Fatigue, Stress, and Strain of Rubber Components - A Guide for Design Engineers

Front Matter......Page 1
Table of Contents......Page 3
1.2 Discovery......Page 8
1.2.4 Production of Rubber......Page 9
1.4 Synthetics......Page 10
1.4.1 Curing and Crosslinking......Page 11
1.4.3 Curing Ingredients......Page 12
1.5 Principal Uses of Several Elastomers......Page 13
Bibliography......Page 14
2.2.1 Low Elastic Modulus, High Elongation at Break, and Non-Linearity......Page 15
2.2.2 Hysteresis......Page 16
2.2.4 Creep......Page 17
2.2.5 Mullins Effect......Page 18
2.2.6 Reinforcement......Page 19
2.2.7 Cyclic Frequency and Strain Rate......Page 20
2.2.9 Immersion Effects......Page 21
2.2.10 Strain Crystallization......Page 22
2.2.12 Recovery......Page 23
Bibliography......Page 24
3.1 Introduction......Page 25
3.2 The Internal Structure of the Vulcanized Elastomer......Page 26
3.3.1 The Coil Spring Analogy......Page 27
3.3.3 Statistical Distribution of Chains in Length and End Point Separation......Page 30
3.3.4 The Presence of van der Waals Bonds......Page 31
3.3.5 Reinforcement by Particle Rotation......Page 34
3.3.6 Migration of Entanglements......Page 37
3.3.7 Temperature-Induced Chain Vibration......Page 38
3.3.9 Parallelism-Induced Crystallization......Page 39
3.4.2 The Mullins Effect......Page 40
3.4.3 Low Elastic Modulus and High Elongation at Break......Page 42
3.4.6 Strain Rate Stiffening......Page 43
3.4.9 Creep and Creep under Cyclic Conditions......Page 44
Acknowledgements......Page 45
References......Page 46
4.2.1 Specimens......Page 48
4.2.2 Testing with the Dumbbell Specimen......Page 49
4.2.2.4 Setting Extension Cycles, Rates and Maximums......Page 50
4.2.2.6 Set and Buckling......Page 51
4.2.2.8 Measuring Failure......Page 52
4.2.2.10 Fatigue Cycling......Page 53
4.2.3.1 Stress-Strain State of the Specimen......Page 54
4.2.3.2 Grips......Page 55
4.2.4 Testing with the Loop Specimen......Page 57
4.3.2.1 Dual Lap Shear......Page 59
4.3.2.4 Measuring Stress and Strain......Page 60
4.3.2.8 Advantages......Page 61
4.4.1.2 Specimen and Fixture......Page 62
4.4.2 The Cross Specimen......Page 68
4.5 Compression Testing......Page 69
References......Page 71
5.1.2 Elastic Constants......Page 73
5.2.1 Pads in Shear......Page 75
5.2.1.1 Stack of Pads in Shear......Page 76
5.2.2.2 Thin Strip......Page 77
5.2.3 Bushings......Page 78
5.2.4.1 Compressive Modulus, Stiffness, and Force......Page 80
5.2.4.3 Compression of a Circular Disk with Slight Compressibility......Page 82
5.2.4.4 Stack of Pads in Compression......Page 83
5.2.5 Compression of a Long Strip......Page 84
5.2.6 Solid Rubber Rollers......Page 85
5.2.8 Compression of a Rubber Sphere......Page 86
5.2.9 Compression of Solid Rubber Tire......Page 87
5.2.11 Solid Rubber Ring with Rectangular Cross-Section......Page 88
5.2.12 Indenter, Flat Ended Cylinder......Page 89
5.2.15 Indenter, Long Narrow Flat End......Page 90
5.3 Summary......Page 91
References......Page 92
6.2 History of the Spherical Bearing......Page 93
6.3 Mathematical Description of the Bearing......Page 95
6.3.2.1 Find the Parameters of the i^th Pad......Page 96
6.4 Shear Strain of Pads under Angular Deflection......Page 99
6.5 Axial Loads......Page 103
6.5.1 Compression of Pads under Axial Force......Page 104
6.5.2 Bulge Shear Strain......Page 105
6.6 Torsional Loads......Page 107
6.6.2 Computational Procedure......Page 108
References......Page 109
7.2 Procedure......Page 110
7.2.3 Element Selection and Meshing......Page 111
7.3 Material Model or Constitutive Equations......Page 112
7.3.2 Higher Order Constitutive Equations......Page 113
7.4 Fitting Equations to Test Data......Page 114
7.5 O-Ring Seal with Pressure......Page 115
7.6 Rubber Boot......Page 117
References......Page 118
8.2 Parameters Affecting the Strain-Life Curve......Page 119
8.3 Failure Criteria......Page 120
8.5 Combined Strain State......Page 121
8.6 Wave Form......Page 123
8.8 Frequency and Strain Rate......Page 124
8.9 Effect of Temperature......Page 125
8.10 Liquid Immersion......Page 126
8.13 Batch Variation......Page 127
References......Page 128
9.2 Development of an Equation for N in epsilon _a , R and T......Page 129
9.3 The Strain-Life Curve Equation with Nagel\'s Equation for Temperature......Page 132
9.4 Employing the Simple Empirical Formula for Temperature......Page 133
Acknowledgements......Page 134
References......Page 135
10.2 Single Wave Form, the epsilon -N Method......Page 136
10.4 The Deterministic Fatigue Spectrum......Page 137
10.5 Sample Calculation of the Miner\'s Number......Page 138
10.6 White Noise......Page 139
10.6.1 Rainflow Counting......Page 140
11.2.2 Derivation......Page 143
11.2.4 Critical Assumptions......Page 146
11.3.2 Application to Rubber......Page 147
11.3.3 State of Critical Assumptions......Page 149
11.4 Shortcut Formulas for T......Page 150
11.5.2 The Change in Definition of Tearing Energy......Page 151
11.6.1 Fatigue Crack Growth Parameter......Page 152
11.6.2 Cycles to Failure by T or epsilon _a ?......Page 154
11.7 Summary and Conclusions......Page 156
References......Page 157
Appendix 1: Rubber Nomenclature......Page 158
C......Page 166
D......Page 167
H......Page 168
M......Page 169
R......Page 170
S......Page 171
Y......Page 172