COMPOSITE MATERIALS DESIGN AND APPLICATIONS © 2003 by CRC Press LLC CRC PRESS Boca Raton London New York Washington, D.C. COMPOSITE MATERIALS DESIGN AND APPLICATIONS Daniel Gay Suong V. Hoa Stephen W. Tsai © 2003 by CRC Press LLC This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microÞlming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. SpeciÞc permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identiÞcation and explanation, without intent to infringe. Visit the CRC Press Web site at www.crcpress.com © 2003 by CRC Press LLC French editions published by Editions Hermès, Paris, 1997 No claim to original U.S. Government works International Standard Book Number 1-58716-084-6 Library of Congress Card Number 2002073794 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper Library of Congress Cataloging-in-Publication Data Gay, Daniel, 1942- [Matériaux composites. English] Composite materials / by Daniel Gay ; translated by Suong V. Hoa, Stephen W. Tsai. p. cm. Translation of: Matériaux composites. 4th ed. Includes bibliographical references and index. ISBN 1-58716-084-6 (alk. paper) 1. Composite materials. I. Title. TA418.9.C6 G39 2002 620.1 ′ 18—dc21 2002073794 CIP TX846 disclaimer Page iv Friday, November 8, 2002 8:38 AM © 2003 by CRC Press LLC PREFACE The economic importance of composite materials is now well known. There are strong indications everywhere that this importance will be increasing in the future. Composite materials now occupy an established position in the aerospace industry. They are also used for many components in the automotive industry and civil infrastructures now have their reinforcements made of composite materials. There is a large range of manufacturing processes for the production of low-cost compo- sites. There is a need by engineers working in composites for a practical source of reference for the design and application of composites. This book fills that need. In the educational sector, composite materials now are taught at many universities around the world. Usually the topic covered is laminate theory. Composites Design courses also exist in a few universities and institutes. The demand from students and also practitioners of composites for knowledge and training in design of composites is increasing. However a good design book has not been available. The content of these design courses concentrates mostly on analysis while appli- cations still remain at the specimen level. This book, initially written by Daniel Gay in French, has been distributed widely in France and in French speaking countries. The authors are of the opinion that having the book in the English language would facilitate the training and dissemination of knowledge to the regions where composites are used the most. The book has been translated to English with modifications and updates. The book consists of four main parts, with increasing levels of complexity. Each part can be studied independently from the other parts. Ⅲ The first part presents an introduction to composite materials, the fabrica- tion processes, the properties of a single ply, sandwich materials, concep- tual design, assembly, and applications of composites in the aerospace and other areas. This part can be used by itself to form a part of a course on advanced materials and associated designs. Ⅲ The second part presents the mechanics of composite materials. This consists of discussion on elastic anisotropic properties, the directional dependence of different properties, and mechanical properties of thin laminates. This part can be used by itself to teach students and engineers on the mechanics of composite materials. Ⅲ The third part presents the orthotropic coefficients that may be conveniently used for design. The Hill–Tsai failure criterion, bending of composite beams, torsion of composite beams, and bending of thick composite plates. This part requires knowledge of strength of materials. Information presented here is more theoretical than in preceding parts. Its main objective is to contribute to a better interpretation of the behavior of composite components. TX846_Frame_FM Page v Thursday, July 11, 2002 5:38 PM © 2003 by CRC Press LLC Ⅲ The fourth part provides numerous (41) numerical examples on the use and design of composites. There are three levels of examples. Level 1 deals with the determination of mechanical properties of composite structures in different forms such as plates, tubes, or composite components made using different processes such as hand-lay-up or filament winding. Level 2 deals with thermoelastic properties of different laminates. Failure analysis is also carried out. Level 3 deals with bonding of cylinders made of compo- sites, buckling of composite sandwich beams, flexural shear in sandwich beams, vibrations of composite This volume can be used to teach students at the first year graduate level as well as the final year undergraduate level. It is also useful for practical engineers who want to learn, on the job, the guidelines for the use of composites in their applications. The authors hope that this volume can make significant contribution to the training of future engineers who utilize composites. Suong V. Hoa Montreal, Quebec, Canada Daniel Gay Toulouse, France Stephen Tsai Stanford, California July 2002 TX846_Frame_FM Page vi Thursday, July 11, 2002 5:38 PM © 2003 by CRC Press LLC CONTENTS PART I: PRINCIPLES OF CONSTRUCTION 1 Composite Materials, Interest, and Properties 1.1 What Is Composite Material? 1.2 Fibers and Matrix 1.2.1 Fibers 1.2.2 Matrix Materials 1.3 What Can Be Made Using Composite Materials? 1.4 Typical Examples of Interest on the Use of Composite Materials 1.5 Examples on Replacing Conventional Solutions with Composites 1.6 Principal Physical Properties 2 Fabrication Processes 2.1 Molding Processes 2.1.1 Contact Molding 2.1.2 Compression Molding 2.1.3 Molding with Vacuum 2.1.4 Resin Injection Molding 2.1.5 Molding by Injection of Premixed 2.1.6 Molding by Foam Injection 2.1.7 Molding of Components of Revolution 2.2 Other Forming Processes 2.2.1 Sheet Forming 2.2.2 Profile Forming 2.2.3 Stamp Forming 2.2.4 Preforming by Three-Dimensional Assembly 2.2.5 Cutting of Fabric and Trimming of Laminates 2.3 Practical Hints on Manufacturing Processes 2.3.1 Acronyms 2.3.2 Cost Comparison 3 Ply Properties 3.1 Isotropy and Anisotropy 3.1.1 Isotropic Materials 3.1.2 Anisotropic Material 3.2 Characteristics of the Reinforcement–Matrix Mixture 3.2.1 Fiber Mass Fraction 3.2.2 Fiber Volume Fraction 3.2.3 Mass Density of a Ply 3.2.4 Ply Thickness TX846_Frame_FM Page vii Thursday, July 11, 2002 5:38 PM © 2003 by CRC Press LLC 3.3 Unidirectional Ply 3.3.1 Elastic Modulus 3.3.2 Ultimate Strength of a Ply 3.3.3 Examples 3.3.4 Examples of “High Performance” Unidirectional Plies 3.4 Woven Fabrics 3.4.1 Forms of Woven Fabric 3.4.2 Elastic Modulus of Fabric Layer 3.4.3 Examples of Balanced Fabrics/Epoxy 3.5 Mats and Reinforced Matrices 3.5.1 Mats 3.5.2 Summary Example of Glass/Epoxy Layers 3.5.3 Spherical Fillers 3.5.4 Other Reinforcements 3.6 Multidimensional Fabrics 3.7 Metal Matrix Composites 3.8 Tests 4 Sandwich Structures 4.1 What Is a Sandwich Structure? 4.2 Simplified Flexure 4.2.1 Stresses 4.2.2 Displacements 4.3 A Few Special Aspects 4.3.1 Comparison of Mass Based on Equivalent Flexural Rigidity (EI) 4.3.2 Buckling of Sandwich Structures 4.3.3 Other Types of Damage 4.4 Fabrication and Design Problems 4.4.1 Honeycomb: An Example of Core Material 4.4.2 Processing Aspects 4.4.3 Insertion of Attachment Pieces 4.4.4 Repair of Laminated Facings 4.5 Nondestructive Quality Control 5 Conception and Design 5.1 Design of a Composite Piece 5.1.1 Guidelines for Values for Predesign 5.2 The Laminate 5.2.1 Unidirectional Layers and Fabrics 5.2.2 Importance of Ply Orientation 5.2.3 Code to Represent a Laminate 5.2.4 Arrangement of Plies 5.3 Failure of Laminates 5.3.1 Damages 5.3.2 Most Frequently Used Criterion: Hill–Tsai Failure Criterion 5.4 Sizing of the Laminate 5.4.1 Modulus of Elasticity. Deformation of a Laminate 5.4.2 Case of Simple Loading 5.4.3 Case of Complex Loading—Approximate Orientation Distribution of a Laminate 5.4.4 Case of Complex Loading: Optimum Composition of a Laminate 5.4.5 Practical Remarks: Particularities of the Behavior of Laminates TX846_Frame_FM Page viii Thursday, July 11, 2002 5:38 PM © 2003 by CRC Press LLC 6 Joining and Assembly 6.1 Riveting and Bolting 6.1.1 Principal Modes of Failure in Bolted Joints for Composite Materials 6.1.2 Recommended Values 6.1.3 Riveting 6.1.4 Bolting 6.2 Bonding 6.2.1 Adhesives Used 6.2.2 Geometry of the Bonded Joints 6.2.3 Sizing of Bonded Surfaces 6.2.4 Examples of Bonding 6.3 Inserts 7 Composite Materials and Aerospace Construction 7.1 Aircraft 7.1.1 Composite Components in Aircraft 7.1.2 Characteristics of Composites 7.1.3 A Few Remarks 7.1.4 Specific Aspects of Structural Resistance 7.1.5 Large Carriers 7.1.6 Regional Jets 7.1.7 Light Aircraft 7.1.8 Fighter Aircraft 7.1.9 Architecture of Composite Parts in Aircraft 7.1.10 Elements of Braking 7.1.11 The Future 7.2 Helicopters 7.2.1 The Situation 7.2.2 Composite Zones 7.2.3 Blades 7.2.4 Yoke Rotor 7.2.5 Other Composite Working Components 7.3 Propeller Blades for Airplanes 7.4 Turbine Blades in Composites 7.5 Space Applications 7.5.1 Satellites 7.5.2 Pressure Vessels 7.5.3 Nozzles 7.5.4 Other Composite Components 8 Composite Materials for Other Applications 8.1 Composite Materials and the Manufacturing of Automobiles 8.1.1 Introduction 8.1.2 Evaluation and Evolution 8.1.3 Research and Development 8.2 Composites in Naval Construction 8.2.1 Competition 8.2.2 Ships 8.3 Sports and Recreation 8.3.1 Skis 8.3.2 Bicycles TX846_Frame_FM Page ix Thursday, July 11, 2002 5:38 PM © 2003 by CRC Press LLC 8.4 Other Applications 8.4.1 Wind Turbines 8.4.2 Compressed Gas Bottles 8.4.3 Buggy Chassis 8.4.4 Tubes for Off-Shore Installations 8.4.5 Biomechanics Applications 8.4.6 Telepherique Cabin PART II: MECHANICAL BEHAVIOR OF LAMINATED MATERIALS 9 Anisotropic Elastic Media 9.1 Review of Notations 9.1.1 Continuum Mechanics 9.1.2 Number of Distinct ϕ ijk ᐉ Terms 9.2 Orthotropic Materials 9.3 Transversely Isotropic Materials 10 Elastic Constants of Unidirectional Composites 10.1 Longitudinal Modulus E ᐉ 10.2 Poisson Coefficient 10.3 Transverse Modulus E t 10.4 Shear Modulus G ᐉ t 10.5 Thermoelastic Properties 10.5.1 Isotropic Material: Recall 10.5.2 Case of Unidirectional Composite 10.5.3 Thermomechanical Behavior of a Unidirectional Layer 11 Elastic Constants of a Ply Along an Arbitrary Direction 11.1 Compliance Coefficients 11.2 Stiffness Coefficients 11.3 Case of Thermomechanical Loading 11.3.1 Compliance Coefficients 11.3.2 Stiffness Coefficients 12 Mechanical Behavior of Thin Laminated Plates 12.1 Laminate with Midplane Symmetry 12.1.1 Membrane Behavior 12.1.2 Apparent Moduli of the Laminate 12.1.3 Consequence: Practical Determination of a Laminate Subject to Membrane Loading 12.1.4 Flexure Behavior 12.1.5 Consequence: Practical Determination for a Laminate Subject to Flexure 12.1.6 Simplified Calculation for Flexure 12.1.7 Case of Thermomechanical Loading 12.2 Laminate without Midplane Symmetry 12.2.1 Coupled Membrane–Flexure Behavior 12.2.2 Case of Thermomechanical Loading PART III: JUSTIFICATIONS, COMPOSITE BEAMS, AND THICK PLATES 13 Elastic Coefficients 13.1 Elastic Coefficients in an Orthotropic Material 13.2 Elastic Coefficients for a Transversely Isotropic Material 13.2.1 Rotation about an Orthotropic Transverse Axis 13.3 Case of a Ply TX846_Frame_FM Page x Thursday, July 11, 2002 5:38 PM © 2003 by CRC Press LLC 14 The Hill–Tsai Failure Criterion 14.1 Isotropic Material: Von Mises Criterion 14.2 Orthotropic Material: Hill–Tsai Criterion 14.2.1 Preliminary Remarks 14.2.2 Case of a Transversely Isotropic Material 14.2.3 Case of a Unidirectional Ply Under In-Plane Loading 14.3 Variation of Resistance of a Unidirectional Ply with Respect to the Direction of Loading 14.3.1 Tension and Compression Resistance 14.3.2 Shear Strength 15 Composite Beams in Flexure 15.1 Flexure of Symmetric Beams with Isotropic Phases 15.1.1 Degrees of Freedom 15.1.2 Perfect Bonding between the Phases 15.1.3 Equilibrium Relations 15.1.4 Constitutive Relations 15.1.5 Technical Formulation 15.1.6 Energy Interpretation 15.1.7 Extension to the Dynamic Case 15.2 Case of Any Cross Section (Asymmetric) 16 Composite Beams in Torsion 16.1 Uniform Torsion 16.1.1 Torsional Degree of Freedom 16.1.2 Constitutive Relation 16.1.3 Determination of the Function Φ ( y , z ) 16.1.4 Energy Interpretation 16.2 Location of the Torsion Center 17 Flexure of Thick Composite Plates 17.1 Preliminary Remarks 17.1.1 Transverse Normal Stress σ z 17.1.2 Transverse Shear Stresses τ xz and τ yz 17.1.3 Hypotheses 17.2 Displacement Field 17.3 Strains 17.4 Constitutive Relations 17.4.1 Membrane Equations 17.4.2 Bending Behavior 17.4.3 Transverse Shear Equation 17.5 Equilibrium Equations 17.5.1 Transverse Equilibrium 17.5.2 Equilibrium in Bending 17.6 Technical Formulation for Bending 17.6.1 Plane Stresses Due to Bending 17.6.2 Transverse Shear Stresses in Bending 17.6.3 Characterization of the Bending, Warping Increments η x and η y 17.6.4 Warping Functions 17.6.5 Consequences 17.6.6 Interpretation in Terms of Energy 17.7 Examples 17.7.1 Homogeneous Orthotropic Plate 17.7.2 Sandwich Plate TX846_Frame_FM Page xi Thursday, July 11, 2002 5:38 PM © 2003 by CRC Press LLC [...]... Thursday, July 11 , 2002 5:38 PM PART IV: APPLICATIONS 18 Applications 18 .1 Level 1 18 .1. 1 18 .1. 2 18 .1. 3 18 .1. 4 18 .1. 5 18 .1. 6 18 .1. 7 18 .1. 8 18 .1. 9 18 .1. 10 18 .1. 11 18 .1. 12 18 .1. 13 18 .1. 14 18 .1. 15 18 .2 Level 2 18 .2 .1 18.2.2 18 .2.3 18 .2.4 18 .2.5 18 .2.6 18 .2.7 18 .2.8 18 .2.9 18 .2 .10 18 .2 .11 18 .2 .12 18 .2 .13 18 .2 .14 18 .2 .15 18 .2 .16 18 .2 .17 18 .3 Level 3 18 .3 .1 18.3.2 18 .3.3 18 .3.4 18 .3.5 18 .3.6 18 .3.7 18 .3.8 18 .3.9... 0.3 2900 3200 2.3 1. 3 -0.2 ¥ 10 -5 0.02 ¥ 10 18 00 390,000 20,000 0.35 2500 0.6 0.08 ¥ 10 10 0 20 2600 3700 400,000 380,000 3400 14 00 0.8 0.4 0.4 ¥ 10 10 2600 200,000 3000 1. 5 14 2550 200,000 2800 1. 3 960 10 0,000 3000 10 2500 86,000 16 2600 74,000 12 7 14 50 17 50 6.5 -5 -5 800 700 14 1 800 700 2 0.03 200 (20∞C) 60 (800∞C) 14 00 800 >15 00 70 70 200 (20∞C) 60 (800∞C) 800 >15 00 14 0 900 500 >10 00 500 50 (20∞C)... TX846_Frame_C 01 Page 1 Monday, November 18 , 2002 10 :34 AM PART I PRINCIPLES OF CONSTRUCTION © 2003 by CRC Press LLC TX846_Frame_C 01 Page 3 Monday, November 18 , 2002 10 :34 AM 1 COMPOSITE MATERIALS, INTEREST, AND PROPERTIES 1. 1 WHAT IS COMPOSITE MATERIAL? As the term indicates, composite material reveals a material that is different from common heterogeneous materials Currently composite materials refers to materials. .. -5 1 1300 600 -5 -5 0.5 ¥ 10 15 0 TX846_Frame_C 01 Page 12 Monday, November 18 , 2002 10 :34 AM © 2003 by CRC Press LLC Table 1. 3 Properties of Commonly Used Reinforcements TX846_Frame_C 01 Page 15 Monday, November 18 , 2002 10 :34 AM Figure 1. 5 Tensile Strength of Glass/Resin Composites Figure 1. 6 Specific Strength of Different Composites © 2003 by CRC Press LLC TX846_Frame_C02 Page 17 Monday, November 18 ,... distribute the fibers and also to transmit the load to the fibers Notes: Composite materials are not new They have been used since antiquity Wood and cob have been everyday composites Composites have also been used to optimize the performance of some conventional weapons For example: Ⅲ In the Mongolian arcs, the compressed parts are made of corn, and the stretched parts are made of wood and cow tendons glued... cost of the composite solution as compared with the conventional solution, one can state that composites fit the demand of aircraft manufacturers 1. 5 EXAMPLES ON REPLACING CONVENTIONAL SOLUTIONS WITH COMPOSITES Table 1. 1 shows a few significant cases illustrating the improvement on price and performance that can be obtained after replacement of a conventional solution with a composite solution 1. 6 PRINCIPAL... Double Bonded Joint Composite Beam with Two Layers Buckling of a Sandwich Beam Shear Due to Bending in a Sandwich Beam Column Made of Stretched Polymer Cylindrical Bending of a Thick Orthotropic Plate under Uniform Loading Bending of a Sandwich Plate Bending Vibration of a Sandwich Beam TX846_Frame_FM Page xiii Thursday, July 11 , 2002 5:38 PM APPENDICES, BIBLIOGRAPHY, AND INDEX Appendix 1 Stresses in the... made of steel and soft iron: the steel part is stratified like a sheet of paste, with orientation of defects 1 and impurities in the long direction (see Figure 1. 1), then formed into a U shape into which the soft iron is placed The sword then has good resistance for flexure and impact One can see in this period the beginning of the distinction between the common composites used universally and the high... radial frames Ⅲ Sports and Recreation Ⅲ Tennis and squash rackets Ⅲ Fishing poles Ⅲ Skis © 2003 by CRC Press LLC TX846_Frame_C 01 Page 9 Monday, November 18 , 2002 10 :34 AM Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Ⅲ Poles used in jumping Sails Surf boards, Roller skates Bows and arrows Javelins Protection helmets Bicycle frames Golf clubs Oars 1. 4 TYPICAL EXAMPLES OF INTEREST ON THE USE OF COMPOSITE MATERIALS In the domain... will describe the principal processes for the formation of composite parts 2 .1 MOLDING PROCESSES The flow chart in Figure 2 .1 shows the steps found in all molding processes Forming by molding processes varies depending on the nature of the part, the number of parts, and the cost The mold material can be made of metal, polymer, wood, or plaster 2 .1. 1 Contact Molding Contact molding (see Figure 2.2) is open . TX846_Frame_FM Page xi Thursday, July 11 , 2002 5:38 PM © 2003 by CRC Press LLC PART IV: APPLICATIONS 18 Applications 18 .1 Level 1 18 .1. 1 Simply Supported Sandwich Beam 18 .1. 2 Poisson Coefficient of. 17 Flexure of Thick Composite Plates 17 .1 Preliminary Remarks 17 .1. 1 Transverse Normal Stress σ z 17 .1. 2 Transverse Shear Stresses τ xz and τ yz 17 .1. 3 Hypotheses 17 .2. 11 Elastic Constants of a Ply Along an Arbitrary Direction 11 .1 Compliance Coefficients 11 .2 Stiffness Coefficients 11 .3 Case of Thermomechanical Loading 11 .3 .1 Compliance Coefficients 11 .3.2