate compliance (according to Koopmans
(1992)) for 1 3 % die gap 150
Figure 7. 4 1 . " K " values versus the Mz/Mn for 1 3 % of die gap 151
Figure 7. 42. Schematic representation of coordinates describing axial and radial flow at
the annular die exit 155
Figure 7. 4 3 . Schematic picture of the thickness profile at the annular die exit 157
Figure 7. 44. Mandrel and die geometry and the parison swell versus distance at several
characteristic relaxation times 159
Figure 7. 4 5 . Thickness swell versus time at several characteristic relaxation times 159
Figure 7. 46. Axial velocity versus time at several characteristic relaxation times 160
Figure 7. 47. Parison length versus time at several characteristic relaxation times 160
Figure 8. 1. Illustration of the work performed in this thesis 161
Figure 8. 2. Schematic flow diagram, which explains the laboratory technique that, can b e
used to predict blow molding die swell using capillary rheometer die
LIST OF T A B L E S
Page
Table 2. 1. World Producers of HDPE, 1998 and 1999. (Modern Plastics, 1999 and
2000) 10
Table 2 . 2 . Asia Pacific Capacity of H D P E , 1998.(Modern Plastics, 1999) 10
Table 2. 3. Latin America capacity of HDPE, 1998. (Modern Plastics, 1999) 10
Table 2. 4. Differences among Injection, Extrusion, and Stretch Blow Molding 11
Table 2. 5. Brief explanation of several constitutive equations that have been used by
several authors trying to predict the rheological properties and/or parison
behavior 20
Table 3 . 1 . Equipment used in the rheological characterization of H D P E resins 30
Table 3. 2. H D P E resins used in this study with lot numbers 40
Table 4. 1. MI2, MI5 , H L M I and density data for the six H D P E resins 42
Table 4. 2. Moments of the M W D and polydispersity indices for the H D P E resins 43
Table 5 . 1 . Crossover point moduli and frequencies 50
Table 5. 2. Shift factors at different temperatures for all six resins to 190°C reference
temperature results 54
Table 5. 3. Horizontal shift activation energy for the six H D P E resins 55
Table 5 . 4 . Parameters from fitting the viscosity curves using the CarreauYasuda
model 62
Table 6. 1. Parameters used to fit the shear viscosity for the Resin F using Osaki's and
Wagner's damping functions 76
Table 6. 2. Parameters used to fit the shear viscosity for the Resin F using P S M ' s and
modifiedPSM's damping functions 79
Table 6. 3. Parameters for equation 6.16, used in the fitting of the relaxation moduli for
the H D P E resins 81
Table 6 . 4 . Parameters for the modifiedPSM's damping function (equation 6.6),
obtained by fitting of the measured shear viscosity. n2 =1.1 82
Table 6. 5. " b l " and "b2" values for each resin used to fit the steady state elongational
viscosity 101
Table 6. 6. Relationship between parameters " b l " and " b 2 " and molecular weight
data 101
Table 7. 1. Results presented by Parnaby et al. (1974) versus our simulation software 126
Table 7. 2. Shear and elongational viscosity parameters at different gaps ( 9, 11 and 13
% ) for the Resin B 127
inside the machine 127
Table 7. 4. Die gap estimation using " G l " and " G 2 " method 128
Table 7. 5. Die gap estimation using the " G 3 " method 129
Table 7. 6. Pressure rise calculated by the model versus experimental pressure rise for
the Resin B using a 9 % of die gap 130
Table 7. 7. Total shear pressure rise calculated versus experimental pressure rise for the
Resin B 133
Table 7. 8. Power law parameters for the shear viscosity 134
Table 7. 9. Parameters for the elongational viscosity using equation 7.39 134
Table 7. 10. Total shear pressure rise calculated versus experimental pressure rise using a
9 % of die gap 135
Table 7. 11. Total shear pressure rise calculated versus experimental pressure rise using
an 11 % of die gap 135
Table 7. 12. Total shear pressure rise calculated versus experimental pressure rise using a
1 3 % of die gap 135
Table 7. 13. Shear rate calculated at three different die gaps for the six H D P E resins 136
Table 7 . 1 4 . Total pressure rise estimated with the Wagner model at steady state using a
9 % of die gap 137
Table 7. 15. Total pressure rise estimated with the Wagner model at transient state (0.01
sec) using a 9 % of die gap 137
Table 7 . 1 6 . Total pressure rise estimated with the Wagner model at steady state b y
decreasing the process melt temperature 30°C less, using a 9 % of die gap 137
Table 7 . 1 8 . " K " values for each H D P E resin using Eggen's equation and M z / M w values.. 150
Table 7. 19. Experimental thickness swell versus calculated thickness swell using
Gottfert's equation ( 9 % die gap) 152
Table 7. 20. Experimental thickness swell versus calculated thickness swell using Eggen
model equation 7.62, using equivalent diameter approach (9 %, 11 %, and
1 3 % of die gap) 153
N O M E N C L A T U R E
A0 Initial area (inside the annular die)
Af Final area (outside the annular die)
ai Weight factors for the relaxation modulus and memory function
aT Temperature shift factor
B0 Instantaneous swell
Bl 0 O Diameter swell at infinite time
B1, Bd Diameter swell
B2 or B Thickness swell
B200 or B00. Thickness swell at infinite time, ultimate swell
Ba Area swell
B H T 2,6 ditertbutylpcresol
C1
t Finger strain tensor
ct Cauchy strain tensor
D Die diameter, capillary diameter
Db Barrel diameter
D e or DE Extrudate cross section
De q Equivalent diameter
Di,d Inside diameter of the annular die
Di,e Inside diameter of the extrudate parison
D o Die outside diameter
Do,d Outside diameter of the annular die
Do,e Outside diameter of the extrudate parison
D p Parison outside diameter
F Load (lbf)
f1 First weighting factor for the damping function
f2 Second weighting factor for the damping function
FRB Fraction high molecular weight content
G Thickness of the annular die
G(t) Linear viscoelastic relaxation modulus
G(t)
G* Complex modulus
G ' Storage modulus
G P C Gel permeation chromatography
H Thickness of the parison
h(I1I2) Damping function
H D P E Highdensity polyethylene
H M H D P E High molecular weight highdensity polyethylene
ho Die thickness gap
hp Parison thickness gap
I. First invariant of the strain rate tensor
I2 Second invariant of the strain rate tensor
J Creep compliance
Je(t) Retarded elastic compliance
Je° Steady state recoverable compliance
Jg
Instantaneous or glassy complianceJr(0) Recovery compliance
Jr(0)Jr(t) Recoverable compliance at a given time
Jr(t) Recovery compliance at any time after the stress ceases
L Length
L C B Long chain branching
L D P E Lineardensity polyethylene
Ls
T( t ) Total length of the parison
L L D P E Linearlow density polyethylene
m(tt')
Memory functionM F I Melt flow index
M W D Molecular weight distribution
n Power law parameter
n1 First strain sensitive parameter for the damping function
N1(t) First normal stress difference
n
2 Second strain sensitive parameter for the damping functionN2( t ) Second normal stress difference
PET Polyethylene terephthalate
PIB Polyisobutylene
P L M Power law model
PP Polypropylene
P V C Polyvinyl chloride
Q Volumetric flow rate
RB Barrel radius
Rm Mandrel radius
T Temperature
t Time
tonnes 1000 kilograms
UHMWPE Ultrahigh molecular weight highdensity polyethylene
v Velocity
VLDPE Very lowdensity polyethylene
<Vz> Axial average velocity
W(I1,I2) Potential function
Greek symbols
a Single parameter exponential damping function
A
Characteristic relaxation time5 Phase shift or "mechanical loss angle" ; unit tensor
P Density
PTm Initial melt density
Pcool Density at mold cooling time
Pa Density at ambient conditions
ع
Elongational rateعH Transverse shrinkage
ع = r/Rdie Dimensionless radius
APT Total pressure drop
APS Shear pressure drop
APE Elongational pressure drop
n(t)
Transient shear viscosityn0
Zero shear viscosity7,
True shear viscosityne
Elongational viscosity
Shear viscosity at rate infinity
*
V
Complex viscosityV'
Dynamic viscosityo12 Shear stress
o0 Zero shear stress
oA Apparent shear stress
o1 True shear stress
oe Elongational stress or stress under uniaxial extension
e
Ai Relaxation time
0 Ratio between the second normal stress coefficient and the first normal
stress coefficient
XD Outer diameter swell
XT Thickness swell
Xa Area swell
Y Shear strain
Y0 Strain amplitude
Yr Recoverable strain
Yw Shear rate at the wall
Y (t) Shear rate
Ψ1 First normal stress coefficient
Ψ2 Second normal stress coefficient
C H A P T E R I
I N T R O D U C T I O N1
Plastic hollow parts, such as bottles and tanks, are made by a process known as blow molding. There
are two principal types of blow molding process: injection blow molding and extrusion blow molding. In
the first one a "preform", often similar to a test tube with a threaded end, is injection molded and
subsequently reheated and inflated inside a mold. This is used oftenly in the production of small containers
and it has an excellent control of thickness distribution and sagging (Dealy et al. 1990). In extrusion blow
molding process, a polymer melt is extruded through an annular die to form a hollow cylindrical tube
known as parison. The resin is mixed, melted and carried forward by a rotating screw in conjunction with
heaters located on the barrel wall. Then, the parison is inflated, to take the shape of a mold with a cold
surface; as the thermoplastic encounters the surface, it cools and becomes dimensionally stable. The mold
opens, the part is removed and the cycle starts again (DiRaddo et al. 1993).
The extrusion process is faster and more economical than the injection process and is preferred in the
production of larger containers (such as gas tanks, ducts and bumpers). In any case, the viscoelastic nature
of the polymer melts plays an important role in blow molding since it greatly affects the thickness
uniformity of the molded part and consequently its mechanical properties and/or its aesthetic aspect.
A. Statement of the problem
The nonuniform thickness distribution of blow molded parts arises, mainly, to three factors: die
geometry, the material's swell and sag behavior and the process conditions. If the part is not designed
properly or the material behavior is overlooked, it will be difficult to make a good piece by only modifying
the process operating conditions.
According to DiRaddo et al. (1992), the viscoelastic nature of the polymer melts during extrusion,
results in two phenomena known as swell and sag. These authors state that swell is caused by the
relaxation (loss of the molecular orientation) of the polymer melt as it exits the die. Swell is composed of
an instantaneous and a slower gradual relaxation. The instantaneous relaxation results from the solid
elastic recoil, and the slower relaxation results from the gradual disorientation of the polymer chains.
It has been noticed that a given resin has a different die swell depending on the type of forming die used
(Eggen et al. 1996, Koopmans 1992, Nakajima 1974). The reason for such differences underlies on the
polymer flow history inside the die.
The die swell phenomenon, also known as Barus effect, memory, jet swell, puffup, etc., is considered
as a manifestation of the melt elasticity of the polymer after a shearing flow through a die. The extrudate
cross section (De) is greater than the cross section of the die diameter (D), that is De/D » 1 , (Koopmans
1988).
The variables usually employed to describe die swell are the swell ratio (B), the fully developed wall
shear rate ( y w), the length to diameter (L/D), the temperature (T), and the time (t) that has passed. While
the die swell is a consequence of the history of the flow inside the die and the nature of the resin, the sag or
"drawdown", is caused by gravitational forces that act on the suspended parison. The degree of sag
depends on processing parameters (such as melt temperature, suspension time and total parison length),
D i R a d d o e t a l . ( 1 9 9 2 ) .
T w o swell values are required to describe the parison dimensions (shape): diameter swell (Bj) and
thickness swell (B2) and both affect the final thickness distribution of a part. Bi is typically defined as the
ratio Dp/Do, where Dp and D o are the outside diameters of the parison and the die respectively. On the
other hand, B2 is commonly defined by the ratio hp/ho , where hp and ho are the parison thickness and die
gap respectively ( D e a l y e t a l . 1985), see Figure 1.1.
Mandrel
V
Dp
Figure 1 . 1 . Symbols used to define swell ratios.
The values of Bi and B2 will have different effects on the blow molded part. For example, if the B2 is
too low, the finished product will be too thin, and the part will be weak and soft, while if B2 is too large,
raw material will be wasted. If B , is too low, a container with a handle will not have it's complete handle
(short shot), Swan et al. (1991).
Several authors (Henze et al. (1973), Nakijama et al. (1974), Kamal et al. (1981), La Mantia et al.
(1983), Dealy et al. (1985), Koopmans (1988)) have proposed empirical correlations to predict die swell
from melt index, molecular weight, geometrical characteristics and operating conditions (shear rate or shear
stress). However, such empirical correlations do not consider the dynamics of the polymer melt and
consequently fail to predict die swell properly.
Other authors like Tanuoe, et al. (1995,1996), Luo et al. (1989), Laroche et al. (1996) have approached
swell). Some of the rheological properties required in the numerical methods are difficult to measure. In
those cases, the authors used constitutive models to obtain some of the lacking rheological properties.
However, because of the complexity of the equations involved, these computations are quite time
consuming. In addition, the results obtained in the prediction of die swell at high shear rates and different
geometries are not fully accomplished yet. It seems that the work done by Eggen et al. (1996b) points in
the right direction for the prediction of die swell and flow instabilities, but just for cylindrical extrudates.
Eggen et al. (1996b) studied the flow using different die geometries in capillary extrusion. This author
used the factorized RivilinSawyers constitutive equation and also proposed a mathematical model for
predicting extrudate swell. It is worth to notice that Eggen does this prediction just for capillary dies.
B. Objectives
To develop a user friendly model to predict pressure rise and die swell for high density polyethylene
(HDPE) resins in different types of blow molding machines.
Try to develop a laboratory technique to predict die swell during blow molding.
The genera] purpose of this project is to study the methods, to incorporate the history of the polymer
melt in the annular die and to use the rheological data (first normal stress difference, N l ( t ) , shear rate, y (t),
and viscosity, r|(t) at the exit of the die) as a way to predict die swell.
C. Expected Benefits
The overall goal of this study is to:
1) develop an analytical tool to expedite the research and development of new blow molding resins.
2) increase the knowledge of the flow history of the polymer melt in annular dies.
3) identify rheological parameters and/or functions that can be related to die swell.
4) to develop easy software to use for the technical service personnel.
D. General Procedure
T o ensure the quality of the results generated in this project special care was taken in rheological
testing and validation of the constitutive model. The considerations taken in different areas are discussed
next.
1. Rheological techniques
The techniques were subjected to a screening procedure to determine the best testing conditions for the
also determined. In general the resins were tested at T=190°C, in duplicates when using the cone and plate
geometry for shear testing, and triplicates in capillary testing.
2. Constitutive model
A program for the integral constitutive Wagner model (Wagner 1976) was implemented and tested with
reliable data (Otsuki, et al. 1997). The merits of using an integral constitutive model of the Wagner type
are the following: first, this model allows the use of linear viscoelastic data to predict nonlinear behavior.
Second, the Wagner model is based on the assumption of the separability of the nonlinear memory
function in the linear memory function and the damping function (Bonilla 1996). Third, several researchers
have been successful in estimating rheological properties for polypropylene resins (Lanfray et al. 1990,
Verney et al. 1995, Bonilla et al. 1996, Revenu, et al. 1996) and for highdensity polyethylene resins by
using this model (Otsuki, et al. 1997).
E. Organization
This thesis is divided in 8 chapters including the present one. Chapter I addresses the importance this
study has in blow molding area, it indicates the purpose pursued in this project, the benefits of the study
and establishes the requirements to produce reliable information.
Chapter II presents a literature review and is divided in five sections: a) production of H D P E resins, b)
blow molding process, c) modeling of the blow molding process, d) constitutive models, and e) rheological
measurements and interpretations.
Chapter III describes a) the experimental techniques typically used for quality control purposes, b) the
rheological techniques, c) the processing methods used in the industry and c) the models and software used.
The chapter provides information about the principle upon which the techniques are based. Special
attention is given to the procedure followed in establishing the testing conditions for the rheological
measurements.
The experimental data are presented in chapters IV and V. Chapter IV presents resins properties as
determined by typical quality control techniques. The resins properties obtained through quality control
techniques are the melt flow index (MFI) and the molecular weight distribution ( M W D ) . Chapter V
presents experimental rheological data. Chapter V deals with oscillatory data, shear and elongational
viscosity. The shear viscosity data from different instruments are combined and fitted with the Careau
Yasuda model.
Chapter VI presents the development and validation of the constitutive model as well as estimations of
rheological properties using the Wagner model. First the relaxation spectra from Chapter V is used to
determine the linear viscoelastic relaxation modulus and the memory function. Second, the viscosity data
from Chapter V were used together with the steady state equations from the Wagner model to obtain the
damping function. Also the model is used to predict transient and steady shear elongational viscosities,
which are compared to the elongational viscosity estimated by Cogswell analysis, presented in Chapter V.
Chapter VII presents the mathematical modeling of a laminar nonNewtonian flow in an annular die for
an extrusion blow molding machine and die swell predictions using different approaches. A momentum
and continuity balances were conducted to determine the pressure rise, the average velocity and the shear
rate. Estimation of die swell is made by using the Wagner model with the shear rates calculated at the die
exit from the program.
Chapter VIII presents a summary of the major findings and gives the conclusions and suggestions for
C H A P T E R II
B A C K G R O U N D
Polyolefins are defined as polymers synthesized from unsaturated aliphatic hydrocarbons containing one
double bond per molecule. At the present time, one of the major commercial polyolefins is polyethylene.
Ethylene monomer has the chemical composition CH2=CH2 and the repeating unit of polyethylene it has
the chemical structure JcH2CH23.
Three types of polyethylenes are typically obtained:
1. Linear lowdensity polyethylene (LLDPE) is a copolymer of ethylene and 512 % by weight of an a
olefin such as 1butene, 1hexene or 1octene. LLDPE resins contain short branches and a 0.94 gr/cm3
(see Figure 2. 1).
2. Lowdensity polyethylene (LDPE) is prepared by methods that involve the use of highpressures (150
350 MPa). L D P E resins contain large branches and normally has a density of 0.92 gr/cm3.
3. Highdensity polyethylene (HDPE) is prepared with lowpressure methods (0.2 a 0.4 MPa). H D P E has
a linear structure and densities from 0.950.96 gr/cm3 density.
1
L D P E
1 1
H D P E
/ / /
\
L L D P E
Figure 2. 1. Schematic representation of the structures of various types of polyethylenes.
It is worth to mention that other types of polyethylene exist such as very lowdensity polyethylene
(VLDPE), high molecular weight highdensity polyethylene (HMHDPE) and ultrahigh molecular weight
polyethylene ( U H M W P E ) .
The material selected for this work was Chromium H D P E resins.
A. Production of H D P E resins
H D P E resins is produced b y four methods. The first three involve solution or slurry processes, which
differ mainly in the catalyst used. The fourth method is carried out in the gas phase.
a) Ziegler processes
Ziegler processes are operated at pressures between 0.20.4 MPa (24 atmospheres) and at temperatures
of 5075 °C. Polymerization is made in the presence of ZieglerNatta catalysts, usually based on titanium
tetrachloride/aluminium alkyl (e.g. diethylaluminium chloride). The catalyst may be prepared in situ by
adding the components separately to the reactor as solutions in diluents such as diesel oil, heptane or
toluene or the components may b e prereacted and the catalyst added as a slurry in a liquid diluent. These
operations must b e conducted in an inert atmosphere (usually nitrogen) since oxygen and water deactivate
the effectiveness of the catalyst. In a typical process, ethylene as well as the catalyst and diluent are fed
continuously into the reactor. At the reaction temperatures generally used, the polymer is only sparingly
soluble in the hydrocarbon diluent and therefore forms as a slurry, which is continuously removed. The
reaction is quenched by the addition of alcohols such as methanol, ethanol or isopropanol and the resulting
metallic residues are extracted with alcoholic hydrochloric acid. Finally, the polymer is centrifuged, dried,
extruded and granulated (Boor, J. 1979).
b) Phillips processes
Phillips processes are usually operated at pressures between 34 MPa (3040 atmospheres) and at
temperatures of 90160°C. Polymerization is conducted in the presence of a chromium oxide catalyst. The
catalyst is prepared b y impregnating silica or silicaalumina with an aqueous solution of a chromium salt
and heating the product in air at 400800 °C. Solution processes are normally run at 120160 °C, at which
temperatures the polymer is soluble in the diluent. Hot polymer solution is continuously drawn from the
reactor; unreacted ethylene is flashed off and suspended catalyst is removed by filtration or centrifuging.
The solution is then cooled to precipitate the polymer, which is separated b y centrifuging. Slurry
processes, on the other hand, are usually run at 90100°C, and at those temperatures the polymer has low
solubility in the diluent. The slurry, which consists of polymer granules each formed around separate
catalyst particles, is drawn off continuously. Unreacted ethylene is flashed off and then the polymer is
separated by centrifuging. The polymer so obtained is contaminated with a small amount of catalyst which
is not usually removed (Saunders, K. J., 1988).
c) Standard Oil processes
Standard Oil processes are operated at pressures between 410 MPa (40100 atmospheres) and at
temperatures of 200300 °C. Polymerization is made in the presence of a metal oxide, such as
molybdenum trioxide on a support, which may b e alumina titanium dioxide or zirconium dioxide.
d) Union Carbide processes
In the Union Carbide processes, ethylene is polymerized in the gas phase. Pressures from 0.72 MPa (7
20 atmospheres) and temperatures around 100 °C are used. Polymerization made with a proprietary
catalyst, which consist of supported organochromium compounds such as chromacene ((C
5H5)
2Cr). The
process uses a fluidized bed and is inherently simple in that ethylene serve as the fluidizing gas (as well as
reactant) and polyethylene is the bed material. The polymer is produced as granules (from which catalyst is
not removed), and can be used directly. Since no solvent is involved, gas phase processes are simpler to
operate and have lower energy consumption than other processes for HDPE (Saunders, K.J., 1988).
2. Processing
Low melting point and high chemical stability facilitate the processing of HDPE by conventional
techniques like: blow molding, injection molding, pipe and film extrusion.
3. Economic Aspects
HDPE major markets for U.S., Japan and Western Europe are shown in Figure 2. 2, Figure 2. 3, and
Figure 2. 4, respectively.
Exports
10%
Extruded goods
30%
Blow molding
30%
1000 kg. = 1 tonnes
Injection molding
17%
Volume = 6,950 x 10 tonnes/year
Extruded goods
39%
Injection molding
9%
1000 kg. = 1 tonnes
Other
19%
Exports
19%
Volume = 1,191 x 10
3tonnes/year
Figure 2. 3. High density polyethylene (HDPE) Japan major markets in 1999. (Modern Plastics, 2000).
Other
5%
Injection molding
yS
\
21%
/
\
y
Extrusion
37%
Volume = 4,406 x 10
3tonnes/year
Blow molding
\
3 7 %• 1000 kg. = 1 tonnes
World Producers are shown in Table 2. 1. Capacities of H D P E for AsiaPacific and Latin America are
shown in Table 2. 2, and Table 2.3 respectively.
Table 2. 1. World Producers of HDPE, 1998 and 1999. (Modern Plastics, 1999 and 2000).
H D P E S E L E C T N A M E P L A T E
C A P A C I T I E S
1 0 0 0 T O N N E S
1 9 9 9
SOLVAY AND PHILLIPS* 2 3 3 0
EQUISTAR* 1 6 5 0
EXXONMOBIL 1 1 1 0
B A S F S H E L L 8 9 0
TOTAL FINAELF A T O C H E M 8 7 0
S O U R C E : MAACK B U S I N E S S S E R V I C E S ( M B S ) * 1 9 9 9 M B S INFORMATION
Table 2. 2. Asia Pacific Capacity of HDPE, 1998.
(Modern Plastics, 1999)
H D P E
S E L E C T A S I A P A C I F I C C A P A C I T I E S B Y C O U N T R Y
COUNTRY
. TONNES 1 9 9 8
AUSTRALIA 1 6 0 , 1 1 7 C H I N A 6 4 9 , 9 9 4
INDIA 3 3 0 , 2 1 4
INDONESIA 1 0 0 , 2 4 3 S I N G A P O R E 2 0 0 , 0 3 3 SOUTH KOREA 1 , 2 6 0 , 0 7 3 T A I W A N . 2 0 0 , 0 3 3
THAILAND 4 0 0 , 0 6 6
Table 2. 3. Latin America capacity of
HDPE, 1998. (Modern Plastics, 1999).
H D P E
S E L E C T L A T I N A M E R I C A N C A P A C I T I E S B Y C O U N T R Y
COUNTRY
TONNES 1 9 9 8
BRAZIL 5 9 1 , 9 3 8 M E X I C O 2 0 0 , 0 0 0 V E N E Z U E L A 1 0 0 , 2 4 4 ARGENTINA 6 2 , 1 4 2 C O L O M B I A 5 9 , 8 7 4
4 . Uses
The acceptance of H D P E for packing bleach, detergent, household chemicals, and milk in the 1960s and
1970s greatly increased blowmolding production (Encyclopedia of Polymer Science and Technology,
1964 ). Blow molding products are the single largest use of H D P E resins, with packaging applications
accounting for the greatest volume. The U.S. blow molding market represents a 3 0 % of total H D P E
consumption. Injection molding products are the second largest application, with approximately 16% of
the H D P E market (Concise Encyclopedia of Polymer Science and Engineering 1990, Modern Plastics,
1998). Uses include blowmolded bottles for milk, and household cleaners and injectionmolded pails,
B. Blow molding process
Blow molding is a very important polymer processing method for manufacturing hollow articles such as
bottles. The process involves first the forming of a molten parison, which is a hollow cylindrical tube. The
parison is inflated to take the shape of the mold with a cold surface; as the thermoplastic encounters the
surface, it cools and becomes dimensionally stable. The mold opens, the part is removed and the cycle
starts again (DiRaddo et al. 1993).
Three blow molding process are used:
a) Injection blow molding, which uses an injectionmolded testtube shaped perform or parison.
b) Extrusion blow molding, which uses an extruded tube parison.
c) Stretch blow molding, which uses an injectionmolded, extrudedtube, or extrusion blowmolded
preform.
Table 2. 4 shows a comparison among the three processes.
Table 2. 4. Differences among Injection, Extrusion, and Stretch Blow Molding
Injection blow molding Extrusion blow molding Stretch blow molding
• Used for small bottles or parts • used for bottles or parts 250 ml. • used for bottles between 500
less than 500 ml. in volume in volume or larger ml. and 2 1. in size
• Scarpfree, with extremely • operator skills are more crucial • the technique is limited to
accurate control of weight and to the control of the part weight simple bottle
neck finish and quality • lowercost material
• Impractical for containers with • containers with handles and off
handles set necks are easily fabricated
• Tooling costs are relative • tooling costs are less expensive
higher
Injection blow molding has basically three stages. In the first stage, plastic melted in a reciprocating
screw extruder is injected into a split steel mold cavity to produce a preform parison, which in turn is
temperature conditioned for later blow molding. The preform is shaped much like a test tube with a screw
finish at the top. The preform is transferred on a core rod to the second and blow molding stage. Here air is
blown through the core rod to expand the conditioned preform against a cold, usually aluminum, blow
mold cavity. The container has now been produced. In the third stage, the container is transferred again on
the core rod. The finished container is transferred to the third stage where it is ejected from the machine
( R o s a t o e t a l . 1989).
In stretch blow molding, mainly polyethylene terephthalate (PET), polyvinyl chloride (PVC),
polypropylene (PP), and polyacryonitrile are used (Fritz, H.G. 1981). This process is based on the
crystallization behavior of the resin. The parison is temperatureconditioned and then it is rapidly stretched
transition temperature. At this point, the resin can be moved without the risk of further crystallization.
(Encyclopedia of Polymer and Science Engineering, 1985).
There are two types of extrusion blow molding process, continuos and intermittent. In both of them a
melted plastic resin is extruded as a tube ( parison) into the air. The parison is captured by the two halves
of the bottle blow mold. A blow pin is inserted through which air enters and expands and then cools the
parison against the mold cavity (Encyclopedia of Polymer and Science Engineering, 1985).
In continuos extrusion blow molding, the parison is continuously formed at the same rate as the article
is molded, cooled, and removed. To avoid interference with the parison formation, the moldclamping
mechanism must move quickly to capture the parison and return it to the blowing station where the blow
pin enters (Encyclopedia of Polymer and Science Engineering, 1985).
In intermittent extrusion blow molding, the parison is quickly extruded after the bottle is removed form
the mold. The clamping mechanism does not need to move to a blowing station. Blow molding, cooling,
and bottle removal all take place under the extrusion head. This permits a simple and rugged clamping
system. Because of the stopstart aspect of extrusion, this process is more suitable for polyolefin and other
heatstable materials (Encyclopedia of Polymer and Science Engineering, 1985).
A modification is the reciprocatingscrew method used for bottles between 250 ml and 10 liters in
volume. After the parison is extruded, the screw moves back, accumulating melt in front of its tip. When
the previously molded bottle has cooled, the mold opens, the bottle is removed, and the screw quickly
moves forward, pushing plastic melt through the extrusion head forming the next parison. A reciprocating
screw extrusion blow molding is shown in Figure 2.5.
Figure 2. 5. ReciprocatingScrew Extrusion Blow Molding Machine Uniloy 250 Rl.
The extrusion blow molding process involves three consecutive stages:
The shape of the parison and its thickness distribution at the moment the mold closes are of central
importance (Dealy et. al., 1990). Diameter and thickness of the parison are not easily controllable because
of the flow rate variation during parison formation and the presence of gravitational forces (Tadmor Z.,
1979).
Factors governing the geometry of the parison include the die design, the resin properties and the
extrusion conditions (see Figure 2. 6). With regard to the resin, it is the rheological properties of the melt
that govern the parison shape, and it is highly desirable to be able to relate parison behavior to laboratory
rheological measurements.
Process conditions
Temperature ^ \ < ^ ^i m e
Extrusion rate ^
Die geometry
Types of angles
Converging Diverging
Parison Formation ^ ( Diameter and thickness
distribution
Swell phenomena Sag phenomena
Figure 2. 6. Variables affecting diameter and thickness distribution of the parison shape.
The dynamics of the development of the parison are basically influenced by the swell and sag or
drawdown phenomena. The die swell phenomenon is also known as Barus effect, memory, jet swell, puff
up, etc., and is to b e considered a manifestation of melt elasticity in a shearing flow through a die, where
the extrudate cross section (De) is greater than the cross section of the die diameter (D), that is De/D » 1 ,
(Koopmans 1988).
The variables usually employed to describe die swell are the swell ratio (B), the fully developed wall
shear rate (y w) , the length to diameter (L/D), the temperature (T), and the time (t) that has passed since
the melt left the die (Dealy et al. 1990).
Sag, or "drawdown", is caused b y gravitational forces that act on the suspended parison. The degree of
sag depends on processing parameters (such as melt temperature, suspension time and total parison length),
DiRaddo e t a l . (1992).
Nakajima N . (1974) established an empirical model to predict die swell. However this model did not
take in consideration material parameters, such as molecular weights, degree of branching, etc., and the die
geometry. H e stated that H D P E resins presented numerous variations for such model to be used in those
Guillet et al. (1965) and Combs et al. (1969) reported that die swell increases as the molecular weight
distribution broadens. These authors also found that the flow index "n" in the power law model decreases
as the molecular weight distribution broadens.
Kamal et al. (1981) calculated the diameter swell distribution using a timedependent equation, and the
calculation agreed with the experimental data, but it was for short extrusion times (2 seconds). Also, Dealy
et al. (1985) found it to b e unrealistic and unreliable. Dealy argued that the model ignored the detailed role
played b y the strain history.
Kamal et al. (1981) used the following timedependent equations:
Bi(t) was defined as: B](t) = Diameter of extrudate/Diameter of die
( A v + A , , ) '
2A v
where D O E = outside diameter of the extruded parison, DI E = inside diameter of the extrudate parison,
DOD = outside diameter of the annular die, and DID = inside diameter of the annular die.
B2(t) was defined as:B2(t) = Thickness of the parison, H/Thickness of the annular die,G.
m
K
. A , . ) / 2
gg
( 0
M A v ) / 2 G
The total length of the parison Ls (t) was given by:
£ f
( 0 = ' S A 4 ( 0
( 2 . 3 )
where N w a s the total number of increments extruded in time t, and
AL's(t)was
the length of the ithelement.
Dealy et al. (1985) found that 6080% of the swell for commercial H D P E resins occurs in the first few
seconds after the parison leaves the die, with an equilibrium value being reached after 58 minutes have
elapsed. They saw that the die swell increased as the die shape (mandrel configuration) was altered in the
following order: diverging, straight, converging.
Koopmans, R. J. (1988) established an empirical relation between capillary die swell and molecular
structure defined b y total weight average weight (Mw T) , molecular weight distribution ( M W D ) , and
fraction high molecular weight content (FRB). The measurements of the die swell were conducted using an
Instron Rheometer with an L/D = 5.25 (D=0.531xl0"2m), at 300s'1 and 190°C. A statistical analysis system
(SAS) program w a s used to generate the interdependence of the 3 independent parameters in relation to
percentage swell (Mw A , MwB, and FRB). The empirical equation was modeled via statistical analysis of
the BoxBehnken experimental design: