Engineering with Rubber

Contents

Preface to Third Edition

Authors

1 Introduction

1.1 Rubber in Engineering

1.2 Elastomers

1.3 Dynamic Application

1.4 General Design Principles

1.5 Thermal Expansivity, Pressure, and Swelling

1.6 Specific Applications and Operating Principles

1.7 Seal Life

1.8 Seal Friction

Acknowledgments.

References.

2 Materials and Compounds

2.1 Introduction

2.2 Elastomer Types

2.2.1 General Purpose

2.2.1.1 Styrene-Butadiene Rubber (SBR)

2.2.1.2 Polyisoprene (NR, IR)

2.2.1.3 Polybutadiene (BR)

2.2.2 Specialty Elastomers

2.2.2.1 Polychloroprene (CR)

2.2.2.2 Acrylonitrile-Butadiene Rubber (NBR)

2.2.2.3 Hydrogenated Nitrile Rubber (HNBR)

2.2.2.4 Butyl Rubber (IIR)

2.2.2.5 Ethylene-Propylene Rubber (EPR, EPDM)

2.2.2.6 Silicone Rubber (MQ, VMQ, PMQ, PVMQ)

2.2.2.7 Polysulfide Rubber (T)

2.2.2.8 Chlorosulfonated Polyethylene (CSM)

2.2.2.9 Chlorinated Polyethylene (CM)

2.2.2.10 Ethylene-Methyl Acrylate Rubber (AEM)

2.2.2.11 Acrylic Rubber (ACM)

2.2.2.12 Fluorocarbon Rubbers

2.2.2.13 Epichlorohydrin Rubber (CO, ECO)

2.2.2.14 Urethane Rubber

2.3 Compounding

2.3.1 Vulcanization and Curing

2.3.1.1 Sulfur Curing

2.3.1.2 Determination of Crosslink Density

2.3.1.3 Influence of Crosslink Density

2.3.1.4 Other Cure Systems

2.3.2 Reinforcement

2.3.3 Anti-Degradants

2.3.3.1 Ozone Attack

2.3.3.2 Oxidation

2.3.4 Process Aids

2.3.5 Extenders

2.3.6 Tackifiers

2.4 Typical Rubber Compositions

Acknowledgment.

References.

Problems for Chapter.2.

Answers to Problems for Chapter.2.

3 Elasticity

3.1 Introduction

3.2 Elastic Properties at Small Strains

3.2.1 Elastic Constants

3.2.2 Relation Between Shear Modulus G and Composition

3.2.3 Stiffness of Components

3.2.3.1 Choice of Shear Modulus

3.2.3.2 Shear Deformations of Bonded Blocks and Hollow Cylindrical Tubes

3.2.3.3 Small Compressions or Extensions of Bonded Blocks

3.2.3.4 Compression of Blocks Between Frictional Surfaces

3.2.3.5 Maximum Allowable Loads in Tension and Compression

3.2.3.6 Indentation of Rubber Blocks by Rigid Indentors

3.2.3.7 Compression of O-rings

3.2.3.8 Protrusion of Rubber Through a Hole or Slit

3.3 Large Deformations

3.3.1 General Theory of Large Elastic Deformations

3.3.2 Forms for W Valid at Large Strains

3.3.3 Stress-Strain Relations in Selected Cases

3.3.3.1 Simple Extension

3.3.3.2 Equibiaxial Stretching

3.3.3.3 Constrained Tension (Pure Shear)

3.3.4 Determining the Strain Energy Function W

3.3.4.1 Elastic Behavior of Filled Rubber Vulcanizates

3.3.4.2 Does Any Strain Energy Function Apply?

3.3.5 Other Stress-Strain Relations Valid at Large Strains

3.3.5.1 Simple Shear

3.3.5.2 Torsion

3.3.5.3 Instability in Torsion

3.3.5.4 Inflation of a Thin-Walled Tube [58]

3.3.5.5 Inflation of a Spherical Shell (Balloon)

3.3.5.6 Inflation of a Spherical Cavity; Explosive Decompression

3.3.5.7 Surface Creasing in Compression

3.4 Molecular Theory of Rubber Elasticity

3.4.1 Elastic Behavior of a Molecular Network

3.4.3 Effective Density of Network Strands

3.4.4 The Second Term in the Strain Energy Function

3.4.5 Concluding Remarks on Molecular Theories

Acknowledgments.

References.

Problems for Chapter.3.

Answers to Selected Problems for Chapter.3.

4 Dynamic Mechanical Properties

4.1 Introduction

4.2 Stress Waves in Rubbery Solids, Transit Times, and Speeds of Retraction

4.3 Viscoelasticity

4.4 Dynamic Experiments

4.5 Energy Considerations

4.6 Motion of a Suspended Mass

4.7 Experimental Techniques

4.7.1 Forced Nonresonance Vibration

4.7.2 Forced Resonance Vibration

4.7.3 Free Vibration Methods

4.7.4 Rebound Resilience

4.7.5 Effect of Static and Dynamic Strain Levels

4.8 Application of Dynamic Mechanical Measurements

4.8.1 Heat Generation in Rubber Components

4.8.2 Vibration Isolation

4.8.3 Shock Absorbers

4.9 Effects of Temperature and Frequency

4.10 Thixotropic Effects in Filled Rubber Compounds

Acknowledgments.

References.

Problems for Chapter.4.

Answers to Problems for Chapter.4.

5 Strength

5.1 Introduction

5.2 Fracture Mechanics

5.2.1 Analysis of the Test Pieces

5.2.2 The Strain Energy Concentration at a Crack Tip

5.3 Tear Behavior

5.4 Crack Growth under Repeated Loading

5.4.1 The Fatigue Limit and the Effect of Ozone

5.4.2 Physical Interpretation of G0

5.4.3 Effects of Type of Elastomer and Filler

5.4.4 Effect of Oxygen

5.4.5 Effects of Frequency and Temperature

5.4.6 Nonrelaxing Effects

5.4.7 Time-Dependent Failure

5.5 Ozone Attack

5.6 Tensile Strength

5.7 Crack Growth in Shear and Compression

5.8 Cavitation and Related Failures

5.9 Conclusions

References.

Problems for Chapter.5.

Answers to Problems for Chapter.5.

6 Mechanical Fatigue

6.1 Introduction

6.2 Application of Fracture Mechanics to Mechanical Fatigue of Rubber

6.3 Initiation and Propagation of Cracks

6.3.1 Fatigue Crack Initiation

6.3.2 Fatigue Life and Crack Growth

6.3.3 Fatigue Crack Propagation: The Fatigue Crack Growth Characteristic

6.3.4 Fatigue Life Determinations from the Crack Growth Characteristics

6.4 Fatigue Crack Growth Test Methodology

6.4.1 Experimental Determination of Dynamic Tearing Energies for Fatigue Crack Propagation

6.4.2 Kinetics of Crack Growth

6.4.3 Effects of Test Variables on Fatigue Crack Growth Characteristics and Dynamic Fatigue Life

6.4.3.1 Waveform

6.4.3.2 Frequency

6.4.3.3 Temperature

6.4.3.4 Static Strain/Stress

6.5 Material Variables and Their Effect on Fatigue Crack Growth

6.5.1 Reinforcing Fillers and Compound Modulus

6.5.2 Elastomer Type

6.5.3 Vulcanizing System

6.5.3 Fatigue of Double Network Elastomers and Blends

6.6 Fatigue and Crack Growth of Rubber under Biaxial Stresses and Multiaxial Loading

6.7 Fatigue in Rubber Composites

6.7.1 Effect of Wires, Cords, and Their Spacing on Fatigue Crack Propagation

6.7.2 Effect of Minimum Strain or Stress

6.7.3 Comparison of S-N Curve and Fatigue Crack Propagation Constants for Rubber-Wire Composites [53]

6.7.4 Fatigue of Two-Ply Rubber-Cord Laminates

6.8 Fatigue Cracking of Rubber in Compression and Shear Applications

6.8.1 Crack Growth in Compression

6.8.2 Crack Growth in Shear

6.9 Environmental Effects

6.10 Modeling and Life Predictions of Elastomeric Components

6.11 Fatigue Crack Propagation of Thermoplastic Elastomers

6.12 Durability of Thermoplastic Elastomers

6.13 Summary

Acknowledgments.

References.

Problems for Chapter.6.

Answers to Problems for Chapter.6.

7 Durability

7.1 Introduction

7.2 Creep, Stress Relaxation, and Set

7.2.1 Creep

7.2.2 Stress Relaxation

7.2.3 Physical Relaxation

7.2.4 Chemical Relaxation

7.2.5 Compression Set and Recovery

7.2.6 Case History Study

7.3 Longevity of Elastomers in Air

7.3.1 Durability at Ambient Temperatures

7.3.2 Sunlight and Weathering

7.3.3 Ozone Cracking

7.3.4 Structural Bearings: Case Histories

7.3.4.1 Natural Rubber Pads for a Rail Viaduct after 100.Years of Service

7.3.4.2 Laminated Bridge Bearings after 20 Years of Service

7.4 Effect of Low Temperatures

7.4.1 Glass Transition

7.4.2 Crystallization

7.5 Effect of Elevated Temperatures

7.6 Effect of Fluid Environments

7.6.1 Aqueous Liquids

7.6.2 Hydrocarbon Liquids

7.6.3 Hydrocarbon and Other Gases

7.6.3.1 Pressurized CO2 for Assessing Interface Quality in Bonded Rubber/Rubber Systems

7.6.4 Effects of Temperature and Chemical Fluid Attack

7.6.5 Effect of Radiation

7.7 Durability of Rubber-Metal Bonds

7.7.1 Adhesion Tests

7.7.2 Rubber-Metal Adhesive Systems

7.7.3 Durability in Salt Water: Role of Electrochemical Potentials

7.8 Life Prediction Methodology

Acknowledgment.

References.

Problems for Chapter.7.

Answers to Problems for Chapter.7.

8 Design of Components

8.1 Introduction

8.2 Shear and Compression Bearings

8.2.1 Planar Sandwich Forms

8.2.2 Laminate Bearings

8.2.3 Tube Form Bearings and Mountings

8.2.4 Effective Shape Factors

8.3 Vibration and Noise Control

8.3.1 Vibration Background Information

8.3.2 Design Requirements

8.3.3 Sample Problems

8.4 Practical Design Guidelines

8.5 Summary and Acknowledgments

Nomenclature.

References.

Problems for Chapter.8.

Answers to Problems for Chapter.8.

9a Finite Element Analysis

9a.1 Introduction

9a.2 Material Specification

9a.2.1 Metal

9a.2.2 Elastomers

9a.2.2.1 Linear

9a.2.2.2 Non-Linear

9a.2.2.2.1 Non-Linear Characteristics

9a.2.2.2.2 Non-Linear Material Models

9a.2.2.2.3 Obtaining Material Data

9a.2.2.2.4 Obtaining the Coefficients

9a.2.2.2.5 Mooney-Rivlin Material Coefficients

9a.2.3 Elastomer Material Model Correlation

9a.2.3.1 ASTM.412 Tensile Correlation

9a.2.3.2 Pure Shear Correlation

9a.2.3.3 Bi-Axial Correlation

9a.2.3.4 Simple Shear Correlation

9a.3 Terminology and Verification

9a.3.1 Terminology

9a.3.2 Types of FEA Models

9a.3.3 Model Building

9a.3.4 Boundary Conditions

9a.3.5 Solution

9a.3.5.1 Tangent Stiffness

9a.3.5.2 Newton-Raphson

9a.3.5.3 Non-Linear Material Behavior

9a.3.5.4 Viscoelasticity (See Chapter.4)

9a.3.5.5 Model Verification

9a.3.6 Results

9a.3.7 Linear Verification

9a.3.8 Classical Verification – Non-Linear

9a.4 Example Applications

9a.4.1 Positive Drive Timing Belt

9a.4.2 Dock Fender

9a.4.3 Rubber Boot

9a.4.4 Bumper Design

9a.4.5 Laminated Bearing

9a.4.6 Down Hole Packer

9a.4.7 Bonded Sandwich Mount

9a.4.8 O-Ring

9a.4.9 Elastomer Hose Model

9a.4.10 Sample Belt

References.

9b Developments in Finite Element Analysis

9b.1 Introduction

9b.2 Material Models

9b.2.1 Hyperelastic Models

9b.2.2 Compressibility

9b.2.3 Deviations from Hyperelasticity

9b.2.3.1 Viscoelasticity

9b.2.3.2 Stress-Softening

9b.3 FEA Modelling Techniques

9b.3.1 Pre- and Post-Processing

9b.3.2 Choice of Elements

9b.3.3 Convergence

9b.3.4 Fracture Mechanics

9b.4 Verification

9b.4.1 Stresses and Strains

9b.4.2 Tearing Energy

9b.5 Applications

9b.5.1 Load Deflection

9b.5.2 Failure

References.

10 Tests and Specifications

10.1 Introduction

10.1.1 Standard Test Methods

10.1.2 Purpose of Testing

10.1.3 Test Piece Preparation

10.1.4 Time Between Vulcanization and Testing

10.1.5 Scope of This Chapter

10.2 Measurement of Design Parameters

10.2.1 Young’s Modulus

10.2.2 Shear Modulus

10.2.3 Creep and Stress Relaxation

10.2.3.1 Creep

10.2.3.2 Stress Relaxation

10.3 Quality Control Tests

10.3.1 Hardness

10.3.1.1 Durometer

10.3.1.2 International Rubber Hardness Tester

10.3.2 Tensile Properties

10.3.3 Compression Set

10.3.4 Accelerated Aging

10.3.4.1 Aging in an Air Oven

10.3.4.2 Ozone Cracking

10.3.5 Liquid Resistance

10.3.5.1 Factors in Swelling

10.3.5.2 Swelling Tests

10.3.6 Adhesion to Substrates

10.3.7 Processability

10.4 Dynamic Properties

10.4.1 Resilience

10.4.2 Yerzley Oscillograph

10.4.3 Resonant Beam

10.4.4 Servohydraulic Testers

10.4.5 Electrodynamic Testers

10.4.6 Preferred Test Conditions

10.5 Tests for Tires

10.5.1 Bead Unseating Resistance

10.5.2 Tire Strength

10.5.3 Tire Endurance

10.5.4 High Speed Performance

10.6 Specifications

10.6.1 Classification System

10.6.1.1 Type

10.6.1.2 Class

10.6.1.3 Further Description

10.6.2 Tolerances

10.6.2.1 Molded Products

10.6.2.2 Extruded Products

10.6.2.3 Load-Deflection Characteristics

10.6.3 Rubber Bridge Bearings

10.6.3.1 Function

10.6.3.2 Design Code

10.6.3.3 Materials Specification

10.6.4 Pipe Sealing Rings

10.6.4.1 Function

10.6.4.2 Materials

10.6.4.3 Tensile Properties

10.6.4.4 Compression Set

10.6.4.5 Low Temperature Flexibility

10.6.4.6 Oven Aging

10.6.4.7 Oil Resistance

10.6.4.8 Closing Remarks

References.

Problems for Chapter.10.

Answers to Problems for Chapter.10.

Appendix: Tables of Physical Constants

Index