systems dept

ConstructionMaterialsThird edition

ConstructionMaterials

Their nature andbehaviour

Third edition

Edited by

J.M. Illston andP.L.J. Domone

London and New York

First published 2001 by Spon Press11 New Fetter Lane, London EC4P 4EE

Simultaneously published in the USA and Canadaby Spon Press29 West 35th Street, New York, NY 10001

Spon Press is an imprint of the Taylor & Francis Group

2001 Spon Press

All rights reserved. No part of this book may be reprinted or reproduced or utilised inany form or by any electronic, mechanical, or other means, now known or hereafterinvented, including photocopying and recording, or in any information storage orretrieval system, without permission in writing from the publishers.

The publisher makes no representation, express or implied, with regard to theaccuracy of the information contained in this book and cannot accept any legalresponsibility or liability for any errors or omissions that may be made.

British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library

Library of Congress Cataloging in Publication DataConstruction materials : their nature and behaviour/edited by J.M. Illston and P.L.J.Domone, 3rd ed.

p. cm.Includes bibliographical references and index.1. Building materials. I. Illston, J.M. II. Domone, P.L.J.

TA403 .C636 2001624.1'8dc21

2001020094

ISBN 0-419-25860-4 (pbk)ISBN 0-419-25850-7 (hb)

This edition published in the Taylor & Francis e-Library, 2002.

ISBN 0-203-47898-3 Master e-book ISBNISBN 0-203-78722-6 (Glassbook Format)

The biggest thing university taught me was thatwith ambition, perseverance and a book you cando anything you want to.

It doesnt matter what the subject is; once youvelearnt how to study, you can do anything youwant.

George Laurer, inventor of the bar code

Contents

Contributors xv

Acknowledgements xviii

Preface P.L.J. Domone and J.M. Illston xix

Part One Fundamentals W.D. Biggs, revised and updated by I.R. McColl and J.R. Moon 1

Introduction 3

1 States of matter 51.1 Fluids 51.2 Solids 71.3 Intermediate behaviour 12

2 Energy and equilibrium 152.1 Mixing 162.2 Entropy 162.3 Free energy 172.4 Equilibrium and equilibrium diagrams 17

3 Atomic structure and interatomic bonding 253.1 Ionic bonding 263.2 Covalent bonding 273.3 Metallic bonding 283.4 Van der Waals bonds 29

4 Elasticity and plasticity 314.1 Linear elasticity 314.2 Consequences of the theory 324.3 Long-range elasticity 334.4 Viscoelasticity 344.5 Plasticity 37

5 Surfaces 395.1 Surface energy 39

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5.2 Water of crystallisation 405.3 Wetting 405.4 Adhesives 415.5 Adsorption 42

6 Fracture and fatigue 446.1 Brittle fracture 456.2 Ductile fracture 466.3 Fracture mechanics 476.4 Fatigue 48

7 Electrical and thermal conductivity 49

Further reading 51

Part Two Metals and alloys W.D. Biggs, revised and updated by I.R. McColl and J.R. Moon 53

Introduction 55

8 Physical metallurgy 578.1 Grain structure 578.2 Crystal structures of metals 588.3 Solutions and compounds 60

9 Mechanical properties of metals 629.1 Stressstrain behaviour 629.2 Tensile strength 639.3 Ductility 649.4 Plasticity 649.5 Dislocation energy 669.6 Strengthening of metals 669.7 Unstable microstructures 68

10 Forming of metals 6910.1 Castings 6910.2 Hot working 7010.3 Cold working 7010.4 Joining 71

11 Oxidation and corrosion 7311.1 Dry oxidation 7311.2 Wet corrosion 7311.3 Control of corrosion 7611.4 Protection against corrosion 76

12 Metals, their differences and uses 7812.1 The extraction of iron 7812.2 Cast irons 78

Contents

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12.3 Steel 7912.4 Aluminium and alloys 8512.5 Copper and alloys 87

Further reading 88

Part Three Concrete P.L.J. Domone 89

Introduction 91

13 Portland cements 9513.1 Manufacture 9513.2 Physical properties 9613.3 Chemical composition 9713.4 Hydration 9813.5 Structure and strength of hardened cement paste 10413.6 Water in hcp and drying shrinkage 10513.7 Modications of Portland cement 10613.8 Cement standards and nomenclature 10813.9 References 109

14 Admixtures 11014.1 Plasticisers 11014.2 Superplasticisers 11114.3 Accelerators 11214.4 Retarders 11314.5 Air entraining agents 11414.6 Classication of admixtures 11514.7 References 116

15 Cement replacement materials 11715.1 Pozzolanic behaviour 11715.2 Types of material 11815.3 Chemical composition and physical properties 11915.4 Supply and specication 120

16 Aggregates for concrete 12116.1 Types of aggregate 12116.2 Aggregate classication: shape and size 12316.3 Other properties of aggregates 12616.4 Reference 127

17 Properties of fresh concrete 12817.1 General behaviour 12817.2 Measurement of workability 12917.3 Factors affecting workability 132

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17.4 Loss of workability 13417.5 References 135

18 Early age properties of concrete 13618.1 Behaviour after placing 13618.2 Curing 13818.3 Strength gain and temperature effects 13918.4 References 142

19 Deformation of concrete 14319.1 Drying shrinkage 14319.2 Autogenous shrinkage 15019.3 Carbonation shrinkage 15019.4 Thermal expansion 15019.5 Stressstrain behaviour 15219.6 Creep 15619.7 References 159

20 Strength and failure of concrete 16120.1 Strength tests 16120.2 Factors inuencing strength of Portland cement concrete 16520.3 Strength of concrete containing CRMs 17020.4 Cracking and fracture in concrete 17120.5 Strength under multiaxial loading 17320.6 References 175

21 Concrete mix design 17621.1 The mix design process 17621.2 UK method of Design of normal concrete mixes 17821.3 Mix design with cement replacement materials (CRMs) 18121.4 Design of mixes containing admixtures 18221.5 References 183

22 Non-destructive testing of hardened concrete 18422.1 Surface hardness rebound (or Schmidt) hammer test 18422.2 Resonant frequency test 18522.3 Ultrasonic pulse velocity test (upv) 18722.4 Near-to-surface tests 19022.5 References 191

23 Durability of concrete 19223.1 Transport mechanisms through concrete 19223.2 Measurements of ow constants for cement paste and concrete 19423.3 Degradation of concrete 19923.4 Durability of steel in concrete 21023.5 Recommendations for durable concrete construction 21523.6 References 216

Contents

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24 High performance concrete 21724.1 High strength concrete 21724.2 Self-compacting concrete 21924.3 References 220

Further reading 221

Part Four Bituminous materials D.G. Bonner 225

Introduction 227

25 Structure of bituminous materials 22925.1 Constituents of bituminous materials 22925.2 Bitumen 22925.3 Types of bitumen 23125.4 Aggregates 23425.5 Reference 236

26 Viscosity and deformation of bituminous materials 23726.1 Viscosity and rheology of binders 23726.2 Measurement of viscosity 23826.3 Inuence of temperature on viscosity 23926.4 Resistance of bitumens to deformation 24026.5 Determination of permanent deformation 24126.6 Factors affecting permanent deformation 24226.7 References 243

27 Strength and failure of bituminous materials 24427.1 The road structure 24427.2 Modes of failure in a bituminous structure 24427.3 Fatigue characteristics 24627.4 References 250

28 Durability of bituminous materials 25128.1 Introduction 25128.2 Ageing of bitumen 25128.3 Permeability 25228.4 Adhesion 25328.5 References 257

29 Practice and processing of bituminous materials 25929.1 Bituminous mixtures 25929.2 Recipe and designed mixes 26229.3 Methods of production 26429.4 References 265

Further reading 266

Contents

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Part Five Brickwork and Blockwork R.C. de Vekey 267

Introduction 269

30 Materials and components for brickwork and blockwork 27330.1 Materials used for manufacture of units and mortars 27330.2 Other constituents and additives 27730.3 Mortar 27830.4 Fired clay bricks and blocks 28230.5 Calcium silicate units 29030.6 Concrete units 29030.7 Natural stone 29330.8 Ancillary devices ties and other xings/connectors 29430.9 References 294

31 Masonry construction and forms 29731.1 Introduction 29731.2 Mortar 29731.3 Walls and other masonry forms 29831.4 Bond patterns 29931.5 Specials 30131.6 Joint-style 30231.7 Workmanship and accuracy 30231.8 Buildability, site efciency and productivity 30231.9 Appearance 30331.10 References 303

32 Structural behaviour and movement of masonry 30432.1 Introduction 30432.2 Compressive loading 30532.3 Shear load in the bed plane 31032.4 Flexure (bending) 31132.5 Tension 31332.6 Elastic modulus 31432.7 Movement and creep of masonry materials 31532.8 References 316

33 Durability and non-structural properties of masonry 31733.1 Introduction 31733.2 Durability 31733.3 Chemical attack 31833.4 Erosion 32133.5 Staining 32233.6 Thermal conductivity 32333.7 Rain resistance 32433.8 Sound transmission 32533.9 Fire resistance 325

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33.10 Sustainability issues 32633.11 References 328

Further reading 329

Part Six Polymers L. Hollaway 333

Introduction 335

34 Polymers: types, properties and applications 33734.1 Polymeric materials 33734.2 Processing of thermoplastic polymers 33834.3 Polymer properties 33934.4 Applications and uses of polymers 34134.5 References 345

Part Seven Fibre composites 347

Introduction 349

Section 1 Polymer composites L. Hollaway 351Introduction 351

35 Fibres for polymer composites 35235.1 Fibre manufacture 35235.2 Fibre properties 35535.3 References 356

36 Analysis of the behaviour of polymer composites 35736.1 Characterisation and denition of composite materials 35736.2 Elastic properties of continuous unidirectional laminae 35836.3 Elastic properties of in-plane random long-bre laminae 35936.4 Macro-analysis of stress distribution in a bre/matrix composite 35936.5 Elastic properties of short-bre composite materials 36036.6 Laminate theory 36036.7 Isotropic lamina 36236.8 Orthotropic lamina 36236.9 The strength characteristics and failure criteria of composite laminae 36436.10 References 368

37 Manufacturing techniques for polymer composites 36937.1 Manufacture of bre-reinforced thermosetting composites 36937.2 Manufacture of bre-reinforced thermoplastic composites 37437.3 References 374

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38 Durability and design of polymer composites 37538.1 Temperature 37538.2 Fire 37638.3 Moisture 37638.4 Solution and solvent action 37738.5 Weather 37738.6 Design with composites 37838.7 References 378

39 Uses of polymer composites 37939.1 Marine applications 38039.2 Applications in truck and automobile systems 38039.3 Aircraft, space and civil applications 38039.4 Pipes and tanks for chemicals 38039.5 Development of uses in civil engineering structures 38039.6 Composite bridges 38139.7 Retrotting bonded composite plates to concrete beams 38139.8 Composite rebars 38439.9 References 384

Section 2 Fibre-reinforced cements and concrete D.J. Hannant 385

40 Properties of bre and matrices 38640.1 Physical properties 38640.2 Structure of the brematrix interface 388

41 Structure and post-cracking composite theory 38941.1 Theoretical stressstrain curves in uniaxial tension 38941.2 Uniaxial tension fracture mechanics approach 39741.3 Principles of bre reinforcement in exure 39841.4 References 402

42 Fibre-reinforced cements 40342.1 Asbestos cement 40342.2 Glass-reinforced cement (GRC) 40542.3 Natural bres in cement 40942.4 Polymer bre-reinforced cement 41142.5 References 414

43 Fibre-reinforced concrete 41543.1 Steel bre concrete 41543.2 Polypropylene bre-reinforced concrete 41943.3 Glass bre-reinforced concrete 42143.4 Reference 421

Further reading 422

Contents

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Part Eight Timber J.M. Dinwoodie 423

Introduction 425

44 Structure of timber and the presence of moisture 42744.1 Structure at the macroscopic level 42744.2 Structure at the microscopic level 42944.3 Molecular structure and ultrastructure 43444.4 Variability in structure 44244.5 Appearance of timber in relation to its structure 44344.6 Massvolume relationships 44744.7 Moisture in timber 45044.8 Flow in timber 45444.9 References 461

45 Deformation in timber 46345.1 Introduction 46345.2 Dimensional change due to moisture 46345.3 Thermal movement 46645.4 Deformation under load 46845.5 References 486

46 Strength and failure in timber 48946.1 Introduction 48946.2 Determination of strength 48946.3 Strength values 49146.4 Variability in strength values 49146.5 Inter-relationships among the strength properties 49446.6 Factors affecting strength 49446.7 Strength, toughness, failure and fracture morphology 50346.8 Design stresses for timber 51046.9 References 513

47 Durability of timber 51547.1 Introduction 51547.2 Chemical, physical and mechanical agencies affecting durability and

causing degradation 51547.3 Natural durability and attack by fungi and insects 51747.4 Performance of timber in re 52047.5 References 523

48 Processing of timber 52548.1 Introduction 52548.2 Mechanical processing 52548.3 Chemical processing 53448.4 Finishes 53948.5 References 541

Further reading 542

Index 543

Contents

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Contributors

Professor D.G. BonnerDepartment of Aerospace, Civil andEnvironmental EngineeringUniversity of HertfordshireHateld CampusCollege LaneHateldHerts AL10 9AB(Bituminous materials)

Professor J.M. Dinwoodie OBE16 Stratton RoadPrinces RisboroughNr AylesburyBucks HP17 9BH(Timber)

Dr P.L.J. DomoneDepartment of Civil and EnvironmentalEngineeringUniversity College LondonGower Street, London WC1E 6BT(Editor and concrete)

Professor D.J. HannantDepartment of Civil EngineeringUniversity of SurreyGuildfordSurrey GU2 5XH(Fibre reinforced cements and concrete)

Professor L. HollawayDepartment of Civil EngineeringUniversity of SurreyGuildfordSurrey GU2 5XH(Polymers and polymer composites)

Professor J.M. Illston10 Merrield RoadFordSalisburyWiltshire SP4 6DF(Previous editor)

Dr I.R. McCollSchool of Mechanical, Materials, ManufacturingEngineering and ManagementUniversity of NottinghamUniversity ParkNottingham NG7 2RD(Fundamentals and metals)

Dr J.R. MoonSchool of Mechanical, Materials, ManufacturingEngineering and ManagementUniversity of NottinghamUniversity ParkNottingham NG7 2RD(Fundamentals and metals)

Dr R.C. de VekeyBuilding Research EstablishmentGarstonWatfordHerts WD2 7JR(Brickwork and blockwork)

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D.G. BonnerProfessor David Bonner graduated in Civil Engi-neering from the University of Leeds where he latergained a PhD in Trafc Engineering. Following aperiod working in the Highways Department ofLincolnshire County Council, he joined the Uni-versity of Hertfordshire (then Hateld Polytech-nic) where he became Reader in ConstructionMaterials. He subsequently became Head of CivilEngineering and is presently Associate Dean(Academic Quality) for the Faculty of Engi-neering and Information Sciences.

J.M. DinwoodieProfessor John Dinwoodie graduated in Forestryfrom Aberdeen University, and was subsequentlyawarded his MTech in Non-Metallic Materialsfrom Brunel University, and both his PhD andDSc in Wood Science subjects from AberdeenUniversity. He carried out research at the UKBuilding Research Establishment for a period of35 years on timber and wood-based panels with aspecial interest in the rheological behaviour ofthese materials. For this work he was awardedwith a special merit promotion to Senior Prin-cipal Scientic Ofcer. Since his retirement fromBRE in 1995, he has been employed as a consul-tant to BRE to represent the UK in the prepara-tion of European standards for wood-basedpanels. In 1985 he was awarded the Sir StuartMallinson Gold Medal for research on creep inparticleboard and was for many years a Fellow ofthe Royal Microscopical Society. In 1994 he wasappointed an Honorary Professor in the Depart-ment of Forest Sciences, University of Wales,Bangor, and in the same year was awarded anOBE. He is author, or co-author, of over onehundred and thirty technical papers and authorof three text books on wood science and techno-logy.

P.L.J. DomoneDr Peter Domone graduated in civil engineeringfrom University College London, where he sub-

Contributors

xvi

sequently completed a PhD in concrete techno-logy. After a period in industrial research withTaylor Woodrow Construction Ltd, he wasappointed to the academic staff at UCL, rst aslecturer and then as senior lecturer in concretetechnology. He teaches all aspects of civil engi-neering materials to undergraduate students, andhis principle research interests have included non-destructive testing, the rheology of fresh concrete,high-strength concrete and most recently, self-compacting concrete.

D.J. HannantProfessor David Hannant is a Professor in Con-struction Materials at the University of Surreyand has been researching and teaching in the eldof bre-reinforced cement and concrete since1968. He has authored a book, patents and manypublications on steel, glass and polypropylenebres and has been active in commercialising thinsheet products to replace asbestos cement.

L.C. HollawayProfessor Len Hollaway is Professor of Compos-ite Structures at the University of Surrey and hasbeen engaged in the research and teaching ofcomposites for more than 30 years. He is theauthor and editor of a number of books and haswritten many research papers on the structuraland material aspects of bre matrix composites.

J.M. IllstonProfessor John Illston spent the early part of hiscareer as a practising civil engineer before enter-ing higher education. He was involved in teachingand researching into concrete technology andstructural engineering as Lecturer and Reader atKings College, London and then Head ofDepartment of Civil Engineering at Hateld Poly-technic. His interest in his discipline took secondplace when he became Director of the Polytech-nic, but, on retirement he undertook preparationof the second edition of this book. He has actedas passive editor of this edition.

I.R. McCollDr Ian McColl is a senior lecturer at the Univer-sity of Nottingham. His rst degree is in physicsand after receiving his PhD from Nottingham hewas involved in industrially sponsored researchand development work at the university beforetaking up a lecturing post in 1988. He teachesmainly in the areas of engineering materials andengineering design. His research interests centrearound the fretting and fatigue properties ofengineering materials, components and assem-blies, and the use of surface engineering toimprove these properties.

J.R. MoonDr Bob Moon is a metallurgist married to therst woman to study civil engineering at the Uni-versity of Nottingham. His PhD was awarded bythe University of Wales (Cardiff) in 1960. He hasworked in the steel industry in South Wales,researched into titanium and other new metals atIMI in Birmingham and into superconductors,magnetic materials and materials for steam tur-bines at C.A. Parsons on Tyneside. He joined thestaff of the University of Nottingham over 30

Contributors

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years ago and has taught materials to civil engi-neers for the majority of that time. He is nowreader in materials science and researches into thetriangle connecting processing, microstructureand properties of materials made from powders.

R.C. de VekeyDr Bob de Vekey studied chemistry at HateldPolytechnic and graduated with the Royal Societyof Chemistry. He subsequently gained a DIC inmaterials science and a PhD from ImperialCollege, London on the results of his work at theBuilding Research Establishment (BRE) on mater-ials. At BRE he has worked on many aspects ofbuilding materials research and development andbetween 1978 and 2000 led a section concernedmainly with structural behaviour, testing, dura-bility and safety of brick and block masonrybuildings. From September 2000 he has relin-quished his previous role and become an associ-ate to the BRE. He has written many papers andadvisory publications and has contributed toseveral books on building materials and masonryand has been involved in the development of UK and international standards and codes forbuilding.

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Acknowledgements

I rst of all want to express my thanks to JohnIllston for his tremendous work and vision thatresulted in the rst two editions of this book, andfor his encouragement and helpful advice in theearly stages of preparing this edition. My thanksalso go to all the contributors who have willinglyrevised and updated their text despite many othercommitments. They have all done an excellentjob, and any shortfalls in the book are entirelymy responsibility. I greatly appreciate the adviceand inspiration provided by my students at UCLand my colleagues at UCL and elsewhere, whohave suffered due to my neglect of other dutieswhilst preparing and editing the manuscript.

Finally, but most importantly, I must acknow-ledge the support given to me by my wife andchildren, who I have neglected most of all, butwho have borne with good grace the many hoursI have spent in my study.

P.L.J. Domone

I wish to express my appreciation to the BuildingResearch Establishment (BRE) and in particularto Dr A.F. Bravery, Director of the Centre forTimber Technology and Construction, not only

for permission to use many plates and guresfrom the BRE collection, but also for providinglaboratory support for the production of thegures from both existing negatives and fromnew material.

Thanks are also due to several publishers forpermission to reproduce gures.

To the many colleagues who have so willinglyhelped me in some form or other in the produc-tion of this revised text I would like to record myvery grateful thanks. In particular, I would like torecord my appreciation to Dr P.W. Boneld andDr Hilary Derbyshire, BRE; Dr J.A. Petty, Uni-versity of Aberdeen; Dr D.G. Hunt, University ofthe South Bank for all their valuable and helpfuladvice. I would also like to thank colleagues atBRE for assistance on specic topics: C.A.Benham, J. Boxall, Dr J.K. Carey, Dr V. Enjily,C. Holland, J.S. Mundy, Dr R.J. Orsler, J.F.Russell, E.D. Suttie and P.P. White. Lastly, mydeep appreciation to both my daughter, who didmuch of the word processing, and my wife forher willing assistance in editing my text and inproof reading.

J.M. Dinwoodie

Preface

This book is an updated and extended version ofthe second edition, which was published in 1994.This has been extremely popular and success-ful, but the continuing recent advances in manyareas of construction materials technology haveresulted in the need for this new edition.

The rst edition was published under the titleConcrete, Timber and Metals in 1979. Its scope,content and form were signicantly changed forthe second edition, with the addition of threefurther materials bituminous materials,masonry and bre composites with a separatepart of the book devoted to each material,following a general introductory part on Funda-mentals.

This overall format has been retained. One newsmall part has been added, on polymers, whichwas previously subsumed within the section onpolymer composites. The other signicantchanges are, rst, in the section on concrete,where Portland cement, admixtures, cementreplacement materials and aggregates now havetheir own chapters, and new chapters on mixdesign, non-destructive testing and high perform-ance concrete have been added; and, second, inthe section on bre reinforced cement and con-crete, which has been rearranged so that eachtype of composite is considered in full in turn.

All of the contributors to the second editionwere able and willing to contribute again, withtwo exceptions. First, the co-author of the rstedition and editor and inspiration for the secondedition, John Illston, is enjoying a well-earnedretirement from all professional engineering andacademic activities, and did not wish to continueas editor for this edition. This role was taken overby Peter Domone, with considerable apprehen-

sion about following such an illustrious predeces-sor and the magnitude of the task. Fortunately,John Illston provided much needed encourage-ment, advice and comments, particularly in theearly stages,

Second, one of the contributors, Bill Biggs, hadsadly died in the intervening period, but two newcontributors have revised, extended and updatedhis Fundamentals and Metals sections. Themost signicant addition is a consideration ofequilibrium phase diagrams.

Objectives and scopeAs before, the book is addressed primarily to stu-dents taking courses in civil or structural engi-neering, where there is a continuing need for theunied treatment of the kind that we have againattempted. We believe that the book providesmost if not all of the information required by stu-dents for at least the rst two years of three- orfour-year degree programmes. More specialistproject work in the third or fourth years mayrequire recourse to the more detailed texts thatare listed in Further reading at the end of eachsection. We also believe that our approach willcontinue to provide a valuable source of interestand stimulation to both undergraduates andgraduates in engineering generally, materialsscience, building, architecture and related disci-plines.

The objective of developing an understandingof the behaviour of materials from a knowledgeof their structure remains paramount. Only inthis way can information from mechanicaltesting, experience in processing, handling andplacing, and materials science, i.e. empiricism,

xix

craft and science, be brought together to give thesound foundation for materials technologyrequired by the practitioner.

The Fundamentals section provides the neces-sary basis for this. Within each of the subsequentsections on individual materials, their structureand composition from the molecular levelupwards is discussed, and then the topics ofdeformation, strength and failure, durability, andmanufacture and processing are considered. Acompletely unied treatment for each material isnot possible due to their different nature and thedifferent requirements for manufacture, process-ing and handling, but a look at the contents listwill show how each topic has been covered andhow the materials can be compared and con-trasted. Cross-references are given throughout thetext to aid this, from which it will also be appar-ent that there are several cases of overlap betweenmaterials, for example concrete and bituminouscomposites use similar aggregates, and Portlandcement is a component of masonry, some brecomposites and concrete.

It is impossible in a single book to cover theeld of construction materials in a fully compre-hensive manner. Not all such materials of con-struction are included, nor has the attempt beenmade to introduce design criteria or to provide acompendium of materials data. Neither is thisbook a manual of good practice. Nevertheless wehope that we have provided a rm foundation forthe application and practice of materials techno-logy.

Levels of informationThe structure of materials can be described ondimensional scales varying from the smallest,atomic or molecular, through materials structuralto the largest, engineering.

The molecular level

This considers the material at the smallest scale,in terms of atoms or molecules or aggregations ofmolecules. It is very much the realm of materialsscience and a general introduction for all mater-

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ials is given in Part One of the book. The sizes ofthe particles are in the range of 107 to 103 mm.Examples occurring in this book include thecrystal structure of metals, cellulose molecules intimber, calcium silicate hydrates in hardenedcement paste and the variety of polymers, such aspolyvinyl chloride, included in bre composites.

As shown in Part One consideration of estab-lished atomic models leads to useful descriptionsof the forms of physical structure, both regularand disordered, and of the ways in which mater-ials are held together. Chemical composition is offundamental importance in determining thisstructure. This may develop with time as chemi-cal reactions continue; for example, the hydrationof cement is a very slow process and the structureand properties show correspondingly signicantchanges with time. Chemical composition is ofespecial signicance for durability which is oftendetermined, as in the cases of timber and metals,by the rate at which external substances such asoxygen or acids react with the chemicals of whichthe material is made.

Chemical and physical factors also cometogether in determining whether or not the mater-ial is porous, and what degree of porosity ispresent. In materials such as bricks, timber andconcrete, important properties such as strengthand rigidity are inversely related to their porosi-ties. Similarly, there is often a direct connectionbetween permeability and porosity.

Some structural phenomena such as dislocationsin metals are directly observable by microscopicand diffractometer techniques, but more oftenmathematical and geometrical models areemployed to deduce both the structure of thematerial and the way in which it is likely tobehave. Some engineering analyses, like fracturemechanics, come straight from molecular scaleconsiderations, but they are the exception. Muchmore often the information from the molecularlevel serves to provide mental pictures which aidthe engineers understanding so that they candeduce likely behaviour under anticipated con-ditions. In the hands of specialists, knowledge ofthe chemical and physical structure may well offera route to the development of better materials.

Materials structural level

This level is a step up in size from the molecularlevel, and the material is considered as a compos-ite of different phases, which interact to realisethe behaviour of the total material. This may be amatter of separately identiable entities withinthe material structure as in cells in timber orgrains in metals; alternatively, it may result fromthe deliberate mixing of disparate parts, in arandom manner in concrete or asphalt or somebre composites, or in a regular way in masonry.Often the material consists of particles such asaggregates distributed in a matrix like hydratedcement or bitumen. The dimensions of the parti-cles differ enormously from the wall thickness ofa wood cell at 5103 mm to the length of abrick at 225mm. Size itself is not an issue; whatmatters is that the individual phases can be recog-nised independently.

The signicance of the materials structural levellies in the possibility of developing a more generaltreatment of the materials than is provided fromknowledge derived from examination of the totalmaterial. The behaviours of the individual phasescan be combined in the form of multiphasemodels which allow the prediction of behaviouroutside the range of normal experimental obser-vation. In formulating the models considerationmust be given to three aspects:

1. Geometry: the shape, size and concentrationof the particles and their distribution in thematrix or continuous phase.

2. State and properties: the chemical and physi-cal states and properties of the individualphases inuence the structure and behaviourof the total material.

3. Interfacial effects. The information under (1)and (2) may not be sufcient because theinterfaces between the phases may introduceadditional modes of behaviour that cannot berelated to the individual properties of thephases. This is especially true of strength, thebreakdown of the material often being con-trolled by the bond strength at an interface.

To operate at the materials structural level

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requires a considerable knowledge of the threeaspects described above. This must he derivedfrom testing the phases themselves, and addition-ally from interface tests. While the use of themultiphase models is often conned to research inthe interest of improving understanding, it issometimes taken through into practice, albeitmostly in simplied form. Examples include theestimation of the elastic modulus of concrete, andthe strength of bre composites.

The engineering level

At the engineering level the total material is con-sidered; it is normally taken as continuous andhomogeneous and average properties are assumedthroughout the whole volume of the materialbody. The materials at this level are thosetraditionally recognised by construction practi-tioners, and it is the behaviour of these materialsthat is the endpoint of this book.

The minimum scale that must be considered isgoverned by the size of the representative cell,which is the minimum volume of the materialthat represents the entire material system, includ-ing its regions of disorder. The linear dimensionsof this cell varies considerably from, say, 103 mmfor metals to 100mm for concrete and 1000mmfor masonry. Properties measured over volumesgreater than the unit cell can be taken to apply tothe material at large. If the properties are thesame in all directions then the material isisotropic and the representative cell is a cube,while if the properties can only be described withreference to orientation, the material isanisotropic, and the representative cell may beregarded as a parallelepiped.

Most of the technical information on materialsused in practice comes from tests on specimens ofthe total material, which are prepared to repre-sent the condition of the material in the engin-eering structure. The range of tests, which can beidentied under the headings used throughoutthis book, includes strength and failure, deforma-tion, and durability. The test data is often pre-sented either in graphical or mathematical form,but the graphs and equations may neither express

the physical and chemical processes within thematerials, nor provide a high order of accuracy ofprediction. However, the graphs or equationsusually give an indication of how the propertyvalues are affected by signicant variables; suchas the carbon content of steel, the moisturecontent of timber, the bre content and orienta-tion in composites or the temperature of asphalt.It is extremely important to recognise that thequality of information is satisfactory only withinthe ranges of the variables used in the tests.Extrapolation beyond those ranges is very risky;this is a common mistake made not only by stu-dents, but also often by more experienced engi-neers and technologists who should know better.

Comparability and variabilityThroughout this book we have tried to excitecomparison of one material with another. Atten-tion has been given to the structure of eachmaterial, and although a similar scientic founda-tion applies to all, the variety of physical andchemical compositions gives rise to great differ-ences in behaviour. The differences are carriedthrough to the engineering level of informationand have to be considered by practitionersengaged in the design of structures who rst haveto select which material(s) to use, and then en-sure that they are used efciently, safely andeconomically.

Selection of materials

The engineer must consider the tness of thematerial for the purpose of the structure beingdesigned. This essential tness-for-purpose is amatter of ensuring that the material will performadequately both during construction and in sub-sequent service. Strength, deformation and dura-bility are likely to be the principal criteria thatmust be satised, but other aspects of behaviourwill be important for particular applications, forexample water-tightness or speed of construction.In addition, aesthetics and environmental impactshould not be forgotten.

Table 0.1 gives some properties of a number of

Preface

xxii

individual and groups of materials. These aremainly structural materials, with some othersadded for comparison. The mechanical propertieslisted stiffness, strength (or limiting stress) andwork to fracture (or toughness) are all denedand discussed in this book. It is immediatelyapparent that there is a wide variety of eachproperty that the engineer can select from (orcope with, if it is not ideal). It is also interestingto note the overall range of each property.Density varies by about two orders of magnitudefrom the least to the most dense (timber tometals). Stiffness varies by nearly three orders ofmagnitude (nylon to diamond), strength by aboutfour orders (concrete to diamond) and work tofracture by the greatest of all, ve orders (glass toductile metals). The great range of the last prop-erty is perhaps the most signicant of all. It is ameasure of how easy it is to break a material,particularly under impact loading, and how wellit copes with minor aws, cracks, etc.; it shouldnot be confused with strength. Low values areextremely difcult for engineers to deal with low strength and stiffness can be accommodatedby bigger section sizes and structural arrange-ments (within limits), but low toughness is muchmore difcult to handle. It is one reason whybre composites have become so popular.

Clearly, in many circumstances more than onematerial satises the criterion of tness-for-purpose; for instance, members carrying tensioncan be made of steel or timber, facing panels canbe fabricated from bre composite, metal, timberor masonry. The matter may be resolved by theengineer making a choice based on his or herjudgement, with often some help from calcula-tions. For example, comparisons of minimumweight or minimum cost options for a simplestructure with different materials, obtained withsome fairly elementary structural mechanics, withdifferent materials gives some interesting results.

Consider the cantilever shown in Figure 0.1.For linear elastic behaviour, the deection at thefree end is given by:

Fl3/3EI

where E is the elastic modulus of the material and

TA

BL

E 0

.1Se

lect

ed p

rope

rtie

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a r

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ne/m

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ss (

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bon

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ylon

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ens.

Preface

xxiv

l

F

FIGURE 0.1 A simple cantilever.

I is the second moment of area. For a rectangularbeam Ibd3/12, where b is the width of thebeam and d is its depth. Usually, the width is adesign constant, e.g. a bridge for four carriage-ways, but the depth can be altered to meet theloading and deection requirements. The depthis:

d (4Fl3/Eb)1/3

The weight is:

W lA lbd lb(4Fl3/Eb)1/3

where is the density.Rearranging, we have:

W l 2b2/3(4F/)1/3(/E1/3) (0.1)

so that, for a given set of design conditions (F, l,b, ), W is minimised by maximising E1/3/. Itturns out that the same condition applies for anytype of beam, of any shape or of any loading con-guration. The parameter E1/3/ is therefore theselection criterion for stiffness at minimumweight.

A similar approach can be taken to derive aselection criterion for the strength of the beam.For the cantilever in Figure 0.1, the maximumtension stress generated is:

max 6Fl/bd 2

Following the argument through as before gives:

W l3/2b1/2(6F)1/2(/1l/i2mit) (0.2)

So, for strength at minimum weight, we want tomaximise 1l /i 2mit /. Note the use of limit, the

maximum useful stress that the material can tol-erate in tension. In dening this, we must takeinto account the variability of materials, dis-cussed below.

The cost of a beam is simply WM, where M isthe cost of the material per unit mass. Workingthe arguments through again give criteria forstiffness and for strength at minimum cost. Theseturn out to be similar to those used before, i.e.E1/3/V and 1/2/V, where V is the material costper unit volumedensitycost per unit mass.

Table 0.2 shows how these four factors relativeto those for structural steel work out for some ofthe materials listed in Table 0.1. Where appropri-ate the mid-range properties have been used,together with the prices given in Table 0.2.Remembering that we are looking for maximumvalues, the most obvious result is that timber isoutstanding in terms of stiffness and strength atboth minimum weight and minimum cost nature clearly got things right without any helpfrom us. Thinking only about weight and neglect-ing cost points to the efciency of diamond (not arealistic option!), titanium, aluminium, epoxyresin and nylon. But when it comes to minimisingcosts, the highest scoring materials other thantimber are steel and concrete.

Table 0.2 does not, of course, give a completepicture. Prices will vary from time to time, andother properties, such as ease of construction,durability and toughness have not been takeninto account. Also, composite systems, such asreinforced concrete and bre reinforced systemshave not been considered. Nevertheless, it doesgive food for thought.

The cost of the energy used in manufacturingthe material and its transport and fabricationmust also not be overlooked, either in simple eco-nomic or in environmental terms. High-strengthversions of all the materials covered in this bookare often sought with the intention of reducingthe volume of material for a given structure, nor-mally with a commensurate saving in energy;and, conversely, lower grade materials are some-times introduced to replace higher grades as, forexample, in the partial replacement of cement bythe waste material, pulverised fuel ash (y ash).

Variability and characteristic strength

An important issue facing engineers is the vari-ability of the properties of the material itself,which clearly depends on the uniformity of itsstructure and composition.

The strength or maximum allowable stress is ofparticular concern. In tension, for ductile mater-ials this can be taken as the yield strength or theproof stress (see Chapter 9), but for brittle mater-ials it may have to be chosen on the basis of theapproach described in Chapter 6. In compression,brittle materials have a well dened maximumstress, but ductile materials may not fail at all,they just continue being squashed.

The variability can be assessed by a series oftests on nominally similar specimens from eitherthe same or successive batches of a material; thisusually gives a variation of strength or maximumstress with a normal or Gaussian distribution asshown in Figure 0.2. This can be represented bythe bell-shaped mean curve given by the equation

y exp (0.3)where y is the probability density, and is thevariate, in this case the strength. The strengthresults are therefore expressed in terms of twonumbers:

1. the mean strength, m, where for n results:

m /n (0.4)

(m)2

2s21

s2

Preface

xxv

Strength N

umbe

r of

res

ults

or

prob

abili

ty d

ensi

tym

FIGURE 0.2 Histogram and normal distribution ofstrength.

2. the range or variability, expressed as the stan-dard deviation, s, given by

s2 [( m)2/(n1)] (0.5)

The standard deviation has the same units as thevariate.

For comparison of different materials or differentkinds of the same material the non-dimensionalcoefcient of variation cv is used, given by

cv s/m (0.6)

cv is often expressed as a percentage.

TABLE 0.2 Weight and cost comparisons for the use of alternative materials for the cantilever of Figure 0.1(all gures relative to mild steel1, material properties as in Table 0.1)

Material Cost Minimum weight Minimum cost(/tonne) Stiffness criterion Strength criterion Stiffness criterion Strength criterion

E1/3/ max1/2/ E1/3/ ./tonne max1/2/ ./tonne

Diamond 2106 3.8 31.8 1.9106 1.6105

Structural steel 1.0 1.0 1.0 1.0 1.0Silica glass 3.4 2.4 2.1 0.8 0.7Titanium and alloys 27.5 1.4 3.0 0.05 0.1Aluminium and alloys 5.0 2.1 3.4 0.4 0.7Spruce (par. to grain) 1.0 6.4 7.7 6.4 7.7Concrete 0.7 1.8 0.6 2.6 0.8Epoxy resin 3.8 1.5 3.2 0.4 0.8Nylon 7.5 1.7 3.6 0.2 0.5

Preface

xxvi

Values of typical mean strengths and their coef-cients of variation for materials in this book aregiven in Table 0.3. Steel and ungraded timber atthe two ends of the scale. The manufacture of steelis a well developed and closely controlled processso that a particular steel can be readily reproducedand the variability of properties such as strength issmall; conversely, ungraded or unprocessed timber,which in its natural form is full of defects such asknots, and inevitably exhibits a wide variation inproperty values. The variability can, however, bereduced by processing so that the coefcient of

TABLE 0.3 Comparison of strengths of construction materials and their coefcients of variation. c compres-sion, t tension

Material Mean strength Coefcient of CommentMPa variation (%)

Steel 460t 2 Structural mild steelConcrete 40c 15 Typical concrete cube strength at 28 daysTimber 30t 35 Ungraded softwood

120t 18 Knot free, straight grained softwood11t 10 Structural grade chipboard

Fibre cement composites 18t 10 Continuous polypropylene bre with 6% volume fraction in stress direction

Masonry 20c 10 Small walls, brick on bed

Area % failure

failure rate

Strength Margin ks

Num

ber

of r

esul

ts

Characteristicstrength

m

FIGURE 0.3 Failure rate, margin and characteristicstrength.

1

10

100

0 0.5 1 1.5 2 2.5k

Failu

re r

ate

(%)

FIGURE 0.4 Relationship between k and failurerate for normally distributed results

variation for chipboard or breboard is appreciablylower than that for ungraded timber.

Engineers need to take both the mean strengthand the strength variation into account in deter-mining a safe strength at which the possibility offailure is reduced to acceptable levels. If the meanstress alone is used, then by denition half of thematerial will fail to meet this criterion, which isclearly unacceptable. The statistical nature of thedistribution of results means that a minimumstrength below which no specimen will ever failcannot be dened, and therefore a value knownas the characteristic strength (char) is used, whichis set at a distance below the mean, called the

Preface

xxvii

margin, below which an acceptably small numberof results will fall.

The total area under the normal distributioncurve of Figure 0.2 represents 100 per cent of theresults, and the area below any particularstrength is the number of results that will occurbelow that strength, or in other words the failurerate (Figure 0.3). The greater the margin, thelower the failure rate. Clearly, if the margin iszero, then the failure rate is 50 per cent. It is aproperty of the normal distribution curve that ifthe value of the margin is expressed as ks where kis a constant, then k is related to the failure rateas in Figure 0.4. Hence

char m ks (0.7)

Engineering judgement and consensus is used tochoose an acceptable failure rate. In practice, thisis not always the same in all circumstances; forexample, 5 per cent is typical for concrete(i.e. k1.64), and 2 per cent for timber (i.e.k1.96).

As we have said, this analysis uses values of sobtained from testing prepared specimens of thematerial concerned. In practice it is also necessary

to consider likely differences between these andthe bulk properties of material, which may varydue to size effects, manufacturing inconsistencies,etc., and therefore further materials safety factorswill need to be applied to the characteristicstrength. It is beyond the scope of this book toconsider these in any detail guidance can beobtained from relevant design codes and designtext books.

Concluding remarksWe hope that this preface has encouraged you toread on. It has described the general content,nature and approach of the book, and sets thescene for the level and type of information on thevarious materials that is provided. It has alsogiven an introduction to some ways of comparingmaterials, and discussed how the unavoidablevariability of properties can be taken into accountby engineers. You will probably nd it useful torefer back to these latter two sections from timeto time.

Enjoy the book.

A note on unitsIn common with all international publications, and with national practice in many countries, the SIsystem of units has been used throughout this text. Practice does however vary between different partsof the engineering profession and between individuals over whether to express quantities which havethe dimensions of [force]/[length]2 in the units of its constituent parts, e.g. N/m2, or with the interna-tionally recognised combined unit of the Pascal (Pa). In this book, the latter is used in Parts 1 to 7, andthe former in Part 8, which reects the general practice in other publications on the materials con-cerned.

The following relationships may be useful whilst reading:1 Pa 1 N/m2

1kPa 103 Pa 103 N/m2 1 kN/m2

1MPa 106 Pa 106 N/m2 1 N/mm2

1GPa 109 Pa 109 N/m2 1 kN/mm2

The magnitude of the unit for a particular property is normally chosen such that convenient numbersare obtained e.g. MPa (or N/mm2) for strength and GPa (or kN/mm2) for modulus of elasticity ofstructural materials.

Part One

Fundamentals

W.D. Biggs

Revised and updatedby I.R. McColl andJ.R. Moon

Introduction

As engineers our job is to design, but any designremains just that and no more until we start touse materials to convert it into a working arte-fact. There are, basically, three things we need toknow about materials:

1. How do they behave in service?2. Why do they behave in the way that they do?3. Is there anything we can do to alter their

behaviour?

This rst section of the book is primarily con-cerned with (2). We include consideration of thefundamental elements of which all matter is com-posed and the forces which hold it together. Theconcept of atomistics is not new. The ancientGreeks and especially Democritus (c.460 BC) had the idea of a single elementary particle buttheir science did not extend to observation andexperiment. For that we had to wait nearly 22centuries until Dalton, Avogadro and Cannizzaroformulated atomic theory as we know it today.Even so, very many mysteries remain unresolved,a fact which is as pleasing as it is provoking. Soin treating the subject in this way we are reachinga long way back into the development of thoughtabout the universe and the way in which it is puttogether.

One other important concept is more recent.Engineering is much concerned with change thechange from the unloaded to the loaded state, theconsequences of changing temperature, environ-ment, etc. The rst scientic studies of change canbe attributed to Sadi Carnot (1824), laterextended by such giants as Clausius, Joule andothers to produce such ideas as the conservationof energy, momentum, etc. Since the early studieswere carried out on heat engines it became

known as the science of thermodynamics, but ifwe take a broader view it is really the art andscience of managing, controlling and using thetransfer of energy whether the energy of theatom, the energy of the tides or the energy of,say, a lifting rig.

In many engineering courses thermodynamicsis treated as a separate topic, or, in many civilengineering courses, not considered at all. But,because its applications set rules which no engi-neer can ignore, a brief discussion is included.What are these rules? In summary (and ratherjocularly) they are:

1. You cannot win, i.e. you cannot get more outof a system than you put in.

2. You cannot break even in any change some-thing will be lost or, to be more precise, it willbe useless for the purpose you have in mind.

All this may be unfamiliar ground so you may skippast the sections relating to this on rst reading.But come back to it because it is important.

We shall not, in the present part, deal speci-cally with item (3) above; later parts will dealwith this in more specic terms. But what everyengineer should remember is that engineering isall about compromise and trade-off. Some pro-perties can be varied strength is one such butsome, such as density, cannot be varied. If wewere designing aircraft we could, in principle,choose between maximum strength and minimumweight, and minimum weight would win becauseit would ensure a higher payload (we must notforget that engineering is also about money*).

3

*An engineer has been dened as a person who can do for100 what any fool could do for 1000.

But, of course, compromise must be sought andengineering is about nding optimal solutions,not necessarily a best solution.

So good luck with your reading. If you reallyunderstand the principles much of what followswill be clearer to you. But, in a few short chapters

we can do little more than describe the highlightsof materials science, and a list of suggestions forfurther reading is given at the end of this part.

We should add a simple philosophy engi-neering is much too important to be left toengineers.

Introduction

4

Chapter one

States of matter

1.1 Fluids1.2 Solids1.3 Intermediate behaviour

We conventionally think of matter (material) asbeing in one of two states, uid or solid. Werecognise these states of matter based on theresponse of the matter to an applied force. Fluids,i.e. gases and liquids, ow easily when a force isapplied, whereas solids resist an applied force.

1.1 FluidsConsider rst the observable characteristics of a gas.

1. Gases are of low mass density, expand to ll acontainer, are easily compressed and have lowviscosity.

2. Gases exert a uniform pressure on the walls oftheir container.

3. Gases diffuse readily into each other.

The rst set of observations suggests that the gasparticles are not in direct contact with each other,the second and third that they are in constantmotion in random directions and at high speeds.

Liquids exhibit most of the above properties;most diffuse into each other readily and their vis-cosities, although some orders of magnitudehigher than those of gases, are still low, so thatthey ow irreversibly under small forces.However, there are two signicant differences.The rst is that liquids are a condensed state andhave much higher mass densities, which are notvery different from solids. The second is that theyare almost incompressible (hydraulic brakingsystems depend on this).

All this suggests that the particles of uids arein contact but are free to move relative to eachother. We shall consider the nature of the inter-action between the particles in Chapter 3. Mean-while, we can think of a liquid as being similar topeople at a well-run party in which the guestskeep circulating from one group to another.

Since the particles are free to move, the appli-cation of even a small force causes irreversibleow. Strictly, this is a shear deformation in whichparts of the material slide past other parts (seeFigure 1.3(c)). In an ideal (Newtonian) liquid therate of shear ow, d/dt, is proportional to theapplied shear stress:

d/dt (1.1)

where uidity.This is generally written in the inverse form:

d/dt (1.2)

where is the coefcient of dynamic viscosity.As might be expected, the viscosities of gasesand liquids differ markedly. For air at 20C,

18105 Pa.s, for water at 20C,

1.5103 Pa.s. At higher temperatures theparticles possess more energy of their own andthe stress required to move them is reduced, i.e.viscosity reduces rapidly as temperature isincreased (e.g. lubricating oil, treacle, asphalt).

1.1.1 Diffusion

We noted above that both gases and liquids diffuseinto each other. Here, for simplicity, we considerthe diffusion of one gas into another, but the samearguments apply broadly to liquids and even tosolids under the appropriate conditions.

5

Diffusion is caused by countless haphazardwanderings of individual atoms or moleculeswhich continually bump into each other. Theatoms or molecules can rebound in any directionand the path of any individual atom or moleculeis unpredictable but, if enough make such move-ments, the result is a steady and systematic ow.

Imagine a box containing a partition (plane),on one side there are C1 particles of gas/unitvolume and on the other C2, where C1 C2. Theparticles are moving randomly and exerting pres-sures of P1 and P2, respectively, on the partition,with P1 P2. Now remove the partition. Both setsof particles will move across the plane into thespace formerly occupied solely by the other.However, because of the higher concentrationmore will move in the direction C1C2 and,eventually, a totally random mixture is formedand pressure is equalised.

Provided certain simplifying assumptions aremade it is easy to show that the total ux J ofparticles (i.e. the number of particles owing inthe x-direction per unit time per unit cross-sectional area) through the plane is:

J DdC/dx (1.3)

which is Ficks rst law of diffusion. The constantD is known as the diffusion coefcient and is pro-portional to the average distance travelled by aparticle before colliding with another and the fre-quency at which the collisions occur. Thus, therate of diffusion is proportional to the concentra-tion gradient dC/dx, and is directed down thegradient, hence the minus sign above. Both ofthese follow directly from the statistical nature ofthe process.

It does not take much imagination to see thattemperature will play an important role. Athigher temperatures the particles are more activeand jump more frequently so that the rate of dif-fusion increases exponentially as the temperaturerises and vice versa. This has many importanttechnological consequences, e.g. in modifying theproperties of metals and alloys by heat treatment.

1.1.2 Vapourliquid transition

Understanding of the vapourliquid transitionderives from the work of Van der Waals. Hepointed out that the perfect gas law PVRTwhich relates pressure P, volume V and tempera-ture T, via a constant R, neglected two importantfactors:

1. the volume of the particles themselves;2. the forces of attraction between the particles.

The rst is fairly obvious and can be corrected bydeducting from the volume a term representingthe volume of the particles. Thus:

P(Vb)RT (1.4)

The second is less obvious, the forces of attractionbetween the particles will have the effect ofdrawing them closer together, just as if additionalpressure were applied. So a correction must beadded to P. Consider a single particle about tostrike the wall of the chamber containing the gas. Itwill be subjected to an attractive force due to theadjacent particles, proportional to the number ofparticles n per unit volume. Furthermore, thenumber of particles striking the wall is also propor-tional to n. So that the total attractive force experi-enced by the particles about to strike the wall isproportional to n2. Now, for a chamber containinga xed number of particles n is inversely propor-tional to the volume of the chamber V, so that theattractive force is proportional to 1/V 2. Thus, theVan der Waals equation is:

(Pa/V 2)(Vb)RT (1.5)

where a is a constant. The consequences of thisare noteworthy. If P is plotted against V for dif-ferent values of T we obtain a set of isotherms asshown in Figure 1.1. Note that at low tempera-tures each curve has a maximum and minimum,at higher temperatures they become smooth.

The minimum and maximum on each curve areconnected by the dotted line. The point C wherethe minimum and maximum coincide at a pointof inection is the critical point and denotes theconditions where liquid and vapour can coexist inequilibrium.

States of matter

6

Real materials, however, behave as shown inFigure 1.2 where we note that starting with aliquid at X at some constant temperature T1 thevolume increases as the pressure is reduced. Even-tually the liquid becomes saturated with vapourand the volume increases with no change of pres-sure, as a saturated vapour, i.e. a vapour satu-rated with liquid, forms. With further decreasesin pressure a true vapour is formed and the liquidis said to have evaporated. The reverse happens ifwe start with a gas and increase the pressurewhile keeping temperature constant.

The particles within a liquid (at constant tem-perature and pressure) may or may not have suf-cient thermal energy to escape. Those whichescape constitute the vapour and the pressurethey exert is the vapour pressure. In a closed con-tainer equilibrium is set up between those parti-cles escaping from the liquid and those returning,this is the saturation vapour pressure. When the

Solids

7

FIGURE 1.1 Isotherms from Van der Waals equa-tion. The values for P, V and T are expressed in termsof their values at the critical point C. In this form theyare dimensionless and independent of their actualvalues.

FIGURE 1.2 PVT curves for water vapour.

saturation vapour pressure is equal to or greaterthan the external pressure the liquid boils. Thusthe boiling point is conventionally dened as thetemperature to which the liquid must be raised inorder for this to occur at atmospheric pressure.As the atmospheric pressure decreases so does theboiling point.

1.2 SolidsIntuitively the rst thing that we notice about asolid is that it resists the application of a force. Aliquid will also resist a force provided that it isapplied equally in all directions. The essential dif-ference is that, unlike gases and liquids, a soliddoes not appear to change shape except by a tinyamount when a modest load is applied in just onedirection. We shall see later that this is notstrictly true; under appropriate conditions allmaterials will ow, but the denition is goodenough for our purpose and accords with normalexperience.

The reason for no apparent shape change issimple, the mechanism quite complex. First, wemust note what mechanics tells us. Any combina-tion of forces can be thought of as a combinationof a hydrostatic pressure (Figure 1.3 (d)) and ashear (Figure 1.3 (c)). Flow in any circumstances

States of matter

8

p

p

p

(d) Hydrostatic loading

G shear modulus /

(c) Behaviour under shear stress

Strain

Str

ess

E Youngs modulus ofelasticity (or stiffness) tan

(a) Linear behaviour under direct stress

Strain

(b) Non-linear behaviour under direct stress

1

3

2

Tan tangent modulusat 1

Tan secant modulusbetween 2 and 3

Str

ess

FIGURE 1.3 Elastic stressstrain behaviour.

other than under pure hydrostatic pressure isreally a response to the shear component. Theatoms of which the solid is composed are physi-cally bonded together into patterns that must bemaintained. When we rst apply a force wedisplace all the atoms of which the solid is com-

posed in a way that nearest neighbour atoms inthe pattern remain nearest neighbours (provided,of course, that the force is not sufcient to breakany bonds). This is quite unlike a liquid in whichthe individual particles move past each other.

1.2.1 The elastic constants

Before discussing the mechanics and con-sequences of bonding we should digress a little todene some of the properties that are used tocharacterise solids.

When a solid is extended or compressed by amodest external force the dimensions change alittle. Conventionally we express the force F interms of the area A over which it acts, this isknown as stress :

F/A (1.6)

Under simple uniaxial tension or compression thematerial either extends or shortens. Convention-ally we express this as an increment of strain l/l, i.e. change in length per unit length.Strain is therefore a ratio and has no dimensions.Integrating the expression for strain between theoriginal length, l0 and the nal length, l1, gives ln(l1/l0) ln(1 l/l0), where l l1 l0. Thisrather cumbersome expression for strain is usedfor analytical purposes when thinking about largestrains, but for most engineering purposes wherel/l0 1, it reduces to the much more convenientand familiar denition:

l/l0 (1.7)

When solids are not strained very much, say upto about 0.001, or 0.1 per cent, the material

reverts to its original dimensions when the load isreleased, i.e. the strain is reversible. The relation-ship between stress and strain is often linear or,at least, linear to a rst approximation (Figure1.3a). This is known as Hookes law, i.e.:

E (1.8)

where E is a material constant known as Youngsmodulus of elasticity, or simply the elasticmodulus, and has units of stress, e.g. N/m2 (orPa) or, more commonly, GPa. Table 1.1 includessome typical values.

In many materials the stressstrain relationshipis not sufciently linear for this denition. Forsuch materials, a modulus value can be dened aseither the slope of the tangent to the stressstraincurve at a particular value of stress giving thetangent modulus or as the slope of the linejoining two points on the curve at two values ofstress giving the secant modulus (Figure 1.3b).When quoting either value, clearly the corre-sponding level of stress must also be quoted, e.g.the tangent modulus at the origin. Values ofsecant modulus are often given for a zero lowervalue of stress, i.e. it is the slope of the line fromthe origin to a point on the curve.

Modulus values arising from similar relation-ships apply for other forms of stress. Thus, inshear (Figure 1.3c) the shear stress produces a

Solids

9

TABLE 1.1 Typical mass densities, elastic constants and Poissons ratios for a range of materials

Material Mass density E G K Mgm3 GPa GPa GPa

Diamond 3.5 1000 417 556 0.20Alumina 4.0 530 217 315 0.22Tungsten carbide 15.8 720 300 400 0.20Iron 7.9 210 79 206 0.33Silica glass 2.5 70 30 35 0.17Titanium 4.5 120 46 105 0.31Spruce (parallel to grain) 0.5 13 500 0.38Aluminium 2.7 69 26 68 0.33Concrete (lightweight) 1.4 15 6 8 0.20Concrete (normal weight) 2.4 25 10 14 0.20Epoxy resin 1.1 4.5 Nylon 1.14 3 1.1 4.5 0.39

shear strain which, when small, is convenientlymeasured as an angle (in radians). For linearbehaviour

G (1.9)

where G is known as the shear modulus.Under hydrostatic pressure (Figure 1.3d) the

volume changes. As before this is expressed non-dimensionally as V/V and

p K(V/V) (1.10)

where p is the hydrostatic pressure and K is thebulk modulus. The minus sign arises as a con-sequence of the fact that as pressure increases,volume decreases.

Youngs modulus is a measure of the stressrequired to produce a given deformation, andengineers often refer to it as the stiffness of thematerial, for that is what it is. It will be apparentthat whereas a liquid can display a bulk modulusit does not possess a shear modulus since itcannot resist shear. Solids, on the other hand,display a bulk modulus and a shear modulus. It isthe resistance to shear that is the fundamental dif-ference between solids and liquids.

1.2.2 Elastic resilience stored energy

We noted that a linearly elastic (Hookean) mater-ial deforms reversibly, i.e. it returns to its originallength when the load is removed. When a bar ofmaterial experiences an extension of l under anapplied force F, mechanical work Fl is done.This work is stored in the material as a slightstretching of the atomic bonds. The total energystored is obtained by integrating this equation.The energy per unit volume of material U, whichis called the strain energy density, is thenobtained by dividing by the volume of materialAl0:

U (1.11)Now, as previously dened, F/A and

l0

l

l0

l, and therefore, for elastic deforma-

tion:

U2 2/2E 2E/2 (1.12)

We can use this to estimate, in a few simple cases,the stresses generated by impact. Figure 1.4shows a simple wire suspended from a support

FlAl0

States of matter

10

l0l0 lS

l0 lD

Staticallyloaded

Dynamicallyloaded

Unloaded

h

M

FIGURE 1.4 Simple arrangement for comparing static and dynamic loads.

and carrying a small tray at its lower end. If aweight of mass M were to be gently lowered ontothe tray, the wire would experience a static forceMg, where g is the acceleration due to gravity,and a stress of s Mg/A, and would strain bys/EMg/AE. If now, the weight were lifted andallowed to fall onto the tray from a height h, theimpact would cause the wire to stretch by morethan the static strain, after which it would oscil-late until it settled at the static strain. Taking themaximum dynamic stretch to be lD, the weightwould lose potential energy Mg(h lD), all ofwhich would be converted into strain energy ofthe wire. Now the wire has a volume of Al0 andso the strain energy at maximum dynamic strainis (DD/2)(Al0). Equating the two energies andremembering that D lD/l0, gives after somemanipulation:

D s 2s s (1.13)Typically, E/s103 and if h l0/2, we haveD/s34. No wonder things can snap when hitwith a hammer!

1.2.3 Poissons ratio

Clearly the application of a force displaces theatoms from their normal positions. Thus, in anelastic solid, the application of a longitudinaltension force causes a transverse contraction, asin Figure 1.5.

Poissons ratio relates the longitudinal andtransverse strains:

transverse strain/longitudinal strain

1.2.4 Relation between elastic constants

We now have all four elastic constants, andtypical values for these are given in Table 1.1. Itis not too difcult using linear elastic analysis toshow that they are not independent, and that theyare related to one another as follows:

K3(1

E

2) (1.14)

2hE

l0

Solids

11

a0 aa0

b b

b

Longitudinal strainl a/a0

Transverse straint b/b0

Poissons ratio t/l

FIGURE 1.5 Poisson effect under a uniaxial tensileload.

G2(1

E

) (1.15)

Thus if any two are known, or measured, theother two can be calculated, which makes theengineers life easier.

It is interesting and instructive to calculate thechange of volume that is brought about by a uni-axial stress. If a cube of side a is stressed in the zdirection, it will extend by:

z az

and in accordance with Poissons ratio:

x y az

The nal volume is:

V (ax)(a y)(az)

Expanding and neglecting second and higherorder terms in which are vanishingly small:

Va3 a2(x y z)a3 a3(x y z)

the change of volume is:

Va3(x y z)a3z(12)

and:

V/Vz(12) (1.16)

For a liquid, the volume remains constant duringdeformation, i.e. the material is incompressible,and V0. K is therefore innite, and, fromequation 1.14, 0.5. In most other materialsthere is a small volume increase when stretchedelastically and a volume decrease when com-pressed. This means that K is nite and positive if it were negative the volume would increasewhen the material is compressed, which does notbear thinking about. Since E is also a positivenumber, then equation 1.14 tells us that 12must be positive, and hence 0.5. Combiningthe two conditions gives

0.5 (1.17)

Table 1.1 shows that for many common materials lies between 0.2 and 0.35. Soft rubber is unusualin having a Poissons ratio close to 0.5, whichmeans that it behaves very like a stifsh uid.

1.3 Intermediate behaviourWe have already emphasised the lack of anydividing line between solids and liquids, thereason being that the response of materials toshear can vary over a wide range. Solids may beeither crystalline or amorphous (Figure 1.6). In acrystalline solid (and metals are an importantgroup) the atoms are arranged in a regular, three-dimensional array or lattice. Amorphous solidsdo not possess this regularity of structure and wecan further subdivide them into glassy and molecu-lar solids.

True glasses are obtained by cooling liquidswhich, because of their elaborate molecular con-guration, lack the necessary activation energy(see Chapter 2) at the melting temperature torearrange themselves in an ordered crystallinearray.

The material then retains, even when rigid, atypically glassy structure involving short rangeorder only and resembling, except for its immo-bility, the structure of the liquid form. Silica givesrise to the commonest form of glass. If cooledsufciently slowly from the melt it can beobtained in the crystalline form which is morestable thermodynamically than the vitreous state.In nature, cooling over long time spans gives riseto beautiful crystals of quartz and other crys-talline forms.

At ordinary cooling rates crystallisation doesnot take place, and the amorphous nature of thesolid gives rise to its most important physicalproperty, its transparency. Most non-metallicsingle crystals are transparent, but in the poly-crystalline state light is scattered from internalreections at aws and internal boundaries, thematerial then becomes translucent in thin sectionsand completely opaque in the mass, as with natu-rally occurring rocks. If it is amorphous, there areno internal boundaries. Polymers may be totallyamorphous and transparent, but most containsmall crystalline regions (spherulites) within theirstructure that act as light scatterers, giving therather milky appearance that we are familiarwith, that is if they do not contain deliberatelyadded colouring matter.

Molecular solids are of two types. So-calledthermoplastic polymers are best exemplied bysoft polymers such as polyethylene, which consistof long, highly convoluted molecules. The bulkstrength depends upon the entanglement of themolecular chains rather than upon three-dimensional bonding. Thermosets, such as Bake-lite, have genuine extended three-dimensionalmolecules. Mostly, these are harder and strongerthan thermoplastics but tend to be rather brittle.

There are, however, more complex structuresinvolving both solid and liquid phases. One of themost familiar of these is the gel, known to mostof us from childhood in the form of jellies andlozenges.

Gels are formed when a liquid contains a fairlyconcentrated suspension of very ne particles,usually of colloidal dimensions (1m). The par-ticles bond into a loose structure, trapping liquid

States of matter

12

in its interstices. Depending on the number oflinks formed, gels can vary from very nearly uidstructures to almost rigid solids. If the links arefew or weak, the individual particles have consid-erable freedom of movement around their points

of contact, and the gel deforms easily. A highdegree of linkage gives a structure that is hardand rigid in spite of all its internal pores. Themost important engineering gel is undoubtedlycement, which develops a highly rigid structure

Intermediate behaviour

13

FIGURE 1.6 Schematic structures of some covalent materials: (a) vitreous silica (glass); (b) crystalline silica; (c)thermoplastic polymer showing crystalline regions (spherulites); (d) thermosetting polymer; (e) gel by compari-son with (d), the links between the chains are weak and easily broken.

(which we will discuss in some detail in Chapter13). When water is added to the cement powder,the individual particles take up water of hydra-tion, swell and link up with each other to giverise to a high-strength but permeable gel ofcomplex calcium silicates. A feature of many gelsis their very high specic surface area; if the gel ispermeable as well as porous, the surface is avail-able for adsorbing large amounts of watervapour, and such a gel is an effective dryingagent. Adsorption is a reversible process (seepages 423); when the gel is saturated it may beheated to drive off the water and its dryingpowers regained. Silica gel is an example of this.

If a gel sets by the formation of rather weaklinks, the linkages may be broken by vigorousstirring so that the gel liquees again. When thestirring ceases, the bonds will gradually link upand the gel will thicken and return to its originalset. Behaviour of this sort, in which an increase inthe applied shear rate causes the material to act ina more uid manner, is known as thixotropy.Not all gels behave in this manner or, if they do,it is only at a certain stage of their setting pro-cedure. Hardened concrete, alas, will not healitself spontaneously after it has cracked, althoughit exhibits a marked degree of thixotropy at anearly state of setting.

The most familiar application of thixotropy isin non-drip paints, which liquefy when stirred

and spread easily when being brushed on, butwhich set as a gel as soon as brushing is com-pleted so that dripping or streaks on vertical sur-faces are avoided. Clays can also exhibitthixotropy. This is turned to advantage on apotters wheel and in the mixing of drilling mudsfor oil exploration. The thixotropic mud serves toline the shaft with an impermeable layer, whilstin the centre it is kept uid by the movement ofthe drill and acts as a medium for removing therock drillings. On the other hand, a thixotropicclay underlying major civil engineering workscould be highly hazardous.

The reverse effect to thixotropy occurs whenan increase in the applied shear rate causes aviscous material to behave more in the manner ofa solid, and is known as dilatancy. It is a lessfamiliar but rather more spectacular phenome-non. Cornourwater mixtures demonstrate theeffect over a rather narrow range of composition,when the viscous liquid will fracture if stirred vig-orously. It is of short duration, however, sincefracture relieves the stress, and the fractured sur-faces immediately liquefy and run together again.

Silicone putty is also a dilatant; it ows veryslowly if left to itself, but fractures if pulled sud-denly, and will bounce like a rubber ball ifthrown against a hard surface. So far, no engi-neering applications of dilatancy have beendeveloped.

States of matter

14

Chapter two

Energy andequilibrium

2.1 Mixing2.2 Entropy2.3 Free energy2.4 Equilibrium and equilibrium diagrams

Although the engineer conventionally expresseshis ndings in terms of force, deection, stress,strain and so on, these are simply the convention.Fundamentally, what he is really dealing with isenergy. Any change, no matter how simple,involves an exchange of energy. The mere act oflifting a beam involves a change in the potentialenergy of the beam, a change in the strain energyheld in the lifting cables, an input of mechanicalenergy from the lifting device which is itself trans-forming electrical or other energy into kineticenergy. The harnessing and control of energy is atthe heart of all engineering.

Thermodynamics teaches us about energy, anddraws attention to the fact that every materialpossesses an internal energy associated with itsstructure. In this section we examine some of thethermodynamic principles which are of import-ance to understanding the behaviour patterns.

We begin by recognising that all systems arealways seeking to minimise their energy, i.e. tobecome more stable. We also note that althoughthermodynamically correct, some changestowards a more stable condition proceed soslowly that the system appears to be stable eventhough it is not. For example, a small ball sittingin a hollow at the top of a hill will remain thereuntil it is lifted out and rolled down the hill. The

ball is in a metastable state and requires a smallinput of energy to start it on its way down themain slope.

Figure 2.1 shows a ball sitting in a depression,its potential energy is P1. It will roll to a lowerenergy state P2, but only if it is rst lifted to thetop of the hump between the two hollows. Someenergy has to be lent to the ball to do this. Ofcourse, the ball returns the energy when it rollsdown the hump to its new position. This bor-rowed energy is known as the activation energyfor the process. Thereafter it possesses free energyas it rolls down to P2. However, it is losing poten-tial energy all the time and eventually (say, at sealevel) it will achieve a stable equilibrium.However, note two things. At P1, P2, etc. it isstable, actually metastable because there areother more stable states available to it, given thenecessary activation energy. Where does the acti-vation energy come from? In materials science itis extracted mostly (but not exclusively) from

15

FIGURE 2.1 Schematic illustration of activationenergy and free energy.

heat. As things are heated to higher temperaturesthe atomic particles react more rapidly and canbreak out of their metastable state into one wherethey can now lose energy.

2.1 MixingIf whisky and water are placed in the same con-tainer, they mix spontaneously. The internalenergy of the solution so formed is less than thesum of the two internal energies before they weremixed. There is no way that we can separatethem except by distillation, i.e. by heating themup and collecting the vapours and separatingthese into alcohol and water. We must, in fact,put in energy to separate them. But, since energycan neither be created nor destroyed, the fact thatwe must use energy, and quite a lot of it, torestore the status quo must surely pose the ques-tion, Where does the energy come from initially?The answer is by no means simple but, as weshall see, every particle, whether water or whisky,possesses kinetic energies of motion and of inter-action.

When a system such as a liquid is left to itself,its internal energy remains constant, but when itinteracts with another system it will either lose orgain energy. The transfer may involve work orheat or both and the rst law of thermodynamics,the conservation of energy and heat, requiresthat:

dEdQdW (2.1)

where E internal energy, Qheat andWwork done by the system on the surround-ings.

What this tells us is that if we raise a cupful ofwater from 20C to 30C it does not matter howwe do it. We can heat it, stir it with paddles oreven put in a whole army of gnomes eachequipped with a hot water bottle, but the internalenergy at 30C will always be above that at 20Cby exactly the same amount. The rst law saysnothing about the sequences of changes that arenecessary to bring about a change in internalenergy.

2.2 EntropyClassical thermodynamics, as normally taught toengineers, regards entropy S as a capacity pro-perty of a system which increases in proportionto the heat absorbed (dQ) at a given temperature(T). Hence the well-known relationship:

dSdQ/T

which is a perfectly good denition but does notgive any sort of picture of the meaning of entropyand how it is dened. To a materials scientistentropy has a real physical meaning, it is ameasure of the state of disorder in the system.Whisky and water combine; this simply says that,statistically, there are many ways that the atomscan get mixed up and only one possible way inwhich the whisky can stay on top of, or, depend-ing on how you pour it, at the bottom of, thewater. Boltzmann showed that the entropy of asystem could be represented by:

SklnN (2.2)

where N is the number of ways in which the par-ticles could be distributed and k is a constant(Boltzmanns constant k1.381023 J/K). Thelogarithmic relationship is important; if the mole-cules of water can adopt N1 congurations andthose of whisky N2 the number of possible cong-urations open to the mixture is not N1 N2 butN1 N2. It follows from this that the entropy ofany closed system will tend to a maximum sincethis represents the most probable array of cong-urations. You should be grateful for this. As youread these words, you are keeping alive bybreathing a randomly distributed mixture ofoxygen and nitrogen. Now it is statistically pos-sible that at some instant all the oxygen atomswill collect in one corner of the room while youtry to exist on pure nitrogen, but only statisticallypossible. There are so many other possible distri-butions involving a random arrangement of thetwo gases that it is most likely that you will con-tinue to breathe the normal random mixture.

Energy and equilibrium

16

2.3 Free energyIt must be clear that the fundamental tendencyfor entropy to increase, that is, for systems tobecome more randomised, must be stopped some-where and somehow. For, if not, the entire uni-verse would break down into chaos. As we shallsee, the reason for the existence of liquids andsolids is that atoms and molecules are not totallyindifferent to each other and, under certain con-ditions and with certain limitations, will associatewith each other in a non-random way.

As we stated above, from the rst law ofthermodynamics the change in internal energy isgiven by:

dEdQdW

From the second law of thermodynamics theentropy change in a reversible process is:

TdSdQ

Hence:

dETdSdW (2.3)

In discussing a system subject to change, it is conve-nient to use the concept of free energy. For irre-versible changes, the change in free energy is alwaysnegative and is a measure of the driving forceleading to equilibrium. Since a spontaneous changemust lead to a more probable state (or else it wouldnot happen) it follows that, at equilibrium, energy isminimised while entropy is maximised.

The Helmholtz free energy is dened as:

HETS (2.4)

and the Gibbs free energy as:

GpVETS (2.5)

and, at equilibrium, both must be a minimum.We shall later in Chapter 4 apply these ideas tothe elastic deformation of materials.

2.4 Equilibrium and equilibriumdiagramsSo far, we have seen that materials can exist asgases, liquids and crystalline or amorphous

solids. We need a scheme that allows us to sum-marise the inuences of temperature and pressureon the relative stability of each state and on thetransitions that can occur between these. Ther-modynamics tells us that we must seek theinternal condition of a m