i

Low Temperature Austenite Decomposition

in Carbon Steels

Albin Stormvinter

Doctoral Thesis

KTH Royal Institute of Technology

School of Industrial Engineering and Management

Department of Materials Science and Engineering

Division of Physical Metallurgy

SE-10044 Stockholm, Sweden

Stockholm 2012

ii

Albin Stormvinter Low Temperature Austenite Decomposition in Carbon Steels

KTH Royal Institute of Technology,

School of Industrial Engineering and Management,

Department of Materials Science and Engineering,

Division of Physical Metallurgy,

SE-10044 Stockholm,

Sweden

ISRN KTH/MSE--12/19--SE+METO/AVH

ISBN 978-91-7501-449-4

Akademisk avhandling som med tillstånd av Kungliga Tekniska högskolan i Stockholm framlägges

till offentlig granskning för avläggande av teknologie doktorsexamen 27 september 2012, kl. 10.00 i

sal F3, Lindstedsvägen 26, Kungliga Tekniska högskolan, Stockholm.

© Albin Stormvinter, August 2012

Printed by Universitetsservice US-AB, Stockholm, Sweden

iii

To Emma

iv

v

Abstract

Martensitic steels have become very important engineering materials in modern society. Crucial parts

of everyday products are made of martensitic steels, from surgical needles and razor blades to car

components and large-scale excavators. Martensite, which results from a rapid diffusionless phase

transformation, has a complex nature that is challenging to characterize and to classify. Moreover the

possibilities for modeling of this phase transformation have been limited, since its thermodynamics

and kinetics are only reasonably well understood. However, the recent development of

characterization capabilities and computational techniques, such as CALPHAD, and its applicability

to ferrous martensite has not been fully explored yet.

In the present work, a thermodynamic method for predicting the martensite start temperature (Ms)

of commercial steels is developed. It is based mainly on information on Ms from binary Fe-X

systems obtained from experiments using very rapid cooling, and Ms values for lath and plate

martensite are treated separately. Comparison with the experimental Ms of several sets of commercial

steels indicates that the predictive ability is comparable to models based on experimental information

of Ms from commercial steels.

A major part of the present work is dedicated to the effect of carbon content on the morphological

transition from lath- to plate martensite in steels. A range of metallographic techniques were

employed: (1) Optical microscopy to study the apparent morphology; (2) Transmission electron

microscopy to study high-carbon plate martensite; (3) Electron backscattered diffraction to study the

variant pairing tendency of martensite. The results indicate that a good understanding of the

martensitic microstructure can be achieved by combining qualitative metallography with quantitative

analysis, such as variant pairing analysis. This type of characterization methodology could easily be

extended to any alloying system and may thus facilitate martensite characterization in general.

Finally, a minor part addresses inverse bainite, which may form in high-carbon alloys. Its coupling to

regular bainite is discussed on the basis of symmetry in the Fe-C phase diagram.

Keywords: Carbon steels, Electron backscattered diffraction, Martensite, Microscopy,

Microstructure, Thermodynamic modeling.

vi

vii

Preface

In the present doctoral thesis I would like to share my knowledge gained during the past four years,

as a PhD student in physical metallurgy at the Department of Materials Science and Engineering at

KTH Royal Institute of Technology, Sweden. The work has mainly been carried out within the

martensite formation project (Supplements 1-5) which runs within the Hero-m research center,

although Supplement 6 addresses inverse bainite and hence belongs to the bainite formation project

within Hero-m. A large part of the characterization work on martensite is the result of two research

stints conducted by the present author: at INP-Grenoble (France) in the spring of 2010 and at

Tohoku University (Sendai, Japan) in the summer of 2011. In particular this doctoral thesis will

discuss the following challenges, which are related to low temperature austenite decomposition in

carbon steels:

Thermodynamically based prediction of the martensite start temperature (Ms)

Quantitative microstructure characterization: The effect of carbon content on the martensite

morphology with emphasis on the transition from lath to plate martensite.

Inverse bainite in hypereutectoid Fe-C alloys.

The outline of this thesis is as follows; In the first chapter, introduction, the topic low temperature

austenite decomposition and the aims and purposes related to the three challenges listed above are

introduced. In Chapters 2-4 my intention has been to condense selected works on three important

subjects related to this work: Phase transformations, Characterization techniques, and

Thermodynamics. I make no claim that these chapters would advance the understanding of low

temperature austenite decomposition further; instead they should be viewed as either an introduction

to the different topics for the novice or as an interpretation of the dense literature on the subjects

done by the present author. The readers are referred to the cited works for more details. The expert

reader may in fact skip Chapters 2-4 and move on to Chapters 5-7 where I summarize the results

from the supplements and discuss them in relation to existing literature.

Albin Stormvinter

Stockholm, 2012-08-01

viii

Appended papers

I. Investigation of Lath and Plate Martensite in a Carbon Steel

A. Stormvinter, P. Hedström and A. Borgenstam

Solid State Phenomena, 172-174, (2011), p. 61-66.

II. Thermodynamically Based Prediction of the Martensite Start Temperature for Commercial

Steels

A. Stormvinter, A. Borgenstam and J. Ågren

Metallurgical and Materials Transactions A, Online first, 2012,

DOI: 10.1007/s11661-012-1171-z

III. A transmission electron microscopy study of plate martensite formation in high-carbon low

alloy steels

A. Stormvinter, P. Hedström and A. Borgenstam

Submitted manuscript

IV. Effect of Carbon Content on the Orientation Relationship between Austenite and bct-

Martensite in Fe-C Alloys resolved by Electron Backscattered Diffraction

A. Stormvinter, G. Miyamoto, T. Furuhara, and A. Borgenstam

Submitted manuscript

V. Effect of Carbon Content on the Variant Pairing of Martensite in Fe-C alloys

A. Stormvinter, G. Miyamoto, T. Furuhara, P. Hedström and A. Borgenstam.

Submitted manuscript

VI. On the Symmetry Among the Diffusional Transformation Products of Austenite

A. Borgenstam, P. Hedström, M. Hillert, P. Kolmskog, A. Stormvinter and J. Ågren

Metallurgical and Materials Transactions A, 42(6), (2010), p. 1558-1574.

* The appended papers will be referred to as [1–6] in the present thesis

ix

My contribution to the appended papers

I. Major part of: literature survey, experimental work, and writing.

II. Major part of: literature survey, modeling work, and writing.

III. Major part of: literature survey, experimental work, analysis, and writing.

IV. Major part of: literature survey, experimental work, analysis, and writing.

V. Major part of: literature survey, experimental work, analysis, and writing.

VI. Part of experimental work, contributed to discussions and took part in the writing.

Other related reports not included in the thesis

A. On the Three-Dimensional Microstructure of Martensite in Carbon Steels

Peter Hedström, Albin Stormvinter, Annika Borgenstam, Ali Gholinia, Bartlomiej Winiarski,

Philip J. Withers, Oskar Karlsson and Joacim Hagström

Proceedings of the International Conference on 3D Materials Science 2012.

Parts of this work have been presented at the following international conferences

1. “Investigation of the Transition from Lath to Plate Martensite in Fe-C”,

Albin Stormvinter, Peter Hedström and Annika Borgenstam,

Solid-Solid Phase Transformations in Inorganic Materials (PTM2010),

6 - 11 June 2010, Avignon, France.

2. “A Phenomenological Model for the Prediction of Martensite Start Temperature in Steels”,

Albin Stormvinter and Annika Borgenstam,

The TMS Annual Meeting & Exhibition 2011 (TMS2011),

27 February - 3 March 2011, San Diego, USA.

3. “Thermodynamically Based Prediction of the Ms Temperature for Commercial Steels”,

Albin Stormvinter and Annika Borgenstam,

International Conference on Martensitic Transformations 2011 (ICOMAT2011),

4 - 9 September 2011, Osaka, Japan.

4. “Martensitic Meso- and Nanostructures in High-Carbon Low-Alloyed Steels”,

Albin Stormvinter, Peter Hedström, and Annika Borgenstam,

The TMS Annual Meeting & Exhibition 2012 (TMS2012),

11 - 15 March 2012, Orlando, USA.

x

xi

Table of Contents

Abstract ................................................................................................................................................................ v

Preface ................................................................................................................................................................ vii

1 Introduction ..................................................................................................................................................... 1

1.1 Aim of the present work ........................................................................................................................ 2

2 Low temperature austenite decomposition ................................................................................................. 5

2.1 Martensite ................................................................................................................................................. 6

2.1.1 Lattice orientation relationship ...................................................................................................... 7

2.1.2 The habit planes ............................................................................................................................... 8

2.1.3 Martensite – A hierarchic structure ............................................................................................... 8

2.2 Bainite and inverse bainite ................................................................................................................... 10

3 Characterization techniques ......................................................................................................................... 13

3.1 Optical microscopy ............................................................................................................................... 13

3.2 Electron microscopy ............................................................................................................................. 15

3.2.1 Scanning electron microscopy ..................................................................................................... 15

3.2.2 Transmission electron microscopy .............................................................................................. 18

4 Thermodynamics ........................................................................................................................................... 21

4.1 Measuring the martensite start temperature ...................................................................................... 23

4.2 Predicting the martensite start temperature....................................................................................... 24

5 Martensite characterization in carbon steels ............................................................................................. 29

5.1 High-carbon martensite investigated by TEM and ASTAR ........................................................... 35

5.2 EBSD – Variant pairing tendency of martensite in Fe-C alloys ..................................................... 41

5.3 Transition between lath and plate martensite.................................................................................... 51

6 Discussion on inverse bainite ...................................................................................................................... 53

7 Thermodynamically based prediction of the martensite start temperature .......................................... 57

8 Concluding remarks and future prospects ................................................................................................ 61

9 Acknowledgments ......................................................................................................................................... 63

10 Bibliography ................................................................................................................................................. 65

xii

1

1 Introduction

Steels are by far the most widely-used metallic material and worldwide the crude steel production

reached 1,527 megatons (Mt) for the year of 2011 [7]. The world production has almost doubled in

ten years (851 Mt crude steel in 2001) and it is the demand from fast developing countries, in

particular China, that drives this expansion [7]. This ever-growing demand for steel is certainly due to

its attractive combination of high strength and high toughness with a low cost and easy recycling.

These material properties make steel ideal for most engineering applications, although unlocking

these inherent properties may not be trivial. It is the basic insight in physical metallurgy that allows

for tailoring of steel properties, such as strength and toughness, by tuning alloying content and heat

treatment processes [8].

The vast majority of engineering steels belong to the category carbon steels, these are steels that are

often loosely classified according to carbon content. The manufacturing of carbon steels relies on

controlling the decomposition of austenite, the high-temperature allotrope of iron. Austenite is not a

stable phase at ambient temperature for carbon steels so it will decompose into ferrite and cementite

on cooling. Figure 1.1 displays the well-known Fe-C phase diagram, which may be used to predict

this decomposition. The phase diagram concept is best applied for phase transformations with fairly

rapid kinetics, i.e. at relatively high temperatures, since diffusion is needed to reach equilibrium.

However, the present work is dedicated to low temperature austenite decomposition. This might

occur by some diffusional process as in the case of bainite formation. On the other hand, it might

also be a diffusionless transformation as in the case of martensite formation. It all depends on the

alloying content and the processing. Regardless whether the austenite decomposition results in

bainite or martensite, phase transformations at low temperatures offer many challenges from a

scientific point of view. These challenges include, but are not limited to: (1) Assessing the

thermodynamics of important alloying systems, since there are very few experimental data available

at such low temperatures. (2) Controlling and analyzing the kinetics of the phase transformations. (3)

Characterizing and analyzing the complex microstructures which the phase transformations give rise

to.

2

Figure 1.1: The Fe-C phase diagram calculated by Thermo-Calc [9], [10]. Solid lines represent the metastable phase

diagram with cementite. Dotted lines represent the stable phase diagram with graphite.

1.1 Aim of the present work

The major part of this work has been dedicated to the effect of carbon on the martensitic

microstructure in carbon steels. This is usually referred to as “well-known”, even though there is no

standardized quantitative method to objectively evaluate this microstructure. Recent advances in

electron microscopy have enabled quantitative characterization based on crystallographic

information. Such techniques are electron backscatter diffraction (EBSD) [11] in the scanning

electron microscope (SEM) and automatic phase and orientation mapping (ASTAR) [12], [13] in the

transmission electron microscope (TEM). Here, these techniques have been applied to martensite

formed in Fe-C alloys with the purpose to develop an objective method to characterize the change in

the microstructure with the carbon content.

3

The second challenge addressed in this work is the prediction of the martensite start temperature

(Ms) as a function of alloying content, which has gained a lot of attention over the past century. It is

quite understandable since it is a key measure for alloy design. Often a pure empirical approach has

been used to model the alloy effect on Ms, although other approaches have been attempted as well

such as neural network models. The problem with both these approaches is that the predictability

may not be sufficient when the full composition range is considered. Therefore several researchers

have attempted a more fundamental approach, based on thermodynamics, for predicting Ms. With a

thermodynamic approach the idea is to model the transformation barrier and how it depends on

alloying content and other parameters, such as prior austenite grain size (PAGS) or prior

deformation. Such transformation barrier model would then be coupled to a reliable thermodynamic

database to calculate the Gibbs free energy of austenite and martensite as a function of alloying

content and temperature. It is this approach that has been attempted in the present work.

Finally, a minor part of this work is devoted to the formation of inverse bainite in high-carbon alloys.

This is a subject that has not received so much attention as it might have deserved in the literature.

Here the decomposition of high-carbon austenite into inverse bainite is characterized and classified

by optical microscopy (OM) and by SEM. The results from the experimental study are discussed in

relation to formation of ordinary bainite, with the main purpose to strengthen the evidence for

bainite being a diffusion controlled transformation.

4

5

2 Low temperature austenite decomposition

Low temperature austenite decomposition in carbon steels may be better described by the word

commonly used for the process, which also explains its purpose: hardening or quench hardening.

The sole purpose of this process is to produce a microstructure that provides strength and hardness

to the final product. In principle the processing may seem trivial: rapid quenching from the austenitic

regime to complete transformation into martensite or bainite. Nevertheless, when studied in more

detail several technological and scientific challenges arise, of which many can be attributed to the fine

microstructure. However, before discussing these challenges in more detail a few words on the

subject hardening should be addressed.

Iron began to replace bronze as the most common metallic material for tools and weapons some

3000 years ago [7]. To craft iron into a hatchet or a sword that could hold an edge and withstand

long wear was not common knowledge, instead it was an art of craftsmanship. The ability to hold an

edge is of course a direct consequence of the quench hardening process, which has to be carried out

with accuracy. At this time there was for obvious reasons no method to study the process in more

detail. So even though hardening had been applied for a few millennia it was not until the

introduction of modern steelmaking and later the birth of metallography that the hardening process

could be studied more in-depth. The hardened microstructure of steels was first described by

Osmond and he named it after another pioneer metallographer: Adolf Martens [8]. Thus, the hard

phase of steels was named martensite.

Ferrous martensite may be produced from austenite by providing sufficient cooling so all diffusional

transformations are omitted, such as formation of ferrite or perlite. It may be convenient to

introduce the concept of hardenability which is defined as the “susceptibility to hardening by rapid

cooling” or as “the property, in ferrous alloys, that determines the depth and distribution of hardness

produced by quenching” [9]. In general, an increase in alloying content permits a decrease in

quenching rate, i.e. increases the hardenability.

6

2.1 Martensite

The martensitic microstructure has a high level of complexity and to resolve its true nature is a

challenge. It is also known that the microstructure varies with composition and especially the carbon

content has a strong influence. A common practice is to distinguish between two major types of

ferrous martensite, namely, lath- and plate martensite [14], [15]. This is a general classification and

several researchers recognize morphologies such as surface martensite [16], butterfly martensite [17],

[18], thin-plate martensite [19], [20], and lenticular martensite [21], [22].

A martensitic transformation is defined by the following characteristics: (a) displacive; (b)

diffusionless; and (c) kinetics and morphology are dominated by the strain energy arising from the

shear-like displacements [23], [24]. Martensitic transformations can occur in many types of metallic

and nonmetallic crystals, minerals, and compounds [25]. A displacive phase transformation is a

structural change in the solid state which occurs by coordinated shifts of atoms [23]. This

coordinated movement of atoms is sometimes referred to as a military phase transformations, which

is in contrast to civilian diffusion-based phase changes that occur by uncorrelated jumps of individual

atoms across an essentially incoherent interface [25]. A characteristic feature of the martensitic

transformation is the shape change that may produce a surface relief if the transformation occurs

near a free surface. In 1924, Bain [26] discussed the nature of the martensitic transformation in steels.

He recognized that a contraction of about 20 percent along one of the austenite <001> axes and an

expansion of about 12 percent along two of the <011> axes perpendicular to the chosen <001> axis

transformed the austenite lattice into a ferrite bcc lattice. Hence, the fcc lattice of austenite could as

well be viewed as a bct lattice with the axial ratio 1.414. This lattice correspondence has been named

as the Bain correspondence and may be illustrated by Figure 2.1, which is reproduced from [27]. The

Bain correspondence demonstrates that the bcc lattice could be generated from the fcc lattice

through a homogeneous distortion. Nevertheless, it lacks some of the fundamental features of a

martensitic transformation, for instance it does not produce an invariant plane. This plane is the

interface between the martensite and the parent phase and should be undistorted and unrotated, and

hence becomes the martensite habit plane. The Bain strain alone does not fulfill the criteria to

produce such a plane, and therefore is not an invariant plane strain [28].

7

Figure 2.1: Bain correspondence in the transformation of (a) austenite into (b) martensite. Annotation: ○, Fe atom;

x, positions available for carbon. Reproduced from Guo et al. [29].

Some 30 years after Bain proposed his theory, works by Wechsler et al. [30] and by Bowles and

Mackenzie [31], [32] established a more solid understanding of martensite formation. These works

applied the principles of matrix algebra to martensitic transformations and established what is now

known as the phenomenological theory of martensite crystallography (PTMC) [33]. The PTMC was

the first martensite theory that could predict experimentally observed habit planes, orientation

relationships, and macroscopic distortions from knowledge only of the crystal structures of the

parent and product phases. The PTMC thus introduced a mathematical and logical route between

experimental observation and theoretical considerations [27].

2.1.1 Lattice orientation relationship

A characteristic feature of the martensitic transformation is the lattice orientation relationship (OR)

between the parent and product phases [27]. Pioneers Kurdjumov and Sachs [34] studied a carbon

steel with 1.4C* by X-ray pole figure analysis and suggested the well-known K-S OR:

(111)γ//(011)α and [-101]γ//[-1-11]α.

The K-S OR states that the closed packed planes (CPP) along with the closed packed directions

(CPD) of martensite (product phase) and austenite (parent phase) are parallel. Other commonly

quoted OR are the Nishiyama-Wasserman (N-W OR) [35], [36] and the Greninger-Troiano (G-T

OR) [37]. These were both determined from studies on high-nickel ferrous alloys containing large

amount of retained austenite using X-ray diffraction techniques. More recently, Kelly et al. [38] and

* Compositions are given in mass% if not stated otherwise

8

Zhang and Kelly [39] have studied martensite formed in low carbon steels by TEM and measured

orientation of thin layers of austenite retained between laths using convergent beam Kikuchi line

diffraction patterns (CBKLDP) to determine the OR, they report:

(111)γ // (101)α and [1-10]γ 2.5°±2° from [1-1-1]α.

Zhang and Kelly [39] pointed out that CBKLDP has an accuracy of ±0.5° and can thereby very

accurately determine the local OR between parent and product phase, given that sufficient amounts

of retained austenite are present. Therefore this method cannot be applied to low-carbon martensite

containing low amounts of retained austenite.

2.1.2 The habit planes

In the early 1940s Greninger and Troiano [40] studied the orientation habit of martensite formed in

plain carbon and nickel steels. They concluded that lenticular martensite did not form along any low-

indices plane of austenite. Instead they reported that the orientation habit of martensite abruptly

changed from a {4 4 10}γ to a {4 10 18}γ habit at roughly 1.4C. Later Greninger and Troiano [37],

[41] extended their analysis of the orientation relationships and were the first to suggest a double

shear mechanism, that later developed into the PTMC [30–32]. In carbon steels the martensite

morphology changes with carbon content and so does the observed habit plane. For lath martensite

it is close to {111}γ or {557}γ, but changes to {225}γ or {259}γ for plate martensite [27].

2.1.3 Martensite – A hierarchic structure

The K-S OR predicts that 24 unique crystallographic martensite variants may develop from a single

parent austenite grain, when annealing twins are disregarded. For lath martensite, these 24 variants

may in turn be divided into four groups, each consisting of six variants with a common habit plane.

These four groups have been named as “packets” [42–44]. By adopting the nomenclature used by

Morito et al. [42] the four packets are made up by the following variant groups: V1-V6, V7-V12,

V13-V18, and V19-V24. The packet may be further subdivided into three “blocks”, which each

consists of two martensite variants with a low degree of misorientation. For instance, the three

blocks of packet V1-V6 are: V1/V4, V2/V5, and V3/V6 [42]. The unique variants, for example V1,

have been named as sub-blocks and are in fact the martensite unit that contains the individual laths.

The lath has been described as a needle-like martensite unit, a few microns long and less than a

9

micron in diameter [45]. The substructure of the laths consists of dislocations arranged in a typical

cellstructure, which are a result of accommodation deformation due to the large shape strain [46].

Adjacent laths may have a misorientation of a few degrees, but are in principal of the same

crystallographic martensite variant. With the lath as the smallest building block, lath martensite may

be regarded as hierarchic structure, which becomes: parent grain – packet – block – sub-block –

individual lath.

For plate martensite, which is found in high-carbon and high-alloyed grades with low martensite start

temperature, it is not at all evident if it exists a hierarchic structure comparable to what has been

shown for lath martensite. When studied by optical microscopy (OM) plate martensite appears as

individual units of various sizes. The unit size is limited by the parent grain size and by preceding

martensite plates, which inhibits growth of a fresh unit. Some characteristic features of plate

martensite are: (1) the midrib, (2) transformation twins, (3) deformation twins, (4) dislocation arrays,

and (5) transverse micro-cracks [47], [48]. Characterization work done on plate martensite have

commonly addressed the irrational habit planes [40] and remarkably few studies have been made on

variant selection. One of the few studies were made by Okamoto et al. [19] who characterized

martensite formed in a Fe-30.70Ni-0.28C alloy. By following Okamoto et al. [19] it may be

concluded that a nucleation event in ferrous alloys with a low Ms temperature will result in the

growth of a “plate group”, which consists of four unique crystallographic martensite variants. The

principle plate group, which is referred to variant V1, becomes: V1, V16, V17, and V6 (again by

adopting the nomenclature used in [42]). In total six unique plate groups may form from a single

parent austenite grain.

The regime between these two extreme morphologies of martensite, i.e. lath- and plate martensite, is

often referred to as a mixed regime with a gradual transition from the former to the later. This

morphological transition has been schematically represented in Figure 2.2. However, this is more or

less a crude simplification since it has been shown that the morphological transition is gradual over

the entire composition range [49], [50]. In a recent review on the martensite morphology by Maki

[51] he pointed out that the factors that determine the morphology and substructure of martensite

remain poorly defined.

10

Figure 2.2: Schematic representation of the transition from lath to plate martensite with increasing carbon content.

As the carbon content is increased the Ms decreases and the martensite morphology changes from lath to plate

martensite. In between these two extremes it is said to be a “mixed” regime.

2.2 Bainite and inverse bainite

The decomposition of austenite into ferrite and cementite in the temperature range below that for

pearlite results in a microstructure that has been named as bainite [52]. Bainite, like pearlite, is a

eutectoid transformation product and may be further subdivided into upper- and lower bainite. Both

these transformation structures are acicular and ferrite is the leading phase in the main growth

direction during the transformation. In bainite, the ferrite has a tendency to form as plate-like units

and grow with an orientation relationship with the austenite [25]. In the case of upper bainite, carbon

will diffuse away from the growing ferrite into the austenite and eventually the carbon content

reaches such a level that cementite nucleates and grows. The shape of the cementite is usually as a

broken lamella in between the ferrite units. At temperatures where lower bainite forms the diffusion

of carbon is slow, which makes the carbides to precipitate in more close relationship with the ferrite.

The resulting carbide dispersed ferrite becomes very fine and may in fact be hard to tell apart from

tempered martensite. Another feature that bainite share with martensite is that it produces a surface

relief effect [53]. This is probably one of the reasons for the uncertainty regarding the mechanism by

which bainite grows: If it forms by a rapid, diffusionless shear mechanism or if it is controlled by

11

carbon diffusion. However, the surface relief should not be taken as a proof of a diffusionless nature,

since it has been shown that Widmanstätten ferrite [54] as well as Widmanstätten cementite [55]

gives a surface relief. Both these transformations are without a doubt diffusion controlled to their

nature. The diffusionless hypothesis was initially proposed by Zener [56] and suggests that a bainite

unit or a sheaf grows by short consecutive steps [57]. Each of them so rapid that there is not enough

time for carbon to diffuse. The carbides are then formed in a subsequent step from the

supersaturated bainitic ferrite, which involves carbon diffusion. The final product, here lower bainite,

may be seen from Figure 2.3. Macroscopically the growth rate of bainite is rather slow and could as

well be controlled by carbon diffusion. This hypothesis, that the nature of bainite growth is diffusion

controlled, has long been supported by Hillert, who in 1957 [58] proposed that there should be a

symmetry among the eutectoid transformation products of austenite in the Fe-C system. He

suggested that pearlite would form if ferrite and cementite behaves as equal partners as the eutectoid

transformation progresses. Bainite forms when ferrite is the leading phase, and the ferrite constituent

is identical to Widmanstätten ferrite. Hillert also introduced, for symmetry reasons, a third

transformation product that would have cementite as the leading phase and he named it as inverse

bainite. Also for inverse bainite the cementite, as the leading phase, should be identical to

Widmanstätten cementite.

Figure 2.3: Lower bainite formed at 618 K (345 °C) in alloyed steel with 0.69C. 10,000 times magnification.

Reproduced from Oblak and Hehemann [57].

12

13

3 Characterization techniques

The science discipline of examining and determining the constitution and structure of metals has

been named metallography. The father of metallography is Henry Clifton Sorby who was the first

person to examine correctly polished and chemically etched metal samples under the microscope in

the 1860s. Today the discipline covers the examination of metals over a wide range of length scales,

from millimeter scale down to the atomic scale [52].

3.1 Optical microscopy

The classical metallographic tool is the optical microscope (OM), which allows for accurate

metallographic examinations of metallic materials of various shapes and sizes. Before the OM

investigation, specimens are usually mechanical polished and chemical etched [52]. This will produce

a proper surface and thus allow for examination of microstructural features which may arise from

solidification or solid state transformations. Features that might be studied are for instance:

Grains (size and shape) and grain boundaries

Phases and phase interfaces

Annealing twins

Composition gradients that affect the microstructure

Inclusions (distribution, size and shape)

Precipitates (distribution, size and shape)

Imperfections (cracks and notches)

Surface structures (Corrosion attacks, fracture surfaces, and cracks)

Figure 3.1 displays an OM micrograph on transformation structures in a high-carbon alloy. This

figure well illustrates the capabilities of accurate metallography using OM. From the figure three

different features can quite easily be distinguished, those are: spiky nodules, plate-like units formed in

zig-zag patterns, and a matrix phase. Since the heat treatment process and alloy composition is

known in this case, these three features may be recognized as inverse bainite, plate martensite, and

retained austenite, respectively. However, there are limitations of the OM technique; those are first

and foremost the limited depth of field and the spatial resolution, which is of the same order of

magnitude as the wavelength of light, i.e. features smaller than a few tens of a micron cannot be

observed. Moreover, the limited depth of field at high magnification makes it difficult to picture

features which are non-planar [52]. The limited depth of field might not be critical for studying

14

martensite and inverse bainite on a polished surface, as seen from Figure 3.1, but to resolve the fine

microstructural features in more detail is beyond the resolution of OM.

Figure 3.1: Microstructure of a 1.67C carbon steel isothermally heat treated at 400 °C for 1 minute after a 10

minutes austenitization at 1100 °C. The dark etching spiky nodules are inverse bainite formed during the isothermal

hold. Apart from inverse bainite the figure shows plate martensite (dark gray) formed during the final quenching to

room temperature. The matrix is retained austenite. The specimen was prepared by mechanical polishing followed by

etching in Nital.

15

3.2 Electron microscopy

Even though the OM is a versatile characterization tool, its limited spatial resolution makes it

insufficient to study the nanostructure of materials. Therefore, it becomes necessary to apply electron

microscopy techniques to resolve such details of the materials structure. By using modern SEM and

TEM it is possible to achieve a resolution better than 1 nm and thus resolve the very fine structural

features. In addition, it is possible to determine the local crystallography as well as the local chemical

composition using electron microscopes, which will add substantial information to the

characterization work.

3.2.1 Scanning electron microscopy

The SEM is primarily used to study the surface, or near surface, structure of bulk specimens.

Electrons are generated from a source and then focused on to the surface by condenser lenses. The

electron source has usually been of the tungsten filament thermionic emission type, although field

emission gun (FEG) sources are growing in popularity since they may achieve higher resolutions and

higher probe currents [59]. The electrons generated from the source will generate various secondary

emissions after interaction with the specimen surface. These emissions and corresponding contrast

mechanisms have been listed in Table 3.1:

Table 3.1: Overview of contrast mechanisms, detectors, and typical lateral and depth resolution [52].

Detected signal Type of detector Information Lateral

resolution

Depth of

information

Secondary electrons Scintillator/photomultiplier Surface topography,

compositional contrast 5–100 nm 5–50 nm

Backscattered electrons Solid-state detector or

scintillator/photomultiplier

Compositional contrast,

surface topography, crystal

orientation, magnetic domains

50–1000 nm 30–1000 nm

Specimen current No external detector

necessary

Complementary contrast to

backscattered plus secondary

electron signal

Same as

backscattered

electrons

Same as

backscattered

electrons

Characteristic X-rays

(primary fluorescence)

Semiconductor detector

(energy-dispersive) or

crystal/proportional counter

(wavelength-dispersive)

Element composition, element

distribution 500–2000 nm 100–1000 nm

Cathodoluminescence Photomultiplier Detection of nonmetallic and

semiconductive phases ... ...

16

All the detectable signals listed in Table 3.1 may be used for materials characterization. For instance,

secondary electrons excel in detecting the surface topography and are more or less insensitive to

atomic number. Instead the contrast depends strongly on the angle between the incident beam and

the specimen surface. By applying a suitable etchant, chemical or electrolytic, interesting features may

be revealed and could then easily be viewed using the SEM in secondary electron mode. Figure 3.2

gives an example on such image, here carbide precipitations as a result of martensite tempering are

revealed.

Backscattered electrons (BSE) are electrons that escape the specimen due to elastic scattering. These

electrons are more energetic than the secondary electrons and their yield have a strong correlation to

the average atomic number. Hence, the backscattered electrons carry information on the local

composition and their signal may be used to produce an image with compositional contrast. In

addition, backscattered electrons carry crystallographic information since the yield also is dependent

on the orientation of a crystal with respect to the incident beam [59]. This effect, known as electron

channeling, is usually much weaker when compared to the atomic number contrast. Figure 3.3

displays a martensitic steel where the microstructure has been revealed by channeling contrast in the

SEM.

Figure 3.2: Plate martensite formed in a high-carbon steel quenched to 200 °C after austenitization at 1000 °C for

10 minutes. Carbide precipitation is clearly visible inside the large martensite unit. These carbides precipitated during a

1 minute tempering at the quenching temperature. The figure is a SE image using an in-lens detector and acquired

using the following setup: 5.0 kV, WD 5 mm, x10,000. The specimen was prepared by mechanical polishing followed

by electrolytic etching.

17

Figure 3.3: Displays plate martensite formed in a high-carbon steel. The figure is a BSE image acquired using the

following setup: 10.0 kV, WD 2.7 mm, x1000. The specimen was prepared by mechanical polishing.

A SEM technique that is rapidly developing is the electron backscattered diffraction technique

(EBSD). It is a fully automated quantitative material characterization technique based on mapping

the crystallography of the investigated specimen. EBSD relies on the detection of Kikuchi patterns,

which arise from subsequent elastic scattering of inelastically scattered electrons [59]. To obtain an

increased amount of electrons, adding to the Kikuchi pattern, the incident beam should be tilted

about 70° relative to the analyzed surface. To be successful the surface should have a mirror finish

and be essentially free from deformation, for instance by using a vibration-assisted final polishing.

The electron beam is scanned across the specimen while the position (x- and y-coordinates) and

Kikuchi patterns are recorded simultaneously. The next step in the EBSD analysis is to index the

collected Kikuchi patterns; this is commonly done using a Hough transform [11]. For every mapped-

point the best possible solution, i.e. phase and crystallographic orientation, is calculated from the

recorded Kikuchi data. Recent EBSD systems may even select the appropriate phases automatically,

given that a reliable database including the current phases is available. The resulting dataset will

contain crystallographic data for every successfully analyzed point within the mapped area of the

analyzed 2-D cross-section. Commercial EBSD software includes numerous post-processing

possibilities, for example the collected dataset can be viewed as a phase colored map or an inverse

pole figure (IPF) colored map as seen in Figures 3.4a and 3.4b respectively. The reader who wants

further insight in the SEM and EBSD techniques are recommended to the excellent monographs by

Goldstein et al. [60] and by Schwartz et al. [11], respectively.

18

Figure 3.4: (a) Phase colored EBSD map of a high-carbon steel where martensite is colored in red and retained

austenite is colored in blue. (b) An inverse pole figure colored EBSD map of martensite that corresponds to (a), the

retained austenite is here colored in gray. The EBSD dataset is 45 by 35 microns and acquired using an OXFORD

system and a 50nm step size.

Besides generating characteristic electrons the beam specimen interaction also gives rise to X-rays.

Among these there are the characteristic X-rays, which are a result of ionization of the atoms in the

material. An electron of the primary beam may knock an electron out from an inner shell and thus

leave an electron vacancy. This vacancy will immediately be replaced by an electron from an outer

shell. As this other shell electron transfers to the new lower energy level it releases some excess

energy. This energy can be lost as an X-ray photon which in turn is characteristic for every element.

Therefore, these X-rays may be used to analyze the local or average chemical composition. However,

there are some overlaps in the X-ray energy spectra which may be difficult to overcome.

3.2.2 Transmission electron microscopy

The transmission electron microscope builds on the same principle as the scanning electron

microscope; that is interaction between the generated electron beam and the specimen. The central

part of the TEM is the vertical vacuum chamber. At its top the electron gun is located, which

accelerates electrons to a voltage of about 40-400 kV. Below the electron gun are two or more

condenser lenses with an aperture present in between. The lenses together with the aperture are used

to change the character of the incident beam, which may be defocused to a parallel beam or focused

to a convergent beam. It all depends on the desired analyzing conditions. Below the lenses lies the

specimen chamber. As the TEM relies on interaction of transmitted electrons the specimen chamber

and holder are a crucial part of the equipment. The holder should allow the operator to move the

19

specimen as well as to tilt it to rather large angles. The electrons that have interacted with the

specimen should also be able to leave the specimen chamber. In addition, X-rays that may have been

generated should be permitted to leave as well. After the specimen the objective lens and the

projector lenses are located. These lenses are used to produce the image. There are several types of

images that may be produced in the TEM, these include: bright field (BF) images, dark field (DF)

images, high angle annular dark field (HAADF) images, selected area electron diffraction (SAED)

images, and convergent beam electron diffraction (CBED) images [59]. It is the objective aperture

that is used to select either the undeflected (bright field) or the diffracted (dark field) beam for the

imaging. The magnified image is often recorded using a charge-coupled device (CCD) array camera.

An example of a BF image is given in Figure 3.5, which displays plate martensite in a high-carbon

steel.

A technique that has many similarities with SEM-EBSD is the automatic phase and orientation

mapping for TEM (ASTAR) [12], [13]. Instead of determining the phase and crystal orientation from

collected Kikuchi patterns, ASTAR is based on template matching of electron diffraction spot

patterns acquired in the TEM. The templates, i.e. theoretical diffraction patterns, are calculated with

the crystal structure as input parameter. The commercial ASTAR technique also contains quality

indicators such as “reliability”, which is comparable to confidence index found in the TSL-EBSD

system. ASTAR is explained in more detail in Rauch and Dupuy [12] and Rauch et al. [13].

Figure 3.5: Displays plate martensite formed in a high-carbon steel. The figure is a BF image acquired using an

acceleration voltage of 300 kV and x6000 magnification. The specimen was prepared by electrolytic polishing.

20

21

4 Thermodynamics

Today computational thermodynamics are a fundamental engineering tool for materials design.

Coordinated international research using CALPHAD (CALculation of PHAse Diagrams) techniques

has provided the engineering society with reliable databases of important alloying systems, such as

carbon steels. Computational thermodynamics rely on accurate descriptions of the Gibbs energies

for the pure elements and relevant compounds of the material of interest. From these modeled

Gibbs energies, the equilibrium state of the system, i.e. steel grade, may be calculated for a certain

alloy content, temperature and pressure. Moreover, it is possible to study the relative difference in

Gibbs energy of stable and metastable phases as a function of temperature. Regarding martensite

formation in carbon steels, it is of interest to know the T0 temperature [56], the temperature where

the Gibbs energies of austenite and ferrite phases with the same composition are equal, i.e.

. At temperatures above T0, austenite is more stable than ferrite, with the same composition, and

below T0 the vice versa is true. Evidently, the total energy of the system would decrease if austenite

would transform into ferrite of the same composition below T0. Hence, there is a positive driving

force for ferrite formation, which may be defined as:

[Eq. 4.1]

In practice, when using computational thermodynamics, martensite may be treated as supersaturated

ferrite and Equation 4.1 thus becomes relevant for martensite formation as well. Ordinary ferrite

forms in a diffusional manner with a different composition than the parent austenite even above T0

but still inside the austenite-ferrite two-phase field of the phase diagram. The compositions of

austenite and ferrite, locally at the migrating phase-interface, are close to those of the equilibrium tie

line in the phase diagram, i.e. not much driving force is needed for the interface to migrate. Most of

the driving force is used to change the composition by diffusion. However, when regarding the

experimental Ms temperature for pure iron, reported as 818 K (545 °C) [61], the calculated available

driving force is considerable. Figure 4.1 displays how the available driving force increases with

decreasing temperature and reaches 1250 J/mol at the experimental Ms. It should be remembered

though that only the chemical part of the change in Gibbs energy is considered in this calculation. In

general, the Gibbs energy of a martensitic phase is higher than that of ferrite, since coherency strain

energy, surface energy, and defect energies needs to be accounted for [62], [63]. These effects may be

22

difficult to quantify and therefore it may be more useful to define the requirement of chemical

driving force to start the martensitic transformation. This may be thought of as a transformation

barrier, which will hereafter be denoted

. The barrier is essentially different from

,

which is the available chemical driving force at a given temperature. The available driving force is a

thermodynamic property, defined in Equation 4.1, which depends on the temperature and alloy

composition. The barrier, on the other hand, depends on the details of the transformation

mechanisms, and will thus account for the elastic and plastic energies stored in the material after the

martensitic transformation. For each steel, the available driving force varies with temperature, and MS

is reached when the available driving force is equal to

.

Commercial multicomponent steel databases, such as TCFE6 [64], do not contain a metastable

martensitic phase. Instead, the user may treat martensite as supersaturated ferrite when extracting

thermodynamic data from the database. This may lead to some concerns, for instance how to treat

the ordering of carbon atoms [56]. The ordering occurs as a consequence of the very rapid

martensitic reaction giving no time for carbon atoms to perform diffusive jumps. In the ferrite

structure there are three times more interstitial sites than in austenite but only one-third of them

corresponds to the interstitial sites where carbon may be located in the austenite. Thus the carbon

atoms are not randomly distributed in the fresh martensite, since the positions are inherited from the

austenite. The ordering of carbon atoms was first discussed by Zener [56] and is therefore sometimes

referred to as Zener ordering. Ordering of carbon atoms has a very small effect on the

thermodynamic properties of the martensite at low carbon contents. On the other hand, it will have

a dramatic impact at high carbon contents. Therefore, this effect should be taken into account when

evaluating the driving force for martensitic transformations in high-carbon alloys. For example, this

has been done in an evaluation by Fisher [65].

23

Figure 4.1: Displays the driving force for martensite formation as a function of temperature for pure iron. The

experimental Ms temperature is taken from Morozov et al. [61] and the Gibbs energies for martensite (ferrite) and

austenite was calculated in the Thermo-Calc system [9], [64].

4.1 Measuring the martensite start temperature

Several methods have been proposed to predict the martensite start temperature for commercial

steels. These include empirical-, neural network-, and thermodynamic methods. They have in

common that they rely on experimental Ms temperatures in some sense. It is interesting to notice that

there is no standard method to evaluate the experimental Ms temperature. Instead several methods

have been used, for example metallography [66–68], dilatometry [69–72], magnetometer [72–74], and

thermal arrest measurements [61], [75–78]. Often the experimental uncertainty of the method used

for determining Ms has not been evaluated. In addition, there are uncertainties related to the effect of

the PAGS, which seems to affect Ms significantly [79–81]. Therefore it is reasonable to believe that

the uncertainty for experimental Ms data is rather large. In a paper by Ghosh and Olson [82] they

suggested it to be ±40 K. On the other hand, Mirzayev et al. [83] claim that the accuracy of their

measurements is not worse than ±15 K.

24

4.2 Predicting the martensite start temperature

Many modern engineering steels rely on the hard phase of martensite, for example: transformation

induced plasticity (TRIP)-assisted steels [84], quenched and partitioned steels [85], and maraging

steels [86]. Therefore, it is no surprise that the prediction of Ms and especially its dependence of

alloying content has gained a lot of attention over the years. An early attempt to rationalize

information on Ms in commercial steels was made by Payson and Savage in 1944 [87] who proposed

an empirical expression that could be used for predicting the Ms temperature of new steels:

[K], [Eq. 4.2]

with alloying content given in mass percent [mass%]. The original equation gave Ms in Farenheit but

has here been recast to give Ms in K. A large number of similar empirical expressions have later been

proposed [67], [88–90] and they have been reviewed a number of times, for instance by Wang et al.

[91], by Skrotzki and Hornbogen [92], and by Sourmail and Garcia-Mateo [93]. These empirical

expressions may have a very practical usage, although they are limited to a certain composition range.

Figure 4.2: Variation of driving force with Ms temperature in binary iron alloys. Reproduced from Raghavan and

Antia [94].

25

A more fundamental approach is to apply a thermodynamic method to model Ms. This can be done

by evaluating the barrier for the diffusionless austenite to martensite transformation at the measured

Ms temperatures and study how it varies with composition. Raghavan and Antia [94] attempted such

analysis. However, they did not use experimentally determined Ms values in their analysis, instead

they accepted the improved Andrews’ [90] equation evaluated by Kung and Rayment [95]. Raghavan

and Antia [94] calculated the driving force at Ms for some binary and ternary systems, within the

composition range covered by the equation, as a function of composition. Their results are presented

in Figure 4.2 and illustrate how they represented the variation of driving force at Ms in binary alloys

with straight lines. In their analysis they concluded that for multicomponent alloys it did not appear

feasible to develop a simple equation for the required driving force at Ms as a function of

composition. However, they suggested that a more useful result would be to derive a correlation

between the required driving force and Ms by statistical fitting. By calculating the driving force at Ms

for a total of 1152 arbitrarily selected low alloy steels within a given composition range they obtained

a dataset for their statistical analysis. A least-squares fit of all 1152 compositions yielded the

following linear equation:

( ) [J/mol], [Eq. 4.3]

Another example of a thermodynamic approach is the expression proposed by Hsu and Chang [96],

obtained by studying information from Fe-C alloys:

( ( )) [J/mol], [Eq. 4.4]

where xc denotes mole fraction of carbon. This expression was intended for use only above xc =

0.02. The last term was supposed to give the temperature dependence of the effect of shear and the

second term was supposed to account for the solution hardening of carbon. The expression could

just as well be written as:

( ) [J/mol], [Eq. 4.5]

26

Wang et al. [97] have also derived an expression for the required driving force as function of

temperature. They selected 104 engineering steel compositions and calculated the driving force

thermodynamically at estimated Ms temperatures, which were obtained from a trained neural

network [98]. They fitted a straight line to the calculated driving forces and obtained:

( ) [J/mol], [Eq. 4.6]

When taking the carbon ordering energy into account they obtained a slightly different expression:

( ) [J/mol], [Eq. 4.7]

It should be noted that Wang et al. [97] did not find it necessary to include the effect of alloying

elements explicitly in their expressions.

A very extensive study was made by Ghosh and Olson in 1994 [99], [100]. They plotted the driving

force, evaluated at the experimental Ms for various alloying contents, xi, as function of that content.

Assuming that the effect of an alloying element on the required driving force should be similar to the

effect on solution hardening they fitted the data with a parabolic curve,

[J/mol], [Eq. 4.8]

where K1, which should hold for pure Fe, was treated as independent of temperature. The second

parameter, , was evaluated for a large number of alloying elements and assuming that the effects

were additive they could then predict the Ms values for a large number of steels and obtained

reasonable agreement with experimental values.

Ghosh and Olson [82], [101] later refined their method by introducing a new multicomponent

database, specially evaluated for martensitic transformations, together with a complex method for

representing the critical driving force for starting the martensitic transformation. In their paper they

concluded that the accuracy of Ms predictions, in ternary and multicomponent systems, was

satisfactory if an experimental uncertainty of ±40 K was accepted.

27

So, even though a lot of work has been invested in predicting Ms there is still no general method

readily available, that one can apply easily. However, it seems like a semi-physical approach that

combines state-of-the-art thermodynamics with key experiments might be the best option to

establish a more general method of predicting Ms.

28

29

5 Martensite characterization in carbon steels

It is well-known that the microstructure of ferrous martensite is affected by the alloying content [15],

[27], [102]. Even though the morphological change may seem obvious, it is still very challenging to

make a qualitative as well as quantitative classification of the observed microstructure. Often

microstructure characterization relies on the experience of the operator, i.e. the metallographer. It

may seem unfair to thus suggest that microstructure characterization is to some extent subjective,

since there are quantitative indicators as well. Those are for instance hardness, strength, and other

measurable material properties, although they all would be indirect measurements.

As discussed in Chapter 2 the martensite morphology changes from lath-like to plate-like as the

alloying content is increased. This progressive change in martensite morphology can be represented

by the Figures 5.1a-5.1e, which display specimens with an increasing carbon content. The figures also

illustrate the complexity of the martensitic microstructure, which consists of individual martensite

units forming together in hierarchic structures. Many of the microstructural features are beyond the

magnification range of the OM and therefore only a qualitative understanding of the microstructural

transition is realistic from this series of OM micrographs.

Figure 5.1: Martensite formation in steels with increasing carbon content, all specimens were mechanical polished and

etched with 3% Nital. (a) Interstitial free steel (Fe-1.48Mn-0.0024C), (b) Fe-0.35C, (c) Fe-0.75C, (d) Fe-1.05C,

and (e) Fe-1.80C. The figure is reproduced from [5].

30

A very useful metallographic technique, which has not been used so extensively in the past decade, is

to study the microstructural change in a specimen with a composition gradient. For instance,

Borgenstam et al. [103] successfully applied the gradient technique to study the critical growth

temperature for martensite and how it was related to Ms. More recently Stormvinter et al. [1] applied

this technique to a carbon steel to qualitatively study the microstructural transition from lath to plate

martensite with increasing carbon content. The steel composition is listed in Table 5.1. After

decarburization using hydrogen, a carbon gradient was obtained close to the surface, as seen from

the wavelength dispersive X-ray spectroscopy (WDS) measurement displayed in Figure 5.2a. They

also measured the hardness versus carbon content and concluded that it agreed well with previously

reported hardness numbers [45], [74], [104], [105], as seen from Figure 5.2b.

Table 5.1: Composition of the carbon steel studied in [1], alloying content is given in mass%.

Carbon Chromium Silicon Manganese

0.20 – 1.67 0.47 0.27 0.23

Figure 5.2: (a) Carbon profile close to the surface, ~0.01-5 mm, after decarburization measured with WDS and

simulated with DICTRA using the actual conditions. (b) Hardness vs. carbon content [1], [45], [74], [104], [105].

The figure is reproduced from [1].

31

Stormvinter et al. [1] used a quenching and tempering procedure when characterizing the martensitic

microstructure in the carbon gradient specimens. This procedure made it possible to separate the

first martensite units that formed, close to the Ms temperature, from units formed during the final

quenching to room temperature (RT). Moreover, any position in a heat-treated specimen could be

related to the local carbon content by using the information in Figure 5.2a and hence it was possible

to see how the martensite formation close to Ms was affected by the carbon content.

Figures 5.3a-5.3c are from carbon gradient experiments [1] and show typical transformation

structures found in carbon steels: lath martensite (Figure 5.3a), plate martensite (Figure 5.3c), and

martensite formation in the transition regime between these two extremes (Figure 5.3b). The

tempered martensite appears dark while the martensite formed during quenching to RT appears

bright. Close to the eutectoid composition the martensite microstructure displays characteristic

features for both lath and plate martensite. For instance, in Figure 5.3b a large martensite plate is

visible to the right that has grown to a considerable size. Moreover, it can be seen how new

martensite units have been autocatalyzed on this primary unit. The autocatalysis of new martensite

units on a primary plate is better seen in Figure 5.4, taken from a Fe-1.80C binary alloy (the same

alloy as seen in Figure 5.1e). Apart from these plate-like martensite units, Figure 5.3b shows small

martensite units without typical features of plate martensite and could as well be lath martensite.

The gradual morphologic transition of martensite in the composition range 0.6 to 1.1C can be seen

in Figures 5.5a-5.5f. It is realized that the individual martensite units become more defined and

midribs, characteristic for plate martensite, are visible in Figures 5.5e and 5.5f. It should further be

noted that the change in hardness also appears to be continuous over this composition range, as seen

from Figure 5.2b.

32

Figure 5.3: OM micrographs of the two main types of martensite and the transition region in between; (a) Quenched

and tempered at 623 K, 100-300 µm, ~0.32C. (b) Quenched and tempered at 473K, 1000-1100 µm ~0.81C. (c)

Quenched to 298 K, >5000 µm, ~1.67C. The figure is reproduced from [1] and the micrometer range refers to the

distance from the surface.

Figure 5.4: Tendency for autocatalysis of new martensite units on a primary martensite unit in a Fe-1.80C binary

alloy.

33

Stormvinter et al. [1] performed SEM-BSE imaging of the carbon gradient specimens, which are

shown in Figures 5.6a and 5.6b. In these BSE images the martensite units become visible through

crystallographic contrast, and hence a change in lattice orientation will be reflected in the images.

Figure 5.6b is centered on a martensite unit, which is also indicated with a white arrow in Figure 5.6a,

and it is clearly seen that this unit contains two lattice orientations. This is most probably due to the

internal transformation twinning that occurs when plate martensite grows from the austenite,

although the twin-relation cannot be confirmed in this imaging mode.

The morphological transition observed in specimens with a carbon gradient by Stormvinter et al. [1]

agrees well with the commonly accepted view of martensite, i.e. lath martensite forms in the

composition range 0 to 0.6C and above 1.0C acicular plate martensite is the dominant morphology

[47]. The transition between these two morphologies is usually observed within the composition

range 0.6 to 1.0C [14], [47], [106]. Maki [51] has emphasized that the substructure and crystallography

of martensite units, which forms in this composition range, is fairly complicated. Moreover, Maki et

al. [107] have shown that the morphology of lath martensite changes with the carbon content and

Greninger and Troiano [40] have observed a change in the morphological appearance of plate

martensite in Fe-C alloys. For 1.5 to 1.8C, they found plate-type martensite with clearly visible

midribs, which form in zig-zag patterns. Below this composition range they reported a sudden

change in morphological appearance of the plate martensite, since two plate-like units seemed to be

emanating from a point and grow with an obtuse angle with much less prominent midribs. This latter

morphology has later been described as butterfly martensite [17], [49] and the former as lenticular

martensite [49].

34

Figure 5.5: Martensite morphology of a sample cooled to RT without tempering, observed in OM: (A) 900-1000

µm, ~0.76C; (B) 1100-1200 µm, ~0.83C; (C) 1300-1400 µm, ~0.92C; (D) 1500-1600 µm, ~0.97C; (E)

1700-1800 µm, ~1.09C; (F) 1900-2000 µm, ~1.11C. The figure is reproduced from [1] and the micrometer range

refers to the distance from the surface.

Figure 5.6: (a) Martensite morphology observed in SEM-BSE, 800-1000 µm ~0.75C; (b) High magnification of

the area marked by the arrow in (a). The figure is reproduced from [1].

35

5.1 High-carbon martensite investigated by TEM and ASTAR

Classic TEM has been used to study martensite since the early 1960s, and it was clear already from

the pioneering works on medium- and high-carbon ferrous martensite that the microstructure and

substructure of plate martensite is complex [45], [108]. Characteristic features that has been reported

are for instance: (a) twins, (b) planar defects, (c) dislocation arrays, (d) midrib region, and (e) micro-

cracks [47], [48]. Pioneers Kelly and Nutting [45] were the first to make examinations of ferrous

martensite using thin-foils in the TEM when they studied martensite in two high-carbon low alloy

steels with 1.0 and 1.4C respectively. They reported that both steels displayed plate-like martensite

units, a few microns long and less than a micron thick. Within these units they observed nano-sized

twinning, which had a 15 to 100 Å interspacing, and reported the twin-plane to be {112}α.

Furthermore, they found some retained austenite in the 1.4C steel and concluded that the {112}α

twins were produced from {110}γ planes. Later, Oka and Wayman [48] studied two high-carbon low

alloy steels with 1.28 and 1.82C. The martensite units found in both these steels also contained

{112}α transformation twins, but in the 1.82C steel {101}α planar defects were observed. They

suggested that the {101}α planar defects were accommodation distortion imposed by the growing

martensite.

There have in fact been surprisingly few studies following the works by Kelly and Nutting [45] and

by Oka and Wayman [48] on plate martensite in high-carbon low alloy steels. On the contrary, when

regarding martensite formation in general a vast number of TEM studies have been reported. In

recent years there has been a significant development of characterization capability, for instance

automated crystallographic techniques as TEM-ASTAR. Therefore, Stormvinter et al. [3] selected

two high-carbon low alloyed steels with the ambition to combine ASTAR with classical TEM to

provide a comprehensive basis for discussing the development of plate martensite in these alloys.

The alloys chosen by Stormvinter et al. [3] for TEM observations contained 1.20 and 1.67C

respectively. Figure 5.7a is from the 1.67C alloy and shows a large plate-like martensite unit on the

right-hand side with a distinct midrib in the vertical direction. On the left-hand side of this large

martensite unit, it can be seen that smaller martensite units have developed in characteristic zig-zag

patterns, which are surrounded by heavily dislocated retained austenite. Stormvinter et al. [3]

confirmed by SAED (Figure 5.7c) that the large martensite unit to the right was internally twinned.

The twins were of {112}α-type and can be seen from Figures 5.7b and 5.7d, which are DF

36

micrographs. The extension of these twins appears limited by a discrete crystallographic plane, as can

be seen from the figures. This limiting plane was determined as {101}α and may in fact be

accommodation distortion of either fault- or twin-type.

Figure 5.7: TEM micrographs of the 1.67C steel. (a) On the right hand side in the BF micrograph a large plate

martensite unit is seen with a midrib in the vertical direction. On the left hand side, areas of retained austenite are

present, which seem to contain a high amount of dislocations. (b) DF micrograph centered on the midrib of the large

plate martensite unit on the right-hand side in Figure 5.7a. There is strong diffraction close to the midrib. (c) SAED

from the midrib area with the 200α-twin spot used for DF indicated. (d) High magnification DF micrograph

corresponding to the central part of Figure 5.7b. It is seen that the strong diffraction is due to nano-sized

transformation twinning along the midrib. The figure is reproduced from [3].

37

Another example of plate martensite in the 1.67C alloy, with transformation twinning on the midrib,

is shown in Figures 5.8a and 5.8b. In addition to classic TEM, Stormvinter et al. [3] attempted

ASTAR on these martensite units. The result of the ASTAR is displayed in Figure 5.9 as an IPF

colored map. When comparing the ASTAR results to the TEM imaging it is realized that the nano-

size transformation twinning was not resolved by ASTAR, since only a small area (Indicated by (1))

shows a crystal orientation that deviates from the primary orientation of unit A. This can easily be

understood from the fact that the size of the twins was in the order of the probe-size (20nm).

However, by decreasing the probe-size to 10nm and analyze only a small fraction, close to the

midrib, of martensite unit A the transformation twinning could be better reproduced by ASTAR.

This result is seen from the insert in Figure 5.9. Stormvinter et al. [3] used a conventional electron

source when conducting the ASTAR; however, by using a FEG source the probe-size could be

further decreased and it is thus likely that the spatial resolution would be good enough to accurately

resolve the transformation twinning. Nevertheless, it will still be very challenging to simultaneously

resolve transformation twinning in multiple martensite units, since only twins aligned parallel to the

electron beam may be accurately analyzed using ASTAR. The reason is simply that for nonparallel

twins the incident electron beam will pass through multiple twins and thus give rise to double

diffraction. This will make the recognition of the diffraction pattern impossible since it does not

correspond to an actual crystal orientation. Still ASTAR can be a very useful technique for studying

martensite formation, since it allows for orientation and phase mapping in materials with large

deformations: i.e. martensitic steels. For example, the martensite-martensite orientation relationships

may be calculated from the ASTAR data. In the study by Stormvinter et al. [3] this was done for the

martensite units annotated A, B and C in Figure 5.9.

38

Figure 5.8: TEM micrographs of the 1.67C steel. (a) BF micrograph of martensite units surrounded by retained

austenite. The midrib of the central unit has been indicated by an arrow. In addition, two kink couplings with adjacent

units have been indicated by arrows. (b) High-magnification DF micrograph on the midrib of the martensite unit

indicated by the arrow in a. The figure is reproduced from [3].

Figure 5.9: IPF colored map of martensite obtained by ASTAR. The area corresponds to the Figure 5.8a where it

is shown in BF. The insert displays an IPF colored map on the midrib of the martensite unit indicated by the arrow in

Figure 5.9a. The figure is reproduced from [3].

39

Based on the microstructural observations in 1.20 and 1.67C steels Stormvinter et al. [3] presented a

schematic on the development of martensite in high-carbon low alloy steels, as seen from Figure

5.10. They concluded that development of plate martensite seems to occur as follows: (A) In the first

stage of the transformation, the growth occurs by formation of {112}α twins. (B) As the martensite

unit continues to grow there is a build-up of elastic stresses, which are represented by the dark-blue

area in the surrounding matrix. These elastic stresses may be partly relieved and become more

uniform by various accommodation components. The accommodation may occur by dislocation

motion, in the martensite unit or in the surrounding austenite. The area of the martensite units,

which are mainly affected by these accommodations, is colored light-green in Figure 5.10. If the

transformation temperature is low, and as found in the 1.67C steel, accommodation may occur

through {101}α twinning/faults, which have been illustrated with black lines. (C) The martensite

transformation progresses by autocatalytic nucleation of new martensite units, which may have a

different shape strain and orientation relationship to the parent phase. Commonly these new units

belong to the same plate group and make a well-defined coupling to the preceding unit, which may

be of kink- or wedge-type. The martensite units from the same plate group in Figure 5.10 “(C)” may

be viewed as a “cluster”. Hence, it may be the result of a single nucleation event with successive

autocatalysis of new martensite units.

It is realized that the formation temperature and alloying content is important to consider when

discussing the development of plate martensite. This may be illustrated by the variety of plate

martensitic microstructures found in the literature, i.e.: butterfly- [17], [18], lenticular- [21], [22], and

thin-plate martensite [19], [109]. On the other hand, when the development of plate martensite is

seen from a more general perspective some common principles may be distinguished: (1) Initial

growth of a midrib, which has a completely twinned substructure. (2) Transverse thickening of the

midrib, given that plastic accommodation can occur by either deformation twinning or dislocation

formation. (3) Subsequent autocatalytic nucleation of other martensite units from the same plate

group. The variety of observed microstructures may be explained by the conditions for these steps to

occur, which most likely are governed by temperature and alloying content.

40

Figure 5.10: Schematic on the development of martensite in high-carbon low alloy steels. (A) Represents the first

stage of transformation, the growth occurs by formation of {112}α twins. (B) As the martensite unit continues to grow

there is a build-up in the elastic stresses, which are represented by the dark-blue area in the surrounding matrix. The

light-green area belongs to the martensite crystal and has been affected by accommodations. However, if the

transformation temperature is low, accommodation may occur through {101}α twinning/faults, which have been

illustrated with black lines. (C) The martensite transformation progresses by nucleation of new martensite units, which

have a different orientation relationship to the parent phase. These new units may form a kink coupling or a zig-zag

pattern with the preceding unit. The figure is reproduced from [3].

41

5.2 EBSD – Variant pairing tendency of martensite in Fe-C alloys

In the previous sections the emphasis has been on qualitative martensite characterization of the

transition from lath to plate martensite [1] and the development of plate martensite in high-carbon

steels [3]. In this final section on martensite characterization the emphasis is on quantitative

martensite characterization by EBSD. The discussion is based on two of the appended supplements;

of which one introduces the methodology and the feasibility for studying tetragonal bct-martensite

[4] and the second presents the effect of carbon content on the variant pairing tendency of

martensite in binary Fe-C alloys [5].

As discussed in Chapter 3 (Section 3.2.1) EBSD is an analysis technique that relies on detection of

the local crystallography of a specimen. The collected data can be used to determine the phase as

well as the crystal orientation. Recently, Miyamoto et al. [110] developed a novel method to

accurately determine the OR between austenite and martensite that is based only on the martensite

crystal orientations acquired by EBSD [110]. Stormvinter et al. [4] extended this methodology to

study martensite formation with large tetragonality formed in Fe-C alloys. For this purpose they

selected high-purity binary alloys having the nominal compositions of 0.35, 0.75, 1.05, 1.80C and an

interstitial free (IF) steel. The chemical compositions of the alloys together with the Ms temperature,

calculated according to Stormvinter et al. [2], are listed in Table 5.2.

Figure 5.11a displays IPF colored martensite units in the 1.80C alloy, which all belong to a single

parent austenite grain with no annealing twins. To interpret the martensite microstructure solely

based on IPF colored maps is rather difficult. However, these martensite units display a very

characteristic pole figure (PF) pattern as seen from Figure 5.11b. The figure displays a standard

<001>α-BCC stereographic projection of experimental data points, which have been superimposed by

the calculated nodes obtained by numerical fitting [110]. This pattern can be compared to the well-

known K-S OR [34]. In agreement with the K-S OR, Figure 5.11b displays 24 unique martensite

orientations, which may be seen from the clustering of 8 martensite variants around every <001>γ.

This circle pattern around every <001>γ is called a Bain circle [111].

Moreover, Stormvinter et al. [4] discussed how the tetragonality of high-carbon martensite would

influence the EBSD data analysis, since in general martensite is treated as bcc rather than bct when

conducting EBSD analysis. They first attempted indexing of martensite as tetragonal bct on the

42

1.80C alloy, since it has the highest c/a ratio. Figures 5.11c and 5.11d from the 1.80C alloy display

[001]α-BCT and [010]α-BCT/[100]α-BCT pole figures of the martensite units displayed in Figure 5.11a when

indexed as tetragonal bct instead of cubic bcc. As can be seen from Figure 5.11c, the [001]α-BCT crystal

direction could be separated from the [010]α-BCT and [100]α-BCT crystal directions. Figure 5.11d on the

other hand contains data belonging to both [100]α-BCT and [010]α-BCT since they are indistinguishable.

Taking Bain correspondence ([1-10]γ // [100]α-BCT, [110]γ // [010]α-BCT, [001]γ // [001]α-BCT) into

account, it can be understood that only [001]α-BCT should be contained in the Bain circle. Stormvinter

et al. [4] attempted bct indexing on the 0.35, 0.75 and 1.05C alloy as well, and the success rate of bct

indexing, can be seen in Figure 5.11e. The success rate is defined as a ratio between the number of

data points, whose [001]α-BCT is contained in the Bain circle, and the total number of data points. It is

clearly seen that the success rate decreases with decreasing tetragonality and reaches 1/3 at 0.35C,

which would be expected from mathematical statistics for the random case. Thus, it could be

concluded that accurate indexing of martensite as tetragonal bct was only feasible for the 1.80C alloy

of the five alloys studied. In addition, Stormvinter et al. [4] showed that bct indexing of the EBSD

data has a minor effect on the OR analysis and thus the simplified bcc indexing is feasible for all

carbon contents.

Table 5.2: Chemical composition, calculated Ms and PAGS for the studied alloys.

C Mn B Fe Calc. Ms PAGS

0.0023 1.48 0.0027 Bal. 726K 320μm

0.345 0.02 - Bal. 672K 200μm

0.74 <0.003 - Bal. 531K 370μm

1.06 <0.003 - Bal. 472K 300μm

1.80 0.004 - Bal. 363K 250μm

43

Figure 5.11: (a) Displays an IPF colored map of martensite units from one single parent austenite grain, in the

1.80C alloy. Only data points with a confidence index higher than 0.2 are displayed. (b) <001>α-BCC PF of

martensite units visible in (a). Experimental data-points have been superimposed by calculated nodes for <001>α-BCC

and <001>γ, which were obtained by fitting to the former. Hence, white circles and black crosses are for martensite

and austenite, respectively. (c) PF [001]α-BCT and (d) PF [010]α-BCT/[100]α-BCT of martensite units visible in (a)

when indexed as tetragonal bct. (e) Variation of success rate of bct indexing as a function of carbon content and

tetragonality. The figure is reproduced from [4].

44

Figure 5.12: The observed change in orientation relationship between parent and product phase with increasing

carbon content expressed as deviation angle between austenite and martensite CPP and CPD. The figure is reproduced

from [4].

However, when calculating the deviation angle between CPP and CPD of martensite and austenite

they found it necessary to consider the martensite tetragonality. This may be understood from the

fact that the CPP and CPD will rotate when going from a cubic to a tetragonal lattice, unlike the

principal cube axes that will stay parallel. Comparing the deviation angle between CPP and CPD of

the parent and product phase is a common way to express the OR. In Figure 5.12 the effect of

carbon content on the OR, as reported by Stormvinter et al. [4], is displayed and it is seen how the

OR shift from close to G-T OR towards K-S OR as the carbon content increases. Moreover, these

results were found consistent with previously reported OR on low-carbon [110] and high-carbon

steels [34].

There may be several factors affecting the OR, such as lattice parameters of martensite and austenite,

austenite strength for accommodation of shape strain and substructure in martensite arising from

lattice invariant shear (LIS) mode. Oka and Okamoto [112] made theoretical predictions of the OR

for an 1.8C alloy by using phenomenological theory of martensitic crystallography (PTMC) with the

assumption of two different LIS systems (112)[-1-11]α and (101)[10-1]α, which correspond to the

45

ORs shown as A and B in Figure 5.12, respectively. (112)[-1-11]α is the ordinary LIS for (112)α twin

and it appears in most of plate martensite in ferrous alloys while (101)[10-1]α corresponds to the

(101)α twin reported only in high carbon martensite [13]. The prediction by Oka and Okamoto [112],

A and B in Figure 5.12, illustrate the significant effect of LIS on OR. It is interesting that the

measured ORs for high carbon alloys agree with the OR B whereas ORs for lower carbon martensite

are rather close to OR A. Stormvinter et al. [4] did however not investigate the mechanism for the

observed change in OR in more detail.

Instead, Stormvinter et al. [5] used the experimentally determined OR to investigate the effect of

carbon content on the variant pairing tendency of martensite formed in these five alloys. Variant

pairing tendency implies quantification of the nearest neighboring of martensite units. In most cases

the number of crystallographically unique martensite-martensite neighbors is limited to 24. The

misorientation, and thus boundary character, of such neighbors may be calculated from the

experimentally determined OR. An EBSD dataset, for example as seen from Figure 5.13, may

contain several thousands of martensite-martensite boundaries and is therefore ideal for variant

pairing determination. Stormvinter et al. [5] showed how the quantified variant pairing can be

interpreted and transposed into knowledge of the martensite microstructure.

Figure 5.13: IPF colored EBSD map taken from the IF steel. The figure is reproduced from [5].

46

Figure 5.14: Variant pairing frequency diagrams which display the length fractions of inter-variant boundaries for

(a) IF steel, (b) 0.35C alloy, (c) 0.75C alloy, (d) 1.05C alloy, and (e) 1.80C alloy. The error bars represent the

standard deviation of three measurements, each acquired from an area of 800x265µm. Reproduced from [5].

The results from the analysis [5] of martensite-martensite boundaries are presented in Figures 5.14a-

5.14e, and show the length fraction of variant boundaries in relation to variant 1. As seen from the

figures there is a clear dominance of intra close-packed plane group (CP group) variant pairing at

lower carbon contents. Moreover, there is a shift from V1/V4 dominance towards V1/V2

dominance as the carbon content is increased. However, the variant pairing tendency of martensite

formed in the 1.80C alloy is in strong contrast, as seen from Figure 5.14e, to that of the other alloys.

For this high-carbon alloy, pairing of V1 with variants V2, V6, V16 and V17 seems to be more

frequent, with a dominance of V1/V16 pairing. This tendency for V1/V16 pairing is also observed

in the 0.75 and 1.05C alloys, although not as pronounced as in the 1.80C alloy.

47

Figure 5.15: IPF colored EBSD map taken from the IF steel. The map shows an area with a dominant martensite

packet and blocks and sub-blocks have been labeled with its corresponding martensite variants. EBSD data from the

region enclosed by the yellow box was used for the analysis by standard stereographic projection. Misorientation

boundaries are colored as follows: (White) 4°-13° and (Black) > 19°. The figure is reproduced from [5].

As seen from Figure 5.14a, martensite formed in the IF steel is dominated by V1/V4 pairing. This

particular variant pair, V1/V4, has previously been associated with sub-block boundaries of low

misorientation [42], [113], [114]. The packet and block martensite microstructure is rather obvious in

the IF steel, as seen from Figure 5.1a. Another noticeable feature of the IF steel is seen from Figure

5.15; the block boundaries are few when compared to the sub-block boundaries. In fact, the large

block-size of the IF steel may be seen from Figures 5.1a and 5.13 as well. Hence, as the sub-block

boundaries, as seen from Figure 5.15, dominates the microstructure it is realized that the V1/V4

boundary also is the most frequently observed, as seen from Figure 5.14a. The smaller block-

size/sub-block-size ratio for the 0.35C explains why the V1/V4 variant pairing is not found to be as

dominant as for the IF steel, although it displays martensite formed in packets and blocks as seen

from Figure 5.1b. In the 0.35C alloy all martensite units that belong to the CP group shows up in the

variant pair frequency analysis. Nevertheless, the sub-block boundaries, V1/V4, are the most

frequent.

The 0.75C alloy, with the close to eutectoid composition, does not display a typical lath martensitic

microstructure, since packets and blocks cannot be easily identified as seen from Figure 5.1c.

However, when the EBSD data is used to color martensite units according to their CP group

association the packets become more evident, as seen from Figure 5.16a. Moreover, the martensite

units, a few microns in size, seem to be separated primarily by high-angle boundaries in this alloy.

Figure 5.16b displays an IPF colored map of a limited number of such martensite units, taken from a

48

single CP group (CP1 in Figure 5.16a). These martensite units have been labeled with their

corresponding martensite variant, V1 through V6, and boundaries are colored as follows: Yellow –

Twin (V1/V2; V3/V4; V5/V6), White – Low angle (V1/V4; V2/V5; V3/V6), and Black – High

angle (All other combinations). High angle boundaries, preferably twin boundaries (yellow), seem to

dominate in this alloy, although there are a considerable fraction of low angle (white) boundaries as

well. This is also seen from the variant pairing analysis, displayed in Figure 5.14c. The results for the

0.75C alloy may be compared with the results for a 0.61C alloy by Morito et al. [42]. Both results

display variant pairing of martensite units that belong to the same CP group. However, no tendency

for block or sub-block formation is observed in either of the alloys. These similarities indicate that an

increase in carbon content from 0.61 to 0.75C does not affect the structure significantly. The

observed strong peak of the V1/V2 variant pairing in Figure 5.14c is an important observation. If

the martensite in the 0.75C alloy may be classified as lath martensite, it indicates that a lower

formation temperature would promote V1/V2 variant pairing. This temperature dependence of

variant pairing has recently been observed by Takayama et al. [114] in low-carbon bainite. They

found that a lowered formation temperature promotes V1/V2 pairing. This variant pairing is unique

since it is the only pairing that is twin-related. In addition, a recent EBSD work [115] by Naraghi et

al. on athermal martensite formed in stainless steels also supports this observation of twin-related

variant pairing at low transformation temperatures.

Figure 5.16: Displays EBSD data from the 0.75C (a) Martensite units from a single prior austenite grain colored

according to CP group belonging. (b) IPF coloring of martensite units from a single CP group. The martensite units

have been labeled with their corresponding crystallographic variant. The boundaries are colored as follows: Yellow –

Twin (V1/V2; V3/V4; V5/V6), White – Low angle (V1/V4; V2/V5; V3/V6), and Black – High angle

(All other combinations). The figure is reproduced from [5].

49

In the 1.80C alloy the variants V1, V6, V16 and V17, which all belong to the same plate group, tend

to be paired more frequently, as seen from Figure 5.14e. The dominance of plate group variant

pairing is supported by the previous studies on variant selection of plate martensite [19], [116], [117].

The strong coupling between the plate group martensite variants may also be seen from Figure 5.17.

Here the EBSD-data from the 1.80C alloy is displayed as an IPF colored map, where the martensite

variants are colored as follows: V1 – Orange, V6 – Dark blue, V16 – Pink, and V17 – Light blue.

According to Okamoto et al. [19], variant pairs V1/V6, V1/V16 and V1/V17 correspond to wedge-,

kink-, spear-type respectively. They reported that wedge and spear variant pairs are favored due to

self-accommodation, while kink type is not. Therefore, Stormvinter et al. [5] supposed that the

observed dominance of V1/V16 pairing (kink type) could be due to the autocatalytic plate

formation.

The results from the variant pairing analysis [5] of 1.05C displayed in Figure 5.14d may be

interpreted as a transition between CP group pairing and plate group pairing. This conclusion agrees

well with the observed microstructure obtained using OM, as seen from Figure 5.1d. In the figure it

can be seen that large plate-like martensite units, with transverse micro-cracks, are embedded in a

matrix of smaller martensite units.

Figure 5.17: IPF colored EBSD map taken from the 1.80C alloy. EBSD data from the region enclosed by the

yellow box was used for the analysis by standard stereographic projection. Martensite variants are IPF colored as

follows: V1 – Orange, V6 – Dark blue, V16 – Pink, and V17 – Light blue and the white regions correspond to

retained austenite. It should be noted how the transverse thickening of the primary plates seems to occur by autocatalytic

nucleation of new martensite units on the former. The figure is reproduced from [5].

50

Based on their results, Stormvinter et al. [5] presented three schematics to illustrate the observed

change of martensite morphology with increasing carbon content. These schematics are presented in

Figures 5.18a-5.18c. Martensite formation in the IF steel is represented by Figure 5.18a, where a

prior austenite grain has transformed into a martensitic packet and block structure. In this figure one

CP group has been highlighted and it contains three blocks, which are colored according to their

corresponding Bain group association. The blocks contain sub-blocks, which are separated by

boundaries colored in light gray. Figure 5.18b displays formation of CP groups in the Fe-0.75C alloy.

The microstructure within every CP group would be very similar to Figure 5.16b, i.e. preferably

V1/V2 twin-type boundaries between the individual martensite variants. The absence of blocks and

sub-blocks seems to be the characteristic feature of this type of medium carbon lath martensitic

microstructure. The well-known characteristic hierarchy of lath martensite is in strong contrast to the

plate martensite formed in the Fe-1.80C alloy displayed in Figure 5.18c. Here the development of

martensite into plate groups is illustrated. This occurs by subsequent autocatalysis of variants which

belong to the same plate group. Every plate group contains four martensite variants and in total there

may be six plate groups present in one prior austenite grain (when disregarding annealing twins).

However, to make the microstructural interpretation easier, only one out of the six plate groups are

displayed here. This also seems reasonable since it is not clear from the present analysis how the

individual plate groups will be distributed within the prior austenite grain.

Figure 5.18: Schematics of martensite formation in (a) IF steel, (b) Fe-0.75C alloy and (c) Fe-1.80C alloy. The

region composed by variants belonging to the same Bain group is represented by the same color. The figure is reproduced

from [5].

51

5.3 Transition between lath and plate martensite

In the present thesis it has been demonstrated how different analyzing tools may provide

information to get a more fundamental understanding of the martensite microstructure. This

includes: (1) OM and classic SEM to analyze apparent morphology of the martensite units. (2)

Classic TEM to get detailed information on the substructure as well as the possibility to do more

detailed crystallographic analysis. (3) Automated crystallographic techniques, such as EBSD and

ASTAR, to analyze orientation relationships as well as martensite-martensite boundary

characteristics, i.e. variant pairing tendency. When interpreting the combined knowledge gathered [1],

[3–5] it seems clear that the complexity of the martensite morphology has to be resolved in multi-

length scale approach, where all these techniques are combined. Moreover it also seems rather clear

that the transition from lath martensite towards plate martensite is gradual and that the two

morphologies makes good reference points for interpreting a material in the mixed regime. In

addition, the recently developed variant pairing analysis may prove a good compliment to traditional

metallography, since it allows for quantification of boundary character, and thus martensite character.

This is well illustrated in Figure 5.19 that shows how the variant pairing tendency changes with the

carbon content. This EBSD technique has a clear advantage over ASTAR, since it can be applied to

an area large enough to be representative for the whole specimen. On the other hand, ASTAR has its

advantages since it can very well reproduce the local microstructure and allows for on-line

interchanging to classic TEM. In conclusion, by combining the strengths from various

characterization techniques it is possible to get a good understanding of the morphological transition

in ferrous martensite with increasing carbon content, although it may still prove very challenging and

time-consuming to perform the characterization.

52

Figure 5.19: Variant pairing tendency given as length fraction of variant boundary versus carbon content and based

on the experimental results from the present work. The figure is reproduced from [5].

53

6 Discussion on inverse bainite

As mentioned in Chapter 2 (Section 2.2), there has been a long debate concerning the nature of the

bainite formation and whether it can be regarded as diffusionless or diffusion controlled. The

conflict has been on-going since the 1940s when Zener [56] presented a comprehensive review of

the mechanisms involved in the austenite decomposition. The experimental results by Ko and

Cottrell [53], that bainite grows with a surface relief, were taken as a strong indication of a

diffusionless nature. However, as pointed out by Hillert [118] the surface relief is an indication of the

displace nature of the transformation, i.e. the fcc lattice is transformed into the bcc lattice in a

military fashion. It does not imply that such transformation omits diffusion of carbon, especially for

a transformation with slow growth rate as for instance the bainite transformation.

Recently, Borgenstam et al. [6] studied the decomposition of high-carbon austenite with the purpose

to test the symmetry among the diffusional transformation products in the Fe-C alloys. The term

symmetry was here used to define the relation between the eutectoid decomposition products as

follows: “Pearlite is the result of cooperative growth of ferrite and cementite where the two phases

behave as equal partners. It is favored by a close-to-eutectoid composition. Bainite forms with ferrite

as the leading phase in the main growth direction, which is identical to the growth direction of

Widmanstätten ferrite. Bainite is favored by a low carbon content. Inverse bainite forms with

cementite as the leading phase in the main growth direction, which is identical to the growth

direction of Widmanstätten cementite. Inverse bainite is favored by a high carbon content.”. The

concept of inverse bainite was first introduced by Hillert in 1957 [58] but has been discussed only a

few times during the elapsed 50 years, mainly by Aaronson and co-workers [119–121]. Evidently, the

diffusionless mechanism cannot be applied to inverse bainite, since it is not possible to imagine the

growth of a low-carbon cementite plate that later enriches in carbon by the onset of a diffusional

process.

Borgenstam et al. [6] based their study on a large number of micrographs from isothermal treatments

of a high-carbon steel. Below the A1 temperature they observed austenite decomposition into pearlite

in a Fe-1.67C-0.22Mn-0.27Si-0.47Cr. However, below 773 K (500 °C) pearlite was replaced by an

acicular eutectoid with cementite as the leading phase. An example of these “spiky nodules” can be

seen from the micrograph by Modin and Modin [122] presented in Figure 6.1.

54

Figure 6.1: Spiky nodules of inverse bainite formed after 60 s at 723 K (450 °C) in a steel with 1.65C. OM

micrograph at 600 times magnification. Reproduced from Modin and Modin [122].

Figure 6.2: Acicular eutectoid (inverse bainite) between plates of cementite, formed after 1 s at 823 K (550 °C) in

steel with 1.34C. The arrows mark inverse bainite ahead of the cementite plate. TEM micrograph on plastic replica at

12,000 times magnification. Reproduced from Kinsman and Aaronson [119].

As the transformation temperature was lowered further the “spikes” of the nodules became less

pronounced and the eutectoid structure appeared more “fan-like” or columnar. At even lower

transformation temperatures the eutectoid structure again appeared spiky with protruding tips.

However, Borgenstam et al. [6] could show that this was in fact a gradual shift from cementite being

55

the leading phase of the hypereutectoid structure towards ferrite as the leading phase. This may be

illustrated by Figure 6.2 that shows how cementite is dominating the growth of inverse bainite in the

upper temperature range. In contrast, Figure 6.3 displays a hypereutectoid structure, transformed at

much lower temperature, where the growth has been dominated by the ferrite. From the figure it can

be seen how the shorter carbide units have been nucleated and grown from a primary ferrite plate.

Hence, the carbides are formed subsequently. This implies that as the isothermal transformation

temperature is lowered the growth of the hypereutectoid transformation structure shifts from a

cementite dominance (Figure 6.2) towards a ferrite dominance (Figure 6.3), i.e. there is a transition

from growth of inverse bainite towards ordinary bainite as the transformation temperature is

lowered. This is not so unlikely when taking the asymmetry of the Fe-C phase diagram into account.

As can be seen from Figure 6.4, the extrapolated A3 and Acm show that the supersaturation with

respect to ferrite increases more rapidly than to the supersaturation with respect to cementite. The

supersaturation may be interpreted as a driving force and hence the nucleation and growth of ferrite

becomes more likely as the temperature decreases.

Figure 6.3: Two thin spikes with a central plate of ferrite (white) and shorter plates of cementite (dark). Formed

after 1 h at 573 K (300 °C) in steel with 1.67C. Etched for carbides. Additional etching in nital was applied in the

insert. Two arrows mark the same platelet of cementite. SEM at 12,000 times magnification. Reproduced from

Borgenstam et al. [6].

56

Figure 6.4: Extrapolated solubility lines for ferrite and cementite in Fe-C austenitee [9], [64]. The figure is

reproduced from [6].

Most of the changes of microstructure of the eutectoid products in high-carbon steels with

temperature are gradual and may be explained by the asymmetry of supersaturation with respect to

ferrite and cementite at decreasing temperature. Moreover, Borgenstam et al. [6] showed that inverse

bainite, which forms by a diffusion controlled process, has many similarities to ordinary bainite. For

instance, they both form with a shape change that gives rise to a surface relief. However, the bainite

controversy will probably survive until a key experiment accepted by the proponents of both sides

can resolve the true nature of the transformation mechanism.

57

7 Thermodynamically based prediction of the

martensite start temperature

Some years ago, Borgenstam and Hillert [123] reviewed a comprehensive amount of experimental Ms

temperatures of binary and ternary ferrous alloys and made some noticeable distinctions in their final

assessment: (a) They used experimental Ms values directly and took them mainly from studies using

very rapid cooling; (b) They distinguished between data for two kinds of martensite yielding separate

plateaux in the cooling curves, where plateau III was supposed to belong to lath martensite and

plateau IV to plate martensite; (c) Results for Fe-Co were included which was an important addition

because it expanded the temperature range to above the value for pure Fe. They also proposed the

following expressions graphically for the requirement of driving force to start a martensitic

transformation into either lath or plate martensite:

( )

[J/mol], [Eq. 7.1]

( )

[J/mol], [Eq. 7.2]

The concept of two separate Ms temperatures, one for lath- and one for plate martensite, is

originating from the works by Morozov et al. [61], [75] who studied how the decomposition of

austenite in pure Fe and in Fe with 0.01C was affected by the cooling rate, from moderate to

extremely rapid cooling. They observed four transformation plateaux, as seen in Figure 7.1, where

plateaux III and IV were identified as caused by lath and plate martensite, respectively. According to

that information one should distinguish between the Ms temperatures for lath and plate martensite,

supposedly 818 K (545 °C) [61] and 693 K (420 °C) [75] for pure iron.

58

Figure 7.1: Beginning of the γ → α transformation in iron as a function of cooling rate, redrawn from Morozov et

al. [75]

In an attempt to construct a sound thermodynamic method to predict Ms of commercial steels,

Stormvinter et al. [2] accepted that the two expressions, Equations 7.1 and 7.2, for the necessary

driving force to form lath and plate martensite by Borgenstam and Hillert [123] holds for pure Fe.

They then referred experimental data on Ms for binary alloys, Fe-X(= C, Cr, Mn, Ni), from rapid

cooling experiments [70], [74], [76], [78], [124–127] to either plateau III or IV. From this information

they calculated the driving force at Ms and the difference from Equations 7.1 and 7.2 was accepted as

an effect of the alloying element and was evaluated as proportional to the content of each alloying

element. A linear superposition law was assumed for the combined effect of alloying elements on the

driving force, yielding the following expressions to be used for predicting the Ms temperature of

commercial steels (compositions given in mole fraction):

( )

( )

( ), [J/mol] [Eq. 7.3]

( )

( )

( ), [J/mol] [Eq. 7.4]

59

In the analysis by Stormvinter et al. [2] Zener ordering of carbon atoms was taken into account, since

it will have a dramatic impact on the Gibbs energy of the fresh martensite at high carbon contents.

In order to use Equations 7.3 and 7.4 to predict Ms of a commercial steel, it is necessary to find the

temperature where the available driving force for the alloy composition equals the required driving

force, i.e. the transformation barrier. To validate their proposed thermodynamic method for

prediction of Ms, they applied it to a number of datasets available in the rich martensite literature

[67], [68], [128], [129]. Both Equations 7.3 and 7.4 were used and the highest predicted Ms

temperature was accepted for each steel. For steels where Equation 7.3 (lath) gave the highest

predicted Ms, open symbols were used in the figures, while filled symbols were used when Equation

7.4 (plate) gave the highest predicted Ms. For example, Figure 7.2 displays a comparison of the

predicted Ms by the model and the experimentally determined Ms by Grange and Stewart [67] and by

Steven and Haynes [68].

Figure 7.2: Comparison between experimental Ms by Grange and Stewart [67], and by Steven and Haynes [68]

and predicted Ms temperatures. The figure is reproduced from [2]. Open symbols: lath martensite and filled symbols:

plate martensite.

60

The thermodynamic model proposed by Stormvinter et al. [2] has been used to develop a simple and

user-friendly software for calculation of Ms. This software is for the moment exclusive for the Hero-

m research center partners and may therefore not be distributed outside Hero-m yet. A screenshot of

the user-interface can be seen in Figure 7.4. It is the belief of the present author that this software

will be developed further, for instance to include the effect by PAGS on Ms.

Figure 7.3: User-interface of the computer program for calculating Ms developed within the Hero-m center.

61

8 Concluding remarks and future prospects

The martensite transformation in steels has a substantial amount of complexity. In addition, it is also

one of the most important phase transformations to account for in process development and

materials design. Some important aspects of the martensitic transformation have been thoroughly

discussed in the present thesis. Those include: (1) The quantification of the martensite

microstructure and how that may be used to classify martensitic steels. (2) The feasibility of

developing a predictive model for Ms that is based on the current state-of-the-art thermodynamics.

Both these subjects may have a true industrial significance, since it may aid engineers in alloy design.

However, there are still challenges left before the full potential of both these methods can be fully

realized. A number of these challenges will be listed here:

The limited amount of experimental Ms data from binary and ternary alloys that is relevant for

steels. It is evident that additional experimental data would make further improvements of the

thermodynamic model as developed here [2], since it in principle relies on experimental Ms data

from binary and ternary alloys. However, it is important to keep in mind that such data should

contain information of experimental conditions, for instance cooling rate and PAGS. Very often

this kind of additional data is left out when the final experimental data is presented.

Improved thermodynamic databases, which are optimized for low temperatures. It is likely that

the never-ending increase in computational power will further fuel the capabilities of doing

computer based experiments. Ab initio and related techniques have already proved that they can

provide reliable data that may be extremely difficult to obtain through an ordinary experiment.

This new information may be used together with experimental data to optimize thermodynamic

databases to handle low temperature phase transformations, as the martensitic for instance.

Improvement of the commercially available EBSD software. For instance, to include easy-to-use

post-processing software to analyze orientation relationships and variant pairing. It is most

probable that EBSD analysis will become more sophisticated since this is a recent developed

area. Especially if one considers the growing popularity of FEG-SEMs equipped with EBSD

detectors.

62

There has been a recent interest in three-dimensional (3D) characterization of materials, for

instance TMS (The Minerals, Metals and Materials Society) hosted an international conference

(3DMS in Seven Springs, Pennsylvania) dedicated to the topic in the past summer (2012). It is

likely that 3D characterization will add substantial information to the structure-property

relationships of materials. 3D characterization includes, among other techniques, 3D EBSD that

allows for detailed analysis of the crystallography of a finite volume. 3D EBSD is already

commercially available and may be applied to study morphology, boundary character, and variant

grouping of martensitic steels.

The growth kinetics of martensite may not yet be categorized as “well-known”. Obviously the

rapid transformation rate has made it difficult to study how the transformation progresses. On

the other hand, synchrotron sources and detector capabilities have improved significantly since

most of the experiments were conducted. It is therefore likely that it would be feasible to study

the growth kinetics using a synchrotron source to gain more insight to this phase transformation.

Steels forming lath martensite would probably be the best candidate to choose, since experiments

indicate that the growth rate can be several orders of magnitude lower when compared to the

growth rate of plate martensite.

63

9 Acknowledgments

First of all I would like to express my sincere gratitude to my principal supervisor Assoc. Prof.

Annika Borgenstam and co-supervisor Prof. John Ågren for giving me this opportunity to do

research on some very interesting aspects of physical metallurgy. I do much appreciate how you

encourage me to find and develop the researcher within me, although always prepared with guidance

if needed. I would also like to express my deepest gratitude to my second co-supervisor, Dr. Peter

Hedström, for non-depleting enthusiasm as well as professional assessment of my work.

I would like to acknowledge Prof. Yves Brechét and his co-workers at INP-Grenoble for a superb

spring in 2010. Also Prof. Tadashi Furuhara and his co-workers should be sincerely acknowledged

for accepting me into their lab in the summer of 2011. A special thanks to Dr. Goro Miyamoto for

his never-ending patience in my struggles to learn crystallography of martensite.

I would also like to acknowledge my colleagues at KTH for providing a welcoming, professional and

inspiring environment for research. A special thanks to Dr. Lars Höglund for being very helpful with

computer related challenges.

I would also like to thank the VINN Excellence Center Hero-m, VINNOVA, Swedish Steel

Industry, and KTH Royal Institute of Technology for providing finance for performing this work.

As well as Stiftelsen Axel Hultgren fond, Ångpanneföreningens Forskningsstiftelse, Stiftelsen

Bergshögskolans jubileumsfond, Knut och Alice Wallenbergs stiftelse, and Stiftelsen De Geerska

fonden for providing travel grants.

Finally, I would like to express my deepest gratitude to my family for their support and

encouragement. I am also in debt to all my friends for giving me such a wonderful time; you know

who you are (Ingen nämnd – Ingen glömd).

64

65

10 Bibliography

[1] A. Stormvinter, P. Hedström, and A. Borgenstam, “Investigation of Lath and Plate Martensite

in a Carbon Steel,” Solid State Phenomena, vol. 172–174, pp. 61–66, Jun. 2011.

[2] A. Stormvinter, A. Borgenstam, and J. Ågren, “Thermodynamically Based Prediction of the

Martensite Start Temperature for Commercial Steels,” Metallurgical and Materials Transactions A,

2012.

[3] A. Stormvinter, P. Hedström, and A. Borgenstam, “A transmission electron microscopy study

of plate martensite formation in high-carbon low alloy steels,” To be published, 2012.

[4] A. Stormvinter, G. Miyamoto, T. Furuhara, and A. Borgenstam, “Effect of Carbon Content

on the Orientation Relationship between Austenite and bct-Martensite in Fe-C Alloys

resolved by Electron Backscattered Diffraction,” To be published, 2012.

[5] A. Stormvinter, G. Miyamoto, T. Furuhara, P. Hedström, and A. Borgenstam, “Effect of

Carbon Content on Variant Pairing of Martensite in Fe-C alloys,” To be published, 2012.

[6] A. Borgenstam, P. Hedström, M. Hillert, P. Kolmskog, A. Stormvinter, and J. Ågren, “On the

Symmetry Among the Diffusional Transformation Products of Austenite,” Metallurgical and

Materials Transactions A, vol. 42, no. 6, pp. 1558–1574, Nov. 2010.

[7] World Steel Association, “World crude steel output increases by 6.8% in 2011,” 2012.

[Online]. Available: http://www.worldsteel.org/media-centre/press-releases/2012/2011-

world-crude-steel-production.html. [Accessed: 24-Jan-2012].

[8] G. Krauss, Steels: processing, structure, and performance. Materials park, OH: ASM International,

2005, pp. 1–658.

[9] J.-O. Andersson, T. Helander, L. Höglund, P. Shi, and B. Sundman, “Thermo-Calc &

DICTRA, computational tools for materials science,” Calphad, vol. 26, no. 2, pp. 273–312,

Jun. 2002.

66

[10] P. Gustafson, “A Thermodynamic Evaluation of the Fe-C System,” Scandinavian Journal of

Metallurgy, vol. 14, no. 5, pp. 259–267, 1985.

[11] A. J. Schwartz, M. Kumar, B. L. Adams, and D. P. Field, Eds., Electron Backscatter Diffraction in

Materials Science, 2nd ed. Boston, MA: Springer US, 2009.

[12] E. F. Rauch and L. Dupuy, “Rapid Spot Diffraction Patterns Identification through Template

Matching,” Archives of Metallurgy and Materials, vol. 50, pp. 87–99, 2005.

[13] E. F. Rauch, J. Portillo, S. Nicolopoulos, D. Bultreys, S. Rouvimov, and P. Moeck,

“Automated nanocrystal orientation and phase mapping in the transmission electron

microscope on the basis of precession electron diffraction,” Zeitschrift für Kristallographie, vol.

225, no. 2–3, pp. 103–109, Mar. 2010.

[14] G. Krauss and A. Marder, “The morphology of martensite in iron alloys,” Metallurgical

Transactions, vol. 2, no. 9, pp. 2343–2357, 1971.

[15] P. G. McDougall and C. M. Wayman, “The Crystallography and Morphology of Ferrous

Martensites,” in Martensite, G. B. Olson and W. S. Owen, Eds. Materials park, OH: ASM

International, 1992, pp. 59–95.

[16] J. A. Klostermann and W. G. Burgers, “Surface martensite in iron-nickel,” Acta Metallurgica,

vol. 12, no. 4, pp. 355–360, Apr. 1964.

[17] M. Umemoto, T. Hyodo, T. Maeda, and I. Tamura, “Electron microscopy studies of butterfly

martensite,” Acta Metallurgica, vol. 32, no. 8, pp. 1191–1203, Aug. 1984.

[18] H. Sato and S. Zaefferer, “A study on the formation mechanisms of butterfly-type martensite

in Fe–30% Ni alloy using EBSD-based orientation microscopy,” Acta Materialia, vol. 57, no. 6,

pp. 1931–1937, Apr. 2009.

[19] H. Okamoto, M. Oka, and I. Tamura, “Couplings of thin-plate martensites in an Fe-Ni-C

alloy,” Transactions JIM, vol. 19, pp. 674–684, 1978.

67

[20] T. Kakeshita, K. Shimizu, T. Maki, and I. Tamura, “Growth behavior of lenticular and thin

plate martensites in ferrous alloys and steels,” Scripta Metallurgica, vol. 14, no. 10, pp. 1067–

1070, 1980.

[21] M. Umemoto, K. Minoda, and I. Tamura, “Some characteristics of the substructure of

lenticular martensite in Fe-Ni-C alloys,” Metallography, vol. 15, no. 2, pp. 177–191, May 1982.

[22] A. Shibata, S. Morito, T. Furuhara, and T. Maki, “Substructures of lenticular martensites with

different martensite start temperatures in ferrous alloys,” Acta Materialia, vol. 57, no. 2, pp.

483–492, Jan. 2009.

[23] M. Cohen, G. B. Olson, and P. C. Clapp, “On the Classification of Displacive Phase

Transformations,” in Proceedings of the International Conference on Martensitic Transformations

ICOMAT 1979, 1979, pp. 1–11.

[24] C. M. Wayman, “The Growth of Martensite Since E.C. Bain - Some Milestones,” Materials

Science Forum, vol. 56–58, pp. 1–32, 1991.

[25] D. A. Porter, K. E. Easterling, and M. Y. Sherif, Phase Transformations in Metals and Alloys, 3rd

ed. CRC Press, 2009.

[26] E. C. Bain, “The nature of martensite,” Transactions AIME, vol. 70, pp. 25–46, 1924.

[27] Z. Nishiyama, Martensitic Transformation. New York: Academic press, 1978.

[28] J. S. Bowles and C. M. Wayman, “The bain strain, lattice correspondences, and deformations

related to martensitic transformations,” Metallurgical Transactions, vol. 3, no. 5, pp. 1113–1121,

May 1972.

[29] Z. Guo, C. S. Lee, and J. W. Morris, “On coherent transformations in steel,” Acta Materialia,

vol. 52, no. 19, pp. 5511–5518, Nov. 2004.

[30] M. S. Wechsler, D. S. Lieberman, and T. A. Read, “On the Theory of the Formation of

Martensite,” Transactions AIME, vol. 197, pp. 1503–1515, 1953.

68

[31] J. S. Bowles and J. K. Mackenzie, “The Crystallography Martensite Transformations I,” Acta

Metallurgica, vol. 2, pp. 129–137, 1954.

[32] J. K. Mackenzie and J. S. Bowles, “The crystallography of martensite transformations II,” Acta

Metallurgica, vol. 2, no. 1, pp. 138–147, 1954.

[33] C. M. Wayman, Introduction to the Crystallopgraphy of Martensitic Transformations. New York: The

Macmillan Company, 1964.

[34] G. Kurdjumow and G. Sachs, “Uber den Mechanismus der Stahlhartung,” Zeitschrift fur Physik,

vol. 64, no. 5–6, pp. 325–343, May 1930.

[35] Z. Nishiyama, “No Title,” Sci. Rep. Tohoku Univ., vol. 23, p. 637, 1934.

[36] G. Wassermann, “No Title,” Mitt. K-W-I Eisenforsch., vol. 17, p. 149, 1935.

[37] A. B. Greninger and A. R. Troiano, “The Mechanism of Martensite Formation,” Transactions

AIME, vol. 185, pp. 590–598, 1949.

[38] P. M. Kelly, A. Jostsons, and R. G. Blake, “The orientation relationship between lath

martensite and austenite in low carbon, low alloy steels,” Acta Metallurgica et Materialia, vol. 38,

no. 6, pp. 1075–1081, 1990.

[39] M. X. Zhang and P. M. Kelly, “Accurate orientation relationship between ferrite and austenite

in low carbon martensite and granular bainite,” Scripta Materialia, vol. 47, no. 11, pp. 749–755,

Dec. 2002.

[40] A. B. Greninger and A. R. Troiano, “Crystallography of Austenite Decomposition,”

Transactions AIME, vol. 140, pp. 307–331, 1940.

[41] A. B. Greninger and A. R. Troiano, “Mechanism of Martensite Formation Summary,”

Transactions AIME, vol. 145, pp. 289–291, 1941.

69

[42] S. Morito, H. Tanaka, R. Konishi, T. Furuhara, and T. Maki, “The morphology and

crystallography of lath martensite in Fe-C alloys,” Acta Materialia, vol. 51, no. 6, pp. 1789–

1799, Apr. 2003.

[43] H. Kitahara, R. Ueji, N. Tsuji, and Y. Minamino, “Crystallographic features of lath martensite

in low-carbon steel,” Acta Materialia, vol. 54, no. 5, pp. 1279–1288, Mar. 2006.

[44] T. Maki, “Recent advance in understanding martensite in steels,” in Proceedings of the

International Symposium on Steel Science IS3-2007, 2007, pp. 1–10.

[45] P. Kelly and J. Nutting, “The Martensite Transformation in Carbon Steels,” Proceedings of the

Royal Society of London Series A, vol. 259, pp. 45–58, 1960.

[46] B. Sandvik and C. Wayman, “Characteristics of lath martensite: Part I. crystallographic and

substructural features,” Metallurgical and Materials Transactions A, vol. 14, no. 4, pp. 809–822,

1983.

[47] A. R. Marder and G. Krauss, “The Morphology of Martensite in Iron-Carbon Alloys,”

Transactions ASM, vol. 60, pp. 651–660, 1967.

[48] M. Oka and C. M. Wayman, “Electron metallography of the substructure of martensite in

high-carbon steels,” Transactions AIME, vol. 62, no. 2, pp. 370–379, 1969.

[49] M. Umemoto, E. Yoshitake, and I. Tamura, “The morphology of martensite in Fe-C, Fe-Ni-C

and Fe-Cr-C alloys,” Journal of Materials Science, vol. 18, no. 10, pp. 2893–2904, 1983.

[50] T. Maki, “Microstructure and Mechanical Behaviour of Ferrous Martensite,” Materials Science

Forum, vol. 56–58, pp. 157–168, 1990.

[51] T. Maki, “Morphology and substructure of martensite in steels,” in Phase transformations in steels.

Volume 2: Diffusionless transformations, high strength steels, modelling and advanced analytical techniques,

1st ed., E. Pereloma and D. V. Edmonds, Eds. Cambridge, UK: Woodhead Publishing

Limited, 2012, pp. 34–58.

70

[52] G. F. Vander Voort, Ed., ASM Handbook, Volume 9, Metallography and Microstructure. Materials

park, OH: ASM International, 2004.

[53] T. Ko and S. A. Cottrell, “The Formation of Bainite,” Journal of The Iron and Steel Institute, vol.

172, pp. 307–313, 1952.

[54] T. Ko, “The Formation of Bainite in an En 21 Steel,” Journal of The Iron and Steel Institute, vol.

175, pp. 16–18, 1953.

[55] G. R. Speich, “Unpublished work, reproduced by H. Warlimont in a report from the Edgar C.

Bain Laboratory for Fundamental Research,” Monroeville, PA, 1961.

[56] C. Zener, “Kinetics of the Decomposition of Austenite,” Transactions AIME, vol. 167, pp.

550–595, 1946.

[57] J. M. Oblak and R. F. Hehemann, “Structure and Growth of Widmanstätten Ferrite and

Bainite,” in Transformation and Hardenability in Steels, Ann Arbor, MI: Climax Molybdenum Co.,

1967, pp. 15–38.

[58] M. Hillert, “The Role of Interfacial Energy During Solid State Phase Transformations,”

Jernkontorets Annaler, vol. 141, pp. 757–789, 1957.

[59] P. J. Goodhew, J. Humphreys, and R. Beanland, Electron Microscopy and Analysis, 3rd ed.

London: Taylor & Francis, 2001, pp. 1–251.

[60] J. Goldstein et al., Scanning Electron Microscopy and X-ray Microanalysis, 3rd ed. New York:

Springer, 2003, pp. 1–586.

[61] O. P. Morozov, D. A. Mirzayev, and M. M. Shteynberg, “The Polymorphous Gamma-Alpha

Transformation in Iron of a High Level of Purity,” Physics of Metals and Metallography, vol. 34,

pp. 114–119, 1972.

[62] J. W. Christian, “Thermodynamics and Kinetics of Martensite,” in Proceedings of the International

Conference on Martensitic Transformations ICOMAT 1979, 1979, pp. 220–234.

71

[63] J. Ågren, “Martensitic transformations,” in A graduate course in the theory of PHASE

TRANSFORMATIONS, Stockholm: US-AB, 2004, pp. 119–134.

[64] “TCFE6 - TCS Steels/Fe-Alloys Database.” Thermo-Calc Software AB, Stockholm, SE.

[65] J. Fisher, “Free Energy Change Accompanying the Martensite Transformation in Steels,”

Transactions AIME, vol. 185, pp. 688–690, 1949.

[66] A. B. Greninger and A. R. Troiano, “Kinetics of the Austenite to Martensite Transformation

in Steel,” Transactions ASM, vol. 28, pp. 537–574, 1940.

[67] R. Grange and H. Stewart, “The temperature range of martensite formation,” Transactions

AIME, vol. 167, pp. 467–501, 1946.

[68] W. Steven and A. Haynes, “The temperature of formation of martensite and bainite in low-

alloy steels,” Journal of the Iron and Steel Institute, vol. 183, no. 8, pp. 349–359, 1956.

[69] S. M. C. van Bohemen, M. Santofimia, and J. Sietsma, “Experimental evidence for bainite

formation below Ms in Fe–0.66C,” Scripta Materialia, vol. 58, no. 6, pp. 488–491, Mar. 2008.

[70] M. Oka and H. Okamoto, “Swing back in kinetics near Ms in hypereutectoid steels,”

Metallurgical and Materials Transactions A, vol. 19, no. 3, pp. 447–452, 1988.

[71] R. B. G. Yeo, “The Effects of Some Alloying Elements on the Transformation of Fe-22.5 Pct

Ni Alloys,” Transactions AIME, vol. 227, pp. 884–890, 1963.

[72] C. L. Magee and R. G. Davies, “On the volume expansion accompanying the f.c.c. to b.c.c.

transformation in ferrous alloys,” Acta Metallurgica, vol. 20, no. 8, pp. 1031–1043, Aug. 1972.

[73] R. Pradhan and G. S. Ansell, “Kinetics of the martensite transformation in athermal Fe-C-Ni-

Cr alloys,” Metallurgical Transactions A, vol. 9, no. 6, pp. 793–801, Jun. 1978.

[74] D. A. Mirzayev, M. M. Shteynberg, T. N. Ponomareva, and V. M. Schastlivtsev, “Influence of

Cooling Rate on the Position of Martensitic Transformation Points. Carbon Steels,” Physics of

Metals and Metallography, vol. 47, no. 1, pp. 102–111, 1980.

72

[75] O. P. Morozov, D. A. Mirzayev, and M. M. Shteynberg, “Some Regularities of

Transformations in Iron Cooled at High Rates,” Physics of Metals and Metallography, vol. 32, pp.

170–177, 1971.

[76] M. M. Shteynberg, D. A. Mirzayev, and T. N. Ponomareva, “Gamma-Alpha Transformation

of Iron-Manganese Alloys During Cooling,” Physics of Metals and Metallography, vol. 43, pp. 143–

149, 1977.

[77] A. Gilbert and W. S. Owen, “Diffusionless transformation in iron-nickel, iron-chromium and

iron-silicon alloys,” Acta Metallurgica, vol. 10, no. 1, pp. 45–54, 1962.

[78] W. D. Swanson and J. G. Parr, “Transformations in Iron-Nickel Alloys,” Journal of The Iron and

Steel Institute, pp. 104–106, 1964.

[79] P. J. Brofman and G. S. Ansell, “On the effect of fine grain size on the Ms temperature in Fe-

27Ni-0.025C alloys,” Metallurgical Transactions A, vol. 14, no. 9, pp. 1929–1931, Sep. 1983.

[80] S.-J. Lee and Y.-K. Lee, “Effect of Austenite Grain Size on Martensitic Transformation of a

Low Alloy Steel,” Materials Science Forum, vol. 479, pp. 3169–3172, 2005.

[81] H. Yang and H. Bhadeshia, “Austenite grain size and the martensite-start temperature,” Scripta

Materialia, vol. 60, no. 7, pp. 493–495, Apr. 2009.

[82] G. Ghosh and G. B. Olson, “Computational thermodynamics and the kinetics of martensitic

transformation,” Journal of Phase Equilibria, vol. 22, no. 3, pp. 199–207, 2001.

[83] D. A. Mirzayev, V. M. Schastlivtsev, and S. Y. E. Karzunov, “Martensitic Points of Fe-C

Alloys,” Physics of Metals and Metallography, vol. 63, pp. 129–132, 1987.

[84] P. J. Jacques, “Phase transformations in transformation induced plasticity (TRIP)-assisted

multiphase steels,” in Phase transformations in steels. Volume 2: Diffusionless transformations, high

strength steels, modelling and advanced analytical techniques, 1st ed., E. Pereloma and D. V. Edmonds,

Eds. Cambridge, UK: Woodhead Publishing Limited, 2012, pp. 213–246.

73

[85] J. G. Speer, “Phase transformations in quenched and partitioned steels,” in Phase transformations

in steels. Volume 2: Diffusionless transformations, high strength steels, modelling and advanced analytical

techniques, 1st ed., E. Pereloma and D. V. Edmonds, Eds. Cambridge, UK: Woodhead

Publishing Limited, 2012, pp. 247–270.

[86] W. Sha, “Phase transformations in maraging steels,” in Phase transformations in steels. Volume 2:

Diffusionless transformations, high strength steels, modelling and advanced analytical techniques, 1st ed., E.

Pereloma and D. V. Edmonds, Eds. Cambridge, UK: Woodhead Publishing Limited, 2012,

pp. 332–362.

[87] P. Payson and C. H. Savage, “Martensite Reactions in Alloy Steels,” Transactions ASM, vol. 33,

pp. 261–275, 1944.

[88] L. A. Carapella, “Computating A’' or Ms (Transformation Temperature on Quenching) from

Analysis,” Metal Progress, vol. 46, no. 108, 1944.

[89] E. S. Rowland and S. R. Lyle, “The Application of Ms Points to Case Depth Measurement,”

Transactions ASM, vol. 37, pp. 27–47, 1946.

[90] K. W. Andrews, “Empirical Formulae for the Calculation of Some Transformation

Temperatures,” Journal of The Iron and Steel Institute, vol. 203, pp. 721–727, 1965.

[91] J. Wang, P. J. van der Wolk, and S. van der Zwaag, “Determination of Martensite Start

Temperature in Engineering Steels Part I. Empirical Relations Describing the Effect of Steel

Chemistry,” Materials transactions JIM, vol. 41, pp. 761–768, 2000.

[92] B. Skrotzki and E. Hornbogen, “Projekt COSMOS -Temperaturen und Verlauf der

martensitischen Umwandlung in Stahlen,” 1991.

[93] T. Sourmail and C. Garcia-Mateo, “Critical assessment of models for predicting the Ms

temperature of steels,” Computational Materials Science, vol. 34, no. 4, pp. 323–334, 2005.

[94] V. Raghavan and D. Antia, “The driving force for martensitic transformations in low alloy

steels,” Metallurgical and Materials Transactions A, vol. 27, no. 4, pp. 1127–1132, 1996.

74

[95] C. Kung and J. Rayment, “An examination of the validity of existing empirical formulae for

the calculation of Ms temperature,” Metallurgical and Materials Transactions A, vol. 13, no. 2, pp.

328–331, 1982.

[96] T. Y. Hsu and H. Chang, “On calculation of Ms and driving force for martensitic

transformation in Fe-C,” Acta Metallurgica, vol. 32, no. 3, pp. 343–348, Mar. 1984.

[97] J. Wang, P. J. van der Wolk, and S. van der Zwaag, “Determination of Martensite Start

Temperature for Engineering Steels Part II. Correlation between Critical Driving Force and

Ms Temperature,” Materials transactions JIM, vol. 41, pp. 769–776, 2000.

[98] J. Wang, P. J. van der Wolk, and S. van der Zwaag, “Effects of Carbon Concentration and

Cooling Rate on Continuous Cooling Transformations Predicted by Artificial Neural

Network,” ISIJ International, vol. 39, pp. 1038–1046, 1999.

[99] G. Ghosh and G. B. Olson, “Kinetics of F.C.C. → B.C.C. heterogeneous martensitic

nucleation—I. The critical driving force for athermal nucleation,” Acta Metallurgica et

Materialia, vol. 42, no. 10, pp. 3361–3370, Oct. 1994.

[100] G. Ghosh and G. B. Olson, “Kinetics of F.c.c. → b.c.c. heterogeneous martensitic

nucleation—II. Thermal activation,” Acta Metallurgica et Materialia, vol. 42, no. 10, pp. 3371–

3379, Oct. 1994.

[101] G. Ghosh and G. B. Olson, “The isotropic shear modulus of multicomponent Fe-base solid

solutions,” Acta Materialia, vol. 50, no. 10, pp. 2655–2675, Jun. 2002.

[102] G. Krauss, “Martensitic Transformation, Structure and Properties in Hardenable Steels,” in

Hardenability concepts with applications to steel, D. V. Doane and J. S. Kirkaldy, Eds. Metallurgical

Society of AIME, 1978, pp. 229–248.

[103] A. Borgenstam, M. Hillert, and J. Ågren, “Critical temperature for growth of martensite,” Acta

Metallurgica et Materialia, vol. 43, no. 3, pp. 945–954, Mar. 1995.

75

[104] A. Litwinchuk, F. X. Kayser, H. H. Baker, and A. Henkin, “The Rockwell C hardness of

quenched high-purity iron-carbon alloys containing 0.09 to 1.91% carbon,” Journal of Materials

Science, vol. 11, no. 7, pp. 1200–1206, 1976.

[105] A. Borgenstam, “Unpublished work.” 2006.

[106] G. Krauss, “Martensite in steel: strength and structure,” Materials Science and Engineering A, vol.

273–275, no. 1–2, pp. 40–57, Dec. 1999.

[107] T. Maki, K. Tsuzaki, and I. Tamura, “The morphology of microstructure composed of lath

martensites in steels,” Transactions ISIJ, vol. 20, pp. 207–214, 1980.

[108] G. Thomas, “Electron microscopy investigations of ferrous martensites,” Metallurgical

Transactions, vol. 2, no. 9, pp. 2373–2385, Sep. 1971.

[109] T. Maki, S. Furutani, and I. Tamura, “Shape Memory Effect Related to Thin Plate Martensite

with Large Thermal Hysteresis in Ausaged Fe-Ni-Co-Ti Alloy,” ISIJ International, vol. 29, pp.

438–445, 1989.

[110] G. Miyamoto, N. Takayama, and T. Furuhara, “Accurate measurement of the orientation

relationship of lath martensite and bainite by electron backscatter diffraction analysis,” Scripta

Materialia, vol. 60, no. 12, pp. 1113–1116, Jun. 2009.

[111] G. Nolze, “Irrational orientation relationship derived from rational orientation relationships

using EBSD data,” Crystal Research and Technology, vol. 43, no. 1, pp. 61–73, Jan. 2008.

[112] M. Oka and H. Okamoto, “Roles of {101} twinnings in Martensite Transformation of a 1.80

mass% Carbon Steel,” Materials transactions JIM, vol. 33, no. 3, pp. 229–234, 1992.

[113] S. Morito, X. Huang, T. Furuhara, T. Maki, and N. Hansen, “The morphology and

crystallography of lath martensite in alloy steels,” Acta Materialia, vol. 54, no. 19, pp. 5323–

5331, Nov. 2006.

76

[114] N. Takayama, G. Miyamoto, and T. Furuhara, “Effects of transformation temperature on

variant pairing of bainitic ferrite in low carbon steel,” Acta Materialia, vol. 60, no. 5, pp. 2387–

2396, Mar. 2012.

[115] R. Naraghi, P. Hedström, and A. Borgenstam, “Spontaneous and Deformation-Induced

Martensite in Austenitic Stainless Steels with Different Stability,” Steel Research International, vol.

82, no. 4, pp. 337–345, Apr. 2011.

[116] J. C. Bokros and E. R. Parker, “The mechanism of the martensite burst transformation in Fe-

Ni single crystals,” Acta Metallurgica, vol. 11, no. 12, pp. 1291–1301, 1963.

[117] M. Umemoto and C. Wayman, “Crystallography and morphology studies of Fe-Pt

martensites: Lenticular to thin plate transition and thin plate morphologies,” Acta Metallurgica,

vol. 26, no. 10, pp. 1529–1549, Oct. 1978.

[118] M. Hillert, “Diffusion in growth of bainite,” Metallurgical and Materials Transactions A, vol. 25,

no. 9, pp. 1957–1966, Sep. 1994.

[119] K. R. Kinsman and H. I. Aaronson, “The inverse bainite reaction in hypereutectoid Fe-C

alloys,” Metallurgical Transactions, vol. 1, no. 5, pp. 1485–1488, 1970.

[120] H. J. Lee, G. Spanos, G. J. Shiflet, and H. I. Aaronson, “Mechanisms of the bainite (non-

lamellar eutectoid) reaction and a fundamental distinction between the bainite and pearlite

(lamellar eutectoid) reactions,” Acta Metallurgica, vol. 36, no. 4, pp. 1129–1140, Apr. 1988.

[121] G. Spanos, H. S. Fang, D. S. Sarma, and H. I. Aaronson, “Influence of carbon concentration

and reaction temperature upon bainite morphology in Fe-C-2 Pct Mn alloys,” Metallurgical

Transactions A, vol. 21, no. 6, pp. 1391–1411, Jun. 1990.

[122] H. Modin and S. Modin, Microstructures in Three Isothermally Transformed Carbon Steels with High-

Carbon Contents. Stockholm, SE: Meritförlaget, 2000.

[123] A. Borgenstam and M. Hillert, “Driving force for f.c.c. --> b.c.c. martensites in Fe---X alloys,”

Acta Materialia, vol. 45, no. 5, pp. 2079–2091, 1997.

77

[124] D. A. Mirzayev, O. P. Morozov, and M. M. Shteynberg, “The Gamma-Alpha Transformation

in Iron and in its Alloys,” Physics of Metals and Metallography, vol. 36, pp. 99–105, 1973.

[125] D. A. Mirzayev, V. N. Karzunov, V. N. Schastlivtsev, I. I. Yakovleva, and Y. V. Kharitonova,

“The Gamma-Alpha Transformation in Low-Carbon Fe-Cr Alloys,” Physics of Metals and

Metallography, vol. 61, no. 2, pp. 114–122, 1986.

[126] D. A. Mirzayev, S. Y. E. Karzunov, V. M. Schastlivtsev, I. L. Yakovleva, and Y. E. V.

Kharitonova, “Peculiarities of Martensite and Bainite Transformation in Chromium Steels,”

Physics of Metals and Metallography, vol. 62, pp. 100–109, 1986.

[127] E. A. Wilson, “Doctoral Thesis,” University of Liverpool, 1965.

[128] H. Finkler and M. Schirra, “Transformation behaviour of the high temperature martensitic

steels with 8-14% chromium,” Steel research, vol. 67, no. 8, pp. 328–342, 1996.

[129] G. Vander Voort, Ed., Atlas of Time-Temperature Diagrams for Nonferrous Alloys. Materials park,

OH: ASM International, 1991, p. 474.