Fractal Approach to Tribology of Elastomers (Materials Forming, Machining and Tribology)

This book summarizes the results of years of research on the problem of strength and fracture of polymers and elastomers. It sets out the modern approach to the strength theory from the standpoint of fractals, the kinetic and thermodynamic theories as well as the meso-mechanic destruction. The dimension reduction method is applied to model the friction processes in elastomers subjected to the complex dynamic loading. Finally, it analyses a relation between the fracture mechanism and the relation phenomena, and provides new experimental data on the sealing nodes in accordance with their specific working conditions where the effect of self-sealing is observed. About the Book 6 Contents 7 Introduction 11 1 About Theoretical Strength of Materials 13 1.1 Theoretical Strength of Solids 14 1.2 The Relationship Between Elastic Modulus and Theoretical Strength 17 1.3 The Concept of Phonon Destruction 18 1.4 The Phonon Theory of Destruction of Polymer Chain 20 1.5 The Relationship Between Mechanical and Thermal Properties of Solids 23 1.6 Some Types of Cracks 25 1.7 Nonlinear Fracture Mechanics and Fracture Criteria 29 1.8 The Griffith Theory of Fracture of Solids 31 Literature 34 2 General Laws of Friction and Wear of Polymers 36 2.1 The Nature and Properties of Elastomer Friction 37 2.2 Principles of Failure of Elastomers 38 2.3 Thermodynamics of Failure and Criticism of Griffith Theory 40 2.4 The General Form of Phenomenological Theory 44 2.5 Statistical Theory of Fatigue Fracture 46 2.6 The Mechanism of Fatigue Failure of Elastomers 49 2.7 The Principles of Scaling and Generalized Variables 51 2.8 The Transition to Dimensionless Parameters. π-Theorem 53 2.9 The Stress-Relaxation in Elastomers and Self-sealing Effect 55 2.10 The Reasons of Absence of Self-sealing Effect in Elastomers 56 Literature 57 3 Fractal Kinetics of Fracture 60 3.1 The Concept of Fractal. Fractal Dimension 60 3.2 Fractals of Condensed Matter Physics 63 3.3 Fractal Properties of Hierarchical Structure of Potential Relief 66 3.4 Kinetics of Fracture from the Point of Theory of Fractals 72 3.5 Analysis of Relationship Between the Fractal Dimension of Dissipative Structure of Pre-destruction Zone, and the Mechanical Properties and the Critical Deformation States of Metals and Alloys 84 3.6 Diagnosis of Contact Interaction of Solids Using Fractal Analysis Method 95 3.6.1 The Emergence of Fractal Structures During Evolution of Complex Systems 96 3.6.2 The Dependence of Contour Pressure Roughness at Elastic and Plastic Contacts 99 3.6.3 The Calculation of Fractal Dimension of the Supporting Surface Curve for the Ultimate Value of Penetration 103 3.6.4 The Calculation of Power Spectrum of Profile Roughness and the Diagnosis of Contact Modes of Metallic Bodies 105 Literature 108 4 Modern Problems of Frictional Contacts of Elastomers 111 4.1 Efficient Linear Viscoelastic Characteristics of Nonhomogenous Elastic (Composites) and Viscoelastic Bodies 111 4.2 Derivation of Expressions of New Efficient Moduli 113 4.3 Analytical Solution of the Problem of Loading Viscoelastic Half-Space 115 4.4 Building Approximate Solutions with Effective Time Moduli 117 4.5 Modification of Efficient Hashin–Shtrikman Moduli for the Two-Component Isotropic Composite 123 4.6 Derivation of Expressions of Effective Hashin–Shtrikman Moduli of Reuss Type 124 4.7 Models of Averaging Effective Characteristics of the Two-Component Elastic Composite 128 4.7.1 Model of Iterative Conversion of Efficiency Characteristics 129 4.7.2 Model of Averaging Effective Characteristics 131 4.8 The Problem of Loading Double-Layer Shell 133 4.9 The Problem of Loading Triple-Layer Plates 136 4.10 Nanotribological Processes During Electric Discharge in Discrete Ohmic Contacts of “Polymer–Metal” Pairs 139 4.10.1 Electrical Currents in Surface and Subsurface Layers of Polymer Lining 141 4.10.2 Electrical Rift in Discrete Ohmic Contacts of Metal–Polymer Pairs of Tribosystems 144 4.10.3 Local Fracturing of Polymer Films in Ohmic Contacts of Tribo-Coupling 147 4.11 The Frictional Interaction in Electric and Thermal Fields of Metal–Polymer Frictional Pairs 149 4.11.1 Electrical Conductivity of Surface Lining of Polymer Lining 149 4.11.2 The Contact–Impulse Interaction of Frictional Pairs with Different Energy Levels of Materials 153 4.11.3 Selection of Materials of Electrodes and Their Behavior at the Transition Phase of the First Kind 158 4.11.4 The General Laws of Electrodynamic Characteristics of the Micro-protrusion Contact Spots at Their Frictional Interaction 159 4.11.5 The Phenomena of Electrical Explosion and Hear Discharge at the Frictional Interaction in Metal–Polymer Pairs 163 4.11.6 The Phenomena of Thermal Explosion at Frictional Interaction of Metal–Polymer Pairs 168 4.12 Fractal Analysis of Disperse-Filled Elastomeric Composites 170 4.12.1 Molecular Modeling of Mesoscopic Polymeric Composite Systems 178 4.12.2 Fractal Analysis of Structure and Properties of Interphase Layers in Disperse-Filled Elastomeric Composites: The Significant Nanoeffect of Strengthening Elastomers by Nanoparticles 184 Literature 189 5 Dimension Reduction as Modeling Method for Elastomers Under Complex Dynamic Loading 194 5.1 Contact Mechanics and Physics of Friction 194 5.1.1 The Depth of Indentation as Steady Controlling Parameter of Contact Configuration 195 5.1.2 The Surface Gradient and the Size of Micro-contact as the Main Surface Parameters 199 5.1.3 Examples of the Generalized Friction Laws 201 5.2 Meso-mechanical Nature of Friction and Numerical Modeling in Tribology 204 5.2.1 Tribology in the Era of Information Technologies 204 5.2.2 Mesoscopic Nature of Friction 205 5.2.3 Method of Dimensionality Reduction 207 5.3 Dimensionality Reduction for Modeling Friction Process in Elastomers 209 5.3.1 Main Principles of Dimensionality Reduction 209 5.3.1.1 Case of Normal Contacts 211 5.3.1.2 Case of Tangential Contacts 217 5.3.1.3 Viscoelastic Contacts and Thermal Effects 219 5.3.1.4 Adhesion at Viscoelastic Contacts 221 5.3.1.5 Normal Contacts on Rough Surfaces 228 5.3.1.6 Friction Force Between the Rigid Rough Surfaces and Elastomers 231 5.3.2 Precise Mapping Based on Dimensionality Reduction of Axisymmetric Contact Problems with and Without Adhesion 234 5.3.2.1 Axisymmetric Contacts Without Adhesion 236 5.3.2.2 Mapping Theorems of Dimensionality Reduction 238 5.3.2.3 Implementation of Adhesion 242 5.4 Dimensionality Reduction for Modeling Friction of Elastomers 248 5.4.1 Modeling Friction of Elastomers Under Complex Dynamic Loading 248 5.4.1.1 Modeling Static Coefficient of Friction 257 5.4.1.2 Studying Oscillations of Pressing Normal Forces with Coefficient of Sliding Friction 262 5.4.2 Modeling Friction of Elastomers at Contact with Rough Surface 265 5.4.2.1 The Dependence of Kinetic Frictional Force on Normal Force at Contact with Random Roughness of Elastomer Surface 265 5.4.2.2 Studying Adhesive Properties of Contacts Between Elastic Bodies with Random Rough Self-affine Surfaces Using Dimensionality Reduction 268 5.4.2.3 Studying Dry Normal Contact Between Fractal Rough Surfaces Using Dimensionality Reduction 278 Literature 284 6 General Problems of Sealing Units and Their Classifications 291 6.1 The Primary Mechanism of Sealing Units 291 6.1.1 Classifications of Sealants 296 6.1.2 Leakage of Sealing Components 299 6.2 Major Groups and Design Types of Rubber Sealants 304 6.2.1 Group of Sealants 317 6.3 Synthesis of Sealing Downhole Packers 318 6.4 Destructive Influence of Two-Phase Fluids on Cuffs of Screw Pumps 328 Literature 334 7 Stress–Strain State of Sealants of Complex Shapes 335 7.1 Strain Characteristics of Casing Sealant 335 7.2 Creeping in Casing Sealant 339 7.3 Strain Characteristics of Casing Sealant of Complex Shape 346 7.4 Examining Stress–Strain State of Sealing Element of Casing 352 7.5 Determination of Sealing Ability of Sealant 356 7.6 Ensuring Effectiveness of Sealant 362 7.7 Effectiveness of Radial Sealant in Hydraulic Cylinder 368 7.8 Influence of Geometric Shape of Sealant on Self-sealing 372 Literature 376 8 Sealing Properties of Elastic Element 378 8.1 Conditions of Self-sealing 378 8.2 Impact of Wicking on Self-sealing 385 8.3 Determination of Optimal Gap Between Elastic Element and Operational Casing 388 8.4 Determination of Forces Applied to Elastic Element 390 8.5 Assessment of Impact Rate of Load to Elastic Element 391 8.6 Impact of Sealant Shape on Stress Relaxation in Contact Zone 398 8.7 Impact of Axial Force Rate on Sealing Process 402 Literature 407 Conclusion 408 Front Matter ....Pages i-xii About Theoretical Strength of Materials (Ahad Kh Janahmadov, Maksim Javadov)....Pages 1-23 General Laws of Friction and Wear of Polymers (Ahad Kh Janahmadov, Maksim Javadov)....Pages 25-48 Fractal Kinetics of Fracture (Ahad Kh Janahmadov, Maksim Javadov)....Pages 49-99 Modern Problems of Frictional Contacts of Elastomers (Ahad Kh Janahmadov, Maksim Javadov)....Pages 101-183 Dimension Reduction as Modeling Method for Elastomers Under Complex Dynamic Loading (Ahad Kh Janahmadov, Maksim Javadov)....Pages 185-281 General Problems of Sealing Units and Their Classifications (Ahad Kh Janahmadov, Maksim Javadov)....Pages 283-326 Stress–Strain State of Sealants of Complex Shapes (Ahad Kh Janahmadov, Maksim Javadov)....Pages 327-369 Sealing Properties of Elastic Element (Ahad Kh Janahmadov, Maksim Javadov)....Pages 371-400 Back Matter ....Pages 401-401