PRINCIPLES OF COMPOSITEMATERIAL MECHANICS

PRINCIPLESOF COMPOSITE

MATERIALMECHANICS

Ronald F. GibsonDepartment of Mechanical Engineering

Wayne State UniversityDetroit, Michigan

McGraw-Hill, Inc.New York St. Louis San Francisco Auckland BogotaCaracas Lisbon London Madrid Mexico City Milan

Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto

This book was set in Times Roman.The editors were John J. Corrigan and Eleanor Castellano;the production supervisor was Louise Karam.The cover was designed by Joseph Gillians.R. R. Donnelley & Sons Company was printer and binder.

PRINCIPLES OF COMPOSITE MATERIAL MECHANICS

Copyright 0 1994 by McGraw-Hill, Inc. All rights reserved. Printed in the United Statesof America. Except as permitted under the United States Copyright Act of 1976, no partof this publication may be reproduced or distributed in any form or by any means, orstored in a data base or retrieval system, without the prior written permission of thepublisher.

234567890DOCDOC90987654

ISBN O -07-023451-5

Library of Congress Cataloging-in-Publication Data

Gibson, Ronald F.Principles of composite material mechanics/Ronald F. Gibson.

cm.-(McGraw-Hill series in mechanical engineering)(Mc&aw-Hill series in aeronautical and aerospace engineering)

Includes bibliographical references and index.ISBN o-07-02345 l-51. Composite materials-Mechanical properties. I. Title.

II. Series. III. Series: McGraw-Hill series in aeronautical andaerospace engineering.TA418.9.C6G53 1 9 9 4620.1. ’ 1892-dc20 93-22119

ABOUT THE AUT-HOR

Ronald F. Gibson is a Professor of Mechanical Engineering and Directorof the Advanced Composites Research Laboratory at Wayne StateUniversity. Dr. Gibson received his B.S. degree in Mechanical Engineer-ing from the University of Florida, his M.S. in Mechanical Engineeringfrom the University of Tennessee, and his Ph.D. in Mechanics from theUniversity of Minnesota. He has held full-time faculty positions at IowaState University, the University of Idaho, and Wayne State IJniversity,and visiting faculty positions at the University of Florida and MichiganState University. He has been a Development Engineer for UnionCarbide Corporation and a Summer Faculty Fellow at the NASALangley Research Center.

Dr. Gibson is an active member of numerous professional societies,including the American Society of Mechanical Engineers, the AmericanSociety for Composites, the American Society for Testing and Materials,the Society for Experimental Mechanics, and the Society for theAdvancement of Material and Process Engineering. He has been therecipient of the Hetenyi Award for Best Research Paper of the Yearfrom the Society for Experimental Mechanics and the College ofEngineering Outstanding Faculty Award from the University of Idaho.The results of his research have been published in numerous scholarlyarticles and presented at a variety of national and international meetings.

vii

To MY WIFE Mary Anne,

MY DAUGHTER Tracy,

AND THE MEMORY OF MY PARENTS,

Jim and Lora Gibson

PRINCIPLES OF COMPOSITEMATERIAL MECHANICS

INTRODUCTION 21

FIGURE 1.19Filament wound composite power transmission shaft. (Cour~sy of Ford Motor Company.Research StaJ)

1.4 FABRICATION PROCESSESAlthough this book is concerned primarily with mechanics of compositematerials, it is essential for the reader to know how these materials aremade. This is because with composites, we design and build not only thestructure, but also the structural material itself. The selection of afabrication process obviously depends on the constituent materials in thecomposite, with the matrix material being the key (i.e., the processes forpolymer matrix, metal matrix, and ceramic matrix composites aregenerally quite different). In this brief summary of fabrication processes

EFFECllVE MODUL, OF A CONTlNUOlJS FIBER-REINFORCED LAMINA 79

The parallel combination of subregions A and B is now loaded by atransverse normal stress and the procedure of Sec. 3.2.1 is followed inorder to find the effective transverse modulus of the RVE. The result, ofcourse, is the rule of mixtures analogous to Eq. (3.20):

(3.48)

Substitution of Eqs. (3.46) and (3.47) in Eq. (3.48) then gives the finalresult

A similar result may be found for G,,. The detailed derivation inRef. [3.11] also includes the effect of a fhird phase, a fiber/matrixinterphase material, which is assumed to be an annular volume surround-ing the fiber. Such interphase regions exist in many metal matrix [3.11]and polymer matrix [3.12] composites. When the fiber diameter is equalto the interphase diameter, the equation for E2 in Ref. [3.11] reduces toEq. (3.49) above. The complete set of equations for effective moduli ofthe three-phase model are given in Ref. [3.11].

In separate publications Chamis [3.13,3.14] presented the so-called“simplified micromechanics equations” (SME), which are based on thissame method of subregions, except that only the terms for subregion B(see Fig. 3.5) are retained. Thus, the simplified micromechanics equationfor E2 would be the same as that for ES2 in Eq. (3.47), and similarequations for the other effective moduli are given in Refs. [3.13] and[3.14]. Also included in these references are tables of fiber and matrixproperties to be used as input to the SME, and these tables arereproduced here in Tables 3.1 and 3.2. It is important to note that in suchtables the transverse fiber modulus, Ef2, and the longitudinal fiber shearmodulus, Gfr2, are not actually measured but are inferred by substitutionof measured composite properties and matrix properties in the SME. Theinferred properties show that fibers such as graphite and aramid arehighly anisotropic, whereas glass and boron are essentially isotropic.Similar back-calculations of anisotropic fiber properties using otheranalytical models have been reported by Kriz and Stinchcomb [3.15] andby Kowalski [3.16]. More recently, direct measurement of fiber transversemoduli has been reported by Kawabata [3.17]. Kawabata’s measure-ments, based on transverse diametral compression of single graphite andaramid fibers, show even greater anisotropy than the inferred propertiesin Tables 3.1 and 3.2. However, Caruso and Chamis [3.18] have shownthat the SME and the corresponding tables of properties give resultswhich agree well with three-dimensional finite element models, as shown

.

MECHANICAL TESTING OF COMPOSITES AND THEIR CONSTITUENTS 415

in Composite Laminates by the Use of Damping Capacity Measurements,” Role ofInterfaces on Material Damping, 79-93, ASM International, Materials Park, OH(1985).

10 . 77 . Mantena, R., Gibson, R. F., and Place, T. A., “Damping Capacity Measurements ofDegradation in Advanced Materials,” SAMPE Quarterly, 17(3), 20-31 (1986).