Messerschmidt U. Dislocation Dynamics During Plastic Deformation

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Ulrich Messerschmidt

Dislocation Dynamics

During Plastic Deformation

123

With291 Figures and 56 Video Sequences

Professor Dr. Ulrich Messerschmidt

Guest Scientist at Max Planck Institute of Microstructure Physics

Weinberg 2, 06120 Halle (Saale), Germany

E-mail: um@mpi-halle.de

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Springer Series in Materials Science ISSN 0933-033X

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Preface

Very many structural materials like metals and ceramics are of crystalline

nature. Under most of the conditions, they undergo plastic deformation before

they fail under load. The plastic deformation is mediated by the genera-

tion and motion of one-dimensional crystal defects, the so-called dislocations.

Thus, the density and dynamic properties of the dislocations determine the

plastic behavior of the respective materials and frequently also their failure.

The dislocation dynamics, that is, the response of the dislocations to an exter-

nal load, is controlled by the interaction between the moving dislocations

with the periodic crystal lattice structure, other crystal defects from point

defects over small clusters to larger precipitates, with other dislocations form-

ing a microstructure through which the mobile dislocations have to move,

and ﬁnally the grain and phase structure of the material. Considering these

diﬀerent interactions, the dislocation motion turns out to be quite a complex

process.

In situ straining experiments in a transmission electron microscope are

a powerful means for studying the microprocesses controlling the dislocation

mobility. With this method, dislocations can directly be observed during their

motion under load. The technique advanced when high-voltage electron micro-

scopes became commercially available at the end of the 1960s, ﬁrst in Japan

and later on also in other countries. These microscopes enable the transmis-

sion of thicker specimens, which have properties similar to macroscopic bulk

specimens. Besides, they oﬀer suﬃcient room for elaborate deformation stages

in the specimen chamber. In the last 30 years, in situ straining experiments

were performed on many materials, both in conventional and in high-voltage

electron microscopes. The present author and his coworkers performed such

experiments over about 30 years, yielding many hours of video recordings of

dislocation motion.

This book gives an introduction into the processes controlling the dislo-

cation dynamics and its role in crystal plasticity. It is divided into two parts.

Part I describes the general properties of dislocation motion in an introductory

way suited also for students without prior knowledge in dislocation properties.

VI Preface

“Dislocations” in a mowed lawn (solarized)

It is based on lectures given in the Physics Department of the Martin

Luther University in Halle (Saale). For easy understanding, the mathe-

matical treatment is presented on a simple level. In Part II, particular

materials are discussed covering semiconductors, ceramic single crystals, met-

als, and alloys including intermetallic alloys and quasicrystals. The whole

text is, whenever possible, illustrated by electron micrographs, partly of

dislocations under load taken during in situ straining experiments in a high-

voltage electron microscope. Besides, video ﬁles can be downloaded from

http://extras.springer.com/2010/978-3-642-03176-2 presenting characteristic

video sequences of moving dislocations. The videos are commented in the

chapters of Part II but are referred to also in Part I. The presentation of

the diﬀerent materials is not exhaustive but intended to explain the processes

shown in the videos. It is a main aim of this work to make the video sequences

available to a greater number of scientists and lecturers.

The experimental work frequently referred to in this book and exploited

for the video clips was carried out in the Institute of Solid State Physics and

Electron Microscopy of the Academy of Sciences of the GDR in Halle (Saale)

and since 1992 in the Max Planck Institute of Microstructure Physics at the

same place. The author is very grateful to all responsible directors, that is,

the late Heinz Bethge, Volker Schmidt, and J¨urgen Kirschner, for creating the

experimental and collaborative environment for these studies. The continuous

high-quality performance of the high-voltage electron microscope was essen-

tially due to Christian Dietzsch. The author acknowledges the contributions

Preface VII

of many scientists to the experiments and interpretations; ﬁrst of all to Fritz

Appel for the work on NaCl, MgO, and some metals, and Martin Bartsch

for the studies on all other materials. He had an essential inﬂuence on the

experiments and the instruction of the PhD students and post-doctoral fel-

lows who worked in projects funded by the Deutsche Forschungsgemeinschaft

and the Volkswagenstiftung. He also saved the original video recordings in

digital form and helped to collect data for the book, and he discussed its con-

tents. Many other scientists were involved in the experiments. Their names are

listed below.

J¨urgen Kirschner supported the preparation of the book after

my retirement. Hans-Rainer Trebin, Boris V. Petukhov, Wolfgang Blum, Hart-

mut Leipner, and Ichiro Yonenaga discussed special topics or helped ﬁnding

suitable references. Video clips were made available by Daniel Caillard and

Volker Mohles. The author is very grateful for all these contributions. The

English of the text was kindly revised by Heike Messerschmidt.

Halle (Saale) Ulrich Messerschmidt

December 2009

Part of the experimental work was carried out by the PhD students and post-

doctoral fellows Susanne Guder, Anna Wasilkowska, Dietmar Baither, Bernd

Baufeld, Ralf Haush¨alter, Dietrich H¨aussler, Bert Geyer, Ludwig Junker, Lars

Ledig, and Aleksander Tikhonovski. Several studies were performed in close

collaboration with other laboratories. In this respect, I thank the late Peter

Haasen, Manfred R¨uhle, Knut Urban, Toru Imura, Masaharu Yamaguchi, Eck-

hard Nembach, Bernd Reppich, Gerhard Sauthoﬀ, Eduard M. Nadgornyi, Peter J.

Wilbrandt, Markus Wollgarten, Michael Feuerbacher, Peter Schall, Mark Aindow,

Ian Jones, Hiro Saka, Yoichi Nishino, Christina Scheu, Easo P. George, Witold

Zielinski, and Michael Mills. Further names will be found in the references.

Contents

Part I General Properties of Dislocation Motion

1 Introduction ............................................... 3

1.1 TheoreticalYieldStrength................................ 4

1.2 PlasticShearby the Motionof Dislocations................. 5

2 Experimental Methods .................................... 11

2.1 MacroscopicDeformationTests ........................... 11

2.2 StressPulse Double Etching Technique..................... 16

2.3 TransmissionElectronMicroscopy ......................... 18

2.4 In Situ Straining Experiments in the Transmission Electron

Microscope ............................................. 20

2.5 OtherMethods.......................................... 26

2.5.1 X-Ray Topography In Situ Deformation Experiments . . 27

2.5.2 SurfaceStudiesofSlipLines........................ 27

2.5.3 InternalFriction................................... 29

2.5.4 NuclearMagneticResonance........................ 33

3 Properties of Dislocations ................................. 35

3.1 GeometricProperties .................................... 35

3.1.1 BurgersVector.................................... 35

3.1.2 Glide and ClimbMotion ofaDislocation ............. 37

3.1.3 Relation Between Dislocation Motion

andPlasticStrainandStrainRate .................. 39

3.2 ElasticPropertiesofDislocations.......................... 40

3.2.1 StressFields ofStraightDislocations................. 41

3.2.2 DislocationEnergy ................................ 43

3.2.3 ForcesonDislocations ............................. 47

3.2.4 Interaction BetweenParallelDislocations............. 50

3.2.5 Interaction Between Nonparallel Dislocations . . . . . . . . . 52

XContents

3.2.6 Elastic Interaction Between Dislocations

andElasticInclusions.............................. 54

3.2.7 Bowed-OutDislocations............................ 57

3.3 DislocationsinCrystals .................................. 65

3.3.1 SelectionofBurgersVectors ........................ 66

3.3.2 StackingFaultsandPartialDislocations.............. 66

3.3.3 Twins............................................ 70

3.3.4 Antiphase Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4 Dislocation Motion ........................................ 73

4.1 ThermallyActivatedOvercomingofBarriers................ 74

4.2 LatticeFriction ......................................... 78

4.2.1 Peierls–NabarroModel............................. 79

4.2.2 Double-KinkModel................................ 83

4.2.3 Characteristics and Experimental Evidence

oftheDouble-KinkModel.......................... 92

4.3 SlipandCrossSlip ...................................... 93

4.4 TheLocking–UnlockingMechanism........................ 99

4.5 OvercomingofLocalizedObstacles ........................101

4.5.1 FriedelStatistics ..................................103

4.5.2 MottStatistics....................................110

4.6 Transition from the Double-Kink Mechanism

tothe OvercomingofLocalizedObstacles ..................113

4.7 OvercomingofExtendedObstacles ........................116

4.8 DislocationIntersections .................................126

4.9 Dislocation Motion at High Velocities

andLowTemperatures...................................129

4.10 DislocationClimb .......................................132

4.10.1 Point Defect Equilibrium Concentrations . . . . . . . . . . . . . 132

4.10.2 ClimbForces .....................................134

4.10.3 Emission-orAbsorption-controlledClimb ............137

4.10.4 Diﬀusion-controlledClimb..........................140

4.10.5 Jog Dragging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

4.11 DragForcesdue toPointDefectAtmospheres...............143

4.12 Dynamic Laws of Dislocation Mobility . . . . . . . . . . . . . . . . . . . . . 150

5 Dislocation Kinetics, Work-Hardening, and Recovery ......155

5.1 DislocationKinetics .....................................155

5.1.1 ModelsofDislocationGeneration....................156

5.1.2 Experimental Evidence of Dislocation Generation. . . . . . 162

5.1.3 Dislocation Immobilization and Annihilation . . . . . . . . . . 166

5.2 Work-HardeningandRecovery ............................171

5.2.1 Work-HardeningModels............................172

5.2.2 Thermal and Athermal Components

oftheFlowStress .................................180