Inhaltsverzeichnis. Contents

Transcription

1 V Contents 1 Introduction Objective Discovery First Vulcanization Early Manufacture of Rubber Products Discovery of Reinforcement Production of Rubber The Rubber Molecule Synthetics Curing and Crosslinking Fillers and Reinforcement Curing Ingredients Other Additives Principal Uses of Several Elastomers... 6 Bibliography Rubber Stress-Strain Behavior Challenges of Rubber Behavior Characteristics of Stress-Strain Behavior Low Elastic Modulus, High Elongation at Break, and Non-Linearity Hysteresis Stress Relaxation Creep Mullins Effect Reinforcement Cyclic Frequency and Strain Rate Temperature Immersion Effects Strain Crystallization Permanent Set Recovery Bibliography A Theory of the Elastomer Stress-Strain Curve Introduction The Internal Structure of the Vulcanized Elastomer Assumptions and Hypotheses The Coil Spring Analogy Chain Segments and Terminations... 24

2 VI Statistical Distribution of Chains in Length and End Point Separation The Presence of van der Waals Bonds Reinforcement by ParticleRotation Migration of Entanglements Temperature-Induced Chain Vibration Bond Breaking and Remaking in Deformation Parallelism-Induced Crystallization Elastomer Behaviors The Non-Linear Stress-Strain Curve The Mullins Effect Low Elastic Modulus and High Elongation at Break Hysteresis Stiffening by Reinforcing Fillers Strain Rate Stiffening Temperature Response Stress Relaxation and Cyclic StressRelaxation Creep and Creep under Cyclic Conditions Permanent Set Recovery Strain Crystallization Acknowledgements References Stress-Strain Testing Introduction Tensile Testing Specimens Testing with the Dumbbell Specimen Testing with the Planar Stress Specimen Testing with the Loop Specimen Shear Testing Stress-Strain State Specimens Biaxial Strain Testing The Bubble Test The Cross Specimen Compression Testing Summary References... 66

3 VII 5 Design Equations Introduction Use of Design Equations Elastic Constants Design Equations forvariousgeometries Pads in Shear Pads in Torsion Bushings Pads in Compression Compression ofalongstrip Solid Rubber Rollers Rubber-Covered Rollers Compression of a Rubber Sphere Compression of SolidRubber Tire Compression of Solid Rubber Ring of Circular Cross-Section Solid Rubber Ring with Rectangular Cross-Section Indenter, Flat Ended Cylinder Indenter, Spherical Head Indenter, Conical Indenter, Long Narrow Flat End Protrusion Through a Round Hole Protrusion Through Long Narrow Gap Summary References Calculation Methods for Spherical Elastomer Bearings Introduction History of the Spherical Bearing Mathematical DescriptionoftheBearing Overall BearingParameters Parameters of Particular Pads Angular Moment Shear Strain of Pads under Angular Deflection Axial Loads Compression of Pads under Axial Force Bulge Shear Strain Summary of Calculations Torsional Loads Shear Strain of Pads under Torsional Rotation Computational Procedure Limitations References

4 VIII 7 Finite Element Analysis Introduction Procedure Symmetry Loads and Boundary Conditions Element Selection and Meshing Material Model or ConstitutiveEquations Simpler Constitutive Equations Higher Order Constitutive Equations Fitting Equations to Test Data O-Ring Seal with Pressure Rubber Boot Summary Acknowledgements References Fatigue Testing Introduction Parameters Affecting thestrain-lifecurve Parameters to BeSpecified Selecting StrainAmplitude Failure Criteria R-Ratio Combined Strain State Wave Form Creep and Stress Relaxation Frequency and Strain Rate Effect of Temperature Liquid Immersion Recovery Scragging Batch Variation Storage Acknowledgements References Fitting the Strain-Life Curve Introduction Development of an Equation for N in ε a, R and T The Strain-Life Curve Equation with Nagel s Equation for Temperature Employing the Simple Empirical Formula for Temperature Acknowledgements References

5 IX 10 Fatigue Life Estimation Introduction Single Wave Form, the ε-n Method The Miner s Number The Deterministic Fatigue Spectrum Sample Calculation of the Miner s Number White Noise Rainflow Counting Fatigue Crack Growth and Tearing Energy Introduction Griffith Strain Energy ReleaseRate Griffith Criterion Derivation Griffith Condition for Fracture Critical Assumptions Rivlin and Thomas and Tearing Energy Modification of Griffith s Criterion for Fracture of Metals Application to Rubber State of Critical Assumptions Shortcut Formulas for T Tearing Energy Applied to Fatigue Crack Growth Pioneering Developments in Fatigue The Change in Definition of Tearing Energy Limitations Fatigue Crack Growth Parameter Cycles to Failure by T or ε a? Summary and Conclusions Acknowledgements References Appendix I. Rubber Nomenclature Appendix 2. Fatigue Terminology Appendix 3. English to Metric Conversion Appendix 4. Fitting the Strain-Life Curve Appendix 5. Derivation of Tearing Energy Equations Appendix 6. Derivation of Equations for Spherical Elastomer Bearings Sachregister