Engineering with Rubber

Transcription

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

2 Gent Engineering with Rubber

3

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

5 The Editor: Dr. Alan N. Gent, 4498 Cobblestone Trail, Ravenna, OH , USA Distributed in North and South America by: Hanser Publications 6915 Valley Avenue, Cincinnati, Ohio , USA Fax: (513) Phone: (513) Distributed in all other countries by Carl Hanser Verlag Postfach , München, Germany Fax: +49 (89) 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 (hardcover) -- ISBN (hardcover) 1. Rubber. 2. Engineering design. I. Gent, Alan N. TA455.R8E dc Bibliografische Information Der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über < abrufbar. ISBN E-Book-ISBN 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, München Coverdesign: Stephan Rönigk Typeset: Manuela Treindl, Fürth Printed and bound by Kösel, Krugzell Printed in Germany

6 Contents Preface to Third Edition... XV Authors... XVII 1 Introduction Rubber in Engineering Elastomers Dynamic Application General Design Principles Thermal Expansivity, Pressure, and Swelling Specific Applications and Operating Principles Seal Life Seal Friction... 8 Acknowledgments... 9 References Materials and Compounds Introduction Elastomer Types General Purpose Styrene-Butadiene Rubber (SBR) Polyisoprene (NR, IR) Polybutadiene (BR) Specialty Elastomers Polychloroprene (CR) Acrylonitrile-Butadiene Rubber (NBR) Hydrogenated Nitrile Rubber (HNBR) Butyl Rubber (IIR) Ethylene-Propylene Rubber (EPR, EPDM) Silicone Rubber (MQ, VMQ, PMQ, PVMQ) Polysulfide Rubber (T) Chlorosulfonated Polyethylene (CSM)... 16

7 VI Contents Chlorinated Polyethylene (CM) Ethylene-Methyl Acrylate Rubber (AEM) Acrylic Rubber (ACM) Fluorocarbon Rubbers Epichlorohydrin Rubber (CO, ECO) Urethane Rubber Compounding Vulcanization and Curing Sulfur Curing Determination of Crosslink Density Influence of Crosslink Density Other Cure Systems Reinforcement Anti-Degradants Ozone Attack Oxidation Process Aids Extenders Tackifiers Typical Rubber Compositions Acknowledgment References Problems for Chapter Answers to Problems for Chapter Elasticity Introduction Elastic Properties at Small Strains Elastic Constants Relation Between Shear Modulus G and Composition Stiffness of Components Choice of Shear Modulus Shear Deformations of Bonded Blocks and Hollow Cylindrical Tubes Small Compressions or Extensions of Bonded Blocks Compression of Blocks Between Frictional Surfaces Maximum Allowable Loads in Tension and Compression Indentation of Rubber Blocks by Rigid Indentors Compression of O rings Protrusion of Rubber Through a Hole or Slit... 55

8 Contents VII 3.3 Large Deformations General Theory of Large Elastic Deformations Forms for W Valid at Large Strains Stress-Strain Relations in Selected Cases Simple Extension Equibiaxial Stretching Constrained Tension (Pure Shear) Determining the Strain Energy Function W Elastic Behavior of Filled Rubber Vulcanizates Does Any Strain Energy Function Apply? Other Stress-Strain Relations Valid at Large Strains Simple Shear Torsion Instability in Torsion Inflation of a Thin-Walled Tube [58] Inflation of a Spherical Shell (Balloon) Inflation of a Spherical Cavity; Explosive Decompression Surface Creasing in Compression Molecular Theory of Rubber Elasticity Elastic Behavior of a Molecular Network Effective Density of Network Strands The Second Term in the Strain Energy Function Concluding Remarks on Molecular Theories Acknowledgments References Problems for Chapter Answers to Selected Problems for Chapter Dynamic Mechanical Properties Introduction Stress Waves in Rubbery Solids, Transit Times, and Speeds of Retraction Viscoelasticity Dynamic Experiments Energy Considerations Motion of a Suspended Mass Experimental Techniques Forced Nonresonance Vibration Forced Resonance Vibration Free Vibration Methods...107

9 VIII Contents Rebound Resilience Effect of Static and Dynamic Strain Levels Application of Dynamic Mechanical Measurements Heat Generation in Rubber Components Vibration Isolation Shock Absorbers Effects of Temperature and Frequency Thixotropic Effects in Filled Rubber Compounds Acknowledgments References Problems for Chapter Answers to Problems for Chapter Strength Introduction Fracture Mechanics Analysis of the Test Pieces The Strain Energy Concentration at a Crack Tip Tear Behavior Crack Growth under Repeated Loading The Fatigue Limit and the Effect of Ozone Physical Interpretation of G Effects of Type of Elastomer and Filler Effect of Oxygen Effects of Frequency and Temperature Nonrelaxing Effects Time-Dependent Failure Ozone Attack Tensile Strength Crack Growth in Shear and Compression Cavitation and Related Failures Conclusions References Problems for Chapter Answers to Problems for Chapter Mechanical Fatigue Introduction Application of Fracture Mechanics to Mechanical Fatigue of Rubber Initiation and Propagation of Cracks Fatigue Crack Initiation...163

10 Contents IX Fatigue Life and Crack Growth Fatigue Crack Propagation: The Fatigue Crack Growth Characteristic Fatigue Life Determinations from the Crack Growth Characteristics Fatigue Crack Growth Test Methodology Experimental Determination of Dynamic Tearing Energies for Fatigue Crack Propagation Kinetics of Crack Growth Effects of Test Variables on Fatigue Crack Growth Characteristics and Dynamic Fatigue Life Waveform Frequency Temperature Static Strain/Stress Material Variables and Their Effect on Fatigue Crack Growth Reinforcing Fillers and Compound Modulus Elastomer Type Vulcanizing System Fatigue of Double Network Elastomers and Blends Fatigue and Crack Growth of Rubber under Biaxial Stresses and Multiaxial Loading Fatigue in Rubber Composites Effect of Wires, Cords, and Their Spacing on Fatigue Crack Propagation Effect of Minimum Strain or Stress Comparison of S N Curve and Fatigue Crack Propagation Constants for Rubber-Wire Composites [53] Fatigue of Two-Ply Rubber-Cord Laminates Fatigue Cracking of Rubber in Compression and Shear Applications Crack Growth in Compression Crack Growth in Shear Environmental Effects Modeling and Life Predictions of Elastomeric Components Fatigue Crack Propagation of Thermoplastic Elastomers Durability of Thermoplastic Elastomers Summary Acknowledgments References Problems for Chapter Answers to Problems for Chapter

11 X Contents 7 Durability Introduction Creep, Stress Relaxation, and Set Creep Stress Relaxation Physical Relaxation Chemical Relaxation Compression Set and Recovery Case History Study Longevity of Elastomers in Air Durability at Ambient Temperatures Sunlight and Weathering Ozone Cracking Structural Bearings: Case Histories Natural Rubber Pads for a Rail Viaduct after 100 Years of Service Laminated Bridge Bearings after 20 Years of Service Effect of Low Temperatures Glass Transition Crystallization Effect of Elevated Temperatures Effect of Fluid Environments Aqueous Liquids Hydrocarbon Liquids Hydrocarbon and Other Gases Pressurized CO 2 for Assessing Interface Quality in Bonded Rubber/Rubber Systems Effects of Temperature and Chemical Fluid Attack Effect of Radiation Durability of Rubber-Metal Bonds Adhesion Tests Rubber-Metal Adhesive Systems Durability in Salt Water: Role of Electrochemical Potentials Life Prediction Methodology Acknowledgment References Problems for Chapter Answers to Problems for Chapter

12 Contents XI 8 Design of Components Introduction Shear and Compression Bearings Planar Sandwich Forms Laminate Bearings Tube Form Bearings and Mountings Effective Shape Factors Vibration and Noise Control Vibration Background Information Design Requirements Sample Problems Practical Design Guidelines Summary and Acknowledgments Nomenclature References Problems for Chapter Answers to Problems for Chapter a Finite Element Analysis a.1 Introduction a.2 Material Specification a.2.1 Metal a.2.2 Elastomers a Linear a Non-Linear a Non-Linear Characteristics a Non-Linear Material Models a Obtaining Material Data a Obtaining the Coefficients a Mooney-Rivlin Material Coefficients a.2.3 Elastomer Material Model Correlation a ASTM 412 Tensile Correlation a Pure Shear Correlation a Bi-Axial Correlation a Simple Shear Correlation a.3 Terminology and Verification a.3.1 Terminology a.3.2 Types of FEA Models a.3.3 Model Building a.3.4 Boundary Conditions a.3.5 Solution...318

13 XII Contents 9a Tangent Stiffness a Newton-Raphson a Non-Linear Material Behavior a Viscoelasticity (See Chapter 4) a Model Verification a.3.6 Results a.3.7 Linear Verification a.3.8 Classical Verification Non-Linear a.4 Example Applications a.4.1 Positive Drive Timing Belt a.4.2 Dock Fender a.4.3 Rubber Boot a.4.4 Bumper Design a.4.5 Laminated Bearing a.4.6 Down Hole Packer a.4.7 Bonded Sandwich Mount a.4.8 O-Ring a.4.9 Elastomer Hose Model a.4.10 Sample Belt References b Developments in Finite Element Analysis b.1 Introduction b.2 Material Models b.2.1 Hyperelastic Models b.2.2 Compressibility b.2.3 Deviations from Hyperelasticity b Viscoelasticity b Stress-Softening b.3 FEA Modelling Techniques b.3.1 Pre- and Post-Processing b.3.2 Choice of Elements b.3.3 Convergence b.3.4 Fracture Mechanics b.4 Verification b.4.1 Stresses and Strains b.4.2 Tearing Energy b.5 Applications b.5.1 Load Deflection b.5.2 Failure References...362

14 Contents XIII 10 Tests and Specifications Introduction Standard Test Methods Purpose of Testing Test Piece Preparation Time Between Vulcanization and Testing Scope of This Chapter Measurement of Design Parameters Young s Modulus Shear Modulus Creep and Stress Relaxation Creep Stress Relaxation Quality Control Tests Hardness Durometer International Rubber Hardness Tester Tensile Properties Compression Set Accelerated Aging Aging in an Air Oven Ozone Cracking Liquid Resistance Factors in Swelling Swelling Tests Adhesion to Substrates Processability Dynamic Properties Resilience Yerzley Oscillograph Resonant Beam Servohydraulic Testers Electrodynamic Testers Preferred Test Conditions Tests for Tires Bead Unseating Resistance Tire Strength Tire Endurance High Speed Performance Specifications Classification System...401

15 XIV Contents Type Class Further Description Tolerances Molded Products Extruded Products Load-Deflection Characteristics Rubber Bridge Bearings Function Design Code Materials Specification Pipe Sealing Rings Function Materials Tensile Properties Compression Set Low Temperature Flexibility Oven Aging Oil Resistance Closing Remarks References Problems for Chapter Answers to Problems for Chapter Appendix: Tables of Physical Constants Index...427

16 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

17

18 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 , 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 , USA Hamed, G. R., Department of Polymer Science, The University of Akron, Akron, Ohio , USA Hertz, Daniel L., Jr., Seals Eastern, Inc., Red Bank, New Jersey 07701, USA James, Frank O., Mechanical Products Division, Lord Corporation, Erie, Pennsylvania , USA Lake, Graham J., University of East London, Dagenham, RM8 2AS, U.K.

19 XVIII Authors Miller, Thomas S., Mechanical Products Division, Lord Corporation, Erie, Pennsylvania , USA Scott, Kenneth W. (deceased) Sheridan, Patrick M., Mechanical Products Division, Lord Corporation, Erie, Pennsylvania , 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

20 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.