Nanostructured metals and alloys - Processing, microstructure, mechanical properties and applications 1845696700, 9781845696702

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Table of contents :
front-matter......Page 1
1 Producing bulk nanostructured metals and alloys by severe plastic deformation (SPD)......Page 36
2 Bulk nanostructured metals and alloys produced by accumulative roll-bonding......Page 73
3 Nanocrystalline metals and alloys prepared by mechanical attrition......Page 92
4 The processing of nanocrystalline steels by solid reaction......Page 118
5 The processing of bulk nanocrystalline metals and alloys by electrodeposition......Page 151
6 Bulk nanocrystalline and nanocomposite alloys produced from amorphous phase......Page 185
7 Severe plastic deformation and the production of nanostructured alloys by machining......Page 211
8 Deformation structures including twins in nanograined pure metals......Page 244
9 Microstructure and mechanical properties of nanostructured low-carbon steel prepared by equal-channel angular pressing......Page 274
10 Characteristic structures and properties of nanostructured metals prepared by plastic deformation......Page 307
11 Strengthening mechanisms in nanocrystalline metals......Page 327
12 Elastic and plastic deformation in nanocrystalline metals......Page 357
13 The mechanical properties of multi-scale metallic materials......Page 403
14 Enhanced ductility and its mechanisms in nanocrystalline metallic materials......Page 458
15 The mechanical behavior of nanostructured metals based on molecular dynamics computer simulations......Page 487
16 The surface deformation and mechanical behavior of nanostructured alloys......Page 509
17 Fatigue behaviour in nanostructured metals......Page 535
18 Superplastic deformation in nanocrystalline metals and alloys......Page 570
19 Creep and high-temperature deformation in nanostructured metals and alloys......Page 622
20 Processing nanostructured metal and metal-matrix coatings by thermal and cold spraying......Page 640
21 Nanocoatings for commercial and industrial applications......Page 688
22 Applying nanostructured steel sheets to automotive body structures......Page 712
23 Production processes for nanostructured wires, bars and strips......Page 740
24 Nanostructured plain carbon-manganese (C-Mn) steel sheets prepared by ultra-fast cooling and short interval multi-pass hot rolling......Page 772
back-matter......Page 812
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1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X

Nanostructured metals and alloys

i © Woodhead Publishing Limited, 2011

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X

Related titles: Fundamentals of aluminium metallurgy (ISBN 978-1-84569-654-2) This authoritative book reviews the latest advances in the study of the metallurgy of aluminium and how this knowledge is applied to the production, casting and processing of the metal and its alloys. It includes a comprehensive range of chapters on topics such as production, casting, alloys and heat treatments, through to physical metallurgy and applications. Corrosion of magnesium alloys (ISBN 978-1-84569-708-2) The book gives a comprehensive account of the corrosion of magnesium alloys. The book covers the better known methods of corrosion, such as atmospheric, as well as the lesser known processes such as corrosion in engine coolants and the corrosion mechanisms of implants. The use of magnesium alloys is increasing in a range of applications and their popularity is growing wherever lightweight materials are needed. The book covers the fundamentals of magnesium alloy corrosion, metallurgical effects, environment-affected behaviour and protected magnesium alloys. Welding and joining of magnesium alloys (ISBN 978-1-84569-692-4) This book covers all aspects of the welding and joining of magnesium alloys. Magnesium and its alloys have been used for many years and their use is increasing due to their superior properties and light weight. Part I includes welding metallurgy, preparation for welding and welding materials. Part II covers the various welding technologies that can be used for joining magnesium alloys and Part III includes other joining technologies, weld defects and corrosion protection. Details of these and other Woodhead Publishing materials books can be obtained by: •฀ visiting฀our฀web฀site฀at฀www.woodheadpublishing.com •฀ contacting฀ Customer฀ Services฀ (e-mail:฀ [email protected];฀ fax:฀ +44฀ (0)฀ 1223฀ 832819;฀ tel.:฀ +44฀ (0)฀ 1223฀ 499410฀ ext.฀ 130;฀ address:฀ Woodhead฀ Publishing฀Limited,฀80฀High฀Street,฀Sawston,฀Cambridge฀CB22฀3HJ,฀UK) If you would like to receive information on forthcoming titles, please send your address฀ details฀ to:฀ Francis฀ Dodds฀ (address,฀ tel.฀ and฀ fax฀ as฀ above;฀ e-mail:฀ francis. [email protected]).฀ Please฀ conirm฀ which฀ subject฀ areas฀ you฀ are฀ interested in.

ii © Woodhead Publishing Limited, 2011

Nanostructured metals and alloys Processing, microstructure, mechanical properties and applications Edited by Sung H. Whang

iii © Woodhead Publishing Limited, 2011

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Published by Woodhead Publishing Limited, 80฀High฀Street,฀Sawston,฀Cambridge฀CB22฀3HJ,฀UK www.woodheadpublishing.com Woodhead Publishing, 1518 Walnut Street, Suite 1100, Philadelphia, PA฀19102-3406,฀USA Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi – 110002, India www.woodheadpublishingindia.com First published 2011, Woodhead Publishing Limited © Woodhead Publishing Limited, 2011 The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials. Neither the authors nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means,฀electronic฀or฀mechanical,฀including฀photocopying,฀microilming฀and฀recording,฀or฀ by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The฀consent฀of฀Woodhead฀Publishing฀Limited฀does฀not฀extend฀to฀copying฀for฀general฀ distribution,฀for฀promotion,฀for฀creating฀new฀works,฀or฀for฀resale.฀Speciic฀permission฀ must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks,฀and฀are฀used฀only฀for฀identiication฀and฀explanation,฀without฀intent฀to฀ infringe. British฀Library฀Cataloguing฀in฀Publication฀Data A catalogue record for this book is available from the British Library. ISBN 978-1-84569-670-2 (print) ISBN 978-0-85709-112-3 (online) The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acid-free and elemental chlorine-free practices. Furthermore, the publisher ensures that the฀text฀paper฀and฀cover฀board฀used฀have฀met฀acceptable฀environmental฀accreditation฀ standards. Typeset฀by฀ReineCatch฀Limited,฀Bungay,฀Suffolk,฀UK Printed฀by฀TJI฀Digital,฀Padstow,฀Cornwall,฀UK

iv © Woodhead Publishing Limited, 2011

Contents

Contributor contact details Introduction

xv xxi

S.H. WHANG, New฀York฀University,฀USA

Part I

Processing bulk nanostructured metals and alloys

1

1

Producing bulk nanostructured metals and alloys by severe plastic deformation (SPD)

3

R.Z. VALIEV, Ufa฀State฀Aviation฀Technical฀University,฀Russia

1.1 1.2 1.3฀ 1.4 1.5 1.6฀ 1.7 2

Introduction The principles of severe plastic deformation (SPD) processing New฀trends฀in฀SPD฀processing฀for฀effective฀grain฀reinement฀ Enhanced properties achieved using SPD processing Innovation potential of bulk nanostructured materials Conclusions฀ References

3 4 8 22 33 34 35

Bulk nanostructured metals and alloys produced by accumulative roll-bonding

40

N. TSUJI, Kyoto฀University,฀Japan

2.1 2.2 2.3 2.4฀ 2.5 2.6฀ 2.7

Introduction The principle of accumulative roll-bonding (ARB) Processing details Change฀in฀microstructures฀during฀the฀process฀ Mechanical properties of nanostructured metals fabricated by ARB Conclusions฀ References

40 41 42 45 53 57 57

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Contents

3

Nanocrystalline metals and alloys prepared by mechanical attrition

59

S. SCUDINO and J. ECKERT, IFW Dresden, Germany

3.1 3.2 3.3 3.4฀ 3.5฀ 3.6 3.7

Introduction Mechanical attrition Nanocrystalline phase formation by mechanical attrition Consolidation฀of฀nanocrystalline฀powders฀ Conclusion฀and฀future฀trends฀ Acknowledgements References

59 60 62 75 80 81 82

4

The processing of nanocrystalline steels by solid reaction

85

F.G.฀CABALLERO ฀and฀C.฀GARCÍA -MATEO , National฀Center฀for฀ Metallurgical฀Research฀(CENIM-CSIC),฀Spain

4.1 4.2฀ 4.3 4.4฀ 4.5 4.6฀ 4.7 4.8฀ 4.9 4.10 4.11 5

Introduction The฀inest฀grain฀structures฀in฀steels฀ Phase transformation theory: a powerful tool for the design of advanced steels, from micro to nano NANOBAIN฀steel:฀a฀material฀going฀to฀extremes฀ Accelerating the bainite reaction at low temperatures Characterizing฀nanocrystalline฀bainitic฀steels฀at฀the฀ atomic scale The mechanical properties of nanocrystalline bainitic steels Conclusion฀and฀future฀trends฀ Sources of further information and advice Acknowledgements References

85 86

98 107 113 114 114 114

The processing of bulk nanocrystalline metals and alloys by electrodeposition

118

89 93 98

U.฀ERB ,฀University฀of฀Toronto,฀Canada฀and฀G.฀PALUMBO and J.L.฀MC C REA , Integran฀Technologies฀Inc.,฀Canada

5.1 5.2 5.3฀ 5.4 5.5฀ 5.6 5.7 5.8 5.9

Introduction Electrodeposition methods Examples฀of฀nanocrystalline฀metals฀and฀alloys฀prepared฀by฀ electrodeposition Mechanical properties of nanocrystalline electrodeposits Corrosion฀properties฀of฀nanocrystalline฀electrodeposits฀ Other properties of nanocrystalline electrodeposits Applications Acknowledgements References

© Woodhead Publishing Limited, 2011

118 119 128 136 141 143 145 146 146

Contents

6

Bulk nanocrystalline and nanocomposite alloys produced from amorphous phase

vii

152

A. INOUE and D.V. LOUZGUINE , Tohoku฀University,฀Japan

6.1 6.2 6.3฀ 6.4 6.5 6.6 6.7฀ 6.8 7

Introduction The formation of bulk metallic glassy alloys The฀formation฀of฀a฀nanostructure฀by฀crystallization฀of฀the฀glassy฀ phase, by deformation or directly from the melt on casting The formation of nano-quasicrystals The mechanical properties of nanocomposite alloys The magnetic properties of nanocomposite alloys Conclusions฀ References

152 153 159 165 167 169 172 173

Severe plastic deformation and the production of nanostructured alloys by machining

178

J.B.฀MANN ,฀M4฀Sciences,฀USA,฀S.฀CHANDRASEKAR ,฀W.D.฀COMPTON , and฀K.P.฀TRUMBLE ,฀Purdue฀University,฀USA,฀C.฀SALDANA , and S. SWAMINATHAN ,฀GE฀John฀F.฀Welch฀Technology฀Center,฀India,฀ W. MOSCOSO and T.G. MURTHY , Indian Institute of Science, India

7.1 7.2 7.3฀ 7.4฀ 7.5 7.6 7.7฀ 7.8 7.9

Introduction The mechanics of severe plastic deformation (SPD) in machining A฀study฀of฀microstructure฀reinement฀ Bulk฀forms฀with฀ultraine-grained฀(UFG)฀microstructure฀ Nanostructured particulate Surface nanostructuring Conclusions฀ Acknowledgements References

Part II Microstructure 8

Deformation structures including twins in nanograined pure metals

178 179 189 196 200 205 207 207 208 211 213

K.฀HATTAR ,฀Sandia฀National฀Laboratories,฀USA

8.1 8.2฀ 8.3฀ 8.4 8.5 8.6 8.7 8.8

Introduction Classical฀defect฀structures฀in฀nanograined฀metals฀ Classical฀defect฀structures฀absent฀in฀nanograined฀metals฀ Novel defect structures in nanograined metals The effect of initial microstructure on deformation structures Future trends Acknowledgements References

© Woodhead Publishing Limited, 2011

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Contents

9

Microstructure and mechanical properties of nanostructured low-carbon steel prepared by equal-channel angular pressing

243

Y.G.฀KO ,฀Yeungnam฀University,฀Republic฀of฀Korea,฀and฀D.H.฀SHIN , Hanyang฀University,฀Republic฀of฀Korea

9.1 9.2฀ 9.3฀ 9.4฀ 9.5฀ 9.6฀ 9.7 10

Introduction The฀microstructural฀evolution฀of฀low-carbon฀steel฀(LCS)฀ The฀mechanical฀response฀of฀a฀nanostructured฀LCS฀alloy฀ Enhanced฀tensile฀properties฀by฀grain฀reinement฀and฀ microstructural฀modiication฀ Continuous฀shear฀drawing:฀a฀new฀processing฀method฀ Conclusion฀ References

243 244 261 268 270 272 272

Characteristic structures and properties of nanostructured metals prepared by plastic deformation

276

X. HUANG , Technical฀University฀of฀Denmark,฀Denmark

10.1 10.2฀ 10.3 10.4 10.5฀ 10.6 10.7

Introduction Characteristic฀microstructures฀ Hardening by annealing and softening by deformation Optimisation of microstructure and mechanical properties Conclusions฀ Acknowledgements References

276 277 286 289 290 294 294

Part III Mechanical properties

297

11

299

Strengthening mechanisms in nanocrystalline metals D.G. M ORRIS , National฀Center฀for฀Metallurgical฀Research฀ (CENIM-CSIC),฀Spain

11.1 11.2฀ 11.3฀ 11.4 11.5฀ 11.6 11.7 11.8฀ 11.9฀ 11.10

Introduction The฀deformation฀of฀polycrystals;฀the฀Hall–Petch฀model฀for฀ strengthening;฀typical฀strength฀and฀hardness฀data฀ Hall–Petch฀breakdown:฀a฀ine฀grain฀size฀limit฀to฀models฀ Hall–Petch breakdown: the importance of defective materials Alternative฀deformation฀mechanisms฀at฀very฀ine฀grain฀sizes฀ Strengthening caused by second-phase particles Strengthening caused by other factors: solute, order, twin boundaries Strengthening฀mechanisms฀in฀materials฀with฀ultraine฀ microstructure prepared by severe plastic deformation Conclusion฀and฀future฀trends฀ References

© Woodhead Publishing Limited, 2011

299 300 303 304 307 314 319 320 324 325

Contents

12

Elastic and plastic deformation in nanocrystalline metals

ix

329

M.Y. GUTKIN , Russian Academy of Sciences, Russia

12.1 12.2 12.3 12.4฀ 12.5 12.6 12.7

Introduction Elastic strains in nanocrystalline metals Plastic deformation in nanocrystalline metals Conclusions฀and฀future฀trends฀ Sources of further information and advice Acknowledgements References

329 330 337 365 367 367 367

13

The mechanical properties of multi-scale metallic materials

375

Y.H. ZHAO ฀and฀E.J.฀LAVERNIA ,฀University฀of฀California฀Davis,฀USA

13.1 13.2 13.3 13.4 13.5฀ 13.6 13.7 14

Introduction Mechanical properties of multi-scale metallic materials Deformation and fracture mechanisms of multi-scale metallic materials Future trends Conclusions฀ Acknowledgements References

375 383 405 425 425 426 426

Enhanced ductility and its mechanisms in nanocrystalline metallic materials

430

I.A. OVID’KO, Russian Academy of Sciences, Russia

14.1 14.2 14.3 14.4 14.5฀ 14.6 14.7 14.8 14.9

Introduction General aspects concerning the tensile ductility of materials Plastic flow mechanisms in coarse-grained metallic polycrystals,฀ultraine-grained฀metals฀and฀nanocrystalline฀ metals with intermediate grains Plastic flow mechanisms in nanocrystalline metals with the฀inest฀grains฀ Speciic฀features฀of฀crack฀nucleation฀and฀growth฀processes฀ in nanocrystalline metallic materials Enhanced ductility of artifact-free nanocrystalline metals with฀narrow฀grain฀size฀distributions฀ Enhanced ductility of nanocrystalline metals due to twin deformation and growth twins Enhanced ductility of nanocrystalline metals due to strain rate hardening Enhanced ductility of single-phase nanocrystalline metals with bimodal structures

© Woodhead Publishing Limited, 2011

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Contents

14.10

Enhanced ductility of nanocrystalline metallic composites with second-phase nanoparticles, dendrite-like inclusions and carbon nanotubes Conclusions฀and฀future฀trends฀ Sources of further information and advice Acknowledgements References

451 452 454 455 455

The mechanical behavior of nanostructured metals based on molecular dynamics computer simulations

459

14.11฀ 14.12 14.13 14.14 15

V.I. YAMAKOV , National฀Institute฀of฀Aerospace,฀USA

15.1 15.2 15.3 15.4฀ 15.5฀ 15.6 15.7 16

Introduction The structure and properties of grain boundaries in nanocrystalline฀(NC)฀metals฀by฀molecular฀dynamics฀(MD)฀ simulation Deformation mechanisms in nanoscale grains Grain฀growth฀and฀microstructure฀evolution฀in฀NC฀metals฀ Conclusions฀ Acknowledgement References

459 461 465 472 476 477 477

The surface deformation and mechanical behavior in nanostructured alloys

481

L.L. SHAW , University฀of฀Connecticut,฀USA

16.1 16.2 16.3฀ 16.4 16.5 16.6 16.7฀ 16.8 16.9 17

Introduction Mechanics aspects during surface severe plastic deformation Changes฀in฀the฀microstructure฀and฀stress฀states฀induced฀by฀ surface severe plastic deformation Tensile properties of metals with a nanocrystalline surface and hardened layer Fatigue resistance of metals with a nanocrystalline surface and hardened layer Wear resistance of metals with a nanocrystalline surface and hardened layer Conclusions฀ Acknowledgements References Fatigue behaviour in nanostructured metals

481 482 484 493 499 501 502 504 504 507

H.W. HÖPPEL and M. GÖKEN , Friedrich-Alexander฀University฀of฀ Erlangen-Nuremberg, Germany

17.1 17.2฀

Introduction and motivation General฀indings฀on฀the฀fatigue฀behaviour฀and฀the฀fatigue฀ lives of nanostructured model materials

© Woodhead Publishing Limited, 2011

507 509

Contents

17.3 17.4 17.5฀ 17.6 18

xi

Light metal alloys Fatigue behaviour and life of nanostructured steels Consequences฀and฀strategies฀for฀optimizing฀fatigue฀lives฀ and cyclic deformation behaviour References

517 532 534 537

Superplastic deformation in nanocrystalline metals and alloys

542

A. SERGUEEVA ,฀The฀Nanosteel฀Company,฀USA฀and฀A.฀MUKHERJEE , University฀of฀California฀Davis,฀USA฀

18.1 18.2 18.3 18.4฀ 18.5 18.6฀ 18.7 18.8 19

Introduction Theoretical predictions Superplasticity in nanocrystalline metals and alloys Speciic฀features฀of฀superplasticity฀in฀nanocrystalline฀ materials Deformation mechanisms Conclusions฀ Acknowledgements References

542 543 546 568 578 587 590 590

Creep and high-temperature deformation in nanostructured metals and alloys

594

W. YIN , Williams฀Advanced฀Materials,฀USA

19.1 19.2฀ 19.3฀ 19.4 19.5฀ 19.6

Introduction Temperature-dependent฀deformation฀in฀ine-grained฀ pure metals Creep฀and฀high-temperature฀deformation฀in฀ nanostructured alloys Deformation mechanisms and modeling Conclusions฀ References

Part IV Applications 20

Processing nanostructured metal and metal-matrix coatings by thermal and cold spraying

594 595 601 603 609 610

613 615

G.E.฀KIM ,฀Perpetual฀Technologies฀Inc.,฀Canada,฀V.K.฀CHAMPAGNE , and M. TREXLER , US฀Army฀Research฀Laboratory฀AMSRD-ARL-WM-MC,฀ USA฀and฀Y.฀SOHN , University฀of฀Central฀Florida,฀USA

20.1 20.2 20.3

Introduction Nanostructured metal-base feedstock Thermal spray processing

© Woodhead Publishing Limited, 2011

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xii

Contents

20.4

Thermal spray processing of nanostructured coatings: tungsten฀carbide-cobalt฀(WC-Co)฀coatings฀ Thermal spray processing of nanostructured coatings: alumina-titania (n-AT) coatings Thermal spray processing of nanostructured coatings: titanium฀oxide฀coatings฀ Thermal spray processing of nanostructured coatings: MCrAlY฀and฀NiCrAlY฀coatings฀ The cold spray process Characteristics฀of฀cold฀spray฀material฀ Cold-sprayed฀processing฀of฀WC-Co฀ Cold-sprayed฀processing฀of฀non-cryogenically฀milled฀ n-WERKZ฀AA5083฀ Future trends Sources of further information and advice Acknowledgements References

20.5 20.6 20.7 20.8 20.9฀ 20.10฀ 20.11฀ 20.12 20.13 20.14 20.15 21

Nanocoatings for commercial and industrial applications

620 621 622 627 644 647 648 651 657 658 658 658 663

J.L.฀MC C REA and G. PALUMBO ,฀Integran฀Technologies,฀Canada฀ and฀U.฀ERB , University฀of฀Toronto,฀Canada

21.1 21.2 21.3฀ 21.4฀ 21.5฀ 21.6

Introduction Overview of nanostructured metals and alloys Commercialization฀of฀nanostructured฀materials฀ Current฀and฀emerging฀applications฀ Conclusions฀ References

663 664 666 669 683 684

22

Applying nanostructured steel sheets to automotive body structures

687

Y. OKITSU and N. TSUJI , Honda฀R&D฀Co.,฀Ltd.,฀Japan

22.1 22.2 22.3฀ 22.4 22.5฀ 22.6฀ 22.7 22.8฀

Introduction The potential demand for nanostructured steels for automotive body structures Fabricating฀nanostructured฀low-C฀steel฀sheets฀ Improving elongation in nanostructured steel sheets Crash-worthiness฀of฀nanostructured฀steel฀sheets฀ Conclusions฀ References Appendix฀

© Woodhead Publishing Limited, 2011

687 688 689 699 706 711 712 713

Contents

23

Production processes for nanostructured wires, bars and strips

xiii

715

S. TORIZUKA , and E. MURAMATSU , National Institute for Material Science,฀Japan,฀T.฀KOMATSU , Komatsuseiki฀Kosakusho฀Co.,฀Ltd.,฀Japan฀ and S. NAGAYAMA , Tokushu฀Kinzoku฀Excel฀Co.,฀Ltd.,฀Japan

23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 24

Introduction The production processes and properties of nanostructured steel bars The production processes and properties of nanostructured steel wire The production processes and properties of nanostructured steel strips Applications of nanostructured steels and their features Future trends Acknowledgements References Nanostructured plain carbon-manganese (C-Mn) steel sheets prepared by ultra-fast cooling and short interval multi-pass hot rolling

715 716 722 725 731 743 745 745

747

T. TOMIDA ,฀K.฀MIYATA , and H. NISHIBATA , Sumitomo Metal Industries Ltd.,฀Japan

24.1 24.2 24.3฀ 24.4฀ 24.5 24.6 24.7฀ 24.8

Introduction The concept of ultra-fast direct cooling and short interval multi-pass฀hot฀rolling฀(UDCSMR)฀and฀an฀experimental฀hot฀ rolling mill Nanostructured฀carbon-manganese฀(C-Mn)฀steel฀sheets฀ produced฀by฀UDCSMR฀ Grain฀reinement฀mechanisms฀ Deformation characteristics Welding and application to some prototype parts Conclusions฀ References

752 757 765 773 784 784

Index

787

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xiv 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X

Contributor contact details

(*฀=฀main฀contact)

Editor

Chapter 3

S. H. Whang Department of Mechanical Engineering Polytechnic Institute New฀York฀University NY 11201 USA E-mail:฀[email protected]

S.฀Scudino฀and฀J.฀Eckert* Institute฀for฀Complex฀Materials Leibniz฀Institute฀for฀Solid฀State฀ and Materials Research Dresden (IFW Dresden) Helmholtzstr.฀20 D-01069 Dresden Germany

Chapter 1

E-mail:฀[email protected][email protected]

R. Z. Valiev Institute of Physics of Advanced Materials Ufa฀State฀Aviation฀Technical฀ University 12฀K.฀Marx฀str. Ufa฀450000 Russia E-mail:฀[email protected]

Chapter 4 F.฀G.฀Caballero*฀and฀ C.฀García-Mateo National฀Center฀for฀Metallurgical฀ Research฀(CENIM-CSIC) Avenida Gregorio del Amo, 8 Madrid 28040 Spain E-mail:฀[email protected]

Chapter 2 N. Tsuji Department of Materials Science and Engineering Graduate School of Engineering Kyoto฀University Yoshida-Honmachi, Sakyo-ku Kyoto฀606-8501 Japan E-mail:฀[email protected]

Chapter 5 U.฀Erb* University฀of฀Toronto Dept. Materials Science & Engineering 184฀College฀Street,฀Room฀140 Toronto, ON M5S 3E4 Canada E-mail:฀[email protected]

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Contributor contact details

G.฀Palumbo฀and฀J.฀L.฀McCrea Integran Technologies Inc. 1 Meridian Road Toronto, ON M9W 4Z6 Canada E-mail:฀[email protected][email protected]

Chapter 6 D.฀V.฀Louzguine*฀and฀A.฀Inoue WPI Advanced Institute for Materials Research Tohoku฀University 2-1-1฀Katahira Aoba-Ku Sendai, 980-8577 Japan E-mail:฀[email protected]@tohoku.ac.jp

Chapter 7 J.฀B.฀Mann M4 Sciences West Lafayette IN 47906 USA

T. G. Murthy Department฀of฀Civil฀Engineering Indian Institute of Science Bangalore, India

Chapter 8 K.฀Hattar Sandia National Laboratories (505) 845-9859 PO฀Box฀5800 Mail Stop 1056 Albuquerque NM 87185-1056 USA E-mail:฀[email protected]

Chapter 9 Y.฀G.฀Ko School of Materials Science and Engineering Yeungnam฀University Gyeongsan 712-749 Republic฀of฀Korea E-mail:฀[email protected]

S.฀Chandrasekar*,฀W.฀D.฀Compton,฀ K.฀P.฀Trumble,฀C.฀Saldana,฀and W. Moscoso Center฀for฀Materials฀Processing฀and฀ Tribology Purdue฀University West Lafayette IN 47907 USA E-mail:฀[email protected]

S. Swaminathan GE฀John฀F.฀Welch฀Technology฀Center Bangalore India

D.฀H.฀Shin* Department of Metallurgical and Materials Science Hanyang฀University Ansan 425-791 Republic฀of฀Korea E-mail:฀[email protected]

Chapter 10 X. Huang Danish-Chinese฀Center฀for฀ Nanometals Materials Research Division Risø National Laboratory for Sustainable Energy Technical฀University฀of฀Denmark DK-4000฀Roskilde Denmark E-mail:฀[email protected]

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xvii

Chapter 11

Chapter 14

D. G. Morris National฀Center฀for฀Metallurgical฀ Research฀(CENIM-CSIC) Avenida Gregorio del Amo, 8 Madrid 28040 Spain

I.A. Ovid’ko Institute of Problems of Mechanical Engineering Russian Academy of Sciences St. Petersburg Russia

E-mail:฀[email protected]

E-mail:฀[email protected]

Chapter 12

Chapter 15

M. Y. Gutkin Institute of Problems of Mechanical Engineering Russian Academy of Sciences Bolshoj 61 Vasilievskii Ostrov St. Petersburg 199178 Russia

V. I. Yamakov Durability and Damage Tolerance Branch NASA฀Langley฀Research฀Center Hampton VA 23681 USA

E-mail:฀[email protected][email protected]

Chapter 13 Y.฀H.฀Zhao* Department฀of฀Chemical฀ Engineering and Materials Science University฀of฀California,฀Davis 1231 Bainer Hall One Shields Avenue Davis CA฀95616-5294 USA E-mail:฀[email protected]

E.฀J.฀Lavernia Department฀of฀Chemical฀ Engineering and Materials Science University฀of฀California,฀Davis Davis CA฀95616-5294 USA

E-mail:฀[email protected]

Chapter 16 L. L. Shaw Department฀of฀Chemical,฀Materials฀ and Biomolecular Engineering University฀of฀Connecticut Storrs CT฀06269 USA E-mail:฀[email protected]

Chapter 17 H.฀W.฀Höppel*฀and฀M.฀Göken Department of Materials Science and Engineering Institute I: General Materials Properties Friedrich-Alexander฀University฀of฀ Erlangen-Nuremberg 91058 Erlangen Germany E-mail:฀[email protected] uni-erlangen.de

E-mail:฀[email protected]

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Chapter 18 A.฀Sergueeva* The฀Nanosteel฀Company Idaho Falls ID 83402 USA E-mail:฀[email protected]

A. Mukherjee University฀of฀California฀Davis California USA E-mail:฀[email protected]

Chapter 19 W. Yin Williams Advanced Materials Inc., Thin Film Products 42 Mount Ebo Road South Brewster NY 10509 USA E-mail:฀[email protected]

Chapter 20 G.฀E.฀Kim* Perpetual Technologies, Inc. 38฀Place฀du฀Commerce Suite 11-163 Ile des Soeurs Quebec H3E 1T8 Canada E-mail:฀[email protected]

V.฀K.฀Champagne US฀Army฀Research฀Laboratory AMSRD-ARL-WM-MC Building 4600 Aberdeen Proving Ground MD 21005-5069 USA

M.฀Trexler US฀Army฀Research฀Laboratory AMSRD-ARL-WM-MC Building 4600 Aberdeen Proving Ground MD 21005-5069 USAY.฀Sohn Advanced Materials Processing and Analysis฀Center฀and฀Department฀ of Mechanical, Materials and Aerospace Engineering University฀of฀Central฀Florida 4000฀Central฀Florida฀Blvd. Orlando FL 32816-2455 USA

Chapter 21 J.฀McCrea*฀and฀G.฀Palumbo Integran Technologies 1 Meridian Road Toronto, ON M9W 4Z6 Canada E-mail:฀[email protected][email protected]

U.฀Erb University฀of฀Toronto Dept. Materials Science & Engineering 184฀College฀Street,฀Room฀140 Toronto, ON M5S 3E4 Canada E-mail:฀[email protected]

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Chapter 22 Y.฀Okitsu* Automobile฀R&D฀Center Honda฀R&D฀Co.,฀Ltd. 4930฀Shimotakanezawa Haga-machi, Haga-gun Tochigi 321-3393 Japan E-mail:฀[email protected] co.jp

N. Tsuji Department of Materials Science and Engineering Graduate School of Engineering Kyoto฀University Yoshida-Honmachi, Sakyo-ku Kyoto฀606-8501 Japan E-mail:฀[email protected]

Chapter 23 S.฀Torizuka*฀and฀E.฀Muramatsu National Institute for Material Science Material Manufacturing and Engineering Station 1-2-1 Sengen, Tsukuba Ibaraki 305-0047 Japan

xix

T.฀Komatsu Komatsuseiki฀Kosakusho฀Co.,฀Ltd. Production Department 942-2 Siga, Suwa Nagano 392-0012 Japan E-mail:฀[email protected]

S. Nagayama Tokushu฀Kinzoku฀Excel฀Co.,฀Ltd. New Functional Materials R&D H.Q. 56 Tamagawa, Tokigawa Saitama 355-0342 Japan E-mail:฀[email protected]

Chapter 24 T.฀Tomida*,฀K.฀Miyata฀and฀ H. Nishibata Sumitomo Metal Industries, LTD. Corporate฀R&D฀Laboratories 1-8,฀Fuso-Cho Amagasaki Hyogo, 660-0891 Japan E-mail:฀[email protected] co.jp

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Introduction S. H. WHANG, New฀York฀University,฀USA Recent nanotechnology for material applications deals with a very wide range of material groups and various aspects of materials problems. Since the volume of the accumulated knowledge and database for the subjects stemming from worldwide research and development has been rapidly escalating, this book intends to limit its coverage to the recent progress on nanostructured metallic materials for structural applications. Since฀‘nanostructured฀materials’฀were฀irst฀deined฀by฀Gleiter,1,2 research and development฀in฀the฀ields฀of฀nanostuctured฀materials฀have฀lourished฀over฀the฀last฀ two฀ decades.฀ Currently฀ nanostructured฀ materials฀ are฀ conveniently฀ deined฀ as฀ materials made of a microstructure less than 100 nm in length in at least one dimension฀whereas฀ultraine-grained฀materials฀(UFG)฀possess฀a฀grain฀size฀range฀ between 200 nm and less than 1 µm in diameter. But, for practical reasons, nanostructured metallic materials that have been prepared for research and development฀ contain฀ a฀ wide฀ range฀ of฀ grain฀ size฀ distribution฀ from฀ tens฀ of฀ nanometers฀ to฀ a฀ submicrometer.฀ For฀ example,฀ research฀ on฀ optimizing฀ the฀ mechanical properties of nanostructured materials requires manipulation of its bimodal฀and฀multimodal฀grain฀size฀distribution.฀In฀this฀case,฀the฀grain฀size฀ranges฀ from฀nano฀size฀(NG)฀to฀submicron฀size฀(UFG).฀Therefore,฀for฀practical฀structural฀ applications, it is envisioned that nanostructured bulk metallic materials may contain both nanoscale as well as submicron-scale microstructures in the future. This฀book฀deals฀with฀metallic฀materials฀that฀have฀various฀grain฀size฀distributions:฀ nanoscale grains or nanomicrostructure other than nanograins or submicron scale grains or submicron microstructure other than submicron grains or a combination of all these. The history of metallic materials shows that an appetite for higher strength/ speciic฀strength,฀and฀better฀ductility฀and฀toughness฀for฀structural฀applications฀has฀ been the main driving force for research and development for better and even better฀materials฀in฀the฀last฀century,฀as฀well฀as฀this฀century.฀Recent฀nanostructurizing฀ approaches to the metallic material systems continue this effort. To achieve this desire, scientists and engineers always look into smaller-scale worlds from micron- to submicron-, and submicron- to nano-dimensions for their solutions. Long before such recent endeavors became a fashion among materials scientists and฀engineers,฀it฀was฀recognized฀that฀nanoscale฀microstructure฀has฀great฀potential฀ for changing the landscape in advanced engineering materials and manufacturing. For฀example,฀new฀high-strength฀aluminum฀alloys฀were฀produced฀for฀the฀irst฀time฀ utilizing฀ the฀ nanoscale฀ Guinier-Preston฀ zone3฀ and฀ ultraine-layered฀ wire฀ with฀ extremely฀ high฀ strength4 long before the current nanotechnology debut. The xxi © Woodhead Publishing Limited, 2011

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Introduction

discovery of the Hall–Petch relationship also suggested that new high-strength materials฀might฀be฀fabricated฀with฀materials฀with฀nanoscale฀grain฀sizes. In the last two decades, research and development into nanostructured metallic materials have been largely focused on metallic materials with two different microstructures: nanograined structures and embedded nanomicrostructures other than฀ nanograins;฀ and฀ also฀ the฀ effort฀ has฀ been฀ largely฀ devoted฀ to฀ four฀ different฀ subject฀areas:฀processing฀and฀fabrication,฀characterization฀of฀material฀properties,฀ microstructural฀characterization,฀and฀engineering฀design฀and฀development฀for฀new฀ products and applications. The฀irst฀hurdle฀to฀overcome฀in฀this฀effort฀has฀been฀the฀large-scale฀processing฀of฀ high quality of nanomaterial for use in research and development. Of course, many technically challenging problems emerge in the course of processing of such nanomaterials. In general, the bulk forms prepared by different processes contain different structural defects and impurities. As a result, the mechanical properties of the specimens of an alloy prepared by different processing routes฀exhibit฀substantial฀deviation,฀particularly฀in฀structure-sensitive฀properties฀ such as deformation behavior, ductility, fatigue, superplasticity and creep. This deviation poses serious problems for scientists in the analysis and interpretation of฀the฀experimental฀results฀and฀in฀arriving฀at฀meaningful฀conclusions.฀In฀addition,฀ many of the processes face other challenging engineering problems that require each process to demonstrate the feasibility of scaling-up for industrial applications. As฀the฀nanomaterials฀research฀ields฀continue฀to฀expand฀and฀the฀accumulation฀ of knowledge from the research escalates, it becomes clear that it is increasingly dificult฀ to฀ cover฀ the฀ progress฀ made฀ in฀ these฀ ields฀ adequately฀ in฀ a฀ single฀ publication. Thus, the focus of the current book is placed on the recent progress on nanostructured metallic materials in bulk forms, in their processing, microstructure, mechanical properties and structural applications. For those who are interested in these subjects and want to know the depth and breath of the issues, there are references available for additional reading, which have reviewed฀and฀summarized฀the฀progress฀made฀in฀these฀areas฀in฀the฀past.5–7 This brief introduction on the subject areas is given for readers who come from other ields.

Processing It฀is฀imperative฀to฀provide฀nanostructured฀metallic฀materials฀of฀suficient฀quality฀ and฀ quantity฀ for฀ research฀ and฀ development฀ in฀ order฀ to฀ realize฀ the฀ envisioned฀ progress฀in฀this฀ield.฀There฀have฀been฀many฀processing฀approaches฀available฀for฀ producing a small quantity of nanostructured metals based on ‘top-down’, and ‘bottom-up’ approaches1 in three different phase forms – vapor, liquid or solid – utilizing฀ all฀ available฀ technological฀ means.฀ The฀ bottom-up฀ approach฀ includes฀ inert gas condensation, chemical vapor condensation, pulse electron deposition,

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etc. Nevertheless, the structural application requires a substantial quantity of nanostructured materials in three dimensions, which eliminates the majority of possible bottom-up processing approaches as candidates for the current effort, at least฀ at฀ this฀ stage.฀ Currently,฀ that฀ leaves฀ only฀ a฀ handful฀ of฀ potentially฀ viable฀ processes for research and development in bulk nanostructured metallic materials. For these reasons, this book includes only those processing methods that could be serious candidates for producing nanostructured metallic materials in the near future. This book introduces several promising processing approaches for nanostructured metallic materials, which include 1) solid deformation processing: equal channel angular฀pressing฀(ECAP),฀high฀pressure฀torsion฀(HPT),฀accumulative฀roll-bonding฀ (ARB),฀mechanical฀attrition฀(MA)฀and฀mechanical฀machining฀process฀(MM);฀2)฀ solid฀ reaction฀ processing:฀ ultraine฀ bainite฀ or฀ pearlite฀ structure฀ in฀ carbon฀ steels฀ using฀ a฀ combination฀ of฀ deformation฀ and฀ thermal฀ reaction;฀ and฀ 3)฀ liquid– solid transformation: involving a transformation from liquid to solid phases, e.g. from฀ the฀ molten฀ phase฀ to฀ metallic฀ glass฀ and฀ subsequently฀ to฀ crystallization;฀ electrodeposition฀processing;฀and฀thermal฀spray฀processing,฀from฀molten฀droplets฀ to฀solidiied฀droplets฀containing฀nanograins.

Severe plastic deformation processes Historically, a large plastic deformation and the resulting microstructural reinement฀ in฀ metals฀ and฀ alloys฀ have฀ been฀ investigated฀ by฀ a฀ number฀ of฀ researchers.8–11 Nevertheless, the concept of relating severe plastic deformation (SPD)฀to฀ultraine฀microstructure฀as฀well฀as฀unique฀properties฀has฀been฀put฀to฀test฀ by Valiev and co-workers in the 1980s and thereafter,12–14 which has contributed to฀ the฀ popularization฀ of฀ current฀ SPD฀ technology฀ for฀ nanostructured฀ metallic฀ materials. Both high pressure torsion (HPT) pressing and equal channel angular pressing฀(ECAP)11 use the same principle: that hydrostatic pressure permits a very large shear deformation in ductile metals, at a strain as high as strain of 4–5, which translates into the dislocation density up to 1014–17 mm–1.15,16 Repeating the process฀cycle฀in฀SPD฀results฀in฀ultraine฀grains฀(100–300฀nm).฀On฀the฀other฀hand,฀ although฀ the฀ ARB฀ process฀ as฀ another฀ form฀ of฀ SPD฀ generates฀ ine-grained฀ microstructure฀by฀a฀large฀accumulative฀deformation฀similar฀to฀ECAP,฀the฀approach฀ is substantially different in that in ARB processing,17,18 a very large accumulative deformation is applied to a thin sheet by a series of repetitive fold-and-roll processes without hydrostatic pressure where the surfaces of sheets in the folded sides฀convert฀to฀grain฀boundaries฀by฀cold฀welding.฀In฀the฀processing,฀the฀ultraine฀ grain฀reinement฀occurs฀by฀the฀introduction฀of฀new฀grains฀in฀the฀old฀grains฀during฀ dynamic฀recovery฀and฀post฀annealing.฀Both฀ARB฀and฀ECAP฀deformation฀generate฀ new grains of high angle grain boundaries, and the fraction of such boundaries increases with an increasing number of cycles. ARB is particularly advantageous for producing a sheet form of nanostructured metallic material.

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There฀are฀many฀roadblocks฀in฀the฀way฀of฀ECAP฀and฀HPT฀becoming฀industrially฀ viable processes. They include the inability to produce the desired dimensions – length, width and thickness of continuous bulk forms – at this stage. Nevertheless, in one area, the wire processing by a large acumulative deformation is successful in producing฀the฀required฀dimensions.฀For฀example,฀a฀ine฀wire฀of฀Mn฀steel฀is฀made฀by฀ drawing 10 mm diameter rods of a dual-phase microstructure of martensite and ferrite฀and฀of฀the฀composition฀of฀Fe-0.2C-0.8Si-1Mn฀(wt-%)฀into฀individual฀strands฀ of 8 µm diameter wire. This wire drawing amounts to a huge deformation of a true strain฀in฀excess฀of฀9.฀The฀dislocation฀cell฀size฀in฀the฀deformed฀wires฀is฀found฀to฀be฀ 10–15 nm.19,20 Another form of SPD is mechanical attrition, which is basically high impact ball-milling, and produces very large plastic deformation. Although an initial development aimed to produce new alloys by mechanical alloying,21 the same technique฀can฀be฀employed฀to฀produce฀microstructural฀reinement.฀In฀the฀process,฀ metallic powders undergo fracture and plastic deformation in which the powders can฀form฀mechanical฀alloying฀or฀generate฀nanoscale฀microstructures฀such฀as฀ine฀ grains฀ or฀ ine฀ precipitates.฀ The฀ deformed฀ nanograins฀ in฀ this฀ process฀ exhibit฀ deformation shear bands22 like any other highly deformed nanograins produced by other processing techniques. Nevertheless, these nanostructured powders are not a inal฀product,฀but฀a฀precursor฀material.฀The฀nanopowders฀may฀be฀consolidated฀into฀ nanostructured bulk materials or they can be sprayed for nanostructured coatings. Consolidating฀powders฀into฀a฀bulk฀material฀is฀a฀challenging฀process฀because฀of฀ pores฀or฀oxides฀or฀other฀potential฀contamination฀introduced฀into฀the฀matrix,฀some฀ of฀ which฀ are฀ produced฀ during฀ milling฀ and฀ consolidation;฀ and฀ second,฀ these฀ precursor powders undergo microstructural coarsening or grain growth during thermal consolidation. A recent approach using a cryogenic atmosphere in mechanical attrition shows clear improvement in effective milling and a reduction in contamination.23฀SPD฀metals฀with฀UFG฀can฀be฀produced฀by฀a฀conventional฀ machining฀ process,฀ whose฀ microstructual฀ reinement฀ mechanisms฀ have฀ been฀ known฀for฀some฀time.฀The฀grain฀size฀produced฀in฀machining฀depends฀on฀processing฀ parameters, but it can be as low as 200 nm. Besides, the machining can produce bulk฀ forms฀ of฀ UFG฀ products฀ such฀ as฀ foils,฀ sheets,฀ or฀ rods,฀ directly฀ from฀ the฀ coarse-grained bulk metals.24 The challenging aspect of this approach is to control the microstructure via machining parameters such as strain, strain rate and temperature฀throughout฀the฀entire฀operation.฀Alternatively,฀individual฀UFG฀chips฀ produced can be consolidated into a bulk form by various consolidation techniques, which are still in the early stage of development.

Solid reaction processes Nanomicrostructures other than nanograin structures can be generated and produced in a controlled manner by thermal reaction and diffusion. One recent interesting฀ approach฀ is฀ to฀ examine฀ the฀ possibility฀ of฀ creating฀ nanostructure฀ in฀

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conventional฀ high-strength฀ steel฀ material,฀ which฀ is฀ dificult฀ to฀ process฀ using฀ conventional SPD approaches due to its high flow stresses. In the past, bainite steels have been in use for a long time, and the nucleation and kinetics of bainite formation have also long been understood. In another recent approach, the bainite reaction can be made to produce nanoscale bainitic ferrite plates (20–40 nm) by heat-treating bainite steel at relatively low temperatures for a longer duration. This is only possible in steels with a relatively high concentration of฀ carbon.฀ For฀ example,฀ in฀ Fe-0.78-0.98฀ C-Si-Mn-Cr-Mo฀ alloys,฀ an฀ enhanced฀ nucleation of ferrite in austenite after supercooling is possible at the low temperatures (125–325oC)฀for฀one฀to฀six฀days’฀holding฀time฀during฀which฀grain฀ growth is suppressed.25,26฀This฀type฀of฀steel฀containing฀nanostructures฀exhibits฀an฀ extremely฀high฀strength฀comparable฀with฀that฀of฀maraging฀steels.฀The฀advantage฀ of bainite steels over martensitic steels is that martensite steel has limited dimensionality due to the fact that it needs a high cooling rate to produce martensite, while nanoscale bainite steels can be produced in larger dimensions due to their lexible฀ heat฀ treatment฀ requirements฀ and฀ no฀ requirement฀ of฀ high฀ cooling.฀ Highsilicon฀bainite฀steels฀also฀exhibit฀a฀combination฀of฀high฀strength฀and฀toughness.26

Liquid–solid transformation processes Liquid–solid transformation processes have two different approaches. First, a molten฀alloy฀is฀solidiied฀into฀an฀amorphous฀phase,฀from฀which฀nanocrystalline฀ precipitates or nanograins can be produced by controlled heat treatment for crystallization.27฀The฀amorphous฀matrix฀turns฀into฀partially฀or฀fully฀nanocrystalline฀ matrix฀depending฀on฀heat฀treatment฀conditions.฀The฀maximum฀dimensions฀of฀a฀ bulk amorphous metal, however, are limited due to the fact that 1) a critical cooling rate is required for amorphous formation and 2) each alloy has its own glass forming ability. The second process includes thermal spray coating, in which the฀feed฀material฀is฀melted฀and฀broken฀into฀ine฀droplets฀before฀solidifying฀on฀the฀ substrate surface. In this process, the stability of the molten phase is important during melting and flight.28 The feedstock could be powders or solid wires. A general rule of thumb is that any material that has a stable molten phase and can be฀processed฀into฀the฀appropriate฀feed฀speciications,฀can฀be฀thermal฀sprayed.฀The฀ heat source used to heat and accelerate the feedstock is generated either chemically via฀oxygen-fuel฀combustion฀or฀electrically฀via฀an฀arc.

Mechanical properties One of the most pronounced mechanical properties of nanostructured metals is their฀extraordinary฀high฀yield฀strength฀compared฀to฀those฀of฀conventional฀coarsegrained metallic materials. But, the downside of this material is its well-known poor ductility. Earlier efforts to test the strengthening behavior of nanometals with respect฀to฀grain฀size฀led฀to฀the฀discovery฀of฀a฀breakdown฀of฀the฀Hall–Petch฀(H–P)฀

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Introduction

relationship.29,30฀ This฀ unexpected฀ behavior฀ was฀ identiied฀ as฀ the฀ ‘inverse฀ H–P฀ relationship’.฀ Since฀ then,฀ this฀ unexpected฀ softening฀ behavior฀ of฀ nanostructured฀ metals has been a subject of intensive research and the center of discussion. Furthermore, not only is strain hardening (the result of characteristic dislocation pile-ups฀in฀coarse-grained฀metals)฀absent฀in฀nanostructured฀metals฀with฀grain฀size฀ less฀than฀approximately฀20฀nm,฀but฀also฀any฀dislocation฀pile-up฀in฀nanograins฀has฀ not been observed using high-resolution microscopy. Thus, in nanograined metals, grain boundary (GB) deformation has to be the main mechanism for plastic deformation, considering the fact that 1) nanograins become an inactive component in deformation, and 2) the volume fraction of grain boundary and triple junction under฀the฀single-digit฀grain฀size฀matrix฀could฀be฀anywhere฀from฀10%฀to฀as฀much฀ as฀30%.฀For฀these฀reasons,฀the฀focus฀of฀research฀moved฀from฀grain฀deformation฀to฀ grain boundary deformation for nanograined metals. For the last two decades, unique deformation mechanisms of nanostructured metals and alloys based on grain boundary deformation mechanisms have been investigated, in which each of different deformation modes such as tensile deformation, superplastic deformation, creep and fatigue failure has been studied separately to capture a complete picture of the deformation mechanisms. Research results on these subjects are presented and discussed throughout various chapters in Parts II and III of this book.

Strength and ductility The Hall–Petch relationship tells us that we could achieve strength in materials that is฀ as฀ high฀ as฀ their฀ own฀ theoretical฀ strength฀ by฀ reducing฀ grain฀ size.฀ Indeed,฀ their฀ strength฀continues฀to฀increase฀with฀decreasing฀grain฀size฀to฀approximately฀20–30฀nm฀ where the strength peaks. Indeed, the peak yield strength of pure nanostructured copper฀with฀grain฀size฀approaching฀approximately฀20฀nm฀can฀reach฀as฀high฀as฀800– 900 MPa 29,31–33 compared to 200 MPa for coarse-grained copper. But decreasing grain฀size฀beyond฀20฀nm฀reverses฀the฀H–P฀effect:฀in฀other฀words฀the฀material฀starts฀ to soften instead of further strengthening. In general, nanostructured metals are characterized฀as฀having฀very฀high฀strength฀with฀poor฀ductility.฀In฀other฀words,฀the฀ strength increase trades off with ductility in nanostructured metallic materials. As฀an฀exception,฀artifact-free฀nanocrystalline฀copper฀with฀a฀grain฀size฀of฀30–60฀ nm was found to possess a very high yield strength, and good ductility such as a fracture strain of 0.06 to 0.12 (Eng).34,35 Such relatively ductile behavior of nanocopper฀ may฀ be฀ explained฀ by฀ a฀ number฀ of฀ models:฀ dislocations฀ stored฀ in฀ larger฀ grains,฀ grain฀ boundary฀ sliding,฀ Coble฀ creep฀ (GB฀ diffusion),฀ localized฀ shear฀ microbands, twinning, etc. For฀nanostructured฀metals฀with฀a฀wide฀distribution฀of฀grain฀size,฀none฀of฀the฀ above฀models฀can฀be฀excluded.฀But,฀when฀the฀grain฀size฀distribution฀is฀narrow฀and฀ its median value is close to 20 nm or less, only grain boundary deformation modes,฀i.e.฀grain฀boundary฀sliding,฀grain฀boundary฀rotation฀or฀Coble฀creep฀must฀

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be considered since the grains are regarded as plastically non-deformable islands that are embedded in the network of grain boundaries. For nanostructured metals, it may be possible that all these GB deformation models are operating in an optimized฀manner.36 Another important factor is the effect of impurities on GB deformation.฀For฀example,฀nano-copper฀with฀contaminants฀does฀not฀exhibit฀such฀ ductile behavior, probably due to the fact that the impurity has a negative influence on GB deformation, which is a subject of future investigation.

Deformation mechanisms In the past, tensile testing of nanostructured metallic materials has been performed with฀various฀grain฀sizes฀from฀the฀ultraine฀scale฀to฀the฀nanoscale,฀as฀small฀as฀10฀nm฀ in diameter. In addition, the samples prepared by different processing routes have contained different levels of atomic as well as macro defects. Thus, one must be careful฀in฀analysing฀and฀interpreting฀the฀experimental฀results฀from฀such฀diversiied฀ material sources. In fact, this has been a challenging aspect for investigating deformation mechanisms of nanostructured metals in the past. In general, the tensile deformation of nanostructured metals shows that the flow stress starts to decline right after yielding, indicating an absence of strain hardening behavior. This is an indicative of the fact that the dislocation pile-up doesn’t occur beyond฀ the฀ yield฀ point฀ in฀ nanostructured฀ metals.฀To฀ explain฀ this฀ behavior,฀ it฀ is฀ proposed that the number of dislocations in the pile-up continues to decline with decreasing฀grain฀size.37,38฀Thus,฀there฀must฀be฀a฀critical฀grain฀size฀where฀a฀single฀ Frank–Read฀ source฀ can฀ operate฀ in฀ a฀ grain.฀ Near฀ such฀ a฀ critical฀ grain฀ size,฀ the฀ dislocation pile-up would no longer occur due to the very high shear stress required for the generation of any additional dislocation, and consequently, the Hall–Petch฀relationship฀cannot฀be฀established.฀This฀would฀explain฀why฀the฀H–P฀ relationship breaks down in nanostructured metals. For these reasons, dislocation pile-up mechanisms would no longer be useful for฀nanostructured฀metals฀with฀a฀grain฀size฀less฀than฀20–30฀nm.฀Thus,฀the฀focus฀ has been shifted to grain boundary deformation in recent years. The fact that the volume฀percentage฀of฀grain฀boundary฀and฀triple฀junction฀signiicantly฀increases฀ and฀reaches฀as฀much฀as฀30%฀for฀a฀grain฀size฀less฀10฀nm฀makes฀GB฀deformation฀ more฀signiicant.฀But฀the฀details฀of฀GB฀deformation฀in฀nanostructured฀metals฀are฀ very฀complex.฀Furthermore,฀direct฀observation฀of฀deformation฀defect฀structures฀ using high-resolution microscopy is scarce. Therefore, research into GB deformation mechanisms has largely taken two tracks: 1) developing theoretical approaches that are based on classical deformation models฀ for฀ superplasticity;฀ 2)฀ performing฀ computer฀ simulations฀ based฀ on฀ molecular dynamics under various stress and temperature conditions. The theoretical approach is considered to test the predetermined framework against experimental฀ measurements฀ whereas฀ MD฀ simulations฀ let฀ atoms฀ and฀ groups฀ of฀ atoms play the game without knowing the outcome.

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From this prospect, MD simulations could provide insightful information about the process and mechanisms of plastic deformation. Since, in nanograined metals, tensile deformation, superplastic deformation and creep have a common thread, i.e.฀grain฀boundary฀deformation,฀it฀may฀be฀possible฀to฀develop฀a฀uniied฀model฀ that can describe these three deformation modes in the future. GB deformation models Although the three different deformation modes – time-independent deformation, superplasticity and creep–are connected through grain boundary deformation mechanisms, conceptually it can be said that each of the modes is made of different levels of contributions by stress-induced GB deformation and thermally-induced GB deformation. In general, it is understood that grain boundary sliding in nanostructured metals occurs by GB dislocations if dislocations are available under applied shear stress, and by thermally activated local shear events, which occur by uncorrelated individual atomic jumps and the movement of small groups of atoms. In particular, nanostructured metals are made of grains whose boundaries are not only nanoscale, but also in the non-equilibrium state (majority). Thus, thermally induced GB deformation becomes important in this type of materials. With฀ such฀ a฀ conceptual฀ background,฀ Conrad฀ et al.39 proposed that the macroscopic shear occurs due to thermally activated atomic shear in the nanograin boundary, i.e. GB sliding. Fu et al., following the idea of a neighbor-grainexchange฀ mechanism฀ in฀ superplastic฀ deformation฀ by฀ Raj฀ et al.,40 introduced a plastic฀ accommodation฀ term฀ to฀ the฀ thermal฀ shear฀ stress฀ in฀ Core–Mantle฀ nanograins.41฀The฀results฀show฀that฀the฀strain฀rate฀in฀nano-copper฀with฀grain฀size฀less฀ than฀ 10฀ nm฀ at฀ 300K฀ could฀ reach฀ a฀ signiicant฀ level฀ indicating฀ that฀ GB฀ sliding฀ would be real possibility under diffusional sliding with plastic accommodation. In recent years, Wang et al.42 suggested that grain rotation and grain coalescence in the direction of shear would be possible during plastic deformation. Ovid’ko demonstrated that such a rotation of grains could be indeed possible by creating disclinations during such a rotation.43 Furthermore, Murayama et al.44 reported that TEM images from a milled Fe sample showed a partial disclination dipole. Another฀deformation฀structure฀reported฀was฀shear฀band฀formation฀as฀a฀localized฀ deformation฀mode฀in฀ultraine-grained฀iron.45 Another important issue is non-equilibrium GB,46 which is a center of dislocation sink and generation. The fraction of non-equilibrium boundary increases฀with฀decreasing฀grain฀size.฀It฀is฀important฀to฀understand฀the฀role฀of฀the฀ non-equilibrium฀ GB฀ in฀ deformation.฀ For฀ example,฀ 1)฀ the฀ emission฀ of฀ partial฀ dislocations from triple junctions and non-equilibrium GB as part of the accommodation mechanisms to local shear events would trigger the formation of stacking faults and twins in nanograins, and 2) non-equilibrium GB acts as a dislocation sink and may assist dynamic recovery during deformation. Despite the

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limited฀success฀of฀analytical฀models,฀it฀is฀not฀possible฀to฀understand฀the฀complex฀ dynamic process of GB sliding by analytical modeling as the process is characterized฀ by฀ the฀ evolution,฀ annihilation฀ and฀ mutual฀ interaction฀ of฀ various฀ defect structures in the process. MD simulations Scientists have often been unable to observe the evolution of deformation microstructure on an atomic scale by high-resolution microscopy. In the past, numerous interesting pieces of defect structures in nanostructured metals have been reported. On the other hand, regular mechanical testing continues to generate a฀large฀volume฀of฀experimental฀results฀that฀were฀usually฀not฀provided฀with฀the฀ related microstructures. Therefore, to establish the property–structure relationship, computer simulations must play a crucial role in bridging the two different types฀of฀observation.฀In฀addition,฀other฀unexpected฀microstructural฀evidence฀that฀ has฀ been฀ observed฀ needs฀ to฀ be฀ explained฀ by฀ theory฀ or฀ demonstrated฀ by฀ MD฀ simulations.฀ For฀ example,฀ some฀ interesting฀ microstructures฀ observed฀ by฀ highresolution microscopy include stacking faults, twins in face-centred cubic (fcc) metals฀such฀as฀Al,฀Cu฀with฀high฀stacking฀faults฀energy,฀stacking฀fault฀tetrahedral,฀ and disclinations. The challenging task is to understand why these defect structures are present only in nanostructured metals. To answer these questions, numerous theoretical models and computer atomic simulation techniques have been employed. In the early stage of investigations, for฀ example,฀ inite฀ element฀ (FE)฀ simulations฀ by฀ Kim฀ et al.47 were used to reproduce฀experimental฀tensile฀test฀results฀as฀well฀as฀the฀H–P฀plot฀for฀nano-Cu฀ with฀grain฀size฀of฀10–1000฀nm.฀Kim฀used฀a฀‘phase฀mixture฀mode’฀in฀which฀nanomaterial consisted of two distinctive phases: initially dislocation-free crystalline matter at the center and the surrounding grain boundary (amorphous-like). Thus, during simulations, the dislocation pile-up was allowed in the crystalline matter while diffusional flow occurred in the grain boundary. The H–P plot generated by this฀ scheme฀ is฀ in฀ good฀ agreement฀ with฀ experimental฀ data.฀ Nevertheless,฀ FE฀ simulations are not equipped to investigate the role of various defects in GB deformation฀or฀to฀predict฀the฀evolution฀of฀unexpected฀defect฀structures.฀In฀recent฀ years, however, molecular dynamic (MD) computer simulations have demonstrated that they are powerful tools in investigating the deformation mechanisms฀ in฀ nanostructured฀ metals.฀ For฀ example,฀ twinning฀ in฀ deformed฀ nanostructured Al was predicted by MD simulations,48฀and฀was฀conirmed฀later฀ by฀experiment.49 The deformation mechanisms in both time-dependent and time-independent deformation have been studied by MD simulations in the past. For time-dependent deformation, MD simulations have been focused on grain boundary diffusion, grain boundary sliding and emission of dislocations, particular partial dislocations and twins from grain boundaries.

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Despite฀ their฀ inherent฀ deiciencies฀ (see฀ Chapter฀ 15),฀ MD฀ simulations฀ have฀ already฀made฀a฀signiicant฀contribution฀in฀elucidating฀deformation฀mechanisms฀of฀ nanostructured materials this decade. Such important events by MD simulations this฀decade฀include฀1)฀conirmation฀of฀the฀inverse฀Hall–Petch฀relationship;50 MD models฀ reasonably฀ explained฀ the฀ transition฀ from฀ the฀ hardening฀ mode฀ to฀ the฀ softening mode in nanostructured metals using two competing mechanisms: grain boundary mediated mechanisms (GB sliding, diffusion)51,52 and transgranular dominant฀mechanisms฀(dislocation฀slip,฀twinning,฀etc.)฀depending฀on฀grain฀size;฀ 2)฀MD฀simulations฀showed฀the฀existence฀of฀Coble฀creep฀in฀nanostructured฀metals฀ at฀ relatively฀ low฀ temperatures;53 3) elucidating grain boundary-mediated deformation mechanisms in which the Shockley partial dislocations emitting from triple junction and GB are also a part of GB sliding.51,54 Yet, there are unresolved problems regarding the fundamental understanding of GB sliding mechanisms. There are two views: either stress-induced free-volume migration or stress-induced long-range atomic migration (diffusion) causes the deformation of nanograined metals. The fact that both GB sliding and GB diffusion฀ are฀ inluenced฀ by฀ applied฀ stress฀ and฀ temperature฀ makes฀ it฀ dificult฀ to฀ separate one from the other. Second, such MD simulations that have been performed on fcc metals are not or almost not available for other crystal structures such฀ as฀ body-centred฀ cubic฀ (bcc),฀ hexgonal฀ close฀ packed฀ (hcp)฀ and฀ tetragonal฀ structures. Thus, it is desired to have MD simulations for other nanostructured metals with different crystal structures other than fcc in the future.

Superplasticity and creep Both superplasticity (SP) and creep were observed in nanostructured metallic materials and in course grained metallic materials. The differences between the two deformation modes lie in the loading conditions: applied stress, strain rate, time duration and temperature. Nevertheless, the main deformation mechanism for both deformation modes remains in the grain boundary deformation regime. Since SP deformation occurs at higher strain rates and higher stresses while creep occurs under relatively low applied stress for a longer time frame, diffusion carries out the bulk of grain boundary deformation. One of the theories about GB sliding in SP deformation is that GB sliding is an operation of the sliding and rotation of entire grain groups along common sliding surfaces. The evidence of such a group sliding฀is฀the฀existence฀of฀steps฀along฀shear฀planes฀on฀a฀surface฀of฀post-deformed฀ materials.฀ Such฀ ‘cooperative฀ grain฀ boundary฀ sliding’฀ (CGBS)฀ was฀ observed฀ indirectly in Ni3Al,55 Pd56 and directly in Nano-Ni3Al.57฀For฀example,฀Ti-6Al-4V฀ with฀ a฀ grain฀ size฀ 100–200฀ nm฀ deformed฀ at฀ 725°฀ at฀ a฀ strain฀ rate฀ range฀ 10–1 to 10–3 s–1฀yielded฀an฀elongation฀more฀than฀500%,฀which฀is฀much฀higher฀than฀that฀in฀ the microcrystalline state.58฀It฀is฀logical฀to฀assume฀that฀higher฀diffusion฀lux฀as฀ a฀ component฀ of฀ CGBS฀ in฀ nanostructured฀ metallic฀ materials฀ would฀ assist฀ GB sliding while lack of intragranular dislocation activity in nanostructured

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metallic materials (NMM) may negatively influence the grain boundary sliding. But, the fundamental classical mechanisms for SP and creep appear to remain in฀ NMM.฀ Understanding฀ of฀ SP฀ and฀ creep฀ mechanisms฀ must฀ start฀ with฀ an฀ understanding of the GB sliding mechanisms in NMM. Nanostructured฀Ni฀(20–40฀nm฀grains)฀exhibits฀creep฀at฀RT.฀The฀test฀results฀well฀ it฀into฀the฀models฀of฀grain฀boundary฀sliding฀aided฀by฀grain฀boundary฀diffusion.59,60 Yin et al.61฀studied฀the฀creep฀of฀nano-Ni฀from฀RT฀to฀473฀K.฀The฀activation฀energy฀ calculated฀ from฀ the฀ temperature฀ dependence฀ curve฀ was฀ 92฀ kJ/mol,฀ which฀ is฀ activation energy for GB diffusion in Ni. Thus, at the moment, both grain boundary sliding and grain boundary diffusion can be considered as candidates for creep in nano-Ni in the temperature range RT to 473k. On the other hand, Yamakov et al.53 performed MD simulations for nano-Pd at elevated temperatures under high stresses assuming no grain growth. The results show฀that฀the฀creep฀was฀characterized฀as฀a฀Coble-type฀creep฀and฀GB฀sliding฀is฀an฀ accommodating mechanism for the creep. The simulations showed a linear dependence of the creep rate with the applied stress. But, the linear relationship was฀unable฀to฀extrapolate฀to฀a฀low฀temperature฀regime,฀e.g.฀RT.฀The฀questions฀ remain whether conditions of high stress and high strain rates at high temperatures used in the simulations can duplicate the real creep situation under low stress, low strain rate at low temperatures because different conditions would alter deformation mechanisms. It would take for a while for MD simulations to carry out creep deformation under reasonable conditions, because currently the limitations imposed on the computations are too severe. Another complication in analysing฀experimental฀data฀for฀creep฀is฀that฀in฀fact฀grain฀growth฀occurs฀in฀nanometals even at relatively low temperatures where the time duration for creep testing฀is฀signiicant฀for฀grain฀growth.฀Although฀both฀GB฀diffusion฀and฀GB฀sliding฀ are฀an฀integral฀part฀of฀the฀creep,฀it฀is฀dificult฀to฀determine฀which฀is฀the฀dominant฀ mechanism for a given stress and temperature at this time.

Fatigue Investigating the fatigue behavior of nanograined metals has rarely been done, mainly due to inadequate nanomaterial supply, and thus the majority of investigation฀has฀been฀focused฀on฀ultraine-grained฀(UFG)฀metals฀and฀alloys฀with฀ a฀grain฀size฀range฀of฀100฀nm–1฀µm.62 Nevertheless, an interesting earlier piece of work on fatigue in nanostructured Ni was reported by Hanlon et al.63฀ In฀ the฀ report,฀ nanocrystalline฀ (NC)฀ Ni฀ was฀ compared฀with฀UFC฀Ni฀and฀microcrystalline฀(MC)฀Ni฀with฀respect฀to฀its฀stresslife฀(S-N)฀fatigue฀behavior.฀NC฀Ni฀sheets฀with฀grain฀size฀20฀to฀40฀nm฀and฀UFC฀Ni฀ sheets฀with฀grain฀size฀300฀nm฀were฀prepared฀by฀electrodeposition฀technique.฀The฀ results฀show฀that฀the฀endurance฀limit฀signiicantly฀increased฀from฀MC฀Ni฀to฀both฀ UFC฀Ni฀and฀NC฀Ni.฀There฀is฀no฀appreciable฀difference฀between฀NC฀Ni฀and฀MC฀ Ni฀in฀terms฀of฀fatigue฀resistance.฀However,฀the฀fatigue฀growth฀rate฀of฀NC฀Ni฀is฀

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higher฀than฀that฀of฀UFC฀Ni,฀and฀much฀higher฀than฀that฀of฀MC฀Ni.฀Depending฀on฀ the฀ grain฀ size,฀ the฀ reinement฀ has฀ a฀ negative฀ inluence฀ on฀ fatigue฀ crack฀ growth฀ resistance. Despite some preliminary evidence for the fatigue properties of nanometals,฀it฀is฀critical฀to฀conduct฀similar฀experiments฀with฀specimens฀of฀artifactfree฀and฀controlled฀impurity฀concentration฀at฀GB฀to฀conirm฀these฀results.฀It฀is฀too฀ early to draw conclusions with only limited information. Fatigue฀ life฀ based฀ on฀ a฀ S-N฀ plot฀ for฀ pure฀ UFG฀ metals฀ –฀ copper,฀ nickel฀ and฀ aluminum฀ –฀ has฀ been฀ investigated.฀ The฀ results฀ show฀ a฀ signiicant฀ increase฀ in฀ fatigue฀life฀in฀all฀these฀UFG฀metals฀compared฀to฀those฀of฀the฀counterpart฀coarsegrained฀metals,฀primary฀due฀to฀the฀increase฀in฀strength฀in฀UFG฀metals.฀Nevertheless,฀ when฀ fatigue฀ life฀ is฀ regarded฀ with฀ respect฀ to฀ the฀ plastic฀ strain฀ amplitude.฀ UFG฀ metals฀ exhibit฀ a฀ deteriorated฀ fatigue฀ life฀ compared฀ to฀ their฀ coarse-grained฀ counterparts.฀ For฀ UFG฀ metals฀ crack฀ initiation฀ is฀ mostly฀ a฀ result฀ of฀ shear฀ band฀ formation฀and฀localized฀plastic฀deformation฀along฀these฀shear฀bands.฀Shear฀band฀ formation appears to be the dominant mechanism to SPD-processed materials at this฀ grain฀ size฀ range.64 But the key is the history of material processing, which would determine the microstructural characteristics and in turn has an influence on fatigue฀life.฀For฀example,฀SPD-processed฀UFG฀metals฀with฀a฀post-heat฀treatment฀ result in a bimodal microstructure, which has a positive influence on fatigue life.65

Applications In฀ the฀ coming฀ decades,฀ structural฀ applications฀ will฀ require฀ energy฀ eficient฀ materials,฀e.g.฀with฀high฀speciic฀strength,฀light฀weight฀and฀excellent฀durability.฀ From this vantage point, nanostructured metals should have a bright future. Nevertheless, the development of products requires long-term commitment by the industry, and the odds that a product under development successfully makes it into the marketplace are still statistically quite low. Currently,฀a฀few฀products฀of฀nanostructured฀metallic฀material฀have฀found฀their฀ way฀ into฀ the฀ marketplace.฀ For฀ example,฀ nanosurface฀ coatings฀ for฀ corrosion฀ protection and wear-resistant applications that are processed by electrodeposition, thermal spray and cold spray are already available for special applications. New nanostructured coating of cobalt-phosphorus alloy,66 as alternative to conventional hard฀ chrome฀ coating,฀ shows฀ excellent฀ wear฀ and฀ corrosion฀ properties.฀ Due฀ to฀ growing฀environmental฀concern฀about฀the฀health฀risks฀of฀hexavalent฀chromium,฀ this alternative looks attractive for practical applications. Thermal spraying of hard฀ metals฀ such฀ as฀ WC-Co67฀ and฀ Ti-oxide,฀ NiCrAlY62 by the high-velocity Oxyfuel฀(HVOF)฀processing฀yields฀high฀dense฀nanostructured฀coatings฀for฀wear฀ and corrosion applications. Nowadays, the structural materials for aerospace and automobile applications and any other applications that are tied to power consumption are increasingly required฀to฀be฀energy฀eficient.฀Riding฀the฀trend,฀there฀is฀considerable฀effort฀to฀ develop nanostructured steels that will meet such demands. But current effort has

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been฀focused฀on฀ultraine-grain฀(UFG)฀ferrite฀single-phase฀steels,69,70 multi-phase steels,71 and nanostructured Bainite steels.25 UFG฀ferrite฀steel฀can฀be฀processed฀by฀hot฀rolling,฀followed฀by฀cold฀rolling฀in฀a฀ conventional฀ way,฀ and฀ the฀ rolled฀ sheets฀ recrystallized฀ at฀ 525–700°C฀ for฀ two฀ minutes฀ in฀ a฀ salt฀ bath.฀ This฀ UFG฀ ferrite฀ steel฀ has฀ been฀ further฀ developed฀ into฀ UFG-multi-phase฀ steel฀ to฀ optimize฀ the฀ strength฀ and฀ ductility฀ balance฀ for฀ highstrength automobile body applications. The multi-phases in this steel include austenite, bainite and martensite, in addition to ferrite grains. For very high strength structural applications, nanostructured bainite steels containing Si, Mn and฀Cr฀would฀be฀economically฀attractive฀compared฀to฀expensive฀maraging฀steels.฀ These bainite steels have a yield strength of 1.4 GPa, a tensile strength of 2.2 GPa and฀fracture฀toughness฀(K1c) of 25 MPam1/2 at room temperature. Other฀ ultraine-grained฀ steel฀ materials฀ come฀ in฀ bar,฀ wire฀ and฀ strip฀ form.72 Ultraine-grained฀bars฀of฀low-carbon฀steel฀can฀be฀processed฀by฀multiple฀caliber฀ rolling฀at฀550°C฀and฀water฀quenching.฀Ultraine-grained฀wires฀were฀made฀using฀a฀ starting฀wire฀of฀6฀mm฀in฀diameter฀and฀by฀oval-square฀rolling฀repeatedly฀at฀500°C฀ until฀its฀diameter฀was฀reduced฀to฀3฀mm.฀The฀UF฀wires฀show฀a฀yield฀strength฀of฀ more than 800 MPa, compared to that of the starting wire of 400 MPa. All these steels฀are฀some฀of฀the฀examples฀currently฀under฀development.

References ฀ 1฀ ฀ 2฀ ฀ 3฀ ฀ 4฀ ฀ 5฀ ฀ 6฀ ฀ 7฀ ฀ 8฀ ฀ 9฀ 10฀ 11฀ 12฀ 13฀ 14฀ 15฀ 16฀ 17฀ 18฀ 19฀

Gleiter฀H.฀Prog฀Mater฀Sci฀1989;33:฀223. Gleiter฀H.฀Acta฀Mater฀2000;48:฀1–29. Guinier,฀A.,฀Preston,฀D.A.฀Nature฀1938;142:฀569–570. Embury฀J.D.,฀Fisher฀R.M.฀Acta฀Metall฀1966;14:฀147–159. Valiev฀R.Z.,฀Langdon฀T.G.฀Prog฀Mater฀Sci฀2006;51:฀881. Koch฀C.C.,฀editor,฀Nanostructured฀Materials฀–฀processing,฀properties฀and฀applications,฀ Noyes publications, William Andrew Publishing, Norwich, New York (2007). Meyers฀M.A.,฀Mishra฀D.J.,฀Benson฀D.J.฀Prog฀Mater฀Sci฀2006;51:฀427–556. Erbel฀S.฀Metals฀Tech฀1979;6:฀482. Langford฀G.,฀Cohen฀M.฀Trans.฀ASM฀1969;82:฀623. Saunders฀I.,฀Nutting฀J.฀Metal฀Sci฀1984;18:฀571. Segal฀V.M.,฀Mater฀Sci฀Eng฀1995;A197:฀157. Valiev฀ R.Z.,฀ Kaibyshev฀ O.A.,฀ Kuznetsov฀ R.I.,฀ Musalimov฀ R.Sh.,฀Tsenev฀ N.K.฀ Dokl฀ Akad฀Nauk฀SSSR฀(Reports฀of฀USSR฀Academy฀of฀Sciences)฀1988;301(4):฀864. Valiev฀R.Z.,฀Krasilnikov฀N.A.,฀Tsenev฀N.K.฀Mater฀Sci฀Eng฀฀A฀1991;137:฀35. Valiev฀R.Z.,฀Korznikov฀A.V.,฀Mulyukov฀R.R.฀Mater฀Sci฀Eng฀A฀1993;186:฀141. Valiev฀R.Z.,฀Islamgaliev฀R.K.,฀Alexandrov฀I.V.฀Prog฀Mater฀Sci฀2000;45:฀103. Ungár฀ T.,฀ Balogh฀ L.,฀ Zhu฀ Y.T.,฀ Horita฀ Z.,฀ Xu฀ C.,฀ Langdon฀ T.G.฀ Mater฀ Sci฀ Eng฀ A฀ 2007;444:฀153. Saito฀Y.,฀Utsunomiya฀H.,฀Tsuji฀N.฀and฀Sakai฀T.฀1999;47:฀579. Tsuji฀T.,฀Saito฀Y.,฀Lee฀S.H.,฀and฀Minamino฀Y.฀Adv.฀Eng.฀Mater,฀2003;5:฀338.฀฀ Bhadeshia฀ H.K.D.H.฀ High฀ strength฀ steels.฀ In฀ Charles฀ J.A.,฀ Greenwood฀ G.W.,฀ Smith฀ G.C.,฀ editors.฀ Future฀ Developments฀ in฀ Metals฀ and฀ Ceramics,฀ London,฀ Institute฀ of฀ Materials, 1992. p.25.

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29฀ 30฀ 31฀ 32฀ 33฀ 34฀ 35฀ 36฀ 37฀ 38฀ 39฀ 40฀ 41฀ 42฀ 43฀ 44฀ 45฀ 46฀ 47฀ 48฀ 49฀ 50฀ 51฀ 52฀ 53฀ 54฀ 55฀ 56฀ 57฀ 58฀ 59฀

Introduction

Bhadeshia฀H.K.D.H.,฀Harada฀H.฀Appl฀Sur฀Sci฀1993;฀67:฀328. Benjamin฀J.S.฀Metall฀Trans฀1970;1:฀2943. Fecht฀H.J.,฀Hellstern฀E.,฀Fu฀Z.,฀Johnson฀W.L.฀Metall฀Trans฀A฀1990;21:฀2333. Perez฀R.J.,฀Huang฀B.,฀Lavernia฀E.J.฀Nanostructure฀Mater฀1996;7:฀565. Brown฀T.L.,฀Saldana฀C.,฀Murthy฀T.G.,฀Mann฀J.B.,฀Compton฀W.D.,฀Trumble฀K.P.,฀King฀ A.H.,฀and฀Chandrasekar฀S.฀Acta฀Mater฀2009;57:฀5491. Caballero฀F.G.,฀Bhadeshia฀H.K.D.H.,฀Mawella฀J.A.,฀Jones฀D.G.,฀Brown฀P.฀Mater฀Sci฀ Technol฀2002;18:฀279. García-Mateo฀C.,฀Caballero฀F.G.,฀Bhadeshia฀H.K.D.H.฀ISIJ฀Int฀2003;43:฀1238. Perepezko฀J.H.฀and฀Hebert฀R.J.,฀J฀Metall฀2002;5:฀34. Kim฀G.E.฀Thermal฀Sprayed฀Nanostructured฀Coatings:฀Applications฀and฀Developments.฀ In฀Koch฀C.C.,฀editor,฀Chapter฀3,฀Nanostructured฀Materials฀Processing,฀Properties,฀and฀ Applications, 2nd Edition, William Andrew Publishing, 2007. Chokshi฀A.H.,฀Rosen฀A.,฀Karch฀J.,฀Gleiter฀H.฀Scripta฀Mater฀1989;23:฀1679. Fougere฀G.E.,฀Weertman฀J.R.,฀Siegel฀R.W.,฀Kim฀S.฀Scripta฀Metall฀Mater฀1992;26:฀1879. Embury฀J.D.,฀Keh฀A.S.,฀Fisher฀R.M.฀Trans฀Metall฀Soc฀AIME฀1966;236:฀1252. Hansen฀N.,฀Ralph฀B.฀Acta฀Metall฀1982;30:฀411. Nieman฀G.W.,฀Weertman฀J.R.,฀Siegel฀R.W.฀Scripta฀Metall฀1989;23:฀2013. Youssef฀K.M.,฀Scattergood฀R.O.,฀Murty฀K.L.,฀Horton฀J.A.,฀Koch฀C.C.฀Appl฀Phys฀Lett฀ 2005;87:฀091904. Cheng฀S.,฀Ma฀E.,฀Wang฀Y.M.,฀Kecskes฀L.J.,฀Youssef฀K.M.,฀Koch฀C.C.,฀Trociewitz฀U.P.,฀ Han฀K.฀Acta฀Mater฀2005;53:฀1521. Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Acta฀Mater฀2009;57:฀2217. Pande฀C.S.,฀Masumura฀R.A.,฀Armstrong฀W.฀Nanostruct฀Mater฀1993;2:฀323–331. Nieh฀T.G.,฀Wadsworth฀J.฀Scripta฀Metall฀Mater฀1991;25:฀955–958. Conrad฀H.,฀Narayan฀J.฀Scripta฀Mater฀2000;42:฀1025. Raj฀R.,฀Ashby฀M.฀J฀Met฀Tans฀1971;2A:฀1113. Fu฀H.H.,฀Benson฀D.J.,฀Meyers฀M.A.฀Acta฀Mater฀2001;49:฀2567–2582. Wang฀Y.M.,฀Ma฀E.,฀Chen฀M.W.฀Appl฀Phys฀Lett฀2002;80:฀2395–2397. Ovid’ko฀I.A.฀Science฀2002;295:฀2386. Murayama฀M.,฀Howe฀J.M.,฀Hidaka฀H.,฀Takaki฀S.฀Science฀2002;295:฀2433–2435. Wei฀Q.,฀Kecskes฀L.,฀Jiao฀T.,฀Hartwig฀K.T.,฀Ramesh฀K.T.,฀Ma฀E.฀Acta฀Mater฀2004;52:฀ 1859–1869. Valiev฀R.Z.,฀Islamgaliev฀R.K.,฀Alexandrov฀I.V.฀Prog฀Mater฀Sci฀2000;45:฀103. Kim฀H.S.,฀Estrin฀Y.,฀Bush฀M.B.฀Acta฀Mater฀2000;42:฀493–504. Yamakov฀V.,฀Wolf฀D.,฀Phillpot฀S.R.,฀Gleiter฀H.฀Acta฀Mater฀2002;50:฀5005. Chen฀M.฀et al.฀Science฀2003;300:฀1275. Kadau฀K.฀et al.฀Metall฀Mater฀Trans฀2004;฀35A:฀2719. Shiiotz฀J.,฀Di฀Tolla฀F.D.,฀Jacobson฀K.W.฀Phys฀Rev฀B฀1999;60:฀11,971. Swygenhoven฀H.V.,฀Spaczer฀M.,฀Caro฀A.,฀Farkas฀D.฀Phys฀Rev฀B฀1999;60:฀22. Yamakov฀V.,฀Wolf฀D.,฀Phillpot฀S.R.,฀Gleiter฀H.฀Acta฀Mater฀2002;50:฀61. Swygenhoven฀H.V.,฀Farkas฀D.,฀Caro฀A.฀Phys฀Rev฀B฀2000;62:฀831. Zelin฀M.G.,฀Mukherjee฀A.K.,฀Acta฀Metall฀Mater฀1995;45:฀2359. Markmann฀J.,฀Bunzel฀P.,฀Rosner฀H.฀Scripta฀Mater฀2003;49:฀637. Sergueeva฀A.V.,฀Mara฀N.A.,฀Krasilnikov฀N.A.,฀Valiev฀R.Z.,฀Mukherjee฀A.K.฀Phil฀Mag฀ 2006;86:฀5797. Sergueeva฀ A.V.,฀ Stolyarov฀ V.V.,฀ Valiev฀ R.Z.,฀ Mukherjee฀ A.K.฀ Mater฀ Sci฀ Eng฀ A฀ 2002;323:฀318. Cai฀B.,฀Kong฀Q.P.,฀Cui฀P.,฀Lu฀L.,฀Lu฀K..฀Scripta฀Mater฀2001;45:฀1407.

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60฀ Sanders฀P.G.,฀Eastman฀J.A.,฀Weertman฀J.R.฀Acta฀Mater฀1997;10:฀4019. 61฀ Yin฀W.M.,฀Whang฀S.H.฀JOM฀2005;1:฀63. 62฀ Höppel฀H.W.,฀Kautz฀M.,฀Xu฀C.,฀Murashkin฀M.,฀Langdon฀T.G.,฀Valiev฀R.Z.,฀Mughrabi฀ H.:฀Int฀J฀Fatigue฀2006,28:฀1001. 63฀ Hanlon฀T.,฀Kwon฀Y.N.,฀Suresh฀S.฀Scripta฀Mater฀2003;49:฀675–680. 64฀ Mughrabi฀H.,฀Höppel฀H.W.฀In:฀Farkas฀D.,฀Kung฀H.,฀Mayo฀M.,฀v.฀Swygenhoven฀H.,฀ Weertman฀ J.,฀ editors.฀ Structure฀ and฀ mechanical฀ properties฀ of฀ nanophase฀ materialstheory฀ and฀ computer฀ simulation฀ vs.฀ experiment,฀ Mat฀ Res฀ Soc฀ Symp฀ Proc฀ Vol฀ 634,฀ Materials฀Research฀Society;฀2001;฀p.฀B฀2.1.1. 65฀ Höppel฀H.W.,฀Valiev฀R.Z.฀Z฀Metallkunde฀2002;93:฀641. 66฀ Erb฀U.,฀El-Sherik฀A.M.฀US฀Patent฀No.฀5,352,266฀(1994). 67฀ He฀J.,฀Ice฀M.,฀Dallek฀S.,฀Lavernia฀E.J.฀Metall฀and฀Mater฀Trans฀A฀2000;31A:฀541. 68฀ Ajdelsztajn฀ L.,฀ Picas฀ J.A.,฀ Kim฀ G.E.,฀ Bastian฀ F.L.,฀ Schoenung฀ J.M.,฀ Provenzano฀ V.฀ Mater฀Sci฀Eng฀2002;A338:฀33. 69฀ Tsuji฀N.,฀Ito฀Y.,฀Saito฀Y.,฀Minamino฀Y.฀Scripta฀Mater฀2002;47:฀893. 70฀ Tsuji฀N.,฀Okuno฀S.,฀Koizum฀Y.,฀Minamino฀Y.฀Mater฀Trans฀2004:45:฀2272. 71 Okitsu Y., Naito T., Takaki N., Sugiura T., Tsuji N. SAE Technical Paper 2010:201001-0438. 72฀ Ohmori฀ A.,฀ Torizuka฀ S.,฀ Nagai฀ K.,฀ Koseki฀ N.,฀ Kogo฀ Y.฀ Tetsu-to-Hagane,฀ 8(2003):฀ 781–788.

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1 Producing bulk nanostructured metals and alloys by severe plastic deformation (SPD) R.Z. VALIEV, Ufa฀State฀Aviation฀Technical฀University,฀Russia

Abstract: Despite its promise, the use of nanostructured metals and alloys as a new generation of structural and functional materials has only recently been realized.฀Only฀in฀recent฀years฀has฀a฀breakthrough฀been฀made฀in฀this฀area,฀ associated both with developing new methods for fabricating bulk nanostructured materials and with investigating the fundamental mechanisms that lead to novel properties in these materials. This chapter presents new concepts and principles in using severe plastic deformation (SPD) techniques to fabricate bulk nanostructured metals with advanced properties. Special emphasis is laid on analysing of the effect of the microstructural features of nanostructured materials fabricated by SPD on mechanical properties such as strength and ductility, fatigue strength and life, and superplasticity, as well as describing฀early฀examples฀of฀their฀innovative฀applications. Key words: bulk nanostructured materials, severe plastic deformation, advanced properties, strength and ductility, equal-channel angular pressing, high pressure torsion.

1.1

Introduction

The฀concept฀of฀‘large฀plastic฀strains’,฀or฀deformations฀that฀are฀characterized฀by฀a฀ high value of true accumulated strain (e ≥฀0.5)฀and฀are฀realized฀at฀relatively฀low฀ temperature (≤ 0.4 melting point), is widely used in the branches of physics and mechanics that deal with the problems of strength and ductility of solid states.1–3 Large฀plastic฀deformations฀are฀actively฀engaged฀in฀practice,฀for฀example,฀in฀metal฀ forming for shaping in the process of manufacturing semi-products and parts as well as for materials hardening. Traditionally, such methods of metal forming as drawing,฀extrusion,฀rolling฀and฀others฀are฀used฀for฀these฀purposes.฀Experimental฀ methods for achieving very large strains are usually based on the rolling of strips or฀thin฀foils,฀e.g.฀with฀initial฀thickness฀of฀~10฀mm฀up฀to฀a฀inal฀one฀of฀~0.1฀mm,฀ which฀is฀equivalent฀to฀a฀99%฀reduction฀in฀thickness฀(true฀strain฀e฀=฀4.6).฀Therefore,฀ true strains 4–4.5 are critical for shaping bulk billets by conventional metal forming methods, and as it was noticed in earlier works, the achievement of larger strains requires radically different processing techniques.4 It was suggested4,5 that such techniques may comprise the die-sets combining shear (torsion) and compression straining as they make it possible to deform the material without changing its form. Fracture in material is another problem encountered when achieving super-high strains.฀As฀ is฀ known,฀ many฀ metallic฀ materials฀ are฀ exposed฀ to฀ quick฀ fracture฀ at฀ room temperature even in the early stages of deformation. However, it is possible 3 © Woodhead Publishing Limited, 2011

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to increase the deformability of metals and alloys by imposing hydrostatic pressure.฀The฀phenomenon฀was฀irst฀studied฀in฀detail฀by฀P.W.฀Bridgman฀(Harvard฀ University),฀who฀was฀awarded฀the฀Nobel฀Prize฀for฀Physics฀in฀1946฀for฀his฀works฀ in the sphere of high pressure.6 In฀ the฀ 1980s฀ these฀ ideas฀ were฀ realized฀ by฀ Polish4 and Russian scientists from Yekaterinburg,฀(formerly฀Sverdlovsk,฀USSR)7฀in฀creating฀experimental฀die-sets฀for฀ combined torsion and compression. The application of these devices achieved very large฀ strains฀ with฀ true฀ strains฀ exceeding฀ 8–10,฀ which฀ resulted฀ in฀ strong฀ grain฀ reinement฀ in฀ metals.฀ The฀ basic฀ work฀ was฀ performed฀ by฀ scientists฀ in฀ Ufa฀ in฀ 1988,8฀where฀this฀method฀was฀demonstrated฀for฀the฀irst฀time,฀of฀producing฀ultrainegrained฀ (UFG)฀ metals฀ and฀ alloys฀ with฀ high-angle฀ grain฀ boundaries฀ that฀ led฀ to฀ new properties. The latter was evidenced by revealing the so-called ‘low-temperature superplasticity’฀in฀an฀UFG฀Al฀alloy.฀Later,฀in฀1991฀UFG฀materials฀were฀irst฀obtained฀ by฀means฀of฀another฀technique฀–฀equal-channel฀angular฀pressing฀(ECAP),9 during which the billet shape is also preserved and therefore very large strains are achieved by฀multi-pass฀processing.฀As฀demonstrated฀below,฀ECAP฀allows฀the฀production฀of฀ UFG฀ structures฀ in฀ bulk฀ billets฀ from฀ different฀ metals฀ and฀ alloys.฀ Moreover,฀ the฀ technique is very promising for practical applications. This new approach to grain reinement,฀based฀on฀the฀achievement฀of฀very฀large฀true฀strains฀with฀e฀≥ 6–8 under high pressure, was termed ‘severe plastic deformation’ (SPD)10 and attracted much attention with the further development of many SPD techniques.11–13 Besides, SPD processing฀ routes฀ and฀ regimes฀ for฀ grain฀ reinement฀ were฀ established฀ for฀ various฀ metals and alloys.14฀ More฀ complete฀ deinitions฀ of฀ SPD฀ processing฀ and฀ ultrainegrained฀ (UFG)฀ materials฀ are฀ presented฀ in฀ several฀ recent฀ overviews.11,12,15,16 It is important฀to฀emphasize฀that฀SPD-produced฀UFG฀materials฀are฀fully฀dense฀and฀their฀ large geometric dimensions make it possible to study their properties thoroughly by means฀of฀mechanical฀and฀other฀tests.฀As฀a฀result,฀the฀subject฀of฀bulk฀ultraine-grained฀ materials฀ produced฀ by฀ severe฀ plastic฀ deformation฀ was฀ introduced฀ into฀ scientiic฀ literature.฀The฀ next฀ important฀ step฀ along฀ with฀ the฀ formation฀ of฀ UFG฀ was฀ inding฀ nanostructural features in SPD-processed metals (non-equilibrium grain boundaries, dislocation substructures, segregations and nanoparticles and other elements) resulting in novel properties16 (see also section 1.3.3, this chapter). At this time, the fabrication of bulk nanostructured materials by SPD is becoming one of the most actively฀developing฀areas฀in฀the฀ield฀of฀nanomaterials.12,17 The present chapter considers new trends in the development of SPD techniques, basic requirements for processing nanostructured materials with enhanced properties by means of SPD, and prospects for their practical applications.

1.2

The principles of severe plastic deformation (SPD) processing

Since฀ the฀ pioneering฀ work฀ on฀ tailoring฀ ultraine-grained฀ structures฀ by฀ SPD฀ processing,9,10 two SPD techniques have attracted close attention and have

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Producing bulk nanostructured metals and alloys by SPD

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recently been further developed. These techniques are high-pressure torsion (HPT)16,18฀and฀equal-channel฀angular฀pressing฀(ECAP).16,19 In the last 10 to 15 years฀there฀have฀appeared฀a฀wide฀diversity฀of฀new฀SPD฀techniques:฀for฀example,฀ accumulative฀roll฀bonding฀(ARB),฀multi-axial฀forging,฀twist฀extrusion฀and฀others฀ (see฀other฀chapters฀for฀details).฀Nevertheless,฀processing฀by฀HPT฀and฀ECAP฀has฀ remained the most popular approach and has recently acquired a new impulse for development฀through฀the฀modiication฀of฀conventional฀die-sets฀and฀demonstrations฀ that new opportunities are now available for involving these procedures in processing (see References 15, 18, 19). The fundamental principles of these two techniques are illustrated schematically in Fig. 1.1. Samples processed under HPT are disc-shaped (Fig. 1 (a) ). In this process, the sample, with a diameter ranging from 10–20 mm and thickness of 0.3–0.8 mm, is placed between anvils and compressed under an applied pressure (P) of several GPa. The lower anvil turns and friction forces lead to a shear straining of the sample.฀Under฀high฀pressure,฀the฀deforming฀sample฀does฀not฀break฀even฀at฀high฀ strains.16 In฀HPT,฀an฀essential฀microstructural฀reinement฀is฀observed฀after฀deformation฀ through฀ one-half฀ or฀ one฀ complete฀ (360°)฀ turn.฀ But฀ to฀ produce฀ a฀ homogeneous฀ nanostructure,฀with฀a฀typical฀grain฀size฀of฀about฀100฀nm฀or฀less,฀deformation฀by฀ several turns is necessary (Fig. 1.2). The important role of applied pressure in the formation of a more homogeneous nanostructured state during HPT is also shown in recent work on nickel.20 Among different SPD techniques, HPT particularly

1.1 Principles of severe plastic deformation: (a) High-pressure torsion: a sample is held between anvils and strained in torsion under an applied pressure (P); (b) Equal-channel angular pressing: a work piece is repeatedly pressed through a special die.

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1.2 Transmission electron microscopy images of ultrafine-grained copper: (a) Copper processed by HPT at room temperature (P = 6 GPa, 5 turns); (b) Copper processed by ECAP (12 passes).

enables฀ a฀ reinement฀ of฀ the฀ microstructure฀ with฀ maximum฀ eficiency฀ and฀ often฀ forms฀a฀UFG฀structure฀with฀a฀grain฀size฀less฀than฀100฀nm.16,18 For this reason, HPT฀ is฀ now฀ widely฀ used฀ as฀ an฀ experimental฀ technique฀ for฀ grain฀ reinement฀ in฀ different laboratories all over the world. Moreover, in recent years it has been further฀developed฀by฀enlarging฀the฀size฀of฀specimens21,22 and by processing ringshaped samples23. Processing฀by฀ECAP฀(Fig.฀1.1฀(b)฀)฀is฀now฀also฀the฀most฀established฀procedure฀ for use with different metals and alloys and it is a very attractive technique for several฀reasons.฀First,฀it฀is฀relatively฀easy฀to฀set฀up฀and฀use฀an฀ECAP฀die.฀Second,฀ exceptionally฀high฀strains฀may฀be฀imposed฀either฀through฀repetitive฀pressing฀of฀ the same sample or by developing special multi-pass dies,24 rotary dies25 or sideextrusion฀facilities.26฀Third,฀although฀ECAP฀is฀generally฀used฀with฀samples฀in฀the฀ form฀of฀bars฀or฀rods,฀the฀process฀may฀be฀applied฀also฀to฀plate฀samples:฀for฀example,฀ a฀recent฀report฀described฀the฀application฀of฀ECAP฀to฀an฀aluminum฀plate.27 Fourth, ECAP฀can฀be฀incorporated฀into฀conventional฀rolling฀mills฀for฀use฀in฀continuous฀ processing28–31฀ or฀ into฀ the฀ ECAP-conform฀ process฀ for฀ the฀ production฀ of฀ longsized฀rods฀and฀wires.32 In view of these many advantages, special attention has been฀paid฀recently฀to฀the฀principles฀of฀processing฀through฀the฀use฀of฀ECAP฀(see฀ the reviews16,19,33). The฀ECAP฀technique฀was฀introduced฀by฀V.฀Segal฀et al. in 1981 as a technique for straining by a simple shear,34 however, as noted above, it was developed and irst฀applied฀for฀producing฀UFG฀metals฀only฀in฀the฀early฀1990s.9,10 Figure฀1.3฀shows฀a฀schematic฀illustration฀of฀the฀ECAP฀procedure.35 A die is constructed containing a channel that is bent through an abrupt angle – this angle is฀90°฀in฀Fig.฀1.3.฀A฀sample฀is฀machined฀to฀it฀in฀the฀channel฀and฀the฀sample฀is฀then฀ pressed through the die using a plunger. It is apparent from the illustration that the sample has the same cross-sectional dimensions before and after pressing, thereby

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1.3 The principle of ECAP processing, including a definition of the three orthogonal planes X, Y and Z.35

permitting repetitive pressings of the same sample. It is important to note also that฀retaining฀the฀same฀cross-sectional฀area฀differentiates฀processing฀by฀ECAP฀in฀ a฀ very฀ signiicant฀ way฀ from฀ more฀ conventional฀ industrial฀ processes,฀ such฀ as฀ rolling,฀extrusion฀or฀drawing,฀where฀the฀sample฀dimensions฀are฀reduced฀in฀each฀ consecutive pass. Three orthogonal planes are illustrated in Fig. 1.3, where X is the transverse plane perpendicular to the flow direction, Y is the flow plane parallel to฀the฀side฀face฀at฀the฀point฀of฀exit฀from฀the฀die฀and฀Z฀is฀the฀longitudinal฀plane฀ parallel฀to฀the฀top฀surface฀at฀the฀point฀of฀exit฀from฀the฀die. The strain imposed on the sample in each passage through the die depends primarily upon the angle, Φ,฀between฀the฀two฀parts฀of฀the฀channel฀(90°฀in฀Fig.฀1.3)฀ and฀also฀to฀a฀minor฀extent฀upon฀the฀angle฀of฀curvature,฀Ψ, representing the outer arc฀ of฀ curvature฀ where฀ the฀ two฀ channels฀ intersect฀ (0°฀ in฀ Fig.฀ 1.3).฀ To฀ achieve฀ optimum฀results,฀ECAP฀is฀generally฀conducted฀using฀a฀die฀having฀a฀channel฀angle฀ of Φ฀=฀90°19,36฀and฀with฀this฀coniguration฀it฀can฀be฀shown฀from฀irst฀principles฀ that฀for฀these฀angles฀the฀imposed฀strain฀on฀each฀pass฀is฀approximately฀equal฀to฀ 1฀ with฀ only฀ a฀ small,฀ and฀ almost฀ insigniicant,฀ Ψ depending upon the arc of curvature.34,37

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1.4 The four processing routes in ECAP.24

When samples are pressed repetitively, different slip systems may be introduced by฀rotating฀the฀samples฀about฀the฀X-axis฀between฀consecutive฀passes฀through฀the฀ die.฀In฀practice,฀four฀separate฀processing฀routes฀have฀been฀identiied฀for฀use฀in฀ ECAP:฀ route฀ A฀ in฀ which฀ the฀ sample฀ is฀ pressed฀ repetitively฀ without฀ rotation฀ between฀passes;฀route฀BA฀in฀which฀the฀sample฀is฀rotated฀through฀90°฀around฀the฀ extrusion฀axis฀in฀alternate฀directions฀between฀each฀pass;฀route฀BC in which the sample฀is฀rotated฀by฀90°฀in฀the฀same฀sense฀between฀each฀pass;฀and฀route฀C฀where฀ the฀sample฀is฀rotated฀by฀180°฀between฀passes.38 These different processing routes are illustrated schematically in Fig. 1.4 and the distinction between these routes is important because the various routes introduce different shearing patterns into the samples39 leading to variations both in the macroscopic distortions of the individual grains in polycrystalline matrices40 and in the capability to develop a reasonably฀homogeneous฀and฀equiaxed฀ultraine-grained฀microstructure.16,19,41–43

1.3

New trends in SPD processing for effective grain refinement

1.3.1 Development of SPD techniques and routes Since฀high-pressure฀torsion฀and฀equal-channel฀angular฀pressing฀were฀irst฀used฀to฀ produce฀ UFG฀ metals฀ and฀ alloys,9,10 processing regimes and routes have been established for many metallic materials, including some low-ductility and hardto-deform฀ materials.฀ High-pressure฀ torsion฀ and฀ ECAP฀ die฀ sets฀ have฀ also฀ been฀ essentially฀modernized.19,44,45

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However, to date these techniques have been usually used for laboratory-scale research.฀The฀requirement฀of฀economically฀feasible฀production฀of฀ultraine-grained฀ metals฀ and฀ alloys฀ essential฀ to฀ successful฀ commercialization฀ raises฀ several฀ new฀ problems in the development of the SPD techniques. Highest priority tasks include reducing the material waste, obtaining uniform microstructure and properties in bulk฀billets฀and฀products,฀and฀increasing฀the฀eficiency฀of฀SPD฀processing. The฀ solution฀ for฀ these฀ tasks฀ has฀ been฀ found฀ by฀ developing฀ continuous฀ ECA฀ pressing32 and multi-step combined SPD processing46,47 for fabrication of longsized฀rods฀aimed฀at฀setting฀aimed฀at฀setting฀up฀production฀of฀nanostructured฀Ti฀ materials for medical applications48 and, later, other metals. Some recent results of these works are presented below. Continuous equal-channel angular (ECA) pressing So฀far,฀of฀all฀SPD฀techniques,฀equal-channel฀angular฀pressing฀(ECAP),฀also฀known฀ as฀equal-channel฀angular฀extrusion฀(ECAE),49 has attracted most attention, because it฀is฀very฀effective฀in฀producing฀UFG฀structures฀and฀can฀be฀used฀to฀produce฀UFG฀ billets฀that฀are฀suficiently฀large฀for฀various฀structural฀applications.16,19,44,45 However,฀the฀ECAP฀technique฀in฀its฀original฀design฀has฀some฀limitations,฀in฀ particular,฀a฀relatively฀short฀length฀of฀work฀piece฀that฀makes฀ECAP฀a฀discontinuous฀ process฀with฀low฀production฀eficiency฀and฀high฀cost.฀In฀addition,฀the฀ends฀of฀a฀ work piece usually contain non-uniform microstructure or macro-cracks and have to฀be฀thrown฀away,฀thus฀a฀signiicant฀portion฀of฀the฀work฀piece฀is฀wasted฀and฀the฀ cost฀of฀the฀UFG฀materials฀produced฀by฀ECAP฀is฀further฀increased. The฀key฀to฀wide฀commercialization฀of฀UFG฀materials฀is฀to฀lower฀their฀processing฀ cost and waste through continuous processing. Several attempts have been made to this฀ end.฀ For฀ example,฀ repetitive฀ corrugation฀ and฀ straightening50,51 have been developed recently to process metal sheets and rods in a continuous manner. The co-shearing process28 and the continuous constrained strip shearing process29 were recently฀also฀reported฀for฀continuous฀processing฀of฀thin฀strips฀and฀sheets฀with฀UFG฀ structures. However, the question of further improving microstructure uniformity and properties remains topical in the development of these techniques. In฀our฀studies฀we฀have฀worked฀on฀combining฀the฀Conform฀process52฀with฀ECAP฀ to฀continuously฀process฀UFG฀materials฀for฀large-scale฀commercial฀production.32 In this invention, the principle used to generate frictional force to push a work piece฀through฀an฀ECAP฀die฀is฀similar฀to฀the฀Conform฀process,฀while฀a฀modiied฀ ECAP฀die฀design฀is฀used฀so฀that฀the฀work฀piece฀can฀be฀processed฀repetitively฀to฀ produce฀UFG฀structures. We฀have฀designed฀and฀constructed฀an฀ECAP-Conform฀set-up฀that฀is฀schematically฀ illustrated฀in฀Fig.฀1.5.฀As฀shown฀in฀the฀igure,฀a฀rotating฀shaft฀in฀the฀center฀contains฀ a groove, into which the work piece is fed. The work piece is driven forward by frictional forces on the three contact interfaces with the groove, which makes the work piece rotate with the shaft. The work piece is constrained to the groove by a

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1.5 A schematic illustration of an ECAP-Conform set-up.

stationary constraint die. The stationary constraint die also stops the work piece and forces฀ it฀ to฀ turn฀ an฀ angle฀ by฀ shear฀ as฀ in฀ a฀ regular฀ ECAP฀ process.฀ In฀ the฀ current฀ set-up,฀the฀angle฀is฀about฀90°,฀which฀is฀the฀most฀commonly฀used฀channel฀intersection฀ angle฀ in฀ ECAP.฀ This฀ set-up฀ effectively฀ makes฀ ECAP฀ continuous.฀ Other฀ ECAP฀ parameters (die angle, strain rate, etc.) can also be used. In our recent work32฀we฀used฀commercially฀pure฀(99.95%)฀coarse-grained฀long฀Al฀ wire with a diameter of 3.4 mm and more than 1 m in length for processing at room temperature฀with฀1–4฀passes฀using฀ECAP฀with฀route฀C,฀i.e.฀the฀sample฀was฀rotated฀ 180°฀between฀ECAP฀passes.฀The฀starting฀Al฀wire฀had฀a฀grain฀size฀of฀5–7฀µm. Figure฀1.6฀shows฀an฀Al฀work฀piece฀at฀each฀stage฀of฀the฀ECAP-Conform฀process,฀ from฀ the฀ initial฀ round฀ feeding฀ stock฀ to฀ rectangular฀Al฀ rod฀ after฀ the฀ irst฀ ECAP฀ pass. As shown, the rectangular cross-section was formed shortly after the wire entered the groove (see the arrow mark). The change is driven by the frictional force between the groove wall and the Al work piece. The frictional force pushes the wire forward, and deforms the wire to make it conform to the groove shape. After the wire cross-section changes to the square shape, the frictional force per unit of wire length increases because of the greater contact area between the groove and the wire. The total frictional force pushes the wire forward from the groove฀into฀the฀stationary฀die฀channel,฀which฀intersects฀the฀groove฀at฀a฀90°฀angle.฀ This฀ part฀ of฀ the฀ straining฀ process฀ is฀ similar฀ to฀ that฀ in฀ the฀ conventional฀ ECAP฀ process. Transmission฀electron฀microscopy฀observations฀have฀shown฀that฀the฀ECAPConform฀ has฀ led฀ to฀ microstructure฀ evolution฀ typical฀ of฀ the฀ ECAP฀ process.41,53 Figure฀ 1.7฀ clearly฀ indicates฀ that฀ the฀ ECAP-Conform฀ process฀ can฀ effectively฀

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1.6 An Al work piece in the process of ECAP-Conform.

1.7 A TEM micrograph from the longitudinal section of Al wire processed by ECAP-Conform with four passes.

reine฀grains฀and฀produce฀UFG฀structures฀in฀Al฀and฀now฀in฀CP฀(commercially฀ pure) Ti.45 The tensile mechanical properties of the as-processed Al samples after 1 to 4 passes฀are฀listed฀in฀Table฀1.1.฀It฀is฀obvious฀that฀the฀ECAP-Conform฀process฀has฀ signiicantly฀increased฀the฀yield฀strength฀(σ0.2) and the ultimate tensile strength (σu),

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Table 1.1 Yield strength σ0.2, ultimate tensile strength σu, elongation to failure δ, and cross-section reduction (necking) ψ of Al samples processed with 1 to 4 passes Processing state

σ0.2, (MPa)

σu, (MPa)

δ, (%)

ψ, (%)

Initial Al rod After 1 pass After 2 passes After 3 passes After 4 passes

47 130 140 130 140

71 160 170 160 180

28 13 12 14 14

86 73 72 76 76

while฀ preserving฀ a฀ high฀ elongation฀ to฀ failure฀ (ductility)฀ of฀ 12–14%.฀ These฀ results฀are฀consistent฀with฀those฀of฀Al฀processed฀by฀conventional฀ECAP.41 We also found฀ that฀ for฀ Ti,฀ the฀ strength฀ increased฀ by฀ more฀ than฀ twice฀ after฀ the฀ ECAP฀ processing as compared to the untreated Ti, and the same is true for Ti subjected to conventional฀ECAP. Thus,฀ the฀ newly฀ developed฀ continuous฀ SPD฀ technique,฀ ECAP-Conform฀ can฀ successfully฀produce฀UFG฀materials.฀The฀continuous฀nature฀of฀the฀process฀makes฀ it฀promising฀for฀producing฀UFG฀materials฀on฀a฀large฀scale,฀in฀an฀eficient฀and฀costeffective manner. However, further study is needed to investigate its ability with respect฀to฀grain฀reinement฀and฀properties฀improvement฀of฀various฀UFG฀materials. Combined SPD processing In solving the problem of fabrication of nanostructured Ti materials for medical applications,฀we฀showed฀the฀advantage฀of฀combining฀ECAP฀with฀other฀techniques฀ of฀metal฀forming฀such฀as฀rolling,฀forging฀or฀extrusion.54,55 The advantages include effective shaping of long semi-products such as sheets, rods, etc as well as further enhancement฀of฀mechanical฀properties฀of฀UFG฀materials.฀For฀example,฀in฀Grade฀ 2฀CP฀Ti฀high-strength฀(YS฀=฀980฀MPa,฀UTS฀=฀1100฀MPa)฀with฀elongation฀to฀ failure δ฀ =฀ 12%฀ was฀ attained฀ using฀ ECAP฀ and฀ extrusion.฀ Also฀ the฀ results฀ of฀ investigations on processing of Ti rods of over 800 mm in length and 6.5 mm in diameter฀by฀a฀combination฀of฀ECAP฀and฀thermomechanical฀treatment฀including฀ forging and rolling are very impressive.46,47 Figure฀1.8฀presents฀TEM฀micrographs฀of฀commercially฀pure฀(CP)฀Ti฀subjected฀ to฀ECAP฀and฀thermomechanical฀treatment฀at฀80%.฀It฀can฀be฀seen฀that฀combined฀ processing฀results฀in฀signiicant฀additional฀grain฀reinement฀down฀to฀100฀nm฀in฀ comparison฀with฀300–400฀nm฀after฀ECAP;฀however,฀a฀considerable฀elongation฀ of฀ grains฀ takes฀ place.฀ Mechanical฀ testing฀ showed฀ (Table฀ 1.2)฀ that฀ in฀ CP฀ Ti,฀ thermomechanical฀treatment฀after฀ECAP฀results฀not฀only฀in฀an฀increase฀in฀strength฀ and recorded values of σ0.2 and σu,฀but฀also฀suficient฀ductility฀is฀preserved.฀It฀is฀ important฀that฀these฀strength฀values฀of฀nanostructured฀CP฀Ti฀are฀visibly฀higher฀

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1.8 Transmission electron microscopy micrographs displaying the microstructure of Grade 2 Ti after ECAP + TMT, 80%: (a) cross section; (b) longitudinal section. Table 1.2 Mechanical properties of the Ti billets at different stages of processing State

σu, (MPa)

σ0.2, (MPa)

δ, (%)

ψ, (%)

Initial ECAP 4 passes ECAP 4 passes + TMT ε = 80%

440 630 1150

370 545 1100

38 22 11

60 51 56

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than฀ that฀ of฀ the฀ Ti-6%Al-4%V฀ alloy,฀ which฀ is฀ widely฀ used฀ in฀ structural฀ and฀ medical applications. It is also interesting that the microstructure and properties of the obtained rods are rather uniform, the dispersion of mechanical properties along the rod length does฀not฀exceed฀±5%.47

1.3.2 Processing of bulk nanocrystalline materials Since฀the฀irst฀works฀dating฀back฀to฀the฀early฀1990s9,10 severe plastic deformation techniques have been used mostly for coarse-grained metals in order to produce ultraine-grained฀materials฀through฀microstructure฀reinement.฀The฀inal฀grain฀size฀ produced depends strongly on both processing regimes and the type of material. For฀pure฀metals฀the฀mean฀grain฀size฀is฀typically฀about฀100–200฀nm฀after฀processing฀ by฀HPT฀(high-pressure฀torsion)฀and฀about฀200–300฀nm฀after฀processing฀by฀ECAP.฀ For฀alloys฀and฀intermetallics฀the฀grain฀size฀is฀usually฀even฀iner฀and฀in฀some฀cases฀ as฀ine฀as฀50–100฀nm.฀However,฀it฀is฀very฀important฀for฀fundamental฀tasks฀and฀ many advanced applications to have bulk nanocrystalline materials with a mean grain฀ size฀ less฀ than฀ 30–50฀ nm.฀ Is฀ it฀ possible฀ to฀ produce฀ such฀ materials฀ using฀ SPD techniques? In recent years this problem has become the object of special investigations and two approaches have been proposed:16;56 SPD consolidation of nanopowders฀and฀SPD-induced฀nanocrystallization฀of฀amorphous฀alloys. SPD consolidation Already in the early work on SPD consolidation of powders57,58 it was revealed that HPT with high pressures of several GPa can provide a rather high density close฀to฀100%฀in฀the฀processed฀disc-type฀nanostructured฀samples.฀For฀fabricating฀ such samples via high-pressure torsion, the consolidation of both conventional powders and powders prepared by ball milling can be used. HPT consolidation of nanostructured Ni and Fe powders prepared by ball milling57,58฀can฀be฀taken฀as฀an฀example.฀The฀conducted฀investigations฀showed฀that฀ the density of the samples processed at room temperature was very high and close to฀ 95%฀ of฀ the฀ theoretical฀ density฀ of฀ bulk฀ coarse-grained฀ metals.฀ After฀ HPT฀ consolidation฀at฀200°฀or฀400°C฀the฀samples’฀density฀was฀even฀higher฀and฀reached฀ 98%.฀ Transmission฀ electron฀ microscopy฀ examinations฀ showed฀ the฀ absence฀ of฀ porosity.฀The฀mean฀grain฀size฀is฀very฀small;฀it฀is฀equal฀to฀17฀nm฀and฀20฀nm฀for฀Ni฀ and Fe, respectively. It is also very interesting to note that the value of microhardness of฀ the฀ Ni฀ samples฀ produced฀ by฀ HPT฀ consolidation฀ was฀ 8.60฀ ±฀ 0.17฀ GPa,฀ the฀ highest value of microhardness mentioned in literature for nanocrystalline Ni. SPD-induced nanocrystallization Recent฀investigations฀also฀show฀that฀SPD฀processing฀can฀control฀crystallization฀ of amorphous alloys that may result in the formation of bulk nanocrystalline

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alloys฀with฀an฀ultraine฀grain฀size฀and฀new฀properties.56,59 Recently this approach has also been used to produce and investigate nanocrystalline Ti-Ni alloys, widely known as alloys with shape memory effects. For this investigation, two alloys of the Ti-Ni system were used: melt-spun Ti50Ni25Cu25 alloy59,60 and cast Ti49.4Ni50.6 alloy.61,62 The amorphous structure of Ti50Ni25Cu25฀ alloy฀ was฀ conirmed฀ by฀TEM฀ and฀ X-ray diffraction (Fig. 1.9 and 1.10).59,60 However, when the alloy was HPT-ed at room฀ temperature,฀ the฀ x-ray฀ diffraction฀ still฀ indicated฀ the฀ presence฀ of฀ an฀ amorphous structure in the alloy, but TEM studies showed a structure full of nanocrystals฀with฀grain฀sizes฀of฀about฀2–3฀nm฀in฀it฀(Fig.฀1.9฀(c)฀). The essential difference between this alloy in the amorphous state and in its HPT-ed state was revealed during subsequent annealing. As it can be seen in Fig. 1.10,฀ the฀ amorphous฀ alloy฀ was฀ crystallized฀ at฀ 450°C,฀ and฀ formed฀ a฀ martensite฀ phase B19 during cooling. The TEM micrograph of the alloy after annealing shows฀that฀the฀grain฀structure฀was฀rather฀non-uniform฀and฀contained฀a฀mixture฀of฀ small฀grains฀and฀large฀grains฀with฀a฀size฀of฀about฀1฀micron฀(Fig.฀1.9฀(c)฀).฀At฀the฀same฀ time฀after฀HPT,฀crystallization฀occurs฀below฀390°C฀and฀its฀micrograph฀shows฀a฀ uniform฀nanocrystalline฀structure฀with฀a฀grain฀size฀of฀less฀than฀50฀nm฀(Fig.฀1.9฀(d)฀).฀

1.9 Transmission electron microscopy image of rapidly-quenched alloy Ti50Ni25Cu25: (a) initial state (dark field); (b) after annealing at 450°C 10 min; (c) after HPT (dark field); (d) after HPT and annealing at 390°C 10 min.

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1.10 X-ray diffraction patterns of the Ti50(Ni, Cu)50 alloy: (a) initial rapidly quenched alloy (1); after annealing at 300°C 5 min (2); after annealing at 450°C 5 min (3) with the phase B19; (b) alloy after HPT(1); after HPT and annealing at 300°C 5 min (2); after HPT and annealing at 400°C 5 min, with the phase B2 (3).

It฀is฀interesting฀to฀note฀that฀the฀structure฀after฀cooling฀was฀an฀austenitic฀B2-phase;฀ in other words, imposing severe plastic deformation on the amorphous alloy resulted฀in฀its฀crystallization฀during฀heating฀and฀changed฀its฀phase฀composition฀ after further cooling to room temperature. In the coarse-grained alloy Ti50Ni25Cu25, the temperature of martensite transformation฀upon฀cooling฀equals฀~80°C,฀which฀explains฀why฀there฀is฀a฀martensite฀ phase฀in฀the฀alloy฀at฀room฀temperature.฀In฀this฀connection,฀the฀existence฀of฀only฀an฀ austenitic฀phase฀after฀HPT฀and฀nanocrystallization฀can฀be฀related฀to฀the฀martensite฀ transformation฀retard฀in฀the฀alloy฀with฀a฀nanocrystalline฀grain฀size.฀This฀inding฀was฀ previously฀reported฀in฀the฀literature฀for฀ultraine-grained฀Ti-Ni฀alloys.63 For the alloy Ti50Ni25Cu25,฀the฀critical฀grain฀size฀for฀martensite฀transformation฀is฀about฀100฀nm,฀ below which the martensite transformation does not take place at room temperature. The amorphous state in Ti49.4Ni50.6 alloy can be obtained directly as a result of HPT processing (P = 6 GPa, n฀=฀5฀ revolutions).61,62 Subsequently, the homogeneous nanocrystalline structure was produced by annealing of the HPT-ed material฀ (Fig.฀ 1.11).฀ For฀ instance,฀ after฀ annealing฀ at฀ 400°C฀ for฀ 0.5฀ h฀ the฀ mean฀ grain฀size฀was฀about฀20฀nm฀(Fig.฀1.11฀(a),฀(b),฀and฀after฀annealing฀at฀500°C,฀it฀was฀ about 40 nm (Fig. 1.11 (c), (d). It is worth mention that according to HREM observations, such annealing removed the amorphous phase and produced welldeined฀grain฀boundaries,฀though฀there฀were฀still฀small฀distortions฀of฀the฀crystal฀ lattice near some of the boundaries.

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1.11 Transmission electron microscopy micrographs of Ti49.4Ni50.6 alloy after HPT and annealing at 400°C (a, b) and at 500°C (c, d) for 0.5 h: (a, c) bright field images; (b, d) dark field images.

Tensile mechanical tests showed that the amorphous nitinol produced by HPT had much higher strength than at the initial microcrystalline state,61 but it was essentially฀brittle.฀Nanocrystallization฀results฀in฀the฀recorded฀value฀of฀yield฀strength฀ for฀this฀material฀equal฀to฀2650฀MPa฀and฀an฀elongation฀to฀failure฀of฀about฀5%. Thus,฀SPD฀consolidation฀of฀powders฀and฀SPD-induced฀nanocrystallization฀can฀ be considered new SPD processing routes for fabricating bulk nanocrystalline materials. One of the advantages of these techniques is the possibility of producing fully฀dense฀samples฀with฀a฀uniform฀ultraine-grained฀structure฀having฀a฀grain฀size฀ less than 40–50 nm. Studies of the properties of these materials are of great interest for ongoing research because deformation mechanisms and, as mentioned above, phase transformations can essentially change the properties of materials with฀a฀small฀grain฀size.64,65

1.3.3 Basic rules for grain refinement For฀the฀formation฀of฀UFG฀structures฀with฀primarily฀high-angle฀grain฀boundaries฀ through฀ SPD฀ processing,฀ there฀ have฀ been฀ deined฀ ive฀ basic฀ rules฀ for฀ grain฀ reinement,66 four of which are related to the requirements for SPD processing regimes฀ and฀ routes฀ while฀ the฀ ifth฀ one฀ is฀ related฀ to฀ the฀ intrinsic฀ nature฀ of฀ the฀

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material under study. These rules are briefly considered below. A detailed description of SPD processing regimes and routes may be found in recent overviews on the subject.16,18,19 1. SPD processing at low temperatures (as a rule, less than 0.4 Tm) is referred to as฀ a฀ rather฀ important฀ requirement฀ for฀ its฀ realization.฀ Only฀ under฀ these฀ conditions is it possible to achieve dislocation densities of 1014 m–2 or higher, up to the limiting values of 1016–1017 m–2,16,67 which are necessary for the formation฀of฀the฀UFG฀structure.฀Higher฀processing฀temperatures฀result฀in฀a฀ lower฀accumulated฀dislocation฀density฀and฀an฀increase฀in฀grain฀size฀to฀more฀ than 1 micron. 2.฀ The฀ degree฀ of฀ strain฀ during฀ processing฀ (true฀ strain)฀ should฀ exceed฀ 6–8.฀ Although฀the฀considerable฀reinement฀of฀the฀microstructure฀and฀the฀attainment฀ of฀ dislocation฀ densities฀ exceeding฀ 1014 m–2 occur at a strain of 1–2,16 the formation฀of฀UFG฀structure฀with฀a฀majority฀of฀high-angle฀grain฀boundaries฀ requires further straining. 3.฀ High฀hydrostatic฀pressures,฀usually฀>1฀GPa,฀are฀important฀for฀eficient฀SPD฀ processing. High pressure contributes to the enhancement of deformability of the processed material and therefore, provides solidity of the billets even under high strain.11,19 Furthermore, the pressure affects the diffusion and thus suppresses the annihilation of deformation-induced lattice defects.68 4.฀ The฀ formation฀ of฀ equiaxed฀ ultraine฀ grains฀ depends฀ on฀ the฀ vorticity฀ of฀ the฀ metal flow. At the macrolevel, the vorticity is related to the non-monotonous character฀ of฀ deformation.฀ For฀ example,฀ the฀ ECAP฀ route฀ BC, in which the billet฀is฀rotated฀by฀90°฀between฀each฀pass,฀is฀considerably฀more฀effective฀for฀ grain฀reinement฀in฀comparison฀with฀route฀C,฀in฀which฀the฀billet฀position฀does฀ not change.19 At the microlevel, the vorticity is associated with grain rotations and displacements.69 5.฀ Grain฀ reinement฀ is฀ also฀ related฀ to฀ the฀ atomic฀ structure฀ of฀ the฀ material฀ processed. The ordering of alloys or low-stacking fault energy (SFE), all other conditions being equal, contributes to the enhancement of accumulated dislocation฀density฀and฀considerably฀reduces฀the฀grain฀size฀produced.16 For example,฀ in฀ Pd-20%Ag฀ alloy฀ with฀ SFE฀ =฀ 125฀ mJ·m–2, in comparison with pure฀Pd฀with฀SFE฀=฀190฀mJ·m–2, during HPT (5 rotations and P฀=฀6฀GPa),฀the฀ grain฀ size฀ produced฀ equals฀ 150฀ nm฀ for฀ Pd-20%Ag฀ and฀ 240฀ nm฀ for฀ Pd,฀ respectively.70 These฀ive฀rules฀are฀required฀and฀typically฀suficient฀conditions for effective grain reinement฀by฀SPD฀processing.

1.3.4 Types of nanostructures Though฀ it฀ is฀ possible฀ to฀ achieve฀ a฀ nanocrystalline฀ structure฀ with฀ a฀ grain฀ size฀ less than 100 nm in a number of metals and alloys by means of HPT, for SPD

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processing฀the฀formation฀of฀ultraine-grained฀(UFG)฀structures฀with฀a฀mean฀grain฀ size฀within฀the฀submicron฀range฀(i.e.฀with฀grains฀200–500฀nm฀in฀size)฀is฀typical. However,฀ in฀ the฀ process฀ of฀ SPD,฀ including฀ ECAP,฀ the฀ formation฀ of฀ other฀ structural elements takes place as well – that is, dislocation substructures, twins, grain boundary segregations and precipitations, which also produce a considerable influence on the properties of the materials after processing. Moreover, semiproducts in the form of rods, wires and sheets are produced by deformation and thermal฀ treatment฀ in฀ sequence฀ after฀ ECAP,฀ which฀ additionally฀ reines฀ their฀ microstructure and enhances their properties. In general, we can single out four types of nanostructural elements in the metals and alloys produced by SPD. It is possible to observe such nanostructures by the application of modern techniques for structural analysis – high-resolution transmission electron microscopy (HRTEM), 3D-atom probe, etc.16,19,71,72 These four types of structures are as follows: 1.฀ Non-equilibrium฀grain฀boundaries.฀For฀example,฀as฀illustrated฀in฀Fig.฀1.12,73 an excessively฀high฀density฀of฀dislocations,฀facets฀and฀steps฀are฀observed฀at฀grain฀ boundaries฀ of฀ the฀ UFG฀ Al-3%Mg฀ alloy฀ after฀ HPT,฀ illustrating฀ the฀ nonequilibrium state of grain boundaries with crystal lattice distortions of 5–7 nm in width near boundaries.16,66 Such non-equilibrium grain boundaries are typical for different materials after SPD processing and their role in the mechanical behavior฀of฀UFG฀materials฀has฀been฀stressed฀in฀a฀number฀of฀works.16,66,74 2. Nanotwins, stacking faults, intragranular cells. These nanostructural elements are฀typical฀for฀the฀materials฀after฀HPT฀or฀ECAP฀at฀lower฀temperatures฀and/or฀ those฀subjected฀to฀additional฀cold฀rolling,฀extrusion,฀and฀drawing.฀Figure฀1.13฀ shows฀the฀TEM฀image฀of฀atom฀resolution฀of฀UFG฀Cu฀after฀ECAP฀and฀cold฀

1.12 Transmission electron microscopy images of non-equilibrium grain boundaries in the UFG Al-3%Mg alloy73 illustrating highresolution photographs of regions A and B.

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1.13 (a) TEM images of typical grain with high density of deformation twins in UFG Cu processed by ECAP with consequent cold rolling; (b) high-resolution TEM image taken from the zone axis. Inset: twin relationship (white lines) and a Frank dislocation at a twin boundary, marked by arrow.75

rolling at liquid nitrogen temperature with clearly observed twins of 10–20 nm฀in฀size.75 Such nanostructured defects also have a considerable effect on material strength,75,76฀for฀example฀increasing฀the฀yield฀stress฀in฀UFG฀Cu฀from฀ 380 to 510 MPa.75 3. Segregation clusters, ‘clouds’. Recent investigations by a 3D atom probe directly testify the formation of impurity as well as alloying element segregations at grain boundaries฀ in฀ the฀ UFG฀ alloys฀ processed฀ by฀ SPD,71,72,77 see e.g. Fig. 1.14.71

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1.14 Grain boundary segregations in the HPT-processed 6061 Al alloy (of system Al-Mg-Si): (a) TEM image of the 6061 Al alloy; (b) grain size distribution; (c) Mg, Cu and Si distribution in a 3D reconstructed volume analysed in the 6061 alloy by HPT (6 × 6 × 40 nm3).71

These฀ segregations฀ form฀ ‘clouds’,฀ and฀ clusters฀ 3–5฀ nm฀ in฀ size฀ inluence฀ the฀ formation and motion of dislocations, which provides additional strengthening of the฀alloys,฀in฀particular฀those฀based฀on฀aluminum,฀by฀more฀than฀40%.71,78 4.฀ Nano-sized฀particles฀–฀second-phase฀precipitations.฀The฀formation฀of฀particles฀ has been observed in many alloys subjected to SPD after solution quenching.15,19 Figure฀1.15฀illustrates฀the฀example฀of฀such฀nanoparticles฀10–20฀nm฀in฀size฀precipitated฀in฀the฀UFG฀alloy฀Al฀6061฀after฀ECAP.79 The presence of nano-particles

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1.15 UFG structure of the alloy Al 6061 after ECAP with parallel channels (4 passes). The formation of nano-sized precipitations is clearly visible inside the grain after processing at selected areas A and B with larger magnification.79

originates from dynamic ageing and provides additional precipitation hardening of the alloys.19,79 Thus,฀ the฀ UFG฀ metals฀ and฀ alloys฀ processed฀ by฀ SPD฀ techniques฀ and,฀ in฀ particular,฀ECAP฀are฀characterized฀by฀a฀number฀of฀nanostructural฀elements฀that฀ considerably influence their properties, as will be shown below. That is why these materials are referred to as the class of ‘bulk nanostructured materials’, and this deinition฀is฀presently฀accepted฀by฀the฀international฀community฀(www.฀nanospd. org).฀It฀is฀important฀that฀the฀strength฀of฀such฀materials฀as฀shown฀in฀the฀next฀section฀ may฀be฀considerably฀higher฀than฀that฀expected฀from฀the฀Hall–Petch฀relation.

1.4

Enhanced properties achieved using SPD processing

The฀ ultraine฀ grain฀ sizes฀ and฀ high-defect฀ densities฀ inherent฀ in฀ UFG฀ materials฀ processed by severe plastic deformation lead to much higher strengths than in their coarse-grained counterparts. Moreover, according to the constitutive relationship for฀superplasticity,฀it฀is฀reasonable฀to฀expect฀the฀appearance฀of฀low-temperature฀and/ or฀high-rate฀superplasticity฀in฀UFG฀metals.8,80–83฀The฀realization฀of฀these฀capabilities฀ is important for the future development of high-strength and wear-resistant materials, advanced superplastic alloys and metals of high fatigue life. The potential for achieving all of these qualities has raised a keen interest among scientists and engineers฀studying฀the฀mechanical฀and฀functional฀properties฀of฀these฀UFG฀materials. In฀this฀connection,฀the฀irst฀works฀on฀the฀fabrication฀of฀bulk฀samples฀and฀billets฀ using SPD were a crucial step in initiating investigations on the properties of

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UFG฀materials,฀because฀the฀use฀of฀SPD฀processing฀made฀it฀possible฀to฀conduct฀a฀ series of systematic studies using various nanostructured metallic materials including commercial alloys.16,84–88

1.4.1 Strength and ductility at ambient temperature During฀the฀last฀decade฀it฀has฀been฀widely฀demonstrated฀that฀major฀grain฀reinement,฀ down to the nanometer range, may lead to considerable hardness and strength in various฀metals฀and฀alloys฀but฀nevertheless฀these฀materials฀invariably฀exhibit฀low฀ ductility under tensile testing.12,15,89,90 A similar tendency is well known for metals subjected฀ to฀ heavy฀ straining฀ by฀ other฀ processes฀ such฀ as฀ rolling,฀ extrusion฀ or฀ drawing. Strength and ductility are the key mechanical properties of any material, but these properties typically have opposing characteristics. Thus, materials may be strong or ductile but they rarely possess both characteristics. This dichotomy shown in properties is of a fundamental nature. As discussed in more detail in earlier reports,64 the plastic deformation mechanisms associated with฀ the฀ generation฀ and฀ movement฀ of฀ dislocations฀ can฀ be฀ different฀ in฀ ultraine฀ grains฀ or฀ in฀ strongly฀ reined฀ microstructures.฀This฀ is฀ generally฀ equally฀ true฀ for฀ SPD-processed materials. Thus, most of these materials have a relatively low ductility฀ but฀ they฀ usually฀ demonstrate฀ signiicantly฀ higher฀ strength฀ than฀ their฀ coarse-grained counterparts. High strength in SPD-processed materials is usually attributed to the formation of฀UFG฀structure฀via฀the฀classic฀Hall–Petch฀relationship,฀according฀to฀which฀the฀ yield stress σy is calculated as:

σy฀=฀σ0 + ky฀*฀d –1/2,

[1.1]

where d฀is฀a฀grain฀size,฀σ0 and k are constant for the material. However,฀it฀has฀been฀found฀that฀in฀many฀cases฀the฀yield฀stress฀value฀in฀the฀UFG฀ materials processed by SPD may be considerably higher than those calculated by the Hall–Petch relation.15,16,91 For฀ example,฀ this฀ was฀ shown฀ in฀ the฀ studies฀ of฀ mechanical฀ behavior฀ of฀ Ni฀ subjected฀ to฀ ECAP฀ and฀ consequent฀ rolling.91 Figure 1.1691,93–95 shows the difference in strength between the states of Ni, where grains contain dislocation substructures inside grains, and the states with grains without substructure. An attempt was made to describe the deviation quantitatively from the Hall– Petch rule by taking into account the presence of two types of boundaries: highangle boundaries (HAB) between grains, and low-angle cell boundaries (LAB) on the yield stress. Following,92 it was assumed that all type of boundaries including฀non-equilibrium฀grain฀boundaries฀with฀extrinsic฀dislocations฀contribute฀ to the yield stress independently:

σy฀=฀σ0 + σLAB + σHAB + σNGBs and

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[1.2]

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1.16 Yield stress as a function of a grain size for Ni. Note: Continuous line: material states with grains without substructure, dashed line: UFG Ni containing dislocation substructure.

σy฀=฀σ0 + Mα Gb((1.5Svθ/b)LAB )1/2 + ky฀*฀d –1/2 + Mα Gb(ρGBDs)1/2,

[1.3]

where σ0 is the threshold stress, M is the Taylor factor (M฀=฀3),฀ α is the constant (α฀=฀0.24),฀G฀is฀the฀shear฀modulus฀(79฀GPa),฀and฀b is the Burgers vector (0.249 nm). The Sv฀is฀associated฀with฀the฀cell฀size,฀θ is the misorientation angle of LAB, ky is the Hall–Petch constant. The d฀is฀the฀average฀grain฀size,฀ρGBDs฀is฀the฀density฀of฀extrinsic฀ GB dislocations. Their numerical values are taken following references.91,92 The contributions of these different components for SPD Ni correspond well to the฀ experimentally฀ obtained฀ data฀ (Table฀ 1.3).฀After฀ HPT฀ a฀ homogeneous฀ UFG฀ structure was formed with mainly high-angle misorientations. So, after several passes, we neglect the contribution of low-angle boundaries. Thus, the analysis of mechanical test data shows that the presence of substructure and the nonequilibrium state of GB contributes stronger to the yield stress of SPD Ni than that predicted by the Hall–Petch rule. In addition to the dislocation substructure and non-equilibrium grain boundaries other฀nanostructural฀elements฀formed฀in฀the฀UFG฀materials฀processed฀by฀SPD,฀as฀ it was shown above in section 1.2.3, may contribute to the change of yield stress and flow stress. This issue has recently been studied in detail for the case of super-strong UFG฀Al฀alloys,78 such as commercial Al alloys 1570 (Al-5.7Mg-0.32Sc-0.4Mn wt. %)฀and฀7475฀(Al-5.7Zn-2.2Mg-1.6Cu-0.25Cr,฀wt.฀%),฀with฀considerable฀magnesium฀ content. Al-Mg system alloys are the basis for most popular commercial Al alloys. For฀grain฀reinement฀the฀solid-soluted฀alloys฀were฀subjected฀to฀high-pressure฀ torsion฀ (HPT),฀ in฀ which฀ UFG฀ structures฀ were฀ produced฀ with฀ applied฀ pressure฀ of 6 GPa and number of anvil rotations equaling to 10. The samples in the

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Table 1.3 The contribution in flow stress for SPD-processed Ni Processing of Ni

YS exp, (MPa)

YS calc, (MPa)

σLAB , (MPa)

σHAB , (MPa)

σGBDs, (MPa)

ECAP + rolling HPT

990 1200

980 1190

510 –

280 460

170 710

Note: YS exp: experimental data, YS calc: calculated by means of equation [1.3].

form of disks 20 mm in diameter and 0.8 mm in width were cut out from the HPT-processed alloys for further tensile tests. Transmission electron microscopy analysis demonstrated that HPT leads to a complete transformation of the initial coarse-grained structure of the alloys into the฀UFG฀structure.฀In฀alloys฀1570฀and฀7475,฀homogeneous฀UFG฀structures฀with฀ a฀ grain฀ size฀ of฀ about฀ 100฀ nm฀ were฀ formed฀ after฀ HPT฀ (Fig.฀ 1.17).฀ It฀ was฀ also฀ determined that HPT processing has a visible effect on the value of crystal lattice parameter a฀ of฀Al฀ alloys.฀ For฀ example,฀ in฀ the฀ alloy฀ 1570,฀ its฀ lattice฀ parameter฀ value after straining was reduced considerably in comparison with that at the initial฀ state฀ –฀ from฀ 4.0765฀ ±฀ 0.0001฀ Å฀ to฀ 4.0692฀ ±฀ 0.0003฀ Å,฀ approaching฀ the฀ lattice parameter of pure Al, which resulted in the formation of Mg segregations at grain boundaries.78 Figure 1.18 shows the results of mechanical tests of the alloys 1570 and 7475. It฀can฀be฀seen฀that฀the฀UFG฀alloys฀after฀HPT฀at฀room฀temperature฀demonstrate฀ recorded฀strength฀that฀exceeds฀more฀than฀two฀times฀the฀level฀of฀strength฀of฀the฀ material subjected to standard hardening.

1.17 Typical UFG structure formed in the alloy 1570 after HPT processing at room temperature (dark field).

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1.18 Engineering stress–strain curves of the UFG alloys 1570 (a) and 7475 (b).

Figure 1.1978 shows the data for a number of Al alloys presented in the form of the Hall–Petch relation in which the yield stress (σ0.2) is plotted against the inverse square฀root฀of฀the฀grain฀size฀(d–1/2)฀for฀a฀UFG฀Al฀alloy฀1100฀produced฀by฀ARBrolling and consequent heat treatment96฀as฀well฀as฀for฀an฀ECAP-processed฀alloy฀ Al-3%฀Mg฀alloy.97 For the Hall–Petch relation in the 1100 alloy,96 the following

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1.19 The Hall–Petch relation for the alloys 1100,96 Al–3%Mg97 and data on the yield stresses of the UFG alloys 1570 and 7475.

parameters were set: σ0฀=฀6.0฀MPa฀and฀ky฀=฀105฀(for฀the฀grain฀sizes฀in฀µm);฀for฀the฀ ECAP-processed฀alloy฀Al-3%฀Mg,97 σ0฀=฀62฀MPa฀and฀ky฀=฀149.฀Figure฀1.19฀also฀ shows฀the฀data฀obtained฀for฀the฀coarse-grained฀(CG)฀and฀UFG฀1570฀and฀7475฀ alloys. From฀the฀available฀data฀it฀is฀seen฀that฀the฀YS฀values฀for฀the฀CG฀quenched฀alloys฀ are฀close฀to฀the฀results฀for฀the฀Al-3%฀Mg฀alloy.฀However,฀for฀the฀UFG฀states฀with฀ a฀grain฀size฀of฀100–130฀nm฀the฀value฀ sy is considerably higher than calculated from฀the฀Hall–Petch฀relation฀for฀these฀grain฀sizes. The physical nature of this unusual effect of super-strength refers to the features of the GB states formed during SPD and, in particular, to the formation of GB segregation of alloying elements.71,77,78฀The฀point฀is฀that฀in฀UFG฀materials฀with฀a฀ grain฀ size฀ of฀ about฀ 100฀ nm฀ the฀ deformation฀ mechanisms฀ controlling฀ the฀ low฀ stress change.98,99฀ In฀ the฀ CG฀ materials฀ the฀ generation฀ of฀ dislocations฀ proceeds฀ relatively easily and hardening is related to the hindering of their movement by various฀ obstacles.฀ In฀ the฀ UFG฀ materials฀ the฀ process฀ of฀ dislocation฀ generation฀ occurs฀at฀the฀GBs฀and฀is฀the฀most฀dificult.74,99 In this connection, the change of GB states and the formation of GB segregants of alloying elements, in particular in Al alloys, may considerably harden the dislocation generation and result in the achievement of a high-strength state.78

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As฀ is฀ well฀ known,฀ the฀ UFG฀ materials฀ are฀ commonly฀ deined฀ as฀ interfacecontrolled materials.100฀At฀the฀same฀time฀in฀the฀UFG฀materials฀produced฀by฀the฀ SPD฀techniques,฀grain฀boundaries฀may฀vary฀signiicantly฀depending฀on฀the฀regimes฀ and routes of processing, and they can belong to high- and low-angle grain boundaries, special and random boundaries, equilibrium and non-equilibrium boundaries as well as containing GB segregations or precipitations.11,64,71,101–104 In this฀context฀there฀appears฀a฀possibility฀of฀controlling฀and฀enhancing฀the฀properties฀ of฀UFG฀materials฀by฀varying฀the฀structure฀of฀GBs฀using฀SPD฀processing.฀This฀ approach can be considered as an application of the principles of GB engineering to฀UFG฀metals฀and฀alloys.64,104,105 The concept of grain boundary engineering or grain boundary design was introduced by T. Watanabe,106 who had proposed that the properties of polycrystalline materials may be effectively changed by deliberate and careful tailoring of the distributions of boundary misorientation angles. This approach has been employed successfully฀in฀several฀studies฀including,฀for฀example,฀improving฀the฀susceptibility฀to฀ intergranular stress corrosion cracking.107฀However,฀there฀are฀generally฀dificulties฀in฀ achieving different boundary distributions in conventional coarse-grained materials. In฀this฀connection,฀UFG฀materials฀in฀which฀GB฀structure฀features฀are฀associated฀with฀ SPD processing regimes allow much more possibilities for GB engineering. The concept of GB engineering is also of special interest regarding recent indings฀of฀extraordinary฀high฀strength฀and฀good฀ductility฀in฀several฀bulk฀ultrainegrained metals produced by severe plastic deformation.80,108–111 Let us consider in detail the three different approaches that were used in these investigations. In฀the฀irst฀study,฀high-purity฀(99.996%)฀Cu฀was฀processed฀at฀room฀temperature฀ using฀ ECAP฀ with฀ a฀ 90°฀ clockwise฀ rotation฀ around฀ the฀ billet฀ axis฀ between฀ consecutive passes in route BC.108฀Cu฀samples,฀which฀were฀prepared฀in฀the฀initial฀ coarse-grained condition as well as in three processed states (cold rolled, 2-pass ECAP฀and฀16-pass฀ECAP 108),฀were฀uni-axial฀tensile-tested฀at฀room฀temperature.฀ The resulting engineering stress–strain curves are shown in Fig. 1.20. It is apparent that฀the฀initial฀coarse-grained฀Cu,฀with฀a฀grain฀size฀of฀about฀30฀µm, typically has low-yield฀stress฀with฀signiicant฀strain฀hardening฀and฀a฀large฀elongation฀to฀failure.฀ At฀the฀same฀time,฀cold฀rolling฀of฀copper฀to฀a฀thickness฀reduction฀of฀60%฀signiicantly฀ increases its strength, as shown by curve 2 in Fig. 1.20, but dramatically decreases its total elongation to failure. This result is consistent with the classical strain hardening฀behavior฀of฀metals.฀The฀same฀tendency฀is฀true฀also฀for฀Cu฀subjected฀to฀2฀ passes฀of฀ECAP.฀However,฀further฀straining฀of฀Cu฀to฀16฀passes฀of฀ECAP,฀as฀shown฀ by curve 4 in Fig. 1.20, simultaneously increases both the strength and the ductility. Furthermore,฀the฀increase฀in฀ductility฀is฀much฀more฀signiicant฀than฀the฀relatively฀ minor increase in strength. Thus,฀the฀data฀for฀Cu฀processed฀by฀ECAP฀shown฀in฀Fig.฀1.20฀clearly฀demonstrate฀ enhanced strength as well as ductility with accumulated deformation on increasing the number of passes from 2 to 16. At the time of the investigation in 2002, this was considered a very remarkable result, which had never been observed before in

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1.20 Tensile engineering stress–strain curves for Cu tested at 22°C with a strain rate of 10–3s–1: the processing conditions for each curve are indicated.108

metals processed by plastic deformation. Accordingly, the effect was termed the ‘paradox฀of฀strength฀and฀ductility฀in฀SPD-processed฀metals’,฀and฀the฀principles฀of฀ this฀ paradox฀ are฀ illustrated฀ in฀ Fig.฀ 1.21,฀ where฀ it฀ is฀ apparent฀ that฀ conventional฀ metals lie within the lower shaded quadrant.108฀As฀seen฀in฀Fig.฀1.21฀for฀Cu฀and฀Al,฀ cold rolling (the reduction in thickness is marked by each datum point) increases the yield strength but decreases the elongation to failure or ductility. The extraordinary฀combination฀of฀high฀strength฀and฀high฀ductility฀shown฀in฀Fig.฀1.21฀ for฀the฀nanostructured฀Cu฀and฀Ti฀after฀processing฀by฀SPD฀clearly฀sets฀them฀apart฀ from the other coarse-grained metals. In recent years, a similar tendency has been reported in a number of metals including Al,114,115฀Cu,116 Ni117 and Ti,80 after processing through various types of severe฀plastic฀deformation฀such฀as฀ECAP,฀high-pressure฀torsion฀or฀accumulative฀ roll฀bonding.฀Concerning฀the฀origin฀of฀this฀phenomenon,฀it฀has฀been฀suggested฀ that it is associated with an increase in the fraction of high-angle grain boundaries with increased straining and with a consequent change in the dominant deformation mechanisms due to an increasing tendency for grain boundary sliding and grain rotation.64,108 An increase in the fraction of high-angle grain boundaries is also an example฀of฀GB฀engineering.105 Another approach to the problem of ductility enhancement that was suggested was฀ the฀ introduction฀ of฀ a฀ bimodal฀ distribution฀ of฀ grain฀ sizes.109 In this study, nanostructured฀ copper฀ was฀ produced฀ through฀ a฀ combination฀ of฀ ECAP฀ and฀ subsequent rolling at the low temperature of liquid nitrogen prior to heating to a temperature฀close฀to฀~450฀K.฀This฀procedure฀gave฀a฀bimodal฀structure฀of฀micrometersized฀ grains,฀ with฀ a฀ volume฀ fraction฀ of฀ around฀ 25%,฀ embedded฀ in฀ a฀ matrix฀ of฀ nanocrystalline฀grains.฀The฀material฀produced฀in฀this฀way฀exhibited฀an฀extraordinarily฀ high ductility but also retained a very high strength. The reason for this behavior is

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1.21 The paradox of strength and ductility in metals subjected to SPD (‘VAZL paradox’): the extraordinary combination of high strength and high ductility in nanostructured Cu and Ti processed by SPD (two upper points) clearly sets them apart from conventional coarse-grained metals (the lower points relating to metals of 99.5–99.9% purity).108

that, while the nanocrystalline grains provide strength, the embedded larger grains stabilize฀ the฀ tensile฀ deformation฀ of฀ the฀ material.฀ Other฀ evidence฀ supporting฀ the฀ importance฀of฀grain฀size฀distribution฀comes฀from฀investigations฀on฀zinc,118 copper119 and an aluminum alloy.120 Furthermore, the investigation of copper119 showed that bimodal structures might increase ductility not only during tensile testing but also during cyclic deformation. This observation is important in improving the fatigue properties of materials. A third approach has been suggested for enhancing strength and ductility based on฀the฀formation฀of฀second-phase฀particles฀in฀the฀nanostructured฀metallic฀matrix,89 where it is anticipated that these particles will modify the shear band propagation during straining and thereby lead to an increase in ductility. The principle of achieving high strength and high ductility by introducing intermediate฀metastable฀phases฀was฀successfully฀realized฀recently฀in฀commercial฀ Al-Zn-Mg-Cu-Zr121฀ and฀ Al-10.8%฀ Ag฀ alloys฀ after฀ processing฀ by฀ ECAP฀ and฀ subsequent ageing.110 The principle of this approach is illustrated in Fig. 1.22 for the Al-Ag alloy where Vickers microhardness is plotted against the ageing time at 373฀K฀for฀samples฀prepared฀by฀three฀different฀pretreatments:฀the฀solution-treated฀ condition฀(ST),฀cold฀rolling฀(CR)฀and฀ECAP.110 For the solution-treated condition, the hardness is initially low but increases with ageing time and reaches a peak

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1.22 Variation of Vickers microhardness with ageing time for the Al-10.8%Ag alloy after solution treatment (ST), cold rolling (CR) and ECAP.110

value after 100 hours (3.6 × 105 s). For the cold-rolled condition, the hardness is higher but there is only a minor increase with ageing. The hardness is even higher after฀ECAP฀and฀further฀increases฀with฀ageing฀to฀a฀peak฀value฀after฀100฀hours.฀The฀ relatively low values of hardness recorded after cold rolling in contrast with those higher฀values฀of฀ECAP฀samples฀is฀because฀the฀equivalent฀strain฀imposed฀on฀the฀ sample฀ is฀ ~1.4฀ for฀ CR฀ and฀ ~8฀ for฀ ECAP฀ so฀ that฀ the฀ microstructure฀ after฀ CR฀ consisted of subgrains or cell boundaries having low angles of misorientation. It was฀shown,฀using฀scanning฀TEM,฀that฀the฀peak฀hardness฀achieved฀after฀ECAP฀ and ageing for 100 hours is due to precipitation within the grains of spherical particles with diameters of ~10 nm and elongated precipitates with lengths of ~20 nm.฀ The฀ spherical฀ particles฀ were฀ identiied฀ as฀ η-zones฀ consisting฀ of฀ arrays฀ of฀ solute atoms lying parallel to the (001) planes and the elongated precipitates were identiied฀as฀the฀plate-like฀γ' particles. It was shown also that additional ageing up to 300 hours led to a growth in the γ'฀particles฀and฀a฀very฀signiicant฀reduction฀in฀ the฀density฀of฀the฀ine฀ η-zones,฀thereby฀giving฀a฀consequent฀loss฀in฀hardening฀at฀ the longest ageing time recorded in Fig. 1.22. The฀introduction฀of฀ageing฀after฀ECAP฀has฀an฀important฀inluence฀on฀the฀stress– strain behavior at room temperature, as demonstrated in Fig. 1.23 where the tensile stress–strain฀ curves฀ of฀ Al-10.8฀ wt%฀ Ag฀ alloy฀ processed฀ under฀ four฀ different฀ conditions:฀1)฀ECAP฀only;฀2)฀ECAP฀and฀subsequent฀100฀h฀annealing฀at฀373฀K;฀3)฀ cold฀rolling฀and฀subsequent฀100฀h฀annealing฀at฀373฀K;฀and฀4)฀solution฀treatment฀ and฀ subsequent฀ 100฀ h฀ annealing฀ at฀ 373฀ K.110 Thus, a combination of solution

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1.23 Tensile plots of stress versus strain at room temperature for the Al-10.8%Ag alloy after solution treatment (ST) or cold-rolling (CR) with ageing at 373 K for 100 h or ECAP without subsequent ageing and ECAP with ageing at 373 K for 100 h.110

treatment฀and฀ageing฀gives฀a฀reasonable฀tensile฀strength,฀an฀extensive฀region฀of฀ uniform฀ strain฀ and฀ good฀ ductility,฀ whereas฀ CR฀ and฀ ageing฀ gives฀ an฀ increased฀ strength but very limited uniform strain and a marked reduction in the total ductility. For฀the฀ECAP-ed฀alloy,฀the฀strength฀is฀high฀in฀the฀absence฀of฀ageing฀but฀there฀is฀a฀ negligible฀region฀of฀uniform฀strain฀and฀no฀signiicant฀strain฀hardening.฀By฀contrast,฀ the฀sample฀processed฀by฀ECAP฀and฀aged฀for฀100฀h฀shows฀a฀similar฀high฀strength,฀ a region of strain hardening and good ductility. In practice, the uniform strain of ~0.14 achieved in this specimen is similar to the uniform strain of ~0.17 in the sample after solution treatment and ageing. The elongation to failure of ~0.40 is comparable฀to,฀and฀even฀slightly฀exceeds,฀the฀elongation฀of฀~0.37฀recorded฀in฀the฀ solution treatment and aged condition. These results demonstrate, therefore, the potential for producing high strength and good ductility in precipitation-hardened alloys. Thus,฀recent฀results฀show฀that฀grain฀reinement฀by฀ECAP฀can฀lead฀to฀a฀unique฀ combination of strength and ductility in metallic materials. However, the achievement of฀these฀properties฀is฀associated฀with฀the฀tailoring฀of฀speciic฀microstructures,฀which,฀ in turn, are determined by the precise processing regimes and origin of any further treatments. In this case the concept of GB engineering plays also an important role in the enhancement of strength and ductility. That is why nowadays nanostructuring of฀metals฀for฀advanced฀properties฀comprises,฀as฀a฀rule,฀scientiic฀as฀well฀as฀artistic฀ aspects of tailoring of materials by means of SPD techniques. In return, strength and ductility are fundamental mechanical properties that are closely connected with many engineering properties of materials, in particular

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fatigue, fracture toughness, durability, wear resistance as well as creep and superplasticity. Such superior mechanical properties are highly desirable for the development฀of฀advanced฀next-generation฀structural฀materials฀and฀this฀has฀been฀ an object of numerous investigations in the sphere of nanoSPD materials in the last several years.15,19,122 In fact, closer attention is now being paid to work on the enhancement of functional properties such as magnetic, electrical, super-elastic ones,฀etc.,฀in฀the฀UFG฀metals฀produced฀by฀SPD.15,123,124 All this is very important in view of innovative applications of bulk nanomaterials.

1.5

Innovation potential of bulk nanostructured materials

Recent฀reports฀documented฀more฀than฀100฀speciic฀market฀areas฀for฀nanostructured฀ metals122,125 and it is evident that many of these new structural applications involve฀ extreme฀ environments฀ where฀ exceptional฀ strength฀ is฀ needed.฀ Potential฀ near-future applications are presented schematically in Fig. 1.24 demonstrating some฀speciic฀examples.122

1.24 Assumed innovation probability in various sectors vs. specific strength. The highest potential may be seen in applications and products under ‘extreme environments and/or with extreme specific strength’ requirements.

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Firstly,฀ due฀ to฀ excellent฀ biological฀ compatibility฀ combined฀ with฀ superior฀ speciic฀ strength,฀ it฀ is฀ probable฀ that฀ UFG฀ titanium฀ will฀ enter฀ the฀ bio-medical฀ market at an ever-increasing pace. Titanium and titanium alloys are currently used extensively฀as฀implant฀materials฀in฀traumatology,฀orthopaedics฀and฀dentistry.126 This฀ is฀ due฀ to฀ several฀ characteristics฀ including฀ their฀ excellent฀ biocompatibility,฀ good฀corrosion฀resistance฀and฀speciic฀strength฀compared฀with฀other฀metals.฀The฀ implant฀ materials฀ used฀ in฀ these฀ areas฀ are฀ subjected฀ to฀ complex฀ loads฀ with฀ additional biomedical and other technical requirements. Signiicant฀progress฀may฀be฀achieved฀here฀by฀increasing฀the฀speciic฀strength฀of฀ the฀implant฀materials,฀and฀thereby฀permitting฀the฀use฀of฀a฀smaller฀size฀with฀less฀ invasive surgery. Recent investigations have shown that, due to nanostructuring, the฀fatigue฀strength฀of฀CP-Ti฀may฀be฀signiicantly฀increased฀to฀a฀level฀exceeding฀ that of the coarse-grained Ti-6Al-4V alloy.48,127 Hence, there is also the potential to฀replace฀more฀expensive฀and฀less฀biocompatible฀alloys฀with฀commercial-purity฀ titanium that is more biocompatible.48 Important requirements in all biomedical applications฀are฀corrosion฀resistance฀and฀excellent฀biocompatibility฀and฀both฀are฀ fulilled฀with฀titanium฀and฀most฀titanium฀alloys.฀Preliminary฀investigations฀of฀the฀ corrosion behavior of nano-titanium suggest that corrosion resistance is improved by฀introducing฀a฀UFG฀microstructure.128฀A฀second฀example฀with฀high฀innovative฀ potential is the superplastic forming of light metals produced by SPD for the fabrication฀of฀products฀with฀both฀complex฀shapes฀and฀high฀speciic฀strengths.฀It฀is฀ anticipated that these products will have a wide range of applications in the aeronautic and automotive sectors as well as in the consumer product industry. The development of superplastic forming capabilities after SPD is now well established.129฀Numerous฀experiments฀show฀that฀these฀superplastic฀properties฀are฀ retained when large billets processed by SPD are subsequently rolled into thin sheets during superplastic forming operations.130–132฀ Furthermore,฀ the฀ ultraine฀ grain฀size฀is฀preserved฀after฀SPD฀forming฀and฀thus฀provides฀a฀very฀high฀strength฀ at ambient temperatures, which is an important consideration for many structural applications. A฀third฀potential฀innovation฀lies฀in฀extreme฀low-temperature฀applications฀as฀in฀ arctic environments and in the special processing applications associated with the oil and gas industries. This is especially important for low carbon and stainless ferritic steels where usually there is a sharp transition from ductile to brittle behavior฀ with฀ decreasing฀ temperature.฀ Extensive฀ grain฀ reinement฀ due฀ to฀ SPD฀ can฀ signiicantly฀ decrease฀ the฀ brittle–ductile฀ transition฀ temperature฀ in฀ these฀ steels133,134 and this is especially important when undertaking construction work at high latitudes.

1.6

Conclusions

Processing฀ by฀ severe฀ plastic฀ deformation฀ provides฀ strong฀ grain฀ reinement฀ and฀ therefore an opportunity to enhance properties of metals and alloys making them

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attractive฀for฀new฀structural฀and฀functional฀applications.฀However,฀inding฀solutions฀ to฀these฀problems฀is฀a฀complex฀challenge฀requiring฀an฀individual฀approach฀to฀the฀ choice of processing routes and regimes and formation of certain nanostructures. The recent progress witnessed in this trend and many new works demonstrate unique opportunities to successfully do this. Limitations on the use of SPDprocessed materials to date, which have arisen primarily from their processing costs and the inherent wastage in conventional processing methods, are now being overcome through the development of new and continuous processing techniques. As these procedures become more developed, it is reasonable to anticipate that there฀will฀be฀signiicant฀advances฀in฀the฀use฀of฀nanomaterials฀in฀different฀areas฀of฀ engineering and bio-medical applications. There is already every reason to believe that this breakthrough will take place in the coming years.

1.7

References

฀ 1฀ Honeycombe฀R.W.K.฀The฀plastic฀deformation฀of฀metals.฀London:฀Edward฀Arnold,฀2฀ Sub edition, 1984. 2 Rybin V.V. Large plastic deformations and fracture of metals. Moscow: Metallurgia, 1986. ฀ 3฀ Sevillano฀G.,฀Van฀Houtte฀P.,฀Aernoudt฀E.฀Prog฀Mater฀Sci฀1980;25(2–4):฀69. ฀ 4฀ Erbel฀S.฀Metals฀Tech฀1979;6:฀482. ฀ 5฀ Saunders฀I.,฀Nutting฀J.฀Metal฀Sci฀1984;18:฀571. 6 Bridgman P.W. Studies in large plastic flow and fracture. New York (NY): McGrawHill, 1952. ฀ 7฀ Smirnova฀N.A.,฀Levit฀V.I.,฀Pilyugin฀V.I.,฀Kuznetsov฀R.I.,฀Davidova฀L.S,฀Sazonova฀V.A.฀ Phys฀Met฀Metallogr฀1986;61:฀1170. ฀ 8฀ Valiev฀ R.Z.,฀ Kaibyshev฀ O.A.,฀ Kuznetsov฀ R.I.,฀ Musalimov฀ R.S.,฀ Tsenev฀ N.K.฀ Dokl฀ Akad฀Nauk฀SSSR฀(Reports฀of฀USSR฀Academy฀of฀Sciences)฀1988;301(4):฀864. ฀ 9฀ Valiev฀R.Z.,฀Krasilnikov฀N.A.,฀Tsenev฀N.K.฀Mater฀Sci฀Eng฀A฀1991;137:฀35. 10฀ Valiev฀R.Z.,฀Korznikov฀A.V.,฀Mulyukov฀R.R.฀Mater฀Sci฀Eng฀A฀1993;186:฀141. 11฀ Valiev฀ R.Z.,฀ Estrin฀ Y.,฀ Horita฀ Z.,฀ Langdon฀ T.G.,฀ Zehetbauer฀ M.J.,฀ Zhu฀ Y.T.฀ JOM฀ 2006;58(4):฀33. 12฀ Zehetbauer฀ M.J.,฀ Zhu฀ Y.T.฀ (eds.),฀ Bulk฀ Nanostructured฀ Materials,฀ WILEY-VCH฀ Verlag฀GmbH฀&฀Co.฀KGaA,฀Weinheim,฀2009. 13฀ Estrin฀ Y.,฀ Maier฀ H.J.฀ (eds).฀ Mater฀ Sci฀ Forum:฀ Nanomaterials฀ by฀ severe฀ plastic฀ deformation฀IV฀2008;฀584–586. 14฀ Langdon฀T.G.,฀Furukawa฀M.,฀Nemoto฀M.,฀Horita฀Z.฀JOM฀2000;52(4):฀30. 15฀ Valiev฀ R.Z.,฀ Alexandrov฀ I.V.,฀ Bulk฀ Nanostructured฀ Metallic฀ Materials:฀ Production,฀ Structure and Properties, Akademkniga Pub., Moscow, Russia, 398 pp., 2007. 16฀ Valiev฀R.Z.,฀Islamgaliev฀R.K.,฀Alexandrov฀I.V.฀Prog฀Mater฀Sci฀2000;45:฀103. 17฀ Horita฀Z.฀(ed.),฀Nanomaterials฀by฀Severe฀Plastic฀Deformation,฀Trans฀Tech,฀Uetikon– Zürich,฀Switzerland,฀2006. 18฀ Zhilyaev฀A.P.,฀Langdon฀T.G.฀Prog฀Mater฀Sci฀2008;53:฀893. 19฀ Valiev฀RZ,฀Langdon฀T.G.฀Prog฀Mater฀Sci฀2006;51:฀881. 20 Zhilyaev A.P., Lee S., Nurislamova G.V., Valiev R.Z., Langdon T.G. Scripta Mater 2001;44:฀2753. 21฀ Sakai฀G.,฀Nakamura฀K.,฀Horita฀Z.,฀Langdon฀T.G.฀Mater฀Sci฀Eng฀A฀2005;406:฀268.

© Woodhead Publishing Limited, 2011

36 22฀ 23฀ 24฀ 25฀ 26฀ 27฀ 28฀ 29฀ 30฀ 31฀ 32฀ 33฀ 34฀ 35 36฀ 37฀ 38 39฀ 40 41฀ 42฀ 43฀ 44฀ 45฀ 46 47฀ 48฀ 49฀ 50฀ 51฀ 52฀ 53฀ 54฀ 55฀

56฀ 57฀

Nanostructured metals and alloys Murashkin฀M.Y.,฀Kilmametov฀A.,฀Valiev฀R.Z.฀Phys฀Met฀Metallgr฀2008;106฀(1):฀93. Harai฀Y.,฀Edalati฀K.,฀Horita฀Z.,฀Langdon฀T.G.฀Acta฀Mater฀2009;57:฀1147. Nakashima฀K.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Mater฀Sci฀Eng฀A฀2000;281:฀82. Nishida฀Y.,฀Arima฀A.,฀Kim฀J-C.,฀Ando฀T.฀Scripta฀Mater฀2001;45:฀261. Azushima฀A.,฀Aoki฀K.฀Mater฀Sci฀Eng฀A฀2002;337:฀45. Kamachi฀M.,฀Furukawa฀M.,฀Horita฀Z.,฀Langdon฀T.G.฀Mater฀Sci฀Eng฀A฀2003;361:฀258. Saito฀Y.,฀Utsunomiya฀H.,฀Suzuki฀H.,฀Sakai฀T.฀Scripta฀Mater฀2000;42:฀1139. Lee฀J-C.,฀Seok฀H-K.,฀Suh฀J-Y.฀Acta฀Mater฀2002;50:฀4005. Han฀J-H.,฀Seok฀H-K.,฀Chung฀Y-H.,฀Shin฀M-C.,฀Lee฀J-C.฀Mater฀Sci฀Eng฀A฀2002;323:฀ 342. Lee฀J-C.,฀Seok฀H-K.,฀Suh฀J-Y.,฀Han฀J-H.,฀Chung฀Y-H.฀Metall฀Mater฀Trans฀2002;33A:฀ 665. Raab฀G.J.,฀Valiev฀R.Z.,฀Lowe฀T.C.,฀Zhu฀Y.T.฀Mater฀Sci฀Eng฀A฀2004;382:฀30. Zhu฀Y.T.,฀Lowe฀T.C.,฀Langdon฀T.G.฀Scripta฀Mater฀2004;51:฀825. Segal฀V.M.,฀ Reznikov฀V.I.,฀ Drobyshevsky฀A.E.,฀ Kopylov฀V.I.฀ Reports฀ of฀ the฀ USSR฀ Academy฀of฀Sciences.฀Metals฀1981;1:฀115. Berbon P.B., Furukawa M., Horita Z., Nemoto M., Langdon T.G. Metall Mater Trans 1999;30A:฀1989. Nakashima฀K.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Acta฀Mater฀1998;46:฀1589. Iwahashi฀Y.,฀Wang฀J.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Scripta฀Mater฀1996;35:฀143. Furukawa M., Iwahashi Y., Horita Z., Nemoto M., Langdon T.G. Mater Sci Eng A 1998;257:฀328. Furukawa฀M.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Mater฀Sci฀Eng฀A฀2002;324:฀82. Iwahashi Y., Furukawa M., Horita Z., Nemoto M., Langdon T.G. Metall Mater Trans 1998;29A:฀2245. Iwahashi฀Y.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Acta฀Mater฀1997;45:฀4733. Iwahashi฀Y.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Acta฀Mater฀1998;46:฀3317. Oh-ishi฀K.,฀Horita฀Z.,฀Furukawa฀M.,฀Nemoto฀M.,฀Langdon฀T.G.฀Metall฀Mater฀Trans฀ 1998;29A:฀2011. Langdon฀T.G.,฀Furukawa฀M.,฀Nemoto฀M.,฀Horita฀Z.฀JOM฀2000;No.4:฀30. Raab฀ G.I.,฀ Valiev฀ R.Z.,฀ Gunderov฀ D.V.,฀ Lowe฀ T.C.,฀ Misra฀ A.,฀ Zhu฀ Y.T.฀ Mater฀ Sci฀ Forum฀2008;584–586:฀80. Semenova I.P., Salimgareeva G.H., Latysh V.V., Lowe T., Valiev R.Z. Mater Sci Eng A 2009;503:฀92. Latysh฀V.V.,฀Semenova฀I.P.,฀Salimgareeva฀G.H.,฀Kandarov฀I.V.,฀Zhu฀Y.T.,฀Lowe฀T.C.,฀ Valiev฀R.Z.฀Mater฀Sci฀Forum฀2006;฀503–504:฀763. Valiev฀R.Z.,฀Semenova฀I.P.,฀Latysh฀V.V.,฀Rack฀H.,฀Lowe฀T.C.,฀Petruzelka฀J.,฀Dluhos฀L.,฀ Hrusak฀D.,฀Sochova฀J.฀Adv฀Eng฀Mater฀2008;10:฀B15. Segal฀V.M.฀Mater฀Sci฀Eng฀A฀1995;197:฀157. Huang฀J.,฀Zhu฀Y.T.,฀Jiang฀H.,฀Lowe฀T.C.฀Acta฀Mater฀2001;49:฀1497. Zhu฀Y.T.,฀Jiang฀H.,฀Huang฀J.,฀Lowe฀T.C.฀Metall฀Mater฀Trans฀2001;32A:฀1559. Etherington฀C.J.฀Eng฀for฀Industry฀1974;8:฀893. Furukawa฀M.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀J฀Mater฀Sci฀2001;36:฀82. Stolyarov฀V.V.,฀Zhu฀Y.T.,฀Lowe฀T.C.,฀Valiev฀R.Z.฀Mater฀Sci฀Eng฀A฀2001;303:฀82. Zhu฀Y.T.,฀Lowe฀T.C.,฀Valiev฀R.Z.,฀Stolyarov฀V.V.,฀Latysh฀V.V.,฀Raab฀G.I.฀USA฀Patent฀ No.6,฀ 399,฀ 215฀ Ultraine-grained฀ titanium฀ for฀ medical฀ implants,฀ published฀ July฀ 4,฀ 2002. Valiev฀R.Z.฀Adv฀Eng฀Mater฀2003;5:฀296. Valiev฀R.Z.,฀Mishra฀R.S.,฀Grosa฀J.,฀Mukherjee฀A.K.฀Scripta฀Mater฀1996;34:฀1443.

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58฀ Shen฀H.,฀Li฀Z.,฀Guenther฀B.,฀Korznikov฀A.V.,฀Valiev฀R.Z.฀Nanostr฀Mater฀1995;6:฀385. 59 Wilde G., Boucharat N., Dinda G.P., Rösner H., Valiev R.Z. Mater Sci Forum 2006;503–504:฀425. 60 Gunderov D.V., Pushin V.G., Valiev R.Z., Valiev E.Z. Deformation and Fracture of Materials฀2006;4:฀22. 61฀ Sergueeva฀A.V.,฀ Song฀ C.,฀Valiev฀ R.Z.,฀ Mukherjee฀A.K.฀ Mater฀ Sci฀ Eng฀A฀ 2003;339:฀ 159. 62฀ Huang฀J.Y.,฀Zhu฀Y.T.,฀Liao฀X.Z.,฀Valiev฀R.Z..฀Phil฀Mag฀Lett฀2004;84:฀183. 63฀ Waitz฀T.,฀Kazykhanov฀V.,฀Karnthaler฀H.P.฀Acta฀Mater฀2004;52:฀385. 64฀ Valiev฀R.Z.฀Nature฀Mat฀2004;3:฀511. 65฀ Zhu฀Y.T.,฀Langdon฀T.G.฀JOM฀2004;56(10):฀58. 66฀ Valiev฀R.Z.฀Int฀J฀Mat฀Res฀(formerly฀Metallkd)฀2009;100:฀757 67฀ Ungár฀ T.,฀ Balogh฀ L.,฀ Zhu฀ Y.T.,฀ Horita฀ Z.,฀ Xu฀ C.,฀ Langdon฀ T.G.฀ Mater฀ Sci฀ Eng฀ A฀ 2007;444:฀153. 68฀ Zehetbauer฀M.J.฀(ed.).฀Advanced฀Engineering฀Materials,฀Special฀Issue฀on฀Nanomaterials฀ by Severe Plastic Deformation (SPD), Vol. 5, 2003. 69฀ Gutkin฀M.Y.,฀Ovidko฀I.A.฀Appl฀Phys฀Lett฀2005;87:฀251916-1. 70฀ Kurmanaeva฀L.,฀Ivanisenko฀Y.,฀Markmann฀J.,฀Kübel฀C.,฀Chuvilin฀A.,฀Doyle฀S.,฀Valiev฀ R.Z.,฀Fecht฀H-J.฀Mater฀Sci฀Eng฀A฀2010;527:฀1776. 71 Nurislamova G., Sauvage X., Murashkin M., Islamgaliev R., Valiev R.Z. Phil Mag Lett 2008;88:฀459. 72฀ Sha฀ G.,฀ Wang฀ Y.B.,฀ Liao฀ X.Z.,฀ Duan฀ Z.C.,฀ Ringer฀ S.P.,฀ Langdon฀ T.G.฀ Acta฀ Mater฀ 2009;57:฀3123. 73฀ Horita฀Z.,฀Smith฀D.J.,฀Furukawa฀M.,฀Nemoto฀M.,฀Valiev฀R.Z.,฀Langdon฀T.G.฀J฀Mater฀ Res฀1996;11:฀1880. 74฀ Valiev฀R.Z.,฀Kozlov฀E.V.,฀Ivanov฀Y.F.,฀Lian฀J.,฀Nazarov฀A.A.,฀Baudelet฀B.฀Acta฀Metall฀ Mater฀1994;42:฀2467. 75฀ Zhao฀Y.,฀Bingert฀J.F.,฀Liao฀X.,฀Cui฀B.,฀Han฀K.,฀Sergueeva฀A.V.,฀Mukherjee฀A.K.,฀Valiev฀ R.Z.,฀Langdon฀T.G.,฀Zhu฀Y.T.฀Adv฀Mater฀2006;18:฀2949. 76฀ Chukin฀M.V.,฀Koptseva฀H.V.,฀Valiev฀R.Z.,฀Yakovleva฀I.L.,฀Zrnik฀J.,฀Covarik฀T.฀Vestnik฀ MGTU฀2008;1฀(in฀Russian). 77฀ Liddicoat฀P.V.,฀Liao฀X.Z.,฀Zhao฀Y.,฀Zhu฀Y.,฀Murashkin฀M.Y.,฀Lavernia฀E.J.,฀Valiev฀R.Z.,฀ Ringer S.P., 2010, submitted to Nat. Commun. 78฀ Valiev฀ R.Z.,฀ Enikeev฀ N.A.,฀ Murashkin฀ M.Y.,฀ Alexandrov฀ S.E.,฀ Goldshtein฀ R.V.฀ Doklady฀Physics฀2010;55(6):฀267. 79฀ Valiev฀R.Z,฀Murashkin฀M.Yu,฀Bobruk฀E.V.,฀Raab฀G.I.฀Mater฀Trans฀2009;50:฀87. 80฀ Valiev฀R.Z.,฀Sergueeva฀A.V.,฀Mukherjee฀A.K.฀Scripta฀Mater฀2003;49:฀669. 81฀ McFadden฀ S.X.,฀ Mishra฀ R.S.,฀ Valiev฀ R.Z.,฀ Zhilyaev฀ A.P.,฀ Mukherjee฀ A.K.฀ Nature฀ 1999;398:฀684 82฀ Valiev฀ R.Z.,฀ Salimonenko฀ D.A.,฀ Tsenev฀ N.K.,฀ Berbon฀ P.B.,฀ Langdon฀ T.G.฀ Scripta฀ Mater฀1997;37:฀1945. 83฀ Kawasaki฀M.,฀Langdon฀T.G.฀J฀Mater฀Sci฀2007;42:฀1782. 84฀ Lowe฀T.C.,฀Valiev฀R.Z.฀Investigations฀and฀applications฀of฀severe฀plastic฀deformation.฀ Kluwer,฀Dordrecht,฀The฀Netherlands,฀2000. 85฀ Zhu฀ Y.T.,฀ Langdon฀ T.G.,฀ Valiev฀ R.Z.,฀ Semiatin฀ S.L.,฀ Shin฀ D.H.,฀ Lowe฀ T.C.฀ (eds.)฀ Ultraine-Grained฀Materials฀III,฀Minerals,฀Metals฀and฀Materials฀Society,฀Warrendale,฀ PA,฀USA,฀2004. 86฀ Zehetbauer฀ M.J.,฀ Valiev฀ R.Z.฀ (eds.)฀ Nanomaterials฀ by฀ severe฀ plastic฀ deformation.฀ Wiley-VCH฀Verlag,฀Weinheim,฀Germany,฀2004.

© Woodhead Publishing Limited, 2011

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87 Zhu Y.T., Varyukhin V. (eds.) Nanostructured materials by high-pressure severe plastic deformation. Springer, Dordrecht, The Netherlands, 2006. ฀ 88฀ Zhu฀Y.T.,฀Langdon฀T.G.,฀Horita฀Z.,฀Zehetbauer฀M.J.,฀Semiatin฀S.L.,฀Lowe฀T.C.฀(eds.)฀ Ultraine-Grained฀Materials฀IV,฀Minerals,฀Metals฀and฀Materials฀Society,฀Warrendale,฀ PA,฀USA,฀2006. ฀ 89฀ Koch฀C.C.฀Scripta฀Mater฀2003;49:฀657. ฀ 90฀ Morris฀D.G.฀Mechanical฀behaviour฀of฀nanostructured฀materials.฀Trans฀Tech,฀UetikonZürich, 1998. ฀ 91฀ Krasilnikov฀N.,฀Pakiela฀Z.,฀Lojkowski฀V.,฀Valiev฀R.Z.฀Sol฀St฀Phen฀2005;101–102:฀49. ฀ 92฀ Hugnes฀D.A.,฀Hansen฀N.฀Acta฀Metall฀2000;48:฀2985. ฀ 93฀ Thompson฀A.W.฀Acta฀Metall฀1975;23:฀1337. ฀ 94฀ Xiao฀C.,฀Mirshams฀R.A.,฀Whang฀S.H.,฀Yin฀W.M.฀Mater฀Sci฀Eng฀A฀2001;301:฀35. ฀ 95฀ Ebrahimi฀F.,฀Bourne฀G.R.,฀Kelly฀M.S.,฀Matthews฀T.E.฀Nanostr฀Mater฀1999;11:฀343. ฀ 96฀ Tsuji฀ N.฀ Unique฀ deformation฀ behaviors฀ of฀ the฀ ultraine-grained฀ aluminum฀ alloys฀ fabricated by accumulative roll bonding. In: Zhu Y.T., Varyukhin V. (eds.) Nanostructured materials by high-pressure severe plastic deformation. Springer Netherlands, 2006. p. 227. 97 Furukawa M., Horita Z., Nemoto M., Valiev R.Z., Langdon T.G. Phil Mag A 1998;78(1):฀203. ฀ 98฀ Meyers฀M.A.,฀Mishra฀A.,฀Benson฀D.J.฀JOM฀2006;58(4):฀41. ฀ 99฀ Pande฀C.S.,฀Cooper฀K.P.฀Prog฀Mater฀Sci฀2009;54:฀689. 100฀ Gleiter฀H.฀Prog฀Mater฀Sci฀1989;33:฀223. 101฀ Dobatkin฀S.,฀Zrnik฀J.,฀Nikulin฀S.,฀Kovarik฀T.,฀submitted฀to฀JPCS฀(Proc.฀of฀the฀15th฀ Int.฀Conf.฀on฀the฀Strength฀of฀Materials),฀2009. 102฀ Zhao฀Y.H.,฀Bingert฀J.F.,฀Zhu฀Y.T.,฀Liao฀X.Z.,฀Valiev฀R.Z.,฀Horita฀Z.,฀Langdon฀T.G.,฀ Zhou฀Y.Z.,฀Lavernia฀E.J.฀Appl฀Phys฀Lett฀2008;92:฀081903. 103฀ Furukawa฀M.,฀Horita฀Z.,฀Langdon฀T.G.฀J฀Mater฀Sci฀2005;40:฀909. 104฀ Valiev฀R.฀Mater฀Sci฀Forum฀2008;584–586:฀22. 105฀ Fujita฀T.,฀Horita฀Z.,฀Langdon฀T.G.฀Mater฀Sci฀Eng฀A฀2004;371:฀241. 106฀ Watanabe฀T.฀Res฀Mech฀1984;11:฀47. 107฀ Watanabe฀T.,฀Fujii฀H.,฀Oikawa฀H.,฀Arai฀K.I.฀Acta฀Metall฀1989;37:฀941. 108฀ Valiev฀R.Z.,฀Alexandrov฀I.V.,฀Zhu฀Y.T.,฀Lowe฀T.C.฀J฀Mater฀Res฀2002;17:฀5. 109฀ Wang฀Y.,฀Chen฀M.,฀Zhou฀F.,฀Ma฀E.฀Nature฀2002;419:฀912. 110฀ Horita฀Z.,฀Ohashi฀K.,฀Fujita฀T.,฀Kaneko฀K.,฀Langdon฀T.G.฀Adv฀Mater฀2005;17:฀1599. 111฀ Zhao฀Y.,฀Topping฀T.,฀Bingert฀J.F.,฀Thornton฀J.J.,฀Dangelewicz฀A.M.,฀Li฀Y.,฀Zhu฀Y.T.,฀ Zhou฀Y.,฀Lavernia฀E.J.฀Adv฀Mater฀2008;20:฀3028. 112 Parker E.R. Materials data book for engineers and scientists. McGraw-Hill, New York,฀NY,฀USA,฀1967. 113 Brandes E.A., Brook G.B. Smithells metals reference book, 7th ed. ButterworthHeinemann,฀Oxford,฀UK,฀Ch.฀22,฀1992. 114฀ Höppel฀H.W.,฀May฀J.,฀Eisenlohr฀P.,฀Göken฀M.฀Metallkd฀2005;96:฀566. 115฀ May฀J.,฀Höppel฀H.W.,฀Göken฀M.฀Scripta฀Mater฀2005;53:฀189. 116฀ Dalla฀Torre฀F.,฀Lapovok฀R.,฀Sandlin฀J.,฀Thomson฀P.F.,฀Davies฀C.H.J.,฀Pereloma฀E.V.฀ Acta฀Mater฀2004;52:฀4819. 117฀ Krasilnikov฀N.,฀Lojkowski฀W.,฀Pakiela฀Z.,฀Valiev฀R.฀Mater฀Sci฀Eng฀A฀2005;397:฀330. 118฀ Zhang฀ X.,฀ Wang฀ H.,฀ Scattergood฀ R.O.,฀ Narayan฀ J,฀ Koch฀ C.C.,฀ Sergueeva฀ A.V.,฀ Mukherjee฀A.K.฀Acta฀Mater฀2002;50:฀4823. 119฀ Mughrabi฀H.,฀Höppel฀H.W.,฀Kautz฀M.,฀Valiev฀R.Z.฀Metallkd฀2003;94:฀1079. 120฀ Park฀Y.S.,฀Chung฀K.H.,฀Kim฀N.J.,฀Lavernia฀E.J.฀Mater฀Sci฀Eng฀A฀2004;374:฀211.

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121฀ Islamgaliev฀R.K.,฀Yunusova฀N.F.,฀Sabirov฀I.N.,฀Sergueeva฀A.V.,฀Valiev฀R.Z.฀Mater฀Sci฀ Eng฀A฀2001;319–321:฀877. 122฀ Valiev฀R.Z.,฀Zehetbauer฀M.J.,฀Estrin฀Y.,฀Höppel฀H.W.,฀Ivanisenko฀Y.,฀Hahn฀H.,฀Wilde฀ G.,฀Roven฀H.J.,฀Sauvage฀X.,฀Langdon฀T.G.฀Adv฀Eng฀Mater฀2007;9:฀527. 123฀ K.฀Suehiro,฀S.฀Nishimura,฀Z.฀Horita,฀Mater฀Trans,฀2008;49:฀102. 124฀ B.฀Straumal,฀S.G.฀Protasova,฀A.A.฀Mazilkin,฀B.฀Baretzky,฀D.฀Goll,฀D.V.฀Gunderov,฀ R.Z.฀Valiev,฀Phil฀Mag฀Lett,฀2009;89:฀649. 125฀ Lowe฀T.C.฀JOM฀2006;58(4):฀28. 126฀ Brunette฀ D.M.,฀ Tengvall฀ P.,฀ Textor฀ M.,฀ Thomsen฀ P.฀ Titanium฀ in฀ med.฀ Springer,฀ Heidelberg, 2001. 127฀ Stolyarov฀V.V.,฀Zhu฀Y.T.,฀Alexandrov฀I.V.,฀Lowe฀T.C.,฀Valiev฀R.Z.฀Mater฀Sci฀Eng฀A฀ 2003;343:฀43. 128฀ Balyanov฀A.,฀ Kutnyakova฀ J.,฀Amirkhanova฀ N.A.,฀ Stolyarov฀ V.V.,฀ Valiev฀ R.Z.,฀ Liao฀ X.Z.,฀Zhao฀Y.H.,฀Jiang฀Y.B.,฀Xu฀H.F.,฀Lowe฀T.C.,฀Zhu฀Y.T.฀Scripta฀Mater฀2004;51:฀225. 129฀ Horita฀Z.,฀Furukawa฀M.,฀Nemoto฀M.,฀Barnes฀A.J.,฀Langdon฀T.G.฀Acta฀Mater฀2000;48:฀ 3633. 130 Akamatsu H., Fujinami T., Horita Z., Nemoto M., Langdon T.G. Scripta Mater 2001;44:฀759. 131฀ Park฀K.T.,฀Lee฀H.J.,฀Lee฀C.S.,฀Nam฀W.J.,฀Shin฀D.H.฀Scripta฀Mater฀2004;51:฀479. 132฀ Nikulin฀I.,฀Kaibyshev฀R.,฀Sakai฀T.฀Mater฀Sci฀Eng฀A฀2005;07:฀62. 133฀ Korznikov฀ A.V.,฀ Safarov฀ I.M.,฀ Nazarov฀ A.A.,฀ Valiev฀ R.Z.฀ Mater฀ Sci฀ Eng฀ A฀ 1996;206:฀39. 134฀ Borisova฀M.Z.,฀Yakovleva฀S.P.,฀Ivanov฀A.M.฀Sol฀St฀Phen฀2006;14:฀97.

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2 Bulk nanostructured metals and alloys produced by accumulative roll-bonding N.฀TSUJI,฀Kyoto฀University,฀Japan

Abstract: This chapter introduces the fabrication of bulk nanostructured metals and alloys by the accumulative roll-bonding (ARB) process. The principles and processing details of ARB are presented and discussed. The formation of ultraine-grained฀structures฀in฀single-phased฀metals฀during฀ARB฀is฀illustrated฀ using฀original฀experimental฀results.฀This฀process฀is฀understood฀in฀terms฀of฀grain฀ subdivision:฀the฀ultraine-grains฀essentially฀have฀the฀characteristics฀of฀ deformation microstructures, which include large misorientation grain boundaries. Post-ARB annealing of aluminum and ferritic steel cause relatively continuous changes in the grain structure by a combination of recovery and grain growth. The ARB process can also fabricate non-equilibrium nanostructured materials, such as a composite of nanocrystals and metallic glass฀in฀the฀Cu฀+฀Zr฀multi-stack฀metal฀system.฀Ultraine-grained฀metals฀ fabricated฀by฀ARB฀exhibit฀two฀to฀four฀times฀more฀strength฀than฀the฀same฀ metals with conventionally coarse-grained structures, but they also show limited tensile ductility, due to early plastic instability that occurs in the nanostructured materials. This observation also suggests the possibility of maintaining both high strength and adequate ductility by making the nanostructures multi-phased. Key words:฀severe฀plastic฀deformation,฀accumulative฀roll-bonding,฀ultraine฀ grains, non-equilibrium structures, grain subdivision, bulk mechanical alloying, mechanical properties.

2.1

Introduction

Accumulative roll-bonding (ARB) is a kind of severe plastic deformation (SPD) process for fabricating bulk nanostructured metallic materials.1 It has been clariied฀ that฀ bulk฀ nanostructured฀ metals฀ and฀ alloys,฀ which฀ are฀ composed฀ of฀ ultraine฀ grains฀ (UFGs)฀ with฀ a฀ mean฀ grain฀ size฀ of฀ several฀ hundreds฀ of฀ nanometers฀or฀nanocrystals฀with฀mean฀grain฀size฀of฀several฀tens฀of฀nanometers,฀ can be fabricated by plastic deformation up to a very high strain (above logarithmic equivalent strain of 4~5), which is often called SPD.2 Various kinds of unique SPD฀processes,฀such฀as฀equal-channel฀angular฀extrusion฀(ECAE),฀high-pressure฀ torsion฀ (HPT),฀ cyclic฀ extrusion฀ and฀ compression฀ (CEC),฀ etc.,฀ have฀ been฀ developed฀for฀realizing฀bulk฀nanostructured฀metals.1,2 Among the SPD processes, ARB is advantageous for continuous production of sheet materials, since it uses rolling deformation in principle. In laboratory scale, ARB has been applied to various kinds of metals and alloys and has succeeded in producing bulky sheets having nanostructures. In this chapter, the principle of the ARB process, 40 © Woodhead Publishing Limited, 2011

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evolution of nanostructures during ARB, and mechanical properties of the nanostructured metals and alloys fabricated by ARB are introduced and summarized.

2.2

The principle of accumulative roll-bonding (ARB)

ARB was developed by Saito et al. in 1998.1,3 The principle of the ARB process is schematically illustrated in Fig. 2.1. ARB is a SPD process using rolling deformation. Rolling is the most advantageous metalworking process for continuous production of bulk materials with shapes of plates, sheets, bars, and so on. However, it is nearly impossible to achieve ultra-high plastic strain above a logarithmic equivalent strain of 4~5 by the conventional rolling, because the dimension of the materials (the thickness of sheets,฀for฀example)฀decreases฀with฀increasing฀total฀plastic฀strain฀applied.฀In฀the฀ ARB฀process,฀for฀example,฀a฀sheet฀2฀mm฀thick฀is฀irst฀rolled฀to฀a฀50%฀reduction฀ in฀thickness.฀The฀rolled฀sheet฀with฀a฀thickness฀of฀1฀mm฀and฀approximately฀twice฀ the length of the original is cut into two, stacked together to make 2 mm thick material (initial thickness) (see Fig. 2.1), and the stack is rolled again. In order to obtain one-body solid material, the rolling in the ARB process is not only a deformation process but also a bonding process, which is known as roll-bonding, used for the production of clad sheets. To achieve good bonding between two stacked sheets, the contact surfaces of the sheets are degreased and wire-brushed typically before being subjected to rolling. Roll-bonding is sometimes carried out at฀elevated฀temperatures฀below฀the฀recrystallization฀temperature฀of฀the฀material,฀ in order to make the bonding better and to reduce the rolling force. By repeating the procedure, one can apply a very large amount of plastic strain to the sheet material without changing the original dimensions. The von Mises equivalent strain (εeq) after n฀cycles฀of฀the฀ARB฀can฀be฀expressed฀as,

2.1 Schematic illustration showing the principle of the accumulative roll-bonding (ARB) process.

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Nanostructured metals and alloys ,

[2.1]

where t0, t, and r are initial thickness of the stacked sheets, the thickness after rollbonding, and the reduction in thickness per cycle, respectively. Geometrical changes฀of฀the฀materials฀in฀the฀ARB฀process฀using฀50%฀reduction฀per฀cycle฀(r฀=฀ 0.5฀in฀equation฀(2.1))฀are฀summarized฀in฀Table฀2.1.฀An฀equivalent฀strain฀of฀4฀can฀ be achieved by 5 ARB cycles in this case, and after 10 ARB cycles the 1 mm-thick sheet contains 1024 original layers.

2.3

Processing details

The฀ARB฀process฀does฀not฀require฀any฀special฀equipment฀except฀for฀a฀rolling฀mill฀ with enough capacity, which is another advantage of this method. Figure 2.2

Table 2.1 Geometrical changes of the material during the ARB where two pieces of the 1 mm thick sheets are stacked and roll-bonded by 50% reduction per cycle No. of cycles

1

2

3

4

5

6

7

8

No. of layers

2

4

8

16

32

64

128

256

512 1024

2n

No. of bonded boundaries

1

3

7

15

31

63

127

255

511 1023

2n –1

7.8

3.9

1.9

Layer 500 250 125 62.5 31.3 15.6 interval (µm)

9

10

1000/2n (1 – 1/2n) × 100

50

75

87.5 93.8 96.9 98.4 99.2 99.6 99.8 99.9

Equivalent strain

0.8

1.6

2.4

4

4.8

5.6

6.4

7.2

n

0.96

Total reduction (%)

3.2

.........

8

2.2 (a) The two-high rolling mill used for the ARB process in the author’s group. (b) A channel guide for the stacked sheets on the entrance side of the mill.

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0.8n

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shows the rolling mill that has been used for the ARB process in the author’s group. The rolling machine is a conventional two-high mill with 310 mm roll diameter. Because the large reduction in 1 pass is necessary to achieve good bonding4฀and฀roll-bonding฀is฀often฀carried฀out฀without฀lubrication฀to฀realize฀quick฀ UFG฀formation,5,6 the rolling force during ARB becomes very large. For instance, the rolling force for a commercial purity aluminum sheet 40 mm in width reaches to 49 tons force in the seventh cycle of ARB at room temperature (RT) without lubrication.2 Thus, the rolling mill is required to have enough capacity. The rolling mill shown in Fig. 2.2 (a) has a capacity of 150 tons. The ARB process has been successfully applied to various kinds of metallic materials and actually produced bulky sheets with nanostructures. In most materials,฀ the฀ ultraine฀ lamellar฀ boundary฀ structures฀ or฀ the฀ pancake-shaped฀ ultraine฀ grains,฀ whose฀ average฀ boundary฀ spacing฀ or฀ grain฀ thickness฀ is฀ much฀ smaller than 1 µm, were formed uniformly in the materials after 5~6 cycles of ARB.1,2฀ The฀ARB-processed฀ sheets฀ with฀ ultraine-grained฀ structures฀ exhibited฀ very high strength, which is two to four times higher than that of the starting materials฀with฀conventional฀grain฀sizes,฀as฀will฀be฀shown฀in฀a฀later฀section. It฀has฀been฀found,฀rather฀unexpectedly,฀that฀roll-bonding฀in฀the฀ARB฀process฀ was฀not฀dificult฀for฀most฀of฀the฀ductile฀metallic฀materials,฀although฀degreasing฀ and wire-brushing the contact surfaces before stacking were an indispensable step for฀a฀good฀bonding.฀The฀minimum฀required฀rolling฀reduction฀in฀1฀pass฀exists฀to฀ achieve a good bonding,4 which depends on the kind of materials in use and the rolling฀conditions.฀The฀critical฀1-pass฀reduction฀in฀ARB฀at฀RT฀is฀roughly฀40~50%.฀ In฀case฀of฀Al฀alloys,฀for฀example,฀oxide฀layers฀quickly฀cover฀the฀surfaces฀of฀the฀ sheet฀even฀if฀wire-brushing฀is฀conducted.฀However,฀the฀oxide฀layers฀are฀very฀thin฀ and฀brittle,฀and฀will฀not฀survive฀rolling.฀When฀a฀50%฀reduction฀is฀used฀in฀rollbonding,฀ the฀ surface฀ area฀ increases฀ by฀ 100%,฀ which฀ means฀ that฀ so฀ many฀ fresh฀ metallic฀atoms฀behind฀the฀oxide฀layer฀come฀to฀the฀surface฀during฀roll-bonding,฀i.e.฀ create฀virgin฀surfaces฀that฀are฀not฀covered฀with฀oxide฀layers.฀The฀fresh฀metallic฀ atoms on both sides of the sheet surfaces make close contact with each other to achieve bonding under great pressure from the roll-bite. This is a possible mechanism of roll-bonding in the ARB process. During repeated ARB cycles, bonding at the interfaces becomes increasingly stronger, since the bonding interfaces are repeatedly elongated to the rolling direction. As a result, even after fracture฀in฀a฀tensile฀test,฀exfoliation฀of฀the฀bonded฀interfaces฀could฀be฀seen฀only฀at฀ the center of the sheet, which corresponds to the bonded interface in the most recent ARB cycle. A serious potential problem in the ARB process is cracking during rolling in some kinds of metals and alloys. The typical appearance of the ARB-processed aluminum alloys is shown in Fig. 2.3. In very ductile materials, such as pure Al, pure฀Cu฀and฀ultra-low-carbon฀steel,฀almost฀no฀cracking฀occurs฀even฀after฀many฀ cycles฀of฀ARB.฀As฀a฀result,฀sound฀and฀large฀sheets฀illed฀with฀the฀UFG฀structures฀ can฀be฀obtained.฀Figure฀2.3a฀is฀such฀an฀example฀of฀the฀1100-Al฀(99%Al)฀sheet฀

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2.3 Appearance of the ARB-processed Al alloy sheets. Thickness of the sheets is 1 mm. (a) 1100-Al ARB-processed by 5 cycles at RT. (b) 5083-Al ARB processed by 2 cycles at RT.

ARB-processed by 5 cycles at RT, whose dimensions are 1 mm thick, 55 mm wide and 320 mm long. On the other hand, some kinds of materials considerably lost฀ workability฀ with฀ increasing฀ARB฀ cycles.฀An฀ example฀ of฀ severely฀ cracked฀ sheet฀of฀the฀5083-Al฀(Al-4.7%Mg)฀ARB-processed฀by฀2฀cycles฀at฀RT฀is฀shown฀in฀ Fig. 2.3 (b). The cracks generally start at the edges of the sheet due to tensile stress, and they sometimes propagate into the center of the sheet (Fig. 2.3 (b) ). Once฀such฀cracking฀occurs,฀it฀is฀dificult฀to฀proceed฀to฀the฀next฀cycle.฀However,฀ there are some small techniques or know-how for avoiding cracking during rollbonding. As a result, the ARB process has been applicable to most of the metallic materials that can be deformed in rolling. The ARB process has been successfully applied฀ to฀ pure฀ metals฀ (Al,฀ Fe,฀ Cu,฀ Ni,฀Ti฀ and฀ Zr),฀ various฀ kinds฀ of฀Al฀ alloys,฀

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Al-matrix฀composites,฀low-carbon฀steels,฀ferritic฀stainless฀steels,฀duplex฀stainless฀ steels,฀high-Ni฀austenitic฀steels,฀dilute฀Cu฀alloys,฀brass,฀Cu-Ag฀alloys,฀and฀even฀ Mg฀alloys,฀and฀UFG฀microstructures฀have฀been฀obtained฀in฀all฀cases฀after฀ARB฀ over 5~6 cycles.2,7–10

2.4

Change in microstructures during the process

2.4.1 Formation of ultrafine grains in ARB In฀this฀section,฀the฀evolution฀of฀UFG฀structures฀during฀the฀ARB฀in฀single-phase฀ metals is shown and discussed. Figure 2.4 shows the boundary misorientation maps obtained by electron backscattering diffraction (EBSD) measurement in a ield-emission฀type฀scanning฀electron฀microscope฀(FE-SEM)฀for฀the฀ultra-lowcarbon฀interstitial฀free฀(IF)฀steel฀ARB-processed฀by฀various฀cycles฀at฀500°C.11 In Fig.฀2.4,฀high-angle฀boundaries฀with฀misorientations฀larger฀than฀15°฀were฀drawn฀ in bold black lines, while low-angle boundaries whose misorientations were between฀ 2°฀ and฀ 15°฀ were฀ drawn฀ in฀ narrow฀ grey฀ lines.฀ After฀ 1-cycle฀ ARB฀ corresponding฀to฀just฀a฀50%฀reduction,฀elongated฀initial฀grains฀involving฀many฀ low-angle boundaries are observed. This is a typical microstructure conventionally seen in deformed metals. It should be noted, however, that newly formed highangle boundaries appeared in the vicinity of initial grain boundaries. The number and the density of the deformation-induced high-angle boundaries increased with more฀ ARB฀ cycles฀ (i.e.฀ strain),฀ and฀ inally฀ the฀ specimen฀ was฀ illed฀ with฀ the฀ elongated grain structure, mostly subdivided by high-angle boundaries. The misorientation distribution in the samples shown in Fig. 2.4 is represented in Fig. 2.5. The ‘fHAGB’ in Fig. 2.5 indicates the fraction of high-angle grain boundaries. The 1-cycle ARB-processed specimen that had a typical deformation microstructure (Fig.฀2.4฀(a))฀was฀mostly฀illed฀with฀low-angle฀boundaries฀(64%).฀It฀should฀be฀noted฀ that฀ in฀ the฀ EBSD฀ analysis฀ the฀ misorientations฀ under฀ 2°฀ were฀ cut฀ off฀ in฀ order฀ to฀ remove inaccuracy due to measurement and analysis in automatic orientation mapping. That is, the actual fraction of the low-angle boundaries must be much larger฀than฀64%.฀The฀fraction฀of฀high-angle฀boundaries฀increased฀with฀increasing฀ strain,฀and฀more฀than฀80%฀of฀the฀observed฀boundaries฀were฀already฀high-angle฀in฀ the specimen ARB-processed by 5 cycles (Fig. 2.5 (d)). Other ARB-processed materials showed similar microstructural evolution to that in the IF steel described above.12,13฀It฀has฀been฀clariied฀in฀various฀metals฀that฀the฀ultraine฀microstructures฀ are quite uniform throughout the thickness of the ARB-processed sheets.14,15 Figure 2.6 shows TEM micrographs of the IF steel (a) and the 1100-Al (b) ARB-processed by 6 cycles. The microstructures were observed from TD. These are the typical microstructures in the single-phased materials that have been ARB-processed by many cycles. Both materials showed quite similar microstructures elongated along RD, which corresponds to Fig. 2.4 (d). These are so-called lamellar boundary (LB) structures, which have been observed in heavily

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2.4 Boundary misorientation maps obtained by FE-SEM/EBSD measurements of the IF steel ARB-processed by (a) 1 cycle, (b) 2 cycles, (c) 3 cycles and (d) 5 cycles at 500°C without lubrication. The measurements were done on the longitudinal sections of the sheets.

rolled฀FCC฀metals.16 The mean spacing of the LBs was about 200 nm for both materials. As is shown statistically in Fig. 2.5, most of the boundaries in these microstructures฀ are฀ already฀ high-angle฀ ones,฀ as฀ has฀ been฀ also฀ conirmed฀ by฀ FE-SEM/EBSD฀and฀Kikuchi-line฀analysis฀in฀TEM.

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2.5 Misorientation distributions of the boundaries observed in the EBSD measurements of the IF steel ARB-processed by (a) 1 cycle, (b) 2 cycles, (c) 3 cycles and (d) 5 cycles at 500°C without lubrication. The data taken throughout thickness of the ARB-processed sheets were summarized.

2.6 Transmission electron microscopy microstructures of singlephased materials ARB-processed by 6 cycles without lubrication. The microstructures were observed from TD of the sheets. (a) IF steel processed at 500°C. (b) 1100-Al processed at RT.

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2.7 Transmission electron microscopy micrograph (a) and corresponding boundary misorientation map (b) of the 1100-Al ARB-processed by 6 cycles at 200°C. Observed from TD. The misorientation angles (in degrees) superimposed in (b) were calculated from the precise orientation of each region measured by TEM/Kikuchi-line analysis.

Figure 2.7 is a TEM microstructure (a) of a commercial purity aluminum (1100-Al)฀ARB-processed฀by฀6฀cycles฀at฀200°C฀together฀with฀the฀boundary฀map฀ (b)฀of฀the฀identical฀area฀obtained฀through฀TEM/Kikuchi-line฀analysis.12,17 In the boundary map (Fig. 2.7 (b) ), the misorientations of the boundaries are also indicated in degrees. It is again shown that most of the observed boundaries (especially lamellar boundaries) are high-angle ones having quite large misorientations. The boundaries between adjacent regions are not broad (or unclear) like dislocation-cell boundaries, but seem quite sharp. It can be concluded, therefore, that the elongated regions surrounded by high-angle boundaries are

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2.8 Schematic illustration showing grain subdivision mechanism during plastic deformation.

certainly ‘grains’ from a viewpoint of misorientation. At the same time, however, the morphology of the grains is elongated along the principal deformation direction, and the microstructure involves many low-angle boundaries and dislocations฀tangled฀within฀the฀grains.฀That฀is,฀the฀ultraine฀grains฀fabricated฀by฀ the ARB process (and by other SPD processes) are essentially deformation microstructures as well. The microstructural evolution during ARB (or during SPD in general) can be understood in terms of grain subdivision.18 The process of grain subdivision is illustrated in Fig. 2.8. Plastic deformation of metallic crystals is born basically by dislocation slips. In polycrystalline materials, the slip patterns (combination and number of slip systems operated) generally differ depending on locations even within an identical crystal. Different slip patterns result in different crystal rotation in producing misorientation between neighboring regions. The boundaries between such regions to bear the misorientation are called geometrically necessary boundaries (GNBs).16,18 In addition, the dislocations stored in the crystal tend to form฀ low-energy฀ conigurations฀ (LEC).฀ The฀ boundaries฀ formed฀ by฀ such฀ LEC฀ dislocations are called incidental dislocation boundaries (IDBs).16,18 The original grain฀(crystal)฀is฀inely฀subdivided฀by฀the฀GNBs฀and฀IDBs฀with฀increasing฀plastic฀ strain, which is the grain subdivision mechanism. The GNBs are especially important฀for฀UFG฀formation,฀as฀their฀misorientation฀increases฀with฀increasing฀ plastic strain applied.16,18 So-called lamellar boundary structure has been reported in heavily cold-rolled aluminum,16 where lamellar boundaries are GNBs. The ultraine฀lamellar฀structures฀observed฀in฀the฀present฀ARB฀specimens฀(Fig.฀2.6)฀are฀ quite similar to the lamellar boundary structure reported in heavily cold-rolled aluminum, though the proportion of high-angle boundaries in the ARB specimens is much higher than in the cold-rolled one.12 Because the mechanism of

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microstructure evolution is grain subdivision,฀ the฀ UFG฀ structures฀ produced฀ by฀ ultra-high straining are naturally deformation microstructures, though the subdivided regions (grains) have large misorientations to each other. This agrees well฀ with฀ the฀ fact฀ that฀ the฀ UFG฀ microstructures฀ obtained฀ through฀ the฀ ARB฀ involves many dislocations and low-angle grain boundaries (Figs. 2.4–2.7). It is also฀interesting฀that฀nano-sized฀deformation฀twins฀have฀been฀observed฀in฀UFG฀ pure฀Cu19 and pure Al20 fabricated by the ARB process, as has been reported in the materials fabricated by other SPD processes.

2.4.2 Change in microstructures during subsequent heat treatments Subsequent annealing could change the microstructures of the ARB-processed materials.17,21,22 Figure 2.9 shows the TEM microstructures of the 1100-Al ARB processed and then annealed at various temperatures.21 During low temperature annealing, the recovery decreases the dislocation density inside the elongated ultraine฀ grains,฀ and฀ the฀ ultraine฀ grains฀ grow฀ slightly.฀ The฀ specimen฀ annealed฀ at฀225°C฀for฀1.8฀ks฀was฀found฀to฀contain฀equiaxed฀grains฀free฀from฀dislocations฀ (Fig.฀2.9฀(d)฀).฀It฀is฀quite฀dificult฀to฀distinguish฀these฀grains฀from฀conventionally฀ recrystallized฀grains.฀It฀should฀be฀noted,฀however,฀that฀the฀mean฀grain฀size฀is฀still฀

2.9 Transmission electron microscopy microstructures of the 1100-Al ARB-processed by 6 cycles at 200°C without lubrication and then annealed at (a) 100°C, (b) 150°C, (c) 200°C, (d) 225°C, (e) 250°C and (f) 300°C for 1.8 ks. Observed from TD.

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around 1 µm, which cannot be achieved through a conventional deformation and recrystallization฀ process.฀ Further฀ annealing฀ causes฀ grain฀ growth,฀ resulting฀ in฀ equiaxed฀grain฀structures฀having฀various฀mean฀grain฀sizes.฀Similar฀microstructural฀ change has been observed in the ARB-processed IF steel as well.21,22 The changes in microstructures during annealing of ARB-processed pure Al and IF steel are fairly homogeneous and continuous. Such a continuous change of the grain structure is sometimes called continuous recrystallization,23 since฀it฀is฀greatly฀different฀from฀conventional฀recrystallization฀characterized฀by฀ nucleation and growth of particular grains (discontinuous recrystallization). However,฀even฀in฀conventional฀recrystallization฀(discontinuous recrystallization), it฀is฀considered฀that฀no฀new฀recrystallized฀grains฀nucleate฀by฀thermal฀luctuation฀ of฀atoms,฀but฀potential฀nuclei฀existed฀in฀the฀deformed฀microstructure฀preferentially฀ grow.24 In that sense, it might be confusing to use the term, continuous recrystallization.฀ In฀ the฀ materials฀ deformed฀ to฀ ultra-high฀ strains,฀ the฀ inely฀ subdivided structure is already full of high-angle grain boundaries, as is shown in Figs. 2.4, 2.5 and 2.7. Thus, it is reasonable to consider that the microstructural change during annealing of SPD processed materials (Fig. 2.9) can be a kind of normal grain growth accompanied by the recovery at grain interior. Here, it should be noted that both pure aluminum (face-centered cubic (fcc) metal with very high stacking fault energy) and IF steel (ferritic iron: body-centered cubic (bcc) metal) are the materials where recovery is enhanced to occur during annealing.฀In฀fact,฀recovery฀quickly฀occurs฀to฀decrease฀signiicantly฀the฀dislocation฀ density at the grain interior in the ARB-processed and annealed Al (Fig. 2.9). In the case of the ARB-processed fcc metals having medium to low stacking fault energy,฀ such฀ as฀ Cu฀ and฀ austenitic฀ steels฀ or฀ the฀ARB-processed฀ Ti,฀ it฀ has฀ been฀ found that as ARB-processed microstructures are similar to Al and IF steel, but recovery฀is฀dificult฀to฀achieve฀and฀discontinuous฀recrystallization฀happens฀during฀ annealing.11,15,25฀One฀example฀of฀discontinuous฀grow฀of฀ultraine฀grains฀during฀ annealing in the commercial purity Ti ARB-processed and annealed is shown in Fig. 2.10. Even in the ARB-processed pure Al, discontinuous growth of particular grains can be observed under certain annealing conditions.13 Figure 2.10 looks like฀conventional฀(discontinuous)฀recrystallization฀by฀nucleation฀and฀growth,฀or฀ abnormal grain growth. On the other hand, the microstructural change shown in Fig. 2.9 are much more like normal grain growth. When the ARB process is carried out after solution treatment of materials, precipitation occurs during heat treatment (ageing) following the ARB. Since the ARB-processed฀specimens฀have฀UFG฀structures฀with฀a฀very฀high฀density฀of฀grain฀ boundaries, the precipitation behaviors of the ARB-processed materials are signiicantly฀different฀from฀those฀of฀the฀conventional฀alloys฀with฀coarse-grained฀ structures.฀ For฀ example,฀ the฀ precipitation฀ kinetics฀ from฀ the฀ UFG฀ materials฀ is฀ much faster than that from coarse-grained ones, and sometimes stable phases directly appear during aging treatment, skipping the formation of the metastable phases that usually appear in conventional alloys.26,27

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2.10 Transmission electron microscopy microstructures of the commercial purity Ti ARB-processed by 6 cycles at RT with lubrication and then annealed at various temperatures for 1.8 ks. Observed from TD. (a) As ARB-processed. Annealed at (b) 200°C, (c) 300°C, (d) 400°C, (e) 450°C, and (f) 500°C.

2.4.3 Formation of non-equilibrium phases in ARB Processes similar to ARB had previously been carried out for bulk mechanical alloying of different metals or for fabricating multi-layered materials.28,29 However, roll-bonding was not used in such attempts, but diffusion bonding at elevated temperatures was carried out between each pressing or rolling procedure. Bulk mechanical alloying by the ARB process is of course possible, and nonequilibrium structures including an amorphous phase have been fabricated.30–32 An฀ example฀ of฀ the฀ formation฀ of฀ non-equilibrium฀ nanostructures฀ by฀ the฀ ARB฀ process฀is฀introduced฀here.฀Sheets฀of฀pure฀Cu฀(99.96%฀purity)฀and฀pure฀Zr฀(99.2%฀ purity), 200 mm in length, 50 mm in width, and 0.2 mm in thickness, were mutually stacked so that the total thickness becomes 1 mm. The overall composition฀of฀the฀multi-stacks฀was฀Cu-29at%Zr.฀The฀ARB฀process฀using฀75%฀ reduction per cycle was carried out at RT with lubrication. The ARB was repeated for up to 10 cycles, with an equivalent strain of 15.8, which corresponds to the conventional rolling of a huge plate with a thickness of 568 m down to 1 mm thickness.฀Figure฀2.11฀shows฀a฀high-resolution฀TEM฀microstructure฀of฀the฀Cu/Zr฀ multi-stacks ARB-processed by 9 cycles at RT. A nano-lamellar structure

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2.11 High-resolution TEM microstructure of the Cu + Zr multi-stacks ARB-processed by 9 cycles (equivalent strain of 13.7) at RT. Observed from TD.

composed฀ of฀ mutual฀ alignment฀ of฀ Cu฀ layers฀ and฀ Zr฀ layers฀ is฀ observed.฀ The฀ thickness฀of฀each฀Cu฀or฀Zr฀layer฀is฀below฀10฀nm.฀In฀some฀thinner฀Zr฀layers,฀no฀ periodical฀ contrast฀ is฀ recognized,฀ indicating฀ that฀ an฀ amorphous฀ phase฀ has฀ been฀ formed฀ (indicated฀ as฀ ‘Amo’).฀Also฀ at฀ the฀ interfaces฀ between฀ Cu฀ layers฀ and฀ Zr฀ layers, thin amorphous regions are observed. EDX analysis using nano-beam has clariied฀ that฀ atomistic฀ scale฀ mixing฀ of฀ Cu฀ and฀ Zr฀ happens฀ at฀ interface฀ regions฀ during the ARB and eventually form an amorphous region.32 It has also been found that the subsequent heat treatment of ARB-processed stacks causes thermally฀induced฀amorphization฀to฀form฀sheets฀of฀nearly฀100%฀metallic฀glass.33

2.5

Mechanical properties of nanostructured metals fabricated by ARB

Figure 2.12 shows the changes in the nominal stress–strain curves of the IF steel and 1100-Al during ARB. The ARB process for the IF and 1100-Al were carried out฀ without฀ lubrication฀ at฀ 500°C฀ and฀ RT,฀ respectively.฀ Both฀ materials฀ showed฀ quite similar changes in the stress–strain curves. The strength and ductility were summarized฀ in฀ Fig.฀ 2.13฀ as฀ a฀ function฀ of฀ the฀ number฀ of฀ the฀ARB฀ cycles.฀ The฀ strength of the materials increased roughly twice by one cycle of ARB, while the elongation greatly decreased. This is a typical mechanical property of strainhardened materials. The flow stress increased with increasing the ARB cycle, keeping similar shapes of the stress–strain curves. The elongation maintained nearly the same value after the second cycle. After seven cycles, the tensile strength reached 910 MPa in the IF steel and 340 MPa in the 1100-Al, respectively,

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2.12 Engineering stress–strain curves of the ARB-processed materials. (a) IF steel ARB processed at 500°C without lubrication. (b) 1100-Al ARB processed at RT without lubrication.

which were more than 3~4 times higher than those of the starting materials. In stress–strain฀ curves,฀ the฀ ARB-processed฀ specimens฀ reached฀ their฀ maximum฀ strength at early stage of the tensile test, followed by macroscopic necking. Consequently,฀ the฀ specimens฀ had฀ limited฀ uniform฀ elongation฀ (about฀ 1~3%),฀ which is a common feature of the ultra-high strained materials independent of the SPD process.34 Actually, the same materials, deformed highly to the equivalent

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2.13 Strength (0.2% proof stress (s0.2) and tensile strength (sB)) and ductility (uniform elongation (eu) and total elongation (et)) obtained by tensile test at RT for the ARB-processed materials. (a) IF steel ARB processed at 500°C without lubrication. (b) 1100-Al ARB processed at RT without lubrication.

amount of strain, show nearly the same strength, regardless of the processes. Different elongation (ductility) has sometimes been reported in the nanostructured materials SPD-processed by different techniques, but we should note that tensile elongation฀ is฀ signiicantly฀ affected฀ by฀ the฀ shape฀ and฀ dimensions฀ of฀ the฀ tensile฀ specimens, and in many cases different types of specimens have been used in different฀ groups.฀ It฀ should฀ be฀ emphasized,฀ however,฀ that฀ the฀ UFG฀ materials฀ fabricated by ARB (SPD) do not lose plasticity, because they can be rolled, compressed or bent to fairly high degrees of deformation. There฀ have฀ been฀ many฀ arguments฀ on฀ whether฀ oxides฀ formed฀ at฀ bonded฀ interfaces affect the mechanical properties of the ARB-processed sheets or not. There฀ must฀ be฀ a฀ certain฀ amount฀ of฀ oxides฀ at฀ bonded฀ interfaces฀ in฀ the฀ ARBprocessed฀ materials.฀ However,฀ even฀ after฀ six฀ ARB฀ cycles฀ that฀ can฀ produce฀ a฀ homogeneous฀UFG฀structure฀(Fig.฀2.4),฀the฀number฀of฀bonded฀interfaces฀within฀ the 1 mm sheet is only 63 and the interval of the bonded interfaces (the thickness of the original sheet) is 15.6 µm (Table 2.1), which is much larger than the mean grain฀size฀(~0.2฀µm).฀The฀total฀volume฀of฀oxides฀would฀thus฀be฀relatively฀small.฀ Therefore,฀it฀is฀believed฀that฀the฀effect฀of฀oxides฀on฀the฀mechanical฀properties฀of฀ the฀ARB-processed฀ sheets฀ is฀ not฀ signiicant฀ below฀ about฀ ten฀ cycles,฀ which฀ is฀ usually฀used฀for฀fabricating฀UFG฀structures. The stress–strain curves of commercial purity aluminum (ARB-processed and then annealed) are shown in Fig. 2.14. The change in microstructures during annealing has been already shown in Fig. 2.9. Flow stress of the material decreases with increasing annealing temperature, but tensile elongation, especially uniform elongation,฀ recovers฀ only฀ after฀ the฀ mean฀ grain฀ size฀ becomes฀ larger฀ than฀ 1฀ µm. Quite similar changes in mechanical properties have been reported in the IF steel (ARB processed and annealed).21 The results show that even if the characteristics

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2.14 Engineering stress–strain curves of the 1100-Al ARB-processed by 6 cycles at 200°C without lubrication and then annealed at various temperatures indicated in the figure for 1.8 ks. Mean grain thickness (dt) in each specimen is also indicated.

of deformation microstructures in the ARB-processed specimens are diminished by฀ annealing,฀ the฀ UFG฀ specimens฀ exhibit฀ limited฀ tensile฀ ductility.฀The฀ limited฀ uniform฀elongation฀of฀the฀UFG฀materials฀is฀understood฀in฀terms฀of฀early฀plastic฀ instability.21 Plastic instability condition, i.e. necking criteria in tensile test, can be simply฀expressed฀in฀the฀Considère฀equation฀shown฀below: [2.2] Here, σ and ε฀are฀true฀stress฀and฀true฀strain,฀respectively.฀Grain฀reinement฀greatly฀ increases flow stress, especially yield strength, of the material. On the other hand, strain-hardening฀ is฀ not฀ enhanced฀ by฀ grain฀ reinement.฀ As฀ a฀ result,฀ the฀ plastic฀ instability฀ expressed฀ in฀ equation฀ (2.2)฀ is฀ easily฀ achieved฀ in฀ UFG฀ materials.฀ Therefore,฀ it฀ is฀ necessary฀ to฀ enhance฀ strain-hardening฀ ability฀ of฀ the฀ matrix฀ in฀ order to manage both high strength and ductility in nanostructured metals.35 Actually, a good balance of strength and ductility has been reported in multiphased nanostructured metals and alloys.35–39 It฀is฀noteworthy฀in฀Fig.฀2.14฀that฀the฀specimens฀having฀mean฀grain฀sizes฀smaller฀ than 3 µm฀ exhibit฀ yield-point฀ phenomena,฀ nevertheless฀ the฀ material฀ is฀ pure฀ aluminum. A number of such unique and unusual mechanical properties have been recently reported in nanostructured metals fabricated by ARB, such as an increase in tensile ductility with increasing ARB strain in particular Al alloys40

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and the hardening by annealing and softening by deformation phenomena, which are totally opposite to metallurgical common sense.41

2.6

Conclusions

In this chapter, the principles and processing details of the ARB process were explained,฀and฀further฀the฀nanostructure฀evolution฀and฀mechanical฀properties฀of฀ the ARB-processed materials were presented and discussed. The ARB process is the only SPD process applicable to continuous production of large bulky materials, while another batch type SPD processes are disadvantageous for practical application. Although to adapt ARB into large-scale mass production of materials, such฀as฀those฀in฀the฀steel฀industry,฀is฀still฀dificult,฀very฀thin฀strips฀(~0.1฀mm฀thick)฀ of฀UFG฀stainless฀steel฀has฀already฀been฀already฀produced฀in฀a฀relatively฀smallscale฀ industry฀ using฀ the฀ principle฀ of฀ the฀ARB฀ (see฀ Chapter฀ 23).42 The present manuscript clearly shows that the ARB is also a nice process at the laboratory scale for obtaining bulky samples having homogeneous nanostructures. By the use of the technique, we have been able to systematically acquire fundamental knowledge of bulk nanostructured metals and alloys.

2.7

References

1 Tsuji N., Saito Y., Lee S.H., and Minamino Y. Adv. Eng. Mater. 2003: 5: 338. 2 Altan B.S., editor. Severe Plastic Deformation toward Bulk Production of Nanostructured Materials. New York: Nova Science Publishers, 2006. ฀ 3฀ Saito฀Y.,฀Tsuji฀N.,฀Utsunomiya฀H.,฀Sakai฀T.,฀and฀Hong฀R.G.฀Scripta฀Mater.฀1998:฀47:฀ 893. 4 Tylecote R.F. The Solid Phase Welding of Metals. London: Edward Arnold, 1968. ฀ 5฀ Lee฀S.H.,฀Saito฀Y.,Tsuji฀N.,฀Utsunomiya฀H.,฀and฀Sakai฀T.฀Scripta฀Mater.฀2002:฀46:฀281. ฀ 6฀ Kamikawa฀N.,฀Sakai฀T.,฀and฀Tsuji฀N.฀Acta฀Mater.฀2007:฀55:฀5873. 7 Tsuji N. in,2 p.545. ฀ 8฀ Terada฀D.,฀Inoue฀M.,฀Kitahara฀H.,฀and฀Tsuji฀N.฀Acta฀Mater.฀2008:฀49:฀41. 9 Dinda G.P., Rosner H., and Wilde G. Scripta Mater. 2005: 52: 577. 10฀ Perez-Prado฀M.T.,฀del฀Valle฀J.A.,฀and฀Ruano฀O.A.฀Scripta฀Mater.฀2004:฀51:฀1093. 11฀ Tsuji฀N.,฀Kamikawa฀N.,฀and฀Minamino฀Y.฀Mater.฀Sci.฀Forum฀2004:฀467–470:฀341. 12 Huang X., Tsuji N., Hansen N., and Minamino Y. Mater. Sci. Eng. A 2003: 340: 265. 13฀ Tsuji฀ N.,฀ and฀ Kamikawa฀ N.฀ Proc.฀ of฀ the฀ 12th฀ Int.฀ Conf.฀ on฀ Aluminum฀ Alloys฀ (ICAA฀12),฀2010,฀The฀Japan฀Institute฀of฀Light฀Metals,฀pp.฀1134–1140. 14฀ Kamikawa฀N.,฀Tsuji฀N.,฀and฀Minamino฀Y.฀Sci.฀Tech.฀Adv.฀Mater.฀2004:฀5:฀163. 15฀ Li฀B.L.,฀Tsuji฀N.,฀and฀Kamikawa฀N.฀Mater.฀Sci.฀Eng.฀A฀2006:฀423:฀331. 16฀ Hansen฀N.,฀and฀Juul฀Jensen฀D.฀Phil.฀Trans.฀R.฀Soc.฀London฀A฀1999:฀357:฀1447. 17฀ Ito฀Y.,฀Tsuji฀N.,฀Saito฀Y.,฀Utsunomiya฀H.,฀and฀Sakai฀T.J.฀Jpn.฀Inst.฀Metals฀2000:฀64:฀ 429. 18 Hansen N. Metall. Mater. Trans. A 2001: 32: 2917. 19฀ Ikeda฀K.,฀Yamada฀K.,฀Takata฀N.,฀Yoshida฀F.,฀Nakashima฀H.฀and฀Tsuji฀N.฀Mater.฀Trans.฀ 2008: 49: 24. 20฀ Ii฀S.,฀Takata฀N.,฀Ikeda฀K.,฀Nakashima฀H.฀and฀Tsuji฀N.฀unpublished฀data.

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21 Tsuji N., Ito Y., Saito Y., and Minamino Y. Scripta Mater. 2002: 47: 893. 22฀ Tsuji฀N.,฀Okuno฀S.,฀Koizumi฀Y.,฀and฀Minamino฀Y.฀Mater.฀Trans.฀2004:฀45:฀2272. 23฀ Humphreys฀F.J.,฀Prangnell฀P.B.,฀and฀Priestner฀R.฀Curr.฀Opinion฀Solid฀State฀Mater.฀Sci.฀ 2001: 5: 15. 24฀ Humphreys฀F.J.,฀and฀Hatherly฀M.฀Recrystallization฀and฀Related฀Annealing฀Phenomena.฀ Oxford:฀Pergamon,฀1995. 25฀ Takata฀N.,฀Yamada฀K.,฀Ikeda฀K.,฀Yoshida฀F.,฀Nakashima฀H.,฀and฀Tsuji฀N.฀Mater.฀Trans.฀ 2007: 48: 2043. 26 Tsuji N., Iwata T., Sato M., Fujimoto S., and Minamino Y. Sci. Tech. Adv. Mater. 2004: 5: 173. 27 Terada D., Sato T., and Tsuji N. Proc. of the 30th Risø Int. Symp. on Mater. Sci. Roskilde: Risø National Laboratory, 2009: 351. 28฀ Atzmon฀M.,฀Unruh฀K.M.,฀and฀Johnson฀W.L.฀J.฀Appl.฀Phys.฀1985:฀58:฀3865. 29฀ Yasuna฀K.,฀Terauchi฀M.,฀Otsuki฀A.,฀Ishihara฀K.N.,฀and฀Singu฀P.H.฀J.฀Appl.฀Phys.฀1997:฀ 82: 2435. 30฀ Sieber฀H.,฀Wilde฀G.,฀and฀Perepzko฀J.H.฀J.฀Non-Cryst.฀Solid฀1999:฀250–252:฀611. 31฀ Sieber฀H.,฀Wilde฀G.,฀Sagel฀A.,฀and฀Perpezko฀J.H.฀J.฀Non-Cryst.฀Solid฀1999:฀250–252:฀ 616. 32฀ Ohsaki฀S.,฀Kato฀S.,฀Tsuji฀N.,฀Ohkubo฀T.,฀and฀Hono฀K.฀Acta฀Mater.฀2007:฀55:฀2885. 33฀ Sun฀Y.F.,฀Todaka฀Y.,฀Umemoto฀M.,฀and฀Tsuji฀N.฀J.฀Mater.฀Sci.฀2008:฀23–24:฀7457. 34฀ Iwahashi฀Y.,฀Wang฀J.,฀Horita฀Z.,฀Nemoto฀M.,฀and฀Langdon฀T.G.฀Metall.฀Mater.฀Trans.฀ A 1998: 29: 2503. 35฀ Tsuji฀N.,฀Kamikawa฀N.,฀Ueji฀R.,฀Takata฀N.,฀Koyama฀H.,฀and฀Terada฀D.฀ISIJ฀Int.฀2008:฀ 48: 1114. 36฀ Tsuji฀N.,฀Ueji฀R.,฀Minamino฀Y.,฀and฀Saito฀Y.฀Scripta฀Mater.฀2002:฀46:฀305. 37฀ Ueji฀R.,฀Tsuji฀N.,฀Minamino฀Y.,฀and฀Koizumi฀Y.฀Acta฀Mater.฀2002:฀50:฀4177. 38฀ Okitsu฀Y.,฀Takata฀N.,฀and฀Tsuji฀N.฀J.฀Mater.฀Sci.฀2008:฀23–24:฀7391. 39฀ Takata฀N.,฀Ohtake฀Y.,฀Kita฀K.,฀Kitagawa฀K.,฀and฀Tsuji฀N.฀Scripta฀Mater.฀2009:฀60:฀590. 40฀ Kim฀H.W.,฀Kang฀S.B.,฀Tsuji฀N.,฀and฀Minamino฀Y.฀Acta฀Mater.฀2005:฀53:฀1737. 41 Huang X., Hansen N., and Tsuji N. Science 2006: 312: 249. 42 Tsuji N. Adv. Eng. Mater. 2010: 12: 701.

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3 Nanocrystalline metals and alloys prepared by mechanical attrition S.฀SCUDINO฀and฀J.฀ECKERT,฀IFW Dresden, Germany

Abstract: This overview discusses the formation of nanocrystalline materials by mechanical attrition. The chapter starts with a description of the methods and the process variables typically employed for producing nanostructured phases฀by฀mechanical฀attrition.฀Experimental฀data฀for฀the฀resulting฀ nanostructures obtained by mechanical milling of single phases as well as by mechanical฀alloying฀of฀phase฀mixtures฀are฀discussed฀for฀selected฀materials฀with฀ an emphasis on the different mechanisms involved. Finally, problems and possible solutions for consolidating nanostructured powders are also addressed at the end of this chapter. Key words: mechanical attrition, mechanical alloying, powder metallurgy, nanocrystalline materials, consolidation.

3.1

Introduction

Nanocrystalline (also referred to as nanostructured or nanophase) materials are single-฀or฀multi-phase฀polycrystals฀with฀particle฀or฀grain฀sizes,฀layer฀thicknesses,฀ or฀ domain฀ sizes฀ in฀ the฀ nanometer฀ range฀ (typically฀ less฀ than฀ 100฀ nm฀ at฀ least฀ in฀ one฀dimension).฀Due฀to฀their฀extremely฀small฀grain฀size,฀an฀appreciable฀fraction฀ of the atoms in nanostructured materials are located in the grain boundaries.1 Such unique microstructural features lead to physical and chemical properties that may฀signiicantly฀differ฀from฀those฀of฀the฀corresponding฀coarse-grained฀materials฀ with the same composition.2–5฀ In฀ particular,฀ a฀ signiicant฀ improvement฀ of฀ the฀ mechanical properties, such as a substantial increase in strength and hardness with respect to conventional coarse-grained materials, has been observed in a number of alloys with nanoscale microstructures.2–5 However, one major drawback for the use of nanocrystalline materials in engineering applications is their often limited room temperature ductility.2–5฀Nevertheless,฀recent฀indings฀have฀shown฀that฀grain฀ reinement฀to฀the฀nanometer฀regime฀may฀also฀lead฀to฀enhanced฀plastic฀deformation,6 therefore, opening up new perspectives for the application of nanocrystalline phases as structural and functional materials. Two main strategies have been used for the preparation of nanocrystalline materials: (i) the bottom-up approach, which consists of building the nanostructure atom-by-atom or layer-by-layer and (ii) the top-down approach that consists of breaking฀down฀the฀microstructure฀into฀a฀nanostructure.฀Examples฀of฀the฀bottom-up approach are inert gas condensation, chemical vapor condensation and pulse electron deposition.1,7,8 The archetype technique of the top-down approach is 59 © Woodhead Publishing Limited, 2011

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mechanical attrition. This processing route has been widely used for the preparation of nanostructured materials and, different from the top-down approach, produces nanophase structures not by cluster assembly but by the structural decomposition of coarser-grained structures as the result of heavy cyclic plastic deformation.4,9 Mechanical attrition is one of the less sophisticated technologies and,฀in฀turn,฀also฀one฀of฀the฀most฀inexpensive฀to฀produce฀nanophase฀powders.฀In฀ addition, it can be used for the processing of essentially all classes of materials.9 This, along with the additional advantage of the possible scaling up to tonnage quantities of processed material, has made mechanical attrition a very popular method for the synthesis of nanocrystalline materials, not only for the laboratory scale but also for potential industrial applications.9 In view of the importance of mechanical attrition as a method for nanocrystalline materials synthesis, this overview starts with a description of the methods and the process variables typically employed for producing nanostructured phases by mechanical฀attrition.฀Experimental฀data฀for฀the฀resulting฀nanostructures฀obtained฀ by mechanical attrition of single- and multi-phase powders will be described for selected materials, and the mechanisms responsible for the formation of the different฀nanophase฀structures฀will฀be฀discussed.฀Consideration฀of฀the฀problems฀ and challenges for the consolidation of nanostructured powders, as well as a discussion of the possible solutions, will also be addressed at the end of this chapter.

3.2

Mechanical attrition

Mechanical฀attrition฀of฀powders,฀irst฀developed฀by฀Benjamin฀and฀coworkers10,11 in the 1970s, is a processing route that can successfully produce new alloys, phases฀and฀phase฀mixtures.฀This฀method฀for฀materials฀synthesis฀can฀circumvent฀ many of the limitations of conventional alloying and allows the preparation of alloys฀ and฀ composites฀ that฀ cannot฀ be฀ synthesized฀ via฀ conventional฀ casting฀ or฀ rapid฀solidiication฀routes.฀Examples฀are฀uniform฀dispersions฀of฀ceramic฀particles฀ in฀a฀metallic฀matrix฀or฀alloys฀of฀metals฀with฀rather฀different฀melting฀points฀with฀ the aim of improving strength and corrosion resistance.10,11 Over the years, mechanical attrition has attracted enormous interest as a versatile non-equilibrium processing technique resulting in solid-state alloying beyond the equilibrium solubility limit and the formation of amorphous, quasicrystalline or nanostructured materials for a broad range of alloys, intermetallic compounds, ceramics and composites.4,9,12,13,14 Mechanical attrition is usually performed in ball mills capable of high-energy impact forces. For this purpose, a variety of different types of ball mills with different characteristics have been developed, including attrition mills, shaker mills, planetary mills, vibratory mills, etc.14 The milling process consists of loading the starting material and the grinding balls (typically steel or tungsten carbide) into a milling container (vial), which is violently shaken or rotated, depending on the

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mill฀used.฀The฀intensity฀of฀milling฀depends฀on฀the฀internal฀mechanics฀of฀the฀speciic฀ mill and, consequently, on the kinetic energy imparted to the grinding balls, as well as฀on฀mass,฀size฀and฀number฀of฀the฀balls.฀One฀serious฀problem฀in฀the฀processing฀of฀ ine฀powders฀by฀mechanical฀attrition฀is฀potential฀contamination฀from฀the฀milling฀ media or atmosphere.4,9,13฀The฀small฀size฀of฀the฀powder฀particles฀and฀the฀consequent฀ availability of large surface area, along with the continuous formation of new fresh surfaces during milling, contribute to the contamination of the powder.14 If, as in most cases, the milling vial and balls are made of steel, iron is the typical contaminant due to debris of the milling tools. The magnitude of contamination appears to depend on both the time and the intensity of milling.9,15 The other major source฀of฀contamination฀is฀from฀the฀milling฀atmosphere,฀i.e.฀oxygen฀or฀nitrogen.฀ Atmospheric contamination is particularly severe for milling of reactive metals, such฀ as฀ titanium฀ and฀ zirconium,9,14 however, it can be drastically reduced by milling in an inert gas atmosphere (e.g. argon). Mostly, mechanical attrition is carried out under dry conditions but also milling with liquid or solid process control agents is possible,13,14 depending on the nature of the milled powders, in order to prevent sticking of the materials to the milling tools. The฀ dynamics฀ of฀ mechanical฀ attrition฀ are฀ extremely฀ complex฀ and฀ strongly฀ depend on the mill characteristics. However, for all types of ball mills the fundamental event of the milling process is the ball–powder collision, as schematically shown in Fig. 3.1. During milling the powder particles are trapped between the colliding balls and are subjected to repeated high-energy impacts, which induce heavy plastic deformations together with fracturing and cold-welding events. For a given composition, the deformation/fracture process, the potential phase฀transformations฀during฀milling฀and฀the฀inal฀structure฀of฀the฀material฀depend฀ on the powder material properties (e.g. hardness, fracture toughness, etc.), being different for single-phase materials or combinations of ductile/ductile, ductile/ brittle or brittle/brittle components,9 as well as on the milling parameters, i.e. the kinetic energy transferred to the powder and the local temperature during the impacts.9,12฀ The฀ temperature฀ that฀ the฀ powders฀ experience฀ during฀ milling฀ also฀ depends on the type of mill used and on parameters such as vibration frequency or rotational฀ velocity.฀ Experimental฀ observations฀ and฀ modeling฀ of฀ the฀ mechanics,฀ kinetics and the energy transfer during collision suggest that the temperature rise during milling is about ≤฀100–200฀K.9,12 Adjusting or changing the milling conditions can affect the phase formation or can lead to phase transitions between different phases. Depending on the chosen experimental฀conditions฀(i.e.฀energy฀input,฀milling฀temperature),฀nanocrystalline฀ and amorphous materials as well as quasicrystalline or crystalline phases can be synthesized฀ by฀ mechanical฀ attrition.฀ In฀ addition,฀ the฀ different฀ phases฀ can฀ be฀ transformed into each other by additional milling at higher or lower milling intensity. In particular, this has been demonstrated for the crystal-to-quasicrystal transition, the crystal-to-amorphous transition, and the quasicrystal-to-amorphous transition.16–18

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3.1 Schematic illustration of the basic event occurring during mechanical attrition showing the trapping of powder particles between colliding balls.

3.3

Nanocrystalline phase formation by mechanical attrition

A fundamental feature of mechanical attrition is the development of nanoscale microstructures. As described above, during milling the powder particles are subjected to severe mechanical deformation from repeated high-energy impacts with the milling tools. Deformation occurs under shear conditions and high strain rates (~103–104 s–1), leading to the incorporation of lattice defects and to฀ a฀ continuous฀ reinement฀ of฀ the฀ initial฀ structure฀ of฀ the฀ powder฀ particles฀ to฀ the฀ nanometer regime.4,13฀Extended฀milling฀may฀eventually฀lead฀to฀phase฀transformations,฀ including nanocrystalline equilibrium and metastable phases.4,13 The฀inal฀structure฀of฀a฀powder฀subjected฀to฀mechanical฀attrition฀may฀depend฀on฀ the starting material used. Accordingly, mechanical attrition can be divided in two different routes depending on the starting material. The mechanical attrition of powders฀with฀different฀compositions฀(the฀mixture฀of฀elemental฀powders฀as฀well฀as฀

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of intermetallic compounds), in which material transfer occurs, is named mechanical alloying (MA), while the mechanical attrition of single composition powders, such as pure elements and single-phase intermetallic compounds, where material transfer is not required, has been termed mechanical milling (MM).19 In the following section, the evolution of nanocrystalline structures produced by mechanical milling of single phases as well as by mechanical alloying of phase mixtures฀ is฀ discussed฀ with฀ emphasis฀ on฀ the฀ different฀ mechanisms฀ involved.฀ Similarly,฀selected฀examples฀of฀phase฀transformation฀during฀milling฀of฀different฀ starting materials are also presented.

3.3.1 Mechanical milling of single-phase materials Grain฀reinement฀to฀the฀nanometer฀regime฀is฀a฀universal฀phenomenon฀of฀the฀milling฀ process and has been observed in almost all mechanically attrited materials, including pure metals, intermetallic compounds and multi-phase materials.4,9,13,14 The microstructural changes induced by mechanical attrition can be estimated by x-ray฀diffraction฀(XRD)฀methods.฀The฀XRD฀patterns฀exhibit฀increasing฀broadening฀ of฀the฀diffraction฀peaks฀as฀a฀function฀of฀milling฀time,฀which฀is฀caused฀by฀size฀as฀ well as internal strain effects.4,13 The individual contributions of these effects to the total broadening can be separated using standard techniques: the peak broadening due฀to฀the฀reduction฀of฀grain฀or฀crystallite฀size฀(the฀average฀coherently฀diffracting฀ domain฀size)฀is฀inversely฀proportional฀to฀cos θ, whereas broadening due to lattice strain is proportional to tan θ.20,21 The฀ characteristics฀ of฀ grain฀ size฀ reinement฀ by฀ mechanical฀ attrition฀ have฀ been฀ studied฀extensively฀in฀the฀past฀years฀with฀particular฀attention฀on฀mechanical฀milling฀ of฀pure฀metallic฀elements.฀For฀example,฀Fecht฀et al.22–24 observed the continuous decrease฀of฀the฀grain฀size฀with฀increasing฀milling฀time฀down฀to฀about฀9฀nm฀for฀the฀ body-centered฀cubic฀(bcc)฀metals฀and฀to฀about฀13฀nm฀for฀the฀hexagonal฀close฀packed฀ (hcp)฀metals.฀Similar฀results฀in฀terms฀of฀grain฀reinement฀with฀milling฀time฀have฀ been also reported for milling of a series of face-centered cubic (fcc) metals.25 Interestingly,฀the฀minimum฀grain฀size฀for฀the฀fcc฀elements฀was฀found฀to฀inversely฀ scale with the melting temperature.25 A similar trend as observed for the fcc metals can be observed for milling of a series of hcp metals spanning over a wide range of melting temperatures (Fig. 3.2). On the other hand, MM bcc metals do not show any signiicant฀variation฀of฀minimum฀grain฀size฀with฀the฀melting฀temperature,22 probably because฀of฀the฀lack฀of฀milling฀experiments฀for฀bcc฀metals฀with฀low฀melting฀point. Along฀ with฀ the฀ grain฀ size฀ reinement฀ to฀ the฀ nanometer฀ regime,฀ milling฀ of฀ powders can introduce a considerable amount of lattice strain, which is most presumably linked to the dislocation density.25 In analogy with the minimum grain฀size,฀the฀maximum฀lattice฀strain฀introduced฀during฀milling฀is฀also฀meltingpoint฀dependent,฀and฀increases฀with฀the฀melting฀temperature฀of฀the฀speciic฀metal฀ (Fig.฀3.3).฀The฀observed฀dependence฀of฀grain฀size฀and฀lattice฀strain฀on฀the฀melting฀ temperature suggests that recovery rates during the milling process correlate with

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3.2 Minimum grain size obtained by mechanical milling for different fcc, hcp and bcc metals as a function of the melting temperature (data from Fecht et al.22, Eckert et al.25 and Nogales et al.31).

Lattice strain, %

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3.3 Lattice strain for different mechanically milled fcc metals versus melting temperature (adapted from Eckert et al.25).

the฀melting฀point฀of฀the฀speciic฀metal,฀thus฀preventing฀very฀small฀grain฀sizes฀for฀ low-melting elements.25 Another important aspect of nanostructure formation by milling is the stored enthalpy, which is accumulated in the material as a result of the heavy mechanical deformation. This energy is released during heating to elevated temperatures due

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Stored enthalpy, kJ/mol

to฀recovery,฀relaxation฀processes฀within฀the฀boundaries฀and฀grain฀growth24 and can฀be฀determined฀using฀differential฀scanning฀calorimetry฀(DSC)฀measurements.฀ As฀a฀typical฀example฀of฀mechanically฀attrited฀metals,฀Fig.฀3.4฀shows฀the฀stored฀ enthalpy฀of฀MM฀Ni฀as฀a฀function฀of฀the฀reciprocal฀grain฀size.25 The stored enthalpy increases฀to฀a฀maximum฀value฀(which฀does฀not฀occur฀at฀the฀minimum฀grain฀size)฀ and฀then฀decreases฀during฀further฀grain฀reinement.฀A฀plausible฀explanation฀for฀ this฀ behavior฀ might฀ be฀ the฀ increase฀ of฀ the฀ impurity฀ content฀ during฀ milling;25 however,฀ a฀ clear฀ motivation฀ for฀ this฀ phenomenon฀ is฀ still฀ missing.฀ The฀ inal฀ energies฀ stored฀ during฀ mechanical฀ attrition฀ largely฀ exceed฀ those฀ resulting฀ from฀ conventional cold working of metals and alloys, such as cold rolling or wire drawing.23,25฀During฀conventional฀deformation฀the฀stored฀enthalpy฀never฀exceeds฀ more than a small fraction of the heat of fusion. However, in the case of mechanical attrition฀the฀energy฀stored฀can฀reach฀values฀corresponding฀to฀about฀40%฀of฀the฀ heat of fusion.25 Point defects and dislocations can account for only a fraction of this energy and, most likely, the major energy contribution is stored in the form of grain boundaries, and related strains within the nanocrystalline grains that are induced through grain boundary stresses.4 The฀ minimum฀ grain฀ size฀ obtainable฀ by฀ milling฀ has฀ been฀ attributed฀ to฀ the฀ competition between the heavy mechanical deformation and recovery by thermal processes฀and,฀in฀turn,฀by฀the฀minimum฀grain฀size฀that฀can฀sustain฀a฀dislocation฀ pile-up within a grain and by the rate of recovery during milling.25 An estimate for the minimum dislocation separation in a pile-up Lc is given by Lc฀=฀3Gb/π(1–ν)h, with shear modulus G, Burgers vector b, Poisson ratio ν, and hardness h of the

3.4 Stored enthalpy in mechanically milled Ni versus reciprocal grain size d (adapted from Eckert et al.25).

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material. Applying this relation to the milled fcc metals shows that the minimum grain฀ size฀ of฀ fcc฀ metals฀ (d) follows a linear relation with Lc (Fig. 3.5, solid symbols).฀This฀gives฀a฀lower฀bound฀for฀the฀grain฀size฀of฀pure฀metals฀and฀reveals฀ that฀ a฀ small฀ grain฀ size฀ itself฀ provides฀ a฀ limit฀ for฀ further฀ grain฀ reinement฀ by฀ milling.25฀In฀addition,฀the฀reduction฀of฀the฀grain฀size฀is฀also฀limited฀by฀the฀rate฀of฀ recovery฀during฀milling,฀which฀may฀be฀signiicant฀for฀metals฀with฀low฀melting฀ points. It has been found22,24 that in the early stages of milling the deformation of milled฀powders฀is฀localized฀in฀shear฀bands฀containing฀a฀high฀dislocation฀density.฀ By increasing the milling time, the lattice strain increases due to the increasing dislocation density and, at a certain strain level, the dislocations annihilate and recombine to small angle grain boundaries, separating the individual grains. The฀ subgrains฀ formed฀ via฀ this฀ route฀ are฀ already฀ in฀ the฀ nanometer฀ size฀ range฀ (about฀20–30฀nm).฀With฀a฀longer฀milling฀time฀the฀grain฀size฀decreases฀gradually฀ and฀ the฀ structure฀ inally฀ evolves฀ into฀ nano-grains฀ separated฀ by฀ high-angle฀ grain฀boundaries.฀At฀this฀stage,฀no฀further฀grain฀reinement฀is฀possible฀but฀only฀ grain฀ boundary฀ sliding฀ can฀ occur,฀ which฀ does฀ not฀ reine฀ the฀ microstructure฀ any further.4 These฀indings฀indicate฀that฀a฀high฀initial฀dislocation฀density฀and,฀thus,฀a฀large฀ lattice฀ strain,฀ is฀ necessary฀ for฀ signiicant฀ grain฀ size฀ reinement฀ by฀ mechanical฀ attrition. This is opposed by the recovery processes whose driving force is the energy฀stored฀in฀the฀grain฀boundaries฀of฀the฀milled฀material.฀Grain฀reinement฀and฀ recovery฀are฀closely฀related฀to฀the฀minimum฀grain฀size฀d through the rate of each

Minimum grain size, nm

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3.5 Minimum grain size obtained by milling of pure metals (solid symbols) and FexCu100–x solid solutions with different compositions (open symbols) versus the minimum distance between two dislocations Lc (adapted from Eckert32).

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process฀expressed฀as฀a฀function฀of฀the฀grain฀size,฀since฀d฀is฀the฀grain฀size฀at฀which฀ the two rates are equal.32 In the case of metals with low melting temperatures, such as Al, the dislocation density is limited by recovery processes and, therefore, the฀minimum฀grain฀size฀achievable฀is฀most฀likely฀governed฀by฀the฀recovery฀rate.฀ On฀the฀other฀hand,฀almost฀no฀recovery฀is฀expected฀to฀occur฀for฀refractory฀metals฀ during milling, but a high level of internal strain is created due to the large number of dislocations and other deformation faults introduced. Therefore, the minimum grain฀size฀for฀these฀elements฀is฀limited฀by฀the฀stress฀required฀for฀plastic฀deformation฀ via dislocation motion rather than by the recovery rate.25 Nanocrystalline phase formation can also be achieved by the mechanical milling฀of฀intermetallic฀compounds.฀For฀example,฀Hellstern฀et al.33,34 investigated the฀stability฀of฀several฀intermetallic฀compounds฀with฀CsCl฀(ordered฀bcc)฀structure฀ under high-energy milling. Like the milling of pure metals, they observed a decrease฀of฀the฀grain฀size฀with฀increasing฀milling฀time฀to฀about฀5–12฀nm.฀This฀was฀ accompanied by disordering of the lattice as shown by the decrease of the longrange order parameter, which became more pronounced with decreasing grain size฀and฀inally฀saturated฀at฀about฀0.7.34 This indicates that the material does not disorder completely and that some residual chemical disorder (i.e. atoms on wrong฀sites.฀For฀example,฀in฀an฀A-B฀compound,฀A฀atoms฀on฀B฀sites฀and฀B฀atoms฀ on A sites) is present within the nanocrystalline grains after milling. Still, an appreciable part of the strain will reside in the disorder, because atoms on the ‘wrong’฀sublattice฀are฀to฀be฀accommodated฀on฀lattice฀sites,฀where฀they฀do฀not฀it.฀ This gives rise to strain.35฀Indeed,฀MM฀of฀CsCl฀intermetallics฀introduces฀a฀lattice฀ strain฀of฀about฀2–3%,฀which฀is฀much฀larger฀than฀what฀is฀generally฀observed฀for฀ pure฀ metals฀ (less฀ than฀ 1%).฀ In฀ addition,฀ milling฀ intermetallic฀ compounds฀ does฀ not฀lead฀to฀a฀peak฀of฀the฀maximum฀stored฀enthalpy,฀as฀is฀typical฀for฀pure฀metals฀ (Fig.฀ 3.4),฀ but฀ the฀ stored฀ energy฀ shows฀ saturation฀ to฀ a฀ maximum฀ value.34 The degree of disordering during mechanical milling of intermetallic phases depends on฀the฀structure฀of฀the฀compound,฀as฀observed฀by฀Jang฀and฀Koch36 for the ordered fcc Ni3Al฀compound,฀which฀exhibits฀complete฀disordering฀during฀milling. Following฀grain฀reinement฀and฀lattice฀disordering,฀the฀mechanical฀attrition฀of฀ intermetallics can lead to mechanically induced phase transformations, such as for the A-15 type Nb3Au compound,37฀ which฀ exhibits฀ the฀ formation฀ of฀ a฀ nanocrystalline bcc solid solution during milling. This behavior can be understood by considering the Au-Nb equilibrium phase diagram.35 The Nb3Au compound is stable at room temperature and transforms to the bcc solid solution of Au in Nb at elevated temperatures. The type of atomic disorder, obtained after milling, appears to be similar to that generated at high temperature. Similarly to high temperature treatments, milling introduces anti-site disorder in Nb3Au and brings the material into an increasingly higher disordered state, which corresponds to heat treatments at progressively higher temperatures.35 Therefore, in terms of disorder, milling is equivalent to an increase of temperature of the compound up to the point where the transition from Nb3Au to the bcc solid solution occurs.35 This was corroborated

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by the observation that the Au2Nb compound transforms to a nanostructured fcc solid solution of Nb in Au during milling, as predicted when considering the equilibrium phase diagram.38 Other possible phase transformations during milling involving฀intermetallic฀compounds฀include฀amorphization฀and฀the฀transformation฀ into฀a฀different฀(complex)฀crystal฀structure฀(for฀a฀review฀see฀Bakker฀et al.35). Another interesting type of mechanically induced phase transition is the allotropic฀ transformation฀ of฀ pure฀ elements฀ during฀ milling.฀ Examples฀ are฀ the฀ elements of the Group IVB Ti, Zr, and Hf that undergo an hcp-to-fcc allotropic transformation during mechanical milling39–41฀and฀Co,42 which shows a reversible hcp-to-fcc transformation that depends on the milling intensity used. Although recent results43 have shown that allotropic transformations in the Group IVB might be due to impurity contamination during milling, thus raising doubts about the real nature of these transformations, this type of transformation further demonstrates the versatility of mechanical attrition as a tool for the formation of new materials.

3.3.2 Mechanical alloying of phase mixtures Mechanical฀ alloying฀ of฀ powders฀ with฀ different฀ compositions฀ (mixture฀ of฀ elemental powders as well as of intermetallic compounds) is perhaps the most used mechanical attrition technique for the preparation of a wide range of materials including supersaturated solid solutions, amorphous, quasicrystalline or nanostructured materials for a broad range of alloys, intermetallic compounds, ceramics and composites.4,9,12,13,14 The mechanism of nanocrystalline formation operating during MA is different with respect to MM of single phases since it involves material transfer during processing. Although the microstructural evolution during MA depends on the mechanical behavior of the powder components (i.e. ductile or brittle), the primary aspect of the process is the reduction of the diffusion distances between the different phases.฀For฀example,฀for฀MA฀of฀ductile/ductile฀components,฀in฀the฀early฀stages฀of฀ mechanical alloying the particles are cold-welded and plastically deformed, leading to a characteristic layered structure consisting of various combinations of the starting constituents, as illustrated in Fig. 3.6.44 With increasing milling time the thickness of the individual layers decreases so much that it is no longer visible under an optical microscope.9,14 The structure undergoes severe deformation, work hardening and fracture. Fragments generated by this mechanism may continue to reduce฀in฀size,฀giving฀rise฀to฀a฀more฀and฀more฀reined฀microstructure.12 Alloying begins to occur at this stage due to the combination of decreased diffusion distances (interlayer spacing), increased lattice defect density, and any heating that may have occurred during the milling operation.14฀ This฀ has฀ been฀ conirmed฀ by฀ Klassen฀ et al.,45 who investigated the microstructure evolution during the early stages of MA of Ti-Al powder blends. For MA powder with composition Ti25Al75, transmission electron microscopy (TEM) investigations revealed that, after the

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3.6 Typical layered microstructure obtained during mechanical alloying.14

initial formation of an hcp solid solution by the diffusion of Al into Ti, a (partially) ordered Ll2฀fcc฀phase฀with฀grain฀size฀of฀about฀10–30฀nm฀is฀formed฀between฀the฀ alternating Ti and Al lamellae. The volume fraction of the Ll2 phase increases with increasing milling time until Al is entirely consumed. No additional phase transformation was observed upon further milling. The authors concluded that the Ll2฀ phase,฀ observed฀ in฀ the฀ inal฀ stage฀ of฀ milling,฀ is฀ already฀ formed฀ in฀ the฀ early฀ stages฀of฀the฀phase฀reaction.฀In฀addition,฀the฀initial฀diffusion฀of฀Al฀into฀the฀Ti฀matrix฀ and฀ the฀ resulting฀ formation฀ of฀ the฀ hcp฀ solid฀ solution฀ permit฀ to฀ exclude฀ that฀ the฀ formation of the Ll2 fcc phase at the interface occurs by the diffusion of Ti into the fcc Al. Therefore, the development of the nanocrystalline structure is not a result of a฀gradual฀grain฀reinement฀process,฀as฀observed฀during฀milling฀of฀pure฀metals,฀but฀ it consists of numerous nucleation events at the Ti/Al interface followed by limited growth of the new phase.46 Another remarkable achievement of MA is the production of a homogeneous mixture฀of฀immiscible฀phases.฀For฀example,฀large฀non-equilibrium฀solid฀solubility฀ has฀been฀attained฀by฀MA฀for฀a฀series฀of฀Fe-Cu฀powders,47 which are essentially

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immiscible฀and฀display฀a฀large฀positive฀enthalpy฀of฀mixing.฀The฀ultimate฀grain฀ size฀of฀the฀binary฀Fe-Cu฀nanostructured฀solid฀solutions฀depends฀on฀the฀composition฀ of฀the฀material฀(Fig.฀3.7).฀The฀grain฀size฀can฀be฀reduced฀to฀only฀20฀nm฀for฀pure฀Cu,฀ whereas it continuously decreases with increasing Fe content, reaching values below฀10฀nm฀for฀the฀Fe-rich฀fcc฀solid฀solutions.฀Similarly,฀the฀grain฀size฀decreases฀ with฀increasing฀Cu฀content฀for฀single-phase฀bcc฀solid฀solutions.฀A฀second฀decrease฀ of฀the฀bcc฀grain฀size฀occurs฀for฀samples฀with฀two-phase฀fcc/bcc฀microstructure,฀ whereas฀the฀fcc฀grain฀size฀in฀this฀region฀is฀independent฀of฀composition.฀When฀the฀ contributions of solution hardening and dispersion hardening are taken into account,32,48฀the฀ultimate฀grain฀size฀of฀the฀Fe-Cu฀alloys฀scales฀with฀the฀minimum฀ dislocation separation in a pile-up Lc (Fig. 3.5, open symbols) in the same manner as the data for pure fcc metals. This indicates that, similarly to MM of pure metals, the฀ minimum฀ grain฀ size฀ in฀ MA฀ Fe-Cu฀ powders฀ can฀ also฀ be฀ attributed฀ to฀ the฀ competition between the plastic deformation and the recovery behavior and demonstrates that both the alloy composition and the microstructure of the material฀determine฀the฀inal฀grain฀size.32 Solid฀ solubility฀ extension฀ far฀ beyond฀ the฀ equilibrium฀ values฀ has฀ also฀ been฀ reported฀for฀mechanically฀alloyed฀nanocrystalline฀Cu-M฀(M฀=฀Ti,฀Nb,฀Ni,฀Cr,฀Fe฀ and฀Co),49 Ti-Ni,50 Ni-Nb51 and Al-Nb52฀(for฀an฀exhaustive฀review฀on฀this฀topic฀ see13).฀Among฀the฀different฀alloys฀characterized฀by฀extended฀solid฀solubility฀when฀ prepared฀by฀MA,฀the฀Al-Mg฀system฀has฀been฀extensively฀investigated฀in฀recent฀ years.53–60 The equilibrium solid solubility of Mg in Al is quite small at room temperature฀(about฀1฀at.%61). However, depending on the initial solute content in the฀elemental฀powder฀mixture,฀the฀milling฀parameters฀and฀the฀presence฀of฀control฀

3.7 Effect of composition on the minimum grain size achievable by mechanical alloying of FexCu100–x powders (adapted from Eckert32).

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processing฀agents,฀an฀extended฀solid฀solubility฀of฀Mg฀in฀Al฀can฀be฀achieved฀by฀ MA฀of฀elemental฀powders.฀For฀example,฀Calka฀et al.53 showed that mechanical alloying฀allows฀to฀extend฀the฀solid฀solubility฀of฀Mg฀in฀Al฀up฀to฀18฀at.%฀in฀the฀case฀ of Al70Mg30฀and฀45฀at.%฀for฀Al50Mg50. Similarly, Zhang et al.54฀and฀Schoenitz฀ et al.56 observed for mechanically alloyed Al60Mg40 the formation of a solid solution฀containing฀23฀at.%฀and฀20.8฀at.%฀Mg,฀respectively. Recently,฀it฀was฀found฀that฀both฀MA฀of฀elemental฀powder฀mixtures฀and฀MM฀of฀ the single-phase intermetallic compound with composition Al60Mg40 lead to the same product, i.e. a supersaturated Al(Mg) solid solution.60,62 Although MA and MM may lead to the formation of the same product (i.e. the Al(Mg) solid solution), the solid-state transformations induced by the two processing routes occur by different฀mechanisms฀due฀to฀the฀different฀starting฀materials฀used฀(phase฀mixtures฀ and single-phase materials, respectively). MA is not a purely mechanical process but฀it฀involves฀interdiffusion,฀driven฀by฀the฀negative฀heat฀of฀mixing,฀of฀alternating฀ thin฀layers฀as฀observed฀for฀the฀interdiffusion฀of฀thin฀ilms฀of฀pure฀metals.63,64 On the฀other฀hand,฀MM฀consists฀of฀energizing฀the฀equilibrium฀crystalline฀compound฀ by the severe cyclic deformation provided by the milling process.19 Mechanical milling increases the energy of the compound by the generation of chemical disorder, point defects such as vacancies, and lattice defects (e.g. dislocations).14,21,35 In addition, an important contribution to the energy increase comes from the reduction฀of฀the฀grain฀size฀to฀the฀nanometer฀level฀and฀the฀consequent฀storage฀of฀ energy in the grain boundaries, which constitute an appreciable fraction of the material volume.14,21,35 This energy is stored in the crystal up to a point at which it becomes฀ unstable.฀ The฀ highly฀ energized฀ material฀ then฀ lowers฀ its฀ energy฀ by฀ transforming into a different atomic structural arrangement, e.g. the supersaturated solid solution. With this in mind, it is possible to draw a schematic illustration of the formation of the supersaturated Al(Mg) solid solution by MA and MM. Instead of lowering the Gibbs free energy of the system, such as for mechanical alloying, during mechanical milling the free energy of the equilibrium crystalline compound is raised to a level equal to or larger than that of the metastable phase. The process can be better understood by referring to Fig. 3.8, which schematically shows the Gibbs free energies for the different phases that may form during mechanical attrition of binary Al60Mg40. The straight line represents the free energy of the elemental฀powder฀mixture฀of฀the฀pure฀elements฀Al฀and฀Mg.฀The฀broad฀curve฀is฀the฀ free energy of the metastable solid solution and the narrow curve is the free energy of the crystalline intermetallic compound β-Al3Mg2 with composition Al60Mg40. From thermodynamic point of view, the two processes are quite different. While for฀MA฀of฀the฀mixture฀of฀pure฀Al฀and฀Mg฀with฀a฀composition฀corresponding฀to฀that฀ of the intermetallic compound β-Al3Mg2 (reaction [1] →  [2]), the initial state has a฀Gibbs฀free฀energy฀larger฀than฀that฀of฀the฀inal฀product฀(i.e.฀the฀solid฀solution),฀for฀ MM of the intermetallic compound β-Al3Mg2 (reaction [3] → [2]), the initial state has฀a฀Gibbs฀free฀energy฀lower฀than฀that฀of฀the฀inal฀product.฀In฀the฀irst฀case฀the฀ negative฀heat฀of฀mixing฀of฀the฀elemental฀powders฀provides฀the฀driving฀force฀for฀

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3.8 Schematic free energy diagram of the Al–Mg system for the different phases that may form during mechanical alloying of elemental powder mixtures and mechanical milling of the single-phase intermetallic compound (adapted from Scudino et al.60).

interdiffusion and eventually for metastable phase formation. On the other hand, no฀ chemical฀ driving฀ force฀ exists฀ for฀ the฀ reaction฀ [3]฀→ [2] In this case, the free energy of the equilibrium intermetallic compound must be raised above that of the metastable solid solution by the mechanism previously mentioned. A฀ microscopic฀ model฀ for฀ MA,฀ which฀ explains฀ intermixing฀ in฀ systems฀ with฀ positive฀mixing฀enthalpy,฀has฀been฀proposed฀by฀Schwarz.65 The model is based on dislocation-mediated฀ intermixing฀ through฀ the฀ diffusion฀ of฀ solutes฀ along฀ the฀ dislocation cores (dislocation pipe diffusion). Mechanical alloying produces fresh metal/metal surfaces and a high density of dislocations. Due to the strong attractive interaction between solutes and dislocations, the solutes can diffuse along the dislocation cores with an activation energy which is about half of that needed for bulk diffusion. When a powder particle is trapped between colliding balls, for short time intervals on the order of milliseconds, it is subjected to a high stress pulse. As a result, some or all the dislocations in the particle are forced to glide and leave their previous positions. However, the solutes that have diffused along the dislocation cores are not able to follow the fast moving dislocations and, consequently, are left behind as strings of solutes in a highly supersaturated state, which฀have฀an฀excess฀chemical฀energy.฀Multiple฀repetition฀of฀this฀process฀leads฀to฀ effective฀alloy฀intermixing฀and/or฀to฀stable฀and฀metastable฀phase฀formation.

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Besides thermodynamic considerations, kinetic aspects also play a central role on the phase selection during mechanical attrition. This is particularly important when฀ different฀ (stable฀ and฀ metastable)฀ phases฀ compete฀ for฀ the฀ inal฀ product.฀ Typical฀examples฀are฀the฀formation฀of฀amorphous฀or฀nanostructured฀quasicrystalline฀ powders by mechanical alloying.12 The amorphous phase and most of the quasicrystalline materials are metastable with respect to the equilibrium crystalline phases,฀ i.e.฀ an฀ energy฀ barrier฀ exists฀ preventing฀ these฀ metastable฀ phases฀ from฀ spontaneous฀crystallization.12,18 The thermodynamically stable state of a system is determined by a minimum in the Gibbs free energy G. In metallic systems, the Gibbs free energy of the equilibrium crystalline state Geq is always lower than that of the metastable phases Gmeta below the melting temperature. In order to form a metastable phase by mechanical attrition, the free energy of the equilibrium phase has฀to฀be฀irstly฀raised฀to฀a฀state฀G0 (Fig. 3.9). This high-energy state can be achieved by mechanical attrition through the mechanisms฀ explained฀ previously.฀ The฀ free฀ energy฀ of฀ the฀ system฀ can฀ be฀ then฀ lowered from G0 either by the formation of the metastable phase with free energy Gmeta or by the formation of the equilibrium phase. The equilibrium phase is thermodynamically favored, since the driving force ∆Geq฀=฀(G0 – Geq) is larger than that for metastable phase formation ∆Gmeta฀ =฀ (G0 – Gmeta). However, the formation of equilibrium or metastable phases depends on thermodynamic as well as on kinetic factors. The formation of the metastable phase is then possible if the system is kinetically restricted from reaching the equilibrium state of lower free energy, i.e. metastable phase formation proceeds considerably faster than the

3.9 Schematic representation of the basic principles of metastable phase formation by mechanical attrition.

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formation of the equilibrium phase from the initial state G0. At the same time, the metastable phase must not transform into the equilibrium phase as the reaction proceeds, i.e. the timescale for transformation of the metastable phase must be longer than that of metastable phase formation. These kinetic constraints can be summarized฀as12,18,66:

τ0→meta 3฀GPa฀already฀exist.27 This kind of martensite is produced in fairly large steel samples by rapid cooling from the austenitic condition. However, the dimensions can be limited by the need to achieve a uniform microstructure, a fact implicit in the original concept of hardenability. To increase hardenability requires฀the฀addition฀of฀expensive฀alloying฀elements.฀The฀rapid฀cooling฀can฀lead฀ to undesirable residual stresses28,29 that can ruin critical components and have to be accounted for in component life assessments. Recently, an innovative design procedure based on phase transformation theory30 has been successfully applied to design strong, tough and affordable nanocrystalline steel without using deformation, rapid heat-treatment or mechanical processing. Furthermore, the material can be produced in a form that is large in all its three dimensions. The new material relies on a microstructure called฀bainite,฀which฀has฀been฀known฀since฀1930;฀the฀novelty฀is฀in฀the฀alloy฀design฀ which฀leads฀to฀the฀ine฀scale฀and฀controlled฀response฀to฀heat฀treatment.

4.3

Phase transformation theory: a powerful tool for the design of advanced steels, from micro to nano

It฀has฀long฀been฀known฀that฀alloying฀the฀steel฀with฀about฀2฀wt.%฀of฀silicon฀can฀in฀ appropriate฀circumstances฀yield฀a฀carbide-free฀microstructure,฀which฀is฀a฀mixture฀ of bainitic ferrite and carbon-enriched residual austenite. The silicon does not dissolve in cementite and hence suppresses its precipitation from austenite. Cementite฀ is฀ a฀ cleavage฀ and฀ void-initiating฀ phase฀ that฀ is฀ best฀ eliminated฀ from฀ strong฀steels.฀However,฀the฀full฀beneits฀of฀this฀carbide-free฀bainitic฀microstructure฀ have฀frequently฀not฀been฀realized.฀This฀is฀because฀the฀transformation฀to฀bainitic฀ ferrite stops well before the equilibrium carbon concentration in austenite is reached.31–34 There remain large regions of untransformed austenite that decompose under stress to hard, brittle martensite. The problem, which is essentially thermodynamic in origin, can be solved by altering the relative stabilities of the austenite and ferrite phases. The essential principles฀ governing฀ the฀ optimization฀ of฀ such฀ microstructures฀ are฀ now฀ well฀ established. Everything must be done that encourages an increase in the amount of bainitic ferrite so as to consume the blocks of austenite.35,36 With careful design, impressive combinations of strength and toughness have been reported for highsilicon bainitic steels.35–39฀More฀recently,฀it฀has฀been฀demonstrated฀experimentally฀

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that models based on the atomic mechanism of displacive transformation can be applied successfully to the design of carbide-free bainitic steels, the only experiments฀needed฀are฀those฀to฀validate฀the฀theoretical฀predictions.40,41 Toughness values of nearly 130 MPa m1/2 were obtained for strength in the range of 1.6–1.7 GPa. This compares well with maraging steels, which are at least ninety times฀more฀expensive.฀The฀details฀of฀the฀design฀method,฀which฀is฀based฀on฀the฀ discipline with which the atoms move during transformation, are as follows. Bainite฀grows฀without฀diffusion฀in฀the฀form฀of฀tiny฀plates฀known฀as฀‘sub-units’;฀ each฀plate฀grows฀to฀a฀limited฀size,฀which฀is฀determined฀by฀the฀plastic฀accommodation฀ of the shape deformation accompanying transformation. One consequence of diffusionless growth is that the plates can be supersaturated with carbon, in which case the carbon partitions into the residual austenite soon after the completion of bainite growth. Diffusionless growth of this kind can only occur if the carbon concentration of the parent austenite is less than that given by the T o′ curve. The To curve is the locus of all points, on a temperature versus carbon concentration plot, where austenite and ferrite of the same chemical composition have the same free energy. The T ′o฀curve฀is฀deined฀similarly,฀but฀taking฀into฀account฀the฀strain฀energy฀ associated with the fact that the shape deformation accompanying the displacive transformation฀is฀accommodated,฀at฀least฀partially,฀by฀plastic฀relaxation. The carbon content of the austenite at the termination of phase transformation for different temperatures in different steels is shown in Fig. 4.2. The calculated values for T o′ and paraequilibrium Ae 3′ phase boundaries are also plotted. Likewise, the same types of calculation, but not considering the stored energies of the related phases, are presented as To and Ae3. The measured concentrations in austenite at temperatures below the BS temperature (see Fig. 4.2) lie closer to the T o′ or To value boundaries and far from the paraequilibrium phase boundaries (Ae3 and Ae 3′ lines) for all the steels. The results are consistent with a mechanism in which the bainite฀ grows฀ without฀ diffusion,฀ but฀ with฀ excess฀ carbon฀ partitioning฀ into฀ the฀ austenite soon after transformation. The reaction is said to be incomplete since transformation stops before the phases achieve their equilibrium compositions. In contrast, the measured carbon content of retained austenite at temperatures above the BS฀temperature฀in฀steels฀with฀a฀carbon฀content฀of฀0.3฀wt.%฀corresponds฀ to that given by the Ae3 and Ae 3′ lines. The presence of Widmanstätten ferrite formed at the highest temperatures in these steels suggests that this trend is consistent with the difference between the growth mechanisms for Widmanstätten and bainitic ferrite formation, the former involving carbon diffusion control with equilibrium partitioning of carbon, and the latter involving that bainite initially forms having a full supersaturation of carbon and grows by a mechanism essentially displacive in nature.42 It฀ follows฀ that฀ the฀ maximum฀ amount฀ of฀ bainitic฀ ferrite฀ that฀ can฀ form฀ in฀ the฀ absence of carbide precipitation is limited by the T o′ ฀ curve;฀ this฀ is฀ a฀ severe฀ limitation if large quantities of blocky austenite remain in the microstructure at the฀point฀where฀transformation฀stops.฀The฀design฀procedure฀avoids฀this฀dificulty฀

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4.2 Calculated phase boundaries for different steel grades together with X-ray experimental data representing the carbon concentration of the austenite that is left untransformed after cessation of the bainite/ Widmanstätten reaction.

in three ways: by adjusting the T o′ curve to greater carbon concentrations using substitutional solutes, by controlling the mean carbon concentration, and by minimizing฀the฀transformation฀temperature. It is worth pointing out that attempts have been made to interpret the T o′ criterion differently. One theory argues that the reason why the bainite reaction stops © Woodhead Publishing Limited, 2011

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prematurely is because of the plastic work done as the plate grows by a displacive mechanism overwhelms the driving force for transformation.43,44 However, the theory is derived incorrectly in that the calculated work is divided by the fraction of remaining austenite, whereas it is in fact per unit quantity of bainite. Furthermore, there฀is฀an฀upper฀limit฀to฀the฀amount฀of฀work฀done฀in฀plastic฀accommodation;฀this฀ is the strain energy associated with an elastically accommodated plate, amounting to฀400฀J฀mol–1.45 An alternative interpretation46 requires local equilibrium at the interface,฀ contradicting฀ atomic฀ resolution฀ experiments฀ that฀ show฀ the฀ absence฀ of฀ substitutional solute partitioning.47,48 Returning now to the design, it is known that blocky austenite should be avoided฀to฀ensure฀good฀toughness.฀The฀size฀of฀these฀blocks฀(which฀may฀transform฀ to brittle martensite under stress) must be less than or comparable to that of other fracture initiating phases such as non-metallic inclusions. A reduction in the scale of฀the฀microstructure฀enhances฀both฀strength฀and฀toughness;฀this฀leads฀naturally฀to฀ the conclusion that the microstructure is best generated at low temperatures. The question then arises, what is the lowest temperature at which bainite can be obtained? In order to answer this question, one must be able to reliably calculate the highest temperature at which bainite can form. This requires a consideration of both nucleation and growth. Bainite can only form below the T o′ temperature when: [4.5] ฀400฀J฀mol–1

bainite42;฀∆Gγα

where GSB is the stored energy of is the free energy change accompanying the transformation of austenite into ferrite without any change฀in฀chemical฀composition.฀The฀irst฀condition฀therefore฀describes฀the฀limit฀ to฀growth.฀The฀second฀condition฀refers฀to฀nucleation;฀thus,฀∆Gm฀is฀the฀maximum฀ molar Gibbs free energy change accompanying the nucleation of bainite. GN is a universal nucleation function based on a dislocation mechanism of the kind associated with martensite.42,49–50 The variation of GN with temperature is well behaved even for the high carbon steels of interest here.51 Together with the growth condition, the function allows the calculation of the bainite start temperature, Bs ,฀ from฀ knowledge฀ of฀ thermodynamics฀ alone.฀ An฀ example฀ calculation is presented in Fig. 4.3, which reveals the important result that extraordinarily฀ low฀ transformation฀ temperatures฀ can฀ be฀ achieved฀ because฀ the฀ bainite and martensite start temperatures remain separated. The rate of reaction is also important since transformation must be achieved in a realistic time. For this purpose, a method34 developed to allow the estimation of isothermal transformation diagrams can be used, with the chemical composition as฀ an฀ input.฀ Calculated฀ time–temperature–transformation฀ (TTT)฀ diagrams฀ indicate the time required to initiate transformation. Such calculations also help design the hardenability of the alloy so as to avoid interfering reactions such as allotriomorphic ferrite and pearlite.

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4.3 Computed martensite-start, Ms, and bainite-start, Bs, temperatures in Fe-2Si-3Mn-C alloy system.

4.4

NANOBAIN steel: a material going to extremes

Low฀transformation฀temperatures฀are฀associated฀with฀ine฀microstructures,฀which฀ in turn possess strength and toughness. The theory described above has been used to฀develop฀steels฀that฀transform฀to฀bainite฀at฀temperatures฀as฀low฀as฀125°C,฀in฀timescales that are practical (Table 4.1). The low Bs temperature is a consequence of the high฀carbon฀concentration฀and,฀to฀a฀lesser฀extent,฀solutes฀such฀as฀manganese฀or฀ chromium,฀which฀in฀the฀present฀context฀increase฀the฀stability฀of฀austenite฀relative฀ to ferrite. The molybdenum is added to ameliorate any temper-embrittlement phenomena due to inevitable impurities such as phosphorus. The alloys all contain suficient฀silicon฀to฀suppress฀the฀precipitation฀of฀cementite฀from฀any฀austenite. In the steels designated NANOBAIN 1 and 2 (Table 4.1), bainite can take between 2 to some 60 days to complete transformation within the temperature range 125– 325°C.52,53 In a commercial scenario it may be useful to accelerate transformation without฀losing฀the฀ability฀to฀utilize฀low฀temperatures.฀Certain฀elements฀increase฀the฀ free energy change when austenite transforms and hence should accelerate its decomposition;฀hence,฀the฀cobalt฀and฀aluminium฀containing฀alloys฀in฀Table฀4.1. Table 4.1 Compositions of NANOBAIN alloys, wt.% Steel NANOBAIN NANOBAIN (at.%) NANOBAIN NANOBAIN

1 2 3 4

C

Si

Mn

Cr

Mo

V

Co

Al

0.79 0.98 (4.34) 0.83 0.78

1.59 1.46 (2.76) 1.57 1.49

1.94 1.89 (1.82) 1.98 1.95

1.33 1.26 (1.28) 1.02 0.97

0.30 0.26 (0.14) 0.24 0.24

0.11 0.09 (0.09) – –

– –

– –

1.54 1.60

– 0.99

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4.4 Microstructure formed by isothermal transformation in NANOBAIN 2 at: (a) 200°C for a day; (b) 200°C for two days; and (c) 200°C for six days.

Micrographs after isothermal transformation of austenite to bainitic ferrite at 200°C฀at฀different฀time฀intervals฀in฀NANOBAIN฀2฀are฀illustrated฀in฀Fig.฀4.4.฀After฀ a฀day฀of฀holding฀time฀at฀200°C,฀bainite฀transformation฀has฀not฀started฀and฀a฀mixture฀ of martensite and retained austenite is obtained by quenching (Fig. 4.4 (a) ). © Woodhead Publishing Limited, 2011

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A longer annealing time (two days) at this temperature was required to obtain a฀ signiicant฀ amount฀ of฀ bainitic฀ transformation,฀ as฀ shown฀ in฀ Fig.฀ 4.4฀ (b).฀ Transformation฀is฀completed฀after฀six฀days฀of฀holding฀time,฀when฀a฀fully฀bainitic฀ microstructure฀(~90%฀bainite)฀is฀obtained฀(Fig.฀4.4฀(c)฀). The calculated34,54,55 TTT diagrams for the initiation of transformation in NANOBAIN฀1฀and฀2฀are฀shown฀in฀Fig.฀4.5,฀which฀also฀contain฀experimental฀data฀ for฀the฀reaction฀times.฀The฀upper฀C-curve฀represents฀the฀onset฀of฀reconstructive฀ transformations such as allotriomorphic ferrite and pearlite, whereas the lower curve is for bainite. The measured values for a detectable degree of transformation are฀ in฀ reasonable฀ agreement฀ with฀ those฀ calculated,฀ except฀ at฀ the฀ highest฀ temperature฀(300–400°C)฀where฀the฀time฀period฀required฀is฀underestimated. X-ray analysis was used to estimate the quantities of retained austenite present at the point where transformation ceases (Fig. 4.6 (a) ). The retained austenite fraction฀ is฀ expected฀ to฀ increase฀ for฀ the฀ higher฀ transformation฀ temperature฀ because฀ less฀ bainite฀ forms;฀ this฀ is฀ in฀ contrast฀ to฀ the฀ situation฀ with฀ low-carbon฀ alloys, where a larger fraction of bainite favours the retention of austenite because of the portioning of carbon into the austenite.

4.5 Calculated TTT diagrams for the initiation of transformation, and measured times for the commencement (filled points) and termination of reaction (open circles): (a) NANOBAIN 1; (b) NANOBAIN 2.

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The฀maximum฀amount฀of฀bainite฀that฀can฀be฀obtained฀at฀any฀temperature฀is฀limited฀ because฀the฀carbon฀content฀of฀the฀residual฀austenite฀must฀not฀exceed฀that฀given฀by฀the฀ T ′o curve. At that point, the enriched austenite can no longer transform into bainite. The carbon concentrations of the austenite and bainitic ferrite as determined from X-ray analysis for NANOBAIN 2 are also presented in Fig. 4.6. The evolution of carbon฀in฀austenite฀and฀bainitic฀ferrite฀during฀transformation฀at฀200°C฀is฀shown฀in฀ Fig. 4.6 (b). Similarly, the carbon content of the austenite and bainitic ferrite at the termination of bainite reaction for different transformation temperatures is shown in Fig. 4.6 (c). The measured carbon concentrations in austenite lie closer to the T o′ value boundary and far from the paraequilibrium phase boundary. This trend is

4.6 X-ray experimental data on: (a) volume fractions of retained austenite; (b) carbon content in bainitic ferrite and retained austenite of the microstructure obtained by isothermal transformation at 200°C for 2 to 10 days in NANOBAIN 2; and (c) X-ray results corresponding at the termination of bainite reaction for different transformation temperatures in NANOBAIN 2. Xo represents the overall carbon content of the steel. To ′ and the paraequilibrium A’3 curves were calculated according to Bhadeshia.55

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4.6 Continued.

consistent with a mechanism in which the bainite grows without any diffusion, but with฀ excess฀ carbon฀ partitioning฀ into฀ the฀ austenite฀ soon฀ after฀ transformation.฀ The฀ reaction is said to be incomplete since transformation stops before the phases achieve their equilibrium compositions. The transmission electron micrograph in Fig. 4.7 illustrates a typical microstructure of low-temperature bainite, with slender plates that are incredibly thin฀ and฀ long,฀ giving฀ a฀ most฀ elegant฀ ine฀ scale฀ structure,฀ which฀ is฀ an฀ intimate฀ mixture฀of฀austenite฀and฀ferrite.฀Dislocation฀debris฀is฀evident฀in฀both฀the฀bainitic฀ ferrite฀and฀the฀surrounding฀austenite.฀Extensive฀transmission฀microscopy฀failed฀to฀ reveal carbides in the microstructure, only a few minute (20 nm wide and 175 nm long) cementite particles in the ferrite within NANOBAIN 1 transformed at

4.7 Transmission electron micrographs of microstructure obtained at 200°C for 15 days in NANOBAIN 2.

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190°C฀for฀two฀weeks.52฀Quite฀remarkably,฀the฀plates฀formed฀at฀200°C฀in฀Steel฀B฀ (Fig. 4.7) have a width that is less than 50 nm, with each plate separated by an even฀ iner฀ ilm฀ of฀ retained฀ austenite.฀ It฀ is฀ this฀ ine฀ scale฀ that฀ is฀ responsible฀ for฀ much฀ of฀ the฀ tenacity฀ of฀ the฀ microstructure,฀ with฀ hardness฀ values฀ in฀ excess฀ of฀ 600฀HV฀and฀strength฀in฀excess฀of฀2.5฀GPa.52฀The฀dispersion฀of฀ilms฀of฀austenite฀ undoubtedly helps render the steel tough. Analysis indicates that the largest effects on plate thickness are the strength of the austenite, the free energy change accompanying transformation and a small independent effect due to transformation temperature.56 In the present case, the observed฀reinement฀is฀a฀consequence฀mainly฀of฀high฀carbon฀content฀and฀the฀low฀ transformation temperature on enhancing the strength of the austenite.

4.5

Accelerating the bainite reaction at low temperatures

Slow transformation gives the ability to transform large components to a uniform฀ microstructure฀ free฀ from฀ residual฀ stresses฀ or฀ complex฀ processing.฀ Suppose, however, that there is a need for more rapid heat treatment. The transformation can easily be accelerated to complete the processing within hours (as opposed to days), by making controlled additions of substitutional solutes to the steel, such that the free energy change as austenite changes into ferrite is enhanced. There are essentially two choices: aluminium and cobalt, in concentrations฀less฀than฀2฀wt.%,฀have฀been฀shown฀to฀accelerate฀the฀transformation฀ in the manner described.57 Both are effective, either on their own or in combination. They฀ work฀ by฀ increasing฀ the฀ driving฀ force฀ for฀ the฀ transformation฀ of฀ austenite;฀ they have therefore been added to make NANOBAIN 3 and 4, which should then transform more rapidly. Fig. 4.8 (a) shows the increase in the reaction rate due฀to฀the฀cobalt;฀the฀effect฀is฀particularly฀large฀when฀both฀elements฀are฀added.฀A฀ further฀rate฀increment฀is฀possible฀by฀reining฀the฀austenite฀grain฀size฀(Fig.฀4.8฀(b)).฀ An increase in the free energy change also means that a greater fraction of bainite is obtained, which may have the additional advantage of increasing the stability of the austenite.57

4.6

Characterizing nanocrystalline bainitic steels at the atomic scale

The฀complexity฀of฀bainite฀formation฀mechanism฀and฀kinetics,฀and฀the฀apparent฀ diversity of its microstructural appearance, gives rise to disagreement in identifying฀its฀correct฀deinition.฀However,฀the฀well-known฀difference฀in฀carbide฀ distribution฀between฀bainite฀formed฀at฀high฀and฀low฀temperatures,฀viz.฀intralath฀ and฀interlath฀respectively,฀appears฀to฀exist฀in฀a฀majority฀of฀steels฀and฀makes฀the฀ classical nomenclature of upper and lower bainite useful, both in describing the microstructural appearance and in classifying the overall reaction mechanism.

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4.8 (a) Kinetics of bainite formation at 200°C in NANOBAIN 2–4 steels; (b) effect of prior austenite grain on bainite formation at 200°C in NANOBAIN 3 steel.

Both upper and lower bainite consist of plates of ferrite, known as sub-units, separated by cementite. The plates of ferrite grow in aggregates called sheaves of bainite. Within each sheaf, the plates of ferrite are parallel and share a common crystallographic orientation. The essential difference between upper and lower bainite is with respect to the carbide precipitation. In upper bainite, the bainitic ferrite฀is฀free฀of฀precipitation;฀carbides฀grow฀from฀the฀regions฀of฀carbon-enriched฀ austenite, which are trapped between the sub-units of ferrite. In contrast, lower bainitic฀ferrite฀contains฀a฀ine฀dispersion฀of฀plate-like฀carbides฀within฀the฀bainitic฀ ferrite plates. The carbide particles usually precipitate in a single crystallographic orientation฀such฀that฀their฀habit฀plane฀is฀inclined฀at฀~60°฀to฀the฀plate฀axis.฀There฀ are many observations that reveal that lower bainitic cementite forms within supersaturated ferrite by a displacive mechanism without the partitioning of substitutional solute.58 The cementite lattice is generated by the deformation of the ferrite crystal structure, at a rate controlled by the diffusion of carbon. The iron/substitutional solute content ratio thus remains constant everywhere and subject฀to฀that฀constraint,฀the฀carbon฀achieves฀equality฀of฀chemical฀potential;฀the฀ cementite is then said to grow by paraequilibrium transformation. In contrast, the precipitation of carbides in upper bainite is a secondary process that฀does฀not฀interfere฀with฀the฀mechanism฀of฀formation฀of฀bainitic฀ferrite฀except฀

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in the sense that any precipitation from austenite will deplete its carbon content, thereby promoting further transformation. In fact, the precipitation of cementite from austenite during bainite formation can be suppressed using silicon as an alloying element because the driving force for precipitation is dramatically reduced when the cementite is forced to inherit the silicon present in the parent phase.59 The bainitic microstructure in high silicon steels, commonly known as carbide-free฀bainite,฀consists฀of฀ine฀plates฀of฀bainitic฀ferrite฀separated฀by฀carbonenriched regions of retained austenite. As฀ mentioned฀ above,฀ extensive฀ transmission฀ electron฀ microscopy฀ (TEM)฀ of฀ this novel microstructure has failed to reveal carbide particles inside the bainitic ferrite. This is indeed an interesting observation, since at these temperatures, the steel with such high carbon levels would transform to a lower-bainitic microstructure.฀After฀extensive฀aging฀at฀200°C฀for฀two฀weeks,฀just฀a฀few฀20฀nm฀ wide and 175 nm long cementite particles have been observed inside a thicker bainitic ferrite plate in NANOBAIN 2.60 The difference between upper and lower bainite comes from a competition between the rate at which carbides can precipitate from ferrite and the rate with which carbon is partitioned from supersaturated ferrite into austenite.61 The precipitation of cementite from฀ lower฀ bainite฀ can฀ occur฀ at฀ temperatures฀ below฀ 125°C,฀ in฀ time฀ periods฀ too short to allow any substitutional diffusion of iron atoms. The long-range diffusion of carbon atoms is of course necessary, but because carbon resides in interstitial฀ solution,฀ it฀ can฀ be฀ very฀ mobile฀ at฀ temperatures฀ as฀ low฀ as฀ –60°C.62 The formation of cementite or other transition carbides of iron such as ε-carbide, in these circumstances of incredibly low atomic mobility, must differ from diffusional decomposition reactions. It has been suggested that63 the cementite lattice is generated by a displacive mechanism with paraequilibrium, i.e. a homogeneous deformation of supersaturated ferrite combined with the necessary diffusion of carbon. The X-ray diffraction analysis results in Fig. 4.6 (b) indicated that the carbon concentration฀ in฀ the฀ bainitic฀ ferrite฀ was฀ much฀ higher฀ than฀ that฀ expected฀ from paraequilibrium thermodynamics between austenite and ferrite.60 This supersaturation was attributed to the trapping of carbon at the dislocations in the bainitic฀ ferrite.฀ Using฀ transmission฀ electron฀ microscopy,฀ Smith64 estimated a mean dislocation density of 4 × 1014 m–2฀in฀a฀Fe-0.07C-0.23Ti฀wt.%฀alloy฀when฀ isothermally฀ transformed฀ to฀ bainite฀ at฀ 650°C.฀ This฀ relatively฀ high฀ dislocation฀ density is attributed to the fact that shape deformation accompanying displacive transformations฀is฀accommodated฀partially฀by฀plastic฀relaxation.65 However, no direct฀ observation฀ has฀ been฀ yet฀ reported฀ of฀ the฀ interstitial฀ carbon฀ Cottrell฀ atmosphere in bainitic ferrite. In฀this฀sense,฀atom฀probe฀tomography฀(APT)฀was฀used฀to฀characterize฀at฀the฀ atomic฀scale฀bainitic฀microstructures฀formed฀at฀200฀and฀300°C฀in฀NANOBAIN฀ 2฀ bainitic฀ steel.฀ The฀ large฀ ield฀ of฀ view฀ and฀ rapid฀ analysis฀ capability฀ of฀ this฀ technique facilitated the analysis of dislocations in these materials.

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4.6.1 Solute distribution during transformation Five฀ at.%฀ carbon฀ isoconcentration฀ surface฀ and฀ concentration฀ proiles฀ from฀ NANOBAIN฀ 2฀ annealed฀ at฀ 200°C฀ for฀ four฀ days฀ are฀ shown฀ in฀ Fig.฀ 4.9.฀ The distribution of carbon atoms in the analysis volume is not uniform and carbon-rich and carbon-depleted regions are clearly distinguishable. As no crystallographic information was available, the carbon-enriched regions of the atom maps are assumed to represent a region of austenite, as its carbon content฀ is฀ higher฀ than฀ the฀ average฀ value฀ of฀ 4.3฀ at.%,฀ and฀ the฀ low฀ carbon฀ (80%฀ of฀ the฀ inest฀ bainitic฀ ferrite฀ present in the microstructures, the contribution is about 1.6 and 1.1 GPa for NANOBAIN฀ 3฀ and฀ 4฀ respectively;฀ on฀ the฀ other฀ hand,฀ the฀ increment฀ due฀ to฀

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4.14 Quantitative microstructure results on NANOBAIN 3 and 4 steels: carbon content in bainitic ferrite, its plate thickness and dislocation density obtained after isothermal transformation at different temperatures and times, ensuring that bainitic transformation was finished.

4.15 Plot showing the relation between ferrite dislocation density and its carbon content following transformation.

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4.16 Strengthening contributions versus transformation temperature after correcting by their corresponding bainitic ferrite fractions.

dislocations is about 0.5 GPa for both alloys. As the transformation temperature increases and the microstructures become coarser and less dislocated, these contributions become weaker, as Fig. 4.16 illustrates for the microstructure obtained฀after฀transformation฀at฀300°C฀in฀both฀steels. It฀is฀dificult฀to฀separate฀the฀effect฀of฀retained฀austenite฀on฀strength฀in฀these฀steel฀ from other factors. Qualitatively, austenite can affect the strength by transforming to martensite during testing, the transformation-induced plasticity (TRIP) effect. The฀low฀yield/ultimate฀tensile฀strength฀ratios฀(YS/UTS)฀in฀Fig.฀4.13฀(a)฀are฀due฀ to the presence of austenite and the large dislocation density in the microstructure.90 Consequently,฀retained฀austenite฀increases฀the฀strain-hardening฀rate฀of฀the฀steel. Similarly, toughness and ductility are controlled by the volume fraction of retained austenite,74 ductile phase compared to the bainitic ferrite, and its ability to transform to martensite under strain. This effect strongly depends on the chemical composition and morphology of the retained austenite.73,91 Thus the microstructures฀obtained฀after฀isothermal฀heat฀treatment฀at฀300°C,฀with฀austenite฀ fractions฀of฀0.25฀and฀0.37฀for฀NANOBAIN฀3฀and฀4฀respectively,฀exhibit฀the฀best฀ results in terms of total elongation and fracture toughness (Fig. 4.13 (b) and (c))

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when฀compared฀with฀the฀microstructures฀obtained฀after฀transformation฀at฀200°C,฀ with austenite fractions of 0.13 and 0.17 for NANOBAIN 3 and 4 respectively. Strain฀hardening฀is฀characterized฀by฀the฀incremental฀strain-hardening฀exponent฀ deined฀ as฀ n฀ =฀ d(ln σ)/d(ln εp), where σ฀ =฀ kε pn represents the flow curve in the region of uniform true plastic deformation (εp) and k฀is฀the฀strength฀coeficient.฀The฀ variation฀of฀the฀incremental฀work฀hardening฀exponent฀n as a function of true strain in NANOBAIN 3 transformed at different temperatures is shown in Fig. 4.17. The straight line corresponds to the instability criterion εp฀ =฀ n. It appears that the different strength-ductility combinations in these advanced bainitic microstructures are associated with completely different work-hardening behaviors. The large true uniform฀strains฀of฀specimen฀treated฀at฀300°C฀are฀due฀to฀a฀high฀retained฀austenite฀ fraction that continuously increases the incremental work-hardening n after a sharp decrease at low plastic strains. In the microstructure obtained by transformation at 250°C,฀after฀reaching฀a฀maximum฀n smoothly decreases until the onset of necking. For฀ the฀ microstructures฀ obtained฀ at฀ 200°C฀ the฀ situation฀ completely฀ differs฀ from฀ that previously described at higher transformation temperatures: a high increase of n฀during฀the฀irst฀stages฀of฀plastic฀deformation฀is฀followed฀by฀a฀drastic฀drop฀that฀ ends at low levels of plastic deformation. The฀ mechanisms฀ occurring฀ during฀ tensile฀ deformation฀ can฀ be฀ explained฀ by฀ the correlation between the shape of n versus true strain curves and the rate at which retained austenite transforms to martensite under strain.92–95฀The฀200°C฀ microstructure, with low fractions and lowest stability of the austenite, rapidly transform฀ at฀ very฀ small฀ strains.฀As฀ a฀ result,฀ there฀ is฀ little฀ beneit฀ of฀ the฀ straininduced transformation. The situation changes as the fraction of more stable

4.17 Curves of the incremental work hardening exponent, n, of bainitic microstructures obtained in NANOBAIN 3 steel by transformation at different temperatures (200, 250 and 300°C) and tested at room temperature. The straight line represents the instability criterion.

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austenite฀ increases฀ in฀ the฀ microstructure.฀ For฀ 250°C฀ microstructure,฀ retained฀ austenite฀ starts฀ to฀ transform฀ immediately฀ after฀ the฀ initial฀ maximum฀ n, and transformation proceeds until the instability criterion is reached. On the other hand,฀high฀fractions฀of฀very฀stable฀austenite฀are฀present฀at฀300°C฀microstructures,฀ as฀ a฀ result,฀ transformation฀ starts฀ well฀ after฀ the฀ maximum฀ n and continues progressively up to necking. Finally, the properties of the present alloys are compared against published data in Fig. 4.18,39,96฀ highlighting฀ the฀ fact฀ that฀ novel฀ bainitic฀ steels฀ exhibit฀ an฀

4.18 Comparison of ultimate strength versus fracture toughness of: (a) conventional quenched and tempered steels (QT), maraging steels, other bainitic steels39 and NANOBAIN steels; and (b) strength versus total elongation of conventional steels96 and NANOBAIN steels. Note: IF: interstitial free, CMn: carbon manganese, BH: bake hardenable, IS: isotropic, DP: dual phase, CP: complex phase.

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exceptional฀ combination฀ of฀ mechanical฀ properties฀ that฀ places฀ this฀ new฀ type฀ of฀ microstructures in an advantageous position for different applications such as transport, construction and offshore industries, as well as defence applications.

4.8

Conclusion and future trends

It is clear that bainite can be obtained by transforming at very low temperatures. There is then very a low possibility that iron or substitutional solutes will diffuse. A consequence of the low transformation temperature is that the plates of bainite are฀extremely฀ine,฀20–40฀nm฀thick,฀making฀the฀material฀very฀strong.฀This฀is฀a฀ bulk nanocrystalline material that is cheap and can be obtained without severe deformation processing. When this feature is combined with the fact that the plates of ferrite are interspersed with austenite, it becomes possible to create novel strong and tough steels. In this regard, the potential for industrial application is large because the alloys are routinely manufactured. As is always the case, there remain many parameters that have yet to be characterized,฀for฀example฀the฀fatigue฀and฀stress฀corrosion฀properties.฀Moreover,฀ the alloys designed so far either transform slowly over a period of many days, or have to be alloyed with cobalt and aluminium in order to accelerate transformation. In the future, it is possible that rapid transformation could be engineered by controlling the manganese concentration. The key will be to do this without compromising properties. Finally,฀ high-carbon฀ steels฀ are฀ dificult฀ to฀ weld฀ because฀ of฀ the฀ formation฀ of฀ untempered,฀ brittle฀ martensite฀ in฀ the฀ coarse-grained฀ heat-affected฀ zones฀ of฀ the฀ joints. The martensite fractures easily, leading to a gross deterioration in the structural integrity of the joint. For this reason, the vast majority of weldable steels have low-carbon concentrations. Therefore, it would be desirable to make the low-temperature bainite with a much reduced carbon concentration. Preliminary calculations indicate that carbon is much more effective in maintaining a difference between the MS and BS temperatures than are substitutional solutes which reduce ∆Gγα simultaneously for martensite and bainite. Substitutional solutes฀ do฀ not฀ partition฀ at฀ any฀ stage฀ in฀ the฀ formation฀ of฀ martensite฀ or฀ bainite;฀ therefore, both transformations are identically affected by the way in which the substitutional solute alters the thermodynamic driving force. It is the partitioning of carbon at the nucleation stage that is one of the distinguishing features of bainite when compared with martensite. This carbon partitioning allows bainite to form at a higher temperature than martensite. This advantage is diminished as the overall carbon concentration is reduced. These results are discouraging from the perspective of฀designing฀a฀low-carbon฀bainite฀with฀a฀ine฀microstructure฀obtained฀by฀transforming฀ at low temperatures. However, the issue is worth investigating further since the original฀ theory฀ has฀ a฀ number฀ of฀ approximations.฀ In฀ the฀ future,฀ the฀ Fe-Mn-Ni-C฀ system฀should฀be฀explored฀in฀the฀context฀of฀these฀calculations,฀bearing฀in฀mind฀the฀ desire to design low carbon alloys in which the BS temperature is suppressed.

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4.9

Sources of further information and advice

Research groups working on NANOBAIN MATERALIA฀ Research฀ Group,฀ CENIM-CSIC,฀ Madrid,฀ Spain฀ http://www. cenim.csic.es/materalia/PaginaWebEnglish/WebMateralia.html Phase฀ Transformations฀ &฀ Complex฀ Properties฀ Research฀ Group,฀ University฀ of฀ Cambridge,฀Cambridge,฀UK฀http://www.msm.cam.ac.uk/phase-trans/

Key books to consult: R.W.K.฀ Honeycombe฀ and฀ H.K.D.H.฀ Bhadeshia:฀ Steels, Microstructure and Properties. Edward Arnold, London (1995). H.K.D.H.฀ Bhadeshia:฀ Bainite in steels, 2nd ed. Institute of Materials, London (2001). M.K.฀ Miller:฀ Atom Probe Tomography.฀ Kluwer฀Academic/Plenum฀ Press,฀ New฀ York (2000).

4.10

Acknowledgements

It฀ is฀ a฀ special฀ pleasure฀ to฀ acknowledge฀ Professor฀ H.K.D.H.฀ Bhadeshia฀ for฀ his support guidelines on NANOBAIN research and development. Research at฀the฀Oak฀Ridge฀National฀Laboratory฀SHaRE฀User฀Facility฀was฀sponsored฀by฀ the฀ Scientiic฀ User฀ Facilities฀ Division,฀ Ofice฀ of฀ Basic฀ Energy฀ Sciences,฀ US฀ Department of Energy.

4.11

References

฀ 1฀ Valiev฀R.Z.,฀Islamgaliev฀R.K.,฀Alexandrov฀I.V.฀Prog฀Mater฀Sci฀2000;฀45:฀103. ฀ 2฀ Valiev฀R.Z.,฀Zehetbauer฀M.J.,฀Estrin฀Y.,฀Hoppel฀H.W.,฀Ivanisenko฀Y.,฀Hahn฀H.,฀Wilde฀ G.,฀Roven฀H.J.,฀Sauvage,฀X.฀Langdon฀T.G.฀Adv฀Eng฀Mater฀2007;฀9:฀527. ฀ 3฀ Ma฀E.฀JOM฀2006;฀58:฀49. ฀ 4฀ Teplov฀V.A.,฀Pilugin฀V.P.,฀Gaviko฀V.S.,฀Chernyshov฀E.G.฀Philos฀Mag฀1993;฀68:฀877. ฀ 5฀ Senkov฀ O.N.,฀ Froes฀ F.H.,฀ Stolyarov฀ V.V.,฀ Valiev฀ R.Z.,฀ Liu฀ J.฀ Scr฀ Mater฀ 1998;฀ 38: 1511. ฀ 6฀ Shabashov฀ V.A.,฀ Litvinov฀ A.V.,฀ Mukoseev฀ A.G.,฀ Sagaradze฀ V.V.,฀ Desyatkov฀ D.V.,฀ Pilyugin฀V.P.,฀Sagaradze฀I.V.,฀Vildanova฀N.F.฀Mater฀Sci฀Eng฀A฀2003;฀361:฀136. ฀ 7฀ Ivanisenko฀Y.,฀Lojkowski฀W.,฀Valiev฀R.Z.,฀Fecht฀H.J.฀Acta฀Mater฀2003;฀51:฀5555. ฀ 8฀ Sauvage฀X.,฀Jessner฀P.,฀Vurpillot฀F.,฀Pippan฀R.฀Scr฀Mater฀2008;฀58:฀1125. ฀ 9฀ Sauvage฀X.,฀Ivanisenko฀Y.฀J฀Mater฀Sci฀2007;฀42:฀1615. 10฀ Ohsaki฀S.,฀Kato฀S.,฀Tsuji฀N.,฀Ohkubo฀T.,฀Hono฀K.฀Acta฀Mater฀2007;฀55:฀2885. 11฀ Embury฀J.D.,฀Fisher฀R.M.฀Acta฀Metall฀1966;฀14:฀147. 12฀ Languillaume฀J.,฀Kapelski฀G.,฀Baudelet฀B.฀Acta฀Mater฀1997;฀45:฀1201. 13฀ Langford฀G.฀Metall฀Trans฀1970;฀1:฀465. 14฀ Kobe฀Steel฀Ltd.฀Kobelco฀technology฀review฀No.฀8,฀Japan,฀1990.

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15฀ Bhadeshia฀H.K.D.H.฀High฀strength฀steels.฀In฀Charles฀J.A.,฀Greenwood฀G.W.,฀Smith฀ G.C.,฀ editors.฀ Future฀ Developments฀ in฀ Metals฀ and฀ Ceramics,฀ London,฀ Institute฀ of฀ Materials,฀1992;฀p.฀25. 16฀ Bhadeshia฀H.K.D.H.,฀Harada฀H.฀Appl฀Sur฀Sci฀1993;฀67:฀328. 17฀ Segal฀V.M.฀Mater฀Sci฀Eng฀A฀2002;฀338A:฀331. 18฀ Saito฀Y.,฀Tsuji฀N.,฀Utsunomiya฀H.,฀Sakai฀T.,฀Hone฀R.J.฀Scr฀Mater฀1998;฀39:฀1221. 19฀ Tsuji฀N.,฀Saito฀Y.,฀Ustunomiya฀H.,฀Tanigawa฀S.฀Scr฀Mater฀1999;฀40:฀795. 20฀ Krauss฀G.฀Steels฀heat฀treatment฀and฀processing฀principles.฀Materials฀Park฀(OH):฀ASM฀ International, 1995. 21฀ Maki฀T.฀Tetsu-to-Hagane฀1995;฀81:฀N547. 22฀ Niikura฀M.,฀Fujioka฀M.,฀Adachi฀Y.,฀Matsukura฀A.,฀Yokota฀T.,฀Shirota฀Y.,฀Hagiwara฀Y.฀J฀ Mater฀Process฀Technol฀2001;฀117:฀341. 23฀ Yokota฀T.,฀Garcia-Mateo฀C.,฀Bhadeshia฀H.K.D.H.฀Scr฀Mater฀2004;฀51:฀767. 24฀ Das฀S.K.,฀Thomas฀G.฀Metall฀Trans฀1970;฀1:฀325. 25฀ Morito฀S.,฀Huang฀X.,฀Maki฀T.,฀Hansen฀N.฀Acta฀Mater฀2006;฀54:฀5323. 26฀ Morito฀S.,฀Nishikawa฀J.,฀Maki฀T.฀ISIJ฀Int฀2003;฀43:฀1475. 27฀ Hornbogen฀E.฀Innovations฀in฀ultrahigh-strength฀steel฀technology.฀In฀Olson฀G.B.,฀Azrin฀ M.,฀Wright฀E.S.,฀editors.฀Proc.฀34th฀Sagamore฀Army฀Conf,฀Boston฀(MA),฀1987;฀p.฀113. 28฀ Withers฀P.J.,฀Bhadeshia฀H.K.D.H.฀Mater฀Sci฀Technol฀2001;฀17:฀355. 29฀ Withers฀P.J.,฀Bhadeshia฀H.K.D.H.฀Mater฀Sci฀Technol฀2001;฀17:฀366. 30฀ Caballero฀ F.G.,฀ Miller฀ M.K.,฀ Garcia-Mateo฀ C.,฀ Capdevila฀ C.,฀ Garcia฀ de฀Andrés฀ C.฀ JOM฀2008;฀60:฀16. 31฀ Bhadeshia฀H.K.D.H.,฀Waugh฀A.R.฀Acta฀Metall฀1982;฀30:฀775. 32฀ Chang฀L.C.,฀Bhadeshia฀H.K.D.H.฀Mater฀Sci฀Eng฀A฀1994;฀A184:฀L17. 33฀ Self฀P.,฀Bhadeshia฀H.K.D.H.,฀Stobbs฀M.฀Ultramicroscopy฀1981;฀6:฀29. 34฀ Bhadeshia฀H.K.D.H.฀Met฀Sci฀1982;฀16:฀159. 35฀ Bhadeshia฀H.K.D.H.,฀Edmonds฀D.V.฀Met฀Sci฀1983;฀17:฀411. 36฀ Bhadeshia฀H.K.D.H.,฀Edmonds฀D.V.฀Met฀Sci฀1983;฀17:฀420. 37฀ Miihkinen฀V.T.T.D.,฀Edmonds฀D.V.฀Mater฀Sci฀Technol฀1987;฀3:฀422. 38฀ Miihkinen฀V.T.T.D.,฀Edmonds฀D.V.฀Mater฀Sci฀Technol฀1987;฀3:฀432. 39฀ Miihkinen฀V.T.T.D.,฀Edmonds฀D.V.฀Mater฀Sci฀Technol฀1987;฀3:฀441. 40฀ Caballero฀F.G.,฀Bhadeshia฀H.K.D.H.,฀Mawella฀J.A.,฀Jones฀D.G.,฀Brown฀P.฀Mater฀Sci฀ Technol฀2001;฀17:฀512. 41฀ Caballero฀F.G.,฀Bhadeshia฀H.K.D.H.,฀Mawella฀J.A.,฀Jones฀D.G.,฀Brown฀P.฀Mater฀Sci฀ Technol฀2001;฀17:฀517. 42฀ Bhadeshia฀H.K.D.H.฀Acta฀Metall฀1981;฀29:฀1117. 43฀ Bouaziz฀O.,฀Quidort฀D.,฀Maugis฀P.฀Rev฀Metall฀Paris฀2003;฀100:฀103. 44฀ Quidort฀D.,฀Bouaziz฀O.฀Can฀Metall฀Quart฀2004;฀43:฀25. 45฀ Bhadeshia฀H.K.D.H.฀Mat฀Sci฀Eng฀A฀2004;฀A378:฀34. 46฀ Hillert฀M.฀ISIJ฀Int฀1995;฀35:฀1134. 47฀ Bhadeshia฀H.K.D.H.,฀Waugh฀A.R.฀An฀atom-probe฀study฀of฀bainite.฀In฀Aaronson฀H.I.,฀ Laughlin฀ D.E.,฀ Sekerka฀ R.F.,฀ Wayman฀ C.M.,฀ editors.฀ Proc.฀ Int.฀ Conf.฀ Solid-Solid฀ Phase฀Trans,฀Warrendale:฀Metall฀Soc฀AIME,฀1981;฀p.฀993. 48฀ Stark฀ I.,฀ Smith฀ G.D.W.,฀ Bhadeshia฀ H.K.D.H.฀ The฀ element฀ redistribution฀ associated฀ with the incomplete-reaction phenomenon in bainitic steels: an atom-probe investigation.฀In฀Lorimer฀G฀editor.฀Proc.฀Int.฀Conf.฀Solid-Solid฀Phase฀Trans,฀London:฀ Inst. of Metals, 1988. p. 211. 49฀ Bhadeshia฀H.K.D.H.฀Bainite฀in฀steels.฀2nd฀ed.,฀London:฀Institute฀of฀Materials,฀2001.฀ p. 132.

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50฀ Olson฀G.B.,฀Cohen฀M.฀Metall฀Trans฀1976;฀7A:฀1897. 51฀ García-Mateo฀C.,฀Bhadeshia฀H.K.D.H.฀Mat฀Sci฀Eng฀A฀2004;฀A378:฀289. 52฀ Caballero฀F.G.,฀Bhadeshia฀H.K.D.H.,฀Mawella฀J.A.,฀Jones฀D.G.,฀Brown฀P.฀Mater฀Sci฀ Technol฀2002;฀18:฀279. 53฀ García-Mateo฀C.,฀Caballero฀F.G.,฀Bhadeshia฀H.K.D.H.฀ISIJ฀Int฀2003;฀43:฀1238. 54฀ Lee฀J.L.,฀Bhadeshia฀H.K.D.H.฀Mat฀Sci฀Eng฀A฀1993;฀A171:฀223. 55฀ Bhadeshia฀ H.K.D.H.฀ Program฀ MAP_STEEL_MUCG46,฀ Cambridge,฀ Materials฀ Algorithms Project. Available from: http://www.msm.cam.ac.uk/map/steel/programs/ mucg46-b.html฀[accessed฀30฀June฀2009]. 56฀ Singh฀S.B.,฀Bhadeshia฀H.K.D.H.฀Mat฀Sci฀Eng฀A฀1998;฀245:฀72. 57฀ García-Mateo฀C.,฀Caballero฀F.G.,฀Bhadeshia฀H.K.D.H.฀ISIJ฀Int฀2003;฀43:฀1821. 58฀ Bhadeshia฀H.K.D.H.฀Acta฀Metall฀1980;฀28:฀1103. 59฀ Kozeschnik฀E.,฀Bhadeshia฀H.K.D.H.฀Mater฀Sci฀Technol฀2008;฀24:฀343. 60฀ Caballero฀F.G.,฀Bhadeshia฀H.K.D.H.฀Curr฀Opin฀Solid฀State฀Mater฀Sci฀2004;฀8:฀251. 61฀ Takahashi฀M.,฀Bhadeshia฀H.K.D.H.฀Mater฀Sci฀Tech฀1990;฀6:฀592. 62฀ Winchell฀P.G.,฀Cohen฀M.฀Trans฀ASM฀1962;฀55:฀347. 63฀ Yakel฀H.C.฀Int฀Met฀Rev฀1985;฀30:฀17. 64฀ Smith฀G.M.฀The฀microstructure฀and฀yielding฀behaviour฀of฀some฀Ti฀steels,฀Cambridge฀ (UK):฀University฀of฀Cambridge,฀1984. 65฀ Bhadeshia฀H.K.D.H.,฀Christian฀J.W.฀Metall฀Trans฀1990;฀21A:฀767. 66฀ Bhadeshia฀H.K.D.H.,฀Edmonds฀D.V.฀Acta฀Metall฀1980;฀28:฀1265. 67฀ Kalish฀D.,฀Cohen฀M.฀Mater฀Sci฀Eng฀1970;฀6:฀156. 68฀ Miller฀ M.K.฀Atom฀ probe฀ tomography.฀ New฀York,฀ Kluwer฀Academic/Plenum฀ Press,฀ 2000;฀p.฀158. 69฀ Cochardt฀A.,฀Schoeck฀G.,฀Wiedersich฀H.฀Acta฀Metall฀1955;฀3:฀533. 70฀ Wilde฀J.,฀Cerezo฀A.,฀Smith฀G.D.W.฀Scr฀Mater฀2000;฀43:฀39. 71฀ Srinivasan฀G.R.,฀Wayman฀C.M.฀Acta฀Metall฀1968;฀16:฀621. 72฀ Nemoto฀M.฀High฀voltage฀electron฀microscopy,฀New฀York,฀Academic฀Press,฀1974;฀p.฀230. 73฀ Bhadeshia฀H.K.D.H.,฀Edmonds฀D.V.฀Metall฀Trans฀1979;฀10A:฀895. 74฀ Sandvik฀B.P.J.,฀Nevalainen฀H.P.฀Met฀Technol฀1981;฀15:฀213. 75฀ Ogura฀T.,฀McMahon฀C.J.,฀Feng฀H.C.,฀Vitek฀V.฀Acta฀Metall฀1978;฀26:฀1317. 76฀ Ogura฀T.,฀Watanabe฀T.,฀Karashima฀S.,฀Masumoto฀T.฀Acta฀Metall฀1987;฀35:฀1807. 77฀ Swiatnicki฀W.,฀Lartigue-Korinek฀S.,฀Laval฀J.Y.฀Acta฀Metall฀Mater฀1995;฀43:฀795. 78฀ Fondekar฀M.K.,฀Rao฀A.M.,฀Mallik฀A.K.฀Metall฀Trans฀1970;฀1:฀885. 79฀ Matas฀S.J.,฀Hehemann฀R.F.฀Trans฀Met฀Soc฀AIME฀1968;฀221:฀179. 80฀ Owen฀W.S.฀Trans฀ASM฀1954;฀46:฀812. 81฀ Roberts฀C.S.,฀Averbach฀B.L.,฀Cohen฀M.฀Trans฀ASM฀1953;฀45:฀576. 82฀ Babu฀S.S.,฀Hono฀K.,฀Sakurai฀T.฀Metall฀Mater฀Trans฀1994;฀25A:฀499. 83฀ Miller฀M.K.,฀Beaven฀P.A.,฀Brenner฀S.S.,฀Smith฀G.D.W.฀Metall฀Trans฀1983;฀14:฀1021. 84฀ Sha฀W.,฀Chang฀L.,฀Smith฀G.D.W.,฀Cheng฀L.,฀Mittemeijer฀E.J.฀Surf฀Sci฀1992;฀266:฀416. 85฀ Thomson฀R.C.,฀Miller฀M.K.฀Acta฀Mater฀1998;฀46:฀2203. 86฀ Bhadeshia฀ H.K.D.H.฀ Mathematical฀ modelling฀ of฀ weld฀ phenomena฀ III.฀ London,฀ Institute฀of฀Materials,฀1997;฀p.฀229. 87฀ Langford฀G.,฀Cohen฀M.฀Trans฀ASM฀1969;฀62:฀623. 88฀ Langford฀G.,฀Cohen฀M.฀Metall฀Trans฀1970;฀1:฀1478. 89฀ Honeycombe฀ R.W.K.,฀ Bhadeshia฀ H.K.D.H.฀ Steels.฀ Microstructure฀ and฀ Properties.฀ London,฀Edward฀Arnold,฀1995;฀p.฀311. 90฀ Coldren฀A.P.,฀Cryderman฀R.L.,฀Semchysen฀M.฀Steel฀Strengthening฀Mechanisms.฀Ann฀ Arbor฀(MI):฀Climax฀Molybdenum,฀1969;฀p.฀17.

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Ballinger฀N.K.,฀Gladman฀T.฀Met฀Sci฀1981;฀15:฀95. Jacques฀P.J.,฀Girault฀E.,฀Harlet฀P.,฀Delannay฀F.฀ISIJ฀Int฀2001;฀41:฀1061. Itami฀A.,฀Takahashi฀M.,฀Ushioda฀K.฀ISIJ฀Int฀1995;฀35:฀1121. Sakuma฀Y.,฀Matlock฀D.K.,฀Krauss฀G.฀Metall฀Trans฀1992;฀23A:฀1233. Sugimoto฀K.,฀Kobayashi฀M.,฀Hashimoto฀S.฀Metall฀Trans฀1992;฀23A:฀3085. World Auto Steel. World Steel Association. Middletown (OH): Available from: http:// www.worldautosteel.org฀[accessed฀1฀July฀2009].

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5 The processing of bulk nanocrystalline metals and alloys by electrodeposition U.฀ERB,฀University฀of฀Toronto,฀Canada,฀G.฀PALUMBO฀ and฀J.L.฀McCREA,฀Integran฀Technologies฀Inc.,฀Canada฀

Abstract: This chapter deals with the synthesis of nanocrystalline metals, alloys฀and฀metal฀matrix฀composites฀using฀the฀electrodeposition฀method.฀The฀ irst฀part฀of฀the฀chapter฀covers฀the฀fundamentals฀of฀electrodeposition฀from฀ aqueous฀solutions฀and฀reviews฀experimental฀details฀for฀several฀speciic฀ nanomaterials. This will be followed by a summary of mechanical, corrosion and other properties reported for these materials over the past two decades. The chapter฀includes฀several฀examples฀of฀industrial฀applications฀for฀these฀advanced฀ materials. Key words: electrodeposition of nanomaterials, metals, alloys and composites, mechanical, corrosion, electrical, thermal and magnetic properties, industrial applications.

5.1

Introduction

There฀are฀ive฀general฀approaches฀to฀making฀nanocrystalline฀materials:฀solid฀state฀ processing, liquid phase processing, vapor phase processing, chemical synthesis and electrochemical฀ synthesis.฀ For฀ each฀ general฀ approach,฀ many฀ different฀ speciic฀ methods have been developed to produce nanomaterials in different shapes including thin฀ ilms,฀ powders,฀ nanodots฀ and฀ nanowires฀ or฀ compact฀ three-dimensional฀ bulk฀ nanomaterials. This chapter deals with electrodeposited bulk nanomaterials. Electrodeposition belongs to the general group of electrochemical synthesis methods. Other methods in this group of techniques include electroless deposition, galvanic displacement deposition฀or฀immersion฀plating,฀and฀electrodeposition฀under฀oxidizing฀conditions.฀ The chapter will focus on recent advances in electrodeposition from aqueous solutions. Electrodeposition from organic solutions, molten salts or ionic liquids will not be covered here. Furthermore, the main focus of this review will be on metals,฀alloys฀and฀metal-matrix฀composites.฀Electrodeposition฀of฀organic฀ilms,฀ conductive฀ polymers,฀ semiconductors฀ and฀ oxides฀ will฀ not฀ be฀ included฀ in฀ this฀ chapter. Electrodeposition has been used for more than a century in several application areas฀including฀primary฀metal฀production฀(e.g.฀electrowinning฀and฀electroreining),฀ direct manufacturing (e.g. electroforming of large structural objects or small components฀ for฀ microelectromechanical฀ systems)฀ and฀ surface฀ inishing฀ (e.g.฀ decorative coatings, corrosion and wear-resistant coatings, functional coatings).1–3 118 © Woodhead Publishing Limited, 2011

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There are numerous reports in the literature that have dealt with electrodeposits with฀ extremely฀ small฀ crystal฀ size฀ and฀ the฀ property฀ enhancements฀ that฀ can฀ be฀ achieved฀ in฀ such฀ materials฀ by฀ grain฀ size฀ reduction.฀ However,฀ it฀ was฀ only฀ throughout the 1980s that the full potential of electrodeposition as a production route฀ for฀ nanocrystalline฀ materials฀ was฀ recognized.4,5 The earliest patents on nanomaterials made by electrodeposition were issued in the mid 1990s.6,7 The superior฀ properties฀ irst฀ observed฀ on฀ nanocrystalline฀ nickel฀ electrodeposits฀ resulted in one of the world’s earliest large-scale industrial applications of nanomaterials in 1994: the so-called electrosleeve process for in situ repair of nuclear steam generator tubing.8–10 This process has been implemented in both฀ Canadian฀ CANDU฀ and฀ US฀ pressurized฀ water฀ reactors.฀ Essentially,฀ this฀ application is a nanocrystalline Ni-P microalloy electroform (~ 1 mm in thickness, 50–100฀nm฀grain฀size)฀deposited฀on฀the฀inside฀of฀steam฀generator฀tubes฀to฀effect฀a฀ complete structural repair at sites where corrosion, stress corrosion cracking and other degradation phenomena compromised the structural integrity of the tubes. The early success of nanocrystalline metal electrodeposits accelerated 1) research efforts in this area by numerous groups around the world, and 2) the development of applications in several sectors, including energy, automotive, aerospace, consumer product and defense industries.11–18 Several review articles on the electrodeposition method have been published over the past decade.19–25

5.2

Electrodeposition methods

The four most important components of a typical electroplating system are 1) an appropriate electrolyte, often referred to as the plating bath, 2) a power supply, usually฀either฀a฀direct฀current฀(DC)฀or฀pulsed฀current฀(PC)฀power฀supply,฀3)฀the฀ cathode onto which the material is electrodeposited and 4) the anode. Figure 5.1 shows that, in addition, a heater and electrolyte stirring are often used, mainly to enhance the diffusion of metal ions and other species in the plating bath.

5.2.1 Electrolyte The electrolyte is an aqueous solution containing several ingredients. The most important is the salt of the metal to be deposited on the cathode. Metal salts include sulfamates, sulfates, chlorides, cyanides, fluoroborates, pyrophosphates and others. These salts provide the initial metal ion concentration in the plating bath.฀ Many฀ baths฀ contain฀ several฀ salts฀ of฀ the฀ same฀ metal.฀ For฀ example,฀ in฀ the฀ so-called Watts nickel plating bath both nickel sulfate and nickel chloride are used, the latter in a much smaller concentration. In addition to providing some Ni2+ ions, the main role of the nickel chloride is to increase the bath conductivity and to aid in the nickel anode dissolution. For alloy deposits that contain two or more metals, salts of each component are added฀ to฀ the฀ bath.฀ For฀ example,฀ to฀ electrodeposit฀ Zn-Ni฀ binary฀ alloys฀ a฀ bath฀

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5.1 Schematic diagrams showing experimental set-up (top) and current versus time curve (bottom) for conventional direct current plating.

containing฀ both฀ zinc฀ chloride฀ and฀ nickel฀ chloride฀ can฀ be฀ used.฀ Other฀ alloying฀ elements include non-metals such as phosphorus or boron, which must also be added฀to฀the฀bath฀in฀the฀right฀concentration.฀An฀example฀is฀Ni-P฀deposited฀from฀a฀ plating bath containing nickel sulfate and phosphorous acid, the latter as the source฀ of฀ phosphorus.฀ Composite฀ deposits฀ can฀ be฀ made฀ by฀ adding฀ a฀ second฀ phase฀in฀the฀form฀of฀ine฀particles,฀whiskers฀or฀ibres฀to฀the฀electroplating฀bath.฀ The฀second฀phase฀is฀then฀codeposited฀with฀the฀metal฀matrix฀to฀form฀the฀composite฀ material.฀Examples฀are฀Ni-SiC,฀Ni-carbon฀nanotubes,฀Cu-Al2O3, etc. Many plating baths contain buffers. Buffers have the property that they maintain the฀plating฀bath฀pH฀by฀neutralizing฀both฀acid฀and฀base฀changes฀in฀the฀solution.฀ Examples฀of฀buffers฀used฀in฀metal฀plating฀are฀boric฀acid฀(H3BO 3) for nickel or zinc–nickel฀plating฀at฀low฀pH฀or฀potassium฀orthophosphate/phosphate฀(KH 2PO 4/ K3PO 4)฀mixtures฀for฀plating฀of฀palladium฀from฀high฀pH฀solutions.1

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Metal ions in an aqueous solution are usually hydrated, i.e. surrounded by several water฀molecules฀(solvation฀sheath),฀usually฀expressed฀as฀shown฀in฀equation฀5.1. [5.1] For฀example,฀for฀Ni2+ the number x is either 4 or 6.1 When water molecules are replaced฀by฀other฀ions฀or฀molecules฀(i.e.฀complexing฀agents)฀the฀metal฀is฀referred฀ to฀ as฀ a฀ metal฀ ion฀ complex.฀ Complex฀ formation฀ can฀ considerably฀ change฀ the฀ properties of the metal ions in the solution and in particular the metal ion deposition,฀ which฀ involves฀ complex฀ dissociation฀ to฀ form฀ free฀ metal฀ ions.฀ Complexing฀agents,฀also฀referred฀to฀as฀ligands,฀are฀particularly฀important฀in฀the฀ co-deposition of alloys where they help to bring the deposition potentials/activities of฀the฀individual฀metals฀closer฀together.฀Complexed฀ions฀are฀usually฀written฀as฀ follows: [5.2] Examples฀are: [5.3] [5.4] Many฀ complexing฀ agents฀ have฀ been฀ used฀ in฀ alloy฀ plating.฀ For฀ example,฀ for฀ Ni-Fe-Cr฀ternary฀alloys฀alone,฀the฀list฀is฀very฀large,฀including฀di-methyl฀formamide฀ (DMF,฀ HCON(CH 3)2), ethylene-diamine-tetra-acetate (EDTA, (HO 2CCH 2)2 NCH 2CH 2N(CH 2CO 2H)2), sodium citrate (Na3C6H5O7 × 2 H2O), urea (NH 2 CONH 2)฀and฀glycolic฀acid฀(HOCH 2CO 2H). Other฀ bath฀ ingredients฀ include฀ addition฀ agents฀ to฀ achieve฀ speciic฀ deposit฀ properties฀in฀terms฀of฀brightening,฀stress฀relief,฀hardening,฀leveling,฀grain฀reining฀ or฀ surface฀ smoothing.฀ One฀ particular฀ example฀ is฀ the฀ use฀ of฀ saccharin฀ (benzoic฀ sulimide฀(C7H5NO 3S)) in nickel electroplating. Saccharin in this plating bath has a฀dual฀purpose.฀It฀is฀a฀grain฀reiner฀and฀stress฀reliever฀at฀the฀same฀time,฀typically฀ added to the plating bath in low concentrations of about a few grams per liter.1

5.2.2 Power supplies in conventional electroplating Most electroplating operations use direct current plating as shown in Fig. 5.1. Direct฀ current฀ is฀ usually฀ supplied฀ from฀ rectiiers,฀ although฀ older฀ rotating฀ DC฀ generators may still be in operation in some industries. In direct current plating, an important plating variable is the current density, I,฀usually฀expressed฀in฀units฀ of mA/cm.2 Electrodeposition often involves more than one single electrochemical reaction at฀each฀the฀anode฀and฀cathode.฀For฀example,฀during฀the฀electrodeposition฀from฀a฀ low pH bath containing Mez+ and H+ ions, the following reactions occur at the cathode:

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The metal deposition process involves various steps including diffusion of ions from the bulk of the electrolyte to the cathode and through the Nernst diffusion layer,฀formation฀of฀the฀irst฀adions฀on฀the฀cathode฀surface,฀surface฀diffusion฀of฀the฀ adions, nucleation of the crystals and growth of the crystals. When charge transfer associated with the metal ion deposition is the slow, rate-determining step, equation 5.7 gives the limit in terms of current density, IL , which is controlled by the transport of Mez+ ions from the bulk of the electrolyte to the cathode:1 [5.7] where D฀is฀the฀diffusion฀coeficient฀of฀the฀deposited฀Mez+ species, F is the Faraday constant, z the number of electrons involved in the metal ion reduction, Cb the concentration of Mez+ ions in the bulk electrolyte and δ the diffusion layer thickness. Direct current electrodeposition at current densities higher than the limiting current density usually produces poor deposits as the process then involves cathodic reactions other than metal ion deposition. The limiting current density is strongly dependent on solution agitation. For example,฀for฀the฀case฀of฀a฀rotating฀electrode฀it฀has฀been฀shown1 that the limiting current density changes with the angular speed of rotation (ω) as follows: [5.8] where ν is the kinematic viscosity of the electrolyte, Cb the concentration of the solution and a is the rotating disk surface area. The weight of the deposit is given by the following equation: [5.9] where I is the applied current density, t is the plating time, A is the atomic weight of the deposited metal, z the number of electrons, and F is the Faraday constant. The฀current฀eficiency฀(CE) of a plating process is a measure of the actual metal deposition (Wmetal) relative to the theoretically possible metal deposition (Wtotal), when no other reactions occur at the cathode. [5.10] In฀most฀cases฀the฀current฀eficiency฀is฀less฀than฀100%,฀indicating฀that฀other฀reactions฀ do indeed occur at the cathode such as the hydrogen evolution reaction given in equation฀5.6.฀For฀example,฀nickel฀plating฀from฀a฀Watts-type฀bath฀has฀a฀high฀current฀

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eficiency฀of฀more฀than฀90%,฀which฀means฀that฀less฀than฀10%฀of฀all฀electrons฀in฀the฀ process฀are฀used฀to฀produce฀hydrogen฀gas.฀On฀the฀other฀hand,฀the฀current฀eficiency฀ for฀chromium฀plating฀is฀much฀lower,฀typically฀of฀the฀order฀of฀10–30%.26

5.2.3 Cathodes and cathodic reactions When฀the฀purpose฀of฀electrodeposition฀is฀to฀create฀a฀permanently฀modiied฀surface,฀ the฀ cathode฀ is฀ usually฀ the฀ inished฀ workpiece.฀ Electroplating฀ is฀ then฀ carried฀ out฀ until the required coating thickness is reached. Subsequently the workpiece is removed from the plating bath, rinsed and dried. Typical plating operations include rack plating, barrel plating, reel-to-reel plating and brush plating. On the other hand, in processes such as electroforming27–29 the cathode is used only as a temporary mandrel or mold to deposit the material in the shape of a speciic฀ inal฀ object.฀ Following฀ the฀ electrodeposition฀ process฀ the฀ electroformed฀ object is separated from the mold by mechanical means. The mold can then be reused฀ to฀ deposit฀ the฀ next฀ piece฀ either฀ in฀ batch฀ processing฀ (Fig.฀ 5.2)฀ or฀ as฀ a฀ continuous process such as in foil plating (Fig. 5.3). Titanium or steel cathodes are frequently used in such processes. The cathodic reactions in terms of overall metal deposition are often given as in equation 5.5. However, it should be noted that the reactions can be much more฀ complex฀ involving฀ several฀ intermediate฀ steps.฀ For฀ example,฀ for฀ the฀ electrodeposition of Ni from a Watts-type bath, the cathodic reaction given in equation 5.11 is usually presented: [5.11] However, it is more likely that deposition involves the following reactions:30,31 [5.12] [5.13]

5.2 Schematic diagram showing net-shape manufacturing of an electroformed product. Source: Courtesy of Nickel Development Institute, Toronto, Canada.

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5.3 Schematic diagram showing continuous electrodeposition of nanocrystalline sheet/foil. Source: Courtesy of Integran Technologies, Inc., Toronto, Canada.

[5.14]

5.2.4 Anodes The anode completes the electric circuit in the plating cell (Fig. 5.1). Two types of anodes฀are฀typically฀used.฀The฀irst฀type฀is฀a฀dissolvable฀anode฀of฀the฀same฀material฀ as the electroplate, which replenishes the bath with metal ions as they are deposited on the cathode. Often the anode material is contained in a mesh basket made of titanium (Fig. 5.1), the latter being inert in many electroplating baths because of the฀protective฀titanium฀oxide฀layer฀on฀the฀surface.฀Anode฀material฀is฀periodically฀ replenished in the anode basket. The second type of anode is referred to as the dimensionally stable anode (DSA). Supplied as sheet or mesh, these anodes are made of platinum coated/clad titanium or niobium with platinum thicknesses typically of the order of 0.1–0.25 mm. These anodes are chemically inert and do not replenish the plating bath with metal ions. Therefore, periodic additions of metal salts to the plating bath are required to maintain the ion concentration within a certain operating range.

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5.2.5 Structure evolution in conventional electrodeposits Under฀conventional฀electroplating฀conditions,฀the฀microstructural฀evolution฀with฀ increasing deposit thickness is as shown in Fig. 5.4. Initially, numerous crystals are nucleated on the cathode, which usually have different crystallographic orientations with respect to the substrate material. With increasing deposit thickness there is a competition฀between฀nucleation฀of฀new฀crystals฀and฀growth฀of฀existing฀crystals.฀ Many operating conditions (e.g. low current density) promote crystal growth where certain crystal orientations grow faster than others. As a result, the initial ine-grained฀structure฀changes฀with฀increasing฀deposit฀thickness฀to฀a฀large-grained,฀ often columnar grain structure as seen in Fig. 5.4 (b) for an iron deposit. The grain size฀in฀the฀initial฀layer฀is฀very฀small฀and฀cannot฀be฀easily฀resolved฀in฀the฀etched฀ cross-section. However, the columnar large grained structure that developed with increasing deposit thickness is clearly visible in Fig. 5.4 (b). It should be noted that the฀ thickness฀ of฀ the฀ initial฀ ine-grained฀ structure฀ is฀ often฀ found฀ to฀ be฀ strongly฀ dependent฀on฀the฀pH฀of฀the฀electrolyte.฀For฀example,฀for฀nickel฀deposited฀from฀a฀ Watts-type bath, the thickness decreased from about 150 µm at a pH of 0.5 to about 20 µm at a pH of 3.0 and completely disappeared at a pH of 3.5.32

5.2.6 Structure evolution in nanocrystalline electrodeposits It has been shown that nanocrystalline metals can be produced by electrodeposition under electrochemical conditions that promote crystal nucleation and suppress crystal growth.6,7,33,34 The conditions leading to massive nucleation of crystals can be achieved by selecting plating parameters that 1) allow for very high

5.4 Schematic diagram (a) and cross-sectional scanning electron micrograph (b) of an iron electrodeposit showing grain size and shape evolution with increasing deposit thickness. Arrows indicate growth direction.

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deposition rates and 2) reduce the diffusion of adatoms over the surface of the growing deposit. The current density applied during plating has two important effects on electrocrystallization.฀It฀increases฀the฀rate฀of฀metal฀ion฀reduction฀on฀the฀surface฀ and฀reduces฀the฀critical฀crystal฀nucleation฀size,฀rc, which is inversely proportional to overpotential, η/current density, I,฀ as฀ shown฀ in฀ the฀ classical฀ Gibbs–Kelvin฀ equation:35 [5.15] where σ is the interfacial tension of the metal/solution interface, M the molecular weight, ρ the density and z · F the molar charge. The effect of over-potential/ current฀density฀on฀the฀critical฀crystal฀size฀is฀shown฀schematically฀in฀Fig.฀5.5฀in฀the฀ form฀of฀free฀energy฀versus฀crystal฀size฀graphs.฀Figure 5.5 clearly shows that higher current฀density฀results฀in฀smaller฀crystal฀sizes. However,฀conventional฀DC฀plating฀is฀limited฀by฀the฀limiting฀current฀density฀ (equation 5.7) above which electrochemical reactions other than metal deposition

5.5 Effect of over-potential/current density on critical crystal nucleation size.

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occur on the cathode. For this reason, pulsed current electrodeposition was introduced,6,7,33 as shown schematically in Fig. 5.6. In this case the current, Ipeak, during the current on time (Ton)฀can฀be฀signiicantly฀ higher฀than฀the฀limiting฀DC฀current฀density.฀However,฀in฀order฀to฀replenish฀the฀ double layer with metal ions by diffusion from the bulk of the electrolyte before other cathode reactions begin to dominate, the current is turned off for a certain period of time, Toff.฀ Usually฀ Toff is longer than Ton. The important electrical parameters during pulse plating include the pulse frequency, f, the duty cycle, θ, and the average current density, Iave: [5.16]

5.6 Schematic diagrams showing experimental set-up (top) and current versus time curve (bottom) for pulsed current plating.

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Nanostructured metals and alloys [5.17] [5.18]

More recent research efforts have concentrated on producing electrodeposited nanomaterials with different structure types. These include structurally graded materials฀in฀which฀the฀grain฀size฀changes฀in฀cross-section,฀materials฀with฀broader฀ or฀ bimodal฀ grain฀ size฀ distribution฀ and฀ nanocomposites฀ consisting฀ of฀ two฀ or฀ several distinct phases36 or nanotwinned electrodeposits.37 Such structures allow for฀interesting฀property฀optimizations,฀such฀as฀high฀strength฀combined฀with฀high฀ ductility or high electrical conductivity.

5.3

Examples of nanocrystalline metals and alloys prepared by electrodeposition

As pointed out in section 5.1, there have been numerous early studies on electrodeposited฀metals฀with฀extremely฀ine฀grain฀size,฀however,฀without฀particular฀ emphasis on identifying in a systematic way those plating parameters that would lead฀to฀nanocrystalline฀materials.฀The฀irst฀alloys฀that฀were฀studied฀with฀emphasis฀on฀ nanocrystalline material formation were Ni-P electrodeposits.4,5 Earlier studies had shown that these alloys could be produced with both conventional polycrystalline and amorphous structures.38 An electrolyte and plating conditions as shown in Table 5.1 were used to study nanocrystal formation.4,5 As฀ can฀ be฀ seen฀ from฀ this฀ table,฀ electrodeposition฀ was฀ carried฀ out฀ using฀ DC฀ plating and the main variable was the concentration of phosphorous acid (H3PO 3) in the plating bath. It was shown that the phosphorus content in the electrodeposit increased with increasing phosphorous acid concentration in the plating bath, likely by the following reactions39 in addition to the reactions for Ni reduction given in equations 5.11 through 5.14: [5.19] Table 5.1 Electrolyte composition and plating conditions used for the synthesis of nanocrystalline Ni-P alloy deposits4,5 Compound

Concentration (g/l)

Plating conditions

Ni2SO 4 × 7H2O NiCl2 × 6H2O

150 45

pH

1.5

H3PO 4 H3PO 3

50 0–40

T (°C) IDC (mA/cm2) Ipeak(mA/cm2) Ton(msec) Toff (msec)

80 100 – – –

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The resulting deposits were supersaturated solid solutions of P in Ni, with P concentrations฀up฀to฀24฀at.%฀for฀the฀highest฀concentration฀of฀phosphorous฀acid฀in฀ the plating bath. It was further shown that the structures of the deposits were crystalline฀for฀low฀P-concentrations฀in฀the฀deposit,฀less฀than฀4฀at.%.฀On฀the฀other฀ hand,฀ deposits฀ containing฀ more฀ than฀ ~฀ 15฀ at.%฀ P฀ were฀ amorphous.฀ For฀ the฀ intermediate฀ concentration฀ range,฀ rapid฀ grain฀ size฀ reduction฀ was฀ observed฀ and฀ nanocrystalline฀deposits฀with฀grain฀sizes฀down฀to฀less฀than฀3฀nm฀and฀towards฀the฀ amorphous limit were observed with increasing phosphorus content. Figure 5.7 shows฀ brightield฀ and฀ darkield฀ transmission฀ electron฀ micrographs฀ of฀ a฀ Ni-5.2฀ at.%฀P฀deposit฀with฀an฀average฀grain฀size฀of฀6.1฀nm. Since the early 1990s numerous other nanomaterials have been produced by electrodeposition,฀ many฀ of฀ which฀ are฀ summarized฀ in฀ Table฀ 5.2.฀ These฀ include฀ pure฀metals฀such฀as฀Ni,฀Co,฀Pd,฀Cu฀and฀Zn,฀binary฀and฀ternary฀alloys฀including฀ Ni-Zn,฀Co-W,฀Co-Fe,฀Ni-F-Cr฀and฀Ni-Zn-P,฀and฀composite฀materials,฀for฀example฀ Ni-Al2O3,฀ Ni-SiC,฀ Ni-P-BN฀ or฀ Ni-carbon฀ nanotubes.฀ It฀ should฀ be฀ noted฀ that฀ many bath formulations and electroplating parameters have been developed for different฀materials฀by฀various฀research฀groups.฀In฀the฀following฀examples฀details฀ will฀be฀given฀for฀several฀speciic฀materials฀produced฀in฀our฀laboratories฀over฀the฀ past 20 years. Table฀ 5.3฀ summarizes฀ the฀ important฀ electrochemical฀ conditions฀ used฀ in฀ the฀ synthesis of nanocrystalline nickel produced from a Watts-type electrolyte.33 Note that these materials were produced by pulsed current deposition using a peak current density of 1900 mA/cm2, which is about 4–5 times higher than the limiting DC฀ current฀ density฀ for฀ nickel฀ plating.฀ In฀ addition,฀ the฀ plating฀ baths฀ contained฀

5.7 Brightfield (a) and darkfield (b) transmission electron micrographs of a Ni – 5.2 at.% P electrodeposit with an average grain size of 6.1 nm in planar section.

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Nanostructured metals and alloys Table 5.2 Examples of nanocrystalline metals, alloys and metal matrix composites that have been produced by electrodeposition Material

References

Material

References

Ni Co Pd Cu Zn Ni-P Ni-Fe Ni-Zn Co-W Co-Fe Pd-Fe

[6, 33] [6, 40] [41] [40, 42] [43] [4, 5] [44, 45] [46, 47] [48] [49] [50]

Ni-Fe-Cr Ni-Zn-P Co-Fe-P Ni-SiC Ni-Al2O3 Cu-Al2O3 Ni-P-BN Ni-MoS2 Ni-Al (particles) Ni-Nanocarbon tubes

[51–53] [54] [55] [56, 57] [58, 59] [60] [18] [18] [61] [62]

Table 5.3 Electrolyte composition and plating conditions used for the synthesis of nanocrystalline Ni deposits33 Compound

Concentration (g/l)

Plating conditions

Ni2SO 4 × 7H2O NiCl2 × 6H2O H3BO 3 C7H5NO 3S

300 45 45 0–10

pH T (°C) IDC (mA/cm2) Ipeak(mA/cm2) Ton(msec) Toff (msec)

2.5 65 – 1900 2.5 45.0

saccharin฀ (C7H5NO 3S)฀ in฀ various฀ concentrations฀ (0–10฀ g/l)฀ as฀ a฀ grain฀ reiner.฀ Figure 5.8 presents scanning electron microscope (SEM) micrographs showing the surface morphology of deposits without and with saccharin additions. These micrographs clearly show that in the absence of saccharin (Fig. 5.8 (a) ) large crystals฀with฀sizes฀in฀the฀micrometer฀range฀are฀obtained.฀These฀deposits฀exhibited฀ a relatively large surface roughness and dull appearance. With increasing saccharin concentration the surface morphology changed to a more colony-type structure in which individual grains cannot be resolved in the SEM (Fig. 5.8 (b) ). Transmission electron฀ microscopy฀ was฀ used฀ to฀ determine฀ the฀ grain฀ size฀ of฀ the฀ deposit฀ as฀ a฀ function฀of฀saccharin฀concentration฀in฀the฀bath;฀the฀results฀are฀given฀in฀Table฀5.4.฀ A฀small฀addition฀(0.5฀g/l)฀of฀saccharin฀is฀suficient฀to฀reduce฀the฀crystal฀size฀from฀ >1µm to about 40 nm. Further increases in saccharin additions to 5 g/l reduced the grain฀size฀further฀to฀about฀10฀nm.฀Even฀higher฀saccharin฀concentrations฀(10฀g/l)฀ had฀no฀major฀additional฀effect฀on฀grain฀size. Figure฀5.9฀shows฀a฀schematic฀diagram฀and฀a฀brightield฀transmission฀electron฀ micrograph of a nanocrystalline nickel electrodeposit in cross-section through the

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5.8 Scanning electron micrographs showing surface structure of electrodeposited polycrystalline nickel without saccharin (a) and nanocrystalline nickel with a saccharin addition of 5.0 g/l in the plating bath (b). Table 5.4 Effect of saccharin concentration on grain size and sulfur content of nanocrystalline nickel electrodeposits produced from a Wattstype plating bath33 Saccharin concentration (g/l)

Grain size (nm)

Sulfur concentration (ppm)

0 0.5 2.5 5.0 10.0

>1000 40 20 10 9

5%)฀ductility฀to฀sustain฀tensile฀deformation฀to฀

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a discernable peak load, equation [5.28] can be used to estimate tensile strength from hardness measurements. For more brittle materials with tensile elongations less฀ than฀ 5%,฀ the฀ relationship฀ given฀ in฀ equation฀ [5.28]฀ was฀ also฀ found฀ to฀ be฀ invalid. Both abrasive and adhesive wear studies have shown that the wear resistance of nanocrystalline฀nickel฀increases฀with฀decreasing฀grain฀size.65,71 Table 5.8 shows the฀effect฀of฀grain฀size฀on฀the฀abrasive฀wear฀resistance฀(Taber฀wear฀index).฀This฀ behavior is in agreement with Archard’s law, which states that the wear resistance is inversely proportional to the hardness of the material, which in turn initially increases฀ with฀ decreasing฀ grain฀ sizes.฀ It฀ is฀ interesting฀ to฀ note฀ that฀ according฀ to฀ Archard’s law the wear resistance should decrease in nanomaterials that show the negative Hall–Petch behavior. This was indeed observed for both Ni-P111 and Ni-W73 electrodeposits.

5.4.3 Ultimate tensile strength and tensile ductility Because฀of฀the฀initial฀material฀size฀and฀shape฀limitations฀and฀the฀impurity฀problems฀ mentioned earlier in this section, it is currently impossible to predict the intrinsic ultimate tensile strengths and ductilities that could potentially be achieved by grain฀ size฀ control฀ in฀ nanocrystalline฀ electrodeposits.฀ Early฀ results฀ were฀ very฀ disappointing฀in฀terms฀of฀ductility.฀For฀example,฀the฀ductility฀of฀Ni฀was฀observed฀ to฀decrease฀from฀over฀50%฀at฀a฀grain฀size฀of฀100฀µm฀to฀about฀1%฀at฀a฀grain฀size฀ of ~10 nm.16 Many other studies also found very low ductilities and many electrodeposits failed in a completely brittle fashion without onset of necking instability. Over the past several years considerable progress has been made in producing nanocrystalline electrodeposits which much improved ductility and very high ultimate tensile strength in cobalt,120,121 nickel-based alloys89 and copper.37,118 For฀ example,฀ for฀ cobalt฀ and฀ some฀ nickel–iron฀ nanodeposits฀ ultimate฀ tensile฀ strength฀values฀in฀excess฀of฀2000฀MPa฀and฀ductilities฀in฀the฀5–15%฀range฀can฀now฀ be achieved. There are several contributing factors for the higher ductility/ultimate tensile strength values observed in more recent studies. First, improved synthesis methods have been developed with much better control of impurities and other deposition defects฀such฀as฀hydrogen฀pits฀or฀co-deposited฀hydroxides.89 Second, thicker and larger samples are now available for testing following standard testing procedures. Early testing was often done on very thin specimens very close to plane stress conditions, which usually yield lower ductility values. Third, the development of nanotwinned electrodeposits has shown that the high density of twin boundaries can produce a unique combination of high strength and high ductility.37,118 Fourth,฀ there฀ is฀ now฀ considerable฀ evidence฀ that฀ wide/bimodal฀ grain฀ size฀ distributions,87 and co-deposited second phase particles can enhance ultimate tensile strength and ductility of nanomaterials57 and even produce superplastic

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behavior in some cases131,132฀when฀the฀nickel฀matrix฀grain฀size฀was฀in฀the฀range฀ of 50–200 nm. Superplasticity was also observed in electrodeposited nickel containing sulfur impurities, deformed at temperatures between 350 and 400°C.68,84฀However,฀the฀interpretation฀of฀these฀results฀is฀dificult฀because฀of฀1)฀ the substantial grain growth before and during high-temperature deformation that produced฀ grain฀ sizes฀ in฀ the฀ micrometer฀ range,฀ and฀ 2)฀ the฀ formation฀ of฀ sulfurenriched grain boundaries that may have resulted in a liquid grain boundary phase.

5.5

Corrosion properties of nanocrystalline electrodeposits

The corrosion properties of electrodeposited nanomaterials have been reported in many studies dealing with Ni and Ni-based alloys,135–153฀nanocrystalline฀Co,154–157 Zn and Zn-Ni alloys158,159฀and฀nanocrystalline฀Cu.160–162 A detailed analysis of the indings฀reported฀in฀the฀various฀investigations฀is฀beyond฀the฀scope฀of฀this฀review.฀ However, the main results of these studies have shown the following. First, contrary to earlier concerns, the high grain boundary and triple junction densities found on the surfaces of electrodeposited nanomaterials do not compromise their corrosion performance.฀ The฀ general฀ shapes฀ of฀ the฀ potentiodynamic฀ polarization฀ curves฀ for various materials in acidic, basic or neutral chloride solutions were not signiicantly฀affected฀by฀grain฀size฀in฀most฀cases.฀Materials฀that฀show฀passivity฀in฀ the polycrystalline form also showed passivity in the nanocrystalline form. Some materials showed slightly higher or lower current densities in some regions of the active,฀passive฀and฀trans-passive฀portions฀in฀the฀polarization฀curves,฀but฀overall฀the฀ nanomaterials and their polycrystalline counterparts showed very similar behavior. Some materials also displayed a shift in open circuit potential indicating that the nanostructure฀catalyzes฀the฀hydrogen฀evolution฀reaction฀on฀some฀materials. Second, for materials that do show passivity, the structure and chemical composition฀of฀the฀passive฀layers฀were฀found฀to฀depend฀on฀grain฀size.฀This฀is฀due฀ to the high density of defects (grain boundaries and triple junctions) that intersect the free surface of the nanomaterials. The defect structure that forms in the passive layer is strongly influenced by the substrate defects. It was also found that impurity atoms in the nanomaterials could have a substantial effect on the nature of the passive฀ ilm.฀ However,฀ even฀ with฀ a฀ defective฀ structure,฀ the฀ passive฀ ilms฀ on฀ nanomaterials฀ still฀ provide฀ considerable฀ protection฀ for฀ the฀ material฀ exposed฀ to฀ various electrochemical conditions. Third, materials that are susceptible to preferential attack along grain boundaries can฀beneit฀enormously฀by฀grain฀size฀reduction.฀This฀is฀clearly฀seen฀in฀Fig.฀5.14฀ which shows cross-sectional micrographs of polycrystalline and nanocrystalline (grain฀size฀20–30฀nm)฀nickel฀both฀containing฀about฀1000฀ppm฀by฀weight฀of฀sulfur฀ after฀potentiodynamic฀polarization฀in฀a฀0.25M฀Na2SO 4 solution at a pH of 6.5.145 The฀polycrystalline฀material฀shows฀excessive฀attack฀along฀the฀grain฀boundaries฀with฀ considerable weakening of the structure deep inside the material. On the other hand,

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5.14 Scanning electron micrographs of cross-sectional corrosion morphologies in polycrystalline (top) and nanocrystalline (bottom) nickel containing 1000 ppm sulfur. Note that σ represents either internal or externally applied stresses.

corrosion฀attack฀on฀the฀nanocrystalline฀nickel฀shows฀numerous,฀but฀only฀supericial,฀ surface pits with no deep penetration into the bulk of the material. In other words, for nanocrystalline nickel, the corrosion attack is more or less spread out over the entire surface rather than being concentrated along the grain boundaries as seen for polycrystalline nickel. This has a tremendous effect on the performance of the materials in service. Many components in application have either internal stresses or฀are฀subjected฀to฀external฀stresses,฀both฀schematically฀indicated฀by฀the฀σ arrows in Fig.฀5.14.฀For฀the฀polycrystalline฀material,฀extensive฀grain฀boundary฀corrosion฀has฀ not only reduced the effective cross-sectional load-bearing capacity, the deep corrosion฀grooves฀at฀the฀grain฀boundaries฀also฀can฀act฀as฀stress฀concentrations;฀both฀ factors contributing to conditions that can lead to unpredictable and catastrophic failures. On the other hand, the more or less uniform corrosion of the nanocrystalline material results in predictable overall thickness reduction. Therefore a component’s lifetime can be easily estimated as long as the average corrosion rate of the nanomaterial฀is฀known,฀for฀example,฀from฀polarization฀or฀immersion฀tests.

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The effect of sulfur impurities on the corrosion behavior of nanocrystalline and polycrystalline฀nickel฀was฀discussed฀by฀Kim฀et al.145 One of the critical points to consider is the distribution of sulfur throughout the material. For constant overall sulfur content, the sulfur concentration per unit grain boundary area is much smaller฀in฀nanocrystalline฀nickel฀compared฀to฀polycrystalline฀nickel.฀For฀example,฀ if it is assumed that all impurities segregate to grain boundaries, it can be shown that฀the฀maximum฀grain฀boundary฀sulfur฀concentration฀decreases฀by฀three฀orders฀ of฀magnitude฀when฀the฀grain฀size฀is฀reduced฀from฀10฀µm฀to฀10฀nm.฀In฀other฀words,฀ at฀constant฀bulk฀sulfur฀concentration,฀nanocrystalline฀nickel฀is฀expected฀to฀have฀ cleaner boundaries than polycrystalline nickel.

5.6

Other properties of nanocrystalline electrodeposits

The physical properties of conventional metals and alloys are either structuresensitive or structure-insensitive.163 Structure-sensitive properties include tensile strength, hardness, electrical resistivity and thermal conductivity at low temperatures, coercivity, magnetostrictiction and magnetic permeability. On the other hand, density,฀ elastic฀ moduli,฀ thermal฀ expansion,฀ speciic฀ heat,฀ heat฀ of฀ fusion฀ and฀ saturation฀magnetization฀belong฀to฀the฀group฀of฀properties฀that฀are฀relatively฀structureinsensitive. Sensitivity and insensitivity are with respect to structural changes, for example฀by฀grain฀size฀reduction,฀increases฀in฀dislocation฀density฀or฀low฀concentrations฀ of solute additions. In section 5.4 on the mechanical properties of nanocrystalline electrodeposits, it has already been shown that tensile strength and hardness are strongly dependent on฀ grain฀ size,฀ while฀ the฀Young’s฀ modulus฀ is฀ relatively฀ grain฀ size฀ independent.฀ Table฀5.9฀shows฀how฀grain฀size฀and฀intercrystalline฀volume฀fraction฀affect฀room฀ temperature electrical resistivity, ρ,฀ saturation฀ magnetization,฀ MS, and thermal expansion,฀α,฀of฀nickel฀over฀a฀grain฀size฀range฀from฀10฀µm฀to฀10฀nm.฀The฀values฀ given฀in฀Table฀5.9฀were฀again฀taken฀from฀grain฀size–property฀graphs฀presented฀ earlier.16 Table 5.9 Electrical resistivity (ρ), saturation magnetization (MS), and thermal expansion coefficient (α) for nickel as a function of grain size and intercrystalline volume fraction Grain size (nm)

Vic (%)

ρ (µΩ cm)

MS (kA/m)

α (x 10–6/K)

10 000 1 000 100 50 20 10

0.03 0.29 2.97 5.88 14.26 27.10

8.5 8.5 8.8 9.0 13.0 20.0

502 500 500 495 489 488

11.2 11.1 11.0 10.8 10.7 10.6

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Table 5.9 shows that the room temperature electrical resistivity is strongly dependend฀on฀grain฀size,฀in฀particular฀for฀grain฀sizes฀less฀than฀100฀nm฀for฀which฀ the฀intercrystalline฀volume฀fractions฀rapidly฀increase.฀This฀is฀as฀expected฀because฀ grain boundaries and triple junctions are very effective electron scattering centers. The฀grain฀size฀dependence฀for฀the฀room฀temperature฀electrical฀resistivity฀of฀nickel฀ was given by the following equation:164 [5.29] where d฀is฀the฀grain฀size.฀In฀this฀equation฀the฀factor฀2.37฀comes฀from฀the฀grain฀shape฀ of the 14-sided tetrakaidecahedron, 2.82 × 10–6 µΩ cm2฀is฀the฀speciic฀grain฀boundary฀ resistivity term and 8.33 µΩ cm is the resistivity due to electron scattering on phonons and other defects in the material including vacancies, dislocations and impurities. On฀the฀other฀hand,฀Table฀5.9฀shows฀that฀saturation฀magnetization,฀MS, changes very฀little฀with฀grain฀size฀in฀nickel.165 This is consistent with results obtained in linear฀mufin-tin฀orbital฀atomic฀sphere฀approximation฀calculations฀that฀evaluated฀ the effect of structural disorder introduced by grain boundaries on the local magnetic moments in nickel.166,167 These studies have shown that the magnetic moments in different types of grain boundaries (e.g. several coincidence site lattice boundaries and a completely amorphous boundary) are not strongly affected฀by฀the฀structure฀of฀boundary฀defects.฀Similarly,฀grain฀size฀had฀very฀little฀ effect฀on฀the฀saturation฀magnetization฀in฀nanocrystalline฀Co,฀Co-Fe,฀Co-W,฀Ni-Fe฀ and Ni-P electrodeposits.168–170 In alloy deposits it is only the composition that controls฀the฀saturation฀magnetization. Table฀ 5.9฀ further฀ shows฀ that฀ grain฀ size฀ and฀ intercrystalline฀ volume฀ fraction฀ have฀no฀signiicant฀effect฀on฀the฀thermal฀expansion฀of฀electrodeposited฀nickel.171 Again this is consistent with results from a molecular-dynamics simulation study,172 which showed that grain boundaries have only a small effect on the thermal฀expansion฀of฀a฀material. Other structure-insensitive properties in nanocrystalline nickel include density173฀ and฀ speciic฀ heat,171 two properties that show structure-insensitivity also for conventional materials. From฀the฀property฀examples฀shown฀in฀Tables฀5.8฀and฀5.9฀it฀is฀interesting฀to฀note฀ that structure-sensitivity and structure-insensitivity observed in conventional materials฀are฀largely฀maintained฀when฀the฀grain฀size฀is฀reduced฀to฀the฀nanometer฀ range in electrodeposited materials in which the main structural defects are the high volume fractions of grain boundaries and triple junctions. This is in contrast to nanomaterials produced by other synthesis methods such as inert gas condensation,฀ball฀milling฀or฀crystallization฀of฀amorphous฀precursors฀that฀often฀ contain other defects such as porosity or residual amorphous phase. In these materials considerable changes have been observed for several structureinsensitive฀properties฀such฀as฀thermal฀expansion,฀speciic฀heat,฀Young’s฀modulus฀

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and฀saturation฀magnetization.฀These฀differences฀have฀been฀discussed฀elsewhere฀in฀ more detail.22,174,175

5.7

Applications

Electrodeposition is a relatively low-cost production route to make nanocrystalline metals, alloys and composite materials. It is a low-temperature, single-step process and produces fully dense nanostructures, free of porosity often found in materials made from nanocrystalline powder precursors. The electrodeposition method฀for฀nanomaterials฀is฀a฀drop-in฀technology฀that฀can฀make฀use฀of฀existing฀ electroplating and electroforming infrastructure and electrolyte ingredients such as metal salts and bath additions. Switching from conventional electroplating to nanoplating฀requires฀only฀modest฀capital฀investment,฀for฀example฀for฀a฀change฀ over฀from฀DC฀plating฀to฀pulse฀plating. From฀an฀engineering฀point฀of฀view,฀electrodeposition฀is฀an฀extremely฀versatile฀ and฀ lexible฀ technology.฀ First,฀ there฀ are฀ many฀ different฀ metals,฀ alloys฀ and฀ composites฀that฀can฀be฀readily฀deposited฀in฀nanocrystalline฀form฀to฀meet฀speciic฀ application needs. Second, these materials can be deposited in a variety of different product shapes and forms including thin and thick coatings, free-standing sheet, foil, tubes, wires, plates, molds and even powders for some applications. Table 5.10

Table 5.10 Various shapes and applications of nanocrystalline products made by electrodeposition and electroforming Shapes

Applications

Thin coatings

Surface modification for wear and corrosion resistance; catalytic surfaces ElectrosleeveTM ; repair of worn components Gaskets; pressure control membranes; hydrogen purification membranes; thermal barriers; solar energy absorbers; microfoils; soft magnets Surgical tools; missile guidance systems; miniature gamma radiation sources Filters; precision sieve screens; razor foils; printing screens; centrifuge screens Structural applications Filters; electromagnetic shielding; battery electrodes; catalyst carriers Embossing tools for holograms; compression, injection and pattern molds Precision bellows; erosion shields for helicopters; trust chambers for rocket engines; components for micromagnetic motors, micro-optics, microactuators and microfiltration; shaped charge liners; precision reflectors and mirrors; nozzles Catalysts; reinforcements

Thick coatings Sheet, foil

Tubes, wire Mesh Plate Foam Molds Free forms

Powder

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summarizes฀typical฀applications฀for฀the฀various฀product฀shapes฀of฀nanocrystalline฀ electrodeposits. Many of these applications have been previously discussed in more detail.11–13,15,18,20,22,55฀ Chapter฀ 22฀ will฀ discuss฀ several฀ of฀ these฀ applications฀ with฀ emphasis on some of the more recently developed nanometal-enabled hybrid materials.

5.8

Acknowledgements

Financial฀support฀from฀the฀Natural฀Sciences฀and฀Engineering฀Research฀Council฀ of฀ Canada฀ (NSERC)฀ and฀ the฀ Ontario฀ Research฀ Fund฀ (ORF)฀ is฀ gratefully฀ acknowledged.

5.9

References

฀ 1฀ Schlesinger฀M.,฀Paunovic฀M.฀Modern฀Electroplating,฀4th฀ed.฀New฀York:฀John฀Wiley฀&฀ Sons;฀2000. 2 Safranek W.H. The Properties of Electrodeposited Metals and Alloys, 2nd ed. Orlando: American฀Electroplaters฀and฀Surface฀Finishers฀Society฀(AESF);฀1986. ฀ 3฀ Dini฀J.W.,฀Electrodeposition.฀Park฀Ridge:฀Noyes฀Publ;฀1993. ฀ 4฀ McMahon฀G.,฀Erb฀U.฀Microstr฀Sci฀1989;17:฀447–457. ฀ 5฀ McMahon฀G.,฀Erb฀U.฀J฀Mater฀Sci฀Lett฀1989;8:฀865–868. ฀ 6฀ Erb฀U.,฀El-Sherik฀A.M.฀US฀patent฀no.฀5,352,266;฀1994. ฀ 7฀ Erb฀U.,฀El-Sherik฀A.M.,฀Cheung฀C.,฀Aus฀M.J.฀US฀patent฀no.฀5,433,797;฀1995. ฀ 8฀ Palumbo฀ G.,฀ Lichtenberger฀ P.C.,฀ Gonzalez฀ F.,฀ Brennenstuhl฀ A.M.฀ US฀ patent฀ no.฀ 5,527,445;฀1996. ฀ 9฀ Palumbo฀ G.,฀ Lichtenberger฀ P.C.,฀ Gonzalez฀ F.,฀ Brennenstuhl฀ AM.฀ US฀ patent฀ no.฀ 5,538,615;฀1996. 10฀ Palumbo฀G.,฀Gonzalez฀F.,฀Brennenstuhl฀A.M.,฀Erb฀U.,฀Shmayda฀W.,฀Lichtenberger฀PC.฀ Nanostr฀Mater฀1997;฀9:฀737–746. 11฀ Rofagha฀ R,฀ Wood฀ D,฀ Erb฀ U.฀ In:฀ AESF฀ SUR/FIN฀ Technical฀ Proc.฀ Orlando฀ (FL):฀ American฀Electroplaters฀and฀Surface฀Finishers;฀1995;฀p.฀197. 12฀ Cheung฀ C.,฀ Wood฀ D.,฀ Erb฀ U.฀ In:฀ Suryanarayana฀ C.฀ et al., editors. Processing and Properties฀of฀Nanocrystalline฀Materials.฀Warrendale฀(PA):฀TMS;฀1996;฀p.฀479. 13฀ Clark฀D.,฀Wood฀D.,฀Erb฀U.฀Nanostr฀Mater฀1997;9:฀755–758. 14฀ Robertson฀A.,฀Erb฀U.,฀Palumbo฀G.฀Nanostr฀Mater฀1999;12:฀1035–1039. 15฀ Erb฀U.,฀Palumbo฀G.,฀Aust฀K.T.฀In:฀Chow฀G.M.฀et al., editors. Nanostructured Films and Coatings,฀ NATO฀ Science฀ Series,฀ 3-High฀ Technology฀ –฀ Vol.฀ 78.฀ Dordrecht,฀ The฀ Netherlands:฀Kluwer฀Academic฀Publishers;฀2000;฀p.฀11. 16฀ Erb฀ U.,฀Aust฀ K.T.,฀ McCrea฀ J.L.,฀ Palumbo฀ G.,฀ Gonzalez฀ F.฀ In:฀ Srivatsan฀ T.S.฀ et al., editors. Processing and Fabrication of Advanced Materials IX. Materials Park (OH): ASM฀International;฀2001;฀p.฀253. 17฀ Palumbo฀ G.,฀ Gonzalez฀ F.,฀ Tomantschger฀ K.,฀ Erb฀ U.,฀ Aust฀ K.T.฀ Plat฀ &฀ Surf฀ Fin฀ 2003;90(2):฀36–45. 18฀ Palumbo฀G.,฀McCrea฀J.L.,฀Erb฀U.฀In:฀Nalwa฀H.S.,฀editor.฀Encyclopedia฀of฀Nanoscience฀ and฀Nanotechnology.฀Stevenson฀Ranch:฀American฀Scientiic฀Publishers;฀2004;฀p.฀89. 19฀ Erb฀U.,฀Palumbo฀G.,฀Zugic฀R.,฀Aust฀K.T.฀In:฀Suryanarayana฀C.฀et al., editor. Processing and฀Properties฀of฀Nanocrystalline฀Materials.฀Warrendale฀(PA):฀TMS;฀1996;฀p.฀93.

© Woodhead Publishing Limited, 2011

The processing of bulk nanocrystalline metals and alloys

147

20฀ Erb฀ U.,฀ Aust฀ K.T.,฀ Palumbo฀ G.฀ In:฀ Koch฀ C.C.,฀ editor.฀ Nanostructured฀ Materials.฀ Norwich฀(NY):฀Noyes฀Publications/William฀Andrew฀Publishing;฀2002;฀p.฀179. 21฀ Erb฀ U.,฀ Baghbanan฀ M.R.,฀ Cheung฀ C.,฀ Palumbo฀ G.฀ In:฀ Srivatsan฀T.S.฀ et al., editors. Processing and Fabrication of Advanced Materials XII. Materials Park (OH): ASM International;฀2004;฀p.฀301. 22฀ Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.฀In:฀Koch฀C.C.,฀editor.฀Nanostructured฀Materials,฀2nd฀ed.฀ Norwich:฀William฀Andrew;฀2007;฀p.฀235. 23฀ Natter฀H.,฀Hempelmann฀R.฀Z฀Phys฀Chem฀2008;222:฀319–354. 24฀ Gurrappa฀I.,฀Binder฀L.฀Sci฀Technol฀Adv฀Mater฀2008;9:฀1–11. 25฀ Bicelli฀L.P.,฀Bozzini฀B.,฀Mele฀C.,฀D’Urzo฀L.฀Int฀J฀Electrochem฀Sci฀2008;3:฀356–408. 26 Tucker R.E. Metal Finishing – Guidebook and Directory, 75th ed. New York: Metal Finishing;฀2007;฀p.฀184. 27 Watson S.A. Applications of electroforming, NDI Technical Series, No. 10054. Toronto,฀ON:฀Nickel฀Development฀Institute;฀1989. 28 Parkinson R. Electroforming – A unique metal fabrication process, NDI Technical Series,฀No.฀10085.฀Toronto,฀ON:฀Nickel฀Development฀Institute;฀1998. 29 Parkinson R. Nickel plating and electroforming, NDI Technical Series No. 10088. Toronto,฀ON:฀Nickel฀Development฀Institute;฀2001. 30฀ Matulis฀J.,฀Slizys฀R.฀Electrochim฀Acta฀1964;9:฀1177–1188. 31฀ Piatti฀R.C.V.,฀Arvia฀A.J.,฀Podesta฀J.J.฀Electrochim฀Acta฀1969;14:฀541–548. 32฀ Gill฀K.S.,฀Davis฀B.,฀Cooper฀W.C.,฀Erb฀U.฀Plat฀Surf฀Fin฀1993;77(10):฀68–72. 33฀ El-Sherik฀A.M.,฀Erb฀U.฀J฀Mater฀Sci฀1995;30:฀5743–5749. 34฀ Choo฀R.T.C.,฀El-Sherik฀A.M.,฀Toguri฀J.,฀Erb฀U.฀J฀Appl฀Electrochem฀1995;25:฀384–403. 35฀ Gunawardena฀G.,฀Hills฀G.,฀Montenegro฀I.,฀Scharifker฀B.฀J฀Electroanal฀Chem฀1982;138:฀ 255–271. 36฀ Erb฀U.฀J฀Appl฀Surf฀Fin฀2006;1:฀16–22. 37฀ Lu฀L.,฀Shen฀Y.,฀Chen฀X.,฀Quian฀L.,฀Lu฀K.฀Science฀2004;304:฀422–426. 38฀ Brenner฀A.฀Electrodeposition฀of฀Alloys.฀New฀York,฀NY:฀Academic฀Press;฀1963. 39฀ Ratzger฀M.,฀Lashmore฀D.S.,฀Pratt฀K.W.฀Plat฀Surf฀Fin฀1986;79(9):฀74–82. 40฀ Bakonyi฀I.,฀Toth-Kadar฀E.,฀Toth฀J.,฀Tarnoczi฀T.,฀Cziraki฀A.฀In:฀Suryanarayana฀C.฀et al., editors. Processing and Properties of Nanostructured Materials. Warrendale (PA): TMS;฀1996;฀p.฀465. 41 Würschum R., Gruss S., Gissibl B., Natter H., Hempelmann R., Schaefer H.E. Nanostr Mater฀1997;9:฀615–618. 42฀ Natter฀H.,฀Hempelmann฀R.฀J฀Phys฀Chem฀1996;100:฀19,525–19,532. 43฀ Saber฀K.,฀Koch฀C.C.,฀Fedkiw฀P.S.฀Mater฀Sci฀Eng฀2003;A341:฀174–181. 44฀ Grimmett฀D.L.,฀Schwartz฀M.,฀Nobe฀K.฀J฀Electrochem฀Soc฀1993;140:฀973–978. 45฀ Cheung฀C.,฀Djuanda฀F.,฀Erb฀U.,฀Palumbo฀G.฀Nanostr฀Mater฀1995;5:฀513–523. 46฀ Alfantazi฀A.M.,฀El-Sherik฀A.M.,฀Erb฀U.฀Scripta฀Metall฀Mater฀1994;30:฀1245–1250. 47฀ Alfantazi฀A.M.,฀Erb฀U.฀J฀Mater฀Sci฀Lett฀1996;15:฀1361–1363. 48฀ Osmola฀D.,฀Renaud฀E.,฀Erb฀U.,฀Wong฀L.,฀Palumbo฀G.,฀Aust฀K.T.฀Mater฀Res฀Soc฀Symp฀ Proc฀1993;286:฀191–196. 49฀ Cheung฀C.฀PhD฀thesis,฀Queen’s฀University,฀Kingston,฀ON,฀Canada;฀2001. 50฀ Bryden฀K.J.,฀Ying฀J.Y.฀Nanostr฀Mater฀1997;9:฀485–488. 51฀ Cheung฀C.,฀Erb฀U.,฀Palumbo฀G.฀Mater฀Sci฀Eng฀1994;A185:฀39–43. 52฀ Cheung฀C.,฀Nolan฀P.,฀Erb฀U.฀Mater฀Lett฀1994;20:฀135–138. 53฀ Cheung฀C.,฀Palumbo฀G.,฀Erb฀U.฀Scripta฀Metall฀Mater฀1994;31:฀735–740. 54฀ Ganesan฀ P.,฀ Kumaraguru฀ S.P.,฀ Popov฀ B.N.฀ In:฀ AESF฀ SUR/FIN฀ Technical฀ Proc.฀ Orlando฀(FL);฀American฀Electroplaters฀and฀Surface฀Finishers;฀2004;฀p.฀1064.

© Woodhead Publishing Limited, 2011

148

Nanostructured metals and alloys

55฀ Palumbo฀G.,฀Erb฀U.,฀McCrea฀J.L.,฀Hibbard฀D.G.,฀Brooks฀I.,฀Gonzalez฀F.,฀Panagiotopoulos฀ K.฀In:฀AESF฀SUR/FIN฀Technical฀Proc.฀Orlando฀(FL);฀American฀Electroplaters฀and฀ Surface฀Finishers;฀2002;฀p.฀204. 56฀ Zimmerman฀A.F.,฀Clark฀D.G.,฀Aust฀K.T.,฀Erb฀U.฀Mater฀Lett฀2002;52:฀85–90. 57฀ Zimmerman฀A.F.,฀Palumbo฀G.,฀Aust฀K.T.,฀Erb฀U.฀Mater฀Sci฀Eng฀2002;A328:฀137–146. 58฀ Erb฀U.,฀El-Sherik฀A.M.,฀Palumbo฀G.,฀Aust฀K.T.฀Nanostr฀Mater฀1993;2:฀383–390. 59฀ Qu฀N.S.,฀Chan฀K.C.,฀Zhu฀D.฀Scripta฀Mater฀2004.50:฀1131–1134. 60฀ Talbot฀J.B.฀In:฀AESF฀SUR/FIN฀Technical฀Proc.฀Orlando฀(FL):฀American฀Electroplaters฀ and฀Surface฀Finishers;฀2003;฀p.฀701. 61฀ Zhou฀Y.,฀Peng฀X.,฀Wang฀F.฀Scripta฀Mater฀2004;50:฀1429–1433. 62฀ Chen฀X.H.,฀Cheng฀F.Q.,฀Li฀S.L.,฀Zhou฀L.P.,฀Li฀D.Y.฀Surf฀Coat฀Tech฀2002;155:฀274–278. 63฀ Hughes฀G.D.,฀Smith฀S.D.,฀Pande฀C.S.,฀Johnson฀H.R.,฀Armstrong฀R.W.฀Scripta฀Metall฀ 1986;20:฀93–98. 64฀ El-Sherik฀ A.M.,฀ Erb฀ U.,฀ Palumbo฀ G.,฀ Aust฀ K.T.฀ Scripta฀ Metall฀ Mater฀ 1992;27:฀ 1185–1188. 65฀ El-Sherik฀A.M.,฀Erb฀U.฀In:฀Smith฀F.N.฀et al.,฀editors.฀Nickel–Cobalt฀97,฀Applications฀ and฀ Materials฀ Performance,฀ Vol.฀ V.฀ Montreal฀ (PQ):฀ Metallurgical฀ Society฀ of฀ CIM;฀ 1997;฀p.฀257. 66฀ Wang฀N.,฀Wang฀Z.,฀Aust฀K.T.,฀Erb฀U.฀Mater฀Sci฀Eng฀1997;A237:฀150–158. 67฀ Ebrahimi฀ F.,฀ Bourne฀ D.G.,฀ Kelly฀ M.S.,฀ Matthews฀ T.E.฀ Nanostr฀ Mater฀ 1999;11:฀ 343–350. 68฀ McFadden฀ S.X.,฀ Zhilyaev฀ A.P.,฀ Mishra฀ R.S.,฀ Mukherjee฀ A.K.฀ Mater฀ Lett฀ 2000;45:฀ 345–349. 69฀ Yin฀W.M.,฀Whang฀S.H.฀Scripta฀Mater฀2001;44:฀569–574. 70฀ Xiao฀C.,฀Mishrams฀R.A.,฀Wang฀S.H.,฀Yin฀W.M.฀Mater฀Sci฀Eng฀2001;A301:฀35–43. 71฀ Jeong฀ D.H.,฀ Gonzalez฀ F.,฀ Palumbo฀ G.,฀ Aust฀ K.T.,฀ Erb฀ U.฀ Scripta฀ Mater฀ 2001;44:฀ 493–499. 72฀ Dalla฀Torre฀F.,฀van฀Swygenhoven฀H.,฀Victoria฀M.฀Acta฀Mater฀2002;50:฀3957–3970. 73฀ Schuh฀C.A.,฀Nieh฀T.G.,฀Yamasaki฀T.฀Scripta฀Mater฀2002;46:฀735–740. 74฀ Ebrahimi฀F.,฀Ahmed฀Z.฀Mater฀Charact฀2002;49:฀373–379. 75฀ Schwaiger฀ R.,฀ Moser฀ B.,฀ Dao฀ M.,฀ Chollacoop฀ N.,฀ Suresh฀ S.฀ Acta฀ Mater฀ 2003;51:฀ 5159–5172. 76฀ Kumar฀ K.S.,฀ Suresh฀ S.,฀ Chisholm฀ M.F.,฀ Horton฀ J.A.,฀Wang฀ P.฀Acta฀ Mater฀ 2003;51:฀ 387–406. 77฀ Ebrahimi฀F.,฀Ahmed฀Z.฀J฀Appl฀Electrochem฀2003;33:฀733–739. 78฀ Hanlon฀T.,฀Kwon฀Y.N.,฀Suresh฀S.฀Scripta฀Mater฀2003;49:฀675–680. 79฀ Wang฀Y.M.,฀Cheng฀S.,฀Wei฀Q.M.,฀Ma฀E.,฀Nieh฀T.G.,฀Hamza฀A.฀Scripta฀Mater฀2004;51:฀ 1023–1028. 80฀ Mishra฀R.,฀Basu฀B.,฀Balasubramaniam฀R.฀Mater฀Sci฀Eng฀2004;A373:฀370–373. 81฀ Dalla฀Torre฀F.,฀Spätig฀P.,฀Schaüblin฀R.฀Acta฀Mater฀2005;53:฀2337–2350. 82 Dalla Torre F., van Swygenhoven H., Schaüblin H., Spätig P., Victoria M. Scripta Mater฀2005;53:฀23–27. 83฀ Wang฀Y.M.,฀Hamza฀A.V.,฀Ma฀E.฀Appl฀Phys฀Lett฀2005;86:241917:฀1–7. 84฀ McFadden฀S.X.,฀Mukherjee฀A.K.฀Mater฀Sci฀Eng฀2005;A395:฀265–268. 85฀ Ebrahimi฀F.,฀Ahmed฀Z.,฀Li฀Q.฀Mater฀Manuf฀Proc฀2006;21:฀687–693. 86฀ Wang฀Y.M.,฀Hamza฀A.V.,฀Ma฀E.฀Acta฀Mater฀2006;54:฀2715–2726. 87฀ Gu฀C.D.,฀Lian฀J.S.,฀Jiang฀Z.H.,฀Jiang฀Q.฀Scripta฀Mater฀2006;54:฀579–584. 88฀ Cavaliere฀P.฀Comp฀Mater฀Sci฀2008;41:฀440–449. 89฀ Brooks฀I.,฀Lin฀P.,฀Palumbo฀G.,฀Hibbard฀G.D.,฀Erb฀U.฀Mater฀Sci฀Eng฀2008;A491:฀412–419.

© Woodhead Publishing Limited, 2011

The processing of bulk nanocrystalline metals and alloys

149

฀ 90฀ Shen฀ Y.F.,฀ Xue฀ W.Y.,฀ Wang฀ Y.D.,฀ Liu฀ Z.Y.,฀ Zuo฀ L.฀ Surf฀ Coat฀ Tech฀ 2008;202:฀ 5140–5145. ฀ 91฀ Kulovits฀A.,฀Mao฀S.X.,฀Wiezorek฀J.M.K.฀Acta฀Mater฀2008;56:฀4836–4845. ฀ 92฀ Kang฀J.X.,฀Zhao฀W.Z.,฀Zhang฀G.F.฀Surf฀Coat฀Tech฀2009;203:฀1815–1818. ฀ 93฀ Wang฀C.L.,฀Zhang฀M.,฀Nieh฀T.G.฀J฀Phys฀D:฀Appl฀Phys฀2009;42:฀115405:฀1–7. ฀ 94฀ Prasad฀M.J.N.V.,฀Suwas฀S.,฀Chokshi฀A.H.฀Mater฀Sci฀Eng฀2009;A503:฀86–91. ฀ 95฀ Wu฀X.L.,฀Zhu฀Y.T.,฀Wei฀Y.G.,฀Wei฀Q.฀Phys฀Rev฀Lett฀2009;103:฀205504:฀1–4. ฀ 96฀ McCrea฀J.L.,฀Palumbo฀G.,฀Hibbard฀G.D.,฀Erb฀U.฀Rev฀Adv฀Mater฀Sci฀2003;5:฀252–258. ฀ 97฀ Li฀H.,฀Ebrahimi฀F.฀Mater฀Sci฀Eng฀2003;A347:฀93–101. ฀ 98฀ Li฀H.,฀Ebrahimi฀F.฀Appl฀Phys฀Lett฀2004;84:฀4307–4309. ฀ 99฀ Li฀H.,฀Ebrahimi฀F.฀Adv฀Mater฀2005;17:฀1969–1972. 100฀ Li฀H.,฀Ebrahimi฀F.฀Acta฀Mater฀2006;54:฀2877–2886. 101฀ Li฀H.,฀Ebrahimi฀F.,฀Choo฀H.,฀Liaw฀P.K.฀J฀Mater฀Sci฀2006;41:฀7636–7642. 102฀ Wei฀H.,฀Hibbard฀G.D.,฀Palumbo฀G.,฀Erb฀U.฀Scripta฀Mater฀2007;57:฀996–999. 103฀ Ebrahimi฀F.,฀Li฀H.฀J฀Mater฀Sci฀2007;42:฀1444–1454. 104฀ Yang฀ Y.,฀ Imasogie฀ B.,฀ Fan฀ G.J.,฀ Liaw฀ P.K.,฀ Soboyejo฀ W.O.฀ Metall฀ Mater฀ Trans฀ 2008;39A:฀1145–1156. 105฀ Li฀L.,฀Ungar฀T.,฀Wang฀Y.D.,฀Fan฀G.J.,฀Yang฀Y.L.,฀Jia฀N.,฀Ren฀Y.,฀Tichy฀G.,฀Lendvai฀J.,฀ Choo฀H.,฀Liaw฀P.K.฀Scripta฀Mater฀2009;60:฀317–320. 106฀ Fan฀G.J.,฀Li฀L.,฀Yang฀B.,฀Choo฀H.,฀Liaw฀P.K.,฀Saleh฀T.A.,฀Clausen฀B.,฀Brown฀D.W.฀ Mater฀Sci฀Eng฀2009;A506:฀187–190. 107฀ Palumbo฀G.,฀Erb฀U.,฀Aust฀K.T.฀Scripta฀Metall฀Mater฀1990;24:฀2347–2350. 108฀ Jeong฀D.H.,฀Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.฀Mater฀Sci฀Forum฀2002;925:฀408–412. 109฀ Zhou฀Y.,฀Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.฀Z฀Metallk฀2003;94:฀1157–1161. 110฀ Jeong฀ D.H.,฀ Erb฀ U.,฀Aust฀ K.T.,฀ Palumbo฀ G.฀ J฀ Metast฀ Nanostr฀ Mater฀ 2003;15–16:฀ 635–642. 111฀ Jeong฀D.H.,฀Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.฀Scripta฀Mater฀2003;48:฀1067–1072. 112฀ Zhou฀Y.,฀van฀Petegem฀S.,฀Segers฀D.,฀Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.฀Mater฀Sci฀Eng฀ 2009;A512:฀39–44. 113฀ Lu฀L.,฀Sui฀M.L.,฀Lu฀K.฀Science฀2000;208:฀1463–1466. 114฀ Lu฀L.,฀Li฀S.X.,฀Lu฀K.฀Scripta฀Mater฀2001;45:฀1163–1169. 115฀ Jia฀D.,฀Ramesh฀K.T.,฀Ma฀E.,฀Lu฀L.,฀Lu฀K.฀Scripta฀Mater฀2001;45:฀613–620. 116฀ Lu฀ L.,฀ Schwaiger฀ R.,฀ Shan฀ Z.W.,฀ Dao฀ M.,฀ Lu฀ K.,฀ Suresh฀ S.฀Acta฀ Mater฀ 2005;53:฀ 2169–2179. 117฀ Hakamada฀ M.,฀ Nakamoto฀ Y.,฀ Matsumoto฀ H.,฀ Iwasaki฀ H.,฀ Chen฀ Y.Q.,฀ Kusuda฀ H.,฀Mabuchi฀M.฀Mater฀Sci฀Eng฀2007;A457:฀120–126. 118฀ Lu฀L.,฀Chen฀X.,฀Huang฀X.,฀Lu฀K.฀Science฀2009;323:฀607–610. 119฀ Zhang฀H.,฀Jiang฀Z.,฀Qiang฀Y.฀Mater฀Sci฀Eng฀2009;A517:฀316–320. 120฀ Karimpoor฀A.A.,฀Erb฀U.,฀Aust฀K.T.,฀Wang฀Z.,฀Palumbo฀G.฀Mater฀Sci฀Forum฀2002; 386–388: 415–421. 121฀ Karimpoor฀A.A.,฀Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.฀Scripta฀Mater฀2003;49:฀651–656. 122฀ Wang฀L.,฀Gao฀Y.,฀Xu฀T.,฀Xue฀Q.฀Mater฀Chem฀Phys฀2006;99:฀96–113. 123฀ Fan฀ G.J.,฀ Fu฀ L.F.,฀ Qiao฀ D.C.,฀ Choo฀ H.,฀ Liaw฀ P.K.,฀ Browning฀ N.D.฀ Scripta฀ Mater฀ 2006;54:฀2137–2141. 124฀ Karimpoor฀A.A.,฀Aust฀K.T.,฀Erb฀U.฀Scripta฀Mater฀2007;56:฀201–204. 125฀ Cavaliere฀P.฀Mater฀Sci฀Forum฀2007;561–565:1299–1302. 126฀ Gu฀C.D.,฀Lian฀J.S.,฀Jiang฀Z.H.฀Adv฀Eng฀Mater฀2006;8(4):฀252–256. 127฀ Ebrahimi฀F.,฀Ahmed฀Z.,฀Li฀H.฀Appl฀Phys฀Lett฀2004;85:฀3749–3751. 128฀ Schuh฀C.A.,฀Nieh฀T.G.,฀Iwasaki฀H.฀Acta฀Mater฀2003;51:฀431–443.

© Woodhead Publishing Limited, 2011

150

Nanostructured metals and alloys

129฀ Giga฀A.,฀Kimoto฀Y.,฀Takigawa฀Y.,฀Higashi฀K.฀Scripta฀Mater฀2006;55:฀143–146. 130฀ Nakamoto฀Y.,฀Yuasa฀M.,฀Chen฀Y.,฀Kusuda฀H.,฀Mabuchi฀M.฀Scripta฀Mater฀2008;58:฀ 731–734. 131฀ Chan฀K.C.,฀Wang฀C.L.,฀Zhang฀K.F.,฀Pang฀C.฀Scripta฀Mater฀2004;51:฀605–609. 132฀ Chan฀K.C.,฀Wang฀G.F.,฀Wang฀C.L.,฀Zhang฀K.F.฀Scripta฀Mater฀2005;53:฀1285–1290. 133฀ Palumbo฀G.,฀Thorpe฀S.J.,฀Aust฀K.T.฀Scripta฀Metall฀Mater฀1990;24:฀1347–1350. 134฀ Shen฀T.D.,฀Koch฀C.C.,฀Tsui฀T.Y.,฀Pharr฀G.M.฀J฀Mater฀Res฀1995;10:฀2892–2896. 135฀ Rofagha฀R.,฀Langer฀R.,฀El-Sherik฀A.M.,฀Erb฀U.,฀Palumbo฀G.,฀Aust฀K.T.฀Scripta฀Metall฀ Mater฀1991;25:2867–2872. 136฀ Rofagha฀R.,฀Langer฀R.,฀El-Sherik฀A.M.,฀Erb฀U.,฀Palumbo฀G.,฀Aust฀K.T.฀Mater฀Res฀Soc฀ Symp฀Proc฀1992;238:฀751–755. 137฀ Rofagha฀ R.,฀ Erb฀ U.,฀ Ostrander฀ D.,฀ Palumbo฀ G.,฀Aust,฀ K.T.฀ Nanostr฀ Mater฀ 1993;2:฀ 1–10. 138฀ Rofagha฀R.,฀Splinter฀S.J.,฀Erb฀U.,฀McIntyre฀N.S.฀Nanostr฀Mater฀1994;4:฀69–78. 139฀ Wang฀S.,฀Rofagha฀R.,฀Roberge฀P.R.,฀Erb฀U.฀Electrochem฀Soc฀Proc฀1995;95–8:฀244–255. 140฀ Tang฀ P.T.,฀ Watanabe฀ T.,฀ Anderson฀ J.E.T.,฀ Bech-Nielsen฀ G.฀ J฀ Appl฀ Electrochem฀ 1995;25:฀347–352. 141฀ El-Sherik฀A.M.,฀Erb฀U.฀Plat฀&฀Surf฀Fin฀1995;82(9):฀85–89. 142฀ Splinter฀S.J.,฀Rofagha฀R.,฀McIntyre฀N.S.,฀Erb฀U.฀Surf฀Anal฀1996;24:฀181–186. 143฀ Gonzalez฀F.,฀Brennenstuhl฀A.M.,฀Palumbo฀G.,฀Erb฀U.,฀Lichtenberger฀P.C.฀Mater฀Sci฀ Forum฀1996;฀225–227:฀831–836. 144฀ Saito฀M.,฀Jamada฀K.,฀Ohashi฀K.,฀Yasue฀Y.,฀Sowaga฀Y.,฀Osaka฀T.฀J฀Electrochem฀Soc฀ 1999;146:฀2845–2848. 145฀ Kim฀S.H.,฀Aust฀K.T.,฀Erb฀U.,฀Ogundale฀G.,฀Gonzalez฀F.฀In:฀AESF฀SUR/FIN฀Technical฀ Proc.฀Orlando฀(FL):฀American฀Electroplaters฀and฀Surface฀Finishers;฀2002;฀p.฀225. 146฀ Benea฀L.,฀Bonora฀P.L.,฀Borello฀A.,฀Martelli฀S.฀Wear฀2002;249:฀995–1003. 147฀ Mishra฀R.,฀Balasubramaniam฀R.฀Corr฀Sci฀2004;46:฀3019–3029. 148฀ Gu฀ C.D.,฀ Lian฀ J.S.,฀ He฀ J.G.,฀ Jiang฀ Z.H.,฀ Jiang฀ Q.฀ Surf฀ &฀ Coat฀ Techn฀ 2006;200:฀ 5413–5418. 149฀ Peng฀X.,฀Zhang฀Y.,฀Zhao฀J.,฀Wang฀F.฀Electrochim฀Acta฀2006;51:฀4922–4927. 150฀ Sriraman฀K.R.,฀Ganesh฀Sundara฀Raman฀S.,฀Seshadri฀S.K.฀Mater฀Sci฀Eng฀2007;A460– 461: 39–45. 151฀ Steward฀R.V.,฀Fan฀G.J.,฀Fu฀L.F.,฀Green฀B.A.,฀Liaw฀P.K.,฀Wang฀G.,฀Buchanan฀R.฀Corr฀ Sci฀2008;50:฀946–953. 152฀ Zamanzad-Ghavidel฀M.R.,฀Raeissi฀K.,฀Saachti฀A.฀Mater฀Lett฀2009;63:฀1807–1809. 153฀ Lee฀H.B.,฀Wuu฀D.S.,฀Lee฀C.Y.฀Lin฀C.S.฀Metall฀Mater฀Trans฀2010;41A:฀450–459. 154฀ Kim฀ S.H.,฀ Aust฀ K.T.,฀ Erb฀ U.,฀ Gonzalez฀ F.,฀ Palumbo฀ G.฀ Scripta฀ Mater฀ 2003;48:฀ 1379–1384. 155฀ Kim฀S.H.,฀Franken฀T.,฀Hibbard฀G.D.,฀Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.฀J฀Metast฀Nanostr฀ Mater฀2003;15–16:฀643–648. 156฀ Aledresse฀A.,฀Alfantazi฀A.M.฀J฀Mater฀Sci฀2004;39:฀1523–1526. 157฀ Jung฀H.,฀Alfantazi฀A.M.฀Electrochim฀Acta฀2006;51:฀1806–1814. 158฀ Youssef฀K.M.S.,฀Koch฀C.C.,฀Fedkiw฀P.S.฀Corr฀Sci฀2004;46:฀51–64. 159฀ Alfantazi฀A.M.,฀Erb฀U.฀Corrosion฀1996;52:฀880–888. 160฀ Yu฀J.K.,฀Han฀E.H.,฀Lu฀L.,฀Wei฀X.J.,฀Leung฀M.฀J฀Mater฀Sci฀2005;40:฀1019–1022. 161฀ Tao฀S.,฀Li฀D.Y.฀Nanotechnology฀2006;17:฀65–78. 162฀ Yu฀B.,฀Woo฀P.,฀Erb฀U.฀Scripta฀Mater฀2007;56:฀353–6. 163฀ Ruoff฀ A.L.฀ Introduction฀ to฀ Materials฀ Science.฀ Englewood฀ Cliffs฀ NJ:฀ Prentice฀ Hall;฀1972.

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164฀ McCrea฀J.L.,฀Aust฀K.T.,฀Palumbo฀G.,฀Erb฀U.฀Mater฀Res฀Soc฀Symp฀Proc฀2000;581;฀ 461–466. 165฀ Aus฀M.J.,฀Szpunar฀B.฀El-Sherik฀A.M.,฀Erb฀U.,฀Palumbo฀G.,฀Aust฀K.T.฀Scripta฀Metall฀ et฀Mater฀1992;27:฀1639–1643. 166฀ Szpunar฀B.,฀Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.,฀Lewis฀L.J.฀Mater฀Res฀Soc฀Symp฀Proc฀ 1994;318:฀447–482. 167฀ Szpunar฀ B.,฀ Erb฀ U.,฀ Palumbo฀ G.,฀ Aust฀ K.T.,฀ Lewis฀ L.J.฀ Phys฀ Rev฀ B฀ 1996;53:฀ 5547–5556. 168฀ Aus฀M.J.,฀Cheung฀C.,฀Szpunar฀B.,฀Erb฀U.฀J฀Mater฀Sci฀Lett฀1998;17:฀1949–1952. 169฀ Szpunar฀B.,฀Aus฀M.J.,฀Cheung฀C.,฀Erb฀U.,฀Palumbo฀G.,฀Szpunar฀J.A.฀J฀Magn฀Magn฀ Mater฀1998;187:฀325–336. 170฀ Cheung฀C.,฀Aus฀M.J.,฀Erb฀U.,฀McCrea฀J.L.,฀Palumbo฀G.฀In:฀Proc,฀6th฀International฀ Conference฀ on฀ Nanostructured฀ Materials.฀ NANO฀ 2002,฀ Rutgers฀ Univ,฀ (NJ):฀ Nanotechnology฀Enterprises฀Inc;฀2002.฀CD-ROM. 171฀ Turi฀T.,฀Erb฀U.฀Mater฀Sci฀Eng฀A฀1995;203:฀34–38. 172฀ Szpunar฀B.,฀Lewis฀L.J.,฀Swainson฀I.,฀Erb฀U.฀Phys฀Rev฀B฀1999;60:฀10,107–10,113. 173฀ Haasz฀T.R.,฀Palumbo฀G.,฀Aust฀K.T.,฀El-Sherik฀A.M.,฀Erb฀U.฀Scripta฀Metall฀et฀Mater฀ 1995;32:฀423–426. 174฀ Erb฀U.,฀Palumbo฀G.,฀Szpunar฀B.,฀Aust฀K.T.฀Nanostr฀Mater฀1997;9:฀261–270. 175฀ Aust฀K.T.,฀Erb฀U.,฀Palumbo฀G.฀In:฀Suryanarayana฀C฀et al., editors. Processing and Properties฀of฀Nanocrystalline฀Materials.฀Warrendale฀(PA):฀TMS;฀1996;฀p.฀11.

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6 Bulk nanocrystalline and nanocomposite alloys produced from amorphous phase A.฀INOUE฀and฀D.V.฀LOUZGUINE,฀Tohoku฀University,฀Japan

Abstract In this chapter we review a large set of the research results related to formation฀and฀characterization฀of฀bulk฀nanocrystalline฀and฀nanocomposite฀ alloys฀produced฀by฀crystallization฀of฀an฀amorphous/glassy฀phase฀or฀directly฀ from the melt on cooling. The formation of bulk glassy alloys and their processing฀routes฀are฀also฀outlined.฀Nanocrystallizing฀glassy฀samples฀leads฀to฀ the formation of composites containing nanoscale crystalline or quasicrystalline particles. The structure, general physical, thermal, mechanical and magnetic properties of these nanostructured materials are discussed. Some of these composites possess a better combination of mechanical properties than those of fully฀glassy฀or฀crystalline฀alloys.฀For฀example,฀nanoscale฀crystalline฀and฀ quasicrystalline฀phases฀play฀a฀very฀important฀role฀in฀ductilization฀of฀bulk฀glassy฀ alloys. Nanostructured ferromagnetic alloys and glassy-nanocrystal composites possess good soft magnetic properties and create an important application area for such materials. Key words: bulk, nano, crystalline, composite, alloy, amorphous, glassy, magnetic, material.

6.1

Introduction

As a rule bulk metallic alloy samples have a polycrystalline structure after solidiication.฀Even฀casting฀of฀commercial฀alloys฀into฀a฀thin฀mould฀(with฀a฀cavity฀ thickness of about 1 mm) produces a crystalline structure that is typical for metallic฀ materials.฀ Although฀ oxide฀ glasses฀ have฀ been฀ known฀ long฀ ago,฀ active฀ research฀activities฀on฀metallic฀glassy฀alloys฀started฀after฀the฀formation฀of฀the฀irst฀ Au-Si sample with an amorphous structure in 1960.1 This became possible by using฀a฀rapid฀solidiication฀technique฀for฀casting฀of฀metallic฀liquids฀at฀a฀very฀high฀ cooling rate of 106฀ K/s฀ when฀ molten฀ Au-Si฀ and฀ Pd-Si฀ alloys฀ undergo฀ glass฀ transition฀(vitriication)฀on฀cooling.฀Such฀alloys฀required฀extremely฀high฀cooling฀ rate฀(from฀metallurgical฀viewpoint)฀for฀vitriication.฀For฀a฀long฀time฀Pd-Cu-Si฀and฀ Pd-Ni-P฀system฀glassy฀alloys฀produced฀in฀a฀bulk฀form฀after฀lux฀treatment,฀which฀ helps to suppress heterogeneous nucleation, were known to be the best metallic glass formers2,3 but remained a laboratory curiosity. However, a large number of bulk฀ glassy฀ alloys฀ (also฀ called฀ bulk฀ metallic฀ glasses)฀ deined฀ as฀ 3-dimensional฀ massive฀ glassy฀ (amorphous)฀ objects฀ with฀ a฀ size฀ not฀ less฀ than฀ 1฀ mm฀ in฀ any฀ dimension฀(by฀other฀deinition฀10฀mm)฀have฀been฀produced฀since฀the฀end฀of฀the฀ 1980s. The high glass forming ability of some alloy compositions has enabled the 152 © Woodhead Publishing Limited, 2011

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production of bulk metallic glasses in the thickness range of 100–102 mm by using various casting processes.4,5,6 Metallic฀glasses฀obtained฀in฀thin฀ilm,฀ribbon฀or฀bulk฀forms฀are฀metastable฀at฀ room฀ temperature฀ and฀ devitrify/crystallize฀ on฀ heating.฀ Such฀ a฀ devitriication฀ process leads to the formation of a nanostructure in many alloys. Nanostructured material฀can฀be฀deined฀as฀a฀substance฀that฀contains฀very฀small฀grains฀or฀particles฀ of฀typically฀1฀to฀100฀nm฀in฀size฀(more฀strictly฀speaking฀in฀one฀or฀more฀dimensions).฀ These฀ nanostructured฀ materials฀ exhibit฀ unique฀ and฀ superior฀ properties,฀ and฀ for฀ this฀ reason฀ they฀ are฀ subjects฀ of฀ high฀ interest฀ to฀ scientists฀ in฀ various฀ ields฀ of฀ physics, chemistry and materials science.7,8 Although the same nanomaterial can be produced using different techniques, the฀production฀technique฀often฀signiicantly฀inluences฀the฀properties฀of฀metallic฀ glass-originated nanomaterials. If the process involves nucleation and growth then a high nucleation rate and a low growth rate of the precipitating phase are required in order to obtain a nanostructure. Such conditions are usually obtained฀under฀primary฀crystallization/devitriication฀with฀a฀long-range฀diffusioncontrolled growth.

6.2

The formation of bulk metallic glassy alloys

Depending upon their glass-forming ability (GFA), glassy (amorphous) alloys can be produced using various processing methods. Alloys having a low GFA can be prepared in an amorphous state by condensation from a vapor phase.9 This method is,฀ however,฀ high฀ on฀ power฀ consumption฀ and฀ not฀ eficient฀ for฀ the฀ preparation฀ of bulk glassy metals. Some glassy alloys can be produced by a solid-state reaction using mechanical attrition10 such as ball milling11 or by severe plastic deformation.12,13 Another method for producing glassy metals is electrodeposition from a solution.14,15฀The฀two฀methods฀mentioned฀above฀are฀eficient฀but฀also฀heavy฀ on฀power฀consumption.฀Much฀more฀productive฀is฀rapid฀solidiication฀from฀a฀liquid฀ phase16฀by฀melt-spinning฀or฀Cu-mold฀casting,฀for฀example,฀or฀from฀quartz฀crucible฀ through฀a฀nozzle฀(Fig.฀6.1),฀liquid฀forging฀and฀so฀on.฀Bulk฀glassy฀alloys฀with฀an฀ extraordinarily฀high฀GFA 4–6,17 among metallic alloys have been widely produced since the breakthrough achieved in the end of 1980s and the beginning of the 1990s.18,19฀They฀are฀greater฀in฀size฀compared฀to฀melt-spun฀ribbons฀or฀thin฀ilms,฀ and thus represent higher commercial interest as structural materials. Since these discoveries, many other bulk glassy alloys have been produced.20–24 They can be produced฀at฀cooling฀rates฀of฀the฀order฀of฀100,฀10,฀1฀K/s฀and฀even฀less,฀which฀is฀ much lower than those of 104–106฀K/s฀required฀for฀vitriication฀of฀marginal฀glassformers฀using฀a฀rapid฀solidiication฀technique. The฀bulk฀glassy฀alloys฀possess฀three฀common฀features฀summarized฀in,4 i.e. 1) the alloys belong to multicomponent systems, 2) the constituent elements have signiicant฀atomic฀size฀ratios฀above฀12%,฀and฀3)฀most฀of฀the฀alloying฀elements฀in฀ such฀alloys฀have฀a฀large฀and฀negative฀mixing฀enthalpy฀with฀each฀other฀(although฀

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6.1 Bulk glassy sample casting technique, scheme.

some฀of฀the฀alloying฀elements฀like฀Ni฀and฀Cu,฀often฀presenting฀in฀the฀bulk฀glassy฀ alloys,฀for฀example,฀have฀a฀moderately฀positive฀mixing฀enthalpy฀with฀each฀other).฀ At present bulk metallic glasses already have some important applications4,6,25 and it is believed that these will increase in the near future.26,27 On฀the฀other฀hand,฀if฀the฀GFA฀of฀the฀alloy฀is฀insuficiently฀glassy฀or฀amorphous,฀ powder฀ samples฀ can฀ be฀ produced฀ by฀ mechanical฀ alloying฀ or฀ gas฀ atomization฀ techniques,28฀for฀example,฀and฀then฀consolidated฀into฀bulk฀form฀by฀hot฀pressing฀ in฀ a฀ WC฀ die,29 spark plasma sintering (SPS)30 technique by applying pulsed direct฀current฀(Fig.฀6.2)฀or฀some฀other฀techniques.฀For฀example,฀Ni-based฀bulk฀ metallic glassy samples31,32฀with฀a฀size฀of฀20฀mm฀were฀fabricated฀by฀spark฀plasma฀ sintering฀ of฀ gas-atomized฀ Ni52.5Nb10Zr15Ti15Pt7.5 glassy powders (Fig. 6.3 and Fig. 6.4). The structure, thermal stability and interface characteristics of the powder particles in the sintered specimens were investigated. Sintered glassy specimens฀with฀nearly฀100%฀relative฀density฀were฀obtained฀by฀the฀SPS฀process฀at฀

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6.2 Schematic representation of spark plasma sintering technique.

6.3 Scanning electron microscope micrograph of the cross section of the sintered Ni52.5Nb10Zr15Ti15Pt7.5 specimen obtained at a sintering temperature of 773 K.

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6.4 Dimensions of the SPS compact.

the฀ sintering฀ temperature฀ of฀ 773฀ K฀ under฀ a฀ loading฀ pressure฀ of฀ 600฀ MPa.฀The฀ consolidation was achieved with a relatively low sintering temperature, a short holding time and rapid cooling during the SPS process. Spark plasma sintering, as a newly developed rapid sintering technique, has great potential for producing dense glassy specimens or nanocrystalline materials in a short sintering time. In the SPS process, pulsed electrical current flows directly through the powder material฀ being฀ sintered,฀ and฀ high฀ heating฀ eficiency฀ is฀ achieved฀ (Fig.฀ 6.2).฀The฀ application฀of฀pulsed฀DC฀voltage฀induces฀various฀phenomena฀caused฀by฀electrical฀ and thermal effects, providing advantages that could not be obtained using conventional sintering processes. Aluminum-based bulk glassy samples of high relative density were obtained by฀ warm฀ extrusion฀ of฀ atomized฀ amorphous฀ powders33 though they have rather low GFA owing to a high density of so-called quenched-in nuclei in some glasses. This฀fact,฀as฀well฀as฀a฀low฀reduced฀glass-transition฀and฀devitriication฀temperature,34 limits the glassy sample’s critical thickness below 1 mm. Owing to the absence of crystalline lattice and dislocations, a unique deformation mechanism35,36฀is฀realized฀in฀bulk฀glassy฀alloys,฀which฀thus฀exhibit฀high฀strength37 (~2฀GPa฀for฀Cu-,฀Ti-,฀Zr-based,฀~3฀GPa฀for฀Ni-based,฀~4฀GPa฀for฀Fe-based,฀~5฀GPa฀ for฀ Co-based฀ alloys),฀ high฀ hardness,฀ good฀ wear฀ resistance38 and large elastic deformation.฀ For฀ example,฀ (Fe,฀ Co)-Cr-Mo-C-B-Tm฀ glassy฀ alloys฀ prepared฀ in฀ a฀ cylindrical฀form฀with฀a฀diameter฀of฀18฀mm฀demonstrate฀an฀excellent฀GFA฀and฀high฀ strength฀exceeding฀4฀GPa.39฀Some฀bulk฀metallic฀glasses฀exhibit฀signiicantly฀higher฀ compressive ductility40,41 compared to the others. Their ductility can be related to Poisson’s ratio ν,42 in situ nanocrystallization43 or glassy phase separation.44 Nevertheless฀localized฀shear฀deformation฀is฀a฀dominant฀plastic-deformation฀mode฀ at room temperature.45 The fatigue-endurance limits of some Zr-based alloys are comparable with those of high-strength structural alloys.46 Many of the metallic glassy alloys have a high corrosion resistance.47,48฀Iron-฀and฀cobalt-based฀alloys฀exhibit฀good฀ soft magnetic properties,49,50 while Nd-based alloys show hard magnetic properties.

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One should also mention that some bulk glassy alloys contain clear mediumrange฀order฀(MRO)฀zones51 or nanoscale particles52฀in฀an฀as-solidiied฀state,฀even฀ though these precipitates do not produce diffraction peaks in the XRD and selected-area electron diffraction pattern (SAED) due to their small volume fraction.฀An฀example฀of฀MRO฀zones฀is฀shown฀in฀Fig.฀6.5. Although฀ binary฀ bulk฀ glassy฀ alloys฀ exist,53,54,55 their GFA is low (a critical thickness฀of฀the฀sample฀that฀achieves฀the฀glassy฀state฀without฀crystallization฀does฀ not฀exceed฀2฀mm),฀some฀of฀them฀were฀reported฀to฀contain฀nanoparticles฀and฀they฀ are formed in narrow composition ranges. On the other hand, an addition of a third element56 enhances their GFA. Bulk glassy alloys can be thermo-mechanically shaped or welded in the supercooled liquid regions by electromechanical shaping technology at low applied stresses due to the high electrical resistivity of glassy alloys.57 Some of the฀glassy฀alloys฀exhibit฀‘superplasticity’฀(actually฀good฀luidity)฀on฀being฀heated฀ to a supercooled liquid region.58 Bonding of glassy alloys can be achieved by laser,59 electron-beam60 and friction welding.61 Several฀attempts฀have฀also฀been฀made฀to฀explain฀the฀GFA฀of฀these฀alloys฀based฀ on different criteria. These include the reduced glass transition temperature, Trg฀=฀ Tg/Tl62 where Tg is the glass-transition temperature and Tl is the liquidus temperature (though overall validity of this criterion has been questioned recently);63,64 the width of the supercooled liquid region (∆Tx)฀deined฀as฀Tx – Tg where Tx฀ is฀ the฀ crystallization฀ onset฀ temperature;65 and the γ฀ =฀ Tx/(Tg + Tl)

6.5 Medium range order zones in Ni50Pd30P20 alloy, encircled in the HRTEM image. The insert in the top left corner is a Fast Fourier Transform of the area encircled in the center. One can admit the existence of sharp spots.

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parameter,66 which somehow combines both ∆Tx and Tg/Tl criteria into a single parameter and many other criteria.67 It has also been clearly shown that purely extrinsic฀factors฀also฀have฀a฀signiicant฀inluence฀on฀the฀GFA.68 The role of minor additions in the formation of metallic glasses was also discussed.69 Another important point relates to the nonequilibrium eutectic, as the best glass-forming฀compositions฀are฀found฀not฀exactly฀at฀the฀equilibrium฀eutectic฀point฀ but somewhat shifted usually towards a more refractory eutectic component,70 while Tg฀is฀not฀signiicantly฀different฀in฀the฀observed฀range.฀This฀most฀likely฀takes฀ place owing to the shift of the eutectic point with supercooling/undercooling at a high enough cooling rate because casting conditions of bulk glassy samples are far from equilibrium.71 However, binary (Si or Ge)-Ni and ternary (Si or Ge)-Ni-Nd alloys showed that the principles for achieving a good GFA known so far are necessary conditions, but฀not฀always฀suficient฀conditions.72 It was found that the higher GFA of the Ge-Ni-Nd฀alloy฀compared฀to฀the฀Si-Ni-Nd฀alloy฀cannot฀be฀explained฀on฀the฀basis฀ of the widely used parameters such as geometrical and chemical factors, viscosity and diffusion data. It was suggested that the electronic structure characteristics,72,73 for฀example฀electronegativity฀difference,฀should฀be฀taken฀into฀consideration.฀The฀ electronegativity of the constituent elements is an important factor influencing the GFA and the temperature interval of the supercooled liquid region of the glass-forming alloys.74 The atomic packing density for non-crystalline structures is a geometrical factor influencing GFA.75฀A฀mixture฀of฀atoms฀with฀different฀sizes฀enables฀their฀ dense฀packing.฀The฀importance฀of฀eficient฀atomic฀packing฀for฀the฀formation฀of฀ metallic glasses was shown recently,76,77฀as฀the฀speciic฀radius฀ratios฀are฀preferred฀ in the compositions of metallic glasses. These features are also closely connected with so-called λ criterion for good GFA.78 It has been also postulated that electron concentration: number of valence electrons per atom (e/a value) affects the GFA79 by analogy with Hume–Rothery phases related to certain valence electron concentration. However, as many glassy alloys contain transition metals which have multiple valences, it is dificult฀to฀decide฀which฀valency฀value฀should฀be฀taken฀into฀consideration฀in฀a฀ particular case. The฀glass-transition฀phenomenon฀in฀metallic฀glasses฀has฀been฀studied฀extensively.฀ Three kinds of approaches have been formulated:80,81,82 the glassy phase is just฀ a฀ frozen฀ liquid,฀ and฀ thus,฀ glass-transition฀ is฀ a฀ kinetic฀ phenomenon฀ and฀ no฀ thermodynamic฀phase฀transformation฀takes฀place;฀glass฀transition฀may฀be฀a฀secondorder transformation as follows from the shape of the curves for the thermodynamic parameters,฀for฀example,฀speciic฀volume฀or฀enthalpy,฀which฀exhibit฀a฀continuity฀at฀ the฀ glass-transition฀ temperature฀ while฀ their฀ derivatives฀ like฀ thermal฀ expansion฀ coeficient฀or฀heat฀capacity฀exhibit฀a฀discontinuity฀(in฀a฀certain฀approximation)฀at฀ the฀glass-transition฀temperature;฀glass฀transition฀may฀be฀a฀irst-order฀transformation.฀ A฀thermodynamic฀aspect฀of฀glass฀transition฀is฀known฀as฀the฀Kauzmann฀paradox.83

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159

The formation of a nanostructure by crystallization of the glassy phase, by deformation or directly from the melt on casting

Nanoscale particles of a crystalline or a quasicrystalline phase can be readily formed฀ by฀ crystallization/devitriication฀ of฀ the฀ glassy฀ alloys.฀ This฀ indirect฀ method of production of the nanostructure requires formation of the glassy phase in฀ the฀ initial฀ stage฀ and฀ its฀ subsequent฀ full฀ or฀ partial฀ devitriication฀ on฀ heating.฀ Such a method leads to the formation of a highly homogeneous dispersion of nanoparticles฀in฀various฀alloys.฀The฀difference฀in฀the฀devitriication฀pathways฀of฀ glassy฀ alloys฀ is฀ often฀ connected฀ with฀ the฀ state฀ of฀ the฀ matrix฀ phase฀ prior฀ to฀ devitriication.฀ It฀ can฀ be฀ amorphous,฀ glassy฀ or฀ supercooled฀ liquid.฀Amorphous฀ alloys฀ like฀ Al-Nd-Ni-Co฀ do฀ not฀ transform฀ to฀ a฀ supercooled฀ liquid฀ before฀ crystallization฀(Fig.฀6.6)฀upon฀conventional฀heating฀rate.฀Glassy฀alloys฀like฀Al-YNi-Co฀ form฀ the฀ supercooled฀ liquid฀ region฀ on฀ heating฀ prior฀ to฀ crystallization฀ (Fig. 6.6) and in general have a better GFA compared to amorphous alloys which do฀ not฀ exhibit฀ Tg฀ on฀ heating.฀ Marginal฀ glass-formers฀ like฀ Al-Y-Ni-Co-Cu฀ (Fig.฀ 6.6)฀ have฀ pre-existing฀ nuclei84 or even nanoparticles in the amorphous matrix,฀and฀thus฀the฀initial฀heat฀low฀signal฀in฀the฀DSC,฀marked฀as฀A,฀is฀related฀to฀ the฀beginning฀of฀growth฀of฀these฀nuclei฀or฀particles.฀Although฀it฀might฀be฀dificult฀ to establish an intrinsic physical difference between amorphous and glassy alloys such฀a฀slightly฀arbitrary฀differentiation฀in฀relation฀with฀the฀devitriication฀behavior฀ is useful. The฀ formation฀ of฀ a฀ supercooled฀ liquid฀ has฀ a฀ signiicant฀ inluence฀ on฀ the฀ devitriication฀process฀in฀metallic฀glasses.85 Alloys devitrifying from the supercooled liquid฀ exhibit฀ a฀ tendency฀ to฀ form฀ metastable฀ phases฀ and฀ phases฀ with฀ high฀ crystallographic฀ symmetry฀ on฀ devitriication฀ compared฀ to฀ similar฀ alloys฀ that฀ crystallize.86 This may be connected with the change of the local atomic structure in the supercooled liquid region due to higher atomic mobility compared to that in the glassy phase. Below Tg฀ the฀ crystalline฀ products฀ of฀ devitriication฀ in฀ some฀ alloys฀ inherit฀the฀as-solidiied฀structure฀of฀the฀metallic฀glass. Four฀types฀of฀phase฀transformations฀were฀found฀to฀occur฀during฀devitriication฀ of the glassy alloys: 1) polymorphous (a product phase has the same composition as the glassy phase), 2) primary (a product phase has a composition different from that of the glassy phase), 3) eutectic (eutectoid) transformation (two or more phases nucleate and grow conjointly) and 4) spinodal/binodal decomposition involving a phase฀separation฀of฀the฀glassy฀phase฀prior฀to฀crystallization/devitriication.87 When the฀devitriication฀occurs฀by฀nucleation฀and฀growth฀mechanism฀(amorphous฀alloy฀ does฀not฀have฀pre-existing฀nuclei),฀a฀high฀nucleation฀rate฀leading฀to฀a฀high฀number฀ density of the precipitates in the order of more than 1021 m–3 and low growth rate of the precipitating phase are required in order to obtain a nanostructure88 in many alloys.฀The฀kinetics฀of฀the฀devitriication฀process฀has฀been฀also฀analyzed.฀It฀is฀also฀

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6.6 Differential scanning calorimetry traces of three representative Al-based alloys exhibiting glass-transition on heating (alloyed with Y), crystallization without glass-transition (alloyed with Nd) and marginal glass-forming alloy which has pre-existing nuclei and nanoparticles (Cu-bearing alloy).

found฀that฀about฀1฀MHz฀frequency฀ultrasonic฀vibrations฀promote฀the฀crystallization฀ of Pd40Ni40P20 bulk glass.89 Devitriication฀of฀glassy฀alloys฀can฀be฀analyzed฀by฀the฀Kolmogorov–Johnson– Mehl–Avrami฀general฀exponential฀equation฀for฀the฀fraction฀transformed฀x(t):90 X(t)฀=฀1฀−฀exp(−Kt n),

[6.1]

where t is time and n฀is฀the฀Avrami฀exponent฀in฀the฀case฀of฀a฀single-stage฀reaction฀ and฀steady-state฀nucleation.฀Crystallization฀kinetics฀of฀many฀glassy฀alloys฀obeys฀ this mechanism. For฀example,฀Fig.฀6.7฀shows฀the฀Avrami฀plot฀for฀a฀Cu45Zr45Ag10 glassy alloy, which฀exhibited฀eutectic-type฀crystallization฀causing฀simultaneous฀formation฀of฀ oC68฀(Cu,Ag)10Zr7฀and฀tP4฀(Ag,Cu)Zr฀solid-solution฀phases฀by฀nucleation฀and฀

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6.7 The Avrami plot for Cu45Zr45Ag10 glassy alloy heat-treated isothermally at 717 K in a DSC device. Coefficient of determination (R2) for linear function fitting is 0.99998. Only every 5th data point is shown as a filled circle for better visibility of the linearity of the plot.

3-dimensional฀interface-controlled฀growth.฀As฀expected,฀the฀Avrami฀exponent฀for฀ this process is close to 4. Nanostructured฀alloys฀are฀readily฀obtained฀from฀the฀primary฀devitriication฀of฀ glasses฀with฀a฀long-range฀diffusion-controlled฀growth.฀The฀primary฀devitriication฀ process of a highly supercooled liquid or amorphous phase often has high nucleation frequency, low crystal growth rate, high concentration gradient of solute element at liquid/solid interface resulting from low atomic diffusivity, formation of metastable phases, formation of a residual amorphous phase with high solute concentration, and so on. Another type of phase transformation in an amorphous solid leading to the formation of a nanostructure is spinodal decomposition.91 There are some data suggesting that in particular cases nanocrystalline structure can be obtained after eutectic92 and polymorphous93฀devitriication฀of฀glassy฀alloys.฀Nevertheless,฀the฀ most common mechanism leading to formation of a nanostructure is primary crystallization. Different฀Al-RE-TM฀ glasses฀ (where฀ RE:฀ rare฀ earth;฀ TM:฀ transition฀ metals)฀ show primary precipitation of the Al solid solution (α-Al) nanoparticles on heating94฀with฀a฀high฀nucleation฀rate฀exceeding฀1020–1021 m–3s–1.95 The formation of α-Al฀at฀the฀primary฀crystallization฀stage฀is฀quite฀typical฀for฀Al-based฀amorphous฀ alloys฀ and฀ glass-formers,฀ for฀ example:฀Al-Y-Ni-Co,96 Al-Fe-Y, Al-Fe-Nd97 and others. The investigations showed very low concentration of the alloying elements in nanocrystalline98 Al in accordance with the phase diagrams of Al-RE and Al-TM.99 Segregation of the RE metal having low trace diffusivity in Al to the α-Al/amorphous phase interface is considered to be one of the most important reasons฀ for฀ their฀ low฀ growth฀ rate.฀ Extended฀ X-ray฀ absorption฀ ine฀ structure฀ analysis of grain boundaries in the nanocrystalline Fe85Zr7B6Cu2 alloys also showed a low Fe content in the grain boundaries between the bcc (body-centered cubic) Fe solid solution nanograins. Although in most of the alloys the

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nanocrystalline precipitates were found not to contain dislocations the addition of Pd฀to฀Al-Y-Ni-Co฀alloys฀caused฀formation฀of฀the฀highly฀dispersed฀primary฀ α-Al nanoparticles฀about฀3–7฀nm฀in฀size฀upon฀solidiication฀homogeneously฀embedded฀ in฀the฀glassy฀matrix,฀and฀the฀direct฀observation฀of฀micro-strain฀and฀dislocations฀ quenched฀in฀nanoparticles฀with฀a฀size฀below฀7฀nm฀is฀provided.100 Clearly฀ heterogeneous฀ nucleation฀ was฀ observed฀ during฀ formation฀ of฀ the฀ Fe nanocrystals.101 The structure of Fe-based soft magnetic alloys like: Fe73.5Cu1Nb3Si13.5B9102 and Fe84Zr3.5Nb3.5B8Cu1103 after annealing consist of bcc Fe฀nanocrystals฀below฀20฀nm฀in฀size฀well฀dispersed฀in฀the฀amorphous฀matrix.฀The฀ devitriication฀ of฀ the฀ Fe73.5Cu1Nb3Si13.5B9 alloy starts from the formation of Cu-enriched฀ zones.104 Precipitation of a nanoscale α-(Fe,Co)฀ phase105 was observed in the Fe40Co40Cu0.5Zr9Al2Si4B4.5 alloy (Fig. 6.8). As฀ has฀ been฀ shown฀ by฀ means฀ of฀ atom฀ probe฀ ield฀ ion฀ microscopy฀ as฀ well฀ as฀ by high-resolution transmission electron microscopy106฀ Cu฀ atoms฀ form฀ nano-฀ clusters in the Fe73.5Si13.5B9Nb3Cu1฀amorphous฀matrix,฀which฀act฀as฀the฀nucleating฀ sites฀ for฀ heterogeneous฀ nucleation฀ of฀ the฀ bcc฀ Fe฀ particles฀ on฀ devitriication.107 The density of the clusters estimated by 3-dimensional atom probe is in the order of 1024 m–3฀at฀the฀average฀cluster฀size฀of฀about฀2–3฀nm.฀Yavari฀and฀Negri108 discussed nanocrystallization฀ process฀ of฀ soft฀ magnetic฀ Fe-based฀ amorphous฀ alloys฀ using฀ the concentration gradients of the elements that are insoluble in the primary crystalline phase. The transformation of the glassy phase to a supercooled liquid region altered the฀ crystallization฀ behavior฀ of฀ Al85Y4Nd4Ni5Co2,109 Al85Y8Ni5Co2 as well as some other Al-based glassy alloys110,111฀which฀exhibited฀different฀devitriication฀

6.8 Bright-field TEM image of Fe40Co40Cu0.5Zr9Al2Si4B4.5 alloy annealed for 15 min at 873 K showing the formation of nanoparticles. Inset shows the selected-area electron diffraction pattern.

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behavior above and below the onset glass-transition temperature (Tg), while no such฀ a฀ feature฀ was฀ found฀ in฀ the฀Al-RE-Ni-Co฀ amorphous฀ alloys฀ (glassy฀ alloys฀ exhibit฀glass-transition฀on฀heating฀while฀amorphous฀do฀not)฀showing฀no฀Tg. Thus, the฀devitriication฀behavior฀of฀Al-RE-Ni-Co฀metallic฀glasses฀can฀be฀classiied฀as฀ follows: (1) If an alloy does not show Tg฀on฀heating฀prior฀to฀devitriication฀(crystallization)฀ and฀ exhibits฀ nucleation฀ and฀ growth฀ transformation฀ mechanism,฀ it฀ forms฀ intermetallic compound(s) (IM) or IM + nanoscale Al particles. (2)฀ If฀an฀alloy฀does฀not฀show฀glass฀transition฀on฀heating฀prior฀to฀devitriication฀ and฀has฀pre-existing฀nuclei,฀it฀forms฀nanoscale฀primary฀Al฀grains. (3)฀ If฀ an฀ alloy฀ shows฀ glass฀ transition฀ on฀ heating฀ and฀ exhibits฀ nucleation฀ and฀ growth transformation mechanism, it forms nanoscale Al particles above Tg and IM + Al or IM below Tg. The฀exception฀found฀in฀Ref.112 with large ribbon thickness of about 40 µm is more likely฀related฀to฀the฀pre-existing฀α-Al nuclei. The฀devitriication฀behavior฀of฀Al-based฀glassy฀and฀amorphous฀alloys฀was฀also฀ recently associated with a topological empirical criterion (λ)฀deined฀as:78,113 [6.2] where Ci is concentration of the i-th alloying element while ri is a solute atom radius and rAl is Al atom radius. The λ฀parameter฀predicts฀whether฀the฀compositions฀exhibit฀supercooled฀liquid฀ region (λ > 0.1) or not (λ < 0.1). Such a transition at different Ni/RE ratio has been also observed in Al-Y-Ni114 and Al-La-Ni alloys.115 Intermetallic฀compounds฀can฀also฀be฀formed฀into฀a฀nanoscale฀size฀of฀precipitates.฀ For฀ example,฀ the฀ devitriication฀ of฀ the฀ Ti50Ni20Cu23Sn7 alloy begins from the primary฀precipitation฀of฀nanoscale฀equiaxed฀particles฀of฀cF96฀(Pearson฀Symbol)฀ Ti2Ni solid solution.116,117 Formation of such a nanoscale cF96 phase has also been observed in the Zr- and Hf-based alloys.118 The growth rate of cF96 phase at a constant temperature is non-linear which indicates the diffusion-controlled growth฀mechanism.฀An฀extremely฀low฀growth฀rate฀of฀cF96฀crystals฀was฀observed฀ on฀the฀primary฀crystallization฀of฀the฀Hf55Co25Al20 glassy alloy.119 Very small cF96 Hf2Co฀clusters฀of฀2–5฀nm฀in฀size฀are฀formed฀in฀the฀sample฀annealed฀at฀907฀K฀for฀ 0.9 ks, which causes appearance of the broad diffraction peaks (Fig. 6.9). These clusters฀are฀not฀visible฀in฀the฀bright-ield฀TEM฀images,119 while XRD pattern of the฀ sample฀ annealed฀ for฀ 0.9฀ ks฀ at฀ 907฀ K฀ is฀ already฀ different฀ from฀ that฀ of฀ the฀ as-solidiied฀state:฀the฀broad฀diffraction฀peak฀from฀about฀30฀to฀45฀degrees฀2θ splits into฀ive฀narrower฀peaks. The฀ factors฀ leading฀ to฀ nano-devitriication฀ can฀ be฀ connected฀ with฀ the฀ occurrence฀of฀heterogeneities฀such฀as฀oxygen฀impurity-enriched฀clusters,฀spinodal฀

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6.9 X-ray diffraction pattern of the Hf55Co25Al20 glassy alloy annealed at 907 K for 0.9 ks. The location of the five strong peaks (Gaussian fitting) corresponds to that of cF96 Hf2Co phase. Source: Louzguine et al.119 reprinted with permission from Elsevier Science.

decomposition in the liquid or glass120 and homogeneous nucleation in partitioning systems.121 In many cases diffusive redistribution of the alloying elements on a short scale precedes฀ crystallization.฀ Mg-Ni-Mm฀ and฀ Mg-Ni-Y-Mm฀ (where฀ Mm฀ denotes฀ Mischmetal฀–฀a฀natural฀mixture฀of฀several฀rare-earth฀metals)฀glassy฀alloys฀show฀ a฀ multistage฀ crystallization฀ behavior.122฀ The฀ local฀ structure฀ of฀ the฀ as-solidiied฀ Mg86Ni10Y2Mm2 and Mg82Ni14Y2Mm2฀metallic฀glasses฀containing฀MRO฀zones฀ changes฀ prior฀ to฀ the฀ formation฀ of฀ the฀ crystalline฀ phases.฀ Changes฀ in฀ the฀ amorphous฀halo฀peak฀occur฀after฀heating฀to฀the฀irst฀DSC฀exothermic฀peak,฀which฀ indicates฀redistribution฀of฀the฀alloying฀elements฀in฀the฀amorphous฀matrix฀forming฀ Mg-enriched฀zones.฀This฀process฀occurs฀without฀an฀incubation฀period. Comparison฀of฀the฀long-term฀thermal฀stabilities฀of฀different฀metallic฀glasses฀has฀ been฀ carried฀ out฀ using฀ continuous฀ heating฀ transformation฀ (CHT)฀ diagrams123 constructed฀by฀applying฀a฀corollary฀from฀the฀Kissinger฀analysis฀method.฀Continuous฀ heating transformation diagrams also can be recalculated from the isothermal ones using a method close to that used for steels. Nanoparticles฀in฀the฀glassy฀matrix฀can฀be฀produced฀directly฀from฀the฀melt.฀A฀ nanomaterial consisting of icosahedral particles with a diameter below 10 nm was obtained in Zr-Pt alloy124 by casting. The formation of the nanoscale icosahedral phase฀during฀casting฀may฀indicate฀that฀the฀icosahedral฀short-range฀order฀exists฀in฀ the melt of Zr-Pt binary alloy. Plastic฀ deformation฀ can฀ cause฀ nanoscale฀ devitriication฀ of฀ a฀ glassy฀ phase.฀ For฀ example,฀ deformation฀ of฀ some฀ Al-RE-TM฀ amorphous฀ alloys฀ at฀ room฀

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temperature causes precipitation of deformation-induced α-Al particles of 7–10 nm in diameter within the shear bands on bending125 or nano-indentation.126 This effect was also observed in a Ni-based glassy alloy.127 It has been suggested that a฀local฀temperature฀rise฀can฀play฀a฀role฀in฀mechanically฀induced฀devitriication.128 One฀should฀also฀mention฀electron-beam฀irradiation฀induced฀crystallization.129,130 A฀general฀observation฀is฀that฀it฀causes฀primary฀nanocrystallization฀even฀in฀alloys฀ that฀exhibit฀eutectic฀transformation฀mechanism฀on฀heating.฀However,฀it฀tends฀to฀ indicate฀a฀non-thermal฀crystallization.

6.4

The formation of nano-quasicrystals

Nanoscale฀quasicrystals฀are฀formed฀on฀devitriication฀in฀various฀metallic฀glassy฀ alloys.131 An icosahedral quasicrystalline phase (a 3-dimensional quasicrystal while฀ 2-฀ and฀ 1-dimensional฀ quasiperiodic฀ structures฀ also฀ exist)฀ having฀ a฀ longrange quasiperiodic translational and an icosahedral orientational order, but with no 3-dimensional translational periodicity, was initially discovered in Al-Mn alloys132 and later in some other binary Al-TM alloys and different ternary Al-based alloys.133 After that the icosahedral phase was observed in Ga-, Ti-, Mg-฀and฀Pd-based฀alloys฀as฀well฀as฀Cd-,฀rare฀earth-฀and฀Zn-based฀alloys.134,135 It฀has฀been฀found฀that฀reduced฀supercooling฀before฀crystallization฀from฀the฀melt฀ was฀ found฀ to฀ be฀ the฀ lowest฀ for฀ quasicrystals,฀ larger฀ for฀ crystal฀ approximants฀ (crystals which structure is somewhat similar to those of certain quasicrystals) and largest for the crystalline phases. The nucleation barrier scales with the supercooling,฀ and฀ thus,฀ local฀ icosahedral฀ order฀ is฀ considered฀ to฀ exist฀ in฀ some฀ supercooled liquids and glasses. A low energy barrier for nucleation of the icosahedral฀ phase฀ may฀ explain฀ the฀ fact฀ that฀ only฀ growth฀ of฀ the฀ pre-existed฀ icosahedral nuclei was observed in the Zr65Ni10Al7.5Cu7.5Ti10Ta10 alloy.136 Formation฀ of฀ the฀ nanoscale฀ icosahedral฀ phase฀ was฀ observed฀ in฀ the฀ devitriied฀ Zr-Cu-Al,฀ Zr-Al-Ni-Cu137฀ and฀ Zr-Ti-Ni-Cu-Al138 glassy alloys containing an impurity฀of฀oxygen฀above฀about฀1800฀mass฀ppm,฀although฀no฀icosahedral฀phase฀is฀ formed฀if฀oxygen฀content฀is฀lower฀than฀1700฀mass฀ppm.฀The฀nanoscale฀icosahedral฀ phase฀ was฀ obtained฀ in฀ devitriied฀ Zr-Al-Ni-Cu-Pd,139 Zr-Pd, Zr-Pt140 and other system฀alloys฀at฀much฀lower฀(about฀800฀mass฀ppm)฀oxygen฀content.฀The฀nanoscale฀ icosahedral฀phase฀has฀been฀produced฀in฀the฀NM฀(noble฀metals)-free฀Zr-Cu-Ti-Ni141 and฀Zr-Al-Ni-Cu142฀glassy฀alloys฀with฀low฀oxygen฀content,฀below฀500฀mass฀ppm. The icosahedral phase in Zr-based alloys is often formed in cooperation with cF96 phase and cI2 βZr solid solution phase.143฀ In฀ the฀ rapidly฀ solidiied฀ TixZryHfzNi20 system alloys the nanoscale icosahedral phase forms in the composition ranges close to that of the cI2 β฀solid฀solution฀phase฀and฀complex฀ cF96 phase formation ranges.144 Moreover, cI2 β solid solution and icosahedral phases were found to have close chemical compositions. A transformation from glassy + β-Zr to glassy + icosahedral structure was observed in Zr65Ni10Al7.5Cu7.5Ti5Nb5 alloy on heating by a single-stage transformation with

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diffusion control. β-Zr solid solution particles were found to dissolve in the glassy phase, while the nanoscale particles of the icosahedral phase precipitate after the completion฀of฀the฀irst฀exothermic฀reaction,145 which is considered to be a singletype reaction somewhat similar to peritectic one. The nanoscale icosahedral quasicrystalline phase has been also produced upon heating glassy Hf-based alloys containing Pd146,147 or Au. Hafnium-based alloys have a higher tendency to form a cubic cF96 phase compared to Zr-based ones. The฀ alloys฀ in฀ the฀ systems฀ in฀ which฀ an฀ equilibrium฀ Hf-based฀ cF96฀ phase฀ exists฀ do฀not฀show฀the฀formation฀of฀the฀icosahedral฀phase฀from฀the฀amorphous฀matrix.฀ The metastable cF96 phase and the icosahedral phase are formed by primary devitriication฀from฀the฀amorphous฀phase฀inheriting฀the฀structure฀of฀the฀icosahedral฀ clusters. As these two phases are obtained in the alloys with similar compositions and due to local structural similarities between these two phases, one can say that these phases are produced from the same clusters and the free energy difference is a leading factor for the formation of one phase or another. The฀formation฀of฀the฀nanoscale฀icosahedral฀phase฀was฀observed฀in฀the฀Cu-based฀ alloys containing Pd148 and Au while Ag- and Pt-bearing alloys did not form the icosahedral฀ phase.฀ Palladium฀ in฀ the฀ Cu60Zr30Ti10 glass-former changes its devitriication฀pathway,149 inducing nucleation and diffusion-controlled growth of a nanoicosahedral phase (Fig. 6.10) from the supercooled liquid region in the initial฀stage฀of฀the฀devitriication฀process.

6.10 Transmission electron microscopy image of the Cu55Zr30Ti10Pd5 alloy annealed at 750 K for 1.2 ks. (a) Bright-field image, (b) dark-field image, and (c) selected-area electron diffraction pattern. The dark-field image was taken with the sharp rings in (c). Nanobeam diffraction patterns of 5-, 3- and 2-fold symmetries are inserted in (a), (b) and (c), respectively. Source: Data taken from Louzguine et al.148 with permission from Elsevier Science.

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A฀ bulk฀ glassy฀ alloy฀ sample฀ of฀ Cu-Zr-Ti฀ was฀ reported฀ to฀ contain฀ nanoscale฀ crystalline฀particles฀(about฀5฀nm฀size)150฀in฀as-solidiied฀state฀whereas฀the฀samples฀ of฀the฀Cu-Zr-Ti-Pd฀alloy฀containing฀5฀at.%฀Pd฀were฀glassy.฀The฀nanoscale฀particles฀ of฀ the฀ cP2฀ (Pearson฀ Symbol)฀ CuZr฀ phase฀ were฀ observed฀ in฀ the฀ as-solidiied฀ Cu50Zr30Ti10Pd10฀bulk฀glassy฀sample.฀The฀dissolution฀of฀the฀CuZr฀nanoparticles฀ took place on heating up to supercooled liquid region owing to the instability of the฀CuZr฀phase฀below฀988฀K.149,151฀According฀to฀the฀Cu-Zr฀phase฀diagram,฀the฀ CuZr฀ phase฀ undergoes฀ eutectoid฀ transformation฀ at฀ 988฀ K,฀ which฀ is฀ above฀ the฀supercooled฀liquid฀region฀of฀the฀Cu50Zr30Ti10Pd10฀alloy฀(about฀750–800฀K).฀ The฀nanoscale฀CuZr฀phase฀becomes฀thermodynamically฀unstable฀and฀dissolves฀ on heating in the supercooled liquid above Tg when atomic diffusion is enhanced by temperature.

6.5

The mechanical properties of nanocomposite alloys

Bulk glassy alloys demonstrate high yield strength (σy),฀nearly฀2%฀elastic฀strain฀ and relatively low Young’s modulus (E). Thus, they have a high performance index฀ σy2/E.152฀ However,฀ highly฀ inhomogeneous฀ deformation฀ localized฀ in฀ shear bands153฀limits฀their฀ductility.฀Thus,฀the฀ductilization฀of฀bulk฀metallic฀glasses฀ is฀an฀important฀technological฀challenge.฀Devitriication฀of฀the฀glassy฀alloys฀leads฀ to the formation of the composite nanomaterials containing crystalline phase precipitates฀in฀the฀residual฀glassy฀phase฀matrix.฀Mechanical฀strength฀and฀ductility฀ of glassy alloys can be improved by the precipitates of nanocrystalline or nanoquasicrystalline฀phase.฀For฀example,฀a฀Zr65Al7.5Cu7.5Ni10Pd10 alloy having nanoscale฀ icosahedral฀ phase฀ particles฀ embedded฀ in฀ the฀ glassy฀ matrix฀ showed฀ a฀ better combination of the mechanical properties compared to the as-cast glassy sample154฀without฀precipitates.฀Its฀Young’s฀modulus,฀0.2%฀proof฀stress,฀ultimate฀ tensile strength, total percentage deformation including elastic deformation are 85฀GPa,฀1640฀MPa,฀1750฀MPa,฀and฀2.2%,฀respectively,฀in฀the฀bulk฀glassy฀form฀ and฀ 88฀ GPa,฀ 1780฀ MPa,฀ 1830฀ MPa,฀ and฀ 3.1%,฀ respectively,฀ in฀ the฀ 2-phase฀ (nanoquasicrystalline + glassy phase) form. The inclusion of a precipitating phase in this alloy causes deviation and blockage of the operating shear bands, which thus improves the plasticity of the alloy. However,฀ because฀ the฀ single-phase฀ icosahedral฀ phase฀ alloys฀ are฀ extremely฀ brittle155฀ it฀ is฀ dificult฀ to฀ consider฀ that฀ the฀ icosahedral฀ phase฀ itself฀ has฀ plastic฀ deformability.฀Thus,฀its฀good฀mechanical฀properties฀are฀attributed฀to฀the฀existence฀ of the residual intergranular glassy phase, while the icosahedral particles can act as a resisting medium against the shear deformation. Also, nanocrystalline precipitates increase the room-temperature mechanical strength of the Zr-AlCu-Pd,156฀Zr-Al-Cu-Pd-Fe฀and฀(Zr/Ti)-Cu-Al-Ni157 bulk glassy alloys. Some bulk glassy-crystal composites with enhanced ductility have been produced by proper alloying in other Zr-158,159฀and฀Cu-based฀alloys.160,161 The nanoscale icosahedral

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(Fig. 6.10) or crystalline particles can act as a resistant agent against the shear deformation. Amorphous฀ alloys฀ of฀ Al-RE-TM฀ possess฀ a฀ high฀ tensile฀ strength฀ exceeding฀ 1200 MPa162 and good bend ductility, that is, showing ability of being bent through฀180°฀without฀fracture.163,164 The homogeneous dispersion of the nanoscale fcc (face-centered cubic) α-Al฀particles฀in฀the฀amorphous฀matrix฀causes฀a฀drastic฀ increase in the tensile fracture strength to 1560 MPa165 which is a record number for the high strength Al-based glassy or crystalline alloys. The Al88Y2Ni9Fe1 amorphous฀alloy฀containing฀7%฀volume฀fraction฀of฀the฀fcc-Al฀particles฀with฀a฀size฀ of about 3–7 nm has a high tensile fracture strength of 1320 MPa and 1260 MPa with฀the฀particle฀volume฀fraction฀of฀24%,฀respectively.166 These particles can be formed฀by฀controlling฀the฀cooling฀rate฀upon฀solidiication฀or฀by฀annealing฀glassy฀ alloys. The largest strength value was obtained when the volume fraction of α-Al phase฀reached฀25%.167฀The฀signiicant฀decrease฀in฀tensile฀fracture฀strength฀by฀the฀ further increase in Vf is due to the embrittlement of the remaining amorphous phase฀ by฀ the฀ progress฀ of฀ structural฀ relaxation฀ and฀ enrichment฀ in฀ the฀ solute฀ elements.168 The (Al0.84Y0.09Ni0.05Co0.02)95Sc5 amorphous alloy has an ultra-high tensile fracture฀ strength฀ slightly฀ exceeding฀ 1500฀ MPa,฀ which฀ surpasses฀ those฀ for฀ all฀ other Al-based fully crystalline and fully amorphous alloys reported to date.169 It opens the possibility of further strengthening such an alloy by nanoscale crystallization. In metallic glasses the deformation is concentrated in the shear bands of maximum฀ shear฀ stress,฀ which฀ maintain฀ about฀ 45°฀ with฀ the฀ load฀ (tensile฀ or฀ compressive) direction. The width of the shear bands is about 10–20 nm. It is considered that the nanoscale α-Al particles can act as an effective barrier against the฀shear฀deformation฀of฀an฀amorphous฀matrix.170 At the same time, it was also suggested171 that the hardening could be attributed mainly to solute enrichment of the฀ residual฀ glassy฀ matrix฀ due฀ to฀ lowering฀ of฀ the฀Al฀ content.฀ This฀ theory฀ well฀ describes the hardening of the material. As the hardness of fully amorphous or partially crystalline alloys correlates well with the solute content in the amorphous phase, it is suggested that not only α-Al฀particles฀but฀also฀the฀amorphous฀matrix฀ has some role in the hardening and embrittlement of the alloy. However, in some cases, formation of the primary α-Al particles was found to deteriorate mechanical properties and decrease the tensile strength and hardness. Partial฀ substitution฀ of฀ Ni฀ by฀ Cu฀ in฀ the฀ Al85Y8Ni5Co2 metallic glass causes formation of the nanoscale α-Al particles and drastically decreases the tensile strength and hardness values of the alloy.172฀ Copper,฀ which฀ has฀ a฀ much฀ lower฀ absolute฀ value฀ of฀ heat฀ of฀ mixing฀ with฀ Al,฀ Y฀ and฀ Co฀ than฀ Ni฀ has฀ with฀ these฀ metals,฀may฀be฀responsible฀for฀such฀a฀decrease฀in฀the฀properties.฀Thus,฀Cu฀may฀ weaken the interaction needed for the stability of the glass, thus resulting in the disappearance of Tg and precipitation of α-Al nanocrystals. In addition, the volume fraction of the α-Al nanocrystals in Al85Y8Ni3Co2Cu2,฀ for฀ example,฀ is฀

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much฀lower฀than฀that฀in฀the฀primarily฀devitriied฀Al85Y8Ni5Co2 metallic glass. It was found that the α-Al inter-particular distances in the Al85Y8Ni3Co2Cu2 metallic฀ glass฀ signiicantly฀ exceed฀ the฀ particle฀ size฀ itself.฀ Thus,฀ α-Al particles cannot act as an effective barrier against the shear deformation in the amorphous matrix.

6.6

The magnetic properties of nanocomposite alloys

Magnetic materials compose another very important and developing application ield฀ of฀ nanostructured฀ alloys.฀ The฀ connection฀ between฀ nanostructure฀ and฀ magnetic properties is a topic of intensive investigations. Ferromagnetic alloys can฀ exhibit฀ hard฀ or฀ soft฀ magnetism฀ depending฀ on฀ their฀ coercivity.฀ Magnetic฀ materials having coercivity above about 104 A/m are considered to be hard while soft magnetic materials have a coercivity below 103 A/m.

6.6.1 Soft magnetic alloys A฀typical฀magnetization฀curve฀of฀a฀soft฀magnetic฀alloy฀(also฀called฀a฀magnetically฀ soft alloy) is given in Fig. 6.11. Classical฀examples฀of฀Fe-based฀soft฀magnetic฀materials฀with฀mixed฀nanocrystalline฀ and฀ amorphous฀ structure,฀ as฀ shown฀ in฀ Fig.฀ 6.7,฀ for฀ example,฀ are฀ Finemet฀ Fe73.5Cu1Nb3Si13.5B9102 and Nanoperm Fe84Zr3.5Nb3.5B8Cu1103 alloys. The structure consists฀ of฀ bcc฀ Fe฀ nanocrystals฀ below฀ 20฀ nm฀ in฀ size฀ inely฀ dispersed฀ in฀ the฀ amorphous฀matrix.฀The฀addition฀of฀Cu,฀Nb฀or฀Zr฀is฀responsible฀for฀bcc฀Fe฀grain฀ reinement฀and฀formation฀of฀a฀nanostructure฀in฀these฀alloys.

6.11 Magnetization curve of a Co-Fe-Ta-B glassy sample. Source: Courtesy of P. Sharma.

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Atom฀probe฀ield฀ion฀microscopy฀and฀high-resolution฀TEM฀studies฀showed173 that฀ Cu฀ formed฀ nanoclusters฀ in฀ the฀ Fe73.5Si13.5B9Nb3Cu1฀ amorphous฀ matrix,฀ which฀work฀as฀heterogeneous฀nucleation฀sites฀for฀bcc฀Fe฀particles฀on฀devitriication.฀ The฀ studies฀ by฀ X-ray฀ absorption฀ ine฀ structure฀ (XAFS)฀ also฀ showed฀ that฀ Cu฀ clusters with near-fcc structure were present from the very early stages of the devitriication฀process.174 The density of the clusters is of the order of 10–24 m–3 while฀the฀average฀cluster฀size฀is฀about฀2฀nm.175 The฀ above-mentioned฀ alloys฀ show฀ high฀ permeability,฀ for฀ example,฀ 100฀000฀ in the case of Fe84Zr3.5Nb3.5B8Cu1฀alloy,฀high฀magnetization฀saturation฀up฀to฀1.5฀T฀ and low hysteresis losses.176฀ Soft฀ magnetic฀ materials฀ of฀ Fe-Zr-B฀ also฀ exhibit฀ high฀magnetization฀saturation฀(Ms)฀of฀1.60–1.70฀T฀under฀an฀applied฀ield฀of฀800฀ kA/m฀as฀well฀as฀high฀effective฀permeability฀of฀13฀000–15฀000฀at฀1฀kHz.฀Typical฀ nanocrystalline bcc Fe89Hf7B4 and Fe84Nb7B9 alloys subjected to the optimum annealing฀ exhibit฀ high฀ magnetization฀ saturation฀ above฀ 1.5฀ T,฀ as฀ well฀ as฀ high฀ effective฀permeability฀at฀1฀kHz฀above฀20,000. For a long time soft magnetic alloys were limited to marginal glass-formers. Soft magnetic฀properties฀of฀thick฀(Fe,฀Co)-RE-B฀glassy฀alloys฀were฀studied.177 Bulk glassy฀ alloys฀ exhibiting฀ a฀ wide฀ supercooled฀ liquid฀ region฀ before฀ crystallization฀ were฀ found฀ in฀ Fe-(Co,Ni)-(Zr,Nb,Ta)-(Mo,W)-B฀ system.178 These alloys have a high Tg฀of฀about฀870฀K฀and฀the฀supercooled฀liquid฀region฀close฀to฀90฀K.฀The฀high฀ thermal stability of the supercooled liquid enabled the production of bulk glassy alloys฀ with฀ diameters฀ up฀ to฀ 6฀ mm,฀ which฀ exhibit฀ a฀ high฀ compressive฀ strength฀ of 3800 MPa, high Vickers hardness of 1360, and high corrosion resistance. These฀glassy฀alloys฀exhibit฀a฀large฀magnetization฀saturation฀of฀0.74–0.96฀T,฀low฀ coercivity฀of฀1.1–3.2฀A/m,฀high฀permeability฀exceeding฀1.2฀×฀104฀at฀1฀kHz,฀and฀low฀ magnetostriction of about 12 × 10–6. Boron addition is reported to suppress growth of bcc-Fe grains and to stabilize฀ the฀ amorphous฀ matrix.฀Alloys฀ of฀ Fe82(Zr,Hf,Nb)7B10Cu1฀ exhibit฀ good฀ soft magnetic properties especially in the high-frequency range.179 Nanocrystalline Fe42.5Co42.5Nb7B8 alloys with a structure consisting of nearly spherical bcc grains with฀size฀from฀5–10฀nm฀dispersed฀in฀the฀residual฀amorphous฀matrix฀exhibit฀a฀high฀ saturation฀magnetization฀of฀1.90฀T฀and฀a฀low฀coercivity฀(Hc) of 60 A/m.180 It also exhibits฀a฀high฀Curie฀temperature฀(Tc)฀exceeding฀1173฀K.฀The฀segregation฀of฀Nb฀ element in the intergranular amorphous phase increases the thermal stability of the amorphous phase and suppresses the grain growth of the bcc phase. The high thermal฀ stability฀ of฀ the฀ structure฀ and฀ the฀ high฀ Curie฀ temperature฀ are฀ necessary฀ properties of a soft magnetic material for high-temperature application. The Fe-M-B฀(M฀=฀Zr,฀Hf,฀or฀Nb)฀alloys฀also฀show฀low฀core฀losses.181 The Fe66Nb4B30 ferromagnetic฀bulk฀glassy฀alloy฀with฀high฀B฀content฀was฀produced฀by฀luxing฀and฀ casting.182฀It฀also฀forms฀a฀nanostructure฀upon฀initial฀crystallization฀on฀heating. Soft magnetic properties are determined by the nature of the nanocrystal-glassy phase coupling. The origin of the good soft magnetic properties is connected with the formation of the nanoscale bcc-Fe structure and the achievement of rather

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strong magnetic coupling between the bcc grains through the intergranular ferromagnetic amorphous phase.

6.6.2 Hard magnetic alloys Hard฀magnetic฀alloys฀(also฀called฀magnetically฀hard฀alloys)฀have฀suficiently฀high฀ coercive฀force฀as฀a฀resistance฀to฀demagnetizing฀ields฀with฀coercivities฀exceeding฀ 10 kA m–1. These alloys can be used as permanent magnet materials with high magnetic induction that is retained because of a strong resistance to demagnetization,฀for฀example,฀as฀a฀result฀of฀high฀anisotropy. Hard฀magnetic฀alloys฀can฀be฀produced฀by฀crystallization฀of฀the฀glassy฀phase.฀For฀ example,฀permanent฀magnetic฀materials฀consisting฀mainly฀of฀Fe3B with Nd2Fe14B phase were obtained by annealing Nd4.5Fe77B18.5฀ rapidly฀ solidiied฀ alloys.183 The microstructure is composed of magnetically soft Fe3B nanoscale grains and magnetically hard Nd2Fe14B phases. High remanence (Br) of 0.8 T is obtained due to฀the฀remanence฀enhancement฀effect฀of฀exchange-coupled฀magnetic฀grains.฀The฀ remanent฀polarization฀(Jr)฀of฀this฀material฀is฀1.2฀T฀and฀the฀maximum฀energy฀product฀ (BH)max฀=฀97฀kJ/m3 while its coercivity Hc฀=฀240฀kJ/m.฀The฀inluence฀of฀the฀heating฀ rate on the microstructure of Fe3B/Nd2Fe14B nanocomposite magnets has also recently been studied.184,185฀ High฀ coercivity฀ values฀ exceeding฀ 300฀ kA/m฀ were฀ obtained in amorphous Nd5Fe72Cr5B18฀ crystallized฀ into฀ Fe3B/Nd2Fe14B state.186 Amorphous฀alloys฀of฀Fe-Nd-B฀containing฀88–90฀at.%฀Fe฀at฀923–1023฀K฀form฀a฀ nanostructure consisting of bcc-Fe, Fe14Nd2B and the residual amorphous phase. They฀exhibit฀good฀hard฀magnetic฀properties,฀i.e.฀Br฀of฀1.28฀T,฀coercive฀ield฀(iHc) of 252 kA/m and (BH)max฀of฀146฀kJ/m3 for Fe89Nd7B4.187 Ferromagnetic Nd90-xFexAl10 bulk amorphous alloys with high coercive force at room temperature were obtained by a copper mold casting method. The maximum฀diameter฀of฀the฀cylindrical฀amorphous฀samples฀with฀a฀length฀of฀50฀mm฀ is about 7 mm. Neither glass transition nor supercooled liquid region was observed in฀ these฀ alloys฀ in฀ the฀ temperature฀ range฀ before฀ crystallization,฀ which฀ makes฀ them฀ different฀ from฀ previous฀ bulk฀ glassy฀ alloys฀ exhibiting฀ a฀ wide฀ supercooled฀ liquid฀region฀before฀crystallization.฀The฀bulk฀amorphous฀Nd70Fe20Al10 alloy has ferromagnetism฀with฀the฀Curie฀temperature฀(Tc)฀of฀about฀600฀K,฀which฀is฀much฀ higher than the highest Tc฀(about฀480฀K)฀for฀the฀Nd-Fe฀binary฀amorphous฀alloy฀ ribbons. The remanence (Br) and intrinsic coercive force (iHc) for the bulk Nd60Fe30Al10 alloy are 0.122 T and 277 kA/m, respectively, in the as-cast state and฀0.128฀T฀and฀277฀kA/m,฀respectively,฀in฀the฀annealed฀state฀for฀600฀s฀at฀600฀K.฀ The Br and iHc฀decrease฀to฀0.045฀T฀and฀265฀kA/m,฀respectively,฀for฀the฀crystallized฀ sample. The hard magnetic properties for the bulk amorphous alloys are presumably due to the homogeneous development of ferromagnetic clusters with large random magnetic anisotropy.188 The low coercivity of Fe3B/Nd2Fe14B magnets imposes a limit on their application. The bcc-Fe/Nd2Fe14B nanomaterials have higher coercivity than

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those for Fe3B/Nd2Fe14B฀ magnets.฀ Coercivity฀ Hc of 480 kA/m and (BH)max of 160฀kJ/m3 are reported for bcc-Fe/Nd2Fe14B nanomaterials. The structure consists of two phases: magnetically hard Nd2Fe14B with nanoparticles of α-iron on grain boundaries.฀Grain฀size฀of฀the฀Nd2Fe14B฀is฀below฀30฀nm฀and฀particle฀size฀of฀the฀ α-iron is below 10 nm.189 The α-Fe/Nd2Fe14B nanostructured magnet of Fe89Nd7B4 composition contains residual amorphous phase and shows Br฀=฀1.22฀T,฀Hc฀=฀240฀kA/m฀and฀(BH)max฀=฀ 130฀kJ/m3. This alloy has high iron and low boron concentration.190 It฀ has฀ been฀ also฀ found฀ that฀ the฀ rapidly฀ solidiied฀ (Fe0.65Pt0.35)83B17 alloy possesses higher coercivity in the annealed state compared to binary Fe-Pt alloys.191 Remanence (Br), Mr /Ms, Hc, and (BH)max฀ of฀ the฀ rapidly฀ solidiied฀ Fe80-xPtxB20 (x฀=฀20,22,24)฀ribbons฀in฀the฀annealed฀state฀are฀in฀the฀range฀of฀0.93– 1.05฀ T,฀ 0.79–0.82,฀ 375–487฀ kA/m,฀ and฀ 118–127฀ kJ/m3, respectively (Br is remanence, Hc is coercivity, Ms฀is฀magnetization฀saturation,฀(BH)max฀is฀maximum฀ energy฀ product).฀ Good฀ hard฀ magnetic฀ properties฀ result฀ from฀ the฀ exchange฀ magnetic coupling between the nanoscale magnetically hard γ1 tP4 FePt and magnetically soft γ cF4 Fe(Pt) solid solution as well as Fe2B phases.192 Rapidly solidiied฀alloys฀of฀Fe-Pt-P฀were฀also฀found฀to฀possess฀good฀magnetic฀properties.193 Although฀these฀are฀rapidly฀solidiied฀samples,฀they฀can฀be฀compacted฀by฀SPS฀or฀ hot pressing. Alloys of (Fe0.75Pt0.25)75–70B25–30 were also found to possess good hard magnetic properties including high intrinsic coercivity values up to 400฀ kA/m฀ in฀ the฀ nanocrystallized฀ state.194 They are promising candidates for฀ nanocomposite฀ permanent฀ magnets.฀ The฀ structure฀ of฀ the฀ rapidly฀ solidiied฀ (Fe0.75Pt0.25)75B25 alloy contains a limited volume fraction of the nanoscale cubic cF4฀ Fe(Pt)฀ solid฀ solution฀ particles฀ of฀ about฀ 4฀ nm฀ in฀ size฀ embedded฀ in฀ the฀ amorphous฀ matrix.฀ The฀ nanoparticles฀ of฀ cF4฀ Fe(Pt)฀ phase฀ start฀ growing฀ at฀ the฀ elevated temperatures and then undergo forming of the tP4 FePt compound of about฀15฀nm฀in฀size฀which฀is฀followed฀by฀the฀formation฀of฀the฀tI12฀Fe2B phase from฀the฀residual฀amorphous฀matrix.

6.7

Conclusions

Nanocrystallization฀ on฀ heating฀ that฀ is฀ observed฀ in฀ various฀ bulk฀ metallic฀ glassy฀ alloys leads to the formation of the composites containing nanoscale crystalline or quasicrystalline particles. The formation of the nanocomposites leads to a better combination of mechanical properties than those of fully glassy and fully crystalline alloys. Nanoscale crystalline and quasicrystalline phases play a฀ very฀ important฀ role฀ in฀ ductilization฀ of฀ bulk฀ glassy฀ alloys฀ as฀ they฀ act฀ as฀ the฀ effective barriers for shear bands propagation. This can open an area for future applications of these alloys as structural materials. Magnetic materials are฀another฀very฀important฀ield฀of฀applications฀of฀nanostructured฀and฀composite฀ metallic฀ materials฀ that฀ are฀ produced฀ by฀ partial฀ crystallization฀ of฀ bulk฀ glassy฀ alloys.

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6.8 ฀ 1฀ ฀ 2฀ ฀ 3฀ ฀ 4฀ ฀ 5฀ ฀ 6฀ ฀ 7฀ ฀ 8฀ 9 10฀ 11฀ 12฀ 13฀ 14฀ 15฀ 16฀ 17฀ 18฀ 19฀ 20฀ 21฀ 22฀ 23฀ 24฀ 25฀ 26฀ 27฀ 28฀ 29฀ 30฀ 31฀ 32฀ 33฀ 34฀ 35฀ 36฀ 37฀ 38฀ 39฀ 40฀

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References

Klement฀W.,฀Willens฀R.H.฀and฀Duwez฀P.฀Nature฀1960;฀187:869. Chen฀H.S.฀Acta฀Metall฀1974;฀22:1505. Kui฀H.W.฀Greer฀A.L.฀and฀Turnbull฀D.฀Appl฀Phys฀Lett฀1982;฀45:716. Inoue฀A.฀Mater฀Trans฀JIM฀1995;฀36:866. Johnson฀W.L.฀MRS฀Bull฀1999;฀24:42. Inoue฀A.฀Acta฀Mater฀2000;฀48:279. Gleiter฀H.฀Progress฀in฀Materials฀Science฀1989;฀33:223. Greer฀A.L.฀Science฀1995;฀267:1947. Gleiter H. Proceedings of the Second Riso International Symposium on Metallurgy and Materials Science (ed. by N. Hansen et al.), Roskilde, 1981, p. 15. Fecht฀H.J.฀Nanostructured฀Materials฀1995;฀6:33 Weeber฀A.W.฀and฀Bakker฀H.฀Physica฀B฀1988;฀153:93. Valiev฀R.Z.฀Mater฀Sci฀Eng฀A฀1997;฀234–236:59. Segal฀V.M.฀Mater฀Sci฀Eng฀A฀1995;฀197:157. Yamasaki฀T.,฀Schlossmacher฀P.,฀Ehrlich฀K.฀and฀Ogino฀Y.฀Nanostruct฀Mater฀1998;฀10:375. Ahmad฀J.,฀Asami฀K.,฀Takeuchi฀A.,฀Louzguine฀D.V.฀and฀Inoue฀A.฀Mater฀Trans฀2003;฀ 44:1942. Cantor฀B.฀Mater฀Sci฀Forum฀1999;฀307:143. Inoue฀A.,฀Takeuchi฀A.฀Mater฀Trans฀2002;฀43:1892. Inoue฀A.,฀Zhang฀T.฀and฀Masumoto฀T.฀Mater฀Trans฀JIM฀1989;฀30:965. Zhang฀T.,฀Inoue฀A.฀and฀Masumoto฀T.฀Mater฀Trans฀JIM฀32,฀1991;฀1005. Peker฀A.฀and฀Johnson฀W.L.฀Appl฀Phys฀Lett฀1993;฀63:2342. Inoue฀A.,฀Nishiyama฀N.฀and฀Matsuda฀T.฀Mater฀Trans฀JIM฀1996;฀37:181. Guo฀F.,฀Poon฀S.J.,฀Shilet฀G.J.฀Appl฀Phys฀Lett฀2003;฀83:2575. Lofler฀J.F.฀Intermetallics฀2003;฀11:529. Egami฀T.฀JOM฀2010;฀62:70. Ashby฀M.F.,฀Greer฀A.L.฀Scripta฀Mater฀2006;฀54:321. Nishiyama฀N.,฀Amiya฀K.฀and฀Inoue฀A.฀J฀Non-Cryst฀Solids฀2007;฀353:3615. Nishiyama฀N.,฀Amiya฀K.฀and฀Inoue฀A.฀Mater฀Sci฀Eng฀A฀2007;฀449:79. Inoue฀A.,฀Progress฀in฀Materials฀Science฀1998;฀43:365. Inoue฀A.฀and฀Kimura฀H.M.฀J฀Metast฀Nanocr฀Mater฀2001;฀9:41. Xie฀G.,฀Zhang฀W.,฀Louzguine-Luzgin฀D.V.,฀Kimura฀H.M.฀and฀Inoue฀A.฀Scripta฀Mater฀ 2006;฀55:687. Xie฀ G.,฀ Louzguine-Luzgin฀ D.V.,฀ Kimura฀ H.M.฀ and฀ Inoue฀A.฀Appl฀ Phys฀ Lett฀ 2007;฀ 90:241902. Lee฀ J.K.,฀ Kim฀ H.J.,฀ Kim฀ T.S.,฀ Shin฀ S.Y.,฀ Kim฀ Y.C.,฀ Bae฀ J.C.฀ Journal฀ of฀ Materials฀ Processing฀Technology฀2007;฀187:801. Inoue฀A.฀and฀Kimura฀H.M.฀J฀Light฀Met฀2001;฀1:31. Allen฀D.R.,฀Foley฀J.C.฀and฀Perepezko฀J.H.฀Acta฀Mater฀1998;฀46:431. Argon฀A.S.฀Journal฀of฀Physics฀and฀Chemistry฀of฀Solids,฀1982;฀43:945. Liu฀ F.X.,฀ Liaw฀ P.K.,฀ Wang฀ G.Y.,฀ Chiang฀ C.L.,฀ Smith฀ D.A.,฀ Rack฀ P.D.,฀ Chu฀ J.P.,฀ Buchanan฀R.A.฀Intermetallics฀2006;฀14:1014. Yavari฀A.R.,฀Lewandowski฀J.J.฀and฀Eckert฀J.฀MRS฀Bull.฀2007;฀32:635. Togashi฀N.,฀Ishida฀M.,฀Nishiyama฀N.฀and฀Inoue฀A.฀Rev฀Adv฀Mater฀Sci฀(RAMS)฀2008;฀฀ 18:93. Amiya฀K.฀and฀Inoue฀A.฀Rev฀Adv฀Mater฀Sci฀2008;฀18:27. Greer฀A.L.฀and฀Ma฀E.฀MRS฀Bull฀2007;฀32:611

© Woodhead Publishing Limited, 2011

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174 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X

Nanostructured metals and alloys

41฀ Schuh฀C,A,,฀Hufnagel฀T.C.฀and฀Ramamurty฀U.฀Acta฀Mater฀2007;฀55:4067. 42฀ Lewandowski฀J.J.,฀Wang฀W.H.฀and฀Greer฀A.L.฀Philos฀Mag฀Lett฀2005;฀85:77. 43฀ Hajlaoui฀K.,฀Yavari฀A.R.,฀Doisneau฀B.,฀LeMoulec฀A.,฀Botta฀W.J.,฀Vaughan฀G.,฀Greer฀ A.L.,฀Inoue฀A.,฀Zhang฀W.,฀Kvick฀A.฀Scripta฀Mater฀2006;฀54:1829. 44฀ Kim฀K.B.,฀Das฀J.,฀Baier฀F.,฀Tang฀M.B.,฀Wang฀W.H.,฀Eckert฀J.฀Appl฀Phys฀Lett฀2006;฀ 88:051911. 45฀ Eckert฀J.,฀Das฀J.B.,฀Baier฀F.,฀Tang฀M.B.,฀Wang฀W.H.,฀Zhang฀Z.F.฀Intermetallics฀2006;฀ 14:876. 46฀ Wang฀G.Y.,฀Liaw฀P.K.,฀Peter฀W.H.,฀Yang฀B.,฀Yokoyama฀Y.,฀Benson฀M.L.,฀Green฀B.A.,฀ Kirkham฀M.J.,฀White฀S.A.,฀Saleh฀T.A.,฀McDaniels฀R.L.,฀Steward฀R.V.,฀Buchanan฀R.A.,฀ Liu฀C.T.฀and฀Brooks฀C.R.฀Intermetallics฀2004;฀12:885. 47฀ Pang฀S.,฀Zhang฀T.,฀Asami฀K.฀and฀Inoue฀A.฀Materials฀Science฀and฀Engineering฀2004;฀A฀ 375:368. 48฀ Peter฀ W.H.,฀ Buchanan฀ R.A.,฀ Liu฀ C.T.,฀ Liaw฀ P.K.,฀ Morrison฀ M.L.,฀ Horton฀ J.A.,฀ Carmichael฀C.A.฀and฀Wright฀J.L.฀Intermetallics฀2002;฀10:1157. 49฀ Makino฀A.,฀Inoue฀A.,฀Masumoto฀T.฀Mater฀Trans฀JIM฀1995;฀36:924. 50฀ Amiya฀K.,฀Urata฀A.,฀Nishiyama฀N.,฀Inoue฀A.฀J฀Appl฀Phys฀2007;฀101:112. 51฀ Louzguine-Luzgin฀D.V.,฀Zeng฀Y.H.฀Setyawan฀A.D.,฀Nishiyama฀N.,฀Kato฀H.,฀Saida฀J.฀ and฀Inoue฀A.฀Journal฀of฀Materials฀Research฀2007;฀22:1087. 52฀ Jiang฀J.Z.,฀Saida฀J.,฀Kato฀H.,฀Ohsuna฀T.,฀Inoue฀A.,฀Appl฀Phys฀Lett฀2003;฀82:4041. 53฀ Inoue฀A.,฀Zhang฀W.,฀Zhang฀T.฀and฀Kurosaka฀K.฀Acta฀Mater,฀2001;฀49:2645. 54฀ Xu฀D.,฀Lohwongwatana฀B.,฀Duan฀G.,฀Johnson฀W.L.฀and฀Garland฀C.,฀Acta฀Mater฀2004;฀ 52:2621. 55฀ Wang฀D.,฀Li฀Y.,฀Sun฀B.B.,฀Sui฀M.L.,฀Lu฀K.฀and฀Ma฀E.฀Appl฀Phys฀Lett฀2004;฀84:4029. 56฀ Desré฀P.J.฀Mater฀Trans฀JIM฀1997;฀38:583. 57฀ Yavari฀A.R.,฀Oliveira฀M.F.,฀Kiminami฀C.S.,฀Inoue฀A.฀and฀Botta฀W.J.,฀Mater฀Sci฀Eng฀A฀ 2004 375:227. 58฀ Kawamura฀Y.,฀Shibata฀T.,฀Inoue฀A.฀and฀Masumoto฀T.,฀Scripta฀Mater,฀1997;฀37:431. 59฀ Louzguine-Luzgin฀D.V.,฀Xie฀G.Q.,฀Tsumura฀T.,฀Fukuda฀H.,฀Nakata฀K.,฀Kimura฀H.M.฀ and฀Inoue฀A.,฀Mater฀Sci฀Eng฀B฀2008;฀148:88. 60฀ Louzguine-Luzgin฀D.V.,฀Yokoyama฀Y.,฀Xie฀G.,฀Abe฀N.฀and฀Inoue฀A.฀Philos฀Mag฀Lett฀ 2007;฀87:549. 61฀ Shoji฀T.,฀Kawamura฀and฀Ohno฀Y.,฀Materials฀Transactions฀2003;฀44:1809. 62฀ Turnbull฀D.฀and฀Cohen฀M.H.,฀J฀Chem฀Phys,฀1961;฀34:120. 63฀ Senkov฀O.N.฀Phys฀Rev฀B฀2007;฀76:104202. 64฀ Louzguine-Luzgin฀ D.V.,฀ Belosludov฀ R.,฀ Saito฀ M.,฀ Kawazoe฀Y,฀ and฀ Inoue฀A.฀ J฀Appl฀ Phys฀2008;฀104:123529. 65฀ Inoue฀A.,฀Zhang฀T.฀and฀Masumoto฀T.฀J฀Non-Cryst฀Solids฀1993;฀156–158:473. 66฀ Lu฀Z.P.฀and฀Liu฀C.T.฀Acta฀Mater฀2002;฀50:3501. 67฀ Guo฀S.,฀Lu฀Z.P.฀and฀Liu฀C.T.฀Intermetallics฀2010;฀18:883. 68฀ Louzguine-Luzgin฀D.V.,฀Miracle฀D.B.฀and฀Inoue฀A.฀Advanced฀Engineering฀Materials฀ 2008;฀10:1008. 69฀ Wang฀H.W.฀Progress฀in฀Materials฀Science฀2007;฀52:540. 70฀ Tan฀H.,฀Zhang฀Y.,฀Ma฀D.,฀Feng฀Y.P.฀and฀Li.฀Y.฀Acta฀Mater฀2003;฀51:4551. 71฀ Louzguine-Luzgin฀D.V.,฀Xie฀G.,฀Zhang฀Q.,฀Suryanarayana฀C.฀and฀Inoue฀A.฀Metallurgical฀ and฀Materials฀Transactions฀A฀2010;฀41A:1664. 72฀ Louzguine฀D.V.,฀Louzguina฀L.V.฀and฀Inoue฀A.,฀Appl฀Phys฀Lett฀2002;฀80:1556. 73฀ Hasegawa฀M.,฀Sato฀H.,฀Takeuchi฀T.,฀Soda฀K.,฀Mizutani฀U.฀J฀Alloys฀Comp.฀2009;฀483:638. 74฀ Louzguine,฀D.V.,฀Inoue฀A.,฀Appl฀Phys฀Lett฀2001;฀79:3410.

© Woodhead Publishing Limited, 2011

Bulk nanocrystalline and nanocomposite alloys

175

฀ 75฀ Bernal฀J.D.,฀Proc.฀R.฀Soc.฀A.,฀1964;฀280:299. ฀ 76฀ Miracle฀D.B,฀Sanders฀W.S,฀Senkov฀O.N.฀Phil฀Mag฀2003;฀83:2409. ฀ 77฀ Sheng฀H.W.,฀Luo฀W.K.,฀Alamgir฀F.M.,฀Bai฀J.M.฀and฀Ma฀E.฀Nature฀2006;฀439:419. ฀ 78฀ Egami฀T.฀and฀Waseda฀Y.฀J฀Non-Cryst฀Sol฀1984;฀64:113. ฀ 79฀ Jiang฀Q.,฀Chi฀B.Q,฀and฀Li฀J.C.฀Appl฀Phys฀Lett฀2003;฀82:1247. ฀ 80฀ Cohen฀M.H.฀and฀Grest฀G.S.,฀Phys฀Rev฀B฀1979;฀20:1077. ฀ 81฀ Van฀Den฀Beukel฀A.฀and฀Sietsma฀J.฀Acta฀Metall฀Mater฀1990;฀38:383. ฀ 82฀ Angell฀C.A.฀The฀Glass฀Transition,฀Pergamon฀Encyclopedia฀of฀Materials:Science฀and฀ Technology฀2001;฀4:3365. ฀ 83฀ Kauzmann฀W.฀Chem฀Rev฀1948;฀43:219. ฀ 84฀ Greer฀A.L.฀Mater฀Sci฀Eng฀A฀1994;฀179–180:41. ฀ 85฀ Louzguine-Luzgin฀D.V.฀and฀Inoue฀A.฀J฀Alloys฀and฀Comp฀2007;฀434–435:121. ฀ 86฀ Louzguine฀D.V฀and฀Inoue฀A.฀Mater฀Sci฀Eng฀A฀2004;฀375–377:346. ฀ 87฀ Louzguine-Luzgin฀D.V.฀and฀Inoue฀A.฀J฀NanoSci฀Nanotech฀2005;฀5:999. ฀ 88฀ Perepezko฀J.H.฀and฀Hebert฀R.J.฀J฀Metall฀2002;฀5:34. ฀ 89฀ Ichitsubo฀T.,฀Matsubara฀E.,฀Kai฀S.,฀Hirao฀M.฀Acta฀Mater฀2004;฀52:2:,฀423. ฀ 90฀ Kolmogorov฀A.N.฀Isz฀Akad฀Nauk฀USSR฀Ser฀Matem฀1937;฀3:355. ฀ 91฀ Cahn฀J.W.฀Acta฀Metall฀1961;฀9:795. ฀ 92฀ Battezzati฀L.,฀Antonione฀C.,฀Riontino฀G.,฀Marino฀F.,฀Sinning฀H.R.฀Acta฀Metall฀Mater฀ 1991;฀39:2107. ฀ 93฀ Koster฀U.฀and฀Meinhardt฀J.฀Mater฀Sci฀Eng฀A฀1994;฀178:271. ฀ 94฀ Kim฀Y.H.,฀Inoue฀A.฀and฀Masumoto฀T.฀Mater฀Trans฀JIM฀1991;฀32:331. ฀ 95฀ Foley฀J.C.,฀Allen฀D.R.฀and฀Perepezko฀J.H.฀Scripta฀Mater฀1996;฀35:655. ฀ 96฀ Bassim฀N.,฀Kiminami฀C.S.,฀and฀Kaufman฀M.J.฀J฀Non-Cryst฀Solids฀2000;฀273:271. ฀ 97฀ Paik,฀J.H.฀Botta฀F.W.J.฀and฀Yavari฀A.R.฀Mater฀Sci฀Forum฀1996;฀225–227:305. ฀ 98฀ Hono฀K.,฀Zhang฀Y.,฀Tsai฀A.P.,฀Inoue฀A.฀and฀Sakurai฀T.฀Scripta฀Mater฀1995;฀32:191. 99 Massalski T.B. Binary Alloy Phase Diagrams, ASM International, Materials Park, Ohio;฀1990. 100฀ Louzguine-Luzgin฀D.V.฀and฀Inoue฀A.฀J฀Mater฀Res฀2006;฀21:1347. 101฀ Yavari฀A.R.฀and฀Drbohlav฀O.฀Mater฀Trans฀JIM฀1995;฀36:896. 102฀ Yoshizawa฀H.,฀Yamauchi฀K.,฀Yamane฀T.฀and฀Sugihara฀H.฀J฀Appl฀Phys฀1988;฀64:6047. 103฀ Suzuki฀K.,฀Kataoka฀N.,฀Inoue฀A.,฀Makino฀A.฀and฀Masumoto฀T.฀Mater฀Trans฀JIM฀1990;฀ 31:743. 104฀ Hono฀K.฀Progress฀in฀Materials฀Science฀2002;฀47:621. 105฀ Mitra฀A.,฀Kim฀H.Y.,฀Louzguine฀D.V.,฀Nishiyama฀N.,฀Shen฀B.,฀Inoue฀A.฀J฀Magnetism฀ Magnetic฀Mater฀2004;฀278:299. 106฀ Hono฀K.,฀Hiraga฀K.,฀Wang฀Q.,฀Inoue฀A.฀and฀Sakurai฀T.,฀Acta฀Metall฀et฀Mater฀1992;฀ 40:2137. 107฀ Botta฀W.J.,฀Negri฀F.D.,฀Yavari฀A.R.฀J฀Non-Cryst฀Sol฀1999;฀247:19. 108฀ Yavari฀A.R.฀and฀Negri฀D.฀Nanostruct฀Mater฀1997;฀8:969 109฀ Louzguine฀D฀V.฀and฀Inoue฀A.฀Appl฀Phys฀Lett฀2001;฀78:3061. 110฀ Louzguine฀D.V.฀and฀Inoue฀A.฀J฀Non-Cryst฀Sol฀2002;฀311:281. 111฀ Guo฀F.Q.,฀Poon฀J.฀and฀Shilet฀G.J.฀MRS฀Symposium฀Proceedings฀2003;฀754:CC11.6. 112฀ Wang฀J.Q.,฀Zhang฀H.W.,฀Gu฀X.J.,฀Lu฀K.,฀Sommer฀F.,฀Mittemeijer฀E.J.฀Appl฀Phys฀Lett฀ 2002;฀18:80. 113฀ Sá฀ Lisboa฀ R฀ D,฀ Bolfarini฀ C,฀ Botta฀ W฀ J฀ and฀ Kiminami฀ C.S.฀Appl฀ Phys฀ Lett฀ 2005;฀ 86:211904. 114฀ Saini฀S.,฀Zaluska฀A.฀and฀Altounian฀Z.฀J฀Non-Cryst฀Sol฀1999;฀250–252:714. 115฀ Sahoo฀K.L.,฀Wollgarten฀M.,฀Haug฀J.฀and฀Banhart฀J.฀Acta฀Mater฀2005;฀53:3861.

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116฀ Louzguine฀D.V.฀and฀Inoue฀A.฀Scripta฀Mater฀2000;฀43:371. 117฀ He฀G.,฀Eckert฀J.฀and฀Loser฀W.฀Acta฀Mater฀2003;฀51:1621. 118฀ Altounian฀Z.,฀Batalla฀E.,฀Strom-Olsen฀J.O.,฀Walter฀J.L.฀J฀Appl฀Phys฀1987;฀61:149. 119฀ Louzguine฀D.V.,฀Kato฀H.,฀Kim฀H.S.฀and฀Inoue฀A.฀J฀Alloys฀and฀Comp฀2003;฀359:198. 120฀ Schneider฀S.,฀Thiyagarajan฀P.,฀Geyer฀U.฀and฀Johnson฀W.฀L฀Physica฀B฀1998;฀241–243:918. 121฀ Kelton฀K.F.,฀Philos฀Mag฀Lett฀1998;฀77:337. 122฀ Louzguine฀D.V.,฀Louzguina฀L.V.฀and฀Inoue฀A.฀Phil฀Mag฀2003;฀83:203. 123฀ Louzguine฀D.V.฀and฀Inoue฀A.฀Scripta฀Mater฀2002;฀47:887. 124฀ Saida฀J.,฀Matsushita฀M.฀and฀Inoue฀A.฀Appl฀Phys฀Lett฀2000;฀77:1287. 125฀ Chen฀H.,฀He฀Y.,฀Shilet฀G.J.฀and฀Poon฀S.J.฀Nature฀1994;฀367:541. 126฀ Jiang฀W.H.,฀Pinkerton฀F.E.฀and฀Atzmon฀M.฀J฀Appl฀Phys฀2003;฀93:9287. 127฀ Lee฀M.H.,฀Bae฀D.H.,฀Kim฀D.H.,฀Kim฀W.T.,฀Sordelet฀D.J.,฀Kim฀K.B.,฀Eckert฀J.฀Scripta฀ Mater฀2008;฀58:651. 128฀ Csontos฀A.A.฀and฀Shilet฀G.,฀J฀Nanostruct฀Mater฀1997;฀9:281. 129฀ Nagase฀T.฀and฀Umakoshi฀Y.,฀Science฀and฀Technology฀of฀Advanced฀Materials฀2004;฀5:57. 130฀ Xie฀G.,฀Zhang฀Q.,฀Louzguine-Luzgin฀D.V.,฀Zhang฀W.฀and฀Inoue฀A,฀Mater฀Trans฀2006;฀ 47:1930. 131฀ Louzguine-Luzgin฀D.V.฀and฀Inoue฀A.,฀Annual฀Review฀of฀Materials฀Research฀2008;฀ 38:403–423. 132฀ Shechtman฀D.,฀Blech฀L.A.,฀Gratias฀D.,฀Cahn฀J.W.฀Phys฀Rev฀Lett฀1984;฀53:1951. 133฀ Inoue,฀A.,฀Nanostruct฀Mater฀1995;฀6:53. 134฀ Kelton฀K.F.฀in฀Crystal฀Structures฀of฀Intermetallic฀Compounds,฀Westbrook฀J.H.฀and฀ Fleischer฀R.L.฀(eds.),฀John฀Wiley฀and฀Sons,฀New฀York฀2000;฀229. 135฀ Ranganathan฀S.฀and฀Inoue฀A.฀Acta฀Mater฀2006;฀54:3647. 136฀ Ouyang฀L.,฀Louzguine฀D.V.,฀Kimura฀H.M.,฀Ohsuna฀T.,฀Ranganathan฀S.฀and฀Inoue฀A.฀ J฀Metast฀Nanocryst฀Mater฀2003;฀18:37. 137฀ Koster฀U.,฀Meinhardt฀J.,฀Roos฀S.฀and฀Liebertz฀H.฀Appl฀Phys฀Lett฀1996;฀69:179. 138฀ Xing฀L.Q.,฀Eckert฀J.,฀Loser฀W.฀and฀Schultz฀L.฀Appl฀Phys฀Lett฀1998;฀73:2110. 139฀ Inoue฀A.,฀Zhang฀T.,฀Saida฀J.,฀Matsushita฀M.,฀Chen฀M.W.,฀and฀Sakurai฀T.฀Mater฀Trans฀ JIM฀1999;฀40:1137. 140฀ Murty฀B.S.,฀Ping฀D.H.,฀Ohnuma฀M.฀and฀Hono฀K.฀Acta฀Mater฀2001;฀49:3453. 141฀ Louzguine฀D.V.฀and฀Inoue฀A.฀Appl฀Phys฀Lett฀2001;฀78:1841. 142฀ Saida฀J.,฀Matsushita฀M.฀and฀Inoue฀A.฀J฀Non-Cryst฀Sol฀2002;฀312:617. 143฀ Yang,฀X.Y.,฀Kramer฀M.J.,฀Rozhkova฀E.A.฀and฀Sordelet฀D.฀J฀Scripta฀Materialia฀2003;฀ 49:885. 144฀ Chen฀N.,฀Louzguine฀D.V.,฀Ranganathan฀S.,฀and฀Inoue฀A.฀Acta฀Mater฀2005;฀53:759. 145฀ Louzguine฀D.V.,฀Ouyang฀L.,฀Kimura฀H.M.฀and฀Inoue฀A.฀Scripta฀Mater฀2004;฀50:973. 146฀ Louzguine฀D.V.,฀Ko฀M.S.,฀and฀Inoue฀A.฀Appl฀Phys฀Lett฀2000;฀76:3424. 147฀ Li฀C.,฀Saida฀J.,฀Matsushita฀M฀and฀Inoue฀A.฀Appl฀Phys฀Lett฀2000;฀77:528. 148฀ Louzguine฀D.V.฀and฀Inoue฀A.฀Scripta฀Mater฀2003;฀48:1325. 149฀ Jiang฀J.Z.,฀Yang฀B.,฀Saksl฀K.,฀Franz฀H.฀and฀Pryds฀N.฀J฀Mater฀Res.฀2003;฀18:895. 150฀ Chen฀Y.,฀Zhang฀T.,฀Zhan฀W.,฀Ping฀D.,฀Hono฀K.,฀Inoue฀A.฀and฀Sakurai฀T.฀Mater฀Trans฀ 2002;฀43:2647. 151฀ Louzguine฀D.V.,฀Yavari฀A.R.฀and฀Inoue฀A.฀Appl฀Phys฀Lett฀2005;฀86:041906. 152฀ Ashby฀M.F.฀and฀Greer฀A.L.฀Scripta฀Mater฀2006;฀54:321. 153฀ Schuh฀C.A.,฀Nieh฀T.G.฀Acta฀Mater฀2005;฀51:87. 154฀ Inoue฀A.,฀Zhang฀T.,฀Chen฀M.W.,฀Sakurai฀T.,฀Saida฀J.฀and฀Matsushita฀M.฀Appl฀Phys฀ Lett฀2006;฀76:967. 155 Takeuchi S. Quasicrystals, Sangyotosho, Tokyo 1992.

© Woodhead Publishing Limited, 2011

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156฀ Inoue฀A.,฀Fan฀C.฀and฀Takeuchi฀A.฀J฀Non-Cryst฀Sol฀1999;฀250–252:724. 157฀ Eckert฀J.,฀Kühn฀U.,฀Mattern฀N.,฀Reger-Leonhard฀A.฀and฀Heilmaier฀M.฀Scripta฀Mater฀ 2001;฀44:1587. 158฀ Inoue฀A.,฀Fan฀C.,฀Takeuchi฀A.฀Mater฀Sci฀Forum฀1999;฀307:1. 159฀ Hufnagel฀TC.,฀Fan฀C.,฀Ott฀R.T.,฀Li฀J.฀and฀Brennan฀S.฀Intermetallics฀2002;฀10:1163. 160฀ Louzguine฀D.V.,฀Kato฀H.฀and฀Inoue฀A.฀Appl฀Phys฀Lett฀2004;฀84:1088. 161฀ Qin฀C.,฀Zhang฀W.,฀Kimura฀H.฀and฀Inoue฀A.฀Mater฀Trans฀2004;฀45:2936. 162฀ Inoue฀A.,฀Ohtera฀K.,฀Tsai฀A.P.฀and฀Masumoto฀T.฀Jpn฀J฀Appl฀Phys฀1988;฀27:L280. 163฀ Inoue฀A.,฀Ohtera฀K.,฀Tsai฀A.P.฀and฀Masumoto฀T.฀Jpn฀J฀Appl฀Phys฀1988;฀27:L479. 164฀ Shilet฀G.J.,฀He฀Y.฀and฀Poon฀S.J.฀J฀Appl฀Phys฀1988;฀64:6863. 165฀ Kim฀Y.H.,฀Inoue฀A.฀and฀Masumoto฀T.฀Mater฀Trans฀JIM,฀1990;฀31:747. 166฀ Kim฀Y.H.,฀Inoue฀A.,฀Masumoto฀T.฀Mater฀Trans฀JIM฀1991;฀32:599. 167฀ Inoue฀A.฀and฀Kimura฀H.M.,฀Mater฀Sci฀Forum฀1997;฀235–238:873. 168฀ Inoue฀A.,฀Nakazato฀K.,฀Kawamura฀Y.,฀Tsai฀A.P.฀and฀Masumoto฀T.฀Mater฀Trans฀JIM฀ 1991;฀32:331. 169฀ Inoue฀A.,฀Sobu฀S.,฀Louzguine฀D.V.,฀Kimura฀H.฀and฀Sasamori฀K.,฀J฀Mater฀Res฀2004;฀ 19:1539. 170฀ Inoue฀A.,฀Kimura฀H.฀and฀Amiya฀K.฀Mater฀Trans฀2002;฀43:2006. 171฀ Zhong฀Z.C.,฀Jiang฀X.Y.฀and฀Greer฀A.L.฀Mater฀Sci฀Eng฀A฀1997;฀226–228:531. 172฀ Louzguine฀D.V.,฀Inoue฀A.฀J฀Mater฀Res฀2002;฀17:1014. 173฀ Hono฀K.,฀Hiraga฀K.,฀Wang฀Q.,฀Inoue฀A.,฀Sakurai฀T.฀Acta฀Metall฀et฀Mater฀1992;฀40:2137. 174฀ Ayers฀J.D.,฀Harris฀V.G.,฀Sprague฀J.A.,฀Elam฀W.T.฀and฀Jones฀H.N.฀Acta฀Mater฀1998;฀ 46:1861. 175฀ Ohnuma฀M.,฀Hono฀K.,฀Onodera฀H.,฀Pedersen฀J.S.฀and฀S.฀Linderoth,฀Nanostr฀Mater฀ 1999;฀12:693. 176฀ Makino฀A.,฀Suzuki฀K.,฀Inoue฀A.฀and฀Masumoto฀T.฀Mater฀Trans฀JIM฀1991;฀32:551. 177฀ Zhang฀W.,฀Inoue฀A.฀Mater฀Trans฀2001;฀429:1835. 178฀ Inoue฀A.,฀Zhang฀T.,฀and฀Takeuchi฀A.฀Appl฀Phys฀Lett฀1997;฀71:464. 179฀ Moon฀Y.M.,฀Kim฀K-S.,฀Yu฀S.C.฀and฀Rao฀K.V.J.฀Magnetism฀and฀Magnetic฀Materials฀ 1998;฀177:968. 180฀ Shen฀B.,฀Kimura฀H.฀and฀Inoue฀A.฀Mater฀Trans฀2002;฀43:589. 181฀ Suzuki฀K.,฀Makino฀A.,฀Inoue฀A.฀and฀Masumoto฀T.฀J฀Appl฀Phys฀1993;฀74:3316. 182฀ Stoica฀M.,฀Kumar฀S.,฀Roth฀S.,฀Ram฀S.,฀Eckert฀J.,฀Vaughan฀G.,฀Yavari฀A.R.฀J฀Alloys฀ Comp฀2009;฀483:632. 183฀ Coehoorn฀R.,฀Mooij฀D.B.,฀Duchateau฀J.P.W.B.฀and฀Buschow฀K.J.H.J.฀de฀Phys฀C฀1988;฀ 8:669. 184฀ Wu฀ Q.Y.,฀ Ping฀ D.H.,฀ Murty฀ B.S.,฀ Kanekiyo฀ H.,฀ Hirosawa฀ S.฀ and฀ Hono฀ K.฀ Scripta฀ Mater฀2001;฀45:355. 185฀ Hirosawa฀S.,฀Kanekiyo฀H.฀and฀Uehara฀M.฀J฀Appl฀Phys฀1993;฀78:6488. 186฀ Hirosawa฀S฀and฀H.฀Kanekiyo.฀Mater฀Sci฀Eng฀A฀1996;฀217/218:367 187฀ Inoue฀A.,฀Takeuchi฀A.,฀Makino฀A.฀and฀Masumoto฀T.฀IEEE฀Trans฀Magn฀1995;฀31:3626. 188฀ Inoue฀A.,฀Zhang฀T.,฀Zhang฀W.฀and฀Takeuchi฀A.฀Mater฀Trans฀JIM,฀1996;฀37:99. 189฀ Manaf฀A.,฀Buckley฀R.A.฀and฀Davies฀H.A.J.฀Magn฀Magn฀Mater฀1993;฀128:302. 190฀ Inoue฀A.,฀Takeuchi฀A.,฀Makino฀A.฀and฀Masumoto฀T.฀Mater฀Trans฀JIM฀1995;฀36:962. 191฀ Inomata฀K.,฀Sawa฀T.,฀Hashimoto฀S.฀J฀Appl฀Phys฀1988;฀64:2537. 192฀ Zhang฀W.,฀Louzguine฀D.V.,฀Inoue฀A.฀Appl฀Phys฀Lett฀2004;฀85:4998. 193฀ Kündig฀A.A.,฀Abe฀N.,฀Ohnuma฀M.,฀Ohkubo฀T.,฀Mamiya฀H.,฀Hono฀K.฀Appl฀Phys฀Lett฀ 2004;฀85:789. 194฀ Inoue฀A.,฀Zhang฀W.,฀Tsurui฀T.฀and฀Louzguine฀D.V.฀Mater฀Trans฀2005;฀46:891.

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7 Severe plastic deformation and the production of nanostructured alloys by machining J.B.฀MANN฀M4฀Sciences,฀USA,฀S.฀CHANDRASEKAR, ฀W.D.฀COMPTON,฀K.P.฀TRUMBLE,฀Purdue฀University,฀USA, C.฀SALDANA฀and S. SWAMINATHAN, GE฀John฀F.฀Welch฀ Technology฀Center,฀India and฀W.฀MOSCOSO฀and T.G.฀MURTHY,฀Indian Institute of Science, India

Abstract: This chapter describes the production of nanostructured materials using severe plastic deformation (SPD) inherent to machining. The SPD can be controlled, in situ, to access a range of strains, strain rates and temperatures, enabling deformation-microstructure maps to be created. By tuning the SPD parameters, various nanoscale microstructures (e.g. nanocrystalline, nanotwinned,฀bimodal)฀can฀be฀engineered;฀and฀by฀constraining฀the฀chip฀formation,฀ bulk฀forms฀(e.g.฀foil,฀sheet฀and฀rod)฀with฀nanocrystalline฀and฀ultrainegrained฀microstructures฀are฀produced.฀Chip฀formation฀in฀the฀presence฀of฀a฀ superimposed modulation enables the production of nanostructured particulate with฀controlled฀shapes฀including฀iber,฀equiaxed฀and฀platelet฀types.฀SPD฀ conditions also determine the deformation history of the machined surface, enabling microstructural engineering of surfaces. These diverse nanostructuring characteristics of machining are united by their common origins in the SPD phenomena฀prevailing฀in฀the฀deformation฀zone.฀Implications฀for฀large-scale฀ manufacturing฀of฀nanostructured฀alloys,฀optimization฀of฀SPD฀microstructures,฀ and consolidation–recycling of industrial machining chips are also briefly discussed. Key words: machining, severe plastic deformation, nanostructured alloys.

7.1

Introduction

The common applications of machining are in producing components with desired geometry and surface topography by the removal of unwanted material in the form of chips. Inherent to this chip formation is a condition of severe plastic deformation฀ (SPD)฀ that฀ is฀ characterized฀ by฀ the฀ development฀ of฀ large฀ plastic฀ strains under controllable strain rates and temperatures. An important consequence of฀ this฀ SPD฀ is฀ the฀ extensive฀ change฀ to฀ the฀ micro-฀ and฀ nanoscale฀ structure฀ of฀ both the chip and machined surface.1 The SPD in machining can be controlled to access a far wider range of deformation parameters than is feasible with conventional฀ SPD฀ methods฀ such฀ as฀ Equal-Channel฀Angular฀ Pressing฀ (ECAP)฀ and฀High-Pressure฀Torsion฀(HPT),฀or฀even฀by฀more฀specialized฀techniques฀such฀ as Dynamic Plastic Deformation (DPD). This enhanced control enables broader studies of the individual and interactive effects of strain, strain rate and temperature 178 © Woodhead Publishing Limited, 2011

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on large-strain deformation phenomena. After a brief review of the underlying mechanics,฀ this฀ chapter฀ will฀ give฀ examples฀ of฀ the฀ employ฀ of฀ machining-based฀ SPD for a host of applications, including fundamental studies of microstructure reinement฀ and฀ bulk-form฀ manufacture฀ of฀ nanostructured฀ materials.฀ First฀ considered are the unique capabilities that chip formation affords to investigations of฀microstructure฀reinement,฀as฀deformation฀parameter฀control฀vis-à-vis฀tunable฀ machining process parameters can be used to engineer novel nanoscale microstructures (e.g. nanostructured, bimodal, nano-twinned) that may otherwise be inaccessible with the usual SPD routes. Important aspects of the associated microstructures developed in these studies are highlighted, while correlating low deformation rate microstructures produced by machining with those of conventional SPD methods. As will be seen in the ensuing, this has particular relevance for the construction of deformation-microstructure maps that are likely of interest to materials researchers and structural designers alike. This is followed by consideration of the design of various machining-based SPD platforms for the creation of nanostructured materials in bulk and particulate forms and the application฀of฀such฀conigurations฀to฀a฀host฀of฀alloy฀systems.฀Finally,฀controlled฀ surface nanostructuring is presented as an emerging area for which the application of machining-based SPD techniques offers promise.

7.2

The mechanics of severe plastic deformation (SPD) in machining

The฀role฀of฀deformation฀in฀microstructure฀reinement฀is฀best฀illustrated฀in฀the฀seminal฀ work of Embury and Fisher2฀on฀deformation฀of฀pearlite฀and฀Langford฀and฀Cohen3 on iron.฀For฀example,฀Langford฀and฀Cohen฀achieved฀large฀plastic฀strains฀by฀repeated฀ wire drawing and found the microstructure of deformed iron wire to be composed of grains฀ in฀ the฀ sub-micrometer฀ size฀ range;฀ these฀ microstructure฀ changes฀ yielded฀ a฀ signiicant฀increase฀in฀the฀low฀stress฀of฀the฀wire.฀The฀use฀of฀deformation฀to฀study฀ microstructure฀reinement฀has฀received฀a฀major฀impetus฀in฀the฀last฀two฀decades฀as฀a฀ result of the development of various Severe Plastic Deformation (SPD) methods. The฀most฀well฀studied฀among฀these฀are฀Equal-Channel฀Angular฀Pressing฀(ECAP),฀ Accumulative Roll-Bonding (ARB) and High-Pressure Torsion (HPT), all of which are designed to impose large plastic strains by the cumulative application of deformation in multiple passes. These methods have been quite effective at producing bulk฀ultraine-grained฀(UFG)฀materials,฀and฀have฀provided฀signiicant฀insights฀into฀ the฀ mechanisms฀ of฀ microstructure฀ reinement.฀ Perhaps฀ more฀ importantly,฀ their฀ emergence฀ has฀ established฀ SPD฀ as฀ the฀ primary฀ route฀ for฀ developing฀ UFG฀ microstructures in bulk metals and alloys.2–5 However, they are not without limitations.฀Firstly,฀the฀physical฀conigurations฀used฀to฀realize฀these฀methods฀typically฀ limit deformation to small strain rates ( 100 mm/s, a fact established by PIV,฀ metallography฀ and฀ microstructure/hardness฀ characterization,7,12–15 and by slip฀line฀ield฀(SLF)฀and฀inite฀element฀analyses.13–14,16 Even when the deformation zone฀is฀somewhat฀thicker,฀the฀largest฀strain฀increments฀remain฀highly฀localized฀in฀ a narrow region reminiscent of the shear plane.10,13–14,16–18 Thus, in general, the approximation฀of฀the฀deformation฀zone฀as฀a฀shear฀plane฀is฀not฀unreasonable฀and฀is฀ used in the present study to estimate thermo-mechanical SPD parameters of strain rate, temperature and strain. The effect of SPD by machining in imposing microstructure changes in the chip is revealed in the optical micrographs of partially formed pure copper and titanium chips, shown in Fig. 7.3 (a) and 7.3 (b) respectively. These chips were created฀in฀specially฀devised฀‘quick-stop’฀experiments฀wherein฀the฀machining฀was฀ suddenly interrupted. While large grains are visible in the bulk, the chips reveal only flow lines indicative of large-strain deformation. Furthermore, the lack of a

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7.3 Quick-stop images of machining process with copper (right) and titanium (left).

visible grain structure in the polished and etched chip portions suggests that the grain฀size฀is฀in฀the฀sub-micrometer฀range.฀The฀change฀in฀the฀microstructure฀from฀ that of the bulk to that of the chip is seen to be quite abrupt, occurring over a narrow฀zone฀–฀the฀shear฀plane.฀Figure฀7.3฀(a)฀also฀lists฀the฀Vickers฀hardness฀values฀ in different regions of the partially formed copper chip sample. The hardness shows more than a two-fold increase across the shear plane, consistent with reinement฀of฀the฀microstructure.

7.2.1 Strain rate In contrast to the conventional SPD methods, machining provides a framework in which฀the฀effective฀strain฀rate฀in฀the฀deformation฀zone฀can฀be฀varied฀over฀a฀broad฀ range by varying the deformation rate, V0.1,19 From PIV measurements, such as those shown in Fig. 7.2, dε/dt฀in฀the฀deformation฀zone฀can฀be฀directly฀measured฀ and a representative value assigned to this deformation parameter for a given set of machining conditions.10฀For฀example,฀dε/dt is ~20 s–1 in the machining of pure copper at V0฀=฀5฀mm/s฀(Fig.฀7.2฀(b)).฀When฀SPD฀is฀carried฀out฀with฀a฀tool฀of฀ixed฀ α, typically a condition of constant strain, then the PIV measurements show that dε/dt฀increases฀approximately฀linearly฀with฀V0 as dε/dt฀=฀KV0, for V0 < 100 mm/s. Similar inferences have been made from grid-based deformation analysis at low speeds.13–14 This range of deformation rates may be termed as low-strain rate deformation with dε/dt values typically in the range of 1 s–1 to 10 3 s–1. While the PIV measurements can be carried out at larger deformation rates of up to a few meters per second, such data are only now becoming available. Nevertheless, the linear dependence of dε/dt on V0 may be used to estimate strain rate at these higher speeds, as this relationship has been shown to be equally valid at larger deformation฀ rates฀ based฀ on฀ metallographic฀ characterization฀ of฀ the฀ deformation฀ zone฀thickness฀and฀SLF฀analysis.8,13–15 This is based on the fact that:

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Nanostructured metals and alloys [7.4]

where ∆฀ is฀ the฀ thickness฀ of฀ the฀ deformation฀ zone,฀ usually฀ determined฀ by฀ one฀ of฀ the฀ aforementioned฀ characterization฀ methods,฀ and฀ γ is estimated using Eq.฀(7.3).฀Observations฀have฀shown฀that,฀to฀irst฀order,฀ ∆ is essentially constant (~ 50 µm) over a wide range of deformation rates, particularly at the higher V0, supporting the linear dependence of dε/dt on V0. These conclusions have been฀ further฀ conirmed฀ by฀ inite฀ element฀ characterization฀ of฀ the฀ deformation฀ zone฀in฀machining.16 Thus, dε/dt can be estimated by taking Eq. (7.4) together with Eq. (7.3) and measurements of ∆,฀or฀by฀extrapolating฀the฀PIV฀measurements฀ to higher V0.฀Based฀on฀PIV฀results฀and฀hardness/microstructure฀characterization฀ of the deformation, ∆ is taken to be 50 µm for V0 > 100 mm/s and 100 µm otherwise.฀ The฀ strain฀ rate฀ in฀ ECAP฀ corresponds฀ to฀ that฀ observed฀ at฀ the฀ lower deformation rates in machining. This is due to the similarity in the deformation฀ rates฀ in฀ ECAP฀ (1฀ mm/s฀ to฀ 10฀ mm/s)฀ and฀ low-speed฀ machining,฀ and฀ the฀ close฀ correspondence฀ between฀ their฀ respective฀ deformation฀ ields,฀ as฀ conirmed฀by฀PIV฀measurements฀of฀the฀deformation.20฀Contours฀of฀constant฀(iso)฀ strain rate in γ – V0 space can be derived from Eq. (7.4). When ∆ is taken as 50 µm for V0฀ >฀ 100฀ mm/s฀ and฀ 100฀ µm฀ otherwise,฀ as฀ in฀ the฀ illustrative฀ example฀ with฀ copper below, the constant dε/dt contours are hyperbolae in these two velocity regions.

7.2.2 Temperature Estimates฀ of฀ the฀ deformation฀ zone฀ temperature฀ can฀ be฀ made฀ using฀ established฀ thermal analyses that are based on the upper-bound model, and which use measured deformation forces and deformation rates as inputs.8,21–22 Typically, these analyses assume heat generation to arise from plastic dissipation at the shear plane and generally all yield similar values for T. Indeed, these analytical temperature estimates agree well with temperatures measured directly using infra-red (IR) thermographic and thermocouple methods.21,23–25 The analysis of Boothroyd21฀may฀be฀used฀to฀estimate฀the฀deformation฀zone฀temperature฀as฀a฀ function of the machining (SPD) variables. This analysis gives: [7.5a] where Γ is the fraction of shear plane heat flowing into the work material, us is฀ the฀ speciic฀ cutting฀ energy฀ (energy/volume)฀ due฀ to฀ shear,฀ c is the heat capacity and ρ is the density of the work material, tw is the chip width and Fs is the shear component of the resultant force, FR,฀ as฀ deined฀ in฀ Fig.฀ 7.1.฀ Γ is obtained as:22

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[7.5b]

where k is the thermal conductivity of the work material. Eq. (7.5) in the form above assumes that all of the plastic work at the shear plane฀ is฀ converted฀ into฀ heat.฀ In฀ practice,฀ this฀ is฀ a฀ good฀ approximation฀ since฀ typically฀the฀fraction฀converted฀is฀measured฀to฀be฀in฀excess฀of฀0.9฀(90%)฀for฀a฀ variety of metals. Direct measurements of the stored energy of cold work carried out using differential scanning calorimetry in copper chips also are in good agreement with this fraction, so Eq. (7.5) can be used in practice to estimate T. The฀duration฀that฀an฀elemental฀volume฀is฀exposed฀to฀this฀temperature฀is฀0.1฀ms฀to฀ 10 ms for the conditions discussed herein.1 Since T is directly determined by the intrinsic plastic deformation-induced heating, the principal variables controlling it are V0 and α in Eq. (7.5a). While these฀parameters฀also฀affect฀the฀strain฀rate฀in฀Eq.฀(7.4),฀the฀speciic฀values฀of฀dε/dt and T prevailing during the SPD can be determined as a function of V0 and α using Eqs. (7.3)–(7.5) and, hence, can be varied in a systematic way. Additional independent control of this temperature is possible through local heating or cooling฀of฀the฀workpiece฀prior฀to฀the฀deformation,฀an฀example฀of฀which฀will฀be฀ seen฀in฀the฀cryo-SPD฀experiment฀presented.

7.2.3 Zener–Hollomon parameter The฀temperature฀and฀strain฀rate฀dependence฀of฀plastic฀deformation฀can฀be฀analyzed฀ using the Zener–Hollomon parameter (Z ), which incorporates both of these variables as: [7.6] where T is the deformation temperature, Q is the activation energy for the operative thermally activated process and R is the gas constant. The Zener–Hollomon parameter was originally proposed to describe the combined effect of strain rate and temperature on flow stress of metals for deformation at or below room temperature.26–27 Z increases with increasing dε/dt and with decreasing T, containing within it the observed equivalence between higher฀ strain฀ rates฀ and฀ lower฀ temperatures.฀ Certain฀ deformation-induced฀ microstructure changes which are influenced by strain rate and temperature could also฀be฀interpreted฀in฀terms฀of฀this฀parameter.฀For฀example,฀the฀equivalence฀of฀ high strain rates and low temperatures has been postulated to hold as well for dynamic recovery involving dislocation annihilation.27–28 Recently, deformation

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twinning in SPD of copper and titanium has been interpreted using the Z parameter.29,30 The selection of an appropriate activation energy in Eq. (7.6), however, requires careful consideration. When deformation conditions and microstructure฀vary฀signiicantly฀across฀a฀narrow฀deformation฀zone,฀as฀in฀SPD,฀it฀ is฀dificult฀to฀justify฀a฀speciic฀value฀for฀Q that is unambiguously characteristic of the deformation. In such conditions, the use of smaller Q values characteristic of the deformation has been suggested.27 In the ensuing analysis, Q for grain boundary diffusion has been used.

7.2.4 Texture When฀chip฀formation฀occurs฀by฀shear฀in฀a฀deformation฀zone฀of฀small฀width,฀the฀ direction฀of฀maximum฀elongation฀in฀a฀sheared฀element฀of฀the฀chip฀is฀oriented฀at฀an฀ angle ψ with respect to the shear plane, as shown in Fig. 7.1. This causes a circle or square element in the initial bulk material to be deformed into an ellipse or parallelogram,฀respectively,฀in฀the฀chip฀(Fig.฀1.2฀(b)฀).฀The฀‘texture’฀angle฀(ψ) may be฀used฀to฀describe฀the฀‘macroscopic฀texture’฀in฀the฀chip฀created฀by฀the฀SPD฀and฀ can be estimated as:31,32 [7.7] The฀ texture฀ angle฀ can฀ be฀ varied฀ within฀ limits฀ by฀ appropriate฀ selection฀ of฀ the฀ machining variables α and λ, highlighting another aspect of SPD by machining. Direct measurement of ψ฀ is฀ possible฀ from฀ PIV฀ characterization฀ of฀ the฀ strain฀ tensor,฀as฀the฀direction฀of฀the฀largest฀principal฀strain฀is฀the฀direction฀of฀maximum฀ elongation. For the SPD condition corresponding to Fig. 7.2, the PIV analysis gives฀an฀angle฀of฀50.7°฀for฀ ϕ + ψ;฀this฀is฀the฀angle฀between฀one฀of฀the฀principal฀ directions and the direction of V0. The corresponding value for ϕ + ψ estimated using฀ Eqs.฀ (7.1–7.3)฀ and฀ (7.7)฀ is฀ 44.3°฀ (ϕ฀ =฀ 23.9°฀ and฀ ψ฀ =฀ 20.4°),฀ which฀ is฀ reasonably close. By combining such estimates with microstructure analysis, correlations can be established between the deformation path and evolution of texture.

7.2.5 Constrained chip formation – Large Strain Extrusion Machining Precise control of the deformation parameters (dε/dt, T and γ ) in conventional machining is limited in that the input variable λ in Eq. (7.3) is only partially controllable. In this regard, a constrained variant of the chip formation process – Large฀ Strain฀ Extrusion฀ Machining฀ (LSEM)฀ –฀ offers฀ capability฀ beyond฀ conventional machining as a controlled method of SPD.33,34 Figure 7.4 (a) shows a฀coniguration฀of฀LSEM฀in฀which฀the฀thickness฀of฀the฀chip฀after฀deformation฀is฀ controlled a priori฀by฀a฀constraining฀tool฀edge.฀An฀analogous฀rotary฀coniguration฀

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7.4 Mechanics of large strain extrusion machining (LSEM): (a) schematic showing geometry of constrained chip formation in a linear press configuration; (b) constrained chip formation in a turning configuration; and (c) variation of shear strain and normalized hydrostatic pressure (p/2k) in the deformation zone with chip thickness ratio (λ). k is the shear yield strength of the material.

is shown in Fig. 7.4 (b). The position of the constraining edge can be set such that the฀chip฀thickness฀at฀the฀die฀exit฀(tc) can be greater or less than that the thickness of฀the฀material฀entering฀the฀deformation฀zone฀(t0). This affords LSEM full control of strain through the chip thickness ratio, λ, unlike in conventional machining where λ฀cannot฀be฀ixed฀a priori. Furthermore, Eqs. (7.3)–(7.5), which relate the deformation parameters to the controllable variables in machining, apply equally as well to SPD by LSEM. These relationships can also be used to estimate the deformation฀parameters฀in฀a฀single฀pass฀of฀ECAP,฀with฀V0 as the pressing speed, tc฀=฀t0, and α฀set฀equal฀to฀the฀die฀inclination฀angle฀minus฀90°. Figure 7.4 (c) shows that the strain in LSEM is independently controlled by λ and α.฀ Indeed,฀ a฀ 2-parameter฀ dependence฀ of฀ strain฀ enables฀ a฀ inal฀ deformation฀ state฀to฀be฀realized฀by฀multiple฀deformation฀paths,฀each฀of฀which฀should฀results฀in฀ a฀unique฀low฀ield฀and฀texture.฀This฀provides฀for฀lexibility฀in฀control฀of฀strain,฀ microstructure฀ and฀ texture.฀ Furthermore,฀ the฀ microstructure฀ of฀ samples฀ created฀ using LSEM has shown a one-to-one correlation with the microstructures

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produced by conventional machining under equivalent SPD conditions. Fig.฀7.4฀(c)฀also฀shows฀that฀extraordinarily฀high฀levels฀of฀strain฀can฀be฀imposed฀in฀ a single pass by LSEM at small λ. The hydrostatic pressure (p/2k) in the deformation฀ zone฀ is฀ also฀ quite฀ large฀ under฀ such฀ conditions,฀ decreasing฀ with฀ increasing λ,฀based฀on฀a฀slip฀line฀ield฀analysis.฀The฀combination฀of฀large฀strain฀ and hydrostatic pressure at small λ makes this process condition somewhat akin to that in HPT, and especially valuable for deformation of alloys of limited workability (e.g. Ti, Mg, cast materials).

7.2.6 Comparison of the deformation field in SPD by machining versus other methods The฀deformation฀ield฀in฀machining฀is฀a฀steady-state฀ield฀that฀involves฀the฀low฀of฀ material฀and฀heat฀through฀the฀deformation฀zone.฀In฀comparison,฀the฀deformation฀ conditions฀ in฀ ECAP฀ represent฀ a฀ relatively฀ narrow฀ band฀ about฀ V0 ~ 1 mm/s in γ – V0 space (see also Fig. 7.5 and the associated discussion). Particle Image Velocimetry฀(PIV)฀measurements฀of฀the฀ECAP฀deformation฀zone฀show฀that฀it฀is฀ quite similar to that observed in machining at small deformation rates (Fig. 7.2). The฀use฀of฀larger฀deformation฀rates฀in฀ECAP฀is฀non-trivial฀given฀the฀layout฀of฀ typical฀ECAP฀conigurations฀and฀inertial฀effects,฀which฀limit฀the฀exploration฀of฀

7.5 Deformation conditions accessed in the SPD of pure copper. Contours of constant strain rate (d/dt) are shown overlaid on the graph. The ‘coordinates’ (a, b) of the points represent the strain rate, d/dt, and the deformation zone temperature, T, respectively.

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the฀combined฀effects฀of฀strain฀rate฀and฀temperature.฀However,฀ECAP฀can฀be฀used฀ to฀ explore฀ strains฀ in฀ excess฀ of฀ machining,฀ albeit฀ using฀ multiple฀ passes฀ of฀ deformation at small deformation rates.35 The deformation rate in HPT can be varied within some range, though much less widely than in machining, by varying the platen rotation speed.35 Furthermore, the฀strains฀that฀can฀be฀realized฀by฀HPT฀are฀much฀larger฀than฀even฀those฀of฀ECAP.฀ However,฀the฀deformation฀ield฀is฀not฀steady฀state,฀depending฀on฀the฀twist฀of฀the฀ sample.฀ The฀ deformation฀ ield฀ also฀ is฀ inhomogeneous฀ and฀ is฀ characterized฀ by฀ gradations in strain rate and strain across the sample. Regarding DPD, moderate strain rates of ~103 s–1 can be imposed at smaller strains (~3) by using multiple deformation passes.29฀The฀ DPD฀ deformation฀ ield฀ also฀ is฀ not฀ steady฀ state,฀ and฀ inertial effects likely hinder imposition of large strains and strain rates.

7.2.7 Machining as an experimental platform As outlined in Sections 7.2.1–7.2.4, the thermo-mechanical deformation parameters฀of฀strain,฀strain฀rate฀and฀temperature฀in฀the฀deformation฀zone฀can฀be฀ systematically varied by appropriate selection of α, λ and V0. This controllability can be leveraged to study material property changes arising in SPD. While this notion฀has฀been฀recognized฀for฀some฀time฀in฀the฀context฀of฀using฀machining฀as฀a฀ property test for estimating constitutive mechanical properties,8,36 it also is the subject of recent interest.37,38 What has not been considered thus far are the applications of machining to study microstructure development. Their use to manufacture bulk material forms has only been considered recently.6,7 These applications are reviewed below.

7.3

A study of microstructure refinement

The versatility of machining to study microstructure development over a wide range of deformation parameter space is illustrated by the results of SPD experiments฀carried฀out฀with฀copper฀of฀high฀purity฀(99.999%,฀Alfa฀Aesar)฀as฀a฀ model material system (Fig. 7.5 and Fig. 7.6). The physical properties of the copper฀were฀an฀initial฀grain฀size฀of฀0.9฀mm,฀Vickers฀hardness฀of฀73฀±฀3฀kg/mm,2 speciic฀heat฀c฀=฀385฀J/kg·K,฀density฀ ρ฀=฀8900฀kg/m3 and thermal conductivity k฀ =฀ 400฀W/m·K.฀A฀ range฀ of฀ deformation฀ conditions฀ –฀ shear฀ strains฀ of฀ 1฀ to฀ 15,฀ strain rates of 10 s–1 to 105 s–1฀and฀deformation฀temperatures฀up฀to฀250°C฀(0.4฀TM) – were imposed in the copper by appropriate selection of the machining input variables, α฀from฀–30°฀to฀50°฀and฀V0฀from฀10฀mm/s฀to฀5฀m/s;฀Eqs.฀(7.3)–(7.5)฀were฀ used to correlate these variables with the SPD conditions.1,19 Microstructure reinement฀ at฀ temperatures฀ well฀ below฀ room฀ temperature฀ (cryo-SPD)฀ was฀ explored฀ by฀ immersing฀ the฀ deformation฀ setup฀ in฀ liquid฀ nitrogen฀ at฀ –196°C.1,19 Chip฀samples฀were฀typically฀50฀mm฀in฀length,฀4฀mm฀in฀width฀and฀0.5฀to฀2.5฀mm฀ in฀thickness.฀The฀microstructure฀of฀the฀samples฀was฀characterized฀by฀transmission฀

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7.6 Transmission electron microscopy images of the microstructure of copper at select experimental conditions of strain and deformation rate. The points A, C, etc. correspond to the identically labeled points in Fig. 7.5, so as to facilitate mapping of the experimental deformation conditions on to the microstructures.

electron microscopy (TEM), orientation imaging microscopy (OIM) and optical microscopy, and hardness by Vickers indentation.1,19,39 Figure 7.5 shows the range of SPD conditions, including temperature and strain rate, mapped in γ – V0 space for copper. The shear strain ranges from about 1 to 15 over the different sets of SPD conditions that are represented in the experimental฀data.฀The฀strain฀rate฀(dε/dt)฀and฀deformation฀zone฀temperature฀are฀ listed as coordinates (dε/dt, T )฀beside฀each฀of฀the฀experimental฀points฀in฀Fig.฀7.5,฀ with higher values of V0 corresponding to larger values of dε/dt and T.฀Contours฀ of฀constant฀strain฀rate฀are฀also฀shown฀in฀the฀igure฀(see฀discussion฀in฀Section฀7.2.1฀ regarding estimation of dε/dt). The dε/dt values range from about 10 to 3 × 105 s–1 and T฀values฀range฀between฀30°C฀and฀250°C฀for฀V0 between 10 mm/s to 5 m/s. The corresponding ln Z values are in the range of 20 to 100.1฀The฀extreme฀left฀ hand side of Fig. 7.5 represents the deformation conditions typically accessible in ECAP.1,5,19,40 The฀microstructure฀and฀hardness฀were฀analyzed฀as฀a฀function฀of฀the฀deformation฀ rate and strain, and also in terms of strain rate and temperature. Figure 7.6 shows TEM micrographs of the microstructure of the copper after the SPD at select

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conditions of V0 and γ. These conditions were selected to highlight key aspects of the฀ microstructure฀ at฀ different฀ combinations฀ of฀ SPD฀ parameters;฀ the฀ points฀ corresponding to these micrographs are labeled with the same corresponding letters as in Fig. 7.5 to facilitate direct comparison with the associated deformation parameters. The general range of hardness values in the different SPD regions are shown in the γ – V0฀ plane฀ in฀ Fig.฀ 7.7;฀ speciic฀ values฀ at฀ select฀ deformation฀ conditions are reported and discussed in detail elsewhere.1฀ The฀ coeficient฀ of฀ variation฀(CV)฀on฀the฀hardness,฀which฀is฀the฀ratio฀of฀the฀standard฀deviation฀to฀the฀ mean, is also provided in Fig. 7.7.

7.3.1 Microstructure evolution at small deformation rates A฀broad฀range฀of฀UFG฀microstructures฀can฀be฀seen฀in฀the฀images฀in฀Fig.฀7.6.฀At฀ γ ~ 2.1 and V0฀=฀13฀mm/s,฀the฀lowest฀strain฀and฀smallest฀deformation฀rate฀used,฀the฀ microstructure consists of cellular structures and elongated subgrains having broad, diffuse boundaries consisting of forest dislocations (point A in Fig. 7.6). Geometrically necessary boundaries (GNBs)41 are also seen to be forming, these indicated by arrows in the micrographs. At this SPD condition, the SAD pattern resembles more of a single-crystal type pattern that is indicative of substructures with very small misorientations. The hardness of this microstructure

7.7 Deformation-microstructure map for copper showing schematically, microstructures characteristic of the different SPD conditions. The dotted curves demarcate, roughly, regions with different microstructures. Average and variance of hardness for these microstructures are also provided.

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(~142 kg/mm2) is substantially greater than that of the bulk material. This suggests rapid initial hardening at low strains (Fig. 7.7). Indeed, this steep initial increase in฀ strength฀ for฀ copper฀ has฀ been฀ noted฀ in฀ ECAP,42฀ uniaxial฀ compression43 and machining.44 At a higher γ of ~5, the microstructure is composed of elongated subgrains฀with฀sharper฀boundaries฀(point฀C,฀Fig.฀7.6)฀and฀the฀distance฀between฀the฀ GNBs decreases from ~190 nm to ~170 nm. The SAD pattern also indicates an increase in misorientation between the dislocation substructures. Higher strains at V0฀=฀13฀mm/s฀give฀grain฀and฀subgrain฀structures฀with฀equiaxed฀morphology฀and฀ larger misorientations (points D and E, Fig. 7.6), the development of which likely involves฀continuous฀dynamic฀recrystallization45 at the relatively small deformation temperatures (T฀~฀40°C)฀characteristic฀of฀this฀set฀of฀SPD฀conditions.฀Furthermore,฀ the฀ equiaxed฀ structures฀ at฀ γ ~ 12 (point E) are somewhat larger (345 nm) than those at γ ~ 8 (270 nm, point D), This likely due to growth associated with increases in strain energy and somewhat higher deformation temperatures.1 This microstructure evolution with increasing strain at small deformation rates, including a switchover from elongated substructures to the highly misoriented equiaxed฀grain฀structures,฀is฀consistent฀with฀what฀has฀been฀demonstrated฀in฀SPD฀ of฀OFHC฀copper฀(99.95%)฀by฀machining.44 It is also consistent with multi-pass SPD฀of฀copper฀by฀ECAP.40,42 For these conditions, the hardness saturates at 150– 160 kg/mm2฀with฀small฀variations฀(CV฀~5%),฀see฀also฀Fig.฀7.7.1

7.3.2 Deformation twinning Next฀we฀consider฀the฀microstructures฀developed฀at฀low฀strains฀when฀the฀strain฀rate฀ is varied from about 102 s–1 to 105 s–1฀by฀examining฀a฀portion฀of฀the฀γ – V0 space along฀ a฀ horizontal฀ line฀ through฀ γ ~ 1.5 in Fig. 7.6. At the higher strain rates, deformation฀ twinning฀ is฀ prevalent,฀ characterized฀ by฀ a฀ dense฀ array฀ of฀ nanoscale฀ twins of width ~20 nm. The twinning was observed at both V0฀ =฀ 1.67฀ m/s฀ and฀ 4.4 m/s (points L and S in Fig. 7.6), corresponding to dε/dt of about 2 × 104 s–1 and 7 × 104 s–1, respectively. The overall microstructure at V0฀=฀1.67฀m/s฀is฀heterogeneous,฀ with some regions consisting of a high density of nanoscale twins and other regions exhibiting฀ low-misorientation฀ dislocation฀ substructures฀ interspersed฀ with฀ twins฀ (point L in Fig. 7.5 and 7.6). A similar dense array of nanoscale twins was observed at V0฀=฀4.4฀m/s.฀The฀twin฀density฀in฀this฀microstructure฀is฀somewhat฀lower,฀possibly฀ due฀to฀a฀higher฀deformation฀zone฀temperature฀that฀promoted฀dislocation฀slip฀at฀the฀ expense฀ of฀ twin฀ formation฀ (T฀ ~฀ 160°C,฀ Fig.฀ 7.5).฀ The฀ hardness฀ of฀ the฀ twinned฀ microstructures corresponding to points L and S is in the range of 120–140 kg/mm2 (Fig. 7.7). While this is lower than the peak hardness levels recorded in copper, it is not฀signiicantly฀different฀from฀that฀of฀the฀subgrain฀microstructures฀produced฀at฀the฀ same strain levels under the small deformation rate condition. Similar nanoscale twinning was observed in cryogenic SPD of copper, with the degree of twinning increasing with increasing strain rate. Figure 7.8 shows a cryoSPD microstructure at dε/dt ~ 103 s–1 and γ ~ 1.6 that is more homogeneous than

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7.8 Transmission electron microscopy images of the copper microstructure after cryo-SPD at γ ~ 1.6 and strain rate of ~103 s–1 showing dense nano-twinning.

that corresponding to points L and S in Fig. 7.6, with most of the grains showing signiicant฀nanoscale฀twinning฀and฀average฀twin฀widths฀of฀~20฀nm.฀The฀hardness฀ of this highly twinned microstructure is 175–200 kg/mm,2 substantially greater than that of the twinned structures of Fig. 7.6. Nano-twinned microstructures are of฀considerable฀interest฀since฀they฀exhibit฀Hall–Petch฀strengthening฀analogous฀to฀ conventional nanostructured materials while also maintaining appreciable ductility.46฀Furthermore,฀they฀have฀been฀found฀to฀exhibit฀unusual฀thermal฀stability฀ characteristics.47

7.3.3 Discontinuous dynamic recrystallization and bimodal microstructures The฀unique฀combination฀of฀deformation฀parameters฀realized฀in฀SPD฀by฀machining฀ enabled฀ characterization฀ of฀ the฀ onset฀ and฀ evolution฀ of฀ discontinuous฀ dynamic฀ recrystallization฀in฀copper.฀This฀can฀be฀seen฀in฀the฀microstructure฀evolution฀as฀a฀ function of γ at V0฀=฀1.67฀m/s฀(points฀L,฀M,฀N฀and฀O฀in฀Fig.฀7.6).฀In฀this฀strain฀rate฀ range of 104 s–1 to 105 s–1, the twinned microstructure gives way to an elongated subgrain structure with small misorientations (point M) at γ  ~ 5, followed by the onset฀of฀a฀discontinuous฀type฀of฀recrystallization฀at฀γ ~ 7 (T฀~฀200°C)฀at฀point฀N.฀ The deformation-induced heating is important, in conjunction with the strain, for facilitating฀this฀type฀of฀recrystallization.45 Indeed, further increase in strain and

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deformation฀ temperature฀ results฀ in฀ large฀ micron-sized฀ grains,฀ as฀ at฀ point฀ O฀ (Fig.฀7.6).฀Figure฀7.7฀shows฀that฀the฀onset฀and฀progression฀of฀dynamic฀recrystallization฀ is also accompanied by a dramatic loss in strength, with hardness values decreasing from about 140 kg/mm2 to 75 kg/mm2 at strains of 7 and higher. The deformation zone฀temperature฀corresponding฀to฀the฀onset฀of฀recrystallization฀is฀in฀the฀range฀of฀ 200–250°C฀(Fig.฀7.5),฀with฀the฀lower฀temperatures฀associated฀with฀larger฀strains. Dynamic฀recrystallization฀accompanying฀a฀similar฀evolution฀of฀microstructure฀ with strain was also observed at larger deformation rates, as in point Q in Fig. 7.6, at V0฀ =฀ 2.5฀ m/s.฀An฀ intriguing฀ feature฀ of฀ this฀ evolution฀ is฀ the฀ occurrence฀ of฀ a฀ bimodal฀(composite)฀type฀of฀microstructure,฀composed฀of฀ultraine฀subgrains฀and฀ micron-sized฀grains฀at฀ γ ~ 4. This microstructure has a hardness of 127 kg/mm2 with฀a฀large฀variation฀(CV฀~฀25%)฀compared฀to฀that฀of฀the฀other฀microstructures฀ (Fig.฀7.7).฀This฀large฀CV฀is฀consistent฀with฀a฀partially฀recrystallized฀microstructure฀ consisting of ‘hard’ and ‘soft’ regions. This was also evident in two distinct distributions฀of฀hardness฀with฀70%฀of฀the฀points฀centered฀at฀145฀kg/mm2 and the remainder distributed about 85 kg/mm.2 Similar large hardness variations were observed at other similar deformation conditions. Bimodal฀microstructures,฀composed฀of฀a฀mixture฀of฀ultraine฀and฀micron-sized฀ grains, are of interest as they have been observed to possess potentially attractive combinations of ductility and strength.48 The most interesting aspect of the current processing, however, is that this microstructure was engineered, in situ, during the SPD by using the intrinsic deformation-induced heating. The creation of bimodal UFG฀ microstructures,฀ to฀ date,฀ has฀ generally฀ involved฀ complex,฀ multi-stage฀ thermo-mechanical deformation processing routes.48,49

7.3.4 Fully recrystallized microstructures When฀ the฀ deformation฀ conditions฀ of฀ temperature฀ and฀ strain฀ exceed฀ threshold฀ levels,฀recrystallization฀of฀the฀copper฀is฀expected฀to฀occur฀in situ. These thresholds for฀complete฀dynamic฀recrystallization฀can฀be฀identiied฀from฀Fig.฀7.6฀and฀7.7.฀ The฀microstructure฀in฀this฀region฀is฀seen฀to฀be฀composed฀of฀a฀mixture฀of฀large฀and฀ small฀grains,฀several฀micrometers฀in฀size฀(Fig.฀7.9).฀As฀in฀the฀partially฀recrystallized฀ microstructure฀ of฀ point฀ Q,฀ annealing฀ twins฀ are฀ seen฀ in฀ fully฀ recrystallized฀ microstructures corresponding to points N and O (Fig. 7.6). The hardness values of these microstructures are ~75 kg/mm,2 similar to those of the copper in an annealed฀condition.฀For฀a฀given฀strain฀rate,฀the฀threshold฀strain฀for฀recrystallization฀ decreases with increasing deformation temperature (Fig. 7.6 and 7.7), typical of classical฀deformation-induced฀recrystallization.27

7.3.5 Homogeneity of microstructure Figure 7.10 shows OIM data for copper chips created at near-ambient deformation conditions39 for three different strains (γ ~ 3, 7 and 11). The inverse pole

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7.9 Optical micrograph corresponding to point R(V0 = 2.5 m/s, = 6.7) showing some large recrystallized grains (>50 µm) interspersed with smaller micrometer-sized grains.

7.10 Orientation imaging microscopy (OIM) analysis, including inverse pole figure (IPF) map, pole figure and misorientation distribution, for copper subjected to shear strain of (a) 3, (b) 7 and (c) 11 (based on Swaninathan et al.39).

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igure฀(IPF)฀map฀for฀a฀strain฀of฀3฀shows฀elongated฀grains฀containing฀dislocation฀ structures within as evident from the color changes within the grain (Fig. 7.10 (a)). The฀high-angle฀boundaries฀(>15°)฀are฀marked฀by฀black฀lines฀in฀the฀IPF฀map.฀The฀ pole฀igure฀shows฀the฀presence฀of฀rotated฀(from฀the฀initial฀material)฀cube฀texture฀ components,฀as฀well฀as฀two฀variants฀of฀the฀B-iber฀shear฀texture฀component.฀At฀ still larger strains, γ฀ ~฀ 7,฀ the฀ IPF฀ map฀ shows฀ presence฀ of฀ ultraine฀ elongated฀ structures฀ (Fig.฀ 7.10฀ (b)).฀ The฀ pole฀ igures฀ at฀ this฀ strain฀ show฀ continuous฀ distributions฀along฀A฀and฀B฀shear฀texture฀ibers฀and฀absence฀of฀any฀cube฀texture฀ components.39฀The฀IPF฀map฀at฀a฀strain฀level฀of฀11,฀however,฀shows฀only฀equiaxed฀ ultraine฀grains฀along฀with฀a฀well-developed฀shear฀texture฀containing฀B-iber฀and฀ the฀ C฀ component.฀ The฀ misorientation฀ distributions฀ show฀ an฀ increase฀ in฀ the฀ population of high-angle boundaries as the strain level increases. An OIM study of the deformation along three mutually orthogonal flow directions in the chip showed uniformity of microstructure throughout the chip volume.39 The development of such a homogeneous microstructure is consistent with a relatively uniform฀ deformation฀ ield฀ at฀ the฀ micro-scale,฀ as฀ conirmed฀ by฀ PIV 1,19,50 and evident฀in฀Fig.฀7.2.฀Inverse฀pole฀igure฀maps฀determined฀for฀each฀of฀the฀chip฀faces฀ using OIM (Fig. 7.10) show characteristic shear deformation components with nearly฀ homogeneous฀ texture฀ in฀ the฀ volume฀ of฀ the฀ chip.฀ These฀ observations฀ of฀ uniformity,฀ both฀ in฀ microstructure฀ and฀ texture,฀ throughout฀ the฀ chip฀ volume฀ are฀ particularly encouraging for production of bulk nanostructured alloys.

7.3.6 Deformation-microstructure map The interactive effects of strain, strain rate and temperature on microstructure development฀ could฀ be฀ extensively฀ explored฀ by฀ using฀ machining฀ to฀ probe฀ the฀ envelope of deformation conditions in Fig. 7.5, a range of conditions substantially more฀diverse฀than฀is฀achievable฀in฀ECAP,฀HPT฀or฀DPD.฀This฀has฀been฀done฀to฀ develop a deformation-microstructure map for copper.19 Figure 7.7 shows such a map฀ that฀ identiies฀ the฀ microstructures฀ observed฀ in฀ different฀ portions฀ of฀ deformation parameter space. Among other uses, this type of map can guide selection฀ and/or฀ optimization฀ of฀ SPD฀ conditions฀ to฀ realize฀ speciic฀ nanoscale฀ microstructures฀(e.g.฀nano-twinned,฀equiaxed,฀bimodal฀and฀combinations฀thereof).฀ Machining also can be used to develop similar maps for other metals and alloys, even฀alloys฀of฀higher฀strength฀that฀are฀dificult฀to฀deform฀to฀large฀plastic฀strains฀ over a range of deformation rates by conventional multi-pass SPD methods.

7.4

Bulk forms with ultrafine-grained (UFG) microstructure

Chip฀formation฀by฀machining,฀as฀demonstrated฀in฀the฀above฀results฀for฀Cu,฀offers฀ a means for producing nanostructured materials with controllable microstructures. While chips of macroscopic dimensions can be created by the unconstrained chip

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formation฀in฀machining,฀shape฀and฀size฀control฀of฀the฀chips฀would฀be฀advantageous฀ and could complement the microstructure control earlier demonstrated. It is in this regard that the constrained chip formation process – LSEM (see Section 7.2.5) – offers capability for applying controlled SPD in the production of geometrically deined฀bulk฀forms,฀including฀sheet,฀foil฀and฀wire.34 LSEM฀ has฀ been฀ implemented฀ in฀ a฀ rotary฀ coniguration฀ for฀ production฀ of฀ continuous foil34฀and฀in฀a฀linear฀coniguration฀for฀production฀of฀sheet.1 The linear coniguration฀enables฀manufacture฀of฀larger-sized฀samples฀due฀to฀the฀increased฀ load฀capacity฀of฀the฀press฀equipment฀used฀in฀this฀coniguration.฀Additionally,฀a฀ non-plane–strain฀ rotary฀ coniguration฀ has฀ been฀ used฀ to฀ produce฀ nanostructured฀ samples฀in฀wire฀and฀rod฀forms.฀Figure฀7.11฀shows฀examples฀of฀sheet,฀rod฀and฀foil฀ created by LSEM in a diverse set of material systems, including pure metals (Ta, Ti฀and฀Cu)฀and฀alloys฀(e.g.฀Al฀6061-T6)฀with฀a฀range฀of฀properties฀in฀terms฀of฀ workability and strength. The microstructure of several of these metal and alloy samples are shown in Fig. 7.12 and 7.13, with the Inconel 718, Ti and Al 6061-T6 composed of sub-100 nm grains at higher strains. All of these samples have substantially higher hardness than the corresponding microcrystalline bulk material,51,52 a consequence of the nanoscale microstructure. Figure 7.14 shows the hardness values for the initial microcrystalline bulk alloy and the nanostructured chips. The microstructure in each case is determined by the interactive effects of strain, strain rate and temperature, as illustrated in the SPD results for copper earlier. In the steels,฀ the฀ reinement฀ is฀ relected฀ in฀ the฀ reduction฀ of฀ interlamellar฀ spacing฀ of฀

7.11 Bulk forms produced by LSEM using a linear press configuration (left) and a rotary lathe configuration (right).

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7.12 Bright-field TEM micrographs of chips cut from (a) commercially pure Ti, γ ~ 3, grain size: 80 nm, (b) 52100 steel with equi-axed nanoscale ferrite grains [330 nm] and dispersed carbide particles, (c) Al 6061-T6, γ ~ 3, grain size: 200 nm and (d) Inconel 718, γ ~ 8, grain size: 120 nm.

7.13 (a) An optical micrograph of bulk 1080 steel showing a coarse pearlite microstructure; (b) microstructure of 1080 steel chip with occurrence of two distinct pearlitic ensembles – refined pearlite and broken pearlite, as a result of the SPD by machining (based on Shankar et al.53).

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7.14 Bar chart showing increases in hardness for a variety of material systems after deformation by machining.

pearlite, including break-up of the cementite at large strains (Fig. 7.13).53 Through single-pass machining-SPD of eutectoid (1080) steel, it has been possible to reproduce the microstructure evolution as a function of strain (up to shear strain of ~6.5) achieved through incremental SPD, as in the pioneering drawing experiments฀of฀Embury฀and฀Fisher฀to฀shear฀strains฀of฀~7.2 The machining route has also demonstrated the creation of precipitation-treatable alloys (Ni-based alloys, Al 6061) with enhanced strength, thermal stability and ageing kinetics. This was achieved by combining SPD of these alloys in the solution-treated and homogenized฀condition,฀followed฀by฀suitable฀thermal฀treatments.17,54 These early results demonstrate the capability to produce bulk forms with nanoscale microstructure in material systems of commercial interest using LSEM. Furthermore, the transformation of an ‘undeformed chip’ of rectangular crosssection into a rod of circular cross-section, as is the case in the rod and wire, indeed shows that large shape transformations can be achieved by LSEM, a likely consequence of the unique (controllable) thermo-mechanical conditions prevailing in฀the฀deformation฀zone.฀Optimization฀of฀microstructure฀for฀speciic฀performance฀ characteristics (e.g. strength, ductility, thermal stability) once completed, will provide฀ the฀ basis฀ for฀ setting฀ the฀ LSEM฀ parameters฀ needed฀ to฀ attain฀ speciic฀ nanoscale microstructures in these bulk forms. These nanocrystalline bulk forms can be used as precursor materials for structural components with enhanced strength and wear resistance. Micro- or macro-manufacturing processes such as EDM, laser machining, punching and stamping, micro-turning and micro-milling55 can be used to ‘cut out’ components from the bulk forms for these components. Figure 7.15 shows a set of small gears for a micro-power system produced from one of the nanostructured Inconel 718 foils using micro-EDM.51 This approach to making micro-scale components from

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7.15 A pair of micro-scale gears created from nanostructured Inconel 718 foil using micro-EDM (Agie AC Vertex 2F). The foil was produced by LSEM with λ = 3.5, γ ~ 4, V0 = 0.5 m/s (based on Saldana et al.51).

nanostructured alloys is quite versatile as it can be applied to manufacture microelectromechanical system (MEMS) components from functional materials, including those suited to withstand severe operating environments.

7.5

Nanostructured particulate

The chip formation process may be scaled down to produce particulate of controlled฀ geometry฀ with฀ ultraine-grained฀ (UFG)฀ microstructures.฀ Potential฀ applications for such materials include reinforcements in structural composites and precursors for powder metallurgy components. These metal particulates are currently produced by a range of processes that imparts characteristic morphology and microstructure to the particles.56฀These฀processes฀generally฀yield฀broad฀size฀ distributions฀ that฀ require฀ classiication.฀ Furthermore,฀ particle฀ morphology฀ and฀ microstructure฀ are฀ highly฀ process-dependent.฀ For฀ example,฀ the฀ evolution฀ of฀ particle฀size,฀shape฀and฀microstructure฀in฀high-energy฀milling฀is฀a฀consequence฀ of several factors including, milling media, initial charge characteristics, environmental conditions and milling time.57 The milling process is also limited by฀ the฀ contamination฀ associated฀ with฀ the฀ high฀ surface฀ area฀ exposed฀ during฀ repetitive฀comminution฀steps฀and฀limited฀control฀of฀the฀particle/agglomerate฀size. Particulate metals also can be produced through a variant of the machining process – modulation-assisted machining (MAM) – that superimposes a lowfrequency฀ modulation฀ ( 5) and decay with depth into the sub-surface.1 Similar inferences pertaining฀to฀the฀strain฀ield฀have฀come฀from฀metallography,฀grid฀deformation13 and electron microscopy.67฀As฀such,฀a฀ine-scale฀microstructure฀may฀be฀expected฀ on฀the฀machined฀surface.฀Indeed,฀UFG฀microstructures฀have฀been฀observed฀on฀ surfaces created by a number of different material removal processes.15 For example,฀copper฀surfaces฀created฀by฀abrasive฀machining฀have฀been฀shown฀to฀be฀ comprised฀of฀equiaxed฀grains,฀~30฀nm,฀with฀an฀orientation฀texture฀similar฀to฀that฀ of rolling.68 A microstructure consisting of ~100 nm grains has also been observed on hard steel surfaces generated under select machining conditions.69–72 These UFG฀ microstructures฀ are฀ analogous฀ to฀ those฀ found฀ in฀ sliding,73 rolling,74 mechanical attrition,75 and HPT. While the occurrence of such features on machined฀surfaces฀has฀long฀been฀recognized,฀what฀has฀not฀been฀explored฀is฀the฀ possibility฀of฀systematically฀engineering฀speciic฀microstructures฀in฀the฀surface.฀ For machining, this concept is based on the close correspondence between the deformation histories of the material evolving into the machined surface and that of the chip.66,76 To demonstrate nanostructuring of surfaces by controlled machining SPD, oxygen-free฀high฀conductivity฀(OFHC)฀copper฀(99.95%,฀Goodfellow)฀and฀brass฀ (70%฀Cu–30%฀Zn)฀samples฀were฀machined฀at฀near-ambient฀temperature฀and฀at฀ –196°C฀under฀plane-strain฀conditions฀using฀a฀sharp,฀high-speed฀steel฀tool.1,66 The samples฀were฀sheets,฀3฀mm฀in฀width,฀with฀initial฀grain฀sizes฀of฀35฀µm฀(Cu)฀and฀ 200฀µm฀(brass),฀and฀Vickers฀hardness฀of฀77฀±฀3฀kg/mm2฀(Cu)฀and฀80฀±฀5฀kg/mm2 (brass). An undeformed chip thickness of 100 µm to 200 µm and machining speeds฀of฀up฀to฀500฀mm/s฀were฀used.฀The฀strain฀imposed฀in฀the฀deformation฀zone฀ was฀varied฀by฀using฀tool฀rake฀angles฀of฀–30°฀to฀+50°. Figure 7.20 shows PIV measurements of strain with depth from the machined surface for brass and copper. The strain values at the surface were estimated as ~5 (+20°฀rake)฀in฀the฀Cu฀and฀~3฀(+10°฀rake)฀and฀~10฀(–30°฀rake)฀in฀the฀brass.฀The฀ strains in the corresponding chips were determined by PIV and are shown by points฀A,฀B฀and฀C.1,47,66 The close correspondence between the chip and surface strains is not surprising, given that the material constituting the bulk of the chip and฀ the฀ machined฀ surface฀ experience฀ similar฀ deformation฀ history.฀ Similar฀ arguments may be made using analysis of particle trajectories in grid deformation experiments.13,67 Further evidence for the similarity between the deformation levels on the machined surface and chip comes from the hardness data for copper presented.66 The hardness of the machined surface is substantially greater than that฀of฀the฀bulk฀material฀prior฀to฀machining฀(dotted฀line฀in฀the฀igure).฀Furthermore,฀ the hardness values at the surface and of the corresponding chip are essentially the same for different machining conditions. This equivalence is especially striking at

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7.20 Variation of strain with depth from the machined surface in copper and brass. The dotted curves are extrapolations used to estimate the strains at the surface. The strain values in the chip are marked as A (brass, +10° rake), B (copper, +20° rake) and C (brass, –30° rake). Inset shows TEM pictures of a microstructure on the machined surface and of a chip created under a similar deformation condition (γ ~ 8). Both of these microstructures are seen to be very similar, highlighting the equivalence between chip and surface microstructures for the same process conditions.

some of the more special deformation conditions, such as in the cryo-SPD and machining฀with฀a฀+50°฀rake฀angle฀tool.฀The฀cryo-SPD฀condition฀shows฀very฀high฀ hardness values (~180 kg/mm2) for both the chip and machined surface, undoubtedly฀a฀consequence฀of฀the฀enhanced฀reinement฀occurring฀in฀both฀of฀these฀ regions฀at฀this฀condition.฀When฀machining฀with฀the฀+50°฀rake฀angle฀tool฀at฀nearambient temperature, the deformation strain is much smaller (γ ~ 1) than with the –10°฀rake฀tool฀(γ฀~฀8),฀resulting฀in฀smaller฀levels฀of฀microstructure฀reinement฀on฀ the machined surface and in the chip.1 The inset TEM images in Fig. 7.20 also show a high degree of similarity between the chip and near-surface microstructures, in฀this฀case฀equiaxed฀UFG฀microstructures฀with฀grain฀size฀of฀~200฀nm,฀relective฀ of essentially identical deformation histories. Electron Backscatter Diffraction (EBSD)฀of฀the฀material฀on฀the฀work฀surface฀and฀deformation฀zone฀also฀supports฀ this microstructure equivalence.18,66

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The basis for controlling microstructure and mechanical properties of surfaces created by machining is provided by the close correspondence between the strains on the machined surface and chip. The SPD parameters can be reasonably estimated using the shear plane model described in Section 7.2, enabling correlation with the controllable machining variables of cutting speed, rake angle and chip thickness ratio. Taken together with a deformation-microstructure map, such as that outlined for copper in Fig. 7.7, the controllable machining variables may฀be฀tuned฀to฀set฀appropriate฀SPD฀conditions฀for฀generating฀speciic฀surface฀ microstructures.

7.7

Conclusions

The deformation that occurs during chip formation can be controlled, in situ, to access a wide range of strains, strain rates and temperatures. This is used in the present study to demonstrate the creation of a variety of nanoscale microstructures in฀the฀chip฀including฀equiaxed,฀bimodal฀and฀nano-twinned฀structures.฀A฀map฀is฀ outlined for SPD of copper that describes the interactive effects of strain, strain rate and temperature on microstructure. This type of map is may be used to optimize฀process฀parameters฀to฀engineer฀materials฀with฀interesting฀combinations฀ of฀ microstructure,฀ texture฀ and฀ mechanical฀ properties.฀ By฀ adding฀ dimensional฀ control to the chip formation process through LSEM, bulk forms such as foil, sheet฀ and฀ rod฀ are฀ produced฀ with฀ controllable฀ nanocrystalline฀ and฀ UFG฀ microstructures. A newly developed chip formation process, modulation-assisted machining (MAM), enables the production of nanostructured particulate with controlled฀ particle฀ shapes฀ (e.g.฀ iber,฀ equiaxed฀ and฀ platelet).฀ Large-scale฀ manufacturing of nanomaterials by LSEM and MAM in structural alloy systems of฀interest฀is฀currently฀being฀explored.฀Lastly,฀the฀SPD฀conditions฀prevailing฀in฀ the฀ deformation฀ zone฀ are฀ shown฀ to฀ determine฀ the฀ deformation฀ history฀ of฀ the฀ machined surface and, consequently, also the microstructure. This suggests that machining฀can฀also฀be฀used฀to฀engineer฀surfaces฀with฀speciic฀micro-฀and฀nanoscale฀ structures. The uses of machining for materials manufacturing represent deformation processing applications of this class of processes. While these applications are diverse, they are united by their foundation in the SPD phenomena that prevails in฀ the฀ deformation฀ zone฀ during฀ chip฀ formation.฀ Furthermore,฀ these฀ newer฀ applications likely are subject to processing constraints similar to those of component manufacture, including those related to tool wear, workability of materials and equipment capability.

7.8

Acknowledgements

This฀work฀was฀supported฀in฀part฀by฀NSF฀grants฀CMMI-0626047฀and฀CMMI0800481;฀the฀Oak฀Ridge฀National฀Laboratory;฀the฀U.S.฀Department฀of฀Energy’s฀

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FreedomCAR฀ Program฀ via฀ Paciic฀ Northwest฀ National฀ Laboratories฀ contract฀ DE-AC06–76RL01830;฀ and฀ a฀ Ford฀ University฀ Research฀ Program฀ award฀ all฀ to฀ Purdue฀ University;฀ NSF฀ grants฀ STTR-0944980฀ and฀ SBIR-0822879฀ to฀ M4฀ Sciences฀LLC;฀and฀an฀NSF฀Graduate฀Research฀Fellowship฀to฀CS.฀Microscopy฀ work at the Oak Ridge National Laboratory’s High Temperature Materials Laboratory฀ was฀ sponsored฀ by฀ the฀ US฀ Department฀ of฀ Energy,฀ Ofice฀ of฀ Energy฀ Eficiency฀and฀Renewable฀Energy,฀Vehicle฀Technologies฀Program.฀We฀are฀grateful฀ to Dr Larry Allard of Oak Ridge for assistance with some of the transmission electron฀ microscopy.฀ Drs฀ S.฀ Lee,฀ B.C.฀ Rao฀ (IIT฀ Madras,฀ India),฀ and฀ M.฀ Ravi฀ Shankar฀(University฀of฀Pittsburgh,฀Pittsburgh,฀USA);฀and฀T.L.฀Brown฀and฀Y.฀Guo฀ (Purdue฀ University)฀ are฀ acknowledged฀ for฀ their฀ contributions฀ to฀ some฀ of฀ the฀ results reported herein. We also appreciate the support of Professor Terry R. McNelley,฀Naval฀Postgraduate฀School,฀Monterrey,฀CA,฀with฀the฀OIM฀analysis.

7.9

References

฀ 1฀ Brown฀T.L.,฀Saldana฀C.,฀Murthy฀T.G.,฀Mann฀J.B.,฀Compton฀W.D.,฀Trumble฀K.P.,฀King฀ A.H.,฀and฀Chandrasekar฀S.฀Acta฀Mater,฀2009;฀57:5491. ฀ 2฀ Embury฀J.D.,฀Fisher฀R.M.฀Acta฀Metall฀1966;฀14:147. ฀ 3฀ Langford฀G.,฀Cohen฀M.฀Trans฀ASME฀1969;฀62:623. ฀ 4฀ Segal฀V.M.,฀Reznikov฀V.I.,฀Drobyshevskiy฀A.E.,฀Kopylov฀V.฀Rus฀Metall฀1981;฀1:99. ฀ 5฀ Valiev฀R.Z.,฀Islamgaliev฀R.K.,฀Alexandrov฀I.V.฀Prog฀Mater฀Sci฀2000;฀45:103. ฀ 6฀ Brown฀T.L.,฀ Swaminathan฀ S.,฀ Chandrasekar฀ S.,฀ Compton฀W.D.,฀Trumble฀ K.P.,฀ King฀ A.H.฀J฀Mater฀Res฀2002;฀17:2484. ฀ 7฀ Swaminathan฀ S.,฀ Shankar฀ M.R.,฀ Lee฀ S.,฀ Hwang฀ J.,฀ King฀A.H.,฀ Kezar฀ R.,฀ Rao฀ B.C.,฀ Brown฀ T.L.,฀ Chandrasekar฀ S.,฀ Compton฀ W.D.,฀ Trumble฀ K.P.฀ Mat฀ Sci฀ Eng฀ A฀ 2005;฀ 410:358. ฀ 8฀ Shaw฀M.C.฀Metal฀cutting฀principles.฀Oxford฀University฀Press,฀New฀York,฀1984. ฀ 9฀ Gnanamanickam฀E.P.,฀Lee฀S.,฀Sullivan฀J.P.,฀Chandrasekar฀S.฀Proceedings฀of฀the฀Society฀ for฀Experimental฀Mechanics฀Annual฀Conference฀and฀Exposition฀on฀Experimental฀and฀ Applied฀Mechanics฀2007;฀1080. 10฀ Lee฀S.,฀Hwang฀J.,฀Shankar฀M.R.,฀Chandrasekar฀S.,฀Compton฀W.D.฀Metall฀Mater฀Trans฀ A฀2006;฀37:1633. 11฀ Thomsen฀ E.G.฀Yang฀ C.T.,฀ Kobayashi฀ S.฀ Mechanics฀ of฀ plastic฀ deformation฀ in฀ metal฀ processing. Macmillan, 1965. 12฀ Keciouglu฀D.฀Trans฀ASME฀1958;฀80:158. 13฀ Oxley฀P.L.B.฀Mechanics฀of฀machining.฀Ellis฀Horwood,฀New฀York,฀1989. 14฀ Oxley฀P.L.B.,฀Hastings฀W.F.฀Proc฀R฀Soc฀Lond฀A฀1977;฀356:395. 15 Samuels L.E. Metallographic polishing by mechanical methods (4th ed). American Society for Materials International, 2003. 16฀ Sevier฀M.,฀Yang฀H.T.Y.,฀Lee฀S.,฀Chandrasekar฀S.฀Metall฀Mater฀Trans฀B฀2007;฀38:927. 17฀ Shankar฀M.R.,฀Chandrasekar฀S.,฀King฀A.H.,฀Compton฀W.D.฀Acta฀Mater฀2005;฀53:4781. 18฀ M’Saoubi฀R.฀and฀Ryde฀L.฀Mat฀Sci฀Eng฀A฀2005;฀405:339. 19฀ Saldana฀C.,฀Swaminathan฀S.,฀Brown฀T.L.,฀Mann฀J.B.,฀Compton฀W.D.฀and฀Chandrasekar฀ S.฀ASME฀J฀Mfg฀Sci฀Eng฀2010;฀132:030908. 20฀ Lee฀S.฀Ph.D฀thesis,฀Purdue฀University,฀2006.฀See฀also฀Chandrasekar฀S.฀and฀Trumble฀ K.P.,฀ In฀ situ฀ characterization฀ of฀ large฀ strain฀ deformation฀ ield฀ in฀ severe฀ plastic฀

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deformation,฀presentation฀at฀Ultraine฀Grained฀Materials฀(UFG)฀2006,฀Kloster฀Irsee,฀ Germany, September 24–26, 2006. 21฀ Boothroyd฀G.฀Proc฀I฀Mech฀E฀1963;฀177:789. 22฀ Weiner฀J.H.฀Trans฀ASME฀1955;฀77:1331. 23฀ Hwang฀J.,฀Kompella฀S.,฀Chandrasekar฀S.,฀Farris฀T.N.฀ASME฀J฀Trib฀2003;฀125:377. 24฀ Narayanan฀V.,฀Krishnamurthy฀K.,฀Hwang฀J.,฀Chandrasekar฀S.,฀T.N.฀Farris,฀Madhavan฀ V.฀Measurement฀of฀Temperature฀Field฀at฀the฀Tool–Chip฀Interface฀in฀Machining,฀NSF฀ Workshop on Research Needs in Thermal Aspects of Material Removal Advanced Technology฀Research฀Center,฀Oklahoma฀State฀University,฀June฀10–12,฀2003. 25฀ Davies฀M.A.,฀Ueda฀T.,฀M’Saoubi฀R.,฀Mullany฀B.,฀Cooke฀A.L.฀CIRP฀Ann฀2007;฀56:581. 26฀ Zener฀C.,฀Hollomon฀J.H.฀J฀Appl฀Phys฀1944;฀15:22. 27 Backofen W.A. Deformation processing. Addison-Wesley, 1972. 28฀ Christian฀J.W.,฀Mahajan฀S.฀Prog฀Mater฀Sci฀1995;฀39:1. 29฀ Li฀Y.S.,฀Zhang฀Y.,฀Tao฀N.R.,฀Lu฀K.฀Acta฀Mater฀2009;฀57:761. 30฀ Saldana฀C.,฀Shankar฀M.R.,฀Murthy฀T.G.,฀Huang฀C.,฀Gnanamanickam฀E.,฀Chandrasekar฀ S.฀Proceedings฀of฀the฀11th฀CIRP฀conference฀on฀Modeling฀of฀Machining฀Operations,฀ NIST, 2008. 31฀ Dautzenberg฀J.H.,฀Zaat฀J.H.฀Wear฀1973;฀23:9. 32฀ Townend฀G.H.฀J฀Appl฀Phys฀1947;฀18:784. 33฀ De฀Chiffre฀L.฀Int฀J฀Mac฀Tool฀Des฀Res฀1976;฀16:137. 34฀ Moscoso฀W.,฀Shankar฀M.R.,฀Mann฀J.B.,฀Compton฀W.D.,฀Chandrasekar฀S.฀J฀Mater฀Res฀ 2007;฀22:201. 35฀ Valiev฀R.Z.฀and฀Langdon฀T.G.฀Prog฀Mater฀Sci฀2006;฀51:881. 36฀ Drucker฀D.C.฀J฀Appl฀Phys฀1949;฀20:1013. 37฀ Maekawa,฀ K.,฀ Obikawa,฀ T.,฀ Yamane,฀ Y.,฀ Childs,฀ T.H.C.,฀ 2000,฀ Metal฀ Machining:฀ Theory฀and฀Applications.฀Butterworth-Heinemann,฀UK. 38฀ Adibi-Sedeh฀A.H.,฀Madhavan฀V.฀and฀Bahr฀B.J.฀ASME฀J฀Mfg฀Sci฀Eng฀2003;฀125:656. 39฀ Swaminathan฀ S.,฀ Brown฀ T.L.,฀ Chandrasekar฀ S.,฀ McNelley฀ T.R.฀ and฀ Compton฀ W.D.฀ Scrip฀Mater฀2007;฀56:1047. 40฀ Mishra฀A.,฀Kad฀B.K.,฀Gregoric฀F.,฀Meyer฀M.A.฀Acta฀Mater฀2007;฀55:13. 41฀ Hughes฀D.A.,฀Hansen฀N.,฀Bamman฀D.J.฀Scrip฀Mater฀2003;฀48:147. 42฀ Torre฀F.D.,฀Lapovok฀R.,฀Sandlin฀J.,฀Thomson฀P.F.,฀Davies฀C.H.J.,฀Pereloma฀E.V.฀Acta฀ Mater฀2004;฀52:4819. 43฀ Steeds฀J.W.฀Proc฀R฀Soc฀Lond฀A฀1966;฀292:343. 44฀ Swaminathan฀ S.,฀ Shankar฀ M.R.,฀ Rao฀ B.C.,฀ Compton฀ W.D.,฀ Chandrasekar฀ S.,฀ King฀ A.H.,฀Trumble฀K.P.฀J฀Mater฀Sci฀2007;฀42:1529. 45฀ Humphreys฀ F.J.,฀ Hatherly฀ M.฀ Recrystallization฀ and฀ related฀ annealing฀ phenomena฀ (2nd฀ed).฀Elsevier,฀Oxford,฀2004. 46฀ Lu฀L.,฀Shen฀Y.F.,฀Chen฀X.H.,฀Qian฀L.H.฀and฀Lu฀K.฀Science฀2004;฀304:422. 47฀ Saldana฀C.,฀Murthy฀T.G.,฀Shankar฀M.R.,฀Stach฀E.A.,฀Chandrasekar฀S.฀Appl฀Phys฀Lett฀ 2009;฀94:021910. 48฀ Wang฀Y.M.,฀Ma฀E.฀Acta฀Mater฀2004;฀52:1699. 49฀ Wang฀Y.M.,฀Chen฀M.,฀Zhou฀F.,฀Ma฀E.฀Nature฀2002;฀419:912. 50฀ Gnanamanickam฀E.P.,฀Lee฀S.,฀Sullivan฀J.P.฀and฀Chandrasekar฀S.,฀Meas฀Sci฀Tech฀2009;฀ 20:095710. 51฀ Saldana฀C.,฀Yang฀P.,฀Mann฀J.B.,฀Moscoso฀W.,฀Gill฀D.D.,฀Chandrasekar฀S.฀and฀Trumble฀ K.P.฀Mat฀Sci฀Eng฀A฀2009;฀503:172. 52฀ Swaminathan฀S.,฀Shankar฀M.R.,฀Rao฀B.C.,฀Compton฀W.D.,฀Chandrasekar฀S.,฀King฀A.H.฀ and฀Trumble฀K.P.฀J฀Mater฀Sci฀2007;฀42:1529.

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53฀ Shankar฀M.R.,฀Verma฀R.,฀Rao฀B.C.,฀Chandrasekar฀S.,฀Compton฀W.D.,฀King฀A.H.฀and฀ Trumble฀K.P.฀Metall฀Mater฀Trans฀A฀2007;฀38:1899. 54฀ Shankar฀M.R.,฀Rao฀B.C.,฀Chandrasekar฀S.,฀Compton฀W.D.฀and฀King฀A.H.฀Scrip฀Mater฀ 2008;฀58:675. 55฀ Rajurkar฀K.P.,฀Levy฀G.,฀Malshe฀A.,฀Sundaram฀M.M.,฀McGeough฀J.,฀Hu฀X.,฀Resnick฀R.฀ and฀DeSilva฀A.,฀CIRP฀Ann฀2006;฀55:643. 56 Lenel F.V. Powder Metallurgy: Principles and Applications, Metal Powder Industries Federation,฀Princeton,฀NJ,฀1980. 57฀ Witkin฀D.B.฀and฀Lavernia฀E.J.,฀Prog฀Mater฀Sci฀2006;฀51:1. 58฀ Mann฀J.B.,฀Shankar฀M.R.,฀Chandrasekar฀S.,฀Compton฀W.D.฀and฀Moscoso฀W,฀Machining฀ Method฀to฀Controllably฀Produce฀Chips฀with฀Determinable฀Shapes฀and฀Sizes,฀US฀Patent฀ 7,628,099,฀ December฀ 8,฀ 2009.฀ See฀ also฀ Mann฀ J.B.,฀ Chandrasekar฀ S.฀ and฀ Compton฀ W.D.,฀ Tool-Holder฀ Assembly฀ and฀ Method฀ for฀ Modulation-Assisted฀ Machining,฀ US฀ Patent 7,587,965, September 15, 2009. 59฀ Toews฀H.G.,฀Compton฀W.D.฀and฀Chandrasekar฀S.,฀Prec฀Engg฀1998;฀22:1–9. 60฀ Chhabra฀P.N,฀Ackroyd฀B.,฀Compton฀W.D.,฀Chandrasekar฀S.฀Proc฀Inst฀Mech฀Engrs฀B฀ 2002;฀216:321. 61฀ Mann฀J.B.,฀Saldana฀C.,฀Chandrasekar฀S.,฀Compton฀W.D.฀and฀Trumble฀K.P.฀Scrip฀Mater฀ 2007;฀57:909. 62 Lenel, F.V. Powder Metallurgy Principles and Applications, Metal Powder Industries Federation,฀Princeton,฀NJ,฀1980. 63฀ Sanders,฀ P.G.,฀ Fougere,฀ G.E.,฀ Thompson,฀ L.J.,฀ Eastman,฀ J.A.฀ and฀ Weertman,฀ J.R.฀ Improvements in the synthesis and compaction of nanocrystalline materials. Nanostruct Mater฀1997;฀8:3,฀243–252. 64฀ Roberts,฀P.R.฀and฀Ferguson,฀B.I.฀Extrusion฀of฀Metal฀Powders,฀Inter฀Mater฀Rev฀1991฀ 36:2, 62–79. 65฀ Clyne,฀T.W.฀and฀Withers,฀P.J.฀An฀Introduction฀to฀Metal–Matrix฀Composites,฀Cambridge,฀ 1995. 66฀ Calistes฀ R.,฀ Swaminathan฀ S.,฀ Murthy฀ T.G.,฀ Huang฀ C.,฀ Saldana฀ C.,฀ Shankar฀ M.R.,฀ Chandrasekar.฀S.฀Scripta฀Mater฀2009;฀60:17. 67฀ Ramalingam฀S.,฀1967,฀Plastic฀Deformation฀in฀Metal฀Cutting,฀Ph.D.฀Thesis,฀University฀ of Illinois. 68฀ Turley฀D.M.,฀Samuels฀L.E.฀Metallog฀1981;฀14:275. 69฀ Rogers฀H.C.฀Ann฀Rev฀Mater฀Sci฀1979;฀9:283. 70฀ Matsumoto฀Y.,฀Barash฀M.M.฀and฀Liu฀C.R.฀J฀Eng฀Indus฀1986;฀108:169. 71฀ Akcan฀S.,฀Shah฀S.,฀Moylan฀S.P.,฀Chhabra฀P.N.,฀Chandrasekar฀S.฀and฀Yang฀H.T.Y.฀Metall฀ Mater฀Trans฀A฀2002;฀33:1245. 72 Ramesh A., Melkote S.N., Allard L.F., Riester L. and Watkins T.R. Mat Sci Eng A 2005;฀390:88. 73฀ Rigney฀D.A.฀Wear฀2000;฀245:1. 74฀ Hughes฀D.A.,฀Chrzan฀D.C.,฀Liu฀Q.,฀Hansen฀N.฀Phys฀Rev฀Lett฀1998;฀81:4664. 75฀ Zhu฀K.Y.,฀Vassel฀A.,฀Brisset฀F.,฀Lu฀K.,฀Lu฀J.฀Acta฀Mater฀2004;฀52:4101. 76฀ Mann฀J.B.,฀Saldana฀C.,฀Moscoso฀W.,฀Murthy฀T.G.,฀Huang฀C.,฀Swaminathan฀S.,฀Rao฀ B.C.,฀ Shankar฀ M.R.,฀ Compton฀W.D.,฀Trumble฀ K.P.,฀ Chandrasekar฀ S.฀ 2008,฀ Unusual฀ Applications฀ of฀ Machining,฀ Proc฀ 23rd฀All฀ India฀ Int฀ Ind฀ Manf฀ Tech฀ Des฀ Res฀ Conf,฀ pp. 47–55.

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8 Deformation structures including twins in nanograined pure metals K.฀HATTAR,฀Sandia฀National฀Laboratories,฀USA

Abstract: This chapter discusses deformation structures observed in nanograined metals and the proposed formation mechanisms associated with each฀defect฀structure.฀This฀review฀is฀limited฀to฀experimental฀observations฀in฀ pure metals and predominately to transmission electron microscopy studies due to the length scale of interest. The defect structures that have been observed and will be discussed include: perfect and partial dislocation structures, twins, dislocation฀loops,฀disclinations,฀and฀other฀unexpected฀defect฀structures.฀Several฀ of these defects are not observed or are not present at equivalent densities in coarse-grained metals, suggesting the activation of alternative deformation mechanisms.฀These฀effects฀will฀be฀highlighted฀by฀a฀few฀key฀experiments.฀ Theory฀and฀modeling฀will฀be฀used฀to฀aid฀the฀interpretation฀of฀the฀experimental฀ results, particularly in cases in which time-resolved results at the appropriate spatial resolution are not available. Key words: deformation structures, transmission electron microscopy (TEM), deformation mechanisms.

8.1

Introduction

8.1.1 Nanograined defects in historical perspective Despite the fact that mechanical deformation and metallurgy date back to antiquity, the study of deformation defect structures in metals began in the 1930s when Orowan, Taylor, and Polanyi proposed the concept of edge dislocations. Since that฀ discovery,฀ extensive฀ research฀ along฀ with฀ new฀ experimental฀ and฀ modeling฀ tools has resulted in the discovery of a multitude of deformation defects in metals. Great฀advances฀in฀the฀discovery฀and฀characterization฀of฀defect฀structures฀in฀metals฀ resulted from the introduction of the transmission electron microscope (TEM), which permitted direct observation of these defects and their interactions with each฀other.฀The฀type,฀size,฀and฀density฀of฀the฀defect฀structures฀found฀in฀structural฀ metals, which vary from nearly perfect single crystals to severely plastically deformed structures, are a result of the materials processing history and composition. In this chapter, we will discuss the defect structures observed in high purity nanograined฀metals฀that฀are฀1–100฀nm฀in฀grain฀size฀and฀produced฀by฀a฀variety฀of฀ methods. Most of the observations will be limited to a variety of TEM characterization฀techniques฀due฀to฀the฀resolution฀needed฀for฀the฀characterization฀ of nanoscale defects in nanograined metals. Real-time TEM observations of the 213 © Woodhead Publishing Limited, 2011

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deformation dynamics will be referenced heavily, as they often provide the greatest insight into the formation and destruction of the deformation structures. This฀chapter฀will฀begin฀with฀a฀characterization฀of฀the฀classical฀defect฀structures฀ observed in nanograined metals including: grain boundaries, twins, and dislocations.฀Classical฀deformation฀structures,฀which฀are฀absent฀from฀nanograined฀ metals such as dislocation networks, cell structures, and pile-ups, will be discussed next.฀The฀third฀main฀topic฀to฀be฀discussed฀is฀the฀unique฀defect฀structures฀that฀have฀ been reported in nanograined metals, but are uncommon in coarse-grained metals. These฀ uncommon฀ defects฀ include฀ ive-fold฀ twin฀ formations,฀ disclinations,฀ and฀ agglomerated grains. The effect of initial microstructure on the active deformation mechanisms฀and฀the฀resulting฀deformation฀defect฀structure฀will฀be฀emphasized.฀ Finally, the chapter will end with a brief description of the potential future trends in฀the฀ield฀and฀suggested฀literature฀for฀the฀reader฀with฀further฀interest฀in฀this฀area.

8.1.2 Short review of well established structures Before discussing the defect structures in nanograined metals, a basic understanding of the common defect structures present in coarse-grained metallic structures is necessary.฀ The฀ defect฀ structures฀ present฀ in฀ metals฀ can฀ be฀ deined฀ by฀ either฀ their฀ dimensionality or the process by which they were introduced into the crystal structure.฀ Using฀ a฀ bubble฀ raft฀ model,฀ Table฀ 8.1฀ illustrates฀ the฀ classical฀ defects฀ commonly found in metal systems based on their dimensionality. The top row has 0-D defects that include the omission of an atom, vacancy, the inclusion of either an atom฀larger,฀smaller,฀or฀different฀in฀some฀capacity฀from฀the฀matrix,฀interstitial฀or฀ substitutional atom. The second row shows an individual edge dislocation, a 1-D defect,฀which฀is฀identiied฀by฀the฀Burgers฀vector฀arrowed.฀The฀third฀row฀shows฀a฀ grain boundary, a misorientation of the same lattice structure, and an interface between different lattice structures. Two-dimensional defects are the most common defect in nanograined metals. Three-dimensional defects include voids, as illustrated in the last row of Table 8.1, and precipitates. The distinction of defect structures produced฀by฀process฀route฀is฀not฀as฀deinitive,฀although฀a฀general฀trend฀suggests฀that฀ the฀greater฀the฀energy฀put฀into฀deformation,฀the฀more฀complex฀the฀defect฀structure.฀ The combination of the defect dimensionality, density, and character has a direct effect on the properties and performance of any material and is thus worthy of investigation.฀Readers฀new฀to฀this฀ield฀are฀referred฀to฀the฀classical฀and฀introductory฀ literature.1–9 The details of the formation and destruction active in many of these structures are still under investigation, although much progress has been made through a combination of in situ TEM investigations and computational models.

8.2

Classical defect structures in nanograined metals

Several฀defect฀structures฀that฀have฀been฀experimentally฀observed฀in฀nanograined฀ metals are also commonly observed in coarse-grained metals, but at densities and

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Deformation structures including twins in nanograined pure metals Table 8.1 Potential defect structures in crystalline lattices arranged by dimensionality

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under circumstances not regularly seen in coarse-grained metals. These defects include dislocations, stacking faults, twins, grain boundaries, and point defect agglomerations. A comparison will be made of the character and density of these defects฀as฀a฀function฀of฀grain฀size.

8.2.1 Perfect dislocations Dislocation motion and interactions are at the core of all deformation and failure mechanisms in ductile metallic systems. As has been discussed throughout the chapters฀of฀this฀book,฀much฀of฀the฀study฀of฀nanograined฀metals฀has฀emphasized฀ the effects of limited grain volume on the hindrance or absence of classical dislocation mechanisms and processes. Dislocation density and dislocation structures฀are฀commonly฀identiied฀by฀TEM฀using฀a฀variety฀of฀imaging฀conditions.฀ Identiication฀of฀dislocations฀becomes฀more฀dificult฀as฀the฀grain฀size฀decreases฀ and multiple grains are present through the thickness of the TEM foil. Despite these฀ dificulties,฀ dislocations฀ have฀ been฀ observed฀ in฀ nanograined฀ metals฀ with฀ grains as small as 10 nm.10 Figure 8.1 (a) illustrates a common dislocation structure seen in a coarse grained Al-Mg-Sc alloy. As is often the case in coarse-grained alloys, the dislocations interact with themselves as well as with grain boundaries, particles,฀ and฀ any฀ other฀ structural฀ defects฀ in฀ the฀ material.฀ As฀ the฀ grain฀ size฀ decreases, the time for which a mobile dislocation is present within a grain decreases;฀ this฀ decreases฀ the฀ probability฀ that฀ the฀ dislocation฀ will฀ have฀ time฀ to฀ interact with other dislocations and limits the interactions with the surrounding grain boundaries. The interaction of a limited number of dislocations on at least two฀slip฀systems฀can฀be฀seen฀in฀Fig.฀8.1฀(b).฀When฀the฀grain฀size฀decreases฀to฀10฀ nm,฀the฀number฀of฀dislocations฀present฀in฀the฀ilm฀decreases฀substantially฀due฀to฀ dislocation repulsion forces. These dislocations are often reported as dislocation dipoles indicated in Fig. 8.1 (c) from Shan et al.’s work on nanograined Ni. The decreased presence of dislocations and, more importantly, of dislocation interactions฀has฀a฀signiicant฀effect฀on฀the฀mechanical฀properties฀of฀nanograined฀ metals. This decreased presence will be discussed in more detail in Section 8.3.

8.1 (a) Common dislocation structure seen in Al-Mg-Sc alloy. (b) Dislocation present within a 1 µm grain of high-purity Al. (c) Dislocation present in a 10 nm diameter grain in Ni.10

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8.2.2 Partial dislocations (stacking faults) Partial dislocations are commonly observed in coarse-grained metals and alloys with low stacking-fault energy. The interactions of these partial dislocations have been฀found฀to฀play฀a฀signiicant฀role฀in฀the฀deformation฀and฀failure฀processes.฀It฀ has฀been฀suggested฀from฀the฀theory฀and฀computational฀models฀that฀as฀grain฀size฀ decreases, perfect dislocations become less dominant and partial dislocations occur more frequently. In order to understand the potential difference in defect structure, Yamakov et al.11 developed a deformation map for nanograined metals in which the deformation mechanism is determined to be simply a function of stress,฀ grain฀ size,฀ and฀ stacking-fault฀ energy,฀ as฀ seen฀ in฀ Fig.฀ 8.2.11 The three dominant mechanisms were determined to be grain boundary mediated deformation, partial dislocation slip, and full dislocation slip. These mechanisms were฀identiied฀by฀simulating฀strain฀in฀nanograined฀Al฀with฀an฀average฀grain฀size฀ of 32 nm and varying the stacking-fault energy. The change in deformation mechanism to grain boundary mediated processes results in a change in the Hall– Petch฀ relationship฀ as฀ the฀ grain฀ size฀ decreases.฀ At฀ the฀ smallest฀ grain฀ size,฀ this฀ results฀in฀an฀inverse฀relationship฀between฀grain฀size฀(d ) and yield stress (σ ):

.

[8.1]

8.2 Deformation map delineating the active deformation mechanism as a function of grain size based on MD computer simulations,11 where r and d are defined in equation 8.2.

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This proposed mechanism and the associated deformation map, Fig. 8.2,11 have resulted฀in฀intense฀discussions฀within฀the฀ield฀and฀have฀been฀accepted฀as฀incomplete฀ due฀ to฀ recent฀ experimental฀ studies.฀ This฀ model฀ does฀ not฀ take฀ into฀ account฀ any฀ deformation mechanisms associated with grain growth that have recently been reported to be active in nanograined metals during deformation.10,12,13 Normalized฀ values฀ of฀ stress฀ (σ∞ /σ∞ )฀ and฀ grain฀ size฀ (r/d ) make Yamakov et al.’s deformation map applicable to a wide variety of metals.

[8.2]

The applied stress (σ )฀ is฀ normalized฀ by฀ the฀ resolved฀ shear฀ stress฀ at฀ which฀ the฀ dislocation฀ splitting฀ distance฀ is฀ ininity฀ (σ∞). This resolved shear stress is the stacking-fault energy (γ ) and a set of constants based on the elastic modulus and the฀ Shockley฀ partial฀ dislocation฀ type.฀ The฀ grain฀ diameter฀ is฀ normalized฀ by฀ the฀ placement of the equilibrium dislocation splitting distance (r0) in the numerator of the abscissa. The term r0, as shown in Equation 8.2, is based on the elastic modulus and the Shockley partial dislocation type, as well as the Burgers vector (b), and the stacking-fault energy (γ ). The mechanism demarcation lines indicated in Fig. 8.2 are dependent on a variable (r) that is a function of the equilibrium dislocation splitting distance (r0 ), the applied stress (σ ), and the resolved shear stress฀at฀which฀the฀dislocation฀splitting฀distance฀is฀ininity฀(σ∞). Although the motion of partial dislocations has been proposed to dominate in many฀ nanograined฀ metals,฀ limited฀ experimental฀ research฀ exists฀ showing฀ the฀ presence of either partial dislocations or partial dislocation structures.14฀Complex฀ partial฀dislocation฀structures฀are฀known฀to฀exist฀in฀coarse-grained฀low฀stackingfault฀energy฀metals;฀these฀structures฀include฀dislocation฀node฀structures฀that฀result฀ in interacting partial dislocations. This is in contrast to the structures seen in deformed nanograined Au, a low stacking-fault metal that does not show signiicant฀ signs฀ of฀ partial฀ dislocation฀ structures.15 Partial dislocations and the subsequent฀stacking฀faults฀have฀been฀reported฀in฀nanograined฀metals.฀For฀example,฀ Liao et al. observed both deformation twins and stacking faults as wide as 6.8 nm in cryogenically ball-milled Al, despite a bulk stacking-fault energy of 166฀mJ฀m–2.16,17 In general, partial dislocations and stacking faults do not appear to play a major role in the deformation structure formed in nanograined metals.

8.2.3 Twins Deformation฀twins฀are฀a฀signiicant฀defect฀structure฀in฀many฀face-centered฀cubic฀ (FCC)฀ metals฀ with฀ low฀ stacking-fault฀ energy.฀ Several฀ suggested฀ mechanisms฀

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8.3 Image of a deformation twin in Al near crack tip.18

exist฀ for฀ the฀ formation฀ of฀ twins฀ from฀ deformation.฀ Figure฀ 8.3฀ shows฀ frames฀ captured from an in situ TEM video of the deformation and failure of sputterdeposited฀Al฀thin฀ilms.18฀An฀interesting฀aspect฀of฀this฀experiment฀is฀the฀presence฀ of a twin in the grain adjacent to the one responsible for blocking the crack. Although the twin is ahead of the blunting crack tip and may have formed because of฀ the฀ stress฀ ield฀ associated฀ with฀ the฀ crack,฀ its฀ formation฀ was฀ not฀ observed฀ dynamically. The density of twins around the fracture surface was greater than in the rest of the gauge section, suggesting that deformation twinning occurred in association with crack blunting.18 These twins have been observed in nanograined and฀ultra-ine฀grained฀FCC฀metals฀with฀low฀and฀high฀stacking-fault฀energy.17,19–22 Several models suggested that a change in activation volume, strain rate sensitivity,฀ or฀ conining฀ pressure฀ as฀ grain฀ size฀ decreases฀ would฀ result฀ in฀ an฀ increased propensity for twinning.23–26 The addition of twins during the deformation process may act to both relieve stress in a given grain and provide an additional defect structure to limit continued slip activity by providing an additional boundary.27 Deformation twinning is therefore an active mechanism in many฀ nanograined฀ metals฀ and฀ may฀ play฀ a฀ signiicant฀ role฀ in฀ the฀ mechanical฀ properties.

8.2.4 Grain boundaries The essential defects of nanograined metals are two-dimensional defect structures known as grain boundaries. The dynamics of grain boundaries and resulting defect structures dictate the mechanical properties of nanograined metals. The types and structures of these grain boundaries are highly dependent on the alloy composition and processing steps in the manufacturing of nanograined metals. In general, nanograined structures produced using bottom-up approaches are more

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prone to possessing voids and greater free volume at the grain boundaries.28,29 In contrast,฀ nanograined฀ and฀ ultra-ine฀ grained฀ metals฀ formed฀ by฀ severe฀ plastic฀ deformation and other top-down approaches often contain dislocations in or near the grain boundary.30 In either case, the multitude and often the types of grain boundaries found in nanograined metals are far-from-equilibrium and thus not always stable under standard temperature and pressure. Recent studies have begun to฀ investigate฀ the฀ effects฀ of฀ controlling฀ both฀ the฀ grain฀ size฀ and฀ grain฀ boundary฀ type in an effort to completely engineer a material from the grain boundary up.31,32 Understanding฀ and฀ controlling฀ the฀ response฀ of฀ grain฀ boundaries฀ during฀ plastic฀ deformation is essential for predicting the mechanical properties of nanograined metals and determining potential applications of these materials. One investigation into the understanding of these instabilities and how they may be controlled,฀ deformation-induced฀ grain฀ growth,฀ will฀ be฀ discussed฀ extensively฀ in฀ Section 8.4.1.

8.2.5 Point defects and resulting structures: dislocation loops and stacking-fault tetrahedra Dislocation loops and stacking-fault tetrahedra are defects associated with the collapse of a large number of point defects into lower energy defect structures. Dislocation฀ loops฀ can฀ either฀ be฀ the฀ absence฀ or฀ addition฀ of฀ an฀ extra฀ plane฀ of฀ atoms within a crystalline structure. Stacking-fault tetrahedra are pyramidal structures฀formed฀in฀FCC฀metals฀in฀which฀the฀faces฀of฀the฀pyramid฀are฀stacking฀ faults that lie on intersecting {111} planes. Dislocation loops have been proposed to be formed from a variety of techniques including dislocation– dislocation฀interactions฀during฀extensive฀deformation.1,33 The high concentration of vacancies that are needed to form stacking-fault tetrahedra have been reportedly produced by a variety of means including rapid quenching from temperatures near Tm,34,35 irradiation with energetic particles,36 dislocation– dislocation interactions,37 diffusion-induced grain boundary migration under speciic฀ temperatures฀ and฀ migration฀ rates,38฀ annealing฀ and฀ recrystallization฀ following severe plastic deformation,39 and high strain rate (as high as 108 s–1) deformation.40฀In฀severe฀plastic฀deformation฀used฀to฀form฀ultra-ine฀grained฀and฀ nanograined metals, it appears that both dislocation loops and stacking-fault tetrahedra can form from mechanical deformation at room temperature. This suggests฀that฀the฀extensive฀plasticity฀of฀either฀nanograined฀or฀ultra-ine฀grained฀ metals provides a source for a supersaturation of vacancies that results in the formation of dislocation loops and stacking-fault tetrahedra. Dislocation loops and฀ stacking-fault฀ tetrahedra฀ were฀ identiied฀ by฀ Dalla฀ Torre฀ et al. in equalchannel฀ angular฀ pressed฀ Cu฀ that฀ was฀ neither฀ irradiated฀ nor฀ quenched.฀ The฀ stacking-fault tetrahedra are black triangles and the dislocation loops are black dots฀or฀black฀and฀white฀lobes฀under฀the฀bright-ield฀imaging฀conditions฀used฀in฀ Fig. 8.4.39

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8.4 Stacking-fault tetrahedra (arrowed) and dislocation loops in ECAP Cu.39

8.3

Classical defect structures absent in nanograined metals

Greater insight into the properties of nanograined metals may be gained from the classical defect structures absent, rather than those present. This section will detail the defect structures that are commonly seen in bulk deformed metals, but are seldom, if ever, reported in nanograined metals. This discussion will include the description of dislocation locks, cell structures, and intergrain sources. A comparison between the microstructure commonly seen in deformed coarsegrained and nanograined metals will be made on the possible mechanistic differences and resulting alteration to the mechanical properties.

8.3.1 Classical structures absent The variety of classical structures commonly seen in deformed coarse-grained FCC฀metals฀is฀not฀present฀in฀nanograined฀metals฀and฀thus฀warrants฀discussion.฀ These structures include dislocation locks, dislocation pile-ups, dislocation tangles, dislocation cell structures, and intergrain dislocation sources. Although all฀ of฀ these฀ structures฀ are฀ different฀ and฀ play฀ signiicantly฀ different฀ roles฀ in฀ the฀ deformation and failure mechanisms as well as the mechanical properties of metals, they all have in common multiple dislocation interactions, which are needed to form them. Much of what has been discussed thus far relates to the possible breakdown of the Hall–Petch relationship between yield strength and grain฀size.฀The฀Hall–Petch฀relationship฀is฀an฀empirical฀observation฀that฀has฀been฀ associated with many of the mobile defect structures that are often absent in nanograined metals.7,41–45 There are a variety of potential dislocation lock

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8.5 A series of micrographs showing (a) dislocation pile-up at a grain boundary; (b) dislocation emission from a grain boundary in stainless steel.46

structures฀possible฀in฀FCC฀metals;฀all฀of฀which฀combine฀two฀or฀more฀dislocations฀ of different slip character within a grain or grain boundary to form sessile dislocation structures from glissile dislocation combinations. Once locks are formed, they provide an impediment to dislocation motion within a grain. This signiicantly฀ decreases฀ the฀ free฀ path฀ along฀ which฀ the฀ dislocation฀ can฀ proceed.฀ Dislocation pile-ups are arrays of dislocations on the same slip plane and of similar character that apply a local stress on an immobile feature in the microstructure. The pile-up can contain a multitude of dislocations, which can result฀ in฀ a฀ signiicant฀ stress฀ concentration฀ as฀ is฀ illustrated฀ in฀ Fig.฀ 8.5฀ (a).฀ The฀ dislocations produced during deformation can either originate from a grain boundary as shown in Fig. 8.5 (b) or internally within a grain by Frank–Read sources.46 Dislocation sources provide the slip and thereby deformation necessary in฀the฀crystal฀without฀inducing฀failure.฀The฀hindrance฀of฀these฀sources฀was฀the฀irst฀ mechanistic฀explanation฀for฀the฀empirical฀Hall–Petch฀effect.฀Dislocation฀tangles฀ and฀cell฀structures฀are฀more฀complex฀structures,฀which฀evolve฀to฀contain฀a฀large฀ number of dislocations. These structures will often include dislocation locks and pile-ups. The range of dislocation structures that include locks, pile-ups, and cell structures฀is฀complex฀and฀important฀to฀many฀of฀the฀properties฀of฀ductile฀metals,฀ but appears to be absent from most nanograined systems.

8.3.2 Reasons for the absence of classical structures in nanograined metals The absence of these features can be directly correlated with the lack of space available for their development within a nanograined structure. This lack of defect-free volume often found in nanograined metals in combination with the short mean free path between boundaries means that the probability of dislocation– dislocation interactions occurring during the time it takes for these defects to proceed฀from฀one฀grain฀boundary฀to฀the฀other฀is฀signiicantly฀less฀than฀in฀coarsegrained metals. This decreased probability of dislocation–dislocation interaction

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results฀in฀fewer฀dislocation฀locks฀and฀other฀complex฀multiple฀dislocation฀structures฀ forming฀within฀the฀matrix฀of฀nanograined฀metals.฀Dislocation฀pile-ups฀containing฀ a few dislocations have been observed in nanograined metals,13,30 but pile-ups of the฀size฀seen฀in฀Fig.฀8.5฀(a)฀are฀physically฀impossible฀in฀nanograined฀metals฀due฀ to dislocation–dislocation repulsion.47฀The฀limitation฀of฀pile-up฀size฀results฀in฀a฀ limit on the stress applied to the grain boundary and a limit on the slip transferred from one side of the grain to the other.48 This lack of pile-up stress hinders the cross-slip of dislocations in the pile-up that results in both slip on other slip systems฀and฀the฀formation฀of฀more฀complex฀dislocation฀structures฀resulting฀from฀ dislocation–dislocation interactions.46 The large amount of stress that is applied from large dislocation pile-ups can result in some of the strain being transferred across the grain boundary in the form of new dislocations being generated from the฀grain฀boundary.฀An฀example฀of฀dislocation฀cross-slip฀and฀slip฀transfer฀across฀ the grain boundary can be seen in Fig. 8.6.46 The lack of defects, mainly dislocations, within the grains, including dislocation locks to pin the grain boundaries on, means that if dislocations were to move across a grain it would occur very rapidly. This type of dislocation motion would

8.6 A series of micrographs showing (a) cross-slip and (b) slip transfer due to the large dislocation pile-up seen in Fig. 8.5 (a) in stainless steel.46

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not฀ result฀ in฀ the฀ development฀ of฀ complex฀ microstructure฀ within฀ the฀ grains,฀ but฀ may฀ have฀ a฀ signiicant฀ effect฀ on฀ the฀ grain฀ boundary฀ character.฀As฀ a฀ result,฀ the฀ grain฀boundaries฀are฀expected฀to฀be฀the฀location฀for฀all฀the฀complex฀interactions฀ that occur during the plastic deformation of nanograined metals.

8.3.3 The effect of missing structures on mechanical properties The฀lack฀of฀these฀complex฀defect฀structures฀that฀result฀from฀dislocation–dislocation฀ interaction in deformed nanograined metals has a substantial impact on the deformation and failure mechanisms. In coarse-grained metals, these defect structures increase in density as the number of dislocations and thus the probability of their interaction increases. The resulting increase in new structures to pin dislocation฀motion฀leads฀to฀work฀hardening,฀which฀can฀signiicantly฀prolong฀the฀ time฀ between฀ initial฀ deformation฀ and฀ inal฀ failure.฀ However,฀ in฀ nanograined฀ metals, the lower probability of interaction results in little to no work hardening. Most nanograined metals show minimal ductility prior to catastrophic failure, signiicantly฀limiting฀their฀application.49–51

8.4

Novel defect structures in nanograined metals

The฀ inal฀ class฀ of฀ defect฀ structures฀ in฀ nanograined฀ high฀ purity฀ metals฀ is฀ the฀ completely฀unexpected฀defect฀structures฀seen฀in฀nanograined฀metals฀that฀are฀not฀ common or have never been reported in traditional coarse-grained metals. The three฀structures฀related฀to฀deformation฀are:฀larger฀agglomerated฀grains,฀ive-fold฀ twin structures, and disclinations.

8.4.1 Agglomerated grains A coarsened microstructure commonly results from deformation processes in high-purity nanograined metals. Deformed metals with an initially nanograined microstructure will often have regions containing larger grains that can be correlated to the regions of the highest stress during deformation.52 These grains come฀in฀a฀variety฀of฀shapes฀and฀sizes฀with฀occasional฀indications฀for฀oblong฀grains฀ in the direction of the greatest stress.52,53฀These฀structures฀have฀been฀identiied฀by฀ both in situ TEM deformation studies and post-mortem TEM analysis.12,53,54 This฀coarsening฀of฀grains฀during฀deformation฀is฀in฀direct฀contrast฀to฀the฀reinement฀ of grain structure during the room temperature deformation of coarse-grained metals. Three possible mechanisms have been proposed for grain growth in nanograined metals. The traditional mechanism is that grain boundaries migrate by the transfer of atoms across the grain boundary, resulting in a change in the dominant grain orientation. The driving force for this change is often associated with grain

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boundary curvature.55 This mechanism is highlighted in Fig. 8.7 (a) and 8.7 (b). In Fig. 8.7 (a), a small concave grain with four sides is present in a microstructure dominated฀ by฀ stable฀ six-sided฀ grains.฀ The฀ shape฀ of฀ the฀ grains฀ produces฀ an฀ instability that results in the shrinkage and elimination of the grain. This likely occurs through atomic shuffling across the grain boundaries resulting in the progression of the grain boundary in the direction highlighted by the arrows. The collapse of this grain boundary results in the formation of two triple junctions with฀angles฀of฀120°56 that are indistinguishable from the surrounding stable grain boundary structure, Fig. 8.7 (b). It should be noted that all polycrystalline systems are theoretically unstable in comparison to single crystals with certain grain boundary types and structures having an energetic local minimum.57–59 Recently, it has been suggested by Molecular Dynamics computer simulations and฀reported฀experimentally฀that฀grain฀growth฀in฀nanograined฀materials฀can฀occur฀ via grain rotation at room temperature under an applied load.10,60,61 In order for this mechanism to occur, a large amount of free volume must be present in the

8.7 Proposed grain boundary migration mechanisms: (a) grain boundary migration and (b) the resulting microstructure; (c) grain rotation and (d) the resulting microstructure; (e) grain boundary elimination and (f) the resulting microstructure.

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grain boundaries of a far-from-equilibrium structure as illustrated by the thicker grain boundaries and the atypical grain shape shown in Fig. 8.7 (c). A small grain with฀extensive฀free-volume฀at฀the฀grain฀boundaries฀is฀highlighted.฀Local฀stresses฀ applied to the grain can result in atomistic shuffling in the grain boundaries that has been predicted to result in grain boundary rotation along the direction of the arrow in Fig. 8.7 (c). If the grains to the left and the right of the grain are of the same orientation, then the rotation of the grain can result in the formation of an oblong฀grain฀as฀seen฀in฀Fig.฀8.7฀(d).฀Cahn฀and฀Taylor฀developed฀a฀mathematical฀ model฀to฀explain฀the฀combination฀of฀grain฀boundary฀sliding฀and฀grain฀rotation.62 In this model, the tangential motion of grain boundaries was a result of biased grain boundary diffusion.62฀Another฀explanation฀of฀grain฀growth฀via฀grain฀rotation฀ was proposed by Rath et al.63 In their model, introducing a simple stable dislocation structure produces a small-angle grain boundary encircling a region that฀is฀rotated฀relative฀to฀the฀surrounding฀matrix.฀This฀dislocation-based฀model฀ shows that grain boundary motion may produce grain rotation if the necessary grain misorientation and grain boundary structure are present.63 In another proposed model, grain growth is caused by grain boundary annihilation or alteration due to the bombardment and accommodation of a large number of mobile dislocations.64–66 Figures 8.7 (e) and 8.7 (f ) illustrate the proposed mechanism for dislocation mediated grain growth. This mechanism is associated with a large active dislocation density and thus is thought to occur in samples฀ under฀ extreme฀ stress฀ states.฀ Figure฀ 8.7฀ (e)฀ shows฀ an฀ unstable฀ grain฀ structure in which a high density of dislocations is piled up on a weak or lowangle grain boundary as indicated. After continued build-up of local stresses, the grain฀ boundary฀ absorbs฀ and฀ emits฀ dislocations฀ into฀ the฀ matrix฀ and฀ potentially฀ along฀the฀grain฀boundary฀to฀the฀extent฀that฀the฀grain฀boundary฀structure฀can฀no฀ longer฀be฀clearly฀identiied.฀Instead,฀the฀orientation฀between฀the฀grains฀becomes฀a฀ general transition associated with high dislocation density and without the clear demarcation of grain orientation found with grain boundaries,1 as is illustrated in Fig. 8.7 (f ). The grain coarsening observed here is in stark contrast to the deformation structures observed in coarse-grained metals after deformation at room temperature. It is typical for intense deformation in coarse-grained microstructures to result in the฀ reinement฀ of฀ the฀ grains.฀ This฀ can฀ be฀ seen฀ in฀ the฀ formation฀ of฀ complex฀ dislocation cell structures that form barriers to further dislocation motion. The 3D structures฀ formed฀ from฀ fatigue฀ deformation฀ of฀ Cu-16%Al฀ single฀ crystals฀ at฀ 28฀ MPa, 34 MPa, and 41 MPa are seen in Fig. 8.8.67 The initial structure seen in the Cu฀alloy฀after฀28฀MPa฀shows฀dislocation฀activity฀on฀two฀slip฀systems.฀As฀the฀extent฀ of fatigue increases, the densities of dislocations and structures resulting from dislocation–dislocation interaction increase. These defects include dislocation loops,฀ dense฀ dislocation฀ arrays.฀ This฀ type฀ of฀ reinement฀ is฀ assumed฀ to฀ be฀ the฀ mechanism฀that฀is฀used฀for฀the฀formation฀of฀ultra-ine฀and฀nanograined฀structures฀ by severe plastic deformation processes. Grain boundaries are known to be

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8.8 Three-dimensional view of dislocation structures in Cu-16%Al after fatigue deformation at (a) 28 MPa, (b) 34 MPa and (c) 41 MPa. The planes are indexed and in (d) the {111} planes are indicated.67

destroyed฀in฀coarse-grained฀metals฀during฀dynamic฀recrystallization.฀This฀process฀ can be seen in Fig. 8.9, in which a triple boundary in an aluminum alloy is destroyed. This process is associated with superplastic forming and is a result of applied load,฀while฀at฀elevated฀temperature.฀The฀grain฀structure฀in฀metals฀can฀be฀reined฀to฀ an฀ultra-ine฀or฀nanograined฀structure฀using฀severe฀plasticity,68 but it has also been shown to undergo grain growth at room temperature from an applied load.53 It is hypothesized฀ that฀ this฀ grain฀ growth฀ due฀ to฀ applied฀ load฀ is฀ seen฀ in฀ nanograined฀ structures฀deformed฀at฀room฀temperature฀because฀of฀the฀lack฀of฀complex฀dislocation฀ interactions necessary for grain boundary formation and the high amounts of stress applied฀ to฀ far-from-equilibrium฀ boundaries.฀ An฀ example฀ of฀ grain฀ growth฀ both฀ directly฀ ahead฀ of฀ the฀ crack฀ tip฀ and฀ in฀ the฀ plastic฀ zone฀ due฀ to฀ room฀ temperature฀ straining will be discussed in Section 8.5. The formation of a coarse-grained structure, as a result of deformation in nanograined฀metals,฀has฀a฀signiicant฀effect฀on฀the฀properties฀and฀performance฀of฀

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8.9 Series of micrographs showing the destruction of a triple junction in Al-4Mg-0.3Sc alloy at nominally the superplastic deformation temperature.69

nanograined฀metals.฀Large฀grains฀found฀in฀localized฀regions฀of฀high฀stress฀reduce฀ the฀ strength฀ signiicantly฀ in฀ the฀ local฀ region฀ and฀ increase฀ local฀ dislocation฀ slip฀ promoting failure to occur within this region.70฀The฀localized฀deformation฀in฀these฀ large฀grain฀regions฀results฀in฀localized฀plasticity฀and฀failure฀with฀limited฀global฀ deformation resulting in premature failure of traditionally ductile metals. The lack of knowledge on the factors controlling the formation of the agglomerated grain deformation฀ structure฀ represents฀ a฀ signiicant฀ hindrance฀ to฀ the฀ application฀ of฀ nanograined materials and is thus an area of intense investigation.12,71

8.4.2 Star twins Another defect structure not observed in coarse-grained metals, but occasionally observed฀in฀nanograined฀metals,฀is฀the฀ive-fold฀twin฀structure,฀also฀known฀as฀star฀ twins.฀This฀structure฀entails฀the฀union฀at฀a฀single฀junction฀of฀ive฀twins฀and฀was฀ irst฀ observed฀ in฀ Au฀ and฀ other฀ FCC฀ nanoparticles.69–72฀ An฀ example฀ of฀ such฀ structure in a gold nanoparticle which is undergoing sintering at elevated temperatures is shown in Fig. 8.10.72 These structures in the nanoparticles have been well studied and have been accredited to the decreased surface energy gained by฀ the฀ formation฀ of฀ the฀ far-from-equilibrium฀ ive-fold฀ twin฀ structure.฀ These฀ structures have been observed in nanograined metals produced by various methods.73,74฀Similar฀to฀nanoparticles฀with฀ive-fold฀symmetry,฀the฀formation฀of฀ these non-equilibrium structures in bulk metals has also been associated with the decreased energy gained by the formation relative to the grain boundary energy.73 In฀ grains฀ of฀ 20฀ nm฀ or฀ less฀ produced฀ by฀ severe฀ plastic฀ deformation,฀ ive-fold฀ deformation twins were observed. These defects are present only in nanograined metals, due to the increasing geometrically necessary lattice strain imposed by the

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8.10 High resolution TEM of a five-fold twinned Au nanoparticle as it undergoes sintering with a neighboring particle.72

increased฀lattice฀mismatch฀as฀the฀structure฀increases฀in฀size.฀From฀these฀results,฀ Zhu et al. were able to develop a proposed mechanism that would permit the formation฀of฀ive-fold฀twins฀from฀severe฀plastic฀deformation.74,75 Five-fold twin structures are not commonly observed in nanograined metals and as a result are not฀believed฀to฀have฀a฀signiicant฀effect฀on฀their฀mechanical฀properties.

8.4.3 Disclinations Disclinations฀are฀line฀defects฀similar฀to฀dislocations฀and฀will฀be฀the฀inal฀defect฀ structure discussed in this chapter. In contrast to dislocations that displace a local region, disclinations are violations in rotation symmetry of the crystal. Disclinations are defects that are not commonly associated with deformation in coarse-grained metals. High-resolution TEM has been used to identify disclination dipoles in mechanically milled nanocrystalline Fe.76,77 The formation of these rotational฀defects,฀seen฀in฀Fig.฀8.11,฀is฀theorized฀to฀permit฀turbulent฀behavior฀in฀ the solid metal during severe plastic deformation. It has been stipulated that these defects are present in nanograined metals not only as a result of severe plastic deformation, but also as a result of the increased reliance on intergrain sliding during the deformation process. The observation of disclinations in nanograined metals supports the hypothesis that nanograined metals deform predominantly via grain boundary mechanisms rather than dislocation slip.76,77

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8.11 (a) Transmission electron microscopy micrograph of nanocrystalline Fe powder. (b) Same micrograph with overlaying lines indicating planes of atoms. (c) Schematic of the plane structure with the location of the two disclinations identified.76

8.5

The effect of initial microstructure on deformation structures

The deformation structure formed in a given nanograined metal is highly dependent on the processing history of the metal and the resulting microstructure. This฀effect฀is฀true฀for฀all฀materials,฀but฀is฀of฀greater฀signiicance฀in฀nanograined฀ structures due to their very high percentage of atoms not in stable lattice correlation. The variety of possible processing histories that can form nanograined structures can result in various percentages of free volume and types of grain boundaries฀within฀the฀microstructure.฀Characterization฀and฀testing฀of฀nanograined฀ metals฀ with฀ the฀ same฀ purity฀ and฀ average฀ grain฀ size฀ but฀ created฀ by฀ different฀ processing routes have shown that neither the microstructure nor the resulting mechanical properties of the two metals are equivalent.28 This suggests that the grain฀size฀distribution,฀types฀of฀defects฀present฀in฀the฀grains,฀and฀grain฀boundaries฀ have฀ a฀ signiicant฀ effect฀ on฀ the฀ active฀ deformation฀ mechanisms฀ and฀ resulting฀ mechanical properties. The microstructures formed during the production of nanograined materials can be controlled to contain many non-equilibrium structures, as demonstrated below. This effect can be clearly observed in a detailed study of the active deformation and failure mechanisms and properties of nanograined pulsed-laser deposited (PLD)฀Ni฀as฀a฀function฀of฀grain฀size.฀The฀three฀microstructures,฀seen฀in฀Fig.฀8.12,฀ chosen฀for฀investigation฀were฀nearly฀monodispersed฀nanograined฀Ni฀ilm฀present฀ in the as-released freestanding condition, Fig. 8.12 (a) and 8.12 (b), the microstructure฀ with฀ maximized฀ bimodal฀ distribution,฀ Fig.฀ 8.12฀ (c)฀ and฀ 8.12฀ (d),฀ and ฀the฀ultra-ine฀grained฀Ni฀ilms,฀Fig.฀8.12฀(e)฀and฀8.12฀(f฀).฀The฀bright-ield฀image,฀ Fig. 8.12 (a), of the as-released microstructure contains only nanograined Ni grains฀ as฀ conirmed฀ by฀ the฀ select฀ area฀ diffraction฀ (SAD)฀ pattern฀ insert฀ that฀ contains฀ uniform฀ rings฀ of฀ constant฀ brightness,฀ which฀ is฀ typical฀ of฀ ine-grained฀ metals฀ with฀ no฀ preferred฀ texture.฀ The฀ histogram฀ associated฀ with฀ Fig.฀ 8.12฀ (a),฀ which฀ quantiies฀ the฀ grain฀ size฀ distribution,฀ is฀ presented฀ in฀ Fig.฀ 8.12฀ (b).฀ The฀ average฀grain฀size฀ranged฀from฀4฀nm฀to฀39฀nm฀with฀a฀mean฀of฀13฀nm.฀This฀resulted฀

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8.12 The microfabricated structure: (a) The initial nanograined microstructure of Ni film after release from Si; (b) Associated histogram of grain size distribution of the nanograined structure; (c) The bimodal microstructure of Ni film after annealing for 1 hour at 548 K; (d) Associated histogram of the mixed structure; (e) The ultra-fine grained microstructure of Ni film after annealing for 1 hour at 598 K; (f) Associated histogram of the ultra-fine grained structure.

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in a standard deviation of 5.3 nm as can be seen in Table 8.2. The vast majority of the฀ 960฀ grains฀ measured,฀ 90%,฀ are฀ within฀ the฀ range฀ of฀ 5฀ nm฀ and฀ 20฀ nm.฀This฀ results฀in฀a฀maximum฀grain฀size฀to฀average฀grain฀size฀ratio฀of฀2.9.฀For฀comparison,฀ the฀ average฀ grain฀ size฀ in฀ these฀ microfabricated฀ samples฀ is฀ larger,฀ and฀ the฀ distribution฀broader,฀than฀that฀in฀the฀as-deposited฀Ni฀ilms.78฀For฀example,฀a฀90฀ nm-thick฀ ilm฀ deposited฀ on฀ rock฀ salt฀ and฀ not฀ subject฀ to฀ microfabrication฀ was฀ found฀to฀have฀an฀average฀grain฀size฀of฀9฀nm฀with฀a฀standard฀deviation฀of฀3฀nm,฀ suggesting that despite both being monodispersed high-purity nanograined metals, the฀ process฀ history฀ associated฀ with฀ microfabrication฀ altered฀ the฀ grain฀ size฀ distribution. A฀bimodal฀grain฀size฀distribution,฀seen฀in฀Fig.฀8.12฀(b),฀was฀achieved฀through฀ a฀ one-hour฀ anneal฀ at฀ 548฀ K.฀ The฀ microstructure฀ contains฀ several฀ large฀ grains฀ with฀ scalloped฀ grain฀ boundaries฀ and฀ a฀ myriad฀ of฀ unexpected฀ internal฀ defects.฀ The SAD pattern inserted in Fig. 8.12 (c) shows that continuous rings are maintained฀due฀to฀the฀nanograined฀matrix,฀but฀the฀rings฀are฀no฀longer฀of฀uniform฀ intensity฀due฀to฀the฀presence฀of฀these฀large฀grains.฀The฀histogram฀of฀grain฀size฀ distribution฀presented฀in฀Fig.฀8.12฀(d)฀shows฀that฀the฀average฀grain฀size฀has฀nearly฀ doubled฀to฀25฀nm฀from฀the฀initial฀grain฀size.฀The฀range฀of฀grain฀sizes฀has฀increased฀ signiicantly,฀varying฀from฀4฀nm฀to฀435฀nm,฀resulting฀in฀a฀standard฀deviation฀of฀ 40฀nm฀as฀seen฀in฀Table฀8.2.฀The฀ratio฀of฀maximum฀grain฀size฀measured฀to฀average฀ grain฀size฀is฀17.2,฀yet฀70%฀of฀the฀grains฀remain฀in฀the฀range฀of฀5฀nm฀and฀20฀nm.฀ The฀line-intercept฀method฀identiied฀25฀ultra-ine฀grains,฀larger฀than฀100฀nm,฀in฀ the฀region฀analyzed.฀This฀accounts฀for฀only฀3.7%฀of฀the฀681฀grains฀measured฀as฀ seen in Table 8.3. The initial microstructure was completely eliminated after annealing for one hour฀at฀598฀K฀and฀developed฀into฀large฀nanograins฀and฀small฀ultra-ine฀grains,฀as฀ can be seen in Fig. 8.12 (e). The SAD pattern, Fig. 8.12 (e) insert, is now neither uniform฀in฀brightness฀nor฀continuous,฀and฀is฀typical฀of฀ultra-ine฀grained฀crystalline฀ structures.฀ The฀ grain฀ size฀ distribution฀ shown฀ in฀ Fig.฀ 8.12฀ (f฀)฀ is฀ signiicantly฀ different฀from฀the฀as-deposited฀distribution,฀Fig.฀8.12฀(b).฀The฀average฀grain฀size฀ has increased by nearly an order of magnitude of 150 nm with a broad distribution Table 8.2 The mean, median, largest, and smallest grain size, as well as the total number of grains for annealing treatments applied to 90 nm-thick PLD Ni films for in situ TEM straining Condition

Total number of grains

As-deposited

960

Mean (nm)

13

Median Standard Maximum Minimum Max (nm) deviation (nm) (nm) mean (nm) 12

5

39

4

3

548 K 1 hr

681

25

15

40

435

4

17

598 K 1 hr

116

150

145

81

436

23

3

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Table 8.3 Ratios derived from the grain size distribution annealing treatments applied to 90 nm-thick PLD Ni films for in situ TEM straining. The 10 × initial average, ultra-fine grain, 5 × average, and Tukey outliers are normalized by the total number of grains per histogram. The deviation from as-deposited and log normality are based on the Kolmogorov–Smirnov analysis Condition

10x 10x Ultra-fine 5x Tukey Log average initial grains average outliers normality (%) average (%) (%) (%) (%) (%)

As-deposited 0.0 548 K 0.6 598 K 0.0

0.0 3.1 54.3

0.0 3.7 69.8

0.0 3.2 0.0

3.3 9.5 0.9

0.0 0.0 1.0

Deviation from asdeposited (%) 0.0 20.6 42.2

ranging from 23 nm to 436 nm (Fig. 8.12 (f ) ). This resulted in a standard deviation of฀81฀nm,฀seen฀in฀Table฀8.2.฀The฀maximum฀grain฀size฀to฀average฀grain฀size฀ratio฀is฀ 2.9,฀comparable฀to฀that฀of฀the฀as-released฀ilms. No฀grains฀remain฀in฀the฀5฀nm฀to฀20฀nm฀range฀and฀ultra-ine฀grains฀account฀for฀ 70%฀ of฀ the฀ 116฀ grains฀ measured฀ in฀ an฀ area฀ of฀ identical฀ size฀ to฀ the฀ previous฀ histograms. This distribution is only one of the three to show any similarity to a log฀normal฀distribution฀based฀on฀the฀Kolmogorov–Simirnov฀test฀as฀seen฀in฀Table฀ 8.3฀and฀described฀by฀Kirkman.79 This control of microstructure permits the study into฀the฀relationship฀of฀grain฀size฀distributions,฀not฀just฀average฀grain฀size,฀with฀ deformation and failure mechanisms active during straining. The฀deformation฀and฀failure฀of฀a฀PLD฀Ni฀freestanding฀ilm฀annealed฀at฀548฀K฀ for 1 hour was observed during in situ฀TEM฀pulsed฀straining฀experiments฀using฀ a฀custom-built฀straining฀device.฀The฀bimodal฀grain฀size฀distribution฀produced฀by฀ annealing฀ of฀ these฀ ilms,฀ evident฀ in฀ Fig.฀ 8.12฀ (c)฀ and฀ 8.12฀ (d),฀ provides฀ the฀ opportunity for a multitude of deformation mechanisms. Evidence for a variety of mechanisms including dislocation pile-ups, twinning, stress-driven grain growth,฀localized฀thinning,฀crack฀blunting,฀ligament฀necking,฀and฀even฀what฀is฀ interpreted to be grain agglomeration were present during the deformation and failure฀of฀the฀ilms฀with฀a฀bimodal฀structure.฀Plasticity฀was฀observed฀up฀to฀2฀µm฀ in฀front฀of฀the฀crack฀tip฀with฀extensive฀plasticity฀observed฀in฀a฀region฀up฀to฀500฀ nm directly vicinal to the tip, as will be discussed in Fig. 8.13 and Fig. 8.14. Dislocation฀ activity฀ was฀ observed฀ in฀ the฀ large฀ grains฀ within฀ the฀ plastic฀ zone฀ without฀any฀observable฀change฀in฀the฀small฀surrounding฀grains.฀The฀solidiied฀Ni฀ droplets,฀or฀splats,฀present฀in฀the฀ilm฀were฀found฀to฀have฀no฀observable฀interaction฀ with฀crack฀propagation฀despite฀it฀propagating฀within฀100฀nm฀of฀the฀splat.฀Closer฀ to the crack tip, severe microstructural rearrangement occurred in both the large grains฀and฀the฀nanograins.฀In฀the฀region฀of฀the฀Ni฀ilm฀directly฀ahead฀of฀the฀crack฀ tip undergoing thinning, the large grains contained active full dislocations whereas the nanograins underwent the process termed grain agglomeration by Shan et al.10 The combination of these processes resulted in a thinning and

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8.13 Still frames taken from an in situ TEM deformation experiment of a custom-built PLD Ni device annealed at 548 K for 1 hour showing grain growth 240 nm ahead of the crack tip: (a) A still frame with migrating boundary outlined; (b) The same region 0.10 seconds later with the new boundary demarked.

eventual฀local฀failure฀of฀the฀ilm.฀No฀observation฀of฀deformation฀or฀failure฀was฀ observed฀to฀occur฀in฀any฀grains฀identiied฀as฀being฀metastable฀hexagonal฀closepacked฀(HCP)฀phased฀despite฀a฀portion฀of฀the฀large฀grains฀being฀of฀this฀character.฀ Deformation฀ was฀ seen฀ in฀ a฀ grain฀ containing฀ a฀ rich฀ debris฀ ield.฀ Despite฀ these฀ observations, no interactions of dislocations with stacking-fault tetrahedra were discernable. This work also provided direct evidence for stress-driven grain growth. An example฀of฀this฀effect฀is฀shown฀in฀the฀images฀presented฀in฀Fig.฀8.13.฀To฀illustrate฀ the grain growth, a portion of the grain boundary of a grain 240 nm from the nearest crack is highlighted. The new position of the boundary after stress-driven grain growth is highlighted in Fig. 8.13 (b). The grain boundary sweeps out an area of 250 nm2 in less than 0.1 s. Grain growth of this nature was observed in several฀grains฀within฀the฀plastic฀zone. The฀progression฀of฀the฀crack฀through฀the฀ilm฀was฀often฀halted฀due฀to฀the฀large฀ grains present in the bimodal microstructure, as is shown in Fig. 8.14 (a). In this image, a crack that was progressing from left to right was halted on the two large grains indicated. The left-most large grain indicated in Fig. 8.14 (a) separates the primary crack from the microcrack, formed on the other side of the grain. The second large grain present in front of the secondary crack also hindered crack progression. In situ TEM observations of this region showed dislocation activity in฀both฀grains฀during฀pulse฀straining฀followed฀by฀extensive฀necking฀in฀the฀thinned฀ region between the crack and microcrack. Figure 8.14 (b) and 8.14 (c) are postmortem micrographs of the fracture surface. A set of large grains along the fracture surface indicates severe plasticity including necking down to nearly a point. One of the large grains contains two dislocation pile-ups present on opposite planes

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8.14 Fracture surface of PLD Ni device annealed at 548 K for 1 hour: (a) A crack temporarily halted with one large grain spanning crack spacing and the other in front of the crack tip; (b) Necked region containing two dislocation pile-ups; (c) Large grain containing both dislocations and a twin.

and originating near the same region containing slightly more than 15 dislocations each in a grain with a length of 130 nm. Figure 8.14 (c) shows another region of large grains along the fracture surface. In this micrograph, both a dislocation pile-up฀ and฀ a฀ twin฀ are฀ labeled.฀The฀ dislocation฀ pile-up฀ contains฀ 12฀ identiiable฀ dislocations.฀The฀thin฀twin,฀near฀an฀area฀previously฀exposed฀to฀high฀stresses,฀was฀ conirmed฀by฀SAD.฀Signiicant฀necking฀was฀evident฀along฀the฀fracture฀surface฀of฀ the฀PLD฀Ni฀ilm฀annealed฀at฀548฀K฀for฀one฀hour,฀but฀not฀on฀the฀fracture฀surface฀of฀ the฀as-deposited฀Ni฀ilm.฀Analysis฀of฀the฀fracture฀surface฀of฀the฀annealed฀PLD฀Ni฀ ilms฀ by฀ both฀ the฀ scanning฀ electron฀ microscope฀ (SEM)฀ and฀ TEM฀ revealed฀

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extensive฀ dislocation฀ activity฀ in฀ the฀ large฀ grains฀ that฀ resulted฀ in฀ signiicant฀ plasticity along the fracture. Further฀insight฀into฀the฀mechanisms฀active฀in฀the฀ilm฀as฀a฀function฀of฀grain฀size฀ and distribution can be gained from the comparison of the fracture surfaces in the three฀freestanding฀PLD฀Ni฀ilms฀produced฀by฀microfabrication฀and฀annealed฀to฀ varying conditions (Fig. 8.15). In฀Fig.฀8.15฀(a),฀the฀ilm,฀after฀release฀from฀the฀substrate,฀failed฀during฀straining฀ in the TEM. The location of crack initiation and propagation was not observed at the฀ time฀ of฀ failure.฀ Cross-sectional฀ SEM฀ images฀ of฀ the฀ ilm฀ show฀ no฀ sign฀ of฀ necking฀ in฀ the฀ ilm.฀ The฀ fracture฀ surface฀ of฀ this฀ ilm฀ shows฀ limited฀ signs฀ of฀ plasticity. On฀ the฀ fracture฀ surface฀ of฀ a฀ PLD฀ Ni฀ ilm฀ annealed฀ at฀ 548฀ K฀ and฀ shown฀ in฀ Fig. 8.15 (b), three different microstructures are encountered. In the center of the image, the fracture surface intersects a nanograined region in which the surface appears similar to that seen in Fig. 8.15 (a). To the left of this region, a cusp is observed along the fracture surface as it cuts through a large grain. Detailed observation of this grain and other large grains along the fracture surface reveals limited necking within the large grains. In the far right of Fig. 8.15 (b), a region is seen in which the fracture surface passes through a nanograined region vicinal to a฀large฀grain฀present฀in฀the฀ilm.฀The฀crack฀propagated฀through฀these฀three฀regions฀ with no tendency to avoid any of them. The฀fracture฀surface฀of฀the฀PLD฀Ni฀sample฀annealed฀at฀598฀K฀for฀one฀hour,฀ Fig. 8.15, is dominated by dislocation motion within a plastic region. Necking of the฀ilm฀can฀be฀seen฀in฀multiple฀grains฀in฀Fig.฀8.15฀(c).฀The฀plasticity฀observed฀in฀ this฀ilm฀is฀similar฀to฀the฀classical฀expectation฀for฀coarse-grained฀foils.1,80,81 The combination of dynamic observation of deformation and failure in bimodal PLD Ni and detailed observation of the fracture surface have shown that a variety of mechanisms฀ can฀ be฀ operative฀ in฀ the฀ same฀ region฀ of฀ the฀ ilm฀ simultaneously฀ dependent on the processing history of the metal.

8.6

Future trends

Current฀trends฀in฀the฀ield฀would฀suggest฀the฀maturation฀of฀studies฀into฀nanograined฀ FCC฀ metals.฀ Since฀ Gleiter’s฀ irst฀ suggestion฀ that฀ nanograined฀ metals฀ may฀ have฀ unique properties over 20 years ago,82 intensive research has been undertaken to develop฀processing,฀characterization,฀and฀testing฀tools,฀and฀evaluate฀the฀structure฀ of฀ nanograined฀ metals.฀ As฀ such,฀ the฀ ield฀ is฀ beginning฀ to฀ lose฀ its฀ novelty฀ and฀ the research is becoming less ground-breaking and more detailed in nature. This is฀ exempliied฀ in฀ the฀ decreased฀ interest฀ in฀ the฀ inverse฀ Hall–Petch฀ relationship฀ by฀leading฀research฀groups.฀Likewise,฀a฀trend฀is฀observed฀in฀the฀expansion฀of฀the฀ ield฀to฀pure฀BCC,฀HCP,฀and฀alloy฀systems฀being฀tested฀by฀increasing฀the฀number฀ of methods for a greater variety of electrical, thermal, mechanical, and other properties.

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8.15 Fracture surfaces of the PLD Ni films produced by microfabrication with: (a) the initial nanograined microstructure; (b) the bimodal grain size distribution from annealing for 1 hour at 548 K, and (c) ultra-fine grained microstructure from annealing for 1 hour at 598 K.

A฀promising฀trend฀in฀the฀ield฀is฀the฀publishing฀of฀more฀thorough฀studies฀into฀ the governing mechanisms and controlling factors that determine the deformation structures formed in nanograined metals. One of the greatest advances in recent history฀is฀the฀development฀and฀reinement฀of฀processes฀for฀producing฀nanograined฀

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metals with lower contamination levels and well-controlled grain boundary structures. The advancement in the processing-microstructure correlation has resulted฀in฀a฀split฀in฀the฀nanograined฀ield฀between฀the฀metals฀produced฀by฀topdown approaches and those produced by the bottom-up approaches. It is generally accepted that these sets of materials have very different initial microstructure, and as a result, will likely have differing active deformation mechanisms and resulting deformation defects. Along with studies of greater depth, the research into deformation defects in nanograined฀ metals฀ should฀ expand฀ in฀ all฀ dimensions฀ to฀ include฀ investigations฀ employing a greater range of techniques and materials systems. These material systems should include alloy systems with both solutes and precipitates, as strengthening฀and฀grain฀size฀stabilizing฀elements;฀more฀applied฀systems฀such฀as฀ nanograined฀ titanium฀ alloys฀ and฀ oxide-dispersed฀ steels;฀ and฀ various฀ crystal฀ systems. The investigation into different crystal systems, alloy compositions, and processing history will assist in the settlement of debate on the effect length-scale transitions have on the active mechanisms and resulting structures, as well as result in a better understanding of the defect structure and the active mechanisms, and development of nanograined metal applications in industry. Beyond the development in processing and analysis, the greatest potential in the identiication฀ of฀ defect฀ structures฀ may฀ come฀ from฀ the฀ recent฀ advances฀ in฀ highresolution฀ microscopy.฀ Three฀ recent฀ techniques฀ that฀ have฀ undergone฀ signiicant฀ development are aberration-corrected TEM, tomography, and atom probe microscopy. Recent developments in spherical and chromatic aberration-corrected TEM provides increased resolution and chemical mapping, which are essential for detailed analysis of nanograined structures. The further potential for increased resolution and a widened pole piece gap offered by spherical and chromatic aberration corrected TEM provides the opportunity to include a wide range of in situ techniques not previously possible. This should result in techniques for better understanding of the unique deformation structures in nanograined metals and the related formation mechanisms. Three-dimensional electron tomography is another technique฀that฀has฀progressed฀signiicantly฀and฀also฀has฀a฀potential฀for฀continued฀ development. The automation of this technique provides three-dimensional structural information with relative ease to a wide variety of sample geometries, microstructures,฀and฀chemistries.฀The฀inal฀technique฀that฀could฀potentially฀have฀a฀ large impact on defect structures in nanograined metals research is atom probe microscopy.฀This฀technique฀identiies฀the฀location฀and฀type฀of฀element฀present฀in฀a฀ material.฀With฀suficient฀increases฀in฀resolution,฀it฀would฀be฀able฀to฀determine฀the฀ exact฀ relationship฀ between฀ local฀ chemistry฀ and฀ microstructure฀ within฀ complex฀ nanograined฀alloys.฀One฀piece฀of฀equipment฀that฀would฀be฀of฀great฀beneit฀to฀the฀ ield,฀ but฀ is฀ not฀ currently฀ available฀ is฀ a฀ non-destructive฀ tool฀ capable฀ of฀ rapid฀ evaluation of the internal and grain boundary defects in bulk nanograined metals. It is also foreseen that current trends in computation capabilities will continue to increase greatly. This will result in the development of more robust computer

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models฀that฀should฀then฀be฀able฀to฀predict฀the฀evolution฀of฀more฀complex฀structures฀ over greater time periods. Overall, it appears that understanding of nanograined deformation and deformation structures through advances in new tools is progressing฀ out฀ of฀ its฀ infancy฀ and฀ expanding฀ into฀ a฀ broad฀ range฀ of฀ ields.฀ For฀ greater depth in mechanical properties,1,47,83 grain boundary structure,84 or electron microscopy85,86฀the฀reader฀should฀consult฀the฀classical฀text฀on฀the฀subject฀ referenced.

8.7

Acknowledgements

This work is supported by the Division of Materials Science and Engineering, Ofice฀of฀Basic฀Energy฀Sciences,฀US฀Department฀of฀Energy฀both฀at฀Sandia฀and฀ under grant DE-FG02–07ER46443. Sandia National Laboratories is a multiprogram฀laboratory฀operated฀by฀Sandia฀Corporation,฀a฀wholly฀owned฀subsidiary฀ of฀ Lockheed฀ Martin฀ Corporation,฀ for฀ the฀ US฀ Department฀ of฀ Energy’s฀ National฀ Nuclear฀Security฀Administration฀under฀contract฀DE-AC04–94AL85000.

8.8

References

฀ 1฀ J.P.฀Hirth฀and฀J.฀Lothe,฀Theory฀of฀Dislocations฀(McGraw-Hill฀Inc.,฀New฀York,฀1968). 2 G.E. Dieter, Mechanical Metallurgy (McGraw-Hill, Boston, 1986). ฀ 3฀ J.E.฀ Gordon,฀ The฀ New฀ Science฀ of฀ Strong฀ Materials฀ (Penguin฀ Science,฀ Middlesex,฀ England, 1978). ฀ 4฀ T.H.฀ Courtney,฀ Mechanical฀ Behavior฀ of฀ Materials฀ (McGraw-Hill฀ Higher฀ Education,฀ 2000). ฀ 5฀ D.S.฀Clark฀and฀W.R.฀Varney,฀Physical฀Metallurgy฀(Van฀Nostrand฀Company,฀Princeton,฀ NJ,฀1959). ฀ 6฀ S.฀Timoshenko฀and฀J.N.฀Goodier,฀Theory฀of฀Elasticity฀(McGraw฀Hill฀Higher฀Education,฀ 1970). ฀ 7฀ A.H.฀Cottrell,฀The฀Mechanical฀Properties฀of฀Matter฀(Krieger฀Pub฀Co,฀1981). ฀ 8฀ A.P.฀ Sutton฀ and฀ R.W.฀ Ballufi,฀ Interface฀ in฀ Crystalline฀ Materials฀ (Oxford฀ University฀ Press, 2007). ฀ 9฀ J.A.฀Weertman฀and฀J.R.฀Weertman,฀Elementary฀Dislocation฀Theory฀(Oxford฀University฀ Press, 1992). 10฀ Z.฀ Shan,฀ E.A.฀ Stach,฀ J.M.K.฀Wiezorek,฀ J.A.฀ Knapp,฀ D.M.฀ Follstaedt฀ and฀ S.X.฀ Mao,฀ Science 305 (2004) 654. 11฀ V.฀Yamakov,฀D.฀Wolf,฀S.R.฀Phillpot,฀A.K.฀Mukherjee฀and฀H.฀Gleiter,฀Nature฀Materials฀ 3 (2004) 43. 12฀ K.J.฀Hemker,฀D.฀Gianola,฀D.฀Warner,฀E.฀Ma,฀J.-F.฀Molinari฀and฀W.฀Sharpe,฀56฀307. 13฀ Z.W.฀Shan,฀J.M.K.฀Wiezorek,฀E.A.฀Stach,฀D.M.฀Follstaedt,฀J.A.฀Knapp฀and฀S.X.฀Mao,฀ Physical Review Letters 98 (2007) 095502. 14฀ X.฀Wu,฀Y.T.฀Zhu,฀M.W.฀Chen฀and฀E.฀Ma,฀Scripta฀Materialia฀54฀(2006)฀1685. 15฀ K.฀ Hattar,฀ J.฀ Han,฀ T.฀ Saif฀ and฀ I.M.฀ Robertson,฀ Conference฀ proceedings฀ from฀ the฀ Microscopy and Microanalysis Society (2004). 16฀ X.Z.฀Liao,฀S.G.฀Srinivasan,฀Y.H.฀Zhao,฀M.I.฀Baskes,฀Y.T.฀Zhu,฀F.฀Zhou,฀E.J.฀Lavernia฀ and H.F. Xu, Applied Physics Letters 84 (2004) 3564.

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17฀ X.Z.฀Liao,฀F.฀Zhou,฀E.J.฀Lavernia,฀D.W.฀He฀and฀Y.T.฀Zhu,฀Applied฀Physics฀Letters฀83฀ (2003) 5062. 18฀ K.฀Hattar,฀J.฀Han,฀M.T.A.฀Saif฀and฀I.M.฀Robertson,฀Journal฀of฀Materials฀Research฀20฀ (2005) 1869. 19฀ J.B.฀Bilde-Sorensen฀and฀J.฀Schiotz,฀Science฀300฀(2003)฀1244. 20฀ M.฀Chen,฀E.฀Ma,฀K.J.฀Hemker,฀H.฀Sheng,฀Y.฀Wang฀and฀X.฀Cheng,฀Science฀300฀(2003)฀ 1275. 21 A.G. Froseth, P.M. Derlet and H. Van Swygenhoven, Advanced Engineering Materials 7 (2005) 16. 22 X.Z. Liao, Y.H. Zhao, S.G. Srinivasan, Y.T. Zhu, R.Z. Valiev and D.V. Gunderov, Applied Physics Letters 84 (2004) 592. 23฀ R.J.฀Asaro฀and฀S.฀Suresh,฀Acta฀Materialia฀53฀(2005)฀3369. 24฀ B.฀Zhu,฀R.J.฀Asaro,฀P.฀Krysl฀and฀R.฀Bailey,฀Acta฀Materialia฀53฀(2005)฀4825. 25 Y.T. Zhu and T.G. Langdon, Materials Science and Engineering A 409 (2005) 234. 26฀ Y.T.฀Zhu,฀X.Z.฀Liao,฀S.G.฀Srinivasan฀and฀E.J.฀Lavernia,฀Journal฀of฀Applied฀Physics฀98฀ (2005) 34319. 27฀ J.W.฀Christian฀and฀S.฀Mahajan,฀Progress฀in฀Materials฀Science฀39฀(1995)฀1. 28฀ R.C.฀Hugo,฀H.฀Kung,฀J.R.฀Weertman,฀R.฀Mitra,฀J.A.฀Knapp฀and฀D.M.฀Follstaedt,฀Acta฀ Materialia 51 (2003) 1937. 29฀ H.฀Van฀Swygenhoven฀and฀J.R.฀Weertman,฀Scripta฀Materialia฀49฀(2003)฀625. 30฀ M.A.฀ Meyers,฀ A.฀ Mishra฀ and฀ D.J.฀ Benson,฀ Progress฀ in฀ Materials฀ Science฀ 51฀ (2006) 427. 31฀ A.C.฀Lund฀and฀C.A.฀Schuh,฀in฀Amorphous฀and฀Nanocrystalline฀Metals฀Symposium,฀ Dec.฀1–4,฀2003฀(Mater.฀Res.฀Soc.,฀Boston,฀MA,฀USA,฀2004)฀p.฀313. 32฀ Y.-H.฀ Zhao,฀ J.F.฀ Bingert,฀ X.-Z.฀ Liao,฀ B.-Z.฀ Cui,฀ K.฀ Han,฀ A.V.฀ Sergueeva,฀ A.K.฀ Mukherjee,฀ R.Z.฀ Valiev,฀ T.G.฀ Langdon฀ and฀ Y.T.฀ Zhu,฀ Advanced฀ Materials฀ 18฀ (2006) 2949. 33฀ Z.฀ Rong,฀ V.฀ Mohles,฀ D.J.฀ Bacon฀ and฀ Y.N.฀ Osetsky,฀ Philosophical฀ Magazine฀ 85฀ (2005) 171. 34 G. Moya, Acta Metall. 23 (1975) 289. 35฀ M.฀de฀Jong฀and฀J.S.฀Koehler,฀Phys.฀Rev.฀L2฀129฀(1963)฀49. 36 N. Nita, R. Schaeublin, M. Victoria and R.Z. Valiev, Phil. Mag. 85 (2005) 723. 37฀ M.H.฀Loretto,฀L.M.฀Clarebrough฀and฀R.L.฀Segall,฀Phil.฀Mag.฀11฀(1964)฀459. 38฀ R.J.฀Jahn฀and฀A.H.฀King,฀Phil.฀Mag.฀A.฀54฀(1986)฀3. 39฀ F.฀Dalla฀Torre,฀R.฀Lapovok,฀J.฀Sandlin,฀P.F.฀Thomson,฀C.H.J.฀Davies฀and฀E.V.฀Pereloma,฀ Acta Materialia 52 (2004) 4819. 40฀ M.฀Kiritani,฀K.฀Yasunaga,฀Y.฀Matsukawa฀and฀M.฀Komatsu,฀in฀Electron฀Microscopy:฀Its฀ Role in Materials Science, Mar. 2–6, 2003 (Minerals, Metals and Materials Society, Warrendale,฀PA฀15086,฀United฀States,฀San฀Diego,฀CA,฀United฀States,฀2003)฀p.฀71. 41 E.O. Hall, Physical Society – Proceedings 64 (1951) 747. 42฀ N.J.฀Petch,฀Iron฀and฀Steel฀Institute฀–฀Journal฀174฀(1953)฀25. 43฀ E.฀Arzt,฀Acta฀Materialia฀46฀(1998)฀5611. 44฀ H.฀ Conrad฀ and฀ K.฀ Jung,฀ Materials฀ Science฀ &฀ Engineering฀ A฀ (Structural฀ Materials:฀ Properties, Microstructure and Processing) 391 (2005) 272. 45฀ J.A.฀Knapp฀and฀D.M.฀Follstaedt,฀Journal฀of฀Materials฀Research฀19฀(2004)฀218. 46฀ T.C.฀Lee,฀I.M.฀Robertson฀and฀H.K.฀Birnbaum,฀Philosophical฀Magazine฀A฀(Physics฀of฀ Condensed฀Matter,฀Defects฀and฀Mechanical฀Properties)฀62฀(1990)฀131. 47฀ J.R.฀Weertman฀and฀J.฀Weertman,฀Elementary฀Dislocation฀Theory฀(Oxford฀University฀ Press, 2000).

© Woodhead Publishing Limited, 2011

Deformation structures including twins in nanograined pure metals

241

48฀ I.M.฀Robertson,฀A.฀Beaudoin,฀K.฀Al-Fadhalah,฀L.฀Chun-Ming,฀J.฀Robach,฀B.D.฀Wirth,฀ A. Arsenlis, D. Ahn and P. Sofronis, Materials Science and Engineering A 400–401 (2005) 245. 49฀ Y.฀Wang,฀M.฀Chen,฀F.฀Zhou฀and฀E.฀Ma,฀Nature฀419฀(2002)฀912. 50฀ D.฀ Farkas,฀ H.฀ Van฀ Swygenhoven฀ and฀ P.M.฀ Derlet,฀ Physical฀ Review฀ B฀ (Condensed฀ Matter and Materials Physics) 66 (2002) 060101. 51 H. Huang and F. Spaepen, Acta Materialia 48 (2000) 3261. 52 F.R.N. Nabarro, Scripta Materialia v 39 (1998) p 1681. 53 D.S. Gianola, S. Van Petegem, M. Legros, S. Brandstetter, H. Van Swygenhoven and K.฀J.฀Hemker,฀Acta฀Materialia฀54฀(2006)฀2253. 54฀ K.฀Hattar,฀D.M.฀Follstaedt,฀J.A.฀Knapp฀and฀I.M.฀Robertson,฀In฀situ฀TEM฀observation฀ of Stress-Induced Grain Growth, (2010). 55฀ T.฀Gladman,฀Grain฀Size฀Control฀(Maney฀Publishing,฀London,฀2004). 56฀ A.C.฀Ferro฀and฀M.A.฀Fortes,฀Interface฀Science฀5฀(1997)฀263. 57฀ E.M.฀ Bringa,฀ A.฀ Caro,฀ Y.฀ Wang,฀ M.฀ Victoria,฀ J.M.฀ McNaney,฀ B.A.฀ Remington,฀ R.F. Smith, B.R. Torralva and H. Van Swygenhoven, Science 309 (2005) 1838. 58฀ H.฀ Van฀ Swygenhoven,฀A.฀ Caro฀ and฀ D.฀ Farkas,฀ Scripta฀ Materialia,฀ 5th฀ International฀ Conference฀on฀Nanostructured฀Materials฀(NANO฀2000),฀Aug.฀20–25,฀2000฀44฀(2001)฀ 1513. 59฀ H.฀Van฀Swygenhoven,฀M.฀Spaczer฀and฀A.฀Caro,฀Nanostructured฀Materials,฀Proceedings฀ of฀the฀1998฀TMS฀Annual฀Meeting฀&฀Exposition,฀Feb.฀15–19,฀1998฀10฀(1998)฀819. 60฀ A.J.฀Haslam,฀S.R.฀Phillpot,฀D.฀Wolf,฀D.฀Moldovan฀and฀H.฀Gleiter,฀Materials฀Science฀&฀ Engineering A (Structural Materials: Properties, Microstructure and Processing) A318 (2001) 293. 61 H. Li, Advanced Engineering Materials 7 (2005) 1109. 62฀ J.W.฀Cahn฀and฀J.E.฀Taylor,฀52฀4887. 63฀ B.B.฀Rath,฀M.฀Winning฀and฀J.C.M.฀Li,฀Applied฀Physics฀Letters฀90฀(2007)฀161915. 64 V. Bata and E.V. Pereloma, Acta Materialia 52 (2004) 657. 65 V. Bata and E.V. Pereloma, Scripta Materialia 51 (2004) 927. 66฀ J.A.฀Wert,฀Scripta฀Materialia฀50฀(2004)฀1487. 67฀ H.฀Inui,฀S.I.฀Hong฀and฀C.฀Laird,฀Acta฀Metallurgica฀38฀(1990)฀2261. 68฀ R.Z.฀Valiev฀and฀I.V.฀Alexandrov,฀58฀1003. 69฀ L.M.฀Dougherty,฀I.M.฀Robertson฀and฀J.S.฀Vetrano,฀Acta฀Materialia฀51฀(2003)฀4367. 70 B.L. Boyce, Proceedings of the SPIE – The International Society for Optical Engineering฀ Reliability,฀ Testing,฀ and฀ Characterization฀ of฀ MEMS/MOEMS฀ II,฀ Jan.฀27–29,฀2003฀4980฀(2003)฀175. 71฀ S.M.฀Allameh,฀Journal฀of฀Materials฀Science฀38฀(2003)฀4115. 72฀ M.฀ Briceno,฀ K.฀ Hattar,฀ J.฀ Damiano,฀ D.฀ Nackashi฀ and฀ I.M.฀ Robertson,฀ In-situ฀ TEM฀ study of the sintering process of gold nanoparticles using ultra-fast heating stage (2010). 73฀ J.฀Urban,฀33฀1009. 74 Y.T. Zhu, X.Z. Liao and R.Z. Valiev, Applied Physics Letters 86 (2005). 75 Y.T. Zhu, X.Z. Liao and R.Z. Valiev, Applied Physics Letters 86 (2005) 103112. 76฀ M.฀Murayama,฀J.M.฀Howe,฀H.฀Hidaka฀and฀S.฀Takaki,฀Science฀295฀(2002)฀2433. 77 I.A. Ovid’ko, Science 295 (2002) 2386. 78฀ K.฀Hattar,฀D.M.฀Follstaedt,฀J.A.฀Knapp฀and฀I.M.฀Robertson,฀56฀794. 79฀ T.W.฀Kirkman,฀Statistists฀to฀Use,฀at฀http://www.physics.csbsju.edu/stats/฀(1996). 80฀ M.P.฀ Dewald฀ and฀ W.A.฀ Curtin,฀ Modelling฀ and฀ Simulation฀ in฀ Materials฀ Science฀ and฀ Engineering 15 (2007) 193.

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81 H.G.F. Wilsdorf, Acta Metallurgica 30 (1982) 1247. 82฀ J.฀Horvath,฀R.฀Birringer฀and฀H.฀Gleiter,฀Solid฀State฀Communications฀62฀(1987)฀319. 83฀ T.H.฀Courtney,฀Mechanical฀Behavior฀of฀Materials฀(McGraw-Hill฀Science,฀1999). 84฀ A.P.฀ Sutton฀ and฀ R.W.฀ Ballufi,฀ Interfaces฀ in฀ crystalline฀ Materials฀ (Clarendon฀ Press,฀ 2007). 85฀ D.B.฀Williams฀and฀C.B.฀Carter,฀Transmission฀electron฀microscopy฀(Plenum฀Press,฀New฀ York, 1996). 86฀ J.C.H.฀Spence,฀High-Resolution฀Electron฀Microscopy฀(Oxford฀University฀Press,฀New฀ York, 1994).

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9 Microstructure and mechanical properties of nanostructured low-carbon steel prepared by equal-channel angular pressing Y.G.฀KO, Yeungnam University,฀Republic฀of฀Korea and D. H. SHIN, Hanyang University,฀Republic฀of฀Korea

Abstract: This chapter reviews the microstructural evolution of nanostructured low-carbon฀steels฀during฀equal-channel฀angular฀pressing฀(ECAP)฀and฀ subsequent heat treatments. Regarding microstructural evolution, most ferrite phase฀grains฀are฀signiicantly฀reined฀by฀grain฀subdivision฀related฀to฀various฀slip฀ systems of {110}, {112} and {123}, which are mainly operated฀by฀ECAP฀shear฀strain,฀while฀pearlite฀colonies฀are฀deformed฀by฀ mechanical fragmentation. When appropriate subsequent heat treatments are selected,฀a฀signiicant฀portion฀of฀carbon฀atoms฀are฀redistributed฀uniformly฀during฀ ECAP฀deformation,฀leading฀to฀a฀uniform฀distribution฀of฀nanoscale฀cementite฀ particles. The mechanical properties of the nanostructured steel samples are also examined,฀focusing฀on฀microstructural฀modiications฀to฀overcome฀their฀inherent฀ mechanical drawbacks arising from dynamic recovery and nanoscale grains. Key words: nanostructured low-carbon steel, equal-channel angular pressing (ECAP),฀microstructural฀evolution,฀mechanical฀properties.

9.1

Introduction

Over the past decade, the materials science and engineering community has paid considerable attention to nanostructured metallic materials due to their unique properties, particularly their superior mechanical properties, which offer opportunities for a variety of structural applications.1–14 Previous studies have shown that the mechanical properties of nanostructured metallic materials differ greatly from those of฀traditional฀coarse-฀and฀ine-grained฀metallic฀materials.15–20 Since the milestone work by Segal et al.,21฀equal-channel฀angular฀pressing฀(ECAP)฀has฀been฀regarded฀as฀ one of the most promising processes for fabricating advanced metallic materials with nanoscale฀grains.฀Its฀advantages฀have฀spurred฀a฀great฀deal฀of฀research฀on฀ECAPed฀ metallic materials, which have found successful applications in metallic systems such as aluminum,22 iron,23–25 and titanium10,14 alloys. Among these materials, a special focus is placed here on the microstructure and mechanical฀properties฀of฀nanostructured฀low-carbon฀steel฀(LCS)฀in฀light฀of฀two฀ main฀ considerations.฀ In฀ conventional฀ LCS฀ steels,฀ structural฀ reinement฀ of฀ the฀ grain฀size฀from฀~10฀to฀~1฀µm฀led฀to฀an฀increase฀in฀yield฀strength฀by฀as฀much฀as฀ ~500 MPa, and a decrease in the ductile–brittle transition temperature below roughly฀–350฀K.฀Thus,฀extensive฀efforts฀have฀been฀devoted฀to฀the฀development฀of฀ 243 © Woodhead Publishing Limited, 2011

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ferrous฀alloys฀with฀submicron-level฀grain฀sizes฀by฀the฀aforementioned฀processing฀ technologies.฀Considering฀the฀enhanced฀mechanical฀properties฀and฀concomitant฀ commercial฀potential฀of฀nanostructured฀low-carbon฀steel฀(LCS),฀an฀overall฀review฀ would provide a fundamental understanding along with assessing the current development฀of฀new฀types฀of฀ferrous฀alloys.฀Second,฀since฀an฀LCS฀alloy฀consists฀ of two phases, i.e. ferrite and pearlite, its deformation behavior differs markedly from that of single-phase materials. Although pearlite has a much smaller volume fraction฀ than฀ ferrite฀ in฀ LCS,฀ its฀ effect฀ on฀ the฀ mechanical฀ properties฀ of฀ steel฀ is฀ disproportionately large. In addition, the microstructural evolution of pearlite during฀ECAP฀is฀expected฀to฀be฀complex฀due฀to฀the฀existence฀of฀hard฀cementite฀ lamellar plates. In this chapter, we reviewed recent progress on microstructural evolution฀and฀the฀resulting฀mechanical฀properties฀of฀nanostructured฀LCS฀samples,฀ which฀ were฀ analyzed฀ through฀ transmission฀ electron฀ microscopy฀ (TEM)฀ based฀ and theoretical approaches. We also reviewed several metallurgical strategies that had intended to overcome the shortcomings of mechanical properties of nanostructured฀LCS,฀such฀as฀a฀lack฀of฀strain฀hardenability.

9.2

The microstructural evolution of low-carbon steel (LCS)

9.2.1 The microstructural evolution of LCS by equal-channel angular pressing (ECAP) Figure฀9.1฀displays฀the฀optical฀microstructure฀of฀an฀ECAPed฀LCS฀as฀a฀function฀ of฀the฀number฀of฀ECAP฀passes฀with฀route฀C฀where฀the฀sample฀is฀rotated฀180°฀ along฀ its฀ longitudinal฀ axis.฀ The฀ X-plane฀ is฀ the฀ plane฀ perpendicular฀ to฀ the฀ longitudinal฀axis฀of฀the฀sample,฀and฀the฀Y-฀and฀Z-planes฀denote฀the฀side-viewed฀ and฀ top-viewed฀ planes฀ along฀ the฀ longitudinal฀ axis฀ of฀ the฀ sample,฀ respectively.฀ The฀ initial฀ sample฀ reviewed฀ here฀ is฀ a฀ LCS฀ sample฀ consisting฀ of฀ pearlite฀ of฀ approximately฀15%฀(dark฀phase)฀with฀the฀remainder฀being฀ferrite฀(bright฀phase)฀ shown฀in฀Fig.฀9.1฀(a).฀Both฀phases฀are฀nearly฀globular฀and฀their฀size฀is฀~30฀µm.฀ Several฀ common฀ microstructural฀ changes฀ with฀ ECAP฀ deformation฀ were฀ noted฀ regardless of the planes: 1) the constituent phases became smaller and more irregular฀with฀repetition฀of฀pressing฀as฀can฀be฀seen฀from฀Fig.฀9.1฀(b)–(e);฀2)฀the฀ ferrite grain boundaries of the sample after a single pass were visible as shown in Fig.฀9.1฀(b),฀but฀there฀existed฀many฀dim฀contours฀inside฀them,฀likely฀indicative฀of฀ the฀fragmentation฀of฀ferrite฀grains฀due฀to฀extensive฀strain;26฀and฀3)฀it฀is฀dificult฀to฀ identify฀the฀initial฀ferrite฀grain฀boundaries,฀and฀the฀dim฀contours฀became฀extensive฀ beyond two or more passes of the pressing as shown in Fig. 9.1 (c)–(f ). Referring to฀the฀pearlite฀colony฀size฀as฀a฀qualitative฀measure฀of฀the฀mechanical฀fragmentation,฀ the fragmentation on the X-plane was even more severe than that on the Y-planes. With an odd number of passes, the micrographs of the Y-plane showed that the grains฀ were฀ severely฀ elongated฀ along฀ the฀ direction฀ of฀ ~30°฀ inclined฀ to฀ its฀

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9.1 Optical micrographs of (a) the initial sample, (b) one-pass, (c) two-pass, (d) three-pass, and (e) four-pass ECAP-deformed samples with respect to the viewing planes (X, Y, and Z planes).24

longitudinal฀axis,฀which฀was฀fairly฀similar฀to฀the฀macro-shear฀direction฀imposed฀by฀ ECAP฀as฀shown฀in฀Fig.฀9.1฀(b)฀and฀(d).฀With฀a฀subsequent฀even฀number฀of฀passes,฀ both฀phases฀restored฀the฀near-equiaxed฀shape฀as฀shown฀in฀Figs.฀9.1฀(c)฀and฀(e). These฀microstructural฀changes฀were฀anticipated฀when฀route฀C฀was฀used.27–29 Despite฀the฀signiicant฀inherent฀difference฀in฀yield฀strength฀and฀plastic฀deformation฀ between pearlite and ferrite phases, the presence of severely elongated phases after฀an฀odd฀number฀of฀passes฀and฀the฀restoration฀of฀their฀equiaxed฀shape฀after฀ a฀ subsequent฀ even฀ number฀ of฀ passes฀ were฀ observable.฀ Under฀ severe฀ plastic฀ deformation conditions, the macroscopic deformation behavior of pearlite was quite similar to that of ferrite. In terms of deformability, no cracking was observed in฀ the฀ LCS฀ samples฀ that฀ were฀ subjected฀ to฀ severe฀ plastic฀ straining฀ while฀ the฀ strength and plastic deformation behaviors of pearlite and ferrite all vary. Two factors could account for this observation: 1) a soft ferrite phase with a large

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volume fraction could accommodate plastic incompatibility between two phases, and 2) a hard pearlite phase is capable of sustaining plastic deformation to some extent. Figure 9.2 (a) presents a TEM image of ferrite in the deformed samples viewed from฀the฀Y-plane.฀The฀initial฀microstructure฀exhibited฀a฀relatively฀low฀dislocation฀ density. After a single pass, the microstructure mainly consisted of parallel shear bands of elongated grains with a length of ~2 µm and width of ~0.5 µm, showing considerable฀grain฀reinement฀(Fig.฀9.2฀(b)฀).฀The฀corresponding฀selected-area฀electron฀ diffraction฀ (SAED)฀ pattern฀ was฀ characterized฀ by฀ individual฀ spots,฀ implying฀ that฀ most฀of฀the฀boundaries฀of฀ine฀grains฀formed฀by฀a฀single฀pass฀would฀be฀of฀low฀angle.฀ The฀microstructure฀after฀two฀passes฀(Fig.฀9.2฀(c)฀)฀contained฀fairly฀equiaxed฀grains฀ with฀widths฀comparable฀to฀those฀of฀grains฀obtained฀by฀the฀irst฀pass.฀However,฀the฀ SAED฀pattern฀showed฀the฀appearance฀of฀additional฀rings฀and฀extra฀spots,฀indicating฀ the฀ formation฀ of฀ high-angle฀ grain฀ boundaries.฀ Near-equiaxed฀ ultra-ine฀ grains฀ of฀ 0.2–0.3฀µm฀diameter,฀which฀were฀iner฀than฀those฀obtained฀at฀two฀passes,฀resulted฀ from four-pass treatment (Fig. 9.2 (d)). In addition, the number of rings in the SAED

9.2 Transmission electron microscopy images of ferrite phase grains in (a) the initial sample, (b) one-pass, (c) two-pass, and (d) four-pass ECAPed LCS samples taken from the Y-plane presenting main shear deformation.24

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pattern increased and the spots became more diffused as compared to the previous observations. The increase in the number of the rings and the spots with repeated passes฀indicates฀that฀the฀grain฀size฀reduction฀rose฀with฀increasing฀number฀of฀pressings฀ by฀evolution฀from฀low-angle฀boundaries,฀which฀appeared฀after฀the฀irst฀pass,฀to฀highangle boundaries. From TEM observations, however, ferrite grain boundaries after ECAP฀ were฀ not฀ well฀ deined฀ and฀ the฀ existence฀ of฀ extensive฀ extinction฀ contours฀ along grain boundaries was evident. These observations indicated that ferrite grain boundaries฀formed฀by฀ECAP฀were฀in฀a฀non-equilibrium฀state฀having฀a฀high฀internal฀ stress due to long-range order lattice distortion. These general features associated with the microstructural changes observed in ferrite phases are consistent with those in฀ECAP-deformed฀aluminum฀alloys฀reported฀in฀the฀literature.7,26,30–32 On the other hand, the deformation behavior of pearlite differed from that of the฀ferrite฀phase฀during฀ECAP.฀The฀initial฀morphology฀of฀pearlite฀in฀the฀LCS฀ sample consisted of a well-developed continuous lamellar structure, as shown in Fig. 9.3 (a).

9.3 Transmission electron microscopy images of pearlite colonies in the initial and ECAP-deformed LCS samples showing the morphological changes in cementite: (a) the initial sample, (b) severely necked cementite after four-pass, (c) mechanically curled and wavy cementite plates after four-pass, and (d) globular cementite and sharp slip lines (marked by two black arrows) after four-pass.24

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After฀four-pass฀ECAP,฀the฀microstructure฀of฀the฀pearlite฀phase฀is฀represented฀by฀two฀ typical฀features฀according฀to฀cementite฀morphology.฀The฀irst฀feature฀is฀that฀cementite฀ plates remained parallel to each other but were in a discrete form, indicating the occurrence฀of฀a฀breakage฀of฀cementite฀lamellae฀during฀ECAP฀(Fig.฀9.3฀(b)฀).฀The฀ second feature is that the discrete cementite lamellae were severely curled and wavy (Fig. 9.3 (c)). The occurrence of severe necking was also evident along the cementite plate length. In some cases, as shown in Fig. 9.3 (d), a globular cementite33,34 and a sharp slip line35 were observed. The observation of both severe necking and a sharp slip line indicated that a breakage of the cementite lamellae occurred. It is of interest that฀the฀cementite฀lamellae฀exhibited฀a฀considerable฀capability฀for฀plastic฀deformation฀ as shown in Fig. 9.3 (b)–(d), given that the cementite is prone to fracture with ease in a฀ brittle฀ manner฀ under฀ uni-axial฀ tensile฀ mode฀ on฀ account฀ of฀ the฀ few฀ slip฀ systems฀ available.36 Such plastic deformation behavior of cementite could be attributed to the presence of severely elongated pearlite after an odd number of passes and the restoration฀of฀its฀equiaxed฀shape฀after฀a฀subsequent฀even฀number฀of฀passes.฀To฀shed฀ light on this unusual behavior, a comparison with the earlier work on a pearlitic steel wire deformed via conventional drawing would be helpful.33฀Under฀the฀nearly฀same฀ effective฀strain,฀severely฀ECAP-deformed฀cementite฀in฀the฀pearlite฀phase฀was฀quite฀ similar to that observed in a heavily cold drawn pearlitic steel wire.33,34 For the heavily cold drawn pearlitic steel wire, it is generally accepted that severely deformed cementite plates are found on the planes of the lamellae aligned along the drawing axis฀while฀curled฀wavy฀cementite฀plates฀are฀observed฀on฀the฀planes฀of฀the฀lamellae,฀ which฀ are฀ not฀ aligned฀ along฀ the฀ drawing฀ axis.฀ When฀ cementite฀ was฀ subjected฀ to฀uni-axial฀tensile฀deformation,฀(001)[010],฀(010)[001]฀and฀(100)[010]฀slip฀systems฀ were฀ operative,฀ but฀ they฀ were฀ insuficient฀ for฀ cementite฀ to฀ deform฀ plastically฀ without฀inducing฀signiicant฀cracks.37 Accordingly, the TEM observations showing considerable plastic deformation of cementite suggested that the additional slip systems฀ might฀ operate฀ under฀ the฀ deformation฀ mode฀ accompanied฀ by฀ ECAP,฀ the฀ deformation mode of which was documented to be shear. In the cold drawing process, pearlite฀was฀subjected฀to฀a฀hydrostatic฀stress฀state.฀Under฀the฀hydrostatic฀stress฀state,฀ – – additional slip systems of (110)[111] and (011)[111]฀ became฀ active.฀ Cementite฀ thereupon฀possessed฀a฀number฀of฀slip฀systems฀suficient฀for฀homogeneous฀plastic฀ deformation.21,38฀Still,฀it฀is฀doubtful฀whether฀the฀stress฀state฀induced฀by฀ECAP฀is฀ comparable to that induced by the cold drawing process. Based on the observation that cementite deformed plastically in Fig. 9.3 (b)–(d), however, it is likely that ECAP฀deformation฀could฀develop฀a฀complex฀stress฀state฀where฀a฀suficient฀number฀ of slip systems for the plastic deformation of cementite are in operation.

9.2.2 Grain refinement mechanism Slip system at the first pass of ECAP Figure฀9.4฀(a)฀presents฀a฀TEM฀micrograph฀of฀a฀LCS฀sample฀viewed฀from฀the฀฀ zone฀axis฀after฀the฀irst฀pass฀of฀ECAP.฀The฀ferrite฀microstructure฀mainly฀consists฀of฀

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parallel฀bands฀of฀elongated฀grains฀having฀a฀width฀of฀0.3฀µm.฀The฀extended฀parallel฀ band boundaries are called lamellar-type boundaries (LBs). The corresponding SAED pattern shows that LBs are mainly low-angled and the direction of the bands is primarily parallel to the direction. Inside the band interior, dislocation cell boundaries฀ (DCBs)฀ were฀ also฀ detected.฀ The฀ dislocation฀ density฀ inside฀ a฀ cell฀ enclosed฀by฀DCBs฀is฀relatively฀low.฀DBs฀were฀typically฀found฀to฀be฀either฀normal฀ to฀LBs฀or฀30°฀and฀60°฀inclined฀to฀LBs.฀This฀kind฀of฀boundary฀structure฀was฀reported฀ to be typical for heavily deformed metallic materials. In฀order฀to฀identify฀the฀slip฀system฀operating฀during฀ECAP,฀irst฀it฀is฀important฀ to฀recognize฀that฀the฀direction฀of฀the฀deformation฀band฀should฀be฀parallel฀to฀the฀ intersecting฀ line฀ between฀ the฀ viewing฀ plane฀ normal฀ to฀ the฀ selected฀ zone฀ axis฀ and the slip plane on which deformation occurred. The direction of the deformation band is thus equivalent to that of the projection of the slip plane, which contains both the slip direction and the direction of the deformation band, on the viewing plane.฀Figure฀9.4฀(b)฀suggests฀a฀probable฀grain฀reinement฀mechanism฀of฀a฀LCS฀ alloy from the standpoint of dislocation slip activities based on analysis of TEM data. A pictorial illustration satisfying this condition is presented in order to –– identify฀ the฀ slip฀ systems฀ operating฀ at฀ the฀ irst฀ pass฀ of฀ ECAP.฀ When฀ the฀ [111] – direction was selected as the viewing direction, two of the slip planes (110) and –– (112) in the body-centered cubic (bcc) crystal system could contain the [110] deformation band direction, which was the major deformation band direction formed฀at฀the฀irst฀pass.฀In฀order฀to฀identify฀the฀slip฀plane฀more฀deinitively,฀it฀was฀ necessary฀to฀rotate฀the฀viewing฀direction฀in฀TEM.฀Using฀this฀tilting฀method,฀the฀ –– – (112) plane with the [111]฀slip฀direction฀was฀characterized฀as฀the฀slip฀plane.฀It฀was฀ noted that, in a different region, planes belonging to the {110} family were also identiied฀as฀the฀slip฀plane.฀Accordingly,฀it฀was฀evident฀that฀the฀slip฀systems฀of฀

9.4 (a) Transmission electron microscopy micrograph of the first pass ECAPed LCS sample and (b) pictorial illustration for formation of the deformation band and identification of the corresponding slip systems operating at the first pass.39

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{110} and {112}, which are typical in a bcc crystal system, were the major฀slip฀systems฀operating฀in฀the฀LCS฀alloy฀during฀the฀irst฀pass฀of฀ECAP. Slip system at the second pass of ECAP Figure฀9.5฀(a)฀shows฀a฀TEM฀micrograph฀of฀a฀LCS฀sample฀viewed฀from฀the฀฀ zone฀axis฀after฀the฀second฀pass฀of฀ECAP.฀Equiaxed฀grains฀were฀formed฀by฀the฀second฀ pass,฀but฀their฀average฀size฀of฀~0.5฀µm฀was฀slightly฀larger฀than฀the฀width฀of฀the฀subgrain฀bands฀formed฀by฀the฀irst฀pass.฀From฀the฀SAED฀pattern,฀it฀was฀obvious฀that,฀at฀ least in this area, the misorientation between sub-grains increased compared with that of฀ the฀ sample฀ deformed฀ by฀ a฀ single฀ pass.฀ Even฀ though฀ the฀ portion฀ of฀ ultra-ine฀ equiaxed฀grains฀was฀large,฀some฀sub-grain฀bands฀remained.฀This฀implies฀that฀twopass฀ ECAP฀ was฀ insuficient฀ to฀ produce฀ a฀ homogeneous฀ structure฀ despite฀ the฀ considerable฀grain฀reinement.฀Many฀boundaries฀were฀aligned฀along฀either฀the฀฀ or directions, similar to those in the sample after a single pass. However, detailed inspection of Fig. 9.5 (a) reveals the presence of additional boundaries having several different angles with respect to the direction. The direction is the alignment direction of LBs as well as sub-grain bands. The observation of sub-grain boundaries with other directions reveals that new slip systems operated in the course of the following deformation. Accordingly, the boundaries appeared to be serrated as shown in regions 1 and 2 in Fig. 9.5 (a). A฀TEM฀analysis฀was฀conducted฀on฀the฀two-pass฀ECAPed฀sample.฀In฀addition฀to฀ the and directions, the boundaries having several different angles with respect to the direction were observed. This reflects that dislocations belonging to several different slip systems moved and, thereby, formed cell boundaries inside the initial sub-grain bands to accommodate the strain energy. To understand the deformation characteristics induced by the second pass, a pictorial illustration is

9.5 (a) Transmission electron microscopy micrograph of the second pass ECAPed LCS sample and (b) pictorial illustration for formation of the deformation band and identification of the corresponding slip systems operating at the second pass.39

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– provided in Fig. 9.5 (b). In the second pass, the [111] direction became the slip – direction if the [111]฀direction฀could฀be฀the฀slip฀direction฀operating฀at฀the฀irst฀pass.฀ – The intersection between the viewing plane of (111) and the slip plane of (110) – – – containing the [111] slip direction was aligned along the [112] direction, displaying the direction of the new deformation band. It was noted that, on the viewing plane of – – – (111), the [112] direction was normal to the [110] direction, which coincides with the direction฀of฀deformation฀bands฀formed฀by฀the฀irst฀pass.฀Accordingly,฀based฀on฀the฀ –– – – TEM image observed in the direction of [111], the boundaries aligned along the [112] direction฀appeared฀to฀be฀normal฀to฀the฀LBs฀formed฀by฀the฀irst฀pass.฀By฀the฀same฀ – logic, boundaries representing the [213] and [101] deformation bands appeared to be – inclined฀79°฀and฀60°,฀respectively,฀to฀the฀LBs฀formed฀by฀the฀irst฀pass.฀The฀[213] and – – – – [101] deformation bands were associated with the (211) and (101) slip systems, respectively. Figure 9.6 (a) provides a TEM micrograph of the serrated

9.6 Transmission electron microscopy micrograph showing an example of the serrated boundaries found in (a) the two-pass ECAPed LCS sample, viewed by a zone axis, and (b) its schematic description including the slip system corresponding to the individual bands and the angular relationship between them.39

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boundary฀observed฀in฀the฀two-pass฀ECAPed฀sample,฀viewed฀by฀the฀฀zone฀axis,฀ as well as its schematic description, including the slip system corresponding to the individual bands and the angular relationship between bands. The angular relationship between฀deformation฀bands฀formed฀by฀the฀irst฀and฀second฀passes฀described฀above฀ was฀in฀excellent฀accordance฀with฀that฀measured฀experimentally฀in฀Fig.฀9.6฀(b).฀Thus,฀ similar฀to฀the฀irst฀pass,฀the฀{112}฀and฀{110}฀systems฀could฀be฀considered฀ as slip systems operating at the second pass. However, the initial shear bands formed at฀the฀irst฀pass฀inhibited฀dislocations฀on฀other฀slip฀systems฀from฀crossing฀the฀bands.฀ As a result, all of the possible slip systems belonging to the {112} and {110} slip system families should operate to accommodate deformation during the second pass. Hence, nanoscale dislocation cells enclosed by the {112} and {110} planes were formed.39–41 Formation of high-angle grain boundary The฀microstructures฀after฀four-pass฀ECAP฀are฀shown฀in฀Fig.฀9.7,฀in฀which฀equiaxed฀ grains฀with฀an฀average฀grain฀size฀of฀0.2–0.3฀µm฀were฀formed.฀Similar฀to฀previous฀ indings,42–45฀this฀conirms฀that฀grain฀reinement฀was฀most฀pronounced฀at฀the฀initial฀ stage฀of฀ECAP฀but฀was฀not฀signiicant฀at฀large฀strains.฀This฀is฀because,฀with฀an฀ increment in the amount of applied strain, the dislocation movement on the new slip systems would be restricted by the presence of the initial shear bands and, thus, they should rotate so as not only to accommodate strain but also to maintain an even shear strain distribution at grain boundaries once sub-grains appear. In฀ order฀ to฀ examine฀ the฀ grain฀ orientation฀ relationship฀ between฀ two฀ adjacent฀ nanostructured฀grains,฀a฀Kikuchi฀pattern฀analysis฀was฀carried฀out.฀Some฀examples฀

9.7 Transmission electron microscopy micrograph of the four-pass ECAPed LCS sample.39 (Hereafter, all samples were subjected to four-pass ECAP).

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9.8 Transmission electron microscopy Kikuchi patterns showing the misorientation relationship between adjacent nanostructured ferrite grains of the ECAPed LCS sample.39

of฀the฀Kikuchi฀patterns฀of฀the฀four-pass฀ECAPed฀sample฀viewed฀from฀the฀฀ zone฀axis฀are฀shown฀in฀Fig.฀9.8.฀As฀illustrated฀above,฀the฀directions฀of฀the฀grain฀ boundaries in grain 1 were aligned along the and directions. The average misorientation angles across the boundaries aligned along the and ฀directions฀were฀~15°฀and฀~10°,฀respectively.฀The฀Kikuchi฀patterns฀and฀the฀ SAED฀patterns฀at฀large฀strains฀conirmed฀that฀the฀portion฀of฀high-angle฀boundaries฀ increased with increasing the number of the pressing passes and that, thereby, they became the dominant structure at the large deformation strain.39

9.2.3 Microstructural evolution of LCS alloy by post-ECAP annealing Annealing behavior of ferrite phase The฀microstructural฀changes฀of฀ferrite฀phase฀in฀LCS฀alloy฀processed฀by฀ECAP฀and฀ post-ECAP฀ annealing฀ treatments฀ are฀ shown฀ in฀ Fig.฀ 9.9.฀ Little฀ grain฀ growth฀

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9.9 Transmission electron microscopy and optical images showing the annealing behavior of nanostructured ferrite grains in the ECAPed LCS sample annealed for 1 h at various temperatures of (a) 723, (b) 753, (c) 783, (d) 813 K, and (e) 873 K.25

occurred฀ at฀ relatively฀ low฀ annealing฀ temperatures฀ of฀ 693–783฀ K.฀As฀ shown฀ in฀ Fig.฀9.9฀(a),฀however,฀the฀portion฀of฀well-deined฀grain฀boundaries฀increased฀and฀a฀ considerable annihilation of lattice dislocations was noticed. Several interesting features฀were฀noticed฀in฀the฀sample฀annealed฀at฀753฀K฀(Fig.฀9.9฀(b)฀):฀1)฀slight฀but฀ notable฀grain฀growth฀took฀place;฀2)฀most฀grain฀boundaries฀were฀well฀deined;฀3)฀in฀ some฀ grains฀ (marked฀ by฀ grain฀฀ A),฀ dislocation฀ cells฀ were฀ observed;฀ and฀ 4)฀ dislocation฀density฀inside฀individual฀grains฀became฀low.฀By฀annealing฀at฀783฀K฀ (Fig.฀ 9.9฀ (c)฀),฀ most฀ boundaries฀ became฀ well฀ deined,฀ but฀ their฀ appearance฀ was฀

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somewhat฀ different฀ from฀ that฀ observed฀ in฀ the฀ sample฀ annealed฀ at฀ 753฀ K฀ (Fig. 9.9 (b)). In฀addition,฀the฀existence฀of฀a฀dislocation฀wall฀(marked฀by฀arrows)฀was฀found,฀ but฀extinction฀contours฀remained.฀These฀facts฀indicate฀that฀recovery฀was฀still฀in฀ process.฀At฀813฀K฀(Fig.฀9.9฀(d)฀),฀large,฀dislocation-free฀grains฀were฀observed฀and฀ recrystallization฀was฀virtually฀completed฀at฀the฀annealing฀temperature฀of฀873฀K฀ (Fig.฀9.9฀(e)฀).฀The฀variation฀of฀ferrite฀grain฀size฀in฀4฀ECAPed฀LCS฀sample฀with฀ annealing temperature is presented in Fig. 9.10. From Fig. 9.10, it is noticed that annealing behavior is different with respect to annealing temperature, resulting in two฀different฀regions฀whose฀boundary฀is฀determined฀at฀783฀K.฀This฀fact฀is฀mainly฀ due฀to฀two฀different฀mechanisms฀such฀as฀recovery฀and฀recrystallization฀operated฀ during heat treatments. Below฀ 783฀ K,฀ the฀ microstructural฀ change฀ during฀ annealing฀ showed฀ that฀ a฀ recovery process was dominant and indicated that recovery could be attributed to a฀ process฀ associated฀ with฀ the฀ dissociation฀ of฀ lattice฀ dislocations฀ into฀ extrinsic฀ boundary฀ dislocations฀ during฀ annealing.฀ This฀ inding฀ is฀ consistent฀ with฀ the฀ experimental฀ observation฀ of฀ an฀ earlier฀ high-resolution฀ electron฀ microscopy฀ (HREM)฀study฀on฀an฀ECAPed฀aluminum฀alloy37฀showing฀the฀existence฀of฀a฀large฀ number฀of฀extrinsic฀dislocations฀at฀the฀non-equilibrium฀grain฀boundary฀region.฀At฀ this฀temperature฀range,฀the฀grain฀size฀did฀not฀increase฀signiicantly฀with฀increasing฀ annealing฀temperature.฀As฀a฀irst฀approximation,฀the฀grain฀growth฀behavior฀in฀this฀ regime฀was฀examined฀by฀applying฀the฀general฀equation฀for฀grain฀growth: [9.1]

9.10 A grain size variation of ferrite phase with annealing temperatures.25

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where d฀is฀the฀grain฀size฀at฀a฀given฀annealing฀time,฀d0฀is฀the฀initial฀grain฀size,฀K0 is a constant, t is the annealing time, n is a constant with a value close to a unity, Q is the activation energy for grain growth and RT฀has฀its฀usual฀meaning.฀Using฀ Eq. [9.1], Q can be obtained by plotting (d2–d02) against (1/T) in a semi-logarithmic scale at the same annealing time. Such a plot is depicted in Fig. 9.11 where d0 was taken as ~0.3 µm. The฀value฀of฀the฀activation฀energy฀was฀calculated฀to฀be฀~106฀kJ/mol.฀This฀value฀ was lower than the activation energies for several kinetic processes associated with฀ferrite฀grain฀growth฀such฀as฀volume฀diffusion฀(~280฀kJ/mol),฀grain฀boundary฀ diffusion฀ (~164฀ kJ/mol)฀ of฀ Fe฀ in฀ alpha-iron,46 grain boundary mobility of pure iron฀(~147฀kJ/mol),47฀and฀carbon฀diffusion฀in฀alpha-iron฀above฀673฀K฀(~141฀kJ/ mol)46 Wang et al.48 reported that the activation energy for grain growth of an ECAPed฀Al-Mg฀alloy฀in฀the฀unrecrystallized฀regime฀was฀only฀20%฀of฀that฀for฀ self-diffusion of pure aluminum. Indeed, activation energy for grain growth in the unrecrystallized฀regime฀was฀~0.35.฀This฀agrees฀well฀with฀the฀suggestion฀that฀nonequilibrium grain boundaries induced by severe plastic straining show higher mobility compared with those subjected to little or less plastic strain.49,50 Above฀783฀K,฀the฀ferrite฀phase฀of฀the฀LCS฀sample฀consisted฀of฀an฀unrecrystallized฀ area฀and฀a฀recrystallized฀area,฀resulting฀in฀a฀bimodal฀grain฀size฀distribution.฀The฀

9.11 A plot of log (d 2–d02) vs. 1/T for the estimation of the apparent activation energy for grain growth of ferrite phase in the ECAPed LCS samples.25

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activation฀energy฀for฀grain฀growth฀in฀this฀regime฀was฀estimated฀as฀~230฀kJ/mol฀by฀ taking,฀ as฀ a฀ irst฀ approximation,฀ the฀ average฀ value฀ of฀ the฀ recrystallized฀ ferrite฀ grain฀size฀at฀each฀temperature฀and฀d0฀=฀0.3฀µm.฀This฀value฀was฀lower฀than฀that฀for฀ volume฀ diffusion฀ (~280฀ kJ/mol)฀ of฀ Fe฀ in฀ alpha-iron.฀ However,฀ it฀ is฀ worth฀ mentioning that the estimation of activation energy for grain growth in this regime is฀less฀meaningful฀than฀that฀for฀the฀regime฀below฀783฀K฀due฀to฀the฀non-uniform฀ distribution฀of฀the฀recrystallized฀ferrite฀grain฀size฀and฀the฀dificulty฀of฀determining฀ the฀initial฀value฀of฀the฀recrystallized฀ferrite฀grain. In฀conclusion,฀up฀to฀783฀K,฀the฀grains฀were฀relatively฀stable฀and฀grain฀growth฀ took฀place฀slowly฀with฀increasing฀annealing฀temperature.฀Above฀783฀K,฀the฀grains฀ seemed฀to฀be฀unstable,฀showing฀a฀bimodal฀grain฀size฀distribution,฀i.e.฀coexistence฀ of coarse grains and nanoscale grains.25,51 Annealing behavior of pearlite structure For฀the฀pearlite฀structure,฀no฀signiicant฀morphological฀change฀was฀observed฀below฀ 753฀K฀compared฀to฀the฀as-ECAPed฀sample฀(Fig.฀9.3).฀However,฀the฀spheroidization฀ of฀ a฀ large฀ portion฀ of฀ cementite฀ started฀ to฀ appear฀ at฀ 783฀ K฀ (Fig.฀ 9.12฀ (a)฀).฀ The฀ spheroidized฀cementite฀particles฀remained฀at฀the฀initial฀cementite฀lamellar฀domain.฀ In฀addition,฀some฀images฀of฀spheroidized฀cementite฀particles฀were฀not฀deinite฀but฀ relatively dim and diffused. This indicates that carbon in cementite dissolved locally฀into฀the฀pearlitic฀ferrite.฀At฀the฀same฀annealing฀temperature฀of฀783฀K,฀the฀ dislocation density in pearlitic ferrite remained high compared to that in the ferrite phase฀(Fig.฀9.9฀(c)฀).฀At฀813฀K฀(Fig.฀9.12฀(b)฀),฀the฀microstructure฀of฀pearlite฀consisted฀ of฀nearly฀spheroidal฀cementite฀particles฀with฀an฀average฀aspect฀ratio฀of฀~2฀and฀ine฀ ferrite฀grains.฀It฀is฀worth฀noting฀that,฀under฀the฀same฀annealing฀conditions,฀the฀size฀ of฀recrystallized฀ferrite฀grains฀within฀the฀pearlite฀structure฀was฀smaller฀than฀that฀in฀ the฀group฀of฀ferrite฀grains฀(Fig.฀9.9฀(d)฀);฀this฀is฀mainly฀due฀to฀a฀grain฀boundary฀ pinning฀effect฀by฀ine฀cementite฀particles.

9.12 Transmission electron microscopy images showing the microstructure change of pearlite in the ECAPed LCS samples annealed for 1 h at various temperatures of (a) 783 and (b) 813 K.25

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As฀ explained฀ above,฀ the฀ spheroidization฀ of฀ cementite฀ was฀ clearly฀ observed฀ above฀753฀K฀and฀nearly฀completed฀at฀813฀K.฀This฀result฀was฀consistent฀with฀the฀ morphological changes of cementite in heavily cold drawn pearlitic steel wire.33 To฀ examine฀ the฀ inluence฀ of฀ intense฀ plastic฀ strain฀ on฀ the฀ enhancement฀ of฀ the฀ spheroidization฀ behavior฀ of฀ cementite,฀ the฀ initial฀ sample฀ prior฀ to฀ ECAP฀ was฀ annealed฀at฀783฀K฀and฀its฀pearlite฀structure฀is฀shown฀in฀Fig.฀9.13. Comparison฀of฀Fig.฀9.12฀(a)฀(ECAPed฀alloy)฀and฀Fig.฀9.13฀(initial฀pre-ECAPed฀ alloy), where both alloy samples were annealed under the same conditions, led to the฀conclusion฀that฀the฀kinetics฀of฀spheroidization฀occurred฀only฀in฀the฀ECAPed฀ sample. It has been established that, in the case of heavily cold drawn pearlitic steel฀wire,฀severe฀plastic฀strain฀leads฀to฀enhanced฀spheroidization฀of฀cementite฀due฀ to relatively easy carbon dissolution from deformed cementite into pearlitic ferrite during bluing treatment.52–55 Gridnev and Garririlyuk56 proposed that easy carbon dissolution during the bluing treatment of heavily cold drawn pearlitic steel wire could be attributed to higher binding energy between dislocations in pearlitic ferrite and carbon atoms than that between the Fe atoms in cementite and the carbon฀ atoms.฀ However,฀ researchers฀ ind฀ fault฀ with฀ this฀ suggestion฀ since฀ both฀ binding energies are roughly the same: the former and the latter are 0.55 and 0.50 eV, respectively.57,58 Languillaume et al.59฀ explained฀ the฀ easy฀ carbon฀ dissolution behavior by suggesting that the driving force for carbon dissolution was increased by an increase in the cementite/pearlitic ferrite interfacial energy due to the formation of slip steps at the cementite/pearlitic ferrite interface during the heavy cold drawing process. In addition, Hong et al.60 suggested that, in the same฀LCS฀materials,฀excessive฀imperfections฀would฀be฀introduced฀into฀cementite฀

9.13 Transmission electron microscopy image of pearlite in the initial LCS sample without ECAP annealed at 783 K for 1 h.25

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by฀ severe฀ plastic฀ deformation฀ and฀ their฀ existence฀ resulted฀ in฀ a฀ comprised฀ nonstoichiometric cementite composition, facilitating easy carbon dissolution. Accordingly,฀given฀that฀the฀microstructural฀change฀of฀pearlite฀in฀the฀ECAPed฀LCS฀ alloy during annealing was very similar to that observed during the bluing treatment of฀ the฀ heavily฀ cold฀ drawn฀ pearlitic฀ steel฀ wire,฀ the฀ enhanced฀ spheroidization฀ of฀ cementite here could be attributed to easy carbon dissolution from cementite into pearlitic ferrite caused by severe plastic deformation of cementite.

9.2.4 Formation of fine cementite precipitates The฀ TEM฀ micrograph฀ of฀ the฀ LCS฀ sample฀ after฀ annealing฀ at฀ 813฀ K฀ for฀ 1฀ h฀ presented in Fig. 9.14 reveals a number of spherical cementite precipitations within a pearlite colony. In some of the colonies, depending on their inclinations to the main shear direction, rod-like cementite particles were restored, whereas they successfully transformed into spherical precipitates during the annealing. From the TEM images taken of the annealed sample, the dislocation density was observed to be of the order of 1014 to 1016 m–2,฀although฀it฀was฀expected฀that฀the฀dislocation฀ density within ferrite grains of the annealed sample would reduced due to the static recovery. As discussed earlier by several researchers,1,61 the decomposition reaction occurred not only during the deformation stage but also during the annealing฀stage.฀As฀such,฀static฀annealing฀of฀the฀ECAPed฀ferrous฀alloy฀at฀813฀K฀ for฀1฀h฀would฀be฀beneicial฀for฀the฀decomposition฀of฀the฀entire฀pearlite฀colonies฀and฀ the฀uniform฀precipitation฀of฀cementite฀particles.฀This฀extraordinary฀phenomenon฀ demonstrates฀ a฀ potential฀ new฀ processing฀ route฀ of฀ forming฀ ine฀ precipitates฀ by฀

9.14 Transmission electron microscopy image of a spheroidized pearlite colony in the ECAPed LCS sample annealed at 813 K for 1 h.61

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the static annealing of severely deformed steel, instead of the conventional heat treatment฀route฀including฀normalizing,฀quenching฀and฀aging฀treatment. As the formation energy of cementite is relatively low and the dislocationcementite฀ interaction฀ energy฀ was฀ estimated฀ to฀ be฀ approximately฀ ~0.5฀ eV,62 the cementite฀ might฀ be฀ decomposed฀ by฀ the฀ interaction฀ with฀ the฀ stress฀ ield฀ of฀ dislocations, as indicated in a previous report.60 In the presence of the internal stress฀ield฀of฀dislocation,฀the฀net฀number฀of฀extra฀carbon฀atoms฀segregated฀per฀ unit length of a dislocation (N/L) was estimated by the following Eq. [9.2]:63 ,

[9.2]

where C0฀is฀the฀equilibrium฀concentration฀in฀the฀matrix,฀b the Burgers vector of the edge component, ν Poisson’s ratio, G equals E/2(1 + ν), E Young’s modulus, Vs the atomic volume of carbon and Va the interstitial site volume of ferrite steel. As฀the฀cementite฀became฀nano-sized,฀the฀experimentally฀determined฀C0 value64 was adjusted using the Gibbs–Thompson relationship.65 For the adjustment, the cementite was assumed to be a sphere of ~20 nm in diameter and has a surface energy฀ of฀ 1฀ J/m2.66฀ Using฀ the฀ above฀ equation,฀ the฀ excess฀ carbon฀ concentration฀ (ECC)฀ was฀ calculated฀ as฀ a฀ function฀ of฀ temperature฀ at฀ different฀ dislocation฀ densities (1014–1016m–2).฀As฀ shown฀ in฀ Fig.฀ 9.15,฀ the฀ ECC฀ value฀ was฀ a฀ strong฀

9.15 Excess carbon concentration calculated as a function of annealing temperature. The dislocation density changed from 1014 to 1016 m–2.65

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function of the dislocation density and became negligible as the density decreased to less than 1014 m–2. Although the rate constant for the decomposition reaction was฀ not฀ determined,฀ the฀ calculated฀ ECC฀ value,฀ which฀ was฀ 10–20%฀ of฀ the฀ equilibrium concentration, was considered to be large enough for the decomposition reaction to proceed at a reasonable rate. Therefore, a group of high dislocation density might promote the decomposition of the cementite via interaction with the dislocations. For a uniform distribution of cementite particles, the carbon atoms released from the decomposition reaction should diffuse away from the colonies toward ferrite grains and precipitate during the static annealing treatment. On the basis of a฀microstructural฀analysis฀utilizing฀TEM,฀the฀dislocation฀density฀in฀the฀pearlite฀ colony฀was฀much฀higher฀than฀that฀inside฀the฀ferrite฀grains.฀As฀the฀ECC฀value฀was฀ sensitive฀to฀the฀dislocation฀density฀as฀shown฀in฀Fig.฀9.15,฀the฀ECC฀value฀in฀the฀ colony was relatively higher, as compared to that inside the ferrite grain, which would฀induce฀a฀diffusion฀lux฀towards฀the฀ferrite฀grains.฀With฀the฀carbon฀diffused฀ away from the colony towards the ferrite grains of low dislocation density, the grain would became supersaturated with carbon atoms, providing a favorable condition for precipitation.

9.3

The mechanical response of a nanostructured LCS alloy

9.3.1 Mechanical properties Figure฀ 9.16฀ shows฀ the฀ deformation฀ behavior฀ of฀ the฀ ECAPed฀ LSC฀ alloy฀ with฀ respect฀to฀the฀number฀of฀ECAP฀operations,฀corresponding฀to฀effective฀strain.฀The฀ increase฀ in฀ hardness฀ was฀ most฀ pronounced฀ at฀ the฀ irst฀ pass฀ and฀ thereafter,฀ the฀ strengthening฀became฀less฀signiicant฀for฀further฀deformation.฀This฀inding฀is฀in฀ line฀with฀the฀observation฀of฀microstructural฀evolution฀that฀grain฀reinement฀was฀ most฀signiicant฀at฀the฀irst฀pass.฀It฀is฀also฀consistent฀with฀previous฀observations฀ reported฀ for฀ various฀ ECAPed฀ materials.14–16 After the initial pressing, the hardening behavior of the ferrite phase was more considerable than that of pearlite. With an increasing number of passes, however, the hardening tendency in both grains was toward saturation. Tensile฀properties฀of฀the฀ECAPed฀LCS฀alloy฀are฀shown฀in฀Fig.฀9.17.฀The฀trend฀ of the variation of yield strength and ultimate tensile strength with the pass number agreed with that of the hardness data (Fig. 9.16). It was found that, without the aid of compositional changes, the nanostructured grains could give rise to tensile strength฀higher฀than฀900฀MPa฀together฀with฀reasonable฀elongation฀of฀~10%.฀This฀ suggested that, among strengthening mechanisms, inducing a nano-grained structure is฀advantageous฀for฀improving฀strength฀without฀signiicant฀loss฀of฀ductility.17 Stress–strain฀ curves฀ of฀ the฀ initial,฀ ECAPed฀ and฀ ECAPed-annealed฀ LCS฀ samples are shown in Fig. 9.18, and the values of their tensile properties are listed

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9.16 A plot of micro-hardness vs. the pass number for each of the constituent phases of the ECAPed LCS sample.17

9.17 Tensile properties of the ECAPed LCS samples with increasing number of operation.17

in Table 9.1. Particular attention should be paid to strain hardening behavior. The initial฀samples฀exhibited฀moderate฀strain฀hardenability฀with฀large฀uniform฀ductility฀ after฀ Lüders฀ strain,฀ whereas฀ the฀ as-pressed฀ and฀ annealed฀ samples฀ exhibited฀ no฀ strain hardening behavior, a general feature of nanostructured metals reported

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9.18 Engineering stress–strain curves of the initial, ECAPed, and ECAPed-annealed LCS samples.18

Table 9.1 Ferrite grain sizes and tensile properties of the LCS samples Treatments

d (µm)

YS (MPa)

UTS (MPa)

ef (%)

As-received As-ECAPed ECAP + Annealed at 753 K for 72 hrs

30 0.2 ~ 0.3 0.45

310 937 683

480 943 720

29.9 10.9 20.2

previously.25,27,39,61 Depending upon the annealing condition, however, this strain hardenability฀was฀successfully฀restored฀with฀a฀sacriice฀of฀strength.

9.3.2 Deformation mechanism Ultra-high strength Similar to the case of other nanostructured metals, the tensile deformation behavior of฀the฀nanostructured฀LCS฀alloy฀was฀characterized฀by฀the฀absence฀of฀strain฀hardening฀ as฀ well฀ as฀ ultra-high฀ strength.฀ Since฀ the฀ nanostructured฀ LCS฀ samples฀ exhibited฀ negligible฀strain฀hardening,฀their฀ultra-high฀strength฀could฀not฀be฀explained฀solely฀ by the dislocation pile-up mechanism. However, as noted by Valiev et al.,50 the

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dislocation฀bow-out฀model,฀which฀was฀used฀to฀explain฀the฀mechanical฀behavior฀of฀ nanostructured฀ materials,฀ is฀ applicable.฀ In฀ the฀ context฀ of฀ the฀ dislocation฀ bow-out฀ model,67,68฀yielding฀occurred฀when฀the฀dislocation฀coniguration฀reached฀a฀semicircle฀ and฀the฀critical฀stress฀for฀this฀condition฀was฀approximated฀by฀the฀following฀expression: ,

[9.3]

where G is the shear modulus, b is the Burgers vector, ν is Poisson’s ratio and L is the฀average฀dislocation฀length.฀For฀grain฀size฀larger฀than฀100฀nm,฀L was equivalent to ρ–½ where ρ is the dislocation density.69 With the aid of Eq. [9.3], the yield stress฀of฀nanostructured฀materials฀could฀be฀expressed฀as: ,

[9.4]

where σ0 is the friction stress and M฀is฀the฀Taylor฀factor.฀Using฀equations฀[9.3]฀ and฀ [9.4],฀ the฀ yield฀ strength฀ of฀ ferrite฀ phase฀ in฀ the฀ ECAPed฀ LCS฀ sample฀ was฀ estimated as 728 MPa with the following values: G฀=฀78฀GPa,฀b฀=฀2.48฀×฀10–10 m, ρ฀=฀1015 m–2, ν฀=฀0.33,฀M฀=฀2.78฀for฀bcc฀structure,฀and฀σ0฀=฀76฀MPa.8 Although there฀existed฀some฀variation฀in฀dislocation฀density฀when฀TEM฀was฀used,฀the฀use฀ of the value of 1015 m–2 does not appear to be erroneous since ρ for several nanostructured฀materials฀by฀the฀ECAP฀process฀was฀reported฀to฀be฀on฀the฀order฀of฀ 1015 m–2.7,49฀ It฀ is฀ also฀ important฀ to฀ consider฀ that฀ the฀ LCS฀ sample฀ consisted฀ of฀ ~85%฀of฀ferrite฀phase฀with฀the฀remainder฀being฀pearlite฀phase.฀Hence,฀the฀yield฀ stress฀of฀the฀ECAPed฀LCS฀sample฀could฀be฀approximated฀by฀the฀rule฀of฀mixture: ,

[9.5]

where V is the volume fraction and the superscripts f and p denote ferrite and pearlite,฀respectively.฀Due฀to฀a฀lack฀of฀reliable฀data฀on฀the฀application฀of฀ECAP฀to฀ high-carbon steel consisting of a fully pearlite structure, σ ysp should be deduced from฀ that฀ of฀ a฀ cold฀ drawn฀ pearlitic฀ steel.฀ Under฀ the฀ same฀ amount฀ of฀ effective฀ strain, σ ysp of the heavily drawn pearlitic steel was in a range of 1800–2000 MPa.34 Our estimation showed a yield stress of 850–880 MPa, which was still lower than obtained above (937 MPa). Valiev et al.49 also used the dislocation bow-out model to predict the strength of nanostructured pure copper at ambient temperature. They argued that some deviation of the estimated value based on dislocation bowout฀from฀the฀experimental฀value฀could฀be฀attributed฀to฀1)฀the฀actual฀dislocation฀ density and 2) the supplementary effect of internal stress. A lack of strain hardenability: dynamic recovery As฀ shown฀ in฀ Fig.฀ 9.18,฀ the฀ nanostructured฀ LCS฀ sample฀ exhibited฀ no฀ strain฀ hardening under tension deformation. The absence of strain hardening in ultraine฀grained฀(UFG)฀steels฀was฀examined฀in฀terms฀of฀dynamic฀recovery.฀During฀

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tensile deformation, dislocations causing intragranular strain are trapped at the grain฀ boundaries฀ if฀ no฀ strong฀ obstacles฀ for฀ lattice฀ dislocation฀ motion฀ existed฀ inside the grains. The kinetics of dynamic recovery is closely related to the spreading of trapped lattice dislocations (TLDs) into the grain boundaries.49,70,71 The change of dislocation density owing to dynamic recovery by TLD spreading into฀the฀grain฀boundaries฀could฀be฀described฀by฀the฀following฀generalized฀equation [9.6]

. where ρ is the dislocation density, t is the time, α is a constant, ε is the strain rate, b is the Burgers vector, d฀is฀the฀grain฀size฀and฀ ξ is the characteristic time for TLD spreading into the grain boundaries. At steady state deformation, i.e. (∂ρ/∂t)฀=฀0: [9.7] For฀the฀ECAPed฀sample,฀ ξ was ~21 s with ρ฀=฀1015 m–2, b฀=฀2.48฀×฀10–10 m, . d฀=฀0.25฀×฀10–6 m, α฀=฀2.4฀and฀ε฀=฀1.33฀×฀10–3 s–1. The deformation time to reach the฀maximum฀point฀in฀stress฀was฀~22฀s.฀Therefore,฀lattice฀dislocations฀contributing฀ to intragranular strain were trapped at interfaces, and they subsequently spread into the grain boundary concurrently during deformation. As a result, there is no accumulation of lattice dislocations and, consequently, no strain hardening is expected.฀ For฀ a฀ sample฀ annealed฀ at฀ 753฀ K฀ for฀ 72฀ hrs,฀ the฀ dislocation฀ density฀ decreased฀by฀several฀orders฀of฀magnitude,฀but฀the฀ferrite฀grain฀size฀increased฀only฀ by a factor of 2. In this case, the value of ξ decreased drastically but the deformation time became more prolonged due to the larger elongation. Accordingly, it was natural฀that฀strain฀hardening฀was฀observed฀to฀some฀extent฀in฀the฀sample฀annealed฀ at฀753฀K฀for฀72฀hrs.18,19 A lack of strain hardenability: mean free length of dislocation Figure 9.19 shows the dislocation distribution observed in tensile-deformed steel without฀ECAP฀(d฀=฀30฀µm)฀at฀different฀strain฀levels.฀Prior฀to฀the฀tension฀test,฀the฀ dislocation฀density฀was฀relatively฀low฀(Fig.฀9.19฀(a)฀);฀but฀after฀5%฀deformation฀ (Fig.9.19 (b)) the dislocations were distributed randomly inside grains with high density. A dislocation cell structure with an average diameter of 0.35 µm was formed at the฀engineering฀strain฀of฀15%฀(Fig.฀9.19฀(c)฀).฀The฀tensile฀deformed฀microstructure฀ of฀the฀steel฀annealed฀at฀753฀K฀for฀72฀hrs฀after฀ECAP฀is฀shown฀in฀Fig.฀9.20.฀Most฀ ferrite฀ grains฀ in฀ the฀ ECAP-deformed฀ sample฀ were฀ elongated฀ (Fig.฀ 9.20฀ (a)฀),฀ indicating that considerable intragranular strain was induced during deformation. In฀addition,฀an฀inspection฀with฀higher฀magniication฀(Fig.฀9.20฀(b)฀)฀revealed฀that฀ the฀dislocations฀were฀not฀distributed฀uniformly฀inside฀the฀grains฀but฀were฀localized฀ in the vicinity of the grain boundaries.

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9.19 Transmission electron microscopy images showing the distribution and density of lattice dislocation in tensile-deformed LCS sample without ECAP at different strain levels: (a) before testing, (b) e = 5% and (c) e = 15%.18

9.20 (a) Transmission electron microscopy image showing tensiledeformed LCS sample annealed at 753 K for 72 hrs after ECAP and (b) magnified image of the same sample showing dislocation distribution near to grain boundaries.18

At the initial stage of plastic deformation, the dislocation density increased and its distribution was relatively uniform at the grain interior, causing strain hardening. As plastic deformation proceeds, a dislocation cell structure was formed due to dislocation฀entanglement.฀Under฀these฀conditions,฀the฀cell฀size฀was฀equivalent฀to฀

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the mean free dislocation length (L).72 The mean free dislocation length was inversely proportional to the shear stress (τ). [9.8] The฀cell฀size฀at฀different฀stress฀levels฀could฀then฀be฀approximated฀by฀the฀following฀ simple relationship for the same material: [9.9] With฀the฀cell฀size฀(δ1฀=฀0.35฀µm)฀measured฀from฀the฀deformed฀sample฀without฀ ECAP฀ and฀ the฀ stresses฀ inferred฀ from฀ Fig.฀ 9.18,฀ the฀ cell฀ size฀ (δ2) of the other sample is estimated from Eq. [9.9] and listed in Table 9.2. In the estimation, the engineering stress in Fig. 9.18 was converted to the corresponding shear stress by the฀generalized฀relationships.฀Two฀indings฀are฀noted฀from฀Table฀9.2.฀First,฀for฀the฀ ECAP-deformed฀ sample฀ annealed฀ at฀ 753฀ K฀ for฀ 72฀ hrs,฀ the฀ measured฀ cell฀ size,฀ 0.35 µm, is almost identical with that estimated from Eq. [9.9], 0.24 µm, thus demonstrating฀ the฀ validity฀ of฀ Eq.฀ [9.9].฀ Second,฀ the฀ ferrite฀ grain฀ sizes฀ of฀ nanostructured฀LCS฀samples฀were฀comparable฀to฀the฀estimated฀cell฀sizes฀within฀a฀ factor of 2 at the corresponding stress levels. The negligible strain hardening during฀tensile฀deformation฀of฀the฀nanostructured฀LCS฀sample฀could฀be฀attributed฀ to the mean free dislocation length at the corresponding stress level being comparable฀ to฀ the฀ ferrite฀ grain฀ size.฀ Consequently,฀ dislocation฀ entanglement฀ largely took place at the grain interior of nanoscale grains, thus affecting strain hardenability. In฀ coarse-grained฀ LCS฀ materials,฀ the฀ equiaxed฀ dislocation฀ cells฀ were฀ not฀ subjected to shape changes even at relatively high strains. This indicates that the cell formation occurred continuously during deformation, implying that the cell formation฀ is฀ a฀ kind฀ of฀ relaxation฀ process฀ that฀ causes฀ a฀ reduction฀ in฀ the฀ strainhardening rate.73 The uniform distribution of lattice dislocation with high density

Table 9.2 Dislocation cell sizes calculated by Eq. 1.9 and ferrite grain sizes of the LCS samples

τ1 As-received

τ2

276

δ1

δ2

δ

0.35

Remarks

30

Strain hardening

As-ECAPed

486

0.20

0.2 ~ 0.3

Weak strain hardening

ECAP + Annealed at 753 K for 72 hrs

396

0.24

0.45

Slight strain hardening

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at the initial stage of deformation, but with further deformation, it changed into a cell structure consisting of hard and soft regions. For the cell structure the hard region is the cell wall region with tangled dislocations while the soft region is the dislocation-free cell interior. In nanostructured materials, the TLDs at the grain boundaries,฀ one฀ of฀ the฀ relaxation฀ processes,฀ occurred฀ at฀ the฀ onset฀ of฀ plastic฀ deformation without a uniform distribution of lattice dislocation, since the grain size฀ is฀ comparable฀ or฀ even฀ smaller฀ than฀ the฀ mean฀ free฀ dislocation฀ length.฀This฀ analysis indicates that the strain-hardening rate would be negligible during plastic flow of nanostructured metallic materials, but the hardening rate would be restored with฀post-ECAP฀annealing.

9.4

Enhanced tensile properties by grain refinement and microstructural modification

9.4.1 LCS alloy containing vanadium carbides Since strain-hardening characteristics rapidly diminish with a decreasing of grain size฀ down฀ to฀ a฀ nanometer฀ level,฀ we฀ introduced฀ ine฀ vanadium฀ carbides฀ to฀ the฀ nanostructured฀LCS฀sample฀in฀order฀to฀alleviate฀the฀inherent฀mechanical฀drawback฀ discussed฀ above.฀A฀ LCS฀ sample฀ with฀ an฀ addition฀ of฀ 0.34฀ wt%฀ vanadium฀ was฀ prepared฀and฀deformed฀by฀ECAP฀with฀the฀same฀working฀conditions.฀Details฀of฀ the procedures have been described elsewhere.20 As indicated by the arrows in Fig. 9.21 (a), nanoscale precipitates of 5–10 nm were observed at the area of high dislocation฀density฀in฀the฀ECAPed฀LCS฀sample,฀which฀did฀not฀contain฀precipitates฀ prior฀to฀ECAP฀operation.฀These฀precipitates฀formed฀during฀ECAP฀at฀623฀K฀were฀ identiied฀as฀V3C4฀by฀an฀energy฀dispersive฀spectra฀analysis฀(Fig.฀9.21฀(b)฀).฀The฀ precipitates are believed to have originated from strain-induced precipitation,

9.21 (a) Transmission electron microscopy image showing the existence of nanoscale vanadium carbides at the area of high dislocation density in the ECAPed LCS sample and (b) qualitative chemical analysis of them.20

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where nucleation sites are the heterogeneous regions such as dislocations of high density฀formed฀by฀ECAP.

9.4.2 Dual-phase LCS alloy Within the framework of strain gradient plasticity, two different kinds of dislocations฀ played฀ different฀ roles฀ on฀ plastic฀ deformation;฀ that฀ is,฀ statistically฀ stored dislocations influence deformation itself, whereas geometrically necessary dislocations (GNDs) operate for strain hardening.74 Among a variety of ferrous alloys, a dual phase structure consisting of ferrite and martensite is a representative structure฀having฀a฀large฀number฀of฀GNDs.฀It฀is฀well฀established฀that฀the฀excellent฀ strain฀hardenability฀of฀dual฀phase฀steel฀is฀mainly฀due฀to฀the฀existence฀of฀glissile฀ dislocations newly formed during intercritical annealing followed by water quenching฀ after฀ ECAP.75–79 These dislocations, which have been observed at ferrite grains close to martensite, act as GNDs, making it possible to achieve high strain hardenability.80 Details of processing conditions can be found in Ref.81 As shown in Fig. 9.22 (a), the microstructure of the nanostructured dual-phase steel consisted฀of฀equiaxed฀ferrite฀grains฀(0.8฀µm฀in฀size)฀and฀martensite฀grains฀(0.9฀µm฀ in฀size).฀Both฀ferrite฀grain฀size฀and฀martensite฀island฀size฀were฀found฀to฀have฀a฀ submicrometer฀scale฀and฀the฀volume฀fraction฀of฀martensite฀was฀about฀~30%. A฀SEM฀micrograph฀with฀higher฀magniication฀(Fig.฀9.22฀(b)฀)฀revealed฀that฀the฀ martensite ('M' in Fig. 9.22 (b)) was in an isolated blocky type82฀and฀existed฀in฀ minute quantities at ferrite/ferrite boundaries. Again, a nanostructured dual phase microstructure with a uniform distribution of each constituent phase could be attained by three distinctive steps associated with thermo-mechanical treatment. First,฀during฀ECAP,฀carbon฀atoms฀from฀pearlitic฀cementite฀were฀dissolved฀and,฀ thereby, diffused toward ferrite phase grains. This uniform distribution of equilibrium/excessive฀carbon฀atoms฀allowed฀an฀austenite฀phase฀to฀form฀uniformly฀ during intercritical annealing. During water quenching, austenite grains were

9.22 Scanning electron microscopy images of (a) the nanostructured dual-phase steel and (b) nanostructured dual-phase steel with higher magnification.81

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transformed into martensite islands, generating a number of mobile dislocations in฀ferrite฀grains฀adjacent฀to฀martensite฀by฀volume฀expansion.฀Tensile฀testing฀of฀the฀ nanostructured dual phase steel showed that, unlike most nanostructured materials that฀show฀a฀poor฀strain-hardening฀rate,฀the฀dual฀phase฀exhibited฀a฀good฀combination฀ of฀high฀strength฀and฀ductility฀(extensive฀strain฀hardenability).฀This฀demonstrates฀ that strain gradient plasticity has a high potential to enhance the strain hardenability of nanostructured materials.

9.5

Continuous shear drawing: a new processing method

Although฀ severe฀ plastic฀ deformation฀ of฀ metals฀ and฀ alloys฀ utilizing฀ ECAP฀ has฀ recently been regarded as a promising method for tailoring nanostructure as well as decomposing฀lamellar฀or฀dendrite฀structure,฀the฀batch฀process฀of฀ECAP฀generated฀a฀ technical problem, which limits its actual applications. Thus, one of the approaches currently being considered to develop a method that is suitable for the continuous processing฀is฀the฀use฀of฀equal-channel฀angular฀drawing฀(ECAD),฀where฀samples฀are฀ deformed in a drawing fashion instead of pressing, as the length of sample would likely no longer be limited by the buckling instability during deformation.83–86 However, Luis et al.,86฀ based฀ on฀ inite฀ element฀ method฀ (FEM)฀ calculations,฀ validated฀what฀was฀found฀by฀actual฀experiments,฀that฀the฀deformation฀of฀ECAD฀is฀ inevitably฀ accompanied฀ by฀ both฀ appreciable฀ corner฀ gap฀ and฀ severely฀ localized฀ necking. This is presumably due to the fact that the deformation is more dominated by drawing than by shearing when the sample passes through the shear plane. We suggested฀ a฀ new฀ type฀ of฀ ECAD฀ termed฀ continuous฀ shear฀ drawing฀ (CSD)฀ in฀ conjunction with an effort to modify the design of the die in order to avoid dimensional inhomogeniety of the sample during deformation. According to an upper bound analysis84 and FEM results,85฀the฀use฀of฀ECAD฀clearly฀caused฀unstable฀ deformation฀of฀a฀number฀of฀ine฀meshes฀when฀the฀inner฀angles฀became฀less฀than฀ 120°.฀As฀shown฀in฀Fig.฀9.23,฀a฀die฀with฀an฀inner฀angle฀of฀135°฀was฀designed฀to฀avoid฀ the฀formation฀of฀pronounced฀necking,฀which฀is฀noxious฀to฀further฀deformation. A฀CSD฀die฀was฀also฀prepared฀by฀reducing฀the฀diameter฀of฀the฀exit฀channel฀so฀ as฀to฀impose฀higher฀strain฀compared฀to฀ECAD.฀Considering฀the฀reduced฀geometry฀ of฀the฀exit฀channel,฀an฀additional฀strain฀was฀imparted฀to฀samples฀when฀the฀samples฀ experienced฀one฀passage.฀The฀total฀effective฀stain฀(εT)฀accumulated฀from฀the฀CSD฀ process was the sum of the shear strain87 and the drawing strain: ,

[9.10]

where φ, li and lf฀are฀the฀half฀of฀inner฀angle฀in฀die฀and฀the฀initial฀and฀the฀inal฀ diameters of sample, respectively. The annealing behavior of three different samples with no deformation, drawing and฀ CSD฀ is฀ shown฀ in฀ Fig.฀ 9.24฀ (a).฀The฀ annealed฀ sample฀ without฀ deformation฀

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9.23 Schematic description of the proposed die used for CSD technique.

9.24 Scanning electron microscopy images showing spheroidization behavior at a subcritical temperature of 973 K (a) for 10 hrs in sample with no prior deformation, (b) for 5 hrs in sample deformed via conventional drawing and (c) for 1 h in sample deformed via CSD method.

shows remnant thin-striped cementite phases. The other samples deformed via drawing฀and฀CSD฀methods฀required฀5฀hrs฀and฀1฀h,฀respectively฀in฀order฀to฀achieve฀ a฀uniform฀microstructure฀with฀ine฀cementite฀(Fig.฀9.24฀(b)฀and฀9.24฀(c)฀).฀From฀ these฀results,฀the฀CSD฀method฀is฀thought฀to฀possess฀a฀commercial฀potential฀for฀

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use as an intermediate step of wire manufacture, as it could reduce annealing time by฀ promoting฀ the฀ rate฀ of฀ spheroidization฀ of฀ the฀ pearlitic-cementite฀ phase.฀ Moreover, as compared to the result yielded by conventional drawing, the use of the฀CSD฀technique฀combined฀with฀an฀annealing฀treatment฀led฀to฀a฀microstructure฀ having฀ ine฀ cementite฀ dispersed฀ uniformly฀ in฀ the฀ ferrite฀ matrix฀ due฀ to฀ straininduced฀spheroidization.

9.6

Conclusion

The change in microstructure and the variations in tensile properties of nanostructured฀ LSD฀ alloy฀ fabricated฀ by฀ ECAP฀ together฀ without/with฀ various฀ post-ECAP฀ annealing฀ treatments฀ have฀ been฀ reviewed.฀The฀ grain฀ reinement฀ of฀ LSD alloy was achieved by grain subdivision due to the operation of multiple slip systems of {110}, {112} and {123}. A comparison between the฀ferrite฀grain฀size฀of฀a฀nanostructured฀LCS฀sample฀and฀the฀dislocation฀cell฀size฀ of its coarse-grained counterpart formed during tensile deformation revealed that the cell formation was unlikely to occur in the former, thus implying that the low strain hardening rate could be attributed to two factors: dynamic recovery and nanoscale grains comparable to the mean free length of dislocations. First, the feasibility฀of฀enhancing฀the฀strain฀hardenability฀of฀the฀nanostructured฀LCS฀sample฀ was฀explored฀by฀comparing฀the฀microstructure฀and฀stress–strain฀behavior฀of฀two฀ LCS฀ samples฀ without/with฀ vanadium฀ carbides.฀ Second,฀ the฀ strain฀ hardening฀ behavior฀of฀a฀dual-phase฀steel฀via฀both฀ECAP฀and฀intercritical฀annealing฀followed฀ by water quenching was investigated. In addition, we developed a continuous approach฀ based฀ upon฀ CSD฀ in฀ which฀ shear฀ and฀ drawing฀ deformation฀ are฀ conjugated.฀It฀appears฀that฀the฀use฀of฀CSD฀would฀be฀advantageous฀for฀achieving฀ a฀ microstructure฀ incorporating฀ ine฀ cementite฀ particles,฀ which฀ are฀ dispersed฀ uniformly฀throughout฀the฀matrix฀due฀to฀strain-induced฀spheroidization.

9.7

References

฀ 1฀ Valiev฀R.Z.,฀Islamgaliev฀R.K.,฀Alexandrov฀I.V.฀Prog฀Mater฀Sci฀2000;45:฀103. ฀ 2฀ Valiev฀ R.Z.,฀ Estrin฀ Y.,฀ Horita฀ Z.,฀ Langdon฀ T.G.,฀ Zehetbauser฀ M.J.,฀ Zhu฀ Y.T.฀ JOM฀ 2006;58:฀33. ฀ 3฀ McFadden฀ S.X.,฀ Mishra฀ R.S.,฀ Valiev฀ R.Z.,฀ Zhilyaev฀ A.P.,฀ Mukherjee฀ A.K.฀ Nature฀ 1999;398:฀684. ฀ 4฀ Kumar฀K.S.,฀Van฀Swygenhoven฀H.,฀Suresh฀S.฀Acta฀Mater฀2003;51:฀5743. ฀ 5฀ Conrad฀H.฀Mater฀Sci฀Eng฀2003;A341:฀216. ฀ 6฀ Valiev฀R.Z.฀Nature฀Mater฀2004;3:฀511. ฀ 7฀ Horita฀Z.,฀Smith฀D.J.,฀Furukawa฀M.,฀Nemoto฀M.,฀Valiev฀R.Z.,฀Langdon฀T.G.,฀Mater฀J฀ Res฀1996;11:฀1880. ฀ 8฀ Valiev฀R.Z.,฀Ivanisenko฀Y.V.,฀Rauch฀E.F.,฀Baudelet฀B.฀Acta฀Mater฀1996;B:฀4705. ฀ 9฀ Chang฀C.P.,฀Sun฀P.L.,฀Kao฀P.W.฀Acta฀Mater฀2000;48:฀3377. 10฀ Ko฀Y.G.,฀Lee฀C.S.,฀Shin฀D.H.,฀Semiatin฀S.L.฀Metall฀Mater฀Trans฀2006;A37:฀381.

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11฀ Wang฀Y.,฀Chen฀M.,฀Zhou฀F.,฀Ma฀E.฀Nature฀2002;419:฀912. 12฀ Mishra฀ R.S.,฀ Stolyarov฀V.V.,฀ Echer฀ C.,฀Valiev฀ R.Z.,฀ Mukherjee฀A.K.฀ Mater฀ Sci฀ Eng฀ 2001;A298:฀44. 13฀ Sergueeva฀A.V.,฀ Stolyarov฀ V.V.,฀ Valiev฀ R.Z.,฀ Mukherjee฀A.K.฀ Mater฀ Sci฀ Eng฀ 2002;฀ A323: 318. 14฀ Ko฀Y.G.,฀Jung฀W.S.,฀Shin฀D.H.,฀Lee฀C.S.฀Scripta฀Mater฀2003;48:฀197. 15฀ Furukawa฀M.,฀Horita฀Z.,฀Nemoto฀M.,Valiev฀R.Z.,฀Langdon฀T.G.฀Acta฀Mater฀1996;44:฀ 4619. 16฀ Nakashima฀K.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Acta฀Mater฀1998;46:฀1589. 17฀ Shin฀D.H.,฀Seo฀C.W.,฀Kim฀J.,฀Park฀K.T.,฀Choo฀W.Y.฀Scripta฀Mater฀2000;42:฀695. 18฀ Shin฀D.H.฀Met฀Mat฀Inter฀2001;7:฀573. 19฀ Park฀K.T.,฀Kim฀Y.S.,฀Lee฀J.G.,฀Shin฀D.H.฀Mater฀Sci฀Eng฀2000;A293:฀165. 20฀ Park฀K.T.,฀Han฀S.Y.,฀Shin฀D.H.,฀Lee฀Y.K.,฀Lee฀K.S.฀ISIJ฀Inter฀2004;44:฀1057. 21฀ Segal฀V.M.฀Mater฀Sci฀Eng฀1995;A197:฀157. 22฀ Chang฀S.Y.,฀Lee฀J.K.,฀Park฀K.T.,฀Shin฀D.H.฀Mater฀Trans฀2001;42:฀1074. 23฀ Shin฀D.H.,฀Kim฀W.J.,฀Choo฀W.Y.฀Scripta฀Mater฀1999;41:฀259. 24฀ Shin฀D.H.,฀Kim฀B.C.,฀Kim฀Y.S.,฀Park฀K.T.฀Acta฀Mater฀2000;48:฀2247. 25฀ Shin฀D.H.,฀Kim฀B.C.,฀Park฀K.T.,฀Choo฀W.Y.฀Acta฀Mater฀2000;48:฀3245. 26฀ Markushev฀ M.V.,฀ Bampton฀ C.C.,฀ Murashkin฀ M.Y.,฀ Hardwick฀ D.A.฀ Mater฀ Sci฀ Eng฀ 1997;A234:฀927. 27฀ Nemoto฀M.,฀Horita฀Z.,฀Furukawa฀M.,฀Langdon฀T.G.฀Met฀Mater฀1998;4:฀1181. 28 Furukawa M., Iwahashi Y., Horita Z., Nemoto M., Langdon T.G. Mater Sci Eng 1998;A257:฀328. 29฀ Berbon฀P.B.,฀Furukawa฀M.,฀Horita฀Z.,฀Nemoto฀M.,฀Tsenev฀N.K.,฀Valiev฀R.Z.,฀Langdon฀ T.G.฀Mater฀Sci฀Forum฀1996;217:฀1013. 30฀ Valiev฀ R.Z.,฀ Sailmomenko฀ D.A.,฀ Tsenev฀ N.K.,฀ Berbon฀ P.B.,฀ Langdon฀ T.G.฀ Scripta฀ Mater฀1997;37:฀1945. 31 Iwahashi Y., Furukawa M., Horita Z., Nemoto M., Langdon T.G. Metall Mater Trans1998;A29:฀2245. 32฀ Nam฀W.J.,฀Bae฀C.M.฀Mater฀Sci฀Eng฀1995;A203:฀278. 33฀ Bae฀C.M.,฀Dissertation฀PhD.฀POSTECH,฀Korea฀1999. 34฀ Porter฀D.A.,฀Eastering฀K.E.฀Acta฀Metall฀1978;26:฀1405. 35฀ Langford฀G.฀Metall฀Trans฀1977;8A:฀861. 36฀ Inoue฀A.,฀Ogura฀T.,฀Masumoto฀T.฀Trans฀JIM฀1977;17:฀143. 37฀ Servillano฀J.G.฀Mater฀Sci฀Eng฀1975;A21:฀221. 38฀ Maurer฀K.,฀Warrington฀D.H.฀Phil฀Mag฀1967;15:฀321. 39฀ Shin฀D.H.,฀Kim฀I.,฀Kim฀J.,฀Park฀KT.฀Acta฀Mater฀2001;49:฀1285. 40฀ Kim฀J.R.,฀Kim฀I.Y.,฀Shin฀D.H.฀Scripta฀Mater฀2001;45:฀421. 41฀ Shin฀D.H.,฀Kim฀J.,฀Park฀K.T.฀Met฀Mater฀Inter฀2001;7:฀431. 42฀ Mishra฀ R.S.,฀ Semiatin฀ S.L.,฀ Suryanarayana฀ C.,฀Thadhani฀ N.N.,฀ Lowe฀T.C.฀ Ultraine฀ Grained Materials, TMS, Warrendale, PA 2000. 43฀ Nakashima฀K.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Mater฀Sci฀Eng฀2000;A281:฀92. 44฀ Gholinia฀A.,฀Prangnell฀P.B.,฀Markushev฀M.V.฀Acta฀Mater฀2000;48:฀1115. 45฀ Iwahashi฀Y.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Acta฀Mater฀1998;46:฀3317. 46฀ Askill฀J.฀Tracer฀Diffusion฀Data฀for฀Metals,฀Alloys฀and฀Simple฀Oxides;฀Plenum฀Press,฀ New฀York฀(NY);฀1970. 47฀ Hillert฀M.฀Metall฀Trans฀1975;6A:฀5. 48฀ Wang฀J.,฀Iwahashi฀Y.,฀Horita฀Z.,฀Furukawa฀M.,฀Nemoto฀M.,฀Valiev฀R.Z.,฀Langdon฀T.G.฀ Acta฀Mater฀1996;44:฀2973.

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49฀ Valiev฀R.Z.,฀Kozlov฀E.V.,฀Ivanov฀Y.F.,฀Lian฀J.,฀Nazarov฀A.A.,฀Baudelet฀B.฀Acta฀Metall.฀ Mater฀1994;42:฀2467. 50฀ Lian฀J.,฀Valiev฀R.Z.,฀Baudelet฀B.฀Acta฀Metall฀Mater฀1995;43:฀4165. 51฀ Park฀K.T.,฀Shin฀D.H.฀Mater฀Sci฀Eng฀2002;A334:฀79. 52฀ Read฀H.G.,฀Reynolds฀W.T.,฀Hono฀JrK,฀Tarui฀T.฀Scripta฀Mater฀1997;37:฀1221. 53฀ Makii฀ K.,฀ Yaguchi฀ H.,฀ Kaiso฀ M.,฀ Ibaraki฀ N.,฀ Miyamoto฀ Y.,฀ Oki฀ Y.฀ Scripta฀ Mater฀ 1997;37:฀1753. 54฀ Makii฀ K.,฀Yaguchi฀ H.,฀ Minamida฀ T.,฀ Kaiso฀ M.,฀ Ibaraki฀ N.,฀ Oki฀Y.฀ Tetsu-to-Hagane฀ 1997;83:฀42. 55฀ Shin฀D.H.,฀Han฀S.Y.,฀Park฀K.T.,฀Kim฀Y.S.,฀Paik฀Y.N.฀Mater฀Trans฀2003;44:฀1630. 56฀ Gridnev฀V.N.,฀Garririlyuk฀V.G.฀Phys฀Metals฀1981;4:฀531. 57฀ Kamber฀K.,฀Keeter฀D.,฀Wert฀C.฀Acta฀Metall฀Mater฀1961;9:฀403. 58฀ Kalish฀D.,฀Kohen฀M.฀Mater฀Sci฀Eng฀1970;A6:฀156. 59฀ Languillaume฀J.,฀Kapelski฀G.,฀Baudelet฀B.฀Acta฀Mater฀1997;45:฀1201. 60฀ Hong฀M.H.,฀Reynolds฀W.J.,฀Tarui฀Jr.฀T.,฀Hono฀K.฀Metall฀Mater฀Trans฀1999;A30:฀717. 61฀ Shin฀D.H.,฀Kim฀Y.S.,฀Lavernia฀E.J.฀Acta฀Mater฀2001;49:฀2387. 62฀ Kubaschewski฀ O.,฀ Alcock฀ C.B.฀ Metallurgical฀ Thermo-Chemistry;฀ Pergamon฀ Press,฀ Oxford฀1979:฀284. 63฀ Hirth฀J.P.,฀Lothe฀J.฀Theory฀of฀Dislocations;฀McGraw-Hill,฀New฀York฀(NY)฀1968:฀464. 64฀ McGannon฀H.E.฀The฀Making,฀Shaping฀and฀Treating฀of฀Steel฀(9th฀ed.);฀USS,฀Pittsburgh฀ (PA) 1971:328. 65฀ Murr฀ L.E.฀ Interfacial฀ Phenomena฀ in฀ Metals฀ and฀Alloys;฀Addison-Wesley฀ Publishing฀ Co,฀New฀York฀(NY)฀1975:฀5. 66฀ Schaffer฀J.P.,฀Saxena฀A.,฀Antolovich฀S.D.,฀Snaders฀Jr฀T.H.฀The฀Science฀and฀Design฀of฀ Engineering฀Materials;฀RD฀Irwi,฀Inc:฀Chicago฀1995:฀92. 67฀ Hirth฀J.P.,฀Lothe฀J.฀Theory฀of฀Dislocations,฀2nd฀edn;฀Wiley:฀New฀York฀(NY)฀1982:฀971. 68฀ Lian฀J.,฀Baudelet฀B.,฀Nazarov฀A.A.฀Mater฀Sci฀Eng฀1993;A172:฀23. 69฀ Kuhlmann-Wilsdorf฀D.฀Mater฀Sci฀Eng฀1989;A113:฀1. 70฀ Lojkowski฀W.฀Acta฀Metall฀Mater฀1991;39:1892. 71฀ Nazarov฀A.A.,฀Romanov฀A.E.,฀Valiev฀R.Z.฀Scripta฀Metall฀Mater฀1990;24:฀1929. 72฀ Khulmann-Wilsdorf฀ D.฀Work฀ Hardening฀ (eds.,฀ Hirth฀ J.P.฀ and฀Weertman฀ J.);฀ Gordon฀ and Breach, New York (NY) 1968: 97. 73฀ Humphreys฀ F.J.,฀ Hatherly฀ M.฀ Recrystallization฀ and฀ Related฀Annealing฀ Phenomena;฀ Pergamon,฀Oxford฀(UK)฀1995:฀25. 74฀ Needleman฀A.,฀Gil฀Sevillano฀J.฀Scripta฀Mater฀2003;48:฀109. 75฀ Matlock฀ D.K.,฀ Zia-Ebrahimi฀ F.,฀ Krauss฀ G.฀ Deformation฀ Processing฀ and฀ Structure,฀ ASM;฀Metals฀Park,฀USA฀1982:฀47. 76฀ Son฀Y.I.,฀Lee฀Y.K.,฀Park฀K.T.,฀Lee฀C.S.,฀Shin฀D.H.฀Acta฀Mater฀2005;53:฀3125. 77฀ Shin฀D.H.,฀Park฀K.T.฀Mater฀Sci฀Eng฀2005;A410–411:฀299. 78฀ Shin฀ D.H.,฀ Kim฀ W.G.,฀ Ahn฀ J.Y.,฀ Park฀ K.T.,฀ Kim฀ Y.S.฀ Mater฀ Sci฀ Forum฀ 2006;503–504:฀447. 79฀ Hwang฀ B.C.,฀ Kim฀ Y.G.,฀ Lee฀ S.H.,฀ Hwang฀ D.Y.,฀ Shin฀ D.H.฀ Metall฀ Mater฀ Trans฀ 2007;A38:฀3007. 80฀ Aldazabal฀J.,฀Gil฀Sevillano฀J.฀Mater฀Sci฀Eng฀2004;A365:฀186. 81฀ Park฀ K.T.,฀ Han฀ S.Y.,฀ Ahn฀ B.D.,฀ Shin฀ D.H.,฀ Lee฀ Y.K.,฀ Um฀ K.K.฀ Scripta฀ Mater฀ 2004;51:฀909. 82฀ Cai฀X.L.,฀Garratt-Reed฀A.J.,฀Owen฀W.S.฀Metall฀Trans฀1985;A16:฀543. 83฀ Chakkingal฀U.,฀Suriadi฀A.B.,฀Thomson฀P.F.฀Mater฀Sci฀Eng฀1999;A266:฀241.

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84฀ Alkorta฀J.,฀Rombouts฀M.,฀Messenmaeker฀J.D.,฀Froyen฀L.,฀Sevillano฀J.G.฀Scripta฀Mater฀ 2002;47:฀13. 85฀ Luis฀C.J.,฀Garcés฀Y.,฀González฀P.,฀Berlanga฀C.฀Mater฀Manuf฀Proc฀2002;17:฀223. 86฀ Zisman฀ A.A.,฀ Rybin฀ V.V.,฀ Van฀ Boxel฀ S.,฀ Seefeldt฀ M.,฀ Verlinden฀ B.฀ Mater฀ Sci฀ Eng฀ 2006;A427:฀123. 87฀ Iwahashi฀Y.,฀Wang฀J.,฀Horita฀Z.,฀Nemoto฀M.,฀Langdon฀T.G.฀Scripta฀Mater฀1996;35:฀143.

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10 Characteristic structures and properties of nanostructured metals prepared by plastic deformation X.฀HUANG,฀Technical฀University฀of฀Denmark,฀Denmark

Abstract: This chapter focuses on describing the characteristic microstructures of nanostructured metals produced by plastic deformation to ultrahigh strains and their correlation with hardening by annealing and softening by deformation. The results suggest that optimising microstructure and the mechanical properties of nanostructured metals can be achieved by a combination of post-process heat treatment and deformation. Key words: nanostructured metals, transmission electron microscopy (TEM), boundary spacing and misorientation, dislocation density, unusual mechanical behaviours.

10.1

Introduction

Nanostructured metals produced by plastic deformation to ultrahigh strains constitute a special class of nanomaterials with characteristic microstructures and properties. Over the last decades progress has been made in many areas: •  New processes have been introduced, such as high-pressure torsion (HPT), equal-channel฀ angular฀ pressing฀ (ECAP),฀ and฀ accumulative฀ roll฀ bonding฀ (ARB),฀ which฀ enable฀ the฀ researcher฀ to฀ impose฀ extremely฀ high฀ strains฀ to฀ a฀ metal without change in the sample geometry. •  Characteristic฀ microstructural฀ parameters฀ and฀ their฀ distribution฀ have฀ been฀ quantiied฀including฀grain฀size,฀boundary฀misorientation฀and฀dislocation฀density. •  Characteristic฀ mechanical฀ properties฀ have฀ been฀ analysed฀ such฀ as฀ strength,฀ tensile ductility, strain rate sensitivity and flow instabilities, and the effect of post-process annealing and deformation on these properties. •  Strengthening mechanisms and the relationship between microstructural parameters฀and฀mechanical฀properties฀have฀been฀explored. •  New approaches for optimising mechanical properties by manipulating the microstructure have been investigated. Some of these areas are reviewed and discussed in other chapters of this book. This chapter will focus on characteristic microstructural parameters in nanostructured face-centred cubic (fcc) Al and body-centred cubic (bcc) interstitialfree฀(IF)฀steel฀produced฀by฀ARB฀at฀room฀temperature฀and฀500°C,฀respectively,฀and฀ fcc Ni produced by HPT at room temperature. The compositions of these metals 276 © Woodhead Publishing Limited, 2011

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Table 10.1 Chemical composition of a commercial purity Al (JIS1100) (mass%) Si 0.11

Fe 0.55

Cu 0.11

Mn 0.01

Mg 0.02

Ti 0.02

B 0.0007

V Ni 0.011 0.003

Al Bal.

Table 10.2 Chemical composition of an IF steel (mass%) C 0.002

N 0.003

Si 0.01

Mn 0.17

P 0.012

Cu 0.01

Ni 0.02

Ti 0.072

Fe Bal.

Table 10.3 Chemical composition of a commercial purity Ni (mass%) C Si Mn P S Cr Fe Al Co Cu Ti Mg Ni 0.006 0.003 0.015 0.025 0.001 0.001 0.44 0.004 0.035 0.012 0.002 0.003 Bal.

are shown in Tables 10.1–10.3. Then the correlation between microstructural characteristics and mechanical properties is discussed with an emphasis on recent observations of unusual mechanical behaviours. The observations and analyses lead to suggestions for new approaches for optimisation of microstructure and properties of nanostructured metals.

10.2

Characteristic microstructures

10.2.1 Microstructural parameters The key microstructural parameters characterising nanostructured metals are microstructural morphology, spacing between boundaries, misorientation across boundaries, fraction of high-angle boundaries, and density of dislocations present in฀dislocation฀boundaries฀(15°)฀ are listed in Table 10.4. Similar bimodal distributions have also been reported for the nanostructured pure Al produced by cold rolling3฀ and฀ ECAP 14–16 and the relationship between the boundary angle distribution and the evolution of microstructure฀and฀texture฀during฀deformation฀to฀large฀strain฀has฀been฀analysed.17 Within the volume between the boundaries, the presence of individual dislocations

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10.1 (a) Transmission electron microscopy image showing a lamellar structural morphology and dislocation configurations in the nanostructured Al (JIS1100, 99.2% pure) processed by six-cycle ARB to εvM = 4.8. (b) Histogram showing the distribution of boundary misorientation angles.13 Table 10.4 Structural parameters of nanostructured commercial purity Al 1100 (99.2%) and IF steel processed by non-lubricated ARB to 6 cycles19 Material

dt(nm) dl(nm)

dl /dt

θav (°)

f (θ ≥ 15°) (%) t (θ < 3°) (%) ρ0(m–2)

Al (JIS1100) IF Steel

180 210

3.3 3.0

27.3 24.2

66.3 59.8

600 620

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1.3 × 1014 6.3 × 1013

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and฀ dislocation฀ tangles฀ is฀ observed.฀ Sample฀ tilting฀ in฀ the฀TEM฀ conirmed฀ that฀ almost all lamellae contain dislocations although the dislocation density varies from lamella to lamella. The average dislocation density was measured to be about 1.3 × 1014 m–2.18

10.2.3 Nanostructured interstitial-free (IF) steel by ARB Figure 10.2 shows the TEM microstructure and the misorientation angle distribution฀for฀an฀IF฀steel฀(see฀Table฀10.2)฀processed฀by฀ARB฀at฀500°C฀for฀six฀ cycles.19฀The฀microstructure฀exhibits฀a฀lamellar฀morphology,฀Fig.฀10.2฀(a),฀similar฀ to that observed in the nanostructured Al sample (Fig. 10.1 (a) ). The presence of loose dislocations and dislocation tangles in the volume between the lamellar boundaries is also clearly seen in the micrograph. Figure 10.2 (b) illustrates a bimodal distribution of misorientation angles, resembling that obtained in

10.2 (a) Transmission electron microscopy image showing a lamellar structural morphology and dislocation configurations in the nanostructured IF steel processed by six-cycle ARB at 500°C to εvM = 4.8. (b) Histogram showing the distribution of boundary misorientation angles.19

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10.2 Continued.

the nanostructured Al (Fig. 10.1 (b) ). The average spacing between the lamellar boundaries and interconnecting boundaries and the density of loose dislocations are given in Table 10.4.

10.2.4 Nanostructured Ni by high-pressure torsion (HPT) The฀ microstructure฀ in฀ a฀ commercial฀ purity฀ Ni฀ (99.5%฀ pure,฀ see฀ Table฀ 10.3)฀ processed by HPT up to a strain of 300 has been analysed in detail by TEM.6 The TEM results were obtained from the longitudinal section parallel to the torsion฀axis฀(see฀Fig.฀10.3)฀rather฀than฀from฀the฀torsion฀plane฀as฀investigated฀in฀ previous studies.20,21 Figure 10.3 shows the microstructure at a strain of 8.7. A typical lamellar microstructure is seen, where the lamellar boundaries are nearly parallel฀ to฀ the฀ torsion฀ plane฀ (±10°).฀ In฀ the฀ volumes฀ between฀ the฀ lamellar฀ and฀ interconnecting boundaries, dislocation clusters and individual dislocations can be observed. These types of microstructural features are maintained at higher strains up to 300, as shown in Fig. 10.4. However, with increasing strain, the lamellar boundaries sharpen and decrease their width. There is a clear tendency for฀the฀microstructural฀morphology฀to฀be฀more฀equiaxed฀at฀extremely฀high฀strains฀ (see Fig. 10.4(b) ) while maintaining some directional appearance characteristic of microstructures at lower strains. In addition to the lamellar boundaries, interconnecting boundaries and loose฀ dislocations,฀ two฀ new฀ microstructural฀ features,฀ namely฀ small฀ equiaxed฀ crystallites (Fig. 10.5(a) ) and deformation twins (Fig. 10.5(b) ), were also observed in samples deformed to strains ≥12.฀The฀equiaxed฀crystallites฀are฀isolated฀in฀the฀ microstructure: they form at triple junctions and are in general surrounded by high-angle฀ boundaries.฀ The฀ sizes฀ of฀ these฀ equiaxed฀ crystallites฀ range฀ from฀

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10.3 (a) A schematic drawing showing the sampling for TEM observation. (b) Transmission electron microscopy micrograph showing a typical lamellar structure formed in pure Ni deformed by HPT to εvM = 8.7. The shear direction is marked by the double arrows.6

30–130 nm. The deformation twins are in general only 10–50 nm wide and they are inclined with respect to the lamellar boundaries (Fig. 10.5 (b) ). The total volume฀fraction฀of฀equiaxed฀crystallites฀and฀deformation฀twins฀is฀quite฀low฀( φ, can be described as: [11.13] where m is the Taylor factor, G the shear modulus, b the Burgers vector and λ the separation of particles on the shear plane.84 The parameter λ฀is฀related฀to฀particle฀size฀ as λ฀ =฀ φ / √ f. Since particles tend to pin grain boundaries, for materials in quasiequilibrium after preparation by annealing (for powder consolidation, precipitation, coarsening,฀etc.)฀grain฀size฀and฀particle฀size฀are฀related,฀for฀example฀by฀the฀Zener฀ relation, d฀=฀0.66฀φ/f,฀and฀hence฀grain฀size฀and฀particle฀separation฀are฀related: [11.14] As such, it is clear that Orowan strengthening models can only be used for materials containing a small volume fraction of second-phase particles, say less than฀10%,฀and฀then฀the฀model฀applies฀independently฀of฀the฀grain฀size,฀nanoscale฀ to microscale. Figure 11.5 shows an analysis of strengthening in copper alloys containing secondphase particles,84 where strength is related, via equation 11.13, through the Orowan mechanism. A good description of the particle strengthening, i.e. σOR proportional to {1/(λ–φ).ln(φ /2b)},฀is฀seen฀down฀to฀particle฀sizes฀of฀about฀7฀nm.฀Figure฀11.6฀shows฀ some microstructures of these deformed particle-strengthened copper materials, where฀particle-dislocation฀interaction฀is฀clear.฀Since฀particle฀size฀can฀be฀related฀to฀ grain฀size,฀equation฀11.14,฀the฀strengthening฀may฀be฀re-expressed฀in฀terms฀of฀grain฀

11.5 Analysis of strengthening in Cu-bcc particle materials in terms of the Orowan strengthening model, see text for details. Source: Morris and Morris.84

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11.6 Transmission electron micrographs illustrating dislocation– particle interactions in Cu-bcc particle materials of fine grain size. Source: Morris and Morris.84

size,฀by฀the฀Hall–Petch฀equation฀(equation฀11.1,฀ σ y฀=฀ σ0 + k d –1/2) with relatively good agreement found. The numerical value of the Hall–Petch slope, k, is 0.28 MPa√ m,฀ however,฀ much฀ greater฀ than฀ the฀ accepted฀ values฀ for฀ a฀ Cu฀ matrix.85,86 This฀ analysis฀ conirms฀ that฀ the฀ major฀ strengthening฀ is฀ due,฀ in฀ this฀ case,฀ to฀ the฀ particles present, and grain boundary strengthening is less important. A quantitative evaluation of Hall–Petch strengthening (equation 11.1) and Orowan hardening (equation฀ 11.13),฀ making฀ use฀ of฀ the฀ particle–grain฀ size฀ relation฀ (equation฀ 11.14)฀ conirms฀ that฀ Orowan฀ particle฀ strengthening฀ will฀ dominate฀ strengthening฀ in฀ Cu฀ for฀ particle฀ sizes฀ below฀ about฀ 20฀ nm฀ and฀ grain฀ sizes฀ below฀ about฀ 200฀ nm฀ (for฀ material฀with฀5–10%฀second฀phase).฀The฀slower฀strengthening฀observed฀in฀Fig.฀11.5฀ as฀ the฀ second-phase฀ particles฀ reine฀ to฀ very฀ ine฀ sizes฀ (the฀ near฀ saturation฀ in฀ Fig. 11.5) may be due to particles shearing or to the loss of a homogeneous particle distribution with many particles trapped at the grain boundaries. Another฀study฀examined฀hardening฀in฀nanocrystalline฀FeAl฀alloys฀and฀related฀ strength฀to฀grain฀size87,88฀(Fig.฀11.7),฀with฀data฀characterised฀by฀exactly฀the฀same฀

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Hall–Petch฀ slope฀ as฀ Fe฀ (Fig.฀ 11.1).฀ These฀ materials฀ also฀ contained฀ ine฀Al2O3 particles,฀from฀oxidation฀during฀powder฀milling฀and฀during฀hot฀consolidation฀to฀ solid฀material.฀The฀oxide฀particles฀are฀very฀ine฀here,฀less฀than฀3฀nm฀(see฀Fig.฀11.8)฀ and dislocations propagate with little effort since, presumably, they can shear the weak฀particles.฀Oxide฀particle฀coarsening฀on฀heat฀treating฀this฀material฀leads฀to฀ initial strengthening, before softening through particle and grain coarsening – this evolution฀is฀indicated฀by฀the฀sequence฀of฀arrows฀in฀Fig.฀11.7.฀More฀signiicant฀ hardening฀has฀been฀produced฀in฀FeAl฀intermetallic฀by฀the฀addition฀of฀30%TiC฀to฀ the material, as indicated by the high-pressure data in Fig. 11.7.89–91 These materials฀retained฀ine฀grain฀size,฀20–30฀nm,฀after฀high-temperature,฀high-pressure฀

11.7 Hardness of several FeAl materials related to grain size by the Hall–Petch relationship. Data points connected by arrows indicate the hardness evolution on ageing, as oxide precipitates form.88 Highest hardness is achieved after high pressure, high temperature consolidation of FeAl-TiC composites.89–91

11.8 Transmission electron micrograph illustrating dislocation–particle interactions (arrowed) in FeAl.88

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consolidation, but hardness can no longer be analysed by the Orowan model since both฀FeAl฀and฀TiC฀are฀of฀similar฀size฀and฀the฀material฀should฀be฀considered฀as฀a฀ composite฀with฀mixed฀grains฀of฀the฀two฀phases. When฀second-phase฀particles฀are฀present฀in฀large฀volume฀proportion฀(>10%)฀or฀ the฀particles฀have฀a฀similar฀or฀larger฀size฀than฀the฀matrix฀grains,฀it฀is฀better฀to฀analyse฀ material฀and฀hardness฀as฀a฀composite,฀where฀the฀rule฀of฀mixtures฀provides฀a฀good฀ description (hardness is an area or volume-adjusted average of the hardness of the components). He and Ma92฀examined฀hardness฀in฀Cu-Fe฀composites,฀with฀an฀Fe฀ content฀between฀15฀and฀90%,฀and฀grain฀sizes฀of฀25–45฀nm฀for฀both฀phases,฀to฀ind฀ material฀hardnesses฀signiicantly฀greater฀than฀expected฀from฀the฀rule฀of฀mixtures,฀ considering฀ nanocrystalline฀ Cu฀ and฀ nanocrystalline฀ Fe.฀ They฀ concluded฀ that฀ the฀ bcc–fcc interphase boundaries were much stronger than usual grain boundaries in either฀single฀phase฀Cu฀or฀single฀phase฀Fe.฀On฀the฀other฀hand,฀in฀studies฀on฀materials฀ of฀Cu฀matrix฀and฀bcc฀second-phase฀additions,93,94฀the฀hardness฀observed฀for฀mixtures฀ with฀Cu฀grain฀sizes฀between฀10฀and฀60฀nm฀it฀well฀to฀the฀Hall–Petch฀relationship฀ with a good value for the slope, k (0.16 MPa√ m). In these cases, however, the volume฀fraction฀of฀bcc฀phase฀was฀small฀(5–10%)฀and฀bcc฀particles฀were฀somewhat฀ larger฀ than฀ the฀ Cu฀ grain฀ size,฀ such฀ that฀ most฀ boundaries฀ present฀ were฀ standard฀ fcc–fcc grain boundaries, and only few were bcc–fcc interphase boundaries. Guduru et al.13฀ also฀ studied฀ Fe฀ mixed฀ with฀Al2O3 and analysed hardness in terms฀ of฀ the฀ rule฀ of฀ mixtures.฀This฀ was฀ justiied฀ since฀ the฀ Fe฀ matrix฀ grain฀ size฀ was about 10 nm but the Al2O3฀particles฀about฀50฀nm.฀The฀experimental฀hardness฀ was฀much฀greater฀than฀predicted฀by฀the฀rule฀of฀mixtures,฀see฀Fig.฀11.9,฀and฀it฀was฀

11.9 Hardness of Fe milled with Al2O3 and with Pb, indicating that the data do not fit to the composite rule of mixtures.13

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argued that the much harder Al2O3 particles created a local heavily work-hardened zone฀ in฀ the฀ neighbouring฀ Fe฀ grains฀ due฀ to฀ the฀ large฀ number฀ of฀ geometrically฀ necessary dislocations that formed there during deformation. While most attention is given to strengthening by second-phase additions, and large second-phase particles seem generally associated with poorer ductility, there฀is฀some฀evidence฀that฀correctly฀sized฀and฀distributed฀second-phase฀particles฀ might improve ductility. Dutta et al.95 found that spherical second-phase particles of฀size฀slightly฀smaller฀than฀the฀matrix฀grain฀size,฀arranged฀on฀grain฀boundaries,฀ might improve ductility by homogenising strain distribution during deformation. Finally,฀ reiterating฀ Koch,96 relatively little has been studied about the role of second-phase particles in affecting strength, toughness and ductility of nanocrystalline materials. There appears to be ample scope for improvement, and this area is one worthy of further investigation.

11.7

Strengthening caused by other factors: solute, order, twin boundaries

There฀ are฀ few฀ studies฀ that฀ explicitly฀ examine฀ the฀ role฀ of฀ solute฀ or฀ order฀ of฀ the฀ nanocrystalline฀matrix฀in฀affecting฀mechanical฀behaviour.฀Guduru฀et al.13฀examined฀ nanocrystalline฀ Fe-Pb฀ mixtures฀ prepared฀ by฀ milling,฀ using฀ X-ray฀ diffraction฀ to฀ conirm฀ that฀ the฀ Pb฀ had฀ been฀ dissolved.฀The฀ disappearance,฀ following฀ milling,฀ of฀ diffraction฀ peaks฀ corresponding฀ to฀ Pb฀ is฀ insuficient,฀ as฀ such,฀ to฀ conirm฀ Pb฀ dissolution since X-ray diffraction is insensitive to the presence of small amounts of second฀phase฀present฀as฀ine฀particles.฀At฀the฀same฀time,฀however,฀the฀researchers฀ observed฀a฀signiicant฀displacement฀of฀the฀matrix฀relections,฀conirming฀the฀likely฀ solution฀ of฀ up฀ to฀ about฀ 5%฀ Pb.฀ Similar฀ results฀ on฀ Pb฀ dissolution฀ during฀ milling฀ have also been observed by other researchers, see13 for details. Fig. 11.9 shows the฀evolution฀of฀hardness฀with฀Pb฀addition,฀with฀a฀large฀increase฀with฀the฀5%฀Pb฀ addition.฀ Hardness฀ would฀ be฀ expected฀ to฀ fall฀ if฀ the฀ Pb฀ were฀ present฀ as฀ secondphase฀particles,฀according฀to฀the฀composite฀rule฀of฀mixtures,฀indicated฀in฀Fig.฀11.9.฀ Examination฀ of฀ expected฀ hardening฀ by฀ the฀ large฀ Pb฀ atoms฀ in฀ the฀ Fe฀ matrix฀ according to the Fleischer solution-hardening model showed, however, that even greater฀ hardening฀ should฀ be฀ expected.฀ The฀ authors฀ speculated฀ that฀ the฀ Pb฀ atoms฀ were not all uniformly distributed in solution and that some Pb could be present as segregation at grain boundaries or as sub-nanometric clusters, too small to be detected by standard diffraction methods. Preparation of nanomaterials by milling techniques often leads to disordering of many intermetallics,97,98 which can modify mechanical behaviour. For nanocrystalline฀ FeAl,฀ subsequent฀ annealing฀ at฀ 150–250°C฀ leads฀ to฀ reordering87,88,98 but, as indicated in Fig. 11.7 by the arrows showing hardness evolution on annealing, there is no noticeable hardness change during this re-ordering.88฀ One฀ possible฀ explanation฀ is฀ that฀ the฀ super-partial฀ dislocation฀ separation is so large for many such intermetallics that it is similar to the

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nanocrystalline฀ grain฀ size฀ and฀ deformation฀ is฀ then฀ accomplished฀ by฀ the฀ partial฀ dislocations฀ that฀ characterise฀ the฀ disordered฀ matrix,฀ somewhat฀ analogous฀ to฀ the฀ operation of partial dislocation sources (Shockley dislocations or twinning dislocations) suggested by molecular dynamics modelling. Finally,฀while฀the฀theoretical฀models฀(Hall–Petch/Core-and-Mantle/Molecular฀ Dynamics)฀do฀not฀clearly฀explain฀the฀role฀of฀solution฀additions฀on฀hardening,฀the฀ evolution from a single perfect dislocation source to a single partial dislocation or twinning dislocation source, however, is clearly eased by alloying to lower stacking fault energy. Improved฀ strength฀ is฀ found฀ also฀ with฀ inely฀ spaced฀ twins฀ introduced฀ by฀ electrodeposition99 or by rapid straining, especially at low temperatures100–102 in materials with low stacking fault energy. Such twin strengthening can be found in grains฀ of฀ any฀ size฀ with฀ the฀ strengthening฀ now฀ determined฀ by฀ twin฀ spacing฀ instead of grain boundary spacing.99฀ A฀ signiicant฀ advantage฀ of฀ nanospaced฀ twin boundaries appears to be that ductility or toughness can remain high at the same time as strengthening is achieved.101,103 Twins appear to act as barriers to dislocation slip operating in the parent grain, in much the same way as grain boundaries, requiring new slip activation in the twinned region or the parentoriented region found behind the subsequent twin boundary.104 Strengthening should then be described by the same formulation as for grain boundaries, such as the Hall–Petch approach. An alternative approach is to consider the twinned regions, which have nanoscale thickness determined by the close spacing of the pairs of bounding parent–twin interfaces, as hard regions of a composite, and then the overall material strength is given by a composite model of฀ mixed฀ hard฀ and฀ soft฀ regions.101 The low-energy, coherent twin boundaries appear, however, to be able to spread stress concentrations much more than occurs at grain boundaries, and hence are not the sites for crack or cavity nucleation as are grain boundaries or their triple points. This ability to suffer plastic deformation and store dislocations means also that the twin-strengthened materials possess some work hardening,101,103 more than for nanoscale grainboundary-strengthened materials, which is a second reason for the improved ductility of these materials.

11.8

Strengthening mechanisms in materials with ultrafine microstructure prepared by severe plastic deformation

Techniques of severe plastic deformation have been developed over the past about 20฀years฀and฀shown฀to฀lead฀to฀microstructural฀reinement,฀towards฀the฀nanoscale,฀ and฀to฀signiicant฀strengthening.105,106฀Techniques฀such฀as฀Equal-Channel฀Angular฀ Pressing฀(ECAP)฀and฀High-Pressure฀Torsion฀(HPT)฀have฀been฀used฀to฀impose฀ strains฀ to฀ of฀ the฀ order฀ of฀ (true฀ strain)฀ and฀ above฀ 100฀ for฀ ECAP฀ and฀ HPT,฀ respectively. Submicron or nanostructures can eventually be achieved at very high

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strains in materials where recovery is slow or where multiple phase components impose฀strong฀microstructural฀reinement. At฀ the฀ relatively฀ low฀ strains฀ (2–8)฀ generally฀ achieved฀ by฀ the฀ popular฀ ECAP฀ technique, however, the microstructure is composed of random dislocations within dislocation cell walls or low-angle grain boundaries (LAGB), contained within a smaller density of grain boundaries, or high-angle grain boundaries (HAGB). For example,฀ deforming฀ Al฀ or฀ Cu฀ by฀ ECAP฀ to฀ strains฀ of฀ 1–2฀ produces฀ elongated฀ dislocation฀ cells;฀ deforming฀ to฀ strains฀ of฀ 4฀ produces฀ more฀ equiaxed฀ dislocation฀ cell/subgrains;฀while฀deforming฀to฀strains฀of฀10฀produces฀microstructures฀of฀scale฀ about฀100–500฀nm,฀where฀50–70%฀of฀the฀boundaries฀have฀misorientations฀above฀ 15°,฀i.e.฀are฀deined฀as฀HAGB.105–107฀Gubizca฀et al.108 obtained similar dislocation cell฀structures฀in฀Al฀and฀Al-Mg฀alloy฀of฀size฀about฀250–75฀nm,฀respectively,฀after฀ deforming to a strain of 2–8, where a dislocation density of 2 × 1014 – 2 × 1015/m2, respectively, was measured. Similar structures are obtained in Fe and FeAl intermetallics,109,110 where dislocation cellular structures are obtained after strains below 10, and nanocrystalline structures after strains above 100 imposed by HPT. After strains of about 3, the microstructure shows many randomly arranged฀ dislocations฀ inside฀ a฀ dislocation฀ cell฀ structure฀ of฀ size฀ 200฀ nm฀ with฀ an฀ average฀misorientation฀of฀10°฀and฀15%฀of฀boundaries฀being฀HAGB.฀A฀histogram฀ of the distribution of boundary misorientations in this material, FeAl rolled to a strain near 3, is illustrated in Fig. 11.10. Various฀explanations฀of฀strengthening฀during฀such฀severe฀plastic฀deformation฀ have been proposed. Valiev et al.109 argued that strengthening was caused by the many grain boundaries, i.e. by Hall–Petch strengthening, after heavy deformation

11.10 Histogram showing distribution of boundary misorientations in Fe3Al rolled to a true strain of 3.3. Analysis by Electron Back-Scatter Diffraction in a Scanning Electron Microscope. Source: Adapted from Morris et al.110

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to฀a฀nanocrystalline฀state.฀Gubizca฀et al.,108 however, related strengthening (∆σρ), through the Taylor equation, to the measured dislocation density (ρloose) as: [11.15] where α is a factor of value about 0.3, M the Taylor factor, G the shear modulus, and b the Burgers vector. Leseur et al.111฀examined฀milled฀Fe฀and฀argued฀that฀a฀ Hall–Petch dependence of hardening, i.e. ∆H α 1/√ d,฀could฀be฀expected฀for฀grain฀ size฀ d฀ above฀ 1฀ µm,฀ but฀ a฀ subgrain฀ size฀ dependence,฀ i.e.฀ ∆H α 1/d, for cells or subgrains smaller than 1 µm, i.e. about 50–1000 nm. In addition, they noted that hardening฀ could฀ be฀ increased฀ by฀ nanosized฀ oxide฀ particles฀ introduced฀ during฀ milling. Hansen85,86 has discussed how dislocation cell boundaries can be regarded essentially as additional dislocations, producing Taylor hardening, by converting cell boundary area and misorientation into equivalent dislocation density, ρeff. This approach seems reasonable but does not take complete account of the interaction฀of฀dislocation฀stress฀ields฀of฀closely฀spaced฀dislocations฀of฀different฀ types, which will partially annihilate and reduce overall effectiveness as a barrier. With this approach, the strengthening from dislocation cell boundaries (LAGB) can be written: [11.16] with ρeff฀=฀Svθ/b฀=฀3θ/dcb, and hence: [11.17] where ρeff is the effective dislocation density inside cell walls, Sv the surface area of boundaries per volume, θ the boundary misorientation, and dc฀ the฀ cell฀ size.฀ Note that equation 11.17 has the same dependency of strengthening on reciprocal square฀root฀of฀size฀as฀the฀Hall–Petch฀equation,฀with฀the฀effective฀Hall–Petch฀slope฀ given by kcell฀ =฀ MαG√ (3θb). For small-cell boundary misorientations, the boundaries are much weaker than usual grain boundaries, but for misorientations reaching฀about฀15°฀the฀value฀of฀kcell฀is฀approximately฀that฀of฀kH-P, justifying the common consideration that this misorientation marks the distinction between LAGB and HAGB. Based on these arguments, the strength of a moderately deformed material should฀be฀seen฀as฀the฀sum฀of฀matrix฀friction฀stress฀ σ0, including any particle or solution terms, a loose dislocation term ∆σρ taking account of dislocations inside cells, a dislocation cell term ∆σcell, and a Hall–Petch term ∆σHP taking account of HAGB strengthening, thus: [11.18] An analysis of strengthening in heavily rolled Fe3Al as strain level increases is shown in Fig. 11.11, where the dislocation hardening term ∆σρ and the

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11.11 Analysis of hardening taking place during heavy rolling of Fe3Al. Flow stress is interpreted as the sum of the initial, undeformed strength, an increase due to dislocation hardening, and hardening by cell boundaries (LAGB) created by deformation. Source: Taken from Morris et al.110,112

cell-LAGB hardening term ∆σcell are seen to add to the initial material strength (σ0 + ∆σHP )฀ to฀ provide฀ a฀ good฀ description฀ of฀ the฀ experimental฀ strength.110,112 It can thus be understood that initial structural changes during deformation will cause rapid hardening as loose dislocations and dislocation cells are introduced, and฀ only฀ later฀ will฀ grain฀ size฀ hardening฀ be฀ signiicant฀ as฀ grain฀ size฀ is฀ reduced฀ signiicantly฀ when฀ LAGB฀ (cell฀ walls)฀ slowly฀ transition฀ to฀ HAGB฀ (grain฀ boundaries).฀Eventually,฀at฀nanoscale฀grain฀sizes,฀dislocation฀and฀cell฀hardening฀ will฀be฀lost.฀A฀simple฀description฀of฀hardness฀as฀related฀to฀grain฀size฀(i.e.฀ ∆H ∝ 1/√ d)฀or฀as฀related฀to฀dislocation฀cell฀size฀(i.e.฀∆H ∝ 1/dc) will have some validity, each in its own given microstructural regime. Figure 11.12109,110,112–115 compares hardening in Fe/Fe3Al/FeAl during severe working, and shows how the 1/d dependence provides a better description of behaviour, with less data scatter, during฀the฀irst฀stage฀of฀microstructure฀reinement,฀whilst฀the฀1/√ d dependence is better฀for฀grain฀sizes฀smaller฀than฀approximately฀100฀nm. As฀a฀inal฀comment,฀however,฀for฀grain฀sizes฀greater฀than฀about฀50฀nm,฀where฀ a certain density of randomly arranged dislocation can be found (after deformation), and฀especially฀for฀grain฀sizes฀greater฀than฀about฀100฀nm,฀where฀dislocation฀cellular฀ substructures฀ are฀ expected,฀ the฀ complete฀ analysis฀ of฀ hardening฀ must฀ rely฀ on฀ equation 11.18, taking account of the density and misorientation of boundaries, as well as the presence of any loose dislocations.

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11.12 Analysis of hardening during cold working or milling of Fe/Fe3Al/ FeAl in terms of (a) reciprocal grain/cell size, or (b) reciprocal square root grain/cell size. Sources: Data taken from Valiev et al.;109 Fecht et al.;113 Todaka et al.;114 Zadra et al.;115 Morris et al.110,112

11.9

Conclusion and future trends

There now appears to be good understanding of the reasons for strengthening by grain฀ size฀ reinement,฀ and฀ especially฀ the฀ evolution฀ from฀ Hall–Petch฀ behaviour,฀ dependent on local stress concentrations in one grain inducing strain in neighbouring regions, to individual dislocation nucleation and glide, and eventually partial dislocation operation. Grain boundaries can be seen as both obstacles for dislocations and as sources, but the role of grain boundary sliding or diffusion, as well as the ideas of some special structure or behaviour of the boundaries, seems to be discredited.

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Studies today concentrate on materials produced by new fabrication methods, including those prepared by severe plastic deformation and the nano-pillar class of samples, and on improving ductility or toughness at the same time as strength. The฀role฀of฀alloying฀to฀complex฀crystal฀structures฀and฀mixed-phase฀microstructures,฀ which will surely improve both nanostructure stability as well as overall mechanical behaviour, remains poorly understood and worthy of further attention. Speciic฀ references฀ have฀ been฀ made฀ throughout฀ this฀ chapter฀ to฀ important฀ scientiic฀ publications.฀ This฀ is฀ invaluable฀ reading฀ for฀ a฀ more฀ profound฀ understanding of this area. For the more general reader interested in a slightly deeper overview understanding of nanostructural strengthening than that presented here, the following reviews or general reports are recommended reading. Morris5 gives a simple, now somewhat outdated overview of fabrication and mechanical behaviour of nanocrystalline metals. Meyers et al.4 present a very complete analysis of strengthening in these materials. The importance of strain rate฀ in฀ analysing฀ deformation฀ is฀ examined฀ in฀ some฀ excellent฀ publications฀ by฀ Asaro and Suresh,2 Wang et al.65 and Dao et al.3 Finally, information on severe plastic deformation and its materials is reviewed by Valiev et al.105 and Valiev and Langdon.106

11.10 References ฀ 1฀ ฀ 2฀ ฀ 3฀ ฀ 4฀ 5 ฀ 6฀ ฀ 7฀ ฀ 8฀ ฀ 9฀ 10฀ 11฀ 12฀ 13฀ 14฀ 15฀ 16฀ 17฀ 18฀ 19฀ 20฀ 21฀ 22฀

Cottrell฀A.H.฀The฀mechanical฀properties฀of฀matter.฀McGraw-Hill,฀New฀York.฀1964. Asaro฀R.J.,฀Suresh฀S.฀Acta฀mater฀2005;53:฀3369. Dao฀M.,฀Lu฀L.,฀Asaro฀R.J.,฀De฀Hosson฀J.T.M.,฀Ma฀E.฀Acta฀mater฀2007;55:฀4041. Meyers฀M.A.,฀Mishra฀A.,฀Benson฀D.J.฀Progress฀in฀mater฀sci฀2006;51:฀427. Morris D.G. Mechanical behaviour of nanostructured materials. Trans Tech Publications. Uetikon-Zurich,฀Switzerland,฀1998. Jang฀J.S.C.,฀Koch฀C.C.฀Scripta฀metall฀et฀mater฀1990;24:฀1599. Fougere฀G.E.,฀Weertman฀J.R.,฀Siegel฀R.W.฀Nanostructured฀mater฀1995;5:฀127. Zhu฀M.,฀Fecht฀H-J.฀Nanostructured฀mater฀1995;6:฀921. Rawers฀J.C.,฀Korth฀G.฀Nanostructured฀mater฀1996;7:฀25. Malow฀T.R.,฀Koch฀C.C.฀Acta฀mater฀1998;46:฀6459. Munitz฀ A.,฀ Livne฀ Z.,฀ Rawers฀ J.C.,฀ Adams฀ J.S.,฀ Fields฀ R.J.฀ Nanostructured฀ mater฀ 1999;11:฀159. Jia฀D,฀Ramesh฀KT,฀Ma฀E.฀Acta฀mater฀2003;51:฀3495. Guduru฀ R.K.,฀ Scattergood฀ R.O.,฀ Koch฀ C.C.,฀ Murty฀ K.L.,฀ Guruswamy฀ S.,฀ McCarter฀ M.K.฀Scripta฀mater฀2006;54:฀1879. Embury฀J.D.,฀Keh฀A.S.,฀Fisher฀R.M.฀Trans฀metall฀soc฀AIME฀1966;236:฀1252. Hansen฀N.,฀Ralph฀B.฀Acta฀metall฀1982;30:฀411. Nieman฀G.W.,฀Weertman฀J.R.,฀Siegel฀R.W.฀Scripta฀metall฀1989;23:฀2013. Chokshi฀A.H.,฀Rosen฀A.,฀Karch฀J.,฀Gleiter฀H.฀Scripta฀metall฀1989;23:฀1679. Nieman฀G.W.,฀Weertman฀J.R.,฀Siegel฀R.W.฀J฀mater฀res฀1991;6:฀1012. Sanders฀P.G.,฀Eastman฀J.A.,฀Weertman฀J.R.฀Acta฀mater฀1997;45:฀4019. Nieman฀G.W.,฀Weertman฀J.R.,฀Siegel฀R.W.฀Scripta฀metall฀et฀mater฀1990;24:฀145. Fougere฀G.E.,฀Weertman฀J.R.,฀Siegel฀R.W.฀Nanostructured฀mater฀1993;3:฀379. Gertsman฀V.Y.,฀Hoffman฀M.,฀Gleiter฀H.,฀Birringer฀R.฀Acta฀metall฀et฀mater฀1994;42:฀3539.

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23฀ Huang฀Z.,฀Gu฀L.Y.,฀Weertman,฀J.R.฀Scripta฀mater฀1997;37:฀1071. 24฀ Youngdahl฀C.J.,฀ Sanders฀ P.G.,฀ Eastman฀ J.A.,฀Weertman฀ J.R.฀ Scripta฀ mater฀ 1997;37:฀ 809. 25฀ Jain฀M.,฀Christman฀T.฀Acta฀metall฀et฀mater฀1994;42:฀1901. 26฀ Hoffman฀M.,฀Birringer฀R.฀Acta฀mater฀1996;44:฀2729. 27฀ Volpp฀T.,฀Goring฀E.,฀Kuschke฀W.M.,฀Arzt฀E.฀Nanostructured฀mater฀1997;8:฀855. 28฀ Trelewicz฀J.R.,฀Schuh฀C.A.฀Acta฀mater฀2007;55:฀5948. 29฀ Li฀J.C.M.,฀Chou฀Y.T.฀Metall฀mater฀trans฀1970;1:฀1145. 30฀ Ashby฀M.F.฀Phil฀mag฀1970;21:฀399. 31฀ Fleck฀ N.A.,฀ Muller฀ G.M.,฀ Ashby฀ M.F.,฀ Hutchinson฀ J.W.฀ Acta฀ metall฀ et฀ mater฀ 1994;42:฀475. 32฀ Meyers฀M.A.,฀Ashworth฀E.฀Phil฀mag฀1982;46A:฀737. 33฀ Benson฀D.J.,฀Fu฀H-H.,฀Meyers฀M.A.฀Mater฀sci฀eng฀2001;A319–321:฀854. 34฀ Carsley฀J.E.,฀Milligan฀W.W.,฀Zhu฀X.H.,฀Aifantis฀E.C.฀Scripta฀mater฀1997;36:฀727. 35฀ Wei฀ Q.,฀ Kecskes฀ L.,฀ Jiao฀ T.,฀ Hartwig฀ K.T.,฀ Ramesh฀ K.T.,฀ Ma฀ E.฀Acta฀ mater฀ 2004; 52:1 959. 36฀ Nieh฀T.G.,฀Wadsworth฀J.฀Scripta฀metall฀et฀mater฀1991;25:฀955. 37฀ Scattergood฀R.O.,฀Koch฀C.C.฀Scripta฀metall฀et฀mater฀1992;27:฀1195. 38฀ Koch฀C.C.฀Nanostructured฀mater฀1993;2:฀109. 39฀ Pande฀C.S,฀Masumara฀R.A,฀Armstrong฀R.W.฀Nanostructured฀mater฀1993;2:฀323. 40฀ Gleiter฀H..฀Progress฀in฀mater฀sci฀1989;33:฀223. 41฀ Thomas฀G.J.,฀Siegel฀R.W.,฀Eastman฀J.A.฀Scripta฀metall฀et฀mater฀1990;24:฀201. 42฀ Cheung฀C.,฀Djuanda฀F.,฀Erb฀U.,฀Palumbo฀G.฀Nanostructured฀mater฀1995;5:฀513. 43฀ Lu฀K.,฀Wei฀W.D.,฀Wang฀J.T.฀Scripta฀metall฀et฀mater฀1990;24:฀2319. 44฀ Wang฀N.,฀Wang฀Z.,฀Aust฀K.T.,฀Erb฀U.฀Mater฀sci฀eng฀1997;A237:฀150. 45฀ Xiao฀C.,฀Mirshams฀R.A.,฀Whang฀S.H.,฀Yin฀W.M.฀Mater฀sci฀eng฀2001;A301:฀35. 46฀ Wang฀Y.M.,฀Cheng฀S.,฀Wei฀Q.M.,฀Ma฀E.,฀Nieh฀T.G.,฀Hamza฀A.฀Scripta฀mater฀2004;51:฀ 1023. 47฀ Ebrahimi฀ F.,฀ Bourne฀ G.R.,฀ Kelly฀ M.S.,฀ Matthews฀ T.E.฀ Nanostructured฀ mater฀ 1999;11:฀343. 48฀ Agnew฀S.R.,฀Elliott฀B.R.,฀Youngdahl฀C.J.,฀Hemker฀K.J.,฀Weertman฀J.R.฀Mater฀sci฀eng฀ 2000;A285:฀391. 49฀ Weertman฀J.R.฀Mater฀sci฀eng฀1993;A166:฀161. 50฀ Sanders฀ P.G.,฀ Fougere฀ G.E.,฀ Thompson฀ L.J.,฀ Eastman฀ J.A.,฀ Weertman฀ J.R.฀ Nanostructured฀mater฀1997;8:฀243. 51฀ Sanders฀ P.G.,฀Witney฀A.B.,฀Weertman฀ J.R.,฀Valiev฀ R.Z.,฀ Siegel฀ R.W.฀ Mater฀ sci฀ eng฀ 1995;A204:฀7. 52฀ Gertsman฀V.Y.,฀Birringer฀R.฀Scripta฀metall฀et฀mater฀1994;30:฀577. 53฀ Nabarro฀F.R.N.฀Report฀conf฀strength฀solids.฀The฀Physics฀Society.฀London.฀1948;฀p.75. 54฀ Herring฀C.฀J฀appl฀phys฀1950;21:฀437. 55฀ Coble฀R.L.฀J฀appl฀phys฀1963;34:฀1679. 56฀ Gifkins฀R.C.฀J฀amer฀ceram฀soc฀1968;51:฀69. 57฀ Luthy฀H.,฀White฀R.A,฀Sherby฀O.D.฀Mater฀sci฀eng฀1979;39:฀211. 58฀ Sanders฀P.G.,฀Rittner฀M.,฀Kiedaisch฀E.,฀Weertman฀J.R.,฀Kung฀H.,฀Lu฀Y.C.฀Nanostructured฀ mater฀1997;9:฀433. 59฀ Wang฀D.L.,฀Kong฀Q.P.,฀Shui฀J.P.฀Scripta฀metall฀et฀mater฀1994;31:฀47. 60฀ Deng฀J.,฀Wang฀D.L.,฀Kong฀Q.P.,฀Shui฀J.P.฀Scripta฀metall฀et฀mater฀1995;32:฀349. 61฀ Kong฀Q.P.,฀Cai฀B.,฀Xiao฀M.L.฀Mater฀sci฀eng฀1997;A234–236:฀91. 62฀ Cai฀B.,฀Kong฀Q.P.,฀Lu฀L.,฀Lu฀K.฀Scripta฀mater฀1999;41:฀755.

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฀ 63฀ Jia฀D.,฀Ramesh฀K.T.,฀Ma฀E.,฀Lu฀L.,฀Lu฀K.฀Scripta฀mater฀2001;45:฀613. ฀ 64฀ Yin฀W.M.,฀Whang฀S.H.,฀Mirshams฀R.,฀Xiao฀C.H.฀Mater฀sci฀eng฀2001;A301:฀18. ฀ 65฀ Wang฀Y.M.,฀Hamza฀A.V.,฀Ma฀E.฀Acta฀mater฀2006;54:฀2715. ฀ 66฀ Wang฀Y.M.,฀Ma฀E.฀Appl฀phys฀letts฀2004;85:฀2750. ฀ 67฀ Vehoff฀ H.,฀ Lemaire฀ D.,฀ Schuler฀ K.,฀ Waschkies฀ T.,฀ Yang฀ B.฀ Int฀ J฀ mater฀ res฀ 2007;98:฀259. ฀ 68฀ Kumar฀K.S.,฀Suresh฀S.,฀Chisholm฀M.F.,฀Horton฀J.A.,฀Wang฀P.฀Acta฀mater฀2003;51:฀387. ฀ 69฀ Chen฀M.,฀Ma฀E.,฀Hemker฀K.J.,฀Sheng฀H.,฀Wang฀Y.,฀Cheng฀X.฀Science฀2003;300:฀1275. 70 Liao X.Z., Zhao Y.H., Srinivasan S.G., Zhu Y.T., Valiev R.Z., Gunderov D.V. Appl phys฀letts฀2004;84:฀592. ฀ 71฀ Zhu฀Y.T.,฀Liao฀X.Z.,฀Srinivasan฀S.G.,฀Zhao฀Y.H.,฀Baskes฀M.I.,฀Zhou฀F.,฀Lavernia฀E.J.฀ Appl฀phys฀letts฀2004;85:฀5049. 72 Budrovic Z., Van Swygenhoven H., Derlet P.M., Van Petegem S., Schmitt B. Science 2004;304:฀273. ฀ 73฀ Shan฀ Z.,฀ Stach฀ E.A.,฀ Wiezorek฀ J.M.K.,฀ Knapp฀ J.A.,฀ Follstaedt,฀ Mao฀ S.X.฀ Science฀ 2004;305:฀654. ฀ 74฀ Asaro฀R.J.,฀Krysl฀P.,฀Kad฀B.฀Phil฀mag฀letts฀2003;83:฀733. ฀ 75฀ Cheng฀S.,฀Spencer฀J.A.,฀Milligan฀W.W.฀Acta฀mater฀2003;51:฀4505. ฀ 76฀ Schiotz฀J.,฀Vegge฀T.,฀Di฀Tolla฀F.D.,฀Jacobsen฀K.W.฀Phys฀rev฀1999;B60:฀11,971. ฀ 77฀ Van฀Swygenhoven฀H.,฀Caro฀A.,฀Farkas฀D.฀Scripta฀mater฀2001;44:฀1513. ฀ 78฀ Derlet฀P.M.,฀Hasnaoui฀A.,฀Van฀Swygenhoven฀H.฀Scripta฀mater฀2003;49:฀629. ฀ 79฀ Van฀Swygenhoven฀H.,฀Caro฀A.฀Phys฀rev฀1998;B58:฀11,246. ฀ 80฀ Van฀Swygenhoven฀H.,฀Derlet฀P.M.,฀Froseth฀A.G.฀Nature฀materials฀2004;3:฀399. ฀ 81฀ Schiotz฀J.,฀Di฀Tolla฀F.D.,฀Jacobsen฀K.W.฀Nature฀1998;391:฀561. ฀ 82฀ Schiotz฀J.,฀Jacobsen฀K.W.฀Science฀2003;301:฀1357. ฀ 83฀ Van฀Vliet฀K.J.,฀Tsikata฀S.,฀Suresh฀S.฀Appl฀phys฀letts฀2003;83:฀1441. ฀ 84฀ Morris฀D.G.,฀Morris฀M.A.฀Acta฀metall฀mater฀1991;39:฀1763. ฀ 85฀ Hansen฀N.฀Scripta฀mater฀2004;51:฀801. ฀ 86฀ Hansen฀N.฀Adv฀eng฀mater฀2005;7:฀815. ฀ 87฀ Morris-Muñoz฀M.A.,฀Dodge฀A.,฀Morris฀D.G.฀Nanostructured฀mater฀1999;11:฀873. ฀ 88฀ Morris฀D.G.,฀Gutierrez-Urrutia฀I.,฀Muñoz-Morris฀M.A.฀Scripta฀mater฀2007;57:฀369. ฀ 89฀ Krasnowski฀M.,฀Witek฀A.,฀Kulik฀T.฀Intermetallics฀2002;10:฀371. ฀ 90฀ Krasnowski฀M.,฀Kulik฀T.฀Intermetallics฀2007;15:฀201. ฀ 91฀ Krasnowski฀M.,฀Kulik฀T.฀Intermetallics฀2007;15:฀1377. ฀ 92฀ He฀L.,฀Ma฀E.฀Nanostructured฀mater฀1996;7:฀327. ฀ 93฀ Botcharova฀E.,฀Freudenberger฀J.,฀Schultz฀L.฀Acta฀mater฀2006;54:฀3333. ฀ 94฀ Venugopal฀T.,฀Prasad฀Rao฀K.,฀Murty฀B.S.฀Acta฀mater฀2007;55:฀4439. ฀ 95฀ Dutta฀A.,฀De฀P.S.,฀Mishra฀R.S.,฀Watson฀T.J.฀Mater฀sci฀eng฀2009;A513–514:฀239. ฀ 96฀ Koch฀C.C.฀Scripta฀mater฀2003;49:฀657. ฀ 97฀ Benameur฀T.,฀Yavari฀A.R.฀J฀mater฀res฀1992;7:฀2971. ฀ 98฀ Morris฀D.G.,฀Amils฀X.,฀Nogues฀J.,฀Surinach฀S.,฀Baro฀M.D.,฀Muñoz-Morris฀M.A.฀Int฀J฀ of฀non-equilib฀proc฀2002;11:฀379. ฀ 99฀ Lu฀L.,฀Shen฀Y.F.,฀Chen฀X.H.,฀Qian฀L.H.,฀Lu฀K.฀Science฀2004;304:฀422. 100฀ Li฀Y.S.,฀Tao฀N.R.,฀Lu฀K.฀Acta฀mater฀2008;56:฀230. 101฀ Zhang฀Y.,฀Tao฀N.R.,฀Lu฀K.฀Acta฀mater฀2008;56:฀2429. 102฀ Tao฀N.R.,฀Lu฀K.฀J฀mater฀sci฀technol฀2007;23:฀771. 103฀ Qin฀E.W.,฀Lu฀L.,฀Tao฀N.R.,฀Tan฀J.,฀Lu฀K.฀Acta฀mater฀2009;57:฀6215. 104฀ Christian฀J.W.,฀Mahajan฀S.฀Prog฀mater฀sci฀1995;39:฀1. 105฀ Valiev฀R.Z.,฀Islamgaliev฀R.K.,฀Alexandrov฀I.V.฀Progress฀in฀mater฀sci฀2000;45:฀103.

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106฀ Valiev฀R.Z.,฀Langdon฀T.G.฀Progress฀in฀mater฀sci฀2006;51:฀881. 107฀ Cabibbo฀M.,฀Evangelista฀E.,฀Kassner฀M.E.,฀Meyers฀M.A.฀Microstructure฀and฀strength฀ of metals processed by severe plastic deformation. In: Zhu Y.T., Langdon T.G., Horita Z.,฀Zehetbauer฀M.J.,฀Semiatin฀S.L.,฀Lowe฀T.C.,฀editors.฀Ultraine฀Grained฀Materials฀ IV,฀TMS,฀Warrendale,฀2006;฀p.237. 108฀ Gubicza฀ J.,฀ Chinh฀ N.Q.,฀ Langdon฀ T.G.,฀ Ungar฀ T.฀ Microstructure฀ and฀ strength฀ of฀ metals processed by severe plastic deformation. In: Zhu Y.T., Langdon T.G., Horita Z.,฀Zehetbauer฀M.J.,฀Semiatin฀S.L.,฀Lowe฀T.C.,฀editors.฀Ultraine฀Grained฀Materials฀ IV,฀TMS,฀Warrendale,฀2006;฀p.231. 109฀ Valiev฀R.Z.,฀Ivanisenko฀Y.V.,฀Rauch฀E.F.,฀Baudelet฀B.฀Acta฀mater฀1996;44:฀4705. 110฀ Morris฀D.G.,฀Gutierrez-Urrutia฀I.,฀Muñoz-Morris฀M.A.฀J฀mater฀sci฀2008;43:฀7438. 111฀ Leseur฀D.R.,฀Syn฀C.K.,฀Sherby฀O.D.฀Mater฀sci฀eng฀2007;A463:฀54. 112฀ Morris฀D.G.,฀Gutierrez-Urrutia฀I.,฀Muñoz-Morris฀M.A.,฀to฀be฀published. 113฀ Fecht฀ H.J.฀ Formation฀ of฀ Nanostructures฀ in฀ Metals฀ and฀ Composites฀ by฀ Mechanical฀ Means.฀ In:฀ Zehetbauer฀ M.J.,฀ Valiev฀ R.Z.,฀ editors.฀ Nanomaterials฀ by฀ Severe฀ Plastic฀ Deformation,฀Wiley-VCH,฀Weinheim,฀2004;฀p.30. 114฀ Todaka฀Y.,฀Umemoto฀M.,฀Yin฀J.,฀Liu฀Z.,฀Tsuchiya฀K.฀Mater฀sci฀eng.฀2007;A462:฀264. 115฀ Zadra฀M.,฀Casari฀F.,฀Lonardelli฀I.,฀Ischia฀G.,฀Molinari฀A.฀Intermetallics฀2007;15:฀1650.

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12 Elastic and plastic deformation in nanocrystalline metals M.Y.฀GUTKIN,฀Russian Academy of Sciences, Russia

Abstract: This chapter discusses theoretical models that describe structure, elastic฀strains฀and฀different฀mechanisms฀of฀strain฀relaxation฀and฀plastic฀ deformation of nanocrystalline metals. Special attention is paid to structure, strained฀state฀and฀the฀pentagonal฀symmetry฀of฀nanoparticles,฀in฀which฀context฀ the฀disclination฀models฀and฀channels฀of฀strain฀relaxation฀are฀reviewed.฀For฀ nanocrystalline metals, various grain boundary stress sources and concentrators are฀examined฀with฀regard฀to฀their฀capacity฀to฀initiate฀the฀mechanisms฀of฀plastic฀ deformation. Theoretical modeling of dislocation generation, deformation twinning, rotational and superplastic deformation, and athermal stress-induced grain growth is considered in detail. Key words: strained state in nanoparticles, mechanisms of plasticity in nanocrystalline metals, generation of dislocations and twins, rotational and superplastic deformation, athermal stress-induced grain growth.

12.1

Introduction

Outstanding฀ mechanical฀ properties฀ of฀ nanocrystalline฀ metals฀ (NCMs)฀ have฀ attracted฀much฀attention฀since฀the฀end฀of฀the฀1980s฀when฀irst฀NCMs฀had฀been฀ fabricated and studied. In particular, it became at once clear that the behavior of defects฀ and฀ mechanisms฀ of฀ plastic฀ deformation฀ in฀ NCMs฀ and฀ conventional฀ polycrystalline metals are rather different.1,2฀However,฀the฀experimental฀study฀of฀ defects฀ in฀ NCMs฀ has฀ met฀ many฀ dificulties,฀ which฀ determines฀ the฀ importance฀ of theoretical modeling and computer simulations. This chapter reviews some analytical฀ theoretical฀ models฀ that฀ describe฀ deformation฀ phenomena฀ in฀ NCMs.฀ Section฀12.2฀is฀devoted฀to฀elastic฀strains฀in฀as-fabricated฀NCMs.฀Our฀view฀is฀that฀ understanding฀ the฀ initial฀ strained฀ state฀ should฀ be฀ considered฀ as฀ the฀ irst฀ and฀ necessary฀step฀in฀modeling฀the฀deformation฀processes฀in฀NCMs.฀Moreover,฀the฀ assumptions฀on฀the฀elastic-state฀characteristics฀of฀a฀representative฀NCM฀volume฀ form the basis of the majority of theoretical models describing various mechanisms of฀plastic฀deformation฀and฀fracture฀in฀NCMs.฀That฀is฀why฀we฀pay฀much฀attention฀ to elastic strains here. Starting from peculiarities of elastic-strain distribution and relaxation฀ in฀ isolated฀ nanoparticles฀ and฀ their฀ conglomerates,฀ we฀ then฀ briely฀ consider฀ grain฀ boundary฀ (GB)฀ stress฀ sources฀ and฀ concentrators฀ in฀ NCMs.฀ In฀ the฀ stress฀ ields฀ of฀ these฀ GB฀ sources฀ and฀ concentrators,฀ various฀ mechanisms฀ of฀ plastic deformation can start working, including dislocation emission from GBs, generation of deformation twins, GB migration, transformation and decay, etc. 329 © Woodhead Publishing Limited, 2011

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Theoretical models of these mechanisms are considered in Section 12.3. Then in the same section the interplay between translational and rotational modes of plastic deformation is discussed together with mechanisms that provide local changes in misorientation angles of GBs and can result in grain rotation. The theoretical models,฀ which฀ describe฀ the฀ effects฀ of฀ strengthening฀ and฀ softening฀ of฀ NCMs฀ under superplastic deformation, are also reviewed there. It is demonstrated that most฀ of฀ the฀ models฀ under฀ discussion฀ can฀ be฀ analysed฀ within฀ a฀ uniied฀ energy฀ approach,฀where฀some฀critical฀values฀of฀parameters฀(for฀example,฀a฀critical฀value฀ of the applied shear stress) are calculated to state the conditions necessary for the barrierless activation of the deformation mechanisms. When possible, theoretical estimates฀ are฀ compared฀ with฀ available฀ experimental฀ data฀ that฀ allows฀ one฀ to฀ conclude that the model is either realistic or is not.

12.2

Elastic strains in nanocrystalline metals

As-fabricated฀ NCMs฀ are฀ always฀ the฀ subject฀ of฀ residual฀ elastic฀ strains.฀ For฀ example,฀ Wunderlich฀ et al.3฀ evaluated฀ one฀ of฀ the฀ irst฀ transmission฀ electron฀ microscopy฀ (TEM)฀ studies฀ of฀ a฀ NCM฀ (nc-Pd฀ with฀ the฀ grain฀ size฀ of฀ 4–9฀ nm,฀ which was fabricated by high-pressure compaction of nanocrystallites condensed from the gas phase) and showed that many GBs have severely distorted nearboundary regions with smaller atomic density and higher level of elastic strains. In฀general,฀their฀sample฀contained฀about฀25%฀of฀highly฀strained฀material.฀Similar฀ conclusions฀ followed฀ from฀ comparison฀ of฀ earlier฀ experimental฀ data฀ from฀ Mössbauer spectroscopy,4 positron lifetime spectroscopy,5,6 X-ray diffraction,7 EXAFS 8 and neutron diffraction.9 Later, in the middle of the 1990s, residual elastic฀ strains฀ were฀ investigated฀ in฀ detail฀ in฀ NCMs฀ obtained฀ by฀ severe฀ plastic฀ deformation.10 The general result was that the elastic strains were distributed inhomogeneously฀ over฀ the฀ grains:฀ they฀ reached฀ their฀ maximum฀ values฀ in฀ the฀ vicinity฀of฀GBs฀and฀demonstrated฀an฀exponential฀slope฀at฀a฀distance฀of฀several฀ nanometers from the GBs. To understand the origin of the residual elastic strains in฀NCMs,฀it฀is฀reasonable฀to฀start฀from฀the฀main฀features฀of฀NCM฀structure. Usually฀ NCMs฀ consist฀ of฀ crystalline฀ grains฀ (ranging฀ from฀ several฀ to฀ approximately฀one฀hundred฀nanometers฀in฀diameter),฀which฀are฀separated฀by฀GBs.฀ The GBs meet each other at linear junctions that are called double if two GBs meet, triple if three GBs meet, etc. In their turn, the GB junctions meet each other at฀point฀nodes,฀which฀can฀be฀fourfold,฀ivefold,฀etc.฀Most฀GB฀junctions฀and฀their฀ nodes are triple and fourfold, respectively. Their total volume fraction drastically increases฀with฀grain฀reinement฀and฀can฀reach฀up฀to฀50%฀in฀ine-grained฀NCMs.1 As฀ follows฀ from฀ these฀ structural฀ peculiarities฀ of฀ NCMs,฀ there฀ are฀ two฀ main฀ reasons฀for฀their฀unique฀mechanical฀and฀physical฀properties:฀the฀irst฀one฀is฀the฀ nanoscopic฀grain฀size,฀and฀the฀second฀one฀is฀the฀unusually฀high฀density฀of฀GBs,฀ GB฀junctions฀and฀junction฀nodes.฀Let฀us฀irst฀consider฀the฀origin฀of฀residual฀elastic฀ strains in isolated nanoparticles (or nanoclusters) and then in their conglomerates.

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12.2.1 Nanoparticles Residual elastic strains appear in isolated nanoparticles due to various reasons such as surface stress, pentagonal symmetry, presence of defects, phase transformations, etc. The physical origin of the surface stress is that the chemical bonding of atoms at the crystal surface is different from the bonding of atoms in the crystal bulk.11 Therefore, the equilibrium distance between the surface atoms differs from that between the bulk atoms, and the subsurface atomic layers occur in elastically strained state. For an isotropic spherical nanoparticle of radius R, there is a rough estimate of the average distortion of the interatomic distance a caused by surface tension that reads2,12: [12.1] where K฀ is฀ the฀ volume฀ compressibility฀ coeficient฀ and฀ γ฀ is฀ the฀ speciic฀ surface฀ energy. For typical values of parameters K ~ 10–11 m3/J,฀γ฀~฀1฀J/m2 and R ~ 10 nm, this฀estimate฀gives฀approximately,฀0.67·10–3, that is about one-tenth of a percent.2 It฀has฀also฀been฀noted฀that฀parameters฀entering฀equation฀[12.1]฀are฀size฀dependent.2 In particular, the surface energy of a nanoparticle depends on its radius R as13 [12.2] where γ0฀is฀the฀speciic฀surface฀energy฀of฀a฀bulk฀crystal,฀α ≈ 1 and β ≈ α2 ≈ 1 are numerical฀ coeficients.฀ Thus,฀ the฀ surface฀ energy฀ γ decreases with decreasing nanoparticle radius R. It is worth noting that the surface energy of nanoparticles also฀ decreases฀ with฀ increasing฀ temperature฀ (see,฀ for฀ example,฀ Jia฀ et al.14 and references therein). Nevertheless, equation [12.1] demonstrates the main contribution of radius R to the elastic strains caused by the surface stress in nanoparticles. The฀majority฀of฀isolated฀nanoparticles฀are฀synthesized฀in฀the฀single฀crystalline฀ state;15 however, they also demonstrate a large variety of structures and shapes. ‘The฀ next฀ most฀ common฀ structure฀ is฀ probably฀ simple฀ twins,฀ although฀ there฀ is฀ rarely any publication of statistical data of particle populations. Of rather lower probability฀except฀for฀gold฀and฀silver฀is฀multiply฀twinned฀particles’฀(Marks,15). Among฀the฀multiply฀twinned฀particles,฀ivefold-twinned฀nano-฀and฀microparticles฀ have attracted much attention due to their pentagonal symmetry, which is impossible฀in฀bulk฀single฀crystalline฀solids฀(see,฀for฀example,฀the฀reviews2,15–22 and recent papers).23–26 Fivefold-twinned nanoparticles can have shapes close to regular decahedra, icosahedra or pentagonal prisms. De Wit27 and Galligan28 independently pointed out a direct relation between the structure฀of฀ivefold-twinned฀nanoparticles฀and฀disclinations฀(see฀also2,19,29). For illustration, de Wit27 suggested considering the undeformed body, which consists

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of฀ive฀face-centered฀cubic฀(FCC)฀crystals฀oriented฀with฀the฀(1฀¯1 0) plane in the plane of the paper (Fig. 12.1 (a) ). Each crystal is in twin orientation with respect to฀the฀adjacent฀one,฀so฀that฀AC,฀AD,฀AE,฀and฀AF฀are฀twin฀boundaries.฀The฀angle฀ between each pair of (1 1 1) and (¯1 ¯1฀1)฀planes฀is฀70°32' . Therefore the resulting polycrystal has a wedge BAB' ฀with฀an฀apex฀angle฀of฀7°20'. If the two sides of this wedge are brought together they will form a twin boundary, while at the same time฀ a฀ positive฀ wedge฀ disclination฀ is฀ created฀ at฀A,฀ where฀ ive฀ twin฀ boundaries฀ terminate฀ (Fig.฀ 12.1฀ (b)฀).฀Thus,฀ the฀ inal฀ coniguration฀ has฀ no฀ wedge-like฀ cusp฀ BAB' but contains a partial disclination of strength ω฀ =฀ 7°20', which creates inhomogeneous elastic strains and stresses in the polycrystal. In the case of decahedral nanoparticles (Fig. 12.2 (a) ) or pentagonal rods (Fig. 12.2 (b) ), there is only one such ‘star disclination’ whose line coincides with the฀pentagonal฀symmetry฀axis.27฀In฀icosahedral฀nanoparticles,฀there฀are฀six฀such฀ disclinations whose lines pass through twelve icosahedron vertices (Fig. 12.2 (c), see Ref. 19 for details). The idea to use the disclination concept has been very productive because it gives฀a฀straightforward฀way฀of฀modeling฀the฀elastic฀strains฀and฀stresses฀in฀ivefoldtwinned฀ nanoparticles.฀ For฀ example,฀ de฀ Wit27฀ approximated฀ the฀ decahedral฀ nanoparticle by a section of a cylinder containing a wedge disclination of strength ω฀along฀its฀axis.฀In฀this฀case฀the฀non-vanishing฀stress฀components฀(in฀cylindrical฀ coordinates r, ϕ and z) read: [12.3]

12.1 De Wit’s schematics27 of partial disclination formation in the core of a fivefold twin in FCC crystals. (a) Initial undeformed state of a polycrystal consisting of five FCC crystals, each in twin orientation with respect to its neighbour; the plane of the paper is (1 1¯ 0) and AC, AD, AE, and AF are twin boundaries. (b) A positive partial wedge disclination at A on which terminate the five twin boundaries AB, AC, AD, AE, and AF.

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12.2 Partial positive wedge disclinations of strength ω in (a) decahedral nanoparticle, (b) pentagonal rod, and (c) icosahedral nanoparticle.

where D฀=฀G/[2π(1–ν)], G is the shear modulus, ν is the Poisson ratio, and R is the cylinder radius. It is seen from equation [12.3] that the central region of the nanoparticle is compressed while its periphery is stretched. Indeed, the hydrostatic stress component σ฀=฀1/3Trσij฀=฀1/3฀Dω (1+ν)[2ln(r/R)+1], is negative at r < 0.6R,฀zero฀at฀r ≈ 0.6R and positive at r > 0.6R. The stresses are singular at r =฀0,฀which฀is฀a฀generic฀feature฀of฀solutions฀for฀defects฀(like฀cracks,฀dislocations,฀ disclinations,฀ etc.)฀ within฀ the฀ classical฀ theory฀ of฀ elasticity.฀ Using฀ an฀ extended฀ version of the elasticity theory (say, the strain-gradient,30,31 non-local32 or nonlinear33 theory of elasticity), one can dispense with such singularities. For example,฀in฀the฀framework฀of฀the฀strain-gradient฀elasticity,฀the฀hydrostatic฀stress฀ component at the line of a positive wedge disclination, which is placed at the distance ~ 1 µm from a negative wedge disclination of the same strength, is estimated as30,31 σ ≈ –6Dω(1+ν), which gives σ ~ –D ~ –G/4 for ω฀=฀7°20' ≈ 0.128 and ν฀=฀0.3.฀Lazar34฀has฀used฀the฀ield฀theory฀of฀elastoplasticity฀to฀consider฀ a wedge disclination in the center of a cylinder of radius R and obtained σ ≈ –1.14Dω(1+ν) at the dislocation line for R฀=฀10/κ, where κ is the gradient coeficient,฀which฀can฀be฀estimated฀as฀~฀10฀nm–1. Then we get σ ~ –D/5 ~ –G/20 for R ~ 1 nm at the same values of ω and ν. Thus, the level of G/20 can be considered as the lower magnitude of σ฀in฀the฀inest฀nanoparticles,฀while฀G/4 as its upper magnitude in the coarse nanoparticles. Anyway, the compression in the nanoparticle center is very high. Moreover, it follows from equation [12.3] that the strain energy (per unit disclination length) is27 WDh฀=฀1/8Dω2R2. Therefore, one฀can฀expect฀the฀activation฀of฀various฀mechanisms฀of฀stress฀relaxation฀when฀the฀ nanoparticle radius will increase. The same results are valid for pentagonal rods, which can be modeled by long elastic cylinders containing positive wedge disclinations฀along฀their฀axes.2,19,29 Howie and Marks35฀ extended฀ the฀ disclination฀ description฀ to฀ icosahedral฀ nanoparticles (Fig. 12.2 (c) ). They considered:

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an฀ elastic฀ sphere฀ having฀ the฀ same฀ missing฀ volume฀ (about฀ 12%),฀ but฀ spread฀ uniformly throughout the sphere. This is equivalent to an angular average of the strains,฀and฀may฀be฀visualized฀as฀a฀multitude฀of฀thin฀radial฀cones,฀each฀subtending฀ a very small solid angle dω at the centre, with small angular gaps between them in฀ the฀ unstrained฀ state.฀ The฀ cones฀ are฀ now฀ constrained฀ by฀ external฀ forces฀ to฀ remain of the same length R while they are distorted sideways until they touch, are then ‘glued’ together. (Howie and Marks35)

This฀process,฀which฀replaces฀the฀discrete฀set฀of฀six฀wedge฀disclinations฀each฀of฀ strength ω ≈฀ 7°21'฀ by฀ continuously฀ distributed฀ cone฀ defects฀ each฀ of฀ ininitely฀ small strength dω, produces the distributed disclination which is now called Marks–Ioffe disclination.36฀The฀Marks–Ioffe฀disclination฀is฀characterized฀by฀the฀ eigenstrain εθθ * ฀=฀εφφ * ฀=฀6ω/4π ≈ 0.0613 and creates the elastic stresses:35 [12.4] where (r, θ, φ) is the spherical coordinate system with the origin in the center of the sphere. Again the central region of the nanoparticle is compressed while its periphery is stretched. The hydrostatic stress σ฀ =฀ 4/3Dω(1+ν)[3ln(r/R)+1] is negative at r < 0.7R,฀zero฀at฀r ≈ 0.7R and positive at r > 0.7R. The stress components [12.4] are singular at r฀=฀0.฀The฀strain฀energy฀is35 WIc฀=฀4/3Dω2(1+ν)R3. Since฀ the฀ strain฀ energy฀ of฀ the฀ ivefold-twinned฀ nanoparticles฀ drastically฀ increases with their radii, the nanoparticle structure is unstable with respect to various transformations. This may concern the surface faceting37 and reconstruction,38฀ structural฀ modiication฀ and฀ transition฀ to฀ ‘normal’฀ single฀ crystalline state,15,18–23฀ and฀ formation฀ of฀ speciic฀ defect฀ structures,฀ which฀ accommodate in part the initial strained state.2,15,18–25,36฀In฀particular,฀Gryaznov฀ et al.39฀have฀theoretically฀considered฀the฀following฀relaxation฀channels฀of฀elastic฀ stresses inside the pentagonal whiskers: 1) creating an edge dislocation inside the whisker, 2) opening a gap in the whisker, 3) creating a compensating negative partial wedge disclination near the whisker surface, 4) splitting the pentagonal axis฀(in฀terms฀of฀splitting฀the฀positive฀wedge฀disclination฀(Fig.฀12.2฀(a)฀)฀into฀a฀pair฀ of similar disclinations of the same total strength), 5) growing a single crystalline (non-pentagonal) region in the whisker center, and 6) displacing the pentagonal axis฀ from฀ the฀ whisker฀ center.฀The฀ authors฀ calculated฀ and฀ compared฀ the฀ energy฀ changes,฀which฀are฀characteristic฀for฀the฀relaxation฀channels,฀and฀concluded฀that฀ the principal channels are dislocation creation, displacement and splitting of the pentagonal฀axis.฀Recently฀Kolesnikova฀and฀Romanov฀have฀analysed฀the฀formation฀ of a circular prismatic dislocation loop in the cross section of a pentagonal whisker40฀and฀growth฀of฀a฀misitting฀layer฀on฀the฀whisker฀surface41 as potential channels฀of฀stress฀relaxation.฀The฀latter฀stress฀relaxation฀channel฀has฀also฀been฀ applied to icosahedral nanoparticles.36 For the case of an atomically heterogeneous pentagonal whisker, Panpurin and Gutkin42 have studied the nucleation of a

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precipitate฀in฀the฀shape฀of฀a฀inite-length฀cylinder฀coaxial฀to฀the฀whisker.฀In฀the฀ approximation฀that฀the฀precipitate฀is฀subject฀of฀an฀axial฀positive฀eigenstrain฀ ε*,฀ they have demonstrated that nucleation and growth of the precipitate are energetically preferable if ε*฀is฀smaller฀than฀a฀critical฀value฀ εc. If the eigenstrain is large (ε* τc (here τc฀=฀1.53฀GPa),฀the฀central฀dislocation฀moved฀far฀away฀from฀ its initial position (see curve 6 in Fig. 12.7 (a)), and the GB decayed as a whole. The analysis of stability of low-angle GBs with different parameters showed that τc grows in a roughly linear way with rising θ (see curve 1 in Fig. 12.7 (b) ). On the other hand, the dependence of τc on the number N of dislocations, and thereby the GB length d฀(=฀Nh) at a constant value of θ, is very weak. This means that very short GBs in very small grains and comparatively long GBs in large grains decay at close values of the critical stress τc, if they have the same misorientation θ. The decay of a low-angle GB results in the formation of moving lattice dislocations that elastically interact with other lattice dislocations composing

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12.7 (a) Temporal dependence of the position x of the 8th dislocation in a low-angle GB with θ = 0.1 and N = 15, for τ = 0.5, 1.0, 1.4, 1.52, 1.53 and 1.54 GPa (curves 1, 2, 3, 4, 5 and 6, respectively). (b) Dependences τc(θ) for ωl = 0°, 1°, 3°, and 5° (curves 1, 2, 3, and 4, respectively).

neighbouring low-angle GBs. This interaction is able to stimulate decays of the neighbouring low-angle GBs and avalanche-like release of new mobile lattice dislocations.153,154 The main results are demonstrated in Fig. 12.7 (b), where the curves τc(θ) are plotted for different values of the strength ωl฀ characterizing฀ a฀ disclination dipole that has been formed after the decay of a neighbouring lowangle฀GB.฀As฀was฀expected,฀the฀critical฀shear฀stress฀ τc decreases with rising ωl. The฀phenomenon฀in฀question฀is฀able฀of฀causing฀plastic฀low฀localization฀(carried฀ by฀lattice฀dislocations฀released฀by฀low-angle฀GBs)฀in฀deformed฀NCMs฀containing฀ high-density ensembles of low-angle GBs. As฀shown฀experimentally,฀high-angle฀GBs฀bow฀(become฀curved)84,159 and emit partial lattice dislocations47,159–164 that can provide deformation twinning in NCMs.฀To฀account฀for฀these฀experiments,฀Bobylev฀et al.153฀extended฀the฀above฀ model to the case of high-angle GBs containing GB dislocations. In general, high-angle GBs contain intrinsic dislocations with small Burgers vectors associated with misorientation of such GBs. They cannot glide easily in the grain interior, in contrast to the lattice dislocations. However, high-angle GBs bow and emit฀ partial฀ dislocations฀ into฀ adjacent฀ grains฀ in฀ mechanically฀ loaded฀ NCMs฀ (Fig. 12.8). Bobylev et al.153฀ irst฀ considered฀ the฀ GB฀ bowing฀ under฀ a฀ shear฀ stress฀ τ by means of 2D dislocation dynamics that account for the additional hampering force due to an increase of the GB length. Solution of the system of dynamics equations, adapted to this case, gives new equilibrium positions of the GB dislocations and, as฀a฀corollary,฀an฀equilibrium฀coniguration฀of฀the฀high-angle฀GB฀in฀its฀curved฀ state (Fig. 12.8 (b)). Now let one of the GB dislocations located at the curved GB split into an immobile GB dislocation and a mobile Shockley dislocation that moves in the adjacent grain interior under a stress τ (Fig. 12.8 (c) ). The authors

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calculated the energetics of the dislocation emission, which was considered as a transformation of the system from its initial state with the energy W1 (Fig. 12.8 (b) ) to฀the฀inal฀state฀with฀the฀energy฀W2 (Fig. 12.8 (c)). The dislocation emission is energetically favourable, if the energy difference ∆W฀=฀W2 – W1 – A is negative. Here A is the work spent to transfer the Shockley dislocation under the stress τ. The energy difference ∆W฀ was฀ analysed฀ for฀ the฀ exemplary฀ case฀ of฀ pure฀ nanocrystalline฀Cu,฀when฀the฀GB฀is฀characterized฀by฀the฀deviation฀ ω of the GB tilt misorientation θ from that, θ0, of a low-energy (favourable) GB in the same material.63 The favourable GB Σ฀ =฀ 5/(210)฀ with165 misorientation angle θ0฀ =฀ 36.87°฀and฀speciic฀energy฀γ฀=฀0.9฀J·m–2 was used. It was shown that an increase in τ enhances the splitting and emission processes (Fig. 12.9 (a) ). At the same time, the dislocation emission is energetically unfavourable at low τ and is hampered with rising ω (Fig. 12.9 (b) ).

12.8 Evolution of a high-angle GB with intrisic GB dislocations: (a) initial state, (b) bowing of GB, and (c) splitting of a GB dislocation and emission of a partial Shockley dislocation. The partial dislocation has Burgers vector with the edge (be) and screw (bs) components. Its glide causes a stacking fault. The immobile GB dislocation has the Burgers vector with the edge (bgb – be) and screw (–bs) components.

12.9 The energy change ∆W via the path lp of the 5th partial dislocation in the case of high-angle GB containing N = 20 GB dislocations, for (a) ω = 3° and τ = 0.4, 0.6, 0.8, and 1.0 GPa (curves 1, 2, 3 and 4, respectively); and (b) τ = 1 GPa and ω = 3°, 5°, 7°, and 9° (curves 1, 2, 3 and 4, respectively).

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Let us discuss now the emission of partial dislocation by a GB disclination. Following Gutkin et al.,166฀ consider฀ a฀ 2D฀ model฀ of฀ a฀ NCM฀ with฀ positive฀ and฀ negative wedge GB disclinations of a mean strength ω. Let such a disclination ensemble฀consist฀of฀disclination฀dipoles฀with฀a฀mean฀arm฀(grain฀size)฀d, which are distant by 2R from each other, and d < R (Fig. 12.10 (a) ). In this case, one can analyse a separate GB disclination dipole as a source for generation of lattice dislocations (Fig. 12.10 (b) ). Within an energy-based approach,฀we฀calculated฀some฀critical฀values฀of฀the฀external฀shear฀stress฀τ which correspond฀to฀the฀generation฀of฀a฀lattice฀dislocation,฀its฀localization฀in฀the฀bulk฀of฀ the grain and its absorption by the opposite GB, depending on the principal parameters of the model: d, θ, and α฀ (see฀ Fig.฀ 12.10฀ (b)฀).฀ For฀ example,฀ in฀ Fig. 12.11,166 the curves τc(θ) are shown which were calculated for the case of pure nanocrystalline Al at ω฀=฀0.1฀(≈6°),฀α฀=฀10°฀and฀d฀=฀10,฀20฀and฀30฀nm.฀The฀ curves τc(θ)฀determine฀(if฀exist)฀those฀regions฀at฀the฀(θ,τ) diagram, where three typical arrangements of partial dislocations must appear in a grain: I, when partial dislocations฀are฀localized฀near฀their฀GB฀sources;฀II,฀when฀they฀are฀spread฀inside฀ the฀grain;฀and฀III,฀when฀they฀cross฀the฀grain฀and฀are฀absorbed฀by฀the฀opposite฀ GBs.฀An฀ increase฀ in฀ the฀ grain฀ size฀ d฀ is฀ accompanied฀ with฀ an฀ extension฀ of฀ the฀

12.10 (a) 2D model of a NCM with positive and negative wedge GB disclinations. (b) Emission of a partial Shockley dislocation from a moving GB disclination. The positive GB disclination moves by a distance l (l = b/[2sin(ω/2)] is the spacing between the intrisic GB dislocations with the Burgers vectors (b), thus emitting a lattice dislocation. This dislocation may be either partial, with the Burgers vector having the edge (b2) and screw (b3) components, or perfect, with the Burgers vector 2b2. At the place of generation, a difference GB dislocation forms, whose Burgers vector has either the edge (b1 = b – b2) and screw (–b3) components, or only the edge component (b – 2b2), respectively. The position of the negative GB disclination sets by the initial dipole arm L ≈ d and the azimuthal angle θ. The angle α determines the orientation of the dislocation gliding plane with respect to the GB.

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12.11 Critical stress τc via the azimuthal angle θ for different values of the grain size: (a) d = 10 nm, (b) d = 20 nm, and (c) d = 30 nm.

θ ranges, where the emission of partial dislocations must occur, and drastic changes in distribution of regions I, II and III (see Gutkin et al.166 for details). It is worth noting that these characteristic types of defect arrangements were observed฀in฀molecular฀dynamics฀simulations฀(for฀example,฀see156,157). As follows from calculations,166฀there฀exist฀two฀characteristic฀grain฀sizes฀in฀nanocrystalline฀ Al: dc1 (≈ 5 nm) and dc2 (≈ 30 nm). When d ≤ dc1, the generation of partial dislocations by GBs needs smaller values of τ than that of perfect dislocations, in the full range of possible values for θ and α. When d ≥ dc2, the generation of perfect dislocations becomes more energetically preferable for any of possible θ and α.฀In฀the฀grains฀of฀intermediate฀size,฀dc1 < d < dc2, the generation of either partial or perfect dislocations may dominate, depending on the values of the angles θ and α. Above we have considered some 2D models. However, the lattice dislocation slip,฀ deformation฀ twinning฀ and฀ GB฀ sliding฀ in฀ real฀ NCMs฀ are฀ 3D฀ processes฀ conducted฀ by฀ dislocation฀ loops฀ (DLs).฀ In฀ this฀ context,฀ a฀ 3D฀ description฀ of฀ the฀ deformation mechanisms in terms of DLs seems to be important. As noted in Ref.167 the effective way of interaction between different modes of plastic deformation฀in฀NCMs฀is฀the฀generation฀of฀new฀DLs฀at฀the฀pre–existent฀DLs฀of฀ other฀types.฀For฀example,฀pre-existent฀grain฀boundary฀DLs฀(GBDLs)฀can฀serve฀ as sources for perfect or partial lattice DLs (Fig. 12.12 (a), 12.12 (b) ) or GBDLs (Fig.฀12.12฀(c)฀).฀The฀pre-existent฀perfect฀or฀partial฀lattice฀DL฀can฀generate฀either฀ a perfect or partial lattice DL into the neighbouring grain (Fig. 12.12 (d) ) or a GBDL฀(Fig.฀12.12฀(e)฀).฀To฀summarize,฀there฀are฀9฀variants฀of฀the฀DL฀generation฀ at฀the฀pre-existent฀DLs,฀depending฀on฀the฀types฀(GB,฀perfect฀lattice,฀partial฀lattice)฀ of these DLs. These variants are called the modes for the DL generation at preexistent฀DLs.฀All฀these฀modes฀were฀analysed฀within฀a฀3D฀energy-based฀approach฀ for฀the฀exemplary฀case฀of฀nanocrystalline฀Al฀with฀the฀grain฀size฀d ranging from 10 to 100 nm.167 The basic results are briefly as follows: 1) loops of perfect lattice dislocations operate as effective sources for GB, partial and perfect lattice DLs฀ (in฀ order฀ of฀ preference);฀ 2)฀ loops฀ of฀ partial฀ lattice฀ dislocations฀ serve฀ as฀

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12.12 Different modes of generation of a new gliding DL at a segment of the initial gliding DL: (a,b) a lattice DL is emitted by a GBDL, (c) a GBDL is emitted by a GBDL, (d) a lattice DL is emitted by a lattice DL, (e) a GBDL is emitted by a lattice DL. In all the cases, a new DL is generated at a GB or at a triple junction of GBs.

effective sources for GB and partial lattice DLs (in order of preference), but are฀ not฀ effective฀ to฀ generate฀ perfect฀ lattice฀ DLs;฀ 3)฀ loops฀ of฀ GB฀ dislocations฀ can be effective sources for GBDLs, while they are not so effective for generation฀ of฀ partial฀ lattice฀ DLs;฀ GBDLs฀ hardly฀ can฀ generate฀ perfect฀ lattice฀ DLs.฀ With฀ these฀ results,฀ grains฀ in฀ NCMs฀ can฀ be฀ divided฀ into฀ the฀ three฀ basic฀ categories: relatively large (d ≈ 30 to 100 nm), intermediate (d ≈ 10 to 30 nm) and฀ inest฀ (d ≈ 3 to 10 nm) grains. The lattice dislocation slip effectively operates in large grains. The most effective sources of new DLs here are loops of perfect lattice dislocations, in which case the lattice slip enhances intense GB sliding. In intermediate grains, the conventional lattice dislocation slip is severely suppressed. The most effective sources of new DLs here are loops of partial (twinning)฀ lattice฀ dislocations,฀ which฀ enhance฀ GB฀ sliding.฀ In฀ the฀ inest฀ grains,฀ GB sliding dominates over the lattice dislocation slip and deformation twinning. Here GBDLs serve as effective sources of new GBDLs that cause intense GB sliding. A further development of these 3D models was conducted by Bobylev et al.168,169฀ with฀ the฀ aim฀ to฀ explain฀ anomalously฀ wide฀ stacking฀ faults฀ (SFs)฀ between partial dislocations in nanocrystalline Al. The theory of DLs was used to calculate the system energy more accurately compared to some earlier models.105,170–173 By means of an original algorithm, the authors investigated both the generation of partial dislocation semi-loops and the dependence of the SF

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width฀on฀the฀grain฀size฀and฀applied฀stress฀level.฀They฀showed฀that฀anomalously฀ wide SFs in nanocrystalline Al are caused by high stresses but not by small grain size฀as฀was฀derived฀in฀the฀earlier฀models.฀On฀the฀other฀hand,฀it฀was฀noted168 that ‘such high stresses are possible in nanocrystalline Al because the normal dislocation฀activity฀is฀suppressed฀by฀the฀small฀grain฀size.฀Therefore,฀although฀the฀ small฀ grain฀ size฀ is฀ not฀ directly฀ connected฀ with฀ anomalously฀ wide฀ SFs฀ in฀ nanocrystalline Al, it represents the primary cause of this phenomenon.’

12.3.2 Generation of deformation twins As is well known, deformation twins (DTs) do not appear in coarse-grained metals with relatively high values of SF energy γ.฀A฀typical฀example฀is฀Al.฀The฀ situation dramatically changes in the case of nanograins. DTs in nanocrystalline Al฀ were฀ observed฀ in฀ electron฀ microscopy฀ experiments.159–161฀ To฀ explain฀ this฀ phenomenon, a number of theoretical models94,105,168–179 have recently been suggested that describe anomalously wide SFs whose overlapping would create DTs in nc-Al. However, some of these models105,168–174,179 deal with only one or two SF strips and cannot directly be used in a description of the generation of thick฀DT฀lamellae฀observed฀experimentally฀in฀nc-Al,160,161฀Cu,47,180,181 Ni,84,182– 187 Pd188 and Ta.189฀ Following฀ the฀ experiment,฀ the฀ DT฀ lamellae฀ have฀ typical฀ thickness of several nanometers and occupy regions between opposite GBs in nanograins.฀ Sometimes฀ DT฀ lamellae฀ form฀ V-,฀ T-฀ and฀ X-shaped฀ conigurations฀ studied in detail by Zhu et al.190 Let us briefly consider some models that describe the generation of thick DT฀ lamella฀ at฀ GBs฀ in฀ NCMs.฀ It฀ seems฀ rather฀ evident฀ that฀ probability฀ of฀ DT฀ nucleation฀ increases฀ in฀ vicinity฀ of฀ stress฀ sources฀ and฀ concentrators.฀ Extrinsic฀ GB dislocations can stimulate the emission of Shockley partials (see Section 12.3.1);฀ however,฀ their฀ density฀ is฀ not฀ so฀ high฀ and฀ their฀ stresses฀ are฀ not฀ strong฀ enough for initiation of thick DT lamella nucleation.176 Possible alternatives are GB disclinations176,177 and cracks,94 which create strong and long-range stress฀ields.฀In฀the฀model,176 a DT lamella is nucleated under the action of an applied฀stress฀and฀the฀stress฀ield฀of฀a฀dipole฀of฀GB฀or฀junction฀wedge฀disclinations฀ (Fig. 12.13 (a)). The model176฀was฀used฀to฀consider฀pure฀nanocrystalline฀Al฀and฀Cu฀with฀d ≈ 30 nm. It was shown that, if the disclination strength ω฀and฀external฀shear฀stress฀τ are฀ high฀ enough฀ (but฀ still฀ realistic฀ for฀ these฀ NCMs),฀ the฀ DT฀ generation฀ is฀ characterized฀by฀the฀absence฀of฀any฀energy฀barrier.฀The฀critical฀stress฀ τc causing the฀emission฀of฀the฀irst฀twinning฀dislocation฀is฀rather฀low฀(≈0.1 GPa and ≈0.3 GPa,฀ for฀ Cu฀ and฀Al,฀ respectively,฀ at฀ ω฀ =฀ 0.5).฀As฀ the฀ DT฀ thickness฀ (equal฀ to฀ δ (n –1), where δ is the distance between neighbouring {111} atomic planes and n is the number of emitted Shockley partials) increases, the critical stress τc (n) of the฀emission฀of฀new฀twinning฀dislocations฀irst฀grows,฀then฀levels฀off,฀and฀again฀ grows (Fig. 12.13 (b) ). Thus, there are two stages of local hardening and an

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12.13 (a) The twinning partial dislocations are emitted from a GB segment AB in nanocrystalline sample with GB disclinations of strength ±ω. The emission occurred in the region (bounded by dashed contour) where the shear stress of the disclination dipole reaches its highest level. The combined action of the external shear stress τ and the disclination stress field causes the emission and glide of partials along the adjacent slip planes. Most of the partials reach the opposite GB at its segment A‘B’. The overlapping stacking faults (generated behind the emitted partials) form the deformation twin lamella AA‘B’B. (b) Dependence of the critical external shear stress τc on the number n of emitted partials in nanocrystalline Cu (solid curves) and Al (dashed curves), for disclination strength ω = 0.5 (curves 1, 1‘), 0.4 (2, 2‘), and 0.3 (3, 3‘).

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intermediate฀ stage฀ of฀ local฀ low฀ of฀ a฀ NCM฀ on฀ a฀ scale฀ of฀ one฀ nanograin.฀ In฀ all฀ stages, τc depends strongly on ω;฀indeed,฀a฀decrease฀in฀ω results in a sharp increase in τc. When studying the dependence of the equilibrium position peq of a twinning dislocation on its ordinal number n, we found the shape of the DT front (Fig. 12.14).177 Depending on the orientation of the disclination-dipole arm, the longitudinal section of DT lamella is close to a rectangle or a blunted wedge, which฀agrees฀well฀with฀the฀results฀of฀aforementioned฀experimental฀observations.฀ The฀estimated฀DT฀thicknesses฀(5.6–7.0฀nm฀for฀Al฀and฀5–6฀nm฀for฀Cu)177 are also consistent฀with฀the฀experimental฀data.47,160,161 The฀model฀of฀DT฀lamella฀nucleation฀at฀an฀extrinsic฀GB฀dislocation฀aside฀of฀a฀ crack tip (Fig. 12.15 (a) ) has given similar results.94 It was shown that, if the external฀ shear฀ stress฀ τ and the crack length L฀ are฀ suficiently฀ large,฀ no฀ energy฀ barrier฀exists฀for฀the฀nucleation฀of฀a฀DT.฀Such฀values฀of฀τ and L fall in the ranges typical฀ of฀ the฀ NCMs฀ under฀ study.฀ For฀ example,฀ in฀ nc-Al฀ with฀ d ≈ 30 nm the critical stress τc฀ required฀ for฀ the฀ nucleation฀ of฀ the฀ irst฀ twinning฀ dislocation฀ at฀ L฀=฀20d฀=฀600฀nm฀is฀approximately฀0.25฀GPa฀(Fig.฀12.15฀(b)฀).฀For฀a฀micro-crack฀ with L฀=฀200d฀=฀6฀µm,฀the฀critical฀stress฀decreases฀to฀approximately฀15฀MPa.฀With฀

12.14 Dependence of the equilibrium position peq of a twinning dislocation on its ordinal number n in nanocrystalline (a, c) Al and (b, d) Cu for the disclination-dipole strength ω equal to 0.3, 0.4, and 0.5. The dipole arm is oriented (a, b) along or (c, d) normal to the grain boundary.

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12.15 (a) Generation of a deformation-twin lamella at an extrinsic grain-boundary edge dislocation in the vicinity of a mixed I and II mode crack of length L. (b)–(c) The critical external shear stress τc and the equilibrium position peq of a twinning dislocation via its ordinal number n in nc–Al, for various values of the normalized crack length: L/d = 3, 10, 20 and 200.

raising the DT thickness, the critical stress of the emission of new twinning dislocations฀irst฀grows,฀then฀saturates,฀and฀again฀grows,฀as฀is฀the฀case฀with฀DT฀ generation฀in฀the฀disclination฀stress฀ield.176,177 In all the stages, the critical stress τc strongly depends on the crack length L. A decrease in L results in an increase in τc. The curves peq(n), which determine the shape of the DT lamella, also depend on L (Fig. 12.15 (c) ). Depending on L, the longitudinal section of DT lamella is฀close฀to฀a฀rectangle฀or฀a฀trapezoid.฀The฀DT฀thickness฀was฀found฀to฀vary฀from฀ 3.5฀ to฀ 9.4฀ nm฀ in฀ nc-Al.฀The฀ lower฀ (higher)฀ limit฀ corresponds฀ to฀ the฀ maximum฀ (minimum) length L฀of฀the฀crack฀under฀discussion฀and฀the฀minimum฀(maximum)฀ value of the applied critical stress τc. The main conclusion is that microcracks can stimulate the nucleation of thick DT lamellae far from the crack tip. Recently Fischer et al.178 have developed a similar micromechanical model and come to the same conclusion.

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12.3.3 Rotational deformation The฀principal฀structural฀features฀of฀NCMs,฀such฀as฀nanoscale฀grains,฀high฀volume฀ fraction of grain boundaries and their triple junctions, and a high density of GB defects (see Section 12.2.2), provide many opportunities for development of rotational plastic deformation.78,132 Rotational modes of plasticity include stressand strain-driven formation of misorientation bands and new boundaries, change in GB misorientation angles and grain rotation, which are the processes of local reorientation of crystalline lattice.66,78,132,191฀These฀processes฀are฀realized฀through฀ the collective behavior of lattice and/or GB dislocations that is effectively described in terms of partial disclinations.27,29,64–67,78,102,132,191–193 Experimental฀ evidence฀ of฀ rotational฀ plasticity฀ in฀ deformed฀ NCMs฀ has฀ been demonstrated in many works.194–205 Recent direct HRTEM observations of Murayama et al.195฀have฀approved฀the฀existence฀of฀partial฀wedge฀disclinations฀in฀ severely฀ deformed฀ nc-Fe.฀ Ke฀ et al.194 observed in situ GB sliding and grain rotation฀near฀the฀tips฀of฀opening฀cracks฀in฀nc-Au฀ilms.฀Shan฀et al.196–198 and Wang et al.203฀reported฀on฀evident฀grain฀rotation฀in฀nc-Ni฀ilms฀deformed฀by฀in situ TEM tensile straining. Similar observations were made by Sergeeva et al.199–201 in nc-Ni3Al. The authors also noted that the mechanism of cooperative grain boundary฀ sliding,฀ which฀ dominates฀ in฀ superplastic฀ deformation฀ of฀ NCMs,฀ is฀ associated with sliding and rotation of entire grain groups. Yagi et al.202 studied the฀surface฀morphology฀and฀the฀crystallographic฀texture฀of฀nc-Au฀and฀nc-Cu฀after฀ creep฀deformation฀and฀concluded฀that฀grain฀rotation฀takes฀place฀along฀the฀localized฀ grain boundary sliding during creep deformation. Wang et al.203 observed that rotation of an individual grain is accompanied by rotation and further coalescence of฀neighbouring฀grains,฀which฀resulted฀in฀grain฀growth.฀Zizak฀et al.204,205 irradiated nc-Ti layers at room temperature with Au ions and studied the bombardmentinduced฀texture฀changes.฀They฀registered฀that฀‘during฀off-normal฀irradiation,฀the฀ nanocrystals฀undergo฀grain฀alignment฀and฀rotation฀up฀to฀~90°฀at฀the฀highest฀ion฀ fluence’.204 Recent computer simulations have also manifested the rotational plastic deformation฀in฀NCMs฀with฀inest฀grains฀(average฀grain฀size฀from฀5฀to฀7฀nm).157,206–210 Both the molecular dynamics206 and quasicontinuum (molecular statics)207–209 methods฀ were฀ used฀ to฀ simulate฀ the฀ evolution฀ of฀ atomic฀ structure฀ of฀ NCMs฀ in฀ nc-Au206 and nc-Al207–209 under spherical nanoindenter. Among some other mechanisms of plasticity, the authors have observed the GB sliding accompanied by grain rotation and coalescence. Shimokawa et al.157 evaluated the molecular dynamics฀ simulation฀ of฀ nc-Al฀ under฀ tensile฀ loading฀ and฀ also฀ the฀ ixed฀ relative฀ rotation of some neighbouring grains. Monk and Farkas210 used the same method for studying the deformation behavior of nc-Ni nanowires under tension. They observed grain growth accompanied by grain rotation and measured the rotation angle of a sample grain in the center of the nanowire as a function of time for different strain rates. Their ‘data show that the grain rotation speed varies

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signiicantly฀ with฀ strain฀ rate,฀ indicating฀ again฀ that฀ it฀ is฀ not฀ a฀ time฀ controlled฀ thermal process and is mostly driven by the strain itself’.210 Summarizing฀ the฀ results฀ of฀ experiments฀ and฀ computer฀ simulations,฀ one฀ can฀ conclude that stress- and strain-driven grain rotation is a typical mechanism of plastic฀deformation฀in฀NCMs฀with฀inest฀grains,฀which฀is฀accompanied฀by฀GB฀ sliding and can lead to grain coalescence. To date there are a number of theoretical models which describe the gradual change in GB misorientation angles in the course of grain rotation. The earlier models211–213 were aimed at the analyses of energetics of splitting of GB disclinations into smaller-strength GB disclinations. It was shown that the split arrangements are always more energetically preferable than the initial disclinations. However these models did not include any mechanism of disclination motion along GBs. Later it was suggested that motion of GB disclinations฀ could฀ be฀ realized฀ through฀ emission฀ of฀ lattice฀ perfect฀ (Fig.฀ 12.16)฀ and partial (Fig. 12.10 (b) ) dislocations into adjacent grains.149,150,166,214,215 This

12.16 Stress-driven displacement of the wedge disclination (black triangle) with the strength +ω from its initial position (dashed triangle) by the distance l is accompanied by the emission of two lattice dislocations with Burgers vectors b1 and b2. The +ω-disclination moves along the grain boundary plane towards another disclination (white triangle) with the strength –ω. See Gutkin et al.150 for details.

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mechanism฀seems฀to฀be฀more฀appropriate฀for฀NCMs,฀which฀may฀contain฀only฀few฀ lattice dislocations inside the grains, than the earlier proposed mechanism66,216 of GB disclination motion through absorption of lattice dislocations from adjacent grains, which is appropriate for microcrystalline metals216,217 containing a high density of lattice dislocations. The scheme that illustrated the contribution of grain฀ rotation,฀ which฀ is฀ realized฀ through฀ motion฀ of฀ GB฀ disclination฀ dipoles,฀ to฀ plastic฀deformation฀of฀a฀NCM,฀was฀presented฀by฀Ovid’ko.218 The above-mentioned theoretical models manifest interplay between the translational (glide of lattice dislocations) and rotational (motion of GB disclinations)฀ modes฀ of฀ plastic฀ deformation฀ in฀ NCMs.฀ For฀ the฀ case฀ where฀ the฀ translational mode is mainly represented by GB sliding (smallest nanograins and/or superplastic deformation), another model (Fig. 12.17) was suggested.219 Its main idea is as follows. GB sliding occurs via the glide of GB dislocations with Burgers vectors, which are parallel to the GB planes along which these dislocations glide (Fig. 12.17 (b) ). Triple junctions of GBs serve as obstacles for the GB dislocation motion. GB dislocations stopped at a triple junction are capable of being split into climbing GB dislocations (Fig. 12.17 (c) ). When this process repeatedly occurs at a triple junction, it results in the formation of two walls of GB dislocations climbing along the GBs adjacent to the triple junction. The climbing GB dislocation walls cause the rotational deformation, in which case the repeatedly occurring splitting of gliding GB dislocations at the triple junction provides the crossover from the GB sliding to the rotational deformation mode (Fig. 12.17 (c), (d) ). This process can be spread over the grain, which has to rotate on an angle as a whole (Fig. 12.17 (e) ). Thus, the stopped GB sliding can stimulate plastic rotation of the neighbouring grain. Obviously this mechanism may only be effective under the condition of intensive GB diffusion of vacancies, which must be capable of providing the necessary velocity of GB dislocation climb. Analysing this model from a thermodynamic point of view, the authors219 concluded that the transition from GB sliding to rotational deformation becomes฀ energetically฀ favourable฀ when฀ the฀ external฀ shear฀ stress฀ achieves฀ its฀ critical฀value,฀and฀this฀depends฀on฀the฀elastic฀properties฀of฀the฀NCM,฀the฀structure฀ of฀ its฀ GBs,฀ its฀ grain฀ size฀ and฀ its฀ shape.฀ Smaller฀ grains฀ require฀ smaller฀ critical฀ stress to rotate. Recent฀ progress฀ in฀ theoretical฀ modeling฀ of฀ rotational฀ deformation฀ in฀ NCMs฀ is mainly related with elaboration of dislocation–disclination models of grain reinement฀ of฀ polycrystalline฀ metals฀ under฀ severe฀ plastic฀ deformation,220–222 interplay between GB sliding and grain rotation223–225 leading to the inverse Hall–Petch฀ relationship฀ in฀ the฀ range฀ of฀ smallest฀ grain฀ sizes,223,224 and GB migration95,96,226–230 and the formation of immobile disclinations whose strengths gradually increase during deformation as a result of grain boundary sliding and diffusion,231 as special mechanisms of rotational plasticity. Some of these models220–224฀have฀been฀reviewed฀extensively฀by฀Romanov฀and฀Kolesnikova.29 The models226–230 are considered in more detail in Section 12.3.5.

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12.17 Combined action of grain boundary sliding and rotational deformation mode. (a) Nanocrystalline specimen in a non-deformed state. (b) Grain boundary sliding occurs via motion of gliding grain boundary dislocations under shear stress action. (c) Gliding dislocations split at triple junction O of grain boundaries into climbing dislocations. (d) The splitting of gliding grain boundary dislocations repeatedly occurs causing the formation of walls of grain boundary dislocations whose climb is accompanied by crystal lattice rotation in a grain. (e) Climbing dislocations reach triple junction O´ where they converge into gliding dislocations causing further grain boundary sliding.

Alternative฀approaches฀to฀theoretical฀modeling฀of฀grain฀rotation฀in฀NCMs฀have฀ been฀represented฀by฀Kim฀et al.232 and Yang and Yang.233 These authors consider the฀kinetics฀and฀size฀effects฀of฀GB฀sliding฀and฀grain฀rotation฀driven฀by฀both฀GB฀ energy฀and฀external฀stress.฀Ignoring฀the฀underlying฀structural฀mechanisms฀of฀GB฀

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sliding and grain rotation, they operate with continuum mechanics in terms of viscous GB gliding and GB diffusion as accommodation mechanisms. Due to its relative simplicity and high effectiveness, this approach looks rather attractive and฀fruitful฀although฀it฀does฀not฀allow฀one฀to฀visualize฀the฀structural฀mechanisms฀ of grain rotation.

12.3.4 Mechanisms of strengthening and softening under superplasticity The฀superplasticity฀of฀NCMs฀has฀attracted฀much฀attention฀in฀the฀past฀decade฀(see฀ original papers234–241 and reviews99,101,108,118,121,122,242). It has been found that the superplasticity in these materials is reached at lower temperatures and higher strain rates, offering strong possibilities for industrial application of this effect. Moreover, it฀has฀been฀discovered฀that฀the฀strength฀of฀a฀material฀increases฀signiicantly฀in฀the฀ course of superplastic deformation. The yield stress and the hardening effect become฀especially฀great฀during฀deformation฀of฀NCMs,฀with฀an฀average฀grain฀size฀ of about 50 nm. In this case, the stress–strain curves are bell-shaped, and demonstrate฀the฀presence฀of฀well-deined฀long฀hardening฀and฀softening฀stages. Among฀the฀main฀mechanisms฀of฀plasticity฀operating฀in฀NCMs฀(see฀Fig.฀12.3),฀ the GB sliding (in combination with accommodation mechanisms, such as GB migration and lattice sliding near GBs) is believed to be the dominant mechanism of฀ superplastic฀ deformation฀ in฀ NCMs.101,241 Therefore, the unusual effects of NCM฀hardening฀in฀the฀initial฀stage฀of฀superplastic฀deformation฀and฀subsequent฀ softening,฀as฀well฀as฀very฀high฀values฀of฀the฀yield฀stress,฀can฀be฀due฀to฀the฀speciic฀ features of GB sliding. These features were described in theoretical models.243–245 First, we considered a situation near an isolated triple junction of GBs along which฀ GB฀ dislocations฀ glide฀ under฀ an฀ external฀ shear฀ stress฀ τ (Fig. 12.18). Following the models,243,244 numerous acts of transfer of GB dislocations across the triple junction results in an increase in the Burgers vector of the difference sessile dislocation in the triple junction, which increases the critical stress τc necessary for dislocation transfer across the triple junction and hence leads to local strengthening. At the same time, the accompanying local migration of GBs leads to an increase in the angle a between the GB planes (adjacent to the triple junction), which decreases τc and hence leads to local softening. The competition between the strengthening and the softening effects is capable of฀crucially฀inluencing฀the฀deformation฀behavior฀of฀NCMs฀exhibiting฀high฀strainrate฀superplasticity.฀In฀particular,฀superplastic฀deformation฀regime฀is฀realized฀if฀ the฀strengthening฀dominates฀over฀the฀softening฀during฀the฀irst฀extensive฀stage฀of฀ deformation฀ (characterized฀ by฀ a฀ plastic฀ strain฀ of฀ hundreds฀ of฀ percent).฀ This฀ strengthening prevents the necking and is responsible for an increase of the flow stress that drives the movement of GB dislocations. With rising plastic strain, local GB migration arranges GB planes to be tentatively parallel to each other in some local regions of a loaded sample. As a result, local softening becomes

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12.18 Numerous acts of transfer of GB dislocations across a triple junction and accompanying local migration of GBs leads to an increase in the angle α. (a) Initial (0th) state of defect configuration; two gliding GB dislocations move towards the triple junction. (b) Sessile dislocation with the Burgers vector b is formed; triple junction is displaced by the vector b2 from its initial position. (c) Generation of two new gliding GB dislocations that move towards the triple junction. (d) New sessile dislocation is formed; the triple junction is transferred by the vector 2b2 from its initial position. (e) The nth generation of two new gliding GB dislocations that move towards the triple junction. (f) The nth sessile dislocation is formed; the triple junction is transferred by the vector nb2 from its initial position.

substantial, which causes gradual macroscopic softening inherent in the second stage฀of฀superplastic฀deformation฀of฀NCMs. Secondly,฀ we฀ expanded฀ these฀ models฀ by฀ taking฀ into฀ account฀ the฀ effect฀ of฀ neighbouring triple junctions and the possible accommodation of the GB defect structure via emission of lattice dislocations (Fig. 12.19).245 In the model used, perfect lattice dislocations are emitted from triple junctions when Burgers vectors of฀sessile฀triple-junction฀dislocations฀reach฀critical฀values.฀After฀the฀irst฀emission฀ of a perfect lattice dislocation, the strength of the sessile dislocation again increases gradually. When its Burgers vector reaches a new critical value, a lattice dislocation฀is฀emitted฀again.฀A฀detailed฀examination฀of฀these฀processes฀allowed฀us฀ to numerically calculate the strain–stress dependence shown by the solid curve in Fig. 12.20,245฀for฀Al฀with฀the฀grain฀size฀of฀100฀nm.฀The฀dashed฀line฀represents฀ experimental฀ data.239฀ It฀ can฀ be฀ seen฀ that฀ the฀ theoretical฀ and฀ experimental฀ values are close to each other. The theoretical curve is serrated due to the contribution from lattice sliding to the superplastic strain. Each elementary event of lattice sliding causes a drop in the critical stress, thereby leading to local softening.

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12.19 Emission of lattice dislocations with the Burgers vector be from a sessile dislocation with the Burgers vector Bm–1 in a triple junction on the mth transfer of GB dislocations across the triple junction.

12.20 External stress σ as a function of the total plastic strain ε.

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Further theoretical investigation of defect structure evolution near triple junctions of GBs during GB sliding has been evaluated recently by Ovid’ko and Sheinerman.246 The authors have taken into account the formation of disclination dipoles near triple junctions and the partial relief of disclination stresses due to GB diffusion. As the irst฀process฀increases฀the฀strain฀hardening,฀while฀the฀second฀one฀decreases฀it,฀these฀ factors could also be used in further theoretical models of superplasticity.

12.3.5 Athermal stress-induced grain growth In recent years, particular attention has been focused on the grain growth during plastic฀ deformation฀ of฀ ultraine-grained247–253 and nanocrystalline72,203,249–269 metals and alloys at room72,203,249–269 and cryogenic253–255 temperatures. Experimental฀ studies฀ on฀ ultraine-grained฀ pure฀ Al247,249–252฀ and฀ Cu248,253 and Al-Mg alloys250,251 and on nanocrystalline pure Al,249–252,259–261,269฀Cu,253–255,267 Ni,203,256–258,267,268 Pd72฀and฀Co-P263,264 and Ni-Fe264–266 alloys have shown that the grain growth is possible during nano-249–252,257 and micro-indentation253–255 of thin฀ilms฀and฀torsion฀of฀them฀under฀high฀pressure,72,256 during compression of powder,247 micropillars258 and macroscopic samples,248,265 during cold-rolling,268 and,฀ inally,฀ during฀ uniaxial฀ tension฀ of฀ thin฀ ilms203,259–262,269 and bulk planar samples.263,264,266 For an understanding of the physical nature of this phenomenon, the฀following฀experimental฀facts฀are฀of฀importance: (i)

At cryogenic temperatures, grains grow more rapidly than at room temperature.254 (ii) The grain growth is the most intensive in the regions of a sample where the elastic stress and its gradient are the largest (e.g. under a nanoindenter249–252,257 or in the immediate vicinity of a microindenter,253–255 near the tip of a slowly developing crack,259,262 in the surface layer of a sample in the vicinity of a neck forming under tension,266 or near specially prepared holes under tension269). (iii) The grain growth is completely suppressed250 or reduced261,263–266 in the presence of impurities. (iv)฀ During฀grain฀growth,฀not฀only฀the฀grain฀size฀but฀also฀the฀character฀of฀the฀grain฀ size฀ distribution฀ are฀ changed;฀ the฀ distribution฀ is฀ broadened฀ and฀ sometimes฀ becomes bimodal,254,259,264 with larger submicron grains occupying up to 15%฀of฀the฀volume254฀and฀ine฀nanograins฀surrounding฀them. (v) The grain growth occurs at relatively low nanoindentation rates257 and during microindentation in the creep mode,253–255 at relatively high compression rates (~10–3–10–1 s–1 258 and 10–3 s–1 265), and at widely ranged tension rates (~10–5 s–1,259–261 10–3 s–1,260,263 10–5–10–2 s–1,264 10–2 s–1 266). (vi) The grain growth somewhat decreases the ultimate strength, but it signiicantly฀increases฀the฀ultimate฀tensile฀strain฀(up฀to฀25%฀in฀pure฀nc-Al259 and฀up฀to฀7.2%฀in฀the฀nc-Ni-Fe฀alloy266), which is accompanied by noticeable hardening and the formation of dislocation structures in coarse grains. In micropillars฀of฀pure฀nc-Ni฀under฀uniaxial฀compression,฀ultrahigh฀plasticity฀

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(up฀to฀200%฀of฀the฀true฀strain)฀was฀observed฀at฀a฀low฀stress฀of฀2.0–2.4฀GPa,฀ which฀ was฀ accompanied฀ by฀ softening฀ (due฀ to฀ equiaxial฀ grain฀ growth)฀ followed by hardening caused by the elongation of grown grains and the accumulation of dislocations and twins in them.258 (vii) With increasing duration of holding of a sample under indenter, the lowangle GBs were observed to increase in number, especially at cryogenic temperatures.255฀ In฀ submicron-sized฀ grains฀ grown฀ during฀ severe฀ plastic฀ deformation,฀ subgrains฀ were฀ observed,฀ which,฀ in฀ turn,฀ were฀ illed฀ with฀ dislocation cells.256 The authors72,203,249–269 believe that the above results unambiguously indicate the athermic character of grain growth, which occurs under elastic stresses forming at earlier stages of plastic flow. The process of grain growth is inhomogeneous over a฀ cross-section฀ of฀ the฀ sample;฀ indeed,฀ the฀ grains฀ that฀ are฀ located฀ in฀ places฀ of฀ concentrated stresses and, in addition, have a favourable orientation, increase in size.฀ When฀ the฀ growing฀ grains฀ become฀ a฀ few฀ hundred฀ nanometers฀ in฀ size,฀ the฀ plasticity mechanisms typical of low-temperature deformation of coarse-grained metals฀begin฀to฀operate฀in฀them.฀For฀example,฀in฀copper,฀dislocation฀glide฀and฀the฀ formation of dislocation pile-ups were observed at room temperature, and deformation฀twinning฀at฀a฀cryogenic฀temperature฀(77฀K).255 Thus, the grain growth during฀plastic฀deformation฀increases฀the฀plasticity฀of฀NCMs,฀while฀the฀low฀stress฀ remains high at low temperatures and relatively high loading rates, which is very important for practical applications.252 Recent computer simulations157,207,208,210,270–274 have shown that lowtemperature฀ stress-induced฀ grain฀ growth฀ in฀ NCMs฀ is฀ athermal.฀ Its฀ basic฀ mechanisms are found to be stress-induced migration of GBs and their triple junctions, GB sliding, grain rotation and coalescence (see also Section 12.3.3). In particular, all of these mechanisms were observed to operate simultaneously in model samples of nc-Al208 and Ni210฀ with฀ a฀ mean฀ grain฀ size฀ of฀ 7฀ and฀ 5฀ nm,฀ respectively, when nanograins rotated through GB sliding under nanoindentation208 or฀uniaxial฀tension.210 The atomic mechanisms of motion of high-angle GBs have been considered in a number of recent works.275–281 Also, stress-induced GB migration and athermal grain growth have been described theoretically with the aid of dislocation-disclination models.95,96,152–154,226–230,282฀For฀example,฀Bobylev฀et al.152–154 have studied the dynamics and decay of a low-angle tilt boundary under an applied shear stress τ (see Section 12.3.1). It was shown that, as the stress τ increases, the tilt boundary is฀irst฀bent฀and฀then฀shifts฀to฀a฀new฀position฀corresponding฀to฀the฀applied฀stress.฀ At a certain critical stress proportional to the misorientation angle θ of the boundary, it becomes unstable and glides irreversibly. The decay of one such boundary฀signiicantly฀decreases฀the฀critical฀stress฀for฀decay฀of฀neighbouring฀lowangle boundaries. As a result, the chain decay of the neighbouring boundaries occurs and the grains separated by them coalesce. The static model of the escape of฀dislocations฀from฀an฀ininite฀straight฀dislocation฀wall฀developed฀by฀Li282 also

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permits one to estimate the critical stress for boundary decay, which is proportional to θ. The stress at which an intrinsic dislocation of a low-angle boundary (with θ฀ =฀ 0.1฀ (≈฀ 5.7°))฀ breaks฀ away฀ from฀ it฀ (estimated฀ from฀ this฀ model฀ to฀ be฀ about฀ 2 GPa for Fe)282 is not far greater than that obtained from dynamic calculations (1.53 GPa).152–154 The model of Li282 also gives lower values of the critical stress for฀ the฀ decay฀ of฀ a฀ boundary฀ in฀ the฀ case฀ where฀ a฀ few฀ intrinsic฀ or฀ extrinsic฀ dislocations break away simultaneously from it. However, the description of the boundary decay assuming that only single dislocations move while the positions of the other dislocations remain unchanged seems incorrect. Gutkin and Ovid’ko226 proposed a continuum disclination model for describing the฀ migration฀ of฀ an฀ arbitrary฀ tilt฀ GB.฀A฀ migrating฀ GB฀ was฀ approximated฀ by฀ a฀ biaxial฀dipole฀of฀partial฀wedge฀disclinations฀capable฀of฀moving฀under฀an฀applied฀ shear stress τ฀in฀the฀elastic฀ield฀of฀a฀similar฀disclination฀dipole฀of฀opposite฀sign฀ that forms when the GB breaks away from the neighbouring GBs (i.e. at the moment when triple GB junctions transform into double junctions) (Fig. 12.21). It was shown that there are two modes of GB migration. When the applied stress฀reaches฀the฀irst฀critical฀value: [12.7] where D฀=฀G/[2π (1–ν)], G is the shear modulus, ν is the Poisson ratio, ω is the disclination strength equal to the misorientation angle of the migrating GB, 2a is the length of the GB and b is the interatomic distance, the GB begins to migrate in the stable mode in which its equilibrium position is determined by a stress level τ ≥ τc1. When the stress τ reaches the second critical value: ,

[12.8]

the฀ GB฀ migration฀ becomes฀ unstable;฀ the฀ equilibrium฀ position฀ of฀ the฀ GB฀ disappears, and the GB migration no longer depends on τ. For pure nc-Al with grain฀size฀d ranging from 30 to 100 nm, the stress τc1 ranges from 7.6 to 23.5 MPa for ω฀=฀5°฀and฀from฀46.5฀to฀144฀MPa฀for฀ω฀=฀30°.฀The฀stress฀τc2 proves to be far greater, namely, 0.4 GPa for ω฀=฀5°฀and฀2.5฀GPa฀for฀ω฀=฀30°,฀irrespective฀of฀the฀ grain฀size.฀We฀note฀that,฀in฀thin฀nc-Al฀ilms฀under฀tension,฀grains฀begin฀to฀grow฀ intensively over the range of true tensile stresses from 130 MPa for d ≈ 90 nm to 190 MPa for d ≈ 40 nm,259,260฀which฀correspond฀to฀the฀maximum฀values฀of฀τ from 65 to 95 MPa lying in the range τ1c < τ < τc2 for GBs with a misorientation angle ω฀=฀5°฀and฀in฀a฀part฀of฀this฀range฀for฀GBs฀with฀ω฀=฀30°.฀Computer฀simulations฀of฀ nanoindentation฀of฀nc-Al฀ilms฀with฀a฀mean฀grain฀size฀of฀7฀nm฀showed208 that the migration฀ of฀ a฀ low-angle฀ tilt฀ boundary฀ with฀ a฀ misorientation฀ angle฀ of฀ 13.5°฀ becomes฀ unstable฀ under฀ local฀ shear฀ stresses฀ exceeding฀ the฀ estimated฀ value฀ 0.7฀ GPa obtained from equation [12.8]. Recently the model226฀has฀been฀extended฀to฀the฀case฀of฀collective฀migration฀of฀ the two opposite boundaries of a grain.227,228 We have considered the stress-induced

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12.21 Stress-induced migration of a low-angle (a,b) or high-angle (c,d) grain boundary (GB3) as a mechanism of rotational deformation realized through the glide of a wall of lattice dislocations (b) or motion of a dipole of wedge disclinations (d), respectively.

grain growth in a model nc-sample under a tensile stress σ (Fig. 12.22) and analysed in detail the situation with one pair of interacting GBs (Fig. 12.23). We have shown that two critical stresses, τc and τm, control the behavior of migrating GBs. When the฀external฀shear฀stress฀τ reaches τc, opposite GBs start to migrate to each other, their migration is stable, and their equilibrium positions are determined by τ ≥ τc. When τ ≥ τm >> τc, the GBs meet. Then the following regimes of cooperative migration are possible at τ > τm, depending on τ level and GB characteristics: 1) GBs annihilate in the very partial case where their misorientations are equal by magnitude and opposite in sign, 2) one GB captures another GB and makes it migrate together in one direction under a moderate τ, 3) GBs coalesce and stand at a local equilibrium position, 4) GBs can overcome their mutual attraction and migrate in opposite directions under a very high τ. In all cases, GB migration leads to฀unstable฀growth฀of฀a฀grain฀by฀annexing฀parts฀of฀its฀neighbours.

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12.22 Grain growth through collective GB migration in a model NCM under uniaxial tension: (a) the initial state of tilt boundaries with misorientation angles ω and Ω at a low tensile stress σ1; (b) at a stress σ2 > σ1, the boundaries begin to migrate into grains I–IV and partial wedge disclinations with strengths ±ω and ±Ω appear in the remaining double junctions and form dipole and quadrupole structures; (c) at a higher stress σ3 > σ2, some boundaries annihilate partially (grain I) or completely (grain II), while others pass through each other and stop only near the next boundaries (grains III, IV); (d) smoothing of the boundaries of the enlarged grains I–IV at a stress σ4 ≥ σ3.

The model226฀has฀also฀been฀extended฀to฀the฀cases฀of฀GB฀migration฀and฀grain฀ nucleation near cracks.95,96,229 It was shown that these processes result in moderate enhancement of fracture toughness96 and in an increase in the equilibrium lengths of the cracks, thus diminishing the probability of their development.229 On the other hand, the stress concentration provided by cracks leads to a decrease in the critical stresses τc1 and τc2.95 Bobylev and Ovid’ko230฀ have฀ considered฀ GB฀ migration฀ in฀ hexagonal฀ grains฀ and found that, depending on the angle between the mobile and immobile GBs, © Woodhead Publishing Limited, 2011

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12.23 Collective migration of (a, b) low-angle and (c, d) high-angle tilt boundaries separating grains G1–G3 under applied shear stress τ: (a, d) geometrical models and (b, c) dislocation and disclination models, respectively.

GBs migrate more easily (at a lower stress level) compared to the previously examined฀ situation226 with rectangular grains. The difference in the stress may reach฀a฀value฀of฀~20฀to฀30%.฀The฀authors230 have concluded that ‘geometry of triple junctions crucially influences their mobility and thereby controls the stress level needed to drive migration of GBs and their triple junctions in deformed nanocrystalline materials’.

12.4

Conclusions and future trends

We have considered some analytical theoretical models that describe elastic strains฀and฀plastic฀deformation฀phenomena฀in฀NCMs.฀Most฀of฀these฀models฀are฀ © Woodhead Publishing Limited, 2011

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based฀on฀the฀theory฀of฀defects,฀a฀uniied฀concept฀that฀allows฀one฀to฀describe฀the฀ structure,฀ the฀ elastic฀ ields฀ and฀ the฀ mechanisms฀ of฀ plastic฀ deformation฀ from฀ a฀ unique physical viewpoint. Based on the results of such theoretical modeling, one can formulate the following general conclusions: (i)฀ Due฀ to฀ their฀ structural฀ and฀ scale฀ features,฀ NCMs฀ always฀ contain฀ many฀ elastic-strain sources and stress concentrators that are capable of initiating various฀mechanisms฀of฀plastic฀deformation฀under฀external฀loading.฀Most฀of฀ the฀stress฀sources฀and฀concentrators฀are฀defects฀localized฀at/near฀GBs.฀At฀the฀ same time, most of these defects can act as carriers of plastic deformation. As a result, GB-mediated mechanisms of plasticity dominate over other possible฀mechanisms฀in฀ine-grained฀NCMs. (ii) The GB mediated mechanisms of plasticity are emissions of partial and perfect฀lattice฀dislocations฀and฀twins฀from฀GBs;฀mass฀transfer฀along฀GBs฀ and฀their฀triple฀junctions;฀GB฀sliding,฀decay฀and฀migration;฀grain฀rotation,฀ growth฀and฀reinement.฀The฀present฀review฀demonstrates฀that฀most฀of฀these฀ deformation฀ mechanisms฀ can฀ be฀ analysed฀ theoretically฀ within฀ a฀ uniied฀ energy approach. In doing so, one can calculate and analyse some critical values of the applied stress, which control the barrier-less activation of the deformation mechanisms and their transition from the stable regime of development฀to฀its฀unstable฀regime.฀Using฀these฀results,฀one฀can฀sometimes฀ conclude which deformation mode is preferable in given conditions. When possible,฀the฀comparison฀of฀theoretical฀estimates฀with฀available฀experimental฀ data and results of computer simulations shows rather good accordance. (iii)฀ Due฀ to฀ the฀ distribution฀ in฀ grain฀ size,฀ different฀ mechanisms฀ of฀ plastic฀ deformation฀ can฀ dominate฀ in฀ different฀ grains;฀ these฀ mechanisms฀ can฀ also฀ compete within the same grains. Interplay between different mechanisms of plasticity฀commonly฀occurs฀in฀NCMs.฀Theoretical฀modeling฀of฀this฀interplay฀ seems to be a good and important challenge at present. This chapter has concentrated mainly on quasistatic theoretical models. Meanwhile,฀ there฀ are฀ a฀ number฀ of฀ models฀ developed฀ for฀ ultraine-grained฀ and฀ nanocrystalline materials within the evolutional dislocation kinetics78,120,283,284 and discrete dislocation dynamics.285,286 It seems that incorporating GB dislocation and disclination terms to these models may be a future trend in this ield.฀One฀more฀future฀trend฀is฀the฀wider฀use฀of฀elastic฀ields฀of฀defects฀calculated฀ in the framework of the strain-gradient elasticity,30,31,84 which allows one to avoid฀the฀classical฀singularities฀in฀elastic฀ields฀of฀defects฀and฀their฀interactions.฀ Some฀examples฀of฀applying฀this฀theory฀to฀dislocation฀behavior฀in฀freestanding287 and in/near embedded nanowires288,289 have recently been demonstrated. Future theoretical฀ models฀ are฀ also฀ expected฀ to฀ describe฀ in฀ more฀ details฀ the฀ interplay฀ between dislocation–disclination and GB diffusion modes of plastic deformation, and between the mechanisms of plasticity and fracture as well.

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Sources of further information and advice

Further information on the topics under discussion in this chapter can be taken from monographs,78,131–133 reviews1,2,10,17–22,29,59,97–130 and other references listed in Section 12.7. The most useful sources of current information are such materials science and physical journals as Acta Materialia, Applied Physics Letters, Journal of Materials Research, Journal of Materials Science, Materials Science and Engineering A, Nature Materials, Philosophical Magazine, Philosophical Magazine Letters, Physical Review B, Physical Review Letters, Physics of Solid State, Progress in Materials Science, Reviews on Advanced Materials Science, Science, Scripta Materialia, etc.

12.6

Acknowledgements

The work was supported by the Russian Foundation of Basic Research (Grant No. 08–02–00304-a).฀I฀am฀deeply฀thankful฀to฀my฀friends฀and฀colleagues฀E.C.฀Aifantis,฀ S.V.฀Bobylev,฀A.A.฀Fedorov,฀A.L.฀Kolesnikova,฀K.N.฀Mikaelyan,฀N.F.฀Morozov,฀ I.A.฀Ovid’ko,฀C.S.฀Pande,฀A.E.฀Romanov,฀A.G.฀Sheinerman฀and฀N.V.฀Skiba฀for฀ helpful discussions and collaboration.

12.7

References

฀ 1฀ ฀ ฀ 2฀ ฀ ฀ 3฀ ฀ ฀ 4฀ ฀ ฀ 5฀ ฀ ฀ 6฀ ฀ ฀ 7฀ ฀ ฀ 8฀ ฀ ฀ 9฀

Gleiter฀H.฀Prog฀Mater฀Sci฀1989;33:฀223. Gryaznov฀V.G.,฀Trusov฀L.I.฀Prog฀Mater฀Sci฀1993;37:฀289. Wunderlich฀W.,฀Ishida฀Y.,฀Maurer฀R.฀Scr฀Metall฀Mater฀1990;24:฀403. Herr฀U.,฀Jing฀J.,฀Birringer฀R.,฀Conser฀U.,฀Gleiter฀H.฀Appl฀Phys฀Lett฀1987;50:฀472. Schaefer฀H-E.,฀Wurshum฀R.฀Phys฀Lett฀A฀1987;119:฀370. Wurshum฀R.,฀Scheytt฀M.,฀Schaefer฀H-E.฀Phys฀Stat฀Sol฀A฀1987;102:฀119. Zhu฀X.,฀Birringer฀R.,฀Herr฀U.,฀Gleiter฀H.฀Phys฀Rev฀B฀1987;35:฀9085. Haubold฀T.,฀Birringer฀R.,฀Lengeler฀B.,฀Gleiter฀H.฀Phys฀Lett฀A฀1989;135:฀461. Jorra฀E.,฀Franz฀H.,฀Peisl฀J.,฀Wallner฀G.,฀Petry฀W.,฀Haubold฀T.,฀Birringer฀R.,฀Gleiter฀H.฀ Phil฀Mag฀B฀1989;60:฀159. 10฀ Valiev฀R.Z.,฀Islamgaliev฀R.K.,฀Alexandrov฀I.V.฀Prog฀Mater฀Sci฀2000;45:฀103. 11฀ Cammarata฀R.C.฀Prog฀Surf฀Sci฀1994;46:฀1. 12฀ Nicholson฀M.M.฀Proc฀Roy฀Phys฀Soc฀Lond฀A฀1955;228:฀490. 13฀ Ono฀S.,฀Kondo฀S.฀Molecular฀theory฀of฀surface฀tension฀in฀liquids.฀Berlin:฀Springer;฀1960. 14฀ Jia฀M.,฀Lai฀Y.,฀Tian฀Z.,฀Liu฀Y.฀Modelling฀Simul฀Mater฀Sci฀Eng฀2009;17:฀015006. 15฀ Marks฀L.D.฀Rep฀Prog฀Phys฀1994;57:฀603. 16฀ Gillet฀M.฀Surf฀Sci฀1977;67:฀139. 17฀ Martin฀T.P.฀Phys฀Rep฀1996;273:฀199. 18฀ Hofmeister฀H.฀Cryst฀Res฀Technol฀1998;33:฀3. 19฀ Gryaznov฀V.G.,฀Heydenreich฀J.,฀Kaprelov฀A.M.,฀Nepijko฀S.A.,฀Romanov฀A.E.,฀Urban฀ J.฀Cryst฀Res฀Technol฀1999;34:฀1091. 20฀ Yacamán฀ M.J.,฀Ascencio฀ J.A.,฀ Liu฀ H.B.,฀ Gardea-Torresdey฀ J.฀ J฀Vac฀ Sci฀Technol฀ B฀ 2001;19:฀1091. 21 Hofmeister H. In: Nalwa H.S., editor. Encyclopedia of nanoscience and nanotechnology, vol.฀3.฀Stevenson฀Ranch:฀American฀Scientiic฀Publishers;฀2004;฀p.431.

© Woodhead Publishing Limited, 2011

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X

368 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X

22฀ 23฀ 24฀ 25฀ 26฀ 27฀ 28฀ 29฀ 30฀ 31฀ 32฀ 33 34฀ 35฀ 36฀ 37฀ 38฀

39฀ 40฀ 41฀ 42฀

43฀ 44฀ 45฀ 46฀ 47 48฀ 49฀ 50฀ 51฀ 52฀ 53฀ 54฀ 55฀ 56฀ 57฀ 58฀ 59฀

Nanostructured metals and alloys Elechiguerra฀J.L.,฀Reyes-Gasga฀J.,฀Yacaman฀M.J.฀J฀Mater฀Chem฀2006;16:฀3906. Vikarchuk฀A.A.,฀Volenko฀A.P.฀Phys฀Solid฀State฀2005;47:฀352. Yasnikov฀I.S.,฀Vikarchuk฀A.A.฀Phys฀Solid฀State฀2006;48:฀1433. Yasnikov฀I.S.฀Phys฀Solid฀State฀2007;49:฀1224. Yasnikov฀I.S.,฀Vikarchuk฀A.A.,฀Denisova฀D.A.,฀Gryzunova฀N.N.,฀Tsybuskina฀I.I.฀Tech฀ Phys฀2007;52:฀1328. de฀Wit฀R.฀J฀Phys฀C:฀Sol฀State฀Phys฀1972;5:฀529. Galligan฀J.M.฀Scr฀Metall฀1972;6:฀161. Romanov฀A.E.,฀Kolesnikova฀A.L.฀Prog฀Mater฀Sci฀2009;54:฀740. Gutkin฀M.Yu.,฀Aifantis฀E.C.฀Phys฀Solid฀State฀1999;41:฀1980. Gutkin฀M.Yu.฀Rev฀Adv฀Mater฀Sci฀2000;1:฀27. Povstenko฀Yu.Z.฀Int฀J฀Engng฀Sci฀1995;33:฀575. Zubov L.M. Nonlinear theory of dislocations and disclinations in elastic bodies. Berlin:฀Springer;฀1997. Lazar฀M.฀Phys฀Lett฀A฀2003;311:฀416. Howie฀A.,฀Marks฀L.D.฀Phil฀Mag฀A฀1984;49:฀95. Dorogin฀L.M.,฀Kolesnikova฀A.L.,฀Romanov฀A.E.฀Tech฀Phys฀Lett฀2008;34:฀779. Marks฀L.D.฀Phil฀Mag฀A฀1984;49:฀81. Rodríguez-López฀ J.L.,฀ Montejano-Carrizales฀ J.M.,฀ Pal฀ U.,฀ Sánchez-Ramírez฀ J.F.,฀ Troiani฀H.E.,฀García฀D.,฀Miki-Yoshida฀M.,฀José-Yacamán฀M.฀Phys฀Rev฀Lett฀2004;92:฀ 196102. Gryaznov฀ V.G.,฀ Kaprelov฀ A.M.,฀ Romanov฀ A.E.,฀ Polonskii฀ I.A.฀ Phys฀ Stat฀ Sol฀ B฀ 1991;167:฀441. Kolesnikova฀A.L.,฀Romanov฀A.E.฀Tech฀Phys฀Lett฀2007;33:฀886. Kolesnikova฀A.L.,฀Romanov฀A.E.฀Phys฀Stat฀Sol฀RRL฀2007;1:฀271. Panpurin฀ S.N.,฀ Gutkin฀ M.Yu.฀ In:฀ Proceedings฀ of฀ All-Russian฀ Inter-University฀ Scientiic-Technical฀Conference฀of฀Students฀and฀PhD฀Students,฀30฀Nov–4฀Dec฀2009,฀ St.฀Petersburg:฀Izdatel’stvo฀Politekhnicheskogo฀Universiteta,฀2009;฀p.142,฀in฀Russian. Li฀D.X.,฀Ping฀D.H.,฀Ye฀H.Q.,฀Qin฀X.Y.,฀Wu฀X.J.฀Mater฀Lett฀1993;18:฀29. Huang฀J.Y.,฀Wu฀Y.K.,฀Ye฀H.Q.฀Acta฀Mater฀1996:44:฀1211. Huang฀J.Y.,฀Yu฀Y.D.,฀Wu฀Y.K.,฀Li฀D.X.,฀Ye฀H.Q.฀J฀Mater฀Res฀1997;12:฀936. Liao฀X.Z.,฀Huang฀J.Y.,฀Zhu฀Y.T.,฀Zhou฀F.,฀Lavernia฀E.J.฀Phil฀Mag฀2003;83:฀3065. Liao X.Z., Zhao Y.H., Srinivasan S.G., Zhu Y.T., Valiev R.Z., Gunderov D.V. Appl Phys฀Lett฀2004;84:฀592. Zhu฀Y.T.,฀Liao฀X.Z.,฀Valiev฀R.Z.฀Appl฀Phys฀Lett฀2005;86:103112. Cao฀A.J.,฀Wei฀Y.G.฀Appl฀Phys฀Lett฀2006;89:฀041919. Bringa฀ E.M.,฀ Farkas฀ D.,฀ Caro฀ A.,฀ Wang฀ Y.M.,฀ McNaney฀ J.,฀ Smith฀ R.฀ Scr฀ Mater฀ 2008;59:฀1267. Shao฀Y.F.,฀Wang฀S.Q.฀Scr฀Mater฀2010;62:฀419. Saada฀G.฀Acta฀Metall฀1979;27:฀921. Horita฀Z.,฀Smith฀D.J.,฀Furukawa฀M.,฀Nemoto฀M.,฀Valiev฀R.Z.,฀Langdon฀T.G.฀J฀Mater฀ Res฀1996;11:฀1880. Horita฀Z.,฀Smith฀D.J.,฀Nemoto฀M.,฀Valiev฀R.Z.,฀Langdon฀T.G.฀J฀Mater฀Res฀1998;13:฀446. Ranganathan฀S.,฀Divakar฀R.,฀Raghunathan฀V.S.฀Scr฀Mater฀2001;44:฀1169. Huang฀J.Y.,฀Zhu฀Y.T.,฀Jiang฀H.,฀Lowe฀T.C.฀Acta฀Mater฀2001;49:฀1497. Huang฀J.Y.,฀Liao฀X.Z.,฀Zhu฀Y.T.,฀Zhou฀F.,฀Lavernia฀E.J.฀Phil฀Mag฀2003;83:฀1407. Valiev฀R.Z.,฀Sergueeva฀A.V.,฀Mukherjee฀A.K.฀Scr฀Mater฀2003;49:฀669. Koneva฀N.A.฀In:฀Altan฀B.S.,฀editor.฀Severe฀plastic฀deformation:฀toward฀bulk฀production฀ of฀nanostructured฀materials.฀New฀York:฀Nova฀Science฀Publishers;฀2006;฀p.249.

© Woodhead Publishing Limited, 2011

Elastic and plastic deformation in nanocrystalline metals

369

60฀ Wu฀X.L.,฀Zhu฀Y.T.฀Appl฀Phys฀Lett฀2006;89:฀031922. 61฀ Koneva฀N.A.,฀Kozlov฀E.V.,฀Popova฀N.A.,฀Zhdanov฀A.N.,฀Fedorischeva฀M.V.฀Mater฀ Sci฀Forum฀2008;584–586:฀269. 62฀ Liu฀ M.P.,฀ Roven฀ H.J.,฀ Ungar฀T.,฀ Balogh฀ L.,฀ Murashkin฀ M.,฀Valiev฀ R.Z.฀ Mater฀ Sci฀ Forum฀2008;584–586:฀528. 63฀ Sutton฀A.P.,฀Ballufi฀R.W.฀Interfaces฀in฀crystalline฀materials.฀Oxford:฀Oxford฀Science฀ Publications;฀1996. 64฀ Likhachev฀V.A.,฀Rybin฀V.V.฀Sov฀Phys฀–฀Solid฀State฀1976;18:93. 65฀ Bollmann฀W.฀Phil฀Mag฀A฀1984;49:฀73. 66 Romanov A.E., Vladimirov V.I. In: Nabarro F.R.N., editor. Dislocations in solids, vol. 9.฀Amsterdam:฀North-Holland;฀1992;฀p.191. 67฀ Rybin฀V.V.,฀Zisman฀A.A.,฀Zolotorevsky฀N.Yu.฀Acta฀Metall฀Mater฀1993;41:฀2211. 68฀ Languillaume฀J.,฀Chmelik฀F.,฀Kapelski฀G.,฀Bordeaux฀F.,฀Nazarov฀A.A.,฀Canova฀G.,฀ Esling฀C.,฀Valiev฀R.Z.,฀Baudelet฀B.฀Acta฀Metall฀Mater฀1993;41:฀2953. 69฀ Valiev฀R.Z.,฀Musalimov฀R.Sh.฀Phys฀Metals฀Metallogr฀1994;78:฀666. 70฀ Alexandrov฀I.V.,฀Zhang฀K.,฀Kilmametov฀A.R.,฀Lu฀K.,฀Valiev฀R.Z.฀Mater฀Sci฀Eng฀A฀ 1997;234–236:฀331. 71฀ Islamgaliev฀R.K.,฀Chmelik฀F.,฀Kuzel฀R.฀Mater฀Sci฀Eng฀A฀1997;234–236:฀335. 72฀ Ivanisenko฀Y.,฀Kurmanaeva฀L.,฀Weissmueller฀J.,฀Yang฀K.,฀Markmann฀J.,฀Rösner฀H.,฀ Scherer฀T.,฀Fecht฀H-J.฀Acta฀Mater฀2009;57:฀3391. 73฀ Godon฀A.,฀Creus฀J.,฀Cohendoz฀S.,฀Conforto฀E.,฀Feaugas฀X.,฀Girault฀P.,฀Savall฀C.฀Scr฀ Mater฀2010;62:฀403. 74฀ Nazarov฀A.A.,฀Romanov฀A.E.,฀Valiev฀R.Z.฀Acta฀Metall฀Mater฀1993;41:฀1033. 75฀ Nazarov฀A.A.,฀Romanov฀A.E.,฀Valiev฀R.Z.฀Nanostruct฀Mater฀1994;4:฀93. 76฀ Nazarov฀A.A.,฀Romanov฀A.E.,฀Valiev฀R.Z.฀Nanostruct฀Mater฀1995;6:฀775. 77฀ Nazarov฀A.A.,฀Romanov฀A.E.,฀Valiev฀R.Z.฀Scr฀Mater฀1996;34:฀729. 78 Gutkin M.Yu., Ovid’ko I.A. Plastic deformation in nanocrystalline materials. Berlin: Springer;฀2004. 79฀ Hahn฀H.,฀Mondal฀P.,฀Padmanabhan฀K.A.฀Nanostruct฀Mater฀1997;9:฀603. 80฀ Van฀Swygenhoven฀H.,฀Spaczer฀M.,฀Caro฀A.฀Acta฀Mater฀1999;47:฀3117. 81฀ Pozdnyakov฀V.A.,฀Glezer฀A.M.฀Phys฀Solid฀State฀2002;44:฀732. 82฀ Markmann฀ J.,฀ Bunzel฀ P.,฀ Rösner฀ H.,฀ Liu฀ K.W.,฀ Padmanabhan฀ K.A.,฀ Birringer฀ R.,฀ Gleiter฀H.,฀Weissmüller฀J.฀Scr฀Mater฀2003;49:฀637. 83฀ Hirth฀J.P.,฀Lothe฀J.฀Theory฀of฀dislocations.฀New฀York:฀Wiley;฀1982. 84฀ Kumar฀K.S.,฀Suresh฀S.,฀Chisholm฀M.F.,฀Horton฀J.A.,฀Wang฀P.฀Acta฀Mater฀2003;51:฀ 387. 85฀ Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Acta฀Mater฀2004;52:฀1201. 86฀ Pozdnyakov฀V.A.,฀Glezer฀A.M.฀Phys฀Solid฀State฀2005;47:฀817. 87฀ Kozlov฀E.V.,฀Popova฀N.A.,฀Ivanov฀Yu.F.,฀Ignatenko฀L.N.,฀Koneva฀N.A.,฀Pekarskaya฀ E.E.฀Ann฀Chim฀1996;21:฀427. 88฀ Ishida฀Y.,฀Ichinose฀H.,฀Kizuka฀T.,฀Suenaga฀K.฀Nanostruct฀Mater฀1995;6:฀115. 89฀ Sanders฀P.G.,฀Weertman฀J.R.,฀Barker฀J.G.฀J฀Mater฀Res฀1996;11:฀3110. 90฀ Sanders฀P.G.,฀Eastman฀J.A.,฀Weertman฀J.R.฀Acta฀Metall฀1998;46:฀4195. 91฀ Agnew฀ S.R.,฀ Elliott฀ B.R.,฀Youngdahl฀ C.J.,฀ Hemker฀ K.J.,฀Weertman฀ J.R.฀ Mater฀ Sci฀ Eng฀A฀2000;285:฀391. 92฀ Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Rev฀Adv฀Mater฀Sci฀2006;11:฀46. 93฀ Bobylev฀S.V.,฀Morozov฀N.F.,฀Ovid’ko฀I.A.฀Phys฀Solid฀State฀2007;49:฀1098. 94฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Phil฀Mag฀2008;88:฀1137. 95฀ Morozov฀N.F.,฀Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Dokl฀Phys฀2008;53:฀144.

© Woodhead Publishing Limited, 2011

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X

370 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X

Nanostructured metals and alloys

96฀ Ovid’ko฀I.A.,฀Skiba฀N.V.,฀Mukherjee฀A.K.฀Scr฀Mater฀2010;62:฀387. 97฀ Gleiter฀H.฀Acta฀Mater฀2000;48:฀1. 98฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Pande฀C.S.฀Rev฀Adv฀Mater฀Sci฀2001;2:฀80. 99฀ Mohamed฀F.A.,฀Li฀Y.฀Mater฀Sci฀Eng฀A฀2001;298:฀1. 100฀ Padmanabhan฀K.A.฀Mater฀Sci฀Eng฀A฀2001;304–306:฀200. 101฀ Mukherjee฀A.K.฀Mater฀Sci฀Eng฀A฀2002;322:฀1. 102฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Rev฀Adv฀Mater฀Sci฀2003;4:฀79. 103฀ Kumar฀K.S.,฀Van฀Swygenhoven฀H.,฀Suresh฀S.฀Acta฀Mater฀2003;51:฀5743. 104฀ Tjong฀S.C.,฀Chen฀H.฀Mater฀Sci฀Eng฀R฀2004;45:฀1. 105฀ Asaro฀R.J.,฀Suresh฀S.฀Acta฀Mater฀2005;53:฀3369. 106฀ Han฀B.Q.,฀Lavernia฀E.J.,฀Mohamed฀F.A.฀Rev฀Adv฀Mater฀Sci฀2005;9:฀1. 107฀ Ovid’ko฀I.A.฀Int฀Mater฀Rev฀2005;50:฀65. 108฀ Ovid’ko฀I.A.฀Rev฀Adv฀Mater฀Sci฀2005;10:฀89. 109฀ Wolf฀D.,฀Yamakov฀V.,฀Phillpot฀S.R.,฀Mukherjee฀A.,฀Gleiter฀H.฀Acta฀Mater฀2005;53:฀1. 110฀ Kozlov฀ E.V.฀ In:฀ Altan฀ B.S.,฀ editor.฀ Severe฀ Plastic฀ Deformation:฀ Toward฀ Bulk฀ Production฀ of฀ Nanostructured฀ Materials.฀ New฀ York:฀ Nova฀ Science฀ Publishers;฀ 2006;฀p.295. 111฀ Ma฀E.฀JOM฀2006;58:฀49. 112฀ Meyers฀M.A.,฀Mishra฀A.,฀Benson฀D.J.฀Prog฀Mater฀Sci฀2006;51:฀427. 113฀ Witkin฀D.B.,฀Lavernia฀E.J.฀Prog฀Mater฀Sci฀2006;51:฀1. 114฀ Valiev฀R.Z.,฀Langdon฀T.G.฀Prog฀Mater฀Sci฀2006;51:฀881. 115฀ Van฀Swygenhoven฀H.,฀Weertman฀J.R.฀Mater฀Today฀2006;9(5):฀24. 116฀ Dalla฀Torre฀F.H.,฀Gazder฀A.A.,฀Pereloma฀E.V.,฀Davies฀C.H.J.฀J฀Mater฀Sci฀2007;42:฀ 1622. 117฀ Dao฀M.,฀Lu฀L.,฀Asaro฀R.J.,฀De฀Hosson฀J.T.M.,฀Ma฀E.฀Acta฀Mater฀2007;55:฀4041. 118฀ Kawasaki฀M.,฀Langdon฀T.G.฀J฀Mater฀Sci฀2007;42:฀1782. 119฀ Koch฀C.C.฀J฀Mater฀Sci฀2007;42:฀1403. 120฀ Malygin฀G.A.฀Phys฀Solid฀State฀2007;49:฀1013. 121฀ Sergeeva฀A.V.,฀Mara฀N.A.,฀Mukherjee฀A.K.฀Mater฀Sci฀Eng฀A฀2007;463:฀8. 122฀ Sergeeva฀A.V.,฀Mara฀N.A.,฀Mukherjee฀A.K.฀J฀Mater฀Sci฀2007;42:฀1433. 123฀ Valiev฀R.Z.฀J฀Mater฀Sci฀2007;42:฀1483. 124฀ Wei฀Q.฀J฀Mater฀Sci฀2007;42:฀1709. 125฀ Zhang฀H.W.,฀Hansen฀N.฀J฀Mater฀Sci฀2007;42:฀1682. 126฀ Kozlov฀E.V.,฀Zhdanov฀A.N.,฀Koneva฀N.A.฀Phys฀Mesomech฀2008;11:฀42. 127฀ Van฀Swygenhoven฀H.฀Mater฀Sci฀Eng฀A฀2008;483–484:฀33. 128฀ Zhilyaev฀A.P.,฀Langdon฀T.G.฀Prog฀Mater฀Sci฀2008;53:฀893. 129฀ Andrievski฀R.A.,฀Glezer฀A.M.฀Physics฀–฀Uspekhi฀2009;52:฀315. 130฀ Pande฀C.S.,฀Cooper฀K.P.฀Prog฀Mater฀Sci฀2009;54:฀689. 131฀ Gusev฀ A.I.,฀ Rempel฀ A.A.฀ Nanocrystalline฀ materials.฀ Cambridge:฀ Cambridge฀ International฀Science฀Publishing;฀2004. 132฀ Koch฀ C.C.,฀ Ovid’ko฀ I.A.,฀ Seal฀ S.,฀ Veprek฀ S.฀ Structural฀ nanocrystalline฀ materials:฀ fundamentals฀and฀applications.฀Cambridge:฀Cambridge฀University฀Press;฀2007. 133฀ Cherkaoui฀M.,฀Capolungo฀L.฀Atomistic฀and฀continuum฀modeling฀of฀nanocrystalline฀ materials:฀ deformation฀ mechanisms฀ and฀ scale฀ transition.฀ Berlin:฀ Springer;฀ 2009. 134฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Appl฀Phys฀Lett฀2006;88:฀211901. 135฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Acta฀Mater฀2008;56:฀1642. 136฀ Xu฀G.,฀Argon฀A.S.฀Phil฀Mag฀Lett฀2000;80:฀605. 137฀ Gutkin฀M.Yu.,฀Ishizaki฀T.,฀Kuramoto฀S.,฀Ovid’ko฀I.A.฀Acta฀Mater฀2006;54:฀2489.

© Woodhead Publishing Limited, 2011

Elastic and plastic deformation in nanocrystalline metals

371

138฀ Cui฀ J.P.,฀ Hao฀ Y.L.,฀ Li฀ S.J.,฀ Sui฀ M.L.,฀ Li฀ D.X.,฀ Yang฀ R.฀ Phys฀ Rev฀ Lett฀ 2009;102:฀ 045503. 139฀ Joós฀B.,฀Ren฀Q.,฀Duesbery฀M.S.฀Phys฀Rev฀B฀1994;50:฀5890. 140฀ Lu฀G.,฀Kioussis฀N,฀Bulatov฀V.V.,฀Kaxiras฀N.฀Phys฀Rev฀B฀2000;62:฀3099. 141฀ Bernstein฀N.,฀Tadmor฀E.B.฀Phys฀Rev฀B฀2004;69:฀094116. 142฀ Van฀Swygenhoven฀H.,฀Derlet฀P.M.,฀Frøseth฀A.G.฀Nat฀Mater฀2004;3:฀399. 143฀ Lazar฀P.,฀Podloucky฀D.C.฀Phys฀Rev฀B฀2007;75:฀024112. 144฀ Wang฀Y.M.,฀Bringa฀E.M.,฀McNaney฀J.M.,฀Victoria฀M.,฀Caro฀A.,฀Hodge฀A.M.,฀Smith฀ R.,฀Torralva฀B.,฀Remington฀B.A.,฀Schuh฀C.A.,฀Jamarkani฀H.,฀Meyers฀M.A.฀Appl฀Phys฀ Lett฀2006;88:฀061917. 145฀ Jia฀D.,฀Ramesh฀K.T.,฀Ma฀E.฀Acta฀Mater฀2003;51:฀3495. 146฀ Koch฀C.C.฀Scr฀Mater฀2003;49:฀657. 147฀ Ma฀E.฀Scr฀Mater฀2003;49:฀663. 148฀ Fedorov฀A.A.,฀Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Acta฀Mater฀2003;51:฀887. 149฀ Gutkin฀M.Yu.,฀Kolesnikova฀A.L.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Phil฀Mag฀Lett฀2002;82:฀ 651. 150฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Mater฀Sci฀Eng฀A฀2003;339:฀73. 151฀ Zghal฀ S.,฀ Hytch฀ S.J.,฀ Chevalier฀ J-P.,฀ Twesten฀ R.,฀ Wu฀ P.,฀ Bellon฀ P.฀ Acta฀ Mater฀ 2002;50:฀4695. 152฀ Bobylev฀S.V.,฀Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀J฀Phys฀D:฀Appl฀Phys฀2004;37:฀269. 153฀ Bobylev฀S.V.,฀Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Acta฀Mater฀2004;52:฀3793. 154฀ Bobylev฀S.V.,฀Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Phys฀Solid฀State฀2004;46:฀2053. 155฀ Wei฀Q.,฀Jia฀D.,฀Ramesh฀K.T.,฀Ma฀E.฀Appl฀Phys฀Lett฀2002;81:฀1240. 156฀ Hasnaoui฀A.,฀van฀Swygenhoven฀H.,฀Derlet฀P.M.฀Phys฀Rev฀B฀2002;66:฀184112. 157฀ Shimokawa฀T.,฀Nakatani฀A.,฀Kitagawa฀H.฀Phys฀Rev฀B฀2005;71:฀224110. 158฀ Haslam฀A.J.,฀Moldovan฀D.,฀Yamakov฀V.,฀Wolf฀D.,฀Phillpot฀S.R.,฀Gleiter฀H.฀Acta฀Mater฀ 2003;51:฀2097. 159฀ Liao฀X.Z.,฀Zhou฀F.,฀Lavernia฀E.J.,฀Srinivasan฀S.G.,฀Baskes฀M.I.,฀He฀D.W.,฀Zhu฀Y.T.฀ Appl฀Phys฀Lett฀2003;83:฀632. 160฀ Chen฀ M.W.,฀ Ma฀ E.,฀ Hemker฀ K.J.,฀ Sheng฀ H.W.,฀ Wang฀ Y.M.,฀ Cheng฀ X.M.฀ Science฀ 2003;300:฀1275. 161฀ Liao฀X.Z.,฀Zhou฀F.,฀Lavernia฀E.J.,฀He฀D.W.,฀Zhu฀Y.T.฀Appl฀Phys฀Lett฀2003;83:฀5062. 162฀ Wu฀X.L.,฀Ma฀E.฀Appl฀Phys฀Lett฀2006;88:฀061905. 163฀ Wu฀X.L.,฀Ma฀E.฀Appl฀Phys฀Lett฀2006;88:฀231911. 164฀ Zhu฀Y.T.,฀Wu฀X.L.,฀Liao฀X.Z.,฀Narayan฀J.,฀Mathaudhi฀S.N.,฀Kecskés฀L.J.฀Appl฀Phys฀ Lett฀2009;95:฀031909. 165฀ Udler฀D.,฀Seidman฀D.N.฀Phys฀Rev฀B฀1996;54:฀R11133. 166฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Phys฀Solid฀State฀2004;46:฀2042. 167฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Phil฀Mag฀2006;86:฀1483. 168฀ Bobylev฀S.V.,฀Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Phys฀Rev฀B฀2006;73:฀064102. 169฀ Bobylev฀S.V.,฀Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Phys฀Solid฀State฀2006;48:฀1495. 170฀ Liao฀X.Z.,฀Srinivasan฀S.G.,฀Zhao฀Y.H.,฀Baskes฀M.I.,฀Zhu฀Y.T.,฀Zhou฀F.,฀Lavernia฀E.J.,฀ Xu฀H.F.฀Appl฀Phys฀Lett฀2004;84:฀3564. 171฀ Bobylev฀S.V.,฀Ovid’ko฀I.A.฀Rev฀Adv฀Mater฀Sci฀2004;7:฀75. 172฀ Zhu฀Y.T.,฀Liao฀X.Z.,฀Srinivasan฀S.G.,฀Zhao฀Y.H.,฀Baskes฀M.I.,฀Zhou฀F.,฀Lavernia฀E.J.฀ Appl฀Phys฀Lett฀2004;85:฀5049. 173฀ Zhu฀Y.T.,฀Liao฀X.Z.,฀Srinivasan฀S.G.,฀Lavernia฀E.J.฀J฀Appl฀Phys฀2005;98:฀034319. 174฀ Asaro฀R.J.,฀Krysl฀P.,฀Kad฀B.฀Phil฀Mag฀Lett฀2003;83:฀733. 175฀ Zhu฀B.,฀Asaro฀R.J.,฀Krysl฀P.,฀Bailey฀R.฀Acta฀Mater฀2005;53:฀4825.

© Woodhead Publishing Limited, 2011

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176฀ 177฀ 178฀ 179฀ 180฀ 181฀ 182฀ 183฀ 184฀ 185฀ 186฀ 187฀ 188฀ 189฀ 190฀ 191฀ 192฀ 193฀ 194฀ 195฀ 196฀ 197฀ 198฀ 199฀ 200฀ 201฀ 202฀ 203฀ 204฀ 205฀ 206฀ 207฀ 208฀ 209฀ 210฀ 211฀ 212฀

Nanostructured metals and alloys Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Phys฀Rev฀B฀2006;74:฀172107. Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Phys฀Solid฀State฀2007;49:฀874. Fischer฀F.D.,฀Oberaigner฀E.R.,฀Waitz฀T.฀Scr฀Mater฀2009;61:฀959. Gu฀P.,฀Kad฀B.K.,฀Dao฀M.฀Scr฀Mater฀2010;62:฀361. Zhao฀Y.H.,฀Liao฀X.Z.,฀Zhu฀Y.T.,฀Horita฀Z.,฀Langdon฀T.G.฀Mater฀Sci฀Eng฀A฀2005;410– 411: 188. Huang฀C.X.,฀Wang฀K.,฀Wu฀Z.F.,฀Zhang฀Z.F.,฀Li฀G.Y.,฀Li฀S.X.฀Acta฀Mater฀2006;54:฀655. Feng฀ X.Y.,฀ Cheng฀ Z.Y.,฀ Zhou฀ J.,฀Wu฀ X.L.,฀Wang฀ Z.Q.,฀ Hong฀Y.S.฀ Chin฀ Phys฀ Lett฀ 2006;23:฀420. Feng฀ X.Y.,฀ Cheng฀ Z.Y.,฀ Wu฀ X.,฀ Wang฀ T.C.,฀ Hong฀ Y.S.฀ J฀ Phys฀ D:฀ Appl฀ Phys฀ 2006;39:฀746. Wu฀X.L.,฀Qi฀Y.,฀Zhu฀Y.T.฀Appl฀Phys฀Lett฀2007;90:฀221911. Wu฀X.L.,฀Ma฀E.฀J฀Mater฀Res฀2007;22:฀2241. Wu฀X.L.,฀Ma฀E.,฀Zhu฀Y.T.฀J฀Mater฀Sci฀2007;42:฀1427. Wu฀X.L.,฀Ma฀E.฀Mater฀Sci฀Eng฀A฀2008;483–484:฀84. Rösner฀H.,฀Markmann฀J.,฀Weissmüller฀J.฀Phil฀Mag฀Lett฀2004;84:฀321. Wang฀Y.M.,฀Hodge฀A.M.,฀Biener฀J.,฀Hamza฀A.V.,฀Barnes฀D.E.,฀Liu฀K.,฀Nieh฀T.G.฀Appl฀ Phys฀Lett฀2005;86:฀101915. Zhu฀ Y.T.,฀ Narayan฀ J.,฀ Hirth฀ J.P.,฀ Mahajan฀ S.,฀ Wu฀ X.L.,฀ Liao฀ X.Z.฀ Acta฀ Mater฀ 2009;57:฀3763. Rybin฀V.V.฀Large฀plastic฀deformations฀and฀fracture฀of฀metals.฀Moscow:฀Metallurgia;฀ 1986 (in Russian). Seefeldt฀M.฀Rev฀Adv฀Mater฀Sci฀2001;2:฀44. Klimanek฀P.,฀Romanov฀A.E.,฀Seefeldt฀M.,฀editors.฀Sol฀State฀Phenom฀2002;87:฀1. Ke฀M.,฀Hackney฀S.A.,฀Milligan฀W.W.,฀Aifantis฀E.C.฀Nanostruct฀Mater฀1995;5:฀689. Murayama฀M.,฀Howe฀J.M.,฀Hidaka฀H.,฀Takaki฀S.฀Science฀2002;295:฀2433. Shan฀ Z.W.,฀ Stach฀ E.A.,฀ Wiezorek฀ J.M.K.,฀ Knapp฀ J.A.,฀ Follstaedt฀ D.M.,฀ Mao฀ S.X.฀ Science฀2004;305:฀654. Shan฀ Z.W.,฀ Stach฀ E.A.,฀ Wiezorek฀ J.M.K.,฀ Knapp฀ J.A.,฀ Follstaedt฀ D.M.,฀ Mao฀ S.X.฀ Science฀2005;308:฀356d. Shan฀Z.W.,฀Mao฀S.X.฀Adv฀Eng฀Mater฀2005;7:฀603. Sergueeva฀A.V.,฀Mara฀N.A.,฀Valiev฀R.Z.,฀Mukherjee฀A.K.฀Mater฀Sci฀Eng฀A฀2005;410– 411: 413. Sergueeva฀A.V.,฀Mukherjee฀A.K.฀Rev฀Adv฀Mater฀Sci฀2006;13:฀1. Sergueeva฀A.V.,฀Mara฀N.A.,฀Krasilnikov฀N.A.,฀Valiev฀R.Z.,฀Mukherjee฀A.K.฀Phil฀Mag฀ 2006;86:฀5797. Yagi฀N.,฀Rikukawa฀A.,฀Mizubayashi฀H.,฀Tanimoto฀H.฀Mater฀Sci฀Eng฀A฀2006;442:฀323. Wang฀Y.B.,฀Li฀B.Q.,฀Sui฀M.L.,฀Mao฀S.X.฀Appl฀Phys฀Lett฀2008;92:฀011903. Zizak฀I.,฀Darowski฀N.,฀Klaumünzer฀S.,฀Schumacher฀G.,฀Gerlach฀J.W.,฀Assmann฀W.฀ Phys฀Rev฀Lett฀2008;101:฀065503. Zizak฀I.,฀Darowski฀N.,฀Klaumünzer฀S.,฀Schumacher฀G.,฀Gerlach฀J.W.,฀Assmann฀W.฀ Nucl฀Inst฀Meth฀Phys฀Res฀B฀2009;267:฀944. Feichtinger฀D.,฀Derlet฀P.M.,฀Van฀Swygenhoven฀H.฀Phys฀Rev฀B฀2003;67:฀024113. Dupont฀V.,฀Sansoz฀F.฀Mater฀Res฀Soc฀Symp฀Proc฀2006;฀903E:0903–Z06–05.1. Sansoz฀F.,฀Dupont฀V.฀Appl฀Phys฀Lett฀2006;89:฀111901. Sansoz฀F.,฀Dupont฀V.฀Mater฀Sci฀Eng฀C฀2007;27:฀1509. Monk฀J.,฀Farkas฀D.฀Phys฀Rev฀B฀2007;75:฀045414. Gutkin฀M.Yu.,฀Mikaelyan฀K.N.,฀Ovid’ko฀I.A.฀Sov฀Phys฀Solid฀State฀1995;37:฀300. Gutkin฀M.Yu.,฀Mikaelyan฀K.N.,฀Ovid’ko฀I.A.฀Nanostruct฀Mater฀1995;6:฀779.

© Woodhead Publishing Limited, 2011

Elastic and plastic deformation in nanocrystalline metals

373

213฀ Gutkin฀M.Yu.,฀Mikaelyan฀K.N.,฀Ovid’ko฀I.A.฀Phys฀Stat฀Sol฀B฀1996;153:฀337. 214฀ Gutkin฀M.Yu.,฀Kolesnikova฀A.L.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀J฀Metastable฀&฀Nanostruct฀ Mater฀2002;12:฀47. 215฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Tech฀Phys฀Lett฀2002;28:฀437. 216฀ Valiev฀R.Z.,฀Langdon฀T.G.฀Acta฀Metall฀Mater฀1993;41:฀949. 217฀ Nyilas฀R.D.,฀Kobas฀M.,฀Spolenak฀R.฀Acta฀Mater฀2009;57:฀3738. 218฀ Ovid’ko฀I.A.฀Science฀2002;295:฀2386. 219฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Acta฀Mater฀2003;51:฀4059. 220฀ Orlova฀T.S.,฀ Romanov฀A.E.,฀ Nazarov฀A.A.,฀ Enikeev฀ N.A.,฀Alexandrov฀ I.V.,฀Valiev฀ R.Z.฀Tech฀Phys฀Lett฀2005;31:฀1015. 221฀ Orlova฀T.S.,฀ Nazarov฀A.A.,฀ Enikeev฀ N.A.,฀Alexandrov฀ I.V.,฀Valiev฀ R.Z.,฀ Romanov฀ A.E.฀Phys฀Solid฀State฀2005;47:฀845. 222฀ Enikeev฀ N.A.,฀ Orlova฀ T.S.,฀ Alexandrov฀ I.V.,฀ Romanov฀ A.E.฀ Sol฀ State฀ Phenom฀ 2005;101–102:฀319. 223฀ Kolesnikova฀A.L.,฀Ovid’ko฀I.A.,฀Romanov฀A.E.฀Tech฀Phys฀Lett฀2007;33:฀641. 224฀ Romanov฀ A.E.,฀ Kolesnikova฀ A.L.,฀ Ovid’ko฀ I.A.,฀ Aifantis฀ E.C.฀ Mater฀ Sci฀ Eng฀ A฀ 2009;503:฀62. 225฀ Bobylev฀S.V.,฀Mukherjee฀A.K.,฀Ovid’ko฀I.A.฀Rev฀Adv฀Mater฀Sci฀2009;19:฀103. 226฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Appl฀Phys฀Lett฀2005;87:฀251916. 227฀ Gutkin฀M.Yu.,฀Mikaelyan฀K.N.,฀Ovid’ko฀I.A.฀Scr฀Mater฀2008;58:฀850. 228฀ Gutkin฀M.Yu.,฀Mikaelyan฀K.N.,฀Ovid’ko฀I.A.฀Phys฀Solid฀State฀2008;50:฀1266. 229฀ Ovid’ko฀I.A.,฀Sheinerman฀A.G.,฀Aifantis฀E.C.฀Acta฀Mater฀2008;56:฀2718. 230฀ Bobylev฀S.V.,฀Ovid’ko฀I.A.฀Rev฀Adv฀Mater฀Sci฀2009;22:฀39. 231฀ Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Scr฀Mater฀2008;59:฀119. 232฀ Kim฀B.N.,฀Hirada฀K.,฀Morita฀K.฀Acta฀Mater฀2005;53:฀1791. 233฀ Yang฀F.,฀Yang฀W.฀Scr฀Mater฀2009;61:฀919. 234฀ Mishra฀R.S.,฀Valiev฀R.Z.,฀Mukherjee฀A.K.฀Nanostruct฀Mater฀1997;9:฀473. 235฀ Mishra฀ R.S.,฀ Valiev฀ R.Z.,฀ McFadden฀ S.X.,฀ Mukherjee฀ A.K.฀ Mater฀ Sci฀ Eng฀ A฀ 1998;252:฀174. 236฀ McFadden฀ S.X.,฀ Misra฀ R.S.,฀ Valiev฀ R.Z.,฀ Zhilyaev฀ A.P.,฀ Mukherjee฀ A.K.฀ Nature฀ 1999;398:฀684. 237฀ Islamgaliev฀ R.K.,฀ Valiev฀ R.Z.,฀ Mishra฀ R.S.,฀ Mukherjee฀ A.K.฀ Mater฀ Sci฀ Eng฀ A฀ 2001;304–306:฀206. 238฀ Mishra฀R.S.,฀Stolyarov฀V.V.,฀Echer฀C.,฀Valiev฀R.Z.,฀Mukherjee฀A.K.฀Mater฀Sci฀Eng฀A฀ 2001;298:฀44. 239฀ Mishra฀ R.S.,฀Valiev฀ R.Z.,฀ McFadden฀ S.X.,฀ Islamgaliev฀ R.K.,฀ Mukherjee฀A.K.฀ Phil฀ Mag฀A฀2001;81:฀37. 240฀ Valiev฀ R.Z.,฀ Song฀ C.,฀ McFadden฀ S.X.,฀ Mukherjee฀A.K.,฀ Mishra฀ R.S.฀ Phil฀ Mag฀A฀ 2001;81:฀25. 241฀ Padmanabhan฀K.A.,฀Gleiter฀H.฀Mater฀Sci฀Eng฀A฀2004;381:฀28. 242฀ Padmanabhan฀K.A.฀J฀Mater฀Sci฀2009;44:฀2226. 243฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀J฀Phys฀D:฀Appl฀Phys฀2003;36:฀L47. 244฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Acta฀Mater฀2004;52:฀1711. 245฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Phys฀Solid฀State฀2005;47;฀1662. 246฀ Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Acta฀Mater฀2009;57:฀2217. 247฀ Haber฀J.A.,฀Buhro฀W.E.฀J฀Am฀Chem฀Soc฀1998;120:฀10,847. 248฀ Valiev฀ R.Z.,฀ Kozlov฀ E.V.,฀ Ivanov฀ Yu.F.,฀ Lian฀ J.,฀ Nazarov฀A.A.,฀ Baudelet฀ B.฀Acta฀ Metall฀Mater฀1994;42:฀2467. 249฀ Jin฀M.,฀Minor฀A.M.,฀Stach฀E.A.,฀Morris฀Jr฀J.W.฀Acta฀Mater฀2004;52:฀5381.

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250฀ Soer฀W.A.,฀De฀Hosson฀J.Th.M.,฀Minor฀A.M.,฀Morris฀Jr฀J.W.,฀Stach฀E.A.฀Acta฀Mater฀ 2004;52:฀5783. 251฀ De฀Hosson฀J.Th.M.,฀Soer฀W.A.,฀Minor฀A.M.,฀Shan฀Z.,฀Stach฀E.A.,฀Syed฀Asif฀S.A.,฀ Warren฀O.L.฀J฀Mater฀Sci฀2006;41:฀7704. 252฀ Jin฀M.,฀Minor฀A.M.,฀Morris฀Jr฀J.W.฀Thin฀Solid฀Films฀2007;515:฀3202. 253฀ Zhang฀K.,฀Weertman฀J.R.,฀Eastman฀J.A.฀Appl฀Phys฀Lett฀2004;85:฀5197. 254฀ Zhang฀K.,฀Weertman฀J.R.,฀Eastman฀J.A.฀Appl฀Phys฀Lett฀2005;87:฀061921. 255฀ Gai฀P.L.,฀Zhang฀K.,฀Weertman฀J.฀Scr฀Mater฀2007;56:฀25. 256฀ Liao฀X.L.,฀Kilmametov฀A.R.,฀Valiev฀R.Z.,฀Gao฀H.,฀Li฀X.,฀Mukherjee฀A.K.,฀Bingert฀ J.F.,฀Zhu฀Y.T.฀Appl฀Phys฀Lett฀2006;88:฀021909. 257฀ Pan฀D.,฀Nieh฀T.G.,฀Chen฀M.W.฀Appl฀Phys฀Lett฀2006;88:฀161922. 258฀ Pan฀D.,฀Kuwano฀S.,฀Fujita฀T.,฀Chen฀M.W.฀Nano฀Lett฀2007;7:฀2108. 259 Gianola D.S., Van Petegem S., Legros M., Brandstetter S., Van Swygenhoven H., Hemker฀K.J.฀Acta฀Mater฀2006;54:฀2253. 260฀ Gianola฀D.S.,฀Warner฀D.H.,฀Molinari฀J.F.,฀Hemker฀K.J.฀Scr฀Mater฀2006;55:฀649. 261฀ Gianola฀D.S.,฀Mendis฀B.G.,฀Cheng฀X.M.,฀Hemker฀K.J.฀Mater฀Sci฀Eng฀A฀2008;483– 484: 637. 262฀ Legros฀M.,฀Gianola฀D.S.,฀Hemker฀K.J.฀Acta฀Mater฀2008;56:฀3380. 263฀ Fan฀ G.J.,฀ Fu฀ L.F.,฀ Qiao฀ D.C.,฀ Choo฀ H.,฀ Liaw฀ P.K.,฀ Browning฀ N.D.฀ Scr฀ Mater฀ 2006;54:฀2137. 264฀ Fan฀G.J.,฀Fu฀L.F.,฀Choo฀H.,฀Liaw฀P.K.,฀Browning฀N.D.฀Acta฀Mater฀2006;54:฀4781. 265฀ Fan฀G.J.,฀Wang฀Y.D.,฀Fu฀L.F.,฀Choo฀H.,฀Liaw฀P.K.,฀Ren฀Y.,฀Browning฀N.D.฀Appl฀Phys฀ Lett฀2006;88:฀171914. 266฀ Fan฀G.J.,฀Fu฀L.F.,฀Wang฀Y.D.,฀Ren฀Y.,฀Choo฀H.,฀Liaw฀P.K.,฀Wang฀G.Y.,฀Browning฀N.D.฀ Appl฀Phys฀Lett฀2006;89:฀101918. 267฀ Brandstetter฀ S.,฀ Zhang฀ K.,฀ Escuadro฀A.,฀Weertman฀ J.R.,฀Van฀ Swygenhoven฀ H.฀ Scr฀ Mater฀2008;58:฀61. 268฀ Kulovits฀A.,฀Mao฀S.X.,฀Wiezorek฀J.M.K.฀Acta฀Mater฀2008;56:฀4836. 269฀ Rupert฀T.J.,฀Gianola฀D.S.,฀Gan฀Y.,฀Hemker฀K.J.฀Science฀2009;326:฀1686. 270฀ Hasnaoui฀A.,฀van฀Swygenhoven฀H.,฀Derlet฀P.M.฀Acta฀Mater฀2002;50:฀3927. 271฀ Schiøtz฀J.฀Mater฀Sci฀Eng฀A฀2004;375–377:฀975. 272฀ Farkas฀D.,฀Frøseth฀A.,฀van฀Swygenhoven฀H.฀Scr฀Mater฀2006;55:฀695. 273฀ Sansoz฀F.,฀Molinari฀J.F.฀Thin฀Solid฀Films฀2007;515:฀3158. 274฀ Dupont฀V.,฀Sansoz฀F.฀Acta฀Mater฀2008;56:฀6013. 275฀ Cahn฀J.W.,฀Mishin฀Y.,฀Suzuki฀A.฀Acta฀Mater฀2006;54:฀4953. 276฀ Zhou฀L.,฀Zhou฀N.,฀Song฀G.฀Phil฀Mag฀2006;86:฀5885. 277฀ Zhang฀H.,฀Srolovitz฀D.J.,฀Douglas฀J.F.,฀Warren฀J.A.฀Acta฀Mater฀2007;55:฀4527. 278฀ Ivanov฀V.A.,฀Mishin฀Y.฀Phys฀Rev฀B฀2008;78:฀064106. 279฀ Mompiou฀F.,฀Caillard฀D.,฀Legros฀M.฀Acta฀Mater฀2009;57:฀2198. 280฀ Caillard฀D.,฀Mompiou฀F.,฀Legros฀M.฀Acta฀Mater฀2009;57:฀2390. 281฀ Mishin฀Y.,฀Asta฀M.,฀Li฀J.฀Acta฀Mater฀2010;58:฀1117. 282฀ Li฀J.C.M.฀Phys฀Rev฀Lett฀2006;96:฀215506. 283฀ Malygin฀G.A.฀Phys฀Solid฀State฀2008;50:฀1032. 284฀ Malygin฀G.A.฀Phys฀Solid฀State฀2009;51:฀1814. 285฀ Lefebvre฀S.,฀Devincre฀B.,฀Hoc฀T.฀J฀Mech฀Phys฀Solids฀2007;55:฀788. 286฀ Li฀Z.,฀Hou฀C.,฀Huang฀M.,฀Ouyang฀C.฀Comp฀Mater฀Sci฀2009;46:฀1124. 287฀ Shodja฀H.M.,฀Davoudi฀K.M.,฀Gutkin฀M.Yu.฀Scr฀Mater฀2008;59:฀368. 288฀ Davoudi฀K.M.,฀Gutkin฀M.Yu.,฀Shodja฀H.M.฀Scr฀Mater฀2009;61:฀355. 289฀ Davoudi฀K.M.,฀Gutkin฀M.Yu.,฀Shodja฀H.M.฀Int฀J฀Solids฀Structures฀2010;47:฀741.

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13 The mechanical properties of multi-scale metallic materials Y.H. ZHAO and฀E.J.฀LAVERNIA,฀ University฀of฀California฀Davis,฀USA

Abstract: Bulk nanostructured metallic materials with a multi-scale grain size฀distribution฀possess฀both฀high฀strength฀and฀good฀ductility,฀and฀therefore฀ are฀expected฀to฀have฀important฀technological฀implications.฀This฀chapter฀ introduces the basic concepts of bulk multi-scale, bimodal and multimodal metallic materials and discusses their development background and preparation฀methods,฀followed฀by฀a฀review฀of฀the฀experimental฀and฀numerical฀ results of mechanical properties (primarily strength and ductility), and deformation and fracture mechanisms of bimodal and multimodal metallic materials,฀and฀ends฀with฀a฀inal฀discussion฀on฀the฀potential฀technological฀ impact and future work. Key words: bulk multi-scale metallic materials, bimodal and multimodal metallic materials, strength and ductility, deformation and fracture mechanisms.

13.1

Introduction

In the case of polycrystalline materials, such as metals, alloys, ceramics and intermetallics,฀ grain฀ size฀ (i.e.฀ fraction฀ of฀ grain฀ boundary฀ volume)฀ is฀ one฀ of฀ the฀ most important microstructural parameters that influence properties and deformation฀mechanisms.฀For฀instance,฀the฀mean฀grain฀size฀generally฀inluences฀ the low-temperature yield strength of polycrystals via the well-known Hall–Petch relationship.฀The฀ grain฀ size฀ of฀ conventional฀ structural฀ polycrystalline฀ materials฀ typically฀ falls฀ in฀ what฀ is฀ widely฀ described฀ as฀ the฀ coarse-grained฀ (CG)฀ regime฀ (>1฀ µm,฀ see฀ Fig.฀ 13.1)฀ which฀ may฀ include฀ the฀ ine-grained฀ sub-regime฀ (1–10 µm).1 Over the past couple of decades, nanocrystalline (or bulk nanostructured, 1.

[14.1]

The฀irst฀term฀on฀the฀left-hand฀side฀of฀Hart’s฀criterion฀[14.1]฀describes฀the฀strainhardening, and m฀is฀the฀strain฀rate฀sensitivity฀(or฀strain฀rate฀hardening)฀deined฀as: . m฀=฀{∂ log σ /∂ ln ε}ε,T. [14.2] If Hart’s criterion [14.1] is valid, a solid under tensile load is stable relative to฀ the฀ necking.฀ Commonly฀ Hart’s฀ criterion฀ [14.1]฀ in฀ nanocrystalline฀ metallic฀ materials with intermediate grains is violated, and these materials are not stable against the necking.16,24฀At฀the฀same฀time,฀there฀are฀several฀examples฀of฀ enhanced tensile ductility of nanocrystalline metals,11–30 in particular, those with intermediate grains. In most nanocrystalline metallic materials with good ductility, the crucial suppression of plastic strain instability is due to strain hardening,฀while฀the฀role฀of฀strain฀rate฀hardening฀(characterized฀by฀m) is negligibly small. Thus,฀ nanocrystalline฀ metals฀ are฀ capable฀ of฀ exhibiting฀ good฀ tensile฀ ductility฀ when plastic strain, crack nucleation and propagation instabilities are suppressed in the metals. In order to understand the origin of these instabilities in nanocrystalline฀metallic฀materials,฀it฀is฀very฀important฀to฀identify฀the฀grain฀size฀ effects on plastic flow and fracture mechanisms operating in these materials. Sections฀14.3–14.5฀briely฀discuss฀the฀speciic฀features฀of฀plastic฀low฀and฀fracture฀ mechanisms in nanocrystalline materials with a particular attention being paid to their฀sensitivity฀to฀the฀grain฀size.

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14.3

435

Plastic flow mechanisms in coarse-grained metallic polycrystals, ultrafine-grained metals and nanocrystalline metals with intermediate grains

First,฀let฀us฀discuss฀the฀effects฀of฀grain฀size฀on฀plastic฀low฀mechanisms฀operating฀ in฀ coarse-gained฀ polycrystalline,฀ ultraine-grained฀ and฀ nanocrystalline฀ metallic฀ materials with intermediate grains. It is well known that the dominant deformation mechanism in conventional coarse-grained polycrystalline metals is lattice dislocation slip occurring in the large grain interiors.37 Its carriers are perfect lattice dislocations generated and stored in the form of dislocation cells/subgrains in the grain interiors during plastic deformation. Grain boundaries serve as obstacles for the movement of lattice dislocations, in which case they influence the level of the yield stress. This effect of grain boundaries in coarse-grained polycrystalline metals is described by the following classical Hall–Petch relationship between the yield stress τ฀and฀grain฀size฀d:38,39

τ฀=฀τ0 + kd –1/2,

[14.3]

with τ0 and k being constant parameters. However, in general, the mechanical behavior of coarse-grained polycrystalline metals is crucially affected by evolution of lattice dislocations in grain interiors, but not grain boundaries. For instance, the deformation-induced storage of lattice dislocations in grain interiors in coarsegrained polycrystalline metals is responsible for strain hardening. It means that the flow stress increases with rising plastic strain. This standard deformation behavior฀ is฀ exhibited฀ by฀ most฀ coarse-grained฀ polycrystalline฀ metals฀ with฀ grain฀ size฀d being larger than 300 nm. With฀ grain฀ reinement,฀ the฀ lattice฀ dislocation฀ slip฀ shows฀ deviations฀ from฀ its฀ standard฀behavior฀due฀to฀both฀the฀nanoscale฀grain฀size฀and฀grain฀boundary฀effects.฀ For฀illustration,฀let฀us฀consider฀ultraine-grained฀metals฀(d ranges from 100 to 300 nm) and nanocrystalline metallic materials with intermediate grains (d ranges from dc to 100 nm). The lattice dislocation slip is still dominant in such materials. However, in contrast to the situation with conventional coarse-grained polycrystals, lattice฀dislocations฀are฀not฀intensively฀stored฀in฀grain฀interiors.฀In฀ultraine-grained฀ metals and nanocrystalline metallic materials with intermediate grains, the flow stress is crucially affected by the dislocation storage and annihilation at grain boundaries.16 The lattice dislocations are generated and move under the applied stress within the grain interiors. Then the lattice dislocations reach grain boundaries where they are transformed into grain boundary dislocations. This process leads to the dislocation storage at grain boundaries. The dislocation storage provides the strain hardening of a metallic material during plastic deformation. At the same time, grain boundary dislocations with opposite Burgers vectors tend to move towards each other and annihilate each other (when they meet). The dislocation annihilation at grain boundaries provides the strain softening (decrease in the flow stress with rising plastic strain) of a material during plastic deformation. Following

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Wang et al.,16 after some initial stage of deformation, the above opposing reaction rates reach an equilibrium by canceling each other. That is, such an equilibrium causes a steady state in which the dislocation generation rate is completely compensated฀by฀the฀dislocation฀annihilation฀rate.฀The฀steady฀state฀is฀characterized฀ by฀an฀approximately฀constant฀low฀stress,฀in฀which฀case฀strain฀hardening฀of฀the฀ material during plastic deformation is practically absent. In this circumstance, the฀irst฀term฀on฀the฀left-hand฀side฀of฀Hart’s฀criterion฀[14.1]฀is฀approximately฀0.฀ The conventional lattice dislocation slip typically results in the strain rate sensitivity m less then 0.1. Therefore, in nanocrystalline metallic materials with intermediate grains deformed by mostly the lattice dislocation slip, Hart’s criterion [14.1] is violated, and these materials under tensile load are unstable leading to the฀necking฀(Fig.฀14.2).฀As฀shown฀in฀many฀experiments,฀this฀deformation฀behavior฀ is฀typical฀for฀most฀ultraine-grained฀materials฀and฀nanocrystalline฀materials฀with฀ intermediate grains.16

14.4

Plastic flow mechanisms in nanocrystalline metals with the finest grains

In฀nanocrystallin฀e฀metallic฀materials฀with฀inest฀grains฀(with฀grain฀size฀lower฀than฀ dc฀ =฀ 10–30฀ nm),฀ the฀ lattice฀ dislocation฀ slip฀ is฀ very฀ limited฀ or฀ even฀ completely฀ suppressed,1–10 because of the two factors. First, grain boundaries (of which there are many) stop gliding lattice dislocations in nanocrystalline materials. Second, the generation of dislocations by Frank–Read and other sources in nanoscale grains฀ requires฀ extremely฀ high฀ stress,฀ which฀ may฀ initiate฀ cracks.7 At the same time,฀alternative฀deformation฀modes฀such฀as฀grain฀boundary฀sliding,฀Coble฀creep,฀ triple-junction diffusional creep, rotational deformation and nanoscale twin deformation effectively operate in nanocrystalline metals.1–10 Of primary importance to the ductility of nanocrystalline metallic materials with฀ inest฀ grains฀ is฀ the฀ role฀ of฀ grain฀ boundary฀ sliding฀ in฀ plastic฀ low.฀ This฀ deformation mode means a relative shearing of neighboring grains, which is localized฀in฀the฀boundary฀between฀the฀grains.฀Since฀grain฀boundaries฀end฀at฀triple฀ junctions, such junctions serve as natural geometric obstacles for grain boundary฀ sliding.฀ In฀ this฀ situation,฀ the฀ uninished฀ plastic฀ shear฀ (or,฀ in฀ terms฀ of฀ grain boundary dislocations, the dislocation Burgers vector) associated with grain boundary sliding is accumulated at triple junctions, which thereby serve as stress sources.฀There฀are฀several฀ways฀to฀accommodate฀of฀the฀uninished฀plastic฀shear฀at฀ the triple junctions in nanocrystalline materials: the emission of lattice dislocations from triple junctions (Fig. 14.4), diffusional accommodation, rotational deformation and void formation (Fig. 14.4 (c) ).40–46 The emission of lattice dislocations from triple junctions seems to be a rather widespread process in various nanocrystalline materials.45,46 Grain boundary sliding฀accommodated฀by฀such฀a฀dislocation฀emission฀process฀is฀characterized฀by฀ creep strain rate:45,46

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Enhanced ductility and its mechanisms . εis ≈ 9bDgb฀·฀d –3฀[exp(2Mτb3/kBT) – 1],

437 [14.4]

where b denotes the lattice parameter, τ the applied shear stress, M the stress concentration factor (at triple junction), kB฀ Boltzmann’s฀ constant,฀ and฀ T the absolute temperature. Following papers,45,46 equation [14.4] is valid in a wide temperature interval, including room and ambient temperatures. (At the

14.4 Grain boundary sliding and its accommodation through lattice dislocation emission from triple junctions. (a) Grain boundary sliding occurs through the movement of grain boundary dislocations along grain boundaries. Grain boundary dislocations are accumulated near triple junctions. (b) Grain boundary dislocations transform into lattice dislocations that are emited from triple junction B and glide within grain I. These processes are accompanied by formation of dipole of wedge disclinations (full and open triangles) A and B. (c) The lattice dislocations reach grain boundary CD where they transform into grain boundary dislocations that climb along this grain boundary. The distance between wedge disclinations A and B increases due to grain boundary sliding. (d) The distance between wedge disclinations A and B increases more due to grain boundary sliding. Nanocrack nucleates in the stress field of the dipole of wedge disclinations A and B.

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same time, there is a restriction concerning grain growth that may destroy the nanocrystalline structure. That is, the temperature should be lower than the temperature at which intensive grain growth starts to occur in a nanocrystalline metal.) According to estimates45,46 for nanocrystalline Ni, strain rate sensitivity m฀ is฀ typically฀ lower฀ than฀ 0.05฀ (except฀ for฀ regimes฀ with฀ extra฀ low฀ strain฀ rate . ε ≤ 10–8 s–1). Besides, grain boundary sliding produces dipoles of wedge disclinations – defects associated with crystal lattice orientation incompatibilities – at and near triple junctions (Fig. 14.4).47–49 (More precisely, a wedge disclination represents a rotational line defect located at either a grain boundary or a triple junction, and is฀ characterized฀ by฀ the฀ disclination฀ strength฀ or,฀ in฀ other฀ words,฀ the฀ rotational฀ misit.50 For instance, a wedge disclination at a tilt grain boundary is the line dividing grain boundary fragments with different tilt misorientation angles, whose difference฀ is฀ the฀ disclination฀ strength.฀ A฀ wedge฀ disclination฀ exists฀ at฀ a฀ triple฀ junction of tilt boundaries if the sum of tilt misorientation angles of these boundaries฀is฀non-zero.50฀The฀non-zero฀sum฀(angle฀gap)฀serves฀as฀the฀disclination฀ strength). Figure 14.4 schematically shows formation of wedge disclination dipoles฀(two฀connected฀arrow฀signs฀in฀the฀igure)฀due฀to฀grain฀boundary฀sliding฀in฀ a฀nanocrystalline฀specimen;฀for฀more฀details,฀see฀Ovid’ko฀and฀Sheinerman.47,49 Following,47,49 wedge disclination dipoles appearing in nanocrystalline metallic materials during grain boundary sliding create very pronounced strain hardening, and this factor can positively influence ductility of such materials (see Section 14.6). Now let us briefly discuss diffusional creep modes operating in nanocrystalline metallic฀ materials฀ with฀ inest฀ grains.฀ The฀ diffusion฀ coeficient฀ Dtj along triple junctions฀ is฀ much฀ larger฀ than฀ the฀ grain฀ boundary฀ diffusion฀ coeficient฀ Dgb,51 which,฀in฀its฀turn,฀is฀by฀several฀orders฀larger฀than฀the฀bulk฀diffusion฀coeficient฀ Dbulk.52 Also, the volume fractions occupied by triple junctions and grain boundaries฀rapidly฀increase฀(at฀the฀expense฀of฀the฀volume฀fraction฀occupied฀by฀ grain฀ interiors)฀ with฀ decreasing฀ the฀ grain฀ size฀ d in nanocrystalline materials53 (Fig. 14.5). In฀ these฀ circumstances,฀ the฀ contributions฀ of฀ Coble฀ creep฀ and฀ triple฀ junction฀ diffusional฀creep฀are฀enhanced฀with฀decreasing฀the฀grain฀size฀d54,55 more rapidly than that of the Nabarro–Herring creep (bulk diffusional creep). This tendency is . . reflected in various strain rates, Nabarro–Herring creep (ε bulk),฀Coble฀creep฀(εgb) . and triple junction diffusional creep (εtj),฀all฀of฀which฀are฀grain฀size฀dependent: . ε bulk ∝ Dbulk฀·฀d –2 σ, . εgb ∝ Dgb฀·฀d –3 σ, . εtj ∝ Dtj฀·฀d –4 σ, [14.5] where σ is the applied tensile stress. Since the diffusional mass transfer is enhanced with rising temperature, grain boundary and triple-junction diffusional

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Enhanced ductility and its mechanisms

439

14.5 Volume fractions of grain boundaries, triple junctions and interfaces (grain boundaries + triple junctions of grain boundaries + quadruple nodes of triple junctions) as a function of grain size d, for nanocrystalline metals with grain boundary thickness = 1 nm. Source: Reprinted from Scripta Materialia with permission from Elsevier.53

creep฀ modes฀ are฀ capable฀ of฀ signiicantly฀ contributing฀ to฀ plastic฀ low฀ in฀ nanocrystalline฀ metallic฀ materials฀ with฀ inest฀ grains฀ at฀ intermediate฀ and฀ high฀ temperatures (Tgbd < T < Tgg, where Tgbd ≈ 0.3 Tm is the minimum temperature at which intensive grain boundary diffusion occurs, Tgg ≈ (0.5–0.6) Tm is the minimum temperature at which intensive grain growth (destroying the nanocrystalline structure) occurs, and Tm is the melting temperature).54,55 Rotational฀deformation฀in฀coarse-grained฀and฀nanocrystalline฀solids฀is฀deined฀ as plastic deformation accompanied by crystal lattice rotations within grains.50,56,57 Rotational deformation is commonly carried out by moving dipoles of grain boundary wedge disclinations.50,56,57 Disclination dipole movement in coarsegrained polycrystals occurs through rearrangement of lattice dislocations in grain interiors.50฀In฀nanocrystalline฀metallic฀materials฀where฀the฀number฀of฀pre-existing฀ lattice dislocations in grain interiors is very limited, rotational deformation occurs through 1) the emission of perfect lattice dislocations from grain boundaries and their฀absorption฀at฀opposite฀grain฀boundaries;57 2) stress-driven migration of grain boundaries;58 and 3) slip and climb of grain boundary dislocations.42,59 In the latter case, the rotational deformation can be effectively initiated by preceding grain boundary sliding and serve as its accommodating mechanism.42 The representations฀ on฀ rotational฀ deformation฀ are฀ well฀ supported฀ by฀ experimental฀ observations of crystal lattice rotations within grains in deformed nanocrystalline metallic materials.40,60–64 Partial dislocations that carry partial dislocation slip and twin deformation have been฀experimentally฀observed฀in฀nanocrystalline฀metals฀with฀inest฀grains.65–72 In

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particular, pairs of partial dislocations emitted from grain boundaries and connected฀ by฀ wide฀ stacking฀ faults฀ have฀ been฀ experimentally฀ observed฀ in฀ nanocrystalline Al,69 whereas their formation in coarse-grained Al is commonly hampered฀due฀to฀high฀values฀of฀the฀speciic฀stacking฀fault฀energy.฀The฀results฀of฀ these฀experiments฀are฀indicative฀of฀the฀strong฀nanoscale฀and฀interface฀effects฀that฀ enhance฀the฀partial฀dislocation฀slip.฀Also,฀twin฀deformation฀has฀been฀experimentally฀ observed฀in฀nanocrystalline฀metals฀like฀Al,฀Cu,฀Ni฀and฀Ta.65–72 Twin deformation plays an important role, in particular, in nanocrystalline metals deformed at high strain rates and low temperatures, in which case grain boundary sliding and grain boundary diffusion are suppressed. Thus, grain boundary sliding, grain boundary diffusional creep, triple junction diffusional creep, partial dislocation slip, rotational and twin deformation modes effectively฀operate฀in฀nanocrystalline฀metallic฀materials฀with฀inest฀grains.฀These฀ deformation฀mechanisms฀are฀characterized฀by฀very฀high฀values฀of฀the฀low฀stress,฀ which฀ are฀ much฀ larger฀ than฀ those฀ characterizing฀ the฀ lattice฀ dislocation฀ slip฀ in฀ conventional฀ coarse-grained฀ polycrystals฀ and฀ ultraine-grained฀ materials.1–10 At the฀same฀time,฀super-strong฀nanocrystalline฀metals฀with฀inest฀grains฀commonly฀ show low tensile ductility, in particular, due to crack nucleation and propagation instabilities (Fig. 14.1). In doing so, the nanocrystalline structure is responsible for the฀ action฀ of฀ speciic฀ crack฀ nucleation฀ and฀ growth฀ mechanisms฀ operating฀ in฀ nanocrystalline metallic materials. This subject will be considered briefly in the next฀section.

14.5

Specific features of crack nucleation and growth processes in nanocrystalline metallic materials

As฀it฀has฀been฀mentioned฀earlier,฀nanocrystalline฀metals฀can฀exhibit฀either฀ductile฀ or brittle fracture behavior, depending on both their structural characteristics and the conditions of mechanical loading. In particular, there are several experimental฀ reports฀ on฀ nanocrystalline฀ metallic฀ materials฀ having฀ an฀ average฀ grain฀ size฀ in฀ the฀ range฀ of฀ around฀ 20฀ to฀ 100฀ nm฀ and฀ showing฀ slow฀ ductile฀ fracture with preceding neck formation and dimpled structures at fracture surfaces.18–23,40฀The฀size฀of฀the฀dimples฀is฀commonly฀considerably฀larger฀than฀the฀ grain฀ size,฀ and฀ ductile฀ fracture฀ is฀ believed฀ to฀ occur฀ through฀ the฀ coalescence฀ of฀ microvoids. At the same time, there are nanocrystalline metallic materials showing the brittle฀ fracture.฀ For฀ instance,฀ nanocrystalline฀ Ni-15%Fe฀ alloy฀ with฀ an฀ average฀ grain฀ size฀ of฀ around฀ 9฀ nm฀ under฀ tensile฀ test฀ at฀ room฀ temperature18,19 and nanocrystalline฀Ni฀specimens฀with฀an฀average฀grain฀size฀of฀around฀30฀nm฀under฀ fatigue test (tension–tension cyclic deformation) at room temperature73฀ exhibit฀ intergranular brittle fracture. In these cases, the main brittle crack is believed to be formed through the multiple generations of intergranular nano/micro-scale cracks and their convergence.

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Brittle and ductile fracture processes in nanocrystalline metallic materials are crucially฀ inluenced฀ by฀ their฀ structural฀ features:฀ nanoscale฀ sizes฀ of฀ grains฀ and฀ large amounts of grain boundaries. In particular, grain boundaries serve as preferable places for nanocrack nucleation and growth because the atomic density is low, and interatomic bonds are weak at grain boundaries compared to the grain interior. In the case of ductile fracture carried by microvoid growth and coalescence in nanocrystalline metals, the microvoid growth by vacancy diffusion mechanism is enhanced in nanocrystalline metals due to the large amounts of grain boundaries characterized฀by฀high฀diffusivity.฀Besides,฀the฀extra฀energy฀of฀grain฀boundaries฀ contributes to the driving force for intergranular fracture with cracks propagating along฀such฀boundaries฀and฀releasing฀the฀extra฀energy,฀compared฀to฀intragranular฀ fracture with cracks propagating through grain interiors. At the same time, grain boundaries are short and curved at numerous triple junctions in nanocrystalline metallic materials. Therefore, if cracks tend to nucleate and grow along grain boundaries,฀crack฀propagation฀can฀be฀delected฀from฀the฀axis฀of฀highest฀stress฀to฀ less฀eficient฀orientations฀directed฀by฀curved฀grain฀boundary฀surfaces.฀This฀leads฀ to increased fracture energy through increased fracture surface area and lower driving forces due to the reduced resolved normal stresses at the crack tip as a result฀ of฀ the฀ delection฀ of฀ the฀ crack฀ tip฀ away฀ from฀ the฀ most฀ eficient฀ (Mode฀ I)฀ loading orientation. As was noted in Section 14.4, plastic deformation in nanocrystalline metallic materials฀ with฀ inest฀ grains฀ occurs฀ at฀ very฀ high฀ stresses,฀ and฀ grain฀ boundary฀ sliding฀ serves฀ as฀ one฀ of฀ its฀ dominant฀ deformation฀ mechanisms.฀ In฀ the฀ context฀ discussed,฀ one฀ expects฀ that฀ crack฀ nucleation฀ and฀ growth฀ processes฀ in฀ nanocrystalline฀ metals฀ with฀ inest฀ grains฀ are฀ inluenced฀ by฀ grain฀ boundary฀ sliding.฀This฀statement฀is฀conirmed฀by฀experiments,฀computer฀simulations฀and฀ theoretical models. In particular, it was theoretically revealed that the enhanced generation฀of฀nanocracks฀in฀deforming฀nanocrystalline฀materials฀with฀inest฀grains฀ can occur at triple junctions with defects produced by intergrain sliding, such as dislocations,43–46 disclination dipoles47,49 (Fig. 14.4 (c) ) and dislocation– disclination฀ conigurations48 serving as dangerous stress concentrators. Such nanocracks฀in฀the฀vicinities฀of฀triple฀junctions฀have฀been฀observed฀by฀Kumar฀et al. in in situ฀ experiments฀ using฀ nanocrystalline฀ Ni฀ with฀ an฀ average฀ grain฀ size฀ of฀ around 30 nm.40 Also, molecular dynamics simulations74 show nanocracks being generated฀ at฀ triple฀ junctions฀ of฀ grain฀ boundaries฀ near฀ tips฀ of฀ pre-existing฀ large฀ cracks฀in฀nanocrystalline฀Ni฀with฀grain฀size฀ranging฀from฀5฀to฀12฀nm.฀With฀these฀ experimental฀data,฀computer฀simulations฀and฀theoretical฀results,฀one฀expects฀that฀ nanocracks at triple junctions of grain boundaries serve as typical elemental carriers฀ (plate-like฀ cracks฀ of฀ smallest฀ size)฀ of฀ brittle฀ fracture฀ in฀ nanocrystalline฀ metallic฀materials฀with฀inest฀grains. Also,฀the฀unique฀structural฀features฀(nanoscale฀sizes฀of฀grains฀and฀large฀amounts฀ of฀ grain฀ boundaries)฀ of฀ nanocrystalline฀ metallic฀ materials฀ cause฀ the฀ speciic฀ features of crack growth in these materials. In most cases, super-strong

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nanocrystalline฀ materials฀ are฀ characterized฀ by฀ low฀ tensile฀ ductility฀ and฀ low฀ fracture toughness at room temperature.1–10 In particular, some nanocrystalline face-centred฀ cubic฀ (fcc)฀ metals฀ exhibit฀ a฀ ductile-to-brittle฀ transition฀ with฀ decreasing฀ grain฀ size.18,19,23 In contrast, good ductility is typically inherent to coarse-grained fcc metals where the emission of lattice dislocations from cracks causes effective crack blunting and thus suppresses their growth. In the light of the discussed difference in the fracture behavior between nanocrystalline and coarse-grained fcc metals, of particular interest is the nature of the sensitivity of the crack-blunting process to nanocrystallinity. In paper,36 a theoretical model was฀suggested฀in฀describing฀the฀grain฀size฀effect฀on฀crack฀blunting฀through฀the฀ emission of lattice dislocations from cracks in nanocrystalline metallic materials (Fig. 14.6 (a) and 14.6 (b) ). Within this model, grain boundaries serve as structural elements that hinder the movement of lattice dislocations emitted from cracks and thereby the blunting of cracks in nanocrystalline materials. In฀these฀circumstances,฀if฀the฀grain฀size฀of฀a฀polycrystalline฀solid฀is฀suficiently฀ large, the emitted dislocations move far enough from the crack tip and do not฀ signiicantly฀ hinder฀ the฀ motion฀ of฀ new฀ dislocations฀ until฀ the฀ number฀ of฀ the emitted dislocations becomes large enough (Fig. 14.6 (c) and 14.6 (d) ). As a result,฀ the฀ dislocation฀ emission฀ along฀ one฀ slip฀ plane฀ can฀ induce฀ signiicant฀ blunting of the crack tip. Following,75,76฀ the฀ signiicant฀ blunting฀ by฀ lattice฀ dislocations stops crack growth and makes the solid ductile. At the same time, in฀ nanocrystalline฀ materials฀ with฀ inest฀ grains,฀ the฀ emission฀ of฀ even฀ one฀ dislocation and its immobility at the nearest grain boundary hinders the emission of the succeeding dislocations along the same plane due to dislocation repulsion (Fig. 14.6 (a) and 14.6 (b) ). In doing so, the dislocation emission does not induce signiicant฀crack฀blunting.฀As฀a฀corollary,฀the฀nanocrystalline฀solid฀tends฀to฀show฀ low crack growth resistance. This conclusion is in good agreement with the experimental฀indings฀that฀most฀nanocrystalline฀materials฀with฀inest฀grains฀are฀ brittle. On฀ the฀ other฀ hand,฀ the฀ experiment77 showed enhancement of crack growth resistance฀ of฀ nanocrystalline฀ Ni฀ with฀ grain฀ size฀ of฀ around฀ 20฀ nm,฀ compared฀ to฀ that฀ in฀ coarse-grained฀ Ni.฀These฀ experimental฀ data,฀ as฀ well฀ as฀ similar฀ data78–81 on enhancement of crack growth resistance of nanocrystalline ceramics, are naturally฀ explained฀ within฀ the฀ theoretical฀ concept82–86฀ that฀ speciic฀ toughening฀ micromechanisms can operate in nanocrystalline materials, which are not effective in coarse-grained polycrystals. Such micromechanisms are suggested to be nanoscale deformation twinning,82 Ashby–Verall creep carried by grain boundary sliding accommodated by grain boundary diffusion and grain rotations,83,84 stressdriven migration of grain boundaries85 and nucleation of nanoscale grains86 near crack tips. However, in most cases, as it has been previously noted, nanocrystalline materials฀with฀the฀inest฀grains฀exhibit฀brittle฀fracture.

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14.6 Grain size effect on crack blunting through emission of lattice dislocations from crack tips. (a) and (b) Emission of even one dislocation and its stop at the nearest grain boundary hinder the emission of subsequent dislocations along the same plane due to dislocation repulsion. As a result, the dislocation emission does not induce significant crack blunting in nanocrystalline specimen. (c) and (d) If the grain size of the solid is sufficiently large, the emitted dislocations move far enough from the crack tip and do not significantly hinder the motion of new dislocations until the number of the emitted dislocations becomes large enough. As a result, the dislocation emission along one slip plane can induce significant blunting of the crack tip in coarse-grained polycrystalline specimen.

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14.6

Enhanced ductility of artifact-free nanocrystalline metals with narrow grain size distributions

Although most nanocrystalline metallic materials show disappointingly low tensile฀ ductility฀ at฀ room฀ temperature,฀ several฀ experimental฀ examples฀ have฀ revealed substantial tensile ductility at room temperature.11–30 Of particular interest฀ are฀ experimental฀ results20–22,27 that support the evidence of enhanced tensile ductility of single-phase nanocrystalline metallic materials with narrow grain฀size฀distributions฀and฀without฀artifacts,฀because฀these฀results฀are฀indicative฀ of intrinsic ductility of the ‘pure’ nanocrystalline structures. (In such materials, ‘extrinsic’฀ factors฀ like฀ composite฀ structures,฀ bimodal/multimodal฀ grain฀ size฀ distributions,฀pre-existent฀pores฀and฀contaminations฀do฀not฀operate.) In฀ the฀ experiments,20–22฀ artifact-free฀ bulk฀ nanocrystalline฀ Cu฀ and฀Al-5%Mg฀ alloy฀ with฀ mean฀ grain฀ sizes฀ of฀ around฀ 23฀ nm฀ and฀ 26฀ nm,฀ respectively,฀ were฀ fabricated by in situ consolidation during mechanical alloying at liquid nitrogen temperature. These artifact-free nanocrystalline materials showed both ultrahigh strength and good tensile ductility20–22 (Fig. 14.7). (Similar good plastic properties were฀ exhibited฀ by฀ the฀ artifact-free฀ nanocrystalline฀ Cu฀ specimens฀ with฀ narrow฀ grain฀size฀distributions฀in฀the฀miniaturized฀disc฀bend฀test.87) They showed strainhardening and ductile fracture mechanism with ductile dimples at fracture surfaces.20–22 The lattice dislocation slip was reportedly active in artifact-free nanocrystalline฀ Cu฀ and฀ Al-5%Mg฀ alloys.฀ With฀ these฀ data,฀ Youseff฀ et al.20–22 attributed the ductile behavior to both the strain hardening and thereby good

14.7 A typical tensile stress–strain curve for the bulk in situ consolidated nanocrystalline Cu sample in comparison with that of a coarse-grained polycrystalline Cu sample (an average grain size larger than 80 µm) and a nanocrystalline Cu sample prepared by an inert gas condensation and compaction technique (with a mean grain size of 26 nm). Source: Reprinted with permission from Applied Physics Letters.20

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ductility of the materials by lattice dislocation storage in grain interiors. However, this฀ explanation฀ did฀ not฀ take฀ into฀ account฀ the฀ microscopic฀ mechanisms฀ of฀ generation฀ and฀ storage฀ of฀ lattice฀ dislocations฀ in฀ interiors฀ of฀ ine฀ grains.฀At฀ the฀ same time, this aspect of the dislocation behavior at the nanoscale level is of crucial importance because, in most cases, the lattice dislocation generation and storage฀in฀inest฀nanoscale฀grains฀are฀very฀limited฀or฀even฀completely฀suppressed.฀ In particular, conventional lattice dislocation sources (like Frank–Read sources) do not operate in nanoscale grains.1–10 Besides, even if the lattice dislocations are generated in nanoscale grains, they tend to move toward grain boundaries (where these dislocations are absorbed) due to the image forces.88–91 The฀experimental฀data20–22 on simultaneously high strength and good tensile ductility฀of฀nanocrystalline฀metallic฀materials฀with฀narrow฀grain฀size฀distributions฀ can฀be฀naturally฀explained฀within฀the฀approach49฀focusing฀on฀the฀optimization฀of฀ grain boundary sliding and diffusion processes. More precisely, grain boundary sliding in nanocrystalline materials results in the emission of lattice dislocations from triple junctions and produces wedge disclination dipoles at triple junctions of grain boundaries10,47,49 (Fig. 14.4). The wedge disclination dipoles create very pronounced strain hardening. The calculated strain hardening47,49 appeared to be so฀high฀that฀it฀leads฀to฀the฀experimental฀values฀of฀the฀ultimate฀stress฀(the฀peak฀ stress฀at฀the฀experimental฀stress–strain฀curve)฀at฀very฀small฀values฀of฀plastic฀strain.฀ For฀instance,฀the฀calculated฀stress฀reaches฀the฀value฀of฀0.23฀GPa฀(approximately฀ equal฀to฀the฀experimental฀ultimate฀stress),฀at฀plastic฀strain฀=฀0.01,฀for฀Cu,฀and฀the฀ value฀of฀0.61฀GPa฀(approximately฀equal฀to฀the฀experimental฀ultimate฀stress)฀at฀ plastic฀strain฀=฀0.02,฀for฀Ni.49 Therefore, one can assume that such dramatic strain hardening (created by grain boundary sliding), although suppressing plastic strain instability to necking, commonly induces early fractures associated with intensive formation฀and฀growth฀of฀cracks.฀Nevertheless,฀experimentally฀detected฀examples฀ of substantial tensile ductility20–22 of nanocrystalline metallic materials showing moderate strain hardening are naturally attributed to the strain hardening caused by grain boundary sliding, if it is relieved by some accommodation mechanisms. In฀particular,฀grain฀boundary฀diffusion฀can฀signiicantly฀reduce฀or฀even฀completely฀ remove the disclination stresses and the associated strain hardening in nanocrystalline materials. Following Ovid’ko and Sheinerman,49 diffusion processes are capable of suppressing crack nucleation and growth and thus result in good tensile ductility of nanocrystalline metallic materials at certain conditions that optimize฀ grain฀ boundary฀ sliding฀ and฀ grain฀ boundary฀ diffusion฀ process.฀ The฀ optimization฀in฀question฀means฀that,฀for฀a฀speciied฀strain฀rate,฀the฀rate฀of฀diffusion฀ should be high enough to decrease strain hardening and suppress nucleation of crack but, at the same time, small enough to suppress plastic strain instability. At the฀same฀time,฀for฀a฀speciied฀strain,฀there฀exists฀an฀interval฀of฀strain฀rates฀and฀ temperatures at which a nanocrystalline specimen is stable to necking and catastrophic fracture.49 With an increase of strain, this interval of strain rates and temperatures shrinks, and at some critical strain it disappears. Above this critical

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strain,฀a฀nanocrystalline฀specimen฀can฀no฀more฀be฀stabilized฀with฀respect฀to฀failure฀ by฀either฀necking฀or฀fracture฀through฀the฀optimization฀of฀its฀deformation฀regime. Also, grain boundary sliding results in the emission of lattice dislocations from triple junctions (Fig. 14.4), and these dislocations cause the following two effects. First, lattice dislocations are absorbed by grain boundaries where they could glide and climb, enhance grain boundary sliding and produce grain boundary vacancies that enhance grain boundary diffusion, respectively.5,10 Second, lattice dislocations emitted฀from฀triple฀junctions฀can฀be฀stored฀in฀grain฀interiors฀due฀to฀Lomer–Cottrell฀ locking92 and/or elastic interaction with other dislocations and grain boundary defects. For instance, intergrain sliding produces the wedge disclination dipoles of wedge disclinations which strongly interact with the lattice dislocations and prevent฀ their฀ movement฀ toward฀ grain฀ boundaries;฀ and฀ thus฀ are฀ capable฀ of฀ enhancing the lattice dislocation storage in grain interiors. In this case, the experimentally฀observed฀lattice฀dislocations,฀as฀noted฀by฀Youseff฀and฀co-workers,20 can contribute to the strain hardening. However, it should be noted that, in the experiments,20 the lattice dislocation storage was observed near growing crack tips. At the same time, the conditions for lattice dislocation generation and storage in฀regions฀near฀crack฀tips฀(where฀extremely฀high฀local฀stresses฀operate,฀and฀the฀ stress screening effects of crack free surfaces are pronounced) are much softer compared to those in nanoscale grain interiors located far from crack tips. Therefore, the lattice dislocation activity may be suppressed in the regions far from crack tips, and its contribution to the strain hardening of nanocrystalline metallic฀materials฀with฀narrow฀grain฀size฀distributions฀may฀be฀insigniicant.฀Thus,฀ the concept49฀on฀the฀optimization฀of฀grain฀boundary฀sliding฀and฀diffusion฀process฀ gives฀at฀least฀a฀semi-quantitative฀explanation฀of฀the฀experimentally฀observed20–22 good tensile ductility of artifact-free nanocrystalline metallic materials with narrow฀grain฀size฀distributions.฀Representations฀of฀this฀concept฀are฀also฀relevant฀ to฀ the฀ description฀ of฀ experimentally฀ observed฀ superplasticity฀ shown฀ by฀ nanocrystalline materials at higher strain rates and lower temperatures,31 compared to their coarse-grained counterparts. In the case of superplasticity, however, one should take into consideration several additional factors like grain growth, strain rate hardening, and formation of mesoscopic sliding surfaces.

14.7

Enhanced ductility of nanocrystalline metals due to twin deformation and growth twins

There฀are฀experimental฀data฀indicating฀on฀the฀special฀role฀of฀twin฀deformation฀in฀ an increase of strain-to-failure of nanocrystalline metals under tensile load. For instance,฀Karimpoor฀and฀co-workers14฀experimentally฀revealed฀both฀high฀strength฀ and฀ enhanced฀ tensile฀ ductility฀ of฀ electroplated฀ nanocrystalline฀ Co฀ (hexagonal฀ close-packed)฀(containing฀0.09฀wt.%฀S฀and฀0.07฀wt.%฀C)฀with฀the฀mean฀grain฀size฀ d฀=฀12฀nm฀at฀room฀temperature.฀These฀fully฀dense฀nanocrystalline฀Co฀specimens฀ exhibited฀ both฀ moderate฀ strain฀ hardening฀ approximately฀ speciied฀ by฀ the฀

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dependence σ฀=฀Kε n, where n฀=฀0.4,฀and฀good฀tensile฀ductility฀characterized฀by฀ strain-to-failure฀ranging฀from฀0.06฀to฀0.09.฀Also,฀the฀nanocrystalline฀Co฀specimens฀ are฀ characterized฀ by฀ the฀ yield฀ and฀ tensile฀ strength,฀ which฀ are฀ about฀ 2–3฀ times฀ higher฀than฀those฀of฀coarse-grained฀polycrystalline฀Co.14 In doing so, the yield and tensile strength increase as the plastic strain rate decreases from 2.5 10–3 s–1 down to 10–4 s–1. Since such a response is typical for a material in which the twin deformation mode is dominant,93฀ Karimpoor฀ with฀ co-workers14 postulated that enhanced฀tensile฀ductility฀of฀nanocrystalline฀Co฀occurs฀due฀to฀the฀dominant฀twin฀ deformation that provides moderate strain hardening. Similar deformation behavior฀of฀electroplated฀nanocrystalline฀Co฀was฀reported฀in฀a฀paper.24 Further, a very฀high฀density฀of฀extremely฀thin฀twins฀was฀observed฀in฀the฀nanocrystalline฀Co฀ specimens฀after฀tensile฀load.฀With฀these฀experimental฀data,฀the฀twin฀deformation฀ mode associated with moderate strain hardening can serve as a micromechanism for฀ enhancing฀ tensile฀ ductility฀ in฀ nanocrystalline฀ Co฀ and,฀ probably,฀ for฀ other฀ metals with low stacking fault energy. In recent years, particular attention has been paid to the unique combination of high strength and enhanced ductility of nanotwinned copper.17,28–30 Nanotwinned copper฀specimens฀have฀ultraine-grained฀structure฀with฀a฀high฀density฀of฀nanoscale฀ growth twins.17,28–30 Thus, the structure at the nanoscale level is composed of nanoscale elements – twins – divided by coherent twin boundaries serving as obstacles฀for฀moving฀lattice฀dislocations.฀Coherent฀twin฀boundaries฀have฀much฀ lower energy (per unit area) and thereby are more stable against migration in nanotwinned materials, compared to high-angle grain boundaries in nanocrystalline materials with the same chemical composition.17,28–30 (The basic driving force for the migration of twin and grain boundaries is related to a decrease in the boundary energy.฀In฀this฀context,฀the฀boundaries฀with฀low฀energy฀(per฀unit฀area)฀are฀more฀ stable against such a migration compared to those with large energy.) In the experiments,17,28–30฀it฀is฀found฀that฀nanotwinned฀Cu฀specimens฀show฀high฀strength฀ and good ductility. For instance, Lu and co-workers29 reported that nanotwinned copper฀(with฀the฀average฀twin฀lamella฀thickness฀of฀around฀15฀nm)฀exhibited฀good฀ tensile ductility (strain-to-failure εf฀=฀0.14),฀high฀values฀of฀the฀yield฀stress฀(900฀ MPa) and the ultimate tensile stress (1068 MPa). These strength values are at least฀ one฀ order฀ of฀ magnitude฀ larger฀ than฀ those฀ characterizing฀ coarse-grained฀ copper. Nanotwinned copper, with an average twin lamellar thickness of 4 nm, shows very good tensile ductility (strain-to-failure εf฀=฀0.3),฀but฀at฀the฀expense฀of฀ the ultimate tensile stress (around 700 MPa).29 Stress–strain฀ curves฀ of฀ nanotwinned฀ Cu฀ specimens฀ under฀ tensile฀ load฀ are฀ indicative of strain hardening.17,28–30 From the microstructural viewpoint, plastic deformation in nanotwinned metals occurs by lattice dislocation slip, which results in strain hardening due to accumulation and transformations of lattice dislocations in twin interiors and at twin boundaries.28–30 With decreasing of the average twin lamellar thickness, the hardening by the interaction between dislocations and twin boundaries increases and becomes dominant over the

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contribution from the hardening by the dislocation–dislocation interaction within twin interiors.29฀In฀this฀context,฀of฀particular฀interest฀are฀the฀speciic฀features฀of฀ the dislocation behavior at twin boundaries in nanotwinned metals and its difference from the dislocation behavior at high-angle grain boundaries in nanocrystalline materials. When lattice dislocations reach coherent twin boundaries, they either keep their identity as lattice defects or transfer across twin boundaries into adjacent crystallites, in which case the residual dislocations are formed at coherent twin boundaries.28–30 As a result, the dislocations are accumulated฀at฀twin฀boundaries฀during฀plastic฀deformation฀and฀thus฀signiicantly฀ contribute to the strain hardening. (This behavior is contrasted to that of lattice dislocations when they reach conventional high-angle grain boundaries in nanocrystalline฀materials฀under฀the฀action฀of฀the฀image฀forces฀and/or฀the฀external฀ stress. The lattice dislocations are commonly absorbed by high-angle grain boundaries where they transform into grain boundary dislocations that intensively climb (due to enhanced diffusivity along high-angle grain boundaries), or glide and come into annihilation reactions or undergo other transformations reducing their density at grain boundaries.5,10 As a result, their accumulation is very limited or even completely suppressed at grain boundaries in nanocrystalline materials.) This activity of lattice dislocations within twin interiors and at coherent twin boundaries can serve as a micromechanism for enhancing the tensile ductility of nanotwinned copper and, probably, other metals with high densities of nanoscale growth twins.

14.8

Enhanced ductility of nanocrystalline metals due to strain rate hardening

In papers,16,24 it was noted that enhanced tensile ductility of nanocrystalline and ultraine-grained฀metallic฀materials฀can฀be฀achieved฀due฀to฀strain฀rate฀hardening,฀ if฀ it฀ is฀ characterized฀ by฀ large฀ strain฀ rate฀ sensitivity฀ (m฀ =฀ 0.5฀ or฀ larger,฀ as฀ with฀ conventional฀ superplasticity฀ of฀ microcrystalline฀ materials;฀ e.g.94,95). This idea was฀indirectly฀illustrated฀by฀experimental฀data16 on simultaneously good ductility (strain-to-failure εf฀ =฀ 0.14)฀ and฀ high฀ strength฀ of฀ ultraine-grained฀ Cu฀ specimen฀ under room temperature tensile tests at a low strain rate of 10–6 s–1.฀Also,฀Champion฀ and co-workers13฀fabricated฀nanocrystalline฀Cu฀that฀has฀large฀grains฀with฀size฀of฀ around 200 nm divided into subgrains (with low-angle boundaries) whose typical sizes฀ are฀ between฀ 50฀ and฀ 80฀ nm.฀ The฀ Cu฀ showed฀ near-perfect฀ elastic–plastic฀ behavior with no strain hardening, absence of neck formation and strain-to-failure of฀14%฀in฀a฀tensile฀test฀at฀a฀low฀strain฀rate฀of฀10–6 s–1.฀However,฀in฀the฀experiment13 there฀ are฀ no฀ direct฀ experimental฀ measurements฀ of฀ the฀ strain฀ rate฀ sensitivity฀ m, while Wang and Ma16 reported low values of the strain rate sensitivity (m฀=฀0.025฀ or lower). In these circumstances, the enhancement of tensile ductility of nanocrystalline metallic materials through pronounced strain hardening rate needs further฀experimental฀and฀theoretical฀examinations.

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In general, strain hardening rate is high (m฀=฀0.5–1)฀in฀nanocrystalline฀materials฀ deformed by diffusional creep mode and grain boundary sliding. In particular, it is the case of creep in which grain boundary deformation processes can provide signiicant฀contribution฀to฀plastic฀low.฀For฀instance,฀Coble฀creep฀(grain฀boundary฀ diffusional฀creep)฀mode฀was฀recognized฀as฀the฀dominant฀deformation฀mechanism฀ in฀tensile฀creep฀test฀of฀nanocrystalline฀Ni฀specimens฀(with฀grain฀size฀of฀around฀ 30 nm) at room temperature.96 However, during the room temperature test, creep rates of these nanocrystalline Ni specimens very quickly diminish to very low . values (ε ≤ 10–9 s–1) under the applied stress close to the yield stress. Such low strain rates hardly allow one to reach reasonable degrees of plastic strain or, in other terms, good ductility at room temperature.

14.9

Enhanced ductility of single-phase nanocrystalline metals with bimodal structures

One of the most effective strategies in achieving high strength in materials without loss of ductility is to fabricate single-phase metallic materials with bimodal structures composed of nanoscopic and comparatively large grains11,15 (Fig. 14.8). Such฀ nanomaterials฀ have฀ two฀ peaks฀ in฀ grain฀ size฀ distribution,฀ one฀ in฀ the฀ nanometer range, and the other in the submicrometer range. Although the micromechanisms responsible for combining high strength and good ductility of nanomaterials with bimodal structures in the course of their plastic deformation are still under discussion,11,15,97–99 the general assumption is that the presence of large grains suppresses crack formation and/or propagation (Fig. 14.8) and provides strain-hardening necessary for good ductility while the nanocrystalline matrix฀provides฀high฀strength฀and฀hardness. Apparently,฀the฀irst฀experimental฀investigation฀of฀metallic฀nanomaterials฀with฀ bimodal structures was performed by Tellcamp et al.,11 who fabricated a nanostructured฀ Al฀ alloy฀ with฀ an฀ average฀ grain฀ size฀ of฀ 30฀ to฀ 35฀ nm.฀ The฀ nanostructured฀alloy฀has฀been฀found฀to฀have฀a฀30%฀increase฀in฀both฀yield฀strength฀ and ultimate strength without the corresponding decrease in elongation. Such enhanced ductility has been attributed to the presence of larger Al grains in the bimodal grains. It is logical to assume that dislocation activity in these grains could blunt the propagating cracks and thereby enhance plasticity.11 In฀the฀experiment,15฀crystallization฀of฀an฀initially฀amorphous฀metallic฀alloy฀–฀ Fe-based metallic glass of the FINEMET type (Virtroperm) – was used as a method of obtaining a nanocrystalline material with a bimodal structure free from pores฀and฀contamination.฀Specimens฀with฀different฀grain฀size฀distributions฀were฀ fabricated:฀ 1)฀ nanocrystalline฀ specimens฀ with฀ a฀ narrow฀ grain฀ size฀ distribution฀ (characterized฀ by฀ the฀ mean฀ grain฀ size฀ 15฀ nm),฀ 2)฀ specimens฀ with฀ a฀ bimodal฀ structure฀ where฀ distinct,฀ large฀ grains฀ (with฀ a฀ grain฀ size฀ of฀ around฀ 200฀ nm)฀ are฀ randomly฀distributed฀in฀a฀nanocrystalline฀matrix฀(with฀a฀mean฀grain฀size฀of฀around฀ 15–20 nm), and 3) specimens with a bimodal structure where large grains (with a

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14.8 Deformation and fracture processes in a specimen with bimodal structure. Large grains suppress crack propagation and provide strain hardening (related to lattice dislocation accumulation) necessary for good ductility while the presence of the nanocrystalline matrix results in high strength and hardness.

grain฀ size฀ of฀ 100–200฀ nm)฀ are฀ arranged฀ in฀ groups฀ randomly฀ distributed฀ in฀ a฀ nanocrystalline฀matrix฀(with฀a฀mean฀grain฀size฀of฀around฀15฀nm).฀These฀specimens฀ showed฀ different฀ deformation฀ behaviors฀ under฀ tensile฀ tests฀ at฀ temperature฀ T฀ =฀ 600°C฀and฀strain฀rate฀of฀10–4 s–1. Nanocrystalline specimens with a narrow grain size฀ distribution฀ are฀ characterized฀ by฀ high฀ strength,฀ low฀ ductility,฀ no฀ strain฀ hardening and strain rate sensitivity m฀=฀0.5.฀Grain฀boundary฀sliding฀speciied฀by฀ m฀=฀0.5฀is฀supposed฀to฀dominate฀in฀these฀materials.฀Homogeneous฀nanocrystalline฀ specimens show low tensile ductility when grain boundary sliding initiates nucleation of nanocracks at triple junctions that grow rapidly.15 Specimens with a bimodal structure containing distinctly separated large grains showed high strength฀(characterized฀by฀the฀ultimate฀tensile฀stress฀=฀1.7฀GPa),฀strain฀hardening฀ and฀good฀tensile฀ductility฀(characterized฀by฀strain-to-failure฀εf฀=฀0.15).฀The฀lattice฀ dislocation activity seems to be responsible for strain accommodation, strain-

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hardening฀and฀good฀ductility,฀while฀the฀nanocrystalline฀matrix฀is฀responsible฀for฀ the high strength.15 Specimens with a bimodal structure containing groups of large฀ grains฀ are฀ characterized฀ by฀ comparatively฀ low฀ strength฀ and฀ intermediate฀ ductility฀ with฀ poor฀ resistance฀ to฀ plastic฀ low฀ localization.฀ The฀ group฀ of฀ large฀ grains most likely deforms by dislocation creep at low stresses. Plastic deformation by the lattice dislocation creep in large grains arranged in groups seems to control low strength and is responsible for neck formation in these materials.15 This฀approach฀–฀fabrication฀of฀materials฀with฀bimodal฀grain฀size฀distributions฀ to฀obtain฀a฀combination฀of฀high฀strength฀and฀good฀ductility฀–฀has฀been฀extended฀ to other alloys with bimodal structures consisting of large grains embedded into ultraine-grained฀matrixes16,100–105 as well as the alloys with multimodal structures with฀ several฀ peaks฀ in฀ grain฀ size฀ distribution.106,107 For instance, Wang and co-workers16,100 fabricated copper specimens with a bimodal structure where large฀grains฀are฀embedded฀into฀an฀utraine-grained฀matrix.฀To฀do฀so,฀they฀used฀ equal-channel angular pressing followed by cryo rolling, i.e. cold rolling at a low temperature,฀ and฀ recrystallization฀ at฀ 200°C.฀ The฀ obtained฀ bimodal฀ structure฀ showed฀both฀good฀plastic฀behavior,฀a฀high฀tensile฀strain-to-failure฀(about฀65%฀in฀ terms of engineering strain), and a high yield stress of more than 300 MPa, several times฀greater฀than฀the฀yield฀stress฀of฀coarse-grained฀Cu.

14.10 Enhanced ductility of nanocrystalline metallic composites with second-phase nanoparticles, dendrite-like inclusions and carbon nanotubes Another strategy in enhancing the ductility of high-strength nanocrystalline metallic materials is to fabricate a composite form of nanocrystalline materials. For instance, nanocrystalline Al alloys with second-phase nanoparticles are found to show high strength, strain hardening and enhanced tensile ductility.26 In the experiment,26 the 7075 Al alloy was solution-treated to obtain a coarse-grained polycrystalline solid solution. This coarse-grained specimen was cryogenically rolled฀into฀a฀nanocrystalline-structured฀sheet฀with฀a฀mean฀grain฀size฀of฀around฀100฀ nm. Finally, the specimen was aged at a low temperature. This procedure produced a nanocrystalline structure with second-phase nanoparticles of a high density distributed within grain interiors.26 The mean interpacing between the nanoparticles was around 25 nm. The following three categories of nanoparticles were distinguished:฀ 1)฀ nanoscale฀ spherical฀ Guinier–Preston฀ zones฀ with฀ coherent฀ boundaries,฀2)฀the฀same฀crystal฀lattice฀as฀the฀matrix฀and฀a฀Zn/Mg฀atomic฀ratio฀of฀ about฀1:1;฀plate-shaped฀nanoparticles฀of฀the฀metastable฀hexagonal฀ η’ phase with semicoherent฀boundaries฀and฀a฀Zn/Mg฀atomic฀ratio฀of฀about฀1.5:1;฀and฀3)฀equiaxed฀ nanoparticles฀of฀the฀stable฀hexagonal฀ η phase with incoherent boundaries and a Zn/Mg atomic ratio of about 2:1. In tensile load test, the nanocrystalline Al alloy with second-phase nanoparticles exhibited฀ high-yield฀ strength,฀ 615฀ Mpa,฀ and฀ functional฀ tensile฀ ductility฀

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characterized฀by฀the฀uniform฀elongation฀7.4%.26 The yield stress value is larger than฀the฀yield฀stress฀values,฀550฀MPa฀and฀145฀MPa,฀characterizing฀nanocrystalline฀ specimens without nanoparticles and coarse-grained specimens of the Al alloy under฀examination.26฀The฀uniform฀elongation฀7.4%฀of฀the฀nanocrystalline฀Al฀alloy฀ with฀second-phase฀nanoparticles฀is฀larger฀than฀that฀(3.3%)฀of฀this฀alloy฀without฀ nanoparticles. Such deformation behavior of the nanocrystalline Al alloy is crucially affected by second-phase nanoparticles. From a microstructural viewpoint, plastic deformation in the alloy occurs by lattice dislocation slip hampered by nanoparticles. After plastic deformation, a large number of lattice dislocations are located at nanoparticle boundaries and in their vicinity, whereas, before the tensile test, very few dislocations are found near nanoparticles.26 With this observation, Zhao and co-workers concluded that the composite structure is responsible฀ for฀ the฀ experimentally฀ documented฀ difference฀ in฀ the฀ deformation฀ behavior between pure nanocrystalline Al alloy and the same alloy with nanoparticles. In particular, the presence of nanoparticles results in strain hardening฀ (characterized฀ by฀ the฀ dependence฀ σ = Aε n, where n฀=฀0.15)฀ due฀ to฀ accumulation of lattice dislocations at and near nanoparticle boundaries.26 Also, enhanced ductility was shown by Ti-based nanocrystalline alloys with large dendrite-like inclusions of the second phase under compressive load. In these฀metallic฀nanocomposites,฀plastic฀low฀is฀localized฀in฀shear฀bands฀propagating฀ within฀ the฀ nanocrystalline฀ matrix.฀ Large฀ dendrite-like฀ inclusions฀ of฀ the฀ second฀ phase stop shear bands and cause the strain hardening that prevents dramatic localization฀ of฀ plastic฀ low.฀ The฀ discussed฀ effect฀ of฀ the฀ composite฀ structure฀ enhances฀compressive฀ductility฀up฀to฀strain-to-failure฀14%.108,109 Very฀ recently,฀ the฀ enhanced฀ ductility฀ of฀ nanocrystalline฀ Cu฀ reinforced฀ by฀ multiwalled carbon nanotubes under compressive load has been reported.110 The nanocomposite฀consists฀of฀a฀nanocrystalline฀Cu฀matrix฀with฀the฀mean฀grain฀size฀ d฀=฀22฀nm฀and฀1%฀wt.฀carbon฀nanotubes฀which฀were฀located฀within฀grain฀interiors฀ and฀ at฀ grain฀ boundaries.฀ In฀ the฀ experiment,110 the compression test of nanocomposite pillars showed good ductility (strain-to-failure εf฀=฀0.28),฀strain฀ hardening and the high yield stress (1125 MPa). Li and co-workers110 noted that the lattice dislocation slip is dominant in these nanomposites, while carbon nanotubes serve as the structural element hampering the dislocation motion. In this case, lattice dislocations tend to be accumulated at interfaces between the nanocrystalline฀Cu฀and฀carbon฀nanotubes,฀and฀this฀accumulation฀causes฀the฀strain฀ hardening and, thereby, enhances compressive ductility.

14.11 Conclusions and future trends Thus,฀ owing฀ to฀ the฀ speciic฀ structural฀ features฀ of฀ nanocrystalline฀ metallic฀ materials, the set of deformation mechanisms in these materials is richer than that in conventional coarse-grained polycrystals. In particular, such deformation mechanisms – grain boundary sliding, grain boundary diffusional creep, triple-

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junction diffusional creep, twin and rotational deformation modes – effectively operate฀in฀nanocrystalline฀metals฀with฀inest฀grains.฀Plastic฀deformation฀carried฀ by฀ grain฀ boundary฀ processes฀ in฀ nanocrystalline฀ metallic฀ materials฀ with฀ inest฀ grains฀ is฀ characterized฀ by฀ very฀ high฀ values฀ of฀ the฀ low฀ stress.฀ Such฀ plastic฀ deformation very quickly leads to intensive nanocrack generation (at local stress sources and concentrators) and growth instabilities followed by macroscopic fractures (Fig. 14.1). The deformation behavior of nanocrystalline metallic materials with intermediate grains is controlled by grain boundaries operating as active sources and sinks of lattice dislocations. Plastic deformation carried by lattice dislocations in nanocrystalline materials with intermediate grains is characterized฀by฀the฀absence฀of฀strain฀hardening฀and฀low฀strain฀rate฀hardening,฀in฀ which case it very quickly leads to plastic strain instability followed by fast ductile fractures (Fig. 14.3). The above factors – the absence of the strain hardening and low strain rate hardening in nanocrystalline materials with intermediate grains as well฀as฀very฀high฀low฀stresses฀in฀nanocrystalline฀materials฀with฀inest฀grains฀–฀ effectively฀ explain฀ numerous฀ experimental฀ data1–10 that are indicative of low tensile฀ ductility฀ exhibited฀ by฀ most฀ nanocrystalline฀ metallic฀ materials฀ at฀ room฀ temperature. At฀the฀same฀time,฀several฀experiments฀revealed฀substantial฀tensile฀ductility฀at฀ room temperature.11–30 Of particular interest for understanding the fundamental micromechanisms of the intrinsic ductility of ‘pure’ nanocrystalline metals are experimental฀ results20–22,27 giving evidence of enhanced tensile ductility of artifact-free฀nanocrystalline฀metallic฀materials฀with฀narrow฀grain฀size฀distributions.฀ These฀results฀can฀be฀explained฀within฀the฀concept49฀that฀is฀based฀on฀the฀optimization฀ of grain boundary sliding and diffusion processes that cause moderate strain hardening฀ and฀ suppression฀ of฀ dangerous฀ stress฀ sources฀ during฀ extended฀ plastic฀ deformation of nanocrystalline materials. Also, enhanced tensile ductility comes into play in nanocrystalline metallic materials due to strain hardening provided by deformation-induced twins,14,24฀ pre-existent฀ (growth)฀ twins17,28–30 and secondphase nanoparticles.26 In addition, nanocrystalline metals with bimodal structures show good tensile ductility,11,15 because large grains embedded in nanocrystalline matrixes฀in฀these฀materials฀both฀provide฀strain฀hardening฀and฀stop฀crack฀growth฀ due to crack tip blunting. Besides, dendrite-like inclusions and carbon nanotubes in nanocrystalline metallic composites serve as structural elements causing strain hardening effects that may enhance (at least, compressive) ductility of such nanocomposites.108–110 In general, a systematic attempt to obtain a combination of high strength and good tensile ductility in nanocrystalline metallic materials at widely ranged conditions (chemical compositions, structural parameters, conditions of mechanical load) represents a very important unresolved problem in nanomaterials science. This฀problem฀is฀of฀large฀signiicance฀for฀development฀of฀structural฀applications฀of฀ nanocrystalline฀ materials.฀ In฀ the฀ context฀ discussed,฀ experimental฀ identiication,฀ computer modeling and theoretical description of micromechanisms enhancing

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tensile ductility of super-strong nanocrystalline metals as well as determination of their฀ structural฀ characteristics฀ and฀ fabrication฀ parameters฀ that฀ control/optimize฀ ductility are the future critical directions of research in this area. In conclusion, let us outline the key points that are of particular interest for the future research of ductility of nanocrystalline metallic materials: (1) Development of methods for systematic fabrication of artifact-free metallic materials฀ with฀ narrow฀ grain฀ size฀ distributions฀ and฀ various฀ chemical฀ compositions฀(in฀extension฀of฀the฀research฀efforts20–22,27). (2)฀ Experimental฀identiication฀and฀theoretical฀description฀of฀plastic฀low,฀fracture฀ and enhanced ductility micromechanisms operating in artifact-free metallic materials฀ with฀ narrow฀ grain฀ size฀ distributions฀ as฀ those฀ having฀ “pure”฀ nanocrystalline structures. (3)฀ Experimental฀ identiication฀ and฀ theoretical฀ description฀ of฀ new฀ micromechanisms for suppression of plastic strain instability in nanocrystalline metallic materials with intermediate grains. (4)฀ Experimental฀ identiication฀ and฀ theoretical฀ description฀ of฀ new฀ micromechanisms for suppression of crack nucleation and growth instabilities in nanocrystalline metallic materials. (5) Enhancement of ductility of nanocrystalline metallic materials with the aid฀ of฀ methods฀ (e.g.฀ fabrication฀ of฀ materials฀ with฀ multimodal฀ grain฀ size฀ distributions,108,109 deformation at cryogenic temperatures111) found to be effective฀in฀ductilization฀of฀ultraine-grained฀materials. (6)฀ Experimental฀ identiication฀ and฀ theoretical฀ description฀ of฀ the฀ inluence฀ of฀ stress-driven grain growth on tensile ductility of nanocrystalline metallic materials. (7) With results of (1)–(6) used as input, determination of structural characteristics and฀ parameters฀ of฀ fabrication฀ and฀ processing฀ that฀ control฀ and฀ optimize฀ strength and tensile ductility of nanocrystalline metallic materials with various structures and chemical compositions.

14.12 Sources of further information and advice Papers16,33,34 discuss the key factors – plastic strain instability as well as crack nucleation and growth instabilities – for suppressing tensile ductility of nanocrystalline metallic materials. Micromechanisms of plastic deformation and their฀ sensitivity฀ to฀ the฀ speciic฀ structural฀ features฀ of฀ nanocrystalline฀ metallic฀ materials are considered in detail in reviews1–9฀and฀Koch฀et al.10 An overview of experimental฀ data,฀ computer฀ simulations฀ and฀ theoretical฀ models฀ concerning฀ fracture฀processes฀in฀nanocrystalline฀materials,฀with฀the฀interface฀and฀grain฀size฀ effects฀taken฀into฀account,฀is฀presented฀in฀Ovid’ko’s฀paper;32฀see฀also฀Koch฀et al.10 Various strategies for enhancement of ductility in such materials are briefly reviewed in Ma’s paper.24฀ Experimental฀ data฀ on฀ enhanced฀ tensile฀ ductility฀ of฀

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artifact-free฀nanocrystalline฀metallic฀materials฀with฀narrow฀grain฀size฀distributions฀ are presented in papers.20–22,27 Ductility enhancement in nanocrystalline metallic materials due to strain hardening is the subject of several papers focusing on the roles of deformation-induced twins,14,24฀ pre-existent฀ (growth)฀ twins,17,28–30 second-phase nanoparticles26฀and฀bimodal฀grain฀size฀distributions.11,15 The effects of the composite structure on ductility of metallic nanocomposites are experimentally฀examined฀in฀papers.108–110

14.13 Acknowledgements This work was supported, in part, by the Russian Foundation of Basic Research (Grant฀ 08–01–00225-a),฀ Russian฀Academy฀ of฀ Sciences฀ Program฀ “Fundamental฀ studies฀in฀nanotechnologies฀and฀nanomaterials”,฀and฀the฀Ministry฀of฀Education฀ and Science of the Russian Federation.

14.14 References ฀ 1฀ Mohamed฀F.A.,฀Li฀Y.฀Mater฀sci฀eng฀A฀2001;298:฀1. ฀ 2฀ Kumar฀K.S.,฀Suresh฀S.,฀Van฀Swygenhoven฀H.฀Acta฀mater฀2003;51:฀5743. ฀ 3฀ Wolf฀ D.,฀ Yamakov฀ V.,฀ Phillpot฀ S.R.,฀ Mukherjee฀ A.K.,฀ Gleiter฀ H.฀ Acta฀ mater฀ 2005;53:฀1. ฀ 4฀ Ovid’ko฀I.A.฀Rev฀adv฀mater฀sci฀2005;10:฀89. ฀ 5฀ Ovid’ko฀I.A.฀Int฀mater฀rev฀2005;50:฀65. ฀ 6฀ Meyers฀M.A.,฀Mishra฀A.,฀Benson฀D.J.฀Progr฀mater฀sci฀2006;51:฀427. ฀ 7฀ Dao฀M.,฀Lu฀L.,฀Asaro฀R.J.,฀De฀Hosson฀J.T.M.,฀Ma฀E.฀Acta฀mater฀2007;55:฀4041. ฀ 8฀ Pande฀C.S.,฀Cooper฀K.P.฀Progr฀mater฀sci฀2009;54:฀689. ฀ 9฀ Padilla฀II฀H.A.,฀Boyce฀B.K.฀Exp฀mech฀2010;50:฀5. 10฀ Koch฀ C.C.,฀ Ovid’ko฀ I.A.,฀ Seal฀ S.,฀ Veprek฀ S.฀ Structural฀ nanocrystalline฀ materials:฀ Fundamentals฀and฀applications.฀Cambridge:฀Cambridge฀University฀Press,฀2007. 11฀ Tellkamp฀V.L.,฀Melmed฀A.,฀Lavernia฀E.J.฀Metall฀mater฀trans฀A฀2001;32:฀2335. 12฀ Lu฀L.,฀Li฀S.X.,฀Lu฀K.฀Scr฀mater฀2001;฀45:฀1163. 13฀ Champion฀Y.,฀Langlois฀C.,฀Guerin-Mailly฀S.,฀Langlois฀P.,฀Bonnentien฀J-L.,฀Hytch฀M.฀ Science฀2003;300:฀310. 14฀ Karimpoor฀A.A.,฀Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.฀Scr฀mater฀2003;49:฀651. 15฀ Sergueeva฀A.V.,฀Mara฀N.A.,฀Mukherjee฀A.K.฀Rev฀adv฀mater฀sci฀2004;7:฀67. 16฀ Wang฀Y.M.,฀Ma฀E.฀Acta฀mater฀2004;52:฀1699. 17฀ Lu฀L.,฀Shen฀Y.,฀Chen฀X.,฀Qian฀L.,฀Lu฀K.฀Science฀2004;304:฀422. 18฀ Li฀H.,฀Ebrahimi฀F.฀Appl฀phys฀lett฀2004;84:฀4307. 19฀ Li฀H.,฀Ebrahimi฀F.฀Adv฀mater฀2005;17:฀1969. 20฀ Youssef฀K.M.,฀Scattergood฀R.O.,฀Murty฀K.L.,฀Horton฀J.A.,฀Koch฀C.C.฀Appl฀phys฀lett฀ 2005;87:฀091904. 21฀ Cheng฀ S.,฀ Ma฀ E.,฀Wang฀Y.M.,฀ Kecskes฀ L.J.,฀Youssef฀ K.M.,฀ Koch฀ C.C.,฀Trociewitz฀ U.P.,฀Han฀K.฀Acta฀mater฀2005;53:฀1521. 22฀ Youssef฀K.M.,฀Scattergood฀R.O.,฀Murty฀K.L.,฀Koch฀C.C.฀Scr฀mater฀2006;54:฀251. 23฀ Ebrahimi฀F.,฀Liscano฀A.J.,฀Kong฀D.,฀Zhai฀Q.,฀Li฀H.฀Rev฀adv฀mater฀sci฀2006;13:฀33. 24฀ Ma฀E.฀J฀mater฀2006;54:฀49.

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Nanostructured metals and alloys Gu฀C.,฀Lian฀J.,฀Jiang฀Z.,฀Jiang฀Q.฀Scr฀mater฀2006;54:฀579. Zhao฀Y.H.,฀Liao฀X.Z.,฀Cheng฀S.,฀Ma฀E.,฀Zhu฀Y.T.฀Adv฀mater฀2006;18:฀2280. Wang฀G.,฀Jiang฀Z.,฀Zhang฀H.,฀Lian฀J.฀J฀mater฀res฀2008;23:฀2238. Lu฀L.,฀Zhu฀T.,฀Shen฀Y.,฀Dao฀M.,฀Lu฀K.,฀Suresh฀S.฀Acta฀mater฀2009;57:฀5165. Lu฀L.,฀Shen฀X.,฀Huang฀X.,฀Lu฀K.฀Science฀2009;323:฀607. Lu฀K.,฀Lu฀L.,฀Suresh฀S.฀Science฀2009;324:฀349. Mukherjee฀A.K.฀Chapter฀18฀in฀this฀book. Ovid’ko฀I.A.฀J฀mater฀sci฀2007;42:฀1694. Koch฀C.C.฀Scr฀mater฀2003;49:฀657. Ma฀E.฀Scr฀mater฀2003;49:฀663. Ovid’ko฀I.A.฀Rev฀adv฀mater฀sci฀2005;10:฀89. Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Scr฀mater฀2009;60:฀627. Hirth฀J.P.,฀Lothe฀J.฀Theory฀of฀dislocations.฀NewYork:฀McGraw-Hill,฀1968. Hall฀E.O.฀Proc฀phys฀soc฀London฀B฀1951;64:฀747. Petch฀N.J.฀J฀iron฀steel฀inst฀1953;174:฀25. Kumar฀K.S.,฀Suresh฀S.,฀Chisholm฀M.F.,฀Norton฀J.A.,฀Wang฀P.฀Acta฀mater฀2003;51:฀ 387. Fedorov฀A.A.,฀Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Acta฀mater฀2003;51:฀887. Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Acta฀mater฀2003;51:฀4059. Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Acta฀mater฀2004;52:฀1201. Asaro฀R.J.,฀Suresh฀S.฀Acta฀mater฀2005;53:฀3369. Mohamed฀F.A.,฀Chauhan฀M.฀Metall฀mater฀trans฀A฀2006;37:฀3555. Mohamed฀F.A.฀Metall฀mater฀trans฀A฀2007;38:฀340. Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Appl฀phys฀lett฀2007;90:฀171927. Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Phys฀rev฀B฀2008;77:฀054109. Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Acta฀mater฀2009;57:฀2217. Romanov A.E., Vladimirov V.I. Disclinations in crystalline solids. In: Nabarro F.R.N., editor.฀ Dislocations฀ in฀ solids,฀ vol.฀ 9.฀Amsterdam:฀ North-Holland฀ Publ.฀ Co.,฀ 1992;฀ p.191. Bokstein฀B.,฀Ivanov฀V.,฀Oreshina฀O.,฀Peteline฀A.,฀Peteline฀S.฀Mater฀sci฀eng฀A฀2001;302:฀ 151. Sutton฀ A.P.,฀ Ballufi฀ R.W.฀ Grain฀ boundaries฀ in฀ crystalline฀ materials.฀ Oxford:฀ Clarendon฀Press,฀1996. Zhou฀Y.,฀Erb฀U.,฀Aust฀K.T.,฀Palumbo฀G.฀Scr฀mater฀2003;48:฀825. Masumura฀R.A.,฀Hazzledine฀P.M.,฀Pande฀C.S.฀Acta฀mater฀1998;46:฀4527. Fedorov฀A.A.,฀Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Scr.฀mater฀2002;47:฀51. Ovid’ko฀I.A.฀Science฀2002;295:฀2386. Gutkin M.Yu., Ovid’ko I.A. Plastic deformation in nanocrystalline materials. Berlin, New York: Springer, 2004. Gutkin฀M.Yu.,฀Ovid’ko฀I.A.฀Appl฀phys฀lett฀2005;87:฀251916. Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Scr฀mater฀2008;59:฀119. Ke฀M.,฀Milligan฀W.W.,฀Hackney฀S.A.,฀Carsley฀J.E.,฀Aifantis฀E.C.฀Nanostruct฀mater฀ 1995;5:฀689. Mukherjee฀A.K.฀Mater฀sci฀eng฀A฀2002;322:฀1. Shan฀ Z.,฀ Stach฀ E.A.,฀ Wiezorek฀ J.M.K.,฀ Knapp฀ J.A.,฀ Follstaedt฀ D.M.,฀ Mao฀ S.X.฀ Science฀2004;305:฀654. Wang฀Y.B.,฀Li฀B.Q.,฀Sui฀M.L.,฀Mao฀S.X.฀Appl฀phys฀lett฀2008;92:฀011903. Zizak฀I.,฀Darowski฀N.,฀Klaumuenzer฀S.,฀Schumacher฀G.,฀Gerlach฀J.W.,฀Assmann฀W.฀ Phys฀rev฀lett฀2008;101:฀065503.

© Woodhead Publishing Limited, 2011

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65฀ He฀J.H.,฀Lavernia฀E.J.฀J฀mater฀res฀2001;16:฀2724. 66฀ Liao฀X.Z.,฀Zhou฀F.,฀Lavernia฀E.J.,฀Srinivasan฀S.G.,฀Baskes฀M.I.,฀He฀D.W.,฀Zhu฀Y.T.฀ Appl฀phys฀lett฀2003;83:฀632. 67฀ Chen฀ M.W.,฀ Ma฀ E.,฀ Hemker฀ K.J.,฀ Sheng฀ H.W.,฀ Wang฀ Y.M.,฀ Cheng฀ X.M.฀ Science฀ 2003;300:฀1275. 68 Liao X.Z., Zhao Y.H., Srinivasan S.G., Zhu Y.T., Valiev R.Z., Gunderov D.V. Appl phys฀lett฀2004;84:฀592. 69฀ Liao฀X.Z.,฀Srinivasan฀S.G.,฀Zhao฀Y.H.,฀Baskes฀M.I.,฀Zhu฀Y.T.,฀Zhou฀F.,฀Lavernia฀E.J.,฀ Hu฀H.F.฀Appl฀phys฀lett฀2004;84:฀3564. 70฀ Wang฀Y.M.,฀Hodge฀A.M.,฀Biener฀J.,฀Hamza฀A.V.,฀Barnes฀D.E.,฀Kiu฀K.,฀Nieh฀T.G.฀Appl฀ phys฀lett฀2005;86:฀101915. 71฀ Wu฀X.,฀Zhu฀Y.T.,฀Chen฀M.W.,฀Ma฀E.฀Scr฀mater฀2006;54:฀1685. 72฀ Li฀B.Q.,฀Sui฀M.L.,฀Li฀B.,฀Ma฀E.,฀Mao฀S.X.฀Phys฀rev฀lett฀2009;102:฀205504. 73฀ Moser฀B.,฀Hanlon฀T.,฀Kumar฀K.S.,฀Suresh฀S.฀Scr฀mater฀2006;54:฀1151. 74฀ Farkas฀D.,฀Van฀Swygenhoven฀H.,฀Derlet฀P.M.฀Phys฀rev฀B฀2002;66:฀060101. 75฀ Rice฀J.R.,฀Thompson฀R.M.฀Philos฀mag฀1974;29:฀73. 76฀ Rice฀J.R.฀J฀mech฀phys฀sol฀1992;40:฀239. 77฀ Mirshams฀R.A.,฀Xiao฀C.H.,฀Whang฀S.H.,฀Yin฀W.M.฀Mater฀sci฀eng฀A฀2001;315:฀21. 78฀ Bhaduri฀S.,฀Bhaduri฀S.B.฀Nanostruct฀mater฀1997;8:755. 79฀ Pei฀Y.T.,฀Galvan฀D.,฀De฀Hosson฀J.T.M.฀Acta฀mater฀2005;53:฀4505. 80฀ Kaminskii฀A.A.,฀Akchurin฀M.Sh.,฀Gainutdinov฀R.V.,฀Takaichi฀K.,฀Shirakava฀A.,฀Yagi฀ H.,฀Yanagitani฀T.,฀Ueda฀K.฀Crystallogr฀rep฀2005;50:฀869. 81฀ Zhao฀Y.,฀Qian฀J.,฀Daemen฀L.L.,฀Pantea฀C.,฀Zhang฀J.,฀Voronin฀G.A.,฀Zerda฀T.W.฀Appl฀ phys฀lett฀2004;84:฀1356. 82฀ Gutkin฀M.Yu.,฀Ovid’ko฀I.A.,฀Skiba฀N.V.฀Philos฀mag฀2008;88:฀1137. 83฀ Yang฀F.,฀Yang฀W.฀Int฀j฀solids฀struct฀2008;45:฀3897. 84฀ Yang฀F.,฀Yang฀W.฀J฀mech฀phys฀solids฀2009;57:฀305. 85฀ Ovid’ko฀I.A.,฀Sheinerman฀A.G.,฀Aifantis฀E.C.฀Acta฀mater฀2008;56:฀2718. 86฀ Ovid’ko฀I.A.,฀Skiba฀N.V.,฀Mukherjee฀A.K.฀Scr฀mater฀2010;62:฀387. 87฀ Youssef฀K.M.,฀Scattergood฀R.O.,฀Murty฀K.L,฀Koch฀C.C.฀Appl฀phys฀lett฀2004;85:฀929. 88฀ Gryaznov฀V.G.,฀Kaprelov฀A.M.,฀Romanov฀A.E.฀Scr฀metall฀1989;23:฀1443. 89฀ Gryaznov฀V.G.,฀Polonsky฀I.A.,฀Romanov฀A.E.,฀Trusov฀L.I.฀Phys฀rev฀B฀1991;44:฀42. 90฀ Evans฀A.G.,฀Hirth฀J.P.฀Scr฀metall฀mater฀1992;26:฀1675. 91฀ Romanov฀A.E.฀Nanostruct฀mater฀1995;6:฀125. 92฀ Wu฀X.L.,฀Zhu฀Y.T.,฀Wei฀Y.G.,฀Wei฀Q.฀Phys฀rev฀lett฀2009;103:฀205504. 93฀ Christian฀J.W.,฀Mahajan฀S.฀Progr฀mater฀sci฀1995;39:฀1. 94฀ Padmanabhan฀K.A.,฀Davies฀J.J.฀Superplasticity.฀Berlin:฀Springer-Verlag,฀1980. 95฀ Nieh฀ T.G.,฀ Wadsworth฀ J.,฀ Sherby฀ O.D.฀ Superplasticity฀ in฀ metals฀ and฀ ceramics.฀ Cambridge:฀Cambridge฀University฀Press,฀1997. 96฀ Yin฀W.M.,฀Whang฀S.H.,฀Mirshams฀R.A.,฀Xiao฀C.H.฀Mater฀sci฀eng฀A฀2001;301:฀18. 97฀ Ovid’ko฀I.A.,฀Sheinerman฀A.G.฀Rev฀adv฀mater฀sci฀2007;16:฀1. 98฀ Pozdnyakov฀V.A.฀Tech฀phys฀lett฀2007;33:฀1004. 99฀ Malygin฀G.A.฀Phys฀sol฀state฀2008;50:฀1032. 100฀ Wang฀Y.,฀Chen฀M.,฀Zhou฀F.,฀Ma฀E.฀Nature฀2002;419:฀912. 101฀ Zhang฀X.,฀Wang฀H.,฀Koch฀C.C.฀Rev฀adv฀mater฀sci฀2004;6:฀53. 102฀ Han฀B.Q.,฀Lavernia฀E.,฀Mohamed฀F.A.฀Rev฀adv฀mater฀sci฀2005;9:฀1. 103฀ Han฀ B.Q.,฀ Lee฀ Z.,฀Witkin฀ D.,฀ Nutt฀ S.R.,฀ Lavernia฀ E.J.฀ Metall฀ mater฀ trans฀A฀ 2005; 36: 957. 104฀ Han฀B.Q.,฀Huang฀J.Y.,฀Zhu฀Y.T.,฀Lavernia฀E.J.฀Acta฀mater฀2006;54:฀3015.

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105฀ Fan฀G.J.,฀Choo฀H.,฀Liaw฀P.K.,฀Lavernia฀E.J.฀Acta฀mater฀2006;54:฀1759. 106฀ Zhao฀Y.H.,฀Topping฀T.,฀Bingert฀J.F.,฀Thornton฀J.J.,฀Dangelewicz฀A.M.,฀Li฀Y.,฀Liu฀W.,฀ Zhu฀Y.T.,฀Zhou฀Y.Z.,฀Lavernia฀E.J.฀Adv฀mater฀2008;20:฀3028. 107฀ Ertorer฀O.,฀Topping฀T.,฀Liu฀W.,฀Moss฀W.,฀Lavernia฀E.J.฀Scr฀mater฀2009;60:฀586. 108฀ He฀G.,฀Eckert฀J.,฀Loeser฀W.,฀Schultz฀L.฀Nature฀mater฀2003;2:฀33. 109฀ He฀G.,฀Hagiwara฀M.,฀Eckert฀J.,฀Loeser฀W.฀Philos฀mag฀lett฀2004;84:฀365. 110฀ Li฀H.,฀Misra฀A.,฀Horita฀Z.,฀Koch฀C.C.,฀Mara฀N.A.,฀Dickerson฀P.O.,฀Zhu฀Y.T.฀Appl฀phys฀ lett฀2009;95:฀071907. 111฀ Wang฀Y.,฀Ma฀E.,฀Valiev฀R.Z.,฀Zhu฀Y.T.฀Adv฀mater฀2004;16:฀328.

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15 The mechanical behavior of nanostructured metals based on molecular dynamics computer simulations V.I.฀YAMAKOV,฀National฀Institute฀of฀Aerospace,฀USA

Abstract: The major advances of the past two decades in the atomistic simulation of the fundamental deformation mechanisms in nanocystalline metals are presented in this chapter. The discussion focuses on an overview of work that has contributed to our understanding of the mechanical behavior of these important emerging materials while also noting several disputed and controversial issues that remain to be resolved. The chapter includes a discussion of the properties of grain boundaries, grain-boundary deformation mechanisms, dislocation processes, grain growth and structure evolution in nanocrystalline metals as seen from the perspective of molecular dynamics simulations. Key words: nanocrystalline metals, molecular dynamics simulation, nanocrystalline deformation.

15.1

Introduction

More฀than฀25฀years฀since฀the฀irst฀nanocrystalline฀(NC)฀materials฀were฀synthesized,฀ there is still very little consensus on their characteristic mechanical properties (for recent reviews see References 1–4). Suggestions range from greatly enhanced ductility5–7 to dramatically increased strength and hardness.8,9 In this state of controversial฀ indings,฀ computer฀ simulations฀ performed฀ at฀ the฀ atomistic฀ level,฀ such as molecular dynamics simulations, are able to provide key insights on the underlying deformation mechanisms in these materials. Though in many cases the outcome฀of฀these฀simulations฀is฀no฀less฀controversial฀than฀the฀experimental฀results,฀ the฀ ability฀ to฀ study฀ a฀ fully฀ characterized฀ model฀ to฀ the฀ extent฀ of฀ knowing฀ the฀ microscopic state of each atom with machine precision is invaluable for better understanding of the deformation process. Among the various atomic-level simulation approaches developed during past decades,฀ including฀ lattice฀ statics,฀ lattice฀ dynamics,฀ Monte฀ Carlo฀ and฀ molecular฀ dynamics (MD), the latter has proven particularly useful for the investigation of plastic deformation. Based on the solution of Newton’s equations of motion for a system of atoms interacting through a prescribed interatomic potential function, MD฀simulations฀are฀capable฀of฀exposing฀the฀real-time฀behavior฀during฀deformation฀ at฀ atomic฀ resolution.฀ In฀ addition฀ to฀ studying฀ equilibrium฀ conigurations,฀ MD฀ simulations฀ can฀ explore฀ the฀ transient฀ responses฀ of฀ the฀ system฀ as฀ it฀ probes฀ and฀ traverses฀ complex,฀ often฀ unanticipated฀ saddle-point฀ conigurations฀ in฀ the฀ 459 © Woodhead Publishing Limited, 2011

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deformation path (for an overview, see Allen and Tildesley10). A particular feature of MD simulations is that the operating deformation mechanisms emerge from the interatomic forces, and are not a prescribed input of the simulation model (such as they are in mesoscale models11). This capability allows not only the study of the anticipated deformation processes, but also the observation of new ones as they appear during simulation. Like any simulation method, MD simulations have inherent limitations and constraints that should always be considered in the interpretation of their results. These limitations are well known. One such limitation is the modeling of systems of฀relatively฀small฀nanometer฀dimensions.฀The฀small฀system฀size฀may฀introduce฀ substantial฀ inite-size฀ effects฀ and฀ an฀ increased฀ interference฀ of฀ the฀ boundary฀ conditions on the system behavior. Another limitation is the very short time period of a few nanoseconds over which the dynamics of the system can be probed. This short time duration is of particular consequence for the simulations of plastic deformation.฀As฀a฀result,฀such฀simulations฀usually฀involve฀extremely฀high฀strain฀ rates (of typically >107/s,฀corresponding฀to฀1%฀strain฀in฀1฀ns)฀that฀are฀many฀orders฀ of฀magnitude฀higher฀than฀in฀conventional฀experiments.฀To฀make฀the฀deformation฀ observable฀ within฀ such฀ a฀ short฀ time฀ window,฀ very฀ high฀ stresses,฀ exceeding฀ substantially฀ the฀ experimentally฀ known฀ yield฀ stress,฀ have฀ to฀ be฀ applied.฀ The฀ reliability of the interatomic potentials used is also of a major concern. The interatomic force descriptions used in most MD simulations are of empirical or semi-empirical origin.12 While the empirical force representation has the advantage฀ of฀ being฀ computationally฀ eficient,฀ it฀ is฀ unable฀ to฀ fully฀ capture฀ the฀ many-bodied฀nature฀of฀electron฀bonding,฀particularly฀the฀complex,฀self-consistent฀ electron density variation as a function of local structure and chemistry in the vicinity of defects. As a consequence of these limitations, deducing the relationship between฀ simulation฀ predictions฀ and฀ experimental฀ observations฀ is฀ not฀ always฀ straightforward,฀and฀has฀to฀be฀extrapolated฀on฀the฀basis฀of฀a฀rigorous฀theoretical฀ analysis. In฀spite฀of฀their฀limitations,฀MD฀simulations฀have฀brought฀signiicant฀advances฀ in฀ understanding฀ the฀ peculiar฀ mechanical฀ properties฀ of฀ NC฀ materials.฀ In฀ NC฀ metals, MD simulations have revealed the intrinsic relationship between various deformation฀ modes.฀ Speciically,฀ MD฀ simulations฀ have฀ shown฀ that฀ the฀ unique฀ mechanical฀properties฀demonstrated฀by฀NC฀metals฀are฀a฀result฀of฀the฀competition฀ between intergranular deformation modes, such as grain-boundary sliding13–15 and diffusion,16,17 and transgranular deformation modes, such as dislocation slip,18,19 deformation twinning,19–21 and in some cases, lattice diffusion.22 While this competition has long been suspected and suggested,23 it has been fully revealed in simulations,24–26฀and฀experiments฀are฀still฀verifying฀most฀of฀the฀processes฀seen฀in฀ the simulations.2–4 Often, simulations are becoming a guiding tool for experimentalists฀by฀helping฀them฀to฀identify฀and฀decouple฀the฀various฀deformation฀ phenomena฀ observed฀ under฀ the฀ microscope.฀ Examples฀ include฀ the฀ studies฀ of฀ dislocation฀ structures฀ in฀ nanograins;27,28 full dislocation emission versus partial

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dislocation emission29 leading to high concentration of stacking faults in the grain interior฀in฀face-centered฀cubic฀(fcc)฀NC฀metals;฀the฀unexpected฀role฀of฀deformation฀ twinning฀in฀nanograins;30,31 grain-boundary diffusion as a plausible deformation mode and its connection to the observed grain-boundary sliding.32 The purpose of this chapter is to give a brief overview of the recent advances in MD฀ simulations฀ of฀ NC฀ metals.฀ The฀ material฀ is฀ presented฀ in฀ several฀ sections฀ summarizing฀focus฀areas฀of฀the฀MD฀simulations.฀In฀Section฀15.2,฀a฀discussion฀on฀ MD studies on the structure and properties of grain boundaries in view of their governing฀role฀in฀the฀overall฀mechanical฀behavior฀of฀NC฀metals฀is฀presented.฀In฀ Section฀ 15.3,฀ the฀ deformation฀ mechanisms฀ operating฀ in฀ nanosized฀ grains฀ are฀ summarized.฀ Section฀ 15.4฀ is฀ devoted฀ to฀ the฀ microstructure฀ evolution฀ in฀ NC฀ metals,฀ discussing฀ grain฀ growth฀ and฀ recrystallization,฀ which฀ are฀ very฀ active฀ in฀ these materials and strongly influence their mechanical behavior with time. Concluding฀discussions฀are฀presented฀in฀Section฀15.5.

15.2

The structure and properties of grain boundaries in nanocrystalline (NC) metals by molecular dynamics (MD) simulation

It฀ is฀ widely฀ acknowledged฀ that฀ grain฀ boundaries฀ (GB)฀ deine฀ to฀ a฀ great฀ extent฀ the฀ mechanical฀ properties฀ of฀ NC฀ metals.฀ Grain฀ boundary-mediated฀ processes,฀ such as GB diffusion and sliding, are responsible for the observed inverse Hall–Petch฀ behavior฀ at฀ grain฀ sizes฀ smaller฀ than฀ 20฀ nm.฀At฀ grain฀ sizes฀ between฀ 20 and 100 nm, GBs become active sources for dislocations and serve as nucleation sides for deformation twins, thus triggering intragranular deformation modes.฀Understanding฀of฀these฀processes฀begins฀with฀the฀structure฀and฀properties฀ of฀GBs.฀Considering฀the฀existence฀of฀a฀vast฀amount฀of฀literature฀on฀GB฀structure฀ and properties (see Mishin et al.33),฀this฀section฀will฀focus฀mainly฀on฀the฀speciics฀ of฀the฀GBs฀in฀NC฀metals.

15.2.1 Grain boundary structural model for NC metals Two฀key฀questions฀related฀to฀the฀role฀of฀GBs฀in฀NC฀materials฀that฀have฀evolved฀ from฀experimental฀studies฀and฀have฀become฀a฀focus฀of฀MD฀simulations฀are: (1)฀To฀ what฀ extent฀ can฀ the฀ atomic฀ structure฀ of฀ the฀ GBs฀ in฀ NC฀ materials฀ be฀ extrapolated฀ from฀ those฀ of฀ coarse-grained฀ polycrystalline฀ materials฀ and฀ bicrystals? (2)฀What฀is฀the฀structural฀and฀thermodynamic฀relationship฀between฀NC฀materials฀ and amorphous solids? The฀signiicant฀body฀of฀atomic-level฀simulations฀suggests฀important฀similarities34,35 as well as some differences36,37 between the GBs in coarse-grained polycrystalline microstructures฀and฀NC฀microstructures.฀A฀series฀of฀studies฀by฀Swygenhoven฀et al.,

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based฀ on฀ a฀ MD฀ model฀ of฀ NC฀ Ni฀ of฀ grain฀ sizes฀ from฀ 5.2฀ to฀ 15฀ nm,34 and 20 nm,35 showed that the GB structural types present in coarse-grained fcc฀metals฀are฀also฀found฀in฀NC฀metals,฀without฀major฀differences.฀However,฀this฀ conclusion was based on a polycrystalline model prepared using Voronoi tessellation, which is known to result in a random, but non-equilibrated GB topology. Contrary฀to฀that฀conclusion,฀Phillpot฀et al.36,37 argued that the most important differences฀between฀GBs฀in฀NC฀and฀coarse-grained฀metals฀arise฀from฀the฀severe฀ microstructural฀ constraints฀ present฀ in฀ NC฀ materials.฀ GBs฀ in฀ NC฀ materials฀ are฀ strongly฀ constrained฀ by฀ the฀ grain฀ morphology฀ (shape,฀ size฀ and฀ misorientation)฀ of the surrounding nanograins. At nanometer dimensions, the discrete atomic structure฀ starts฀ to฀ affect฀ the฀ grain฀ morphology.฀ For฀ example,฀ constraining฀ the฀ grain฀size฀to฀a฀whole฀number฀of฀interplanar฀lattice฀spacings฀leads฀to฀the฀appearance฀ of so-called incompatibility strain inside the grains. Because of this constrained morphology,฀ GBs฀ in฀ NC฀ materials฀ cannot฀ achieve฀ their฀ minimum-free-energy฀ thermodynamic state within a nanocrystal as in the coarse-grained materials or bicrystal฀interfaces,฀which฀at฀0฀K฀are฀of฀a฀crystalline฀structure. Grain boundaries in MD simulations36,37฀ where฀ NC฀ microstructures฀ were฀ synthesized฀by฀modeling฀a฀recrystallization฀process฀in฀a฀super-cooled฀Lennard– Jones฀melt,฀into฀which฀small฀crystalline฀seeds฀of฀random฀orientations฀had฀been฀ inserted,฀ showed฀ the฀ structural฀ and฀ dynamic฀ characteristics฀ of฀ a฀ frozen฀ liquid,฀ similar to the well known Rosenhain’s ‘amorphous-cement’ GB model.38 In Phillpot et al,36,37 GB energy was found to be uniform for all GBs and independent of the misorientation. Even when the grain seeds were oriented to form a coherent twin boundary, which is the interface between two twins in a fcc lattice and is expected฀ to฀ have฀ a฀ perfectly฀ ordered฀ crystalline฀ atomic฀ structure,฀ the฀ resulting฀ GBs฀ again฀ showed฀ a฀ highly฀ disordered฀ structure฀ of฀ high฀ excess฀ energy.฀ This฀ disorder฀arises฀from฀the฀highly฀constrained฀NC฀microstructure,฀in฀which฀the฀rigidbody฀translations฀of฀the฀grains฀parallel฀to฀the฀GB฀plane฀cannot฀be฀fully฀optimized,฀ by฀contrast฀with฀an฀unconstrained฀GB฀in฀a฀bicrystal฀interface.฀The฀extension฀of฀ the work on fcc metals to silicon39 further elucidated the connection between the GBs฀present฀in฀NC฀and฀coarse-grained฀microstructures.฀The฀simulations฀of฀NC฀ Si,39฀involving฀grain฀sizes฀of฀up฀to฀about฀7฀nm,฀revealed฀the฀presence฀of฀highly฀ disordered฀GBs฀of฀a฀uniform฀thickness.฀Similar฀simulations฀for฀NC฀Pd40 using a many-body embedded atom method (EAM) interatomic potential41 yielded qualitatively identical results. Therefore,฀while฀NC฀and฀coarse-grained฀polycrystalline฀microstructures฀appear฀ to contain the same structural types of GBs (synthesis and processing dependent), the most important measure of their differences probably lies in their GB-energy distribution฀functions.฀Whereas฀coarse-grained฀materials฀usually฀exhibit฀a฀broad฀ distribution฀of฀GB฀energies,฀the฀severe฀microstructural฀constraints฀present฀in฀NC฀ microstructures฀seem฀to฀have฀the฀effect฀of฀signiicantly฀increasing฀the฀fraction฀of฀ high-energy฀GBs฀at฀the฀expense฀of฀the฀low-energy฀boundaries:฀It฀appears฀that฀the฀ more severe the microstructural constraints become (e.g. by decreasing the grain

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size฀or฀by฀the฀use฀of฀a฀highly฀non-equilibrium฀synthesis฀route),฀the฀larger฀is฀the฀ fraction of the high-energy boundaries in the system. Grain-boundary structure changes with temperature. Many of the earlier simulations of high-temperature GB structure predicted ‘premelting’ at the GBs, i.e. GB disordering below the bulk melting point, Tm (for a critical review, see42). By contrast with thermodynamic melting, in which a liquid phase forms at T฀=฀Tm, the GB premelting takes place through the formation of a liquid-like GB layer at T < Tm.฀ This฀ liqueied฀ layer฀ is฀ characterized฀ by฀ increased฀ structural฀ disorder and by enhanced diffusion within it. The width of the layer gradually diverges as T → Tm. A series of more recent simulations (reviewed in2) suggested that the highly disordered high-energy GBs in Si39 and Pd43 undergo a continuous reversible฀ structural฀ and฀ dynamical฀ transition฀ at฀ elevated฀ temperatures.฀ Upon฀ heating฀from฀0฀K฀to฀melting,฀the฀high-energy฀GBs฀in฀the฀polycrystal฀undergo฀a฀ transition฀from฀a฀low-temperature,฀semi-crystalline฀solid฀GB฀structure฀to฀a฀mixed฀ vitriied฀ solid฀ with฀ liqueied฀ conined฀ volumes฀ of฀ higher฀ diffusivity฀ at฀ high฀ temperature.43 Above a certain transition temperature, Tc (Tc < Tm), which depends฀on฀the฀GB฀energy,฀a฀small฀fraction฀of฀liqueied฀volume฀is฀formed฀within฀ the highly disordered, solid GB until, at T → Tm,฀the฀liqueied฀volume฀ills฀the฀ entire,฀still฀highly฀conined,฀GB฀region.฀Possibly,฀the฀closest฀analogy฀of฀Tc can be฀made฀with฀the฀temperature฀of฀vitriication,฀Tg, in amorphous solids. Finally, for T ≥ Tm,฀the฀highly฀conined฀liquid฀GB฀layer฀spreads฀to฀induce฀thermodynamic฀ melting.43฀From฀a฀thermodynamic฀standpoint฀this฀behavior฀can฀be฀explained฀in฀ terms฀of฀heterophase฀luctuations,฀as฀suggested฀by฀Suzuki฀and฀Mishin44 based on an฀independent฀MD฀simulation฀of฀GB฀solid–liquid฀transition฀in฀Cu.

15.2.2 Grain-boundary diffusivity Grain-boundary diffusivity is directly related to GB structure and energy. In general, high-energy GBs of more disordered amorphous-like structure have higher and more isotropic diffusivity compared to the low-energy dislocation GBs with a pipeline diffusivity along the dislocation cores, or the low-energy special GBs45 with almost crystalline structure and very low diffusivity. Molecular dynamic฀ simulations฀ have฀ been฀ extensively฀ used฀ to฀ study฀ GB฀ diffusivity฀ as฀ dependent on structure, energy and temperature in both flat bicrystalline GBs and GBs฀in฀NC฀microstructures. The microscopic mechanisms of GB diffusion at the atomic level in a flat GB interface฀in฀Cu฀have฀been฀thoroughly฀investigated฀by฀Suzuki฀and฀Mishin.44 At low temperature, GB diffusion occurs through individual vacancies and interstitials that can move by a large variety of diffusion mechanisms, including the collective motion of small clusters. At high temperature, GB premelting substantially changes฀the฀diffusion฀mechanism,฀which฀becomes,฀to฀a฀great฀extent,฀independent฀ of฀the฀GB฀structure.฀There฀is฀still฀no฀clear฀picture฀of฀the฀exact฀atomistic฀mechanisms฀ of diffusion in a premelted GB layer.44

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15.1 Schematic diagram, adapted from,43 illustrating the transition in the GB diffusivity, D, at the temperature of premelting Tc, dependent on the grain-boundary energy, EGB , and at the melting temperature Tm. Note that at Tc, D is continuous, while at Tm it is discontinuous.

Macroscopically, the change of the GB-diffusion mechanism at high temperatures is revealed by a jump in the diffusion activation energy at a critical temperature Tc < Tm (Fig. 15.1).43 This change of the diffusion mechanism correlates with the appearance of a liquid phase in the GB layer as discussed in the previous subsection 15.2.1.43฀ It฀ is฀ important฀ to฀ emphasize฀ that฀ while฀ the฀ diffusion฀coeficient฀at฀T < Tc฀is฀speciic฀for฀each฀GB,฀at฀T > Tc GB diffusivity was found to be independent of the GB structure and becomes a universal property of the material.43฀ This฀ universality฀ has฀ been฀ widely฀ exploited฀ in฀ follow-up฀ MD฀ simulation studies of GB diffusion creep as it allows the construction of a polycrystalline-microstructure model with GBs of uniform diffusivity.

15.2.3 Grain-boundary mobility Grain boundary mobility governs grain growth and microstructure evolution in NC฀materials฀at฀elevated฀temperatures.฀A฀large฀number฀of฀MD฀simulations฀on฀GB฀ mobility46–49 have been performed using different types of microstructure models, exploring฀different฀types฀of฀GB-migration฀driving฀forces,฀such฀as฀elastic-driven฀ or curvature-driven migration. A central point of all of these studies was to relate GB฀ mobility฀ to฀ GB฀ diffusion฀ following฀ the฀ experimental฀ knowledge฀ that฀ GB฀ diffusion฀governs฀GB฀mobility.฀In฀the฀irst฀of฀these฀studies,฀Schoenfelder฀et al.46 used elastic anisotropy to drive the migration of a flat, high-angle (001) φ฀=฀43.60°฀ (Σ 29)฀ twist฀ GB฀ in฀ an฀ elastically฀ strained฀ Cu฀ bicrystal.฀ Later,฀ this฀ study฀ was฀ repeated฀and฀extended฀to฀cover฀the฀whole฀spectrum฀of฀(001)฀twist฀GBs.47 Both studies found a clear qualitative correlation between GB migration and diffusion that shows a similar transition from slow to fast migration/diffusion due to

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high-temperature premelting. Quantitatively though, the activation energy for migration was two to three times lower than that of diffusion. Similar results were reported for capillarity-driven migration of curved tilt boundaries in aluminum, irst฀ in฀ two-dimensional,48 and later in three-dimensional49 simulation models. These simulation studies lead naturally to the conclusion that the mechanism of GB migration is not based on diffusion. In Schoenfelder et al.46 it was found that the estimated migration activation energy is close to the latent heat of fusion, supporting a GB migration mechanism proposed half a century earlier by Mott.50 According to Mott,50 GB migration involves local disordering, or ‘melting’, of small groups of atoms at the boundary, thereby enabling atoms belonging to one grain to reshuffle collectively while aligning themselves with the opposite grain. Compared฀to฀experimental฀results,฀the฀simulations฀of฀a฀family฀of฀(001)฀twist฀ GBs฀ in฀ Cu47 reproduced the observed dependence of the GB mobility on GB misorientation, although the activation energies from the simulations were consistently฀ much฀ lower฀ than฀ the฀ experimental฀ ones.฀ In situ฀ experiments฀ on฀ elastic-strain-induced GB migration in Zn bicrystals51 revealed distinct activation energies of low-angle vs. high-angle and symmetric tilt GBs. While low-angle฀GBs฀exhibited฀values฀close฀to฀the฀activation฀energy฀of฀volume฀diffusion,฀ high-angle฀ GBs฀ exhibited฀ a฀ value฀ close฀ to฀ that฀ of฀ GB฀ diffusion.฀ A฀ possible฀ explanation฀for฀the฀role฀of฀diffusion฀in฀the฀experimental฀indings51 was that the impurities,฀ always฀ present฀ in฀ the฀ experimental฀ samples,฀ cause฀ a฀ drag฀ on฀ the฀ migrating GBs, thus increasing the activation energy to that for GB or volume diffusion,฀depending฀on฀the฀GB฀type.฀The฀inite฀mobility฀of฀GB฀vertices,52 which is diffusion governed, may also be a factor that connects GB diffusion to GB migration. In conclusion, while MD simulations have revealed many details of the structural properties of GBs, the full picture is far from complete. There is still no consensus฀ on฀ the฀ difference฀ between฀ GBs฀ in฀ NC฀ materials฀ and฀ their฀ coarsegrained equivalents. The details of the atomistic mechanisms of GB diffusion and migration and their relation at elevated temperatures are not yet clear and require more studies. A thermodynamic picture of GB melting based on heterophase fluctuations in a constrained system has yet to emerge.

15.3

Deformation mechanisms in nanoscale grains

Most of the deformation mechanisms known to operate in coarse-grained metals are฀also฀found฀in฀NC฀metals.฀What฀is฀notable฀though,฀is฀the฀striking฀difference฀in฀ the regimes at which these mechanisms operate in a nanograin compared to a large฀ micron-size฀ grain,฀ and฀ in฀ the฀ intrinsic฀ relation฀ and฀ competition฀ between฀ these mechanisms, which result in unique mechanical properties. The key to the mechanical฀behavior฀of฀NC฀metals฀lies฀in฀their฀speciic฀microstructure฀consisting฀ of small grains of crystalline matter embedded inside a dense GB network. Consequently,฀ the฀ intragranular฀ processes฀ such฀ as฀ dislocation฀ slip฀ or฀ lattice฀

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diffusion are suppressed or have to compete with the enhanced GB-mediated mechanisms฀ such฀ as฀ GB฀ sliding฀ and฀ GB฀ diffusion.฀ Beneitting฀ from฀ the฀ small฀ grain฀size฀of฀NC฀metals,฀MD฀simulations฀proved฀to฀be฀very฀eficient฀in฀capturing฀ the฀ mechanical฀ properties฀ of฀ these฀ materials฀ and฀ in฀ the฀ study฀ of฀ their฀ speciic฀ deformation mechanisms at atomic level.

15.3.1 Grain sliding Grain฀sliding฀is฀found฀in฀a฀large฀number฀of฀MD฀simulations฀of฀NC฀metals฀both฀at฀ low temperatures (T < 0.3Tm)24,26,53 and at elevated temperatures (T > 0.5Tm).17 At present,฀there฀is฀a฀irm฀consensus฀among฀researchers฀that฀GB฀sliding฀is฀an฀important฀ deformation฀mode฀in฀NC฀metals,฀but฀the฀debate฀continues฀regarding฀its฀nature฀and฀ the underlying atomistic mechanism. Two opinions have been introduced: 1) GB sliding is a result of ‘atomic shuffling’ and ‘stress-assisted free-volume migration’,53 and 2) GB sliding is due to GB diffusion,17 which at low T involves individual movement of vacancies and interstitials or collective motion of small clusters of atoms.44 At high T, sliding is assisted by volume diffusion through the premelted GB layer.17 The difference between 1) and 2) is that while diffusion is a randomwalk process, the stress-assisted migration is a directed movement in response to the applied load. The latter is mostly reported in low- or room-temperature models where฀ diffusion฀ is฀ too฀ slow฀ to฀ accommodate฀ deformation฀ at฀ the฀ extremely฀ high฀ strain rates of 107 s–1 inherent in MD simulations.53 Sliding through GB diffusion (Fig. 15.2) has been unambiguously demonstrated in simulations performed at high temperatures฀as฀an฀accommodation฀mechanism฀for฀Coble฀creep.17 In฀coarse-grained฀metals,฀this฀type฀of฀GB฀sliding฀is฀known฀as฀Lifshitz฀sliding.54 The focus of debate is how reliably the diffusion-governed GB sliding at high temperatures฀can฀be฀extrapolated฀to฀low฀temperatures฀and฀low฀strain฀rate฀of฀the฀ order฀of฀the฀typical฀experimental฀values฀of฀10–1 to 102 s–1. It is still a challenge for MD simulations to probe low-temperature–low-strain-rate regimes and to give a deinitive฀answer฀to฀this฀question.

15.3.2 Diffusion creep The฀role฀of฀diffusion฀creep฀as฀a฀possible฀deformation฀process฀in฀NC฀materials฀is฀ currently under debate, with several conflicting reports arising from both the experimental฀and฀computer฀simulation฀communities.฀Gleiter,55฀who฀irst฀proposed฀ this฀notion,฀rationalized฀that฀the฀abundance฀of฀GBs฀together฀with฀the฀absence฀of฀ conventional฀ dislocation฀ activity฀ would฀ result฀ in฀ plasticity฀ localized฀ in฀ the฀ GB฀ regions, namely diffusion and sliding, even at ambient temperatures. So฀far,฀MD฀simulation฀indings฀on฀diffusion฀creep฀in฀NC฀metals฀were฀reported฀ only at temperatures that are close to the melting point of the material (T > 0.8 Tm).16,17 Simulations at lower temperatures24,26,53 report GB sliding as a dominant deformation mode.

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15.2 Atomic structure simulation snapshot of 8 nm size grains at 4% deformation during Coble creep at T = 1200 K in Pd. Strips of black lines, initially drawn in parallel at the beginning of the simulation, are used to monitor the deformation. The line offsets, seen at the GBs indicate GB sliding that has taken place to accommodate the diffusion creep. For clarity, only the GB and the strip atoms are visualized.

Molecular dynamics (MD) simulations of Si16 and fcc Pd17฀on฀idealized฀threedimensional฀microstructures฀have฀clearly฀captured฀steady-state฀Coble฀creep.฀The฀ microstructures for these simulations were carefully chosen to consist of grains with฀uniform฀size฀and฀shape฀thus฀eliminating฀the฀topological฀driving฀force฀for฀grain฀ growth. The grains were randomly misoriented to form high-energy, structurally disordered GBs of uniform diffusivity as discussed in Section 15.2.2. During uniaxial฀loading,฀Coble฀creep฀was฀evidenced฀by฀several฀key฀signatures฀including:฀ 1) equal activation energies for both the strain rate and GB diffusion, 2) the deformation was homogeneous over the entire simulation cell, and 3) observation of฀ the฀ accommodating฀ Lifshitz-sliding฀ mechanism54 (Fig. 15.2). The strain rate dependence฀ on฀ stress฀ and฀ grain฀ size฀ was฀ also฀ consistent฀ with฀ the฀ Coble฀ creep฀ formulation56฀after฀taking฀into฀account฀the฀inite฀width฀of฀the฀diffusive฀GB฀layer.17 Recent MD simulations22,57฀in฀NC฀Mo฀(of฀body-centered฀cubic฀(bcc)฀structure)฀ showed฀ the฀ unexpected฀ result฀ of฀ creep฀ via฀ lattice฀ diffusion฀ (Nabarro–Herring฀

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creep58) and enhanced by GB-assisted vacancy nucleation. The observation of bulk self-diffusion facilitated by GB-nucleated vacancies opens up interesting possibilities for future atomistic studies of the role of vacancies and interstitials on the mechanical properties of materials that have traditionally been thought of as inaccessible by MD simulation.

15.3.3 Dislocation slips The฀role฀of฀dislocations฀in฀the฀deformation฀of฀NC฀metals฀has฀been฀a฀central฀focus฀of฀ interest. This interest was mainly driven by the numerous, and in many cases controversial, reports on the break down of the Hall–Petch hardening effect at grain sizes฀below฀20฀nm,฀which฀is฀replaced฀by฀softening,฀known฀as฀an฀inverse฀Hall–Petch฀ effect (as reviewed in3).฀It฀is฀believed฀that฀a฀modiied฀dislocation–GB฀interaction฀ mechanism฀in฀NC฀metals฀is฀responsible฀for฀reversing฀of฀the฀Hall–Petch฀effect. In฀MD฀simulations฀of฀fcc฀metals฀(Cu,13,14 Ni34)฀of฀very฀small฀grain฀sizes฀> 1 are active in generating dislocations using GBs as nucleation sites (Fig. 15.3 (a)) and deformed mainly through฀ dislocation฀ slip.฀As฀ the฀ grain฀ size฀ approaches฀ the฀ size฀ of฀ the฀ splitting฀ stacking fault, d/r ≈ 1 (Fig. 15.3 (b)), the dislocation activity decreases. Grains with d/r < 1 (Fig. 15.3 (c)) soon become saturated by stacking faults which suppress dislocation motion and prevent further dislocation nucleation. These grains continue to deform mainly through GB mechanisms. Figure 3 (d) presents partial dislocation emission in a larger grain of a material of very low SFE,฀ characterized฀ by฀ d/r < 1. The situation is similar to Fig. 15.3 (c). After saturating the grains with stacking faults, the dislocation activity ceases. Taken together, Figs. 15.3 (c) and 15.3 (d) illustrate the parallel between the deformation modes in small grains of high SFE (Fig. 15.3 (c)) and large grains of low SFE (Fig. 15.3 (d)). This parallel suggests the notion of the splitting distance as a length scale parameter.

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d = 32; ESF = 120

15.3 Atomistic snapshots revealing dislocation processes in a nanocrystalline simulation model of grains of different size, d (in nm), and stacking fault energy, ESF (in mJ/m2). (a) Continuous GB emission of full dislocations (1) governs the deformation in a large grain. (b) In grains of size approaching the size of the splitting stacking fault (2), which separates the two partial dislocations (1a) and (1b), the dislocation slip is suppressed. In (c) and (d) an analogy between a material of small d and high ESF, and a material of large d and low ESF is demonstrated.

The concept of the splitting distance as a length scale in the deformation properties฀ of฀ NC฀ fcc฀ metals฀ was฀ generalized฀ in฀ a฀ deformation-mechanism฀ map61 in terms of reduced units of stress, σ/σ∞,฀vs.฀inverse฀grain฀size,฀ro/d. The parameters, σ∞ and ro, are the theoretical shear strength limit and the equilibrium splitting distance of the material. The deformation map captures the transition from dislocation to GB-based deformation processes and the transition from conventional to partial slip as observed in the simulations.

15.3.4 Deformation twinning One important result from MD simulation studies of the deformation behavior of NC฀Al฀that฀was฀corroborated฀by฀experiments฀was฀the฀initiation฀of฀deformation฀ twinning.19–21฀Twins฀ start฀ to฀ appear฀ in฀ nanograins฀ of฀ size฀ larger฀ than฀ 40฀ nm฀ at฀ relatively฀high฀strain฀(>8%).฀Two฀mechanisms฀of฀twin฀nucleation฀were฀initially฀ identiied:฀heterogeneous฀nucleation฀from฀GBs฀by฀coordinated฀emission฀of฀partial฀ dislocations and homogeneous nucleation by overlapping of stacking faults conined฀by฀the฀dense฀GB฀network฀in฀the฀nanocrystal.20

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In view of the classic understanding of deformation twinning (see62) as a phenomenon฀ limited฀ to฀ relatively฀ large฀ grain฀ size฀ (>10฀ µm)฀ and฀ materials฀ with฀ relatively฀low฀SFE,฀such฀as฀Cu,63฀these฀observations฀for฀NC฀Al฀were฀very฀unexpected.฀ However,฀ previous฀ simulations฀ for฀ NC฀ Cu฀ had฀ already฀ shown฀ the฀ emission฀ of฀ extrinsic฀stacking฀faults฀from฀GBs฀early฀in฀the฀deformation฀process,64 but they did not show the development of deformation twinning during the later stages of the deformation฀ because฀ of฀ the฀ small฀ grain฀ size฀ to฀ which฀ these฀ simulations฀ were฀ limited. Deformation฀twinning฀in฀NC฀Al฀has฀been฀conirmed฀experimentally,30,31 and several฀additional฀twinning฀mechanisms฀in฀NC฀metals฀have฀been฀recently฀found.65 Similar฀indings฀have฀been฀reported฀for฀other฀fcc฀metals,฀such฀as฀Cu66 and Ni.67 Of particular interest is the report by Rösner et al.68 of similar deformationtwinning processes in another high-SFE fcc metal, Pd. A comparison between the Al30 and Pd68฀experiments฀with฀the฀Al฀MD฀simulations19–21 showed similarities in the way that deformation twins formed. However, in contrast to the MD simulations, in both Pd and Al, twins were found to form on only one slip plane per฀ grain;฀ thus,฀ the฀ twins฀ were฀ always฀ coplanar฀ within฀ each฀ grain.฀As฀ one฀ slip฀ plane is not enough to accommodate a general deformation, an additional deformation mechanism is required. Rösner et al. suggested that grain rotation would allow the grains to orient their active twin plane along the principal shear direction. By contrast, the MD simulations21 indicated the appearance of twin networks where two twin planes operate on an equal basis. A possible reason for this might be the much higher strain rates in the MD simulations compared to the experimental฀studies. The฀effect฀of฀twinning฀on฀the฀mechanical฀properties฀of฀NC฀metals฀can฀be฀twofold. During early deformation, when the grain interiors are practically free of dislocations, twinning can facilitate deformation by additional slip systems or by assisting฀ the฀ transfer฀ between฀ existing฀ slip฀ systems฀ through฀ dislocation–twin฀ reactions. Once twins have formed, they can repel certain types of gliding dislocations and give rise to pile-ups with consequent strain hardening of the material.

15.3.5 The strongest size: competition between different deformation modes The well known and almost universal Hall–Petch relation, stating that the yield strength of a polycrystal is inversely proportional to the square root of the grain size,฀suggests฀that฀NC฀materials฀should฀acquire฀very฀high฀strength฀approaching฀ the฀theoretical฀strength฀of฀a฀perfect฀crystal.฀Though฀in฀general,฀NC฀metals฀show฀ much higher strength than their coarse-grained versions – more than an order of magnitude in some cases – theoretical strength is never attained. The reason is the breakdown of the Hall–Petch hardening effect observed below a certain grain size.฀ The฀ underlying฀ reason฀ for฀ this฀ breakdown฀ is฀ the฀ increased฀ role฀ of฀ the฀ GB-mediated฀deformation฀processes.฀Ultimately,฀the฀overall฀strength฀is฀a฀result฀of฀

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a competition between intragranular deformation mechanisms that provide hardening, and intergranular mechanisms that provide softening of the material. This reasoning, formulated by S. Yip,23฀leads฀to฀the฀conclusion฀of฀the฀existence฀of฀ a characteristic length at which both softening and hardening mechanisms are equally฀strong.฀A฀polycrystal฀of฀that฀grain฀size,฀‘the฀strongest฀size’,23 would have the highest practically achievable mechanical strength. Two MD simulation studies on fully 3D microstructures25,26 have been performed฀to฀capture฀the฀full฀range฀of฀grain฀sizes฀over฀which฀the฀crossover฀from฀ dislocation to GB mediated deformation takes place and, thus, to elucidate the nature฀ of฀ the฀ ‘strongest฀ grain฀ size’,฀ dc,฀ in฀ NC฀ fcc฀ metals.฀ The฀ irst฀ of฀ these฀ studies,25฀ considered฀ NC฀ Al฀ microstructures฀ consisting฀ of฀ four฀ grains฀ in฀ a฀ periodically฀repeated฀simulation฀cell.฀This฀simple฀setup฀enabled฀exploration฀of฀a฀ range฀of฀grain฀sizes฀from฀7–32฀nm,฀thus฀incorporating฀sizes฀below฀and฀above฀dc for Al, and allowing the transition from GB-dominated processes (for d < dc) to dislocation-dominated processes (for d > dc) to be probed. These simulations have demonstrated directly the coupling between the crossover in the deformation mechanism and the resulting mechanical behavior. In addition to yielding a value of dc ~ 18 nm for Al, these simulations showed unambiguously that the crossover in the mechanical behavior is, indeed, due to a transition in the dominant deformation process. These simulations, also, related dc to the splitting distance, r, as discussed in the previous section (15.3.4). In฀ the฀ second฀ study,฀ Schiotz฀ and฀ Jacobsen26 determined the flow stress of NC฀Cu฀with฀grain฀sizes฀ranging฀between฀5฀and฀50฀nm.฀These฀simulations฀revealed฀ the฀ expected฀ crossover฀ in฀ the฀ low฀ stress,฀ from฀ normal฀ to฀ inverse฀ Hall–Petch฀ behavior, at a value of dc฀~14฀nm฀for฀Cu.฀As฀in฀Yamakov฀et al.,25 this crossover in the mechanical behavior was accompanied by a change in the underlying mechanism from dislocation-mediated plasticity, dislocation slip and deformation twinning, to GB sliding.

15.4

Grain growth and microstructure evolution in NC metals

Due฀to฀the฀extremely฀small฀grain฀size,฀NC฀metals฀are฀inherently฀unstable฀against฀ grain growth (GG). In these materials, GG is not limited to high-temperature conditions but can occur even at relatively low temperature.69 Since the mechanical properties฀of฀NC฀metals฀are฀strongly฀dependent฀on฀the฀grain฀size,฀they฀are฀very฀ sensitive฀to฀GG.฀For฀this฀reason,฀it฀is฀of฀signiicant฀practical฀importance฀to฀study฀ GG and to determine the factors that have an influence on it. Experimental฀ studies฀ on฀ NC฀ GG฀ are฀ dificult฀ to฀ perform฀ because฀ of฀ the฀ substantial฀ problems฀ in฀ fully฀ characterizing฀ NC฀ microstructures฀ and฀ their฀ evolution.฀ For฀ example,฀ Malow฀ and฀ Koch70฀ have฀ studied฀ GG฀ in฀ NC฀ Fe฀ using฀ X-ray฀diffraction฀to฀determine฀the฀grain฀size฀by฀the฀broadening฀of฀the฀diffraction฀ peaks. To ensure that the internal lattice strain, which also causes peak broadening,

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does฀not฀affect฀the฀measurements,฀the฀estimated฀grain฀size฀had฀to฀be฀conirmed฀by฀ TEM.฀ Since฀ thin฀ metallic฀ ilms฀ make฀ it฀ easier฀ to฀ measure฀ grain฀ size,฀ NC฀ GG฀ experiments฀are฀mostly฀performed฀on฀NC฀thin฀ilms.71,72 Theoretical studies of GG฀ encounter฀ considerable฀ complexities฀ in฀ fully฀ accounting฀ for฀ the฀ dynamic฀ topological features of evolving microstructures. These฀dificulties฀have฀led฀to฀extensive฀simulation฀studies฀on฀grain฀growth.฀The฀ need to include large number of grains in statistically representative simulated systems required the use of mesoscale types of models (Potts models, front-tracking models,฀phase-ield฀models,฀etc.฀reviewed฀in11), which consider the microstructure at the level of grains and GBs rather than at the level of atoms. While highly computationally฀eficient,฀these฀models฀require฀an฀input฀of฀prescribed฀parameters฀ such฀as฀GB฀and฀vertex฀mobility,฀GB฀energy,฀etc.฀that฀may฀not฀be฀known฀a priori. The unaccounted effects of additional GG mechanisms or GG driving forces, not incorporated in the mesoscale models, may lead to qualitatively false predictions. The ability of atomistic simulations to generate GG driving forces through atomic interactions provides a fundamental understanding of the GG processes, which is not possible in the mesoscale models. The combined effect of a relatively small number฀of฀atoms฀per฀grain฀and฀a฀high฀driving฀force฀due฀to฀extremely฀small฀grain฀ size,฀ makes฀ the฀ observation฀ of฀ GG฀ at฀ MD฀ time฀ and฀ length฀ scales฀ possible.฀ At฀ present,฀ NC฀ materials฀ are฀ the฀ only฀ systems฀ where฀ GG฀ can฀ be฀ studied฀ by฀ MD฀ simulations.

15.4.1 Grain growth due to grain-boundary migration As in coarse-grained metals, curvature-driven grain-boundary migration, i.e. the motion of GBs towards the center of their curvature,73,74 is also a dominant GG mechanism฀in฀NC฀metals.฀The฀driving฀force฀for฀such฀GG฀is฀proportional฀to฀the฀ GB curvature, which for a given grain diameter, d, is of the order of 1/d. This makes฀GG฀very฀active฀in฀NC฀materials.฀In฀idealized,฀fully฀dense฀and฀impurityfree microstructures at temperatures close to the melting point where GB mobility is฀maximal,฀GG฀is฀fast฀enough฀to฀be฀observed฀and฀successfully฀studied฀by฀MD฀ simulations on a timescale of 1 to 10 ns. This has been demonstrated in a series of papers by Haslam et al.75–78฀in฀NC฀Pd.฀A฀system฀of฀25฀grains฀of฀average฀d฀=฀15฀ nm75 has been simulated at T฀=฀0.95฀Tm for the period of 10 ns system evolution time. As a result of the GG, only 9 grains remained at the end of the simulation. The฀ MD฀ model฀ has฀ been฀ reproduced฀ by฀ a฀ mesoscale฀ kinetic฀ Monte฀ Carlo฀ GG฀ simulation,76฀where฀the฀GB฀mobility฀and฀GB฀energy฀parameters฀were฀extracted฀ from the MD simulation. The good agreement between the two models in reproducing฀similar฀topological฀patterns฀in฀the฀microstructure฀evolution฀conirmed฀ the฀GG฀mechanism฀through฀curvature-driven฀migration.฀This฀provides฀an฀example฀ of a bottom-up multiscale approach where an atomistic simulation is used to provide parameters for a continuum-level model. In addition, the MD simulation revealed a series of processes taking place at the GBs and in the grain interiors

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during GG. Some of these processes, such as production of residual dislocations in the grains from GB disintegration, were a result of GG.77 Others, such as grain rotation and grain coalescence,75,76 present additional mechanisms of GG, which will฀be฀discussed฀in฀the฀next฀subsection. An important question to be addressed by MD simulations is ‘What is the activation฀energy฀of฀GG?’฀The฀expected฀answer,฀based฀on฀experimental฀evidence฀ that relates the activation energy of GG to that of GB or lattice diffusion, may not฀ be฀ trivial฀ in฀ view฀ of฀ the฀ indings฀ for฀ the฀ GB-migration฀ activation฀ energy฀ in impurity-free MD simulations. As discussed in Section 15.2.3, the activation energy of GB migration was found to be substantially lower than that of GB diffusion, suggesting non-diffusion-related GB migration mechanisms.46,47 To address this issue and to evaluate the activation energy of curvature-driven GG,฀an฀idealized฀MD฀model฀of฀a฀polycrystal฀of฀bimodal฀grain฀size฀distribution฀ was used.79 In this model, four-sided square grains were embedded between eight-sided octagonal grains. At high temperature, T > 0.8 Tm, all GBs were of uniform diffusivity and mobility, representing an isotropic system. As expected฀ from฀ the฀ von฀ Neumann–Mullins฀ rule,80 the octagonal grains grow at the฀ expense฀ of฀ the฀ square฀ grains.฀ The฀ activation฀ energy฀ of฀ the฀ grain฀ growth฀ process was found to be equal to the GB diffusion activation energy. This result suggested that while migration of a single GB may not involve diffusion, GG in a polycrystal is diffusion assisted. One possible role of diffusion is to accommodate฀ the฀ excess฀ free฀ volume฀ generated฀ during฀ GG฀ (because฀ of฀ the฀ decreasing GB network, the density of the polycrystal increases). Alternatively, GB฀ diffusion฀ might฀ be฀ related฀ to฀ the฀ vertex฀ mobility,฀ which฀ can฀ be฀ the฀ rate฀ limiting mechanism for GG.52

15.4.2 Grain growth due to grain rotation and grain coalescence A฀ novel฀ mechanism฀ for฀ GG,฀ speciic฀ for฀ NC฀ materials฀ and฀ shown฀ by฀ MD฀ simulations, is grain coalescence due to grain rotation. In this mechanism, the driving force results from the dependence of the GB energy on the misorientation angle. This dependence creates a torque to rotate the grain to form less energetic GBs. When two grains assume the same orientation, they coalesce to form a single฀ larger฀ grain.฀ This฀ process฀ is฀ found฀ in฀ NC฀ materials81,82 due to their extremely฀ small฀ grain฀ size,฀ resulting฀ in฀ relatively฀ high฀ grain฀ mobility฀ towards฀ rotation.83 The mechanism of grain-rotation coalescence results in a power-law grain growth with time t, given as d ~ tν,฀with฀a฀universal฀scaling฀exponent,฀ν. A combined theoretical and simulation study84 demonstrated that the value of this exponent฀depends฀on฀the฀assumed฀mechanism฀by฀which฀the฀grain฀rotations฀are฀ accommodated, being ν฀=฀1/4,฀for฀GB฀diffusion,฀or฀ ν฀=฀1/3,฀for฀lattice฀diffusion฀ accommodated฀grain฀rotation,฀respectively.฀For฀comparison,฀the฀growth฀exponent฀ for isotropic curvature-driven GG is ν฀=฀1/2.

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15.4.3 Deformation-driven grain growth Experimental฀ studies฀ on฀ superplastic฀ deformation฀ of฀ both฀ metallic85,86 and ceramic87฀materials฀have฀shown฀that฀high-temperature฀deformation฀of฀ine-grained฀ polycrystals generally enhances the rate of GG compared to that at thermal annealing. This enhancement phenomenon is known as dynamic GG. As an extreme฀case฀of฀ine-grained฀materials,฀NC฀materials฀were฀also฀found฀to฀experience฀ dynamic฀ GG฀ under฀ various฀ conditions฀ including฀ uniaxial฀ tension88,89 and compression,90 high-pressure torsion91,92 and nanoindentation.93 A comprehensive MD simulation analysis of the relation between GG and deformation has been performed in two consecutive papers by Haslam et al.77,78 The฀irst฀paper,77 described the effect of deformation on the enhancement of the GG in฀a฀25฀grain฀NC฀model฀of฀Pd฀as฀compared฀to฀GG฀in฀the฀same฀microstructure฀under฀ thermal annealing.75,76 The second paper,78 considered the converse effect of GG on deformation,฀ identiied฀ as฀ Coble฀ creep฀ in฀ this฀ particular฀ model.฀ Based฀ on฀ the฀ analysis, detailed in,77,78 mechanisms of deformation-accelerated GG were found to be: stress-enhanced GB migration, stress-induced grain rotation, dislocationassisted grain rotation, and dislocation emission due to grain coalescence. An example฀ of฀ the฀ relationship฀ between฀ some฀ of฀ these฀ mechanisms฀ is฀ presented฀ in฀ Fig. 15.4. The combined operation of GB-diffusion creep and GB-diffusion-assisted grain rotation resulted in splitting a grain in two parts, followed by a grain switching

15.4 Overall evolution of a MD-simulated Pd microstructure at σ = 0.6 GPa and T = 1200 K performed by Haslam et al.77,78 (unpublished figure). (a) Initial configuration. (b) Diffusion creep elongates grain B. (c) Stress-induced grain rotation separates grain B in two. (d) Neighborswitching event between grains A, B1, B2, and C is taking place according to the