Phase transformations in steels Volume 1: Fundamentals and
diffusion-controlled transformations (ISBN 978-1-84569-970-3)
Edited by two leading experts in the field, and with contributions
from some of the most distinguished figures in steel research, this
two-volume work summarises the vast amount of recent research on
phase transformations in steels. The book covers both fundamental
aspects (thermodynamics, diffusion, etc.) and more particular
features (bainite, martensite, etc.). Volume 1 reviews
fundamentals, diffusion-controlled, bainite and
diffusional-displacive transformations.
Microstructure evolution in metal forming processes: Modelling and
applications (ISBN 978-0-85709-074-4) Metal forming processes
involve varying degrees of deformation to the metal substrate. This
deformation results in changes to the microstructure of the metal.
These microstructural changes need to be monitored and controlled.
This book looks at the evolution of microstructure during metal
forming processes and its modelling and control to produce steels
and other metals with the right properties.
Nanostructured metals and alloys: Processing, microstructure,
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Nanostructured metals and alloys have enhanced tensile strength,
fatigue strength and ductility and are suitable for use in
applications where strength or strength-to-weight ratios are
important. Part I of this important book reviews processing
techniques for bulk nanostructured metals and alloys. Parts II and
III discuss microstructure and mechanical properties, whilst Part
IV outlines applications of this new class of material.
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ii
techniques
Oxford Cambridge Philadelphia New Delhi
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iv
Part I Diffusionless transformations 1
1 Crystallography of martensite transformations in steels 3
P. M. Kelly, The University of Queensland, Australia
1.1 Introduction 3 1.2 Martensite transformations in steels 4 1.3
Phenomenological theory of martensite crystallography
(PTMC) 10 1.4 The post phenomenological theory of martensite
crystallography (PTMC) period 18 1.5 Strain energy – the
Eshelby/Christian model and the
infinitesimal deformation (ID) approach 23 1.6 Interfacial
dislocation models 25 1.7 Future trends 28 1.8 Conclusions 29 1.9
References 30
2 Morphology and substructure of martensite in steels 34 T. Maki,
Kyoto University, Japan
2.1 Morphology and crystallographic features of martensite in
ferrous alloys 34
2.2 Morphology and substructure of lath martensite 38 2.3
Morphology and substructure of lenticular martensite 46 2.4
Morphology and substructure of thin plate martensite 50 2.5
Conclusions 54 2.6 References 56
Contents
v
© Woodhead Publishing Limited, 2012
3 Kinetics of martensite transformations in steels 59 G. B. Olson
and Z. D. Feinberg, Northwestern University, USA
3.1 Introduction 59 3.2 Mechanism and kinetics of martensitic
transformation 60 3.3 Mechanically induced transformations 63 3.4
Transformation plasticity constitutive relations and
applications 66 3.5 Conclusions 79 3.6 References 80
4 Shape memory in ferrous alloys 83 D. Dunne, University of
Wollongong, Australia
4.1 Introduction 83 4.2 Fe-Pt alloys 89 4.3 Fe-Ni and Fe-Ni-C
alloys 93 4.4 Fe-Ni-Co-based alloys 96 4.5 Austenitic stainless
steels with low stacking fault energy
(SFE) 99 4.6 Fe-Mn-based alloys 100 4.7 Summary 115 4.8
Acknowledgements 118 4.9 References 118
5 Tempering of martensite in carbon steels 126 G. Krauss, Colorado
School of Mines, USA
5.1 Introduction 126 5.2 Martensitic microstructures prior to
tempering heat
treatments 127 5.3 Classification of aging and tempering stages:
general
considerations 130 5.4 Changes in martensitic fine structure due to
aging 131 5.5 The stages of tempering 132 5.6 Conclusions 145 5.7
References 145
Part II Phase transformations in high strength steels 151
6 Phase transformations in microalloyed high strength low alloy
(HSLA) steels 153
R. C. Cochrane, University of Leeds, UK
6.1 Introduction to microalloyed high strength low alloy (HSLA)
steels 153
viiContents
© Woodhead Publishing Limited, 2012
6.2 Brief historical review of the development of microalloyed
steels 155
6.3 Solubility of microalloying elements in austenite and ferrite
157 6.4 Precipitation 161 6.5 Effects of microalloying on
transformation kinetics 177 6.6 Phase transformations during high
strength low alloy
(HSLA) steels processing 185 6.7 Controlled processed
ferrite/bainite and acicular ferrite
steels 199 6.8 Conclusions and future trends 205 6.9
Acknowledgements 207 6.10 References 207
7 Phase transformations in transformation induced plasticity
(TRIP)-assisted multiphase steels 213
P. J. Jacques, Université Catholique de Louvain (UCL),
Belgium
7.1 Introduction 213 7.2 Historical perspectives on the emergence
of transformation
induced plasticity (TRIP)-assisted multiphase steels 215 7.3
Influence of parameters of the thermomechanical process
on the formation of multiphase microstructures containing retained
austenite 223
7.4 Conclusion and future trends 242 7.5 References 243
8 Phase transformations in quenched and partitioned steels
247
J. G. Speer, Colorado School of Mines, USA
8.1 Introduction to the quenching and partitioning concept 247 8.2
Microstructure development fundamentals and alloy designs 252 8.3
Mechanical behavior, potential applications, and
implementation status 260 8.4 Conclusions 267 8.5 References
268
9 Phase transformations in advanced bainitic steels 271 F. G.
Caballero and C. Garcia-Mateo, National Centre for
Metallurgical Research (CENIM-CSIC), Spain
9.1 Introduction 271 9.2 Design of third generation of advanced
high strength steels 273 9.3 Carbide-free bainitic steels: a
material ready for the
nanocentury 283
viii Contents
© Woodhead Publishing Limited, 2012
9.4 Conclusions and future trends 290 9.5 Acknowledgement 291 9.6
References 291
10 Phase transformations in high manganese twinning-induced
plasticity (TWIP) steels 295
B. C. De Cooman, Pohang University of Science and Technology, South
Korea
10.1 Introduction 295 10.2 Fe-Mn-X alloys 297 10.3 Strain-induced
twinning 307 10.4 Twinning-induced plasticity (TWIP)
industrialization 327 10.5 Conclusions 327 10.6 Acknowledgements
328 10.7 References 328
11 Phase transformations in maraging steels 332 W. Sha, Queen’s
University Belfast, UK, H. Leitner, University of
Leoben, Austria, Z. Guo, Sente Software Ltd, UK and W. Xu,
ArcelorMittal Global R&D Gent, Belgium
11.1 State of the art of ultra high strength steels 332 11.2 Types
of maraging steels 334 11.3 Microstructure and precipitates in
maraging steels 339 11.4 Reverted austenite and mechanical
properties 342 11.5 Evolution of precipitates and the overall
process 346 11.6 Precipitation kinetic theory in Fe-12Ni-6Mn
maraging type
alloy 349 11.7 Research trends 356 11.8 References 359
Part III Modelling phase transformations 363
12 First principles in modelling phase transformations in steels
365
M. H. F. Sluiter, Delft University of Technology, The
Netherlands
12.1 Introduction 365 12.2 Ab initio description of phase stability
of pure iron 370 12.3 Ab initio phase stability of iron carbides
374 12.4 Substitutional alloying elements 377 12.5 Ab initio
description of diffusivity in bcc Fe 381 12.6 Future trends 384
12.7 References 385
ixContents
13 Phase field modelling of phase transformations in steels
405
M. Militzer, The University of British Columbia, Canada
13.1 Introduction 405 13.2 Phase field methodology 406 13.3
Austenite formation 414 13.4 Austenite decomposition 418 13.5
Future trends 428 13.6 References 429
14 Molecular dynamics modeling of martensitic transformations in
steels 433
H. M. Urbassek and L. Sandoval, Universität Kaiserslautern,
Germany
14.1 Introduction 433 14.2 Interatomic interaction potentials 434
14.3 Martensitic transformations in iron: case studies 443 14.4
Transformations in ferrous nanosystems 449 14.5 Conclusions and
future trends 459 14.6 Acknowledgement 460 14.7 References
460
15 Neural networks modeling of phase transformations in steels
464
C. Capdevila, National Centre for Metallurgical Research
(CENIM-CSIC), Spain
15.1 Introduction 464 15.2 Essence of the method 465 15.3 On the
quest of critical temperatures 472 15.4 Determining microstructural
parameters 488 15.5 Development of continuous cooling
transformation (CCT)
diagrams 496 15.6 Conclusions and future trends 498 15.7 References
500
Part IV Advanced analytical techniques for studying phase
transformations in steels 505
16 Application of modern transmission electron microscopy (TEM)
techniques to the study of phase transformations in steels
507
D. Boyd and Z. Yao, Queen’s University, Canada
x Contents
preparation 508 16.3 Conventional transmission electron microscopy
(CTEM)
of steels 510 16.4 Modern transmission electron microscopy (TEM) of
steels 513 16.5 In-situ transmission electron microscopy (TEM) 524
16.6 Future trends: emerging transmission electron microscopy
(TEM) techniques 525 16.7 Sources of further information and advice
528 16.8 Conclusions 529 16.9 References 529
17 Atom probe tomography for studying phase transformations in
steels 532
M. K. Miller, Oak Ridge National Laboratory, USA
17.1 Introduction 532 17.2 Outline of the technique 533 17.3
Specimen requirements 535 17.4 Recent developments 536 17.5
Interpretation of data 537 17.6 Characterizing and understanding
phase transformations
in various steels 538 17.7 Future trends 553 17.8 Conclusion 554
17.9 Acknowledgments 554 17.10 References 554
18 Electron backscatter diffraction (EBSD) techniques for studying
phase transformations in steels 557
S. Zaefferer, N.-N. Elhami and P. Konijnenberg, Max Planck
Institute for Iron Research, Germany
18.1 Introduction 557 18.2 Fundamentals of electron backscatter
diffraction
(3D-EBSD) technique 558 18.3 The current standard of 2D electron
backscatter diffraction
(EBSD) applications 561 18.4 3D electron backscatter diffraction
(3D-EBSD) 569 18.5 Conclusions and future development of the
technique 579 18.6 References 583
xiContents
19 Application of synchrotron and neutron scattering techniques for
tracking phase transformations in steels 588
S. S. Babu, The Ohio State University, USA
19.1 Introduction 588 19.2 X-ray and neutron scattering techniques
590 19.3 Measurements of phase transformation in steels 605 19.4
Conclusions and future trends 624 19.5 Acknowledgements 625 19.6
References 625
Index 634
E-mail:
[email protected]
Professor David Edmonds Institute for Materials Research School of
Process, Environmental
and Materials Engineering University of Leeds Leeds LS2 9JT
UK
E-mail:
[email protected]
Division of Materials School of Mechanical and Mining
Engineering The University of Queensland Brisbane Queensland 4072
Australia
E-mail:
[email protected]
Chapter 2
Dr Tadashi Maki Nippon Steel Corporation 20-1, Shintomi, Futtsu
Chiba 293-8511 Japan
E-mail:
[email protected]
(* = main contact)
Chapter 3
G. B. Olson* and Z. D. Feinberg Department of Materials
Science
and Engineering Northwestern University 2220 Campus Drive Evanston,
IL 60208 USA
E-mail:
[email protected]
Chapter 4
Emeritus Professor Druce Dunne Faculty of Engineering University of
Wollongong Northfields Avenue Wollongong NSW 2522 Australia
E-mail:
[email protected]
Chapter 5
Products Research Center The George S. Ansell Department
of Metallurgical and Materials Engineering
Colorado School of Mines Golden, CO 80401 USA
E-mail:
[email protected]
Chapter 6
R. C. Cochrane University of Leeds Formerly British Steel Professor
of
Ferrous Metallurgy UK
E-mail: r.cochrane.cochrane@btinternet. com
(UCL) Institute of Mechanics Materials and Civil Engineering
(iMMC) Division of Engineering of
Materials and Processes (IMAP) Place Sainte Barbe, 2 B-1348
Louvain-la-Neuve Belgium
E-mail:
[email protected]
Chapter 8
Products Research Center The George S. Ansell Department
of Metallurgical and Materials Engineering
Colorado School of Mines Golden, CO 80401 USA
E-mail:
[email protected]
National Centre for Metallurgical Research (CENIM-CSIC)
Av. Gregorio del Amo, 8 E-28040 Madrid Spain
E-mail:
[email protected]
Chapter 10
B. C. De Cooman Materials Design Laboratory Graduate Institute of
Ferrous
Technology Pohang University of Science and
Technology Pohang South Korea
Wei Sha* School of Planning, Architecture
and Civil Engineering Queen’s University Belfast Belfast BT7 1NN
UK
E-mail:
[email protected]
Early Stages of Precipitation University of Leoben
Franz-Josef-Straße 18 A-8700 Leoben Austria
Zhanli Guo Sente Software Ltd Surrey Technology Centre 40 Occam
Road Guildford GU2 7YG UK
Wei Xu OCAS ArcelorMittal Global R&D Gent BE-9060 Zelzate
Belgium
Chapter 12
Marcel H. F. Sluiter Department of Materials Science
and Engineering, 3ME Delft University of Technology Mekelweg 2 2628
CD Delft The Netherlands
E-mail:
[email protected]
Chapter 13
Process Engineering The University of British Columbia 309-6350
Stores Road Vancouver BC Canada V6T 1Z4
E-mail:
[email protected]
Fachbereich Physik und Forschungszentrum OPTIMAS
Universität Kaiserslautern Erwin-Schrödinger-Straße D-67663
Kaiserslautern Germany
E-mail:
[email protected]
Chapter 15
C. Capdevila Materalia Group Department of Physical Metallurgy
National Centre for Metallurgical
Research (CENIM-CSIC) Avda. Gregorio del Amo, 8 E-28040 Madrid
Spain
E-mail:
[email protected]
Chapter 16
Materials Engineering Queen’s University Kingston, ON Canada K7L
3N6
E-mail:
[email protected]
Chapter 17
Division Oak Ridge National Laboratory Oak Ridge, TN 37831-6136
USA
E-mail:
[email protected]
Chapter 18
Dr Stefan Zaefferer*, Nahid-Nora Elhami, Peter Konijnenberg
Department of Microstructure Physics and Alloy Design Max Planck
Institute for Iron
Research Max-Planck-Str. 1 D-40237 Duesseldorf Germany
E-mail:
[email protected];
[email protected];
Sudarsanam Suresh Babu Department of Materials Science
and Engineering The Ohio State University 1248 Arthur E. Adams
Drive #130, Columbus, OH 43221 USA
E-mail:
[email protected]
© Woodhead Publishing Limited, 2012
A new and comprehensive book on phase transformations in steels is
both timely and welcome. It is gratifying near the beginning of a
new, technology- dominated, century to see a group of experts and
well accomplished researchers, some of whom have devoted major
parts of their professional activities to this area, as well as a
group of younger researchers and steel users, all willing to
assemble together a new two-volume publication on steels.
Strikingly, unlike many other groups of important metallic
materials, it is the onset of transformations in steels resulting
from the various thermal and mechanical treatments that make steels
so special. This is possible mainly because of the unique
properties of iron (Fe) which exhibits three different simple
crystal structures; bcc, fcc and bcc again, as temperature rises.
Even more unique is the fact that contrary to the usually observed
order of the sequence of phase changes observed with temperature,
the gamma phase at higher temperatures, is the ‘more open’ phase
than the bcc alpha phase, and hence more able to absorb substantial
amounts of alloying element additions. As a result, on quenching or
cooling, and other heat treatments, all kinds of phase
transformations can take place, and their understanding,
manipulation, and utilization constitutes the essence of the
importance that steels have exhibited in the past in the
development of civilizations and related technologies. The various
chapters bring nicely up to date the vast assembled knowledge of
steel transformations in the literature: from the more basic
aspects (thermodynamics, diffusion, kinetics, etc.), through the
more particular transformation features (nucleation and growth,
bainite, martensite, massive, shape memory, etc.), to some aspects
of the more recent and advanced analytical possibilities
(synchrotron, atom probe, etc.). Perhaps it is fitting also to
mention that the bewildering role of magnetism in iron is the basis
of much of this behavior. It is well documented that the
ferromagnetic transition in the bcc-Fe phase makes the bcc phases
more stable at lower temperatures than the fcc-gamma phase, but
still too few people realize that it is the anti-ferromagnetic
transition in the gamma phase at temperatures near 0 K that makes
the crystalline closed-packed (therefore
Foreword
xvii
© Woodhead Publishing Limited, 2012
‘wrong’) gamma phase return to stability on heating. Without these
unusual features of iron, phase transformations in steels would not
take place and the enormous versatility and benefits of steels in
the progress of society would be lost. It may also be time to admit
that the ferromagnetic alpha phase has actually a bc-tetragonal
symmetry due to the magnetic moments, if the more modern standards
of phase definition are adopted, and so the bcc (and paramagnetic)
beta phase which has been banished from the iron phase diagrams
since the 1920s should be rightfully restored to its original
position. Undoubtedly, research on transformations in steels will
continue in the future, as more sophisticated heat treatments are
devised and more advanced techniques are brought into use to study
the results, particularly at the micro and nano scales. The present
book is likely to serve here as a good basis for future
advances.
Ted Massalski Professor of Materials Science, Engineering and
Physics
Carnegie Mellon University
Introduction
Steel has been available as a high tonnage engineering material for
nearly two centuries. During this time it has had a very creditable
track record and one which is crucial to engineering progress,
especially in providing the infrastructure in underdeveloped and
developing parts of the world, which still dwarf in size and
population the more developed nations. This is why the volume of
steel production continues to increase, leading to the continual
need to consider more economic ways of manufacturing using steel in
order to minimise energy consumption and preserve natural
resources. Despite commendable efforts by scientists and engineers
to understand fully the processing-microstructure-property
relationships in steels, these continue to present new challenges
to researchers because of the complexity of the phase
transformation reactions and the wide spectrum of microstructures
and properties achievable. Thus, an important theme and objective
of this book is to follow the development of our understanding of
phase transformations in iron alloys and steels through to the
development of modern commercial steels, and in particular to
highlight the clear connection between phase transformation
studies, no matter how isolated and remote they may seem at the
outset, to the emergence of new steels with enhanced engineering
properties. Unlike many other metals, the combination of several
characteristics, such as magnetism, allotropic phase changes and
the different solubility and diffusion behaviour of interstitial
and substitutional elements, makes iron- based alloys unique and is
responsible for a diversity of phase transformations. The first
chapter of this book provides a historical perspective on the first
pioneering attempts to gain insight into the complexity of these
reactions. All aspects of phase transformations (thermodynamics,
diffusion, kinetics and crystal structure) must be properly
understood in order to develop a complete picture of the
transformation reactions in steels. Thus it was deemed necessary to
devote the first section of the book to the fundamental principles
of thermodynamics, diffusion and kinetics, and in addition, owing
to its growing importance in helping to understand transformations,
the phase boundary interface separating parent and product, now
much more amenable to observation and analysis using the increased
power of modern metallographic instrumentation, as well as
modelling.
xix
xx Introduction
Starting from the earliest studies on phase transformations in
steels, a large number of theories and definitions have emerged
leading to continual debates amongst researchers. Only with the
development of more advanced experimental capabilities have some of
these issues been satisfactorily resolved while others still
provoke conflicting opinions. This book aims to represent the
current status of knowledge on steel phase transformations whilst
also highlighting the challenges facing future researchers in this
field. As mentioned in the Foreword, and demonstrating how the Fe-C
system continues to generate important issues, magnetism plays an
important role in the phase transformations of iron and steels due
to the ferromagnetic and anti-ferromagnetic transitions that take
place. Thus it is suggested that paramagnetic beta phase should be
restored to the Fe-C phase diagram. The most important
transformations in steels, and the area where almost all research
has been concentrated, are those which result in the final
microstructure and properties. These involve decomposition of the
high temperature g-phase, austenite, which takes place on cooling
and, dependent upon steel alloying and cooling conditions and also
whether mechanical working occurs, could follow different paths
resulting in a large diversity of lower temperature phase types and
their mixtures. These phase transformations could be classified
based upon microstructure, thermodynamics or mechanisms and in the
present book the phase transformations are classified according to
their mechanism. In this scheme the phase transformations in steels
are customarily divided into two major groups, which are named
according to whether long-range diffusion of atoms occurs or not,
namely diffusional or non-diffusional (diffusionless). Each type of
phase transformation is then characterised by a set of specific
features, including but not limited to composition, crystal
structure, shape change and carbon mobility. It is generally
accepted that the formation mechanisms of proeutectoid grain
boundary allotriomorphs (of a-ferrite and cementite) and pearlite
are diffusional. These reactions take place within the higher
temperature region of the low temperature phase field with slow
kinetics and generally do not require significant undercooling
below the g Æ a transition temperature. In contrast, the formation
of martensite with a structure change but composition inherited
from parent austenite occurs by a diffusionless transformation at
rapid cooling and/or large undercoolings. In-depth presentations of
the current state of phase transformation theory for the former
type of reactions are given in Volume 1, Part II, whereas the
latter is addressed in Volume 2, Part I. These constitute the more
traditional microstructures which have long been studied; Henry
Clifton Sorby, for example, first identified pearlite around the
middle of the 19th century. Moreover, they have long provided the
properties of the high-tonnage carbon and alloy steels used in
construction and many engineering applications. Nevertheless, as
described in these sections, significant progress has been made in
understanding their
© Woodhead Publishing Limited, 2012
xxiIntroduction
formation, both for ferrite/pearlite and for basic martensite, in
the latter case the phenomenological theory of martensite
crystallography and, more recently, the proposals deriving from
interface mechanics embodied in the so-called topological model,
which attempt to describe the mechanistic aspects of the
transformation. This demonstrates the rich variety of
transformations in iron- based alloys, especially when one also
adds the shape memory effect, which is of immense interest and
commercialisation in non-ferrous systems. Although significant
advances have been made in developing a basic understanding of the
nucleation and growth processes, and in validation of various
theories, questions still remain due to the limitations of even the
most powerful experimental techniques and the complexities of
multiphase microstructures forming under a variety of conditions,
generally at elevated temperatures. Examples include: elucidating
the exact path for carbon diffusion; determining the embryo
structure, location and evolution; measuring the effect of
so-called ‘solute drag’ on interface migration; determining the
diffusivities and binding energies of elements in multi-component
systems; accurately measuring interfacial and strain energies;
providing explanations on the differences between the predicted
rates of diffusion of substitutional elements at low temperatures
and the observed solute clustering. Proving again the complexity,
even previously well-accepted ideal cases of partitioning of
alloying elements under local equilibrium (LE) or paraequilibrium
(PE) conditions for diffusional transformations are now challenged
by assumption of negligible partitioning of substitutional elements
under local equilibrium (NP-LE). However, the issues most difficult
to resolve, not unexpectedly, have been related to the intermediate
products formed between the classical diffusional (e.g.
ferrite/pearlite) and diffusionless (e.g. martensite) ones. A
variety of morphologies of these products including Widmanstätten
ferrite, upper bainite, lower bainite and carbide-free bainite, as
well as granular bainite and the so-called ‘acicular ferrite
microstructures’, are considered to exhibit a mixture of
characteristics familiar to both classes of transformation, which
has fuelled continuous debate regarding the exact formation
mechanisms. Perhaps the main discord concerned with the
fundamentals of the reaction mechanism has been related to the
nature of the bainite transformation (Volume 1, Part III), which
essentially reduces to the behaviour and location of carbon during
the formation of the bainitic ferrite crystals. As mentioned above,
better resolution of such questions might evolve from real-time
measurement of carbon concentrations in parent austenite and
product ferrite during transformation at elevated temperatures.
Nevertheless, there have been significant positive advances in
these phase transformation studies. In this quest for greater
understanding of the bainite reaction mechanism, experimental
steels have been developed which contain untransformed austenite,
useful for studying features of the transformation
© Woodhead Publishing Limited, 2012
xxii Introduction
mechanism, but which have subsequently been shown can impart
valuable properties to a new generation of formable high strength
steels for automotive use that has eventually led to
commercialisation, e.g. transformation induced plasticity (TRIP)
steels. Chapters on these new steels can be found in Volume 2, Part
II, alongside comparative chapters on the new twinning induced
plasticity (TWIP) steels and high alloyed maraging steels. Almost
all modern high-volume metal production processes are continuous,
involving continuous cooling, often associated with mechanical
forming, such that complex dynamic changes are more often the norm
and sometimes even difficult to simulate in a laboratory
environment. Thus, near-equilibrium microstructures are not always
the ones which could lead to commercial success. Consequently,
given the different industrial processes required in the production
of steel in all its various forms, which are continually being
updated or modified, a section dealing with parameters involved in
transformation other than temperature was considered necessary.
External factors, such as deformation, heating rate or application
of electromagnetic field could either accelerate or retard the
phase transformations depending upon the chosen set of conditions
(Volume 1, Part IV). Although a significant body of evidence has
been accumulated over time on the effects of these parameters, the
underlying mechanisms are not yet fully understood. The phenomenon
of restoration of prior austenite morphology and orientation at
slow or fast heating rates and absence of it at intermediate
heating rates continues to puzzle physical metallurgists. The
explanations put forward for this structural inheritance also lack
direct and comprehensive experimental evidence. Many of the
significant advances to our understanding of phase transformations
in the evolution of steel microstructure during the last 50 years
would not have been possible without the parallel development of
higher resolution microscopes and related techniques. In the last
two decades significant advances have been made in many
characterisation techniques (Volume 2, Part IV) and microstructure
observations have moved from only ex-situ to also in-situ ones. It
is now possible using in-situ transmission electron microscopy,
neutron and synchrotron scattering or electron backscattering
diffraction coupled with energy dispersive X-ray spectroscopy, to
observe the progress of phase transformations not only on heating
or cooling, but under external load too. Recent leaps in the
development of atom probes and aberration corrected transmission
electron microscopes enable the collection of compositional and
crystallographic information with atomic resolutions (<0.1 nm).
The ability to gather microanalytical data at high resolutions has
become increasingly important with the realisation that relatively
low bulk concentrations of alloying elements can have
disproportionately large effects on transformation behaviour. The
exact structure of grain and interphase boundaries and solute
segregation to them can now be revealed more clearly.
© Woodhead Publishing Limited, 2012
xxiiiIntroduction
The improved resolution limit is especially valuable with the
increased trend towards production of steels with ultrafine and
nano-sized grains and precipitates. Perhaps it should be mentioned
that more and more use of 3D techniques in addition to more
customarily utilised 2D provides invaluable information on the
morphology and distribution of various phases and their
crystallography, which helps to fine-tune existing theories and
indicates the route for other experiments. But whilst researchers
should remain vigilant to artefacts related to each technique and
continue to analyse data diligently, these newly developed
techniques will allow gathering of the essential information for
advancement or validation of existing theories and models, as well
as provide the necessary input data for rapidly developing
modelling methodologies. However, we must remain mindful that these
instruments and their applications, as will be evident from this
section in the book, have become extremely specialised and
expensive, and are not widely available, and consequently much of
the metallographic work on commercial steel microstructures is
still conducted at much lower resolutions by more conventional
microscopy. This emphasises the need for consistent descriptions
and classifications of microstructure and transformation behaviours
across the length scales. As far as has been possible, we have
tried to maintain a similar nomenclature throughout the book. The
major new inclusion in this book derives from probably the most
significant and totally new topic or field of activity in phase
transformations to emerge during the latter part of the main period
covered, namely phase transformations modelling. A full section
(Volume 2, Part III) has been devoted to this fairly embryonic but
rapidly growing field, including all of the well-known approaches:
first principles, phase field, molecular dynamics, neural networks.
The models provide qualitative and semi-quantitative insight into
phase transformations. Some good examples of the preliminary
applications to ferrous transformations will be found, some of
which have already produced useful advances whilst others are
meeting the extensive challenges arising from the complexity of the
subject. The hope exists that eventually steels may be designed
from first principles taking into account the complexities of phase
change associated with those of processing on a large scale, so
often difficult to reproduce accurately in the laboratory, or
alternatively to study during commercial production. However, it is
clear that despite the progress made, the lack of reliable
experimental data for input into the models hinders their
development. For first principles models reliable experimental data
are needed for validation of the potentials. As mentioned
previously, quantitative interfacial and strain energy data, data
on diffusivities and nucleation, are urgently required to further
advance modelling and the theories of ferrous phase
transformations.
© Woodhead Publishing Limited, 2012
xxiv Introduction
Finally, the success of applying the knowledge of phase
transformations to design of advanced high strength steels should
be acknowledged (Volume 2 Part II). This part begins with a chapter
on high strength low alloy (HSLA) or microalloyed steels which have
probably been the category of steels that have seen the most
resource-intensive development during the latter part of the period
covered by this book, and still do, driven mainly by the ever more
stringent engineering requirements for steels needed in the
recovery and transmission of oil and gas. In the quest for greater
strength and toughness combined with weldability, extensive data
and understanding have been accumulated on the influence of
alloying and controlled deformation processing and cooling on the
phase transformation and precipitation reactions. The pathway from
the development of quenched and tempered steels and HSLA steels to
dual phase, transformation-induced plasticity, nanostructured
bainitic (‘Nanobain’), twinning-induced plasticity and quenched and
partitioned steels is marked by gradual increase in complexity of
processing schedules and the microstructures formed. In the latter
steels, the direct application of phase transformation sequences in
the design of processing schedules led to either significant
strength advantage or desirable combinations of high strength/high
ductility in formable steels. These manipulations of steel
microstructures also enable the achievement of cost savings due to
leaner steel compositions and consequently the reduced use of
natural resources, coupled with socio-economic benefits. This
project would not have been possible without support from Woodhead
Publishing staff and the enthusiasm and co-operation of authors and
co-authors in joining us in this task – which apart from confirming
our inception of the idea, has made it a more worthwhile and also
an enjoyable activity over the last two years. Our authors must
also be congratulated on their efforts to produce comprehensive
overviews of the topics, including fair and balanced treatments of
various theories and models where appropriate. There can be no
doubt that it has been an immense task and we can attest to the
considerable work which has gone into the production of the
manuscript for this book. It will always be a snapshot of where we
have reached in this discipline by the year of publication, but it
will also we hope, and because of the quality of the chapters
provided, stand as a useful source for reference, advanced teaching
and learning for a long time to come. In particular, it is hoped
that this book will inspire a young generation of scientists and
engineers to further advance the knowledge on phase transformations
in steels, which remains a fascinating and significant field to
explore.
Elena Pereloma University of Wollongong
David Edmonds University of Leeds
© Woodhead Publishing Limited, 2012
P. M. Kelly, The University of Queensland, Australia
Abstract: This chapter describes the unique features of martensitic
transformations in steels. It covers the characteristics that serve
to distinguish and identify the different types of ferrous
martensite and then moves on to tackle the most impressive, but
often complex and mathematically inscrutable, theory of phase
transformations ever produced – the phenomenological theory of
martensite crystallography (the PTMC). The approach concentrates on
what the mathematics attempts to achieve and not on the mathematics
itself. A general comparison between theory and experiment is
included as well as attempts to identify features that have proved
difficult to explain and hence led to subsequent improvements in
the theory. Finally, the chapter identifies the need for further
work, either to provide critical experimental evidence to test the
theories or to suggest fruitful areas for future research.
Key words: martensite, crystallography, habit plane, orientation
relationship, shape strain.
1.1 Introduction
© Woodhead Publishing Limited, 2012
of the crystallography of martensite is often never fully
appreciated. In this chapter the emphasis is on describing what the
mathematics attempts to achieve and not on the mathematics itself.
Wherever possible, the approach will be descriptive and will avoid
becoming submerged in what is often regarded as incomprehensible
mathematics. Important concepts that are essential foundation
stones for the PTMC will be explained. The various alternative
theoretical treatments and modifications to the PTMC will be
discussed and compared with the original theory. However, because
of its unsurpassed success as a predictive theory, the PTMC will
receive the lion’s share of attention and, in many cases, shown to
be at least equivalent to the later models/theories. The strength
of any predictive theory rests on its ability to account for any
experimental observations. Hence, the comparison between theory and
experiment will be covered, but not in minute detail. There is an
extensive amount of quite sophisticated experimental data on the
crystallography of ferrous martensites in steels that has been
collected over more than half a century, and it is impossible to
cover all of this individual detail in a single chapter. Instead
the emphasis will be on summaries that have appeared in textbooks
or reviews and the reader is encouraged to go back to these sources
for information on individual sets of observations. Wherever
appropriate this comparison between theory and experiment will
attempt to identify particular features that have proved difficult
to explain via the PTMC. These examples have often led to
developments/improvements in the theoretical treatment. Hence this
theoretical/experimental comparison will serve not only to test the
theories themselves, but also to provide a historical perspective
on the development of our understanding of martensite
crystallography in the last five decades. It is hoped it will also
identify the need for further work, either to provide critical
experimental evidence to test the theories or to suggest fruitful
areas for future research. Finally, the success of this chapter on
the crystallography of martensite will depend on its ability to
demonstrate the power of the PTMC and to encourage others to face
the mathematical maelstrom of matrix algebra in the hope of
appreciating its contribution to the understanding of a unique form
of phase transformation in solids.
1.2 Martensite transformations in steels
1.2.1 The characteristics of martensite transformations
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this form of transformation are that it leads to a change in
crystal structure that occurs in an athermal, diffusionless fashion
involving the simultaneous, co-operative movement of atoms over
distances less than an atomic diameter and is accompanied by a
macroscopic change of shape of the transformed volume (Bilby and
Christian, 1955; Christian, 1965, 1975, 1990; Petty, 1970;
Nishiyama, 1978; Cohen et al., 1979). While the co-operative atom
movements may involve some small ‘shuffles’ (Christian, 1990),
there is no need to ‘reconstruct’ the crystal structure of the
matrix, as there is in a conventional diffusional transformation
(Christian, 1975). From the point of view of the crystallography of
the transformation, the displacive character is particularly
important. The shape change that results from this displacive
component is relatively large and dominated by shear, as opposed to
the relatively small changes in volume that accompany the
transformation. In a surface polished prior to the transformation,
the shape change associated with the formation of a martensite
plate leads to surface tilts and the change in direction of surface
scratches, as illustrated in Fig. 1.1. The shape change, its
magnitude and direction, therefore constitute the most important
and defining features associated with a martensitic
transformation.
Surface polished before transformation
Polished and etched cross-section
LIS Slip or twinning
© Woodhead Publishing Limited, 2012
The other important crystallographic characteristics of martensite
in steels are its morphology, the orientation relationship between
the matrix and product martensite phases, the internal substructure
of the martensite itself and the nature of the interface. These
crystallographic features need to be referred to particular phases,
such as the face centred cubic (fcc) parent phase austenite denoted
by the subscript F, the body centred cubic (bcc) or tetragonal
(bct) martensite phase denoted by the subscript B and the
relatively rare hexagonal close-packed (hcp) epsilon (e) martensite
denoted by the subscript H. Martensite in steels is often
plate-like with a well-defined habit plane – the plane defined by
the plate itself. Laths are another relatively common morphology.
Martensite laths are ruler-shaped particles that have a habit
plane, as well as a specific crystallographic long direction. On
rare occasions, rod-like or multi-faceted lath shaped particles may
form. The habit plane of a plate or the major facet plane of a lath
is often used as a means of distinguishing between the various
types of martensite formed in different steels, or in the same
steel under differing conditions. The major types of ferrous
martensite consist of the {259}F martensite plates formed in Fe-Ni
alloys with more than 29% Ni, Fe-Ni-C, Fe-24.5at%Pt, and Fe-Al-C,
the {225}F martensite plates formed in high carbon and/or high
alloyed carbon steels, the {557}F lath martensite typical of low
carbon steels and the {1 12}F bcc laths and {111}F hexagonal
close-packed epsilon martensite formed in low stacking fault energy
stainless steels (Nishiyama, 1978; McDougall and Wayman, 1992). It
must be remembered that these so-called habit planes are generally
‘irrational’, i.e. they cannot strictly be represented by simple,
single-digit Miller indices. However, rather than use a more
complex system to represent the habit plane, they are usually, in
the interests of brevity at the expense of precision, expressed in
terms of the nearest low-index plane. The actual habit planes do
not coincide exactly with these low-index planes – the so-called
{225}F habit plane is more like {2 2 4.9}F, the reported {259}F
habit is closer to {3 10 15}F and {557}F is more accurately
described as a plane close to, but not exactly of the form {hhl}F
that is between 9° and 11° from {111}F. An orientation relationship
(OR) expresses the relationship between planes and directions in
one phase, such as the austenite matrix (F) with corresponding
planes and directions in the other phase, i.e. the martensite (B).
Typical austenite-martensite ORs are the Kurdjumov–Sachs (K-S) OR
(Kurdjumov and Sachs, 1930):
(111)F//(101)B
the Nishiyama–Wasserman (N-W) OR (Nishiyama, 1934; Wassermann,
1935):
© Woodhead Publishing Limited, 2012
[121]F//[101]B
and the intermediate Greninger–Troiano (G-T) OR (Greninger and
Troiano, 1949):
(111)F//(101)B
[110]F 2.5° from [111]B
[121]F 2.5° from [101]B
© Woodhead Publishing Limited, 2012
are responsible for the actual transformation from austenite to
martensite must satisfy certain requirements. For a martensite
transformation to occur, these interface dislocations must be
completely mobile and capable of rapid movement as the interface
propagates. Because of its diffusionless nature, any interface
dislocation movement associated with the transformation must be
conservative and not involve any net atom flux or the creation or
destruction of lattice sites. In developing a dislocation model of
the austenite/martensite interface or in postulating details of the
transformation mechanism that may involve the creation of interface
dislocations, all of these relatively strict conditions must be
met. By comparison, in the case of a diffusion-controlled
transformation, this interface dislocation movement criterion
associated with no atom flux is not necessary, as non-conservative
climb is possible and the interface dislocations merely have to
satisfy geometric considerations. The combination of these
crystallographic characteristics has a pronounced impact on the
development of a satisfactory theoretical model for a martensitic
transformation. A successful theory must be capable of predicting a
planar interface that corresponds to the habit plane of a
martensite lath or plate, must derive the correct features of the
OR and shape change, must be consistent with any internal
substructure within the martensite plates, and finally, must only
result in totally glissile arrangements of dislocations in the
interface. How this is done is covered in the following
sections.
1.2.2 Early theories of martensite crystallography
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© Woodhead Publishing Limited, 2012
Frank also considered the {225}F transformation and developed a
model where the close-packed planes (111)F and (101)B in the two
phases met along the common close-packed directions [110]F and
[111]B lying in the {225}F habit plane interface (Frank, 1953). The
spacing of the close-packed planes in the two phases differed
slightly, and to achieve perfect matching a small rotation about
their common intersection in the habit plane was necessary. In
addition, a shear on the (112)B planes produced by an array of
screw dislocations in the interface is needed to ensure that
matching between successive planes remains ‘in-step’. This is
essentially the same as the inhomogeneous second shear proposed by
Greninger and Troiano. This two-dimensional model was criticised
because it only applied to the {225}F transformation where the
matching close-packed directions lie in the habit plane and it did
not account for the {259}F habit plane. This was subsequently
remedied when a three-dimensional prism matching theory was later
developed (Bilby and Frank, 1960). The geometric matching
conditions were obviously far more complex, but a second shear on
(112)F was still required. This prism matching model predicted an
elliptical locus of habit plane positions. The magnitude of the
shape deformation varied along this habit plane locus and was a
minimum at a position that corresponded to {259}F. For the same set
of lattice parameters this was identical with the predictions
arrived at somewhat earlier using the PTMC.
1.3 Phenomenological theory of martensite crystallography
(PTMC)
1.3.1 Key features of the PTMC
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austenite cell shown in Figs 1.2 (b) and (c) has the carbon atoms
arranged in these very specific positions. Adding interstitial
carbon atoms at random to this bct unit cell would result in it
having a c/a ratio greater than unity. In other words, the
interstitial carbon atoms in the martensite will make its
Fe atoms C atom positions
[001]F [001]F
[100]F
[001]B
(d) Austenite Martensite
© Woodhead Publishing Limited, 2012
unit cell tetragonal, with the degree of tetragonality linearly
proportional to the carbon content. This provides the experimental
proof that completely justifies the choice of correspondence.
Figure 1.2 illustrates another important point. The variant of the
correspondence shown in Fig. 1.2 is such that:
[100]F becomes [110]B,
[010]F becomes [110]B, and,
[001]F becomes [001]B.
There are two other major variants of this correspondence, one with
[100]F becoming [001]B and one with [010]F becoming [001]B. This
latter major variant is the one selected by Bowles and Mackenzie.
With the correspondence shown in Fig. 1.2 and the lattice
parameters of the austenite and the martensite, the total strain
necessary to convert the matrix austenite to the product martensite
can be derived. This total strain is known as the Bain strain B.
Note that throughout this chapter ‘bold sans serif’ type will be
used to represent matrices (in capitals) and vectors (in lower
case). If the fcc austenite lattice parameter is aF and the lattice
parameters of the bct martensite are aB and cB, then the Bain
strain can be represented by three components h1, h2 and h3 along
the [100]F, [010]F and [001]F directions in the austenite lattice,
where:
h1 = h2 = ÷2(aB/aF),
h3 = (cB/aF)
© Woodhead Publishing Limited, 2012
(Christian, 1976). This concept meant that the shape strain
associated with a martensite transformation had to be an invariant
plane strain of the type illustrated in Fig. 1.3 – in other words a
shear g in a direction parallel to the habit plane, plus an
expansion (or contraction) x normal to the habit plane. The Bain
strain B is sufficient to convert the matrix austenite crystal
structure to that of the product martensite, but it seldom
satisfies the two very stringent conditions required to produce an
invariant plane strain. The first of these is that one of the
principal strains must be zero and the second, equally important
condition, is that the other two principal strains must be of
opposite sign, i.e. one strain must be an expansion, while the
other is a contraction (Bilby and Christian, 1955; Christian,
1956). If the strain involved in the martensite transformation can
be made to satisfy these two conditions, then it will be possible
to form a martensite plate where the habit plane of the plate is
invariant. The two versions of the PTMC were both aimed at ensuring
that the shape strain of the martensite transformation was an
invariant plane strain. The final point about the PTMC is that the
WLR and BM theories are both phenomenological. This means that all
the theories attempt to do is to relate the crystallographic
features of the final transformed martensite product to those of
the original matrix austenite. This is a purely ‘before and after’
description. Although governed by the very stringent conditions
associated with the invariant plane concept, the PTMC does not
pretend to offer any information about the actual mechanism of
transformation. It is
Austenite Martensite Transforms to:
Habit plane Habit plane
x = DV
© Woodhead Publishing Limited, 2012
not a mechanistic model that describes individual atom movements.
All the PTMC does is to specify, via an elegant analysis based on
matrix algebra, the very strict geometrical conditions that must be
met to get from the initial state to the final state. The
mathematical steps taken in this process and the order in which
they are carried out do not necessarily bear any particular
relevance to the way the transformation actually occurs. This is
pure mathematical manipulation, designed to go from ‘before’ to
‘after’. The PTMC predictions of the habit plane, the orientation
relationship between austenite and martensite and the magnitude and
direction of the shape strain can then be compared with
experimental observations.
1.3.2 How the PTMC works
© Woodhead Publishing Limited, 2012
quadratic equation, there will be two solutions for g, both of
which lead to an invariant line strain (Wechsler et al., 1953).
Normally, the smaller of the two is adopted on the grounds that
this minimises the strain components of the LIS L. To convert this
invariant line strain BL to an invariant plane strain, the other
two principal strains of BL must be opposite in sign. This is the
second condition that must be satisfied and means that BL will
generate at least one other undistorted line in addition to the
original invariant line. This pair of undistorted lines defines an
undistorted plane. However, only the original undistorted line is
both undistorted and unrotated. The second undistorted line is not
necessarily unrotated, but can be made completely invariant, i.e.
undistorted and unrotated, via a rigid body rotation R about the
original invariant line. This rigid body rotation has no effect on
the morphological or crystallographic features of the ‘rigid body’
that is rotated. All it does is to ensure that there is now a pair
of invariant lines that define an invariant plane. In other words
the combination RBL is an invariant plane strain, which is exactly
what is required by the theory to represent the shape strain S. The
WLR formulation of the theory can therefore be represented via the
matrix algebra ‘short-hand’ notation as:
S = RBL [1.1]
Because the theory is phenomenological, the mathematical steps
taken to generate the shape strain S in eq. [1.1] do not
necessarily indicate actual physical processes that have occurred
during the transformation. However, the resultant shape strain has
real, physically measurable characteristics.
Outline of block of austenite that has
transformed to martensite
has transformed to martensite
Surface of austenite crystal
Surface of austenite crystal
{225}F Habit (b) Twinning on
(112)[111]B
© Woodhead Publishing Limited, 2012
The habit plane corresponds to the invariant plane and, on a
pre-polished surface, measurements of the surface tilts and change
in direction of scratches illustrated in Fig. 1.1 can be used to
determine the direction and magnitude of the shape strain S.
Similarly, the orientation relationship between the austenite and
the martensite depends on the correspondence, on which B is based,
and the rotation R. The LIS L has no effect on the orientation
relationship, but the shear that gives L its lattice invariant
characteristics may be experimentally observable as regular slip or
twinning, as shown in Figs 1.1 and 1.4. The BM treatment of the
PTMC follows directly from the original observation (Greninger and
Troiano, 1949) that the shape strain S is, on its own, not capable
of transforming fcc austenite to bcc (or bct) martensite. Hence the
BM approach begins with the invariant plane strain S and combines
this with an ‘invisible’ second shear H, which also deforms the
crystal lattice. The total deformation that results from the BM
combination SH must then be equal to the WLR total deformation RB
and so the BM version of the PTMC can be represented as:
SH = RB [1.2]
In order to maintain the ‘invisibility’ of the ‘second’ shear H and
to ensure that it cannot make up part of the shape change, the
shape deformation S must equal SHH–1, where H–1 is the inverse of
H. In other words, H–1 must be an equally opposite lattice
invariant deformation that exactly balances any shape changes
resulting from H. So, Eq. [1.2] can be written as:
SHH–1 = S = RBH–1 [1.3]
© Woodhead Publishing Limited, 2012
or {3 10 15}F habit plane in iron-nickel and iron-nickel carbon
alloys with low martensite start (Ms) temperatures. The PTMC was
able to explain all the crystallographic features of the {259}F
martensite, which was not surprising, since Greninger and
Trioiano’s work on this type of martensite was the catalyst that
lead to the development of the PTMC. However, there was a measure
of marked disappointment when the PTMC appeared to have some
difficulties in relation to the {225}F type of ferrous martensite.
The need to account for {225}F martensite had always been
recognised. It appears in Bowles initial introduction of the
concept of an ‘invisible’ second shear (Bowles, 1951) and was the
basis for Frank’s original lattice matching model (Frank, 1953).
Hence, it was not surprising to see a number of attempts to adapt
the PTMC to the case of the {225}F transformation. The first of
these had already been incorporated in the BM version of the PTMC.
Bowles and Mackenzie purposely permitted a small relaxation to the
invariant plane condition by introducing a small dilatation
(<2%) that allowed the distances in the habit plane to be
slightly different in the two phases. So, the habit plane was
nearly invariant, but it was still an unrotated plane in the two
phases. This allowed the PTMC to be more versatile, and increasing
the dilatation parameter d from unity (an exactly invariant habit
plane) to around 1.015 (1.5% strain allowed in the habit plane) the
predicted habit plane moved from {259}F to {225}F (see, for
example, fig. 2.11 in Petty, 1970, or fig. 5 in Bowles and
Mackenzie, 1954b). No satisfactory physical explanation of the
significance of this dilatation was put forward and consequently
this explanation for {225}F martensite was occasionally regarded
with some suspicion by other workers in the field. Wechsler, Otte
and Wechsler, Lieberman and Read all adopted a different approach
in an attempt to account for the {225}F martensite habit plane.
They tried different rational slip or twinning systems in the
austenite or the martensite as the LIS (Wechsler, 1959; Otte, 1960;
Wechsler et al., 1960). These LIS systems were capable of
predicting a variety of habit planes, but only a few came close to
{225}F and even these possible solutions were not always really
convincing. In some cases the variant of {225}F predicted was not
correct and in others the magnitude g of the LIS was relatively
large.
1.4 The post phenomenological theory of martensite crystallography
(PTMC) period
1.4.1 Experiments and more trials of the theory
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© Woodhead Publishing Limited, 2012
martensite forms as bands on the {111}F planes of the austenite and
can be produced by a change in the stacking sequence from fcc to
hcp via a shear of a/6<112>F on every second {111}F plane,
with no need for a LIS or ‘second’ shear. This shear can occur
inhomogeneously by distributing the transformation shear over the
three <112>F directions lying in the {111}F plane of a single
band. This could lead to the fcc austenite to hcp e transformation
occurring with essentially no shape change. The bcc a martensite
can form within a band of hexagonal e, via a single invariant plane
strain, plus a slight ‘shuffle’ of atoms on adjacent (000l)e
planes. Alternatively, the fcc austenite to bcc martensite
transformation can occur directly with a LIS on (111)/[121]F
(Kelly, 1964, 1965). In this case the LIS corresponds to the
formation of stacking faults within the parent austenite. Hence,
the bcc martensite will always be associated with bands of faulting
in the austenite and these faulted bands could be close to the hcp
e structure, so that the bcc martensite could appear as if it had
formed from the hexagonal e. The predicted habit plane for this bcc
martensite is (1 12)F at a maximum dilatation (d = 1.018), and it
is possible to form twin-related bcc martensite plates with this
same habit plane arranged at right angles to the bands of faulting
or hexagonal e. In such situations the shape strains of the
twin-related pair would have shear components that are exactly
opposite and would effectively cancel each other (Kelly, 1965). For
values of the dilatation parameter d closer to unity, a habit plane
of the type {225}F is predicted. But this habit plane is (2 25)F
and is close to 90° from the close- packed fcc plane (111)F that is
parallel to (101)B. This is not the same as the normal {225}F
martensite, where the habit plane is less than 30∞ away from the
close-packed fcc plane (111)F that is parallel to (101)B. The
orphan child in all of this burgeoning experimental work and
further applications of the PTMC was the lath martensite formed
primarily in low carbon steels. The main reason for the dearth of
experimental attention devoted to what was subsequently to become
known as the ‘{557}F lath transformation’ was that it invariably
formed at high temperatures and it was difficult to find any
retained austenite matrix to use as the basis for measurements of
the habit plane, orientation relationship or shape strain. In fact
even now, nearly half a century later, there has never been a
reliable measurement of the shape strain of lath martensite in
steels. little theoretical attention was devoted to lath martensite
in the decade or two that followed the development of the PTMC,
mainly because of the obsession with explaining the plate-like
{225}F martensite that was much easier to deal with
experimentally.
1.4.2 Alternative theories
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© Woodhead Publishing Limited, 2012
© Woodhead Publishing Limited, 2012
the time this comment was made, the various published applications
of the double shear theory had not been able to account for all of
these observed crystallographic features of {225}F martensite.
However, some two decades later an extended series of systematic
double shear trials, where the larger of the two LIS shears
incorporated a component of the twinning shear observed in {225}F
martensite (Kelly, 1992c), led to a number of double shear
combinations that simultaneously accounted for, not only the
observed habit plane, orientation relationship and shape strain,
but was also able to account for the previously observed real
variation in shape strain direction of 40° or more (see Muddle et
al., 1976, and fig. 9 in McDougall and Wayman, 1992). A similar
application of the double shear theory (Kelly, 1992a, 1992b) was
able to account for all the currently known crystallographic
features of {557} F lath martensite, including the apparently large
values of the shape strain, the orientation relationship and the
observed array of a/2[11 1]B dislocations in the
austenite/martensite interface (Sandvik and Wayman, 1983). All of
this is amply reviewed in the section on ‘The {557}F lath
transformation’ in McDougall and Wayman (1992). While the
criticisms of the generalised double shear versions of the PTMC
mentioned above are difficult to justify and, in this modified
form, the theory appears to provide the required flexibility to
account very well for the majority of the crystallographic features
of martensite in steels and other materials, there is still room
for doubt. One question often raised in informal discussions was
whether or not such a double shear arrangement could still lead to
an array of interface dislocations that were sufficiently mobile to
permit the extremely rapid propagation of the austenite/martensite
interface. Despite these niggling doubts about the mechanistic
viability of the double shear versions of the theory, the PTMC has
to be regarded as probably the best predictive, as opposed to
explanatory, theory of phase transformations in crystalline solids.
No other theory of martensitic or diffusional phase transformations
would appear to even come close to the PTMC in this regard.
1.5 Strain energy – the Eshelby/Christian model and the
infinitesimal deformation (ID) approach
© Woodhead Publishing Limited, 2012
© Woodhead Publishing Limited, 2012
(Shibata-Yanagisawa and Kato, 1990; Navruz and Durlu, 1999; Navruz,
2001). If valid, the infinitesimal strain approximation allows
strain and rotation matrices to be added, rather than multiplied,
so that in ID terms the PTMC equation [1.1], namely S = RBL,
becomes:
T i = Si = Ri + Bi + Li [1.4]
While this certainly simplifies the subsequent mathematical
manipulation, unless at least two of the terms on the right-hand
side of eq. [1.4] satisfy the infinitesimal strain approximation by
having strains that are less than 0.01, T i is not going to be
equal to Si and the predictions of the ID theory will no longer be
the same as those of the PTMC, as they should be. For example, in
the case of {259}F martensite, the strains in Bi are in the range
0.13–0.24 and the magnitude of the LIS in Li is >0.2 (Wayman,
1964). These are clearly not infinitesimal strains by any stretch
of the imagination and the predictions made by the matrix addition
version of the ID theory in this case, and in any other application
to martensite in steels for that matter, will not be consistent
with those of the PTMC. If the infinitesimal strain approximation
is not used when it is inappropriate and the ID analysis is
conducted in a rigorous fashion with matrix multiplication where
necessary, then the predictions will be exactly the same as those
of the PTMC (Mura et al., 1976; Kato et al., 1977; Hayakawa and
Oka, 1984; Ledbetter and Dunn, 1999, 2000; Kelly, 2003).
Unfortunately, there is now little simplification in the
mathematics of the rigorous ID approach.
1.6 Interfacial dislocation models
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(Olson and Cohen, 1986). The emphasis on what was termed the
‘topological’ characteristics of interface dislocations has the
potential to provide an atomistic mechanism for the martensite
transformation that goes well beyond the purely phenomenological
approach in theories like the PTMC. Recently, Pond and co-workers
have developed an interfacial dislocation theory termed the
‘Topological Model’ (TM) (Pond and Celotto, 2003; Pond et al.,
2003, 2006, 2007). This was based on a habit plane made up of
terraces and steps/disconnections, as shown in Fig. 1.5, and the
martensitic transformation proceeds by the movement of the
interface dislocations associated with these regularly spaced
disconnections. The initial version was essentially two-dimensional
and avoided the need to incorporate a lattice invariant shear. The
mathematics was relatively simple compared with the PTMC and the TM
offered considerable promise as a means of exploring the more
mechanistic aspects of martensite formation. The determination of
the overall interface habit plane orientation was based on the
premise that the array of interface dislocations must lead to a
situation where there is ‘no long range strain’ in the habit plane.
The analysis in appendix B of Pond et al. (2003) and section 3.2 of
Pond et al. (2007) led to the following equation for the angle q of
the habit plane to the terrace planes lying in the xy plane of Fig.
1.5:
bztan2q + bytanq + heyy = 0 [1.5]
A martensite interface with no long range strain is in effect
equivalent to the invariant plane strain concept used in the PTMC
and it was to be expected
a
b
h
bcy = heyy/tanq bz = (hb – ha) h/d = tanq
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© Woodhead Publishing Limited, 2012
1.7 Future trends
© Woodhead Publishing Limited, 2012
crystallographic features of martensite in steels. For example,
although this type of analysis is capable of justifying the change
in habit plane position from {259}F to {225}F as the t/R ratio
increases from zero to ~0.1, it does not obviously account for the
fact that there do not appear to be any martensite habit planes
located between these two positions. Why the dramatic change in
habit plane, with no evidence for a gradual movement from one to
the other? A recent possible explanation for this sudden transition
introduces another important factor: the role of the interfacial
surface energy in determining the crystallographic characteristics
of martensite (Kelly, 2006). Why should the reduction of strain
energy completely dominate the features of a displacive martensitic
transformation? Is it not possible that the interfacial surface
energy also plays a role? If so, how important are the relative
influences of strain and surface energy in martensite
transformations? Surely a strain energy dominated transformation
can make some sacrifices in order to achieve a reduction in surface
energy. Is this reduction in interfacial surface energy sufficient
to compensate for the increase in strain energy associated with the
change from the {259}F habit to the {225}F habit when the t/R ratio
is increased to ~0.1? All this string of questions does is to
highlight what would appear to be a promising area for future
research, namely the role of interfacial surface energy in
governing the crystallographic characteristics of martensite in
steels. All the required theoretical and experimental tools are
available for a concerted attack on this topic. On the theoretical
side, interfacial dislocation models like the TM, combined with the
elegant O-lattice formulation developed by Zhang and her co-workers
(Zhang and Weatherly, 2005), should be able to make predictions
that can be verified (or otherwise) by HRTEM examination of
martensite interface dislocation structures. This particular aspect
of martensitic transformations is crying out for further, more
sophisticated analysis, verified by careful experiments.
1.8 Conclusions
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Kelly, P M (1964) Metallurgical developments in high-alloy steels.
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Kelly, P M (1965) ‘The martensite transformation in steels with low
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martensite in steels
T. Maki, kyoto University, Japan
Abstract: Martensite in ferrous alloys exhibits various
morphologies, chiefly lath, lenticular and thin plate, depending on
chemical compositions and Ms temperature. This chapter reviews
crystallographic features and substructures for each of these
specific forms. Furthermore, the chapter discusses crystallographic
features of packet and block in lath martensite, the origin of
dislocation structure in lath and lenticular martensites, and the
origin of the midrib in lenticular martensite.
Key words: morphology of ferrous martensite, lath martensite,
lenticular martensite, thin plate martensite, substructure of
ferrous martensite.
2.1 Morphology and crystallographic features of martensite in
ferrous alloys
© W
(a)
(d)
(b)
(e)
(c)
(f)
20 µm20 µm20 µm
© Woodhead Publishing Limited, 2012
0 0.5 1.0 1.5 2.0 C content (mass%)
600
500
400
300
200
100
0
)
2.2 Formation range of various types of a¢ martensite (lath,
butterfly, lenticular and thin plate) as a function of formation
temperature (Ms) and carbon content in Fe-Ni-C alloys (Maki and
Tamura, 1984).
© Woodhead Publishing Limited, 2012
remain poorly defined. However, the Ms temperature, the strengths
of parent austenite and product martensite, the critical resolved
shear stress for slip and twinning in martensite, and the stacking
fault energy of austenite are considered to be important factors
(Davies and Magee, 1971; Krauss and Marder, 1971; Maki et al.,
1972; Carr et al., 1978). Lath and lenticular are the two major
morphologies of a¢ martensite (Reed, 1