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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
4.2.1 Mechanical Response and Work Hardening Behavior of the Fe-30Mn Alloy at 77 K . . . . . . . . . . . . . . . . . . . . . . . 117
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
5.1.1 Mechanical Response and Work Hardening Behavior of the Fe-24Mn Alloy at 293 K . . . . . . . . . . . . . . . . . . . . . . . 143
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
5.2.1 Mechanical Response and Work Hardening Behavior of the Fe-24Mn Alloy at 77 K . . . . . . . . . . . . . . . . . . . . . . . 173
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
4.6 SEM images of microstructures of the Fe-30Mn alloy after T = 5%tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.7 SEM images of microstructures of the Fe-30Mn alloy after T = 10%tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.8 SEM images of microstructures of the Fe-30Mn alloy after T = 20%tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.9 SEM images of microstructures of the Fe-30Mn alloy after T = 30%tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 103
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
4.24 Mechanical response of the Fe-30Mn alloy at 77 K: (a) Engineeringstress strain plot and (b) True stress strain plot. . . . . . . . . . . 118
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
5.2 Mechanical response of the Fe-24Mn alloy at 293 K: (a) Engineeringstress strain plot and (b) True stress strain plot. . . . . . . . . . . 144
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
5.6 SEM images of microstructures of the Fe-24Mn alloy after T = 5%tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.7 SEM images of microstructures of the Fe-24Mn alloy after T = 10%tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.8 SEM images of microstructures of the Fe-24Mn alloy after T = 20%tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.9 SEM images of microstructures of the Fe-24Mn alloy after T = 30%tensile strain at 293 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 152
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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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