Chapter 1 Applications of Composite Materials....................................................1
References.............................................................................................5
Section I E lectromagnetic Properties
of Composites: Static Electromagnetic
Properties of Composites
Chapter 2 Electrical Conductivity of Composites............................................... 11
2.1 Background............................................................................... 11
2.2 Electrical Conductivity of Composites..................................... 12
2.2.1 Empirical Rules of Mixtures....................................... 12
2.2.2 Theoretical Models...................................................... 13
2.3 Electrical Percolation in Composites....................................... 21
2.4 Phase Inversion in Composites.................................................26
References...........................................................................................29
Chapter 3 Dielectric Properties of Composites.................................................... 31
3.1 Background............................................................................... 31
3.2 Dielectric Constant of Composites........................................... 33
3.3 Influence of Interphase Region on Dielectric Behavior of
Composites............................................................................... 39
References........................................................................................... 43
Chapter 4 Magnetic Properties of Composites.................................................... 45
4.1 Background............................................................................... 45
4.2 Magnetic Properties of Composites.........................................48
4.3 Upper and Lower Bounds on Magnetic Permeability of
Composites............................................................................... 51
References........................................................................................... 53
Section II EII EII EII EII E
electromagnetic Properties of Composites: General Treatment of Electromagnetic Phenomena in Composites
Chapter 5 Maxwell Equations and the Generalized Conductivity Principle.......57
5.1 Maxwell Equations...................................................................57
5.1.1 Constitutive Equations................................................58
5.1.2 Boundary Conditions..................................................58
5.2 Time-Independent Electromagnetic Phenomena......................60
5.2.1 Electrostatic Phenomena.............................................60
5.2.2 Steady Electrical Phenomena......................................61
5.2.3 Magnetostatic Phenomena...........................................62
5.2.4 Summary.....................................................................62
5.3 Time-Harmonic Electric and Magnetic Fields.........................63
5.3.1 Quasistationary Approximation..................................66
5.3.2 Boundary Conditions..................................................67
5.3.3 Comparison of Governing Equations..........................68
Supplemental Reading.........................................................................69
Chapter 6 Complex Electromagnetic Properties of Composites..........................71
6.1 Complex Permittivity of Composites.......................................71
6.1.1 Models for Complex Permittivity of Composites........76
6.1.2 Comparison of Model Predictions with Experimental Data......................................................79
6.1.3 Influence of Interphase Region on the Complex Permittivity of Composites..........................................82
6.2 Complex Magnetic Permeability of Composites......................90
6.2.1 Models for Complex Magnetic Permeability of Composites..................................................................93
6.2.2 Experimental Observations on Complex Magnetic Permeability of Composites........................95
References...........................................................................................98
Section
III III III
Mechanical Properties of Composites
Chapter 7 Mechanical Properties of Dilute Particulate-Filled Composites......101
7.1 Background.............................................................................101
7.2 Empirical Rules of Mixtures..................................................102
7.2.1 Voigt Rule of Mixtures..............................................102
7.2.2 Reuss Rule of Mixtures.............................................103
7.3 Theoretical Models.................................................................103
7.3.1 Dilute Composites with Spherical Particles..............103
7.3.1.1 Composites with Rigid Spherical Particles.....................................................107
7.3.1.2 Composites with Incompressible Matrix......108
7.3.1.3 Composites with Pores...............................108
7.3.2 Dilute Composites with Disk-Shaped Particles.........109
7.4 Bounds for the Effective Elastic Properties of Particulate Composites.............................................................................112
References.........................................................................................117
Chapter 8 Mechanical Properties of Concentrated Pore-Solid Composites......119
8.1 Introduction............................................................................119
8.2 Pal Models for Elastic Moduli of Concentrated Pore- Solid Composites...........................................................120
8.3 Comparison of Model Predictions with Experimental Data.......123
8.4 Bulk Modulus and Poisson’s Ratio of Concentrated Pore- Solid Composites...........................................................126
References.........................................................................................128
Chapter 9 Effective Young’s Modulus of Concentrated Composites.................131
9.1 Introduction............................................................................131
9.2 Background.............................................................................131
9.3 Pal Models for Young’s Modulus of Concentrated Composites.............................................................................133
9.3.1 Model Predictions of Young’s Modulus....................136
9.3.2 Comparison of Model Predictions with Experimental Data....................................................140
9.4 Concluding Remarks..............................................................144
References.........................................................................................145
Chapter 10 Effective Shear Modulus of Concentrated Composites....................147
10.1 Introduction............................................................................147
10.2 Single-Parameter Shear Modulus Equations for Composites.....149
10.3 Two-Parameter Shear Modulus Equations for Composites....153
10.4 Analogy between Shear Modulus of Composites and Viscosity of Suspensions........................................................156
10.5 Comparison of Experimental Data with Predictions of Shear Modulus Equations.......................................................158
10.6 Concluding Remarks..............................................................161
References.........................................................................................161
Chapter 11 Mechanical Properties of Concentrated Composites of Randomly Oriented Platelets.............................................................165
11.1 Introduction............................................................................165
11.2 Pal Models for Concentrated Composites of Randomly Oriented Platelets...................................................................166
11.2.1 Model Predictions.....................................................170
11.2.2 Comparison of Model Predictions with Experimental Data....................................................173
11.3 Composites of Three-Phase Core-Shell-Type Platelets..........176
References.........................................................................................179
Chapter 12 Interfacial and Interphase Effects on Mechanical Properties of Composites........................................................................................181
12.1 Background.............................................................................181
12.2 Poor Adhesion between Particles and Matrix........................185
12.3 Effect of Interphase Layer......................................................186
12.4 Comparison of Model Predictions with Experimental Data........191
12.5 Concluding Remarks..............................................................195
References.........................................................................................196
Chapter 13 Viscoelastic Behavior of Composites................................................199
13.1 Introduction............................................................................199
13.2 Elastic–Viscoelastic Correspondence Principle.....................200
13.3 Complex Moduli of Dilute Composites..................................200
13.4 Complex Moduli of Concentrated Composites......................208
13.4.1 Complex Shear Modulus of Concentrated Composites................................................................209
13.4.2 Complex Young’s Modulus of Concentrated Composites................................................................214
13.5 Concluding Remarks..............................................................218
References.........................................................................................218
Section
I
V T T Transport Properties of Composites: Heat Transfer in Composites
Chapter 14 General Introduction to Heat Transfer..............................................223
14.1 Different Modes of Heat Transfer..........................................223
14.1.1 Conductive Heat Transfer..........................................223
14.1.1.1 Rate Equation for Heat Conduction...........223
14.1.1.2 Mechanisms of Heat Conduction...............224
14.1.2 Convective Heat Transfer..........................................225
14.1.2.1 Rate Equation for Convection....................226
14.1.3 Radiative Heat Transfer.............................................227
14.1.3.1 Nature of Thermal Radiation.....................227
14.1.3.2 Thermal Radiation Exchange....................228
14.1.4 Summary...................................................................228
14.2 Energy Balance.......................................................................229
Supplemental Reading.......................................................................231
Chapter 15 Fundamentals of Conductive Heat Transfer......................................233
15.1 Heat Flux Vector and Temperature Gradient.........................233
15.2 Fourier’s Law of Heat Conduction.........................................234
15.3 General Heat Conduction Equation........................................235
15.3.1 Boundary and Initial Conditions...............................236
15.4 Steady-State Heat Conduction................................................238
15.4.1 One-Dimensional Steady-State Heat Conduction.....238
15.4.2 Analogy between Heat Flow and Electric Current Flow.............................................................241
15.4.3 Temperature-Dependent Thermal Conductivity.......242
15.4.4 Composite Systems with and without Contact Resistance..................................................................244
15.4.5 Conduction with Convection at the Boundaries........245
15.4.6 Heat Conduction with Thermal Energy Generation.....247
15.4.7 Heat Transfer from Extended Surfaces.....................249
15.5 Transient Heat Conduction.....................................................253
15.5.1 Lumped Capacity Analysis.......................................255
15.5.2 Transient Conduction with Nonnegligible Internal Resistance....................................................256
Supplemental Reading.......................................................................258
Chapter 16 Thermal Conductivity of Composites...............................................259
16.1 Empirical Rules of Mixtures..................................................259
16.2 Theoretical Models.................................................................261
References.........................................................................................274
Chapter 17 Thermal Conductivity of Composites of Core-Shell Particles..........277
17.1 Dilute Composites of Core-Shell Particles.............................277
17.2 Nondilute Composites of Core-Shell Particles.......................278
17.3 Model Predictions...................................................................281
17.4 Comparison of Model Predictions with Experimental Data.......286
17.5 Concluding Remarks..............................................................287
References.........................................................................................288
Chapter 18 Influence of Interfacial Contact Resistance on Thermal Conductivity of Composites..............................................................289
18.1 Introduction............................................................................289
18.2 Thermal Conductivity Models for Composites with Contact Resistance.................................................................290
18.2.1 Spherical Filler Particles...........................................290
18.2.2 Nonspherical Filler Particles.....................................294
References.........................................................................................294
Chapter 19 Thermal Diffusivity and Coefficient of Thermal Expansion of Composites........................................................................................295
19.1 Thermal Diffusivity of Composites.......................................295
19.2 Coefficient of Thermal Expansion of Composites.................296
19.2.1 Models for CTE of Composites.................................297
19.2.2 Upper and Lower Bounds of CTE of Composites.....300
19.2.3 Comparison of Model Predictions with Experimental Data....................................................301
References.........................................................................................301
Chapter 20 Radiative Heat Transfer and Radiative Properties of Composites.........303
20.1 Fundamentals of Radiative Heat Transfer..............................303
20.1.1 Nature of Thermal Radiation....................................303
20.1.1.1 Emissive Power, Irradiation, and Radiosity....................................................304
20.1.1.2 Absorptivity, Reflectivity, and Transmissivity............................................305
20.1.1.3 Black Bodies..............................................306
20.1.1.4 Real Bodies................................................307
20.1.1.5 Some More Definitions..............................308
20.1.1.6 Kirchhoff’s Radiation Law........................308
20.1.2 Radiative Heat Transfer between Surfaces...............308
20.1.2.1 Radiation Heat Exchange between Two Real Surfaces.............................................311
20.1.3 Radiation Shielding...................................................313
20.1.4 Radiative Heat Transfer Coefficient..........................314
20.2 Radiative Properties of Composites.......................................315
20.2.1 Estimation of Thermal Emissivity of Composites........316
References.........................................................................................318
Supplemental Reading.......................................................................318
Section V T T Transport Properties of Composites: Mass Transfer in Composites
Chapter 21 Fundamentals of Diffusion Mass Transfer........................................321
21.1 Introduction............................................................................321
21.2 Fick’s Law of Diffusion..........................................................322
21.3 Some Definitions and Concepts.............................................322
21.3.1 Velocities...................................................................322
21.3.2 Fluxes........................................................................323
21.4 Relationship between Fluxes..................................................324
21.4.1 Mass Fluxes...............................................................324
21.4.2 Molar Fluxes.............................................................325
21.5 Differential Mass Balance Equations.....................................326
21.6 Special Cases..........................................................................330
21.6.1 Equimolar Counter Diffusion...................................330
21.6.2 Diffusion of Species A through Stagnant B (Dilute Binary System without Chemical Reaction)..................330
21.6.2.1 Steady-State Diffusion in Planar Geometry...................................................331
21.6.2.2 Steady-State Diffusion in Cylindrical Geometry...................................................333
21.6.2.3 Steady-State Diffusion in Spherical Geometry...................................................335
21.6.3 Diffusion of Species A through Stagnant B (Dilute Binary System with Chemical Reaction)......336
21.6.4 Diffusion of Species A through Stagnant B (Nondilute Binary System)........................................337
21.6.5 Transient Diffusion....................................................339
Supplemental Reading.......................................................................340
Chapter 22 Diffusion Mass Transfer in Composite Membranes.........................341
22.1 Particulate-Filled Polymer Composite Membranes...............341
22.1.1 Background...............................................................341
22.1.2 Permeation Models for Particulate-Filled Polymer Composite Membranes...............................343
22.1.3 Effects of Interfacial Layer.......................................345
22.1.3.1 Predictions of the Pal–Felske Model.........348
22.1.3.2 Comparison of Model Predictions with Experimental Data.....................................351
22.2 Porous Membranes.................................................................354
22.2.1 Diffusion in Porous Membranes and Porous Media.....354
References.........................................................................................356
Chapter 23 Fundamentals of Convective Mass Transfer.....................................359
23.1 Governing Equations..............................................................359
23.2 External Flows........................................................................360
23.2.1 Integral Analysis of Boundary Layer........................361
23.2.2 Mass Transfer Coefficient.........................................361
23.2.2.1 Laminar Flow over Flat Plate....................362
23.2.2.2 Turbulent Flow over Flat Plate..................364
23.2.3 Other External Flows................................................364
23.3 Internal Flows.........................................................................365
23.3.1 Laminar Flow............................................................366
23.3.2 Turbulent Flow..........................................................368
23.4 Interphase Mass Transfer.......................................................369
23.4.1 Individual Mass Transfer Coefficients and Interface Concentrations...........................................370
23.4.2 Concept of Overall Mass Transfer Coefficient..........371
23.4.3 Mass Transfer Coefficients Using Mole Fraction Difference as the Driving Force................................374
23.4.3.1 Liquid-Phase Mass Transfer Coefficients (kL and kx)..............................375
23.4.3.2 Gas-Phase Mass Transfer Coefficients (kG and ky)..................................................375
23.4.3.3 Overall Mass Transfer Coefficients Based on Liquid Phase (KL and Kx)..........376
23.4.3.4 Overall Mass Transfer Coefficients Based on Gas Phase (K G and K y)..............376
23.4.3.5 Relationship between Overall Mass Transfer Coefficient Kx and Individual Mass Transfer Coefficients kxand ky.........376
23.4.3.6 Relationship between Overall Mass Transfer Coefficient Ky and Individual Mass Transfer Coefficients kxand ky.........377
References.........................................................................................377
Supplemental Reading.......................................................................377
Chapter 24 Convective Mass Transfer in Composite Materials..........................379
24.1 Mass Transport across Composite Membrane with Convection at Boundaries.......................................................379
24.1.1 Porous Membranes....................................................379
24.1.1.1 Separation of Gas Mixtures.......................379
24.1.1.2 Separation of Liquid Mixtures..................381
24.1.2 Dense Particulate Composite Membranes................384
24.2 Convective Mass Transfer within Composite Materials........389
24.2.1 Convective Mass Transfer from Single Particle........389
24.2.2 Convective Mass Transfer in Packed Bed of Particles.....................................................................391
24.2.3 Interphase Mass Transfer in Packed Bed of Inert Particles.....................................................................392
References.........................................................................................399
Electromagnetic, Mechanical, and Transport Properties of Composite Materials,
