Engineering with Rubber

Alan N. Gent Engineering with Rubber How to Design Rubber Components 3 rd Edition

Gent Engineering with Rubber

Alan N. Gent Engineering with Rubber How to Design Rubber Components 3 rd Edition Hanser Publishers, Munich Hanser Publications, Cincinnati

The Editor: Dr. Alan N. Gent, 4498 Cobblestone Trail, Ravenna, OH 44266-8249, USA Distributed in North and South America by: Hanser Publications 6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USA Fax: (513) 527-8801 Phone: (513) 527-8977 www.hanserpublications.com Distributed in all other countries by Carl Hanser Verlag Postfach 86 04 20, 81631 München, Germany Fax: +49 (89) 98 48 09 www.hanser.de The use of general descriptive names, trademarks, etc., in this publication, even if the former are not especially identified, 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, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Library of Congress Cataloging-in-Publication Data Engineering with rubber : how to design rubber components / [edited by] Alan N. Gent. -- 3rd ed. p. cm. Includes bibliographical references and index. ISBN 978-3-446-42764-8 (hardcover) -- ISBN 978-1-56990-508-1 (hardcover) 1. Rubber. 2. Engineering design. I. Gent, Alan N. TA455.R8E54 2012 620.1 94--dc23 2011045185 Bibliografische Information Der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über <http://dnb.d-nb.de> abrufbar. ISBN 978-3-446-42764-8 E-Book-ISBN 978-3-446-42871-3 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or by any information storage and retrieval system, without permission in writing from the publisher. Carl Hanser Verlag, Munich 2012 Production Management: Steffen Jörg Coverconcept: Marc Müller-Bremer, www.rebranding.de, München Coverdesign: Stephan Rönigk Typeset: Manuela Treindl, Fürth Printed and bound by Kösel, Krugzell Printed in Germany

Contents Preface to Third Edition... XV Authors... XVII 1 Introduction... 1 1.1 Rubber in Engineering... 1 1.2 Elastomers... 2 1.3 Dynamic Application... 3 1.4 General Design Principles... 3 1.5 Thermal Expansivity, Pressure, and Swelling... 4 1.6 Specific Applications and Operating Principles... 5 1.7 Seal Life... 8 1.8 Seal Friction... 8 Acknowledgments... 9 References... 9 2 Materials and Compounds... 11 2.1 Introduction... 11 2.2 Elastomer Types... 12 2.2.1 General Purpose... 12 2.2.1.1 Styrene-Butadiene Rubber (SBR)... 12 2.2.1.2 Polyisoprene (NR, IR)... 13 2.2.1.3 Polybutadiene (BR)... 14 2.2.2 Specialty Elastomers... 14 2.2.2.1 Polychloroprene (CR)... 14 2.2.2.2 Acrylonitrile-Butadiene Rubber (NBR)... 15 2.2.2.3 Hydrogenated Nitrile Rubber (HNBR)... 15 2.2.2.4 Butyl Rubber (IIR)... 15 2.2.2.5 Ethylene-Propylene Rubber (EPR, EPDM)... 15 2.2.2.6 Silicone Rubber (MQ, VMQ, PMQ, PVMQ)... 16 2.2.2.7 Polysulfide Rubber (T)... 16 2.2.2.8 Chlorosulfonated Polyethylene (CSM)... 16

VI Contents 2.2.2.9 Chlorinated Polyethylene (CM)... 16 2.2.2.10 Ethylene-Methyl Acrylate Rubber (AEM)... 17 2.2.2.11 Acrylic Rubber (ACM)... 17 2.2.2.12 Fluorocarbon Rubbers... 17 2.2.2.13 Epichlorohydrin Rubber (CO, ECO)... 17 2.2.2.14 Urethane Rubber... 17 2.3 Compounding... 18 2.3.1 Vulcanization and Curing... 18 2.3.1.1 Sulfur Curing... 18 2.3.1.2 Determination of Crosslink Density... 21 2.3.1.3 Influence of Crosslink Density... 22 2.3.1.4 Other Cure Systems... 23 2.3.2 Reinforcement... 23 2.3.3 Anti-Degradants... 25 2.3.3.1 Ozone Attack... 26 2.3.3.2 Oxidation... 26 2.3.4 Process Aids... 28 2.3.5 Extenders... 29 2.3.6 Tackifiers... 29 2.4 Typical Rubber Compositions... 30 Acknowledgment... 34 References... 34 Problems for Chapter 2... 35 Answers to Problems for Chapter 2... 35 3 Elasticity... 37 3.1 Introduction... 37 3.2 Elastic Properties at Small Strains... 38 3.2.1 Elastic Constants... 38 3.2.2 Relation Between Shear Modulus G and Composition... 41 3.2.3 Stiffness of Components... 44 3.2.3.1 Choice of Shear Modulus... 44 3.2.3.2 Shear Deformations of Bonded Blocks and Hollow Cylindrical Tubes... 45 3.2.3.3 Small Compressions or Extensions of Bonded Blocks.. 47 3.2.3.4 Compression of Blocks Between Frictional Surfaces... 50 3.2.3.5 Maximum Allowable Loads in Tension and Compression... 52 3.2.3.6 Indentation of Rubber Blocks by Rigid Indentors... 53 3.2.3.7 Compression of O rings... 55 3.2.3.8 Protrusion of Rubber Through a Hole or Slit... 55

Contents VII 3.3 Large Deformations... 56 3.3.1 General Theory of Large Elastic Deformations... 56 3.3.2 Forms for W Valid at Large Strains... 58 3.3.3 Stress-Strain Relations in Selected Cases... 59 3.3.3.1 Simple Extension... 59 3.3.3.2 Equibiaxial Stretching... 61 3.3.3.3 Constrained Tension (Pure Shear)... 61 3.3.4 Determining the Strain Energy Function W... 63 3.3.4.1 Elastic Behavior of Filled Rubber Vulcanizates... 65 3.3.4.2 Does Any Strain Energy Function Apply?... 67 3.3.5 Other Stress-Strain Relations Valid at Large Strains... 67 3.3.5.1 Simple Shear... 67 3.3.5.2 Torsion... 70 3.3.5.3 Instability in Torsion... 72 3.3.5.4 Inflation of a Thin-Walled Tube [58]... 73 3.3.5.5 Inflation of a Spherical Shell (Balloon)... 74 3.3.5.6 Inflation of a Spherical Cavity; Explosive Decompression... 76 3.3.5.7 Surface Creasing in Compression... 77 3.4 Molecular Theory of Rubber Elasticity... 78 3.4.1 Elastic Behavior of a Molecular Network... 78 3.4.3 Effective Density of Network Strands... 81 3.4.4 The Second Term in the Strain Energy Function... 82 3.4.5 Concluding Remarks on Molecular Theories... 83 Acknowledgments... 84 References... 84 Problems for Chapter 3... 87 Answers to Selected Problems for Chapter 3... 88 4 Dynamic Mechanical Properties... 89 4.1 Introduction... 89 4.2 Stress Waves in Rubbery Solids, Transit Times, and Speeds of Retraction... 90 4.3 Viscoelasticity... 92 4.4 Dynamic Experiments... 96 4.5 Energy Considerations...100 4.6 Motion of a Suspended Mass...102 4.7 Experimental Techniques...106 4.7.1 Forced Nonresonance Vibration...106 4.7.2 Forced Resonance Vibration...106 4.7.3 Free Vibration Methods...107

VIII Contents 4.7.4 Rebound Resilience...107 4.7.5 Effect of Static and Dynamic Strain Levels...108 4.8 Application of Dynamic Mechanical Measurements...108 4.8.1 Heat Generation in Rubber Components...108 4.8.2 Vibration Isolation...109 4.8.3 Shock Absorbers...109 4.9 Effects of Temperature and Frequency...110 4.10 Thixotropic Effects in Filled Rubber Compounds...114 Acknowledgments...116 References...116 Problems for Chapter 4...116 Answers to Problems for Chapter 4...117 5 Strength...119 5.1 Introduction...119 5.2 Fracture Mechanics...119 5.2.1 Analysis of the Test Pieces...122 5.2.2 The Strain Energy Concentration at a Crack Tip...123 5.3 Tear Behavior...125 5.4 Crack Growth under Repeated Loading...131 5.4.1 The Fatigue Limit and the Effect of Ozone...132 5.4.2 Physical Interpretation of G 0...133 5.4.3 Effects of Type of Elastomer and Filler...135 5.4.4 Effect of Oxygen...135 5.4.5 Effects of Frequency and Temperature...137 5.4.6 Nonrelaxing Effects...137 5.4.7 Time-Dependent Failure...138 5.5 Ozone Attack...138 5.6 Tensile Strength...142 5.7 Crack Growth in Shear and Compression...144 5.8 Cavitation and Related Failures...147 5.9 Conclusions...148 References...149 Problems for Chapter 5...152 Answers to Problems for Chapter 5...153 6 Mechanical Fatigue...159 6.1 Introduction...159 6.2 Application of Fracture Mechanics to Mechanical Fatigue of Rubber.. 161 6.3 Initiation and Propagation of Cracks...163 6.3.1 Fatigue Crack Initiation...163

Contents IX 6.3.2 Fatigue Life and Crack Growth...164 6.3.3 Fatigue Crack Propagation: The Fatigue Crack Growth Characteristic...166 6.3.4 Fatigue Life Determinations from the Crack Growth Characteristics...168 6.4 Fatigue Crack Growth Test Methodology...170 6.4.1 Experimental Determination of Dynamic Tearing Energies for Fatigue Crack Propagation...170 6.4.2 Kinetics of Crack Growth...171 6.4.3 Effects of Test Variables on Fatigue Crack Growth Characteristics and Dynamic Fatigue Life...172 6.4.3.1 Waveform...172 6.4.3.2 Frequency...172 6.4.3.3 Temperature...172 6.4.3.4 Static Strain/Stress...174 6.5 Material Variables and Their Effect on Fatigue Crack Growth...176 6.5.1 Reinforcing Fillers and Compound Modulus...176 6.5.2 Elastomer Type...178 6.5.3 Vulcanizing System...179 6.5.3 Fatigue of Double Network Elastomers and Blends...181 6.6 Fatigue and Crack Growth of Rubber under Biaxial Stresses and Multiaxial Loading...182 6.7 Fatigue in Rubber Composites...184 6.7.1 Effect of Wires, Cords, and Their Spacing on Fatigue Crack Propagation...185 6.7.2 Effect of Minimum Strain or Stress...185 6.7.3 Comparison of S N Curve and Fatigue Crack Propagation Constants for Rubber-Wire Composites [53]...187 6.7.4 Fatigue of Two-Ply Rubber-Cord Laminates...188 6.8 Fatigue Cracking of Rubber in Compression and Shear Applications.. 189 6.8.1 Crack Growth in Compression...189 6.8.2 Crack Growth in Shear...192 6.9 Environmental Effects...193 6.10 Modeling and Life Predictions of Elastomeric Components...194 6.11 Fatigue Crack Propagation of Thermoplastic Elastomers...194 6.12 Durability of Thermoplastic Elastomers...195 6.13 Summary...197 Acknowledgments...198 References...198 Problems for Chapter 6...200 Answers to Problems for Chapter 6...201

X Contents 7 Durability...205 7.1 Introduction...205 7.2 Creep, Stress Relaxation, and Set...207 7.2.1 Creep...208 7.2.2 Stress Relaxation...208 7.2.3 Physical Relaxation...209 7.2.4 Chemical Relaxation...211 7.2.5 Compression Set and Recovery...211 7.2.6 Case History Study...213 7.3 Longevity of Elastomers in Air...214 7.3.1 Durability at Ambient Temperatures...214 7.3.2 Sunlight and Weathering...215 7.3.3 Ozone Cracking...215 7.3.4 Structural Bearings: Case Histories...216 7.3.4.1 Natural Rubber Pads for a Rail Viaduct after 100 Years of Service...216 7.3.4.2 Laminated Bridge Bearings after 20 Years of Service...217 7.4 Effect of Low Temperatures...220 7.4.1 Glass Transition...220 7.4.2 Crystallization...221 7.5 Effect of Elevated Temperatures...222 7.6 Effect of Fluid Environments...224 7.6.1 Aqueous Liquids...229 7.6.2 Hydrocarbon Liquids...232 7.6.3 Hydrocarbon and Other Gases...235 7.6.3.1 Pressurized CO 2 for Assessing Interface Quality in Bonded Rubber/Rubber Systems...240 7.6.4 Effects of Temperature and Chemical Fluid Attack...240 7.6.5 Effect of Radiation...242 7.7 Durability of Rubber-Metal Bonds...243 7.7.1 Adhesion Tests...243 7.7.2 Rubber-Metal Adhesive Systems...245 7.7.3 Durability in Salt Water: Role of Electrochemical Potentials...246 7.8 Life Prediction Methodology...248 Acknowledgment...251 References...251 Problems for Chapter 7...253 Answers to Problems for Chapter 7...256

Contents XI 8 Design of Components...259 8.1 Introduction...259 8.2 Shear and Compression Bearings...261 8.2.1 Planar Sandwich Forms...261 8.2.2 Laminate Bearings...267 8.2.3 Tube Form Bearings and Mountings...269 8.2.4 Effective Shape Factors...274 8.3 Vibration and Noise Control...275 8.3.1 Vibration Background Information...276 8.3.2 Design Requirements...278 8.3.3 Sample Problems...278 8.4 Practical Design Guidelines...287 8.5 Summary and Acknowledgments...288 Nomenclature...289 References...290 Problems for Chapter 8...290 Answers to Problems for Chapter 8...291 9a Finite Element Analysis...295 9a.1 Introduction...295 9a.2 Material Specification...297 9a.2.1 Metal...297 9a.2.2 Elastomers...298 9a.2.2.1 Linear...298 9a.2.2.2 Non-Linear...303 9a.2.2.2.1 Non-Linear Characteristics...303 9a.2.2.2.2 Non-Linear Material Models...303 9a.2.2.2.3 Obtaining Material Data...304 9a.2.2.2.4 Obtaining the Coefficients...309 9a.2.2.2.5 Mooney-Rivlin Material Coefficients...310 9a.2.3 Elastomer Material Model Correlation...311 9a.2.3.1 ASTM 412 Tensile Correlation...311 9a.2.3.2 Pure Shear Correlation...312 9a.2.3.3 Bi-Axial Correlation...312 9a.2.3.4 Simple Shear Correlation...312 9a.3 Terminology and Verification...313 9a.3.1 Terminology...313 9a.3.2 Types of FEA Models...314 9a.3.3 Model Building...315 9a.3.4 Boundary Conditions...317 9a.3.5 Solution...318

XII Contents 9a.3.5.1 Tangent Stiffness...318 9a.3.5.2 Newton-Raphson...319 9a.3.5.3 Non-Linear Material Behavior...319 9a.3.5.4 Viscoelasticity (See Chapter 4)...319 9a.3.5.5 Model Verification...320 9a.3.6 Results...320 9a.3.7 Linear Verification...322 9a.3.8 Classical Verification Non-Linear...323 9a.4 Example Applications...325 9a.4.1 Positive Drive Timing Belt...325 9a.4.2 Dock Fender...326 9a.4.3 Rubber Boot...329 9a.4.4 Bumper Design...331 9a.4.5 Laminated Bearing...333 9a.4.6 Down Hole Packer...335 9a.4.7 Bonded Sandwich Mount...337 9a.4.8 O-Ring...339 9a.4.9 Elastomer Hose Model...339 9a.4.10 Sample Belt...340 References...342 9b Developments in Finite Element Analysis...345 9b.1 Introduction...345 9b.2 Material Models...345 9b.2.1 Hyperelastic Models...346 9b.2.2 Compressibility...350 9b.2.3 Deviations from Hyperelasticity...351 9b.2.3.1 Viscoelasticity...351 9b.2.3.2 Stress-Softening...352 9b.3 FEA Modelling Techniques...353 9b.3.1 Pre- and Post-Processing...353 9b.3.2 Choice of Elements...354 9b.3.3 Convergence...355 9b.3.4 Fracture Mechanics...356 9b.4 Verification...356 9b.4.1 Stresses and Strains...357 9b.4.2 Tearing Energy...358 9b.5 Applications...359 9b.5.1 Load Deflection...359 9b.5.2 Failure...360 References...362

Contents XIII 10 Tests and Specifications...365 10.1 Introduction...365 10.1.1 Standard Test Methods...365 10.1.2 Purpose of Testing...366 10.1.3 Test Piece Preparation...366 10.1.4 Time Between Vulcanization and Testing...367 10.1.5 Scope of This Chapter...367 10.2 Measurement of Design Parameters...367 10.2.1 Young s Modulus...368 10.2.2 Shear Modulus...370 10.2.3 Creep and Stress Relaxation...372 10.2.3.1 Creep...373 10.2.3.2 Stress Relaxation...374 10.3 Quality Control Tests...374 10.3.1 Hardness...375 10.3.1.1 Durometer...375 10.3.1.2 International Rubber Hardness Tester...376 10.3.2 Tensile Properties...378 10.3.3 Compression Set...380 10.3.4 Accelerated Aging...381 10.3.4.1 Aging in an Air Oven...381 10.3.4.2 Ozone Cracking...382 10.3.5 Liquid Resistance...384 10.3.5.1 Factors in Swelling...384 10.3.5.2 Swelling Tests...385 10.3.6 Adhesion to Substrates...385 10.3.7 Processability...388 10.4 Dynamic Properties...390 10.4.1 Resilience...392 10.4.2 Yerzley Oscillograph...393 10.4.3 Resonant Beam...394 10.4.4 Servohydraulic Testers...395 10.4.5 Electrodynamic Testers...396 10.4.6 Preferred Test Conditions...397 10.5 Tests for Tires...397 10.5.1 Bead Unseating Resistance...398 10.5.2 Tire Strength...399 10.5.3 Tire Endurance...400 10.5.4 High Speed Performance...400 10.6 Specifications...401 10.6.1 Classification System...401

XIV Contents 10.6.1.1 Type...402 10.6.1.2 Class...403 10.6.1.3 Further Description...403 10.6.2 Tolerances...406 10.6.2.1 Molded Products...406 10.6.2.2 Extruded Products...408 10.6.2.3 Load-Deflection Characteristics...408 10.6.3 Rubber Bridge Bearings...409 10.6.3.1 Function...409 10.6.3.2 Design Code...410 10.6.3.3 Materials Specification...411 10.6.4 Pipe Sealing Rings...413 10.6.4.1 Function...413 10.6.4.2 Materials...413 10.6.4.3 Tensile Properties...413 10.6.4.4 Compression Set...414 10.6.4.5 Low Temperature Flexibility...414 10.6.4.6 Oven Aging...415 10.6.4.7 Oil Resistance...415 10.6.4.8 Closing Remarks...415 References...416 Problems for Chapter 10...419 Answers to Problems for Chapter 10...420 Appendix: Tables of Physical Constants...423 Index...427

Preface to Third Edition The two former editions of Engineering with rubber have served as handbooks and teaching texts in a rather specialized branch of materials science and engineering the design, testing and use of engineered products incorporating rubber for two generations of students, engineers and scientists who have encountered this unusual and fascinating branch of engineering technology. During this period, applications of rubber in engineering have increased significantly, notably in seals (for example in oil wells and transmission lines) and in flexible mountings to protect buildings against earthquake shocks. However, the second edition of the book has become out-of-print, and some of the material in it, particularly the references, has become out-dated. This third edition includes revised versions of most of the previous chapters and also contains a new chapter reviewing recent developments in the use of finite-element programs, an important advance in methods of designing rubber products. We hope that the book will continue to help scientists and engineers as they study and apply the basic principles governing the use of rubber components in engineering applications. Alan N. Gent The University of Akron August 1, 2011

Authors Campion, Robert, Materials Engineering Research Laboratory (MERL Ltd.), Wilbury Way, Hitchin, Hertfordshire, SG4 0TW, England Ellul, Maria D., ExxonMobil Chemical Company, 388 S. Main Street, Akron, Ohio 44311 1059, USA Finney, Robert H., HLA Engineers, Inc., 5619 Dyer Street, Suite 110, Dallas, Texas, 75206, USA Gent, Alan N., College of Polymer Science and Polymer Engineering, The University of Akron, Akron, Ohio 44325 3909, USA Hamed, G. R., Department of Polymer Science, The University of Akron, Akron, Ohio 44325 3909, USA Hertz, Daniel L., Jr., Seals Eastern, Inc., Red Bank, New Jersey 07701, USA James, Frank O., Mechanical Products Division, Lord Corporation, Erie, Pennsylvania 16514 0039, USA Lake, Graham J., University of East London, Dagenham, RM8 2AS, U.K.

XVIII Authors Miller, Thomas S., Mechanical Products Division, Lord Corporation, Erie, Pennsylvania 16514 0039, USA Scott, Kenneth W. (deceased) Sheridan, Patrick M., Mechanical Products Division, Lord Corporation, Erie, Pennsylvania 16514 0039, USA Sommer, John G., 5939 Bradford Way, Hudson, OH 44236, USA Stevenson, Andrew, Materials Engineering Research Laboratory (MERL Ltd.), Wilbury Way, Hitchin, Hertfordshire, SG4 0TW, England Thomas, Alan G., Queen Mary and Westfield College, University of London, E1 4NS, U.K. Yeoh, Oon Hock, Freudenberg-NOK General Partnership, Plymouth, MI 48170, USA

1 Introduction Daniel L. Hertz, Jr. 1.1 Rubber in Engineering Elastomers (natural and synthetic rubber) are amorphous polymers to which various ingredients are added, creating what the rubber chemist refers to as a compound. After heating and reaction (vulcanization), these materials become rubber. While they are elastic and rubbery, they also dissipate energy because of their viscoelastic nature. Their strength is high, especially under shear and compressive deformations. But, as with any mechanically loaded component, failure can occur as a result of fatigue. Thus the long-term durability of rubber has to be predictable. Simple design criteria should be made available. Computer-aided design and analysis would be desirable. Specifications are required to control product quality. Physical constants, as with any engineering material, should be readily available. These are the reasons for this book: Engineering Design of Rubber Components. The next question is: Which are the necessary chapters to read? Answer: All of them sooner (the reason you probably bought the book) or later (the reason you are rereading the book), when you have problems. Many failures of rubber components are due to a basic lack of understanding of the nature of rubber. Rubber is an engineering material. Consider now the process of designing a longlived rubber component. To be successful, we must understand: Polymers and the rubbery state General design principles This is not as daunting a task as it appears. Chapters 2 to 4 provide a background for polymers and the rubbery state, and Chapters 5 to 10 give some general design principles. Without attempting to preempt the authors, let me present a sometimes overly simplistic view as I might use in addressing a fellow engineer.