Table Of ContentMechanical Engineering Series
Frederick F. Ling
Series Editor
Springer-Verlag Berlin Heidelberg GmbH
Mechanical Engineering Series
Introdnctory Attitude Dynamics
F.P. Rimrott
Balancing of High-Speed Machinery
M.S. Darlow
Theory of Wire Rope, 2nd ed.
G.A Costello
Theory of Vibration: An Introduction, 2nd ed.
AA Shabana
Theory of Vibration: Discrete and Continuous Systems, 2nd ed.
A.A. Shabana
Laser Machining: Theory and Practice
G. Chryssolouris
Underconstrained Structural Systems
E.N. Kuznetsov
Principles of Heat Transfer in Porous Media, 2nd ed.
M. Kaviany
Mechatronics: Electromechanics and Contromechanics
D.K. Miu
Structural Analysis of Printed Circuit Board Systems
P.A Engel
Kinematic and Dynamic Simulation of Multibody Systems:
The Real-Time Challenge
J. Garcia de Jalon and E. Bayo
High Sensitivity Moire:
Experimental Analysis for Mechanics and Materials
D. Post, B. Han, and P. Ifju
Principles of Convective Heat Transfer
M. Kaviany
(continued after index)
Jean-Marie Berthelot
Composite Materials
Mechanical Behavior and
Structural Analysis
Translated by J. Michael Cole
With 360 Figures
Springer
Jean-Marie Berthelot Translator
Acoustics & Mechanics Institute J. Michael Co1e
Universite du Maine 17 St. Mary's Mount
Avenue Olivier Messiaen Leyburn, North Yorkshire DL8 5JB, UK
72085 Le Mans, Cedex 9, France
Series Editor
Frederick F. Ling
Ernest F. Gloyna Regents Chair in Engineering
Department of Mechanical Engineering
The University of Texas at Austin
Austin, TX 78712-1063, USA
and
Williarn Howard Hart Professor Emeritus
Department of Mechanical Engineering,
Aeronautical Engineering and Mechanics
Rensselaer Polytechnic Institute
Troy, NY 12180-3590, USA
Library of Congress Cataloging-in-Publication Data
Berthelot, Jean-Marie.
Composite materials: mechanical behavior and structural analysis
/ Jean-Marie Berthelot.
p. cm. - (Mechanical engineering series)
Revised translation from the French.
Includes index.
ISBN 978-1-4612-6803-1 ISBN 978-1-4612-0527-2 (eBook)
DOI 10.1007/978-1-4612-0527-2
1. Composite materials. I. Title. 11. Series: Mechanical
engineering series (Berlin, Germany)
TA418.9.C6B467 1998
620.1' 18-DC21 97-48885
Printed on acid-free paper.
© 1999 Springer-Verlag Berlin Heidelberg
Originally published by Springer-Verlag Berlin Heidelberg New York in 1999
All rights reserved. This work may not be translated or copied in whole or in pati without the written petmission
of the publisher (Springer-Verlag Berlin Heidelberg GmbH), except for btief excerpts in connection with reviews
or scholarly analysis. Use in connection with any fOlm of infOlmation storage and retrieval, electronic adaptation,
computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The
use of general descriptive names, trade names, trademarks, etc., in this publication, even if the fOlmer at-e not es
pecially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchan
dise Marks Act, may accordingly be used ft-eely by anyone.
Production managed by A. Orrantia; manufacturing supervised by Thomas King.
Typeset by Integre Technical Publishing Co., Inc., Albuquerque, NM.
9 8 7 6 543 2 1
SPIN 10658148
Series Preface
Mechanical engineering, an engineering discipline borne of the needs of the in
dustrial revolution, is once again asked to do its substantial share in the call for
industrial renewal. The general call is urgent as we face profound issues of produc
tivity and competitiveness that require engineering solutions, among others. The
Mechanical Engineering Series features graduate texts and research monographs
intended to address the need for information in contemporary areas of mechanical
engineering.
The series is conceived as a comprehensive one that covers a broad range of
concentrations important to mechanical engineering graduate education and re
search. We are fortunate to have a distinguished roster of consulting editors on the
advisory board, each an expert in one of the areas of concentration. The names
of the consulting editors are listed on the next page of this volume. The areas
of concentration are applied mechanics, biomechanics, computational mechan
ics, dynamic systems and control, energetics, mechanics of materials, processing,
thermal science, and tribology.
Austin, Texas FREDERICK F. LING
Mechanical Engineering Series
Frederick F. Ling
Series Editor
Advisory Board
Applied Mechanics F.A Leckie
University of California,
Santa Barbara
v.c.
Biomechanics Mow
Columbia University
Computational Mechanics H.T. Yang
University of California,
Santa Barbara
Dynamical Systems and Control KM. Marshek
University of Texas, Austin
Energetics l.R. Welty
University of Oregon, Eugene
Mechanics of Materials 1. Finnie
University of California, Berkeley
Processing KK Wang
Cornell University
Production Systems G.-A Klutke
Texas A&M University
Thermal Science AE. Bergies
Rensselaer Polytechnic Institute
Tribology W.O. Winer
Georgia Institute of Technology
Preface
The growth of the use of composite materials in structures has required the de
velopment of the necessary tools for modeling their mechanical behavior and for
the analysis of laminate or sandwich structures. The objective of this book is to
establish a synthesis of the analysis of the mechanical behavior and the theory
of laminate or sandwich plates and to apply them to the problems of bending,
buckling, and vibrations.
The contents and sequence of this book were conceived with four principal
objectives: (1) to treat a composite material as a traditional material; (2) to provide
engineers with the necessary basic elements for the treatment of design problems
of laminate or sandwich structures by processes of computer aided design; (3) to
have a progression of difficulty that will help readers less familiar with the concepts
of the mechanics of deformable media; (4) to continually compare models with
the actual behavior of the materials or structures.
The book is divided into five parts. The first part, Composite Materials, has the
objective of setting out the context within which the problem of the mechanical
analysis of laminate or sandwich structures exists. Chapter 1 introduces compos
ite materials in a general way. The constituents (matrix and fibers) are studied in
Chapter 2. Chapter 3 describes the principles of the different processes of the man
ufacture of composite structures, with the architecture oflaminates and sandwiches
being analyzed next.
To develop the concepts of the mechanical analysis of composite materials
and structures one needs the basic theory of the mechanics of deformable media.
We have chosen to make a synthesis of the necessary basics in the second part,
Basic Concepts oft he Mechanical Behavior ofM aterials, where the classical tools
viii Preface
are developed: stresses (Chapter 5); strains (Chapter 6); the elastic behavior of
materials (Chapter 7); mechanics of deformable solids (Chapter 8).
The third part, Mechanical Behavior ofC omposite Materials, develops the anal
ysis of the local mechanical behavior of composites. Chapter 9 treats the elastic
behavior of a unidirectional composite material: the law of behavior, estimation
of moduli, and comparison of results with experiments. Composites with a cloth
reinforcement are orthotropic materials whose elastic behavior is studied in Chap
ter 10. Laminated composite materials are formed of successive layers whose
principal directions are changed from one layer to another. Chapter 11 analyzes
the elastic behavior of a layer off its principal axes. Part of the chapter is devoted to
the state called plane stress, a state whose importance will appear in the theory of
laminates. Lastly, Chapter 12 presents the basic mechanisms of fracture observed
in composite materials, and develops the criteria for fracture that a designer will
have available for evaluating the mechanical resistance of a laminate.
The fourth part, Modeling the Mechanical Behavior ofL aminates and Sandwich
Plates, develops the basics of the theory of laminate and sandwich plates. The
general assumptions of the various theories are introduced first in Chapter 13.
The classical theory oflaminates is developed next in Chapter 14. The study of the
effect of the stacking oflayers (Chapter 15) allows us to understand the phenomena
of coupling between stretching, bending, and twisting. The classical theory of
laminates also allows us to estimate the elastic behavior of layers reinforced with
cloths or mats. Chapter 16 develops the fundamental equations of the classical
theory of laminates as well as the energy formulation. The boundary conditions
are also analyzed. Accounting for transverse shear in the theory of laminates is
next developed in Chapter 17. Lastly, Chapter 18 analyzes the theory of sandwich
plates.
The fifth part, Analysis oft he Mechanical Behavior ofC omposite Material Struc
tures, treats problems of bending, buckling, and vibrations of structures made of
composite materials. Chapters 19 and 20 treat the problems of bending for which
the theory of plates can be reduced to a one-dimensional analysis. The first type
of problem concerns cylindrical bending (Chapter 19). The second type is that
of the behavior of the bending of beams (Chapter 20). Chapter 21 next studies
the bending of orthotropic laminated plates for which there is neither bending!
twisting-stretching coupling nor twisting-bending coupling. Chapter 22 consid
ers the bending of symmetric laminates, cross-ply laminates, and angle-ply lam
inates, and shows the difficulty of finding analytical solutions. Chapter 23 treats
the study of the buckling of beams and laminate or sandwich plates, including the
governing equations for buckling and analytical solutions. The determination of
the natural frequencies of beams and plates that are laminates or sandwiches is
next developed in Chapter 24. Hygrothermal effects and the behavior of laminate
plates are analyzed in Chapter 25. Lastly, the book is ended by a chapter devoted
to the predesigning of laminate and sandwich structures, creating a synthesis of
all the concepts developed in the course of the text.
The intention of this book is to provide a fundamental and unified approach to the
basic mechanical behavior of composite materials and composite structures. The
Preface ix
different parts have been carefully developed to provide continuity of the concepts
and theories. It is hoped that this book will provide the necessary elements for
advancing the reader's understanding of the mechanical behavior of materials and
structures.
Vallouise, France JEAN-MARIE BERTHELOT
April, 1997
Translator's Preface
I am very greatly indebted to the author for his considerable assistance in providing
me with much technical terminology and usage in this field, especially where the
French use of one term covers two quite different notions in the subject's English
usage.
For this translation the author has made some significant alterations to the orig
inal French edition, in addition to the correction of some errors. A number of the
later chapters have been altered, some substantially; other small parts have been
completely rewritten. Exercises have been added to almost all chapters. A few
tables have been altered and one or two figures omitted. Throughout the book the
author has changed the way in which he expressed his arguments and descriptions
in the original French edition. This translation edition is therefore, paradoxically,
to a great extent both different from and the same as the original.
It is appropriate to make a few comments about the translation. Mathematicians
and physicists of a theoretical bent should keep in mind that the author's preferred
term "directions" is used instead of "axes"; in the earlier part of the book composites
are described as being "constituted of" their constituent elements in order to avoid
any confusion with a process of formation that "made of" might imply if not infer,
but in the latter chapters it is very apparent that the constitution of a composite
is usually being referred to rather than its process of formation, and therefore the
much less clumsy "made of" is freely used.
As to style I have sought to avoid the use of nouns and proper names as adjec
tives, a practice quite improper in formal English text. Also punctuation has been
kept to the proper level, which is low; the prevalent error of almost amputating
the introductory phrase of a sentence by a comma has been eschewed as far as
any potential for ambiguity allows. The pandemic practice of hyphenating sim-
