Alan N. Gent
Engineering with Rubber
How to Design Rubber Components
Contents
6
Preface to Third Edition
16
Authors
18
1 Introduction
20
1.1 Rubber in Engineering
20
1.2 Elastomers
21
1.3 Dynamic Application
22
1.4 General Design Principles
22
1.5 Thermal Expansivity, Pressure, and Swelling
23
1.6 Specific Applications and Operating Principles
24
1.7 Seal Life
27
1.8 Seal Friction
27
Acknowledgments.
28
References.
28
2 Materials and Compounds
30
2.1 Introduction
30
2.2 Elastomer Types
31
2.2.1 General Purpose
31
2.2.1.1 Styrene-Butadiene Rubber (SBR)
31
2.2.1.2 Polyisoprene (NR, IR)
32
2.2.1.3 Polybutadiene (BR)
33
2.2.2 Specialty Elastomers
33
2.2.2.1 Polychloroprene (CR)
33
2.2.2.2 Acrylonitrile-Butadiene Rubber (NBR)
34
2.2.2.3 Hydrogenated Nitrile Rubber (HNBR)
34
2.2.2.4 Butyl Rubber (IIR)
34
2.2.2.5 Ethylene-Propylene Rubber (EPR, EPDM)
34
2.2.2.6 Silicone Rubber (MQ, VMQ, PMQ, PVMQ)
35
2.2.2.7 Polysulfide Rubber (T)
35
2.2.2.8 Chlorosulfonated Polyethylene (CSM)
35
2.2.2.9 Chlorinated Polyethylene (CM)
35
2.2.2.10 Ethylene-Methyl Acrylate Rubber (AEM)
36
2.2.2.11 Acrylic Rubber (ACM)
36
2.2.2.12 Fluorocarbon Rubbers
36
2.2.2.13 Epichlorohydrin Rubber (CO, ECO)
36
2.2.2.14 Urethane Rubber
36
2.3 Compounding
37
2.3.1 Vulcanization and Curing
37
2.3.1.1 Sulfur Curing
37
2.3.1.2 Determination of Crosslink Density
40
2.3.1.3 Influence of Crosslink Density
41
2.3.1.4 Other Cure Systems
42
2.3.2 Reinforcement
42
2.3.3 Anti-Degradants
44
2.3.3.1 Ozone Attack
45
2.3.3.2 Oxidation
45
2.3.4 Process Aids
47
2.3.5 Extenders
48
2.3.6 Tackifiers
48
2.4 Typical Rubber Compositions
49
Acknowledgment.
53
References.
53
Problems for Chapter.2.
54
Answers to Problems for Chapter.2.
54
3 Elasticity
56
3.1 Introduction
56
3.2 Elastic Properties at Small Strains
57
3.2.1 Elastic Constants
57
3.2.2 Relation Between Shear Modulus G and Composition
60
3.2.3 Stiffness of Components
63
3.2.3.1 Choice of Shear Modulus
63
3.2.3.2 Shear Deformations of Bonded Blocks and Hollow Cylindrical Tubes
64
3.2.3.3 Small Compressions or Extensions of Bonded Blocks
66
3.2.3.4 Compression of Blocks Between Frictional Surfaces
69
3.2.3.5 Maximum Allowable Loads in Tension and Compression
71
3.2.3.6 Indentation of Rubber Blocks by Rigid Indentors
72
3.2.3.7 Compression of O-rings
74
3.2.3.8 Protrusion of Rubber Through a Hole or Slit
74
3.3 Large Deformations
75
3.3.1 General Theory of Large Elastic Deformations
75
3.3.2 Forms for W Valid at Large Strains
77
3.3.3 Stress-Strain Relations in Selected Cases
78
3.3.3.1 Simple Extension
78
3.3.3.2 Equibiaxial Stretching
80
3.3.3.3 Constrained Tension (Pure Shear)
80
3.3.4 Determining the Strain Energy Function W
82
3.3.4.1 Elastic Behavior of Filled Rubber Vulcanizates
84
3.3.4.2 Does Any Strain Energy Function Apply?
86
3.3.5 Other Stress-Strain Relations Valid at Large Strains
86
3.3.5.1 Simple Shear
86
3.3.5.2 Torsion
89
3.3.5.3 Instability in Torsion
91
3.3.5.4 Inflation of a Thin-Walled Tube [58]
92
3.3.5.5 Inflation of a Spherical Shell (Balloon)
93
3.3.5.6 Inflation of a Spherical Cavity; Explosive Decompression
95
3.3.5.7 Surface Creasing in Compression
96
3.4 Molecular Theory of Rubber Elasticity
97
3.4.1 Elastic Behavior of a Molecular Network
97
3.4.3 Effective Density of Network Strands
100
3.4.4 The Second Term in the Strain Energy Function
101
3.4.5 Concluding Remarks on Molecular Theories
102
Acknowledgments.
103
References.
103
Problems for Chapter.3.
106
Answers to Selected Problems for Chapter.3.
107
4 Dynamic Mechanical Properties
108
4.1 Introduction
108
4.2 Stress Waves in Rubbery Solids, Transit Times, and Speeds of Retraction
109
4.3 Viscoelasticity
111
4.4 Dynamic Experiments
115
4.5 Energy Considerations
119
4.6 Motion of a Suspended Mass
121
4.7 Experimental Techniques
125
4.7.1 Forced Nonresonance Vibration
125
4.7.2 Forced Resonance Vibration
125
4.7.3 Free Vibration Methods
126
4.7.4 Rebound Resilience
126
4.7.5 Effect of Static and Dynamic Strain Levels
127
4.8 Application of Dynamic Mechanical Measurements
127
4.8.1 Heat Generation in Rubber Components
127
4.8.2 Vibration Isolation
128
4.8.3 Shock Absorbers
128
4.9 Effects of Temperature and Frequency
129
4.10 Thixotropic Effects in Filled Rubber Compounds
133
Acknowledgments.
135
References.
135
Problems for Chapter.4.
135
Answers to Problems for Chapter.4.
136
5 Strength
138
5.1 Introduction
138
5.2 Fracture Mechanics
138
5.2.1 Analysis of the Test Pieces
141
5.2.2 The Strain Energy Concentration at a Crack Tip
142
5.3 Tear Behavior
144
5.4 Crack Growth under Repeated Loading
150
5.4.1 The Fatigue Limit and the Effect of Ozone
151
5.4.2 Physical Interpretation of G0
152
5.4.3 Effects of Type of Elastomer and Filler
154
5.4.4 Effect of Oxygen
154
5.4.5 Effects of Frequency and Temperature
156
5.4.6 Nonrelaxing Effects
156
5.4.7 Time-Dependent Failure
157
5.5 Ozone Attack
157
5.6 Tensile Strength
161
5.7 Crack Growth in Shear and Compression
163
5.8 Cavitation and Related Failures
166
5.9 Conclusions
167
References.
168
Problems for Chapter.5.
171
Answers to Problems for Chapter.5.
172
6 Mechanical Fatigue
178
6.1 Introduction
178
6.2 Application of Fracture Mechanics to Mechanical Fatigue of Rubber
180
6.3 Initiation and Propagation of Cracks
182
6.3.1 Fatigue Crack Initiation
182
6.3.2 Fatigue Life and Crack Growth
183
6.3.3 Fatigue Crack Propagation: The Fatigue Crack Growth Characteristic
185
6.3.4 Fatigue Life Determinations from the Crack Growth Characteristics
187
6.4 Fatigue Crack Growth Test Methodology
189
6.4.1 Experimental Determination of Dynamic Tearing Energies for Fatigue Crack Propagation
189
6.4.2 Kinetics of Crack Growth
190
6.4.3 Effects of Test Variables on Fatigue Crack Growth Characteristics and Dynamic Fatigue Life
191
6.4.3.1 Waveform
191
6.4.3.2 Frequency
191
6.4.3.3 Temperature
191
6.4.3.4 Static Strain/Stress
193
6.5 Material Variables and Their Effect on Fatigue Crack Growth
195
6.5.1 Reinforcing Fillers and Compound Modulus
195
6.5.2 Elastomer Type
197
6.5.3 Vulcanizing System
198
6.5.3 Fatigue of Double Network Elastomers and Blends
200
6.6 Fatigue and Crack Growth of Rubber under Biaxial Stresses and Multiaxial Loading
201
6.7 Fatigue in Rubber Composites
203
6.7.1 Effect of Wires, Cords, and Their Spacing on Fatigue Crack Propagation
204
6.7.2 Effect of Minimum Strain or Stress
204
6.7.3 Comparison of S-N Curve and Fatigue Crack Propagation Constants for Rubber-Wire Composites [53]
206
6.7.4 Fatigue of Two-Ply Rubber-Cord Laminates
207
6.8 Fatigue Cracking of Rubber in Compression and Shear Applications
208
6.8.1 Crack Growth in Compression
208
6.8.2 Crack Growth in Shear
211
6.9 Environmental Effects
212
6.10 Modeling and Life Predictions of Elastomeric Components
213
6.11 Fatigue Crack Propagation of Thermoplastic Elastomers
213
6.12 Durability of Thermoplastic Elastomers
214
6.13 Summary
216
Acknowledgments.
217
References.
217
Problems for Chapter.6.
219
Answers to Problems for Chapter.6.
220
7 Durability
224
7.1 Introduction
224
7.2 Creep, Stress Relaxation, and Set
226
7.2.1 Creep
227
7.2.2 Stress Relaxation
227
7.2.3 Physical Relaxation
228
7.2.4 Chemical Relaxation
230
7.2.5 Compression Set and Recovery
230
7.2.6 Case History Study
232
7.3 Longevity of Elastomers in Air
233
7.3.1 Durability at Ambient Temperatures
233
7.3.2 Sunlight and Weathering
234
7.3.3 Ozone Cracking
234
7.3.4 Structural Bearings: Case Histories
235
7.3.4.1 Natural Rubber Pads for a Rail Viaduct after 100.Years of Service
235
7.3.4.2 Laminated Bridge Bearings after 20 Years of Service
236
7.4 Effect of Low Temperatures
239
7.4.1 Glass Transition
239
7.4.2 Crystallization
240
7.5 Effect of Elevated Temperatures
241
7.6 Effect of Fluid Environments
243
7.6.1 Aqueous Liquids
248
7.6.2 Hydrocarbon Liquids
251
7.6.3 Hydrocarbon and Other Gases
254
7.6.3.1 Pressurized CO2 for Assessing Interface Quality in Bonded Rubber/Rubber Systems
259
7.6.4 Effects of Temperature and Chemical Fluid Attack
259
7.6.5 Effect of Radiation
261
7.7 Durability of Rubber-Metal Bonds
262
7.7.1 Adhesion Tests
262
7.7.2 Rubber-Metal Adhesive Systems
264
7.7.3 Durability in Salt Water: Role of Electrochemical Potentials
265
7.8 Life Prediction Methodology
267
Acknowledgment.
270
References.
270
Problems for Chapter.7.
272
Answers to Problems for Chapter.7.
275
8 Design of Components
278
8.1 Introduction
278
8.2 Shear and Compression Bearings
280
8.2.1 Planar Sandwich Forms
280
8.2.2 Laminate Bearings
286
8.2.3 Tube Form Bearings and Mountings
288
8.2.4 Effective Shape Factors
293
8.3 Vibration and Noise Control
294
8.3.1 Vibration Background Information
295
8.3.2 Design Requirements
297
8.3.3 Sample Problems
297
8.4 Practical Design Guidelines
306
8.5 Summary and Acknowledgments
307
Nomenclature.
308
References.
309
Problems for Chapter.8.
309
Answers to Problems for Chapter.8.
310
9a Finite Element Analysis
314
9a.1 Introduction
314
9a.2 Material Specification
316
9a.2.1 Metal
316
9a.2.2 Elastomers
317
9a.2.2.1 Linear
317
9a.2.2.2 Non-Linear
322
9a.2.2.2.1 Non-Linear Characteristics
322
9a.2.2.2.2 Non-Linear Material Models
322
9a.2.2.2.3 Obtaining Material Data
323
9a.2.2.2.4 Obtaining the Coefficients
328
9a.2.2.2.5 Mooney-Rivlin Material Coefficients
329
9a.2.3 Elastomer Material Model Correlation
330
9a.2.3.1 ASTM.412 Tensile Correlation
330
9a.2.3.2 Pure Shear Correlation
331
9a.2.3.3 Bi-Axial Correlation
331
9a.2.3.4 Simple Shear Correlation
331
9a.3 Terminology and Verification
332
9a.3.1 Terminology
332
9a.3.2 Types of FEA Models
333
9a.3.3 Model Building
334
9a.3.4 Boundary Conditions
336
9a.3.5 Solution
337
9a.3.5.1 Tangent Stiffness
337
9a.3.5.2 Newton-Raphson
338
9a.3.5.3 Non-Linear Material Behavior
338
9a.3.5.4 Viscoelasticity (See Chapter.4)
338
9a.3.5.5 Model Verification
339
9a.3.6 Results
339
9a.3.7 Linear Verification
341
9a.3.8 Classical Verification – Non-Linear
342
9a.4 Example Applications
344
9a.4.1 Positive Drive Timing Belt
344
9a.4.2 Dock Fender
345
9a.4.3 Rubber Boot
348
9a.4.4 Bumper Design
350
9a.4.5 Laminated Bearing
352
9a.4.6 Down Hole Packer
354
9a.4.7 Bonded Sandwich Mount
356
9a.4.8 O-Ring
358
9a.4.9 Elastomer Hose Model
358
9a.4.10 Sample Belt
359
References.
361
9b Developments in Finite Element Analysis
364
9b.1 Introduction
364
9b.2 Material Models
364
9b.2.1 Hyperelastic Models
365
9b.2.2 Compressibility
369
9b.2.3 Deviations from Hyperelasticity
370
9b.2.3.1 Viscoelasticity
370
9b.2.3.2 Stress-Softening
371
9b.3 FEA Modelling Techniques
372
9b.3.1 Pre- and Post-Processing
372
9b.3.2 Choice of Elements
373
9b.3.3 Convergence
374
9b.3.4 Fracture Mechanics
375
9b.4 Verification
375
9b.4.1 Stresses and Strains
376
9b.4.2 Tearing Energy
377
9b.5 Applications
378
9b.5.1 Load Deflection
378
9b.5.2 Failure
379
References.
381
10 Tests and Specifications
384
10.1 Introduction
384
10.1.1 Standard Test Methods
384
10.1.2 Purpose of Testing
385
10.1.3 Test Piece Preparation
385
10.1.4 Time Between Vulcanization and Testing
386
10.1.5 Scope of This Chapter
386
10.2 Measurement of Design Parameters
386
10.2.1 Young’s Modulus
387
10.2.2 Shear Modulus
389
10.2.3 Creep and Stress Relaxation
391
10.2.3.1 Creep
392
10.2.3.2 Stress Relaxation
393
10.3 Quality Control Tests
393
10.3.1 Hardness
394
10.3.1.1 Durometer
394
10.3.1.2 International Rubber Hardness Tester
395
10.3.2 Tensile Properties
397
10.3.3 Compression Set
399
10.3.4 Accelerated Aging
400
10.3.4.1 Aging in an Air Oven
400
10.3.4.2 Ozone Cracking
401
10.3.5 Liquid Resistance
403
10.3.5.1 Factors in Swelling
403
10.3.5.2 Swelling Tests
404
10.3.6 Adhesion to Substrates
404
10.3.7 Processability
407
10.4 Dynamic Properties
409
10.4.1 Resilience
411
10.4.2 Yerzley Oscillograph
412
10.4.3 Resonant Beam
413
10.4.4 Servohydraulic Testers
414
10.4.5 Electrodynamic Testers
415
10.4.6 Preferred Test Conditions
416
10.5 Tests for Tires
416
10.5.1 Bead Unseating Resistance
417
10.5.2 Tire Strength
418
10.5.3 Tire Endurance
419
10.5.4 High Speed Performance
419
10.6 Specifications
420
10.6.1 Classification System
420
10.6.1.1 Type
421
10.6.1.2 Class
422
10.6.1.3 Further Description
422
10.6.2 Tolerances
425
10.6.2.1 Molded Products
425
10.6.2.2 Extruded Products
427
10.6.2.3 Load-Deflection Characteristics
427
10.6.3 Rubber Bridge Bearings
428
10.6.3.1 Function
428
10.6.3.2 Design Code
429
10.6.3.3 Materials Specification
430
10.6.4 Pipe Sealing Rings
432
10.6.4.1 Function
432
10.6.4.2 Materials
432
10.6.4.3 Tensile Properties
432
10.6.4.4 Compression Set
433
10.6.4.5 Low Temperature Flexibility
433
10.6.4.6 Oven Aging
434
10.6.4.7 Oil Resistance
434
10.6.4.8 Closing Remarks
434
References.
435
Problems for Chapter.10.
438
Answers to Problems for Chapter.10.
439
Appendix: Tables of Physical Constants
442
Index
446
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