Mechanics of Particle- and Fiber-Reinforced Polymer Nanocomposites: From Nanoscale to Continuum Simulations

Learn to model your own problems for predicting the properties of polymer-based composites Mechanics of Particle- and Fiber-Reinforced Polymer Nanocomposites: Nanoscale to Continuum Simulations provides readers with a thorough and up-to-date overview of nano, micro, and continuum approaches for the multiscale modeling of polymer-based composites. Covering nanocomposite development, theoretical models, and common simulation methods, the text includes a variety of case studies and scripting tutorials that enable readers to apply and further develop the supplied simulations. The book describes the foundations of molecular dynamics and continuum mechanics methods, guides readers through the basic steps required for multiscale modeling of any material, and correlates the results between the experimental and theoretical work performed. Focused primarily on nanocomposites, the methods covered in the book are applicable to various other materials such as carbon nanotubes, polymers, metals, and ceramics. Throughout the book, readers are introduced to key topics of relevance to nanocomposite materials and structures—supported by journal articles that discuss recent developments in modeling techniques and in the prediction of mechanical and thermal properties. This timely, highly practical resource: Explains the molecular dynamics (MD) simulation procedure for nanofiber and nanoparticle reinforced polymer composites Compares results of experimental and theoretical results from mechanical models at different length scales Covers different types of fibers and matrix materials that constitute composite materials, including glass, boron, carbon, and Kevlar Reviews models that predict the stiffness of short-fiber composites, including the self-consistent model for finite-length fibers, bounding models, and the Halpin-Tsai equation Describes various molecular modeling methods such as Monte Carlo, Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann methods Highlights the potential of nanocomposites for defense and space applications Perfect for materials scientists, materials engineers, polymer scientists, and mechanical engineers, Mechanics of Particle- and Fiber-Reinforced Polymer Nanocomposites is also a must-have reference for computer simulation scientists seeking to improve their understanding of reinforced polymer nanocomposites.

Table of Contents:
Preface xiii Biography xvi 1 Introduction 1 1.1 Nanoparticle-Reinforced Composites 2 1.2 Nanoplatelet-Reinforced Composites 3 1.3 Nanofiber-Reinforced Composites 3 1.4 Carbon Nanotube-Reinforced Composites 4 1.5 Nanomaterials 5 1.5.1 Woven Fabric 8 1.5.2 Fibers 12 1.5.3 Types of Fibers 15 1.5.4 Boron Fiber 16 1.5.5 Carbon Fiber 17 1.5.5.1 Fabrication of C Fiber Using PAN 17 1.5.5.2 Fabrication of C Fiber Using Pitch 19 1.5.6 Glass Fiber 20 1.5.7 Aramid (Kevlar) Fiber 22 1.5.8 Matrices 24 1.5.8.1 Polymer Matrix Composite 24 1.5.8.2 Metal Matrix Composites 25 1.5.8.3 Ceramic Matrix Composites 25 1.6 Manufacturing Methods 26 1.6.1 Polymer Matrix Composites 26 1.6.1.1 Thermoset Matrix Composites 26 1.6.1.2 Thermoplastic Matrix Composites 36 1.6.2 Metal-Matrix Composites 38 1.6.2.1 Liquid-State Processes 38 1.6.2.2 Solid-State Processes 43 1.6.2.3 In Situ Processes 47 1.6.3 Ceramic Matrix Composites 47 1.6.3.1 Cold Pressing and Sintering 47 1.6.3.2 Hot Pressing 48 1.6.3.3 Reaction Bonding 49 1.6.3.4 Infiltration 50 1.6.3.5 Polymer Infiltration and Pyrolysis 51 References 54 2 Literature Review of Different Modeling Methods 55 2.1 Material Development 55 2.2 Nanostructured Materials 56 2.3 Methods of Modeling 58 2.3.1 Atomistic, Molecular Methods 59 2.3.2 Coarse Grain Methods 60 2.3.3 Continuum Methods 62 2.3.4 Effective Continuum Approach 63 2.4 Literature Review of Different Methods of Modeling 64 2.4.1 Micromechanics/FEM 64 2.4.2 Effective Continuum 72 2.4.3 Molecular Dynamics 73 2.5 Conclusion 76 References 77 3 Modeling of Nanocomposites 83 3.1 Notation 84 3.2 Average Properties 85 3.3 Theoretical Models 86 3.3.1 Cox Shear Lag Model 87 3.3.2 Eshelby’s Equivalent Inclusion 91 3.3.3 Dilute Eshelby’s Model 93 3.3.4 Mori–Tanaka Model 94 3.3.5 Chow Model 98 3.3.6 Modified Halpin–Tsai or Finegan model 99 3.3.7 Hashin–Shtrikman Model 104 3.3.8 Lielens Model 106 3.3.9 Self-Consistent Model 106 3.3.10 Finite Element Modeling (FEM) 108 3.3.10.1 Introduction 108 3.3.10.2 Representative Volume Elements (RVEs) 109 3.3.10.3 Modeling for E11 112 3.3.10.4 Modeling for E22 117 3.3.10.5 Modeling for G23 123 3.3.10.6 Modeling for G31 127 3.3.10.7 Theoritical Formulation 132 3.3.10.8 Comparison of Results 132 3.4 Fast Fourier Transform Numerical Homogenization Methods 143 3.4.1 FFT-based Homogenization Method 145 3.4.2 Implementation of FFT-based Homogenization Method 148 3.5 Conclusion 149 References 150 4 Prediction of Mechanical Properties 155 4.1 Storage Moduli 155 4.1.1 Longitudinal Storage Modulus (E′11) 155 4.1.1.1 Variation of E′11 with Vf 155 4.1.1.2 Variation of E′11 with l/d 157 4.1.2 Transverse Storage Modulus (E′22) 159 4.1.2.1 Variation of E′22 with Vf 159 4.1.2.2 Variation of E′22 with l/d 161 4.1.3 Transverse Shear Storage Modulus (G′23) 163 4.1.3.1 Variation of G′23 with Vf 163 4.1.3.2 Variation of G′23 with l/d 164 4.1.4 Longitudinal Shear Storage Modulus (G′12) 166 4.1.4.1 Variation of G′12 with Vf 166 4.1.4.2 Variation of G′12 with l/d 168 4.2 Loss Factors 170 4.2.1 Longitudinal Loss Factor (𝜂11) 171 4.2.1.1 Variation of 𝜂11 with Vf 171 4.2.1.2 Variation of 𝜂11 with l/d 172 4.2.2 Transverse Loss Factor (𝜂22) 174 4.2.2.1 Variation of 𝜂22 with Vf 174 4.2.2.2 Variation of 𝜂22 with l/d 175 4.2.3 Transverse Shear Loss Factor (𝜂23) 178 4.2.3.1 Variation of 𝜂23 with Vf 178 4.2.3.2 Variation of 𝜂23 with l/d 181 4.2.4 Longitudinal Shear Loss Factor (𝜂12) 183 4.2.4.1 Variation of 𝜂12 with Vf 183 4.2.4.2 Variation of 𝜂12 with l/d 184 4.3 Conclusions 187 Reference 189 5 Experimental Work 191 5.1 Materials 191 5.2 Principles of DMA – Forced Nonresonance Technique 192 5.2.1 Terms and Definitions 192 5.2.2 Choice of Sample Geometry 193 5.2.3 Geometry Choice Guidelines 195 5.3 Experimental Procedure for Dual Cantilever Mode 195 5.4 Theoretical Formulations/Modeling 197 5.5 Results and Discussion 198 5.6 Conclusions 202 References 203 6 Molecular Dynamics Simulation 205 6.1 Molecular Dynamics 205 6.2 Monte Carlo Simulation 206 6.3 Brownian Dynamics 207 6.4 Dissipative Particle Dynamics 207 6.5 Lattice Boltzmann Method 208 6.6 Basic Concepts 208 6.6.1 Force Field 208 6.6.2 Potentials 214 6.6.2.1 Tersoff Model 216 6.6.2.2 Brenner Model 216 6.6.2.3 Morse Potential 217 6.6.2.4 Lennard–Jones Potential 218 6.6.3 Ensemble 219 6.6.4 Thermostat 220 6.6.4.1 Andersen’s Method 221 6.6.4.2 Berendsen Thermostat 221 6.6.4.3 Nosé–Hoover Thermostat 222 6.6.5 Boundary Conditions 224 6.6.5.1 Periodic Boundary Condition 224 6.6.5.2 Lees–Edwards Boundary Condition 225 6.7 Molecular Dynamics Methodology 225 6.7.1 Initial Positions 228 6.7.1.1 Spherical Systems 228 6.7.1.2 Nonspherical Systems 230 6.7.2 Initial Velocities 233 6.7.2.1 Spherical Systems 233 6.7.2.2 Nonspherical Systems 234 6.8 Molecular Potential Energy Surface 235 References 237 7 Molecular Dynamics Simulation-Case Studies 239 7.1 Carbon Nanofiber–Reinforced Polymer Composites 239 7.1.1 Molecular Modeling of CNF and CNF/PP Composites 242 7.1.2 Modeling of CNFs 243 7.1.3 Modeling of CNF–PP Composites 243 7.1.4 Damping in CNF–PP Composites 247 7.1.5 Results and Discussion 248 7.1.5.1 Elastic Moduli 248 7.1.5.2 Damping 253 7.1.6 Conclusions 256 7.2 Silica Nanoparticle/Hydroxyapatite Fiber Reinforced bis-GMA/TEGDMA Composites 256 7.2.1 Molecular Dynamics Methodology 259 7.2.1.1 Molecular Models of Unfilled Polymers 259 7.2.1.2 Molecular Models of Filled Polymer Composites 259 7.2.1.3 MD Methodology 259 7.2.2 Results and Discussion 263 7.2.2.1 Chain Configuration 263 7.2.2.2 Effect of Hydrogen Bonding 263 7.2.2.3 Prediction of Mechanical Properties 267 7.2.2.4 Coefficient of Diffusion 269 7.2.3 Conclusion 272 References 274 8 Coupling of Scales-Continuum Mechanics and Molecular Dynamics 279 8.1 Introduction 279 8.2 Structural Mechanics Review 280 8.3 Carbon Nanotubes: Structural Mechanics Approach 282 8.4 Stiffness Parameters and Force Field Constants: Linkage 285 8.5 Young’s Modulus of Graphene and CNT 286 8.5.1 Modeling of Polymer Matrix 292 8.6 Modeling of CNT/Polymer Interface 292 8.7 Elastic Buckling of CNT/Polymer Composite 294 8.8 Conclusions 296 References 296 9 Conclusions and Future Scope 299 Index 301

About the Author :
SUMIT SHARMA is Assistant Professor at Dr B R Ambedkar National Institute of Technology in Jalandhar, India. He has published thirty scholarly articles and a book related to simulations of composite materials. His research interests include viscoelasticity, fracture mechanics, phase transformations, and solid mechanics.