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Structure and Mechanical Properties of Fe-Mn

Alloys


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Structure and Mechanical Properties of Fe-Mn

Alloys

By

Xin Liang, B.Eng.

A Thesis

Submitted to the School of Graduate Studies

in Partial Fulfilment of the Requirements

for the Degree of

Master of Applied Science

McMaster University

Copyright by Xin Liang, July 2008


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Master of Applied Science (2008) McMaster University

(Materials Science and Engineering) Hamilton, Ontario

TITLE: Structure and Mechanical Properties of Fe-Mn Alloys

AUTHOR: Xin Liang, B.Eng.

(University of Science and Technology Beijing)

SUPERVISORS: Professor J.D. Embury, Dr. H.S. Zurob

and Dr. J.R. McDermid

NUMBER OF PAGES: xxii, 254

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ABSTRACT

Materials for automobile applications need both the high strength and good

ductility. A combination of these beneficial mechanical properties requires sustained

high strain hardening rate throughout the course of plasticity. Fe-Mn alloys are a

good example of demonstrating such exceptional mechanical behaviour, and thus

become an attractive research subject in both the academic fields and industry. In

the present work, structure of the Fe-24Mn and Fe-30Mn alloys were investigated and

characterized, and their mechanical properties were evaluated.

Fe-30Mn possesses a single phase austenitic structure and its work hardening

behaviour at room temperature can be interpreted by applying the Kocks and Meck-

ings model. The persistent high work hardening rate of Fe-30Mn is attributed to its

low stacking fault energy (SFE). The mechanical behaviour of Fe-30Mn at 77 K is

understood by taking into account both a reduced SFE and introduction of strain

induced phase transitions at the late stage of deformation.

It has been shown that Fe-24Mn starts with a complex microstructure which

has approximately 50% of martensite. The stress strain behaviour presents a

pronounced elastic-plastic transition stage and much higher level of flow stress than

Fe-30Mn. This behaviour is essentially due to a co-deformation process of austenite

and martensite, and in the current work, we used an Iso-work model to analyze the

plasticity of Fe-24Mn at both 293 and 77 K.

Furthermore, we also evaluated the fracture behaviour of the two alloys at 293

and 77 K. It has been found that the fracture process of Fe-30Mn appears to be strain

limited, whereas that of Fe-24Mn appears to be dominated by a critical fracture stress.

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The austenite in both the Fe-24Mn and Fe-30Mn alloys are found to be ther-

mally stable, as no appreciable martensitic phase transformation occurs whencooled down to 77 K.

In addition, the large deformation behaviour by plane strain compression for

both alloys was also studied, but to a limited extent.

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ACKNOWLEDGEMENT

Two years of my master program is approaching the end, and it is hard to

believe that time flies so fast. I could not have completed this thesis without the

help from many people, and my first and foremost thanks go to my supervisors:

Professor David Embury, Dr. Hatem Zurob and Dr. Joseph McDermid.

It has been greatly fortunate for me to be under the supervision of Profes-

sor David Embury, and I am sincerely indebted to him for all his guidance, advice,inspiration and encouragement over the past two years. His incredible knowledge and

deep insight in the field of materials science always made his suggestions most valu-

able. I am greatly impressed by his devotion to materials science and his dedication

to teaching and advising me. He was always available when I had questions, and I

always got a reply from him. Instead of giving me the answer directly, he inspired

me to think and guided me to find the correct answer. In this way, he taught me

the methods of learning and discovering the fantastic world of materials science. It

has always been an enjoyable experience to have those inspiring discussions with him,

through which I was learning how to critically and creatively conduct research. He

cared for my way of thinking and analyzing the problem even more than the progress

of the project. It has been a very memorable and productive period of time in 2008

summer when he advised me to develop the discussion chapter of the present the-

sis by face-to-face discussions at least once a day, including weekends and holidays!

I am also deeply grateful for his time and great patience of helping me to develop

my academic capabilities. It has been a great honor and sincere privilege to be his

student.

Dr. Hatem Zurob is a wonderful supervisor. It has been a great pleasure

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for me to work with him for the past two years. His knowledge in thermodynamics

and phase transformations is impressive, and he has advised me to understand the

problems in a different way, for example, in terms of energies. He is a very thoughtful

and considerate professor, and was always there when I need the help. It has been an

unforgettable experience in which he advised and helped me to build up the thermal

system. It has been his knowledge, optimism and encouragement that helped me to

overcome a number of obstacles over the past two years. Dr. Hatem Zurob spent so

much time on reading my thesis, giving me so many helpful and valuable suggestionson improving it. I know that it is a quite tough work, as the original draft of thesis

was huge more than 300 pages. I am sincerely grateful for his help. Dr. Hatem

Zurob is also one of the best instructors at McMaster University, and I was also

fortunate to be a teaching assistant for him.

I would like to express my sincere thankfulness to my co-supervisor Dr. Joseph

McDermid for his constant strong support throughout my Master research project.His knowledge and experience in industry always helped me to understand the present

study from the sense of engineering applications, by which the scientific interests and

technological significance were well combined. His encouragement and advice on my

research project is well appreciated.

My special thanks are given to Dr. Xiang Wang, for his help with the transmis-

sion electron microscopy (TEM) part of the present work, and I am greatly impressed

by his TEM expertise. I would also like to thank Professor Yves Brechet of Institut

National Polytechnique de Grenoble (INPG) and Dr. Oliver Bouaziz at Arcelor-Mittal

for the helpful discussions with them during their visit to McMaster University.

I would like to appreciate the help of the technical staff of Canadian Center for

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Electron Microscopy (CCEM) at McMaster University. Mr. Christ Butcher deserves

special thanks for his helpful suggestions on metallography as well as the time he spent

on teaching me to conduct the Electron Backscattered Diffraction analysis (EBSD).

I wish to express sincere thanks to Dr. Steve Koprich for his teaching me to operate

the Scanning Electron Microscopy (SEM) and Electron Dispersive Spectrum (EDS)

Analysis. He offered the efficient and professional help when I encountered problems

with microscope. A thank-you goes to Mr. Fred Pearson for teaching me to work

on the conventional TEM. I would like to thank Mr. Andy Duft for his help withIon Beam Milling and Atomic Force Microscopy (AFM). Dr. Glynis de Silveira also

offered a number of help and assistance with my experiments at CCEM.

Dr. James Britten and Mr. Wen He Gong at Brockhouse Institute for Materials

Research (BIMR) at McMaster University offered me a lot of help and suggestions

on X-ray diffraction analysis, which are also acknowledged. Sincere thanks are also

given to the technical staff at the Department of Materials Science and Engineeringfor their constant help and support, who are Mr. Doug Culley, Mr. John Rodda and

Mr. Ed McCaffery.

For the past two years, I also obtained enormous help from my friends inside

and outside of the lab. In particular, I am truly grateful to Erika Bellhouse, Yankui

Bian, Kai Cui, Nana Ofori-Opoku, Hossein Seyedrezai, Yang Shao, Tao Wu, Tom

(Tihe) Zhou (in last name based alphabetic order) and other good friends for their

kind help on various aspects of my living in Canada.

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TABLE OF CONTENTS

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii

1 Introduction 1

1.1 High Manganese Alloys: Background . . . . . . . . . . . . . . . . . . 21.2 Research Motivation: Mechanical Behavior of High Manganese Alloys 3

1.3 Objectives and Structure of the Thesis . . . . . . . . . . . . . . . . . 5

2 Critical Literature Review 8

2.1 Isotropic and Kinematic Strain Hardening . . . . . . . . . . . . . . . 9

2.1.1 Analysis of Isotropic Strain Hardening . . . . . . . . . . . . . 9

2.1.2 Kinematic Strain Hardening Bauschinger Effect . . . . . . 14

2.2 Phase Transitions in High Manganese Alloys and Their Thermal Driv-ing Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Mechanical Twinning . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.2 Martensitic Phase Transformations . . . . . . . . . . . . . . . 26

2.2.3 Thermal Driving Force for Phase Transitions Stacking FaultEnergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

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2.3 Interaction between Phase Transitions and Plasticity . . . . . . . . . 38

2.3.1 Phase Transitions Induced Plasticity: TWIP and TRIP Effects 38

2.3.2 Plasticity Induced Phase Transitions: Mechanical Driving Force 44

2.4 Correlation between Phase Transitions and Fracture Behaviour . . . . 48

2.4.1 Influence of Deformation Induced Martensitic Transformationon Fracture Properties . . . . . . . . . . . . . . . . . . . . . . 48

2.4.2 Interrelation between Mechanical Twinning and Fracture Process 50

2.5 Critical Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3 Experimental Techniques and Methods 61

3.1 Materials under Study . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.1.1 Choice of Materials and Composition Analysis . . . . . . . . . 62

3.1.2 Thermal Treatment . . . . . . . . . . . . . . . . . . . . . . . . 63

3.2 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.2.1 Machining, Cutting and Mounting . . . . . . . . . . . . . . . . 67

3.2.2 Metallographic Preparation . . . . . . . . . . . . . . . . . . . 67

3.2.3 Tint Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.2.4 Electropolishing . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.2.5 TEM Specimen Preparation . . . . . . . . . . . . . . . . . . . 70

3.2.6 Iron Plating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.3 Characterization Techniques . . . . . . . . . . . . . . . . . . . . . . . 72

3.3.1 Optical Microscopy . . . . . . . . . . . . . . . . . . . . . . . . 72

3.3.2 X-ray Diffraction Measurements . . . . . . . . . . . . . . . . . 73

3.3.3 Scanning Electron Microscopy with X-ray Energy DispersiveSpectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.3.4 Electron Backscattered Diffraction . . . . . . . . . . . . . . . 75

3.3.5 Transmission Electron Microscopy . . . . . . . . . . . . . . . . 80

3.4 Mechanical Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

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3.4.1 Vickers Micro-hardness Measurement . . . . . . . . . . . . . . 81

3.4.2 Uniaxial Tensile Testing . . . . . . . . . . . . . . . . . . . . . 82

3.4.3 Cold Rolling Experiments . . . . . . . . . . . . . . . . . . . . 90

3.5 Fracture Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.5.1 Fractography . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

3.5.2 Estimation of Fracture Stress and Strain . . . . . . . . . . . . 92

4 Experimental Results for Fe-30Mn: A Single-phase High ManganeseTWIP-TRIP Alloy 93

4.1 Mechanical Response, Microstructural Development and Fracture Be-havior of the Fe-30Mn Alloy due to Uniaxial Tension at 293 K . . . . 94

4.1.1 Mechanical Response and Work Hardening Behavior of the Fe-30Mn Alloy at 293 K . . . . . . . . . . . . . . . . . . . . . . . 94

4.1.2 Evolution of Microstructures in the Fe-30Mn Alloy as a Func-tion of True Strain at 293 K: An Overall Picture . . . . . . . 95

4.1.3 Evolution of Microstructures in the Fe-30Mn Alloy as a Func-tion of True Strain at 293 K: Further Investigations . . . . . . 105

4.1.4 Fracture Behavior and Damage Nucleation in the Fe-30Mn Al-loy by Uniaxial Tensile Deformation at 293 K . . . . . . . . . 111

4.2 Mechanical Behavior of the Fe-30Mn Alloy due to Uniaxial Tensionat 77 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116


4.2.2 Microstructural Development in the Fe-30Mn Alloy after 48.2%Uniform Tensile Deformation at 77 K . . . . . . . . . . . . . . 120

4.2.3 Damage Events and Fracture Behavior of the Fe-30Mn Alloyat 77 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.3 Mechanical Behavior of the Fe-30Mn Alloy due to Uniaxial TensionInvolving a 77 K Treatment . . . . . . . . . . . . . . . . . . . . . . . 130

4.4 A Study of the Fe-30Mn Alloy after 70% Plane Strain Compressionat 293 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

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4.4.1 An Overview of the 70% Cold Rolled Fe-30Mn Alloy: Mechan-

ical Data and XRD Results . . . . . . . . . . . . . . . . . . . 1324.4.2 Development of Microstructure in the 70% cold rolled Fe-30Mn

alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

4.4.3 Damage Nucleation in the Fe-30Mn Alloy by Plane Strain Com-pression at 293 K . . . . . . . . . . . . . . . . . . . . . . . . . 139

5 Experimental Results for Fe-24Mn: A Dual Phase High Man-ganese TRIP Alloy with Complex Microstructures 141

5.1 Mechanical Response, Microstructural Development and Fracture Be-

havior of the Fe-24Mn Alloy due to Uniaxial Tension at 293 K . . . . 142


5.1.2 Evolution of Microstructures in the Fe-24Mn Alloy as a Func-tion of True Strain at 293 K: An Overall Picture . . . . . . . 146

5.1.3 Evolution of Microstructures in the Fe-24Mn Alloy as a Func-tion of True Strain at 293 K: Further Investigations . . . . . . 153

5.1.4 Fracture Behavior and Damage Nucleation in the Fe-24Mn Al-

loy by uniaxial tensile deformation at 293 K . . . . . . . . . . 1695.2 Mechanical Behavior of the Fe-24Mn Alloy during Uniaxial Tension

at 77 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172


5.2.2 Microstructural Development in the Fe-24Mn Alloy after 15.7%Uniform Tensile Deformation at 77 K . . . . . . . . . . . . . . 176

5.2.3 Damage Events and Fracture Behavior of the Fe-24Mn Alloyat 77 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

5.3 Mechanical Behavior of the Fe-24Mn Alloy due to Uniaxial TensionInvolving a 77 K Treatment . . . . . . . . . . . . . . . . . . . . . . . 187

5.4 A Study of the Fe-24Mn Alloy after 70% Plane Strain Compressionat 293 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

5.4.1 An Overview of the 70% Cold Rolled Fe-24Mn Alloy: Mechan-ical Data and XRD Results . . . . . . . . . . . . . . . . . . . 190

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5.4.2 Development of Microstructure and Damage Nucleations in the

70% Cold Rolled Fe-24Mn alloy . . . . . . . . . . . . . . . . . 191

6 Discussions 200

6.1 Summaries of Experimental Results for High Manganese Alloys . . . 201

6.1.1 The Fe-30Mn Alloy . . . . . . . . . . . . . . . . . . . . . . . . 201

6.1.2 The Fe-24Mn Alloy . . . . . . . . . . . . . . . . . . . . . . . . 204

6.1.3 General Comments . . . . . . . . . . . . . . . . . . . . . . . . 207

6.2 Strain Hardening Behaviour and Microstructural Evolution of the Fe-

Mn Alloys: Experimental and Modeling . . . . . . . . . . . . . . . . . 208

6.2.1 Analysis of Plasticity of the Fe-30Mn Alloy . . . . . . . . . . . 209

6.2.2 Analysis of Plasticity of the Fe-24Mn Alloy . . . . . . . . . . . 224

6.2.3 Comments on Kinematic Hardening Behaviour of Fe-Mn Alloys 235

6.3 Fracture Behaviour of Fe-Mn Alloys . . . . . . . . . . . . . . . . . . . 235

6.4 Influence of Thermal and Strain Path . . . . . . . . . . . . . . . . . . 237

6.5 Microstructural Evolution during Large Plane Strain Compression of

Fe-Mn Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2386.5.1 The Fe-30Mn Case . . . . . . . . . . . . . . . . . . . . . . . . 239

6.5.2 The Fe-24Mn Case . . . . . . . . . . . . . . . . . . . . . . . . 240

7 Conclusions 242

8 Future Work 245

Bibliography 247

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LIST OF FIGURES

1.1 Typical mechanical properties of several classes of steels. . . . . . . . 3

2.1 Work hardening stages of single crystals. . . . . . . . . . . . . . . . . 10

2.2 Evolution of energy storage as a function of true stress in pure nickel. 11

2.3 Normalized plots for Cu polycrystals at different temperaturesand strain rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 (V/)1/2 versus

kTb3 ln

0

1/2plots. . . . . . . . . . . . . . . . . . . 14

2.5 Illustration of the Bauschinger effect. . . . . . . . . . . . . . . . . . . 15

2.6 Simulated and experimental results on backstress. . . . . . . . . . . . 19

2.7 TEM image of dislocation pile-ups at the twin boundary. . . . . . . . 20

2.8 Twinning elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.9 Organization of twinning by stacking of micro-twins. . . . . . . . . . 23

2.10 Dislocation models of twinning. . . . . . . . . . . . . . . . . . . . . . 24

2.11 Bullough dislocation model of twins. . . . . . . . . . . . . . . . . . 25

2.12 Pole mechanism for the growth of a twin. . . . . . . . . . . . . . . . . 26

2.13 Effect of austenite grain size on the type of martensite morphology. 28

2.14 HRTEM image of the substructure of martensite. . . . . . . . . . . 29

2.15 Stacking sequence of the FCC and HCP crystal structures togetherwith those of the twin, intrinsic, and extrinsic stacking faults. . . . . 32

2.16 Tensile strain stress curves for the Fe-22 wt.% Mn-0.6 wt.% C steel(grain size = 15 m) at different temperatures. . . . . . . . . . . . . 35

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3.7 The Euler angle colouring scheme for EBSD mapping. . . . . . . . . . 77

3.8 The inverse pole figure colouring schemes for EBSD mapping. . . . . 78

3.9 Phase colouring scheme for EBSD mapping. . . . . . . . . . . . . . . 79

3.10 Legend for grain boundaries and twin boundaries in EBSD mapping. 80

3.11 Geometry of tensile specimen for all 293 K tensile tests. . . . . . . . . 83

3.12 Loading-unloading tensile tests on Fe-30Mn alloy at 293 K. . . . . . . 87

3.13 Illustration of calculating the backstress at T=10%. . . . . . . . . . . 88

4.1 Mechanical response of the Fe-30Mn alloy at 293 K: (a) Engineeringstress strain plot and (b) True stress strain plot. . . . . . . . . . . 96

4.2 Work hardening behavior of the Fe-30Mn alloy at 293 K: work hard-ening rate vs. true stress. . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.3 Development of the backstress in the Fe-30Mn alloy at 293 K: plot ofboth true flow stress and backstress versus true strain. . . . . . . . . 98

4.4 SEM images of microstructures of the annealed Fe-30Mn alloy. . . . . 98

4.5 SEM images of microstructures of the Fe-30Mn alloy after T = 2%tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 100





4.10 SEM images of microstrcutres in uniformly elongated portion of frac-tured Fe-30Mn tensile sample at 293 K, T = 37.3%. . . . . . . . . . . 104

4.11 Evolution of martensite phase volume fraction with plastic strainat 293 K by X-ray diffraction measurements: the Fe-30Mn alloy. . . . 105

4.12 Optical metallographs of microstructures in the annealed Fe-30Mn alloy.106

4.13 EBSD mapping of microstructures in the annealed Fe-30Mn alloy. . . 107

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4.14 TEM micrographs of microstructures in the annealed Fe-30Mn alloy. . 108

4.15 TEM images of microstructures of the Fe-30Mn alloy at T = 20% bytension at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.16 EBSD mapping of microstructures in the uniform elongated part offractured Fe-30Mn sample at 293 K, T = 37.3%. . . . . . . . . . . . 110

4.17 Misorientation profiles for the two paths in Figure 4.16(a). . . . . . . 110

4.18 Fracture stress and strain of the Fe-30Mn alloy at 293 K, superimposedwith its T T curve. . . . . . . . . . . . . . . . . . . . . . . . . . . 112

4.19 Stereoscopic images of fracture portion of Fe-30Mn tensile sample after

monotonic tensile test at 293 K: (a) Top view and (b) Thickness sectionview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4.20 SEM images of fracture surface of Fe-30Mn tensile sample after mono-tonic tensile test at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . 114

4.21 Optical metallographs of necked region on thickness section of Fe-30Mntensile sample, after monotonic tensile test at 293 K. . . . . . . . . . 115

4.22 SEM images of the thickness section close to the fracture surface ofFe-30Mn tensile sample, after monotonic tensile test at 293 K. . . . . 115

4.23 SEM-EDS analysis of inclusions that cause decohesion in the Fe-30Mn

alloy at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116


4.25 Work hardening behavior of the Fe-30Mn alloy at 77 K: work hardeningrate versus true stress. . . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.26 Work hardening behavior of the Fe-30Mn alloy at 77 K: dT/dT vs.(T 0) plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.27 Optical images of microstructures in the Fe-30Mn alloy after an uni-axial tensile strain of 48.2% at 77 K. . . . . . . . . . . . . . . . . . . 122

4.28 FEG-SEM observations of microstructures and damage events in theFe-30Mn alloy after an uniaxial tensile strain of 48.2% at 77 K. . . . 123

4.29 SEM-EBSD analysis of microstructures in the Fe-30Mn alloy after anuniaxial tensile strain of 48.2% at 77 K. . . . . . . . . . . . . . . . . . 125

4.30 Fracture stress and strain of the Fe-30Mn alloy at 293 Kand 77 K,superimposed with T T curves. . . . . . . . . . . . . . . . . . . . 126

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4.31 Stereoscopic images of fracture portion of Fe-30Mn tensile sample after

monotonic tensile test at 77 K: (a) Top view and (b) Thickness sectionview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.32 FEG-SEM observations of the fracture surface in the Fe-30Mn alloyafter monotonic tensile test at 77 K: brittle fracture. . . . . . . . . . 128

4.33 FEG-SEM observations of the fracture surface in the Fe-30Mn alloyafter monotonic tensile test at 77 K: ductile fracture. . . . . . . . . . 129

4.34 Optical and FEG-SEM observations of fractured portion of Fe-30Mntensile sample after monotonic tensile test at 77 K: thickness sectionview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

4.35 Mechanical response of the Fe-30Mn alloy in Type I tensile test: truestress strain plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

4.36 Uniform and post-uniform deformation behavior of the Fe-30Mn alloyat 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

4.37 FEG-SEM images of microstructures on the ND surface of the 70%cold rolled Fe-30Mn alloy. . . . . . . . . . . . . . . . . . . . . . . . . 134

4.38 EBSD analysis of microstructures on ND surface of the 70% cold rolledFe-30Mn alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

4.39 TEM images of well-developed deformation bands in 70% cold rolledFe-30Mn alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

4.40 TEM images of mechanically transformed martensite in 70% coldrolled Fe-30Mn alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

4.41 Optical observations of microstructures on TD surface of 70% coldrolled Fe-30Mn alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

4.42 FEG-SEM images of microstructures on the TD surface of the 70%cold rolled Fe-30Mn alloy. . . . . . . . . . . . . . . . . . . . . . . . . 139

4.43 SEM observations of microscopic damage events on TD section of 70%

cold rolled Fe-30Mn alloy at 293 K. . . . . . . . . . . . . . . . . . . . 140

5.1 SEM images of microstructures of the annealed Fe-24Mn alloy. . . . . 143


5.3 Work hardening behavior of the Fe-24Mn alloy at 293 K: work hard-ening rate vs. true stress. . . . . . . . . . . . . . . . . . . . . . . . . . 145

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5.4 Development of the backstress in the Fe-24Mn alloy at 293 K: plot of

both true flow stress and backstress versus true strain. . . . . . . . . 1465.5 SEM images of microstructures of the Fe-24Mn alloy after T = 2%

tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 148





5.10 Evolution of martensite phase volume fraction with plastic strainat 293 K by X-ray diffraction measurements: the Fe-24Mn alloy. . . . 153

5.11 Optical metallographs of microstructures in the annealed Fe-24Mn alloy.154

5.12 SEM-EBSD analysis of microstructures in the annealed Fe-24Mn alloy. 156

5.13 An overall TEM observations of microstructures in the annealed Fe-24Mn alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

5.14 TEM micrographs of stacking faults in the annealed Fe-24Mn alloy. . 1575.15 TEM micrographs of complex microstructure in the annealed Fe-24Mn

alloy: fine retained plates between thermally transformed martensite.159

5.16 TEM images of different variants of martensite in the annealed Fe-24Mn alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

5.17 SEM-EBSD analysis of microstructures in the Fe-24Mn alloy after T =20% at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

5.18 TEM micrographs of two sets of martensite in the 20% deformedFe-24Mn tensile sample; note the thickening of the martensite due to

deformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

5.19 TEM micrographs of deformation bands in the Fe-24Mn alloy afterT = 20% tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . 164

5.20 TEM micrographs of intersection of deformation bands with thin martensite plates in the Fe-24Mn alloy after T = 20% tensile strainat 293 K; note that deformation bands which propagate through thethin martensite plates. . . . . . . . . . . . . . . . . . . . . . . . . . 165

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5.21 TEM micrographs of intersection of deformation bands with relatively

thick martensite plates in the Fe-24Mn alloy after T = 20% ten-sile strain at 293 K; note that the propagation of deformation bandsstopped at martensite plates. . . . . . . . . . . . . . . . . . . . . . 166

5.22 TEM micrographs of intersection of different variants of martensiteplates in the Fe-24Mn alloy after T = 20% tensile strain at 293 K;note that one set of plates went through the other. . . . . . . . . . 167

5.23 TEM micrographs of intersections of different variants of martensitein the Fe-24Mn alloy after T = 20% tension at 293 K; note that a new martensite formed at the intersection site. . . . . . . . . . . . . . . 168

5.24 Fracture stress and strain of the Fe-24Mn alloy at 293 K, superimposedwith its T T curve. . . . . . . . . . . . . . . . . . . . . . . . . . . 170

5.25 Stereoscopic images of the fracture portion of the Fe-24Mn tensile sam-ple after monotonic tensile test at 293 K: (a) Top view and (b) Thick-ness section view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

5.26 SEM images of the fracture surface of the Fe-24Mn tensile sample aftermonotonic tensile test at 293 K. . . . . . . . . . . . . . . . . . . . . . 171

5.27 FEG-SEM images of the microscopic damage events on the neckedsection of the fractured Fe-24Mn tensile sample after monotonic tensile

test at 293 K: thickness section view. . . . . . . . . . . . . . . . . . . 1725.28 Mechanical response of the Fe-24Mn alloy at 77 K: (a) Engineering

stress strain plot and (b) True stress strain plot. . . . . . . . . . . 174

5.29 Work hardening behavior of the Fe-24Mn alloy at 77 K: work hardeningrate versus true stress. . . . . . . . . . . . . . . . . . . . . . . . . . . 175

5.30 Work hardening behavior of the Fe-24 alloy at 77 K: dT/dT vs.(T 0) plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

5.31 Optical images of microstructures in the Fe-24Mn alloy after an uni-axial tensile strain of 15.7% at 77 K. . . . . . . . . . . . . . . . . . . 178

5.32 FEG-SEM observations of microstructures in the Fe-24Mn alloy afteran uniaxial tensile strain of 15.7% at 77 K. . . . . . . . . . . . . . . . 178

5.33 SEM-EBSD analysis of microstructures in the Fe-24Mn alloy after anuniaxial tensile strain of 15.7% at 77 K. . . . . . . . . . . . . . . . . . 180

5.34 Fracture stress and strain of the Fe-24Mn alloy at 293 K and 77 K,superimposed with T T curves. . . . . . . . . . . . . . . . . . . . 182

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5.35 Stereoscopic images of the fracture portion of the Fe-24Mn tensile sam-

ple after monotonic tensile test at 77 K: (a) Top view and (b) Thicknesssection view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

5.36 FEG-SEM observations of the fracture surface of the Fe-24Mn tensilesample after monotonic tensile test at 77 K. . . . . . . . . . . . . . . 183

5.37 Optical metallographs of the fractured portion of the Fe-24Mn tensilesample after monotonic tensile test at 77 K: thickness section view. . 184

5.38 FEG-SEM observations of the microscopic damage events on the thick-ness section of the Fe-24Mn tensile sample after monotonic tensile testat 77 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

5.39 Mechanical response of the Fe-24Mn alloy in Type I tensile test: (a)Engineering stress strain plot and (b) True stress strain plot. . . . 188

5.40 Work hardening behavior of the Fe-24Mn alloy in Type I tensile test:work hardening rate versus true stress. . . . . . . . . . . . . . . . . . 189

5.41 Uniform and post-uniform deformation behavior of the Fe-24Mn alloyat 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

5.42 FEG-SEM images of microstructures on the ND surface of the 70%cold rolled Fe-24Mn alloy. . . . . . . . . . . . . . . . . . . . . . . . . 192

5.43 EBSD analysis of microstructures on ND surface of the 70% cold rolledFe-24Mn sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

5.44 TEM micrographs of a fully martensite area with deformation twins,in the 70% cold rolled Fe-24Mn alloy. . . . . . . . . . . . . . . . . . . 195

5.45 TEM micrographs of different sets of deformation twins in the fully martensite regions, in the 70% cold rolled Fe-24Mn alloy. . . . . . . . 196

5.46 TEM micrographs of fine complex microstructures developed by the martensitic phase transformation at different stages of deformation, inthe 70% cold rolled Fe-24Mn alloy. . . . . . . . . . . . . . . . . . . . 197

5.47 FEG-SEM images of the microstructure and damage events on the TDsurface of the 70% cold rolled Fe-24Mn alloy. . . . . . . . . . . . . . . 199

6.1 True stress strain behaviour of Fe-30Mn and pure Cu-polycrystalsat 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

6.2 Evolution of dislocation storage as a function of applied stress in Fe-30Mn and pure Cu-polycrystals at 293 K. . . . . . . . . . . . . . . . 212

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6.3 Normalized strain hardening behaviour of Fe-30Mn and pure Cu-polycrystals

at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2136.4 Comparison between experimental results and modeling for strain hard-

ening behaviour of Fe-30Mn at 293 K. . . . . . . . . . . . . . . . . . 216

6.5 Comparison between experimental results and modeling for strain hard-ening behaviour of Fe-30Mn at 77 K. . . . . . . . . . . . . . . . . . . 219

6.6 Comparison between experimental results and modeling for strain hard-ening behaviour of Fe-30Mn at 77 K. Phase transitions were considered.222

6.7 Fitting plot of evolution of volume fraction of martensite with truestrain in Fe-24Mn at 293 K. . . . . . . . . . . . . . . . . . . . . . . . 226

6.8 Iso-work modeling results for strain partition in the Fe-24Mn alloyat 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

6.9 Iso-work modeling results for evolution of flow stress of austenite and martensite as a function of global strain in the Fe-24Mn alloy at 293 K.229

6.10 Iso-work modeling results for stress partition in the Fe-24Mn alloyat 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

6.11 Iso-work modeling results for intrinsic true stress strain behaviour of martensite together with the experimental stress strain behaviour

of Fe-24Mn and Fe-30Mn (austenite) at 293 K. . . . . . . . . . . . . . 2306.12 Iso-work modeling results for strain partition in the Fe-24Mn alloy

at 77 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

6.13 Iso-work modeling results for evolution of flow stress of austenite and martensite as a function of global strain in the Fe-24Mn alloy at 77 K.233

6.14 Iso-work modeling results for stress partition in the Fe-24Mn alloyat 77 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

6.15 Iso-work modeling results for intrinsic true stress strain behaviour of martensite together with the experimental stress strain behaviourof Fe-24Mn and Fe-30Mn (austenite) at 77 K. . . . . . . . . . . . . . 234

6.16 Summaries of fracture strength and strain for Fe-Mn alloys at 293 and77 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

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LIST OF TABLES

3.1 Results of composition analysis in Fe-24Mn and Fe-30Mn binary alloys. 62

3.2 Summaries of Vickers micro-hardness testing results (HV). . . . . . . 65

4.1 Evolution of phase volume fractions in the Fe-30Mn alloy with plasticstrain at 77 K by X-ray diffraction measurements, %. . . . . . . . . . 121

4.2 Evolution of phase volume fraction of the Fe-30Mn alloy after T = 70%plane strain compression at 293 K by X-ray diffraction measurements,%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

5.1 Evolution of phase volume fractions in the Fe-24Mn alloy due to uni-axial uniform tensile deformation at 77 K by X-ray diffraction mea-surements, %. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

5.2 Evolution of phase volume fractions of the Fe-24Mn alloy due to 70%plane strain compression at 293 K by X-ray diffraction measurements,%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

6.1 Numerical values of physical constants and calculated parameters forpure Cu-polycrystals and Fe-30Mn which are involved in the preset

models. Data for Cu-polycrystals were take from Kocks and Meckingswork (2003) and were further analyzed. . . . . . . . . . . . . . . . . . 223

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CHAPTER

ONE

INTRODUCTION

For many applications, materials need to possess a combination of high strength

and good ductility. The high strength can be defined in terms of plastic resistance,

whereas there are two aspects of ductility to be considered. One is the maximum uni-

form strain in tensile deformation, and the other is the total ductility up to fracture.

To achieve this combination of mechanical properties, we need a high work hardening

rate plus a sustained work hardening rate during the whole plastic resistance. One

way of doing this is to have phase transitions which occur during plasticity. Iron high

manganese alloys are a good example of this behaviour, and thus they constitute thesubject of the present thesis.

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M.A.Sc. Thesis by Xin Liang Materials Science & EngineeringMcMaster 2008

SECTION 1.1

High Manganese Alloys: Background

Weight reduction and improved safety standards are the current trends in the

automobile industry. Materials for automobile applications should thus have high

strength for structural reinforcement and exceptional ductility for easy forming and

energy absorption (crash resistance). These requirements spur the development of

automobile materials with a good combination of high strength and excellent tough-

ness (Grassel et al., 2000; Frommeyer et al., 2003; Scott et al., 2005).

Iron-high manganese alloys are an attractive and promising candidate for au-

tomobile applications. Figure 1.1 presents several classes of steels based on their

combination of total elongation and UTS (Ultimate Tensile Strength). It can be

clearly seen that high manganese TWIP/TRIP alloys (designated as HMS on the

figure) possess both high UTS and high total elongation.

The origin of high manganese alloys dates back to the late nineteenth century

when Sir Robert Hadfield invented them, and the name Hadfield steels was then

given to this type of alloy. The class of Hadfield steel generally has 1014 wt.% man-

ganese and 1.01.4 wt.% carbon content, and it was found to be fully austenitic after

the normal quenching (Dastur & Leslie, 1981). However, the high carbon content in

Hadfield steels makes it difficult to process due to carbon precipitation, and also leads

to the poor weldability (Scott et al., 2005). To surmount this problem, the carbon

content is reduced or even removed from the alloying system, and more manganese is

added so that the austenite stability is not compromised. Accordingly, a new gener-

ation of austenitic high manganese alloys were designed, which typically have 2230

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wt.% manganese and 00.6 wt.% carbon (Scott et al., 2005).

Figure 1.1: Typical mechanical properties of several classes of steels (Bleck & Phiu-On,2005). Note the position of high manganese alloys on this diagram.

SECTION 1.2

Research Motivation: Mechanical Behavior of

High Manganese Alloys

There have been a number of works on austenitic high manganese alloys, aimed

at understanding the strain hardening mechanisms that are responsible for their ex-

ceptional mechanical properties. Most of the works concluded that it is strain induced

phase transitions, such as mechanical twinning and/or deformation induced marten-

sitic reactions, that lead to a combination of both the high strain hardening and

dramatically enhanced ductility (Remy & Pineau, 1976, 1977; Remy, 1978b; From-

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meyer et al., 2003; Grassel et al., 2000; Bracke et al., 2006). These are so called

TWIP (Twinning Induced Plasticity) and TRIP (Transformation Induced Plas-

ticity) effects, and we will generally name these alloys as Transformable Alloys or

Steels in which deformation induced phase transition can occur.

The Fe-Mn alloy system is an interesting one because, unlike conventional

pure metals which are hardened by accumulation of dislocations, Fe-Mn alloys can

have additional hard planar obstacles added, for instance, by mechanical twinning

or strain induced martensitic reactions. We then get additional strain hardening

which is kinematic strain hardening. It has its name because the kinematic strain

hardening component has the memory of the loading direction due to the build-up of

elastic strain in the embedded hard phases or at the planar obstacles.

The investigation of kinematic hardening behaviour is important in that, from

the perspective of scientific interests, it distinguishes between the contributions to

work hardening behaviour from different kinds of dislocation mechanisms; on the side

of engineering practice, an good understanding of the kinematic hardening contri-

bution will help to define the relationship between the applied stress state and flow

strength for strain path other than simple monotonic straining (Bate & Wilson, 1986).

The influence of phase transitions on the strain hardening behaviour of trans-

formable alloys needs to more clearly understood. For example, whether phase tran-

sitions make a softening or hardening contribution, and what is the net effect. In-

vestigations of microscopic damage mechanisms and association of them with phase

transition processes in transformable alloys are also needed.

What is equally important and interesting is that in the present literatures

available, there seems to be a missing part for the study of mechanical behaviour

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of austenitic high manganese alloys, that is, the strain hardening behaviour of non-

transformable high manganese alloys. It should be noted that these non-transformable

high manganese alloys possess high ductility in terms of total elongation (Tomota

et al., 1986), which are considerably better than the transformable ones. Their general

mechanical properties, including the level of strength that they can achieve, are still

appreciably superior to other types of non-transformable alloys such as copper or

micro-alloying steels.

Last but not least, it is of importance to look into the effect of thermal path and

strain path on the strain hardening behaviour as well as the deformation mechanisms

in Fe-Mn alloys. Such studies not only provide an insight into both the thermal and

mechanical driving force for phase transitions, but also provide valuable correlation

to engineering processes such as metal forming operations.

SECTION 1.3

Objectives and Structure of the Thesis

The investigation and understanding of the relationship of processing

structure properties applications has always been one of the main goals of

the Materials Science and Engineering. The objective of the present work is thus to

develop a good comprehension of the structure (mechanical) properties relation-ship in high manganese steels, as this thesiss title implies.

To achieve this goal, we have chosen two Fe-Mn binary alloys, which are Fe-

24Mn and Fe-30Mn. Fe-30Mn possesses an austenite single phase microstructure

after annealing whereas Fe-24Mn has a mixture of austenite and (HCP) martensite.

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Furthermore, the stacking fault energies (SFEs) of two alloys are quite different, as

is their strain hardening behaviour. According to a recent SFE model by Allain et

al. (2004a), Fe-24Mn has a SFE of about 8 mJ/m2, whereas Fe-30Mn possesses a SFE

of around 15 mJ/m2.

The mechanical properties of the Fe-Mn alloys were investigated by a series of

mechanical tests. The initial microstructure and the evolution of microstructure as

a function of applied strain in the Fe-Mn alloys were carefully and comprehensively

evaluated. The strain hardening behaviour of Fe-Mn alloys can be well understood

by correlating it with the evolution of microstructure and measurement of the kine-

matic hardening contribution which comes in part from deformation induced phase

transitions. The fracture behaviour of both alloys were also investigated. The effect

of thermal path and strain path on the both alloys are also examined.

The structure of the current thesis is as follows. Chapter 2 gives a systematic

review of the literatures related to essential aspects regarding the present work, focus-

ing on the deformation mechanisms and strain hardening behaviour of high manganese

alloys. Following this review, Chapter 3 will describe the experimental methods and

techniques that we applied in the present work. Chapter 4 and 5 will mainly present

the experimental results for the Fe-24Mn and Fe-30Mn alloys, respectively, and both

chapters will follow an organization as follows. The mechanical behaviour of the Fe-

Mn alloys at 293 K will be investigated, followed by a focus on the strain hardening

behaviour at 77 K. The effect of thermal path and strain path are evaluated by some

mechanical tests other than simple monotonic tensile tests. In Chapter 6, we will

make intensive discussions on our experimental results. We will start with a brief

summary of the experimental results for the both alloys. The Kocks and Meckings

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model will then be extended to investigate the effects of both the SFE and strain

induced phase transitions on the work hardening behaviour of the Fe-30Mn alloy. As

for Fe-24Mn, we applied the Iso-work model to analyze its plasticity and deduce the

intrinsic mechanical behaviour of martensite. In the modeling work for both alloys,

the correlation between microstructural evolution and strain hardening behaviour is

emphasized. After that, we will briefly discuss the fracture behaviour of Fe-Mn alloys

at 293 and 77 K, the effect of thermal path as well as the deformation mechanisms

at large plane strain compression. The conclusions of the present work as well assuggestions for future study are given in Chapter 7 and 8, respectively.

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CHAPTER

TWO

CRITICAL LITERATURE REVIEW

The high manganese steels demonstrate interesting mechanical properties,

which are mainly due to a complex combination of different deformation mechanisms

occurring during the deformation process. In this chapter, we will review some impor-

tant ideas by starting off with a general description, i.e. the isotropic and kinematic

strain hardening behaviour. Then we will switch to several aspects of phase tran-

sitions in high Mn alloys, followed by a review of the complex interaction between

phase transitions and plasticity. Along with the sequence of deformation, we will

then focus on the interrelationship between phase transitions and fracture behaviour.Finally, we like to make a brief critical assessment to conclude the present chapter.

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SECTION 2.1

Isotropic and Kinematic Strain Hardening

The strain hardening behaviour of metals and alloys is generally classified into

two categories: isotropic and kinematic behaviour. The material which presents a

symmetrical mechanical response after a change of the strain path is considered to

demonstrate the isotropic work hardening behaviour. Kinematic hardening can be

thought of as an additive component on top of the isotropic hardening behaviour,

which is due to internal or polarized stress developed in the body being deformed.

We will first review the Kocks-Meckings model (2003) on the strain hardening

behaviour in the FCC case, in which only isotropic hardening is considered. In dis-

cussions, We will apply their model with critical assessment to investigate the Fe-Mn

alloy system. The second part of this section will then review the kinematic strain

hardening, with emphasis on the transformable alloys.

2.1.1 Analysis of Isotropic Strain Hardening

The plastic deformation of FCC single crystal metals usually exhibit three

stages of strain hardening behaviour (Tegart, 1966). The material typically begins

with the Stage I deformation which corresponds to the easy glide on only one slip

system, whereas Stage II starts with the activation of a secondary slip system. The

beginning of the Stage III is generally associated with the appearance of a dynamic

recovery process. For polycrystals, however, Stage I is absent and Stage II is hard to

be identified except at low temperatures. The Stage III starts after general yielding of

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the material, and it constitutes a significant portion of the strain hardening behaviour,

as can be seen from Figure 2.1. The Kocks-Meckings model (2003) mainly addresses

the Stage III strain hardening behaviour. Their essential ideas and methodologies

will be briefly reviewed in the following content.

Figure 2.1: Schematic sketch of hardening coefficient versus flow stress illustrating thehardening stages for polycrystals in comparison to those for single crystals deformed insingle slip (Kocks & Mecking, 2003).

2.1.1.1 Essential Concepts and Core Ideas

The core concept of Kocks-Meckings model is that the flow stress or the

strain hardening behaviour is directly linked with the storage of dislocations in the

material during the deformation process. It is then appropriate to correlate the

strain hardening with the change in dislocation structure, which could be considered

as the combination of two processes. The first process is related to the fraction of the

previously mobile dislocations that get trapped in the material. The second process is

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the rearrangement of these remanent dislocations involving dislocation annihilation,

which is the thermally activated dynamic recovery process. A typical behaviour

demonstrating a combination of these two processes is shown in Figure 2.2, which is

the plots of dislocation storage T (dT/dT) against the true stress T for pure nickel

with two different grain sizes. It can be clearly seen that the storage of dislocation

initially increases, and then goes through a maximum before decreasing, which is

ascribed to the dynamic recovery process. However, it should be noted that both

the dislocation accumulation and dynamic recovery processes occur simultaneouslyin most cases during the straining of FCC polycrystal metals, although they may be

treated separately in experimental results and modeling.

Figure 2.2: Evolution of energy storage as a function of true stress in pure nickel of twodifferent grain sizes (Kocks & Mecking, 2003).

A mathematic model was proposed to describe these two processes, which is

given as follows:

= 0 Rd/1/n (2.1)

where = dT/dT is the net work hardening rate in the polycrystals (its counter-

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part in single crytals is = d/d). 0, is the athermal strain hardening contribution

which reflects the initial dislocation storage dictated by geometry, and thus is ather-

mal. The second term is the contribution from the dynamic recovery, and the negative

sign indicates its softening effect by removing dislocations. The parameters, Rd and

n vary with temperature but are independent of stress and strain rate .

2.1.1.2 Phenomenological Approach

Following a sketch of the important concepts in the Kocks-Meckings model,

we will now review their phenomenological approaches to investigate the Stage III

strain hardening behaviour in FCC metals. The typical methods they proposed can

be generalized into two master curves, by which for the same material, the strain

hardening curves for a large range of temperature and strain rates could be unified.

The first master curve, the / /V plot, is based on the Voce hardening

law, which is given as

= 0

1

V

(2.2)

or in a general form:

0= E

V

(2.3)

where E is an arbitrary function that should be determined for each case, and also has

generality for a wide set of temperatures and strain rates. V is the scaling stress, and

it indicates the point at which the net strain hardening rate = 0, as can be realized

from Eq. 2.2. From the view of dislocation structure evolution, V implies the level of

stress upon which the dislocation accumulation in the material is equally balanced by

the dislocation annihilation or removement, i.e. via dynamic recovery process. Both

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the athermal strain hardening rate 0 and the scaling stress V are proportional to

the shear modulus (T); V also depends on the strain rate and temperature.

The athermal strain hardening rate and scaling stress can be derived from the

strain hardening rate plot, i.e. the plot of against . The athermal strain hardening

rate 0 can be determined from the intercept of a tangent to the straight middle part

of the curve on the axis, whereas the exploration of this tangent to = 0

gives the scaling stress V. An illustration of extracting the two parameters can be

referred back to Figure 2.1. An example of this type of master curve is presented in

Figure 2.3.

Figure 2.3: Normalized plots for Cu polycrystals at five temperatures from RT to400 at the two strain rates, 104 s1and 1 s1. The dotted line is the Voce approximation

with / = 0.05 (Kocks & Mecking, 2003).

The second master curve has several forms, but they all posses the same basis,

namely, that the scaling stress V is a function solely of deformation temperature and

strain rate. One type of the plot is in the form of (V/)1/2 versus

kTb3 ln

0

1/2, as

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is shown in Figure 2.4. The two border lines for the values zero and infinity of the

stacking fault energy are obtained by the extrapolation method. The second master

curve thus provides a quite useful method to investigate the stacking fault energy

(SFE) dependence of the strain hardening behaviour of FCC materials.

Figure 2.4: (V/)1/2 versus kTb3 ln 0

1/2plots for Ag-, Cu-, Ni-, and Al-

polycrystals (Kocks & Mecking, 2003). is the stacking fault energy.

2.1.2 Kinematic Strain Hardening Bauschinger Effect

The presence of an anisotropic mechanical behaviour due to a change of the

strain path is referred to the Bauschinger effect. Investigation of the Bauschinger

effect will help to refine the relationship between the microstructure and strain hard-

ening behaviour of the materials. We will briefly review the basic concepts of the

Bauschinger effect, followed by a look into a few cases in transformable alloys.

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2.1.2.1 Phenomenology and Physics of the Bauschinger Effect

The Bauschinger effect, which is usually appreciable in dual or multi-phase

materials, can be revealed in mechanical tests which involve a change of loading

direction, for example, a forward tension followed by a compression. The common

observation of the corresponding mechanical response during the reverse loading (i.e.

the compression) is a reduced elastic point, a rounded appearance of yielding portion

and possibly a permanent softening compared with the forward flow stress strain

curve (Sowerby et al., 1979). Figure 2.5 illustrates such features of the Bauschinger

effect. One should note that a forward compression followed by tension would also

yield similar phenomenon.

Figure 2.5: Illustration of the Bauschinger effect: uniaxial stress strain behaviour ofmany real metals during forward and reverse flow tests (Sowerby et al., 1979).

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Both the transient and permanent softening observed in such mechanical tests

are associated with the presence of internal stress. Theoretical explanations have

been proposed to understand the Bauschinger effect from different approaches, or

more accurately, from views of different length scales, as reviewed by Sowerby et

al (1979). From a macroscopic sense, the continuum view considers the difference

between the isotropic and kinematic hardening as follows. The initial yield surface

expands uniformly when isotropic work hardening occurs; in contrast, the yield surface

would translates in stress space without changing its initial form and orientation whenkinematic work hardening occurs. On the other hand, from the microscopic approach,

the Bauschinger effect is thought of as a result of incompatibility among different

phases in the material, for example between the matrix and reinforcement particles,

which can be ascribed to the heterogeneity of plastic flow in the level of dislocation

motion. The internal stress or backstress is then generated.

A micro-mechanical model was proposed by Bate and Wilson (1986) to un-derstand the kinematic strain hardening behaviour, as is given below

flow = 0 + iso + kin (2.4)

where flow is the flow stress, 0 is the initial yield strength, and the second term on the

right side of the above equation, iso, is the isotropic hardening contribution coming

from the dislocation storage process, as have been described in the Kocks-Meckings

model in section 2.1.1. This term is non-directional, i.e. independent of loading

direction. The last term kin reflects the kinematic strain hardening contribution,

which arises from the unrelaxed internal stress or backstress and would then aid the

reverse flow. Obviously, the kinematic hardening component kin is directional and

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its sign might be reversed when the strain path changes.

Before switching to a review of the Bauschinger effect in transformable alloys,

it is also worthwhile to comment it in the case of non-transformable alloys. It is

well established that the Bauschinger effect occur in the dispersion hardened alloys.

For example, there is early research work on the internal tress in the copper alloys

containing SiO2 particles (Atkinson et al., 1974). Also, a study on co-deformation of

two phases Cu-Cr alloys by Sinclair et al. (2005) shows that both the elastic and plastic

behaviour in embedded Cr fibres is accompanied by large internal stress. However, one

should not overlook the build-up of the backstress due to the evolution of dislocation

substructures, without the presence of second phases. For instance, if cell structure

forms during the deformation process, the Bauschinger effect would be notable due

to a polarization of the dislocation substructure and the consequent build-up of the

internal stress or backstress, although the magnitude of the backstress might not be as

high as in precipitate strengthened alloys. More specifically, there will be high forwardstresses inside the cell walls in which a high dislocation density exists, whereas low

back-stresses in the relatively clean cell interior (Kocks & Mecking, 2003).

Moreover, stacking fault energy (SFE) also plays a role in the kinematic strain

hardening in non-transformable alloys, in addition to its significant influence on the

isotropic strain hardening behaviour. In their studies on FCC Cu-Al alloys, Abel and

Muir (1973) found that the Bauschinger effect becomes larger as the SFE decreases,

and that the alloys of low SFE possess a large capacity to store energy associated with

plastic deformation in a reservable manner. These observations might be understood

from the view of dislocation reactions, more strain reversal due to the more planar

nature of the slip.

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2.1.2.2 Bauschinger Effect in Transformable Alloys

There is far less work on the kinematic strain hardening behaviour in trans-

formable alloys (i.e. TWIP and/or TRIP alloys) compared with that in conventional

non-transformable steels such as dispersion strengthened alloys. Nevertheless, it is of

both scientific and technological significance to investigate the Bauschinger effect in

materials in which deformation induced phase transitions can occur. The challenge of

understanding the Bauschinger effect in transformable alloys lies in that it is a pro-

cess, as new obstacles such as mechanical twins and deformation induced martensite

are being added into the microstructure during the deformation process, which would

further change the dislocation substructures on top of that produced by dislocation

glide and thus affects the evolution of the backstress in a manner different from the

process solely controlled by dislocation slip.

Bouaziz et al. (2008) have proposed a model to describe the kinematic harden-

ing behaviour of Fe-22Mn-0.6C, which is a type of TWIP steel. The basic scheme of

their work is to link the hardening behaviour with the density of dislocations stored in

the material, and the key idea is to treat deformation twins, in a similar way to grain

boundaries, as strong obstacles to the progress of mobile dislocations. A description

of the evolution of the mechanically twinned fraction was included in their studies.

Their model can predict well the overall strain hardening as a whole, but seems to

underestimate the kinematic strain hardening, as can be seen in Figure 2.6.

To exclude the effect of grain boundaries, Karaman et al. (2001; 2002) evalu-

ated the Bauschinger effect in the Fe-12.3Mn-1.03C Hadfiled single crystals in which

mechanical twinning is a possible deformation mode. They correlate the Bauschinger

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Figure 2.6: Comparison between the simulated and experimental monotonic tensile be-haviour and back-stress evolution for the alloy with 3 m grain size (Bouaziz et al., 2008).

effect with the deformation mechanisms that are operating during the preceding for-

ward loading path. They found that whenever mechanical twinning is the primary

deformation mode in forward loading, there is a significant lowering in the reverse

yield strength and thus a prominent Bauschinger effect; the homogeneous slip, how-ever, results in a lower Bauschinger effect. Karaman et al. further conclude, from

their microscopic observations of the dislocation structures such as that shown in Fig-

ure 2.7, that the high Bauschinger effect observed in this type of material is attributed

to the long-range backstress arising from dislocation pile-ups that are accumulated

at twin boundaries, which are strong barrier to dislocation motion at low strains.

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Figure 2.7: Two-beam bright-field image showing the dislocation arrangement near amicro-twin at 3% tensile strain. Note the dislocation pile-ups near the twin boundary.After Karaman et al. (2002).

SECTION 2.2

Phase Transitions in High Manganese Alloys and

Their Thermal Driving Force

A number of studies concluded that the excellent mechanical properties of

the high manganese alloys originate from the complex combination of deformation

mechanisms in addition to dislocation glide, which are mechanical (or deformation)

twinning (Dai et al., 1999; Karaman et al., 2000a; Grassel et al., 2000; Remy, 1978a,b;

Klassen-Neklyudova, 1964; Frommeyer et al., 2003; Karaman et al., 2002; Hyoung Cheol

et al., 1999; Remy, 1977c) and deformation induced martensitic reactions (Tomota

et al., 1986, 1988; Sato et al., 1982; Hyoung Cheol et al., 1999; Frommeyer et al., 2003;

Bracke et al., 2006). To be concise in some of the text, these two types of deformation

modes will be unified into one name, i.e. phase transitions, in order to distinguish

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them from the process of dislocation glide. The present section will briefly review

some of the basic concepts about these two deformation modes. The temperature

and composition dependence of mechanical twinning and martensitic phase transfor-

mation will be also reviewed. Discussion of the effect of phase transitions on the

strain hardening behaviour will be presented in section 2.3.1.

2.2.1 Mechanical Twinning

Generally speaking, there are two ways of producing twins. First, twinned

crystals can be produced during growth from vapor, liquid or solid; alternatively,

crystals can also become twinned by mechanical deformation, which is called me-

chanical or deformation twinning (Kelly et al., 2000). In the present studies, only

the mechanical (or deformation) twinning is primarily concerned.

We like to give a brief review on mechanical twinning in the following struc-

ture. The crystallographic aspects of deformation twinning are first introduced. The

morphology and structure of twinning will be discussed from both the experimental

observations and dislocation models, followed by a description of the pole mechanisms

for the twinning growth.

2.2.1.1 Crystallographic Theory of Twinning

Twinning elements:

Deformation by twinning, unlike dislocation glide which preserves the crystal

structure in the same orientation, reproduces the crystal structure in a specific new

orientation (Klassen-Neklyudova, 1964). Thus, it is necessary to have a geometric

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description of the twinning structure. Usually, four twinning elements (1, 2, 1, 2)

and the scalar magnitude of shear s are used to describe the crystallography of twin-

ning. 1 is the invariant plane of twinning (termed as twining plane or composition

plane), which is neither distorted nor rotated; 2 is the second undistorted plane

(conjugate twinning plane), it has its name because of the feature that all vectors in

2 plane are unchanged in length after twinning (only rotated); 1 is the shear direc-

tion and 2 the conjugate shear direction. The illustration of the twinning elements

is made in Figure 2.8.

Figure 2.8: The four twinning elements. After Klassen-Neklyudova (1964).

Twin structures in FCC and HCP crystals:

We will now discuss the twin structures in three types of crystal structures,

i.e. FCC and HCP, which are prevalent structures in Fe-Mn alloys. For FCC metals,

twinning elements are as follows: 1 = (111), 1 = [112], 2 = (111), 2 = [112]

and with a magnitude of twinning shear of 0.707. This amounts to displacing each(111) layer in the twin by 1/6[112] over the layer underneath. For HCP metals,

limited nature of the common slip modes in these metals makes twinning a necessary

component of their deformation. Twinning elements for HCP metals are found to be:

1 = (1012), 1 = [1011], 2 = (1012), 2 = [1011], and the magnitude of twinning

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shear varies with the c/a ratio but is always small ranging from 0.175 for Cd to -0.186

for Be (Kelly et al., 2000).

2.2.1.2 The Morphology and Structure of Mechanical Twinning

Experimental observations:

The twinned regions are usually in the form of plates parallel to 1 plane.

Sometimes, the plate is very thin and the twin is a lamella whose faces are accuratelyparallel to 1 plane. Under optical microscope, a twin appears as a band about 0.5-

2 m. However, transmission electron microscopy shows that it consists in fact of

many thin twins or micro-twins which are at most a few nanometers thick (Remy,

1978b). Illustration of understanding this organization of twinning as well as the

TEM observations of stacks of micro-twins in high manganese alloys (Allain et al.,

2004b) are shown in Figure 2.9.

(a) Illustration of stacks of micro-twins (b) TEM dark field micrographs

of stacks of micro-twins (Fe-22wt.%Mn-0.6wt.%C, after 33%strain).

Figure 2.9: Organization of twinning by stacking of micro-twins (Allain et al., 2004b).

Dislocation Models of Twinning:

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If a rigid twin is embedded in a perfectly rigid matrix, and if it is everywhere

firmly bounded to that matrix, then the only possible interface is the undistorted and

unrotated plane 1. For a twin of any other form, the matrix has to accommodate

itself to the shape change of the twinned region. If the accommodation required is

small enough, it may be obtained by elastic strain. Under this condition, a finite

lamella must taper to an edge at its sides and be lens-shaped. The corresponding

elastic strain field can be represented by an appropriate array of dislocations (Kelly

et al., 2000), which is shown in the Figure 2.10 (a) and (b).

Figure 2.10: (a) Twin lamella intersecting a surface AB; (b) Dislocation model of thesame lamella; (c) Dislocation model of a thin twin lamella.

If the lamella is thin and tapered, a pile-up of dislocations on a single plane

will represent the stress field adequately. This kind of dislocation model is shown in

Figure 2.10 (c). The shear stress due to a pile-up ofn screw dislocations at sufficiently

large distances from the head of the pile-up is given by

=nb

2r=

hg

2r(2.5)

where is shear modulus, b is the Burgers vector, r the radial distance from dis-

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location core, h the thickness fo the twin lamella at any point and g the twinning

shear. Derivation of equation 2.5 are omitted here. The product hg determines

the magnitude of accommodation stress and strain in this case and also in the more

general case of mixed dislocations where both tensile and shear strains are produced.

At the tip of a twin that has been blocked by some obstacle, the tensile strain may

be large enough to nucleate a crack. However, it is also found that the stresses at the

edge of twin can be relieved by accommodation via slip, which can be described by a

model of emissary dislocations (Kelly et al., 2000).

The dislocation model described in Figure 2.10 (b) is usually called Frank

dislocation model. This classical configuration makes sense if the dislocations are

glissile in the plane of interface and have their Burgers vectors in the same plane.

Another dislocation model of twins, based upon the concept of continuous surface

dislocations, is the Bullough dislocation model (Cahn, 1964). In this model, the

twin interfaces are believed to consist of edge dislocations forming a tilt boundary ofinvariant angle, as shown in Figure 2.11. This model is geometrically self-consistent,

and motion of such an array of edge dislocations or the tilt boundary thickens the

twin lamella.

Figure 2.11: Bullough dislocation model of twins.

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2.2.1.3 Pole Mechanism for the Growth of a Twin

Dislocation mechanisms for the nucleation and growth of a twin are illustrated

in Figure 2.12. A dislocation PQ creates a twin by gliding over successive planes that

are parallel to 1 (twin plane). PQ intersects with PP, whose b has a component

perpendicular to twin planes and equal to their spacing. The twin planes are there-

fore turned into a spiral ramp on which the twinning dislocation PQ glides. The

dislocation PP, which PQ spirals about, is called the pole. In FCC metals, the

dislocation PP may be dissociated into a Shockley partial PQ and a Frank partial.

Only the Shockley partial PQ can spirals about the pole PP and Frank partial is

sessile in the twin plane (Kelly et al., 2000).

Figure 2.12: Pole mechanism for the growth of a twin.

2.2.2 Martensitic Phase Transformations

Unlike in the description of mechanical twinning where the shear is com-

monly used as it seems to be an essential nature of twinning in most cases, people

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tend to describe the martensitic phase transformation from the views of phase sta-

bility (thermodynamics) and/or dislocation reactions (e.g. stacking faults) probably

due to the birth of a new phase. The present review will thus adopt this custom.

In fact, there has been a comprehensive review in Spencers PhD thesis (2004) on

deformation induced martensite transformation.

The crystallography of the deformation induced martensite phase trans-formation is found to follow a general rule that the closest packed planes and directions

of both the parent and product phases are well aligned (Olson & Cohen, 1976). A

recent study by Bracke et al. (Bracke et al., 2006) in the Fe-Mn-Cr alloys shows that

martensite could also form in a sequence of , and its closest packedplanes and directions are also parallel to those of the other two phases. The ori-

entation relationship of the two types of martensitic phase transformations can be

summarized as follows,

(111) (0001) (101)[110] [1210] [111]

Olson et al. (1976) found that the martensitic embryo nucleation consists a

faulting process which originates from an existing defect. Brooks et al. (1979b; 1979a)

found in their direct observations of martensite nuclei in stainless steel that such de-

fects are usually the irregularly spaced stacking faults. Further transmission electron

microscopic investigations revealed that there are two possible processes which are re-

sponsible for the formation of martensite: the regular overlapping of stacking faults

on {111} slip planes and the irregular overlapping process (Fujita & Ueda, 1972). Forthe latter process, the overlapping of stacking faults occurs irregularly at first and

then gradually changes to the regular sequence. Different from the formation of

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martensite, Brooks et al. (1979b; 1979a) reported that the martensite nucleation

is associated with dislocation pile-ups on the active slip plane.

Both the growth and morphology of martensite seems to be strongly influ-

enced by the original austenite grain size. In a study of the Fe-15Mn alloy, Takaki

et al. (1993) summarized their findings on the effect of austenite grain size on the

morphology of martensite into a diagram, as is shown in Figure 2.13. It is found

that when the grain size is less than 30 m, plates transverse austenite grains from

one side to the other. When the grain size is larger than 30 m, a lot of plates

with different length and thickness intersect with each other inside austenite grains.

In their studies, they concluded that the formation of multi-variants of marten-

site comes from the branching of which takes place at the tip of a pre-formed

martensite. Such branching behaviour will be stopped due to constraint from grain

boundaries, and implies a suppressive effect in the phase transformation by

the refinement of austenite grains.

Figure 2.13: Effect of austenite grain size on the type of martensite morphology (Takakiet al., 1993).

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Putaux and Chevalier (1996) further investigated the morphology of martensite phase transformation in a Fe-Mn-Si-Cr-Ni shape memory alloy by both

the conventional and high resolution TEMs. Their TEM observations reveal that a

large martensite plate appears to be composed of thinner -layers having a thickness

ranging from a few to a few dozen atomic planes and separated by layers of retained

austenite. Figure 2.14 shows one of their typical high resolution TEM observations.

Figure 2.14: High resolution image showing the layered substructure of a large -plate (Putaux & Chevalier, 1996). The processed image is inset on the right. It is assumedthat the atoms are white.

They postulated that the martensite phase transformation is achievedby the correlated glide of Shockley partial dislocations, shearing the austenite matrix

on every other {111} plane, and they further proposed a model for the growth of martensite, in which they postulated that the thermal martensite develops by

the nucleation of new layers and the propagation of pre-formed ones rather than

thicknening of the ones already formed.

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2.2.3 Thermal Driving Force for Phase Transitions Stack-

ing Fault Energy

It is generally accepted that the choice of deformation mechanisms in metals

and alloys, or more specifically, the activation of phase transitions, mainly depends on

both the thermal driving force and mechanical driving force. We focus on the aspect

of the thermodynamic driving force in the present part, and start with the important

concept or definition of stacking faults (SF) and stacking fault energy (SFE), as well as

its relationship with deformation mechanisms. A brief review of the thermodynamic

model of SFE will be followed, but only the fundamental function is given and we

will refer to a couple of original works for those readers who are interested in this

topic. Finally, we will look into which factors affect SFE and thus the deformation

mechanisms. The investigation of this issue is essentially important for the study of

mechanical properties of high manganese alloys in terms of both the scientific interests

and engineering materials design. Note that the present review mainly addresses the

FCC crystal structure, i.e. austenite in steels.

2.2.3.1 SF, SFE and phase transitions

It is of value to consider how SFE correlates with the activation of phase

transitions (i.e. mechanical twinning and martensitic phase transformation). Now

let us start with the formation of a stacking fault. In materials of low SFE, the

general process of the formation of a stacking fault is considered to consist of two

steps (Courtney, 2005). The first step is that a perfect dislocation is dissociated in

FeMnAlloys HB

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