Contact, Adhesion and Rupture of Elastic Solids

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1 D. Maugis Contact, Adhesion and Rupture of Elastic Solids With 186 Figures Springer

Contents г 1. Elements of Surface Physics 1 1.1 Introduction 1 1.2 Van der Waals Forces Between Molecules 3 1.2.1 The Keesom Theory (1921) 3 1.2.2 The Debye Theory (1920) 7 1.2.3 The London Theory (1930) 8 1.

2 Contents г 1. Elements of Surface Physics Introduction Van der Waals Forces Between Molecules The Keesom Theory (1921) The Debye Theory (1920) The London Theory (1930) Lennard-Jones Potential Retarded van der Waals Forces Van der Waals Forces Between Solids Nonretarded Forces Retarded Forces Derjaguin Approximation Early Experiments Lifschitz's Theory of van der Waals Forces Van der Waals Disjoining Pressure Experimental Verifications of Lifshitz's Theory Surface Energy Surface Energy of a Lennard-Jones Solid Surface Energy of Metals Theoretical Stress: Orowan's Model Adhesive Avalanche Wetting Films Kinetics of Spreading and Precursor Films De-wetting of Films Surface Tension Mechanical Definition of the Surface Tension of a Liquid Surface Tension of Thin Films Surface Tension of Solids Mechanical Effects Due to the Surface Tension of Solids The Relation Between 7 and a Shuttleworth's Equation Surface Stress g in Any Reversible Stretching 65

Contents 1.7 Surface Thermodynamics 67 1.7.1 Dividing Surface and Adsorption 67 1.7.2 Plastic Stretching: Gibbs Adsorption Formula 69 1.7.3 The Case of Reversible Stretching: the Gibbs-Eriksson Equation 71 1.

3 Contents 1.7 Surface Thermodynamics Dividing Surface and Adsorption Plastic Stretching: Gibbs Adsorption Formula The Case of Reversible Stretching: the Gibbs-Eriksson Equation Thermodynamics of the Energy of Adhesion 71 References 77 Elements of Elasticity Stress Tensor at a Point Definitions Principal Stresses and Principal Axes Deviatoric Stress Tensor and von Mises Criterion Description of a Stress Field Basic Equations Equations of Equilibrium Compatibility Equations Constitutive Equations Expressing the Linear Elastic Relationship Between Stresses and Strains Plane State Problems Plane Strain Plane Stress Remark Axisymmetric Problems Resolution of ЛАФ = 0 in Plane Elasticity Analytic Functions The Method of Kolossov and Muskhelishvili The Old Method of Westergaard Resolution of ЛЛФ 0 in Axisymmetry The Inglis Elliptical Cavity: Stress Concentration Factors Elliptical Coordinates Complex Potentials Isotropic Loading Uniaxial Loading with ß = 7г/ General Case Elliptical Cavity Subjected to Hydrostatic Pressure Stresses Crossing an Interface 129 References 131 Rupture and Adherence of Elastic Solids Introduction The Thermodynamic Aspect Stability of the Equilibrium and Adherence Force Berry's Representation Multiple Loadings and Mutual Energy 144

Contents XI 3.3 The Calculation of Griffith 145 3.4 Study of Cracks: Stress Intensity Factors 147 3.4.1 Exact Solution for a Straight Internal Crack in a Plate 147 3.4.2 Power Expansion 158 3.4.3 Comparison with the Exact Solution 163 3.

4 Contents XI 3.3 The Calculation of Griffith Study of Cracks: Stress Intensity Factors Exact Solution for a Straight Internal Crack in a Plate Power Expansion Comparison with the Exact Solution Direct Calculation of the Stress Intensity Factors Cracks Carrying Interior Tractions Straight Crack in Plate Penny-Shaped Crack External Circular Crack Calculation of G, Irwin's Formula, and the J Integral Irwin's Formula Remarks The J Integral The Dugdale Model Straight Crack in a Plate Penny-Shaped Crack 199 References Ffictionless Elastic Contact Introduction Method of Hankel Transforms Some General Theorems Influence of the Surface Energy Concentrated Force Displacements Stresses The Circular Flat Punch Study of the Displacements Study of the Stresses Stresses and Displacements at the Edge of the Contact Adherence of a Flat Punch Contact of Spheres: the Hertz Theory Elementary Method Stored Elastic Energy Use of the General Theorems Calculation of Stresses and Displacements Study of the Stresses Study of Displacements Impact Between Two Spheres Contacts of Spheres: the JKR Theory Thermodynamic Method Use of the Sneddon General Theorems Equilibrium Relations and Adherence Force 267

5 XII Contents Energies of the System and Berry's Representation Profile of a Surface The Stress Tensor Contacts of Spheres: the DMT Theory Contacts of Spheres: the JKR-DMT Transition Study of Stresses Study of Displacements Penetration Energy Release Rate Equilibrium Curves Application to a Liquid Meniscus Conical Punch General Theorems Calculation of Displacements and Stresses Study of Stresses Study of displacements Adherence of a Conical Punch Impact and Rebound of a Cone Liquid Bridges Contact and Adherence of Rough Elastic Solids Description of a Rough Surface Models of Rough Surfaces Contact and Adherence of Two Rough Planes 323 References Study of Some Geometries Background Bending of a Cantilever Beam Beam on Elastic Foundation Elastoplastic Bending The Double Cantilever Beam Elementary Theory Influence of the Shear Force Rotation of the Built-in Section Cleavage Stresses Asymmetric Double Cantilever Beam Influence of an Intercalary Film Peeling Elementary Theory Shape of a Peeled Band Rotation of the Built-in Section Cleavage Stresses Shear Stresses Influence of Prestresses Peeling at Small Angles: Dislocations 381

XIII 5.4 The Lap Joint 383 5.4.1 Elementary Theory 383 5.4.2 "Dislocations" in Lap Joints 388 5.4.3 Other Examples of Spontaneous Peeling 391 5.

6 XIII 5.4 The Lap Joint Elementary Theory "Dislocations" in Lap Joints Other Examples of Spontaneous Peeling Double Torsion Elementary Theory Influence 'of the Thickness The Blister Test 396 References 400 Appendix A 403 References 409 Appendix В 411 Index 413

Contents. Preface XI Symbols and Abbreviations XIII. 1 Introduction 1

Contents. Preface XI Symbols and Abbreviations XIII. 1 Introduction 1 V Contents Preface XI Symbols and Abbreviations XIII 1 Introduction 1 2 Van der Waals Forces 5 2.1 Van der Waals Forces Between Molecules 5 2.1.1 Coulomb Interaction 5 2.1.2 Monopole Dipole Interaction