Composite Materials Design and Applications Part 1 pot

COMPOSITE MATERIALS DESIGN AND APPLICATIONS Daniel Gay Suong V... The first part presents an introduction to composite materials, the tion processes, the properties of a single ply, sand

COMPOSITE MATERIALS

DESIGN AND APPLICATIONS

CRC PR E S S

Boca Raton London New York Washington, D.C

COMPOSITE MATERIALS

DESIGN AND APPLICATIONS

Daniel Gay Suong V Hoa Stephen W Tsai

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.

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© 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, [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

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The economic importance of composite materials is now well known There arestrong 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 civilinfrastructures now have their reinforcements made of composite materials There

is a large range of manufacturing processes for the production of low-cost sites

compo-There is a need by engineers working in composites for a practical source ofreference for the design and application of composites This book fills that need

In the educational sector, composite materials now are taught at many universitiesaround the world Usually the topic covered is laminate theory Composites Designcourses also exist in a few universities and institutes The demand from studentsand also practitioners of composites for knowledge and training in design ofcomposites 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 distributedwidely in France and in French speaking countries The authors are of the opinionthat having the book in the English language would facilitate the training anddissemination of knowledge to the regions where composites are used the most.The book has been translated to English with modifications and updates Thebook consists of four main parts, with increasing levels of complexity Each partcan be studied independently from the other parts

 The first part presents an introduction to composite materials, the tion processes, the properties of a single ply, sandwich materials, concep-tual design, assembly, and applications of composites in the aerospaceand other areas This part can be used by itself to form a part of a course

fabrica-on advanced materials and associated designs

 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 Thispart can be used by itself to teach students and engineers on the mechanics

of composite materials

 The third part presents the orthotropic coefficients that may be convenientlyused for design The Hill–Tsai failure criterion, bending of composite beams,torsion of composite beams, and bending of thick composite plates Thispart 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

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 The fourth part provides numerous (41) numerical examples on the useand design of composites There are three levels of examples Level 1 dealswith the determination of mechanical properties of composite structures

in different forms such as plates, tubes, or composite components madeusing 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 sites, buckling of composite sandwich beams, flexural shear in sandwichbeams, vibrations of composite

compo-This volume can be used to teach students at the first year graduate level aswell as the final year undergraduate level It is also useful for practical engineerswho want to learn, on the job, the guidelines for the use of composites in theirapplications The authors hope that this volume can make significant contribution

to the training of future engineers who utilize composites

Suong V HoaMontreal, Quebec, Canada

Daniel GayToulouse, FranceStephen TsaiStanford, California

July 2002

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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

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

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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

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

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6 Joining and Assembly

6.1 Riveting and Bolting

6.1.1 Principal Modes of Failure in Bolted Joints for Composite Materials

6.2.2 Geometry of the Bonded Joints

6.2.3 Sizing of Bonded Surfaces

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

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 ϕijk Terms

9.2 Orthotropic Materials

9.3 Transversely Isotropic Materials

10 Elastic Constants of Unidirectional Composites

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

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

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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

15.1.7 Extension to the Dynamic Case

15.2 Case of Any Cross Section (Asymmetric)

16 Composite Beams in Torsion

16.2 Location of the Torsion Center

17 Flexure of Thick Composite Plates

17.1 Preliminary Remarks

17.1.1 Transverse Normal Stress σz

17.1.2 Transverse Shear Stresses τxzand τyz

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 ηxand ηy

PART IV: APPLICATIONS

18 Applications

18.1 Level 1

18.1.1 Simply Supported Sandwich Beam

18.1.2 Poisson Coefficient of a Unidirectional Layer

18.1.3 Helicopter Blade

18.1.4 Transmission Shaft for Trucks

18.1.5 Flywheel in Carbon/Epoxy

18.1.6 Wing Tip Made of Carbon/Epoxy

18.1.7 Carbon Fiber Coated with Nickel

18.1.8 Tube Made of Glass/Epoxy under Pressure

18.1.9 Filament Wound Vessel, Winding Angle

18.1.10 Filament Wound Reservoir, Taking the Heads into Account

18.1.11 Determination of the Volume Fraction of Fibers by Pyrolysis

18.1.12 Lever Arm Made of Carbon/PEEK Unidirectional and Short Fibers

18.1.13 Telegraphic Mast in Glass/Resin

18.1.14 Unidirectional Ply of HR Carbon

18.1.15 Manipulator Arm of Space Shuttle

18.2 Level 2

18.2.1 Sandwich Beam: Simplified Calculation of the Shear Coefficient

18.2.2 Procedure for Calculation of a Laminate

18.2.3 Kevlar/Epoxy Laminates: Evolution of Stiffness Depending

on the Direction of the Load

18.2.4 Residual Thermal Stresses due to Curing of the Laminate

18.2.5 Thermoelastic Behavior of a Tube Made of Filament-Wound Glass/Polyester

18.2.6 Polymeric Tube Loaded by Thermal Load and Creep

18.2.7 First Ply Fracture of a Laminate—Ultimate Rupture

18.2.8 Optimum Laminate for Isotropic Stress State

18.2.9 Laminate Made of Identical Layers of Balanced Fabric

18.2.10 Wing Spar in Carbon/Epoxy

18.2.11 Determination of the Elastic Characteristics of a Carbon/Epoxy Unidirectional Layer from Tensile Test

18.2.12 Sailboat Shell in Glass/Polyester

18.2.13 Determination of the In-Plane Shear Modulus of a Balanced Fabric Ply

18.2.14 Quasi-Isotropic Laminate

18.2.15 Orthotropic Plate in Pure Torsion

18.2.16 Plate Made by Resin Transfer Molding (R.T.M.)

18.2.17 Thermoelastic Behavior of a Balanced Fabric Ply

18.3 Level 3

18.3.1 Cylindrical Bonding

18.3.2 Double Bonded Joint

18.3.3 Composite Beam with Two Layers

18.3.4 Buckling of a Sandwich Beam

18.3.5 Shear Due to Bending in a Sandwich Beam

18.3.6 Column Made of Stretched Polymer

18.3.7 Cylindrical Bending of a Thick Orthotropic Plate under Uniform Loading

18.3.8 Bending of a Sandwich Plate

18.3.9 Bending Vibration of a Sandwich Beam

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PART I

PRINCIPLES OF CONSTRUCTION

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COMPOSITE MATERIALS, INTEREST, AND PROPERTIES

1.1 WHAT IS COMPOSITE MATERIAL?

As the term indicates, composite material reveals a material that is different fromcommon heterogeneous materials Currently composite materials refers to materialshaving strong fibers—continuous or noncontinuous—surrounded by a weakermatrix material The matrix serves to distribute the fibers and also to transmit theload 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:

In the Mongolian arcs, the compressed parts are made of corn, and thestretched parts are made of wood and cow tendons glued together

Japanese swords or sabers have their blades made of steel and soft iron:the steel part is stratified like a sheet of paste, with orientation of defectsand impurities in the long direction1 (see Figure 1.1), then formed into a

U shape into which the soft iron is placed The sword then has goodresistance for flexure and impact

One can see in this period the beginning of the distinction between the commoncomposites used universally and the high performance composites

The composite material as obtained is

Very heterogeneous

Very “anisotropic.” This notion of “anisotropy” will be illustrated later inSection 3.1 and also in Chapter 9 Simply put this means that the mechanicalproperties of the material depend on the direction

1

In folding a sheet of steel over itself 15 times, one obtains 215 = 32,768 layers.

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