PRINCIPLES OF COMPOSITE MATERIAL MECHANICS
PRINCIPLES OF COMPOSITE MATERIAL MECHANICS
Ronald F. Gibson Department of
Mechanical Engineering Wayne State University Detroit, Michigan
McGraw-Hill, Inc. New York St. Louis San Francisco Auckland Bogota Caracas 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 States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher.
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-5 1. Composite materials-Mechanical properties. I. Title. II. Series. III. Series: McGraw-Hill series in aeronautical and aerospace engineering. TA418.9.C6G53 1994 620.1. ’ 1892-dc20
93-22119
ABOUT THE AUT-HOR
Ronald F. Gibson is a Professor of Mechanical Engineering and Director of the Advanced Composites Research Laboratory at Wayne State University. Dr. Gibson received his B.S. degree in Mechanical Engineering from the University of Florida, his M.S. in Mechanical Engineering from the University of Tennessee, and his Ph.D. in Mechanics from the University of Minnesota. He has held full-time faculty positions at Iowa State University, the University of Idaho, and Wayne State IJniversity, and visiting faculty positions at the University of Florida and Michigan State University. He has been a Development Engineer for Union Carbide Corporation and a Summer Faculty Fellow at the NASA Langley Research Center. Dr. Gibson is an active member of numerous professional societies, including the American Society of Mechanical Engineers, the American Society for Composites, the American Society for Testing and Materials, the Society for Experimental Mechanics, and the Society for the Advancement of Material and Process Engineering. He has been the recipient of the Hetenyi Award for Best Research Paper of the Year from the Society for Experimental Mechanics and the College of Engineering Outstanding Faculty Award from the University of Idaho. The results of his research have been published in numerous scholarly articles and presented at a variety of national and international meetings.
vii
To
MY
MY AN D
THE
MEMORY
WIFE
Mary Anne,
DAUGHTER
OF
MY
Tracy, PARENTS,
Jim and Lora Gibson
PRINCIPLES
OF
COMPOSITE
MATERIAL MECHANICS
INTRODUCTION
FIGURE
21
1.19
Filament wound composite power transmission shaft. (Cour~sy
of Ford Motor
Company.
Research StaJ)
1.4 FABRICATION PROCESSES Although this book is concerned primarily with mechanics of composite materials, it is essential for the reader to know how these materials are made. This is because with composites, we design and build not only the structure, but also the structural material itself. The selection of a fabrication process obviously depends on the constituent materials in the composite, with the matrix material being the key (i.e., the processes for polymer matrix, metal matrix, and ceramic matrix composites are generally 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 a transverse normal stress and the procedure of Sec. 3.2.1 is followed in order to find the effective transverse modulus of the RVE. The result, of course, 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 final result
A similar result may be found for G,,. The detailed derivation in Ref. [3.11] also includes the effect of a fhird phase, a fiber/matrix interphase material, which is assumed to be an annular volume surrounding the fiber. Such interphase regions exist in many metal matrix [3.11] and polymer matrix [3.12] composites. When the fiber diameter is equal to the interphase diameter, the equation for E2 in Ref. [3.11] reduces to Eq. (3.49) above. The complete set of equations for effective moduli of the 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 this same method of subregions, except that only the terms for subregion B (see Fig. 3.5) are retained. Thus, the simplified micromechanics equation for E2 would be the same as that for ES2 in Eq. (3.47), and similar equations for the other effective moduli are given in Refs. [3.13] and [3.14]. Also included in these references are tables of fiber and matrix properties to be used as input to the SME, and these tables are reproduced here in Tables 3.1 and 3.2. It is important to note that in such tables the transverse fiber modulus, Ef2, and the longitudinal fiber shear modulus, Gfr2, are not actually measured but are inferred by substitution of measured composite properties and matrix properties in the SME. The inferred properties show that fibers such as graphite and aramid are highly anisotropic, whereas glass and boron are essentially isotropic. Similar back-calculations of anisotropic fiber properties using other analytical models have been reported by Kriz and Stinchcomb [3.15] and by Kowalski [3.16]. More recently, direct measurement of fiber transverse moduli has been reported by Kawabata [3.17]. Kawabata’s measurements, based on transverse diametral compression of single graphite and aramid fibers, show even greater anisotropy than the inferred properties in Tables 3.1 and 3.2. However, Caruso and Chamis [3.18] have shown that the SME and the corresponding tables of properties give results which 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 of ASM International, Materials Park, OH
Interfaces on Material Damping, 79-93, (1985). 10.77.
Mantena, R., Gibson, R. F., and Place, T. A., “Damping Capacity Measurements of Degradation in Advanced Materials,” SAMPE Quarterly, 17(3), 20-31 (1986).
