Engineering Design with Polymers and Composites

James C. Gerdeen Harold W. Lord Ronald A. L. Rorrer

A CRC title, part of the Taylor & Francis imprint, a member of the Taylor 8E Francis Group, the academic division of T&F Informa pic.

Table of Contents

Chapter 1 Introduction to Polymers and Composites 1

1.1 Introduction 1 1.2 History of Polymers 2 1.3 History of Composites 2 1.4 Examples of Polymers and Composites 4 1.5 Definitions and Classifications 6 1.6 Raw Materials and Production of Polymers 8 1.7 Chemical Structures 11 1.8 Glass-Transition Temperature 18 References 22 Homework Problems 22

Chapter 2 Mechanical Properties of Polymers 25

2.1 Introduction 25 2.2 Tensile Properties 25

2.2.1 Elongation 26 2.2.2 Elastic Modulus 26 2.2.3 Ultimate Tensile Strength 27 2.2.4 Yield Strength 28

2.3 Creep Properties 32 2.4 Relaxation Properties 34 2.5 Dynamic Properties 35

2.5.1 Dynamic Tests 35 2.5.2 Dynamic Modulus and Damping 36 2.5.3 Dynamic Property Data 38

2.6 Large-Strain Definitions 40 2.7 Analysis of Damping 41 2.8 Time-Hardening Creep 44 2.9 Isochronous Creep Curves 45 References 46 Homework Problems 47

Chapter 3 Viscoelastic Behavior of Polymers 49

3.1 Mechanical Models 49 3.2 Mathematical Models 50 3.3 The Maxwell Fluid 52

3.4 The Kelvin Solid 55 3.5 The Four-Parameter Model 58 3.6 The Boltzmann Superposition Principle 60 3.7 Advanced Viscoelastic Models 63 3.8 The Viscoelastic Correspondence Principle 64 3.9 The Time-Temperature Equivalence Principle 67 References 70 Homework Problems 70

Chapter 4 Composite Materials 77

4.1 Introduction 77 4.2 Composite Material Nomenclature and Definitions 77 4.3 Analysis of Composite Structures 81

4.3.1 Micromechanics of a Unidirectional Fiber-Reinforced Composite Layer (Lamina) 84 4.3.1.1 Determination of Apparent Longitudinal

Young's Modulus 85 4.3.1.2 Determination of Major Poisson's Ratio

of Unidirectional Lamina 87 4.3.1.3 Apparent Transverse Young's Modulus 89 4.3.1.4 Apparent Shear Modulus 92 4.3.1.5 Summary of Results from Micromechanics

Analysis of Lamina Elastic Moduli 94 4.3.1.6 Prediction of Tensile Strength in Fiber Direction 95

4.3.2 Macromechanics of a Unidirectional Fiber-Reinforced Composite Layer of Lamina 97 4.3.2.1 Stress-Strain Relations for Isotropic Materials 98 4.3.2.2 Anisotropic Materials—Contracted Notation 99 4.3.2.3 Orthotropic Lamina—Hooke's Law in

Principal Material Coordinates 101 4.3.2.4 Stress-Strain Relationships for Off-Axis

Orientation 104 4.4 Experimental Determination of Engineering Elastic Constants 111 4.5 Strength Properties and Failure Theories 114

4.5.1 A Review of Failure Theories for Isotropic Materials 115 4.5.2 Strength and Failure Theories for an

Orthotropic Lamina 117 4.5.3 Failure by Fiber Pullout 121

4.6 Stiffness of Laminated Composites 122 4.6.1 Sandwich Beam 122 4.6.2 Orthotropic Plate 124 4.6.3 Laminated Plates 128 4.6.4 Thermal Stresses 133

4.7 Summary 133

Bibliography 134 References 134 Homework Problems 135

Chapter 5 Creep Failure and Fatigue Failure 139

5.1 Creep Failure Under Tension 139 5.2 Creep Failure Under Compression 142 5.3 Fatigue of Polymers 144 5.4 Notch Sensitivity Under Fatigue 150 5.5 Creep Buckling of Shells 150 References 152 Homework Problems 152

Chapter 6 Impact and Other Properties 155

6.1 Impact Strength 155 6.1.1 Adjusted Impact Properties 160 6.1.2 Combined Stiffness and Impact Properties 162

6.2 Fracture Toughness 166 6.2.1 Brittle Fracture 166 6.2.2 Ductile Fracture 171 6.2.3 General Theory of Fracture Instability 171

6.3 Thermal Properties 178 6.4 Electrical Properties 179 References 180 Homework Problems 181

Chapter 7 Selection of Polymers for Design Applications 185

7.1 Introduction 185 7.2 Basic Material Properties 185 7.3 Performance Parameters 186 7.4 Loading Conditions and Geometrical Configurations 186 7.5 Availability of Materials 186 7.6 A Rectangular Beam in Bending 187 7.7 Weighting-Factor Analysis 190 7.8 Thermal Gradient Through a Beam 191 7.9 Rating Factors for Various Loading Requirements 193 7.10 Design Optimization 194

7.10.1 Graphical Solution 194 7.10.2 Computer Solution 199 7.10.3 Microsoft Excel Solver Routine 201

7.11 Computer Database Design Selection Procedure 205 7.11.1 Example Problem of Impact of a Beam 205

References 206 Homework Problems 207

Chapter 8 Design Applications of Some Polymers 209

8.1 Phenolic Resins with Fillers 209 8.2 Polycarbonate 211 8.3 Example Design with PC—Fan Impeller Blade 211

8.3.1 Creep Strain 213 8.3.2 Impact Failure 215

8.4 Example Design with PC—Snap/Fit Design 216 8.5 Example Design of Polyvinyl Chloride Pipe 217 8.6 Design with Fluorocarbon Resins 221 References 224 Homework Problems 224

Chapter 9 Polymer Processing 227

9.1 Extrusion 227 9.2 Manufacture of PVC Pipe by Extrusion 229 9.3 Injection Molding 233 9.4 Sheet Forming 235 9.5 Blow Molding 236

9.5.1 Inflation 238 9.5.2 Cooling Phase 243

References 250 Homework Problems 250

Chapter 10 Adhesion of Polymers and Composites 253

10.1 Introduction 253 10.2 Fundamentals of Adhesion 253

10.2.1 Wetting and Work of Adhesion 253 10.2.2 Measurement of Adhesion 256 10.2.3 Viscoelasticity of Adhesion 259

10.3 Adhesives 261 10.3.1 Common Polymeric Adhesives 261 10.3.2 PSA Polymers As Matrix Materials (In-Situ Adhesives)

in Polymeric Composites 262 10.4 Enhancement of Adhesion in Composites 263 10.5 Curing of Adhesives 265 10.6 Summary 268 References 268 Homework Problems 269

Chapter 11 Tribology of Polymers and Composites 271

11.1 Introduction 271 11.2 Contact Mechanics 272 11.3 Surface Topography 274 11.4 Friction 275

11.4.1 Static and Dynamic Coefficients of Friction 279 11.4.2 Adhesive and Abrasive Friction 280

11.5 Wear 280 11.5.1 Archard Wear Law 281

11.6 PV Limit 282 11.7 Rolling and Sliding 283 11.8 Modification of Polymers for Friction and Wear Performance 284

11.8.1 Internal Lubricants 285 11.8.2 Reinforcements 286

11.9 Composites 288 11.10 Wear of Composites 291 11.11 Heat Generation in Sliding-Polymer Systems 292

11.11.1 Bulk Surface-Temperature Calculations 292 11.11.2 Flash Temperature 293

11.12 Special Considerations 293 11.12.1 Polymer-on-Polymer Sliding 293 11.12.2 Coatings 294 11.12.3 Effect of Surface Topography on Friction and

Wear 294 11.12.4 Effect of Environment on Friction and Wear 294 11.12.5 Friction-Induced Vibration 294

11.13 Simulative Laboratory Testing 296 References 297 Homework Problems 297

Chapter 12 Damping and Isolation with Polymers and Composites 299

12.1 Introduction 299 12.2 Relevance of Thermomechanical Spectrum of Polymers 300 12.3 Damping of Materials 301

12.3.1 Reduced-Frequency Nomograph 302 12.4 Materials 303 12.5 Fundamentals of Vibration Damping and Isolation 304 12.6 Role of Dampers 312 12.7 Damping Layers 313 References 317 Homework Problems 317

Appendices Appendix A Conversion Factors 319 Appendix В Area Moments of Inertia 321 Appendix С Beam Reactions and Displacements 323 Appendix D Laminate Analysis MATLAB® Code 329 Appendix E Sample Input/Output for Laminate Program 339 Appendix F Composite Materials Properties 343

Index 347