《纺织复合材料》课程参考文献（Composite materials science and applications，Second Edition）Contents

Engineering Materials and Processes

Engineering Materials and Processes

Series Editor Professor Brian Derby,Professor of Materials Science Manchester Materials Science Centre,Grosvenor Street,Manchester,M1 7HS,UK Other titles published in this series: Fusion Bonding of Polymer Composites Computational Quantum Mechanics C.Ageorges and L.Ye for Materials Engineers Composite Materials L.Vitos D.D.L.Chung Modelling of Powder Die Compaction Titanium P.R.Brewin,O.Coube,P.Doremus G.Lutjering and J.C.Williams and J.H.Tweed Corrosion of Metals Silver Metallization H.Kaesche D.Adams,T.L.Alford and J.W.Mayer Microbiologically Influenced Corrosion Corrosion and Protection R.Javaherdashti E.Bardal Modeling of Metal Forming Intelligent Macromolecules and Machining Processes for Smart Devices P.M.Dixit and U.S.Dixit L.Dai Electromechanical Properties in Composites Microstructure of Steels and Cast Irons Based on Ferroelectrics M.Durand-Charre V.Yu.Topolov and C.R.Bowen Phase Diagrams Charged Semiconductor Defects and Heterogeneous Equilibria E.G.Seebauer and M.C.Kratzer B.Predel,M.Hoch and M.Pool Modelling Stochastic Fibrous Materials Computational Mechanics with Mathematica® of Composite Materials M.Kaminski W.W.Sampson Ferroelectrics in Microwave Devices, Gallium Nitride Processing for Electronics. Circuits and Systems Sensors and Spintronics S.Gevorgian S.J.Pearton,C.R.Abernathy and F.Ren Materials for Information Technology Porous Semiconductors E.Zschech,C.Whelan and T.Mikolajick F.Kochergin and H.Foll Fuel Cell Technology Chemical Vapor Deposition N.Sammes C.-T.Yan and Y.Xu Casting:An Analytical Approach A.Reikher and M.R.Barkhudarov

Series Editor Professor Brian Derby, Professor of Materials Science Manchester Materials Science Centre, Grosvenor Street, Manchester, M1 7HS, UK Other titles published in this series: Fusion Bonding of Polymer Composites C. Ageorges and L. Ye Composite Materials D.D.L. Chung Titanium G. Lütjering and J.C. Williams Corrosion of Metals H. Kaesche Corrosion and Protection E. Bardal Intelligent Macromolecules for Smart Devices L. Dai Microstructure of Steels and Cast Irons M. Durand-Charre Phase Diagrams and Heterogeneous Equilibria B. Predel, M. Hoch and M. Pool Computational Mechanics of Composite Materials M. Kamiñski Gallium Nitride Processing for Electronics, Sensors and Spintronics S.J. Pearton, C.R. Abernathy and F. Ren Materials for Information Technology E. Zschech, C. Whelan and T. Mikolajick Fuel Cell Technology N. Sammes Casting: An Analytical Approach A. Reikher and M.R. Barkhudarov Computational Quantum Mechanics for Materials Engineers L. Vitos Modelling of Powder Die Compaction P.R. Brewin, O. Coube, P. Doremus and J.H. Tweed Silver Metallization D. Adams, T.L. Alford and J.W. Mayer Microbiologically Influenced Corrosion R. Javaherdashti Modeling of Metal Forming and Machining Processes P.M. Dixit and U.S. Dixit Electromechanical Properties in Composites Based on Ferroelectrics V.Yu. Topolov and C.R. Bowen Charged Semiconductor Defects E.G. Seebauer and M.C. Kratzer Modelling Stochastic Fibrous Materials with Mathematica® W.W. Sampson Ferroelectrics in Microwave Devices, Circuits and Systems S. Gevorgian Porous Semiconductors F. Kochergin and H. Föll Chemical Vapor Deposition C.-T. Yan and Y. Xu

Deborah D.L.Chung Composite Materials Science and Applications Second Edition 包Springer

Deborah D.L. Chung Composite Materials Science and Applications Second Edition 123

Deborah D.L.Chung,PhD State University of New York,Buffalo Dept.Mechanical Aerospace Engineering 318 Jarvis Hall NY 14260-4400.Buffalo USA ddlchung @buffalo.edu ISSN1619-0181 ISBN978-1-84882-830-8 e-ISBN978-1-84882-831-5 D0I10.1007/978-1-84882-831-5 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number:2010920533 Springer-Verlag London Limited 2010 Apart from any fair dealing for the purposes of research or private study,or criticism or review.as permitted under the Copyright,Designs and Patents Act 1988.this publication may only be reproduced, stored or transmitted,in any form or by any means,with the prior permission in writing of the publishers. or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copy- right Licensing Agency.Enquiries conceming reproduction outside those terms should be sent to the publishers. The use of registered names,trademarks,etc.,in this publication does not imply,even in the absence of a specific statement,that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation,express or implied,with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. The publisher and the authors accept no legal responsibility for any damage caused by improper use of the instructions and programs contained in this book and the DVD.Although the software has been tested with extreme care,errors in the software cannot be excluded. Cover design:eStudio Calamar,Figueres/Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Deborah D.L. Chung, PhD State University of New York, Buffalo Dept. Mechanical & Aerospace Engineering 318 Jarvis Hall NY 14260–4400, Buffalo USA ddlchung@buffalo.edu ISSN 1619-0181 ISBN 978-1-84882-830-8 e-ISBN 978-1-84882-831-5 DOI 10.1007/978-1-84882-831-5 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2010920533 © Springer-Verlag London Limited 2010 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copy￾right Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. The publisher and the authors accept no legal responsibility for any damage caused by improper use of the instructions and programs contained in this book and the DVD. Although the software has been tested with extreme care, errors in the software cannot be excluded. Cover design: eStudio Calamar, Figueres/Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

In Celebration of the 20th Anniversary of the Composite Materials Research Laboratory, University at Buffalo, State University of New York With thanksgiving for the past twenty years and excitement for the future,I dedicate this book to the Composite Materials Research Lab- oratory,which I founded at the University at Buffalo,State University of New York,in 1989.With the highly appreciated involvement of a large number of researchers,including students,postdoctoral asso- ciates,visiting scholars,faculty members and industrial participants, the Laboratory has made advances in the science and technology of composite materials,as shown by 400 peer-reviewed journal publica- tions that cover composites with polymer,cement,and metal matrices, including those for aerospace,automotive,civil,electronic,energy and thermal applications.The Laboratory has emphasized material devel- opment that is application driven and process oriented,as partly de- scribed in this book.Our most notable breakthroughs relate to smart concrete,vibration damping materials,cement-based pn-junctions, thermoelectric materials,multifunctional structural materials,carbon nanofiber applications,electromagnetic interference shielding mate- rials,electronic packaging materials and thermal interface materials. The graduation of over 30 doctoral students is particularly heart- warming.Special appreciation is extended to Mr.Mark A.Lukowski, for twenty years of technical support. In further celebration of the anniversary,the Laboratory has com- missioned Kenneth C.K.Yip (composer)and I (lyrics and narration writer)to write a musical that merges science and music.The piece is entitled Materials Are Needed to Make Anything,and is for per- formance by a chorus and two vocal soloists and percussion accom- paniment.This is the first musical work that centers on engineering materials!Choirs interested in performing this 30-minute piece are welcome to contact me. Deborah D.L.Chung Director and Professor Composite Materials Research Laboratory Buffalo,NY June1,2009

In Celebration of the 20th Anniversary of the Composite Materials Research Laboratory, University at Buffalo, State University of New York With thanksgiving for the past twenty years and excitement for the future, I dedicate this book to the Composite Materials Research Lab￾oratory, which I founded at the University at Buffalo, State University of New York, in 1989. With the highly appreciated involvement of a large number of researchers, including students, postdoctoral asso￾ciates, visiting scholars, faculty members and industrial participants, the Laboratory has made advances in the science and technology of composite materials, as shown by 400 peer-reviewed journal publica￾tions that cover composites with polymer, cement, and metal matrices, including those for aerospace, automotive, civil, electronic, energy and thermal applications. The Laboratory has emphasized material devel￾opment that is application driven and process oriented, as partly de￾scribed in this book. Our most notable breakthroughs relate to smart concrete, vibration damping materials, cement-based pn-junctions, thermoelectric materials, multifunctional structural materials, carbon nanofiber applications, electromagnetic interference shielding mate￾rials, electronic packaging materials and thermal interface materials. The graduation of over 30 doctoral students is particularly heart￾warming. Special appreciation is extended to Mr. Mark A. Lukowski, for twenty years of technical support. In further celebration of the anniversary, the Laboratory has com￾missioned Kenneth C.K. Yip (composer) and I (lyrics and narration writer) to write a musical that merges science and music. The piece is entitled Materials Are Needed to Make Anything, and is for per￾formance by a chorus and two vocal soloists and percussion accom￾paniment. This is the first musical work that centers on engineering materials! Choirs interested in performing this 30-minute piece are welcome to contact me. Deborah D.L. Chung Director and Professor Composite Materials Research Laboratory Buffalo, NY June 1, 2009 v

Preface to the Second Edition The field of composite materials has progressed greatly over the last few decades,as shown by the widespread use of fibrous composite ma- terials for airframes,sporting goods and other lightweight structures. Enabling this technological progress is scientific understanding of the design and mechanics of composite materials that involve continuous fibers as the reinforcement. Current challenges in the field of composite materials are associated with the extension of the field of composite materials from structural composites to functional and multifunctional composites,the devel- opment of composite materials for electrical,thermal and other func- tional applications that are relevant to current technological needs,and the improvement of composite materials through processing.Exam- ples of functions are joining (e.g.,brazing),repair,sensing,actuation, deicing(as needed for aircraft and bridges),energy conversion (as needed to generate clean energy),electrochemical electrodes,elec- trical connection,thermal contact improvement and heat dissipation (i.e.,cooling,as needed for microelectronics and aircraft).Processing includes the use of additives(which may be introduced as liquids or solids),the combined use of fillers (including discontinuous ones)at the micrometer and nanometer scales,the formation of hybrids(such as organic-inorganic hybrids),the modification of the interfaces in a composite,and control over the microstructure.In other words,the development of composite materials for current technological needs must be application driven and process oriented.This is in contrast to the conventional composites engineering approach,which focuses on mechanics and purely structural applications. The second edition is aimed at providing in an organized manner the concepts and technical details for addressing the challenges mentioned above.Compared to the first edition,the second edition has been greatly expanded(with hundreds of illustrations added),extensively reorganized and almost totally rewritten. As a part ofa comprehensive treatment of composite tailoring meth- ods,numerous examples of methods,in addition to data and micro- graphs that support their effectiveness,have been added to the second vii

Preface to the Second Edition The field of composite materials has progressed greatly over the last few decades, as shown by the widespread use of fibrous composite ma￾terials for airframes, sporting goods and other lightweight structures. Enabling this technological progress is scientific understanding of the design and mechanics of composite materials that involve continuous fibers as the reinforcement. Current challenges in the field of composite materials are associated with the extension of the field of composite materials from structural composites to functional and multifunctional composites, the devel￾opment of composite materials for electrical, thermal and other func￾tional applications that are relevant to current technological needs, and the improvement of composite materials through processing. Exam￾ples of functions are joining (e.g., brazing), repair, sensing, actuation, deicing (as needed for aircraft and bridges), energy conversion (as needed to generate clean energy), electrochemical electrodes, elec￾trical connection, thermal contact improvement and heat dissipation (i.e., cooling, as needed for microelectronics and aircraft). Processing includes the use of additives (which may be introduced as liquids or solids), the combined use of fillers (including discontinuous ones) at the micrometer and nanometer scales, the formation of hybrids (such as organic–inorganic hybrids), the modification of the interfaces in a composite, and control over the microstructure. In other words, the development of composite materials for current technological needs must be application driven and process oriented. This is in contrast to the conventional composites engineering approach, which focuses on mechanics and purely structural applications. The second edition is aimed at providing in an organized manner the concepts and technical details for addressing the challenges mentioned above. Compared to the first edition, the second edition has been greatly expanded (with hundreds of illustrations added), extensively reorganized and almost totally rewritten. As a part of a comprehensive treatment of composite tailoring meth￾ods, numerous examples of methods, in addition to data and micro￾graphs that support their effectiveness, have been added to the second vii

viii edition.Topics added to the second edition include vibration damping, degradation,durability,mechanical joining,electrical connection and nanocomposites.Composites with polymer,cement,metal and carbon matrices are covered in terms of the structure,properties,fabrication and applications.Up-to-date information on lightweight structural materials and civil infrastructure materials is provided.Materials for structural,electrical and thermal applications are comprehensively covered with much information that is not in the first edition.The emphasis on process-oriented composite design,application-oriented functional properties and multifunctional structural materials makes this book different from all other books on composite materials. Due to the large amount of up-to-date and down-to-earth informa- tion,the book is also suitable for use as a reference book for students and professionals that are interested in the development of compos- ite materials.Due to the tutorial style,basic concept coverage,ex- ample problems and review questions,the book is also suitable for use as a textbook for undergraduate and graduate students that have had a semester of an introductory materials science course.The rel- evant academic disciplines include materials,chemical,mechanical, aerospace,electrical and civil engineering Deborah D.L.Chung Buffalo,NY April 16,2009 http://alum.mit.edu/www/ddlchung

viii edition. Topics added to the second edition include vibration damping, degradation, durability, mechanical joining, electrical connection and nanocomposites. Composites with polymer, cement, metal and carbon matrices are covered in terms of the structure, properties, fabrication and applications. Up-to-date information on lightweight structural materials and civil infrastructure materials is provided. Materials for structural, electrical and thermal applications are comprehensively covered with much information that is not in the first edition. The emphasis on process-oriented composite design, application-oriented functional properties and multifunctional structural materials makes this book different from all other books on composite materials. Due to the large amount of up-to-date and down-to-earth informa￾tion, the book is also suitable for use as a reference book for students and professionals that are interested in the development of compos￾ite materials. Due to the tutorial style, basic concept coverage, ex￾ample problems and review questions, the book is also suitable for use as a textbook for undergraduate and graduate students that have had a semester of an introductory materials science course. The rel￾evant academic disciplines include materials, chemical, mechanical, aerospace, electrical and civil engineering. Deborah D.L. Chung Buffalo, NY April 16, 2009 http://alum.mit.edu/www/ddlchung

Preface to the First Edition Books on composite materials are essentially limited to addressing the fabrication and mechanical properties of these materials,because of the dominance of structural applications(such as aerospace appli- cations)for traditional composite materials.However,nonstructural applications are rapidly increasing in importance due to the needs of the electronic,thermal,battery,biomedical and other industries. The scientific concepts that guide the design of functional compos- ites and that of structural composites are quite different,as both the performance and cost requirements are different.Therefore,this book is different from related books in its emphasis on functional com- posite materials.The functions addressed include structural,thermal, electrical,electromagnetic,thermoelectric,electromechanical,dielec- tric,magnetic,optical,electrochemical and biomedical functions.The book provides the fundamental concepts behind the ability to pro- vide each function,in addition to covering the fabrication,structure, properties and applications of the relevant composite materials. Books on composite materials tend to emphasize polymer-matrix composites,though cement-matrix composites are the most widely used structural materials,and metal-matrix,carbon-matrix and ce- ramic-matrix composites are rising in importance.In contrast,this book covers composite materials with all of the abovementioned ma- trices. The most common approach for books on composite materials is to emphasize mechanics issues,due to the relevance of mechanics to structural applications.A less common approach for books on com- posite materials is to categorize composite materials in terms of their matrices and cover the composites in accordance with their matrix materials.In contrast,this book takes a new approach,namely the functional approach-covering composites in accordance with their functions.The functional approach allows the readers to appreciate how composites are designed for the needs of various industries.Such appreciation is valuable for students who are preparing themselves for industrial positions (most students are)and for professionals work- ing in various industries.Moreover,the functional approach allows ix

Preface to the First Edition Books on composite materials are essentially limited to addressing the fabrication and mechanical properties of these materials, because of the dominance of structural applications (such as aerospace appli￾cations) for traditional composite materials. However, nonstructural applications are rapidly increasing in importance due to the needs of the electronic, thermal, battery, biomedical and other industries. The scientific concepts that guide the design of functional compos￾ites and that of structural composites are quite different, as both the performance and cost requirements are different. Therefore, this book is different from related books in its emphasis on functional com￾posite materials. The functions addressed include structural, thermal, electrical, electromagnetic, thermoelectric, electromechanical, dielec￾tric, magnetic, optical, electrochemical and biomedical functions. The book provides the fundamental concepts behind the ability to pro￾vide each function, in addition to covering the fabrication, structure, properties and applications of the relevant composite materials. Books on composite materials tend to emphasize polymer-matrix composites, though cement-matrix composites are the most widely used structural materials, and metal-matrix, carbon-matrix and ce￾ramic-matrix composites are rising in importance. In contrast, this book covers composite materials with all of the abovementioned ma￾trices. The most common approach for books on composite materials is to emphasize mechanics issues, due to the relevance of mechanics to structural applications. A less common approach for books on com￾posite materials is to categorize composite materials in terms of their matrices and cover the composites in accordance with their matrix materials. In contrast, this book takes a new approach, namely the functional approach—covering composites in accordance with their functions. The functional approach allows the readers to appreciate how composites are designed for the needs of various industries. Such appreciation is valuable for students who are preparing themselves for industrial positions (most students are) and for professionals work￾ing in various industries. Moreover, the functional approach allows ix

an organized presentation of numerous scientific concepts other than those related to mechanical behavior,thereby enabling a wide scientific scope to be covered. The book is tutorial in style,but it is up-to-date,and each chapter includes an extensive list of references.The readers need to have taken a course on introductory materials science.They do not need to have taken any prior course on composite materials.Therefore,the book is suitable for use as a textbook for upper-level undergraduate students and for graduate students.It is also suitable for use as a reference book for students,engineers,technicians,technology managers and marketing personnel. Because of the wide scientific scope enabled by the functional ap- proach,the book is expected to be useful to all kinds of engineers (including electrical,thermal,chemical and industrial engineers).In contrast,the conventional approach that emphasizes mechanical be- havior limits the readership to materials,mechanical,aerospace and civil engineers. Deborah D.L.Chung Buffalo,NY April 1,2002

x an organized presentation of numerous scientific concepts other than those related to mechanical behavior, thereby enabling a wide scientific scope to be covered. The book is tutorial in style, but it is up-to-date, and each chapter includes an extensive list of references. The readers need to have taken a course on introductory materials science. They do not need to have taken any prior course on composite materials. Therefore, the book is suitable for use as a textbook for upper-level undergraduate students and for graduate students. It is also suitable for use as a reference book for students, engineers, technicians, technology managers and marketing personnel. Because of the wide scientific scope enabled by the functional ap￾proach, the book is expected to be useful to all kinds of engineers (including electrical, thermal, chemical and industrial engineers). In contrast, the conventional approach that emphasizes mechanical be￾havior limits the readership to materials, mechanical, aerospace and civil engineers. Deborah D.L. Chung Buffalo, NY April 1, 2002

Contents 1 Composite Material Structure and Processing............. 1 1.1 Introduction...................................... 1 1.2 Composite Material Structure....................... 1.2.1 Continuous Fiber Composites................ 5 1.2.2 Carbon-Carbon Composites................. 6 1.2.3 Cement-Matrix Composites.................. 7 1.3 Processing of Composite Materials.................. 8 1.3.1 Polymer-Matrix Composites................. 8 1.3.2 Metal-Matrix Composites.................... 14 1.3.3 Carbon-Matrix Composites 21 1.3.4 Ceramic-Matrix Composites................. 25 1.3.5 Cement-Matrix Composites.................. 26 1.4 Composite Design Concepts........................ 27 1.5 Applications of Composite Materials................. 30 Review Questions ..................................... 32 References…… 33 Further Reading… 33 2 Carbon Fibers and Nanofillers 35 2.1 Carbons.............. 35 22 Carbon Fibers....… 36 23 Nanofillers.… 40 Review Questions ..................................... 45 Further Reading.… 46 3 Mechanical Properties 47 3.1 Property Requirements ........................... 47 3.2 Basic Mechanical Properties........................ 49 3.2.1 Modulus of Elasticity.....…… 49 3.2.2 Strength.…… 57 3.2.3 Ductility................................... 61 3.3 Effect of Damage on the Mechanical Properties....... 61 3.4 Brittle vs.Ductile Materials......................... 62 3.5 Strengthening 62 xi

Contents 1 Composite Material Structure and Processing ............. 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Composite Material Structure . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Continuous Fiber Composites . . . . . . . . . . . . . . . . 5 1.2.2 Carbon–Carbon Composites . . . . . . . . . . . . . . . . . 6 1.2.3 Cement-Matrix Composites . . . . . . . . . . . . . . . . . . 7 1.3 Processing of Composite Materials . . . . . . . . . . . . . . . . . . 8 1.3.1 Polymer-Matrix Composites . . . . . . . . . . . . . . . . . 8 1.3.2 Metal-Matrix Composites . . . . . . . . . . . . . . . . . . . . 14 1.3.3 Carbon-Matrix Composites . . . . . . . . . . . . . . . . . . 21 1.3.4 Ceramic-Matrix Composites . . . . . . . . . . . . . . . . . 25 1.3.5 Cement-Matrix Composites . . . . . . . . . . . . . . . . . . 26 1.4 Composite Design Concepts . . . . . . . . . . . . . . . . . . . . . . . . 27 1.5 Applications of Composite Materials . . . . . . . . . . . . . . . . . 30 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2 Carbon Fibers and Nanofillers . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.1 Carbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2 Carbon Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3 Nanofillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.1 Property Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2 Basic Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.1 Modulus of Elasticity . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.2 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.2.3 Ductility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3 Effect of Damage on the Mechanical Properties . . . . . . . 61 3.4 Brittle vs. Ductile Materials . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.5 Strengthening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 xi