design data for plastics engineers - rao n. s
TRANSCRIPT
Natti Rao / Keith O'Brien
Design Data forPlastics Engineers
Hanser Publishers, Munich
Hanser/Gardner Publications, Inc., Cincinnati
The Authors:Dr.-Ing. NattiRao, Schieferkopf 6,67434 Neustadt, Germany; Dr. Keith T. O'Brien, Vistakon, Ing., 4500 Salisbury Road,Jacksonville, FL 32216-0995, USA
Distributed in the USA and in Canada byHanser/Gardner Publications, Inc.6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USAFax: (5B) 527-8950Phone: (5B) 527-8977 or 1-800-950-8977Internet: http: //www.hansergardner.com
Distributed in all other countries byCarlHanserVerlagPostfach 86 04 20,81631 Munchen, GermanyFax:+49 (89) 9812 64
The use of general descriptive names, trademarks, etc., in this publication, even if the former are not especiallyidentified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act,may accordingly be used freely by anyone.
While the advice and information in this book are believed to be true and accurate at the date of going to press, neitherthe authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may bemade. The publisher makes no warranty, express or implied, with respect to the material contained herein.
Library of Congress Cataloging-in-Publication DataRao,NattiS.Design data for plastics engineers / Natti Rao, Keith O'Brien.
p. cm.Includes bibliographical references and index.ISBN l-56990-264-X(softcover)1. Plastics. I. O'Brien, Keith, T. II. Title.TP1120.R325 1998668.4—dc21 98-37253
Die Deutsche Bibliothek - CIP-EinheitsaufnahmeRao, Natti S.:Design data for plastics engineers / Natti Rao/Keith O'Brien. -Munich: Hanser; Cincinnati: Hanser/Gardner, 1998
ISBN 3-446-21010-5
All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic ormechanical, including photocopying or by any information storage and retrieval system, without permission in writingfrom the publisher.
© Carl Hanser Verlag, Munich 1998Camera-ready copy prepared by the authors.Printed and bound in Germany by Druckhaus "Thomas Muntzer", Bad Langensalza
Preface
Mechanical, thermal and rheological properties of polymers form the basic group ofproperty values required for designing polymer machinery. In addition, knowledge of theproperties of the resin such as stock temperature of the melt is necessary for optimizing theprocess. Furthermore, while designing a plastic part, performance properties of the resindepending on the application are to be considered, examples of which are flammability,weather resistance and optical properties, to quote a few. Hence, a variety of propertyvalues is needed to accomplish machine design, part design and process optimization.
Comprehensive as well as specific overviews of polymer property data exist in theliterature. Also the data banks of resin manufacturers offer quick information onthermophysical properties of polymers. But there are few books dealing with both resinand machine design data based on modern findings.
The intent of this book is first of all to create an easy to use quick reference workcovering basic design data on resin, machine, part and process, and secondly, to show as tohow this data can be applied to solve practical problems. With this aim in mind numerousexamples are given to illustrate the use of this data. The calculations involved in theseexamples can be easily handled with the help of handheld calculators.
Chapters 1 to 5 deal with the description of physical properties - mechanical, thermal,rheological, electrical and optical - of polymers and principles of their measurement. InChapter 6 the effect of external influences on the performance of polymers is treated.General property data for different materials such as liquid crystal polymers, structuralfoams, thermosetting resins and reinforced plastics are given at the end of this chapter.
In Chapter 7 the processing properties and machine related data are presented forcontinuous extrusion processes namely blown film, pipe and flat film extrusion. Resin andmachine parameters for thermoforming and compounding have also been included in thischapter.
Chapter 8 deals with blow molding and the influence of resin and machine variableson different kinds of blow molding processes. Finally, Chapter 9 covers resin-dependentand machine related parameters concerning the injection molding process.
Machine element design covered in Chapters 7 to 9 includes screw design forextruders and injection molding machines, die design for extruders, mold design for
molding and forming operations and downstream equipment for extrusion. Whereverappropriate, the properties and machine related parameters are described by mathematicalformulas which are, as already mentioned, illustrated by worked-out examples. Thesolution procedure used in these examples describes the application of polymer data tosolve practical problems. On the basis of this approach the importance of polymer data indealing with design and process optimization is explained.
This book is intended for beginners as well as for practicing engineers, students andteachers in the field of plastics technology and also for scientists from other fields whodeal with polymer engineering.
We wish to express our sincere thanks to Professor Stephen Orroth of the University ofMassachusetts at Lowell, U.S.A., for his valuable suggestions, criticism and review of themanuscript. He also suggested to write a book on the lines of Glanvill's PlasticsEngineer's Data Book. Our work is based on the findings of modern plastics technology,and can be considered as an extension to Glanvill's book.
The authors also wish to express particular thanks to Dr. Giinter Schumacher ofUniversity of Karlsruhe, Germany, for his constructive comments and his great help inpreparing the manuscript.
Neustadt, GermanyJacksonville, U.S.A.
Natti S. Rao, Ph.D.Keith T. O'Brien, Ph.D.
AFINALWORD
There are many other processes in wide application such as reaction injection molding,compression and transfer molding used to produce parts from thermosetting resins. It wasnot possible to cover all these processes within the scope of this book. However, the natureof data needed for designing machinery for these processes is similar to the one presentedin this work.
Authors
Natti S. Rao obtained his B.Tech(Hons) in Mechanical Engineering and M.Tech inChemical Engineering from the Indian Institute of Technology, Kharagpur, India. Afterreceiving his Ph.D. from the University of Karlsruhe, Germany he worked for theBASF AG for a number of years. Later on he served as a technical advisor to theleading German Plastics machine manufacturers.Natti has published over 50 papers on different aspects of plastics engeneering andauthored 3 books on designing polymer machinery with computers. Prior to startinghis consultancy company in 1987, he worked as a visiting professor at theIndian Institute of Technology, Chennai(Madras), India. Besides consultancy work,he also holds seminars teaching the application of his software for designingextrusion and injection molding machinery.
Keith O'Brien has a B.Sc.(Eng) from the University of London, and M. Sc. andPh.D. degrees from the University of Leeds in Mechanical Engineering. Keith hasover 100 published works to his credit, and also edited the well-known book,1 Computer Modeling for Extrusion and other Continuous Processes'. Before hejoined Johnson & Johnson, he was professor of mechanical engineering at theNew Jersey Institute of Technology.
vii This page has been reformatted by Knovel to provide easier navigation.
Contents
Preface .................................................................................... v
A Final Word ............................................................................ vii
Authors .................................................................................... viii
1. Mechanical Properties of Solid Polymers ...................... 1 1.1 Ideal Solids .............................................................................. 1 1.2 Tensile Properties ................................................................... 1
1.2.1 Stress-Strain Behavior ............................................ 2 1.2.2 Tensile Modulus ...................................................... 5 1.2.3 Effect of Temperature on Tensile Strength .............. 6
1.3 Shear Properties ..................................................................... 6 1.3.1 Shear Modulus ........................................................ 6 1.3.2 Effect of Temperature on Shear Modulus ................ 7
1.4 Compressive Properties .......................................................... 9 1.4.1 Bulk Modulus .......................................................... 10
1.5 Time Related Properties ......................................................... 11 1.5.1 Creep Modulus ....................................................... 11 1.5.2 Creep Rupture ........................................................ 12 1.5.3 Relaxation Modulus ................................................ 13 1.5.4 Fatigue Limit ........................................................... 14
viii Contents
This page has been reformatted by Knovel to provide easier navigation.
1.6 Hardness ................................................................................. 15 1.7 Impact Strength ....................................................................... 17 1.8 Coefficient of Friction .............................................................. 17
2. Thermal Properties of Solid and Molten Polymers ....... 23 2.1 Specific Volume ....................................................................... 23 2.2 Specific Heat ........................................................................... 26 2.3 Thermal Expansion Coefficient ............................................... 27 2.4 Enthalpy ................................................................................... 29 2.5 Thermal Conductivity .............................................................. 29 2.6 Thermal Diffusivity ................................................................... 31 2.7 Coefficient of Heat Penetration ............................................... 32 2.8 Heat Deflection Temperature .................................................. 34 2.9 Vicat Softening Point ............................................................... 35 2.10 Flammability ............................................................................ 35
3. Transport Properties of Molten Polymers ...................... 39 3.1 Newtonian and Non-Newtonian Fluids ................................... 39 3.2 Viscous Shear Flow ................................................................ 41
3.2.1 Apparent Shear Rate .............................................. 41 3.2.2 Entrance Loss ......................................................... 42 3.2.3 True Shear Stress ................................................... 42 3.2.4 Apparent Viscosity .................................................. 44 3.2.5 True Shear Rate ..................................................... 47 3.2.6 True Viscosity ......................................................... 47
3.3 Rheological Models ................................................................. 47 3.3.1 Hyperbolic Function of Prandtl and Eyring .............. 48 3.3.2 Power Law of Ostwald and De Waele ..................... 48 3.3.3 Polynomial of Muenstedt ......................................... 50
Contents ix
This page has been reformatted by Knovel to provide easier navigation.
3.3.4 Viscosity Equation of Carreau ................................. 53 3.3.5 Viscosity Formula of Klein ....................................... 55
3.4 Effect of Pressure on Viscosity ............................................... 56 3.5 Dependence of Viscosity on Molecular Weight ...................... 57 3.6 Viscosity of Two-Component Mixtures ................................... 59 3.7 Melt Flow Index ....................................................................... 59 3.8 Tensile Viscosity ...................................................................... 60 3.9 Viscoelastic Properties ............................................................ 60
3.9.1 Primary Normal Stress Coefficient Θ ....................... 61 3.9.2 Shear Compliance Je .............................................. 61 3.9.3 Die Swell ................................................................. 62
4. Electrical Properties ........................................................ 65 4.1 Surface Resistivity ................................................................... 65 4.2 Volume Resistivity ................................................................... 65 4.3 Dielectric Strength ................................................................... 65 4.4 Relative Permittivity ................................................................. 66 4.5 Dielectric Dissipation Factor or Loss Tangent ........................ 66 4.6 Comparative Tracking Index (CTI) .......................................... 68
5. Optical Properties of Solid Polymers ............................. 73 5.1 Light Transmission .................................................................. 73 5.2 Haze ........................................................................................ 73 5.3 Refractive Index ...................................................................... 73 5.4 Gloss ....................................................................................... 75 5.5 Color ........................................................................................ 75
6. External Influences .......................................................... 77 6.1 Physical Interactions ............................................................... 77
6.1.1 Solubility ................................................................. 77
x Contents
This page has been reformatted by Knovel to provide easier navigation.
6.1.2 Environmental Stress Cracking (ESC) .................... 77 6.1.3 Permeability ............................................................ 79 6.1.4 Absorption and Desorption ...................................... 80 6.1.5 Weathering Resistance ........................................... 80
6.2 Chemical Resistance .............................................................. 81 6.2.1 Chemical and Wear Resistance to Polymers .......... 81
6.3 General Property Data ............................................................ 82
7. Extrusion .......................................................................... 91 7.1 Extrusion Screws .................................................................... 92 7.2 Processing Parameters ........................................................... 92
7.2.1 Resin-Dependent Parameters ................................. 92 7.2.2 Machine Related Parameters .................................. 98
7.3 Extrusion Dies ......................................................................... 124 7.3.1 Pipe Extrusion ......................................................... 126 7.3.2 Blown Film .............................................................. 135 7.3.3 Sheet Extrusion ...................................................... 137
7.4 Thermoforming ........................................................................ 142 7.5 Compounding .......................................................................... 146 7.6 Extrudate Cooling .................................................................... 149
7.6.1 Dimensionless Groups ............................................ 152
8. Blow Molding .................................................................... 155 8.1 Processes ................................................................................ 155
8.1.1 Resin Dependent Parameters ................................. 155 8.1.2 Machine Related Parameters .................................. 161
9. Injection Molding .............................................................. 169 9.1 Resin-Dependent Parameters ................................................ 170
9.1.1 Injection Pressure ................................................... 170
Contents xi
This page has been reformatted by Knovel to provide easier navigation.
9.1.2 Mold Shrinkage and Processing Temperature ........ 172 9.1.3 Drying Temperatures and Times ............................. 174 9.1.4 Flow Characteristics of Injection-Molding
Resins ..................................................................... 175 9.2 Machine Related Parameters ................................................. 179
9.2.1 Injection Unit ........................................................... 179 9.2.2 Injection Molding Screw .......................................... 180 9.2.3 Injection Mold .......................................................... 183
Index ....................................................................................... 205
1 Mechanical Properties of Solid Polymers
The properties of polymers are required firstly to select a material which enables desiredperformance of the plastics component under conditions of its application. Furthermorethey are also essential in design work to dimension a part from a stress analysis or topredict the performance of a part under different stress situations involved. Knowledge ofpolymer properties is, as already mentioned in the preface, a prerequisite for designing andoptimizing polymer processing machinery.
In addition to the physical properties there are certain properties known asperformance or engineering properties which correlate with the performance of thepolymer under varied type of loading and environmental influences such as impact,fatigue, high and low temperature behavior and chemical resistance. The followingsections deal with the physical as well as important performance properties of polymers.
1.1 Ideal Solids
Ideal elastic solids deform according to Hookean law which states that the stress is directlyproportional to strain. The behavior of a polymer subjected to shear or tension can bedescribed by comparing its reaction to an external force with that of an elastic solid underload. To characterize ideal solids, it is necessary to define certain quantities as follows [3]:
1.2 Tensile Properties
The axial force Fn in Fig. 1.1 causes an elongation A/ of the sample of diameter d0 andlength I0 fixed at one end. Following equations apply for this case:Engineering strain:
(1.2.1)
Fig. 1.1: Deformation of a Hookean solid by a tensile stress [10]
1.2.1 Stress-Strain Behavior
As shown in Fig. 1.2 most metals exhibit a linear stress-strain relationship (curve 1),where as polymers being viscoelastic show a non-linear behavior (curve 2). When thestress is directly proportional to strain the material is said to obey Hooke's law. The slopeof the straight line portion of curve 1 is equal to the modulus of elasticity. The maximumstress point on the curve, up to which stress and strain remain proportional is called theproportional limit (point P in Fig. 1.2) [I].
Hencky strain:
Tensile stress:
Reference area:
Poisson's ratio:
(1.2.2)
(1.2.3)
(1.2.4)
(1.2.5)
Fig. 1.2: Typical stress-strain curves of metals and polymers
Most materials return to their original size and shape, even if the external load exceedsthe proportional limit. The elastic limit represented by the point E in Fig. 1.2 is themaximum load which may be applied without leaving any permanent deformation of thematerial. If the material is loaded beyond its elastic limit, it does not return to its originalsize and shape, and is said to have been permanently deformed. On continued loading apoint is reached at which the material starts yielding. This point (point Y in Fig. 1.2) isknown as the yield point, where an increase in strain occurs without an increase in stress.It should however be noted that some materials may not exhibit a yield point. The point Bin Fig. 1.2 represents break of the material.
Stre
ss c
Stres
s 6
Strain z
Strain E
Fig. 1.3: Secant modulus [3]
Owing to their non-linear nature it is difficult to locate the straight line portion of thestress-strain curve for polymeric materials (Fig. 1.3). The secant modulus represents the
ratio of stress to strain at any point (S in Fig. 1.3) on the stress-strain diagram and is equalto the slope of the line OS. It is an approximation to a linear response over a narrow, butpre-specified and standard level of strain [2], which is usually 0.2%.
The initial modulus is a straight line drawn tangent to the initial region of the stress-strain curve to obtain a fictive modulus as shown in Fig. 1.4. As this is ambiguous, theresin manufacturers provide a modulus with the stress, for example, G05 corresponding to astrain 0.5 % to characterize the material behavior on a practical basis (Fig. 1.4) [3], Thisstress G0 is also known as the proof stress.
Stress
6Ten
sile s
tress
Tensile
stre
ss
N/mm2
%Strain S
mm2
psi
Fig. 1.4: Stress at a strain of 0.5% [3]
Elongation %
Fig. 1.5: Tensile stress diagram of a number of materials at 23°C [ 4 ]: a: steel,b: copper, c: polycarbonate, d: PMMA, e: PE-HD, f: rubber, g: PE-LD, h: PVC-P
Stress-strain diagrams are given in Fig. 1.5 for a number of materials [4]. It can be seenfrom Fig. 1.5 that the advantage of metals lies in their high strength, where as that ofplastics lies in their high elongation at break.
1.2.2 Tensile Modulus
According to Eq. (1.2.1) and Eq. (1.2.3) one obtains for the modulus of elasticity E whichis known as Young's Modulus
E = az/ 8 (1.2.6)
The modulus of elasticity in a tension test is given in Table 1.1 for different polymers [7].
Table 1.1: Guide Values of Modulus of Elasticity of Some Plastics [4]
Material Modulus of elasticityN mm'2
PE-LD 200/500PE-HD 700/1400PP 1100/1300PVC-U 1000/3500PS 3200/3500ABS 1900/2700PC 2100/2500POM 2800/3500PA6 1200/1400PA66 1500/2000PMMA 2700/3200PET 2600/3100PBT 1600/2000PSU 2600/2750CA 1800/2200CAB 1300/1600Phenol-Formaldehyde-Resins 5600/12000Urea-Formaldehyde-Resins 7000/10500Melamin-Formaldehyde-Resins 4900/9100Unsaturated Polyester Resins 14000/20000
The 3.5 % flexural stresses of thermoplastics obtained on a 3-point bending fixture(Fig. 1.6) [6] lie in the range 100 to 150 N mm"2 and those of thermosets from around 60to 150 N mm"2 [7].
Fig. 1.6: Three point bending fixture [6]
1.2.3 Effect of Temperature on Tensile Strength
The tensile strength is obtained by dividing the maximum load (point M in Fig. 1.2) the speci-men under test will withstand by the original area of cross-section of the specimen. Fig.1.7 shows the temperature dependence of the tensile strength of a number of plastics [4].
1.3 Shear Properties
Figure 1.8 shows the influence of a shear force Ft acting on the area A of a rectangularsample and causing the displacement AU. The valid expressions are defined by:
Shear strain:
(1.3.1)
Shear stress
(1.3.2)
1.3.1 Shear Modulus
The ratio of shear stress to shear strain represents the shear modulus G. From theequations above results:
(1.3.3)
Applied load
Fig. 1.8: Deformation of a Hookean solid by shearing stress [10]
1.3.2 Effect of Temperature on Shear Modulus
The viscoelastic properties of polymers over a wide range of temperatures can be bettercharacterized by the complex shear modulus G* which is measured in a torsion pendulumtest by subjecting the specimen to an oscillatory deformation Fig. 1.9 [2]. The complexshear modulus G* is given by the expression [2]
(1.3.4)
The storage modulus G' in Eq. (1.3.4) represents the elastic behavior associated withenergy storage and is a function of shear amplitude, strain amplitude and the phase angle
Tensile
stre
ss
Tensile
stre
ss
Nmm2
psi
Temperature0C
Fig. 1.7: Temperature dependence of the tensile stress of some thermoplasticsunder uniaxial loading [4]; a: PMMA, b: SAN, c: PS, d: SB, e: PVC-Uf: ABS, g: CA, h: PE-HD, i: PE-LD, k: PE-LD-V
Fig. 1.9: Torsion pendulum; Loading mode and sinusoidal angular displacement t [2]
The tangent of the phase angle 8 is often used to characterize viscoelastic behaviorand is known as loss factor. The loss factor d can be obtained from
(1.3.5)
The modulus-temperature relationship is represented schematically in Fig. 1.10 [2], fromwhich the influence of the transition regions described by the glass transition temperatureTg and melting point Tm is evident.
This kind of data provides information on the molecular structure of the polymer. Thestorage modulus G' which is a component of the complex shear modulus G* and the lossfactor d are plotted as functions of temperature for high density polyethylene in Fig. 1.11[4]. These data for various polymers are given in the book [4].
DEFO
RMAT
ION
RESI
STAN
CE
TEMPERATURE
Fig. 1.10: Generalized relationship between deformation resistance and temperature foramorphous (solid line) and semi-crystalline (broken line) high polymers [2]
HARDTOUGHSOLID
VISCOUSMELT
BRITTLESOLID
RUBBERY
5 between stress and strain. The loss modulus G" which is a component of the complexmodulus depicts the viscous behavior of the material and arises due to viscous dissipation.
TIME (t)8
8
Fig. 1.11: Temperature dependence of the dynamic shear modulus, G' andthe loss factor d, obtained in the torsion pendulum test DIN 53445 [4]:PE-HD (highly crystalline), PE-HD (crystalline), PE-LD (less crystalline)
1.4 Compressive Properties
The isotropic compression due to the pressure acting on all sides of the parallelepipedshown in Fig. 1.12 is given by the engineering compression ratio K .
(1.4.1)
where AV is the reduction of volume due to deformation of the body with the originalvolume F0.
Dyna
mic s
hear
modu
lus G
'
Mech
anica
l loss
facto
r d
psi N/mm2
°CTemperature
Fig. 1.12: Hookean solid under compression [44]
V0-LV P
P
1.4.1 Bulk Modulus
The bulk modulus K is defined byK =-p IK (1.4.2)
where A: is calculated from Eq. (1.4.1). The reduction of volume, for instance for PE-LD,when the pressure is increased by 100 bar follows from Table
AV / V0 = -100/(0.7 • 104) = -1.43% .
Furthermore, the relationship between E, G and K is expressed as [3]E = 2 G(I + JU) = 3K(I- 2ju) . (1.4.3)
This leads for an incompressible solid (K —> oo, /j —> 0.5 ) toE = 3G. (1.4.4)
Typical values of moduli and Poisson's ratios for some materials are given in Table 1.2[10]. Although the moduli of polymers compared with those of metals are very low, atequal weights, i.e. ratio of modulus to density, polymers compare favorably.
Table 1.2: Poisson ratio ju, density p, bulk modulus K and specific bulk modulus forsome materials [10]
Material
Mild steelAluminumCopperQuartzGlassPolystyrenePolymethyl-methacrylatePolyamide 66RubberPE-LDWaterOrganic liquids
Poisson ratio ju
0.270.330.250.070.230.330.33
0.330.490.450.50.5
Density p at200Cg/cm3
7.8.2.78.9
2.652.51.051.17
1.080.910.92
10.9
Bulk modulus KN/m2
1.66-1011
7-1010
1.344011
3.9-1010
3.7-1010
3-109
4.1-109
3.3-109
0.033-109
0.7-109
2-109
1.33-109
Specific bulkmodulus KJp
m2/s2
2.1-107
2.6107
1.5-107
1.47-107
1.494 O7
2.85407
3.5407
2.3407
0.044 O7
3.7407
24 O6
1.5406
1.5 Time Related Properties
1.5.1 Creep Modulus
In addition to stress and temperature, time is an important factor for characterizing theperformance of plastics. Under the action of a constant load a polymeric materialexperiences a time dependent increase in strain called creep. Creep is therefore the resultof increasing strain over time under constant load [6]. Creep behavior can be examined bysubjecting the material to tensile, compressive or flexural stress and measuring the strainfor a range of loads at a given temperature.
The creep modulus Ec № in tension can be calculated from
Ec(t) = W£-(t) (1.5.1)
and is independent of stress only in the linear elastic region.As shown in Fig. 1.13 the creep data can be represented by creep plots, from which the
creep modulus according to Eq. (1.5.1) can be obtained. The time dependence of tensilecreep modulus of some thermoplastics at 2O0C is shown in Fig. 1.14 [5]. The 2 % elas-ticity limits of some thermoplastics under uniaxial stress are given in Fig. 1.15. Creep datameasured under various conditions for different polymers are available in [4].
Stra
in £
Stre
ss 6
Stre
ss 6
Time /
Time t Strain £
a
b
Fig. 1.13: Long-term stress-strain behavior [3]
Stress duration
Fig. 1.15:2% elasticity limits of some thermoplastics under uniaxial stress at 200C [4]a: SAN, b: ABS, c: SB, d: chlorinated polyether, e: PE-HD, f: PE-LD
1.5.2 Creep Rupture
Failure with creep can occur when a component exceeds an allowable deformation orwhen it fractures or ruptures [6]. Creep rupture curves are obtained in the same manner ascreep, except that the magnitude of the stresses used is higher and the time is measured up
h
Tens
ile str
ess
Tens
ile s
tress
Tens
ile C
reep
Mod
ulus
GN
/m2
Nmm2 psi
Time (hours)
Fig. 1.14: Tensile creep modulus vs time for engineering thermoplastics [5]
Nylon 6620 MN/m2
200P Polyethersulfone28 MN/nf
Polysulfone28 MN/m2
Polycarbonate20.6 MN/m2
Acetal copolymer20 MN/m2
1 Year
Data for polysulfooe, polycarbonate,acretal copolymer and nylon 66from Modern Plastics Encyclopaedia
1 Week
to failure. Data on creep rupture for a number of polymers are presented in [4]. Accordingto [4] the extrapolation of creep data should not exceed one unit of logarithmic time and astrain elongation limit of 20 % of the ultimate strength.
1.5.3 Relaxation Modulus
The relaxation behavior of a polymer is shown in Fig. 1.16 [3]. Relaxation is the stressreduction which occurs in a polymer when it is subjected to a constant strain. This data isof significance in the design of parts which are to undergo long-term deformation. Therelaxation modulus of PE-HD-HMW as a function of stress duration is given in Fig. 1.17[4]. Similar plots for different materials are to be found in [4].
7r
Relax
ation
mod
ulus
t
t>
t-Fig. 1.16: Relaxation after step shear strain y0 [3]
psi N/mm2
hStress duration
Fig. 1.17: Relaxation modulus of PE-HD-HMW as a function of stress duration at 23°C [4]
1.5.4 Fatigue Limit
Fatigue is a failure mechanism which results when the material is stressed repeatedly orwhen it is subjected to a cyclic load. Examples of fatigue situations are components sub-jected to vibration or repeated impacts. Cyclic loading can cause mechanical deteriorationand fracture propagation resulting in ultimate failure of the material.
Fatigue is usually measured under conditions of bending where the specimen issubjected to constant deflection at constant frequency until failure occurs. The asymptoticvalue of stress shown in the schematic fatigue curve (S-N plot) in Figs. 1.18 and 1.19 [6]is known as the fatigue limit. At stresses or strains which are less than this value failuredoes not occur normally.
Stre
ssSt
ress
S-N cuive
Log cycles
Fig. 1.18: Fatigue curve [6]
Fatigue limit
Log cycles (to failure)
Fig. 1.19: Fatigue limit [6]
Log cycles (to failure)
Fig. 1.20: Endurance limit [6]
For most plastics the fatigue limit is about 20 to 30 % of the ultimate strengthmeasured in short-term tensile investigations [6]. The Woehler plots for oscillatingflexural stress for some thermoplastics are given in Fig. 1.21. Fatigue limits decrease withincreasing temperature, increasing frequency and stress concentrations in the part [4].
1.6 Hardness
Various methods of measuring the hardness of plastics are in use. Their common feature ismeasuring the deformation in terms of the depth of penetration which follows indentationby a hemisphere, cone or pyramid depending on the test procedure under defined loadconditions. According to the type of indenter (Fig. 1.22) used the Shore hardness, forexample, is given as Shore A or Shore D, Shore A data referring to soft plastics and ShoreD to hard plastics. The results of both methods are expressed on a scale between 0 (verysoft plastics) and 100 (very hard surface).
The ball-indentation hardness which represents the indentation depth of a sphericalsteel indenture is given in Table 1.3 for some thermoplastics [2].
Stres
s
Some materials do not exhibit an asymptotic fatigue limit. In these cases, theendurance limit which gives stress or strain at failure at a certain number of cycles is used(Fig. 1.20) [6].
Endurance limit
Cycles to failure
Fig. 1.21: Flexural fatigue strength of some thermoplastics [4]a: acetal polymer, b: PP, c: PE-HD, d: PVC-U
Table 1.3: Ball-Indentation Hardness for Some Plastics [7]
Material HardnessN/mm2
PE-LD 13/20PE-HD 40/65PP 36/70PVC-U 75/155PS 120/130ABS 80/120PC 90/110POM 150/170PA6 70/75PA66 90/100PMMA 180/200PET 180/200PBT 150/180Phenol-Formaldehyde-Resins 250 -320Urea-Formaldehyde-Resins 260/350Melamin-Formaldehyde-Resins 260/410Unsaturated Polyester Resins 200/240
Stres
s am
plitud
epsi
Nmm2
Fig. 1.22: Types of indenter [7]a: shore, b: shore C and A
1.7 Impact Strength
Impact strength is the ability of the material to withstand a sudden impact blow as in apendulum test, and indicates the toughness of the material at high rates of deformation.The test procedures are varied. In the Charpy impact test (Fig. 1.23) [2] the pendulumstrikes the specimen centrally leading to fracture.
Fig. 1.23: Charpy impact test [2]
1.8 Coefficient of Friction
Although there is no consistent relationship between friction and wear, the factorsaffecting the two processes such as roughness of the surfaces, relative velocities of theparts in contact and area under pressure are often the same. Table 1.4 shows thecoefficients of sliding friction and sliding wear against steel for different materials [4]. Inapplications where low friction and high wear resistance are required, smooth surface andlow coefficient of friction of the resin components involved are to be recommended.
a; b)
radiusr
Impa
ct va
lueC
harp
y Im
pact
Stre
ngth
(kj/
m2)
A typical impact curve as a function of temperature is shown in Fig. 1.24 [6]. This typeof data provides the designer with information about the temperature at which the ductilefracture changes to brittle fracture thus enabling to evaluate the performance of thematerial in a given application. The results of impact tests depend on the manufacturingconditions of the specimen, notch geometry and on the test method. Impact strengths forvarious plastics are given by Domininghaus [4]. Charpy notched impact strengths of someplastics as functions of notch radius are given in Fig. 1.25 [5].
Ductilebehaviour
Ductile/brittletransition
Brittlebehaviour
Temperature
Fig. 1.24: Impact curve [6]
Radius (mm)
PVCPolyethersulfone
Nylon 66 (dry)
Acetal
ABSGlass-filled
nylon
Acrylic
Fig. 1.25: Charpy impact strength vs. notch radius for some engineering thermoplastics [5]
Example [8]:The following example illustrates the use of physical and performance properties ofpolymers in dealing with design problems.
The minimum depth of the simple beam of SAN shown in Fig. 1.26 is to bedetermined for the following conditions:
The beam should support a mid-span load of 11.13 N for 5 years without fracture andwithout causing a deflection of greater than 2.54 mm.
Solution:The maximum stress is given by
(1.8.1)
Table 1.4: Coefficient of Sliding Friction of Polymer/Case Hardened Steelafter 5 or 24 Hours [4]
Polymer
Polyamide 66Polyamide 6Polyamide 6 {in situ polymer)Polyamide 610Polyamide 11PolyethyleneterephthalateAcetal homopolymerAcetal copolymerPolypropylenePE-HD (high molecular weight)PE-HD (low molecular weight)PE-LDPolytetrafluoroethylenePA 66 + 8% PE-LDPolyacetal + PTFEPA 66 + 3% MoS2
PA 66 - GF 35PA 6 - GF 35Standard polystyreneStyrene/Acrylonitrile copolymerPolymethylmethacrylatePolyphenylene ether
Coefficient ofsliding friction
0.25/0.420.38/0.450.36/0.430.36/0.440.32/0.38
0.540.340.320.300.290.250.580.220.190.21
0.32/0.350.32/0.360.30/0.35
0.460.520.540.35
Slidingfrictional wear
0.090.230.100.320.80.54.58.9
11.01.04.67.4
21.00.100.160.70.160.28
11.5234.8
90
where F = load (N)l,h,d = dimensions in (mm) as shown in Fig. 1.26.
The creep modulus Ec is calculated from
(1.8.2)
where f is deflection in mm.The maximum stress from Fig. 1.27 at a period of 5 years (= 43800 h) is
crmax = 23.44 N/mm2.
Working stress crw with an assumed safety factor S = 0.5:
o-w = 23.44-0.5 = 11.72 NJmm1 .
Creep modulus Ec at cr < crw ^ d a period of 5 years from Fig. 1.27:
Ec = 2413 NI mm2.
Creep modulus with a safety factor S = 0.75:
Ec = 2413-0.75 = 1809.75 NJmm2 .
The depth of the beam results from Eq. (1.8.1)
The deflection is calculated from Eq. (1.8.2)
Under these assumptions the calculated/is less than the allowable value of 2.54 mm.This example shows why creep data are required in design calculations and how they
can be applied to solve design problems.
Fig. 1.26: Beam under mid-span load [8]
Fig. 1.28: Creep modulus of SAN [8]
Literature
1. Nat, D.S.: A Text Book of Materials and Metallurgy, Katson Publishing House, Ludhiana,India 1980
2. Birley, A. W.: Haworth, B.: Bachelor, T.: Physics of Plastics, Hanser, Munich 19913. Rao, NS.: Design Formulas for Plastics Engineers, Hanser, Munich, 19914. Domininghaus, K: Plastics for Engineers, Hanser, Munich 19935. Rigby, R.B.: Polyethersulfone in Engineering Thermoplastics: Properties and Applications.
Ed.: James M. Margolis. Marcel Dekker, Basel 19856. General Electric Plastics Brochure: Engineering Materials Design Guide7. Schmiedel, K: Handbuch der Kunststoffpriifung (Ed.), Hanser, Munich 1992
Time th
Cree
p mo
dulus
Nmm2
Initia
l app
lied
stres
s
Fig. 1.27: Creep curve of SAN [8]
Time at ruptureh
mm2
8. Design Guide, Modem Plastics Encyclopedia, 1978-799. Brochure: Advanced CAE Technology Inc. 199210. Pahl, M.; Gleifile, W.; Laun, KM.: Praktische Rheologie der Kunststoffe und Elastomere,
VDI-Kunststofftechnik, Dusseldorf 1995
2 Thermal Properties of Solid and MoltenPolymers
In addition to the mechanical and melt flow properties thermodynamic data of polymersare necessary for optimizing various heating and cooling processes which occur in plasticsprocessing operations.
In design work the thermal properties are often required as functions of temperatureand pressure [2]. As the measured data cannot always be predicted by physical relation-ships accurately enough, regression equations are used to fit the data for use in designcalculations.
2.1 Specific Volume
The volume-temperature relationship as a function of pressure is shown for a semi-crystalline PE-HD in Fig. 2.1 [1] and for an amorphous PS in Fig. 2.2 [I]. The p-v-Tdiagrams are needed in many applications, for example to estimate the shrinkage ofplastics parts in injection molding [19]. Data on p-v-T relationships for a number ofpolymers are presented in the handbook [8].
According to Spencer-Gilmore equation which is similar to the Van-der-Waal equationof state for real gases the relationship between pressure p, specific volume v andtemperature T of a polymer can be written as
(2.1.1)
In this equation b* is the specific individual volume of the macromolecule, p*, the cohesionpressure, W, the molecular weight of the monomer and R, the universal gas constant [9].
The values p* and b* can be determined from p-V-T diagrams by means of regressionanalysis. Spencer and Gilmore and other workers evaluated these constants frommeasurements for the polymers listed in Table 2.1 [9], [18].
Spe
cific
vol
ume
(cm
3/g)
SPECIFIC VOLUME (cm3/g)
TEMPERATURE(0C)
Fig. 2.1: Specific volume vs. temperature for a semi-crystalline polymer (PP) [1]
Temperature (0C)
Fig. 2.2: Specific volume vs. temperature for an amorphous polymer (PS) [1]
Example:Following values are given for a PE-LD:
W = 28.1 g/Molb* = 0.875 cm7gp* = 3240 arm
Calculate the specific volume at
T = 190°Candp- lbar
Solution:Using Eq. (2.1.1) and the conversion factors to obtain the volume v in crnVg, we obtain
y = 10 -8.314.(273, 190) + =
28.1-3240.99-1.013The density p is the reciprocal value of specific volume so that
1P = -
vThe p-v-T data can also be fitted by a polynomial of the form
v = A(0)v + A(l)v -p+ A(2)v-T+ A ( 3 ) v T p (2.1.2)
if measured data is available (Fig. 2.3) [10], [11], [17]. The empirical coefficientsA(0)v... A(3)v can be determined by means of the computer program given in [H]. Withthe modified two-domain Tait equation [16] a very accurate fit can be obtained both forthe solid and melt regions.
Table 2.1: Constants for the Equation of State [9]
Material
PE-LD
PP
PS
PC
PA 610
PMMA
PET
PBT
W
g/mol
28.1
41.0
104
56.1
111
100
37.0
113.2
atm
3240
1600
1840
3135
10768
1840
4275
2239
b*
cmVg
0.875
0.620
0.822
0.669
0.9064
0.822
0.574
0.712
Fig. 2.3: Specific volume as a function of temperature and pressure for PE-LD [2], [13]
2.2 Specific Heat
The specific heat cp is defined as
- - ( S i ) ,
where h = enthalpyT = Temperature
The specific heat cp gives the amount of heat which is supplied to a system in areversible process at a constant pressure in order to increase the temperature of thesubstance by dT. The specific heat at constant volume cv is given by
C - [^lwhere u = internal energy
T = Temperature
In the case of cv the supply of heat to the system occurs at constant volume.
cp and cv are related to each other through the Spencer-Gilmore equation Eq. (2.1.1)
Spec
ific v
olume
v
cm3/g
Temperature T
0C
measuredpolynomial
/> = 1bar
OJObar
800 bar
The numerical values of cp and cv differ by roughly 10 %, so that for approximate calcula-tions cv can be made equal to cp.
Plots of cp as function of temperature are shown in Fig. 2.4 for amorphous, semi-crystalline and crystalline polymers.
Fig. 2.4: Specific heat as a function of temperature for amorphous (a), semi-crystalline (b) andcrystalline polymers (c) [14]
As shown in Fig. 2.5 measured values can be fitted by a polynomial of the type [11]
Fig. 2.5: Comparison between measured values of cp [13] and polynomial for PE-LD [2]2.3 Thermal Expansion CoefficientThe expansion coefficient aY a* constant pressure is given by [14]
(2.3.1)
(2.2.3)
(2.2.4)
Temperature T'C
Speci
fic he
at c p
JiLkg K
measuredpolynomial
a) b) c)
The isothermal compression coefficient yk is defined as [14]
r, - - 1 [£) (2-3.2)v \dpJT
ay and yk are related to each other by the expression [14]Cp - Cv + ^ ^ (2.3.3)
The linear expansion coefficient alin is approximately
tflin = - CCv (2.3.4)
Table 2.2 shows the linear expansion coefficients of some polymers at 20 0C. The linearexpansion coefficient of mild steel lies around 11 x 10"6 [K"1] and that of aluminum about25 x 10~6 [K"1]. As can be seen from Table 2.2 plastics expand about 3 to 20 times morethan metals. Factors affecting thermal expansion are crystallinity, cross-linking and fillers
Table 2.2: Coefficients of Linear Thermal Expansion [1], [5]
Polymer
PE-LDPE-HDPPPVC-UPVC-PPSABSPMMAPOMPSUPCPETPBTPA 6PA 66PTFETPU
Coefficient of linear expansionat 20 0C alin
106K1
25020015075
180709070100506565708080100150
2.4 Enthalpy
Eq. (2.2.1) leads todh = cp -dT (2.4.1)
As shown in Fig. 2.6 the measured data on h = h(T) [13] for a polymer melt can be fittedby the polynomial
Fig. 2.6: Comparison between measured values of h [13] and polynomial for PA6 [11]
The specific enthalpy defined as the total energy supplied to the polymer divided by thethroughput of the polymer is a useful parameter for designing extrusion and injectionmolding equipment such as screws. It gives the theoretical amount of energy required tobring the solid polymer to the process temperature. Values of this parameter for differentpolymers are given in Fig. 2.7 [14].
If, for example, the throughput of an extruder is 100 kg/h of polyamide (PA) and theprocessing temperature is 260° C, the theoretical power requirement would be 20 kW. Thiscan be assumed to be a safe design value for the motor horse power, although theoreticallyit includes the power supply to the polymer by the heater bands of the extruder as well.
2.5 Thermal Conductivity
The thermal conductivity X is defined as
(2.5.1)
Temperature T
h-hn
0C
kg polynomial measured
(2.4.2)
Fig. 2.7: Specific enthalpy as a function of temperature [14]
where Q = heat flow through the surface of area A in a period of time t(T1-T2) = temperature difference over the length 1.
Analogous to the specific heat cp and enthalpy h the thermal conductivity X as shown inFig. 2.8 can be expressed as [2]
Fig. 2.8: Comparison between measured values of A, [13] and polynomial for PP [2]
The thermal conductivity increases only slightly with the pressure. A pressure increasefrom 1 bar to 250 bar leads only to an increase of less than 5 % of its value at 1 bar.
(2.5.2)
Therm
al co
nduc
tivity
A
Temperature J-
Entha
lpy
Temperature I
mK polynomialmeasured
0C
9C
kWhkg
VC
PCPSPA
As in the case of other thermal properties the thermal conductivity is, in addition to itsdependence on temperature, strongly influenced by the crystallinity and orientation and bythe amount and type of filler in the polymer [I]. Foamed plastics have, for example,thermal conductivities at least an order of magnitude less than those of solid polymers [I].
2.6 Thermal Diffusivity
Thermal diffusivity a is defined as the ratio of thermal conductivity to the heat capacityper unit volume [1]
a = - ^ - (2.6.1)P 'Cp
and is of importance in dealing with transient heat transfer phenomena such as cooling ofmelt in an injection mold [2]. Although for approximate calculations average values ofthermal diffusivity can be used, more accurate computations require functions of Z, pand cp against temperature for the solid as well as melt regions of the polymer. Thermaldiffusivities of some polymers at 20 0C are listed in Table 2.3 [14], [15].
Table 2.3: Thermal Diffusivities of Polymers at 20 0C
Polymer I Thermal diffusivity at 20 0C a106m2/s
PE-LD 012PE-HD 0.22
PP 0.14
PVC-U 0.12
PVC-P 0.14
PS 0.12
PMMA 0.12
POM 0.16
ABS 0.15
PC 0.13
PBT 0.12
PA 6 0.14
PA 66 0.12
PET 0.11
Exhaustive measured data of the quantities cp, h, X and pvT diagrams of polymers aregiven in the VDMA-Handbook [8]. Approximate values of thermal properties of use toplastics engineers are summarized in Table 2.4 [14], [15].
Experimental techniques of measuring enthalpy, specific heat, melting point and glasstransition temperature by differential thermal analysis (DTA) such as differential scanningcalorimetry (DSC) are described in detail in the brochure [12]. Methods of determiningthermal conductivity, pvT values and other thermal properties of plastics have been treatedin this brochure [12].
Table 2.4: Approximate Values for Thermal Properties of Some Polymers [14]
2.7 Coefficient of Heat Penetration
The coefficient of heat penetration is used in calculating the contact temperature whichresults when two bodies of different temperature are brought into contact with each other[2], [16].
As shown in Table 2.5 the coefficients of heat penetration of metals are much higherthan those of polymer melts. Owing to this the contact temperature of the wall of aninjection mold at the time of injection lies in the vicinity of the mold wall temperaturebefore injection.
Polymer
PSPVCPMMASANPOMABSPCPE-LDPE-LLDPE-HDPPPA6PA 66PETPBT
Thermalconductivity
(20 0C) XW/m-K
0.120.160.200.120.250.150.230.320.400.490.150.360.370.290.21
Specific heat(20°C)cp
kJ/kgK1.201.101.451.401.461.401.172.302.302.252.401.701.801.551.25
Density(20 0C) p
g/cm3
1.061.401.181.081.421.021.200.920.920.950.911.131.141.351.35
Glass transitiontemperature Tg
0C10180105115-73115150
-120/-90-120/-90-120/-90
-1050557045
Melting pointrange Tm
0C
ca. 175
ca. 110ca. 125ca. 130160/170215/225250/260250/260ca. 220
The contact temperature #Wmax of the wall of an injection mold at the time of injection
is [17]
_ bw flWmin + bp Bu n0W~ " bw + bp {JA)
where b = coefficient of heat penetration= J / l p c
wmjn = temperature before injection
0u = melt temperatureIndices w and p refer to mold and polymer respectively.
Table 2.5: Coefficients of Heat Penetration of Metals and Plastics [17]
Material Coefficient of heat penetration bW • s0 5 • m'2 • K-1
Beryllium Copper (BeCu25) 17.2 x 103
Unalloyed Steel (C45W3) 13.8 x 103
Chromium Steel (X40Cr 13) 11.7 x 103
Polyethylene (PE-HD) 0.99 x 103
Polystyrene (PS) 0.57 x 103
Stainless Steel 7.56 x 103
Aluminum 21.8 x 103
The values given in Table 2.5 refer to the following units of the properties:
Thermal conductivity X: W/(m-K)Density p: kg/m3
Specific heat c: kJ/(kg-K)
The approximate values for steel are
1 = 50 W/(mK)r = 7850 kg/m3
c = 0.485 kJ/(kg-K)
The coefficient of heat penetration is
2.8 Heat Deflection Temperature
Heat Deflection Temperature (HDT) or the Deflection Temperature under load (DTUL) isa relative measure of the polymer's ability to retain shape at elevated temperatures whilesupporting a load. In amorphous materials the HDT almost coincides with the glass tran-sition temperature Tg. Crystalline polymers may have lower values of HDT but aredimensionally more stable at elevated temperatures [5]. Additives like fillers have moresignificant effect on crystalline polymers than on amorphous polymers. The heatdeflection temperatures are listed for some materials in Table 2.6. Owing to the similarityof the measuring principle Vicat softening point, HDT and Martens temperature lie oftenclose to each other (Fig. 2.9) [6].
Table 2.6: Heat Deflection Temperatures (HDT) According to theMethod A of Measurement [3], [6]
Material I HDT (Method A)°_C
PE-LD 35PE-HD 50PP 45PVC 72PS 84ABS 100PC 135POM 140PA6 77PA66 130PMMA 103PET 80PBT 65
VlCAT MARTENS HDT
load
heat transferliquid
specimenc)
load
load
specimenoven
b)
specimenstandardized
needle
heat transferliquid
a)
Fig. 2.9: Principles of measurement of heat distortion of plastics [6]
2.9 Vicat Softening Point
Vicat softening point is the temperature at which a small lightly loaded, heated test probepenetrates a given distance into a test specimen [5].
The Vicat softening point gives an indication of the material's ability to withstandcontact with a heated object for a short duration. It is used as a guide value for demoldingtemperature in injection molding. Vicat softening points of crystalline polymers havemore significance than amorphous polymers, as the latter tend to creep during the test [5].Both Vicat and HDT values serve as a basis to judge the resistance of a thermoplastic todistortion at elevated temperatures.
Guide values of Vicat softening temperatures of some polymers according toDIN 53460 (Vicat 5 kg) are given in Table 2.7 [6].
Table 2.7: Guide Values for Vicat Softening Points [6]
Polymer Vicat softening pointC
PE-HD 65PP 90PVC 92PS 90ABS 102PC 138POM 165PA 6 180PA 66 200PMMA 85PET 190PBT I 180
2.10 Flammabi l i ty
Most plastics are flammable and can act as fuel in a fire situation. The aim of variousflammability tests is to measure the burning characteristics of plastics materials onceignition has occurred. The Critical Oxygen Index is the most accepted laboratory test. Itmeasures the minimum volume concentration of oxygen in a mixture of oxygen andnitrogen, which is required to initiate combustion of the plastic and propagate flame-burning to a pre-specified extent (a flame-spread time or a distance along the test sample)[I]. Data are presented in the form of Limiting Oxygen Index (LOI) value. These values
are summarized in Table 2.8 [I]. The non-flammability of PTFE is manifested by itsexceptionally high LOI value. Other flame-resistant plastics include thermosets, PVC andPVDC. Resistance to flammability can be enhanced by adding flame retarding additives tothe polymer [I].
Table 2.8: Limiting Oxygen Indices (LOI) of polymers (23 0C) [1]
Material I LOIPOM 14.9/15.7PMMA 17.4PE 17.4PP 17.4PS 17.6/18.3ABS 18.3/18.8PET 20.0PA 66 24/29PSU 30/32PI 36.5PVDC 60.0PVC (chlorinated) 60.0/70.0PTFE 95.0
CLAMPPLASTICSSPECIMEN
IGNITIONSOURCE
(V) (H)
Fig. 2.10: Typical arrangements for the UL flammability test: (V) UL 94 vvertical small flame ignitibility (variable sample thickness); (H) UL 94HB horizontal small flame ignitibility / flame spread [1]
Underwriters' Laboratory test (UL 94) is a rating system which classifies flammabilitybehavior of plastics according to their ability to maintain combustion after the flame isremoved (see Fig. 2.10 [I]). In general, plastics which extinguish rapidly and do not dripflaming particles obtain high ratings. Ratings are given on the basis of minimum wallthickness of the material which corresponds to a particular flame class [I]. These thick-nesses are important for designing plastics component design.
The temperature index determined on the basis of the tensile half-life concept of theUnderwriters' Laboratories is shown for various polymers in Fig. 2.11 [4]. The smokeemission for a number of plastics is given in Fig. 2.12 [4].
Tem
pera
ture
0C
Fig. 2.11: UL temperature index for some thermoplastics [4]
Fig. 2.12: Smoke emission behavior of some thermoplastics [4]
Literature
1. Birley, A. W.: Haworth, B.: Bachelor, T.: Physics of Plastics, Hanser, Munich 19912. Rao, N. S.: Design Formulas for Plastics Engineers, Hanser, Munich, 19913. Domininghaus, K: Plastics for Engineers, Hanser, Munich 19934. Rigby, R.B.: Polyethersulfone in Engineering Thermoplastics: Properties and Applications.
Ed.: James M. Margolis. Marcel Dekker, Basel 19855. General Electric Plastics Brochure: Engineering Materials Design Guide6. Schmiedel, K: Handbuch der Kunststoffpriifung (Ed.), Hanser, Munich 19927. Design Guide, Modern Plastics Encyclopedia, 1978-798. Kenndaten fur die Verarbeitung thermoplastischer Kunststoffe, Teil I, Thermodynamik,
Hanser, Munich 19799. Mckelvey, JM.: Polymer Processing, John Wuley, New York 196210. Miinstedt, K: Berechnen von Extrudierwerkzeugen, VDI-Verlag, Diisseldorf, 197811. Rao, N.S.: Designing Machines and Dies Polymer Processing, Hanser, Munich 198112. Brochure: Advanced CAE Technology Inc. 199213. Proceedings, 9. Kunststofftechnisches !Colloquium, IKV, Aachen 197814. Rauwendal, C: Polymer Extrusion, Hanser, Munich 1986.15. Ogorkiewicz, RM.: Thermoplastics Properties and Design, John Wuley, New York 197316. Martin, H.: VDI-Warmeatlas, VDI-Verlag, Diisseldorf 198417. Wubken, G: Berechnen von SpritzgieBwerkzeugen, VDI-Verlag, Diisseldorf 197418. Progelhof, R.C., Throne, J.L.: Polymer Engineering Principles - Properties, Processes, Tests
for Design, Hanser, Munich 199319. Kurfess, W.: Kunststoffe 61 (1971), p 421
Speci
fic Op
tical D
ensity
, DM (
corr.)
Test Conditions:American National Bureau ofStandarts Smoke3-2 mm SamplesFlamming Condition
3 Transport Properties of Molten Polymers
The basic principle of making parts out of polymeric materials lies in creating a melt fromthe solid material and forcing the melt into a die, the shape of which corresponds to that ofthe part. Thus, as Fig. 3.1 indicates, melt flow and thermal properties of polymers play animportant role in the operations of polymer processing.
Plastics solids
Part removal
Fig. 3.1: Principle of manufacturing of plastics parts
3.1 Newtonian and Non-Newtonian Fluids
Analogous to the ideal elastic solids there exists a linear relationship between stress andstrain in the case of Newtonian fluids (Fig. 3.2).
Plastication
Melt
Shaping
Cooling
SHEAR RATE
Fig. 3.2: Flow curves of idealized fluids [1]
The fluid between the upper plate in Fig. 3.3 moving at a constant velocity Ux and thelower stationary plate experiences a shear stress x (see Fig. LIB also).
Fig. 3.3: Shear flow
The shear or deformation rate of the fluid is equal to
H dy
The shear viscosity is then defined as
TJ = - (3.1.3)
rFor an extensional flow, which corresponds to the tension test of Hookean solid, we get
(3.1.4)
where
(3.1-1)
Ux
H
SHEARSTRESSDilatant
Bingham
Newtonian
Pseudoplastic
GZ = normal stressA = Trouton viscositye = strain rate
Analogous to Eq. (1.4.4) one obtainsI = 3TJ (3.1.5)
3.2 Viscous Shear Flow
Macromolecular fluids like thermoplastic melts exhibit significant non-Newtonianbehavior. This is noticed in the marked decrease of melt viscosity when the melt issubjected to shear or tension as shown in Fig. 3.4 and in Fig. 3.5. The flow of melt in thechannels of dies and polymer processing machinery is mainly shear flow. Therefore,knowledge of the laws of shear flow is necessary for designing machines and dies forpolymer processing. For practical applications the following summary of the relationshipswas found to be useful.
3.2.1 Apparent Shear Rate
The apparent shear rate for a melt flowing through a capillary is defined as
, - $
where Q is the volume flow rate per second and R, the radius of capillary.
Fig. 3.4: Tensile viscosity and shear viscosity of a polymer melt as a function of strain rate [14]
<9£o.tgft
Igq.
lg/i
Mo= 31«
SHEAR RATE du/dr
Fig. 3.5: Shear stress as a function of shear rate for different types of plastics [24]
3.2.2 Entrance Loss
Another rheological parameter which is of practical importance is the entrance loss pc
representing the loss of energy of flow at the entrance to a round nozzle. This is correlatedempirically by the relation [4]
Pc=cTm (3.2.2)
where c and m are empirical constants and r the shear stress. These constants can bedetermined from the well-known Bagley curves as shown in Fig. 3.6. The values of theseconstants are given in Table 3.1 for some of the thermoplastics. The dimensions of shearstress and entrance loss used in the calculation of c and m are Pa.
3.2.3 True Shear Stress
The flow curves of a particular PE-LD measured with a capillary rheometer are given inFig. 3.7. The plot shows the apparent shear rate y a as a function of the true shear stress r
SHEA
R ST
RESS
, TBINGHAM PLASTIC
NEWTONIAN
ST. VENANT BODY
DILATANT
PSEUDOPLASTIC
at the capillary wall with the melt temperature as a parameter. The entrance loss pc wasobtained from the Bagley plot shown in Fig. 3.6.Thus, the true shear stress z is given by
2(1/ R)
where L = length of the capillaryR = radius of the capillary respectively.p = pressure of the melt (see Fig. 3.6)
Fig. 3.6: Bagley plots of a polystyrene with the capillary length L and radius R [15]
Table 3.1: Resin-Dependent Constants c and m in Eq. (3.2.2) [4]
ProductPolypropylene (Novolen 1120 H)Polypropylene (Novolen 1120 L)Polypropylene (Novolen 1320 L)PE-LD (Lupolen 1800 M)PE-LD (Lupolen 1800 S)PE-LD (Lupolen 1810 D)PE-HD (Lupolen 601 IL)PE-HD (Lupolen 6041 D)Polyisobutylene (Oppanol BlO)Polyisobutylene (Oppanol B15)
C
2.55 HO"5
1.463-10-4
2.87M0-7
1.176-101
6.984-10°5.688-10-4
3.9404 O2
1.788-10°6.401-10"3
1.02M0-7
m
2.1161.9762.4691.4341.0721.9051.3991.1871.5752.614
R= 1mmR=0,6 mm
Pres
sure
p
Capillary geometry L/R
Pc
Fig. 3.7: Flow curves of a PE-LD [2]
3.2.4 Apparent Viscosity
The apparent viscosity rja is defined as
Va=- (3-2.4)Ya
and is shown in Fig. 3.8 as a function of shear rate and temperature for a PE-LD. Viscosityfunctions for several polymers are given in Figs. 3.9 and 3.10.
U X
||5O3SI/\
Shea
r rate
f •
Fig. 3.8: Viscosity functions of a PE-LD [2]
Shear rate js"1
Pa-s
Shear stress TPa
s]
Melt v
iscos
ity (P
a s)
melt v
iscos
ity (P
a s)
Shear viscosity of different polymer melts
Shear rate ( s1 )
shear viscosity of different polymer melts
melt temperature (0C)
Fig. 3.9: Shear viscosity of some polymer melts
PBT
PP
PA6ABS
PA66
PE-HDPOM
PE-LD
PE-LD (2000C)
ABS(2500C)
PE-HD (19O0C)
POM (21 OX)PA66 (2800C)
PP (260°C)
PA6 (275°C)
PBT (290°C)
Visc
osity
Ns/m
2V
ISC
OS
ITY
, P
a
s
Pois
e
SHEAR RATE 1OD SECS.1
POLYSULFbNE
POLYCARBONATE
TEMPERATURE, 0C
Fig. 3.10: Shear viscosity of some engineering thermoplastics [3], [16]
Shear Stress N/m2
Polyethersulfone 300P: 3500CPolyethersulfone 200P: 3500CPolysulfone : 3500CPolycarbonate : 2700CRigid PVC i : 1800C
3.2.5 True Shear Rate
The true shear rate y t is obtained from the apparent shear rate by applying the correctionfor the non-Newtonian behavior of the melt according to Rabinowitsch
The meaning of the power law exponent n is explained-in Section 3.3.2.
3.2.6 True Viscosity
The true viscosity rjw is given by
^ = - (3.2.6)Yt
In Fig. 3.11 the true and apparent viscosities are plotted as functions of the correspondingshear rates at different temperatures for a polystyrene. As can be seen, the apparentviscosity function is a good approximation for engineering calculations.
Fig. 3.11: True and apparent viscosity functions of a polystyrene at different temperatures [4]
3.3 Rheological Models
Various fluid models have been developed to calculate the apparent shear viscosity r\a [2].The following sections deal with an important few of these relationships, which arefrequently used in design calculations.
Appa
rent v
iscos
ity 7} a
True
visco
sity 7
? w
Pa-s Polystyrene
s"1
Apparent shear rate faTrue shear rate fx
3.3.1 Hyperbolic Function of Prandtl and Eyring
The relation between shear rate y a and shear stress r according to the fluid model ofEyring [19] and Prandtl [20] can be written as
ra=-Csinh(r/A) (3.3.1)
where C and A are temperature-dependent material constants.The evaluation of the constants C and A- for the flow curve of PE-LD at 1900C in
Fig. 3.12 leads to C = 4s"1 and A = 3-104 N/m2. It can be seen from Fig. 3.12 that thehyperbolic function of Prandtl and Eyring holds good at low shear rates.
Fig. 3.12: Comparison between measurements and values calculated with Eq. (3.3.1) [2]
3.3.2 Power Law of Ostwald and De Waele
The power law of Ostwald [21] and De Waele [22] is easy to use, hence widely employedin design work [5]. This relation can be expressed as
fa=Kr" (3.3.2)
or
ra=K\rn-l\T (3.3.3)
where K denotes a factor of proportionality and n the power law exponent. Another formof power law often used is
(3.3.4)
Shear stress TN/mz
Shear
rate
j
PE-LO19O0C
S"1
In this case, nR is the reciprocal of n and KR- K nR .From Eq. (3.3.2) the exponent n can be expressed as
« = ^ P (3.3.6)dlgr
As shown in Fig. 3.13 in a double log-plot the exponent n represents the local gradient ofthe curve y a vs. T.
Fig. 3.13: Determination of the power law exponent n in the Eq. (3.3.2)
Furthermore1 = d\gr = d\grja + d\gya = d\grja | n d\gya d\gya d\gy a
The values of K and n determined from the flow curve of PE-LD at 1900C shown inFig. 3.14 were found to be K= 1.06-1011 and «=2.57.As can be seen from Fig. 3.14, the power law fits the measured values much better thanthe hyperbolic function of Prandtl [20] and Eyring [19]. The deviation between the powerlaw and experiment is a result of the assumption that the exponent n is constant throughout
(3.3.5)
or
Shea
r rate
j
Shear stress T
PE-LOM50°C
s'1
Pa
the range of shear rates considered, whereas actually n varies with the shear rate. Thepower law can be extended to consider the effect of temperature on viscosity as follows:
ria=KOR-e*v(-p-T)-y**-x (3.3.8)
where K0R = consistency indexP = temperature coefficientT = temperature of melt.
Fig. 3.14: Comparison between measured values and power law
Example:Following values are given for a PE-LD:
nR = 0.3286P = 0.008630C1
KOR = 135990N-snR -nf1
The viscosity % at T= 2000C and ya =500 s1 is calculated from Eq. (3.3.8)
r\a = 373APa-s
3.3.3 Polynomial of Muenstedt
The fourth degree polynomial of Muenstedt provides a good fit for the measured values ofviscosity. For a definite temperature this is expressed as
(3.3.9)
Shea
r rate
f
Shear slress T
measured
PE-IO19O0C
N/m2
s]
where A0, Ax, A2, A3, A4 represent resin-dependent constants. These constants can bedetermined with the help of the program of Rao [13], which is based on multiple linearregression.
This program in its general form fits an equation of the type y=ao+apcl+ajc2+...arpcn
and prints out the coefficients a0, Ci1 and so on for the best fit.
3.3.3.1 Shift Factor for Crystalline Polymers
The influence of temperature on viscosity can be taken into account by the shift factor aT
[4]. For crystalline polymers this can be expressed asaT = bx(T0)exV(b2/T) (3.3.10)
where bh b2 = resin-dependent constantsT = melt temperature (K)T0 = reference temperature (K)
3.3.3.2 Shift Factor for Amorphous Polymers
The shift factor O1. for amorphous polymers is derived from the WLF equation and can bewritten as
C2 +(T-T0)
where C1, c2 - resin-dependent constantsT = melt temperature (0QT0 = reference temperature (0C)
The expression for calculating both the effect of temperature and shear rate on viscosityfollows from Eq. (3.3.9)
(3.3.12)
(3.3.13)
The power law exponent is often required in the design work as a function of shear rateand temperature. Fig. 3.15 illustrates this relationship for a definite PE-LD. The curvesshown are computed with Eqns. (3.3.10) and (3.3.13). As can be inferred from Fig. 3.15,the assumption of a constant value for the power law exponent holds good for a widerange of shear rates.
With Eq. (3.3.7) we get
Fig. 3.15: Power law exponent of a PE-LD as a function of shear rate and temperature
Example:A0 = 4.2541A1 = -0.4978A2 = -0.0731A3 = 0.0133A4 = -0.0011b, = -5.13-10"6
b2 = 5640 K
at y a =500 s1 and T= 2000C.
Solution:aT from Eq. (3.3.10)aT= 5.13-106-exp(5640/473) = 0.774
With X = lg(aT.ya)
X = lg(0.774-500) = 2.588
rja from Eq. (3.3.12)= lQ(^aT + A0+A\X+A2X
2+A3X3+A4X
4)
Substituting the values of A0, A1 and so on one gets77, = 351.78 Pa -s
The power law exponent is obtained from Eq. (3.3.13)
n = (1 + A1 +2A2X+ 3A3X2 +4^4X3)"1
Using the values of A0, A1 and so onw= 3.196
Powe
r law
exp
onen
t n
Shear rate fs-1
PE-LD
15O0C 19O0C 23O0C27O0C
3.3.4 Viscosity Equation of Carreau [23]
As shown in Fig. 3.16, the Carreau equation gives the best fit for the viscosity functionreproducing the asymptotic form of the plot at high and low shear rates correctly.
Fig. 3.16: Determination of Carreau parameters from a viscosity function [9]
The equation is expressed as
rja = p (3.3.14)
where A, B, C are resin-dependent constants. By introducing the shift factor aT intoEq. (3.3.14) the temperature-invariant form of the Carreau equation can be given as(Fig. 3.17)
Va = ^ - c <3-3-15)(\ + BaTfaf
For a number of resins the shift factor can be calculated as a function of temperature fromthe following equation with good approximation [5], [6]
lor (T r , 8.86(ri-Ta-) 8.86(r2~7V) , , , l6)
where T1 (0C) is the temperature, at which the viscosity is given and T2 (0C), thetemperature, at which the viscosity is to be found out.
The standard temperature TST is given by [6]
TST = Tg+50° C (3.3.17)
Data on typical glass transition temperatures of polymers are given in Table 2.4.The power law exponent n can be obtained from Eq. (3.3.15):
(3.3.18)
Visco
sity 7}
Shear rate /
Slope: -C
Vis
cosi
ty
r|
Red
uced
vis
cosi
ty
rj/a
T
Shif
t fac
tor
a T
Reduced shear rate y/aT
[Pa-s][Pas]
Shear rate y
Is"1]
[-]
Reciprocal absolute temperature 1/T
[103IC1]
Fig. 3.17: Use of shift factor aT for calculating temperature invariant viscosity [17]
0C
LDPE
PS
PP
HDPE
LDPE
master curve T = 150 0C
KM
For high shear rates n becomes [4]
« = j ^ (3.3.19)
Computer disks containing the resin-dependent constants A9 B, C can be obtained for therespective resins from the resin manufacturers [12]. These constants can also bedetermined by using the software VISRHEO [13], and can be stored in a data bank forviscosity data.
Example:Following constants are given for a particular PE-LD.
A = 32400 Pa • sB = 3.1sC = 0.62TST = -133 CT1 = 190 C
The viscosity is to be calculated atT2 = 2000C and Y0=SOOs1
Solution:One obtains from Eq. (3.3.16)
Y _ 8.86(TI-TST) _ 8.86(190-(-133)) _ 6 ? / )
101.6+ Cr 1 -7V) 101.6+ (190-(-133))
and
y_ 8.86(T2-TsT) _ 8.86(200-(-133)) _ 6 ? 9
101.6 + (T2 ~ TST) 101.6 + (200- (-133))
The power law exponent is calculated from Eq. (3.3.18)
n = + lV' = r -°- 6 2- 1 3 7 9- 5 + l)=2.63
v i + z ; v 1 + 1379.5 ;The viscosity r\a follows from Eq. (3.3.15)
32400-0.89(1 + 1379-5)-0.62
3.3.5 Viscosity Formula of Klein
The regression equation of Klein et al. [25] is given by
IgT1n = a0+U1In/a+an(lnya)2+a2T+a22T
2+auT\nya (3.3.20)
T= Temperature of the melt (0F)rja = Viscosity (lbf-s/in2)
The resin-dependent constants a0 to a22 can be determined with the help of the computerprogram given in [13], as has been the case in finding out the A-coefficients in Eq. (3.3.9).
Example:
Following constants are valid for a particular type of PE-LD. What is the viscosity rja atra=500sJ and T= 2000C?
a0 = 3.388a, = -6.35M01
au = -1.815-10'2
a2 = -5.975-103
a22 = -2.5 MO'6
a12 = 5.187-104
Solution:T(0F) = 1.8 • T(0C) + 32 = 1.8 • 200 + 32 = 392
With the constants above and Eq. (3.3.20) one gets
T]n = 0.066 Ibfs/in2
and in Si-units
T]n = 6857 • 0.066 = 449.8 Pa • s
The expression for the power law exponent n can be derived from Eq. (3.3.7) andEq. (3.3.19). The exponent n is given by
- = l + ax +2au\nya +au T (3.3.21)n
Putting the constants ah ..., a12 into this equation one obtains« = 2.919
3.4 Effect of Pressure on Viscosity
Compared to the influence of temperature the effect of pressure on viscosity is not ofmuch significance.However, the relative measure of viscosity can be obtained from [8], [6], [4]
r/p = rjoexip(ap'p) (3.4.1)
where r/p = viscosity at pressure/? and constant shear stress T0
T]0 = viscosity at constant shear stress T0
ap = pressure coefficientFor styrene polymers T]p is calculated from [8]
17P = ^oGXP(P/KM)) (3.4.2)
where p = pressure in bar.
Thus the change of viscosity with the pressure can be obtained from Eq. (3.4.2). Table3.2 shows the values of viscosity calculated according to Eq. (3.4.2) for a polystyrene ofaverage molecular weight. It can be seen that a pressure of 200 bar causes an increase ofviscosity of 22% compared to the value at 1 bar. The pressure coefficient of PE-LD is lessthan that of PS by factor of 3 to 4 and the value PE-HD is again less than a factor of 2 thanthat of PE-LD. This means that in the case of polyethylene an increase of pressure by 200bar would enhance the viscosity only by 3 to 4%. Consequently, the effect of pressure onviscosity can be neglected in the case of extrusion 'processes, in which generally lowpressures exist. However, in injection molding where usually one has to deal with highpressures the dependence of viscosity on pressure has to be considered.
Table 3.2: Effect of Pressure on Viscosity for Polystyrene, Eq. (3.4.2)
bar
30 1.03%100 1.105%200 1.221%300 1.35 Tj0
500 1.65%1000 2.72%3000 I 20%
Figure 3.18 shows the melt viscosity at constant stress and temperature as a function ofpressure for some polymers [7].
3.5 Dependence of Viscosity on Molecular Weight
The relationship between viscosity and molecular weight can be described by [ 10]
T111= K'Ml5 (3.5.1)
where Mw = molecular weightK' = resin dependent constant.
The approximate value of K' for PE-LD is^'=2.28-10-4
and for Polyamide 6JT= 5.2U0"14
according to the measurements of Laun [10]. These values are based on zero viscosity.
Vis
cosi
ty/v
isco
sity
at
refe
ren
ce p
ress
ure
Excess pressure ( bar)
Fig. 3.18: Melt viscosity at constant stress and temperature as a function of pressure [7]
Temperature above2100C only
3.6 Viscosity of Two-Component Mixtures
The viscosity of a mixture consisting of the component A and the component B can beobtained from [11]
Ig T1M = CA Ig T1A + C 5 Ig T1n (3.6.1)
where T1 = viscosityC = weight percent
Indices:M: mixtureA, B: components
3.7 Melt Flow Index
The Melt Flow Index (MFI) which is also known as the Melt Flow Rate (MFR) indicatesthe flowability of a constant polymer melt, and is measured by forcing the melt through acapillary under a dead load at constant temperature (Fig. 3.19). The MFI value is the massof melt flowing in a certain time. A MFR or MFI of 2 at 2000C and 2.16 kg means, forexample, that the melt at 200 0C flows at a rate of 2 g in ten minutes under a dead load of2.16 kg.
In the case of Melt Volume Rate which is also known as Melt Volume Index (MVI)the volume flow rate of the melt instead of mass flow rate is set as the basis. The unit hereisml/lOmin.
The effect of MFI on the properties of polyethylene, as an example, is illustrated inFig. 3.20 [18]. Ranges of melt indices for common processing operations are given inTable 3.3 [18].
Table 3.3: Ranges of MFI Values (ASTM D1238) for Common Processes [18]
Process MFI rangeInj ection molding 5/100Rotational molding 5/20Film extrusion 0.5/6Blow molding 0.1/1Profile extrusion 0.1/1
Fig. 3.19: Melt flow tester [6]
3.8 Tensile Viscosity
Although the flow of melt in the channels of dies and machines of polymer machinery ismainly shear flow, elongational flow is of importance in such applications as film blowingand blow molding. The elongational or tensile viscosity can be measured with a tensilerheometer [1], and is much higher than shear viscosity. As shown in Fig. 3.4 the tensileviscosity of a Newtonian fluid is three times the shear viscosity. The tensile viscosity isdefined as
// = | (3.8.1)
* -riwhere / = length at any instant of a volume element
t = time
3.9 Viscoelastic Properties
Polymer machinery can be designed sufficiently accurate on the basis of the relationshipsfor viscous shear flow alone. However, a complete analysis of melt flow should includeboth viscous and elastic effects, although the design of machines and dies by consideringmelt elasticity is rather difficult and seldom in use. Similar attempts to dimension the diestaking elastic effects into account have been made as described in the work of Wagner[26] and Fischer [27].
weight
barrel
heater
piston
capillary
Fig. 3.20: Melt index and density vs. polymer properties [18]
To give a more complete picture of melt rheology the following expressions for theviscoelastic quantities according to Laun [10], [14] are presented.
The material functions characterizing the elastic behavior of a polymer melt are shearcompliance and primary normal stress coefficient which are defined as follows [14], [2]:
3.9.1 Primary Normal Stress Coefficient 0 :
0 = (3.9.1)
N1: normal stress difference, y0 : shear rate
3.9.2 Shear Compliance Je:
U=7-- (3-9-2)TO
yrs: recoverable shear strain, T0: shear stressFurther on we have [14]
(3.9.3)
Increasing melt index
Incr
easi
ng d
ensi
ty
A. Barrier propertieshardnesstensile strengthchemical resistance
B. Flexibilityelongation
C. Rigiditycreep resistanceheat resistance
D. Clarityreduced shrinkage
E. Surface gloss
F. Toughnessstress crack resistance
A
B
C E
FD
The equations above shown as functions of shear rate can be determined frommeasurements with a cone and plate rheometer (Fig. 3.21) [I].
Fig. 3.21: Schematic diagram of a cone and plate rheometer [1]
The limiting values of these equations are 0O , Tj0 and J° (Fig. 3.22).
Fig. 3.22: Parameters for steady shear flow [14] (I = linear region, II = nonlinear region)
3.9.3 Die Swell
Die swell which can be measured with a capillary viscometer gives a measure of theelastic deformation of the melt. Die swell is shown in Fig. 3.23 [14] as a function of lengthL to radius R of the capillary. The value is highest for an orifice of negligible length wherethe effect of converging entrance flow is largest. With increasing L/R ratios the molecularorientation decays, and the swell attains a constant value. For certain applications smallerL/R ratios of dies are preferred in order to have a high molecular orientation.
Cone
Sample
Plate
ig-U
g7?,
ig0
ig %
Fig. 3.23 Die swell vs length to radius IVR [14]
The viscoelastic behavior of polymer melts is treated in [2] in more detail.
Literature
1. Birley, A.W.: Haworth, B.: Bachelor, T.: Physics of Plastics, Hanser, Munich 19912. Rao, KS.: Design Formulas for Plastics Engineers, Hanser, Munich, 19913. Rigby, KB.: Polyethersulfone in Engineering Thermoplastics: Properties and Applications.
Ed.: James M. Margolis. Marcel Dekker, Basel 19854. Miinstedt, K: Berechnen von Extrudierwerkzeugen, VDI-Verlag, Diisseldorf, 19785. Rao, KS.: Designing Machines and Dies Polymer Processing, Hanser, Munich 19816. Rauwendal, C: Polymer Extrusion, Hanser, Munich 19867. Ogorkiewicz, R.M.: Thermoplastics Properties and Design, John Wuley, New York 19738. Avenas, P., Agassant, J.F., Sergent, J.Ph.: La Mise en Forme des Materieres Plastiques,
Technique & Documentation (Lavoirier), Paris 19829. Hertlein, T., Fritz, KG.: Kunststoffe 78, 606 (1988)10. Laun, KM.: Progr. Colloid & Polymer Sai, 75, 111 (1987)11. Carley, J.F.: ANTEC 84, p. 43912. CAMPUS Databank13. Rao, KS., O'Brien, K.T. and Harry, D.K: Computer Modeling for Extrusion and other
Continous Polymer Processes. Ed. Keith T. O'Brien, Hanser, Munich 199214. Laun, KM.: Rheol. Acta 18, 478 (1979)
UR
die s
well
i"PA 6T C9CJ
15. BASF Brochure: Kunststoff-Physik im Gesprach, 197716. Harris, J.E.: Polysulfone in Engineering Thermoplastics: Properties and Applications. Ed.:
James M. Margolis, Marcel Dekker, Basel 198517. Geiger, K.: Private Communication.18. Rosato, D. V., Rosato, D. V.: Plastics Processing Data Handbook, Van Nostrand Reinhold,
New York 199019. Eyring, K: I. Chem. Phys. 4, 283 (1963)20. Prandtl, L: Phys. Blatter 5, 161 (1949)21. Ostwald, W.: Kolloid-Z., 36, 99 (1925)22. De Waele, A.: Oil and Color Chem. Assoc. J., 6, 33 (1923)23. Carreau, PJ.: Dissertation, Univ. Wisconsin, Madison (1968)24. Bernhardt, E. C.: Processing of Thermoplastic Materials, Reinbold, New York (1963)25. Klein, L; Marshall, D.I; Friehe, CA.: Soc Plastic Engrs. J. 21, 1299 (1965)26. Wagner, M.K: Dissertation, Univ. Stuttgart (1976)27. Fischer, E.: Dissertation, Univ. Stuttgart (1983)
4 Electrical Properties
The use of plastics in the electrical industry as insulators for wire and cable insulation iswell known. The application of engineering resins to make miniature electric components,printed circuit boards, conductive housings of computer equipment and the like, althoughnot so well known, is increasing. Some of the electrical properties which are of importancein selecting a resin for these applications are treated in this section.
4.1 Surface Resistivity
Surface resistivity is defined as the ratio of electrical field strength to the current density ina surface layer of an insulating material. It is the measure of a material's ability to resist theflow of current along its surface when a direct voltage is applied between surface mountedelectrodes of unit width and unit spacing. The unit of surface resistivity is ohm [1], [3].
4.2 Volume Resistivity
Volume resistivity is the volume resistance reduced to a cubical unit volume of thematerial. Volume resistance is the ratio of the direct voltage applied to the electrodes incontact with the test material, to the steady-state current flowing between them [1], [3].The unit of volume resistivity is ohm-m (Wm) or ohm-cm (Wcm).
4.3 Dielectric Strength
Dielectric strength is the measure of the electrical breakdown resistance of a materialunder an applied voltage [I]. It is the ratio of the voltage reached just before breakdown tothe material's thickness and is expressed as kv/mm or Mv/m. Dielectric strength data forsome materials are given in Table 4.1.
Table 4.1: Dielectric Strength Data for Plastics (Method ASTM D149) [6]
Material Dielectric strengthkv/25jim
PE-LD >700PE-HD > 700PP 800PVC 300PS 500ABS 400PC 350POM 700PA 6 350PA 66 400PMMA 300PET 500PBT 500
4.4 Relative Permittivity
Relative permittivity (%), formerly known as dielectric constant is the ratio of capacitance(C) of a given configuration of electrodes with the plastics material as the dielectricmedium, to the capacitance (Cv) of the same configuration of electrodes with vacuum asthe dielectric [1], [3].
SR = r (4 A 1)Cv
The performance of plastics as insulators increases with decreasing relative permittivity.
4.5 Dielectric Dissipation Factor or Loss Tangent
Dielectric dissipation factor is the ratio of the electrical power dissipated in a material tothe total power circulating in the circuit. It is the tangent of the loss angle (S) and isanalogous to tan5 which is the ratio between loss and storage moduli described in Section1.3.2. A low dissipation factor is important for plastics insulators in high frequencyapplications such as radar and microwave equipment. Relative permittivity and dissipationfactor are dependent on temperature, moisture, frequency and voltage [3]. Typical valuesof volume resistivity, relative permittivity and loss tangent are given in Table 4.2 for somepolymers [1], [5] (see also Fig. 4.1 [2]).
Temperature C
Fig. 4.1: Loss tangent as a function of temperature for some engineering thermoplastics [2]
Table 4.2: Typical Values of Volume Resistivity, Relative Permittivityand Loss Tangent [1], [5]
Material Volume Relative Dielectric dissipation factorresistivity permittivity or loss tangent tan<5 • 104
ohm x cm at 50 Hz at 200C and 1 MHzPE-LD 1017 2.3 1.2PE-HD 1017 2.35 2PP 1017 3.5 400PVC 1015 2.27 230PS 1017 2.5 1ABS 1015 2.9 200PC 1017 3 7POM 1015 3.7 50PA 6 1012 3.8 300PA 66 1012 8.0 800PMMA 1015 3.3 40PET 1016 4.0 200PBT 1016 3,0 200
Loss
Tan
gent
(ta
n S
at
60
Hz)
PolyimidoType H
Polyethyleneterephthalate
PolycarbonatePolysulfone
Polyethersulfone
4.6 Comparative Tracking Index (CTI)
Comparative tracking index indicates a plastics material's ability to resist development ofan electrical conducting path when subjected to current in the presence of a contaminatingsolution [1], [3]. Contaminants, such as salt and moisture, allow increased conduction overthe surface which may lead to tracking, the appearance of conducting paths over thesurface. The deterioration of the surface quality is hence the cause of failure of highvoltage insulation systems [I]. The CTI is given in terms of maximum voltage, at whichno failure occurs, according to different test procedures. Typical values of CTI are given inTable 4.3 [5].
Table 4.3: Typical Values of Comparative Tracking Index [5]
"Material I Test method KBPE-LD >600PE-HD > 600PP > 600PVC 600PS 200ABS 300PC > 600POM > 600PA 6 > 600PA 66 > 600PMMA > 600PBT I 450
Owing to their high electrical resistance plastics retain electrostatic charge which leadsto such undesirable effects as marked attraction of dust or creation of discharges when thematerial comes into contact with other surfaces. This situation can be alleviated by usinganti-static agents in the polymer formulation. Polymers with intrinsic electricalconductivity can also be used as anti-static coatings [I].
In addition to the properties treated in the foregoing sections the optical properties ofplastics products such as transparency and gloss of films play an important role inselecting a resin in applications where these properties are required. The test procedures tomeasure the optical properties are treated in [I].
A list of properties for which data can be obtained from the resin manufacturers, forexample, on CAMPUS computer disks is presented in Table 4.4. Example of material dataused as input to the software VISMELT [4] for designing extruders is given in Table 4.5.
Table 4.4: List of Properties Obtainable from Resin Manufacturers
Tensile strengthTensile elongationTensile modulusFlexural strengthFlexural modulusCompressive strengthHardnessAbrasionIzod impact strength
Material densityBulk densitypvT diagramsSpecific heatEnthalpyThermal conductivityVicat temperatureHDT (Heat distortion temperature)Flammability UL 94 ratingLOI (Limiting Oxygen Index)
Dielectric strengthSurface resistivityVolume resistivityRelative permittivityDielectric dissipation factor or loss tangentComparative Tracking Index (CTI)
Melt Flow Rate (MFR)Melt Volume Rate (MVR)Shear viscosity as a function of shear rate and temperature of melt
Table 4.5: Example of Input Data to the Software Design Package VISMELT [4]
Type of Polymer: PE-HD
Trade name of polymer: HOECHST GM 9255 F
thermal properties :
melting point TM = 130.0 Grad Celsius
specific heat of melt CPM = 2.51 kJ / (kg K)specific heat of solid CPS = 2.3 0 kJ / (kg K)thermal conductivity of melt KM = .2700 W / (m K)thermal conductivity of solid KS = .2800 W / (m K)heat of fusion LAM = 200.000 k J / k gdensitiy of melt RHOM = .78 g / cm**3density of solid RHOS = .9430 g / cm**3bulk density RHOS0 = .40 g / cm**3Viscosity coefficients :
Carreau-coefficients :A = 28625. Pa S B = .7126 SC = .6535TO = 200.0 Grad Celsiusb = 2447. K
Muenstedt-coefficients :AO = 4.2410 Al = -.01304A2 = -.55251 A3 = .222252A4 = -.033758TO = 200.0 Grad Celsiusb = 2425. K
Klein-coefficients :
Light transmissionRefractive Index
AO = .653721E+01 Al = -.722213E+00All = -.989580E-02 A2 = -.213261E-OlA22 = .204288E-04 A12 = .473881E-03
Power law coefficients :NR = .4022BETA = .003919 l/Grad Celsius KOR = 60889. N s**n / m**2
Literature
1. Birley, A.W.: Haworth, B.: Bachelor, T.: Physics of Plastics, Hanser, Munich 19912. Rigby, R.B.: Polyethersulfone in Engineering Thermoplastics: Properties and Applications.
Ed.: James M. Margolis. Marcel Dekker, Basel 19853. General Electric Plastics Brochure: Engineering Materials Design Guide4. Rao, N.S., O'Brien, K.T. and Harry, D.H.: Computer Modeling for Extrusion and other
Continous Polymer Processes. Ed. Keith T. O'Brien, Hanser, Munich 19925. BASF Brochure: Kunststoff-Physik im Gesprach, 19776. Domininghaus, H.: Plastics for Engineers, Hanser, Munich 1993
5 Optical Properties of Solid Polymers
5-1 Light Transmission
The intensity of light incident on the surface of a plastic is reduced as the light enters theplastic because some light is always reflected away from the surface. The intensity of lightentering the plastic is further reduced as the light passes through the plastic since somelight is absorbed, or scattered, by the plastic. The luminous transmittance is defined as thepercentage of incident light which is transmitted through the plastic. For comparisonpurposes the exact test parameters are documented in ASTM D 1003. Some typical lighttransmission values are presented in Table 5.1 for most common optical plastics. Lighttransmission is a measurement of the transparency of a plastic.
5.2 Haze
Haze is defined as the percentage of transmitted light which deviates from the incidentlight beam by more than 2.5 degrees. Its measurement is also defined by ASTM D 1003.Some typical haze values are presented in Table 5.2 for most common optical plastics.Haze is a measure of the clarity of a plastic.
5.3 Refractive Index
The refractive index n of an isotropic material is defined as the ratio of the speed of lightin the material v to the speed of light in a vacuum c, that is,
n = v/cThe speed of light in vacuum is 300 Mm/s. The refractive index decreases as thewavelength of the light increases. Therefore the refractive index is measured and reported
at a number of standard wavelengths, or atomic emission spectra (AES) lines, as indicatedin Table 5.3.
Table 5.1: Light Transmission, or Luminous Transmittanceof Some Common Optical Plastics
Material Luminous. Transmittance D 1003
ABS 85PC 89PMMA 92PMMA/PS 90PS 88SAN I 88
Table 5.2: Haze of Some Common Optical Plastics
Material Haze
~ABS TOPC 1-3PMMA 1-8PMMA/PS 2PS 3SAN I 3
Table 5.3: Refractive Indices as Functions of Wavelength
AES lineFDC
Wavelength486 nm589 ran651 nm
PMMA1.4971.4911.489
PS1.6071.5901.584
PC1.5931.5861.576
The refractive index is usually measured using an Abbe refractometer according to ASTMD542. The Abbe refractometer also measures the dispersions, which is required for lensdesign. An extensive list of refractive indices is provided in Table 5.4. Since speed of lightin the polymer v is a function of the density, polymers which exhibit a range of densitiesalso exhibit a range of refractive indices. Since density is a function of crystallinity, therefractive index is dependent on whether the polymer is amorphous or crystalline, and on
5.4 Gloss
Surface gloss is the percentage of light intensity reflected relative to that reflected by anideal surface. Also called specular reflectance or specular gloss, the gloss is measuredwithin a specific angular range of the ideal reflected angle. It is then compared to astandard, polished black glass with a refractive index of 1.567, which possesses a speculargloss of 100%. The gloss reduces rapidly as the surface roughness increases. The speculargloss is measured according to ASTM D 523-80.
5.5 Color
Color may be measured using tristimulus colorimeters (a.k.a. colorimeters), orspectrophotometers (a.k.a. spectrocolorimeters). These instruments measure color byilluminating a sample and collecting the reflected light. Colorimeters use filters tosimulate the color response of the eye. They are used for quick and simple measurementsof color differences. Spectrocolorimeters measure color as a certain wavelength of light.The color is reported as three numbers. The L-value measures the grayness, with purewhite scoring 100 and pure black scoring 0. The a-value measures the redness whenpositive and the greenness when negative. The b-value measures the yellowness when
its degree of crystallinity. Since density is also a function of temperature, decreasing astemperature increases, the refractive index also decreases with increasing temperature.
Table 5.4: Refractive Indices of Some Plastics as Functions of Density [1]
Polymer
PE-LDPE-HDPPPVCPSPCPOMPA 6PA 66PMMAPET
Refractive indexn2
D°1.511.53
1.50/1.511.52/1.55
1.591.581.481.521.531.491.64
Densitykg/m3
914/928940/960890/910
1380/155010501200
1410/142011301140
1170/12001380
Transparency
transparentopaque
transparent/opaquetransparent/opaque
transparenttransparent
opaquetransparent/opaquetransparent/opaque
transparenttransparent/opaque
positive and the blueness when negative. So from the L, a, and b values a color can bedefined.
Literature
1. Domininghaus, K: Plastics for Engineers, Hanser, Munich 1993
6 External Influences
Plastics parts are often used in an environment, in which an interaction between thepolymer and a fluid like water, gas or organic liquids can take place. This may lead todeterioration or even failure of the part. Furthermore, plastics used in certain applicationsas in packaging foodstuffs should be resistant to the entry of oxygen or moisture, so thatthe contents do not deteriorate during the prescribed time span.
The behavior of polymers under external influences is dependent on the combinationof polymer and fluid, exposure time, temperature, stress level and processing history [I].The properties of polymers which manifest themselves under external effects are the topicof this section.
6.1 Physical Interactions
6.1.1 Solubility
Most thermoplastics have a solubility parameter [1], [3]. Common solvents are paraffins,ethers, ketones, alcohols and chlorinated organic liquids. The solvation leads to swelling,weight and dimensional changes together with property loss.
6.1.2 Environmental Stress Cracking (ESC)
ESC is a failure mechanism which occurs under conditions when an external or residualstress is imposed on the part which is in contact with an external environment such asliquid or vapor. It is the combination of stress and the liquid medium, which gives rise topremature failure. The failure is initiated by microcrazing into which the aggressive liquidor vapor penetrates [I]. The term ESC is applied to amorphous polymers, where as in thecase of crystalline polymers the failure is denoted as stress corrosion failure.
One of the standard ESC tests is the Bell Telephone technique, in which bent strips ofmaterial containing a defect are totally immersed in a chemical medium before beingexamined for visible signs of damage (Fig. 6.1) [I]. The environmental behavior of someplastics is presented in Fig. 6.2 [7] and Fig. 6.3 [4].
STR
ESS
(psi
)ST
RESS
(psi
)
Fig. 6.1: Bell test for determining ESC [1]
ENVIRONMENT' ISOOCTANE/TOLUENE 7 0 / 3 0 by volume
SAMPLEJIG
LIQUID
POLYARYLETHERSULFONE
POLYARYLATE
POLYSULFONE
MODIFIEDPOLYARYLATE
POLYCARBONATE
MODIFIED PPO
TIME TO RUPTURE (seconds)
Fig. 6.2: ESC resistance of polyarylate vs. other thermoplastics [7]
POLYCARBONATEPOLYSULFONE
NORYL SE-I
TIME TO RUPTURECSECONDS)
Fig. 6.3: ES rupture comparison of several engineering thermoplasticsin a 70/30 isooctane/toluene mixture at 25°C [4]
6.1.3 Permeability
Plastics are to some extent permeable to gases, vapors and liquids. The diffusional charac-teristics of polymers can be described in terms of a quantity known as permeability.
The mass of the fluid permeating through the polymer at equilibrium conditions isgiven by [3]
m = P t A - ( P ' - ^ (6.1.1)S
wherem = mass of fluid permeating [g]
r g iP = permeability — - —
[m-s-PaJt = time of diffusion [s]A = Area of the film or membrane [m2]P1 p2 = partial pressures on the side 1 and 2 of the film [Pa]s = thickness of the film [m]
Besides its dependence on temperature the permeability is influenced by the difference inpartial pressures of the fluid and thickness of the film. Other factors which affect perme-ability are the structure of the polymer film such as crystallinity and type of the fluid.
Permeability is a barrier property of plastics and is important in applications likepackaging. Permeation data for some resins is summarized in Table 6.1 [3].
Table 6.1: Relative Permeability of Various Polymers Compared to PVDC [3]
Polymer
PVDCPCTFEPETPA6PVC-UCAPE-HDPE-LDPPPSButyl RubberPolybutadieneNatural Rubber
Gas permeability
N2
13.195.328.51
42.552982872021479309332862
8600
O2
110.644.157.17
22.64147200103843420824536044400
CO2
12.485.285.5234.52351211214317303179
48004517
H2O (250C, 90% R.H.)1
0.2193
500111
53579.35749857
Table 6.2: Relative Permeability to CO2 of Different PolymersCompared to PET [3]
Polymer Relative permeabilityPET 1PVC-U 6.53PP 60PE-HD 23PE-LD 230
One of the reasons for using PET for making bottles for carbonated drinks is that PET isrelatively impermeable to carbon dioxide, as can be seen from Table 6.2 [3].
6.1.4 Absorption and Desorption
The process by which a fluid is absorbed or desorbed by a plastics material is time-depen-dent, governed by its solubility and by the diffusion coefficient [3]. The period untilequilibrium value is reached, can be very long. Its magnitude can be estimated by the half-life of the process given by [3]
0.04919 s2 , , , ~t0.5 = ( 6 1 2 )
where t05 = half-life of the processs = thickness of the polymer assumed to be penetrated by one sideD = diffusion coefficient
The value of t05 for moisture in PMMA for D = 0.3 x 10"12 m2/s and s = 3 mm is
0.04919-3-3-10~6 __, ,to 5 = T^ = 17-1 days
0.3-10~12-3600-24when the sheet is wetted from one side only [3], However, the equilibrium absorptiontakes much longer, as the absorption rate decreases with saturation.
6.1.5 Weathering Resistance
Weathering is the deterioration of the polymer under atmospheric conditions which by theaction of oxygen, temperature, humidity, and above all, ultra-violet radiation on the resinlead to loss of properties and finally failure of the part. Performance data of the resin underweathering is supplied by resin makers (see also Table 6.4) [8].
Rating: 1: resistant; 2: sufficiently resistant; 3: conditionally resistant;4: mostly not resistant; 5: completely nonresistant
Data on chemical resistance of resins can be obtained from resin manufacturers.
6.2.1 Chemical and Wear Resistance to Polymers
As polymers are converted into products they contact the walls of the various machines inwhich they are converted. Such walls include barrel walls, the plasticating screw surfaces,the interior die surfaces and the mold cavity surfaces. It is important that the correctmaterials be chosen for these surfaces or reduced performance and premature failure may
6.2 Chemical Resistance
Good chemical resistance of polymers is of importance in many applications. Table 6.3shows the performance of some polymers according to a rating when they are in directcontact with the chemical agents listed in the Table 6.3 [6].
Table 6.3: Chemical Resistance of Resin to Different Liquid Agents [6]
Polymer
PE-LDPE-HDPVC-UPMMAPSPAPCPOMPTFE
111111111
221335251
112554411
111335511
111111111
545554511
335551521
311551211
231111111
315551531
315551551
311551511
Salt
solu
tion
Con
cent
rate
d ac
ids
Org
anic
aci
ds
Con
cent
rate
d ba
ses
Alip
hatic
hyd
roca
rbon
s
Hal
ogen
ated
hyd
roca
rbon
s
Aro
mat
ic h
ydro
carb
on
Mon
vale
nt a
lcoh
ols
Oils
and
gre
ases
Ket
ones
Est
ers
Est
hers
arise. In the case of screws and barrels, the contacting surfaces must also exhibit wearresistance to each other.
One of the approaches is to select the barrel which provides the greatest resistance tocorrosion and wear by particular plastic, including any additives, fillers or reinforcements.Then to select a material for the screw flights which performs well against that particularbarrel material, and finally to select a coating for the remaining surfaces of the screwwhich exhibits the greatest corrosion and wear resistance to the plastic.
6.3 General Property Data
General property data for some plastics is presented in Tables 6.5 to 6.11. Some propertiesof the reinforced plastics are illustrated in Fig. 6.4 [5]. The comparability of different testmethods is discussed in Table 6.12.
Table 6.4: Ultraviolet, Thermal and Biological Resistance of Some Plastics [8]
Polymer
AcetalsPolyamidesPCPolyethylenePolypropylenePSPolysulfonePVCEpoxy, aromaticEpoxy, cycloaliphaticPolyurethanesSiliconesButyl rubber
Service temperaturerange
0C90/104-50/150
12075/100
1107517055
100/150100/150100/130
260-45/150
Ultravioletresistance
fairpoor
excellentpoorpoorfairfair
poorfair to good
excellentfair
excellentexcellent
Fungus resistance
excellentexcellentexcellent
poorexcellentexcellentexcellent
poorpoorpoorpoor
excellentexcellent
Strength
Modulus of Elasticity
Specific Gravity
PlasticsComposites / Reinforced Plastics
WoodSteel
AluminumGlass
Concrete - Stone
Fig. 6.4: Reinforced plastics and composites vs. other materials [5]
PlasticsComposites / Reinforced Plastics
WoodSteel
AluminumConcrete
PlasticsComposites / Reinforced Plastics
WoodSteel
AluminumConcrete
MPa
3x 10 psi
6x 10psi
GPa
Table 6.5: Polymer Parameters and Their Influence Properties [8]
Density
Increases Decreases
Molecular weight
Increases Decreases
Molecular weightdistribution
Broadens Narrows
Environmental stressImpact strengthStiffnessHardnessTensile strengthPermeationWarpageAbrasion resistanceFlow processibilityMelt strengthMelt viscosityCopolymer content
Table 6.6: Properties of Some Thermoplastic Structural Foams (Physical PropertiesGuidelines at 0.25 Wall with 20% Density Reduction) [9]
Property
Specific gravityDeflection temperature [0C]under load at 0.462 N/mm2
atl.85N/mm2
Coefficient of thermal expansion [K"1-105]Tensile strength [N/mm2]Flexural modulus [N/mm2]Compressive strength 10% deformation [N/mm2]
PE-HD
0.6
54.234.2229.284012.9
ABS
0.86
86788.9
27.3196031
modifiedPPO0.85
96826.9
23.8182736.4
PC
0.9
1381273.6442.7250036.4
Table 6.7: General Properties of Liquid-Crystal Polymers [8]
Property ValueFlexural strength, N/mm2 147/308Unnotched izod, J/m 150/300Notched izod, J/m 400/500Rockwell hardness M62/99Dielectric constant, 103 Hz 2.9/4.5Dissipation factor, 103 Hz 4-6x 103
Volume resistivity, W • cm 1012/l 013
Dielectric strength, V/mil 780/1000Arc resistance, s 63/185Water absorption, equilibrium at 23 0C, % 0.02/0.04Specific gravity 1.4/1.9Glass transition temperature, 0C -Melt temperature, 0C 275/330Heat distortion temperature, 0C
at 0.455 N/m2 250/280at 1.848 N/m2 180/240
Continuous-use temperature, 0C 200/240Coefficient of thermal expansion, ppm/°C 0-25 x 106 flow direction
25-5OxIO'6 transverseFlammability, UL-94 V/OOxygen index 35/50Tensile modulus, N/mm2 9.8/40.6Tensile strength, yield N/mm2 140/245Tensile elongation, % 1.2/6.9Flexural modulus, N/mm2 9.8/35
Table 6.8: Some Physical Properties of Polyurethane Structural Foams [9]
Property vs specific gravity
Specific gravityFlexural strength pST/mm2]Flexural modulus pS[/mm2]Tensile strength [N/mm2]Heat deflection temperature [0C] at 0.462 n/mm2
Charpy impact, unnotched [kT/m2]Skin hardness, D scale
Property vs thickness
ThicknessSpecific gravityFlexural strength (N/mm2)Flexural modulus (N/mm2)Tensile strength (N/mm2)Charpy impact, unnotched (ft • lb/in2)
0.424.56029.881
13.2570
l/4in0.637.8109218.212.0
0.532.274212.691
18.175
3/8in0.637.8100117.511.0
0.636.484716.8962180
l/2in0.636.484716.810.0
Table 6.9: Properties of Some Thermosetting Resins [8]
Specific gravityWater absorption [% 24h]Heat deflection temperatureat 1.85 N/m2 [0C]Tensile strength [N/mm2]Impact strength [T/m)] [Izod]Coefficient of thermal expansion[10-5 • K"1]Thermal conductivity [W/m • k]
Epoxyglassfilled
1.80.2204
210530.43.1
0.864
mineralfilled
2.10.04121
10521.4
4
generalpurpose
1.450.7172
7016
4.55
0.043
Phenolicsglassfilled
1.950.5204
49187
0.05
mineralfilled
1.830.5260
778011.76
0.03
Table 6.10: Properties of Some Elastomers [8]
Property
Tensile strength (N/mm2)Tensile modulus (N/mm2)ElongationResilienceBrittleness temperature (0C)Thermal expansioncoefficient (105 • K1)Durometer hardnessCompression set
EPM/EPDM
3.5/24.5700/21000
100/700good-5558
30A/90A20/60
Chloroprene
3.5/24.5700/21000
100/800excellent
-4562
30A/95A20/60
Fluoro-elastomers
10.51400/14000
150/450fair
-15/-5055
55A/95A15/30
Naturalrubber
16.8/32.23360/5950300/750
outstanding-6067
30A/100A10/30
Table 6.11: Comparative Physical Properties of Metals and Reinforced Plasticsat Room Temperature [10]
Property
Density [kg/m3]Coefficient of thermalexpansion [k1 • 10'6]Modulus of elasticity[N/mm2]Tensile strength[N/mm2]Yield strength [N/mm2]Thermal conductivity[W/m • k]Ratio of tensile strengthto density
Carbon steel1020
786011.83
210000
462
23148.5
0.0588
Stainless steel316
791616.7
196000
595
24516.3
0.0752
Hastelloy C
896811.5
196000
560
35411.3
0.0624
Aluminium
271224
70000
84
28234
0.031
Glassmatlaminate
138431
4900/7000
63/84
63/842.6
0.0607
Compositestructure glassmat
woven roving152224
7000/10500
84/140
84/1402.6
0.092
Glass reinforcedepoxy filament
wound1800
16.4/22
21000
420/700
420/7002.6/3.5
0.39
Table 6.12: Comparability of DIN/ISO and ASTM Test Methods for Plastics [2]
Test
Density
Melt index
Standard
DINl 306DIN53479
ASTM D 792ASTM D 1505DIN 53735(-ISO/R 292)ASTM D 1338
Symbol
d
d23C
MFI
Units
g/cm3at 200Cg/mlat 23°Cg/lOmin
g/lOmin
Comparability
comparable at sametemperature
comparable under sameconditions
(cont. next page)
Test
Mechanical properties
Elastic modulus
Shear modulus
Torsion modulus
Torsional stiffness
Stiffness propertiesTensile propertiesTensile strength(at maximum load)
Elongation at maximumforcePercentage elongation
Ultimate tensile strength
Tensile strength(at break)Percentage elongation(at break)
Yield stress(Yield point)Yield pointYield strengthPercentageElongation (at yield)Flexural propertiesFlexural strengthLimiting flexural stressFlexural stress(at 5% strain or atconventional deflection)Flexural impactImpact resistanceImpact strength
*)kgf=kiloforce = dN
Standard
DIN 53457ASTM D 638(Tensile)ASTM D 695(Compression)ASTM D 790(Fluxural)ASTM D 882(Film)DIN 53445(ISO/DR 533)ASTM D 2236
DIN 53447(ISO/DR 458)ASTMD 1043
DIN 53455(ISO/DR 468)DIN 53371ASTM D 638ASTM D 882DIN 53455DIN 53371ASTM D 638ASTM D 882DIN 53455DIN 53371ASTM D 638ASTM D 882DIN 53455DIN 53371ASTM D 638ASTM D 882DIN 53455DIN 53371ASTM D 638ASTM D 882DIN 53455ASTM D 882DIN 53452ASTM D 790DIN 53452ASTM D 790
DIN 53453(ISO/R 179)ASTM D 256(ISO/R 180)
Symbol
EE
E0
G
G
T
G(!)
<*B
^ B
eB
5Pmax
%E1
<*R
<*R
°u
SR
SR
Es
°bB
<*bG
Units
kN/mm2psi(=lb/sq.in.)
psi
kgf/cm2 •>
kN/mm2
dyn/cm2
psikN/mm2
dN/cm2
N/mm2
N/mm2
psidN/cm2
%%%%N/mm2
N/mm2
psidN/cm2
%%%%N/mm2
N/mm2
psidN/cm2
%%N/mm2
psiN/mm2
psi
kJ/m2
J/m
Comparability
comparable only under sameconditions: shape and stateof specimen, measuredlenght, test rate
comparable
comparable
comparable only under sameconditions:shape and state of specimen,measured length, test rate
comparable only under sameconditions:shape and state of specimen,measured length, test rate
limited comparability
not comparable
Test
Impact strength(notched)
Shore hardness
Durometer (Shorehardness)Ball indention hardnessct-Rockwell hardnessThermal propertiesVicat softening point
Martens heat distortiontemperatureHeat distortiontemperatureDeflection temperature(HDT)Water absorbtion
Electrical properties
Volume resistivity
Surface resistivity
Dielectrical constant
Dissipation factor (tan 8)
Dielectrical loss factor(e= tan 8)Dielectrical strength
Arc resistance
Tracking resistance
Standard
DIN 53453(ISO/R179)ASTM D 256(ISO/R180)DIN 53505
ASTM D 1706ASTM D 2240DIN 53456ASTM D 785
DIN 53460(ISO/R 306)ASTMD 1525DIN 53458
DIN 53461(ISO/R 75)ASTM D 648
DIN 53472DIN 53475(ISO/R 62)
ASTM D 570
DIN 53482(VDE 0303 Part 3)ASTM D 257DIN 53482(VDE 0303 Part 3)ASTM D 257DIN 53483(VDE 0303 Part 4)ASTMD 150DIN 53483(VDE 0303 Part 4)ASTMD 150
ASTM D 150DIN 53481(VDE 0303 Part 2)ASTM D 149
DIN 53484(VDE 0303 Part 5)ASTM D 495DIN 53480(VDE 0303 Par t i )ASTM D 2132
Symbol
aK
HH
VSP
MSO
PD
P
R0
a
6
D -
Ed
Units
kJ/m2
J/m
Shore scaleA, C, DScale A5 DgramforceN/mrri2
Rockwell scale
0C
0C0C
0C
0C 50F
22°C,4d, mg23°C,24h, mg23°C,24h, %2h
Q-cm
Q-cmQ
Q
kV/mm
V/mil(1 mil=25|im)sec
sec
Comparability
not comparable
comparable
not comparable
comparable if measuredunder same load in liquid
comparable if load,specimen shape and slate arethe same
comparable (converted), ifpre- and post-treatment,specimen and times are thesame
comparable
comparable
comparable
comparable
not comparable
not comparable
not comparable
Literature
1. Birley, A.W.: Haworth, B.: Bachelor, T.: Physics of Plastics, Hanser, Munich 19912. Domininghaus, H.: Plastics for Engineers, Hanser, Munich 19933. Ogorkiewicz, RM.: Thermoplastics Properties and Design, John Wiley, New York 19734. Harris, J.E.: Polysulfone in Engineering Thermoplastics: Properties and Applications. Ed.:
James M. Margolis, Marcel Dekker, Basel 19855. Rosato, D.V., Rosato, D. V.: Plastics Processing Data Handbook, Van Nostrand Reinhold,
New York 19906. Schmiedel, K: Handbuch der Kunststoffprufung (Ed.), Hanser, Munich 19927. Maresca, LM., Robeson, LM.: Polyarylates in Engineering Thermoplastics, Properties and
Applications. Ed. James M. Margolis, Marcel Dekker, Basel, 19858. Alvino, WM.: Plastics for Electronics - Materials, Properties and Design Applications,
Mcgraw Hill, New York 19949. Wendle, BA.: Structural Foam, A purchasing and Design Guide, Marcel Dekker, New York
198510. Mallinson, J.H.: Corrosion-resistant Plastic Composites in Chemical Plant Design, Marcel
Dekker, New York 1969
7 Extrusion
Extrusion is one of the most widely used unit operations of polymer processing. Basicallyit consists of transporting the solid polymer in an extruder by means of a rotating screw,melting the solid, homogenizing the melt, and forcing the melt through a die (Fig. 7.1).
Fig. 7.1: Plasticating extrusion [2]
The extruder screw of a conventional plasticating extruder has three geometricallydifferent zones (Fig. 7.1a) whose functions can be described as follows:
feed zonetransport and preheating of the solid materialtransition zonecompression and plastication of the polymermetering zonemelt conveying, melt mixing and pumping of the melt to the die
However the functions of a zone are not limited to that particular zone alone. Theprocesses mentioned can continue to occur in the adjoining zone as well.
PlasHcat-ion Metering
Feed zone Molten polymer
Fig. 7.1a: Three zone screw
7.1 Extrusion Screws
To perform these processing operations optimally screws of varied geometry as shown inFig. 7.2 are used. Higher melting capacities compared to the three zone screws (Fig. 7.1)are achieved with screws having shearing and mixing devices (Fig. 7.2a). Barrier typescrews enable the separation of solids polymer from the melt, and thus lead to lower andconstant melt temperatures over a wide range of screw speeds (Figs. 7.2c/d). Devola-tilizing screws are applied to extract volatile components from the melt (Fig. 7.2b) [27].
Twin screw extruders are mainly used in the compounding of polymers, such as, forexample, in the pelletizing and compounding of PVC or in the profile extrusion of PVC.The positive conveying characteristics of the twin screw extruders are achieved by forcingthe material to move in compartments formed by the two screws and the barrel. Thedegree of intermeshing between the flight of one screw and the channel of the other screw,sense of rotation and speed distinguish the different kinds of screws (Fig. 7.3 [9]) from oneanother.
7.2 Processing Parameters
The factors affecting extrusion can be classified into resin-dependent and machine relatedparameters.
7.2.1 Resin-Dependent Parameters
Resin-dependent parameters are not the physical constants which one obtains bymeasuring the physical properties of the polymeric material. They are, however, similar tothese constants with the difference that they relate more to the process and processingconditions. If, for example, the processing temperature of a polymer is too high,degradation of the material leading to adverse material properties of the product mightoccur. Too low a processing temperature on the other hand may create a melt containingunmelted solids. The appropriate processing temperatures and pressures suited to aparticular resin and process are usually quoted by the resin manufacturers. These valuescan be maintained during the process by optimizing the processing conditions and, ifnecessary, the machinery such as extrusion screw or die [I].
SHANK FEED SECTIONCONSTANT ROOT DIA
TRANSITION SECTIONTAPERED ROOT DlA
-METERING SECTION-CONSTANT ROOT OIA!
Fig. 7.2: Geometries of some extrusion screws [20], [27]
e. KIM screw
d. Maillefer screw (variable pitch and constant depth)
c. Barr screw (variable depth and constant pitch)
b. Devolatilizing screw Extractionsection
a. Maddock mixing screw
feed transition metering
Pin mixing screw
feed transition meteringTwo stage screw
Metering screwfeed transition first meter vent transition second meter or pump
transition/compressionfeed
MAIN FLIGHT
SOLIDS CHANNELBARRIER FLIGHT
MELT CHANNEL
a b
counter-rotating corotating
non-intermeshing
closely intermeshing
Fig. 7.3: Geometries of some twin screws [9]
Melt temperature and pressure are important resin-dependent parameters which affect thequality of the product. Guide values of these parameters are given below for a few resinsand extrusion processes. They refer to the temperature and pressure of the melt at the dieentrance as shown in Fig. 7.4. These values are also known in the practice as stocktemperature and stock pressure, and depend not only on the type of the resin but also onthe grade of the resin used, which is characterized, for example, by the MFR value.
Fig.7.5: Blown film [9]
Blown Film (Fig. 7.5)
Characteristic values of melt temperature and pressure are given in Table 7.1.
basketrolls
bubble
winderextruder
air entry
Fig. 7.4: Position of measurement of melt pressure and melt temperature [9]
melt pressuremelt temperature
screen pack
breaker plate
flangedie
Table 7.1: Typical Values of Melt Temperature and Pressure for Blown Film
Pipe Extrusion (Fig. 7.6)
Table 7.2 shows some guide values of melt temperature and pressure for pipe extrusion.
Fig. 7.6: Pipe extrusion [9]
Table 7.2: Typical Values of Melt Temperature and Melt Pressure for Pipe Extrusion
Material
PE-LDPE-HDPE-LLDPPPA 6PCPETEVAEVOH
Melt temperature0C
140/210180/230190/230220/240270/280260/290260/280150/200200/220
Melt pressurebar
100/300150/300250/350200/300160/200150/250150/250100/200100/200
Material
PVC-UPVC-PPEHDPP
Melt temperature0C
180/185160/165180/200230/240
Melt pressurebar
100/200100/200150/250150/200
hopper withfeed controlextruder
diecalibration
water bath
haul off
air
Sheet Extrusion
A flat die is used in both flat film and sheet extrusion processes. Depending on thethickness of the product the term film or sheet is applied. Typical values for sheetextrusion are presented in Table 7.4.
Wire Coating
Melt temperatures for wire coating are approximately the same as those used for pipeextrusion. However, depending on the type of extrusion the pressure can range from 100bar to 400 bar.Melt temperatures and pressures for other resins and processes can be obtained from resinmakers. Data on processing conditions suited to attain resin compatible melt temperaturesis also supplied by resin manufacturers. This data includes values on extruder barrel
Fig. 7.7: Flat film extrusion [9]
Table 7.3: Typical Values of Melt Temperature and Pressure for Flat Film Extrusion
Material
PPPA 6PELDPEHD
Melt temperature0C
230/260260/280220/250220/230
Melt pressurebar
150/200100/200100/250150/250
Flat Film Extrusion (Fig. 7.7)
Typical values of melt temperature and pressure for flat film extrusion are given in Table7.3.
die
melt
Chill - roll
7.2.2 Machine Related Parameters
Although machine related parameters include effects due to resin properties, they are moreinfluenced by the geometry of the machine elements involved such as extrusion screw anddie than by resin properties. Fol lowing examples taken from single screw extrusion illus-trate the influence of the geometry of machinery on the target quantities of the process.
7.2.2.1 Extruder Output
Depending on the type of extruder the output is determined either by the geometry of thesolids feeding zone alone as in the case of a grooved extruder [11] or by the solids andmelt zones to be found in a smooth barrel extruder.
Feed Zone
The solids transport is largely influenced by the fiictional forces be tween the solidpolymer and barrel and screw surfaces. A detailed analysis of the solids conveyingmechanism was performed b y Darnell and MoI [16]. In the following example anempirical equation which gave good results in the practice is presented [1], [2].
Example:The geometry of the feed zone of a screw (Fig. 7.8), is given by the following data:
barrel diameter D b = 30 m mscrew lead s = 30 m mnumber of flights v = 1flight width wFLT = 3 m mchannel width W = 28.6 m m
Material
PSP M M ASBABSPETPVC-UPVC-P
Melt temperature0C
190/220200/230210/230220/240280/285180/185160/165
Melt pressurebar
150/250200/250150/250150/250150/200100/20075/150
temperature, die temperature, screw speed, and depending on the process haul-off ratesand draw-ratios.
Table 7.4: Typical Values of Melt Temperature and Pressure for Sheet Extrusion
depth of the feed zone H = 5 mm
conveying efficiency r|F = 0.436
screw speed N = 250 rpm
bulk density of the polymer p0 = 800kg/m3
Fig. 7.8: Screw zone of a single screw extruder
The solids conveying rate in the feed zone of the extruder can be calculated according to
[2]W
G = 60 - /vN. /7 F - , r 2 -H .Db ( D b - H ) — sin ^ . cos (f> (7.2.1)W + WFLT
with the helix angle O
$ = tan"1 [s/ (n -Db)] (7.2.2)
The conveying efficiency rj¥ in Eq. (7.2.1) as defined here is the ratio between the actualextrusion rate and the theoretical maximum extrusion rate attainable under the assumptionof no friction between the solid polymer and the screw. It depends on the type of polymer,bulk density, barrel temperature, friction between the polymer, barrel and the screw.Experimental values of r/¥ for some polymers are given in Table 7.4A.
Solution:Inserting the values above with the dimensions in meters into Eq. (7.2.1) and Eq. (7.2.2)we get
G = 60 • 800 • 250 • 0.44 • n2 • 0.005 • 0.03 • 0.025 • ° > 0 2 5 6 • 0.3034 • 0.9530.0286
Hence G « 50 kg/h
flight clearance 5FLT
screw channel
screw
screw lead s
barrel
Metering Zone (Melt Zone)
Starting from the parallel plate model and correcting it by means of appropriate correctionfactors [3] the melt conveying capacity of the metering zone can be calculated as follows[3]:
Although the following equations are valid for an isothermal quasi-Newtonian fluid,there were found to be useful for many practical applications [I].These equations can be summarized as follows:Volume flow rate of pressure flow Q (Fig. 7.8A):
(7.2.3)
Fig. 7.8A: Drag and pressure flow in screw channel
Table 7.4A: Conveying Efficiency r\Y for Some Polymers
PolymerPE-LDPE-HDPPPVC-PPAPETPCPS
Smooth barrel0.440.350.250.450.20.170.180.22
Grooved barrel0.80.750.60.80.50.520.510.65
BARREL SURFACE
PRESSURE FLOW1 SxpDRAGFLOW, v2p
SCREW ROOT
COMBINED DRAG AND PRESSURE FLOW
OPENDISCHARGE
CLOSEDDISCHARGE
h
Mass Flow Rate rhp
mp = 3600-1000 QpPm (7.2.4)
Drag Flow Qd (Fig. 7.8A)
(7.2.5)
Mass Flow Rate ma
rh d = 3600-1000 Q d p m (7.2.6)
Leakage Flow QL
To avoid metal to metal friction, extrusion screws have a small clearance between the topof the flight and the barrel surface. This clearance reduces the pumping rate of the meltbecause it enables the polymer to leak across the flights. The net flow rate Q is therefore
(7.2.7)
The melt conveying rate of the metering zone can be finally calculated from [1]
(7.2.8)
where ad = - mp / md and J = 5FLT /H
Average shear rate in the metering channel
K = n Db N/ 60- H (7.2.9)
Symbols and units used in the equations above
Db : Barrel diameter [mm]H : Channel depth [mm]e : Flight width [mm]s : Screw lead [mm]8 F L T : Flight clearance [mm]L : Length of metering zone [mm]Q ' Qd : Volume flow rate of pressure and drag flow, respectively [m3/s]
ihp, riid' Mass flow rate of pressure and drag flow respectively [kg/h]rh : Extruder output [kg/h]
Ap : Pressure difference across the metering zone [bar]v : Number of flightsr|a : Melt viscosity [Pa • s]y a : average shear rate [s1]pm : density of the melt [g/cm3]ad : Ratio of pressure flow to drag flowN : Screw speed [rpm]
Example:For the following conditions the extruder output is to be determined:melt viscosity r|a = 1406.34 P a s ; N = 80 rpm Ap = 300 bar; pm = 0.7 g/cm3
Geometry of the metering zone (Fig. 7.8)Db = 6 0 m m ; H = 3 m m ; e = 6 m m ; s = 6 0 m m ; 5FLT = 0 .1mm;L = 600 mm; v = 1Substituting these values into the equations above one obtains
nip = 3.148 k g / h Eq. (7.2.4)
ihd = 46.59 k g / h Eq. (7.2.6)m = 41.88 k g / h Eq. (7.2.8)
Leakage flow mi = rhd + m p - rh = 1.562 k g / hWith the help of Eq. (7.2.8) the effect of different parameters on the extruder output is
presented in Figs. 7.9A-H by changing one variable at a time and keeping all othervariables constant. The dimensions of the screw used in these calculations are taken fromthe example above.
extru
der o
utput
(kg/h)
screw speed (rpm)Fig. 7.9A: Effect of screw speed on extruder output
extru
der o
utput
(kg/h
)ex
trude
r outp
ut (kg
/h)
channel depth (mm)
Fig. 7.9B: Effect of channel depth on extruder output
flight clearance (mm)
Fig. 7.9C: Effect of flight clearance on extruder output
extru
der o
utput
(kg/h)
extru
der o
utpu
t (kg
/h)
melt pressure (bar)
Fig. 7.9D: Effect of melt pressure on extruder output
melt viscosity (Pa s)
Fig. 7.9E: Effect of melt viscosity on extruder output
extru
der o
utpu
t (kg
/h)
extru
der o
utpu
t (kg
/h)
screw lead (mm)
Fig. 7.9G: Effect of screw lead on extruder output
melt temperature ("C)
Fig. 7.9F: Effect of melt temperature on extruder output
channel length (mm)
Fig. 7.9H: Effect of channel length on extruder output
Correction FactorsTo correct the infinite parallel plate model for the flight edge effects following factors canbe used along with the equations above:With sufficient accuracy the shape factor Fd for the drag flow can be obtained from [27]
Fd = 1-0.571 ^ (7.2.10)
and the factor Fp for the pressure flow
Fp = 1-0.625 ^ - (7.2.11)W
The expressions for the corrected drag flow and pressure flow would then be
Qdk = Fd-Qd (7.2.12)
andQpK = Fp-Op (7-2-13)
The correction factor for the screw power which is treated in the next section can bedetermined from [1]
Fx = ex - x3 + 2.2 x2 - 1.05x (7.2.14)
with x =H/W.Eq. (7.2.14) is valid in the range 0 < HAV < 2. For the range of commonly occurring
H/W-ratios in extruder screws the flight edge effect accounts for only less than 5% andcan therefore neglected [27]. The influence of screw curvature is also small so that Fx can
extru
der o
utput
(kg/h)
be taken as 1. Although the above mentioned factors are valid only for Newtonian fluids;their use for polymer melt flow is accurate enough for practical purposes.
7.2.2.2 Melting Parameter
The melting rate is described by TADMOR [2] through the parameter Op which is ex-pressed as [2], [1] (see also Fig. 7.10).
(7.2.15)
Fig. 7.10: Velocity and temperature profiles in the melt and solid bed after TADMOR [2]
The numerator represents the heat supplied to the polymer by conduction through thebarrel and dissipation, where as the denominator shows the enthalpy required to melt thesolid polymer. The melting rate increases with increasing Op. The dimensionless meltingparameter \\J is defined as [2]
K -HrW05" = - l ^ G - C«.I6)
This parameter is the ratio between the amount of melted polymer per unit down channeldistance to the extruder output per unit channel feed depth.The symbols and units used in the Eqns (7.2.15) and (7.2.16) are as follows:
Barrel temperature Tb 0C
Melting point of the polymer Tm 0C
Viscosity in the melt film r|f Pa • sVelocity of the barrel surface Vb cm/s
Velocity component Vbx cm/s (Fig. 7.10)Relative velocity V ; cm/sOutput of the extruder G g/sDepth of the feed zone H1 m mWidth of the screw channel W m mMelt density p m g/cm3
Specific heat of the solid polymer p p kJ/(kg • K)
Temperature of the solid polymer T s 0C
Thermal conductivity of the melt Xm W/(m • K)Heat of fusion of the polymer im kJ/kg
Numerical examples illustrating the calculation of melting rate and melting parameteraccording to Eqns. (7.2.15) and (7.2.16) have been given by R A O in his book [ I ] .
7.2.2.3 Melting Profile
The melting profile gives the amount of unmelted polymer as a function of screw length(Fig. 7.11), and is the basis for calculating the melt temperature and pressure along thescrew. It shows whether the polymer at the end of the screw is fully melted. Theplasticating and mixing capacity of a screw can be improved by incorporating mixing andshearing devices into the screw. The melting profile enables to judge the suitablepositioning of these devices in the screw [4]. Methods of calculating melting profile, melttemperature and melt pressure are given in the book by R A O [4].
Fig. 7.11: Solid bed and melting profiles XAV and Gs/G [2]G: total mass flow rate; Gs: mass flow rate of solids
7.2.2.4 Screw Power
The screw power consists of the power dissipated as viscous heat in the channel and flightclearance and the power required to raise the pressure of the melt. The total power Z N istherefore for a melt filled zone [5]
X/W.Gs
/G
Axial distance along the screwCross-section of screw channel
Melt Solid bed Melt film
Barrel
Screw
ZN = Zc + ZFLT + ZAp (7.2.17)
where Zc = power dissipated in the screw channelZFLT = power dissipated in the flight clearanceZAp
= power required to raise the pressure of the meltThe power ZAp is small in comparison with the sum Zc + ZFLT, and can be neglected. Ingeneral the power due to dissipation £d can be expressed for a Newtonian fluid as [1]
Ed = V Y2 (7.2.18)
Using the respective shear rates for the screw channel (Eq. (7.2.9)) and flight clearance theequation for the screw power can be derived [I].The power dissipated in the screw channel Zc is given by [1]
(7.2.19)
(7.2.20)
(7.2.21)
(7.2.22)
(7.2.23)
The symbols and units used in the equations above are given in the following example:
Example:For the following conditions the screw power is to be determined:
Resin: PE-LDOperating conditions:Screw speed N = 80 rpmmelt temperature T = 200 0Cdie pressure Ap = 300 barGeometry of the metering zone:Db =60 mm; H = 3mm; e = 6mm; s = 60mm; 8FLT = 0.1mm;AL = 600 mm; v = 1
Solution:Power Zc in the screw channel: DFLT = 59.8 mm from Eq. (7.2.22)
The power dissipated in the flight clearance can be calculated from [1]
The power required to raise the pressure of the melt ZAp can be written as
The flight diameter DFLT is obtained from
and the channel width W
Viscosity of the melt in the screw channel r|c at the average sheer rate 83.8 s"1
according to the Eq. (7.2.9) and T = 200 0C from the viscosity function of resinr|c = 1406.34 Pa • s
Channel width W = 51.46 from Eq. (7.2.23)Number of flights v = 1Length of the metering zone AL = 600 mmFactorFx:
Fx = 1 for HAV = 3/51.46 = 0.058 from Eq. (7.2.14)
Power in the screw channel Zc from Eq. (7.2.19)
_ lV-59.82-802-51.46-1406.34-600(l-cos217.66o+4-sin217.66°)_^ Qg1 wc 36-1014- 3-sinl7.66°
Power in the flight clearance ZFLT:Flight width WFLT(Fig. 7.8)
WFLT = e cos O = 6 • cos 17.66° = 5.7 mmViscosity at the average shear rate in the flight clearance
y = "Db-N , 2 5 1 3 .3 s->
and T = 200 0C from the viscosity function of the resinr|FLT = 219.7 Pa-s
Power in the flight clearance ZFLT from Eq. (7.2.20):
= lV.59.8 2 -8f600-5 .7-219.7 = L 5 6 k W
36-1014-0.1-0.303
Power to raise the melt pressure ZAp:Pressure flow Q :
Q from the example in Section 7.2.2.1
Qp = 1.249 -10-6m3/s
Die pressure Ap:
Ap = 300 bar
ZAp from Eq. (7.2.20):
ZAp = 100 • 1.249 • 10"6 A- 300 = 0.0375 kW
Hence the power ZAp is negligible in comparison with the sum Zc + ZFLT.
With increasing flight clearance, as it might occur due to wear in extruders the meltconveying capacity is reduced, since the leakage flow over the flight increases. Tocompensate for this reduction the screw speed has to be increased, if the output were toremain the same. This leads to an increase in the power ZN as shown in Table 7.4B.
7.2.2.5 Melt Temperature and Melt Pressure
Melt Temperature
The exact calculation of melt temperature can be done only on an iterative basis as shownin the computer program given in [4]. The temperature rise AT in an increment of thescrew can be found from [5]
4 T . ( T - _ T J . """-fa * Z r * NH) ( 7 2 2 4 )m-Cpm
where Zc, ZFLT = (see Section 7.2.2.4) (kW)NH = heat through the barrel (kW)rh = extruder output (kg/h)Tout = temperature of the melt leaving the increment (0C)Tm = melting point of the polymer (0C)
The average temperature 0.5 (Tin + Tout) can be taken as the stock temperature in theincrement, where Tin denotes the temperature of the melt entering the increment.
Temperature Fluctuation
Fluctuations of melt temperature in an extruder serve as a measure of the stability of ex-trusion and extrudate quality.
The temperature variation AT can be estimated for a 3-zone screw from the followingempirical relationship developed by Squires [19]:
A T = - (7.2.25)9 [4 .31 N Q - 0 . 0 2 4 J
for 0 . 1 K NQ < 0.5. The parameter NQ is given by
The power in the flight clearance ZFLT does mot vary much as the opposing effects ofviscosity and flight clearance nearly balance each other.
Table 7.4B: Effect of Flight Clearance on Screw Power for a PE-LD
5FLT
mm
0.10.150.2
0.250.3
ZFLT
kW
0.7110.710.65
0.6260.6
zckW2.732.832.933.0
3.15
ZN
kW
3.443.543.583.633.75
Nrpm
8081.5838486
where AT = temperature variation 0CDb = barrel diameter cmG = output g/sL = Length of screw zone in diametersH = depth of the screw zone cm
Example:Db = 6cm; G-15 g/s; L H L/H
9 0.9 103 0.6 (mean value) 3.339 0.3 30
Hence L/H = 43.33
NQ from Eq. (7.2.26)
NQ = 14.7 - 1 0 " 4 ~ -43.33 = 0.153
AT from Eq. (7.2.25)
AT = - I \ 1 = 7.22° C or ±3.61° C9|_4.31-0.1532-0.024j
The constants occuring in the Eqs. (7.2.26) and (7.2.25) depend on the type of polymerused. For screws other than 3-zone screws the geometry term in Eq. (7.2.26) has to bedefined in such a way that NQ correlates well with the measured temperature fluctuations.
Melt Pressure
The melt or stock pressure can be obtained from the pressure flow by means of Eq. (7.2.4)[1], [5]. The more exact calculation of the melt pressure profile in an extruder shouldconsider the effect the ratio of pressure flow to drag flow, the so-called drossel quotient asshown in [5].
Pressure Fluctuation
The effect of pressure fluctuations of the melt on the flow rate can be estimated by therelation [2]
(7.2.27)
Example:pressure drop Ap1 = 200 bar; Ap2 = 210 bar
flow rate Q1 = 39.3 Cm3/s
(7.2.26)
power law exponent n for PE-LD = 2.5Calculate the flow rate variation.
Solution:
Q1ZQ2 = 39.7/Q2 = (200/ 21O)25 = 0.885
Q2 = 44.9 cm3/s
44 9 - 39 7flow rate variation = (Q2 - Q1) / Q1 = — — = 13%
Ap 2 -Ap 1 210-200pressure variation = — L = = 5%
Ap1 200This means that a pressure variation of 5% can cause a flow rate fluctuation of 13%.
The influence of machine related parameters and operating variables on the melting ofsolid polymer is shown in Figs. 7.12A-L [2].
For given resin the fluctuation of the melt temperature depends mainly on the screwgeometry and output rate as shown in Fig. 7.13 [2].
Empirical design data for different screw geometries, resins and processes is given inFigs. 7.14A-E[Il].
REDU
CED
SOLID
BED
WID
TH X
/W
AXIAL DISTANCE
increasingoutput
screw
Fig. 7.12A: Influence of increasing output on solids melting in an extruder [2]
REDU
CED
SOLID
BED
WIDT
H XT
WRE
DUCE
D SO
LID B
ED W
IDTH
X/W
Fig. 7.12C: Influence of increasing screw speed and outputon solids melting in an extruder [2]
AXIAL DISTANCE
increasingscrew speed and
output
screw
Fig. 7.12B: Influence of increasing screw speed on solids melting in an extruder [2]
AXIAL DISTANCE
increasingscrew speed
screw
LEN
GTH
OF
MEL
TIN
G
LENG
TH O
F M
ELTI
NG
range ofextruder operation
SCREW LEAD
Fig. 7.12D: Relationship between length of meltingand screw lead in an extruder [2]
Fig. 7.12E: Relationship between flight clearance and length ofmelting for different resins in an extruder [2]
FLIGHT CLEARANCE
PPLDPE
LDPE PVC
MEL
T PR
ESSU
RE
Leng
th o
f mel
ting
Fig. 7.12G: Relationship between melt pressure and screwlength at increasing screw speed[2]
AXIAL DISTANCE FROM START OF THREAD
Number of channels in parallel
Fig. 7.12F: Relationship between length of melting andnumber of channels in an extruder [2]
screw
increasingscrew lead
MELT
PRE
SSUR
E
LENG
TH O
F M
ELTI
NG
Fig. 7.121: Relationship between melt pressure and screw length atconstant screw speed and increasing output [2]
AXIAL DISTANCE FROM BEGINNING OF THREAD
increasingoutput
Fig. 7.12H: Relationship between length of melting and barreltemperature at constant screw speed [2]
BARREL TEMPERATURE
constantsrew speed
MEL
T TE
MPE
RATU
REM
ELT
PRES
SURE
increasingoutput
SCREW LENGTH
Fig. 7.12J: Relationship between melt temperature andscrew length at increasing output [2]
screw
CONSTANTSCREWSPEEO
ANDOUTPUT
increasingscrew lead
SCREWLENGTH
Fig. 7.12K: Relationship between melt pressure and screw length at constantoutput and screw speed and increasing screw lead [2]
Tem
pera
ture
Flu
ctua
tion
Ampl
itude
POW
ER
Fig. 7.13: Relationship between melt temperature fluctuation, screw geometry and output [2]
Output
very shallow metering channel
shallow metering channel
deep metering channel
Fig. 7.12L: Relationship between power and barrel temperature at increasing output [2]
BARREL TEMPERATURE
increasingoutput
front edge of the
feed opening
Fig. 7.14A: Empirical screw design data [11]
L = 20 D to 24 D
"Wh t
lh,
mm
mmD
kg/hn m
«. -1mm
D
Fig. 7.14B: Empirical screw design data [11]
n [m
in ]
N A [k
W]
m
[kg/h
]
m /
n [kg
min
/h]
e [kW
h / k
g]
h,,h
3
L/D=20
mmD
mm
Fig. 7.14C: Empirical screw design data [11]
mmD
n mi, [
min ]
N mix[k
Vv]
h[mm]
m I n
[kg m
in /h]
D
Design data for a series
of grooved extruders
Fig. 7.14D: Empirical screw design data [11]
170=20; s=0,80
Screw built from standard modules for grooved blow molding extruders
screw flights screw tiphomogenizing
shearing section section
effective length L/D = 20
L =16-17D L =2-2,5D L =2,0-2,5 D
D
Comparison of specific through-put rates m/n of conventional and groovedextruders (material: HDPE, Lupolen 5021 D)a grooved extruder m/n = 6.6- 10"6D19 , bconventional extruder m/n = 3.1 • 10"6 • D17
Fig. 7.14E: Empirical screw design data [11]
7.3 Extrusion Dies
Extrusion dies can be designed by calculating shear rate, die pressure and residence timeof the melt as functions of the flow path of melt in the die [6]. Of these quantities the diepressure is most important as the desired throughput cannot be attained if the die pressuredoes not match with the melt pressure. The interaction between screw and die is shown inFig. 7.15.
Common shapes of flow channels occurring in extrusion dies are shown in Fig. 7.16.Detailed treatment of die design is presented in the book [1] and in [17]. Following areasof application of extrusion dies serve as examples to illustrate the relationship between diegeometry and processing parameters:
Dmm 2
m/n
kg min / h
extru
der o
utput
(kg/h)
extru
der o
utput
(kg/h)
Material: PA6
screw characteristics
die characteristics
channel depth: 3mmdie opening: 5mm
melt pressure (bar)
Fig. 7.15A: Effect of screw and die temperature
deep channel H=5mm Material: PA6
melt Temperature: 275°C
shallow channelH=3mm
large dieDiA=5mm
small dieDiA=4mm
melt pressure (bar)
Fig. 7.15B: Effect of channel depth and die opening
Fig. 7.16: Common shapes of flow channels in extrusion dies [1]
7.3.1 Pipe Extrusion
The spider die shown in Fig. 7.17 is employed for making tubes and pipes and also forextruding a parison required to make a blow-molded article. It is also used in blown filmprocesses.
Mandrel support die
Mandrel
Mandrelsupport"(spider)
Or breakerplate
Spiderlegs
Fig. 7.17: Mandrel support die with spider or break plate [17]
For a circular channel the shear rate is calculated from Eq. (3.2.1). For an annulus,which represents the pipe cross-section it is given by
(7.3.1)
(7.3.2)
(7.3.3)
(7.3.4)
for W/H > 20. For W/H < 20, Gslit has to be multiplied by the correction factor Fp given inFig. 7.18 as a function of HAV. The die constant Gannulus is calculated from
H = R 0 -R, (7.3.5)
W = Ti(R0 + ^ ) (7.3.6)
Gannuius follows then from
Gannulus ~
for (R0+ R4)/(R0-R1) £ 3 7 .For smaller values of this ratio Gannulus has to be multiplied by Fp given in Fig. 7.18. Theheight H and the width W are obtained in this case from Eqns. (7.3.5) and (7.3.6).
Facto
r Fp
Fig. 7.18 Correction factor Fp as a function of HAV [ 19]
Ratio H/W
WH
The pressure drop is obtained from [7]
where G, the die constant follows from
(7.3.7)
General Cross Section
By means of the substitute radius defined by Schenkel [18] the pressure drop in crosssections other than the ones treated above can be calculated. The substitute radius is ex-pressed by [18]
(7.3.8)
where R111 = substitute radiusA = cross-sectional areaB = circumference
On the basis of the substitute radius the pressure drop in the channel is calculated as inthe case of the circular channel [I].
Another method of calculating the pressure drop in channels of varied cross section ispresented in Fig. 7.19 [17], [19]. The correction factor Fp and the flow coefficient fj, havethe same values in comparable ranges of height to width of the channel.
In Table 7.5 the shear rates and die constants for different channel shapes are summarized.
Table 7.5: Shear Rates and Die Constants for Some Die Channel Shapes (Fig. 7.16) [1]
Channel shape
Circle
Slit
Annulus
Triangle
Square
Shear rate y [s1] Die constant G
Shape factor - g -
Fig. 7.19: Flow coefficient fp as a function of shape factor H/B [17]
The symbols and units used in the equations above are explained in the followingexample:
Example:It is required to calculate the pressure drop Ap of a PE-LD melt at 200 0C flowing throughan annular channel with an outside radius R0 = 40 mm, an inside radius R1 = 39 mm andlength L = 100 mm at a mass flow rate m = 10 g/ s.
Solution:
Volume flow rate Q = — = — = 14.29 —Pm 0.7
Flo
w c
oeffi
cien
t f P
Narrow slit
Rectangle
According to Squires
Square(Tp= 0,4217)
Circle
(f = 127T )[ p 1 2 8 }
Semicircle(f,=0,447)
Ellipse
mm
Length of flow path I
Fig. 7.20A: Melt pressure in a spider die [6]
or Q = 1.429-1(T5In3/swhere pm = melt density = 0.7 g/cm3
Shear rate from Eq. (7.3.1)
, = ^ ~2 = 6 ' L 4 2 9 ' 1 0 " 5 , - 3 5 4 . 4 7 . -n (R0 + R1) (R0 - R1)
2 n (0.04 + 0.039) (0.001)2
The given resin-dependent values which can also be calculated from flow curves (seeSection 3.2.7.2) are
n = 2.907T] = 579.43 Pa • sK=1.34-10'13
Pre
ssur
e dr
op A
P
bar
LDPE
m = 40kg/hTM= 1600C
Length of flow path I
Fig. 7.20B: Residence time in a spider die [6]
The die constant Gannulus follows from Eq. (7.3.7)
( w\ 2^907 - — 2 Il
.(0.04 + 0.39)2907 -(0.00I)2907
r = S^lvJannulus O A 1
As the ratio Tc(R0+ RJV(R 0 -R 4 ) = 248.19 is greater than 37, no correction is necessary.
Therefore, Gannulus = 1.443 • 105.The pressure drop Ap is obtained finally from Eq. (7.3.2)
Ap = 400.26 bar
The residence time t in a channel of length AL can be written as
t = A L / u
mm
Res
iden
ce t
ime
t
s LDPE
m = 40 kg/hTM= 1600Chr = 2 mm
Length of flow path I
Fig. 7.20C: Shear rate in a spider die [6]
The average velocity u can be expressed in terms of shear rate, channel cross section andvolume flow rate. The adiabatic temperature increase of the melt in the die can be obtainedfrom
AT = A P (K) (7.3.9)1 O ' /VCpm
where AT = temperature rise (K)Ap = pressure difference (bar)pm = melt density (g/cm3)c p m = specific heat of the melt kJ/(kg K)
mm
She
ar r
ate
if
S"1
LDPETM ,1600Chr = 2mm
Using the equations above, the shear rate, residence time and pressure of the melt along aspider die are calculated and shown in Figs. 7.20A-C. As seen from these figures the diegap has a marked influence on the pressure [6].
Drawdown and Haul-Off Rates
Drawdown occurs when the velocity of the haul-off is greater than the velocity of theextrudate at the die exit. This leads to a reduction of the extrudate cross-section. The drawratio DR can be expressed as (Fig. 7.21)
Fig. 7.21: Draw-down in pipe extrusion
DR = D *! " 1 ^ t e l (7.3.10)ODpipe " IDpipe
The draw ratio is dependent on the resin and on the haul-off rate. In Fig. 7.22 [8] the ratioof die diameter to pipe diamteter which is referred in practice as the draw ratio is shown asa function of the haul-off rate for a PA resin. For other resins this ratio has to bedetermined experimentally.
Ratio
ofDie
diame
ter to
pipe d
iamete
r
Hauloffrate (m/min)
Fig. 7.22: Relationship between draw ratio and haul-off rate [8]
DdIe
mandrelODpipe
'Dpipe
pipedie
Table 7.6 shows typical data obtained on twin screw extruders for pipes. Design data forpipe dies and sizing units (Fig. 7.23) is given in Table 7.7 [12].
Table: 7.6: Typical Data for Twin-Screw Extruders for Pipes out of Rigid PVC [12]
Screw diameter Dmm
60/7080/90
100/110120/140
Screw lengthL/D18/2218/2218/2218/22
Screw speedmin"1
35/5030/4025/3820/34
Screw powerkw
15/2528/4058/7065/100
specific energykwh/kg0.1/0.140.1/0.140.1/0.140.1/0.14
Table 7.7: Die and Calibration Unit Dimensions Based on Empirical Results [12]
Pipe rawmaterial
PVC
PE
PP
PA121
PA122
PA122
Outerdiameterof pipe
mm201602016020160
82022
A
mm201602116821168
14.228.230.0
B
mm20.16161.3
21167.2
21167.2
8.620.8523.0
S in % ofnominal
wallthickness
479100100100100
2.03.33.3
a atpressure6 to 10
mm3015020
40/1751
2040/1751
S[mm]
2525/303
35/503
b
mm100/150500/600
15040150640
130130130
Haul-offspeed
m/min20/352.0/3.525/301.2/2.225/301.0/2.0
55/6012/1510/12
1WaIl thickness 1 mm2wall thickness 2 mm
dependent on wall thickness
Fig. 7.23: Design data for pipe dies and sizing units (see Table 7.7) [12]
7.3.2 Blown Film
The blow ratio is the ratio between the diameter of blown film to the die lip diameter(Fig. 7.24). The effect of operating variables such as coolant temperature in the case ofwater-cooled films on some film properties like gloss and haze is shown in Fig. 7.25 [9].Depending on the material and the type of film blow ratios range from 1.3 : 1 to 6 : 1 [26].
bQ
B •A
d i a m e t e r o f
b u b l e
d i a m e t e r o f
d i e l i p
b u b b l e
c o o l i n g r i n g
d i e
extruder
Fig.7.24: Blow-up in blown film
Fig. 7.25A: Effect of film thickness on haze [9]
Extruder throughputs for blown film lines for polyethylene are given in Table 7.8 [13].
Table 7.8: Data for High Performance PE-LD Blown Films Lines [13]
Side fed and spiral mandrel dies are employed in processes, in which the extruder is atan angle, usually 90°, to the direction of the extrudate (Fig. 7.26 [17]). These processesinclude making annular parisons for blow molding, cable coating and pipe jacketing, tomention a few examples.
In the extrusion of blown film spiral mandrel dies (Fig. 7.26 [17]) are widely usedtoday. The mixing of spiral flow and annular flow of the melt in these dies leads touniform flow distribution at the die exit, and owing to the lack of spider legs which disturbthe melt flow in a spider die there will be no weld lines on the film.
Side fed and spiral dies can also be designed using the equations given in the Section7.3.1. The principle here is to divide the die into a number of segments and by applyingthe pressure balance.
^ P spiral flow in the channel ^ P annular flow in the gap
to each segment calculate the height of the channel required for uniform flow. This can bedone conveniently by means of a computer program such as VISPIRAL [20].
haze
film thickness
Screw diameter Dmm6090120150
Maximum throughputkg/h200400550900
Extruder powerkW55110170300
glos
sha
ze
Fig. 7.25B: Effect of coolant temperature on haze [9]
coolant temperature
coolant temperature
Fig. 7.25C: Effect of coolant temperature on gloss [9]
7.3.3 Sheet extrusion
Dies for sheet and flat film extrusion have a rectangular exit cross-section (Fig. 7.16),where the die width W is usually much larger than the height of the slit H. The shear ratein a rectangular channel is calculated from
(7.3.11)
stiffn
ess
impa
ct str
engt
h
coolant temperature
Fig. 7.25D: Effect of coolant temperature on stiffness [9]
coolant temperature
Fig. 7.25E: Effect of coolant temperature on impact strength [9]
ease
of d
raw-
down
ease
of d
raw-
down
Fig. 7.25G: Effect of frost line on ease of draw-down [9]
height of frost line
Fig. 7.25F: Effect of blow-up ratio on ease of draw-down [9]
blow-up ratio
Fig. 7.26: Side-fed spiral mandrel dies [17]
The pressure drop in a sheet die can be obtained from the relation given by Chung andLohkamp [10]. For a uniform flow distribution the radius R(x) along the manifold(Fig. 7.27) is deduced to be [10]
Fig. 7.27: Scheme of a typical coat-hanger die [6]
In Fig. 7.28 the calculated manifold radius R(x) is shown as a function of the distance xalong the manifold [6]. The pressure drop in the die lip section is given in Fig. 7.28A as afunction of the die gap.
where n, is the reciprocal of the power law exponent n in Eq. (3.2.8).
(7.3.12)
Side fed die Spiral mandrel die
Mandrel
Spiral mandrelmanifold
ManifoldCoat-hanger section
Damper sectionChoker barsDie-lip section
Radi
us R
Distance x
Fig. 7.28: Manifold radius R(x) as a function of the distance x along the manifold [6]
mm
mm
pressure [bar]
die gap [mm]
Fig. 7.28A: Pressure drop in a flat die as a function of die gap
7.4 Thermoforming
In thermoforming the material initially in the form of a sheet or film is shaped undervacuum or pressure after it has reached a particular temperature. At this temperature thepolymer must have a sufficiently strong viscous component to allow for flow under stressand a significant elastic component to resist flow in order to enable solid shaping. Thus theoptimal conditions for thermoforming occur at a temperature corresponding to thematerial's transition from a solid rubber state to a viscous liquid state [21].
The effect of different factors related to thermoforming is presented in Figs. 7.29A-E[22] [23]. Some data including machine dependent parameters are given in the Tables 7.9to 7.12.
Dra
w r
atio
Stra
in
(Cold)rupture
Detailsnotreproduced
Discolorationdegradation
Holesand
splits
Temperature
Fig. 7.29A: Parametrical relationship for thermoforming:Draw ratio vs temperature
Acceptablequality
Optimum
Area ofrupture
Strainlevelreachedinfixed
time
Increasing strainingrate under fixed load
Fig. 7.29B: Parametrical relationship for thermoforming:Strain vs temperature
Temperature
INT
ER
NA
L S
TR
ES
S O
F F
OR
ME
D P
AR
TEN
ERG
Y FO
R FO
RMIN
G
HOT
STRE
NGTH
Fig. 7.29C: Parametrical relationship for thermoforming: Internal stress vs. sheet temperature
SHEET TEMPERATURE
SHEETTEMPERATURE
Fig. 7.29D: Parametrical relationship for thermoforming: Energy vs. temperature
CRYSTALLINEPOLYMER
AMORPHOUSPOLYMER
SHEET TEMPERATURE
Fig. 7.29E: Parametrical relationship for thermoforming: Hot strength vs. sheet temperature
The production rates for flat and thermoformable films are given in Figs. 7.30A/B [14]and in Table 7.9 [14]. Table 7.10 shows the thermoforming temperature ranges for variousthermoplastics [14].
take
-off
spee
d vmin
film thickness s
PE-LDPPPA-6
Fig. 7.30A: Production rates for flat films [14]
Table 7.9: Guide to Thermoforming Processing Temperatures [0C] [24]
Polymer
PE-HDABSPMMAPSPCPVCPSU
Mold tem-perature
7182888512960160
Lowerprocessing
limit
127127149127168100200
Normalforming
heat
146163177146191135246
Upper limit
166193193182204149302
Set tem-perature
8293939313871182
Table 7.10: Extruder Outputs for Thermoformable Film Extrusion(Film Thickness Range: 0.4 to 2.0 mm) [14]
Screwdiameter D
mm
7590105120150
Screw length
30/36 D30/36 D30/36 D30/36 D30/36 D
Outputkg/h
PP
180/200260/290320/350480/550650/750
SB
300/320450/500600/650750/850
1100/1200
ABS
220/250360/400450/480600/650850/900
PET
120/140180/220240/280320/360480/540
take -
off s
peed
v
min
Fig. 7.30B: Production rates for thermoformable films [14]
Table 7.11: Ranges of Melt and Roll Temperature Ranges Used inThermoformable Film [14]
film thickness smm
SB
ABS
PP
Material
PPSB
ABSPET
Melt temperature0C
230/260210/230220/240280/285
Chill roll temperature0C
15/6050/90
60/10015/60
Table 7.12: Shrinkage Guide for Thermoformed Plastics [24]
Polymer Shrinkage %PE-LD imoPE-HD 3.0/3.5ABS 0.3/0.8PMMA 0.2/0.8SAN 0.5/0.6PC 0.5/0.8PS 0.3/0.5PP 1.5/2.2PVC -U 0.4/0.5PVC-P 0.8/2.5
7.5 Compounding
In the compounding of polymers such as polyolefins and PVC twin screw extruders find awide application. Some machine data are given in the tables below.
Table 7.13: Machine Data of Non-Interrneshing Counter-Rotating Twin-ScrewMachines for Degassing [25]
Screw diameter Dmm150200250305380400
Screw speed nmin1
100/18087/15078/13570/12063/11058/100
Drive power NkW
120/250220/460370/750
600/1200970/20001500/3000
Throughput Gkg/h
670/12501200/23002000/37503300/60005400/100008300/15000
Table 7.14: Machine Data of Intermeshing, Co-Rotating Twin-Screw Extruders (ZSK)for the Concentration of Melts [25]
Screw diameter Dmm130170240300
Screw speed nmin"1
180/300150/250140/230110/180
Drive power NkW
150/240300/490
680/11001200/2000
Throughput Gkg/h
850/15001750/30004000/70007000/12000
Table 7.15: Data for the Reifenhaeuser-Bitruder with Intermeshing Counter-RotatingScrews for Compounding and Pelletizing of PVC-U and PVC-P [23]
Extruder
BT 80 -12 GBT 80-16 GBT 100-14 GBT 100-18 GBT 150-17 G
Screwdiameter
mm77779898150
Screw length
L/D1216141817
Drive powerN
kW25253337133
Heatingcapacity
kW1717313688
Output
kg/h120/230200/400300/550450/750650/1200
Coextrusion
In many cases a plastics product made from a single polymer cannot meet therequirements imposed on it. To create layered structures and benefit from the properties ofseveral resins in combination, coextrusion is evidely employed. Examples includemultiple layer flat and tubular films, cables with multiple layer insulation, multiple layerblow molded articles and many more.
To achieve these objectives, dies of different designs are used as shown in Fig. 7.30Cand in Fig. 7.30D [17]. A multilayer extrudate can be produced by conventional dies whenan adapter is used to feed the individual melt streams into the die inlet. They flow togetherthrough the die and leave it as a coextrudate (Fig. 7.30C) [17].
Fig. 7.30C: Adapter dies: a) Flat slit die, b) Blown film die
In the multi-manifold dies (Fig. 7.30D) [17] each melt is first fed separately anddistributed into the desired form. These partial streams are then combined just prior to theland area.
Fig. 7.30D: Multimanifold dies: a) Flat slit die, b) Blown film die [17]
a) b)
a) b)
Some advantages and disadvantages of adapter and multi-manifold dies aresummarized in Table 7.15A.
Table 7.15A: Comparison Between Adapter (Feedblock) Dies andMulti-Manifold Dies [17]
Type of die
Adapter(Feedblock) dies
Multi-manifold dies
Advantages
Any number of individuallayers can be combined.
1. Each melt can be adjustedindividually, if appropriateadjustment is available.2. The method of combiningthe melts inside the die underpressure improves the mutualadhesion of the layers.3. Materials with different flowbehavior (Table 7.16) and melttemperature can be processed
Disadvantages
Polymers used must havealmost identical flow behaviorand processing temperatures.
1. Die design is complicated.2. It is difficult to solve theproblem of thermal insulationof the individual channels fromeach other.3. For a combination of morethan four layers this type of diebecomes very complex andcostly.
Table 7.16: Examples of Compatibility Between Plastics for Co-Extrusion [24]
PE-LD
PE-HD
PP
IONOMER
PA
EVA
PE-LD
3
3
2
3
1
3
PE-HD
3
3
2
3
1
3
PP
2
2
3
2
1
3
IONOMER
3
3
2
3
3
3
PA
1
1
1
3
3
1
EVA
3
3
3
3
1
3
1: Layers easy to separate2: Layers can be separated with moderate effort3: Layers difficult to separate.
7.6 Extrudate Cooling
The cooling of extrudate is an important operation in downstream extrusion processing, asit sets a limit to the production rate. It is an unsteady heat transfer process, in which mostlyconduction and convection determine the rate of cooling. Transient conduction can bedescribed by means of Fourier number and simultaneous conduction and convection byBiot number. The magnitude of heat transfer coefficients which are necessary to estimatethe rate of cooling is given in Table 7.17 for different cooling media.
Table 7.17: Heat Transfer Coefficients for Different Types of Cooling
Mode of cooling Heat transfer coefficient a[W/(m2 • K)]
Air cooling by natural convection 5/10Air cooling by forced convection 20/80Water bath 1000/1800Water sprays | 2000/2500
Example [28]:A wire of polyacetal of diameter 3.2 mm is extruded at 190 0C into a water bath at 20 0C.Calculate the length of the water bath to cool the wire from 19O0C to a center-linetemperature of 140 0C for the following conditions:
Heat transfer coefficient cca = 1700 W/(m2 • K)Thermal diffusivity plastic = 10"7m2/sThermal conductivity \lastic = 0.23 W/(m • K)Haul-off rate of the wire VH = 0.5 m/s
Solution:
The Biot number Bi = ^ -A
where R = radius of the wire
Bi = 1 7 0Q-1-6 = 11.13 ; -L = 0.08461000-0.23 Bi
The temperature ratio 0Th :
( T ^ U = 140-20 = 120 = ( ) 7 0 6
(Ta-Tw) 190-20 170
The temperature ratio #Tb based on the center-line temperature is given in Fig. 7.31 as a
function of the Fourier number with the recoprocal of Biot number as parameter [29].
Fig. 7.31: Midplane temperature for an infinite plate [29]
The Fourier number Fo for #Tb =0.706 and 1/Bi = 0.0846 from Fig. 7.31 is
approximately Fo = 0.16.The cooling time tk follows from the definition of the Fourier number
—— — —— — — 0.16R2 (1.6-10"3)2 2.56-10
tk = 4.1 s
The length of the water bath is therefore
VH-tk = 0.5- 4 .1= 2.05 m
If the wire is cooled by spraying water on to ist as it emerges from the extruder, a heattransfer coefficient of oca = 3500 W / (m2 • k) can be assumed.
The Biot number is then
Bi = 3500 -1.6/ (1000 • 0.23) = 24.35
1/Bi = 0.041
The Fourier number from Fig. 7.31 is approximately
F0 «0.15
The cooling time tk follows froma • tk / R
2 = 10"7 • tk / (1.6 • 10"3)2 = 0.15
tk = 3.84s
Tempera
ture rat
io &\ b
Fourier number F0-a-t/X2
This value is not significantly less than the one in the case of cooling in the water bath,since the resistance to heat flow is mainly due to conduction.
Example:Cooling of a blown film for the following conditions:
thickness of the film: 70 JJ,melt temperature: 220 0Cfrost line temperature: 110 0Cair temperature: 20 0Coca = 120W/(m 2 -K)W = 0.242 W / ( m - K )thermal diffusivity a: 1.29 • 10"3 cm2/shaul-off speed: 60 m/min
The cooling time tk is to be calculated.
Solution:Temperature ratio Sn
0-n, = (110 - 20) / 220 - 20) = 0.45
Biot number Bi
Bi = 120 • 35 • 106/ 0.242 = 0.01736
1/Bi = 57.6
F0 from Fig. 7.31 for Sn = 0.45 and 1 / Bi = 57.6F0 = 42.5
n v ,- x2 'F 0 35-35-42.5-IQ3
Cooling time t k = - ^ - = ^ - ^ = 0.4 s
At a haul-off speed of 1 m/s the height of the film to the frost line will be approximately0.4 m.
Example:Cooling of a sheet for the following conditions:
thickness of the sheet s = 0.25 mmmelt temperature T0 = 240 0Croll temperature Tw = 20 0Cthermal diffusivity a = 1.13 • 10"3 mVs
^lastic = 0.12W/(m2.K)Ct3 = 1000 W/(m2-K)
haul-off speed =130 m/minThe length of contact between the sheet and the roll required to attain a sheet temperatureof 70 0C is to be calculated.
Solution:
The Biot number Bi = ^ ^X
Bi = 1000-0.125/0.12 = 1.04
1/Bi = 0.96
Gn = (70 -120) / 240 - 20) = 50 / 220 = 0.227The Fourier number F0 for 1 / Bi = 0.96 and Qn from Fig. 7.31
n v . + 0.125-0.125-2-103 _ . _ ,Cooling time tk = = = 0.276 s
k 102-1.13At a haul-off speed of 2.17 m/s the length of contact is L = 2.17 • 0.276 = 0.6 m. For a rolldiameter of D = 250 mm this amounts to 1.31 times the roll circumference.
The above examples give only a rough estimate of the actual values. More realisticresults can be obtained by using the software POLYFLOW [20].
7.6.1 Dimensionless Groups
Dimensionless groups can be used to describe complicated processes which are influencedby a large number of variables with the advantage that the whole process can be analyzedon a sound basis by means of a few dimensionless parameters.
The foregoing example shows their application in heat transfer applications. Their usein correlating experimental data and in scaling-up equipment is well known.
Table 7.18 shows some of the dimensionless groups which are often used in plasticsengineering.
Nomenclature:a : thermal diffusity [m2/s]g : acceleration due to gravity [m/s2]1 : characteristic lengthp : pressure [N/m2]tD : memory time [s]tp : process time [s]AT : temperature difference [K]w : velocity of flow [m/s]ota : outside heat-transfer coefficient [W/(m2 • K)]P : coefficient of volumetric expansion [K'1]PT : temperature coefficient in the power law of viscosity [1] [K"1]Ps : mass transfer coefficient [m/s]5d : diffusion coefficient [m2/s]r\ : viscosity [Pa • s]X : thermal conductivity (index i refers to the inside value) [W/(m • k)]v : kinematic viscosity [m2/s]tv : residence t ime [s]t : time [s]p : density [kg/m3]
Table 7.18: Dimensionless Groups
Symbol
BiBrDebFoGrGzLeN aN uPePrReShScSk
Name
Biot numberBrinkman numberDeborah numberFourier numberGrashof numberGraetz numberLewis numberNahme numberNusselt numberPeclet numberPrandtl numberReynolds numberSherwood numberSchmidt numberStokes number
Definition
a a • IA1
T]W2Z(X • AT)
a t / 1 2
g . ' p . A T - l 2 / v 2
l2/(a-tv)a/5d
Px • w2 • TiA.alA,wl/av/apwl/r)
v/8d
P • 1/(Tl • W)
Literature
1. Rao, KS.: Design Formulas for Plastics Engineers. Hanser, Munich 19912. Tadmor, Z., Klein, L: Engineering Principles of Plasticating Extrusion, Van Nostrand
Reinhold, New York (1970)3. Bernhardt, E. C.: Processing of Thermoplastic Materials, Reinhold, New York (1963)4. Rao, KS.: Computer Aided Design of Plasticating Screws, Hanser, Munich 19865. Klein, L, Marshall, DJ.: Computer Programs for Plastic Engineers, Reinhold, New York
19686. Rao, N. S.: Designing Machines and Dies for Polymer Processing with Computer Programs,
Hanser, Munich 19817. Procter, B.: SPE J. 28 (1972) p. 3248. Brochure: EMS Chemie 19929. Brochure: BASFA. G. 199210. Chung, CL, Lohkamp, D.T.: SPE 33, ANTEC 21 (1975), p. 36311. Fritz, HG.: Extrusion blow molding in Plastics Extrusion Technology, Ed. F. Hensen,
Hanser, Munich, 198812. Predohl, W., Reitemeyer, P.: Extrusion of pipes, profiles and cables in Plastics Extrusion
Technology, Ed. F. Hensen, Hanser, Munich, 198813. Winkler, G.: Extrusion of blown films in Plastics Extrusion Technology, Ed. F. Hensen,
Hanser, Munich, 198814. Bongaerts, H: Flat film extrusion using chill-roll casting in Plastics Extrusion Technology,
Ed. F. Hensen, Hanser, Munich, 198815. Rauwendaal, CJ.: Polymer Engineering and Science, 21 (1981), p. 109216. Darnell, W.H., andMoI, E.A.J.: Soc. Plastics Eng. J., 12,20 (1956)17. Michaeli, W.: Extrusion Dies, Hanser, Munich 199218. Schenkel, G.: Private Communication19. Squires, RH.: SPE-J. 16(1960), p. 26720. Rao, N.S., O'Brien, KT. and Harry, D.H: Computer Modelling for Extrusion and Other
Continuous Polymer Processes. Ed. Keith T. O'Brien, Hanser, Munich 199221. Eckstein, Y., Jackson, R.L.: Plastics Engineering, 5(1995)22. Ogorkiewicz, R.M.: Thermoplastics - Effects of Processing. Gliffe Books Ltd, London 196923. Titow, W. V.: PVC Technology, Elsevier Applied Science Publishers, London 198424. Rosato, D. V., Rosato, D. V.: Plastics Processing Data Handbook, Van Nostrand-Reinhold,
New York 199025. Hermann, H: Compound Lines in Plastics Extrusion Technology, Ed. F. Hensen, Munich
198826. Hensen, F.: Plastics Extrusion Technology, Hanser, Munich 198827. Rauwendaal, C: Polymer Extrusion, Hanser, Munich 198628. Ogorkiewicz, RM.: Thermoplastics and Design, John Wiley, New York 197329. Kreith, F., Black, W.Z.: Basic Heat Transfer, Harper & Row, New York 1980
8 Blow Molding
8.1 Processes
The different processes of blow molding, namely extrusion blow molding, injection blowmolding and stretch blow molding are illustrated in the Fig. 8.1 to 8.4 [1], [2], In Fig. 8.5[2], in addition to the aforementioned processes the principle of dip molding is brieflyexplained.
8.1.1 Resin-dependent Parameters
Melt Temperature and Pressure
Typical values of melt temperature and melt pressure for extrusion blow molding aregiven in Table 8.1.
Table 8.1: Melt Temperature and Pressure for Extrusion Blow Moldingof Some Polymers
Material
PE-LDPE-HDPPPVC-UPVC-P
Melt temperature0C
140/150160/190230/235180/210160/165
Melt pressurebar
100/150100/200150/200100/20075/150
Fig. 8.1: Extrusion blow molding [1]
Blown containerbeing ejected
Compressed air inflatesparison
Parison being extruded
PRESSPLATEN
Fig. 8.2: Injection blow molding [1]
Injecting preform Blow molding and ejection
1 2 3
4 5 6
Fig. 8.3: Extrusion stretch blow molding [2]
Fig. 8.4: Injection stretch blow molding [2]
Parison Swell
The wall thickness of the molding is related to the swelling ratio of the parison. Referringto Fig. 8.11 [3] the swelling thickness of the parison is given by
Bt = y h d (8.1.1)
and the swelling of the parison diameterBp = D1ZD, (8.1.2)
Using the relationship [4]Bt = B2
p (8.1.3)
it follows
K = K-KThe swell ratio Bp depends on recoverable strain [4], and can be measured.
Inject preform Reheat preform
Stretch blow molding andejection
EXTRUSION BLOWMOULDING
EXTRUSIONSTRETCHJ3LOW
MOULDING
INJECTIONBLOW MOULDING
INJECTIONSTRETCH_BLOW
MOULDING
DIP (DISPLACEMENT)BLOW MOULDING
MOULDEDARTICLE
MOULDEDARTICLE
Fig. 8.5: Sequence of operations in different blow molding processes [2]
transfer to second(article) mould,
stretch and blow,cool
MOULDEDARTICLE
PREFORM(CLOSE-ENDED
TUBE WITHFULLY FORMED
NECK)•pjnoui (appJB)
puo3ds O) JajsuBjj
blow, coot
MOULDEDARTICLE
MOULDED(ORIENTED)
ARTICLE
PREFORM(CLOSE-ENDED
TUBE WITHFULLY FORMED
NECK)
HOT MELTIN CAVITY
PREFORM(CLOSE-ENDED
TUBE WITHFULLY FORMED
NECK)
OPEN-ENDEDTUBE
(PARISON)
enclousc in mould
Mow, cool
enclose in first(preform) mould.
blow(possibly cool)
extrusionPLASTICSFEEDSTOCK
PLASTICSFEEDSTOCK
PLASTICSFEEDSTOCK
injectionmoulding
extrusion
or injection
transfer to second(article) mould,
blow, cool
transfer to second(article)mould,
blow, cooT
dip mandrel into meltin cavity
complete shaping ofpreform round mandrelby piston push on melt
Average parison swell for some polymers is given in Table 8.2 [I].
Table 8.2: Average Parison Swell for Some Polymers [1]
Polymer Swell%
PE-HD (Phillips) 15/40PE-HD (Ziegler) 25/65PE-LD 30/65PVC-U 30/35PS 10/20
_PC I 5/10
Processing Data for Stretch Blow Molding
Table 8.3: Data on Stretch Blow Molding for Some Polymers [1]
Polymer
PETPVCPPPAN
Melt temperature0C
250200170210
Stretch orientationtemperature 0C
88/11699/116121/136104/127
Maximum stretchratio16:17: 16: 19 :1
Volume Shrinkage
Table 8.4: Volume Shrinkage of Stretch Blow Molded Bottles (Seven Days at 270C) [1]
Type of bottle I Percent
Extrusion blow molded PVCImpact-modified PVC (high orientation) 4.2Impact-modified PVC (medium orientation) 2.4Impact modified PVC (low orientation) 1.6Non-impact modified PVC (high orientation) 1.9Non-impact modified PVC (medium orientation) 1.2Non-impact modified PVC (low orientation) 0.9PET 1.2
8.1.2 Machine Related Parameters
Blow Molding Dies
As the parison is always ejected downward and the position of the extruder beinggenerally horizontal, the term cross-head dies may be applied to blow molding dies. Thesecan be of the spider type (Fig. 8.6) [5] or side fed dies as shown schematically in Fig. 7.26[6]. As mentioned earlier, these dies can be designed by using the equations given inSection 7.3.1.
The interaction of various factors influencing blow molding operations is presented inFigs. 8.7-8.9 [7] and Fig. 8.10 [8]. Data on air blowing pressures and temperatures forcavities in blow molds are given in Tables 8.6 and 8.7 respectively.
Table 8.6: Data on Air Blowing Pressures [1]
Polymer Pressurebar
Acetal 6.9/10.34PMMA 3.4/5.2PC 4.8/10.34PE-LD 1.38/4.14PE-HD 4.13/6.9PP 5.2/6.9PS 2.76/6.9PVC-U 5.2/6.9ABS 3.4/10.34
Choice of Material
Table 8.5: Data for Choosing Blow Molding Materials [8]
Polymer
High-impact PVC-UPE-LDLow-impact PVC-UHigh-impact PPPE-HDLow-impact PP
Appearance in blowmolded form
clear high glosstransculent, high glossvery clear, high gloss
rather opaque, low glossrather opaque, low gloss
transculent, moderate gloss
Cost for equivalent stiffness(PE-LD=IOO)
10410087797671
Table 8.7: Recommended Temperature for Cavities in Blow Molds [1]
Polymer Temperature0C
PE and PVC 15/30PC 50/70PP 30/60PS 40/65PMMA 40/60
Elbow joint
Tip of Mandrel
Spider legs
die body
mandrel
die ring
parison
Extruder
Fig. 8.6: Application of spider die in blow molding [3]
BottleweightDieswell
Melt temperature
Bottleweight
Polymer die swell
Polymerdieswell
Die land length
Output Output Output
Wall thickness Melt temperature Blowing pressure
Circum-ferentialwailthicknessvariation
Criticalshearrate
Parisondraw-down(sag)
Extrusion rate Die gap Melt index
Parisondraw-down(sag)
Parisondraw-down(sag)
Parisondraw-down(sag)
Extrusion rate Parison weight Parison formation time
Pinchoffproper-ties
Pinchoffproper-ties
DielinesPartingline
Melt temperature Melt index Blowing pressure
Fig. 8.7: Relationship between machine and materialvariables in extrusion blow molding process [7]
Degreeof orien-tation inmolding
Shrinkage
ComponentIZODimpactstrengthalong lineof flow
Density ofcrystallinepolymers
Unit moldclampingpressure
Densityof crys-tallinepolymers
Weldtensilestrength
Neatdistortiontemper-ature
Shrinkage
Shrinkage Coolingtime
Partweight
Moldinggloss
Pressurelossthroughgate
Compo-nent f.w.impactstrength
Mold temperature
k Jthicicness Injectionpressure
PackingtimeMelttemperature
Melt temperature Melt temperature
With flow
Across flow
Mold temperature Packing time Melt temperatureMold temperature
With flow
Across flow
Melt temperature Cavity thickness Packing time/pressure
Mold temperature Melt temperature
Restricted gate
Open gate
Packing time
Long flowpath
Shortflow path
Cavity thickness Distance from gate injection pressure
Fig. 8.8: Relationship between machine and materialvariables in injection blow molding process [7]
Fig. 8.9: Relationship between machine and materialvariables in injection blow molding process
Melt temperature
Weldtensilestrength
Cavity thickness Injection rate Mold temperature
ShrinkageRestrictedgate
Open gate
Pressurelossthroughrunner
Impactstrength
Along line of flow
Across line of flow
Packing time Melt temperature Packing pressure
Heatdistortiontemper-ature
Densityofcrystal-linepolymers
Cavitypressure
Density ofcrystallinepolymers
Flexuralandtensilestrengthin lineof flow
Cavity thickness Melt temperature
Differen-tialshrinkage
Melt temperature
Cavity thicknessGate areaDistance from gate
Weldtensilestrength
Shrinkagein lineof flow
Coolingtime
Post moldingshrinkageofcrystallinepolymer
Ageing time Gate area Melt temperature
Impactstrength
Pressurelossthroughgate
Cold moldHot mold
Annealed
Along line of flow
Across line of flow
STIFFN
ESSTHIC
KNESS
FOR EQ
UIVALEN
T STIFF
NESS
COST FO
R EQUIV
ALENT
STIFFNE
SS
DENSITY IN g / c m J
Variation of stiffness with density for polyethylene
DENSITY IN g/cmJ
Relationship between thickness for equivalent stiffnessand density for polyethylene
DENSITY IN g/cm1
Relationship between cost for equivalent stiffness anddensity for polyethylene
Fig. 8.10: Relationship between product stiffness, materialdensity and cost in blow molding process [8]
Fig. 8.11: Wall thickness of parison and molding in blow molding [3]
Literature
1. Rosato, D. V., Rosato, D. V.: Plastics Processing Data Handbook, Van Nostrand-Reinhold,New York 1990
2. Titow, W.V.: PVC Technology, Elsevier Applied Science Publishers, London 19843. Morton-Jones, D.H.: Polymer Processing, Chapman and Hall, New York 19814. Cogswell, F.N.: Polymer Melt Rheology, John Wiley, New York 19815. BASF Brochure on Blow Molding 19706. Michaeli, W.: Extrusion Dies, Hanser, Munich 19927. Rosato, D. V., Rosato, D. V.: Injection Molding Handbook, Van Nostrand-Reinhold, New
York 19868. Glyde, BS.: Blow Moulding in Thermoplastics, Effects of Processing, Ed. R.M.
Ogorkiewicz, Gliffe Books Ltd, London 1969
molding
mold
DP
Dm
9 Injection Molding
Among the polymer processing operations injection molding (Fig. 9.1) has found thewidest application for making articles which can be put to direct use.
Fig. 9.1: The three stages of injection molding: injection, plastication, ejection [1]
The molding equipment consists of an injection unit, an injection mold and a moldtemperature control unit. The quality of the part depends on how well the interactionbetween these components functions.
Part is ejectedNozzle oreoks o<f
Stage 3. EjectionMote opens
Screw rotatesat the end of
holding pressure
Mold fitted.Port is cooling
Stoge 2 . Holding Pressure end Plostication
Heater band
advances
Screw
Feed hoDOerStoge 1 . Injection
Moid partially filled
Barrel
At an appropriate point in the typical molding cycle (Fig. 9.1) the screw remains sta-tionary in the forward position (Fig. 9.1A) as indicated by phase 5 in Fig. 9.1B [22]. At theend of dwell or holding pressure the screw begins to rotate conveying plastic material anddeveloping a pressure ahead of the screw. This pressure pushes the screw to move back apredetermined distance which is dependent on the desired volume of the molded part. Thescrew is then idle in the back position while the previously molded plastic continuescooling in the mold, and while the mold is open and part ejected. After the mold closes,the screw is forced forward by the hydraulic pressure, causing the newly recharged shot infront of the screw to flow into the empty mold. A valve, such as a cheek ring (Fig. 9.7A),prevents back flow during injection. The screw then maintains pressure on the moldedplastic for a specific time called dwell or hold time, thus completing the cycle [7].
Fig. 9.1A: Injection molding process [22]
The important processing variables in an injection molding process and their effect onthe plastic material and part are shown in Fig. 9.1C, in which the cavity pressure isillustrated as a function of time during the molding of a part [I].
As in extrusion, the processing parameters can be classified into resin-dependent andmachine-related parameters.
9.1 Resin-Dependent Parameters
9.1.1 Injection Pressure
Injection pressure is the pressure exerted on the melt in front of the screw tip during theinjection stage, with the screw acting like a plunger [I]. It affects both the speed of the
step 1: start of ptastication step 4: start of injection
step 2- end of plastication step S: end of injection and cooling of the molding
step 3: closing the mold step 6 = ejection of molding
advancing screw and the process of filling the mold cavity with the polymer melt, andcorresponds to the flow resistance of the melt in the nozzle, sprue, runner and cavity. Theinjection pressures needed for some resins are given in Table 9.1 [I]. The maximuminjection pressure is approximately 1.2 times the pressure listed in Table 9.1.
Table 9.1: Injection Pressure Required for Various Plastics [1]
Material
ABSPOMPEPAPCPMMAPSRigid PVCThermosetsElastomers
NLow viscosityheavy sections
80/11085/10070/10090/110100/120100/12080/100100/120100/14080/100
ecessary injection presMedium viscositystandard sections
100/130100/120100/120110/140120/150120/150100/120120/150140/175100/120
sure [MPa]High viscosity
thin sections, small gates130/150120/150120/150>140< 150< 150
120/150>150
175/230120/150
closing the moldinjection unit forwardfilling
injection cycle
startpnriopening the moldpart ejection
holding pressure
injection unit backwardplasticating
Fig. 9. IB: Molding cycle [22]
cdounq
Fig. 9.1C: Cavity pressure profile over time [1]
9.1.2 Mold Shrinkage and Processing Temperature
Due to their high coefficients of thermal expansion components molded from plasticsexperience significant shrinkage effects during the cooling phase. Semi-crystallinepolymers tend to shrink more, owing to the greater specific volume difference betweenmelt and solid. Shrinkage S can be defined by [2]
S = 1 ^ (9.1.1)
where V is any linear dimension of the mold and L, the corresponding dimension of thepart when it is at some standard temperature and pressure. As a consequence of moldshrinkage it is necessary to make core and cavity slightly larger in dimension than the sizeof the finished part.
Processing temperature, mold temperature and shrinkage are given in Table 9.2 for anumber of materials [I].
The parameters influencing shrinkage behavior are shown in Fig. 9.2 [17].
Cavit
y pr
essu
re
Holding pressurestage-Effects from:temperature ofcavity waitdeformation of moldstability ofclamping unitmagnitude ofclamping forceEffects ona. material:crystallinitymolecular orientatiorinside the partshrinkageb. parts:weightdimensionsvoidssink marksrelaxationease of ejection
Compressionstage-Effects from*•switch-over toholding pressure•control ofpressure reserveEffects on-crystallinity•anisotropyb. parts:completenessof molded part•flash formationweight
Injection stage-Effects from:injection speedtemperature ofhydraulic oil.melt and mold•viscosity ofmaterialpressuredependencyof screw driveEffects ono. material:viscositymoleculardegradationcrystallinitymolecularorientationin part surfaceb. parts:surfacequality
Injection stageCompression stage
TimeHolding pressure stage
Table 9.2: Processing Temperatures, Mold Temperatures, and Shrinkage for the MostCommon Plastics Processed by Injection Molding [1]
Material
PSHI-PSSANABSASAPE-LDPE-HDPPPPGRIBPMPPVC-softPVC-rigidPVDFPTFEFEPPMMAPOMPPOPPO-GRCACABCPPCPC-GRPETPET-GRPBTPBT-GRPA 6PA 6-GRPA 66PA 66-GRP A I lPA 12PSOPPSPURPFMFMPFUPEP
Glass fiber content%
30
30
10/30
20/30
30/50
30/50
30/35
40
30/80
Processingtemperature 0C
180/280170/260180/270210/275230/260160/260260/300250/270260/280150/200280/310170/200180/210250/270320/360
210/240200/210250/300280/300180/230180/230180/230280/320300/330260/290260/290240/260250/270240/260270/290260/290280/310210/250210/250310/390
370195/23060/8070/8060/8040/60ca.70
Mold temperature0C
10/105/75
50/8050/9040/9050/7030/7050/7550/80
7015/5030/50
90/100200/230
50/70>90
80/10080/10050/8050/8050/8080/100100/120
140140
60/8060/8070/12070/12070/12070/12040/8040/80
100/160> 15020/40
170/190150/165160/180150/170150/170
Shrinkage%
0.3/0.60.5/0.60.5/0.70.4/0.70.4/0.61.5/5.01.5/3.01.0/2.50.5/1.2
1.5/3.0>0.5-0.53/6
3.5/6.0
0.1/0.81.9/2.30.5/0.7<0.70.50.50.50.8
0.15/0.551.2/2.01.2/2.01.5/2.50.3/1.20.5/2.20.3/1
0.5/2.50.5/1.50.5/1.50.5/1.5
0.70.20.91.2
1.2/20.8/1.80.5/0.8
0.2
shrin
kage
shrin
kage
shrin
kage
shrin
kage
shrin
kage
shrin
kage
Sch
rinka
ge
wall thickness holding pressure time holding pressure
wall temperature melt temperature injection speed
cavity pressure
PE-HDPP
PS
Fig. 9.2: Qualitative relations between individual process parametersand shrinkage behavior [17]
9.1.3 Drying Temperatures and Times
As already mentioned in Section 6.1.4 plastics absorb water at a rate depending on therelative humidity of the air in which they are stored (Table 9.3) [3].
9.1.4 Flow Characteristics of Injection-Molding Resins
The flow behavior of injection-molding materials can be determined on the basis of meltflow in a spiral channel. In practice a spiral-shaped mold of rectangular cross-section withthe height and width in the order of a few millimeters is often used to classify the resinsaccording to their flowability (Fig. 9.3). The length L of the solidified plastic in the spiralis taken as a measure of the viscosity of the polymer concerned (Fig. 9.4).
Table 9.3: Equilibrium Moisture Content of Various Plastics Stored in Air at 230Cand Relative Humidity 50% [3]
Equilibriummoisture (%)Water contentacceptable forinjectionmolding [%]
CA2.2
0.2
CAB1.3
0.2
ABS1.5
0.2
PA63
0.15
PA662.8
0.03
PBT0.2
0.02
PC0.19
0.08
PMMA0.8
0.05
PPO0.1
0.02
PET0.15
0.02
Moisture and monomers have an adverse effect on processing and on the part. To removemoisture, materials are dried in their solid or melt state. Table 9.4 shows the drying tempe-ratures and times for different resins and dryers [I].
Table 9.4: Drying Temperatures and Times of Various Dryers [1]
Material
ABS
CA
CAB
PA 6
PA 66,6.10
PBT, PET
PC
PMMA
PPO
SAN
Drying temperature0C
fresh air/mixedair dryers
80
70/80
70/80
not recomm.it
120
120
80
120
80
dehumidifyingdryers
80
75
75
75/80
75/80
120
120
80
120
80
Drying timeh
fresh air/mixedair dryers
2/3
1/1.5
1/1.5
3/4
2/4
1/2
1/2
1/2
dehumidifyingdryers
1/2
1
1
2
2
2/3
2
1/1.5
1/1.5
1/1.5
flo
w l
ength increasing
spiral height
Fig. 9.3: Flow length in a spiral test as a function of the resin MFI
spiralcoolingchannelcooling channel
moUSng rumer cooling channel
Fig. 9.4: Flow Length L as function of the spiral height H [4]
Fig. 9.4 shows the experimentally determined flow length L as a function of the heightH of the spiral for polypropylene. A quantitative relation between L and the parametersinfluencing L such as type of resin, melt temperature, mold temperature and injectionpressure can be developed [4] by using the dimensionless numbers as defined by Thorne[5]. As shown in [4] the Graetz number correlates well with the product Re-Pr- Br.
Gz = f (Re-Pr-Br), (9.1.2)
from which an explicit relationship for the flow length L can be computed.
Example [4]:This example illustrates the calculation of the dimensionless numbers Gz, Re, Pr and Brfor the given data and for resin-dependent constants given in [4]:
Width of the spiral W = 10 mmHeight of the spiral H = 2 mmFlow length L = 420 mmMelt density p = 1.06 g/cm3
Specific heat cp = 2kJ/(kg-K)Thermal conductivity X = 1.5W/(m-K)Melt temperature TM = 27O0CMold temperature Tw = 7O0CMass flow rate G = 211.5kg/h
Solution:The conversion factors for the units used in the following calculation of the dimensionlessnumbers are
F1=O-OOl ; F2=IOOO ; F3 = 3600
The Graetz number Gz is calculated from
Flow
length
L
Spiral height H
mm
PP
mm
with G in kg/h and L in mm.From the above data Gz = 186.51.The Reynolds number is obtained from
F T V ( 2 " n R ) - O- FT* n R
Re = ^ - ^ - £ - ^ (9.1.4)k
where Ve = velocity of the melt front in m/sH* = half-height of the spiral in mmnR = reciprocal of the power law exponent
The viscosity r| can be calculated from the melt temperature and shear rate [4].For the given values Re = 0.03791 [4].With H* in m and Ve in m/s we get for the Prandtl number Pr
Fvk*-Cn-H*(1"nR)
* 2 K C p H
A-V^n R )
Pr= 103 302.87
The Brinkman number Br [5]Br = * — ^ S (9.1.6)
A - ( T M - T W )
Ve follows from Ve = - ^ - with Q = —.W-H p
Br =1.9833
Finally the product Re-Pr- Br is 7768.06.From the plot of Gz vs Re-Pr-Br (Fig. 9.5) [4], which is obtained by measuring the
flow length at different values of spiral height, melt temperature and flow rate the Graetznumber corresponding to the calculated product of Re-Pr-Br is read and finally the flowlength L calculated from this number.
Symbols and units used in the formulas above:
Br Brinkman numbercp Specific heat kJ/kg-KY Shear rate s"1
G Mass flow rate kg/hGz Graetz numberH Height of the spiral mmH* Half-height of the spiral mm
(9.1.3)
L Length of the spiral mmUx Reciprocal of the power law exponentPr Prandtl number
Q 0 Volume flow rate m3 /sRe Reynolds numberTM Melt temperature 0CT w Mold temperature 0CV e Velocity of the melt front m/sW Width of the spiral m mX Thermal conductivity W/m-Kp Melt density g/cm3
rj Melt viscosity Pas
In the case of thermosetting resins the flow can be defined as a measure of melt viscosity,gelation rate and subsequent polymerization or cure [18].
Fig. 9.5: Dimensionless groups for determining the flow length L in s spiral test
9.2 Machine Related Parameters
9.2.1 Injection Unit
The average travel velocities of injection units (Fig. 9.6) [1] are given in Table 9.5 [I].Table 9.6 [1] shows the common forces with which the nozzle is in contact with the spruebushing. This contact pressure prevents the melt from leaking into the open at the interfacebetween nozzle and sprue bushing [I].
Grae
tz num
ber G
z
RePrBr
Fig. 9.6: Components of a reciprocating screw injection [1]
9.2.2 Injection Molding Screw
The plastication of solids in the reciprocating screw of an injection molding machine ia abatch process consisting of two phases. During the stationary phase of the screw meltingtakes place mainly by conduction heating from the barrel. The melting during screwrotation time of the molding cycle is similar to that in an extrusion screw but time-dependent. At long times of screw rotation it approaches the steady state condition ofextrusion melting [6], [7].
Table 9.5: Travel Velocity of the Injection Unit [1]
Table 9.6: Contact Force Between Nozzle and Sprue Bushing [1]
Clamping force Contact forcekN kN
lOO 50/801000 60/905000 170/22010 000 220/28020 000 I 250/350
Clamping forcekN
<500501/20002001/10 000> 10 000
Maximum velocitymm/s
300/400250/300200/250
200
Minimum velocitymm/s20/4030/5040/6050/100
Feedhopper
ReciprocatingscrewNon return valveScrew tip
ThermocoupleBarrelHeater bandsCylinder headNozzle
Design of injection molding screws can be performed by using the software of Rao [8].Essential dimensions are the lengths and depths of the feed zone and the metering zone(Fig. 9.7). Table 9.7 shows these data for several screw diameters [I].
Table 9.7: Significant Screw Dimensions for Processing Thermoplastics [1]
Diameter
30406080100120>120
Flight depth(feed) hF
mm
4.35.47.59.110.712
max 14
Flight depth(metering) hM
mm
2.12.63.43.84.34.8
max 5.6
Flight depthratio
2 : 12.1 : 12.2:12.4: 12.5:12.5:1
max 3 : 1
Radial flightclearance
mm
0.150.150.150.200.200.250.25
Fig. 9.7: Dimensions of an injection molding screw [1]
Non-return Valves
A non-return valve is a component at the tip of the screw that prevents back flow of theplasticated material during the injection and holding pressure stages. A comparisonbetween the main categories of the non-return valves used (Fig. 9.7A) is given in Table9.7A [21].
Screw geometries for other polymers are given by Johannaber [I].
Ls-20DLM (20%) Lc(20%) Lp (60%)-
INSERTBALL
DISCHARGEBODY
iNLETS
Front Discharge Ball Check
DISCHARGE BALLBALL SEAT
NOSE CONE
INLETS
BODY
RETAINER P!N
Side Discharge Ball Check
Fig. 9.7A: Non-return values [21], [22]
Table 9.7A: Comparison Between Sliding Ring Valves and Ball Check Valves [21]
Sliding ring valve - Advantages Ball check valve - Advantages1. Greater streamling for lower material 1. More positive shut off
degradation 2. Better shot control2. suitable for heat sensitive materials3. less barrel wear4. less pressure drop across valve5. well suited for vented operation6. easy to clean.
Disadvantages Disadvantages1. Lower positive shut-off in large machines 1. Less streamlined, hence more degradation2. lower shot control. of materials
2. more barrel wear and galling3. greater pressure drop, hence more heat4. poor for vented operation5. harder to clean.
Nozzle
The plasticating barrel ends at the mold in a nozzle, which is forced against the spruebushing of the mold prior to injection and produces a force locking connection there [I].Examples of commonly used types of nozzles are given in Fig. 9.7B [1], [22].
9.2.3 Injection Mold
The quantitative description of the important mold filling stage has been made possible bythe well-known computer programs like MOLDFLOW [9], CADMOULD [10], C-MOLD[19] and others.
The purpose of this section is to touch upon the basic principles of designing injectionmolding dies using rheological and thermal properties of polymers.
9.2.3.1 Runner Systems
The pressure drop along the gate or runner of an injection mold can be calculated from thesame relationships used for dimensioning extrusion dies (Section 7.3).
Example:A part is to be made from polycarbonate using a runner of length 100 mm and diameter3 mm and with the melt at a temperature 300 0C. The volume flow rate of the plastic meltthrough the runner is 2.65 cmVs. The pressure drop in the runner is to be calculated.
Floating or sliding shutoff nozzle (with self-closing spring action)
Fig. 9.7B: Examples of nozzles [22]
Solution:
shearrate, = *± = ^ ^ = 1000 s"1
At 300 0C, a shear rate of 1000 s"1 corresponds to a viscosity r| = 420 Pa • s according tothe resin manufacturer's data.The shear stress
T=Tf-Y = 420-1000 = 0.42 MPa
The pressure drop across the runner can be calculated by using Eq. (3.2.3)2-T-L 2-0.42-100
Ap = = = 56 MPaH R 1.5
screw tip
springslidingdiameter
sprue brushing
neater bond
Shutoff nozzle with internal needle (with self-closing spring action)
spring
needle
IDeIt byposs
screw tip
heater bond
It is accepted practice that the pressure drop across the runner should be less than70 MPa [23]. Otherwise the size of the runner should be increased. The pressure drop inrunners of non-circular cross-sections can be calculated by using the Eq. (7.2.35) given inSection 7.3.
Different cross-sections for runners, their advantages, disadvantages and practicaldesign relationships are summarized in Fig. 9.8 [20].
Empirical guidelines for dimensioning cross sections of runners are presented inFig. 9.9 [20].
Circular cross-section Cross sections for runners
Advantages: smallest surface relative to cross-section, slowestcooling ratet low heat and frictional losses, center ofchannel freezes last therefore effective holdingpressure
Disadvantages: Machining into both mold halves is difficult andexpensive
Advantages: best approximation of circular cross section, simplermachining in one mold half only (usually movableside for reasons of ejection
Disadvantages: more heat losses and scrap compared with circularcross section
Alternative to parabolic cross section
Disadvantages: more heat losses and scrap than parabolic crosssection
Unfavorable cross sections have to be avoided
Fig. 9.8: Advantages and disadvantages of some runner cross-sections [20]
W = 1.25-0
Trapezoidal cross-section
W = 125-DD = smQX +1,5mm
Parabolic cross-section
0= smax •*• 1.5 rn m
Fig. 9.9: Nomogram for dimensioning runner cross-sections [20]
9.2.3.2 Design of Gates
Suggested dimensions of some commonly used gates are shown in Fig. 9.10 [20] andthose of sprues in Fig. 9.11 [20].
By means of the software mentioned in Section 9.2.3 the entire melt entry system ofthe mold as well as the mold can be designed with good success.
Gig
)
G(g
)
L
k
Diagram 3rnrn^
D'(mm) D'(mm)
Diagram 1 Diagram 2
Diagram 1applicable for PS, ABS, SAN, CAB
Diagram 2applicable for PE, PP, PA, PC, POM
Symbols
s: wall thickness of part (mm)D': diameter of runner (mm)G: weight of part (g)L: length of runner to one cavity (mm)fL: correction factor
Procedure (Diagram 3)
1. determine G and s2. take D' from diagram for material consid-
ered3. determine L4. take fL from diagram 35. correct diameter or runner: D = D'fL
Fig. 9.10: Guidelines for dimensioning gates [20] a: pinpoint, b: tunnel, c: edge gate withcircular distributor channel, d: disk gate, e: ring gate with circular cross-section
Fig. 185 Ring gate with circular cross section [5, 6]D = s+1.5mm to fs + kL =0.5 to 1.5 mmH = § s to 1 to 2 mmr =0.2 sk = 2 for short flow lengths and thick sectionsk =4 for long flow lengths and thin sections
Fig. 175 Edge gate with circular distributor channel[1,5]D = s to § s + kk = 2 mm for short flow lengths and thick sectionsk =4 for long flow lengths and thin sectionsL =(0.5 to 2.0) mmH =(0.2 to 0.7) s
Fig. 9.11: Guidelines for dimensioning a sprue [20]
9.2.3.3 Injection Pressure and Clamp Force
To determine the size of an injection molding machine suited to produce a given part,knowledge of the clamp force required by the mold is important in order to prevent themold from flashing.
As already mentioned, the mold filling process was treated extensively in the programs[9], and [10] and later on by Bangert [H]. Analytical expressions for the injection pressureand clamp force have been given by Stevenson [12] on the basis of a model for moldfilling. The main parameters characterizing this model are fill time x and Brinkmannumber Br, which can be used as machine related parameters for describing injectionmolding in general. According to the solution procedure of Stevenson [12] injectionpressure and clamp force are calculated assuming isothermal flow of melt in the cavity andthen modified to obtain actual values. The empirical relationships used for thismodification are functions of fill time and Brinkman number.
Following example shows the calculation of fill time and Brinkman number for a disc-shaped cavity [4], [12]:
The material is ABS with nR = 0.2655, which is the reciprocal of the power lawexponent n.
The viscosity constant k, [4] is k,. = 3.05 • 104
Constant injection rate Q = 160cm3/sPart Volume V = 160 cm3
Half-thickness of the disc b = 2.1mmRadius of the disc r2 = 120 mmNumber of gates N = IInlet melt temperature Tm = 245 0CMold temperature Tw = 5O0CThermal conductivity of the melt X = 0.174 W/(m • K)Thermal diffusivity of the polymer a = 7.72 • 10"4 cm2/sMelt flow angle [12] 0 = 360°
Calculate fill time and Brinkman number.
Solution:The dimensionless fill time x which characterizes the cooling of the flowing melt in thecavity is defined as [12]
Inserting the numerical values we have
f , 1 6 0 . 7 . 7 2 - 1 0 ^
160-(0.105)2
The Brinkman number which characterizes viscous heating is given by
B , = ^ ^ f » * • > , T - ' ( « . ,10 4 -X - (TM-TW) L N - Q ^ b 2 T 2 J
Introducing the given values we get
Br = 01f-305-104 { 160'360 2 I '"5 5 = 0.771
104-0.174-195 U-360-2;r-(0.105)2-12jTable 9.7B shows the results of simulating the mold filling of a large rectangular opencontainer (Fig, 9.1 IA) [24] according to the model of Stevenson [12].
Fig. 9.1 IA: Mold filling of rectangular open container according to the model of Stevenson [12]
Relative to the standard conditions the results in Table 9.7B show that Ap is decreased by10 percent when T1 is increased 20 0C, by 4 percent when Tw is increased 20 0C, by 24percent when the material is changed, by 37 percent when the number of gates is increasedto four, and by 63 percent when all of the above changes are made. The optimal conditionswhich correspond to the lowest Ap and F occur when these changes are combined with thechange of the resin.
Symbols in Table 9.7B:T1: inlet melt temperatureTw: mold wall temperatureAp: injection pressure dropF: clamp forceN: Number of gates
Operating Conditions:injection rate = 2000 crnVsfill time = 3.81 shalf-thickness of the part = 0.127 cmdimensionless fill time T = 0.1824
A rough estimate of the clamp force can be made as follows:The pressure drop in a plate mold AP1N for the melt flow of an isothermal, Newtonian fluidcan be calculated from Eqns. (7.3.2) and (7.3.4) given in Section 7.3 by putting n = 1.AP1N is then
Substituting the injection rate for the volume flow rate Q 0 we get
Q = ^ (9.2.4)
where V = W H Land t = injection time = L/uwith u = injection velocityIntroducing the equations above into Eq. (9.2.3) we obtain
A P i N = 1 i r ' r u ' ; 7 (925)
Example with symbols and units in Eq. (9.2.5)
Table 9.7B: Simulations of Injection Pressure and Clamp Force at DifferentProcessing Conditions [24]
Resin
AAABAB
N
111144
T10K501520500500500500
Tw0K301301321301301301
Br
1.3810.9621.5360.8490.6250.299
ApMPa302273290229192113
FkN
1910001750001810001470006780040400
part thickness H = I mmflow length L = 100 mminjection velocity u = 100 mm/smelt viscosity r| = 250 P • s
Solution:
1O 100 1 100-250 O A A UAP l N = 12- — ™ — ^ - = 300bar
In Fig. 9.1 IC AP1N is plotted over the part thickness H for different ratios of flow length Lto part thickness H [25]. The injection velocity is assumed to be 10 cm/s and the meltviscosity 250 Pa • s.The pressure Apm is then corrected by the following correction factors [26]:Correction Factor CFshape
Depending on the complicacy of the part geometry the factor CFshape can have valuesbetween 1.1 to 1.3.Correction Factor CFresin
The correction factors for the flow behavior of the resin CFresin are given in Table 9.7C forsome resins.
Table 9.7C: Correction Factor CFresin [26]
"Resin |CFresin
PE, PP, PS 1.0PMMA, PPO 1.5PA, SB 1.2PC5PVC 1.7ABS, SAN, CA 11.3
Finally the actual cavity pressure ApAp = APlN. CFshape • CFresin
and the clamp force F [kN]
A p(bar) • projected area of the part (c m2)100
unco
rrec
ted
cavi
ty p
ress
ure
unco
rrec
ted
cavi
ty p
ress
ure
[bar]
ratio of flow lengthto part thickness
part thickness [mm]
(a)
[bar]ratio of flow lengthto part thickness
part thickness [mm]
(b)
Fig. 9.1 IB: Cavity pressure as a function of part thickness andratio of flow length to part thickness [25]
Example:Disk-shaped mold (see Fig. 9.1 IA)Thickness H = I mmRadius R =100 mmCorrection factor CFshape =1.2Resin: ABSCFresin from Table CFresin= 1.3
Solution:Ratio of flow length to part thickness L/H
L/H=100
AP1N from Fig. 4.1 IB for L/H = 100 and H = 1
AP1N = 300 bar
Actual cavity pressure Ap
Ap = 3001.2-1.3 =468 bar
Clamp force F (kN)
F = ^ M * 147OkN100
In Fig. 9.12 the relationship between shot size and clamping force is presented for somecommercially available injection molding machines [I]. Here a and a0 are the ratiosbetween working (injection) capacity and clamping force and Fcx and Fco the clampingforces.
The following example shows as to how the maximum shot weight can be calculated ifthe clamping force is known.
Example:Clamping force: 3500 kNValue of the ordinate corresponding to the dashedline 3 in Fig. 9.12b: 0.39Maximum shot weight for polystyrene assuminga density of 0.9: 3500 x 0.39 x 0.9 « 1230 gEffective maximum shot weight with a factor of 0.8: 1230 x 0.8 « 980 gThe range for the maximum shot weight is approximately [1] 1230 ± 500 g.
Two-dimensional and three-dimensional diagrams as shown in Fig. 9.13 [18] are helpfulin the practice for finding out the useful working range of an injection molding machine[18].
Max
sho
t si
ze /
clam
ping
for
ceM
ax s
hot
size
/ cl
ampi
ng f
orce
Fig. 9.12: Calculation of maximum shot weight by means of model laws [1]
kNClamping force F c
cm3
kN
Model law( Fc f 3
a = ao 7"Max. shot size 3 ^
a = JCULclamping force kN
Clamping force F ckN
.cm5
kN
Model law
a = a ° i d_ Max. shot size 3 ^
clamping force ^N
Ram
press
ure ps
iRa
m pre
ssure
Mold temperature
F lash area
Short shot area
Molding 'area
Fig. 9.13: Mold Area Diagram (MAD) and Mold Volume Diagram (MVD) [18]a: MAD, b: MVD
9.2.3.4 Thermal Design of Mold
Cooling of Melt in Mold
The analytical solution for the transient one-dimensional heat conduction for a plate can bewritten as [13]
* - M ^ fe£]Although this equation is valid only for amorphous polymers, it has given good results inthe practice for semi-crystalline and crystalline polymers as well, so that its general use forall thermoplastic materials is justified.
Example with symbols and units:Cooling of a part in an injection mold for the following conditions [5]:resin: PE-LDthickness of the plate s = 12.7 mmtemperature of the melt Ta = 243.3 0Cmold temperature Tw
= 21.10Cdemolding temperature Tb = 76.7 0Cthermal diffusivity of the melt a = 1.29-10"3 cm2/sThe temperature Tb in Eq. (9.2.6) refers to the centerline temperature of the part.
Solution:The temperature ratio 0Th :
Q1 b = ^ Z J ^ = 7 6 - 7 - 2 U =0.25
Tb T3-Tw 243.3-21.1
cooling time tk according to Eq. (9.2.6)
tk = 2 L2?2 3 - lnf±—1 = 206.5 s
The cooling time tk can also be found from Fig. 9.14 in which the ratio 0Th is plotted overthe Fourier number for bodies of different geometry [14].Fourier number F0 from Fig. 9.14 at 0Th = 0.25
F0 = 0.66
Cooling time tk:s 12.7 , . _
x = - = = 6.35 mm2 2
coo
ling
tim
e (s
)
Temp
eratur
e ra
tio <
9j b •
Fig. 9.15: Cooling time vs. wall thickness
wall thickness (mm)
Fig. 9.14: Axis temperature for multidimensional bodies [14]
Fourier number F^at/X1
The cooling time as a function of wall thickness of the molding is shown in Fig. 9.15.Calculations of cooling time based on the average demolding temperature are given in
the book by Rao [4].Convective heat transfer is to be taken into account if the mold is cooled by a coolant
such as circulating water by calculating the Biot number as shown in Chapter 7.In practice the temperature of the mold wall is not constant, as it is influenced by the
heat transfer between the melt and the cooling water. Therefore the geometry of thecooling channel lay-out, thermal conductivity of the material and velocity of cooling wateraffect the cooling time significantly (Fig. 9.16).
demo
lding
temp
eratur
e
Fig. 9.16: Cooling time as a function of demolding temperature and wall thickness
The influence of the cooling channel lay-out on cooling time can be simulated bymeans of equations given in the book [4] by changing the distances x and y (Fig. 9.16) asshown in Figs. 9.17 and 9.18. The effects of the temperature of cooling water and of watervelocity are presented in Figs. 9.19 and 9.20 respectively. From these results it followsthat the cooling time is significantly determined by the cooling channel lay-out.
cooling time
Cooli
ng ti
meCo
oling
time
Cooli
ng ti
me
Fig. 9.19: Influence of the temperature of cooling water on cooling time [4]
Fig. 9.18: Effect of cooling channel distance X on cooling time [4]
Fig. 9.17: Effect of cooling channel distance Y on cooling time [4]
Cooling water temperature
0C
s
5= 1.5mm/=25 mmK= 15 mm
Distance from channel to channel /mm
s W20°C
W='o°c
Distance between mold surface and cooling channel Y
mm
s W-20°C
W=W0C
Fig. 9.20: Influence of the velocity of cooling water on cooling time[4]
9.2.3.5 Mechanical Design of Mold
The cooling channels should be as close to the surface of the mold as possible so that heatcan flow out of the melt in the shortest time possible. However, the strength of the moldmaterial sets a limit to the distance between the cooling channel and the mold surface. Theallowable distance z (Fig. 9.21) taking the strength of the mold material into account wascalculated by Lindner [15] according to the following equations:
^ ^ (9.2.7)
r=™** (9.2.8)Z
f=iooo^r__d^+ai5lz U2-E-Z2 GJ J
where p = melt pressure N/mm2
d,z = distances mm, see Fig. 9.21E = tensile modulus N/mm2
G = shear modulus N/mm2
cb = tensile stress N/mm2
T = shear stress N/mm2
f = deflection of the mold material above the cooling channel jamThe minimization of the distance z such that the conditions
^ b ^ ^bmax
* < - w
(fmax: maximum deflection; abmax: allowable tensile stress; xmax: allowable shear stress)are satisfied, can be accomplished by a computer program [16]. The results of a samplecalculation are shown in Table 9.8.
Velocity of coojing waterm/s
Cooli
ng ti
me
sW-20°CS= 1.5mm
/=25 mmY-- 15mm
Min
imum
coo
ling
chan
nel d
ista
nce
z (m
m)
moldsurface
b=0.7 d
channel form
Channel dimension d (mm)
Fig. 9.21: Cooling channel distance z for different cavity pressuresand channel dimensions with steel as mold material
Table 9.8: Results of Optimization of Cooling Channel Distance
Inputmelt pressure p = 4.9 N/mm2
maximum deflection ^12x = 2.5 |j,m
modulus of elasticity E = 70588N/mm2
modulus of shear G = 27147 N/mm2
allowable tensile stress abmax = 421.56 N/mm2
allowable shear stress Xn^ = 294.1 N/mm2
channel dimension d = 10 mm
Outputchannel distance z = 2.492 mmdeflection f= 2.487 pmtensile stress a = 39.44 N/mm2
shear stress % = 14.75 N/mm2
The equations given above are approximately valid for circular channels as well. Thedistance from wall to wall of the channel in this case should be roughly around channellength 1 or channel diameter depending on the strength of mold material.
Fig. 9.21 shows for steel as mold material the minimum cooling channel distance z fordifferent cavity pressures.
Literature
1. Johannaber, F.: Injection Molding Machines, Hanser, Munich 19832. McKelvey, JM.: Polymer Processing, John Wiley, New York 19623. Hensen, F. (Ed,): Plastics Extrusion Technology, Hanser, Munich 19884. Rao, KS.: Design Formulars for Plastics Engineers, Hanser, Munich 19915. Thome, J.L.: Plastics Process Engineering, Marcel Dekker Inc., New York 19796. Rao, KS.: Computer Aided Design of Plasticating Screws, Hanser, Munich 19867. Donovan, R. C.: Polymer Engineering and Science 11 (1971) p. 3618. Rao, KS., O'Brien, K.T. and Harry, D.H.: Computer Modeling for Extrusion and other
Continuous Polymer Processes. Ed. Keith T. O'Brien, Hanser, Munich 19929. Austin, C: CAE for Injection Molding, Hanser, Munich 198310. CADMOULD: DCV Aachen11. Bangert, K: Systematische Konstruktion von SpritzgieBwerkzeugen unter Rechnereinsatz,
Dissertation RWTH Aachen 198112. Stevenson, J.F.: Polymer Engineering and Science 18 (1978), 9. 57313. Martin, H.: in VDI-Warmeatlas, VDI-Verlag, Dusseldorf 198414. Welty, J.R., Wicks, CE., Wilson, R.E.: Fundamentals of Momentum, Heat and Mass
Transfer, John Wiley, New York 198315. Lindner, E.: Berechenbarkeit von SpritzgieBwerkzeugen, VDI-Verlag, Dusseldorf 1974, p.
10916. Rao, KS.: Designing Machines and Dies for Polymer Processing with Computer Programs,
Hanser, Munich 198117. Zoellner, O., Sagenschneider, U.: Kunststoffe 84 (1994) 8, p. 102218. Rosato, D.V., Rosato, D.V.: Plastics Processing Data Handbook, Van Nostrand-Reinhold,
New York 199019. C-MoId: Advanced CAE Technology Inc.20. Menges, G., Mohren, P.: How to make Injection Molds, Hanser, Munich 199321. Brochure ofSpirex Corporation U.S.A., 199522. Potsch, G., Michaeli, W.: Injection Molding - An Introduction, Hanser, Munich 199523. Cracknell, P.S., Dyson, R.W.: Handbook of Thermoplastics Injection Mold Design, Blackie
Academic & Professional, London 199324. Stevenson, J.F., Hauptfleisch, R.A.: Handbook Methods for Predicting Pressure Drop and
Clamp Force in Injection Molding: Technical Report No. 7, July 30, 197625. Brochure of Mannesmann-Demag 1992
205 This page has been reformatted by Knovel to provide easier navigation.
Index
Index terms Links
A Absorption 80
B Barrel 98
diameter 98 108 temperature 98 108
Bagley plot 42
Barr screw 92
Biot number 152
Blown film 135
Blow molding 155
Brinkman number 152
Bulk modulus 10
C Chemical resistance 81
Clamp force 188
Color 75
Comparative tracking index 68
Compounding 146
Composites 83
Contact temperature 32
206
Index terms Links
This page has been reformatted by Knovel to provide easier navigation.
Cooling channels 196 200
Cooling of melt 196 in mold 196
Cooling time 196 198
Correction factors 106 drag flow 106 pressure flow 106 127
Creep modulus 11
Creep rupture 12
D Deborah number 152
Desorption 80
Design of mold 183 196 200 mechanical 200 thermal 196
Dielectric strength 65 dissipation factor 66
Diffusion coefficient 80
Dimensionless numbers 152
Die swell 62
Drying temperature 174 time 175
E Enthalpy 29
Elastomers 87
Entrance loss 42
Environmental stress cracking 77
207
Index terms Links
This page has been reformatted by Knovel to provide easier navigation.
External influences 77
Extrudate cooling 149
Extruder output 98
Extrusion dies 124 annulus 127 pressure drop 127 residence time distribution 131 shear rate 41 47 slit 126 127 128 substitute radius 128
Extrusion screws 92 channel depth 122 103 clearance 101 channel length 106 flight diameter 101
Extrusion screws lead 115 power 109 122 speed 102
F Fatigue 14
Flammability 35
Fluid 39 Newtonian 39 non-Newtonian 39
Fluctuation 112 111 pressure 113 temperature 112
Friction 19
208
Index terms Links
This page has been reformatted by Knovel to provide easier navigation.
G Gates 170 186
Gloss 75
H Hardness 16
Haze 73
Heat defection temperature 34
Heat penetration 32
I Ideal solid 1
Impact strength 17
Injection molding 169 mold 183 pressure 170 processing temperature 173 resin 170 runner systems 183 screw 181 unit 179
L Light transmission 73
Liquid crystal polymers 85
Loss tangent 66
M Melt flow index 59
209 Index terms Links
This page has been reformatted by Knovel to provide easier navigation.
Melting parameter 107
Melting profile 108
Melt pressure 111 temperature 111
Mold shrinkage 172
N Normal stress coefficient 61
Nozzle 183 184
P Parameter 92
machine related 98 resin dependent 92
Permeability 79 80
Permittivity 66 relative 66
Pipe extrusion 126
R Reinforced plastics 83
Refractive index 73
Relaxation modulus 13
Rheological model 47 Carreau 53 Muenstedt 50 power law 48 Pradtl and Eyring 48
Runner 183
210 Index terms Links
This page has been reformatted by Knovel to provide easier navigation.
S Shear compliance 61
Shear modulus 6 effect of temperature 6
Shear rate 41 apparent 41 true 47
Shear stress 42 true 42
Sheet extrusion 137
Shrinkage 172
Solubility 77
Specific volume 23
Specific heat 23
Spider die 131
Spiral die 136
Stress strain behavior 2
Structural foam 84
Surface resistivity 65
Tensile modulus 5 effect of temperature 6
T Tensile strength 6
effect of temperature 6
Thermal conductivity 29
Thermo forming 142
Thermal diffusivity 31
211 Index terms Links
This page has been reformatted by Knovel to provide easier navigation.
Thermal expansion coefficient 27
Twin screws 92
V Volume resistivity 65
Viscosity 41 apparent 44 effect of molecular weight 57 shear 44 true 47 two-component mixtures 59
W Weathering resistance 80