Ph.D Fatigue, Stress, and Strain of Rubber Components

Guide for Design Engineers
1. Auflage 2012
ISBN: 978-3-446-43340-3
Verlag: Carl Hanser Fachbuchverlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 226 Seiten

This text emphasizes the mechanical behavior of elastomers. It discusses the molecular and micro configuration of the rubber matrix and how they produce the observed mechanical behavior.

The fatigue testing of specimens, curve fitting of equations to the test data, and the use of such equations in life prediction are covered compehensively. Stress-strain testing and behavior are covered to the extent relevant to fatigue analysis. Also, the text covers the application of finite element analysis to components to determine high stress points which are vulnerable to fatigue failure.
The book presents a very useful reference for practicing engineers charged with responsibility to design structural rubber components where fatigue life is a concern. It is aimed at aiding the design engineer in practical service life estimations and testing of rubber materials to that end.

Autoren/Hrsg.

Ph.D,

Inhaltsverzeichnis

1;Inhaltsverzeichnis;6
2;1 Introduction;12
2.1;1.1 Objective;12
2.2;1.2 Discovery;12
2.2.1;1.2.1 First Vulcanization;13
2.2.2;1.2.2 Early Manufacture of Rubber Products;13
2.2.3;1.2.3 Discovery of Reinforcement;13
2.2.4;1.2.4 Production of Rubber;13
2.3;1.3 The Rubber Molecule;14
2.4;1.4 Synthetics;14
2.4.1;1.4.1 Curing and Crosslinking;15
2.4.2;1.4.2 Fillers and Reinforcement;16
2.4.3;1.4.3 Curing Ingredients;16
2.4.4;1.4.4 Other Additives;17
2.5;1.5 Principal Uses of Several Elastomers;17
2.6;Bibliography;18
3;2 Rubber Stress-Strain Behavior;20
3.1;2.1 Challenges of Rubber Behavior;20
3.2;2.2 Characteristics of Stress-Strain Behavior;20
3.2.1;2.2.1 Low Elastic Modulus, High Elongation at Break, and Non-Linearity;20
3.2.2;2.2.2 Hysteresis;21
3.2.3;2.2.3 Stress Relaxation;22
3.2.4;2.2.4 Creep;22
3.2.5;2.2.5 Mullins Effect;23
3.2.6;2.2.6 Reinforcement;24
3.2.7;2.2.7 Cyclic Frequency and Strain Rate;25
3.2.8;2.2.8 Temperature;26
3.2.9;2.2.9 Immersion Effects;26
3.2.10;2.2.10 Strain Crystallization;27
3.2.11;2.2.11 Permanent Set;28
3.2.12;2.2.12 Recovery;28
3.3;Bibliography;29
4;3 ATheory of the Elastomer Stress-Strain Curve;30
4.1;3.1 Introduction;30
4.2;3.2 The Internal Structure of the Vulcanized Elastomer;31
4.3;3.3 Assumptions and Hypotheses;32
4.3.1;3.3.1 The Coil Spring Analogy;32
4.3.2;3.3.2 Chain Segments and Terminations;35
4.3.3;3.3.3 Statistical Distribution of Chains in Length and End Point Separation;35
4.3.4;3.3.4 The Presence of van der Waals Bonds;36
4.3.5;3.3.5 Reinforcement by Particle Rotation;39
4.3.6;3.3.6 Migration of Entanglements;42
4.3.7;3.3.7 Temperature-Induced Chain Vibration;43
4.3.8;3.3.8 Bond Breaking and Remaking in Deformation;44
4.3.9;3.3.9 Parallelism-Induced Crystallization;44
4.4;3.4 Elastomer Behaviors;45
4.4.1;3.4.1 The Non-Linear Stress-Strain Curve;45
4.4.2;3.4.2 The Mullins Effect;45
4.4.3;3.4.3 Low Elastic Modulus and High Elongation at Break;47
4.4.4;3.3.4 Hysteresis;48
4.4.5;3.4.5 Stiffening by Reinforcing Fillers;48
4.4.6;3.4.6 Strain Rate Stiffening;48
4.4.7;3.4.7 Temperature Response;49
4.4.8;3.4.8 Stress Relaxation and Cyclic Stress Relaxation;49
4.4.9;3.4.9 Creep and Creep under Cyclic Conditions;49
4.4.10;3.4.10 Permanent Set;50
4.4.11;3.4.11 Recovery;50
4.4.12;3.4.12 Strain Crystallization;50
4.5;Acknowledgements;50
4.6;References;51
5;4 Stress-Strain Testing;54
5.1;4.1 Introduction;54
5.2;4.2 Tensile Testing;54
5.2.1;4.2.1 Specimens;54
5.2.2;4.2.2 Testing with the Dumbbell Specimen;55
5.2.3;4.2.3 Testing with the Planar Stress Specimen;60
5.2.4;4.2.4 Testing with the Loop Specimen;63
5.3;4.3 Shear Testing;65
5.3.1;4.3.1 Stress-Strain State;65
5.3.2;4.3.2 Specimens;65
5.4;4.4 Biaxial Strain Testing;68
5.4.1;4.4.1 The Bubble Test;68
5.4.2;4.4.2 The Cross Specimen;74
5.5;4.5 Compression Testing;75
5.6;4.6 Summary;77
5.7;References;77
6;5 Design Equations;80
6.1;5.1 Introduction;80
6.1.1;5.1.1 Use of Design Equations;80
6.1.2;5.1.2 Elastic Constants;80
6.2;5.2 Design Equations for Various Geometries;82
6.2.1;5.2.1 Pads in Shear;82
6.2.2;5.2.2 Pads in Torsion;84
6.2.3;5.2.3 Bushings;85
6.2.4;5.2.4 Pads in Compression;87
6.2.5;5.2.5 Compression of a Long Strip;91
6.2.6;5.2.6 Solid Rubber Rollers;92
6.2.7;5.2.7 Rubber-Covered Rollers;93
6.2.8;5.2.8 Compression of a Rubber Sphere;93
6.2.9;5.2.9 Compression of Solid Rubber Tire;94
6.2.10;5.2.10 Compression of Solid Rubber Ring of Circular Cross-Section;95
6.2.11;5.2.11 Solid Rubber Ring with Rectangular Cross-Section;95
6.2.12;5.2.12 Indenter, Flat Ended Cylinder;96
6.2.13;5.2.13 Indenter, Spherical Head;97
6.2.14;5.2.14 Indenter, Conical;97
6.2.15;5.2.15 Indenter, Long Narrow Flat End;97
6.2.16;5.2.16 Protrusion Through a Round Hole;98
6.2.17;5.2.17 Protrusion Through Long Narrow Gap;98
6.3;5.3 Summary;98
6.4;References;99
7;6 CalculationMethods for Spherical Elastomer Bearings;100
7.1;6.1 Introduction;100
7.2;6.2 History of the Spherical Bearing;100
7.3;6.3 Mathematical Description of the Bearing;102
7.3.1;6.3.1 Overall Bearing Parameters;103
7.3.2;6.3.2 Parameters of Particular Pads;103
7.3.3;6.3.3 Angular Moment;106
7.4;6.4 Shear Strain of Pads under Angular Deflection;106
7.5;6.5 Axial Loads;110
7.5.1;6.5.1 Compression of Pads under Axial Force;111
7.5.2;6.5.2 Bulge Shear Strain;112
7.5.3;6.5.3 Summary of Calculations;114
7.6;6.6 Torsional Loads;114
7.6.1;6.6.1 Shear Strain of Pads under Torsional Rotation;115
7.6.2;6.6.2 Computational Procedure;115
7.6.3;6.6.3 Limitations;116
7.7;References;116
8;7 Finite Element Analysis;118
8.1;7.1 Introduction;118
8.2;7.2 Procedure;118
8.2.1;7.2.1 Symmetry;119
8.2.2;7.2.2 Loads and Boundary Conditions;119
8.2.3;7.2.3 Element Selection and Meshing;119
8.3;7.3 Material Model or Constitutive Equations;120
8.3.1;7.3.1 Simpler Constitutive Equations;121
8.3.2;7.3.2 Higher Order Constitutive Equations;121
8.4;7.4 Fitting Equations to Test Data;122
8.5;7.5 O-Ring Seal with Pressure;123
8.6;7.6 Rubber Boot;125
8.7;7.7 Summary;126
8.8;Acknowledgements;126
8.9;References;126
9;8 Fatigue Testing;128
9.1;8.1 Introduction;128
9.2;8.2 Parameters Affecting the Strain-Life Curve;128
9.2.1;8.2.1 Parameters to Be Specified;129
9.2.2;8.2.2 Selecting Strain Amplitude;129
9.3;8.3 Failure Criteria;129
9.4;8.4 R-Ratio;130
9.5;8.5 Combined Strain State;130
9.6;8.6 Wave Form;132
9.7;8.7 Creep and Stress Relaxation;133
9.8;8.8 Frequency and Strain Rate;133
9.9;8.9 Effect of Temperature;134
9.10;8.10 Liquid Immersion;135
9.11;8.11 Recovery;136
9.12;8.12 Scragging;136
9.13;8.13 Batch Variation;136
9.14;8.14 Storage;137
9.15;Acknowledgements;137
9.16;References;137
10;9 Fitting the Strain-Life Curve;138
10.1;9.1 Introduction;138
10.2;9.2 Development of an Equation for N in ?a , R and T;138
10.3;9.3 The Strain-Life Curve Equation with Nagel’s Equation for Temperature;141
10.4;9.4 Employing the Simple Empirical Formula for Temperature;142
10.5;Acknowledgements;143
10.6;References;144
11;10 Fatigue Life Estimation;146
11.1;10.1 Introduction;146
11.2;10.2 Single Wave Form, the ?-N Method;146
11.3;10.3 The Miner’s Number;147
11.4;10.4 The Deterministic Fatigue Spectrum;147
11.5;10.5 Sample Calculation of the Miner’s Number;148
11.6;10.6 White Noise;149
11.6.1;10.6.1 Rainflow Counting;150
12;11 Fatigue Crack Growth and Tearing Energy;154
12.1;11.1 Introduction;154
12.2;11.2 Griffith Strain Energy Release Rate;154
12.2.1;11.2.1 Griffith Criterion;154
12.2.2;11.2.2 Derivation;154
12.2.3;11.2.3 Griffith Condition for Fracture;157
12.2.4;11.2.4 Critical Assumptions;157
12.3;11.3 Rivlin and Thomas and Tearing Energy;158
12.3.1;11.3.1 Modification of Griffith’s Criterion for Fracture ofMetals;158
12.3.2;11.3.2 Application to Rubber;158
12.3.3;11.3.3 State of Critical Assumptions;160
12.4;11.4 Shortcut Formulas for T;161
12.5;11.5 Tearing Energy Applied to Fatigue Crack Growth;162
12.5.1;11.5.1 Pioneering Developments in Fatigue;162
12.5.2;11.5.2 The Change in Definition of Tearing Energy;162
12.6;11.6 Limitations;163
12.6.1;11.6.1 Fatigue Crack Growth Parameter;163
12.6.2;11.6.2 Cycles to Failure by T or ?a ?;165
12.7;11.7 Summary and Conclusions;167
12.8;Acknowledgements;168
12.9;References;168
13;Appendix I. Rubber Nomenclature;170
14;Appendix 2. Fatigue Terminology;178
15;Appendix 3. English to Metric Conversion;188
16;Appendix 4. Fitting the Strain-Life Curve;190
17;Appendix 5. Derivation of Tearing Energy Equations;198
18;Appendix 6. Derivation of Equations for Spherical Elastomer Bearings;204
19;Index;224