Extrusion Dies For Plastics And Rubber - Hanser Publications
Sample PagesChristian Hopmann, Walter MichaeliExtrusion Dies for Plastics and RubberDesign and Engineering ComputationsBook ISBN: 978-1-56990-623-1eBook ISBN: 978-1-56990-624-8For further information and order or contact your bookseller. Carl Hanser Verlag, München
Hopmann, MichaeliExtrusion Dies for Plastics and Rubber
Christian HopmannWalter MichaeliExtrusion Dies forPlastics and RubberDesign and Engineering Computations4th EditionWith Contributions byDr.-Ing. Ulrich Dombrowski Dr. Ulrich Hüsgen Dr.-Ing. Matthias Kalwa Dr.-Ing. Stefan Kaul Dr.-Ing. Michael Meier-Kaiser Dr.-Ing. Boris Rotter Dr.-Ing. Micha Scharf Dr.-Ing. Claus Schwenzer Dr.-Ing. Christian Windeck Nafi Yesildag, M.Sc.Hanser Publishers, MunichHanser Publications, Cincinnati
The Authors:Prof. Dr.-Ing. Christian Hopmann,Head of the Institute of Plastics Processing (IKV) at RWTH Aachen University, Aachen, GermanyProf. Dr.-Ing. Dr.-Ing. E.h. Walter Michaeli,former Head of the Institute of Plastics Processing (IKV) at RWTH Aachen University, Aachen, GermanyDistributed in the Americas by:Hanser Publications6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USAFax: (513) 527-8801Phone: (513) 527-8977www.hanserpublications.comDistributed in all other countries by:Carl Hanser VerlagPostfach 86 04 20, 81631 München, GermanyFax: 49 (89) 98 48 09www.hanser-fachbuch.deThe 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 MarksAct, may accordingly be used freely by anyone. While the advice and information in this book are believed to be trueand accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legalresponsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied,with respect to the material contained herein.The final determination of the suitability of any information for the use contemplated for a given application remains the sole responsibility of the user.Cataloging-in-Publication Data is on file with the Library of CongressAll rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronicor mechanical, including photocopying or by any information storage and retrieval system, without permission inwriting from the publisher. Carl Hanser Verlag, Munich 2016Editor: Mark SmithProduction Management: Jörg StrohbachCoverconcept: Marc Müller-Bremer, www.rebranding.de, MünchenCoverdesign: Stephan RönigkTypesetting: Kösel Media GmbH, KrugzellPrinted and bound by Hubert & Co GmbH, GöttingenPrinted in GermanyISBN: 978-1-56990-623-1E-Book ISBN: 978-1-56990-624-8
PrefaceIn January 2003, this book was published in its 3rd edition in English. Sincethen, an unrelenting demand for the book has been observed, both for the Germanand English versions. In order to meet this demand, it is our pleasure that Hansernow publishes this 4th edition. With this edition, “Extrusion Dies” has for thefirst time two editors: In April 2011 Prof. Dr.-Ing. Christian Hopmann succeededProf. Dr.-Ing. Dr.-Ing. E. h. Walter Michaeli as holder of the Chair of Plastics Processing and Head of the Institute of Plastics Processing (IKV) at RWTH AachenUniversity, Aachen, Germany. We are very pleased that this book with its longhistory with Hanser is continued into the next IKV generation.This update will continue to help you in your work and life while hopefully also providing pleasure in reading. We have retained the structure of the book, which hasproven itself over many years and received much positive resonance from readers.When we say “we”, we particularly refer to Dr.-Ing. Christian Windeck, former headof the IKV extrusion department, and his successor Nafi Yesildag, M.Sc., who havecritically analyzed, checked, and supplemented the contents, equations, and reference lists. We would like to express our special thanks to both of them.We further thank Mark Smith and Jörg Strohbach of Hanser for their support in thepublication of our work.Once again, suggestions obtained from the plastics and rubber industry were takenup and addressed in this fourth edition. We thank all those who provided theirsuggestions and help. Many research and development efforts of the IKV form thefundament of some of the facts described in this book. Against this background,we thank the Federal Ministry for Economic Affairs and Energy (BMWi), Berlin,for the promotion of many industrial research projects through the German Federation of Industrial Research Associations (AIF e. V.), Cologne, the DeutscheForschungsgemeinschaft (DFG), Bonn-Bad Godesberg, the Federal Ministry of Education and Research (BMBF), Bonn, and the European Commission, Brussels, withrespect to extrusion dies.Walter MichaeliChristian Hopmann
ContentsPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .VPreface to the Third Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .VIIPreface to the Second Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .IXPreface to the First Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XI1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.1Reference of Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72Properties of Polymeric Melts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92.1 Rheological Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.1 Viscous Properties of Melts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.1.1 Viscosity and Flow Functions . . . . . . . . . . . . . . . . . . . . . . .2.1.1.2 Mathematical Description of the PseudoplasticBehavior of Melts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.1.3 Influence of Temperature and Pressure on theFlow Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.1.2 Determination of Viscous Flow Behavior . . . . . . . . . . . . . . . . . . . .2.1.3 Viscoelastic Properties of Melts . . . . . . . . . . . . . . . . . . . . . . . . . . . .910101926322.2 Thermodynamic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2.1 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2.2 Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2.3 Specific Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2.4 Thermal Diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2.5 Specific Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3839414243432.3 References of Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4612
XIVContents3Fundamental Equations for Simple Flows . . . . . . . . . . . . . . . . . . . .493.1 Flow through a Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .503.2 Flow through a Slit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .563.3 Flow through an Annular Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .603.4 Summary of Simple Equations for Dies . . . . . . . . . . . . . . . . . . . . . . . . . . .643.5 Phenomenon of Wall Slip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.5.1 Model Considering the Wall Slip . . . . . . . . . . . . . . . . . . . . . . . . . . .3.5.2 Instability in the Flow Function - Melt Fracture . . . . . . . . . . . . . .7474793.5 References of Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .824Computation of Velocity and Temperature Distributionsin Extrusion Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .854.1 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.1.1 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.1.2 Momentum Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.1.3 Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .858687884.2 Restrictive Assumptions and B oundary Conditions . . . . . . . . . . . . . . . . .924.3 Analytical Formulas for Solution of the Conservation Equations . . . . . .944.4 Numerical Solution of Conservation Equations . . . . . . . . . . . . . . . . . . . .4.4.1 Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.4.2 Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.4.3 Comparison of FDM and FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.4.4 Examples of Computations of Extrusion Dies . . . . . . . . . . . . . . . .1001011041091124.5 Consideration of the Viscoelastic Behavior of the Material . . . . . . . . . . .1264.6 Computation of the Extrudate Swelling . . . . . . . . . . . . . . . . . . . . . . . . . . .1304.7 Methods for Designing and Optimizing Extrusion Dies . . . . . . . . . . . . . .4.7.1 Industrial Practice for the Design of Extrusion Dies . . . . . . . . . . .4.7.2 Optimization Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.7.2.1 Practical Optimization Objectives . . . . . . . . . . . . . . . . . . .4.7.2.2 Practical Boundary Conditions and ConstraintsWhen Designing Flow Channels . . . . . . . . . . . . . . . . . . . .4.7.2.3 Independent Parameters during Die Optimization . . . . .4.7.2.4 Dependent Parameters during Die Optimization andTheir Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.7.3 Optimization Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.7.3.1 Gradient-Free Optimization Methods . . . . . . . . . . . . . . . .4.7.3.2 Gradient-Based Optimization Methods . . . . . . . . . . . . . . .4.7.3.3 Stochastic Optimization Methods . . . . . . . . . . . . . . . . . . . .136137140140141142142144146149150
Contents4.7.3.4 Evolutionary Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.7.3.5 Treatment of Boundary Conditions . . . . . . . . . . . . . . . . . .4.7.4 Practical Applications of Optimization Strategies for theDesign of Extrusion Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.7.4.1 Optimization of a Convergent Channel Geometry . . . . . .4.7.4.2 Optimization of Profile Dies . . . . . . . . . . . . . . . . . . . . . . . .1501524.8 References of Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1625154154156Monoextrusion Dies for Thermoplastics . . . . . . . . . . . . . . . . . . . . . 1675.1 Dies with Circular Exit Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1.1 Designs and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1671671755.2 Dies with Slit Exit Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.1 Designs and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.2.1 T-Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.2.2 Fishtail Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.2.3 Coathanger Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.2.4 Numerical Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2.2.5 Considerations for Clam Shelling . . . . . . . . . . . . . . . . . . .5.2.2.6 Unconventional Manifolds . . . . . . . . . . . . . . . . . . . . . . . . .5.2.2.7 Operating Performance of Wide Slit Dies . . . . . . . . . . . . .1801801871901901922032052062095.3 Dies with Annular Exit Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.1 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.1.1 Center-Fed Mandrel Support Dies . . . . . . . . . . . . . . . . . . .5.3.1.2 Screen Pack Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.1.3 Side-Fed Mandrel Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.1.4 Spiral Mandrel Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.2.1 Pipe Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.2.2 Blown Film Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.2.3 Dies for the Extrusion of Parisons for Blow Molding . . . .5.3.2.4 Coating Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.3 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.3.1 Center-Fed Mandrel Dies and Screen Pack Dies . . . . . . . .5.3.3.2 Side-Fed Mandrel Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.3.3 Spiral Mandrel Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3.3.4 Coating Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 Formulas for the Computation of the Pressure Loss in Flow Channel Geometries other than Pipe or Slit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .250XV
XVIContents5.5 Dies with Irregular Outlet Geometry (Profile Dies) . . . . . . . . . . . . . . . . .5.5.1 Designs and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.5.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2552552645.6 Dies for Foamed Semifinished Products . . . . . . . . . . . . . . . . . . . . . . . . . .5.6.1 Dies for Foamed Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.6.2 Dies for Foamed Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2722742745.7 Special Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.7.1 Dies for Coating of Profiles of Arbitrary Cross Section . . . . . . . . .5.7.2 Dies for the Production of Profiles with Reinforcing Inserts . . . .5.7.3 Dies for the Production of Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.7.4 Slit Die with Driven Screw for the Production of Slabs . . . . . . . . .2762762772782795.8 References of Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2826Coextrusion Dies for Thermoplastics . . . . . . . . . . . . . . . . . . . . . . . . 2896.1 Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.1.1 Externally Combining Coextrusion Dies . . . . . . . . . . . . . . . . . . . .6.1.2 Adapter (Feedblock) Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.1.3 Multimanifold Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.1.4 Layer Multiplication Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2902902912942946.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2.1 Film and Sheet Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2.2 Blown Film Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2.3 Dies for the Extrusion of Parisons for Blow Molding . . . . . . . . . .2962962982996.3 Computations of Flow and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.3.1 Computation of Simple Multilayer Flow with Constant Viscosity6.3.2 Computation of Coextrusion Flow by the Explicit Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.3.3 Computation of Velocity and Temperature Fields by theFinite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.3.4 Computation of Velocity Fields in Coextrusion Flows by FEM . . .3003036.4 Instabilities in Multilayer Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3166.5 References of Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3237308311314Extrusion Dies for Elastomers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3257.1 Design of Dies for the Extrusion of Elastomers . . . . . . . . . . . . . . . . . . . . .3257.2 Fundamentals of Design of Extrusion Dies for Elastomers . . . . . . . . . . .7.2.1 Thermodynamic Material Data . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.2.2 Rheological Material Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .327327328
Contents7.2.3 Computation of Viscous Pressure Losses . . . . . . . . . . . . . . . . . . . .7.2.3.1 Formulas for Isothermal . . . . . . . . . . . . . . . . . . . . . . . . . . .7.2.3.2 Approaches to Nonisothermal Computations . . . . . . . . . .7.2.4 Estimation of the Peak Temperatures . . . . . . . . . . . . . . . . . . . . . . .7.2.5 Consideration of the Elastic Behavior of the Material . . . . . . . . . .3313313343353367.3 Design of Distributor Dies for Elastomers . . . . . . . . . . . . . . . . . . . . . . . . .3377.4 Design of Slotted Disks for Extrusion Dies for Elastomers . . . . . . . . . . .7.4.1 Computation of Pressure Losses . . . . . . . . . . . . . . . . . . . . . . . . . . .7.4.2 Extrudate Swelling (Die Swell) . . . . . . . . . . . . . . . . . . . . . . . . . . . .7.4.3 Simplified Estimations for the Design of a Slotted Disk . . . . . . . .3393393423467.5 References of Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3548Heating of Extrusion Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3578.1 Types and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.1.1 Heating of Extrusion Dies with Fluids . . . . . . . . . . . . . . . . . . . . . .8.1.2 Electrically Heated Extrusion Dies . . . . . . . . . . . . . . . . . . . . . . . . .8.1.3 Temperature Control of Extrusion Dies . . . . . . . . . . . . . . . . . . . . .3583583593608.2 Thermal Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.2.1 Criteria and Degrees of Freedom for Thermal Design . . . . . . . . . .8.2.2 Heat Balance of the Extrusion Die . . . . . . . . . . . . . . . . . . . . . . . . . .8.2.3 Restrictive Assumptions in the Modeling . . . . . . . . . . . . . . . . . . . .8.2.4 Simulation Methods for Thermal Design . . . . . . . . . . . . . . . . . . . .3623623643693698.3 References of Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3789Mechanical Design of Extrusion Dies . . . . . . . . . . . . . . . . . . . . . . . . 3819.1 Mechanical Design of a Breaker Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . .3829.2 Mechanical Design of a Die with Axially Symmetrical Flow Channels .3879.3 Mechanical Design of a Slit Die . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3979.4 General Design Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4019.5 Materials for Extrusion Dies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4029.6 References of Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40910 Handling, Cleaning, and Maintaining Extrusion Dies . . . . . . . . . 41110.1 References of Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .414XVII
XVIIIContents11 Calibration of Pipes and Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41511.1 Types and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.1.1 Friction Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.1.2 External Calibration with Compressed Air . . . . . . . . . . . . . . . . . .11.1.3 External Calibration with Vacuum . . . . . . . . . . . . . . . . . . . . . . . . .11.1.4 Internal Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.1.5 Precision Extrusion Pullforming (the Technoform Process) . . . . .11.1.6 Special Process with Movable Calibrators . . . . . . . . . . . . . . . . . . .41841841942042442542611.2 Thermal Design of Calibration Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.2.1 Analytical Computational Model . . . . . . . . . . . . . . . . . . . . . . . . . . .11.2.2 Numerical Computational Model . . . . . . . . . . . . . . . . . . . . . . . . . . .11.2.3 Analogy Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.2.4 Thermal Boundary Conditions and Material Data . . . . . . . . . . . . .42642843243744011.3 Effect of Cooling on the Quality of the Extrudate . . . . . . . . . . . . . . . . . . .44111.4 Mechanical Design of Calibration Lines . . . . . . . . . . . . . . . . . . . . . . . . . . .44211.5 Cooling Dies, Process for Production of Solid Bars . . . . . . . . . . . . . . . . . .44211.6 References of Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .446Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
2Properties ofPolymeric MeltsWhen we choose a theoretical description of the process correlations in the extrusion die and calibration unit for a reliable design of those systems, there are twothings in particular to be considered: Simplifications and boundary conditions based on the physical models alwayshave to be analyzed critically with regard to the problem at hand. Data pertaining to the processed material and that are being entered into themodels become of key importance. These are data that characterize flow, deformation, and relaxation behaviors and heat transfer; in other words, its rheological and thermodynamic data [1]. 2.1 Rheological BehaviorA general flow is fully described by the law of conservation of mass, impulse, andenergy, as well as by the rheological and thermodynamic equations of state. Therheological state equation, often referred to as the material law, describes the correlation between the flow velocity field and the resulting stress field. All theflow properties of the given polymer enter this equation. The description, explanation, and measurement of the flow properties are at the core of the science of deformation and flow called rheology [2].Rheology will be introduced in this chapter to the extent to which it is needed forthe design of extrusion dies. Polymeric melts do not behave as purely viscous liquids; they also exhibit a substantial elasticity. Their properties therefore lie between ideal Newtonian (viscous) fluids and ideal Hookean (elastic) solids. This isreferred to as viscoelastic behavior or viscoelasticity. When describing rheologicalmaterial behavior, a clear distinction is made between purely viscous behavior andthe combination of viscous and time-dependent elastic behavior.
102 Properties of Polymeric Melts2.1.1 Viscous Properties of MeltsDuring the process of flow as it occurs in extrusion dies, the melt is subjected toshear deformation. This shearing flow is caused by the fact that melts adhere to thedie walls. This is called Stokean adhesion. A change in flow velocity through theflow channel area is the result of this, and it is represented by the following equation:γ uydυ, (2.1)dyFlow velocityDirection of shearDuring the steady-state shear flow, a shear stress t occurs between two layers ofthe fluid at any point. In the simplest case of a Newtonian fluid, this shear stress tis proportional to the shear rate g :τ η γ . (2.2)The constant of proportionality h is called the dynamic shear viscosity or simplyviscosity. Its dimension is Pa·s. The viscosity is the measure of the internal resistance to flow in the fluid under shear.Generally, polymeric melts do not behave in a Newtonian fashion. Their viscosity isnot constant but is dependent on the shear rate. In reference to Equation (2.2) validfor Newtonian fluids, this can be expressed in the following manner:τ η (γ ) γ (2.3)orη (γ ) τ const. (2.4)γ Note: Many polymers exhibit more or less pronounced time-dependent viscosity(thixotropy, rheopexy, lag in viscosity at sudden onset of shear or elongation [2,3]).This time dependence is usually not considered in the design of dies; hence it willbe ignored in the following sections.2.1.1.1 Viscosity and Flow FunctionsWhen plotting the viscosity h in dependence on the shear rate g in a log-log graph,we obtain a function shown in Fig. 2.1 valid for polymers at constant temperature.It can be seen that for low shear rates the viscosity remains constant; however,with increasing shear rate at a certain point it changes linearly over a relativelybroad range of shear rates in a log-log graph.
2.1 Rheological BehaviorThis, the reduction of viscosity with increased shear rate, is referred to as pseudoplastic or shear-thinning behavior. The constant viscosity at low shear rates iscalled zero-shear viscosity, h0.Figure 2.1 Representation of the dependence of viscosity on the shear rate by a viscositycurveBesides the graphic representation of viscosity vs. shear rate, the so-called viscosity curve, the relationship between shear stress and shear rate (also in a log-loggraph) is referred to as a flow curve (Fig. 2.2). For a Newtonian fluid, the shear rateis directly proportional to the shear stress. A log-log graph therefore is a straightline with a slope of 1, which means that the angle between the abscissa and theflow curve is 45 . Any deviation from this slope directly indicates a non-Newtonianbehavior. Figure 2.2 Representation of the dependence of the shear rate on theshear stress by a flow curve11
122 Properties of Polymeric MeltsFor a pseudoplastic fluid, the slope is greater than 1, meaning that the shear rateincreases progressively with increasing shear stress. Conversely, the shear stressincreases with the shear rate in a less-than-proportional relationship (see alsoChapter 3).2.1.1.2 Mathematical Description of the Pseudoplastic Behavior of MeltsVarious models describing the viscosity and flow curves were developed mathematically. They differ in the mathematical methods used on one hand and in theadaptability and hence accuracy on the other. An overview and examples are givenin the literature [2,4]. The most widely used models for thermoplastics and rubberswill be discussed in the following section. Power Law of Ostwald and de Waele [5,6]When plotting the flow curves of different polymers in a log-log graph, curves areobtained that consist of two approximately linear sections and one transition region (Fig. 2.3). In many cases we can operate in one of those two regions, so thesesections of the curve can be mathematically represented in the following generalform:γ φ τ m (2.5)Equation (2.5) is called the power law of Ostwald and de Waele. The parameters arem, the flow exponent, and f, the fluidity. Characteristic for the ability of a materialto flow and its deviation from Newtonian behavior is the flow exponent m. It can beexpressed by the following relation:m D lg γ . (2.6)D lg τNote that m is also the slope of the flow curve in the given sections of the log-logdiagram (Fig. 2.3).The value of m for polymeric melts lies between 1 and 6; for the range of shearrates between approximately 100 and 104 s–1 applicable to the design of extrusiondies, the corresponding values of m are between 2 and 4. For m 1, f 1/h,which is the case of a Newtonian flow.Sinceη τ γ
2.1 Rheological Behaviorwe obtain from Equation (2.5):η φ 1 τ1 m φ 1mBy substituting k fcosity function: 1 1 γ m .1m (2.7)and n 1we obtain the usual representation of the vismη k γ n 1. (2.8)The factor k is called the consistency factor. It represents the viscosity at a shearrate of g 1/s. The viscosity exponent n is equal to 1 for Newtonian behavior, andits value for most polymers is between 0.2 and 0.7. It represents the slope of theviscosity curve in the observed range.The power law is very simple mathematically: it allows an analytical treatment ofalmost all simple flow problems that can be solved for Newtonian fluids (see Chapter 3). The disadvantage of the power law is that when the shear rate drops to zero,the viscosity value becomes infinity, and therefore the shear-rate-independentNewtonian region cannot be depicted. Another disadvantage is that the flow exponent m enters into the dimension of the fluidity. Figure 2.3 Approximation of the flow curve by the power law13
142 Properties of Polymeric MeltsGenerally, the power law can be used to represent a flow or viscosity curve with anacceptable accuracy over only a certain range o
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1.2 Understanding the Extrusion Process A good understanding of the extrusion process is necessary to solve extrusion problems efficiently. It is recommended for the reader new to extrusion to take classes covering the material characteristics of plastics,typical features of extrusion machinery,instrumentation
extrusion. The processing pos-sibilities range from film, pipe, and profile extrusion to sheet, ram, and cold extrusion up to coextrusion. Ceresana analyzes in this study the world market for plastics for extrusion. In 2015, about 51% of the plastics used for ex-trusion were used in the Asia-Pacific; North America and
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Tool steel properties for extrusion dies and tooling 6 Material selection for dies and extrusion tooling parts 8 Manufacturing of dies and tooling 12 Tool steel product programme . Qualitative comparison of critical steel properties (the longer the bar, the better). Fig. 3. Qualitative comparison of resistance to different tool failures (the .
extrusion is also performed for soft metals like Aluminum, lead etc. Difficult to form metals like stainless steels, nickel based alloys and high temperature metals can also be extruded. History; Originally the principle of extrusion was applied to make lead pipe and lead sheathing of electrical cables. Types of Extrusion 1) Direct Extrusion
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Mapping of global plastics value chain and plastics losses to the environment onment 2 Table of contents Table of contents List of Acronyms 4 Types of plastics 5 Executive summary 6 Technical summary 9 1 oduction Intr 17 1.1. Objective 19 1.2. General methodology 19 1.3. Report structure 21 2 Global plastics value chain 23
