EBOOK composite materials design and applications third edition (daniel gay) Thiết kế vật liệu composite và ứng dụng phiên bản thứ ba

Design and and Applications Applications design COMPOSITE materials MATERIALS Composite Materials Science/Mechanical Engineering Materials Science/Mechanical Engineering T h i r d E d i T i o n T H I R D E D I T I O N Composite COMPOSITEmaterials MATERIALS design and Applications Design and Applications “This book covers the topics related to the mechanics of composite matopics to the mechanics of composite terials“This in abook very covers simplethe way itrelated is addressed to graduate and under-materialsstudents in a very It is addressed graduate graduate as simple well asway to practical engineers to who want toand en- undergraduate students as well as to practical engineers who want hance their knowledge and learn the guidelines of the use of composite to enhance their book knowledge learn the guidelines of the use a of good composmaterials This is a and good classroom material [and] ite materials This book is good classroom material [and] a good reference.” reference.” —Dr Pierre Rahme, University of Notre Dame, Indiana, USA —Dr Pierre Rahme, University of Notre Dame, Indiana, USA Considered to have contributed greatly to the pre-sizing of composite structures, Composite Materials: Design andtoApplications is aofpopular Considered to have contributed greatly the pre-sizing composite reference book for designers of heavily loaded composite parts Fully structures, Composite Materials: Design and Applications is a popular updated to mirror the exponential growth and development of composreference book for designers of heavily loaded composite parts Fully ites, this English-language Third Edition: updated to mirror the exponential growth and development of composites, this English-language Third Edition: • Contains all-new coverage of nanocomposites and biocomposites • Contains all-new coverage ofprocesses nanocomposites and biocomposites • reflects the latest manufacturing and applications in the • Reflects the latest manufacturing processes and applications in the aerospace, automotive, naval, wind turbine, and sporting goods aerospace, automotive, naval, wind turbine, and sporting goods industries industries • Provides a design method to define composite multilayered plates • Provides a design method to define composite multilayered plates underunder loading, along withwith all numerical information needed for for loading, along all numerical information needed implementation implementation • Proposes original studystudy of composite beams of any section shapes • Proposes original of composite beams of any section shapes and thick-laminated composite plates, leading to technical formulaand thick-laminated composite plates, leading to technical formulathat not are found not found in literature the literature tions tions that are in the • Features numerous examples of the pre-sizing of composite parts, • Features numerous examples of the pre-sizing of composite parts, processed from industrial cases and reworked to highlight key processed from industrial cases and reworked to highlight key in- information formation • Includes test cases for the validation of computer software using • includes test cases for the validation of computer software using finite elements finite elements Consisting of three main parts, plus a fourth on applications, Composite Consisting of three main parts, plus a fourth on applications, Composite Materials: Design and Applications, Third Edition features a technical Materials: Design and Applications, Third Edition features a technical level that rises in difficulty as the text progresses, yet each part still can level that rises in difficulty as the text progresses, yet each part still can be explored independently While the heart of the book, devoted to the be explored independently While the heart of the book, devoted to the methodical pre-design of structural parts, retains its original character, methodical pre-design of structural parts, retains its original character, the contents have been significantly rewritten, restructured, and expandthe contents have been significantly rewritten, restructured, and expanded to better illustrate the types of challenges encountered in modern ed to better illustrate the types of challenges encountered in modern engineering practice engineering practice 6000 Broken Sound Parkway, NW 6000 Broken Sound NW Suite 300, BocaParkway, Raton, FL 33487 Suite 300, Boca Raton, FL 33487 711 Third Avenue 711 Third NewAvenue York, NY 10017 an informa business New York, NY 10017 an informa business Park Square, Milton Park Square, Milton OxonPark OX14 4RN, UK www.taylorandfrancisgroup.com2 ParkAbingdon, Abingdon, Oxon OX14 4RN, UK www.taylorandfrancisgroup.com TT h H iI r R d D ED d Ii TT Ii O oN n E Composite COMPOSITE materials MATERIALS design Applications Design and Applications Gay Gay TThHi rI RdD I OnN EEdDi TI Ti o K19063 K19063 ISBN: 978-1-4665-8487-7 90000 781466 584877 Daniel Gay daniel Gay T h i r d E d i T i o n Composite materials design and Applications This page intentionally left blank T h i r d E d i T i o n Composite materials design and Applications daniel Gay Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20140611 International Standard Book Number-13: 978-1-4665-8488-4 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface .xix Acknowledgments .xxi Author xxiii Section I  PRINCIPLES OF CONSTRUCTION   Composite Materials: Interest and Physical Properties .3 1.1 1.2 1.3 1.4 1.5 1.6 What Is a Composite Material? 1.1.1 Broad Definition 1.1.2 Main Features Fibers and Matrices 1.2.1 Fibers 1.2.1.1 Definition 1.2.1.2 Principal Fiber Materials 1.2.1.3 Relative Importance of Different Fibers in Applications 1.2.2 Materials for Matrices What Can Be Made Using Composite Materials? A Typical Example of Interest Some Examples of Classical Design Replaced by Composite Solutions 10 Main Physical Properties .10   Manufacturing Processes 17 2.1 2.2 Molding Processes 17 2.1.1 Contact Molding 17 2.1.2 Compression Molding 18 2.1.3 Vacuum Molding 18 2.1.4 Resin Injection Molding 19 2.1.5 Injection Molding with Prepreg 20 2.1.6 Foam Injection Molding 20 2.1.7 Molding of Hollow Axisymmetric Components 20 Other Forming Processes 22 2.2.1 Sheet Forming 22 2.2.2 Profile Forming 23 2.2.3 Forming by Stamping 23 v vi  ◾  Contents 2.3 2.2.4 Preforming by Three-Dimensional Assembly 24 2.2.4.1 Example: Carbon/Carbon 24 2.2.4.2 Example: Silicon/Silicon 24 2.2.5 Automated Tape Laying and Fiber Placement 24 2.2.5.1 Necessity of Automation 24 2.2.5.2 Example 24 2.2.5.3 Example 25 2.2.5.4 Example: Robots and Software for AFP—Automatic Fiber Placement Coriolis Composites (FRA) 25 Practical Considerations on Manufacturing Processes 26 2.3.1 Acronyms 26 2.3.2 Cost Comparison 27   Ply Properties 29 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Isotropy and Anisotropy 29 3.1.1 Isotropic Materials 31 3.1.2 Anisotropic Material 32 Characteristics of the Reinforcement–Matrix Mixture 33 3.2.1 Fiber Mass Fraction 34 3.2.2 Fiber Volume Fraction 34 3.2.3 Mass Density of a Ply .35 3.2.4 Ply Thickness 35 Unidirectional Ply 36 3.3.1 Elastic Modulus 36 3.3.2 Ultimate Strength of a Ply 38 3.3.3 Examples 39 3.3.4 Examples of High-Performance Unidirectional Plies 41 Woven Ply .41 3.4.1 Forms of Woven Fabrics 41 3.4.2 Elastic Modulus of Fabric Layer 42 3.4.3 Examples of Balanced Fabric/Epoxy 43 Mats and Reinforced Matrices .45 3.5.1 Mats 45 3.5.2 Example: A Summary of Glass/Epoxy Layers 45 3.5.3 Microspherical Fillers .45 3.5.4 Other Classical Reinforcements 48 Multidimensional Fabrics 49 3.6.1 Example: A Four-Dimensional Architecture of Carbon Reinforcement 49 3.6.2 Example: Three-Dimensional Carbon/Carbon Components 50 Metal Matrix Composites 50 3.7.1 Some Examples 50 3.7.2 Unidirectional Fibers/Aluminum Matrix 52 Biocomposite Materials 53 3.8.1 Natural Plant Fibers 53 3.8.1.1 Natural Fibers 53 3.8.1.2 Pros 53 Contents  ◾  vii 3.8.1.3 Cons 53 3.8.1.4 Examples 54 3.8.2 Natural Vegetable Fiber–Reinforced Composites 54 3.8.2.1 Mechanical Properties 54 3.8.2.2 Biodegradable Matrices 54 3.8.3 Manufacturing Processes 56 3.8.3.1 With Thermosetting Resins 56 3.8.3.2 With Thermoplastic Resins .57 3.9 Nanocomposite Materials 57 3.9.1 Nanoreinforcement 57 3.9.1.1 Nanoreinforcement Shapes .57 3.9.1.2 Properties of Nanoreinforcements 58 3.9.2 Nanocomposite Material 61 3.9.3 Mechanical Applications 62 3.9.3.1 Improvement in Mechanical Properties 62 3.9.3.2 Further Examples of Nonmechanical Applications 64 3.9.4 Manufacturing of Nanocomposite Materials 64 3.10 Tests 66   Sandwich Structures 69 4.1 4.2 4.3 4.4 4.5 What Is a Sandwich Structure? 69 4.1.1 Their Properties Are Surprising 69 4.1.2 Constituent Materials 70 Simplified Flexure 71 4.2.1 Stress 71 4.2.2 Displacements 72 4.2.2.1 Contributions of bending moment M and of shear force T 72 4.2.2.2 Example: A Cantilever Sandwich Structure 73 Some Special Features of Sandwich Structures 74 4.3.1 Comparison of Mass for the Same Flexural Rigidity 〈EI〉 74 4.3.2 Deterioration by Buckling of Sandwich Structures 74 4.3.2.1 Global Buckling 75 4.3.2.2 Local Buckling of the Skins 75 4.3.3 Other Types of Damage 76 Manufacturing and Design Problems 76 4.4.1 Example of Core Material: Honeycomb 76 4.4.2 Shaping Processes 77 4.4.2.1 Machining 77 4.4.2.2 Deformation 77 4.4.2.3 Some Other Considerations 77 4.4.3 Inserts and Attachment Fittings 78 4.4.4 Repair of Laminated Facings 79 Nondestructive Inspection 80 4.5.1 Main Nondestructive Inspection Methods 80 4.5.2 Acoustic Emission Testing 81 viii  ◾  Contents   Conception: Design and Drawing .85 5.1 5.2 5.3 5.4 Drawing a Composite Part 85 5.1.1 Specific Properties 85 5.1.2 Guide Values of Presizing 86 5.1.2.1 Material Characteristics 86 5.1.2.2 Design Factors 88 Laminate 88 5.2.1 Unidirectional Layers and Fabrics 88 5.2.1.1 Unidirectional Layer 88 5.2.1.2 Fabrics 89 5.2.2 Correct Ply Orientation 89 5.2.3 Laminate Drawing Code 90 5.2.3.1 Standard Orientations 90 5.2.3.2 Laminate Middle Plane 90 5.2.3.3 Description of the Stacking Order 93 5.2.3.4 Midplane Symmetry 93 5.2.3.5 Specific Case of Balanced Fabrics 94 5.2.3.6 Technical Minimum 95 5.2.4 Arrangement of Plies 96 5.2.4.1 Proportion and Number of Plies 96 5.2.4.2 Example of Pictorial Representation 97 5.2.4.3 Case of Sandwich Structure 97 Failure of Laminates 98 5.3.1 Damages 98 5.3.1.1 Types of Failure 98 5.3.1.2 Note: Classical Maximum Stress Criterion Shows Its Limits 99 5.3.2 Most Frequently Used Criterion: Tsai–Hill Failure Criterion 100 5.3.2.1  Tsai–Hill Number 100 5.3.2.2 Notes 101 5.3.2.3 How to Determine the Stress Components σℓ, σt, and τℓt in Each Ply .101 Presizing of the Laminate 102 5.4.1 Modulus of Elasticity—Deformation of a Laminate .102 5.4.1.1 Varying Proportions of Plies 102 5.4.1.2 Example of Using Tables 103 5.4.2 Case of Simple Loading 103 5.4.3 Complex Loading Case: Approximative Proportions According to Orientations .109 5.4.3.1 When the Normal and Tangential (Shear) Loads Are Applied Simultaneously 109 5.4.3.2 Example 114 5.4.3.3 Note .117 5.4.4 Complex Loading Case: Optimum Composition of a Laminate 119 5.4.4.1 Optimum Laminate 119 5.4.4.2 Example 122 Contents  ◾  ix 5.4.4.3 Example 125 5.4.4.4 Notes 126 5.4.5 Notes for Practical Use Concerning Laminates 127 5.4.5.1 Specific Aspects for the Design of Laminates 127 5.4.5.2 Delaminations 128 5.4.5.3 Why Is Fatigue Resistance So Good? 129 5.4.5.4 Laminated Tubes 133   Conception: Fastening and Joining 135 6.1 6.2 6.3 Riveting and Bolting 135 6.1.1 Local Loss of Strength 135 6.1.1.1 Knock-Down Factor .135 6.1.1.2 Causes of Hole Degradation 136 6.1.2 Main Failure Modes in Bolted Joints of Composite Materials 138 6.1.3 Sizing of the Joint 138 6.1.3.1 Recommended Values .138 6.1.3.2 Evaluation of Magnified Stress Values 140 6.1.4 Riveting 140 6.1.5 Bolting 141 6.1.5.1 Example of Bolted Joint 141 6.1.5.2 Tightening of the bolt 143 Bonding .143 6.2.1 Adhesives Used .143 6.2.2 Geometry of the Bonded Joints 145 6.2.3 Sizing of the Bonding Surface Area 146 6.2.3.1 Strength of adhesive .146 6.2.3.2 Design 147 6.2.3.3 Stress in Bonded Areas 148 6.2.3.4 Example of single-lap adhesive joint 150 6.2.4 Case of Bonded Joint with Cylindrical Geometry 150 6.2.4.1 Bonded Circular Flange 150 6.2.4.2 Tubes Fitted and Bonded into One Another 150 6.2.5 Examples of Bonding 150 6.2.5.1 Laminates .150 Inserts 152 6.3.1 Case of Sandwich Parts 152 6.3.2 Case of Parts under Uniaxial Loads 154   Composite Materials and Aerospace Construction 155 7.1 Aircraft 155 7.1.1 Composite Components in Aircraft 155 7.1.2 Allocation of Composites Depending on Their Nature 156 7.1.2.1 Glass/Epoxy, Kevlar/Epoxy 156 7.1.2.2 Carbon/Epoxy 157 7.1.2.3 Boron/Epoxy 157 7.1.2.4 Honeycombs 157 7.1.3 Few Comments 158 Appendix B: Buckling of Orthotropic Structures The stability of orthotropic plates and shells is not treated in this book However, in what follows, we give the way to estimate the magnitude order of loads that can lead to buckling due to compression or shear in orthotropic panels and tubes B.1  Buckling of Rectangular Panels Figures B.1 through B.6 allow calculating the critical plane flux resultants* in compression and in shear for different support conditions * See Section 5.2.4 or 12.1.1 for the definition of these load resultants See in Equation 12.16 the definition of constants C11, C22, C12, and C33 that appear in the figures 585 586  ◾  Appendix B: Buckling of Orthotropic Structures (k – 2C) C= 12 C12 + 2C33 √C11 × C22 a 10 y b Nx = k π2 critical x √ C11 × C22 b2 Simply supported on four sides 2.5 2.17 2.08 a × b C22 C11 2.05 1/4 Figure B.1  Buckling of a rectangular panel under in plane loading simply supported on four sides Appendix B: Buckling of Orthotropic Structures  ◾  587 14 k a Clamped 12 b y Simply supported Simply supported x Nx = kπ2 critical Simply supported 10 √C11 × C22 b2 C= C12 + 2C33 C= √C11 × C22 1.0 0.8 0.6 0.4 0.2 0.0 2 a × b C22 C11 1/4 Figure B.2  Buckling of a rectangular panel under in plane loading simply supported on three sides and clamped on the fourth side 588  ◾  Appendix B: Buckling of Orthotropic Structures k 14 a Clamped y Simply b supported 12 Simply supported x Clamped 10 Nx = k π2 critical √ C11 × C22 b2 C= 1.0 0.8 0.6 0.4 0.2 0.0 C= 2 a × b C22 C11 1/4 C12 + 2C33 √C11 × C22 Figure B.3  Buckling of a rectangular panel under in plane loading simply supported on two sides and clamped on the other two sides Appendix B: Buckling of Orthotropic Structures  ◾  589 k 3.5 a Free y 3.0 Simply b supported x 2.5 Simply supported Clamped Nx = k π2 critical √ C11 × C22 b2 2.0 C= 1.5 C12 + 2C33 √C11 × C22 C= 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.5 0.0 a × b C22 C11 1/4 Figure B.4  Buckling of a rectangular panel under in plane loading simply supported on two opposite sides, clamped on the third side, and free on the fourth side 590  ◾  Appendix B: Buckling of Orthotropic Structures k a 3.0 Simply b supported Free y Simply supported x Simply supported 2.5 Nx = kπ2 critical √ C11 × C22 b2 2.0 1.5 1.0 C= C12 + 2C33 √C11 × C22 C= 0.5 0.0 a × b C22 C11 1.0 0.8 0.6 0.4 0.2 0.0 1/4 Figure B.5  Buckling of a rectangular panel under in plane loading simply supported on three sides and free on the fourth side Appendix B: Buckling of Orthotropic Structures  ◾  591 k a 12 y x b Txy = kπ2 critical 10 Simply supported on four sides C= S A b C12 + 2C33 √C11× C22 C= A 1.0 0.8 0.6 0.4 S √ C11×2 C22 0.2 S symmetric buckling A a × b C22 C11 antisymmetric buckling 1/4 Figure B.6  Buckling of a rectangular panel under in plane shear simply supported on four sides 592  ◾  Appendix B: Buckling of Orthotropic Structures B.2  Buckling of Orthotropic Tubes ◾◾ Buckling in bending, giving rise to ovalization of the thin tube (Figure B.7) Bending leads to ovalization of the cross section The moment of inertia for bending that contributes to the bending stiffness decreases, leading to the unstable process The phenomenon is known as the Brazier effect 1/ M critical bending  Ex × E y  2 = πro e   1 − v xy v yx  ◾◾ Buckling due to external pressure The notations in Figure B.7 are kept L is the length of the tube making the container that is subject to buckling: E p = 0.83 × ×  x  critical Ex   E y 1 − 0.1  Ey   Ey T 5/ r e × o ×  L  ro  ◾◾ Buckling due to torsion (Figure B.8) The critical shear resultant in torsion is given by 1/ 1/    xy critical π2  e  = 12  ro3 L2  1/8   E 3E x y  ×  (1 − ν xy ν yx )    ◾◾ Buckling due to axial compression This aspect is not considered here, because the occurrence of elastic instability is strongly influenced by the geometry defects in the orthotropic cylinder r0 y x e Figure B.7  Flexural buckling of a thin-walled orthotropic tube Mbending Appendix B: Buckling of Orthotropic 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Bâle, Switzerland, May 1990 Volkersen O., Recherches sur la Théorie des Assemblages Collés, La Construction Métallique, 4, 3–13, 1965 Walder A., Les Matériaux pour Moteurs d’Avion du Présent et de l’Avenir: les Alliages Base de Nickel pour Disques, les Composés Intermétalliques, les Composites Céramiques, Journée SF2M/Section Nord: Les matériaux pour applications haute température, les matériaux pour moteurs d’avions du présent et de l’avenir, Lille, France, December 1999 Weiss J and Bord C., Les Matériaux Composites, Publication du Ministère de l’Industrie et de la Recherche, et du CETIM, 1983 Design and and Applications Applications design COMPOSITE materials MATERIALS Composite Materials Science/Mechanical Engineering Materials Science/Mechanical Engineering T h i r d E d i T i o n T H I R D E D I T I O N Composite COMPOSITEmaterials MATERIALS design and Applications Design and Applications “This book covers the topics related to the mechanics of composite mato haveway contributed greatly to the pre-sizingand of composite terialsConsidered in a very simple it is addressed to graduate understructures, Composite Designengineers and Applications is atopopular graduate students as well Materials: as to practical who want enreference book for designers of heavily loaded composite parts Fully hance their knowledge and learn the guidelines of the use of composite materials to This bookthe is a good classroom material [and] a good updated mirror exponential growth and development of composreference.” ites, this English-language Third Edition: —Dr Pierre Rahme, University of Notre Dame, Indiana, USA • Contains all-new coverage of nanocomposites and biocomposites Considered to have contributed greatly to the pre-sizing of composite • Reflects the latest manufacturing processes and applications in the structures,aerospace, Compositeautomotive, Materials: Design and Applications is a popular naval, wind turbine, and sporting goods referenceindustries book for designers of heavily loaded composite parts Fully updated to mirror the exponential growth and development of compos• Provides a design method to define composite multilayered plates ites, this English-language Third Edition: under loading, along with all numerical information needed for • Contains all-new coverage of nanocomposites and biocomposites implementation • reflects the latest manufacturing processes and applications the • Proposes original study of composite beams of any sectionin shapes aerospace, automotive, composite naval, wind turbine, andtosporting and thick-laminated plates, leading technicalgoods formulaindustries tions that are not found in the literature • Provides a design method to define composite multilayered plates • Features numerous examples of the pre-sizing of composite parts, underprocessed loading, from along with allcases numerical information needed key for inindustrial and reworked to highlight implementation formation • Proposes original study of beams any section shapes • Includes test cases forcomposite the validation of of computer software using and thick-laminated finite elements composite plates, leading to technical formulations that are not found in the literature Consisting of three main parts,of plus fourth on applications, • Features numerous examples thea pre-sizing of compositeComposite parts, Materials: from Design and Applications, Edition technical processed industrial cases and Third reworked to features highlightakey inlevel that rises in difficulty as the text progresses, yet each part still can formation be explored While the heart of the book, devoted to the • includes test independently cases for the validation of computer software using methodical pre-design of structural parts, retains its original character, finite elements the contents have been significantly rewritten, restructured, and expandConsisting threeillustrate main parts, plus aoffourth on applications, Composite ed to of better the types challenges encountered in modern Materials: Design and Applications, Third Edition features a technical engineering practice level that rises in difficulty as the text progresses, yet each part still can be explored independently While the heart of the book, devoted to the methodical pre-design of structural parts, retains its original character, the contents have been significantly rewritten, restructured, and expanded to better illustrate the types of challenges encountered in modern engineering practice 6000 Broken Sound Parkway, NW 6000 Broken Sound NW Suite 300, BocaParkway, Raton, FL 33487 Suite 300, Boca Raton, FL 33487 711 Third Avenue 711 Third NewAvenue York, NY 10017 an informa business New York, NY 10017 an informa business Park Square, Milton Park Square, Milton OxonPark OX14 4RN, UK www.taylorandfrancisgroup.com2 ParkAbingdon, Abingdon, Oxon OX14 4RN, UK www.taylorandfrancisgroup.com TT h H iI r R d D ED d Ii TT Ii O oN n E Composite COMPOSITE materials MATERIALS design Applications Design and Applications Gay Gay TThHi rI RdD I OnN EEdDi TI Ti o K19063 K19063 ISBN: 978-1-4665-8487-7 90000 781466 584877 Daniel Gay daniel Gay ...T h i r d E d i T i o n Composite materials design and Applications This page intentionally left blank T h i r d E d i T i o n Composite materials design and Applications daniel Gay Boca... composite materials since the last quarter of a century have made this area popular due to the breadth and universality of applications The annual global growth rate of composites is 5%–6%, and. .. microspheres, powders,* and nanoreinforcements.† * See Section 3.5.3 † See Section 3.9 6  ◾  Composite Materials: Design and Applications 1.2.1.3  Relative Importance of Different Fibers in Applications