Trim Size: 6in x 9in Agarwal ffirs.tex V2 - 09/12/2017 8:24am Page ii

�

� �

�

Trim Size: 6in x 9in Agarwal ffirs.tex V2 - 09/12/2017 8:24am Page i

�

� �

�

ANALYSIS ANDPERFORMANCE OF

FIBER COMPOSITES

Trim Size: 6in x 9in Agarwal ffirs.tex V2 - 09/12/2017 8:24am Page ii

�

� �

�

Trim Size: 6in x 9in Agarwal ffirs.tex V2 - 09/12/2017 8:24am Page iii

�

� �

�

ANALYSIS ANDPERFORMANCE OF

FIBER COMPOSITES

FOURTH EDITION

Bhagwan D. AgarwalConsultant

Hoffman Estates, Illinois, USA

Lawrence J. BroutmanConsultant

Chicago, Illinois, USA

K. ChandrashekharaMissouri University of Science and Technology

Rolla, Missouri, USA

Trim Size: 6in x 9in Agarwal ffirs.tex V2 - 09/12/2017 8:24am Page iv

�

� �

�

This edition first published 2018

© 2018 John Wiley & Sons, Inc.

Edition HistoryJohn Wiley and Sons, Inc. (3e, 2006)

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, ortransmitted, in any form or by any means, electronic, mechanical, photocopying, recording orotherwise, except as permitted by law. Advice on how to obtain permission to reuse material fromthis title is available at http://www.wiley.com/go/permissions.

The right of Bhagwan D. Agarwal, Lawrence J. Broutman, and K. Chandrashekhara to beidentified as the authors of this work has been asserted in accordance with law.

Registered Office(s)John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USAJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

Editorial OfficeThe Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

For details of our global editorial offices, customer services, and more information about Wileyproducts visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Somecontent that appears in standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of Warranty

While the publisher and authors have used their best efforts in preparing this work, they make norepresentations or warranties with respect to the accuracy or completeness of the contents of thiswork and specifically disclaim all warranties, including without limitation any implied warrantiesof merchantability or fitness for a particular purpose. No warranty may be created or extended bysales representatives, written sales materials or promotional statements for this work. The fact thatan organization, website, or product is referred to in this work as a citation and/or potential sourceof further information does not mean that the publisher and authors endorse the information orservices the organization, website, or product may provide or recommendations it may make. Thiswork is sold with the understanding that the publisher is not engaged in rendering professionalservices. The advice and strategies contained herein may not be suitable for your situation. Youshould consult with a specialist where appropriate. Further, readers should be aware that websiteslisted in this work may have changed or disappeared between when this work was written andwhen it is read. Neither the publisher nor authors shall be liable for any loss of profit or any othercommercial damages, including but not limited to special, incidental, consequential, or otherdamages.

Library of Congress Cataloging-in-Publication Data is Available

ISBN 9781119389989 (Hardback)ISBN 9781119390008 (e-PDF)ISBN 9781119389972 (e-pub)

Cover images: tennis racket © Sylvie Bouchard/Shutterstock, Inc.; Boeing 787 DreamlinerComposition © www.BoeingImages.com; graphs courtesy of the authorsCover design by Wiley

Set in 10.7/12pt of TimesLTStd by SPi Global, Chennai, India.

10 9 8 7 6 5 4 3 2 1

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page v

�

� �

�

CONTENTS

Preface xvAbout the Companion Website xvii

1 Introduction 1

1.1 Definition / 1

1.2 Classification / 2

1.3 Particulate Composites / 2

1.4 Fiber-Reinforced Composites / 5

1.5 Applications of Fiber-Reinforced Polymer Composites / 7

Exercise Problems / 15

References / 16

2 Fibers, Matrices, and Fabrication of Composites 17

2.1 Reinforcing Fibers / 172.1.1 Glass Fibers / 192.1.2 Carbon and Graphite Fibers / 252.1.3 Aramid Fibers / 292.1.4 Boron Fibers / 302.1.5 Other Fibers / 31

2.2 Matrix Materials / 332.2.1 Polymers / 332.2.2 Metals / 44

2.3 Fabrication of Fiber Composite Products / 452.3.1 Fabrication with Thermosetting Resin Matrices / 452.3.2 Fabrication with Thermoplastic Resin Matrices / 592.3.3 Sandwich Composites / 61

v

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page vi

�

� �

�

vi CONTENTS

2.3.4 Fabrication with Metal Matrices / 632.3.5 Fabrication with Ceramic Matrices / 64

Suggested Reading / 65

3 Micromechanics of Unidirectional Composites 67

3.1 Introduction / 673.1.1 Nomenclature / 683.1.2 Volume and Weight Fractions / 68

3.2 Longitudinal Loading: Deformation, Modulus, and Strength / 703.2.1 Model / 703.2.2 Deformation under Small Loads / 713.2.3 Load Sharing / 743.2.4 Behavior beyond Initial Deformation / 763.2.5 Failure Mechanism and Longitudinal Strength / 783.2.6 Factors Influencing Longitudinal Strength

and Stiffness / 80

3.3 Transverse Loading: Modulus and Strength / 833.3.1 Model / 833.3.2 Elasticity Methods of Stiffness Prediction / 853.3.3 Halpin–Tsai Equations for Transverse Modulus / 863.3.4 Transverse Strength / 89

3.4 Shear Modulus / 92

3.5 Poisson’s Ratios / 96

3.6 Expansion Coefficients and Transport Properties / 973.6.1 Thermal Expansion Coefficients / 973.6.2 Moisture Absorption and Expansion Coefficients / 993.6.3 Transport Properties / 100

3.7 Failure of Unidirectional Composites / 1053.7.1 Microscopic Failure Events / 1053.7.2 Failure under Longitudinal Tensile Loads / 1083.7.3 Failure under Longitudinal Compressive Loads / 1113.7.4 Failure under Transverse Tensile Loads / 1153.7.5 Failure under Transverse Compressive Loads / 1163.7.6 Failure under In-Plane Shear Loads / 120

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page vii

�

� �

�

CONTENTS vii

3.8 Typical Properties of Unidirectional Fiber Composites / 120

Exercise Problems / 121

References / 126

4 Short-Fiber Composites 129

4.1 Introduction / 129

4.2 Load Transfer to Fibers / 1304.2.1 Simplified Analysis of Stress Transfer / 1304.2.2 Stress Distributions from Finite-Element Analysis / 134

4.3 Predicting Modulus and Strength of Short-Fiber Composites / 1364.3.1 Average Fiber Stress / 1364.3.2 Longitudinal and Transverse Modulus of Aligned

Short-Fiber Composites / 1374.3.3 Modulus of Randomly Oriented Short-Fiber

Composites / 1384.3.4 Longitudinal Strength of Aligned Short-Fiber

Composites / 1424.3.5 Strength of Randomly Oriented Short-Fiber

Composites / 143

4.4 Influence of Matrix Ductility on Properties / 144

Exercise Problems / 148

References / 149

5 Macromechanics Analysis of an Orthotropic Lamina 151

5.1 Introduction / 1515.1.1 Orthotropic Materials / 151

5.2 Stress–Strain Relations for Unidirectional Composites / 1535.2.1 Engineering Constants in Longitudinal

and Transverse Directions / 1535.2.2 Off-Axis Engineering Constants / 1565.2.3 Transformation of Engineering Constants / 158

5.3 Hooke’s Law and Stiffness and Compliance Matrices / 1675.3.1 General Anisotropic Material / 1675.3.2 Transformation of Stress, Strain, and Elasticity

Constants / 169

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page viii

�

� �

�

viii CONTENTS

5.3.3 Stress–Strain Relations for Orthotropic Materials / 1695.3.4 Transversely Isotropic Material / 1705.3.5 Isotropic Material / 1715.3.6 Orthotropic Material under Plane Stress / 1725.3.7 Compliance Tensor and Compliance Matrix / 1735.3.8 Relations between Engineering Constants and

Elements of Stiffness and Compliance Matrices / 1745.3.9 Restrictions on Elastic Constants / 1775.3.10 Transformation of Stiffness and Compliance

Matrices / 1785.3.11 Invariant Forms of Stiffness and Compliance

Matrices / 182

5.4 Strengths of an Orthotropic Lamina / 1855.4.1 Maximum-Stress Theory / 1865.4.2 Maximum-Strain Theory / 1885.4.3 Maximum-Work Theory / 1905.4.4 Importance of Sign on Off-Axis Strength

of Composites / 193

Exercise Problems / 196

References / 200

6 Analysis of Laminated Composites 202

6.1 Classical Lamination Theory / 2026.1.1 Introduction / 2026.1.2 Laminate Displacements and Strains / 2026.1.3 Laminate Stresses / 2056.1.4 Resultant Forces and Moments / 2066.1.5 Laminate Constitutive Relations / 207

6.2 Laminate Description System / 213

6.3 Design, Construction, and Properties of Laminates / 2156.3.1 Symmetric Laminates / 2156.3.2 Unidirectional, Cross-Ply, and Angle-Ply Laminates / 2156.3.3 Quasi-isotropic Laminates / 216

6.4 Failure of Laminates / 2246.4.1 Initial Failure / 2246.4.2 Laminate Analysis after Initial Failure / 228

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page ix

�

� �

�

CONTENTS ix

6.5 Hygrothermal Stresses in Laminates / 2386.5.1 Concepts of Thermal Stresses / 2386.5.2 Hygrothermal Stress Calculations / 240

6.6 Laminate Analysis through Computers / 251

Exercise Problems / 255

References / 259

7 Analysis of Laminated Plates and Beams 260

7.1 Introduction / 260

7.2 Governing Equations for Plates / 2617.2.1 Equilibrium Equations / 2617.2.2 Equilibrium Equations in Terms of Displacements / 264

7.3 Application of Plate Theory / 2667.3.1 Bending of Specially Orthotropic Laminates / 2667.3.2 Buckling / 2767.3.3 Free Vibrations / 281

7.4 Deformations Due to Transverse Shear / 2867.4.1 First-Order Shear Deformation Theory / 2877.4.2 Higher-Order Shear Deformation Theory / 290

7.5 Analysis of Laminated Beams / 2937.5.1 Governing Equations for Laminated Beams / 2937.5.2 Application of Beam Theory / 295

Exercise Problems / 299

References / 301

8 Advanced Topics in Fiber Composites 302

8.1 Interlaminar Stresses and Free-Edge Effects / 3028.1.1 Concepts of Interlaminar Stresses / 3028.1.2 Determination of Interlaminar Stresses / 3048.1.3 Effect of Stacking Sequence on Interlaminar

Stresses / 3068.1.4 Approximate Solutions for Interlaminar Stresses / 3088.1.5 Summary / 312

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page x

�

� �

�

x CONTENTS

8.2 Fracture Mechanics of Fiber Composites / 3138.2.1 Introduction / 3138.2.2 Fracture Mechanics Concepts and Measures

of Fracture Toughness / 3158.2.3 Fracture Toughness of Composite Laminates / 3238.2.4 Whitney–Nuismer Failure Criteria for Notched

Composites / 327

8.3 Joints for Composite Structures / 3328.3.1 Adhesively Bonded Joints / 3338.3.2 Mechanically Fastened Joints / 3378.3.3 Bonded-Fastened Joints / 339

Exercise Problems / 339

References / 340

9 Performance of Fiber Composites: Fatigue, Impact,and Environmental Effects 345

9.1 Fatigue / 3459.1.1 Introduction / 3459.1.2 Fatigue Damage / 3469.1.3 Factors Influencing Fatigue Behavior / 3549.1.4 Empirical Relations for Fatigue Damage and

Fatigue Life / 3619.1.5 Fatigue of High-Modulus Fiber-Reinforced

Composites / 3629.1.6 Fatigue of Short-Fiber Composites / 366

9.2 Impact / 3719.2.1 Introduction and Fracture Process / 3719.2.2 Energy-Absorbing Mechanisms and Failure Models / 3739.2.3 Effect of Materials and Testing Variables on Impact

Properties / 3779.2.4 Hybrid Composites and Their Impact Strength / 3839.2.5 Damage Due to Low-Velocity Impact / 387

9.3 Environmental-Interaction Effects / 3919.3.1 Fiber Strength / 3919.3.2 Matrix Effects / 397

Exercise Problems / 405

References / 406

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page xi

�

� �

�

CONTENTS xi

10 Experimental Characterization of Composites 414

10.1 Introduction / 414

10.2 Measurement of Physical Properties / 41510.2.1 Density / 41510.2.2 Constituent Weight and Volume Fractions / 41510.2.3 Void Volume Fraction / 41610.2.4 Thermal Expansion Coefficients / 41710.2.5 Moisture Absorption and Diffusivity / 41710.2.6 Moisture Expansion Coefficients / 418

10.3 Measurement of Mechanical Properties / 41910.3.1 Properties in Tension / 41910.3.2 Properties in Compression / 42310.3.3 In-Plane Shear Properties / 42510.3.4 Flexural Properties / 43310.3.5 Interlaminar Shear Strength and Fracture Toughness / 43810.3.6 In-Plane Fracture Toughness Tests / 44210.3.7 Impact Tests / 45010.3.8 Tests for Aerospace Applications / 455

10.4 Damage Identification Using Nondestructive EvaluationTechniques / 45710.4.1 Ultrasonics / 45710.4.2 Acoustic Emission / 46010.4.3 X-Radiography / 46110.4.4 Thermography / 46310.4.5 Laser Shearography / 464

10.5 General Remarks on Characterization / 464

Exercise Problems / 468

References / 470

11 Emerging Composite Materials 475

11.1 Nanocomposites / 475

11.2 Carbon–Carbon Composites / 477

11.3 Biocomposites / 47811.3.1 Biofibers / 47811.3.2 Wood–Plastic Composites (WPCs) / 48011.3.3 Biopolymers / 481

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page xii

�

� �

�

xii CONTENTS

11.4 Composites in “Smart” Structures / 482

11.5 Further Emerging Trends / 483

Suggested Reading / 484

Appendix 1 Matrices and Tensors 488

A1.1 Matrix Definitions / 488

A1.2 Matrix Operations / 493

A1.3 Tensors / 498

References / 509

Appendix 2 Equations of Theory of Elasticity 510

A2.1 Analysis of Strain / 510

A2.2 Analysis of Stress / 514

A2.3 Stress–Strain Relations for Isotropic Materials / 518

References / 520

Appendix 3 Laminate Orientation Code 521

A3.1 Standard Code Elements / 521

A3.2 Positive and Negative Angles / 522

A3.3 Symmetric Laminates / 524

A3.4 Sets / 524

A3.5 Hybrid Laminates / 525

Appendix 4 Properties of Fiber Composites 527

Appendix 5 Computer Programs for Laminate Analysis 532

Appendix 6 Introduction to MATLAB 534

A6.1 Introduction: Getting Started / 534

A6.2 Vectors and Matrices / 537A6.2.1 Defining Matrices / 537A6.2.2 Basic Matrix Functions / 537

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page xiii

�

� �

�

CONTENTS xiii

A6.2.3 Extracting Parts of Matrices / 539A6.2.4 Basic Matrix Operations / 539

A6.3 Programming in MATLAB / 540A6.3.1 Logical and Relational Operators / 540A6.3.2 Loop and Logical Statements / 540A6.3.3 MATLAB Functions: Saving Programs / 540A6.3.4 Input/Output Functions / 541A6.3.5 Controlling the Appearance of Floating Point

Number / 541

A6.4 Plotting Tools / 542A6.4.1 Basic Plot Commands / 542A6.4.2 Line Styles and Colors / 543

Index 545

Trim Size: 6in x 9in Agarwal ftoc.tex V1 - 09/12/2017 8:24am Page xiv

�

� �

�

Trim Size: 6in x 9in Agarwal fpref.tex V2 - 09/09/2017 7:28am Page xv

�

� �

�

PREFACE

The need to include composite materials courses in engineering and sciencecurricula at colleges and universities has been steadily increasing over the past40 years. This need is caused by the growing worldwide usage of compos-ite materials. The advantages of fiber composites in structural applicationsinclude outstanding mechanical properties, design versatility, light weight,corrosion and impact resistance, and excellent fatigue strength. In addition,their strength and stiffness properties are easily controlled by their fiber andlayer composition. No wonder that these materials are now a major player inthe universe of materials available to the design engineer. Thus, engineeringand science students, particularly civil, materials, mechanical, and aerospaceengineers need to be educated on all aspects of composites from the materialsscience to the engineering design of products manufactured from composites.The inclusion of new courses into a curriculum is greatly aided by theavailability of suitable textbooks. This also lessens the need for the teacher tobe an expert in the specific field. Prior editions of the book have well servedthe needs of colleges and universities for over three decades. The revisededition, with updates and extensive rewrites and reorganization, providesan improved teaching tool and is better focused for students and practicingengineers using the book for reference. The new edition was substantiallydeveloped from the feedback of students who used previous editions in theircomposites courses.

The book retains its complete coverage of the subject, with chapters onmaterials and manufacturing, micro- and macromechanics analyses, structuralanalysis, and test methods. Additional examples are presented of polymercomposites used in demanding applications such as the Boeing Dreamlinerpassenger jet, the Bell-Boeing V-22, and the Ford Raptor truck.

A very useful structural analysis software, MATLAB, has been described ina new appendix and its use demonstrated by example problems in chapters 5,6, and 7. The MATLAB code for exercise problems is provided in a solutionsmanual for instructors.

The authors would like to acknowledge the help of Zhen Huo, SudharshanAnandan, Gurjot S. Dhaliwal, Bo Wang, Cheng Yan, and Shouvik Ganguly,all graduate students at the Missouri University of Science and Technology,Rolla. They provided useful suggestions, aided in typing the manuscript,

xv

Trim Size: 6in x 9in Agarwal fpref.tex V2 - 09/09/2017 7:28am Page xvi

�

� �

�

xvi PREFACE

prepared many new figures, and developed MATLAB codes for the solution ofexample and exercise problems. The authors also thank Dr. Sanjay Mazumdarfor providing several updated as well as new figures.

Bhagwan D. AgarwalLawrence J. Broutman

K. ChandrashekharaMay 2017

Trim Size: 6in x 9in Agarwal flast.tex V2 - 09/14/2017 1:10pm Page xvii

�

� �

�

ABOUT THE COMPANIONWEBSITE

This book is accompanied by a companion website:

www.wiley.com/go/agarwal/fiber

Password: industry

The website includes a solutions manual.

xvii

Trim Size: 6in x 9in Agarwal flast.tex V2 - 09/14/2017 1:10pm Page xviii

�

� �

�

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 1

�

� �

�

1

INTRODUCTION

1.1 DEFINITION

The word composite means “consisting of two or more distinct parts.” Thus, amaterial having two or more distinct constituent materials or phases may beconsidered a composite material. However, we recognize materials as com-posites only when the constituent phases have significantly different physicalproperties, and thus the composite properties are noticeably different from theconstituent properties. The difference in properties will be more obvious whenthe properties of one constituent are much greater (≥5 times) than the other,when this phase is in fiber or platelet form, and its volume fraction is greater than10%. Many combinations of constituents do not result in a new material withsignificantly different properties. Such materials are not classified as compos-ites. For example, common metals almost always contain unwanted impuritiesor alloying elements; plastics generally contain small quantities of fillers, lubri-cants, ultraviolet absorbers, and other materials for commercial reasons such aseconomy and ease of processing, yet these generally are not classified as com-posites. In the case of metals, the constituent phases often have nearly identicalproperties (e.g., modulus of elasticity), the phases are not generally fibrous incharacter, and one of the phases usually is present in small-volume fractions.Thus, the modulus of elasticity of a steel alloy is insensitive to the amount of thecarbide present, and metallurgists generally have not considered metal alloysas composites, particularly from the point of view of analysis. Nevertheless,two-phase metal alloys are good examples of particulate composites in termsof structure. Although plastics, which are filled with small amounts of addi-tives to reduce cost, are composites, they need not be considered as such iftheir physical properties are not greatly affected by the additives.

1

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 2

�

� �

�

2 INTRODUCTION

Within the wide range of composite materials, a definition may be adopted tosuit one’s requirements. For the purpose of discussion in this book, compositescan be considered to be materials consisting of two or more chemically distinctconstituents, on a macroscale, having a distinct interface separating them. Thisdefinition encompasses the fiber composites, which are of primary interest inthis text. This definition also encompasses many other types of composites thatare not treated specifically in this book.

1.2 CLASSIFICATION

Composites consist of one or more discontinuous phases embedded in acontinuous phase. The discontinuous phase usually has higher stiffness andstrength than the continuous phase and is called the reinforcement or rein-forcing material, whereas the continuous phase is termed the matrix. Ceramicmatrix composites could be exceptions since matrix may have higher stiffnessthan the reinforcement. Properties of composites are strongly influenced bythe properties of constituent materials, their distribution, and the interactionamong them. Therefore, proper description of a composite material as a systemrequires, besides the constituent materials and their properties, the geometryof the reinforcement (shape, size, and size distribution) and its concentration,concentration distribution, and orientation with reference to the system.

Most composite materials have, so far, been developed to improve mechan-ical properties such as strength, stiffness, toughness, and high-temperatureperformance. The mechanism of improving these properties strongly dependson the geometry of the reinforcement. Therefore, it is quite convenient toclassify composite materials on the basis of the microstructure of a repre-sentative unit of reinforcement to study together the composites that havea common strengthening mechanism. Figure 1.1 represents a commonlyaccepted classification scheme for composite materials. With regard tothis classification, the distinguishing characteristic of a particle is that it isnonfibrous in nature with all its dimensions approximately equal. It may bespherical, cubic, tetragonal, a platelet, or of other regular or irregular shape.A fiber is characterized by its length being much greater than its cross-sectionaldimensions. Particle-reinforced composites are sometimes referred to as par-ticulate composites. Fiber-reinforced composites are, understandably, calledfiber composites.

1.3 PARTICULATE COMPOSITES

Particle-reinforced composites are called particulate composites. A particlegenerally has no long dimension, with the exception of platelets. The dimen-sions of the reinforcement determine its capability of contributing its properties

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 3

�

� �

�

1.3 PARTICULATE COMPOSITES 3

Multilayeredcomposites (Laminates)

Composite materials

Fiber-reinforcedcomposites

(Fiber composites)

Particle-reinforcedcomposites

(Particulate composites)

Lamina or single-layer composites

Discontinuous-fiber-reinforcement(Short-fiber composites)

Continuous-fiber-reinforcement

Unidirectionalreinforcement

Bidirectional or multidirectionalreinforcement

(woven or stitched reinforcement)

Randomorientation

Preferredorientation

Figure 1.1. Classification of composite materials.

to the composite. Also, a reinforcement with a long dimension inhibits thegrowth of cracks normal to the reinforcement that otherwise might lead tofailure, particularly with brittle matrices. Therefore, particles, in general, arenot very effective in improving fracture resistance. However, particles of rub-berlike substances in brittle polymers improve fracture resistance by promotingand then arresting crazing in the brittle matrices. Other types of particles, suchas ceramic, metal, or inorganic particles, produce reinforcing effects in metallicmatrices by different strengthening mechanisms. The particles, because theyare harder than the matrix, restrict deformation of the matrix material betweenthem and thus increase stiffness of the material. The particles also share theload, but to a much smaller extent than the fibers that are parallel to the load.Thus, the particles enhance the stiffness of the composites but do not offermuch potential for strengthening. On the other hand, hard particles placed ina brittle matrix reduce strength because they produce stress concentrations inthe adjacent matrix. Particle fillers, however, are used widely to improve otherproperties of matrix materials, such as the thermal and electrical conductivities,improve performance at elevated temperature, reduce friction, increase wearand abrasion resistance and machinability, increase surface hardness, andreduce shrinkage. In many cases, they are used simply to reduce cost.

The particles and matrix material in a particulate composite can be any com-bination of metallic and nonmetallic materials. The choice of a particular com-bination depends on the desired end properties. Particles of lead are mixedwith copper alloys and steel to improve their machinability. In addition, leadis a natural lubricant in bearings made of copper alloys. Particles of many

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 4

�

� �

�

4 INTRODUCTION

brittle metals such as tungsten, chromium, and molybdenum are incorporatedinto ductile metals to improve their elevated temperature performance whilemaintaining ductile characteristics at room temperature. Particles of tungsten,molybdenum, or their carbides are used widely in silver and copper matricesfor electrical-contact applications, which require high thermal and electricalconductivities, high melting point, and low friction and wetting characteris-tics. These materials are also used for electrodes and related applications in thewelding industry.

Cermets are composites of ceramic and metal. Oxide-based cermets are usedextensively as tool materials for high-speed cutting, thermocouple protectiontubes, furnace mufflers, and a variety of high-temperature erosive applications.Carbide-based cermets mostly have particles of tungsten, chromium, and tita-nium carbides. Tungsten carbide in a cobalt matrix produces very high surfacehardness and is widely used in cutting tools, wiredrawing dies, valve parts, andprecision gauges. Chromium carbide in a cobalt matrix is highly resistant tocorrosion and abrasion and has a coefficient of thermal expansion close to thatof steel. This makes it useful for valve parts, nozzles, and high-load bearingsthat operate at very high temperatures. Titanium carbide in a nickel or cobaltmatrix is well suited for high-temperature applications such as turbine parts,torch tips, and hot-mill parts.

Inorganic fillers are extensively used to improve properties of plastics,such as surface hardness and shrinkage reduction, and to eliminate crazingin moldings, improve fire retardancy, provide color and improve appearance,modify the thermal and electrical conductivities, and, most important, greatlyreduce cost without necessarily sacrificing the desirable properties. Manycommercially important elastomers are filled with carbon black or silicato improve their strength and abrasion resistance while maintaining theirnecessary extensibility. Cold solders consist of metal powders suspended inthermosetting resins so that the composite is hard and strong and conductsheat and electricity. Copper in epoxy increases its conductivity immensely.Lead content in plastics acts as a sound deadener and shield against gammaradiation. Fluorocarbon-based plastics are being used as bearing materials.Metallic inclusions are incorporated to increase thermal conductivity, lowerthe coefficient of expansion, and drastically reduce the wear rate.

Thin flakes offer attractive features to be effective reinforcement. They havea primarily two-dimensional geometry and thus impart equal strength in alldirections in their plane compared with fibers that are unidirectional reinforce-ments. Flakes, when laid parallel, can be packed more closely than fibers orspherical particles. Mica flakes are used in electrical and heat-insulating appli-cations. Composites of mica flakes in a glassy matrix can be machined easilyand are used in electrical applications. Aluminum flakes in paints and othercoatings orient themselves parallel to the surface and give the coating excep-tionally good properties. Silver flakes are employed where good conductivityis required. It has not been possible to fully exploit the attractive possibilitiesof flake-reinforced composites because of fabrication difficulties.

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 5

�

� �

�

1.4 FIBER-REINFORCED COMPOSITES 5

Nanocomposites, which are emerging new composites, are discussed inChapter 11. Clay-reinforced nanocomposites are particulate composites.While nanotubes are fibers by character, their size is very small compared withconventional reinforcing fibers. Therefore, nanotube-reinforced compositesmay also be analyzed as particulate composites, especially since nanotubeconcentration is very small.

Particulate composites are an important class of composite materials. Thediscussion in this text, however, deals primarily with fiber composites.

1.4 FIBER-REINFORCED COMPOSITES

The fiber-reinforced composites, or simply fiber composites, have becomethe most important class of composite materials because they are capable ofachieving high strength and have found applications in industries such as auto-motive, construction, appliances, marine, corrosion, electrical insulation, andaerospace. The fiber composites achieve high strength because the reinforcingfibers possess high strength and high stiffness. Properties of some commonfibers are given in Table 1.1, along with properties of some conventionalmaterials. For comparison of properties on the weight basis, specific strengthand specific modulus are also given. Strength and specific strength of fibers are

Table 1.1 Properties of Fibers and Conventional Bulk Materials

Material

TensileModulus

(E)(GPa)

TensileStrength

(𝜎u) (GPa)

Density(𝜌)

(g/cm3)

SpecificModulus

(E/𝜌)

SpecificStrength(𝜎u/𝜌)

FibersE-glass 72.4 3.5a 2.54 28.5 1.38S-glass 85.5 4.6a 2.48 34.5 1.85Graphite (high modulus) 390.0 2.1 1.90 205.0 1.1Graphite (high tensile strength) 240.0 2.5 1.90 126.0 1.3Boron 385.0 2.8 2.63 146.0 1.1Silica 72.4 5.8 2.19 33.0 2.65Tungsten 414.0 4.2 19.30 21.0 0.22Beryllium 240.0 1.3 1.83 131.0 0.71Kevlar 49 (aramid polymer) 130.0 2.8 1.50 87.0 1.87Conventional materialsSteel 210.0 0.34–2.1 7.8 26.9 0.043–0.27Aluminum alloys 70.0 0.14–0.62 2.7 25.9 0.052–0.23Glass 70.0 0.7–2.1 2.5 28.0 0.28–0.84Tungsten 350.0 1.1–4.1 19.30 18.1 0.057–0.21Beryllium 300.0 0.7 1.83 164.0 0.38

aVirgin strength values. Actual strength values prior to incorporation into composites are approxi-mately 2.1 (GPa).

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 6

�

� �

�

6 INTRODUCTION

superior to those of conventional bulk materials. Graphite, boron, and Kevlar49 fibers also have much higher specific modulus, but glass fibers have specificmodulus comparable only with that of aluminum. Thus, importance of fibersin achieving high strengths is obvious from Table 1.1.

The high strength of glass fibers is attributed to being defect free or beingfree from inherent flaws, which, in bulk glass and other brittle materials, dras-tically reduces strength. Graphite, Kevlar 49 (aramid fibers), and many otherpolymeric fibers attain high strength as a result of improved orientation of theiratomic or molecular structure. E-glass fibers are the most important reinforcingfibers because they are relatively inexpensive yet very effective reinforcementfor polymers. However, boron, graphite, and the Kevlar 49 (aramid polymer)fibers are most exceptional because of their high stiffness, which is an essentialrequirement for effective reinforcement. Of these, the graphite fibers offer thelargest number of combinations of strength and modulus values because theirstructure can be effectively controlled during manufacturing.

Fibers, because of their small cross-sectional dimensions, are not directlyusable as structural materials. They are, therefore, embedded in matrix materialto form fiber composites. The matrix binds the fibers together to provide shapeto the fiber composite, transfers applied load to the fibers, and protects themagainst environmental attack and damage due to handling.

The practical structural elements of fiber composites are multilayered,with several distinct layers. Each layer or lamina is usually very thin (typicalthickness of 0.1 mm) and hence cannot be used directly. When all layers ofa multilayered composite are made of the same constituent materials, it iscalled simply laminate. When layers are made up of different constituentmaterials, the composite is called hybrid laminate or hybrid composite. Forexample, one layer of a hybrid laminate may be a glass-fiber-reinforced epoxy,whereas another layer may be graphite-fiber-reinforced epoxy. It is possible,but not as common, to find a hybrid laminate having different fibers within thesingle layer.

The single-layer composites may actually consist of several distinct layers,with each layer having the same orientation and properties, so that the entirelaminate is considered a single-layer composite. In the case of a composite fab-ricated from nonwoven mats, the fibers are randomly oriented in each layer,and the resulting composite would be considered a single-layer composite eventhough there is a thin resin-rich layer between each reinforcement layer. Inmolded composites made with discontinuous or short fibers, the planar fiberorientation is not uniform through the thickness but there are no distinct layers.Therefore, they are also classified as single-layer composites.

Reinforcing fibers in a single layer of composite may be long or short com-pared with its overall dimensions. Composites with long fibers are sometimescalled continuous-fiber-reinforced composites. Composites with short fibers arecalled short-fiber composites or discontinuous-fiber-reinforced composites.

Continuous fibers can be easily aligned to obtain a composite with highstrength and stiffness in the fiber direction. The aligned fiber composites are

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 7

�

� �

�

1.5 APPLICATIONS OF FIBER-REINFORCED POLYMER COMPOSITES 7

called the unidirectional composites. They are very strong in the fiber direc-tion but are generally weak in the perpendicular direction. Therefore, they arestacked together with different orientations to form an angle ply laminate, whichhas desired properties in all directions. Fiber strands (or bundles of alignedfibers) may be woven to obtain bidirectional or multidirectional reinforcements,which are used to produce composites with high strength and stiffness in morethan one direction. Directional properties of woven fabric–reinforced compos-ites are governed by the weaving pattern. For example, the strength and stiffnessin two mutually perpendicular directions can be made equal or any other ratiodepending on the weaving pattern. However, glass fiber adhesive tapes, whichhave essentially unidirectional reinforcement, are widely used for heavy-dutysealing applications. Some unidirectional composites are also used for fishingpoles and other long or rodlike structures. Thus, continuous fiber composites,due to their potential for high strength and stiffness, are extensively used inload-bearing composite laminates and structures.

Short-fiber composites are widely used in automobiles, consumer products,appliances, and many other applications. They are made with both thermoplas-tics and thermosetting resins. With thermoplastics, they are made by injectionmolding or thermostamping. With thermosetting resins, several manufacturingmethods are used. Premixes are often prepared in the form of bulk molding andsheet molding compounds to make final product by compression molding. Thechopped fibers may be sprayed simultaneously with a liquid resin against a moldto build up a short-fiber plastic structure. Alternatively, chopped fibers may beconverted to a lightly bonded mat or preform that can be later impregnated withresin to fabricate single-layer composites.

Short-fiber composites have fiber length generally in the range of 0.4 mm(1/64 inch) to 50 mm (2 inch). The fiber orientation cannot be easily controlledin short-fiber composites, which limits their ability to achieve high strengthcomparable to that of continuous-fiber composites. This limitation is signifi-cantly offset by the use of a faster production process (molding), which lowerscost. Use of chopped strand mat or preforms produces randomly orientedcomposites, which have approximately equal properties in all directions.However, in the molding process, considerable fiber orientation can occur inthe flow direction, and the molding can get preferential orientation in certainareas. This is particularly applicable to injection molding so that differentareas of a single molding can have quite different fiber orientations and,consequently, properties.

1.5 APPLICATIONS OF FIBER-REINFORCEDPOLYMER COMPOSITES

Fiber-reinforced polymer matrix composites are the most widely used fibercomposites. The U.S. polymer composite industry has grown at an average rateof 6% since 1960, which is approximately twice the growth rate of the U.S.economy [1]. Growth of polymer composites is compared with that of steel,

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 8

�

� �

�

8 INTRODUCTION

100

1960

1964

1968

1972

1976

1980

1984

1988

1992

1996

2000

2004

2008

2012

2015

300

Index 1

960=

100

500

700

900

1100

1300

1500

1700

1900

2100

2300

2500

Steel Aluminum GDP Composites

Since 1960...Steel has grown 1.5 timesGDP has grown 5 timesAluminum has tripledComposites have grown 24 times

Figure 1.2. Growth of composites in the United States over five decades: comparison withsteel, aluminum, and GDP. (Courtesy: S. Mazumdar, CEO of Lucintel [1]) See plate section forcolor representation of this figure.

aluminum, and the U.S. gross domestic product (GDP) in Figure 1.2. Between1960 and 2015, the U.S. consumption of steel grew to 1.5 times, the GDP grewto 5 times, consumption of aluminum tripled, and polymer composites grew to24 times their respective values in 1960. It is estimated that in 2015, the U.S.composites industry shipped 2.61 × 109 kg (5.8 billion lb) of finished prod-ucts to domestic customers [1]. These composites have found applications inmany industries, such as transportation, aerospace, automotive, construction,appliance, marine, corrosion, and electrical. The percentage consumption byapplication industries is shown in Figure 1.3 [1]. For comparison, compositesconsumption in Europe is estimated as 2.24 × 109 kg (5.0 billion lb) in 2015.Percentage consumption by application industries is shown in Figure 1.4 [1].

Growth of polymer composites can be attributed to the following outstandingproperties they offer:

1. Mechanical properties (high strength and stiffness)2. Light weight3. Ease of fabrication4. Corrosion resistance5. Flexibility in design6. High fatigue resistance7. Properties can be tailored

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 9

�

� �

�

1.5 APPLICATIONS OF FIBER-REINFORCED POLYMER COMPOSITES 9

Estimated U.S. composites consumption in 2015: 2.61 × 109 kg (5.8 billion lb)

Electrical & Electronics11%

Consumer Goods7%

Transportation36%

Marine5%

Wind Energy3%

Aerospace1%

Pipe & Tank11%

Construction22%

Others4%

Figure 1.3. Use of composites in U.S. by application industries: Estimates for year 2015. (Cour-tesy: S. Mazumdar, CEO of Lucintel [1]) See plate section for color representation of this figure.

Estimated composites consumption in Europe in 2015: 2.24 × 109 kg (5.0 billion lb)

Electrical & Electronics11%

Consumer Goods7%

Transportation44%

Marine3%

Wind Energy7%

Aerospace1%

Pipe & Tank8%

Construction15%

Others4%

Figure 1.4. Use of composites in Europe by application industries: Estimates for year 2015.(Courtesy: S. Mazumdar, CEO of Lucintel [1]) See plate section for color representation of thisfigure.

Trim Size: 6in x 9in Agarwal c01.tex V2 - 09/09/2017 7:28am Page 10

�

� �

�

10 INTRODUCTION

Fiber reinforcement contributes high strength and stiffness to the polymercomposites while polymer matrix is responsible for light weight, ease offabrication, and corrosion resistance. Polymer composites are fabricated atlower temperatures than the metals and are thus easier to fabricate. Many poly-mer composites can be fabricated at room temperature. Machining of metalsrequires application of large force and energy. Many structural forms that areinconvenient or impossible to manufacture with metals can be manufacturedwith polymer composites. Flexibility in design arises from the fact that theproperties can be changed easily by changing material and manufacturingvariables such as the type of fibers, fiber volume fraction, fiber orientation in alamina, laminate layup, and so on. Therefore, the use of polymer compositesis increasing continuously in many industries.

Good mechanical properties (strength and stiffness) are an important consid-eration in the use of fiber composites. The strength and modulus of commonlyused bidirectional polymer composites are compared with those of conven-tional structural materials in Table 1.2. Properties of bidirectional laminates(e.g., cross-ply laminates) are used in Table 1.2 for a fair comparison with met-als, which have equal properties in all directions. Bidirectional laminates havestrengths and moduli approximately one-half of the longitudinal strength andmodulus of unidirectional composites. They have equal properties in two princi-pal directions and show smaller variation of properties with direction. Polymercomposites generally are superior to metals with respect to specific strength andmodulus (Table 1.2). However, glass-fiber composites are inferior to both steeland aluminum with respect to specific modulus. In applications where weightis an important consideration, it is more appropriate to make comparisons onthe basis of specific properties of the materials rather than the absolute values.Very high specific stiffness of carbon-fiber-reinforced polymers (CFRPs) has

Table 1.2 Properties of Conventional Structural Materials and Bidirectional (Cross-ply)Fiber Composites

Material

FiberVolumeFraction

(Vf )(%)

TensileModulus

(E)(GPa)

TensileStrength

(𝜎u)(GPa)

Density(𝜌)

(g/cm3)

SpecificModulus

(E/𝜌)

SpecificStrength(𝜎u/𝜌)

Mild steel 210.0 0.45–0.83 7.80 26.9 0.058–0.106Aluminum

2024-T4 73.0 0.41 2.70 27.0 0.1526061-T6 69.0 0.26 2.70 25.5 0.096

E-glass–epoxy 57 21.5 0.57 1.97 10.9 0.260Kevlar 49–epoxy 60 40.0 0.65 1.40 29.0 0.460Carbon fiber–epoxy 58 83.0 0.38 1.54 53.5 0.240Boron-epoxy 60 106.0 0.38 2.00 53.0 0.190