Thesis_CEIC_Ohlund_FINAL.

Tempering of martensitic
steel for fasteners
Effects of micro-alloying on microstructure
and mechanical property evolution
Proefschrift
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben;
voorzitter van het College voor Promoties,
in het openbaar te verdedigen op
vrijdag 18 september, 2015 om 12:30 uur
Door
Carin Emmy Ingrid Christersdotter Ö HLUND
Master of Science in chemical engineering with engineering physics,
Chalmers University of Technology
geboren te Alnö, Sweden
1
This dissertation has been approved by the
promotor: Prof. dr. ir. J. Sietsma and
copromotor: Dr. ir. S.E. Offerman
Composition of the doctoral committee:
Rector Magnificus
Prof. Prof. dr. ir. J. Sietsma promotor
Dr. ir. S.E. Offerman copromotor
Independent members:
Prof. dr. ir. L.A.I. Kestens
Prof. dr. T. Ohmura
Prof. dr. ir. R. H. Petrov
Prof. dr. J. Ågren
Dr. ir. P.J. van der Wolk
MSE, TU Delft
Nat. Inst. For Materials Science
University of Gent
Kungliga Tekniska Högskolan
Tata Steel
The research described in this thesis was performed in the department of Materials Science and
Engineering, of the Delft University of Technology, Delft, the Netherlands. This research was fully
funded by Koninklijke Nedschroef Holding B.V.
ISBN/EAN:
978-94-6186-519-9
To my parents,
who raised me to believe that
I can become anything I want
3
Table of Contents
Summary.......................................................................................................................11
1 Introduction ...........................................................................................................23
1.1 The scope and aim of this thesis ......................................................................24
1.2 The outline of this thesis .................................................................................27
1.3 References ......................................................................................................28
2 Background ............................................................................................................29
2.1 Fasteners for the automotive industry.............................................................29
2.1.1
2.1.2
2.1.3
2.1.4
2.1.5
2.2
Strength and temperature resistance of metals ...............................................42
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
2.3
Introduction ............................................................................................................... 29
Definition and purpose of a bolted joint ..................................................................... 30
Force distribution in a bolted joint ............................................................................. 31
Mechanical properties of a fastener ........................................................................... 37
Choice of fastener material ........................................................................................ 39
Introduction ............................................................................................................... 42
Definitions of strength and temperature resistance of metals .................................... 42
Dislocations and dislocation movements.................................................................... 44
The microstructural components that strengthen metals ........................................... 46
Creep ......................................................................................................................... 57
Precipitation strengthening of Martensite .......................................................65
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.3.6
2.3.7
2.3.8
2.3.9
Introduction ............................................................................................................... 65
Formation of martensite in steel ................................................................................ 65
Crystallography of martensite .................................................................................... 67
Strength of martensite ............................................................................................... 69
Tempering of martensite ........................................................................................... 71
Nucleation of precipitates .......................................................................................... 74
Growth and coarsening of precipitates....................................................................... 79
The thermodynamics of TiC-precipitate nucleation and growth in steel ..................... 81
References ................................................................................................................. 83
3 The kinetics of softening and microstructure evolution of martensite in Fe-C-Mn steel
during tempering at 300°C ............................................................................................87
Abstract .....................................................................................................................87
3.1 Introduction ....................................................................................................88
3.2 Experimental procedures ................................................................................89
3.3 Results and discussion .....................................................................................91
3.3.1
3.3.2
3.3.3
3.3.4
SEM studies ............................................................................................................... 91
Nano-indentation studies........................................................................................... 92
EBSD studies .............................................................................................................. 93
Softening and microstructure evolution ..................................................................... 95
3.4 Conclusions ................................................................................................... 100
3.5 References .................................................................................................... 101
4 Effect of Ti on evolution of microstructure and hardness of martensitic Fe-C-Mn steel
during tempering ........................................................................................................ 103
5
Abstract ................................................................................................................... 103
4.1 Introduction .................................................................................................. 104
4.2 Method ......................................................................................................... 105
4.3 Results........................................................................................................... 107
4.3.1
Cementite particle size evolution ............................................................................. 107
4.3.2
Martensite block size and area fraction of block boundaries and regions of high
dislocation density .................................................................................................................. 109
4.3.3
TiC-precipitate size................................................................................................... 110
4.3.4
Hardness in matrix and boundaries .......................................................................... 112
4.4
Discussion ..................................................................................................... 113
4.4.1
4.4.2
4.4.3
Hardness and microstructure evolution ................................................................... 113
Diffusional TiC-precipitate growth............................................................................ 118
Comparison of TiC growth models ........................................................................... 122
4.5 Conclusions ................................................................................................... 123
4.6 References .................................................................................................... 125
5 Modelling the evolution of multiple hardening mechanisms during tempering of Fe-CMn-Ti martensite ........................................................................................................ 127
Abstract ................................................................................................................... 127
5.1 Introduction .................................................................................................. 128
5.2 Modelling the evolution of multiple hardness components during tempering129
5.3 Modelling the nucleation and growth of TiC-precipitates during tempering .. 132
5.3.1
5.3.2
5.4
5.5
Experimental ................................................................................................. 136
Model fitting ................................................................................................. 138
5.5.1
5.5.2
5.6
Nucleation of TiC ..................................................................................................... 132
Growth of TiC ........................................................................................................... 134
Input parameters ..................................................................................................... 138
Fitting approach ....................................................................................................... 139
Results and discussion ................................................................................... 140
5.6.1
5.6.2
5.6.3
Fitting parameters ................................................................................................... 140
TiC-precipitates and recovery................................................................................... 142
Evolution of multiple hardening components during tempering ............................... 145
5.7 Conclusions ................................................................................................... 148
5.8 References .................................................................................................... 149
6 A comparison between ultra-high-strength and conventional high-strength fastener
steels: mechanical properties at elevated temperature and microstructural mechanisms
………………………………………………………………………………………………………………………..151
Abstract ................................................................................................................... 151
6.1 Introduction .................................................................................................. 152
6.2 Experimental ................................................................................................. 153
6.2.1
6.2.2
6.2.3
6.3
Mechanical testing of KNDS4, 34Cr4 and 33B2 fasteners .......................................... 153
Characterization of alloy carbides in KNDS4 and 34Cr4............................................. 156
Optimization of the thermal processing of KNDS4 .................................................... 156
Results and Discussion ................................................................................... 157
6.3.1
6.3.2
6.3.3
Mechanical testing ................................................................................................... 157
Characterization of the alloy carbides ...................................................................... 160
Optimizing the thermal processing of KNDS4 ........................................................... 163
6.4 Conclusions ................................................................................................... 172
6.5 References .................................................................................................... 173
7 Conclusions .......................................................................................................... 175
Acknowledgements .................................................................................................... 179
About the author ........................................................................................................ 181
List of publications ...................................................................................................... 182
7
List of abbreviations
A is a constant used in the generalized creep model
AN is a constant used for dislocation creep
Ap is the projected contact area for nano-indentation
Ai is the interface area of the ith interface
a is the interatomic distance
b is the Burgers vector
𝐶𝑖 is the concentration of element i
D is the diffusivity
𝐷0 is the pre-exponential factor for diffusivity
𝐷𝐿 is lattice diffusivity
𝐷𝑃 is pipe diffusivity in dislocations
𝑑𝑔 is the grain size
𝑑𝑝 is the diameter of a precipitate
Ei is the Young’s modulus for material or component i
F is load
Fi is the force in component i
Ff friction force between the clamped parts
f is the volume fraction of precipitate phase
G is the shear modulus
∆𝐺𝑉 is the formation energy of vacancies
∆𝐺 ∗ is the activation energy for nucleation
g is the cross sectional area of dislocation pipe per unit area of matrix
∆𝑔𝑠 is the misfit strain energy
∆𝑔𝑑 is the change in free energy related to defects in the parent phase, which are
annihilated during the nucleation of the phase 𝛽
∆𝑔𝑣 is the driving force for nucleation
h is the indentation depth during nano-indentation
hc is the contact depth during nano-indentation
kB is Boltzmanns constant
𝑘𝑖 is the spring constant/stiffness of component i
kD is the Hall-Petch term
Ki is a proportionality constant for the ith element in solid solution
Ks is the solubility product
k’ is a constant that depends on the geometry of the indenter for nano-indentation
L is the distance between pinning points in the lattice
Lc, is the clamp length of a bolted joint
∆𝑙𝑏𝑜𝑙𝑡 is the elongation of the bolt
∆𝑙𝑏𝑎𝑠𝑒 is the compression of the clamped parts
M is the Taylor factor
N is the density of potential nucleation sites
Nj is the number of atoms that are within one atomic jump distance to the nuclei
n is an exponent of stress
𝑛𝑎 is the number of atoms in the nucleus
𝑛𝑎∗ is the number of atoms in the critical nucleus
ns is an exponent used for solid solution strengthening
Pmax is the maximum applied load during nano-indentation
p is an exponent used for grain size dependence of creep
QC is the activation energy for the creep
QD is the activation energy for diffusion
R is the universal gas constant
Rn is the radius of a growing precipitate
Rm is the ultimate tensile strength
Rp0,2 is the yield strength
rc is the capture radius of a dislocation
rp is the radius of a precipitate
S is the contact stiffness of nano-indentation
S* is the surface of the nuclei
T is the temperature
Tm is the melting temperature
t is the time
ts is the moment of nucleation
𝑈𝑎 is the activation energy for recovery
𝑉𝑎 is the and activation volume for recovery
𝑉𝛽 is the volume of the new phase 𝛽
∆𝕧 is the volume difference between matrix and solute atoms
𝑋𝑉𝑒 is the mole fraction of vacancies
Z is the non-equilibrium Zeldovich factor
Zs is the settlement in the bolted joint
𝛼 is an empirical parameter
𝛼𝑗 is the number of atoms that are within one atomic jump distance to the nuclei
𝛽 ∗ is the frequency factor
𝛾𝑖 is the area and energy of the ith interface
𝜀 is strain
𝜀̇ is strain rate
ρ is the dislocation density
𝜎𝐶 is the characteristic stress during nano-indentation
9
𝜎𝑙 is the lattice friction
𝜎𝑠𝑠 is solid solution strengthening
𝜎𝑔𝑏 is grain boundary strengthening
𝜎𝑑 is dislocation strengthening
𝜎𝑝 is precipitation strengthening
𝜏 is the incubation time
𝑣 is the growth rate of spherical precipitates
𝜈𝑑 is Debye frequency
Φ is the stiffness relationship between the bolt and the base material
Γ is the atomic jump frequency
Summary
The research presented in this thesis aims to deepen our understanding of the effect of microalloying on the microstructure and mechanical property evolution during tempering of
martensitic steel for fasteners. The ongoing trend of engine down-sizing has led to the need
for stronger and more temperature resistant fasteners than currently available according to
international standards. A new martensitic fastener steel called KNDS4 has been developed,
that combines higher strength with improved resistance to hydrogen embrittlement. The
higher strength is the result of the addition of small amounts of alloying elements such as Ti,
V and Mo that can form alloy carbides. The improved resistance to hydrogen embrittlement
is ascribed to the presence of nano-sized alloy carbides. However, in addition to enhancing
strength and resistance to hydrogen embrittlement, alloy carbides are also able to improve
the creep resistance of steels via pinning of dislocations at elevated temperature. It might
therefore be possible to use the new fastener steel at higher service temperatures than the
current high-strength fasteners. In order to optimize the properties of the new fastener steel,
a fundamental understanding is needed of the relationship between the evolution of the
microstructure and the hardness/strength during heat treatment. The research questions of
the research are: (i) To which extent do different hardening mechanisms contribute to the
strength of martensitic fastener steels? (ii) How do the different hardening mechanisms
evolve as a function of time during annealing? (iii) What are the effects of a strong carbide
forming element such as titanium on the microstructure and hardening mechanisms of
martensitic fastener steel? (iv) Can the strength and temperature resistance of a martensitic
fastener steel be improved by addition of carbide forming elements?
The initial part of the research is based on a model alloy without the presence of any carbide
forming elements that is compared to a model alloy with only one carbide forming element,
Ti, in order to study the influence of a single alloy carbide on the microstructure and properties.
Thereafter, industrial fastener steels, with multiple carbide forming elements, are studied,
where complex alloy carbides form.
Chapter 2 describes the industrial context that lead to the research described in this PhDthesis. This background chapter consist of three main sections.
Section 2.1 gives an introduction on bolted joints in the automotive industry. The
bolted joint is defined as the system consisting of the bolt itself, and the components that are
held together by the bolt. The purpose of the bolt, to keep the assembled components
together by compression via a clamp force, is discussed and the distribution of external forces
into the bolted joint is reviewed for different load cases. The influence of settlement (loss of
clamping force due to localized plastic deformation in the joint after assembly) is reviewed
and the fatigue properties of the bolt in a bolted joint are briefly discussed, in terms of
distribution of an alternating external load into the bolted joint. The chapter ends with a
11
review of the key mechanical properties of engine fasteners and an explanation of how
current fastener steels are chosen.
Section 2.2 introduces the concept of strength and hardness and temperature
resistance of metals. The theory of dislocations and dislocation movement is briefly explained
and the mechanisms behind different types of dislocation movements are presented. The link
between dislocation movement and strength of metals is explained and the different
microstructure components that contribute to the total strength and hardness of a metal are
reviewed. Equations for quantification of the strengthening mechanisms are presented and
literature values related to steel are given. The (nearly) instantaneous and time-dependent
(creep) effects of an external load at elevated temperature on the strength and deformation
of steel are described. Creep is the time-dependent and permanent deformation of a metal
under constant external loading. The mechanical behavior during the different stages of creep
is discussed and the microstructural mechanisms behind creep are reviewed. Expressions for
different mechanisms of creep are given. Section 2.2 ends with a review of different methods
to measure creep, with special focus on the indentation creep method, since this method was
used for the research of this Ph.D. study.
Section 2.3 presents martensite formation and precipitation-strengthening of
martensite. The Fe-C phase diagram and the theory of martensite formation, according to the
Bain theory, is discussed. The crystallography of lath martensite is presented and related to
the strength via the hardening mechanisms presented in section 2.2. The evolution of the
microstructure which takes place during tempering of martensite is summarized. Nucleation
of precipitates, according to the classical nucleation theory, is presented and the energy terms
which influence the nucleation of new phases are reviewed. The mechanisms of diffusion- and
interface-controlled growth are presented. The Zener or diffusional growth is reviewed in
more detail. Section 2.3 ends with a summary of the characteristics of TiC precipitates and the
kinetic data related to the nucleation and growth of TiC in steel, since this precipitate type is
specifically studied in the thesis.
Chapter 3 is an experimental study of the evolution of the hardness and microstructure in FeC-Mn martensite (that is free of alloy carbides) during isothermal annealing at 300°C. The
hardness near martensite block boundaries is significantly higher than the hardness inside the
block matrix, due to a higher dislocation density in the regions adjacent to the block
boundaries (called boundary regions). The boundary regions soften with increasing tempering
time, whereas the nano-hardness of the tempered matrix remains approximately constant
with increasing tempering time. The softening kinetics of Fe-C-Mn martensite can be
described by three stages, which are related to the evolution of the microstructure: Stage I (05 min) is characterized by fast macroscopic softening kinetics that is strongly related to: (a)
fast and simultaneous softening and reduction in area fraction of boundaries regions (b) fast
reduction in area fraction of non-tempered matrix regions. Stage II (5-10 min) is characterized
by slow macroscopic softening kinetics that is related to slow softening and reduction in area
fraction of the boundaries regions. Stage III (10-60 min) is characterized by very slow softening
kinetics that is related to very slow softening and reduction in area fraction of boundary
regions.
Chapter 4 is an experimental study of the influence of the addition of 0.042wt% Ti on the
evolution of the microstructure and hardness of Fe-C-Mn steel during isothermal annealing at
300°C and at 550°C. The macroscopic hardness of Ti-containing and Ti-free Fe-C-Mn steel
reduces rapidly during the first 5 minutes of tempering, due to (i) the redistribution of
interstitially dissolved carbon into cementite and (ii) rapid recovery. The macroscopic
hardness thereafter remains stable during continued annealing for the Ti-free steel, but the
Ti-containing steel increases in hardness after 30 minutes of annealing at 550°C. The hardness
increase of Ti-containing Fe-C-Mn-Ti steel is related to the formation of TiC-precipitates at
550°C. Nucleation of TiC-precipitates starts in the regions close to the martensite block
boundaries (between 5-10 minutes) and subsequently nucleates in the block matrix (between
10-30 minutes) due to the higher dislocation density in the regions close to the block
boundaries. The formation of TiC-precipitates slows down the recovery in the regions close to
the martensite block boundaries, especially between 5 and 10 minutes of annealing. The
growth of TiC-precipitates in martensite is simulated in good agreement with experimental
observations with a model that takes capillarity effects, the overlap of the titanium diffusion
fields and the effects of pipe diffusion of titanium atoms into account.
Chapter 5 is a computational study on the evolution of the hardening mechanisms in Fe-CMn-Ti steel during isothermal annealing. The hardness of martensite is simulated as a linear
addition of multiple strengthening mechanisms. This hardness model is combined with a
microstructural model based on the Kampmann-Wagner-Numerical (KWN) approach for a
multi-component and multi-phase system to simulate the nucleation and growth of TiCprecipitates. The model is fitted to experimental results and used to simulate the hardness
contribution of different microstructure components as a function of annealing time. The two
microstructural components which contribute most to the overall hardness of the investigated
Fe-C-Mn-Ti steel are Fe3C precipitates (88 HV) and dislocations (54 HV) on a total of 284 HV.
Both contributions decrease rapidly during the initial stages of annealing and stabilise after 10
minutes of annealing. The addition of titanium to the steel gives a minor hardness contribution
via Ti-atoms in solid solution and TiC precipitates. Ti atoms in solid solution give a hardness
contribution which increases slightly during the first few minutes of annealing and then
remains stable (at 25 HV). The direct contribution of TiC precipitates to the overall hardness
is limited (3.5 HV). However, TiC-precipitates also contribute to the overall hardness by
pinning of dislocations during the recovery that takes place during the tempering. The model
predicts that only a small volume fraction of TiC-precipitates forms during isothermal
annealing at 550°C due to the large misfit strain (1.34 GJ/m3) and the low density of potential
nucleation sites.
Chapter 6 presents a comparative study of the evolution of mechanical properties at elevated
temperature and the underlying microstructural mechanisms of ultra-high-strength and
13
conventional high-strength steels for fasteners. The mechanical properties of the ultrahighstrength steel KNDS4 of fastener grade 14.9 (strength 1400 MPa, yield-to-strength ration 0.9)
and of conventional, high-strength steels 34Cr4 of fastener grade 12.9 (strength 1200 MPa,
yield-to-tensile-strength ration 0.9) and 33B2 of grade 10.9 (strength 1000 MPa, yield-totensile-tensile-strength ration 0.9) are measured at room temperature and at elevated
temperature. The alloy carbides in the steels are examined in order to investigate the
underlying microstructural mechanisms that give rise to the different properties of the three
fastener steels. KNDS4 steel has a higher yield strength ratio than both conventional high
strength steels at 500°C, which have similar yield strength ratios at 500°C. Increasing the
soaking time from 5 seconds up to 100 hours at elevated temperatures does not have an
impact on the yield strength ratio. The nano-indentation creep rate shows a weak trend in
which the tendency for deformation during constant load nano-indentation is lower in KNDS4
than in the 34Cr4 and 33B2 steels. This is measured both at similar indent depths and at the
same indent time. The improved mechanical properties of the KNDS4 steel compared to the
conventional high-strength steels are related alloy carbides in the microstructure that hinder
dislocation movement. The alloy carbides in KNDS4 are smaller than the alloy carbides in
34Cr4 steel, and the properties are therefore better. Changing the standard industrial heattreatment from an austenitization temperature of 940 to 1350°C can increase the hardness of
KNDS4 by 8%. The increase stems from more effective dissolution of mainly Ti during the
austenitization treatment. Titanium in solid solution enables nucleation and growth of
precipitates, which generates precipitation strengthening during subsequent tempering.
However, the standard industrial heat treatment results in a smaller martensite block size,
which might be more beneficial for the toughness of the steel.
The study of martensitic model alloys showed that the martensite block structure remain
stable at temperatures up to 550°C, whereas the redistribution of alloying elements such as
carbon is rapid and cannot be prevented. The study of the model alloys furthermore
confirmed that addition of a strong carbide forming element, such as Ti, results in nucleation
of a fine dispersion of alloy carbides that prevents recovery and thereby adds both
precipitation strengthening and dislocation strengthening to the steel. Our study of the
industrial fastener steels thereafter confirmed that alloy carbides in martensite increases the
temperature resistance of the steel, by maintaining a high yield strength at elevated
temperatures. The study of the industrial steels furthermore showed that the tendency to
material creep at room temperatures is reduced in steels with alloy carbide precipitates.
Development of more temperature resistant high strength steels for fasteners shall
therefore be based on the strengthening mechanisms of grain boundaries and on alloy carbide
precipitates. Our research furthermore showed that there is a need for further studies of
traditional, axial creep testing, to fully understand and evaluate the beneficial effects of alloy
carbides in martensitic steels.
For the application of the existing KNDS4 steel we find that, independent of the heat
treatment, the mechanical performance of KNDS4 fasteners at elevated temperature and the
low nano-indentation creep rates are two strong indicators that fasteners made from KNDS4
steel might be used at higher service temperatures than traditional high strength fasteners,
due to the presence of small alloy carbides in the microstructure of KNDS4. Higher strength of
a fastener steel enables development of smaller, but stronger fasteners. These fasteners can
be used in critical applications inside the engine, to down-size e.g. connecting rods, which will
make it possible to significantly reduce the size and weight of modern combustion engines.
Furthermore, the improved temperature resistance of new martensitic fastener steels will
allow using the fastener at elevated service temperatures. These fasteners can therefore be
used in applications where the temperature exceeds the recommended service temperature
of 150°C (with the maximum upper boundary of 300°C) as stated in ISO898-1. This make is
possible to reduce the use of highly alloyed high temperature fasteners (which are designed
for service temperatures of 500°C or more) that are used in engines today due to the lack of
cost efficient, resource-efficient, micro-alloyed fastener steels suitable for service at 300500°C.
15
Samenvatting
Het onderzoek in dit proefschrift is er op gericht om onze kennis te verdiepen over het effect
van kleine hoeveelheden legeringselement op de ontwikkeling van de microstructuur en de
mechanische eigenschappen tijdens het ontlaten van martensitisch staal dat wordt gebruikt
voor de productie van schroeven voor de automobielindustrie. De aanhoudende trend van
het verkleinen van de motor van auto’s heeft geleid tot de vraag naar sterkere en meer
temperatuurbestendige schroeven dan momenteel beschikbaar zijn volgens de internationale
normen. Hiervoor is een nieuw martensitisch staal ontwikkeld dat KNDS4 wordt genoemd. Dit
staal combineert een hogere treksterkte met een verbeterde weerstand tegen
waterstofbrosheid, door toevoeging van carbidevormende elementen zoals Ti, V, Cr en Mo.
Behalve voor een hogere treksterkte en een verbeterde weerstand tegen waterstofbrosheid,
kunnen deze carbiden, door het (tijdelijk) vasthouden van dislocaties bij verhoogde
temperatuur, ook de kruipweerstand van stalen verbeteren. Daarom is het wellicht mogelijk
om dit nieuwe staal bij hogere temperaturen te gebruiken dan wat mogelijk is met de huidige
staalsoorten die gebruikt worden voor hogesterkte verbindingselementen. Om de
eigenschappen van de nieuwe staalsoort te optimaliseren, is een fundamenteel begrip van het
verband tussen de veranderingen van de microstructuur en het verloop van de
hardheid/treksterkte tijdens de warmtebehandeling nodig. De onderzoeksvragen behorende
bij dit proefschriftzijn: (i) in welke mate verschillende microstructurele mechanismen
bijdragen aan de sterkte van martensitische staalsoorten voor bouten? (ii) Hoe evolueren de
verschillende verstevigingsmechanismen tijdens het ontlaten van het staal? (iii) Wat zijn de
effecten van een sterk carbide-vormend element, zoals titanium, op de microstructuur en
verstevigingsmechanismen van martensitische staal? (iv) Kan de sterkte en
temperatuurbestendigheid van een martensitische staal voor bouten worden verbeterd door
toevoeging van carbidevormende elementen?
De eerste stap in dit onderzoek is het bestuderen van een modellegering zonder enige
carbidevormende elementen, die vervolgens vergeleken wordt met een modellegering met
slechts één carbidevormend element: Ti. Hiermee wordt de invloed van één enkel type
carbide op de ontwikkeling van de microstructuur en de eigenschappen bestudeerd tijdens
het ontlaten van martensitisch staal. Daarna worden voor bevestigingselementen gebruikte
industriële staalsoorten met meerdere carbidevormende elementen, waaronder complexe
carbiden, onderzocht.
Hoofdstuk 2 geeft een samenvatting van de industriële context waaruit dit PhD
onderzoek is ontstaan. Dit hoofdstuk bestaat uit drie secties. Sectie 2.1 geeft een inleiding op
boutverbindingen in de automobielindustrie. Een boutverbinding wordt gedefinieerd als het
systeem van een bout en de onderdelen die erdoor bijeen worden gehouden. Het doel van de
bout bestaat uit het samenhouden van geassembleerde componenten middels een
klemkracht. De invloed van externe krachten op de boutverbinding voor verschillende
17
belastingen, de invloed van het zetgedrag van de verbinding (dit is het verlies van klemkracht
als gevolg van lokale plastische vervormingen in de contactoppervlakken van de
boutverbinding na de montage) en de invloed van een wisselende externe belasting op het
vermoeiingsgedrag van de bout in een geassembleerde boutverbinding worden besproken.
Het hoofdstuk eindigt met een overzicht van de belangrijkste mechanische eigenschappen van
verbindingselementen die in de motor worden gebruikt en een uitleg hoe de huidige
staalsoorten voor verbindingselementen zijn gekozen.
Sectie 2.2 introduceert het concept van sterkte en temperatuurbestendigheid van
metalen. De theorie van dislocaties en dislocatiebeweging wordt kort uitgelegd en de
mechanismen achter verschillende soorten dislocatiebewegingen worden geëvalueerd. De
relatie tussen dislocatiebeweging en de sterkte van metalen wordt toegelicht. De
verschillende microstructuurcomponenten die bijdragen aan de sterkte van een metaal wordt
uitgelegd.
Wiskundige
vergelijkingen
voor
het
kwantificeren
van
de
verstevigingsmechanismen in metalen worden gepresenteerd en literatuurwaarden voor
verschillende staalsoorten worden gegeven. De momentane en de tijdafhankelijke invloed van
een temperatuurverhoging op de verschillende microstructuren wordt onderzocht.
Vervolgens komt kruip van metalen aan bod. Kruip is de tijdafhankelijke plastische vervorming
van een metaal onder een externe belasting. Het mechanische gedrag van de verschillende
stadia van kruip en de microstructurele mechanismen achter kruip worden besproken. Ook
worden er vergelijkingen voor verschillende mechanismen van kruip gegeven. Sectie 2.2
eindigt met een overzicht van verschillende methoden om kruip te meten, met speciale
aandacht voor de methode om kruip middels een nano-indrukking te meten aangezien deze
methode gebruikt wordt in het onderzoek van dit proefschrift.
Sectie 2.3 presenteert de versterking van martensiet middels precipitaten. Het Fe-Cdiagram en theorieën met betrekking tot martensietvorming - waaronder die van Bain worden besproken. De kristallografie van lath martensiet is onderzocht en gekoppeld aan de
verstevigingsmechanismen van sectie 2.2. Daarnaast is een samenvatting toegevoegd met de
microstructuurprocessen die plaatsvinden tijdens het ontlaten van het martensiet. De
kinetische theorie achter vaste-stof nucleatie en groei van legeringscarbiden wordt uitgelegd.
Nucleatie volgens de klassieke nucleatietheorie en de energetische factoren die de nucleatie
van nieuwe fasen beïnvloeden worden besproken. De groeimechanismen achter diffusie- en
grensvlakgecontroleerde groei, worden gepresenteerd. Zener-groei wordt in meer detail
uitgelegd. Het hoofdstuk eindigt met een samenvatting van de kenmerken van TiCprecipitaten, de thermodynamische gegevens achter nucleatie en de groei van TiC in staal,
omdat dit type precipitaten specifiek in dit proefschrift worden bestudeerd.
Hoofdstuk 3 is een experimentele studie naar het verloop van de hardheid en de
microstructuur in Fe-C-Mn martensiet (deze is vrij van legeringscarbiden) tijdens het ontlaten
op 300°C. De hardheid van het grensvlak tussen de martensiet blokken is aanzienlijk hoger
dan de hardheid in de kern van het blok, als gevolg van een hogere dislocatiedichtheid rondom
het grensvlak tussen de martensietblokken (deze regio’s worden blokgrensvlak-regio’s
genoemd). Tijdens het ontlaten wordt de hardheid rondom het grensvlak tussen de blokken
meer gereduceerd dan in de kern van het blok. De kinetiek van het ontlaten van Fe-C-Mn
martensiet kan worden beschreven door drie stadia waarin de microstructuur verandert. Deze
stadia/fasen zijn: Fase I (0-5 min) wordt gekenmerkt door een snelle macroscopische
hardheidsverlagende kinetiek, die sterk gerelateerd is aan (a) snel en gelijktijdig verlagen van
de hardheid en vermindering van het aandeel van blokgrensvlak-regio’st en (b) snelle
vermindering van het aandeel gebieden dat niet is ontlaten in de kern van het martensiet blok.
Fase II (5-10 minuten) wordt gekenmerkt door een trage macroscopische
hardheidsverlagende kinetiek, die wordt bepaald door een langzame hardheidsverlaging en
een vermindering van het aandeel van blokgrensvlak-regio’s. Fase III (10-60 minuten) wordt
gekenmerkt door een zeer trage hardheidsverlagende kinetiek, bepaald door een zeer
langzame hardheidsverlaging van en een vermindering van de blokgrensvlak-regio’s.
Hoofdstuk 4 is een experimentele studie naar de invloed van een toevoeging van 0.042wt% Ti
op het verloop van de microstructuur en de hardheid van Fe-C-Mn staal tijdens het ontlaten
op 300°C en 550°C. De macroscopische hardheid van Ti-houdend en Ti-vrij staal vermindert
snel tijdens de eerste 5 minuten van het ontlaten als gevolg van (i) herverdeling van
interstitieel opgelost koolstof tot de vorming van cementiet en (ii) snel herstel. De
macroscopische hardheid van Ti-vrij staal blijft daarna stabiel tijdens aanhoudend ontlaten. In
tegenstelling hiertoe toont Ti-houdend staal een hardheidsstijging na 30 minuten ontlaten bij
550°C. De verhoging van de hardheid van Ti-houdend Fe-C-Mn-Ti staal is gerelateerd aan de
vorming van TiC-precipitaten bij 550°C. Nucleatie van TiC-precipitaten begint dicht bij het
blokgrensvlak (na 5-10 minuten) en vervolgens in de kern van het blok (na 10-30 minuten). De
oorzaak hiervan is de hogere dislocatiedichtheid dicht bij het blokgrensvlak. De vorming van
TiC-precipitaten vertraagt het herstel dicht bij het blokgrensvlak na 5 tot 10 minuten ontlaten.
Het is mogelijk om de groei van TiC-precipitaten in martensiet te simuleren met behulp van
een model dat rekening houdt met capillaire werking, het overlappen van de titaandiffusievelden en de effecten van pijpdiffusie van titaanatomen.
Hoofdstuk 5 is een theoretische studie naar het verloop van de verschillende
versterkingsmechanismen in Fe-C-Mn-Ti staal tijdens isotherm ontlaten. De hardheid van
martensiet wordt gesimuleerd als een lineaire superpositie van meerdere
versterkingsmechanismen. Dit hardheidsmodel wordt gecombineerd met een
microstructureel model, gebaseerd op een Kampmann-Wagner-Numerical (KWN) model, om
de nucleatie en groei van TiC-precipitaten binnen een multi-component en multi-fase systeem
te simuleren. Het model is wordt gevoed met experimentele resultaten en gebruikt de
hardheidsbijdrage van de verschillende microstructurele componenten om de ontlaattijd te
simuleren. De twee microstructurele componenten die het meest tot de totale hardheid van
het onderzochte Fe-C-Mn-Ti staal bijdragen zijn Fe3C-precipitaten (88 HV) en dislocaties (54
HV) vanuit een total hardheid van on 284 HV. Beide bijdragen verminderen snel tijdens de
eerste stadia van het ontlaten en stabiliseren na 10 minuten. De toevoeging van titanium aan
het staal geeft een kleine hardheidsbijdrage, via Ti-atomen in vaste oplossing en via TiCprecipitaten. Ti-atomen in vaste oplossing geven een hardheidsbijdrage die iets toeneemt
19
tijdens de eerste minuten van het gloeien en daarna stabiel blijft (op 25 HV). De directe
bijdrage van TiC-precipitaten tot de totale hardheid is beperkt (3,5 HV). Maar TiC-precipitaten
dragen ook aan de totale hardheid bij door het (tijdelijk) vasthouden van dislocaties zodat
minder herstel plaatsvindt tijdens het ontlaten. Het model voorspelt dat slechts een kleine
volumefractie TiC-precipitaten gevormd wordt tijdens ontlaten op 550°C als gevolg van een
hoge “misfit strain energy” (1,34 GJ/m3) en een lage dichtheid van potentiële kiemplaatsen.
In hoofdstuk 6 wordt een vergelijkende studie gepresenteerd van de mechanische
eigenschappen bij verhoogde temperatuur en de microstructurele mechanismen tussen ultrahogesterkte en conventionele hogesterktestaalsoorten die gebruikt worden voor
verbindingselementen. De mechanische eigenschappen van verbindingselementen gemaakt
van het nieuwe ultra-hogesterkte staal KNDS4 met sterkteklasse 14.9 (treksterkte 1400 MPa
en een rekgrensverhouding van 0,9), het conventionele hogesterkte staal 34Cr4 met
sterkteklasse 12.9 (treksterkte 1200 MPa en een rekgrensverhouding van 0,9) en 33B2 met
sterkteklasse 10.9 (treksterkte 1000 MPa en een rekgrensverhouding van 0,9) worden bij
kamertemperatuur en bij verhoogde temperatuur gemeten. De legeringscarbiden in de stalen
worden onderzocht om de onderliggende microstructurele mechanismen die leiden tot de
verschillende mechanische eigenschappen van de drie materialen te kunnen verklaren. KNDS4
heeft een hogere verhouding tussen de vloeispanning op 500°C en de vloeispanning op
kamertemperatuur dan conventionele hogesterkte staalsoorten. De twee conventionele
staalsoorten hebben een soortgelijke verhouding tussen de vloeispanning op 500°C en de
vloeispanning op kamertemperatuur bij. Deze verhouding blijkt voor alle drie de stalen niet te
veranderen als de tijd wordt verlengd van 5 seconden naar 100 uur waarop het staal op hoge
temperatuur wordt gehouden. De kruip, zoals gemeten door nano-indrukking, toont een
zwakke trend richting een geringere deformatie tijdens nano-indrukking met constante kracht
in KNDS4 dan in 34Cr4 en 33B2. De betere mechanische eigenschappen van KNDS4 worden
veroorzaakt door de aanwezigheid van legeringscarbiden - die dislocatiebewegingen
belemmeren - in de microstructuur. De legeringscarbiden in KNDS4 zijn kleiner dan de
legeringscarbiden in 34Cr4 en de eigenschappen zijn daarom beter. Wijzigen van de standaard
industriële warmtebehandeling met een austeniteertemperatuur van 940°C naar een
austeniteertemperatuur van 1350°C kan de hardheid van KNDS4 met 8% verhogen. Deze
stijging komt door het meer effectieve oplossen (i.p.v. vergroven) van bestaande TiCprecipitaten tijdens het austenitiseren. Titanium in vaste oplossing kan leiden tot nucleatie en
groei van precipitaten, die op hun beurt de versteviging veroorzaken tijdens het ontlaten.
Maar de standaard industriële warmtebehandeling resulteert in kleinere martensietblokken
die mogelijk gunstig zijn voor de taaiheid van het staal.
De studie van de martensitische modellegering toont aan dat de martensiet blok structuur
stabiel blijft bij temperaturen tot 550 ºC, maar dat de herverdeling van legeringselementen,
zoals koolstof, snel is en niet verhinderd kan worden. Bovendien heeft de studie van de modellegeringen bevestigd dat toevoeging van een sterk carbide vormend element, zoals Ti,
resulteert in nucleatie van een fijne dispersie van TiC precipitaten, hetgeen herstel voorkomt
en daardoor versteviging door zowel precipitaten als dislocaties aan het staal toevoegt. Onze
studie van de industriële staalsoorten voor verbindingselementen heeft daarna bevestigd dat
carbides van legeringselementen in martensiet de temperatuurbestendigheid van het staal
verhogen, door het behoud van een hoge vloeispanning bij hoge temperaturen. De studie van
de industriële stalen heeft bovendien aangetoond dat de kruip bij kamertemperatuur in stalen
met carbides van legeringselementen gereduceerd is.
De ontwikkeling van meer temperatuurbestendige hoge sterkte staalsoorten voor
verbindingselementen zal daarom moeten worden gebaseerd op de versterking mechanismen
van martensitiche blok grenzen en op carbides van legeringselementen. Ons onderzoek toont
bovendien aan dat er is een behoefte aan verdere studies van traditionele, axiale kruip testen,
om de positieve effecten van carbides van legeringselementen in martensitische stalen
volledig te begrijpen en evalueren.
Onafhankelijk van de gevolgde warmtebehandeling zijn de verbeterde mechanische
eigenschappen van KNDS4 bij verhoogde temperatuur en de lage vervorming tijdens nanoindrukkingen twee belangrijke indicaties om KNDS4 voor verbindingselementen te gaan
gebruiken. Het is mogelijk om kleinere, maar sterker bouten met hogere strekte staal te
ontwikkelen. Deze bouten kunnen gebruikt worden voor kritische toepassingen in de motor,
bijvoorbeeld de drijfstangen, waardoor het mogelijk wordt om de grootte en het gewicht van
moderne verbrandingsmotoren te verminderen.
Daarnaast kan de verbeterde temperatuurbestendigheid van de nieuwe martensitische
staalsoorten mogelijkerwijseen verhoogde gebruikstemperatuur toegestaan. Deze bouten
kunnen daarom mogelijk gebruikt worden in toepassingen waar de temperatuur boven de
aanbevolen gebruikstemperatuur van 150°C uit komt (met de maximale bovenste grens van
300°C) zoals vermeld in ISO898-1. Dit maakt het mogelijk om hoog-gelegeerde en hoge
temperatuur materialen voor bouten (die zijn ontworpen voor een gebruikstemperatuur van
500°C of meer) te vervangen, die vandaag worden gebruikt in motoren door het huidige
gebrek aan kostenefficiënte, resource-efficiënte en micro-gelegeerd staalsoorten die geschikt
zijn voor temperaturen tussen 300-500°C.
21
1 Introduction
When you turn the key to the ignition of your car you immediately put a high load on more
than 200 fasteners that are located in the combustion engine of your car. If you drive a hybrid
the clutch and electrical engine will add approximately 200 fasteners to the combustion
engine. When you drive out on the road, you start using an additional 1500-2500 screws, bolts
and nuts located in the driveline, the cassis, the body and the interior of your car, depending
on which car size and model you drive [1].
Figure 1.1. Cylinder head and the cylinder head
bolts of an Opel Ampera. This vehicle was
disassembled at Nedschroef Techno Centre in
order to study the fasteners of a modern hybrid
car. The cylinder head bolts have a length of
122 mm.
Screws and nuts are today completely integrated into the everyday life of every modern
society, as they are used within engineering products ranging from buildings and
infrastructure, to all kinds of transport vehicles, computers and electronics, medicine,
furniture and even jewelry.
23
Nedschroef is the largest supplier of fasteners for the automotive industry in Europe.
Nedschroef has produced and developed fasteners since 1896. The company has never before
focused so intensely on research and development as it does today. The major influence for
the developments of new fasteners comes from the trends and developments of the
automotive industry, which is the largest customer of Nedschroef. I therefore choose an
example from the automotive industry, the internal combustion engine, in order to describe
which development are taking place at Nedschroef.
The first four-stroke combustion engine was invented in the second half of the
nineteenth century [2]. This means that the combustion engine and our products are more or
less of the same age. Even though the combustion engine is old, the basics of the engines in
the latest F1 car are still the same as the original invention. The pistons move inside the
cylinders due to the combustion of an air/fuel mixture and thereby generate the rotation of
the crank-shaft which is used to drive the cars. This means that most of the developments of
the four stroke engine are fine-tuning of existing constructions and concepts. In fact, the high
performance of the F1 vehicles is mainly based on extremely specialized materials and
coatings for the majority of the components in the engine and on the vehicle itself. The
development of modern mass-produced cars follows the same concepts as the F1 industry,
although with more focus on cost and resource efficiency. Today, materials Science is the main
innovative field for the development of new engines as well as new combustion fasteners.
The reason behind this is that the focus of engine development has changed
course during the last decade. The general awareness of climate change and scarce oil and
raw material resources have forced large changes upon the automotive industry. Image, which
used to be measured in horse powers and fast acceleration, is now measured in low emissions
and low fuel consumption instead. Even the F1 industry has introduced restrictions for fuel
consumption since the start of the season of 2014 [3]. This development of low-emission drive
lines has resulted in smaller but more powerful engines (down-sizing) and the mechanical and
thermal loading of the engines are increasing. For us at Nedschroef this means we need to
develop fasteners which are stronger and more temperature resistant (but of course, not
more expensive).
1.1 The scope and aim of this thesis
The scope of this PhD study is to investigate the possibility to optimize the microstructure, in
order to increase both the strength and the temperature resistance, of the industrially
available ultra-high tensile strength fastener steel KNDS4. The requirements for the current
high-strength engine fasteners are listed in the international fastener standard ISO898 [4].
This standard covers fasteners up to class 12.9, which means a nominal strength of 1200 MPa
and a yield point of minimum 90% of the ultimate tensile strength. The ISO standards
furthermore recommend a maximum service temperature of 150°C. The industrial aim of the
presented research is to develop a fastener steel with a tensile strength that exceeds Rm=1200
MPa and that can be used at service temperatures up to 400°C.
There are three main boundary conditions that must be fulfilled for the development of new
engine fasteners. The first condition is related to the traditions and standards within the
automotive industry; in order for an ultra-high strength fastener (ultimate tensile strength
larger than 1200 MPa) to be accepted by the automotive industry, it must be produced and
have properties in line with the currently used, high-strength fasteners. This means that the
fastener must have a martensitic microstructure and that the heat treatment must be
performed with a tempering temperature of minimum 425°C [4].
The second condition is related to cost. In order to keep the production cost low, the
fastener must be produced via cold forming from an annealed wire. This means that the
chemical composition of the steel must contain low concentrations of alloying elements
(preferably maximum 1 wt% per single alloying element), and that the elements themselves
must be abundantly available. The background for reducing the concentration of alloying
elements in the steel is twofold. Firstly, most alloy additions result in solid-solution
strengthening and possible precipitate strengthening of the steel. This can reduce the
formability and will increase the forging loads needed during cold forming, thereby leading to
higher tool wear, higher risk for material cracking and higher energy consumption. Secondly,
lower concentrations of alloying elements means that we can use our natural resources more
efficiently.
The third condition is related to the heat-treatment of the fastener. In order to develop
products which can be produced in high volumes, the heat treatment must be done in existing
industrial quench and temper equipment and the temperature is limited to maximum
temperature of 920-940°C for hardening (austenitization) and a maximum temperature of
600°C for tempering. Higher temperatures will lead to increased CO 2-emission, higher energy
consumption and a higher need for furnace maintenance.
The strength of martensitic steels, which are used for the current engine fasteners, originates
mainly from the following strengthening mechanisms: (i) elements in solid solution, (ii) grain
boundaries, (iii) dislocations and (iv) iron carbides [5-6]. Carbides are phases that consist of
metal atoms, combined with carbon atoms, to form a second phase. Carbides in steel are
formed only by iron and metals that are located to the left of iron in the periodic table of
elements. The metals that have high affinity to carbon and to form carbides, are called carbide
forming elements. Common strong carbide-forming elements are niobium (Nb), titanium (Ti),
vanadium (V), molybdenum (Mo) and chromium (Cr), which are listed in order of increasing
affinity to carbon. Iron carbides consist of Fe and C atoms and alloy carbides, as described in
this thesis, consist of carbide forming elements and C atoms. The most common iron carbide
in tempered steels is cementite (Fe3C). Cementite tends to coarsen more rapidly in steel at
increased temperatures due to increased diffusivity of carbon atoms in steel. Alloy carbides
can be of many forms; MC, M2C, M3C, M7C3, M6C and M23C6 [7] where M can be a mix of
different carbide forming elements [8]. Alloy carbides typically are smaller than cementite and
25
coarsen at a slower rate due to limited solubility and diffusivity of the carbide forming
elements in the steel matrix.
The new, ultra-high strength steels that have been developed for stronger fasteners are based
on the addition of precipitation strengthening and grain refinement via alloy carbides [9],
similar to what is used in HSLA steels [10]. The alloy carbides contain carbide-forming
elements such as Ti, V, Mo and Cr. The alloy carbides in the new steel increase the ultimate
tensile strength of the fastener above 1200 MPa. The tempering temperature that is required
for the nucleation and growth of alloy carbides is in the range of 550°C, which fits with the
requirement of ISO 898-1 and the upper limit of industrial tempering furnaces. The low level
of alloy additions needed for precipitation strengthening furthermore enables the steel to be
cold formed. More importantly, TiC-precipitates have been shown to have the potential to act
as hydrogen traps and improve the resistance to hydrogen-induced damage [11-12] during
processing and service of the fastener. The original design of the chemical composition for
these new high strength fastener steels was merely targeting higher strength levels and
resistance to hydrogen embrittlement. However, thermally stable precipitates are also known
to improve the creep properties of steels [13-15] and the tensile strength at elevated
temperatures [16], by acting as pinning points for dislocation movement. The high thermal
stability of TiC precipitates [17] due to low solubility and low diffusivity of Ti in the steel matrix
combined with coherent or semi-coherent interfaces between the TiC-precipitates and the
steel matrix therefore makes medium-carbon steel with a small addition of Ti an interesting
candidate for the development of ultra-high strength martensitic engine fasteners suitable for
service temperatures up to 400°C.
The mechanical properties and performance of the next generation of high
strength engine fasteners is based upon a martensite microstructure that is further
strengthened with alloy carbides. A fundamental understanding of the relation between the
evolution of the microstructure and the evolution of the strengthening mechanisms in
martensite is required in order to optimize the heat-treatment process and the properties of
new engine fasteners. Our hypothesis is that the next generation of high strength fastener
steels, which is based on alloy carbides, can reach higher strength levels, as well as improved
temperature resistance compared to conventional high-strength steels for fasteners.
This approach requires further knowledge development. The following research questions
were answered during this research project:
1- To which extent do different hardening mechanisms contribute to the strength of
martensitic fastener steels?
2- How do the different hardening mechanisms evolve as a function of time during
annealing?
3- What are the effects of a strong carbide forming element such as titanium on the
microstructure and hardening mechanisms of martensitic fastener steel?
4- Can the strength and temperature resistance of a martensitic fastener steel be
improved by addition of carbide forming elements
1.2 The outline of this thesis
This thesis consists of a background chapter, which summarizes the industrial context that led
to the research described in this PhD-thesis, four chapters that are based on the research
performed within this PhD study, and a concluding chapter.
Chapter 2 consist of three background sections. Section 2.1 gives a short introduction to
bolted joints and the use of fasteners in the automotive industry. The key mechanical
properties of a fastener are reviewed and the choice of traditional fastener steels is briefly
explained. Section 2.2 describes the strength and temperature resistance of metals. The
microstructural components that contribute to the strength of metals are discussed and
equations for calculating the strength contribution of each hardening mechanism is given. The
influence of elevated temperatures on each microstructural feature is reviewed. The
phenomena and mechanisms are explained that are behind the creep of metals and different
methods to measure creep. Section 2.3 presents martensite formation and precipitationstrengthening of martensite. The basics of martensite formation and the crystallography and
microstructure of martensite is discussed. The different strengthening mechanisms of
martensite are reviewed and the microstructural processes that take place during tempering
of martensite are explained. The kinetic theory behind nucleation and growth of precipitates
is presented and the data needed for describing precipitation strengthening based on TiC is
summarized, since this precipitate type is studies during the PhD research.
Chapter 3 is based on an experimental study focusing on the evolution of the hardness and
microstructure of Fe-C-Mn martensite (without precipitation strengthening of TiC) during
tempering at two different temperatures. The results presented give a reference level for the
research on the Ti-containing martensite.
Chapter 4 is an experimental study which examines the influence of adding 0.04wt.% of Ti on
the evolution of the microstructure and hardness of a Fe-C-Mn steel during tempering. The
research confirmed that the precipitation of TiC results in a macroscopic hardness increase of
the martensite and that the high dislocation density of martensite significantly increases the
rate of TiC growth in martensite.
Chapter 5 is a computational study of TiC nucleation and growth and the evolution of the
hardness of martensitic steel during tempering. A multiphase, multi-component hardness
model is combined with a Kampmann-Wagner-Numerical (KWN) model for the nucleation and
growth of precipitates. The models are subsequently fitted to the experimental results of
chapter 4.
Chapter 6 is a comparative study of the mechanical properties at room temperature and
elevated temperatures of the new ultra-high tensile strength fastener steel KNDS4
(containing strong carbide forming elements) and conventional high strength fastener steels.
27
The difference in mechanical properties is explained on the base of the underlying
microstructural mechanisms and potential alternative heat treatments of KNDS4 are
explored, to further improve the mechanical behaviour.
1.3 References
[1] Statistics based on a tear-down project of an Opel Ampera, performed at Nedschroef
Technocentre, 2013
[2] E. Eckerman: World history of the automobile, Society of Automotive Engineers,
Warrendale, USA, 2001
[3] http://www.formula1.com/inside_f1/rules_and_regulations/sporting_regulations/12877/
[4] ISO898-1, Mechanical properties of fasteners made of carbon steel and alloy steel-Part 1.
Fifth edition, Switzerland, 2013
[5] T. Gladman: The physical metallurgy of microalloyed steels, The University press, London,
UK,1997
[6] G. Krauss: Mater. Sci. Eng., A273-275(1999), 40-57
[7] DA. Porter and KE. Easterling: Phase transformations in metals and alloys, Van Norstrand
Reinhold, New York, USA, 1981
[8] ADB. Gingell, HKDH. Bhadeshia, DG. Jones and KJA Mawella: J. Mater. Sci., 32(1997),
4815-4820
[9] Y. Namimura, N. Ibaraki, W. Urushihara and T. Nakayama: Wire J. Int., January(2003), 6267
[10] CY. Chen, HW. Yen, FH. Kao, WC. Li, CY. Huang, JR. Yan and SH Wang: Mater. Sci. Eng. A.,
499(2009), 162-166
[11] F-G. Wei, T. Hara, T. Tsuchida and K. Tsuzaki: ISIJ Int., 43(2003), 539-547
[12] J. Takahashi, K. Kawakami, Y. Kobayashi and T. Tarui: Scripta Mater., 63(2010), 261-264
[13] RL. Klueh, N. Hashimoto, FR. Buck and MA. Sokolov: J. Nuclear Mater., 283-287(2000),
697-701
[14] RL. Klueh, N. Hashimoto and PJ. Maziasz: J. Nuclear. Mater., 367-370(2007), 48-53
[15] K. Maruyama, K. Sawada and J-I. Koike: ISIJ Int., 41(2001), 641-653
[16] P. Michaud, D. Delagnes, P. Lamesle, MH. Masthon and C. Levaillant: Acta Mater.,
55(2007), 4877-4889
[17] M. Taneike, N. Fujitsuna and F. Abe: Mater. Sci. Tech., 20(2004), 1455-1461
2 Background
This background chapter describes the industrial context that led to the research described in
the subsequent chapters in this PhD-thesis. Chapter 2 consist of three main sections: Section
2.1 gives an introduction to fasteners for the automotive industry, which describes forces
acting on bolted joints and the required material properties of fasteners that are used in the
automotive industry. Section 2.2 zooms into the underlying mechanisms that give strength
and temperature resistance to metals, which are two important material properties for
automotive fasteners. Section 2.3 describes the relation between the processing, properties
and microstructure of martensite that is strengthened with precipitates, which could
potentially give the desired combination of strength and temperature resistance to
automotive fasteners.
2.1 Fasteners for the automotive industry
2.1.1
Introduction
Fasteners have been used to join automotive components since the very first production of
automotive vehicles for human transport (steam powered), in the eighteenth century [1]. The
threaded fastener joining method has a major advantage over other joining methods such as
welding, brazing, and gluing; the joint can easily be disassembled at any time. For modern cars,
where the life cycle of the vehicle is expected to be followed by sorting and recycling of all
vehicle components, bolted joints are therefore the key fastening method applied. The
fasteners which are used for modern, mass produced cars, are strictly regulated via
international standards that stipulate the material, the microstructure and the mechanical
properties of the fastener.
29
2.1.2
Definition and purpose of a bolted joint
A fastener is an element that is used to join two or more components together. Examples of
fasteners are a screw, a clip and a rubber band. The work that is described in this thesis is
related to screws and bolts. A bolted joint consists of a bolt or a screw, the components that
are joined by the bolt/screw and in some cases a nut. The components that are joined are
commonly referred to as the clamped parts or the base material. The female thread (which
the bolt/screw is assembled into) is present in the form of either a nut or as a threaded hole
in one of the clamped parts. The distance measured from under the bolt head to the first
engaged thread is called the clamp length, Lc, as shown in Figure 2.1.
Figure 2.1 Schematic drawing of a
bolted joint, showing the clamp
length, Lc, the clamped parts (or
base material), the bolt and the nut
(at the bottom of the drawing.
The working principle of a bolted joint is based on the creation of a traction force over the
clamped parts, which hold the clamped parts together. This traction force is called the clamp
force (Fc). Figure 2.2 shows (a) a properly assembled bolted joint, and (b) an insufficiently
assembled bolted joint. The clamp force Fc is illustrated by blue arrows, the force in the bolt
(Fbolt) is illustrated by green arrows, the external force acting on the joint (Fe) is illustrated by
the red arrows and the friction force between the clamped parts (Ff) is illustrated by orange
arrows. The clamp force is created by tightening the bolt.
The purpose of the clamp force is to compress the clamped parts so that relative movement
or separation of the clamped components is prevented, when external forces are applied to
the joint. The task of the fastener is thus to transfer and absorb the forces applied to the
joint rather than to act as a “stopping-pin” as demonstrated in Fig. 2.2(b).
Figure 2.2 Schematic drawing of bolted joints showing a) a properly assembled bolted joint in
which the clamp length (Lc) the clamping force (Fc) and the external forces acting on the joint
(Fe) are indicated and b) a bolted joint with insufficient clamping force. Panel b shows that the
external forces create unwanted slip at the interface between the clamped parts, because the
frictional forces, Ff, are too low to prevent movement of the clamped parts.
2.1.3
Force distribution in a bolted joint
This section based on the guideline VDI2230 [2], the thesis by G. Toth [3] and the instructions
for design of screw joints used by Volvo Cars [4]. The VDI is developed by the German
automotive industry and is the most widely applied standard for calculations related to the
design of bolted joints that is used within the automotive industry.
The relationship between the bolt elongation, the compression of the clamped parts, the
clamp force and external forces in a bolted joint is commonly illustrated in a so called jointdiagram. A joint diagram can be created from a force/elongation diagram, and is a useful tool
to understand the distribution of forces in a bolted joint during external loading.
The joint diagram describes the bolted joint as a system of two springs; (i) the screw which
acts as a tension spring and (ii) the base material which acts as a compression spring. The
stiffnesses of the two springs are of interest as they influence the distribution of external loads
between the screw and the base material.
2.1.3.1 Assembled condition
During assembly of a bolt, the section of the bolt that is within the clamp length is elongated
by the length of one thread pitch, minus the elastic compression of the clamped parts, for
every 360° rotation of the bolt head. The elastic elongation of the section of the bolt that is
within the clamp length, creates a tensile force ⃑Fbolt in the bolt and a compressive force ⃑Fbase
in the clamped parts or base material in accordance to Hooke’s law. Without the presence of
external loads on the joint, the tensile force of the bolt will be equal in magnitude and opposite
⃑ base . Note that
in direction to the compressive force exerted on the clamped parts: ⃑Fbolt = −F
the clamp length of the joint will decrease slightly during tightening, due to elastic (and
sometimes plastic) stresses in the base material.
Figure 2.3 illustrates the tensile force of the bolt, Fbolt (N), the elongation of the bolt, ∆𝑙𝑏𝑜𝑙𝑡
(m), the compressive force on the clamped parts, Fbase (N), and the compression of the
clamped parts ∆𝑙𝑏𝑎𝑠𝑒 (m) in a Force/Elongation diagram.
31
Figure 2.3 Force
distribution
during assembly
Since the bolted joint is described as a system of springs, Hooke’s law can be used to define
the elongation and compression of the bolt and the base material according to the following
basic relationship between forces and elastic deformation:
𝐹𝑏𝑜𝑙𝑡 = 𝑘𝑏𝑜𝑙𝑡 ∆𝑙𝑏𝑜𝑙𝑡 ,
Equation 2.1
𝐹𝑏𝑎𝑠𝑒 = 𝑘𝑏𝑎𝑠𝑒 ∆𝑙𝑏𝑎𝑠𝑒 ,
Equation 2.2
where 𝑘𝑏𝑜𝑙𝑡 and 𝑘𝑏𝑎𝑠𝑒 are the spring constants of the bolt and the clamped parts respectively.
The spring constants describes the stiffness of the bolt and base material.
Figure 2.4 shows the resulting joint diagram which is created from the curves in Fig. 2.3. The
joint diagram is made by rotating and mirroring the characteristic line for the clamped parts
onto the characteristic line for the bolt, so that they intersect at point A.
The clamp force of the joint, Fc, is measured at the intersection of the curves. In the absence
⃑ bolt .
of external forces; ⃑Fc = ⃑Fbase = −F
Figure 2.4 Joint
diagram
showing the
clamping force
⃑⃑⃑c in an
F
assembled joint.
The stiffness of the bolt, kbolt, is equal to the slope of the characteristic line of
the bolt and can be expressed as:
𝑘𝑏𝑜𝑙𝑡 = 𝐴𝑏𝑜𝑙𝑡 𝐸𝑏𝑜𝑙𝑡 ⁄𝐿 𝐶 ,
Equation 2.3
where Abolt is the stress area of the bolt, Ebolt is the Young’s modulus of the bolt material
and Lc is the clamp length of the bolt. However, since the bolt head, the bolt shank and
the threaded section of the bolt (with stiffnesses kbh, kbs and kbt ) will be affected
individually by the loading, the stiffness of the bolt consist of several springs, arranged in
series, due to which the bolt stiffness can be expresses as:
1
𝑘𝑏𝑜𝑙𝑡
=
1
𝑘𝑏ℎ
+
1
𝑘𝑏𝑠
1
+𝑘
Equation 2.4
𝑏𝑡
The stiffness of the base material, kbase, is equal to the slope of the characteristic line of
the base material and can be expressed as:
𝑘𝑏𝑎𝑠𝑒 = 𝐴𝑏𝑎𝑠𝑒 𝐸𝑏𝑎𝑠𝑒 ⁄𝐿𝐶 ,
Equation 2.5
where Lc is the clamp length and Ebase is the Young’s modulus of the compressed parts.
The area of the compressed section of the base material depends on the design of the
clamped parts, and the diameter of the hole where the bolt is fitted. If the joint consist of
two or more clamped parts the resulting stiffness of the base material shall be calculated
as a series of springs, similar to the stiffness of the bolt;
1
𝑘𝑏𝑎𝑠𝑒,𝑡𝑜𝑡𝑎𝑙
= ∑𝑖
1
𝑘𝑏𝑎𝑠𝑒,𝑖
Equation 2.6
,
where the index i refers to the number of clamped parts.
33
2.1.3.2 External loading
Most bolted joints in an automotive vehicle are subjected to external loads. An external
load (force) can be illustrated as a vertical line in the joint diagram, according to Fig. 2.5.
External loads are applied to the bolted joint in the assembled condition. The origin of the
external force is therefore the intersection of the lines for the bolt and the clamped parts.
If the external load is acting to separate the clamped parts, acting in positive direction of
Y-axis, the bolt will experience this as a continued elongation of the clamp length
(continue the characteristic line of the bolt). The external load is at the same time acting
to reduce the compression of the clamped parts.
Figure 2.5 shows the force distribution in a bolted joint where an external force, Fe, is
acting to separate the clamped parts (the external force is applied symmetrically around
the center line of the joint, directly under the bolt head). The external load has a positive
direction (see the red arrow in Fig. 2.5) and will act to further elongate the bolt. The
characteristic line of the bolt is therefore extended (see the blue dotted extension of the
bolt line in Fig. 2.5). The external force is fitted to the magnitude of the force between
the extended characteristic line of the bolt and the original characteristic line of the
clamped parts, originating from point A.
Figure 2.5 Joint
diagram showing the
force distribution of
an axial external
force applied to a
bolted joint
The distribution of the external force into the bolt resp. the base material of the joint
can then be illustrated as the blue double headed arrows, Fe,bolt and Fe,base respectively.
The distribution of the external load into the bolt and into the base material is
proportional to the stiffness relationship between the bolt and the base material, Φ,
which is given by
𝑘
Φ = |𝑘 𝑏𝑜𝑙𝑡 |
𝑏𝑎𝑠𝑒
Equation 2.7
The load increase in the bolt becomes Φ𝐹𝑒 and the load decrease in the base material
becomes(1 − Φ)𝐹𝑒 . The remaining load in the bolt and the base material of the externally
loaded joint becomes:
𝐹𝑏𝑜𝑙𝑡,𝑟 = 𝐹𝑏𝑜𝑙𝑡 + Φ𝐹𝑒
Equation 2.8
𝐹𝑏𝑎𝑠𝑒,𝑟 = 𝐹𝑏𝑎𝑠𝑒, − (1 − Φ)𝐹𝑒
Equation 2.9
In Fig. 2.5, the base material has a higher stiffness than the bolt material. The result of an
external load is an increase of the elongation of the bolt and a reduction of the
compression of the clamped parts (unloading of the clamped parts by the magnitude of
Fe,base). The remaining clamp force in the joint is Fc,r. Note that this remaining clamp force
must be large enough to prevent relative movements in the joint , via the friction forces
(see Fig. 2.2) in case also shear forces are applied.
Figure 2.6 shows an example of an external load which is increased to the point where
the base material is completely unloaded, Fc,r =0. The remaining clamp force is now
reduced to zero and the complete external load is distributed into the bolt. In the case
that the clamp force is reduced to zero, relative movements of the clamped parts cannot
be prevented.
Figure 2.6 Joint
diagram showing
complete loss of
clamp force due to
overload.
2.1.3.3 Settlement
Any process which reduces the elastic elongation of the bolt in a bolted joint is called
settlement. Settlement can occur in all contact surfaces of the joint, including the threads.
The parameters which determine the extent of the settlement are surface roughness,
surface hardness and parallelism of clamped parts and the fastener. Clamp force losses
due to creep can also be included in settlements.
35
Figure 2.7 Joint
diagram showing
the impact of
settlement Z in a
bolted joint.
Figure 2.7 shows how settlements can be visualized in the joint diagram. Settlement is
measured in distance (m) and is commonly given the name Z in joint diagrams. Z can be
visualized by a horizontal line (along x-axis) with a length equal to the sum of the
reduction of bolt elongation and the base material compression, due to settlements. The
starting point for Z in the joint diagram is the intersection of the two characteristic lines
of the bolt and the clamped parts after assembly. Settlements will lead to a reduction of
the clamp force and is therefore fitted (given in magnitude along the X-axis) between the
characteristic lines for bolt and clamped parts, below their intersection point. After fitting
the Z-line, a new characteristic line for the base material can be drawn (with the same
slope as the old line) from the intersection of Z and the characteristic line of the bolt, see
the new solid line for the base material. The remaining clamp force in the joint can then
be shown as Fc,r. The elongation of the bolt is reduced, as well as the compression of the
clamped parts.
2.1.3.4 Fatigue
Fatigue is failure, at relatively low stress levels, of structures that are subjected to
fluctuating and cyclic stresses. Failure of the material by fatigue is characterized by three
distinct steps. The first step is the initiation of small cracks that form at high stress
concentrations at the surface or internal flaws. Secondly, the crack slowly propagate with
each stress cycle during which the crack advances incrementally. Thirdly final failure
occurs very rapidly once the advancing crack has reached critical size. A greater applied
stress range (load amplitude) results in a higher crack growth and therefore sooner
fracture of the structure (short fatigue life).
The distribution of an altering load in a bolted joint will follow the same
principle as discussed in section 2.1.3.2. The part of the external load that is distributed
into the bolt will determine the amplitude of the cyclic loading that acts upon the bolt.
The fatigue life of the fastener is therefore very dependent on the stiffness relationship
between the bolt and the base material. The methods to improve fatigue life of the
fastener itself include avoiding surface damages and assuring a large radius of curvature
under the bolt head and in the thread roots in order to minimize stress concentrations.
Additional improvements of fatigue life of threaded fasteners can also be achieved by
producing the threads on the bolt via deformation (rolling) after the heat treatment,
thereby introducing compressional stresses on the thread surface, and by the choice of
the material (and microstructures) with good fatigue properties.
2.1.4
Mechanical properties of a fastener
2.1.4.1 Tensile strength
The tensile strength of the fastener material (together with the diameter of the fastener)
determines the maximum clamp force which can be achieved in a bolted joint.
As described in section 2.3.1 the clamp force in the joint is generated by an elongation of
the section of the bolt, within the clamp length of the joint, during tightening (see Figs.
2.3 and 2.4). However, the assembly torque that is applied in order to rotate the bolt head
and elongate the bolt will generate both axial and torsional stresses in the bolt material,
as shown in Fig. 2.8. If the friction between the bolt and the female threads in the joint is
high during assembly, the torsional stresses will be high. The outer diameter of the bolt,
in the section within the clamp length of the joint, experiences the highest stresses (a
combination between axial and torsional stress) and yielding of the bolt material starts
here, if the combined stresses becomes too high during assembly. As soon as the
assembly torque is removed, the majority of the torsional stresses disappear (with the
exception for bolts with very long clamp length).
Figure 2.8 Stresses
in a fastener during
tightening, redrawn
after ref. [4].
Tightening a fastener to a point close to or over the ultimate tensile strength of the
fastener should be avoided as this will lead to changes of the thread pitch (of the threads
37
which are present in the clamp length section of the bolt), work hardening of the material
in the clamp length section of the bolt, possible necking of the bolt and the risk of
elongating the bolt beyond the design of the joint. With respect to the strenght of the
joint, once the yield point of the bolt material is reached, extended deformation of the
bolt will only lead to a marginal increase of clamp force. A high yield point in relation to
the ultimate tensile strength is therefore preferred, as this will make it possible to achieve
a higher clamp force without deforming the bolt plastically.
2.1.4.2 Stiffness
The stiffness of the bolt (in relation to the stiffness of the clamped parts) will determine
how the external forces are distributed in the bolted joint. A low bolt stiffness compared
to the stiffness of the clamped parts is desirable as this will generate a small Φ according
to Eq. 2.7 and therefore limit the distribution of external forces into the bolt. If a smaller
portion of the external loads is distributed into the bolt, the fatigue life of the bolt will
improve, since the amplitude of the dynamic load is reduced.
In addition to low material stiffness, a long clamp length of the fastener is
desirable as this reduces the stiffness of the bolt itself according to Eq. 2.3. A long clamp
length will furthermore enable a longer distance that can be elongated elastically, thereby
making the joint more robust for settlements (see Fig. 2.7).
2.1.4.3 Toughness
The toughness of a fastener material can affect both impact behavior and fatigue life of a
bolted joint. Engine fasteners are in most cases subjected to dynamical loading from the
rotation speed of the engine, as well as vibrations from driving conditions. High toughness
is therefore desirable, as this can improve fatigue life.
Furthermore, the fastener material needs to have a high impact toughness, in order to be
able to absorb large amounts of energy during loading peaks originating from driving
conditions (pot holes in the road) or in the worst case during crash.
In addition to this, high toughness of the fastener material will contribute to improved
resistance to hydrogen embrittlement, which might occur in service environments that
can generate hydrogen (such as corrosion).
2.1.4.4 Creep
The result of creep of a fastener material during service is a reduction of the clamp force
of the joint. The decrease will manifest itself as a settlement, as described in section
2.1.3.3. High creep resistance of fastener materials is therefore desirable. As the clamp
length of a joint seldom changes during service (with the exception of high temperature
joints, where thermal expansion of all components will change the conditions), creep of
fastener materials will lead to stress relaxation (stress relief under constant strain).
2.1.5
Choice of fastener material
Several factors have to be taken into account when a material is chosen for a specific
fastener. The factors are typically (i) standards and customer demands, (ii) price, (iii)
availability as raw material wire and (iv) tradition. The most commonly applied standards
for the choice of fastener materials within the European automotive industry are listed in
the international ISO and DIN standardization systems. The ISO and DIN standards set
restrictions to the mechanical properties, the chemical composition, the microstructure
and the heat-treatment process for the production of the fastener.
2.1.5.1 Current high strength fasteners
The majority of all high-strength fasteners used within the European automotive industry
are defined according to the standard ISO 898-1 (screws) [5]. ISO898-1 covers fasteners
with a nominal strength ranging up to 1200 MPa, so called grade 12.9 (screws). The first
number in the grade name indicates the ultimate tensile strength Rm (in multiples of 100
MPa) and the second digit expresses the yield strength Rp0,2 (as expressed in 1/10
fractions of Rm). In the case of the example: Rp0,2 = 0.9 Rm. The ISO898-1 standard
recommends a maximum service temperature of 150°C. The ISO system furthermore
stipulates that high-strength fasteners grades (Rm≥800 MPa) should be made from carbon
steel, boron-alloyed carbon steel or alloyed steel (typically alloyed with Cr). The
microstructure of the fastener should be tempered martensite. Fasteners are typically
produced via cold forming from a well annealed (ferritic/perlitic or spheroidized) wire and
thereafter heat treated to attain the final mechanical properties and microstructure of
the fastener product.
Table 2.1 shows the ISO898-1 demands on chemical composition for high strength
fasteners. The fastener manufacturers are free to choose any steel that fulfills the
requirements related to the concentrations of the chemical elements C, P, S and B and
that fulfils the requirements related to the mechanical properties after a quench and
temper treatment using a minimum tempering temperature of 425°C.
The demands of table 2.1 allow for a large variety of steels to be applied, and different
fastener manufacturers apply different steels, based on price, tradition, availability (as
wire) and possibly customer specific demands.
39
Table 2.1 Steel chemistry for 8.8, 10.9 and 12.9 grade fasteners according to ISO898-1 [5]
Property
Class
Material and
heat
treatment
8.8f
Carbon steel
with additives
(e.g Boron or
Mn or Cr)
quenched and
tempered
Carbon steel
quenched and
tempered
Alloy steel
quenched and
temperedg
Carbon steel
with additives
(e.g. Boron or
Mn or Cr)
quenched and
tempered
Carbon steel
quenched and
tempered
Alloy steel
quenched and
temperedg
Alloy steel
quenched and
temperedg
10.9f
12.9f,h,i
E
F
G
H
I
Chemical composition limits (cast analysis, wt.%)
C
P
S
B
min
max
max
max
max
0.15e
0.40
0.025
0.025
0.25
0.55
0.025
0.025
0.20
0.55
0.025
0.025
0.20e
0.55
0.025
0.025
0.25
0.55
0.025
0.025
0.20
0.55
0.025
0.025
0.30
0,50
0.025
0.025
Tempering
Temperature
˚C
min
0.003
425
0.003
425
0.003
425
In case of plain carbon boron steel with a carbon content below 0,25% (cast analysis), the minimum
manganese content shall be 0,6% for property class 8.8 and 0,7% for 10.9
For the materials of these property classes, there shall be sufficient hardenability to ensure a structure
consisting of approximately 90% martensite in the core of the threaded sections for the fasteners in the “ashardened” condition before tempering.
This alloy steel shall contain at least one of the following elements in the minimum quantity given: chromium
0,30%, nickel 0,30%, molybdenum 0,20%, vanadium 0,10%. Where elements are specified in combinations of
two, three or four and have alloy contents less than those given above, the limit value to be applied for steel
class determination is 70% of the sum of the individual limits shown above for the two, three or four elements
concerned.
A metallographically detectable white phosphorus layer is not permitted for property class 12.9. It shall be
detected by a suitable test method
Caution is advised when the use of property class 12.9 is considered. The capability of the fastener
manufacturer, the service conditions and the wrenching methods should be considered. Environments may
cause stress corrosion cracking of fasteners as processed as well as those coated
Literature also lists some steels for ultra-high tensile strength fasteners (Rm >1400 MPa)
like the W.nr steel 1.7783, 1.6359 and 1.4534 [6]. These materials are at present not
applied for high volume serial production due to high price of the raw material and poor
formability in cold forging.
2.1.5.2 Current high temperature fasteners
The high temperature fasteners that are approved for use by the European automotive
industry are defined according to DIN EN10269 [7]. This standard lists several types of
metals: alloy steels, stainless steels of austenitic and martensitic structures and nickel
based alloys. DIN ISO 10269 specifies the chemical composition, the heat treatment
process parameters and the mechanical properties of the fastener. However, due to high
raw material prices and poor availability of the metals in DIN ISO 10269 as wire, only a
few of the listed metals are found in high volume automotive applications. The high
temperature metals commonly have limited formability in cold forging and require heat
treatments that are time consuming and expensive.
Table 2.2 lists the few high temperature metals that are commercially available as
fasteners and commonly used within the automotive industry.
Table 2.2 Common high temperature fastener materials
Material
1.7709
1.7711
1.4923
1.4980
2.4952
21CrMoV5-7
40CrMoV4-6
X22CrMoV12-1
X6NiCrTiMoVB25-15-2
NiCr20TiAl
Microstructure
components
Ferrite/martensite
Ferrite/martensite
Martensite
Austenite
Austenite (Nickel base)
41
Service temperature range
Up to 500°C
Up to 500°C
Range 500-550°C
Up to 700°C
Up to 1000°C
2.2 Strength and temperature resistance of metals
2.2.1
Introduction
This section is written to give an introduction to the strength and temperature resistance
of metals. Section 2.2.2 gives the definition of strength and temperature of metals.
Section 2.2.3 is related to dislocations and dislocation movement. The concept of
dislocations is explained and the mechanisms behind different types of dislocation
movement are laid out. In section 2.2.4, the link between dislocations and the strength of
metals is examined and the different microstructure components that contribute to the
strength are reviewed in separate sub-sections. The strengthening mechanism behind
each microstructural component is discussed and equations for the quantification of the
strengthening effect, together with literature values related to steel are given. Each
subsection ends with a brief statement of the influence that elevated temperatures have
on each microstructure component. Section 2.2.5 is related to the phenomena of creep.
Creep is the time-dependent and permanent deformation of a metal under external
loading. The mechanical behavior during the different stages of creep is discussed.
Thereafter, the microstructural mechanisms underlying creep are discussed.
Subsequently, expressions are given for the different mechanisms of creep. Section 2.2.5
ends with a description of the different methods to measure creep, with special focus on
the indentation creep method, since this method was used within the research of this
PhD study.
2.2.2
Definitions of strength and temperature resistance of metals
The strength of a metal can be defined as the ability to withstand deformation during
exposure to external mechanical load. Deformation of metals can be divided into two
different stages: (i) Elastic deformation in which the material returns to its original shape
in case the external load is removed and (ii) plastic deformation, in which the shape of
the material is permanently changed [8], see Fig. 2.9. Elastic deformation of metals is the
result of the stretching of atomic bonds (without the breaking and forming of atomic
bonds) and reversible dislocation motion. Plastic deformation of metals is the result of
breaking and re-forming of bonds via the movement of dislocations.
Figure 2.9 Schematic drawing of the engineering stress-strain curve of a metal as measured
during tensile testing, which show two important stages of deformation: elastic and plastic
deformation. In practice, the proportional limit, which indicates the transition from elastic to
plastic deformation, might be difficult to determine. Therefore the yield strength (Rp0.2) is defined
as the stress required to produce a plastic strain of 0.2%. The (ultimate) tensile strength (Rm) is
the maximum engineering stress, in tension, that may be sustained without fracture.
The proportional limit of a metal is the stress at which elastic deformation changes into
plastic deformation. For most engineering applications the strength of a metal reflects
the resistance to plastic deformation and the yield strength therefore is the central
characterization of material strength. Also the hardness of a metal is an indication of a
metal’s resistance to plastic deformation. Strength and hardness are therefore
considered as proportional within this thesis [8].
The temperature resistance of a metal can be defined as the ability of the metal to
withstand plastic deformation and oxidation at elevated temperatures. The oxidation
resistance of metals at elevated temperatures falls outside the scope of this thesis,
because fasteners made out of steel can be coated to avoid oxidation. It is important to
consider the temperature resistance of steel for fasteners, because engine fasteners are
used at elevated temperatures.
Plastic deformation of metals due to an external load at elevated temperatures can take
place quickly after applying the external load or can take place a long time after applying
the external load. In the former case, the external load has to exceed the yield strength
of the metal at elevated temperatures before plastic deformation takes place at relatively
short time scales. In the former case it is important to know how the yield strength of the
metal decreases with increasing temperature. In general, the yield strength ratio, i.e. the
43
yield strength Rp0.2(T) at temperature T divided by the yield strength Rp0.2(25°C) at room
temperature, will change with temperature, as schematically shown in Fig. 2.10(a).
In the latter case, creep is the dominant mechanism by which plastic deformation takes
place. Creep is the time-dependent plastic deformation of a metal when subjected to a
load or stress that can be lower than the yield stress, which typically takes place at
elevated temperature. Figure 2.10(b) schematically shows the evolution of the strain of a
metal as a function of time during creep at elevated temperature. The ability of a metal
to withstand plastic deformation is directly related to the microstructure of the metal. In
case that heating the metal to elevated temperatures leads to changes in the
strengthening components of the microstructure, the strength of the metal is affected.
Figure 2.10 The effect of temperature on a) the yield strength and b) the creep behavior during
constant load and temperature exposure.
2.2.3
Dislocations and dislocation movements
This section is mainly based on Ref. [9]. Plastic deformation of a metal takes place via the
motion of dislocations in response to an applied shear stress. A dislocation is a linear
crystallographic defect in the metal lattice, around which there is atomic distortion. The
magnitude and direction of the lattice misalignment that is caused by the presence of a
dislocation is commonly called the Burgers vector, b. The Burgers vector can be found by
following the lattice in a square around the dislocation, as illustrated in Fig. 2.11. When a
square in a dislocation-free lattice is investigated each parallel side of the square has an
equal number of lattice steps. However, when a dislocation is present in the lattice (right
pane), one of two parallel sides of the square will contain one extra lattice site. The length
of this extra step is the magnitude of the Burgers vector, and the direction of the extra
step is the direction of the burgers vector, see Fig. 2.11.
Figure 2.11 Burgers vectors illustrated for an edge dislocation, redrawn after [9]
Dislocations can be of three types; (i) edge, (ii) screw, and (iii) mixed dislocations.
Dislocations are present in all metals and form during solidification and solid-to-solid
phase transformations. During plastic deformation of metals the dislocation density
strongly increases.
Figure 2.12 Edge dislocation (left) and screw dislocation (right)
Dislocation movement in a lattice is illustrated for an edge dislocation in Fig. 2.13. The
force that is required to move the dislocation through the lattice is significantly lower
than the force that would be required to move the entire plane of atoms over the adjacent
plane over an interatomic distance. This is why deformation occurs via movement of
dislocations and at a much lower stress than the theoretical strength of a perfect crystal.
As the dislocations move, the material is plastically deformed.
45
Figure 2.13 Movement of an edge dislocation, redrawn after [8]
Dislocation movements can be of two types; (i) glide (also called slide) or (ii) climb.
Dislocation glide is a dislocation movement which takes place along a slip plane of the
host lattice and along a slip direction. The combination of slip plane and direction is
commonly referred to as a slip system.
Cross-slip is a type of glide movement, where the dislocation changes direction
from one slip plane into another slip plane (still moving along the slip planes). As there
are only a limited number of slip systems available within a lattice, the number of possible
dislocation glide movements is restricted. Note that different lattice types contain a
different number of available slip systems.
Dislocation climb is a movement where the dislocation moves out of the slip plane
of the host lattice, atom by atom. This migration outside the slip plane requires the
presence of vacancies in the host lattice. Climb is a thermally activated process and can
allow dislocations to circumvent obstacles. Climb primarily takes place at elevated
temperatures as the number of vacancies and the atomic mobility is increased at elevated
temperatures.
2.2.4
The microstructural components that strengthen metals
All dislocations are surrounded by small strain fields, as illustrated in Fig. 2.14. These
dislocation strain fields can interact with other strain fields that might be present in the
lattice.
Figure 2.14 Strain field surrounding a dislocation
The interactions between different strain fields that might be present in the lattice and
the dislocation strain fields commonly lead to reduced dislocation mobility. As described
previously, the yield strength of metals is related to the stress that is required to move
dislocations through the lattice. This stress can be described according to the general
expression:
𝜎𝑦 ∝
𝑀𝐺𝑏
𝐿
Equation 2.10
,
where M is the Taylor factor, L is the distance between pinning points in the lattice, G is
the shear modulus and b is the Burgers vector. Pinning can be due to interacting stress
fields or, in general, due to obstacles. The most common interaction between dislocations
and microstructure features which result in reduced dislocation mobility are called the
strengthening mechanisms of metals [8].
The total strength of a metal at ambient temperatures is built up from contributions from
five microstructure components; (i) the lattice friction, 𝜎𝑙 , (ii) solid solution strengthening,
𝜎𝑠𝑠 , (iii) grain boundary strengthening, 𝜎𝑔𝑏 , (iv) dislocation strengthening, 𝜎𝑑 and (v)
precipitation strengthening 𝜎𝑝 . The last four components involve strengthening of the
metal by providing obstacles for the motion of dislocations and are commonly referred
to as the strengthening or hardening mechanisms of metals.
There are several methods for expressing the interaction and superposition of the
different microstructure components to the total strength of metals. The most simple and
common method is linear superposition: the total strength is a linear addition of all
microstructure components. The linear superposition can be expressed as [10]:
𝜎𝑡𝑜𝑡 = 𝜎𝑙 + 𝜎𝑠𝑠 + 𝜎𝑔𝑏 + 𝜎𝑑 + 𝜎𝑝
Equation 2.11
These 5 microstructural components are discussed separately in next sections.
47
2.2.4.1 Lattice friction
The lattice friction characterizes the force which is needed for glide movement of a
dislocation along one slip-plane. This force is called the Peierls-Nabarro force and is
representative for a pure crystal without any additional strengthening mechanisms [11].
The lattice friction depends on the atomic bonding energy between neighboring atoms in
the lattice. The bonding energy is the energy required to separate two atoms that are
chemically bonded to each other. The lattice friction can be regarded as the intrinsic
strength of a metal.
The lattice friction of a metal is affected at increased temperature via a reduction of in
atomic bonding energy. Rising the temperature of a metal leads to increased vibrations
and increased vibrational energy of the atoms in the lattice. In case the temperature of a
metal rises, the mean distance between the atoms increases and the bonding energy
between the atoms decreases. A decrease in the bonding energy decreases the lattice
friction, which means that the intrinsic strength of the metal is reduced.
The binding energy between atoms is an intrinsic property of the metal. The
reduction in the intrinsic strength of a metal due to an increase of the temperature cannot
be prevented. However, the effect is reversible: reducing the temperature will lead to an
increase in the intrinsic strength of the metal.
2.2.4.2 Solid solution
Solid solution is the solution of solute atoms into a solvent host lattice, in the solid state.
In metals the solute atoms are commonly referred to as impurity atoms or alloy atoms.
The position of the solute atom in the host lattice depends on the atom sizes. If the solute
atom is small in comparison to the host lattice atom type, the solute atoms fit into
interstitial positions, according to Fig. 2.15(a). If the solute atoms are similar in size, or
larger, in comparison to the host lattice the solute atoms take substitutional positions,
according to Fig. 2.15(b).
Figure 2.15 Solid solution by (a) interstitial elements and (b) by substitution elements.
The strengthening mechanism of solid solution stems from the local strain fields which
form around the solute atoms. These strain fields are caused by (i) the difference in atom
size comparing foreign atom and host atoms, including the interstitial atoms being larger
than voids, and (ii) the differences in bonding characteristics comparing host-to-host
atom bonds and host-to-solute atom bonds [12]. The strain fields around the solute atoms
interact with dislocations and reduces the dislocation mobility.
The strength increase which can be achieved from solid solution in metals depends on
the atomic characteristics and concentration of the solute atoms. Solid solution
strengthening can be expressed as a simple additive power law [13]:
𝜎𝑠𝑠 = ∑𝑖 𝐾𝑖 ∙ (𝐶𝑖 )𝑛𝑠 ,
Equation 2.12
where Ki is a proportionality constant for element i, Ci is the concentration of element i
and ns usually ranges between 1/3 and 2.
The solid solution strengthening of low concentrations of alloy elements in steel (bcc
ferrite structure) is commonly assumed to be approximately linear, ns=1, at low
concentrations [14]. The strengthening effects of several alloying elements is
schematically represented in Fig. 2.16. Note that interstitial elements C, N and P are more
effective than the substitutional elements
Figure 2.16 Solid solution
strengthening by alloy
elements in steel [14]
Solid solution strengthening is affected at increased temperature via increased diffusivity.
Diffusivity describes the mobility of atoms. The diffusivity can also be called the diffusion
coefficient, and is given the SI unit m2/s. The increase in diffusivity at elevated
temperatures can be described according to [15]:
49
𝐷 = 𝐷0 exp (
−𝑄𝐷
𝑘𝑇
),
Equation 2.13
where 𝐷0 is the pre-exponential factor, QD is the activation energy for diffusion, k is
Boltzmann’s constant and T is the temperature. Increased diffusivity of solute atoms at
elevated temperature leads to higher mobility of the solute atoms than of the dislocations,
with the result that the solute atoms no longer restrict the mobility of the dislocations
[16].
Diffusion is a time dependent process that can lead to both irreversible and reversible
yield strength loss. When the increased temperature is reduced again, the mobility of
solute atoms is also reduced, and the solute atoms go back to contribute to solid solution
strengthening. However, solute atoms that segregate into grain boundaries or lattice
defects such as interphases of precipitates, cause an irreversible yield strength loss.
Increased diffusion can in some specific cases lead to increased solid solution
strengthening. Interstitial solute atoms, such as carbon and nitrogen in steel, can diffuse
to dislocations in order to relax their solute strain field and the dislocation strain field.
This is called a Cottrell atmosphere. The effect of a Cottrell atmosphere is reduced
dislocation mobility because the solute atoms in the Cottrell atmosphere increase their
energy when the dislocation moves away. The phenomenon of decreased dislocation
mobility due to Cottrell atmospheres is called strain ageing [17]. Strain ageing is
particularly marked in mild steel and soft iron.
Strain ageing is time- and strain dependent [18]. The rate of strain ageing depends
on the migration rate of the solute atoms to the dislocation. The ageing temperatures
which normally are involved in strain ageing vary for different metals; e.g. austenitic
stainless steel show strain ageing due to carbon and nitrogen atoms in the temperature
range of 200-600°C [19].
2.2.4.3 Grain boundaries
A grain boundary is the interface between neighboring crystals of the same crystal
structure but varying crystallographic orientations (each crystal is called a grain). Grain
boundaries can be sub-divided in several ways, where the coarsest subdivision is into two
categories: (i) low angle grain boundaries and (ii) high angle grain boundaries. The angle
refers to the crystallographic mis-orientation between the neighboring grains. The
distinction between low and high angle is usually drawn at 15°. Low-angle grain
boundaries are made up of rows of dislocations, as for an example shown in Fig. 2.17 for
a tilt boundary. Early theories suggested that high-angle grain boundaries consisted of a
thin disordered layer, but now it is known that these boundaries consist of regions of good
and bat matching between the two grains. This theory is known as the concept of the
coincidence site lattice (CSL). The coincident site lattice (CSL) theory considers the fit of
the outermost atom layer of two neighboring grains. This theory is based on counting the
fraction of lattice sites which coincide between the two lattices of the neighboring grains.
A boundary that contains a high density of lattice points in a CSL has a good atomic fit.
Figure 2.17 A tilt
boundary, which is a
type of low angle grain
boundary consisting of
misfit dislocations
Grain boundaries act as barriers to dislocation motion for two reasons: (i) there is a
change in the direction of the slip planes at the grain boundary between two neighboring
grains according, as illustrated in Fig. 2.18, and (ii) there is a discontinuity between the
slip planes of the two neighboring grains. In the case of high angle grain boundaries, the
dislocations tend to ‘pile’ up at the grain boundaries, which introduces stress
concentrations ahead of their slip planes. This generates new dislocation in the adjacent
grains.
Figure 2.18
Neighboring grains
which have different
orientation of slip
plane.
51
The strength increase which can be achieved via grain boundary strengthening depends
on the grain size and is commonly estimated via the empirical Hall-Petch equation [2021]:
𝜎𝑔𝑏 = 𝑘𝐷 ∙ 𝑑𝑔 −1⁄2 ,
Equation 2.14
where 𝑑𝑔 is the grain size and kD is the strengthening coefficient (Hall-Petch term). The
strengthening coefficient is different for different metals. The strengthening coefficient
kD for micro-alloyed steel varies, but is often found to be consistent within the range of
17.4 to 23.5 MPa mm-1/2 [14, 22].
Grain boundary strengthening is affected at increased temperature via grain coarsening.
Grain coarsening involves the migration of grain boundaries. The driving force for grain
coarsening is the reduction of the total grain boundary energy in the metal. It is common
that high energy grain boundaries have a higher mobility than low energy grain
boundaries and therefore enable faster coarsening. Grain coarsening leads to a reduction
of the grain boundary strengthening contribution, since grain coarsening results in
increased mean grain sizes.
Grain coarsening is a time dependent process that leads to irreversible yield
strength loss. When the temperature is reduced, the yield strength is permanently
reduced. The rate at which grain coarsening takes place depends on the temperature, the
type of grain boundaries (e.g. low-angle or high-angle grain boundaries), the composition
of the metal and the density of obstacles for grain boundary migration. It is possible to
reduce the rate of grain coarsening via solute atoms and via precipitates of a second
phase. Certain solute atoms (impurities as well as alloying elements) can segregate to
grain boundaries, in order to reduce their energy. The segregation leads to a higher solute
concentration in and around the grain boundaries. Locally higher concentrations of solute
atoms reduce the grain boundary mobility since motion of the grain boundary increase
the energy of the solute atom cloud (similar to strain ageing). The phenomenon is related
to solute drag [23-24]. Precipitates in a metal can reduce, or even stop, grain coarsening,
as the precipitates can exert a pinning effect on the boundary [25]. However, if coarsening
of precipitates takes place this will lead to less efficient pinning of grain boundaries and
continued grain coarsening.
2.2.4.4 Dislocations
The strain fields which surround a dislocation can interact with the strain fields of
neighboring dislocations. This interaction between dislocations can lead to dislocations
repelling each other or attracting each other, depending on their Burgers vectors. If two
dislocations of the similar Burgers vector approach each other, they repel each other,
which reduces dislocation mobility. Furthermore, intersecting dislocations can pin each
other.
The strength increase which can be achieved via dislocation strengthening, 𝜎𝑑 , depends
on the dislocation density and can be expressed according to Bailey-Hirsch [26] by:
𝜎𝑑 = 𝑀𝛼𝐺𝑏 ∙ 𝜌1⁄2 ,
Equation 2.15
where 𝛼 is an empirical parameter and ρ is the dislocation density. The parameter 𝛼
varies from 0.05 to 1.2 [9, 22, 27].
In case of work hardening the metal is strengthen by the accumulation of dislocations,
which are generated by plastic deformation. Metals therefore become harder/stronger
when they are plastically deformed, hence the name work hardening.
Dislocation strengthening is affected at increasing temperature via recovery and
recrystallization. Recovery is the term for the combined processes of (i) annihilation of
dislocations of opposite signs acc. to Fig. 2.19(a)-(b), (ii) annihilation of single dislocations
by migration to grain boundaries and (iii) rearrangement of dislocations of similar signs
into polygonized structures acc. to Fig. 2.19(b)-(c). A polygonized dislocation structure is
a low energy structure where dislocations are arranged into relatively stable arrays.
Recovery reduces the mechanism of dislocation strengthening due to that recovery
reduces the dislocation density. Recovery is a time dependent process that leads to
irreversible yield strength loss. The rate of recovery depends on the temperature and on
the density of pinning points for dislocation movements. It is possible to reduce the rate
of recovery via precipitates of a second phase, which can pin dislocations and prevent
them from moving.
53
Figure 2.19 Strained lattice
showing slip planes as lines
and dislocations (a) before
recovery, (b) after
annihilation and (c) after
polygonization
Recrystallization is the formation of new grains, with the same phase as the parent phase,
in cold worked or strained metals. Recrystallization results in roughly equi-axed grains
with a low dislocation density. Recrystallization is a slower process than recovery and
typically requires a higher temperature to start. The two processes can interact, since
recovery affect the dislocation density, which constitutes the driving force for
recrystallization. Recrystallization reduces the mechanism of dislocation strengthening
since recrystallization reduces the dislocation density. Recrystallization can also affect the
contribution of grain boundary strengthening, if the new grains are of a different size than
the parent grains. Recrystallization is a time dependent process that leads to an
irreversible yield strength loss. The rate of recrystallization depends on the temperature
and the strain level in the metal.
2.2.4.5 Precipitates
A precipitate is a particle of a second phase, 𝛽 , inside a host lattice, phase α. The
strengthening mechanism of precipitates originates from small precipitates that are
located on the slip plane of a dislocation and that act as obstacles, or pinning points for
dislocations. The dislocation will need extra force to bypass by the precipitate, which
reduces the dislocation mobility.
The strength contribution of precipitates depends on the volume fraction of precipitates
in the lattice, the precipitate size, the precipitate strength and the interface between the
precipitate and the matrix. There are several expressions for calculating precipitation
strengthening. One of the most common expressions used for steel is the Orowan-Ashby
relationship [28]:
𝜎𝑝 = (
0.538𝐺𝑏𝑓1⁄2
𝑑𝑝
𝑑
) 𝑙𝑛 (2𝑏𝑝 ),
Equation 2.16
where f is the volume fraction of precipitate phase and 𝑑𝑝 is the diameter of the
precipitates. This expression was originally derived for incoherent particles, but has
shown good correlation also to coherent particles in steel [28].
There are three major mechanisms by which a dislocation can bypass a precipitate; (i)
particle cutting (shearing), (ii) local climbing and (iii) Orowan looping [29].
i.
Dislocation bypass of precipitates via cutting means that the dislocation travels
through the precipitate. Dislocation cutting takes place when the precipitate is
soft or small and has a slip plane which fits to the matrix slip plane. The
strengthening effect of cutting is commonly called chemical hardening. The
increase in force that is needed for the dislocation to cut the precipitate origins
from two different phenomena: (i) the particle/matrix interface area is increased
by the cutting of the particle according to Fig. 2.20, and/or (ii) an anti-phase
boundary or a stacking fault is created inside the precipitate by the dislocation
passage. A different lattice friction within precipitate will also affect the cutting
process.
Figure 2.20 Dislocation passage via cutting, redrawn after [29]
ii.
Dislocation bypass of precipitates via local climb means that the section of the
dislocation that is closest to the precipitate moves out of the slip plane, by climb,
and surmounts the precipitate as illustrated in Fig. 2.21 [30]. Climb mainly takes
place at elevated temperatures and is discussed in more detail later in the section.
Figure 2.21 Bypassing of
particle via local climb,
redrawn after [29]
55
iii.
The process of Orowan looping begins with the dislocation bowing around a
precipitate in the slip plane. As the bowing of the dislocation around the
precipitate increases the dislocation can finally leave a closed loop behind [31] as
illustrated in Fig 2.22. Orowan looping takes place when the slip plane of the
matrix is not extended into the precipitate and when the precipitate is too hard to
cut.
Figure 2.22 Orowan
looping around a
precipitate, redrawn
after [29].
The strengthening effect of Orowan looping stems from the increase in dislocation
line length from the bowing itself, and from the remaining loop around the
precipitates. Orowan looping can therefore be said to lead to localized dislocation
strengthening.
Precipitation strengthening is affected at increased temperature by the presence of
vacancies and by the coarsening of precipitates. An increased density of vacancies in the
lattice reduces the effectiveness of precipitation strengthening since vacancies make
dislocation climb possible [30]. A vacancy is a point defect, consisting of one vacant lattice
site. The density of vacancies in a metal lattice is increased at elevated temperature
according to [15]:
𝑋𝑉𝑒 = 𝑒𝑥𝑝 (
−∆𝐺𝑉
𝑅𝑇
),
Equation 2.17
where 𝑋𝑉𝑒 is the mole fraction of vacancies, ∆𝐺𝑉 is the formation energy of vacancies and
R is the universal gas constant.
Dislocation climb is a time-dependent process that can lead to both reversible and
irreversible yield strength loss. If dislocation climb leads to recovery, the yield strength
loss becomes permanent. However, dislocation climb as a mechanism to bypass an
obstacle is reversibly dependent on the temperature since the number of vacancies in the
lattice is reversible with temperature, and will reduce when the temperature is reduced.
The rate of dislocation climb depends on the temperature, since the temperature affects
the density of vacancies and the diffusional jump frequency.
Coarsening of precipitates leads to a reduction in the number density of precipitates and
to larger precipitate sizes. Coarsening of precipitates is accelerated for precipitates when
(i) the solute atoms (from which the precipitate form) have high solubility in the matrix,
(ii) the interface energy between matrix and precipitate is high and/or (iii) the diffusivity
of the solute atoms from the matrix to the precipitate is high. Coarsening of precipitates
leads to a reduction of the precipitate strengthening, since a reduced number density of
precipitates implies increased pinning distance, L.
Precipitate coarsening is a time dependent process that leads to irreversible yield
strength loss. The rate of precipitate coarsening can be controlled via alloy design to
achieve a thermally stable dispersion of precipitates based on precipitate elements that
have low solubility in the matrix of the metal, precipitates that have a low interface energy
to the matrix and precipitate elements with low diffusivity in the matrix.
2.2.5
Creep
Creep is the time-dependent and permanent deformation of a material, at a stress, which
is lower than the yield stress. Creep becomes important at temperature of 0.4Tm, in which
Tm is the melting temperature, for metals. Elastic and plastic deformation, as discussed in
section 2.2.2, are the time independent responses to mechanical loading, whereas creep
can be described as the viscoplastic, time-dependent response to loading. Section 2.2.5
(with the exception of 2.2.5.4) is mainly based on the book by F.R.N. Nabarro [32].
2.2.5.1 Stages of creep
Creep can be divided into three different regions; (i) primary creep, (ii) secondary creep
and (iii) tertiary creep, as illustrated in Fig. 2.23.
Figure 2.23 The
three stages of
creep in metals. The
time scale depends
on the stress and
the temperature
and can be
measured in years.
Primary creep is the first stage of creep. Primary creep is characterized by an initially high
strain rate, which decreases with increasing time. When the strain rate stabilizes, at the
minimum rate, the secondary creep stage has begun. The secondary creep stage is
57
characterized by nearly constant strain rate (at constant temperature and stress) and
secondary creep is therefore commonly referred to as steady-state creep. Creep
parameters are usually extracted from the secondary creep stage. Tertiary creep is the
last stage of creep. Tertiary creep is characterized by increasing strain rate and void
formation followed by fracture of the material.
The creep rate of a material depends on the temperature, the loading level and
the creep stage. Higher temperatures and higher load levels typically result in higher
strain rates. Expressions for the creep rate are given in section 2.2.5.3.
2.2.5.2 Mechanisms of creep
The microstructural processes that cause creep are commonly referred to as mechanisms
of creep [33]. The main mechanisms of creep are (i) dislocation movements, (ii) diffusion,
(iii) grain boundary sliding and (iv) recrystallization. The time scale and the temperature
for these four types of creeps are different.
The creep mechanisms can be summarized into so called deformation mechanisms maps.
Deformation maps show which creep mechanism is dominant for a specific homologous
temperature, 𝑇⁄𝑇𝑀 , (where 𝑇𝑀 is the melting temperature of the metal), and normalized
stress, 𝜎⁄𝐺 , (where G is the shear modulus). Iso-strain rates lines are represented in the
maps. Fig. 2.24, shows a general sketch of a deformation mechanism map for stainless
316 steel.
Figure 2.24 Schematic
representation of a
deformation
mechanism map of
stainless 316 steel
redrawn after [34].
2.2.5.2.1
Dislocation movements
Dislocation creep takes place due to increased dislocation mobility at increased
temperatures, according to all processes discussed in section 2.2.4, since the thermal
energy helps the dislocations to overcome obstacles. Dislocation creep is time-dependent
because the bypass mechanisms are time dependent. Dislocation creep can be reduced
via every microstructural feature that exerts a strong pinning effect on dislocations at
elevated temperatures. A common approach to create temperature resistant metals is to
create a fine dispersion of thermally stable precipitates [35]. Also solid solution
strengthening can be utilized to reduce dislocation creep.
2.2.5.2.2
Diffusion
Diffusion assisted creep takes place via the movement of vacancies. When vacancies
move, the atoms in the lattice move. Diffusion assisted creep is increased at elevated
temperature due to increased diffusivity and increased number of vacancies at elevated
temperatures, according to Eq. 2.13 and Eq. 2.17. The diffusive flow of vacancies results
in deposition of atoms at the grain boundaries. The atoms deposit at the grain boundaries
in order to relax the stress in the metal by changing the shape of the grain. Diffusion
assisted creep can be divided into two types depending on the path of the diffusive flow;
(i) Nabarro-Herring creep, during which diffusion occurs through the lattice and (ii) Coble
creep during which diffusion occurs via grain boundaries.
Figure 2.25 Diffusive
creep. Grey areas
symbolize regions
where atoms deposit.
Nabarro-Herring diffusion is dominant at low stress and high temperatures and Coble
creep (grain boundary diffusion) is increased by small grain sizes in a material. The most
59
common approach to minimize diffusional creep is to increase the grain size, in order to
reduce Coble creep.
2.2.5.2.3
Grain boundary sliding
Creep via grain boundary sliding takes place via sliding of individual grains past each other,
along the grain boundaries. When a polycrystalline material is externally loaded local
stress concentrations form at grain boundaries. Grain boundary sliding takes place
because of the bonding strength at the grain boundaries being lower than the bonding
strength in the grain interior. Furthermore, the local stress concentrations can result in
local plastic strain of the boundary regions, at loads that are smaller than required to
deform the metal at ambient temperature. Creep via grain boundary sliding can be
reduced by large grain sizes. Metals with large grains have lower density of grain
boundaries which can slide. However, creep properties due to grain boundary sliding also
depend on the so called grain aspect ratio (GAR). GAR is the ratio of grain dimension
parallel to the tensile stress direction and the grain dimension perpendicular to the tensile
stress direction. Creep strength is increased by high GAR.
2.2.5.2.4
Recrystallization
Dynamic recrystallization may take place during creep at relatively high strain rates and
temperatures [36]. Recrystallization takes place at higher temperatures than relevant for
this thesis and is therefore not discussed more in detail in this thesis.
2.2.5.3 Expressions for creep
The rate of creep in metals depends on the stress level, the temperature and time. In
addition to these three parameters, the creep rate also depends on the microstructure of
the metal and the creep stage. There are therefore many models for describing creep.
During the design of engineering components primary and secondary creep stages are
often the stages of most interest. Therefore are, as mentioned in section 2.2.5.1, creep
characteristics of metals commonly taken from the secondary, steady-state creep region.
The creep mechanisms of secondary creep can vary. However most models be
generalized according to [37-38]:
𝜀̇ = 𝐴
𝐷𝐺𝑏
𝑘𝑇
𝑏
𝑝
𝜎 𝑛
(𝑑 ) ( 𝐺 ) ,
𝑔
Equation 2.18
where A is a constant, D is the diffusivity (as given by Eq. 2.15), T is the absolute
temperature, 𝜎 is the applied stress and n and p are exponents of stress and grain size
respectively. Equation 2.18 is mainly used for describing creep that is related to the grain
size of a metal.
Creep via grain boundary sliding is described by p=2 and n=2 and using the lattice
diffusivity of the metal for D [39].
Diffusion assisted Nabarro-Herring creep is described by p=2 and n=1 and using
the lattice diffusivity of the metal for D [40-41].
Diffusion assisted Coble creep is described by p=3 and n=1 and using the grain
boundary diffusivity of the metal for D [42].
For creep mechanisms that are based on dislocation movements, the dependence on
grain size is not relevant (p=0), and secondary creep is commonly modelled according to:
𝑄
𝜀̇ = 𝐴𝑁 𝜎 𝑛 exp(− 𝑅𝑇𝐶 ),
Equation 2.19
where 𝐴𝑁 is a constant, n is called the Norton exponent (stress exponent) and QC is the
activation energy for the creep. Dislocation creep in pure metals is commonly described
by n≈5 [38].
2.2.5.4 Measurement of creep
When a metal specimen is externally loaded at an elevated temperature the metal
undergoes creep if the load and temperature are sufficiently high.
2.2.5.4.1
Uniaxial creep measurement
Uni-axial creep measurements are performed by monitoring the length of a material
specimen while the specimen is subjected to temperature and uni-axial loading. There
are two main methods for uni-axial creep testing, (i) measurement at constant load and
(ii) measurement at constant stress. The measured creep life is shorter in the constant
load test, since the stress in the material increases from the area reduction of the test
specimen. Before a uni-axial creep measurement starts, the unloaded test specimen is
heated to the test temperature and the initial gauge length is measured. The specimen is
thereafter loaded (quickly but without shock) and the extension of sample length is
measured at a frequent intervals during the remainder of the test. The test duration of a
uni-axial creep test is commonly 2000-10000 hours and the test is typically performed on
specimens of several centimetres in length.
2.2.5.4.2
Indentation creep measurement
This section is mainly based on Ref. [43]. When an indenter is pressed into a material, it
penetrates the material first by elastic and plastic deformation. If the loaded indenter is
allowed to reside on the material it will continue to penetrate the material via creep.
61
Indentation creep tests are done with a fine scale indenter that is pressed into the test
specimen, while the indent displacement is continuously monitored. Indentation creep
tests can be performed using constant load, constant strain rate, constant depth or
constant rate of loading. The most common method is constant-load testing. The test
duration of indentation creep test is commonly several minutes and the test can be
performed on specimens that are measured in millimetres or smaller.
Within the research presented in this thesis we use indentation creep to compare the
creep behaviour of different fastener steels. This comparison is based on the report that
indentation creep can be used to rank different materials to each other for a certain given
temperature and load [43]. We point out that at present there is no accepted, validated
method of analysing and interpreting indentation creep data. Indentation creep
measurement methods have been investigated since 1960 [44-45]. It has been shown that
several materials, including several metals, show good correlation between indentation
creep data and traditional uni-axial creep data when described via a steady-state power
law (Eq. 2.19) [46-49]. In the next section, the theory is presented that led to the
development of the indentation technique for creep measurements.
The link between indentation creep measurements and steady state power law creep
During an indentation experiment, stress and strain fields are generated in the deformed
zone under the indenter. The deformed zone under the indenter has an approximately
hemispherical shape. The theoretical arguments for using indentation measurements too
measure creep is based on the relation between the size of the deformed zone and the
depth of the indent
In 1970 Johnson [50] suggested that during indentation, the tip of the indenter is encased
in a core, according to Fig. 2.26. Inside the core the pressure is hydrostatic. Since there
are no shear stresses, and no chemical-potential gradients in the hydrostatic core, creep
does not take place within the hydrostatic core. Outside the hydrostatic core there is a
plastic-elastic hemispherical zone of a certain radius. Within the elastic-plastic
hemisphere the stress field ranges from high stresses, in the vicinity of the hydrostatic
core, to low stresses as the distance from the hydrostatic core is increased. Indentation
creep is assumed to take place within this elastic-plastic zone. Creep results in an
expansion of the elastic-plastic zone (the radius of the elastic-plastic zone increases)
which generates an expansion of the hydrostatic core as well. Creep therefore results in
further penetration of the indenter into the material.
When indentation experiments are performed with equipment that can monitor the
indent depth (the displacement) it is therefore possible to measure the evolution of the
material creep within the elastic-plastic hemisphere under the indenter of the tested.
Figure 2.26
Schematic
representation of the
hydrostatic core and
elastic-plastic zone
under an indenter, redrawn after [33]
The conversion of indentation displacement measurement data into creep is performed
in three steps; (i) definition of the characteristic stress, (ii) definition of the creep strain
rate and (iii) assuming that the creep follows a power law such as Eq. 2.19. Since there is
not a single value of the stress in the material under the indenter, a characteristic stress
must be defined. The characteristic value of the stress is commonly defined in a similar
manner as hardness is defined; the applied load, F, is divided by the cross section area of
the indenter at the depth of the indent (called the projected contact area, see Fig. 2.26),
Ap, rather than the actual contact surface area:
𝐹
𝜎𝐶 = 𝐴
Equation 2.20
𝑝
The projected area is related to the indent depth via the contact depth, hc which is the
depth of the indenter in contact with the sample under load according to [51]:
ℎ𝑐 = ℎ𝑚𝑎𝑥 − 𝑘′
𝑃𝑚𝑎𝑥
𝑆
Equation 2.21
,
where S is the contact stiffness, Pmax and hmax are the maximum applied load and the
penetration depth at maximum load respectively and k’ is a constant that depends on the
geometry of the indenter. Oliver and Pharr [52] derived the method to derive S from the
indentation measurement data, and the projected contact area of a Berkowitz indenter
(such as used within the research of this PhD thesis) is derived to be Ap=24,56hc2 [53].
The strain rate during indentation experiments is defined by Mayo and Nix [54] as:
1 𝑑ℎ
𝜀̇ = ℎ 𝑑𝑡
Equation 2.22
63
If the time-dependent plastic deformation of the material, as measured by the
displacement of the indenter, is generated by power-law creep, Eq. 2.19 applies.
The measured displacement is thereafter plotted as a function of time, according to Fig.
2.27. The creep parameters can be extracted by fitting Eq. 2.19 to the data.
Figure 2.27 Creep
parameters from
indentation
measurement
2.3
2.3.1
Precipitation strengthening of Martensite
Introduction
Martensite is the strongest and hardest microstructural constituent of steel. Tempered
martensite combines high strength with good toughness and is therefore the key
microstructure for high strength fasteners. New fastener steels have been developed
which are based on precipitation strengthening of the martensite via alloy carbides, to
increase the strength and the resistance to hydrogen related damage of the fastener.
These improvements of properties are based on a fine dispersion of alloy carbideprecipitates, which act like pinning points for dislocations and hinder dislocation motion.
A clear understanding of the relation between the microstructure, the strength and the
processing conditions that are needed to form alloy carbides in martensite is essential for
the development of fasteners out of these steels.
The formation, crystallography, and microstructure of martensite are described in
next two sections. The hardening mechanisms that contribute to the strength of
martensite are discussed in section 2.3.4. Section 2.3.5 describes the changes that take
place in the microstructure during tempering of martensite. Section 2.3.6 to 2.3.8 discuss
the thermodynamics and kinetics of the nucleation, growth and coarsening of precipitates
and section 2.3.9 describes the specific details related to the thermodynamics of the
nucleation and growth of TiC in martensite. The main content of sections 2.3.2-2.2.5 is
based on the book by Olsen and Owen [13] and the main content of section 2.3.9 is based
on the book by Porter and Easterling [15]
2.3.2
Formation of martensite in steel
Steel is iron with up to 2.14wt% carbon, and usually some other alloying elements. Steel
consists of an iron lattice with carbon atoms that are located at interstitial positions,
dislocations, interfaces or in carbides. The iron lattice can – at ambient temperatures –
be ordered in two different lattice structures under equilibrium conditions: (i) Bodycentered-cubic (BCC) which is referred to as ferrite (α-iron at low temperatures and 𝛿ferrite closer to the melting temperature) and (ii) face-centered-cubic (FCC), which is
referred to as austenite or ɣ-iron. Figure 2.28 shows the iron-carbon phase diagram,
which shows the equilibrium phases as a function of temperature and carbon
concentration. The Fe-C diagram is commonly shown with the meta-stable phase of
cementite (Fe3C). The maximum solubility of carbon in the austenite is approximately
100 times higher than in ferrite. Austenite can dissolve slightly more than 2 wt% of carbon,
whereas ferrite only can dissolve up to 0.02wt% carbon (depending on temperature). The
65
higher solubility of carbon in austenite than in ferrite makes it possibility to form a
martensitic microstructure in carbon steels.
Martensite is created via a rapid cooling from the austenite range (high temperature).
This rapid cooling is referred to as “quenching”. At the high temperature, all carbon atoms
can be in solid solution, due to the higher solubility of carbon in austenite. Quenching of
austenite transforms the FCC structure into the BCC (or BCT as will be explained in the
next section) structure. As the cooling is performed rapidly, there is no time for the carbon
atoms to diffuse and form carbides. The carbon atoms will therefore remain in the
positions of the former austenite phase (FCC) through the transformation from FCC to
BCC structure. The carbon atoms become trapped in the interstitial positions of the
parent FCC phase.
Figure 2.28 The Fe-C phase diagram showing the phases of ferrite (𝛼 𝑎𝑛𝑑 𝛿), austenite (𝛾). Fe3C
and liquid (L)
The exact mechanism behind the nucleation of martensite is not yet fully clarified.
However, once the nucleation barrier is overcome, the martensite crystals grow rapidly
(at almost the velocity of sound in steel) until they hit an obstacle, such as a former
austenite grain boundary. In 1924 Bain proposed that the martensite transformation is a
shear deformation, in which the FCC structure is transformed into BCC. Figure 2.29 shows
the crystallographic relationship between the FCC and the BCC structures. The BCC and
FCC crystal structures are related by rotating the horizontal axes, x and y to x’ and y’
around the vertical (z) axis of the parent FCC cell and by expanding the horizontal axes
[55].
Figure 2.29 Bain model of the FCC-to-BCC transformation. Iron atoms are shown as white circles
and the positions where carbon can be trapped in the resulting BCC structure are shown as dark
grey circle
The Bain model predicts that carbon atoms will be trapped in positions on the vertical axis
of the BCC unit cell of ferrite, turning it into a BCT unit cell (Body Centered Tetragonal).
Later research has, however, shown that the tetragonality of the BCT cell only appears in
martensite that contains more than 0,18 wt.%C (at RT). Martensite that contains less
carbon remains cubic [56]. The Bain model has not been experimentally confirmed and
cannot fully describe all the details of martensite transformation. However, the model
describes the general mechanism of martensite transformation in a concise way.
The martensite transformation is accomplished by a crystallographic misfit
between the growing martensite and the parent austenite lattice. The misfit results in
high shear stresses at the interface of the growing martensite crystals. Dislocations are
formed at the growing interface to accommodate for these stresses. A microstructure
that fully consists of martensite, therefore contains a high density of dislocations.
The cooling rate that is required to avoid the formation of ferrite and bainite, and
to form martensite depends on the chemical composition of the steel and the grain size
of the parent austenite phase. Steels that allow for a slow cooling rate, and yet achieve a
fully martensitic microstructure, are said to have good hardenability.
2.3.3
Crystallography of martensite
Martensite can exhibit several types of crystallographic aspects. These crystallographic
aspects depend on the chemical composition of the steel and the transformation process.
The most general classification is the differentiation between plate martensite and lath
67
martensite. Steel with a carbon concentration below 0.4 wt% typically form lath
martensite whereas steel with higher carbon concentration form plate martensite [5758]. The carbon concentration of high-strength fastener steels range from 0.15 wt% to
0.55 wt% [5]. This makes lath martensite the dominant martensite type found in engine
fasteners and the scope of this thesis therefore covers lath martensite. This thesis
therefore does not cover the formation mechanism and the details about twinned
martensite plates, although some of the fastener steels may contain small fractions of
this microstructure type.
The microstructure of lath martensite can be described in a hierarchical manner. The
largest constituent is the parent austenite grain structure. A single austenite grain is
divided into packets, which in turn are sub-divided into blocks. Each block is built up of
more or less parallel laths, according to Fig. 2.30 [59].
Figure 2.30 Microstructure
of martensite showing
former austenite grain
boundary, packets, blocks
and laths [59].
The formation of martensite take place along a so called habit plane of the parent
austenite phase [60]. A habit plane is a plane among which certain phenomena such as
twinning can occur. The habit plane is a crystallographic common plane that is common
to both the parent austenite and the martensite and that remains intact during the
martensite transformation. There is a special crystallographic orientation relationship (OR)
between the parent austenite grain and the product martensite.
Recent investigations by Morito et al have shown that the orientation relationship
between the martensite and the former austenite follows a near Kurdjumov-Sachs (K-S)
OR, [59, 61], which deviates with a few degrees from the Nishiyama-Wasserman (N-W)
OR. There are 24 and 12 different variants of the KN’ and NW orientation relationships,
respectively. This means that –for the KS OR – there are 24 different combinations of
parallel crystallographic planes and parallel crystallographic directions between the FCC
and the BCC lattices.
The possible misorientations between different crystallographic variants of the KS OR are
10.53˚, 14.88 ˚, 20.61˚, 21.06˚, 47.11˚, 49.47˚, 50.51˚, 51.73˚, 57.21˚ or 60.00˚ [62]. Morito
et al. furthermore measured that the packets in martensite in low carbon and alloy steel
contain blocks made of six of the ten possible variants. The reason why only 6 out of 10
possible variants form is not clear. The misorientation between martensite blocks ranges
from 10.53° to 60°, according to the variants described above. The block can therefore be
considered as the smallest effective ‘grain’ in lath martensite [63].The individual blocks
contain parallel laths. The parallel laths within one block are of the same variant. In case
of low carbon steels, the block can be further divided into two groups (sub-blocks) of laths
of two variants with the misorientation of about 10° [59]. The individual laths of
martensite are separated by walls of entangled dislocations at a distance of approx. 200
nm [64]. The misorientation between neighbouring laths is only a few degrees.
2.3.4
Strength of martensite
Solid solution strengthening, dislocation strengthening and grain size strengthening are
commonly listed as the main strengthening components of martensite [57]. However,
also precipitation strengthening via alloy carbides and/or small iron carbides can add to
the total strength of martensite.
2.3.4.1 Solid solution strengthening effect of carbon
Martensite can be considered as a ferrite matrix that is super-saturated with carbon
atoms. The carbon atoms are located at interstitial octahedral positions of the BCC/BCT
lattice or are segregated into lattice defects. Recent investigations have shown that after
quenching only approx. 0.02wt% of the carbon atoms are located in true interstitial solid
solution in the martensite matrix [65]. The majority of the carbon atoms are thus
segregating to lath boundaries and dislocations during quenching. The segregated carbon
atoms have however been shown to contribute to the strength of as-quenched
martensite to the same extent as true interstitial carbon atoms. The solid solution
strengthening of carbon in martensite can be expressed according to [57]:
⁄
𝜎𝑠𝑠 (𝑀𝑃𝑎) = 1720 ∙ 𝐶𝑐1 2 ,
Equation 2.23
where 𝐶𝑐 is the carbon concentration given in wt.%. The carbon concentration of the steel
furthermore influences the crystallography and the dislocation density of the martensite,
as higher carbon concentration results in smaller packet and block sizes [57, 59] and
higher dislocation density [66].
69
2.3.4.2 Dislocation strengthening
The martensite formation results in the creation of a high dislocation density at the edge
of each growing martensite lath. This high dislocation density will contribute to the
strength of martensite according to Eq. 2.15:
𝜎𝑑 = 𝑀𝛼𝐺𝑏 ∙ 𝜌 1⁄2 ,
Equation 2.24
For calculations of dislocation strengthening of martensite the G and b for ferrite are
commonly applied. Furthermore, the following values is used for the product 𝑀𝛼 = 0.34
[67]. Table 2.3 lists the typical dislocation density of lath martensite of different carbon
concentration measured by TEM [66].
Table 2.3 Dislocation density of lath martensite in the as-quenched state [66]
Alloys
Fe-0.0026C
Fe-0.18C
Fe-0.38C
Dislocation density [x1014 m-2]
Average
Max
6.5
6.9
11.1
13.3
14.2
16.1
Min
5.5
8.9
12.4
The influence of carbon concentration on the dislocation density originates from the
formation of a Cottrell atmosphere around the dislocation. The carbon atoms segregate
to dislocations and reduce the recovery during quenching of the martensite. A higher
carbon concentration therefore increases the dislocation density of the martensite in the
as-quenched state. Nordstrom [68] and Kehoe et. al [69] therefore suggests that the
strengthening effect of segregated carbon in martensite should be calculated via the
dislocation density (via dislocation strengthening) and not via solid solution strengthening.
2.3.4.3 Grain boundary strengthening
The transformation of the parent austenite into the smaller martensite blocks add grain
boundary strengthening to martensite. The contribution of grain boundary strengthening
to martensite can be based on the grain size of the martensite blocks, and is expressed
according to Eq. 2.14 [22]:
𝜎𝑔𝑏 = 17.4 ∙ 𝑑𝑔 −1⁄2
Equation 2.25
Literature reports that the block size decreases when the carbon concentration in steel
increases [59] and that refining of the austenite grain size results in a decrease of the
block width and packet size [70].
2.3.5
Tempering of martensite
Directly after quenching the martensite is called virgin martensite. This is the hardest and
most brittle state of martensite. Tempering is an isothermal heat treatment of martensite
performed to increase the toughness of the steel. Tempering is performed at
temperatures which are high enough to allow changes in the martensite microstructure,
but below the austenite formation temperature, A1. The hardness decreases during
tempering, but the toughness of the microstructure is significantly increased.
The microstructural changes which takes place in the martensite during tempering
have been extensively studied by many experimental techniques and are nicely
summarized in [58, 71]. The main processes that take place during tempering of Fe-C
martensite are (listed in their order of appearance and/or at higher temperatures); (i)
carbon clustering and segregation into lattice defects, (ii) iron carbide precipitation (iii)
decomposition of retained austenite, (iv) coarsening of iron carbides, (v) recovery of
dislocation structures, and (vi) recrystallization of the martensite into equi-axed ferrite.
The processes may overlap and each process may individually be affected by alloy
additions to steel. Furthermore, each of these processes has a direct effect on the
hardening mechanisms of martensite.
2.3.5.1 Carbon clustering and segregation
The first process that takes place during the tempering of martensite involves carbon
segregation and the formation of carbon clusters. This process is sometimes called
martensite ageing. Segregation is the redistribution of carbon atoms from interstitial
positions to lower-energy sites, such as individual dislocations, vacancies and lath
boundaries.
Carbon clustering is the accumulation of carbon atoms into clusters or
modulations in the martensite lattice. The driving force for carbon clustering is the
reduction of the total elastic energy of the lattice [58]. The carbides which form during
later stages of tempering are primarily forming from carbon clusters, and not from
segregated carbon atoms [72-73].
71
2.3.5.2 Iron carbide nucleation and growth
The first type of iron-carbides which form during tempering are so called ɛ-carbides,
which are Fe2.3C-particles with a HCP crystal structure. The formation of ɛ-carbides is
homogeneous in the lattice and is commonly called the first stage of tempering, even
though it takes place after carbon clustering and segregation. The first stage of tempering
proceeds during a few minutes of tempering at 100-200°C, but can also start during autotempering: tempering that takes place during the quenching. . The shape of ɛ-carbides
have been reported to range from needle-, rod-, lath- to disk-like, depending on the
tempering temperature [74]. ɛ-carbides are metastable transition carbides, which
dissolve during the later stages of tempering.
The second type of iron-carbides which form during tempering of martensite is cementite.
The formation of cementite is called the third stage (the second stage is discussed later)
of tempering and takes place at a high rate at temperatures of 200-300°C. Cementite has
the composition Fe3C and an orthorhombic lattice structure.
Figure 2.31 Cementite particles in KNDS4 as observed by SEM on nital etched specimens after 60
minutes of annealing at 550°C
Cementite nucleates primarily on lath and block boundaries and the initial shape of
cementite is needle- or disc-like which evolves into plate or lath shapes [58, 71], as shown
in Fig. 2.31. At higher tempering temperatures (400-600°C) the cementite particles will
start to become more spherical in shape. Coarsening of cementite take place via Ostwald
ripening. The larger particles grow by consuming the smaller particles.
2.3.5.3 Decomposition of retained austenite
Meta-stable austenite can be retained in martensite after quenching. Retained austenite
is usually only present in martensitic steels with carbon content above 0.4wt% and is
therefore not common in lath martensite. The decomposition of retained austenite takes
place at 200-300°C and is commonly called the second stage of tempering since it can
take place before cementite formation and growth. Retained austenite is commonly
transformed into bainite [58, 71].
2.3.5.4 Dislocation recovery, recrystallization and grain coarsening
Dislocation recovery is generally said to start at temperatures above 400°C. The recovery
process of the dislocation structure in martensite is comparable to the process of
recovery in cold worked metals. Recovery of martensite result in a reduction of the
dislocation density in the martensite.
The degree of recovery depends on the tempering temperature, where higher
temperatures typically results in a higher degree of recovery [75]. Recovery is followed by
recrystallization. The recrystallization of martensite results in equi-axed ferrite grains. At
elevated temperatures recrystallization of martensite can be followed by grain growth.
Recrystallization and martensite grain coarsening usually starts at 600-700°C.
Recrystallization is slowed down by the pinning of carbides. The processes of
recovery/recrystallization/grain growth and cementite coarsening can take place in
parallel.
73
2.3.6
Nucleation of precipitates
Nucleation is the localized formation of a new β-phase, in a parent α-phase. Nucleation
starts with the formation of a cluster of the solute atoms (the atoms which make up the
β-phase) which form the nucleus of the new β-phase. The classical nucleation theory
describes the change in Gibbs free energy, during the nucleation event of one nucleus of
𝛽-phase in the host matrix of 𝛼-phase, as [15, 76];
∆𝐺 = −𝑉𝛽 ∆𝑔𝑣 + ∑𝑖 𝐴𝑖 𝛾𝑖 + 𝑉𝛽 ∆𝑔𝑠 − ∆𝑔𝑑 ,
Equation 2.26
where 𝑉𝛽 is the volume of the new β -phase and ∆𝑔𝑣 is the free energy difference,
𝑔𝛼 − 𝑔𝛽 , between 𝛼-phase and 𝛽-phase per unit volume of the β-phase (also called the
chemical driving force for nucleation). Ai and 𝛾𝑖 are the area and energy of the ith interface
of the nucleus or of the grain boundary of the parent phase that is removed during the
nucleation. The product Ai 𝛾𝑖 is taken to be negative in case grain boundary area is
removed during nucleation. The product Ai𝛾𝑖 is taken to be positive for the new interfaces
that are created during nucleation. ∆𝑔𝑠 is the strain energy per unit volume of formed βphase and ∆𝑔𝑑 is the change in free energy related to defects in the parent phase, which
are annihilated during the nucleation of the β-phase. The nucleation process of the new
β-phase is a balance between the negative terms and the positive terms in Eq. 2.26.
Nucleation only takes place in case the activation energy, G*, for nucleation is overcome,
see Figure 2.32. This point defines the critical nucleus size, which is generally indicated
with the symbol *. Subsequent attachment of atoms to the critical nucleus will reduce the
Gibbs free energy of the system.
Figure 2.32 The
change in Gibbs
free energy
(solid line) as a
function of
nucleus size
The critical dimensions of the nucleus can be found by differentiation of Eq. 2.26 with
respect to the precipitate dimension, equating to zero, and solving the equation for the
precipitate dimension. An assumption of the nucleus shape is necessary for this step, as
the exact shape of critical nuclei is not known.
2.3.6.1 Driving force for nucleation, ∆𝒈𝒗
The driving force for the nucleation is the free energy difference between phase α-phase
and β -phase per unit volume of the β -phase. For any given temperature there is a
maximum concentration of solute atoms that can dissolve into the parent α-phase. This
is called the solubility limit of the α-phase. By exceeding this critical concentration, a
driving force for nucleation of precipitates of β-phase arises. The solubility of the atoms
of the β-phase can be expressed in terms of solubility products. For a carbide precipitate
of type MmCn (M=metallic, such as Ti, V and Nb etc.) the following relationship is valid [77]:
𝐵
log 𝐾𝑠 = 𝐴 − 𝑇 ,
Equation 2.27
where Ks = [M]m[C]n is the solubility product and A and B are experimentally determined
parameters. [M] and [C] are the atomic percentages or mole fractions of element M and
C respectively. The unit of the solubility product therefore depends on the stoichiometric
composition of the precipitate phase, and the unit is concentration to the power of m +
n. In case the solubility limit is exceeded, the solution is said to be supersaturated. The
solubility product is a function of temperature, and the driving force for nucleation is
therefore also directly dependent on temperature.
2.3.6.2 Interface energy, 𝜸𝒊
The interface energy of Eq. 2.26 refers to either the energy of the interface between the
precipitate of β-phase and the matrix of the parent α-phase or to the energy of a grain
boundary in the parent phase that is removed during the nucleation. The interface
between β -phase and the parent α -phase can be divided into three main types; (i)
coherent, (ii) semi-coherent and (iii) incoherent, see Fig. 2.33.
75
Figure 2.33 Interfaces between two different phases (grey and white) showing (a) a perfectly
coherent interface, (b) a semi-coherent interface and (c) an incoherent interface.
Coherent interfaces form when the host lattice and precipitate lattice have the same or
nearly the same inter-atomic spacing at the position of the interfaces between the two
phases. This implies that there is a specific orientation relationship between the
crystallographic planes of the two phases. Less than perfect matching of the lattice
parameters of coherent interfaces will result in straining of one or both of the lattices.
This straining is called coherency strain and is included in the volume strain energy term
∆𝑔𝑠 in Eq. 2.26 [78]. The energy of a coherent interface is normally in the range of 1-200
mJ/m2.
Semi-coherent interfaces form when it becomes energetically more favorable to replace
a coherent interface with large strains by an interface with misfit dislocations that are
periodically spaced to reduce the strain energy. The dislocations form to accommodate
the strain, and the interface becomes semi-coherent. The higher the misfit between the
two phases, the closer the misfit dislocations will be placed. Similar to coherent interfaces,
semi-coherent interfaces are associated to a specific orientation relationship between the
two phases. The surface energy of a semi-coherent interface includes the energy of the
dislocations which are part of the interface. The energy of semi-coherent interfaces is
typically in the range of 200-500 mJ/m2
Incoherent interfaces arise when there is no atomic fit at the meeting interfaces between
the two phases. Incoherent interfaces are not associated to a specific orientation
relationship. They are generally associated with high energies, 500-1000 mJ/m2
2.3.6.3 Misfit strain energy, ∆𝒈𝒔
The misfit strain energy of Eq. 2.26 refers to the straining of the host lattice around a
precipitate. This strain energy is therefore closely linked to the coherency strains and is
dependent on the lattice parameter and elastic constants of the 𝛽-phase, the 𝛼-phase
and the temperature of the system.
Misfit strain energies are difficult to measure, but they can be approximated via
first-principles calculations [79]. The misfit strain energy is commonly ignored in Eq. 2.26.
2.3.6.4 Defect energy, ∆𝒈𝒅
The defect energy of Eq. 2.26 refers to the defects in the parent phase 𝛼 which are
annihilated (consumed) due to the nucleation of the new 𝛽-phase. Defects that can be
annihilated during the nucleation of a new phase are vacancies and (part of) dislocations.
The magnitude of ∆𝑔𝑑 depends on the type and the dimensions of the defects that are
removed by the nucleation.
The defect energies for dislocations can be calculated from the length of the dislocation
line which is consumed, and the line energy of the dislocation itself.
2.3.6.5 Homogeneous and heterogeneous nucleation
During homogeneous nucleation the precipitates nucleate within the matrix phase. Truly
homogeneous nucleation does not result in any annihilation of defects. However, it may
be difficult to experimentally determine if nucleation did or did not involve the removal
of a vacancy during nucleation. During homogeneous nucleation there is no site
preference, and all the atoms in the host lattice can act as potential nucleation points for
the nucleating precipitates. Usually, this results in a uniform distribution of precipitates
throughout the host phase. Homogeneous nucleation of spherical precipitates requires
precipitates which have the same interface energy in all directions. However, nonspherical nuclei may appear during homogeneous nucleation due to the crystallographic
nature of the matrix and precipitating phase. For truly homogeneous nucleation the
defect energy term is zero.
During heterogeneous nucleation the precipitates nucleate at grain boundaries, edges or
corners, or other defects. Heterogeneous nucleation results in annihilation of defects.
Figure 2.34 shows two examples of heterogeneous nucleation. This restricts the number
of possible positions for nucleation within the host lattice. Heterogeneous nucleation
therefore results in a distribution of precipitates throughout the host phase, similar to the
distribution of the defects which the precipitates nucleate on.
During heterogeneous nucleation the precipitates form with the help of defects in the
host lattice; so called site preference. Heterogeneous nucleation is therefore linked to the
interfaces and the defect energy terms of Eq. 2.26.
77
Figure 2.34 Heterogeneous nucleation at (a) a grain boundary and (b) at a grain edge.
2.3.6.6 Nucleation rate
Nucleation is a time dependent process. The time-dependent nucleation rate (m-3s-1) can
be described as [76, 80]:
∆𝐺 ∗
𝜏
𝐽 = 𝑁𝑍𝛽 ∗ 𝑒𝑥𝑝 (− 𝑘 𝑇 ) 𝑒𝑥𝑝 (− 𝑡 ),
𝐵
Equation 2.28
where N is the density of potential nucleation sites, Z is the non-equilibrium Zeldovich
factor, 𝛽 ∗ is the frequency factor (the rate at which single atoms are added to the subcritical nucleus), ∆𝐺 ∗ is the activation energy for nucleation, T is the absolute
temperature at which the nucleation takes place and 𝜏 is the incubation time.
The non-equilibrium Zeldovich factor takes into account that when a nucleus reaches the
critical size (at the top of the energy barrier in Fig. 2.32) it can either grow or it can dissolve.
The general equation for the non-equilibrium Zeldovich factor is commonly described as
[81]:
1
𝑍 = √2𝜋𝑘 𝑇 (−
𝐵
𝜕 2 ∆𝐺
2
𝜕𝑛𝑎
) ,
∗
𝑛𝑎
Equation 2.29
where 𝑛𝑎 is the number of atoms in the nucleus and 𝑛𝑎∗ is the number of atoms in the
critical nucleus.
The frequency factor covers the rate at which single atoms are added to the nucleus. The
frequency factor can be described according to [80]:
𝛽 ∗ = 𝑁𝑗 ∙ Γ
Equation 2.30
where Γ is the atomic jump frequency and Nj is the number of atoms that are within one
atomic jump distance to the nuclei (𝛼𝑗 ).
If the surface of the nuclei is described as S* and a is the interatomic distance we can
approximate:
𝑆∗
𝑁𝑗 ≈ 𝑎2
Equation 2.31
The atomic jump frequency Γ can be expressed in terms of the diffusivity of the solute
atom according to:
Γ=
6𝐷
Equation 2.32
𝛼𝑗2
The incubation time is given by [80]:
1
𝜏 = 2𝑍 2𝛽∗ .
Equation 2.33
The incubation time for nucleation of alloy carbide precipitates in steel can be of the order
of seconds or even less (the nucleation of TiC precipitates in the simulations presented in
chapter 5 started already during heating up to the isothermal annealing temperature [82]).
2.3.7
Growth and coarsening of precipitates
When the critical nuclei have formed the precipitate will grow by migration of the
interface into the host matrix. The growth of a precipitate is highly dependent on the
diffusivity of the atoms that form the precipitate phase. The growth mechanism of
precipitates can be of three types; (i) diffusion controlled, (ii) interface controlled, or (iii)
mixed-mode.
Diffusion controlled growth is governed by the long-range diffusion of solute atoms to the
growing precipitate. Interface controlled growth is governed by the rearrangement of the
atoms near the interface by short range diffusion. During diffusion controlled growth local
equilibrium of the solute atoms will form at the interface of the precipitate. As the
attachment of solute atoms to the surface is rapid, the close vicinity of the matrix near
the precipitate will be depleted of solute atoms. This depleted zone creates a
concentration gradient which will cause diffusion of solute atoms towards the growing
precipitate. We give an example for a precipitate of 𝛽 -phase with equilibrium
𝐴,𝑒𝑞
concentration 𝐶𝛽
of A atoms, in a matrix of 𝛼 -phase which is supersaturated
𝐴,𝑒𝑞
𝐴
(𝐶𝛼,0
> 𝐶𝛼 ) in A.
79
Figure 2.35 The concentration profile of A atoms showing the equilibrium concentration of A
𝐴,𝑒𝑞
atoms in the precipitate, 𝐶𝛽 , the concentration of A atoms in the matrix near the
𝐴
interface of a growing precipitate, 𝐶𝛼,𝑒
and the concentration of A atoms in the bulk matrix
of 𝛼-phase outside the diffusion filed of the precipitate during diffusion controlled growth.
Figure 2.35 shows the concentration profile of solute A atoms near the interface of a
growing precipitate during diffusion controlled growth. The concentration of A atoms in
𝐴
the bulk matrix of 𝛼 -phase, outside the diffusion field of the precipitate is 𝐶𝛼,0
. The
concentration of A atoms in the matrix, near the precipitate interface is 𝐶𝑒𝐴 and the
concentration of A atoms in the precipitate 𝛽-phase is 𝐶𝛽𝐴 .
The growth rate, v, of spherical precipitates can be described according to Zener [83]:
𝐴 −𝐶 𝐴
𝐷 𝐶𝛼0
𝛼,𝑒
𝑣=𝑟
𝑝
𝐴
𝐶𝛽𝐴 −𝐶𝛼,𝑒
,
Equation 2.34
where D is the diffusivity of the solute atom A in the host matrix of 𝛼-phase and 𝑟𝑝 is
radius of the growing precipitate.
For small precipitates this growth rate can be affected by the so called Gibbs-Thompson
effect [84]. The Gibbs-Thompson effect describes the influence of a curved interface
between precipitate and matrix on the solubility limits of solute atoms in the matrix. A
high curvature increases the interface energy, which in turn increases the free energy at
the surface. This will increase the solubility limit of the solute atoms. Small precipitates
with a high radius of curvature are therefore surrounded by a matrix where the local
equilibrium concentration of solute atoms is higher than it is in the surrounding of large
precipitates. This reduces the concentration gradient near the surface of small
precipitates which reduced reduces the growth rate of the precipitate. Moreover, the
Gibbs-Thompson effect enables the dissolution of small precipitates in comparison to
large precipitates during coarsening.
2.3.8
The thermodynamics of TiC-precipitate nucleation and growth in steel
Titanium is a carbide forming element, which can be used to create a fine dispersion of
precipitates in steel. The carbide which is formed by titanium consists of one carbon atom
per titanium atom; TiC. The crystal structure of TiC is of the NaCl type, see Fig. 2.36. The
reported lattice parameters of TiC is 0.432 nm [85].
The Baker-Nutting orientation relationship has been observed between TiC and ferrite
[86]. TiC precipitates in steel are reported to be fully coherent at small sizes and to grow
into semi-coherent discs/platelets at a critical dimension [87-88]. The broad interface of
the TiC platelet is parallel to the {100} plane of the ferrite. The lattice parameter of TiC is
larger than the inter-atomic spacing of ferrite, and the result is a misfit of approx. 6-7%
[79, 88] along the direction of the plate. Normal to the broad interface the misfit is
significantly higher. As a result the distance between the mis-fit dislocations becomes 4.2
nm at the diameter of the disk, and 0.82 nm at the edge/height of the disk [87]. The
interface energy between small TiC precipitates and ferrite is commonly reported to be
in the range of 0.3 J/m2 [79, 89-92].
Figure 2.36 NaCl
crystal structure
of TiC.
The nucleation of TiC in steel is heterogeneous and takes place near dislocations [93].
Literature reports that the nucleation rate is enhanced by the strain field which surrounds
the dislocations and that the position of nucleation is next to the dislocation. [94].
Experimental studies show that TiC nucleation in martensite requires an isothermal
annealing temperature of 500°C or higher [87-88] and calculations of the time dependent
nucleation rate, from classical nucleation theory, show that the nucleation rate of TiC in
81
steel at 580°C is up to 1019 m-3s-1 in case the steel contains a dislocation density of 1013 m2
[91].
The solubility of TiC in ferrite is low, but it is possible to fully dissolve TiC in austenite.
Figure 2.37 shows a ThermoCalc simulation (TCFE6) of stable equilibrium phase of TiC in
KNDS4 steel. TiC is stable up to temperatures of approx. 1250°C.
Mole Fraction
0.002
Figure 2.37 Mole
fraction of stable TiC
in steel KNDS4, as a
function of
temperature. Data
calculated by
ThermoCalc (TCFE6).
0.0015
0.001
0.0005
0
900
1000
1100
1200
1300
1400
1500
Temperature [˚C]
The solubility data for TiC in ferrite is reported to be [77]:
log[𝑇𝑖 ][𝐶] = 2.75 −
7000
𝑇
(at.%)2
Equation 2.35
This low solubility in ferrite results in a high supersaturation of Ti in ferrite if quenching is
done from temperatures where Ti is in solid solution. The driving force for nucleation
during subsequent tempering of martensite is therefore high. Literature report values of
∆𝐺𝑣 (580℃) = 3.2𝑥109 J/m3 [91] and ∆𝐺𝑣 (0𝐾) = 81.9𝑥109 kJ/mol [79].
The diffusivity of titanium in ferrite follows the general equation for diffusivity:
𝐷𝑇𝑖 (𝑇) = 𝐷0,𝑇𝑖 exp (−
𝑄𝐷,𝑇𝑖
𝑅𝑇
) ,
Equation 2.36
where the most commonly applied diffusivity data are the values reported by Ogilvie and
Moll [95]. Ogilvie and Moll examined Fe-Ti alloys with low Ti concentration to study the
interdiffusion data; D0,Ti = 0.315x10-3 m2/s and QD,Ti= 247.7 kJ/mol [95]. This data was
measured in polycrystalline ferrite. The tracer diffusion coefficient of Ti in single crystal
α-iron have been measured by [96] via the serial sectioning method and established that
the temperature dependence of the diffusion coefficient can be described according to:
𝐷𝑇𝑖 (𝑇) = 0.21exp (−
𝑘𝐽
𝑚𝑜𝑙
293.2
𝑅𝑇
(1 + 0.079𝑀2 (𝑇))) m2 s−1 ,
Equation 2.37
where M is the ratio of the spontaneous magnetization (at temperature T) to the
saturation magnetization of ferrite. The spontaneous magnetization is given by [97]:
(1−𝑡) 𝛽
𝑀𝑠 (𝑇) = 𝑀0 (1−𝛽𝜗+𝐴𝜗 3⁄2 −𝐶𝜗7⁄2 )
Equation 2.38
𝑀0 = 𝑀1 (1 − 𝛽 + 𝐴 − 𝐶),
Equation 2.39
and
where = 𝑇⁄𝑇𝑐 , 𝑇𝑐 is the Curie temperature and the constants 𝛽 = 0.368, A=0.110 and
C=0.129. Equation 2.37 deviates from a linear Arrhenius relationship, as given in Eq.
2.36, due to the magnetic spin ordering, that is accounted for by the parameter M.
2.3.9
References
[1] E. Eckerman: World history of the automobile, Society of Automotive Engineers,
Warrendale, USA, 2001
[2] VDI 2230-1, Systematic calculation of high duty bolted joints – Joints with one
cylindrical bolt. VDI-Gesellschaft Entwicklung Konstruktion Vertrieb, Dussledorf,
Germany, 2003
[3] G. Toth: Torque and Angle Controlled Tightening Over the Yield Point of a Screw,
Chalmers Univeristy of Technology, Gothenburg, Sweden, 2002
[4] Volvo Car Corporation, Design Instructions, PV3-1997, Standards VCC, Gothenburg,
Sweden, 1997
[5] ISO898-1, Mechanical properties of fasteners made of carbon steel and alloy steelPart 1. Fifth edition, Switzerland, 2013
[6] K.-H. Kloos and W. Thomala: Schrauben verbinduingen; Grundlagen, berechnungen,
Eigenschaften, Handhabung,. Springer, Berlin Heidelberg, Germany, 2007
[7] DIN EN 10269, Stähle und Nickellegierungen für Befestigungselemente für den
Einsatz bei erhöhten und/oder tiefen Temperaturen, Berlin, Germany, 2006
[8] WD. Callister Jr.: Materials Science and Engineering, An introduction. Seventh Ed.
John Wiley & Sons, New York, 2007
[9] D. Hull and D.J Bacon: Introduction to dislocations. Fifth Ed. Pergamon, Oxford, UK,
2011
[10] D. Chandrasekaran: Grain size and solid solution strengthening in metals, Royal
Institute of Technology, Stockholm, Sweden, 2003
[11] FRN Nabarro: Mater Sci Eng. A 234-236(1997), 67-76
[12] EW. Collings and HL. Geel: Physics of solid solution strengthening. AIME, Plenum
Press, New York, USA, 1973
[13] GB. Olson and WS. Owen (Eds.), Martensite, ASM International, Materials Park,
Ohio, USA, 1992
83
[14] T. Gladman: The physical metallurgy of microalloyed steels, The University press,
London, UK, 1997
[15] DA. Porter and KE. Easterling: Phase transformations in metals and alloys, Van
Norstrand Reinhold, New York, USA, 1981
[16] R. Viswanathan: Damage Mechanisms and Life assessment of High Temperature
Components, ASM International, USA, 1989
[17] AH. Cottrell and BA Bilby: Proc. Phys. Soc., A(1949), 49-62
[18] AH. Cottrell: Dislocations and plastic flow in crystals, Clarendon Press, Oxford, UK,
1961
[19] U. Ehrnsten, M. Ivanchenko, V. Nevdacha, Y. Yagodzinskyy, A. Toivonen and H.
Hanninen: Proceedings of the 12th international conference on environmental
degradation of materials in nuclear power system – water reactors-,. TMS, 2005in
Nitrogen
[20] EO. Hall: Proceedings of the Physical SocietyB, 64 (1951), 747-753
[21] NJ. Petch: J. Iron Steel Inst., 174 (1953), 25-28
[22] Y. Han, J. Shi, L. Xu, WQ Cao and H. Dong: Mater. Sci. Eng. A,. 503(2011), 643-651
[23] K. Lucke and K. Detert: Acta Metallurgica., 5(1956) 628-637
[24] JW. Cahn: Acta Metall., 10(1962), 789-798
[25] T. Gladman: Proceedings of the Royal Society of London, Series A, Mathematical
and Physical Sciences, 294(1966), 298-309
[26] JE. Bailey and PB. Hirsch: Philos. Mag., 5:53(1960), 485-497
[27] R. Lagneborg and B. Bergman: Metal. Sci., 10(1976), 20-28
[28] T. Gladman: Mater. Sci. Tech., 15(1999), 30-36
[29] DC. Chrzan and JW. Morris, Jr YN. Osetsky, RE. Stoller, SJ. Zinkle: MRS Bulletin.,
34(2009), 173-177
[30] R. Lagneborg: Scripta Metall., 7(1973), 605-614
[31] E. Orowan: Symposium on International Stresses, Inst. of Metal, London, UK,
1947
[32] FRN. Nabarro and HL. de Villiers: The physics of creep and creep-resistant alloys,
CRC Press, 1995
[33] WB. Li, JL. Henshall, RM. Hooper and KE. Easterling: Acta Metall. Mater., 39(1991),
3099-3110
[34] http://engineering.dartmouth.edu/defmech/
[35] DR. Muzyka, Eds CT Sims and WC Hagel: The Superalloys, John Wiley & Sons, New
York, 1972
[36] ME. Kassner: Fundamentals of creep in metals and alloys., Elsevier, 2015
[37] W. Blum, P. Eisenlohr and F. Breutinger: Metall Mater Trans A., 33A(2002). 291-303
[38] ME. Kassner and MT Perez-Prado: Prog. Mater. Sci., 45(2000), 1-102
[39] TG. Langdon: Acta Metall. Mater., 42(1994), 2437-2443
[40] FRN. Nabarro: Report of a Conference on Strength of solids, Physical Society,
London, 1948
[41] C. Herring: J. Appl. Phys., 212(1950), 437-445
[42] RL. Coble, J. Appl. Phys., 34(1963), 1679-1682
[43] R. Goodall and TW Clyne: Acta Mater., 54(2006), 5489-5499
[44] TO. Mulhearn and D. Tabor: J. Inst. Metals., 89(1960), 7-12.
[45] AG. Atkins, A. Silverio and D. Tabor: J. Inst. Met., 94(1966), 369-378.
[46] H. Takagi, M. Dao, M. Fujiwara and M. Otsuka: Mater. Trans., 47(2008), 2006-2014
[47] Z-F. Yue, J-S Wan and Z-Z Lu: App. Mathematics and Mechanics., 24(2003), 307-317
[48] M. Fujiwara and M. Otsuka: Mater. Sci. Eng., A319-312(2001), 929-933
[49] PM. Sargent and MF. Ashby: Mater. Sci. Tech., 8(1992), 594-601
[50] KL. Johnson: J. Mech. Phys. Solids., 18(1970), 115–126
[51] GZ. Voyiadjis, AH. Almasri and T. Park: Mech. Res. Com., 37(2010), 307-314
[52] WC. Oliver and GM. Pharr: J. Mater. Res., 7(1992), 1564-1580
[53] X. Li and B. Bhushan: Mater. Characterization., 48(2002), 11-36
[54] MJ. Mayo and WD. Nix: Acta Metall., 36(1988), 2183–2192.
[55] EC. Bain: Transactions of the American Institute of Mining and Metal Engineering.,
70(1924), 25-46
[56] L. Xiao, Z. Fan and Z. Jinxiu: Phys. Review B., 52(1995), 9970-9978
[57] G. Krauss: Mater. Sci. Eng., A273-275(1999), 40-57
[58] GR. Speich and WC. Leslie: Metall Trans., 3(1972), 1043-1054
[59] S. Morito, H. Tanaka, R. Konishi, T. Futuhara and T. Maki: Acta Mater., 54(2003),
1789-1799
[60] JA Klosterman: J. less common Met., 28(1972), 75-79
[61] S. Morito, X. Huang, T. Futuhara, T. Maki and N. Hansen: Acta Mater., 54(2006),
5323-5331
[62] G. Kurdjumov and G. Sachs: Zeitschrift fur Physik, 64(1930), 325-343
[63] T. Ohmura, M. Hayakawa, K. Miyahara, S. Matsuoka, K. Tsuzaki and
T. Takahashi: Proceedings of 20th Risa International Symposium on Materials
Science. Deformation-Induced Microstructures: Analysis and Relation to Properties
Roskilde, Denmark, (1999), 443-439
[64] F-G. Wei and T. Tsuzaki: Scripta Mater., 52(2005), 467-472
[65] B. Hutchinson, J. Hagstrom, O. Karlsson, D. Lindell, M. Tornberg, F. Lindberg and M.
Thuvander: Acta Mater., 59(2011), 5845-5858
[66] S. Morito: ISIJ Int. 43(2003), 1475-1477
[67] G. Thomas and J. Washburn (Eds): Electron Microscopy and Strength of
Crystals, John Wiley & Sons Inc, New York, USA, 1963
[68] LA. Nordstrom: Scand. J. Metall., 5(1976), 159-165
[69] M. Kehoe and PM Kelly: Scripta Metall., 4(1970), 473-476
[70] S. Morito, H. Saito, T. Ogawa, T. Furuhara and T. Maki: ISIJ Int., 45(2005), 91-94
[71] RN. Caron and G. Krauss: Metall. Trans., 3(1972)2381-2389
[72] GR. Speich: Trans. Metal. Soc. AIME., 245(1969)2553-2564
[73] C. Zhu, A. Cerezo and GDW. Smith: Ultramicroscopy., 109(2009), 545-552
[74] Y. Ohmori and I. Tamura: Metall Trans A, 23A(1992), 2737-2751
[75] S Takebayashi, T. Kunieda, N. Yoshinaga, K. Ushioda and S. Ogata., ISIJ Int. 50(2010),
875-882
[76] J.W. Christian, The Theory of transformations in metals and alloys, 1st edition,
Pergamon, Oxford, UK, 2002.
[77] J. Strid and KE. Easterling: Acta Metall., 33(1985), 2057-2074
85
[78] M. Enemoto, JK. Lee and HI. Aaronson, Mechanisms of diffusional phase
transformations in metals and alloys, CRC press, Taylor and Francis, London, UK, 2010.
[79] JH. Jang, C-H. Lee, Y-U. Heo and D-W. Suh: Acta. Mater., 60(2012), 208-217
[80] H. Landheer., Nucleation of ferrite in austenite, The role of crystallography, TU
Delft, Delft, The Netherlands, 2010
[81] KC. Russell: Acta Metall., 16(1968), 761-769
[82] CEIC. Ohlund, D.den Ouden, J.Weidow, M.Thuvander and SE. Offerman: ISIJ Int,,
55(2015), 883-892
[83] C. Zener: J. Applied Phys., 20(1949), 950-953
[84] M. Perez: Scripta Mater., 52(2005), 709-712
[85] A. Teresiak and H. Kubsch: NanoStructured Mater., 6(1995), 671-674
[86] Z-G. Yang and M. Enemoto: Mater. Sci. Eng. A., 322(2002), 184-192
[87] F-G. Wei, K. Tsuzaki: Metall. Mater. Trans. A., 37A(2006), 331-353
[88] F-G. Wei, T. Hara, T. Tsuchida and K. Tsuzaki: ISIJ Int., 43(2003), 539-547
[89] W-S. Jung, S-C. Lee and S-H. Chung: ISIJ Int., 48(2008), 1280-1284
[90] H-K. Kim, W-S Jung and B-J. Lee: Acta Mater., 57(2009), 3140-3147
[91] A. Sawahata, M Enemoto, K. Okuda and T. Yamashita: Tetsu-to-Hagane., 94(2008),
21-29
[92] DHR. Fors and G Wahnstrom: Phys. Review. B., 82(2010), 1-13
[93] W. Kesternich: Philos Mag A., 52(1985), 533-548
[94] Z. Wang, X. Mao, Z. Yang, X. Sun, Q. Yong, Z. Li and Y. Weng: Mater. Sci. Eng. A.,
A529(2011), 459-467
[95] Moll SH and Ogilvie RE: Trans. Metal. Soc. AIME., 2015(1959), 613-618
[96] P. Klugkist and CHR Herzig: Phys. Stat. Sol., 148(1995), 413-421
[97] AS. Arrott and B. Heinrich: J. Appl. Phys., 52(1981), 2113-2115
3 The kinetics of softening and microstructure
evolution of martensite in Fe-C-Mn steel during
tempering at 300°C
C. Emmy I.C. Ohlund, Erik Schlangen and S. Erik Offerman
Materials Science & Engineering A, 560 (2013) 351-357
Abstract
A fundamental understanding of the properties of tempered martensitic steel during the
production and service of fasteners helps the development of cost-effective, microalloyed, medium-carbon steel for future automotive fasteners, which have to fulfill more
stringent requirements due to the on-going trend of down-sizing the car engine. We have
studied the relation between the softening kinetics of martensite and the kinetics of the
evolution of the microstructure in high-purity Fe-C-Mn steel during tempering at 300˚C
by means of nano-indentation, SEM, and EBSD. The as-quenched specimen consist of
martensite blocks that are auto-tempered and non-tempered. We find that the nanohardness that is measured directly at the martensite boundaries is significantly higher
than the nano-hardness that is measured in the martensite matrix. The boundary regions
soften with increasing tempering time, whereas the nano-hardness of the tempered
matrix remains approximately constant with increasing tempering time. The kinetics of
martensite softening can be described by three stages that are related to the evolution
of the microstructure. However, most of the softening takes place during the first stage
of tempering: The macroscopic softening of martensite is mainly related to: (i) the nanoscale softening of boundary regions, (ii) the reduction in area fraction of the boundaries
regions, and (iii) the reduction in area fraction of the non-tempered matrix regions.
87
3.1 Introduction
Tempered martensitic steel is the most commonly used material for high-strength
fasteners in mass-produced car engines today. The tensile strength of these fasteners is
up to class 12.9, which means a tensile strength of 1200MPa and a recommended
maximum temperature during service of 150˚C. The trend for car engines is down-sizing,
which means that future generations of fasteners are required to have the capability to
(1) carry higher loads and (2) resist creep at higher temperatures as compared to today’s
fasteners. In addition to enhanced requirements for the mechanical properties during
service of the fasteners, there are the requirements for the production of the fasteners:
the steel needs to be cold formed and heat treated on an industrial scale. Moreover, from
a business perspective the steel for the fastener is required to have low levels of alloying
elements.
A fundamental understanding of the kinetics of martensite softening in relation to
the kinetics of the evolution of the microstructure during tempering is essential for the
development of cost-effective, micro-alloyed, medium-carbon steel for future
automotive fasteners. Research on as-quenched martensite has shown that the
strength/hardness is related to the morphology, carbon concentration, dislocation
density, carbide density and the block size of martensite [1-2]. More recently, Ohmura et
al. showed that the macroscopic hardness of martensite is the result of the matrix
hardness and the hardness of grain boundaries (the grain boundary/size effect). They
have observed this by measuring the ratio of the matrix nano-hardness Hn and the
macroscopic hardness Hv [3-7]. A recent study by Hutchinson et al. concluded that
segregation of carbon atoms to defects during quenching is the largest single factor
controlling the strength of as-quenched martensite. Furthermore, the study of
Hutchinson concludes that the amount of carbon existing in solid solution after quenching
is very small (0.02 wt.%) and independent of the total carbon content of the steel [8].
From these observations we derive the hypothesis that the nano-hardness at grain
boundaries should be significantly higher than in the matrix of as-quenched martensite in
medium carbon steels.
The strength of martensitic steel is known to reduce during temperature exposure. The
factors causing softening, listed in the order they appear in time and for increasing
temperatures are: migration of carbon atoms, decomposition of retained austenite,
precipitation and coarsening of cementite, recovery of dislocation structure and
recrystallization [9-12]. More recently, Ohmura et al. characterized the temper-softening
behavior of Fe–C martensitic steels by nano-indentation. They found that both the matrix
hardness and the grain size/boundary effect decrease with increasing tempering
temperatures [13-17]. However, no studies have been performed on the time-
dependency of the softening kinetics of martensite during isothermal tempering by using
nano-indentation. Moreover, no studies have been conducted to measure if there is a
difference in the softening kinetics of the grain boundaries and of the matrix of martensite
by using nano-indentation.
The aim of this study is to determine the relation between the softening kinetics
and the microstructure evolution during isothermal tempering of Fe-C-Mn martensite.
We specially focus on the hardness of grain boundaries, since previous research has
shown that the strength of as-quenched medium-carbon, martensitic steel strongly
depends on these boundary regions.
For the purpose of evaluating the softening of the grain boundaries we have
developed and validated a methodology to differentiate between nano-hardness
measurements performed directly at grain boundaries and measurements performed in
the matrix by using the technique of continuous stiffness measurement (CSM) nanoindentation [18]. Moreover, we have studied the kinetics of other microstructural factors
potentially leading to martensite softening during tempering: strain relief, carbide
precipitation and coarsening, and martensite block coarsening.
3.2 Experimental procedures
The material investigated is a ternary, high-purity Fe-C-Mn alloy. The composition is given
in table 3.1. The steel is received with a carbon concentration of 0.011 wt.%, machined
into cylinders with a diameter of 4 mm and subsequently carburized to 0.39 wt.%C.
Table 3.1 Steel composition (wt.%)
C
0,39
Mn
0,87
Si
0,0035
P
0,0010
S
0,0007
Al
0,0050
Cu
0,0021
Cr
0,0018
O
0,0008
V
0,0023
The steel cylinders are cut into 10 mm long specimens for heat-treatment in a Bähr 805
A/D dilatometer (Bär-Thermoanayse GmbH, Hüllhorst Germany). A homogenization
treatment is performed at 1100˚C for 207 minutes followed by cooling to 500˚C.
Thereafter, the steel is austenitized at 940˚C for 40 minutes, followed by quenching to
room temperature with He at a rate of 45 ˚C/s between the martensite start (M s) and
finish (Mf) temperatures. Tempering treatments are performed at 300˚C for 5, 10, 30, 60
and 600 minutes. All heating rates are 2 ˚C/s. After heat treatment all samples are
prepared by grinding and polishing down to 1 µm. After full homogenization the carbon
concentration was verified by line scans with Electron probe micro-analysis.
Scanning electron microscopy (SEM, JEOL JSM-6500F with field emission gun) is
performed on nital etched surfaces to determine the kinetics of the evolution of the
89
microstructure during tempering: the area fraction of tempered regions, the carbide
dimensions, and carbide number density.
Conventional micro-vickers hardness measurements and CSM nano-hardness
measurements are performed in order to study the softening kinetics during tempering.
Micro-Vickers hardness is measured at twenty locations on polished specimens using a
load of 500g and reflects the macroscopic hardness of the investigated steel. CSM nanoindentation measurements are performed on electro-polished specimens.
Electropolishing is conducted in a solution of 8 % perchloric, 10 % butylcellosolve, 60 %
ethanol and 22 % water at 0°C under a potential of 55V. An Agilent G200 nano-indenter
equipped with a Berkovich-indenter and a oscillation amplitude of 2nm is employed. The
tip is calibrated using a reference specimen of fused silica. The hardness values are
determined following the method of Oliver and Pharr [19]. We performed 8 x 8 indents
to a depth of 60 nm on each steel specimen. An additional array of 5 x 5 indents to a depth
of 400 nm is made on the as-quenched sample to verify that the macroscopic hardness
and E-modulus of the steel are reached. We determined the location (at a boundary or in
the matrix of the martensite) of the nano-indents on the as-quenched specimens by using
EBSD. A step-size of 150-175 nm is used for identification of the position of the nanoindents. The accuracy of the nano-hardness measurements is 14 % for the CSM nanoindenter that we used, which we determine by measuring the hardness of 8 nano-indents
on a single ferrite grain in the steel with the as-received composition of 0.011 wt% C. A
single ferrite grain is studies instead of a single martensite grain, because a single ferrite
grain is possible to make larger and is microstructurally more homogenous than
(tempered) martensite.
Electron-back scatter diffraction (EBSD with a Nordlys detector) measurements
are performed on electropolished surfaces to determine the kinetics of the evolution of
the microstructure during tempering: the martensite grain size and the width of the
boundary region. The EBSD-data are acquired and post-processed with the Channel 5
software. A step size of 100nm is used during the EBSD-mapping. The diameter of the
electron-beam is 16nm during the EBSD-measurements, which gives a spot size of
16x35nm due to the tilt of the sample.
3.3 Results and discussion
3.3.1
SEM studies
Fig. 3.1 shows SEM images of the specimens annealed for different times at 300˚C. Fig.
3.1(a) shows that the as-quenched microstructure is comprised of two types of regions:
(1) rough, carbide-containing regions and (2) smooth, carbide-free regions.
Figure 3.1 SEM images of the microstructure of the heat treated specimens: (a) as quenched and
the specimen tempered at 300˚C for (b) 5 minutes, (c) 10 minutes, (d) 30 minutes and (e) 60
minutes.
The two different regions correspond to auto-tempered regions (containing carbides) and
non-tempered regions (smooth). Auto-tempering means that tempering started during
the quenching process, i.e. carbon diffusion resulting in segregation and modulation of
carbon atoms and carbide precipitation. The observed difference in etching depth
between auto-tempered and non-tempered regions is most likely due to the different
concentration of carbon atoms in solid solution in the two different regions and not due
to differences in crystal orientations between grains. In case the crystal orientations were
the main reason for different etching depths, similar effects would be present also in the
tempered specimens, which is not the case. The presence of both tempered and nontempered regions in the as-quenched state is believed to be a direct result of the
martensite formation kinetics during quenching. During martensite transformation [20]
the full volume of the steel is not transformed into martensite instantaneous. The volume
fraction of transformed martensite is a function of time during the quenching process. As
a result, the interstitial carbon atoms inside the first formed martensite crystals will have
more time to diffuse at elevated temperature, as compared to the interstitial carbon
atoms in the last volume fraction of transformed martensite.
Fig. 3.1(b)-(e) shows the microstructure of tempered specimens, which consists of
only rough, tempered, carbide-filled regions.
91
3.3.2
Nano-indentation studies
Fig. 3.2 shows the average nano-hardness <Hn> and the average E-modulus as measured
by CSM nano-indentation at the boundaries, tempered matrix, and non-tempered matrix
of martensite of the as-quenched specimen as a function of the indent depth. Examples
of nano-indents located in the matrix of martensite and at boundaries as measured on
the as-quenched sample by EBSD are shown in Fig. 3.2(b) and (d) respectively.
Figure 3.2 The average (a) nano-hardness<Hn> and (c) E-modulus measured in the matrix and at
the grain boundaries as a function of indent depth. Examples of EBSD scans of a nano-indent
located (b) in the matrix and (d) on a boundary. The nano-indents are located within the triangle
and boundaries exceeding 10˚ misorientation are marked with black lines. The error bars
represent the 95% confidence interval and is chosen at 5 different indent depth to indicate the
spread of the measurements over the full indent depth.
Thirteen indents are found on martensite boundaries, which separate areas of different
crystal orientations with misorientations that are exceeding 10˚, see e.g. the IPF map in
Fig. 3.2(d). Seventeen indents are found to be located inside the matrix as they are placed
in regions of similar crystal orientations according to the IPF map, see e.g. Fig 3.2(b). The
matrix indents of the as-quenched sample can thereafter be further divided into nontempered matrix regions and tempered matrix regions by looking for the presence of
carbides in the SEM images, see Fig 3.1. Seven matrix indents are found in tempered
regions according to SEM.
Fig. 3.2(a) shows that the that the nano-hardness of the martensite boundaries is
significantly higher than the nano-hardness of the non-tempered matrix, which is in turn
significantly higher than the nano-hardness of the tempered matrix. This observation
confirms our hypothesis and is in line with the observations of Hutchinson et al. [8]. We
further observe that the nano-hardness of matrix indents continues to increase from
indent depths of 20 nm to indent depths of 60 nm whereas the nano-hardness of
boundaries has reached final hardness already at indent depths of 20-30 nm. We make
use of this difference in the shape of the curves for the nano-hardness as a function of
indent depth to distinguish between measurements of nano-indents at boundaries and
in the matrix for the annealed specimens, see Fig 3.2(a).
Fig. 3.2(c) shows that the E-modulus as a function of indent depth reaches a stable
value at a depth of approximately 60 nm. According to the hemispherical approximation,
the plastically deformed zone of an indent to a depth of 60 nm is approx. 560 nm [7] which
fits inside the average size of the martensite block which is measured to be 3.5 m2, see
below. For these two reasons, the reported nano-hardness values in the remainder of this
paper are measured at a depth of 60 nm, which is also in correspondence to earlier
literature [4, 13-16]. Moreover, the validation measurements on the as-quenched
specimen to a depth of 400 nm show that at depths exceeding 150 nm the curves of the
nano-hardness and of the E-modulus have converged to the same values: the
macroscopic properties of the steel. At all indent depths lower than 150 nm the matrix
hardness is lower than the macroscopic hardness.
3.3.3
EBSD studies
Fig. 3.3 show EBSD-measurements of the microstructures of the as-quenched sample (a)(c) and the sample tempered for 60 min. EBSD measurements of the microstructures of
the intermediate tempering times were also measured, but are not shown. During EBSD
mapping of the as-quenched specimen, no points were indexed as austenite.
93
Figure 3.3 EBSD-images of the microstructure of the as-quenched specimen (a-c) and the
specimen tempered for 60 minutes (d-f).The Left column (a and d) shows the band contrast prior
to noise reduction where non-indexed pixels show as light blue, the middle column (b and e)
shows the misorientation mapping after noise reduction in which boundaries exceeding 10˚ are
represented as black lines, and the right column (c and f) shows the inverse pole figure (IPF)
maps in which boundaries of less than 10˚ misorientation are represented as thin white lines.
The EBSD-images in Fig. 3.3(a) and (d) show the band contrast of the as-quenched
specimen and the specimen tempered for 60 minutes as measured prior to noise
reduction, respectively. The band contrast is a measure of the quality of the Kikuchi
pattern and is shown on a black-white scale, where poor band-contrast is shown as dark
areas. Reduction of pattern quality is typically a result of surface roughness, grain
boundaries and dislocations which induce strain in the measured lattice [21]. Fig. 3.3(a)
and (d) shows that the band contrast is degraded close to non-indexed regions. Nonindexed points, which are shown as white pixels, arise during EBSD mapping when the
Kikuchi patterns cannot be identified at all.
Fig. 3.3(b) and (e) shows the misorientation-profiles of the same EBSD-images as
shown in Fig. 3.3(a) and (d), but after noise reduction. The grain boundaries are defined
as boundaries between two neighboring pixels with a misorientation that exceeds 10˚
(shown as black lines). We observe that all grain boundaries exceeding 10˚ are located
inside formerly non-indexed regions. These grains structures are interpreted as block
boundaries in accordance to earlier literature [6-7, 14-15]. The misorientation profiles are
calculated from the average misorientation within sections of 3x3 pixels, all belonging to
the same grain, i.e. with a smaller misorientation than 10˚ between the pixels. Fig. 3.3(b)
and (e) shows that the misorientation increase towards the martensite boundaries.
Fig. 3.3(c) and (f) shows the inverse pole figures (IPF). Block boundaries are again
marked with black lines. The average block size is measured to be 3.5 µm2 for all tempered
specimens. No block coarsening take place during the 60 min of annealing. A slightly
higher block size is measured for the as-quenched state. This is an artifact of the post
processing of the EBSD data as non-indexed regions become integrated in larger
neighboring grains.
The non-indexed points in Fig. 3.3(a) and (d) are observed at and around block
boundaries. Comparison of Fig. 3.3(a) and (d) further shows that the area fraction of nonindexed regions decreases with increasing annealing time. The width of the non-indexed
regions is measured via the line intercept method in the horizontal and vertical direction
of each scan. The line intercept analysis showed the same average width, independent of
measurement direction, demonstrating that the asymmetric geometry of the beam spot
has no influence on the results. The average width of the non-indexed regions is 350nm
and 200 nm for the as-quenched sample and the sample tempered for 60 min,
respectively. A recent study performed with high-resolution EBSD on an extensively
tempered low carbon steel has shown that the width of the region within which the lattice
orientation is distorted over a grain boundary has a thickness of 40 nm [22]. These results
indicate that the minimum block boundary thickness we can expect to measure by EBSD
exceeds 40 nm.
The above results (band contrast and misorientation mapping) show that the strain levels
in the martensite increases closer to non-indexed regions. The results further show that
the non-indexed regions contain the block boundaries of the martensite and that no block
coarsening take place during tempering at 300 ˚C. As the surface roughness should be
comparable for all test specimens (the electropolishing was carried out using the same
parameters), the non-indexed regions are considered to be a result of high strain due to
high dislocation density. The relative change of non-indexed points for different
tempering times is considered to be a direct result of dislocation annihilation within the
non-indexed regions. In this study, we define the width of the non-indexed regions as the
boundary region. A quantitative analysis of the images in Fig. 3.3 is given in the next
section.
3.3.4
Softening and microstructure evolution
Fig. 3.4(a) shows the macroscopic hardness Hv measured as a function of tempering time.
The hardness reduces from 543.8 HV for the as-quenched specimen to 422.7 HV after 60
min of tempering. The hardness loss is highest during the first 5 min of tempering, but
continues after 10 min of tempering. Extended tempering from 60 to 600 min resulted in
only a minor hardness drop of 5 HV and therefore the 60 min tempering state is
considered the full tempering level in the present investigation. Fig. 3.4(a) also shows the
95
ratio of the nano-hardness, Hn, to the macroscopic hardness Hv. In agreement with
Ohmura et al. [13-17] we observe that the Hn/Hv-ratio increases with tempering time.
For the curve with the filled box-shaped symbols we used the nano-hardness of the
tempered matrix (see Fig. 3.4(b)) for Hn. The present study shows that the increase
of the Hn/Hv-ratio becomes less with increasing tempering time. The open-boxshaped symbol in Fig. 3.4(a) represents the Hn/Hv-ratio based on the average nanohardness of matrix, as calculated from the relation of area fractions of tempered and
non-tempered matrix in the as quenched state (black and red line in Fig 3.4(c)).
Fig. 3.4(b) shows the nano-hardness of the tempered matrix, non-tempered
matrix, and of boundaries, measured at 60 nm depth, as a function of tempering
time. We observe that the nano-hardness of boundaries is significantly higher than
the nano-hardness of the matrix (both tempered and non-tempered matrix), at
each investigated tempering time. We further observe that the nano-hardness of
the non-tempered matrix is significantly higher than the nano-hardness of the
tempered matrix in the as-quenched sample.
Only one data point, at 0 min, exists for non-tempered matrix because these regions
disappear within 5minutes of tempering (see Fig 3.4(c)). The nano-hardness of boundaries
reduces significantly during the first 5 min of tempering and thereafter reduces only
slightly during tempering from 5 to 60 min. The nano-hardness of tempered matrix does
not change upon tempering.
Fig. 3.4(c) shows the area fraction of tempered and non-tempered martensite as
measured by SEM and the area fraction of boundary regions as measured by EBSD, as a
function of tempering time. The area fraction of non-tempered martensite is reduced to
0 within 5minutes of tempering. The area fraction of boundary regions reduces from 0.44
in the as-quenched state to 0.27 after 60 min of tempering due to dislocation annihilation.
The block boundaries are assumed to be located in the center of the boundary regions as
measured by EBSD.
Figure 3.4 Macro- and nano-hardness and microstructural parameters as a function of annealing
time: (a) Macroscopic hardness, Hv, [HV0,5] and the ratio of the matrix nano-hardness and the
macroscopic hardness (Hn/Hv), (b) Nano-hardness, Hn, [GPa], (c) Area fraction of tempered, nontempered and boundary regions and (d) carbide length[nm], width[nm] and number density [µm-2]
97
Fig. 3.4(d) shows the carbide dimensions and number density as measured by SEM as a
function of tempering time. The carbide dimensions initially increase via a combined
length and width increase. After 10 min of tempering, spheroidization starts, the carbide
length decreases while the width increases. The initial number density of the small
carbides observed in the tempered regions of the as-quenched sample exceeds
200 µm-2. This number density is reduced to approx. 50 µm -2 after 5 min of tempering.
After 60 min of tempering the number density of carbides is reduced to approx. 39 µm -2.
The low macroscopic hardness of the as-quenched specimen is most likely a result of
auto-tempering during quenching. An artificial hardness value for comparison with
virgin martensite of 0.39 wt.%C can be calculated from the nano-hardness of nontempered matrix regions combined with the nano-hardness of boundary regions. The
area fraction of boundary regions in the as-quenched specimen is shown in Fig. 3.4(c)
and the remaining area is for the calculation assumed to consist only of non-tempered
matrix. An average hardness value calculated following these principles result in 6.99
GPa, which correlates to 713 HV. This value is in line with literature reports of hardness
of 0.39 wt.%C virgin martensite where quenching has been performed in liquid nitrogen
to avoid auto-tempering and formation of retained austenite [2].
The higher nano-hardness measured at boundaries, for all tempering times, can
be related to carbon atoms being present at defects, as we derive from the research of
Hutchinson [8] and the high dislocation density observed in the boundary regions, see Fig.
3.3 and Fig. 3.4(c). Fig. 3.4(c) show that dislocation annihilation in boundary regions
continues throughout the majority of the tempering process. Retained austenite in block
and lath boundaries can also contribute to added hardness of boundary regions in the asquenched sample. Retained austenite would cause deformation-induced transformation
to high carbon martensite during indentation. Based on the lack of points indexed as
austenite during EBSD measurements of the as-quenched sample, in combination with
literature reports of very low expected volume fractions of retained austenite in 0.39
wt.%C steels [2] we neglect the possible contribution of retained austenite to the
hardness.
The higher nano-hardness of non-tempered matrix is related to the redistribution
of carbon atoms in solid-solution in the non-tempered matrix to carbon in carbides in the
tempered regions during quenching.
The lack of nano-scale softening of the tempered matrix during tempering can be
related to the lower amount of dislocation annihilation inside the matrix. Furthermore we
calculate that the possible hardness change due to changes in carbide size and number
density in the tempered matrix is in the range of 0.2 GPa according to the Orwan-Ashby
model [23], based on the carbide length. This is within the error of the measurement
method and is therefore difficult to distinguish.
Fig. 3.5(a) shows the macroscopic softening rate during tempering. During the first 5
minutes of tempering the softening rate is highest (18.0 HV/min), followed by a large
reduction in softening rate to 3.0 HV/min between 5 and 10 min. After 10 min, the
softening rate continues to reduce to 0.54 HV/min and after 30 min minor softening
occurs at a rate of 0.19 HV/min.
Figure 3.5 Kinetics of the softening
processes during annealing at 300˚C,
showing (a) The rate of macroscopic
softening [HV min-1]and (b) The rate
of
nano-scale softening of the
tempered matrix regions and the
boundary region; nano-hardness Hn,
multiplied by the area fraction, f, per
unit time [GPa min-1]
Fig. 3.5(b) shows the change in nano-scale hardness Hn multiplied by the area fraction f
per unit time, i.e. (Hn·f)/t, which is proportional to the relative contributions of the two
microstructural regions to the macro-scale softening rate: boundary regions (BR) and nontempered matrix (NTM). The nano-hardness value of the boundary regions at 10 min of
tempering is estimated by interpolating the values measured at 5 and 60 min tempering.
From Fig. 3.5 we can distinguish the following three stages in the kinetics of martensite
softening in the Fe-C-Mn alloy during tempering at 300 ˚C. The distinction between the
tempering stages, is based on the hardness measurements of a limited number of
measurement points (5 minutes, 10 minutes, 30 minutes and 60 minutes).The three
stages identified are:
I.
Stage I (0-5 min) is characterized by fast macroscopic softening kinetics
(18,0HV/min) that are strongly related to: (a) fast and simultaneous softening
and reduction in area fraction of boundaries regions, i.e. HnBR·fBR/Δt = 0.24
GPa/min, and (b) fast reduction in area fraction of non-tempered matrix regions
99
II.
III.
ΔHnNTM·fNTM/Δt = 0.42 GPa/min. The microstructure processes of stage I are
redistribution of carbon atoms, recovery, and growth of iron carbides from Ɛcarbides to cementite. Figure 3.1 (a)-(b) and Fig 3.4 (c)-(d) show that these
processes take place in parallel and at different rates. Carbon redistribution is
most rapid, followed by carbide growth. Recovery appears to be the slowest
process.
Stage II (5-10 min) is characterized by slow macroscopic softening kinetics (3.0
HV/min) that is related to slow softening and reduction in area fraction of the
boundaries regions (HnBRfBR = 0.091 GPa/min). The microstructure processes
that dominate stage II are recovery and cementite growth. Figure 3.4(c)-(d)
shows that these processes take place in parallel and at different rates. The
recovery process is more rapid than the cementite growth process. The recovery
process appears to stop during stage II.
Stage III (10-60 min) is characterized by very slow softening kinetics (0.54-0.19
HV/min) that is related to very slow softening and reduction in area fraction of
boundary regions HnBR·fBR/Δt = 0.0041 GPa/min). The microstructure process of
stage III is cementite coarsening (see Fig 3.4 (d)).
3.4 Conclusions
We conclude the following from our investigation on the softening kinetics and the
kinetics of the evolution of the microstructure of martensite in high-purity Fe-C-Mn steel
during tempering at 300˚C:
1) The nano-hardness measured directly at the martensite boundaries is significantly
higher than the nano-hardness measured in the matrix for the as-quenched specimen.
2) The boundary regions soften with increasing tempering time, whereas the nanohardness of the tempered matrix remains approximately constant with increasing
tempering time.
3) The kinetics of martensite softening can be described by three stages, which are
related to the evolution of the microstructure. However, most of the softening takes
place during the first stage of tempering. The macroscopic softening of martensite is
mainly related to: i) the nano-scale softening of boundary regions, ii) the reduction in
area fraction of the boundaries regions, and iii) the reduction in area fraction of the
non-tempered matrix regions.
3.5 References
[1] GB. Olson and W.S. Owen (Eds.): Martensite, ASM International, Materials Park,
Ohio, USA, 1992
[2] G. Krauss: Mater. Sci. Eng., A 273 (1999) 40-57
[3] T. Ohmura, M Hayakawa, K. Miyahara, S. Matsuoka, K. Tsuzaki and T. Takahashi:
(1999) 20th RISO International Symposium on Materials Science (p. 433) Roskilde,
Denmark
[4] T. Ohmura, K. Tsuzaki and S. Matsuoka: Scripta Mater., 45 (2001) 889-894
[5] J. Li, T. Ohmura, F. Wei and K. Tsuzaki: Mater. Sci. Forum., 475-479 (2005) 4109-4112
[6] J. Li, T. Ohmura and K. Tsuzaki: Materials Transaction., 46 (2005) 1301-1305
[7] J. Li, T. Ohmura and K. Tsuzaki: Sci. China. Ser E: Technol. Sci., 49 (2006) 10-19
[8] B. Hutchinson, J. Hagstrom, O. Karlsson, D. Lindell, M. Tornberg, F. Lindberg and M.
Thuvander: Acta Mater., 59 (2011) 5845-5858
[9] KA. Taylor and M. Cohen: Progr. Mater. Sci., 36 (1992) 225-272
[10] GT. Eldis and M. Cohen: Metall. Mater. Trans., A 14A (1983) 1007-1012
[11] GR. Speich and WC. Leslie: Metall. Mater. Trans., B 3(1972) 1043-1054
[12] RN. Caron and G. Krauss: Metall. Mater. Trans., B 3 (1972) 2381-2389
[13] T. Ohmura, K. Tsuzaki and S. Matsuoka: Phil. Mag. A., 82 (2002) 1903-1910
[14] T. Ohmura, T. Hara and K. Tsuzaki: Scripta Mater., 49 (2003) 1157-1162
[15] T. Ohmura, T. Hara and K. Tsuzaki: J. Mater. Res., 18 (2003) 1465-1470
[16] T. Ohmura and K. Tsuzaki: J. Phys. IV France., (2003) 267-270
[17] T. Ohmura and K. Tsuzaki: Mater. Sci. Forum., 475-479 (2005) 4113-4116
[18] X. Li, B. Bhushan: Mater. Charact., 48 (2002) 11-36
[19] WC. Oliver and GM. Pharr: J. Mater. Res., 7 (1992) 1564-1583
[20] SMC van Bohemen, J. Sietsma, MJM Hermans and IM Richardson: Acta Mater. 51
(2003) 4183-4196
[21] SI. Wright, MM Nowell and DP. Field: Microsc. Microanal., 17 (2011) 316-329
[22] CJ. Gardner, BL. Adams, J. Basinger and DT. Fullwood: Int. J. Plasticity., 26 (2010)
1234-1247
[23] T. Gladman, Precipitation hardening in metals, The Institute of Materials, The
University Press, London, UK,1997
101
4 Effect of Ti on evolution of microstructure and
hardness of martensitic Fe-C-Mn steel during
tempering
C.Emmy I.C. Ohlund, Jonathan Weidow, Mattias Thuvander
and S.Erik Offerman
ISIJ International, Vol 54 (2014), No. 12, pp. 2090-2899
Abstract
The effect of the addition of 0.042 wt.% of titanium on the relation between the
evolution of the microstructure and the softening kinetics of quenched martensite in
high-purity Fe–C–Mn steel has been studied during tempering at 300 and 550C. The
evolution of the microstructure is characterized by measuring the cementite particle
size, the martensite block size, the area fraction of martensite regions which contain a
high dislocation density, the macroscopic hardness , the nano-hardness of martensite
blocks boundaries, the nano-hardness of the matrix and the TiC-precipitate size during
tempering. Nucleation of TiC-precipitates take place during annealing at 550°C and
starts earlier in regions close to the block boundaries, after 5-10 minutes, and
thereafter in the matrix, after 10-30 minutes, due to the higher dislocation density in
the regions close to the block boundaries. The TiC-precipitates slow down the recovery
in regions of high dislocation density compared to the alloy without TiC-precipitates.
The TiC-precipitates increase the macroscopic hardness of the steel after 30 minutes
annealing at 550°C. The growth of TiC-precipitates in martensite is simulated in good
agreement with experimental observations by a model that takes into account: 1)
capillarity effects, 2) the overlap of the titanium diffusion fields between TiCprecipitates, and 3) the effect of pipe diffusion of titanium atoms via multiple
dislocations. The average, experimentally-observed, TiC-precipitate size is 69±48 Ti
atoms.
103
4.1 Introduction
Tempered martensitic steel of strengths up to 1200 MPa is the most commonly used
material for high-strength fasteners in mass-produced car engines today. The
recommended maximum temperature during service is 150˚C [1]. These are the typical
requirements for the service conditions of fasteners for mass-produced passenger cars.
However, the current trend of engine down-sizing has resulted in higher mechanical
and thermal loading of the engines. There is a need for stronger (and yet tough) steels
at higher temperatures for engine fasteners. The design of this steel must fulfil
additional requirements. The alloying elements should be abundantly available and
should be added in low quantities to assure cost and material formability. Furthermore,
heat-treatment must be possible using industrial heat-treatment equipment and
tempering temperatures above 425 °C according to the ISO898-1 standard [1].
Precipitates have for decades been used in steels in order to improve
mechanical properties of steel. Good examples are the improved fire-resistance of
construction steel [2], the temperature and wear resistance of tool and high-speed
steels [3], and the creep-resistance of 9-12Cr martensitic steels for the power
generation industry [4-6]. These improvements of properties are based on a fine
dispersion of precipitates, which act like pinning points for dislocations and hinder
dislocation movement and recovery. Recent research suggests that TiC-precipitates are
good candidates for improving the strength of martensite at elevated temperature due
to their slow coarsening rate [7]. Martensitic steel with medium carbon content and a
small addition of Ti (around 0.04 wt%) is therefore an interesting candidate steel for
making steels for fasteners that are stronger at higher temperatures. Furthermore are
TiC-precipitates known to act as hydrogen traps [8-10] and improve the resistance to
hydrogen-induced damage, a very desirable feature when creating a high-strength
steel for the automotive industry.
In order to optimize the microstructure and properties of the steel we need
fundamental understanding of the relation between the evolution of the
microstructure and the softening kinetics during tempering of martensite with small
additions of titanium. Previous research has shown that the strength of as-quenched
and tempered, medium-carbon, martensitic steel strongly depends on the grain
boundaries [11-14]. The grain boundaries of the martensite blocks bring a so called
grain boundary effect to the steel; the boundaries are harder than the grain interior
and therefore increase the macroscopic strength.
We know that TiC-precipitates nucleate near dislocations and that the
nucleation rate is increased by increasing dislocation density [15-21]. However, the
interplay is not clear between the nucleation and early growth of TiC-precipitates and
the softening of the martensite due to the redistribution of carbon and titanium atoms
into cementite and TiC and the dislocation annihilation during tempering.
The aim of this study is to determine the effect of titanium in solid solution and
TiC on the evolution of the microstructure and the softening kinetics of quenched
martensite in Fe–C–Mn steel during tempering at 300 and 550 C. A special focus of our
research is to differentiate between the hardness of block boundaries and the matrix,
because previous research has shown that the strength of medium-carbon, martensitic
steel strongly depends on martensite block boundaries [11-14].
4.2 Method
One Ti-containing and one Ti-free alloy of Fe-C-Mn is investigated. The steel
compositions are given in table 1. Both steels are received with a carbon concentration
of 0.011 wt%, machined into cylinders with a diameter of 4 mm and subsequently
carburized to a carbon concentration of 0.39 wt.%C. The steel cylinders are cut into 10
mm long specimens for heat-treatment in a Bähr 805 A/D dilatometer (BärThermoanayse GmbH, Hüllhorst Germany). Both steels are given a homogenization
treatment before quenching to martensite The Ti-free steel is homogenized at 1100 ˚C
for 207 min, followed by natural cooling to 500°C to form ferrite. The steel is thereafter
transformed to austenite again, at 940˚C for 40 min, to create smaller austenite grain
sizes. The Ti-containing steel is homogenized at 1350˚C for 30 min to assure that all Tiatoms are in solid solution.
Both steels are quenched to room temperature from their respective
homogenization/austenization temperatures, using He-gas, at a cooling rate of approx.
175-180 °C/s from the start of quench to the martensite start (M s) temperature and a
cooling rate of approx. 45 ˚C/s between the M s and finish (Mf) temperatures. The Ms
temperature is approx. 360-370 °C and 380-390 °C for the Ti-free and the Ti-containing
steel respectively. Tempering treatments are subsequently performed at 300 ˚C and
550°C for 5, 10, 30 and 60 min. The heating up time to the tempering temperature is
138 s. The tempering temperature of 300 °C is chosen to assure that all Ti atoms remain
in solid solution and the tempering level of 550 °C is chosen to assure that TiC
nucleation and growth takes place during tempering [8-9].
All specimens are prepared by grinding and polishing to 1 µm diamond
dispersion, followed by 5 % nital etching or electro-polishing conducted in a solution of
8 % perchloric, 10 % butylcellosolve, 60 % ethanol and 22 % water. Electron probe
micros-analysis (EPMA) is performed to verify that the specimens are indeed
homogeneous in composition after the homogenization treatment, as determined with
a spatial resolution of 1 µm. The cementite particle size is measured by scanning
105
electron microscopy (SEM, JEOL JSM-6500F with field emission gun) on nital etched
surfaces. The size of the martensite blocks and the boundaries between the martensite
blocks is measured by electron back-scatter diffraction (EBSD with a Nordlys detector),
on electro-polished surfaces. The EBSD data are acquired and post-processed with
Channel 5 software. The beam diameter during EBSD mapping is approx. 16 nm,
resulting in a spot dimension of 16 x 35 nm. This spot dimension is combined with a
step size of 100 nm.
Transmission electron microscopy (TEM) is used to control that no TiCprecipitates are present in the steel after quenching and Atom probe tomography (APT)
is used to measure the TiC precipitate size after annealing of the martensite. The TEM
specimens are produced with the in-situ lift-out method [22] using a FEI Strata DB235
DualBeam workstation combining a focused ion beam with a scanning electron
microscope (FIB-SEM). The TEM specimens are analysed in a FEI Tecnai G2 transmission
electron microscope working at 200 kV with a LaB 6 filament. APT specimens are
produced with an in-situ lift-out method [23] using the FEI Strata 235 DualBeal
workstation. The specimen is sharpened by Ga+ sputtering using a pattern shaped as
an annulus circle. The voltage used is 30 kV with an initial current of 3000 pA which is
decreased as the specimen becomes sharper. The final sputtering is performed at 10
kV and 300 pA in order to decrease the gallium implementation in the specimen.
The APT specimens are analysed in an Imago LEAP 3000X HR atom probe
tomography instrument. The analyses are performed using laser pulsing at 200 kHz and
the laser energy of 0.2 nJ. The specimen temperature is 30-50 K and the evaporation
rate is 1 %. The reconstruction and data evaluation is performed using IVAS 3.6.1
software. The quantitative analysis is based on isotope distributions of different ions of
relevant atom types [24]. Overlaps involving Ti atoms exist at 24 Da (given by 48Ti2+ or
one molecular ion consisting of two 12C+) and 16 Da (given by 48Ti3+ or O+). We correct
the number of Ti counts at 24 Da with the Ti counts in the surrounding peaks, 23, 23.5,
24.5 and 25 Da. The surrounding peaks have no overlap with other atom types and the
Ti count at 24 Da is scaled according to the natural isotope abundance. For the Ti atoms
in the TiC precipitates the oxygen ion count at 16 Da is compared with the known
nominal concentration of oxygen in the steel and the excess count is attributed to Ti.
The quantitative APT analysis of C atoms is based on ions detected at 6, 6.5, 12
and 13 Da, plus all ions which exceeded the expected Ti level at 24 Da (as two C ions).
The detection and visualization of TiC-precipitates is done via isoconcentrationsurfaces enclosing regions which contain a Ti concentration that exceeds the nominal
steel concentration by 20 times (high enough to avoid local fluctuations or segregations
of Ti atoms and low enough to avoid ruling out very small TiC precipitates). The
diameter of the precipitates is determined from the number of Ti atoms measured by
APT, together with the lattice parameter of TiC. We count 4 Ti atoms per unit cell of TiC.
Micro-Vickers hardness is measured at 20 locations on polished specimens using
a load of 500 g. CSM nano-indentation measurements are performed on electropolished specimens using an Agilent G200 nano-indenter equipped with a Berkowichindenter and oscillation amplitude of 2 nm. The tip is calibrated using a reference
specimen of fused silica and the hardness values are determined following the method
of Oliver and Pharr [25]. We perform 8 x 8 indents to a depth of 70 nm on each sample.
The location of each individual indent is derived via the methodology developed by
Ö hlund et al [11]. The method is based on the fact that the shape of the nano-hardness
and the E-module curves, as a function of indent depth, has a steeper increase during
the first 20-25 nm for indents located at block boundaries, whereas indents located in
the matrix show a gradual increase of the values. The method was validated previously
by us by determining the location of the indents by EBSD measurements [11] where 13
indents on block boundaries and 17 indents in the matrix were compared. Block
boundaries were defined as boundaries with a misorientation that exceeded 10° and
IPF mapping revealed that the majority of all block boundaries in the investigated
specimen had a misorientation in the range of 45-60°.
4.3 Results
4.3.1
Cementite particle size evolution
Fig. 4.1 shows SEM images of Ti-free martensite (a)-(b) and Ti-containing martensite
(c)-(d) in the as-quenched condition and after tempering for 60 min at 550 °C. The
intermediate tempering times at both 300 °C and 550 °C were also examined by SEM
but are not shown here.
The SEM images in Fig. 4.1(a) and (c) show that the microstructures of both steels are
similar in the as-quenched state. Two types of regions exist: auto-tempered regions
which contain small iron-carbides and non-tempered regions which are smooth and
carbide-free [11]. The area fraction of tempered martensite in the as-quenched state is
larger in the Ti-containing steel. The SEM images in Fig. 4.1(b) and (d) show that the
microstructures of both steels consists of tempered martensite with cementite
particles after tempering at 550 °C for 60 min.
107
Figure 4.1 SEM pictures of nital-etched specimens showing the Ti-free martensite and the Ticontaining martensite in the following two states: as-quenched in (a) and (c) and after
tempering for 60 min at 550 °C in (b) and (d).
Fig. 4.2 shows the average cementite particle radius and number density as a function
of annealing time during annealing at 300 °C and 550 °C, which are derived from the
SEM images.
30
300
25
250
550 °C
300 °C
20
200
15
150
10
100
5
50
0
Number density of carbides (um-2)
(open symbols)
Average carbide radius (nm)
(solid symbols)
Ti-free
Ti
0
0
10
20
30
40
50
60
Tempering time (minutes)
Figure 4.2 Cementite carbide size and number density as a function of annealing time during
annealing at 300°C and 550°C as measured in the Ti-free and the Ti-containing martensite.
The error-bars represent a 95% confidence interval.
We observe that the average cementite particle size is larger during annealing at 550°C
than during annealing at 300°C, for each annealing time. Furthermore, we observe that
the average cementite particle size is larger in the Ti-containing martensite than in the
Ti-free martensite during the first 10 min of tempering at 550 °C. Both steels show
comparable carbide sizes during tempering at 300 °C. The number density of cementite
particles decreases rapidly between 5-10 min and is thereafter decreasing at a slower
rate.
4.3.2
Martensite block size and area fraction of block boundaries and regions of high
dislocation density
Fig. 4.3 shows the martensite blocks and the boundaries between the martensite blocks,
as measured by EBSD, of the Ti-free and the Ti-containing martensite after quenching
and after tempering at 550 °C for 60 min.
Figure 4.3 EBSD-images of the microstructure showing Ti-free and Ti-containing martensite in
the as-quenched state (a-d) and after annealing at 550°C for 60minutes (e-h). The left panel
shows the band contrast prior to noise reduction where non indexed points show as white
pixels and the right panel shows the inverse pole figure (IPF) maps after noise reduction where
grain boundaries exceeding 10° misorientation are represented as black lines.
The left hand panels (Fig. 4.3(a), (c), (e) and (g)) show the band contrast (BC) prior to
noise reduction: dark grey regions indicate poor band contrast, light grey regions
indicate good band contrast, and white regions indicate such poor band contrast that
crystallographic indexing is not possible. Degradation of the band contrast typically
arises from surface roughness, grain boundaries, elastic strain, and strain induced by
dislocations [26]. We observe that the BC is degraded close to non-indexed (white)
regions. Furthermore we observe that the BC is improved and that the width of the
109
non-indexed regions is reduced during annealing (compare Fig. 8.3(a) and (c) with 8.3(e)
and (f), respectively).
The right hand panels views (Fig. 4.3(b), (d), (f) and (h)) show the inverse pole figure
(IPF) maps of the same EBSD images as the left view (created after noise reduction)
where martensite block boundaries are marked by black lines. The martensite block
boundaries are defined as boundaries located between two neighbouring pixels which
have a misorientation that exceeds 10° in agreement with Morito et al [27-28]. We
observe that the block boundaries are located in formerly non-indexed regions.
There is no significant difference (95% confidence interval) comparing the block size of
Ti-containing and Ti-free martensite, and no block coarsening takes place during 60 min
of annealing at both tempering temperatures. As no grain coarsening take place during
annealing and the surface roughness and elastic strain is comparable for all specimens
(specimen preparation was the same), we derive that all improvements of Kikuchi
pattern quality during annealing is a result of recovery. We note that non-indexed
regions cover both martensite block boundaries and areas adjacent to the block
boundaries. Indexing of block boundaries is not affected by annealing. The reduction of
non-indexed points is therefore representative for recovery within areas of the
martensite block matrix that are directly adjacent to the martensite block boundary.
We call these regions boundary regions. The boundary regions are expected to consist
of parallel laths separated by lath boundaries, similar to the matrix in the centre of the
martensite block.
We observe that no significant improvement of indexing takes place after 10
min of annealing. Therefore, we consider the 60 min level to be representative for the
fully recovered state within the boundary regions for the annealing temperature
applied. The area fraction of non-indexed points is hereafter used to estimate the area
fraction of boundary regions and the evolution of recovery within these regions.
4.3.3
TiC-precipitate size
The TEM investigation did not reveal the presence of any TiC-precipitates in the asquenched state of the Ti-containing steel.
Fig 4.4 shows the APT measurements of the Ti-containing martensite specimen
where (a) displays Ti atoms in solid solution and TiC-precipitates and (b) displays C
atoms, after 60 min of tempering at 550 °C.
Figure 4.4 ATP images (90 x 90 x 120 nm) of the Ti-containing martensite after 60 minutes of
tempering at 550°C showing (a) distribution of Ti atoms in solid solution and iso-concentration
surfaces surrounding TiC-precipitates and (b) distribution of C atoms. The small window in a)
shows the five lower TiC-precipitates from the view of the single upper TiC-precipitate
Fig. 4.4(a) shows that both TiC-precipitates and Ti atoms in solid solution are present in
the martensite after 60 min of tempering at 550 °C .The amount of Ti in solid solution
is measured to be 0.015 at% which indicate that approx. 67 % of all Ti atoms have
precipitated as TiC. The number of Ti atoms in the largest TiC particle is approximately
160 Ti atoms and the smallest particle contains approximately 35 Ti atoms (here the
detection efficiency of 37 % has been accounted for). The average precipitate size,
based on all six precipitates is 69±46 Ti atoms (standard deviation). 69 Ti atoms
correspond to a diameter of 1.39nm.
Fig. 4.4(b) shows that there is an increase in the carbon concentration along a planar
feature in the examined volume. This planar feature could correspond to a lath
boundary in the martensite [29]. The concentration of carbon atoms in the lath
boundary is 0.21 at% and the concentration of carbon atoms in the matrix outside the
lath boundary is 0.012-0.030 at%. We observe that five out of the six TiC-precipitates
in Fig. 4.4(a) are located on the lath boundary that is visible in Fig. 4.4(b). The average
number of atoms in the five precipitates inside the lath boundary is 76±48 Ti atoms
(standard deviation).
The small TiC-precipitates in the APT reconstruction are close to spherical and the larger
TiC-precipitates appear to be more ellipsoidal. We expect that some degree of
compression in the analysis direction can take place and the true shape of the larger
precipitate can therefore be closer to spherical. APT measurements on specimens with
shorter annealing time were not performed due to that the expected TiC precipitate sizes
111
in these samples are too small to allow us to accurately differentiate between local
fluctuations or possible Ti atom segregation and TiC precipitates.
4.3.4
Hardness in matrix and boundaries
Fig. 4.5 shows the (a) macroscopic hardness and (b)-(c) the nano-hardness of the
boundary regions and the matrix of both steels as a function of annealing time at 300 °C
and at 550 °C.
Figure 4.5 Martensite hardness
measured as a function of
annealing time at 300°C and
550°C showing (a) the
Microvickers hardness (HV0.5) of
both steels and (b)-(c) the nanohardness measurement the Tifree martensite and the Ticontaining martensite
respectively, where the nanohardness of boundaries, nontempered matrix and matrix are
separated. The extrapolated line
in (a) represents the expected
martensite hardness if no TiC
nucleation would take place and
the black arrow shows the
hardness increase due to Ti in
solid solution. The error-bars
represent a 95% confidence
interval
Fig. 4.5(a) shows that the addition of Ti to the steel increases the macroscopic hardness
of the steel. Both steels soften rapidly during early stages of annealing, where a higher
annealing temperature result in a higher degree of softening. After 10 min of annealing
the softening decreases or stops. We observe a hardness increase (approx. 18 HV) for
the Ti-containing martensite between 30 and 60 min of annealing at 550 °C.
Fig. 4.5(b)-(c) shows the nano-hardness of the tempered matrix (both autotempered and normal tempered regions), non-tempered matrix and of boundaries,
measured at 60 nm depth, as a function of annealing time for (b) the Ti-free martensite
and (c) the Ti-containing martensite at 300 °C and at 550 °C. Only one data point exists
for non-tempered matrix, at t=0 minutes, because these regions disappear within 5 min
of annealing. We observe that both steels have a higher nano-hardness in the
boundaries as compared to the tempered matrix, for each tempering time, at both
annealing temperatures.
Fig. 4.5(b) shows that the majority of the nano-hardness reduction in all regions
of the Ti-free martensite takes place during the first 5 min of annealing. After 5 min no
significant further softening takes place for both annealing temperatures.
Fig. 4.5(c) shows that the nano-hardness reduction of the Ti-containing
martensite at 300 °C is similar to the nano-hardness reduction of Ti-free martensite,
the majority of the hardness reduction takes place during the first 5 min of annealing
and thereafter no further softening take place. However, at 550 °C we observe an
increase of the boundary nano-hardness in the Ti-containing martensite between 5 and
10 min of annealing followed by a nano-hardness increase of the matrix between 10
and 30 min. We furthermore observe that the average nano-hardness of the
boundaries remains unchanged between 10 and 30 min and that after 30 min the nanohardness of both the boundaries and the tempered matrix increase in parallel.
4.4 Discussion
4.4.1
Hardness and microstructure evolution
The influence of Ti in solid solution is a macroscopic hardness increase estimated to 32
HV (marked with a black arrow in Fig. 4.5(a)). This is estimated by comparing the Ti-free
and the Ti-containing steel during annealing at 300 °C and by knowing that no TiCprecipitates were present after quenching and that no TiC-precipitates nucleate at
300 °C [8-9]. The influence of TiC precipitates on the macroscopic hardness of
martensite can be observed first after 30-60 min of annealing at 550 °C, see Fig. 8.5(a).
The measured hardness increase of 16 HV shows that the TiC-precipitates we observe
by APT have added precipitation strengthening to the steel. We calculate the
precipitate strengthening after 60 minutes of annealing according to [30]:
𝜎𝑝 =
0.538𝐺𝑏𝑓 1⁄2
𝑑𝑝
𝑑
𝑙𝑛 (2𝑏𝑝 ),
Equation 4.1
where G is the shear modulus (81600 MPa for iron), b is the Burgers vector in iron, f is the
volume fraction of TiC and dp is the average precipitate diameter of 1.39 nm (69 Ti atoms
acc. to APT). The volume fraction of TiC is 67% of the equilibrium volume fraction (0.00084)
as measured by APT and calculated by ThermoCalc, (TCFE6). The strengthening effect is
113
100
Macroscopic
softening rate
(HV/min)
Degree of dislocation
Ratio of boundary
recovery with respect to
to matrix
fully annealed state
nano-hardness
in boundary regions (%)
approx. 105 MPa which correlate to approx. 35 HV, according to the conversion Rp (in
MPa)=3.0 HV [29]. This precipitation hardening effect is counteracted by the
redistribution of Ti atoms from solid solution to TiC, where 67 % of the solid solution
strengthening effect will disappear. This correspond to a hardness reduction of approx.
21.4 HV. We furthermore calculate that the smallest precipitate size which gives a
strengthening effect to the martensite is approximately 35 Ti atoms. The net effect of TiC
precipitates on the Ti-containing steel can be estimated using two methods. The first
method is the linear addition of the hardening mechanisms [31], which have been
suggested for quenched low carbon martensite. The second method is based on separate
treatment of dislocations and hard particles [32] and had successfully been applied on
high strength low alloy aluminium.
Linear addition results in a net hardness increase of approx. 13.6 HV, which is in good
agreement with the measured hardness increase of 16 HV and the approximation in Fig.
4.5(a) (see the extrapolated line in Fig. 4.5(a)). For the separate treatment of dislocations
and hard particles we need to consider the recovery of the martensite.
a)
b)
Ti-free
Ti
80
60
40
20
300oC
550oC
0
c)
1,8
d)
1,6
1,4
1,2
1,0
60
f)
e)
40
20
2
0
0
10
20
30
40
50
Tempering time (Minutes)
60 0
10
20
30
40
50
60
Tempering time (Minutes)
Figure 4.6 The influence of Ti in solid solution and TiC during annealing at 300°C and 550°C
showing (a-b) the degree of dislocation recovery, (c-d) the ratio of boundary and matrix nanohardness and (e-f) the macroscopic softening rate as a function of annealing time for both Tifree and Ti-containing martensite. The left column shows annealing temperature 300°C and
the right column shows annealing temperature 550°C. The error-bars represent a 95%
confidence interval.
Fig. 4.6 shows the effect of Ti in solid solution and as TiC-precipitates on the hardness
and microstructure evolution of martensite during annealing at 300°C (left column) and
at 550 °C (right column). Fig. 4.6(a)-(b) shows the evolution of dislocation recovery, with
respect to the fully annealed state, in boundary regions (a) at 300°C and (b) at 550 °C.
The degree of recovery is calculated from the EBSD indexing results. We consider the
indexing result measured at 60 min to be representative for full recovery (100%) at the
respective tempering temperature, and the indexing result in the as-quenched state to
be representative for 0 % recovery. We observe that the evolution of recovery is similar
in both steels during annealing at 300 °C. As no TiC-precipitates are present at this
tempering temperature, we conclude that Ti atoms in solid solution have no effect on
the recovery rate.
Annealing at 550 °C results in different recovery evolution in the Ti-free and the
Ti-containing steel. The Ti-free steel is similar to the two steels at 300°C; rapid recovery
during the first 10 min, followed by no recovery during the remainder of the 60 min.
The lack of recovery after 10 min of annealing and the EBSD map (see Fig. 4.3(e))
suggest that the non-indexed regions, which remain in the Ti-free steel after 10 min of
annealing, mainly consist of martensite block boundaries.
The Ti-containing steel shows a delay in the recovery process between 5 and 10
minutes (at 55 % of the fully recovered level), followed by slow recovery from 10 to 60
min. At 60 min the Ti-containing steel reaches a similar recovery level as the Ti-free
steel. The complete recovery stop between 5-10 min indicates that the dislocations
present at 5 min are pinned and cannot annihilate. The pinning of the dislocations is
believed to be caused by the presence of TiC precipitates. We calculate the hardness
contribution to the steels, due to dislocation strengthening, at different annealing
times according to the expression derived by Bailey and Hirsch [29, 33]:
𝜎 = 𝑀𝛼𝐺𝑏𝜌1⁄2 ,
Equation 4.2
where 𝛼 is the dislocation hardening factor, M is the Taylor factor (M𝛼 =0.34 for pure
iron [34]) and 𝜌 is the dislocation density. The dislocation density in the as-quenched
state is set to the average value of 14.2×1014 m-2 [35] and the dislocation density after
full recovery at 550 °C is set to 0.025𝜌𝐴𝑠𝑄 [36]. The dislocation density after 5 min of
annealing at 550 °C correlate to 55 % of the fully recovered state (see Fig. 4.6(b)).
The hardness contribution to the steel due to dislocation strengthening in the fully
recovered state is expected to be homogeneous in the material (no boundary regions
remain) and is calculated to 15 HV for both steels.
The hardness contribution due to dislocation strengthening after 10 min of annealing
is different in the Ti-free and the Ti-containing steel. The Ti-free steel will have a
115
hardness contribution that reflects a fully recovered structure (15.0 HV), whereas the
hardness of the Ti-containing steel is affected by the boundary regions where recovery
only has reached 55 % of the fully recovered level. The boundary regions in the Ticontaining steel (excluding the block boundaries) account for 9 % of the material and
have a higher hardness due to the higher dislocation density. The average hardness
contribution due to dislocation strengthening of the Ti-containing steel, taking the
boundary regions into account, is thereby calculated to be 19.0 HV. This higher degree
of dislocation induced hardness is however counteracted by the hardness loss caused
by redistribution of titanium and carbon atoms from solid solution to TiC via nucleation
of TiC-carbides in the boundary regions. These newly nucleated TiC precipitates are
most likely smaller than 35 atoms, and will not add any precipitate strengthening.
Linear addition of the hardening mechanisms is therefore possible. We estimate that
the hardness loss due to reduction of Ti atoms in solid solution caused by the nucleation
of TiC-precipitates in the time interval between 5 and 10 min, is approx. 3.9 HV. We
here assume that the critical TiC nucleus size is 14 Ti atoms (one unit cell of TiC), which
is approx. 18 % of the average TiC-precipitate size we measure in the laths after 60 min
of annealing by APT. We furthermore assume that no further nucleation of new
precipitates take place after 10 min as the TiC nucleation rate is reported to be high
[21]. The hardness decrease due to depletion of Ti atoms in solid solution during
nucleation is therefore expected to be approx. 18 % of the total hardness reduction due
to depletion of Ti atoms from solid solution as measured after 60 min of annealing at
550 °C (21.4 HV acc. to earlier paragraph). The hardness change of the Ti-containing
steel at 10 min of annealing due to dislocation density and redistribution of Ti atoms is
therefore close to 0 HV (not taking the depletion of carbon atoms into account). We
now compare the methods of linear addition [32] and separate treatment of
dislocations and hard particles [32] to estimate the net hardness increase of the Ticontaining steel after 60 min of annealing at 550 °C, including precipitation
strengthening of TiC, Ti atoms in solid solution and dislocation strengthening. Linear
addition predict a net hardness increase (comparing the state after 10 min of annealing
and the state after 60 min of annealing) of 5.7 HV and the separate treatment of
dislocations and hard particles predict a hardness reduction of 6.2 HV. We conclude
that linear addition is suitable for martensitic steel containing TiC precipitates.
Fig. 4.6(c)-(d) shows the ratio of the boundary-to-matrix nano-hardness, as a
function of annealing time, calculated from the nano-hardness measurements (c) at
300 °C and (d) at 550 °C. The evolution of the ratio of boundary to matrix nano-hardness
shows if the nano-hardness evolution is different in these two regions during annealing.
Fig. 4.6(c) shows that the evolution of the nano-hardness ratio is similar for the Ti-free
and the Ti-containing martensite during annealing at 300 °C. Therefore, we conclude
that Ti atoms in solid solution have little effect on the nano-hardness evolution of
martensite. Fig. 4.6(d) shows that the nano-hardness ratios of the two steels are similar
during the first 5 min of annealing at 550°C. This indicates that nucleation of TiC
precipitates has not yet taken place. However, between 5 and 10 min of annealing at
550°C the nano-hardness ratio is increased in the Ti-containing martensite followed by
a decrease between 10 and 30 min of annealing at 550°C. The ratio increase is believed
to be the result of the nucleation of TiC-precipitates in the boundary regions close to
the block boundaries. The higher dislocation density of boundary regions promotes
faster TiC nucleation due to a higher number of possible nucleation sites (the
nucleation of TiC-precipitates is reported to take place on/near dislocations [16, 18-19])
and the possibility of rapid pipe diffusion for solute Ti atoms. Fig. 4.5(c) clearly shows a
small increase in nano-hardness of the martensite block boundary regions and a
parallel decrease in the nano-hardness in the matrix during annealing from 5-10 min at
550 °C. The former can be the result of the small hardness increase caused by a lower
degree of recovery due to TiC nucleation in boundary regions and the latter indicates
that nucleation of TiC-precipitates has not started yet in the matrix. The reduction in
the nano-hardness ratio between 10 and 30 min annealing at 550°C for the Ticontaining steel is the result of the onset of TiC nucleation in the matrix (see the
hardness increase of the matrix in Fig. 6c during annealing between 10-30 min at 550°C).
After 30 min of tempering the ratio remains unchanged as the nano-hardness of the
boundaries and the matrix increase in parallel (see Fig. 8.6(c)).
Fig. 4.6(e)-(f) shows the macroscopic softening rate during annealing, as a
function of annealing time (e) at 300°C and (f) at 550°C, calculated from the
macroscopic hardness measurements. We observe that the softening rate is slightly
higher in the Ti-containing steel than in the Ti-free steel during the first 5 min of
annealing and thereafter (5 to 10 min) the macroscopic softening rate is lower in the
Ti-containing steel, at both annealing temperatures. This higher initial (0-5 min)
softening kinetics of the Ti-containing martensite is the result of the faster cementite
formation in the Ti-containing martensite, as shown in Fig. 4.2, which is in agreement
with the fact that titanium is a cementite stabilizer [37].
We furthermore observe that after 30 min of annealing at 550 °C the Ticontaining steel shows a negative softening rate due to the hardness increase
measured at 60 min (see Fig. 4.6(a)). The hardness increase is a direct result of
precipitation hardening from the TiC-precipitates we observe by APT (in the size of
approximately 70 Ti-atoms), see Fig. 4.4.
117
4.4.2
Diffusional TiC-precipitate growth
The high dislocation density of martensite is expected to influence the growth rate of
TiC in martensite, as compared to nucleation and growth of TiC in ferrite or austenite.
Our results indicate that the nucleation of TiC-precipitates starts earlier in boundary
regions (which have a higher dislocation density), than in the matrix of martensite.
We model the growth of spherical TiC-precipitates in martensite according to
three different models, in order to investigate the influence of the dislocations on the
growth of TiC. In all three models we assume that the nucleation of TiC starts in the
regions close to martensite block boundaries after 5 minutes of annealing, based on
the measured recovery results (Fig. 4.6(b)).
Furthermore, we model the start of nucleation of TiC-precipitates in the matrix
regions between 10-30 min of annealing, based on the increase of the nano-hardness
measured for the same time interval (see Fig. 4.5(c), matrix, 550°C, Ti-containing steel).
We assume that all TiC-precipitates nucleate at the same time in each region since the
nucleation rate of TiC-precipitates in ferrite is reported to be high [21]. The influence
of cementite on the growth of TiC-precipitates is considered to be negligible in the
calculations, because the majority of the volume fraction of cementite has formed
before 5 min of annealing (prior to nucleation of TiC in both regions).
In the first model, the growth is modelled to be controlled by volume diffusion
only). In the second and the third model, the growth rate is assumed to be controlled
by a combination of volume diffusion and diffusion along dislocations. We use the
tracer diffusivity of 44Ti, as measured in large single Fe crystals [38], as the lattice
⁄
diffusivity of Ti in martensite, 𝐷𝐿𝑇𝑖 𝑀 for all three models. The diffusivity data of Ti in αiron, as measured by Moll and Ogilvie [39] is not used for the calculations as this data
is derived from polycrystalline materials, which is believed to overestimate the lattice
diffusivity. We furthermore assume that the concentration of carbon (interstitial
element) of the martensite does not influence the diffusivity of Ti (substitution element)
[40]. ThermoCalc simulations (TCFE6) show that the atomic fraction of Mn in the TiC
phase is in the range of 0.2 at% and we therefore do not expect Mn to have a significant
influence on the nucleation and growth of TiC due to partitioning.
4.4.2.1 Volume-diffusion growth
The growth of TiC-precipitates is modelled according to classical diffusion-controlled
growth theory. The early stages of precipitate growth, when the diffusion fields of
neighbouring TiC grains do not overlap, is described by the Zener model where the
radius of a growing precipitate, Rn, as a function of time, is given by [41]:
𝐶 𝑚 −𝐶 𝑚
𝑒𝑞
0
𝑅𝑛 (𝑡) = 2.102 (𝐶 𝑇𝑖𝐶
)
−𝐶 𝑚
𝑒𝑞
0,5871
0
√〈𝐷𝑇𝑖 〉(𝑡 − 𝑡𝑠 )
Equation 4.3
𝑚
𝑇𝑖𝐶
Where ts is the moment of nucleation and t is the annealing time. 𝑐𝑒𝑞
and 𝑐𝑒𝑞
are the
equilibrium concentrations of Ti in the matrix and in the TiC-precipitate, respectively,
and 𝑐0𝑚 is the concentration of Ti atoms in the parent phase far away from the
precipitate. 〈𝐷𝑇𝑖 〉 is the average diffusion coefficient of Ti in martensite.
For the later stages of TiC-precipitate growth, when the diffusion fields have
started to overlap, we describe the growth by a model involving the transition from
non-overlapping to overlapping diffusion fields developed by Offerman et al [42], see
Fig. 4.7.
<d>
R1
CTiC
eq
C0
Cm
(r)
c
TiC
Martensite
L1
R2
L2
TiC
C
Cm
eq
r
Figure 4.7 Model for growth of TiC-precipitates involving overlapping diffusion fields. The
concentration of Ti-atoms, CTi, is shown as a function of the distance r where two spherical
TiC-precipitates with different radii, R1 and R2, are separated by an average distance <d>.
Local equilibrium is assumed at the interface of the TiC-precipitates (𝐶𝑇𝑖𝐶
𝑒𝑞 ) and the in the
𝑚
𝑚
matrix (𝐶𝑒𝑞 ). The overall Ti-concentration of the alloy is indicated by 𝐶0 . The concentration of
Ti-atoms at the position where the two diffusion profiles cross during precipitate growth, 𝐶𝑚
𝑐 ,
is approximated using linear concentration gradients over the distances L1 and L2
119
The model still uses Zener-type concentration profiles to calculate the velocity of the
interfaces but uses linear concentration profiles to estimate the concentration of Tiatoms at the position where the diffusion fields overlap.
For the growth of TiC-precipitates during overlapping diffusion fields, the Zener model is
still used, but the concentration 𝑐0𝑚 in Eq. 4.3. is replaced by 𝑐𝑐𝑚 , which is the
concentration of Ti at the position where the linear diffusion profiles intersect:
𝑚)
𝑐𝑐𝑚 = 𝑐0𝑚 − (𝑐0𝑚 − 𝑐𝑒𝑞
2𝑅+2𝐿−〈𝑑〉
2𝐿
Equation 4.4
,
where 〈𝑑 〉 is the average distance between the neighbouring precipitates and the
length L of the linear concentration profile is given by [42]:
1
𝐿 = { (44 + 54𝐵 + 6√54 + 132𝐵 + 81𝐵2 )
3
1⁄3
−
2
3(44+54𝐵+6√54+132𝐵+81𝐵 2)
4
} 𝑅𝑛
1⁄3
−
Equation 4.51
3
where
𝐵=
𝑇𝑖𝐶
𝑐0𝑚 −𝑐𝑒𝑞
Equation 4.6
𝑚 −𝑐 𝑚
𝑐𝑒𝑞
0
The Gibbs-Thomson effect is accounted for by expressing the Ti concentration at the
interface of the growing precipitate according to43):
2𝜎𝑣 𝑇𝑖𝐶
𝑎𝑡
𝑚
𝑚
𝑐𝑒𝑞,𝑟
= 𝑐𝑒𝑞
𝑒𝑥𝑝 (𝑐 𝑇𝑖𝐶𝑅(𝑡)𝑘𝑇
),
Equation 4.7
𝑒𝑞
where 𝜎 is the surface tension (approx. 0.3J/m2) [21, 44-45].
The numerical calculation of the TiC-precipitate radius is done according to:
𝑑𝑅
𝑅𝑛 = 𝑅𝑛−1 + ( 𝑑𝑡 )
𝑡=𝑡𝑛−1+1/2∆𝑡
∙ ∆𝑡,
Equation 4.8
where Rn-1 is the radius in the previous time step 𝑡𝑛−1 and t=(tn-tn-1). The equilibrium
𝑚
𝑇𝑖𝐶
concentration of titanium in the matrix and in TiC at 550°C, 𝑐𝑒𝑞
and 𝑐𝑒𝑞
, are calculated
using ThermoCalc. 𝑐0𝑚 (𝑡 = 0) is calculated from the initial steel composition, after
removing the equilibrium volume fraction of cementite at 550°C (as calculated by
ThermoCalc). 〈𝐷𝑇𝑖 〉 is set to be the lattice diffusion coefficient of Ti in martensite,
𝐷𝐿𝑇𝑖
1
⁄𝑀
.
3
4
Correction of typing error in the original publication, from 4 to 3
4.4.2.2 Dislocation assisted growth
We model dislocation assisted growth according to two mechanisms. The first mechanism
is developed by Wang and Shiflet [46]. This model describes how the growth rate of a
precipitate is affected by the diffusion of solute atoms along a single dislocation attached
to the precipitate, and was successfully applied to the growth of precipitates in a well
annealed binary alloy of Al-Li. The second mechanism describes dislocation assisted
growth of a precipitate by the diffusion of solute atoms along multiple dislocations that
are in close proximity to the precipitate. The effective diffusivity of the solute atoms is
described as a net diffusivity of solute atoms through the lattice and along dislocations.
4.4.2.2.1
Single dislocations model
The single-dislocation-assisted growth of spherical precipitates is given by [46]:
𝑑𝑅
|
𝑑𝑡 𝑡𝑜𝑡𝑎𝑙
where
𝑑𝑅
𝑑𝑅
=
𝑑𝑅
|
𝑑𝑡 𝐿𝑎𝑡𝑡𝑖𝑐𝑒
|
𝑑𝑡 𝐿𝑎𝑡𝑡𝑖𝑐𝑒
+ 𝑑𝑡 |
𝑃𝑖𝑝𝑒
Equation 4.9
,
is expressed via Eq. 4.3-4.8. The growth rate of the TiC-precipitate due
to pipe diffusion is expressed as:
𝑑𝑅
𝑐 𝑚 −𝑐 𝑚 √2𝑟
|
𝑑𝑡 𝑝𝑖𝑝𝑒
𝑇𝑖/𝑀
𝐷𝑃
0
0
√𝐷𝐿𝑇𝑖
= 𝑐 𝑚𝑒𝑞−𝑐 𝑇𝑖𝐶
𝜋𝑅2
𝑒𝑞
⁄𝑀
𝑒𝑞
𝐷𝑃𝑇𝑖
⁄𝑀
√𝑓(𝑡 ′ )
Equation 4.10
is the pipe diffusivity of Ti in martensite, r0 is radius of the cylindrical dislocation
pipe, 𝑡 ′ = 𝐷𝐿𝑇𝑖
⁄𝑀
∞
𝑓 (𝑡 ′ ) = ∫0
𝑡/𝑟02 and 𝑓(𝑡 ′ ) is the integral:
exp (−𝑡 ′ 𝑥 2 )
𝑥[𝐽02(𝑥)+𝑌02 (𝑥)]
𝑑𝑥,
Equation 4.11
where 𝐽0 (𝑥) and 𝑌0 (𝑥) are the zeroth order Bessel functions of the first and second
kind respectively. For r0 we use the Burgers vector in α-iron.
4.4.2.2.2
Multiple dislocations model
The multiple dislocation assisted growth of TiC-precipitates is expressed according to
Eq. 4.3-4.8, where 〈𝐷𝑇𝑖 〉 in Eq. 4.3 is replaced by an expression of the effective
diffusivity according to [47]:
121
𝑇𝑖/𝑀
〈𝐷𝑇𝑖 〉
𝐷𝐿
𝑇𝑖/𝑀 = 1 + 𝑔
𝐷𝑝
Equation 4.12
𝑇𝑖/𝑀
𝐷𝐿
where g is the cross sectional area of dislocation pipe per unit area of matrix. We
𝑇𝑖/𝑀
express the ratio of pipe diffusivity to lattice diffusivity,
𝐷𝑝
for Ti diffusion in
𝑇𝑖/𝑀
𝐷𝐿
martensite via the ratio of pipe diffusivity to lattice diffusivity of iron in iron and a scale
𝑇𝑖⁄𝐹𝑒
factor according to the ratio of diffusivities for Ti and Fe in iron (𝐷𝐿
𝑇𝑖/𝑀
𝐷𝑝
𝑇𝑖/𝑀
𝐷𝐿
=
𝑇𝑖/𝐹𝑒
).
𝐹𝑒/𝐹𝑒
𝐷𝐿
𝐷𝑝
𝐷𝐿
𝐷𝐿
𝐹𝑒/𝐹𝑒 ∙
𝐹𝑒⁄𝐹𝑒
and 𝐷𝐿
Equation 4.13
𝐹𝑒/𝐹𝑒
𝑇𝑖/𝐹𝑒
The scale factor,
𝐷𝐿
𝐹𝑒/𝐹𝑒
𝐷𝐿
accounts for the different atom radius of Ti and Fe, which is
believed to affect pipe diffusion of Ti in iron, according to the same proportion as lattice
diffusion of Ti in iron is affected.
The effective pipe radius of a dislocation is set equal to the burgers vector in α-iron, b,
and we express the cross sectional area of dislocation per unit area of martensite in Eq.
4.12 as:
𝑔 = 𝜌𝜋𝑏2 ,
Equation 4.14
where 𝜌 is the dislocation density. We extend Eq. 4.12 to include the recovery during
isothermal annealing by expressing g as a function of time:
𝑔(𝑡) = 𝜌𝐴𝑠𝑄 𝜋𝑏2 − 𝐹(𝑡)[𝜌𝐴𝑠𝑄 𝜋𝑏2 − 𝜌𝑅 𝜋𝑏2 ] ,
Equation 4.15
where ρAsQ is the dislocation density in the as-quenched state, ρR is the dislocation
density after recovery and F(t) is a function that describes the evolution of the recovery
process. We use the same dislocation densities as in section 4.4.2.1. F(t) is modelled to
follow the evolution of dislocation recovery as measured by EBSD (Fig 4.7(b)).
𝐹𝑒/𝐹𝑒
The ratio
4.4.3
𝐷𝑝
𝐹𝑒/𝐹𝑒
𝐷𝐿
= 57100 at 550°C [48] and
𝑇𝑖/𝐹𝑒
𝐷𝐿
𝐹𝑒/𝐹𝑒
𝐷𝐿
is calculated to be 0.30 at 550°C [49].
Comparison of TiC growth models
Table 4.2 shows the calculated average precipitate sizes after 60 min of annealing at
550 °C in boundary and matrix regions for all three models and the APT measurements.
We assume that the precipitates measured in the lath boundary is representative for
boundary regions due to the high dislocation density of martensite laths. The volume
diffusion model predicts too small precipitate sizes, and we therefore conclude that
pipe diffusion strongly contributes to the growth of TiC in martensite.
Table 4.2 Precipitate size (number of Ti atoms)
Kinetics
Volume
Diffusion along
Diffusion
diffusion single dislocation along
multiple
dislocations
Boundary
Matrix
21
17-20
252
168-236
91
68-85
Measured
by APT
(Standard
deviation)
Number of
measurements
(APT)
76±48
35
5
1
Table 4.2 furthermore shows that the single dislocation model overestimates the
precipitate size. The reason for the overestimated precipitate size by the singledislocation model is that the size of the TiC-precipitates within this research is so small
that pipe diffusion becomes dominant in the model (small values for the radii results in
r
high values of the term R02 in Eq. 4.8). The single dislocation model does also not take
into account the reduction in the dislocation density due to recovery. Moreover, as
Wang and Shiflet [46] point out, the model does not take into account the competition
for Ti atoms between neighbouring TiC precipitates along the same dislocation line,
which would slow down precipitate growth.
The multiple dislocation-assisted growth model predict TiC-precipitate sizes
which are in agreement with the APT measurement. The model takes into account the
recovery, which means that the model takes into account a reduction in the overall
diffusivity of Ti-atoms due to the reduction in dislocation density.
4.5 Conclusions
Two martensitic steels with and without the addition of 0.042 wt.% of Ti are compared
at annealing temperatures of 300 °C and 550 °C. The macroscopic hardness in both
steels and at both temperatures reduces quickly during the first 5 min of tempering,
due to the redistribution of interstitially dissolved carbon into cementite and due to
rapid recovery. The macroscopic hardness remains more or less the same during
continued annealing, except for the Ti-containing steel that is tempered at 550 °C. This
is related to the formation of TiC-precipitates at 550 °C. Nucleation of TiC-precipitates
starts first in the regions close to the martensite block boundaries (between 5-10 min)
and thereafter in the block matrix (between 10-30 min) during annealing at 550°C, due
to the higher dislocation density in the regions close to the block boundaries. The
123
formation of TiC-precipitates has the following effects on the evolution of the
microstructure and the hardness:
1. TiC-precipitates slow down the recovery in the regions close to the martensite
block boundaries compared to the alloy without TiC-precipitates.
2. The TiC-precipitates increase the macroscopic hardness of the steel after 30 min
annealing at 550 °C.
The growth of TiC-precipitates in martensite is simulated with three models: 1) a model
taking into account capillarity effects and the overlap of the titanium diffusion fields, 2)
a model that takes into account the above effects plus the effect of the diffusion of
titanium atoms along a single dislocation attached to the precipitate, and 3) a model
that takes into account the effects of the first model and the effect of pipe diffusion of
titanium atoms via multiple dislocations. The third model predicts a TiC-precipitate size
that correspond the closest to the experimentally observed TiC-precipitate sizes.
4.6 References
[1] ISO898-1, Mechanical properties of fasteners made of carbon steel and alloy steelPart 1. Fifth edition, Switzerland, 2013
[2] EG. Dere, H. Sharma, RH. Petrov, J. Sietsma and SE. Offerman: Scr. Mater.,
68(2013), 651
[3] LS. Kremnev: Metal. Sci. Heat. Treat., 33(1991), 428
[4] RF. Buck and WMJr. Garrison: Adv. Mater. Process. 150(1996), 27
[5] RL. Klueh, N. Hashimoto, RF. Buck and MA. Sokolov: J Nucl Mater., 283-287(2000),
697
[6] F. Abe, M. Taneike and K. Sawada: K,: Int. J. Press. Vessel Pip., 87(2007), 3
[7] M. Taneike, M. Fujitsuna and F. Abe: Mater. Sci. Technol., 20(2004), 1455
[8] F-G. Wei, T Hara, T. Tsuchida and K Tsuzaki: ISIJ Int. 43(2003), 539
[9] F-G. Wei, T. Hara and K. Tsuzaki: Metall Mater. Trans. B., 35b(2004), 587
[10] J. Takahashi, K. Kawakami, Y. Kobayashi and T. Tarui: Scr. Mater., 63(2010), 261
[11] CEIC. Ohlund, SE. Offerman and E. Schlangen: Mater. Sci. Eng. A., 560(2013), 351
[12] T. Ohmura, M. Hayakawa, K. Miyahara, S. Matsuoka, K. Tsuzaki and T.
Takahashi: Proc. of 20th Riso Int. Symp. on Materials Science, Roskilde,
Denmark,(1999), 433
[13] T. Ohmura, T. Hara and K. Tsuzaki: Scr. Mater., 49(2003), 1157
[14] T. Ohmura, AM. Minor, EA. Stach and JWJr. Morris: .J Mater. Res. 19(2004), 3626
[15] DM. Barnett: Scr. Metall., 5(1971), 261
[16] W. Kesternich: Philos. Mag. A., 52(1985), 533
[17] SQ. Xiao and P Haasen: Scr. Metall., 23(1989), 365
[18] P. Gopalan, R. Rajarman, B. Viswanathan, KP. Gopinathan and S. Venkadesan: J.
Nuc. Mat., 256(1998), 229
[19] SY. Hu, and LQ. Chen: Acta Mater., 49(2001), 463
[20] Z. Wang, X. Mao, Z. Yang, X. Sun, Q. Yong, Z. Li and Y. Weng: Mater. Sci. Eng. A.,
529(2011), 459
[21] M. Sawahata, M. Enomoto, K. Okuda and T. Yamashita: Tetsu-to-Hagane.,
94(2008), 21
[22] MHF. Overwijk, FC. Van den Heuvel and CWT.Bulle‐Lieuwma: J. Vac. Sci.
Technol. B., 11(1993), 2021
[23] DJ. Larson, DT. Foord, AK. Petford-Long, TC. Anthony, IM. Rozdilsky, A Cerezo and
GWD. Smith: Ultramicrosc., 75(1998), 147
[24] M. Thuvander, J. Weidow, J. Angseryd, LK. Falk, M. Sonestedt, K. Stiller and HO.
Andre’n: Ultramicrosc., 111(2011), 604
[25] WC. Oliver and GM Pharr: J. Mater. Res., 7(1992), 1564
[26] SI. Wright and MM. Nowell: Microsc. Microanal., 17(2011), 316
[27] S. Morito, H. Tanaka, R. Konishi, T. Furuhara and T. Maki: Acta Mater., 51(2003),
1789
[28] S. Morito, X. Huang, T. Furuhara, T. Maki and N. Hansen: Acta Mater., 54(2006),
5323
125
[29] D. Hutchinson, J. Hagstrom, O. Karlsson, D. Lindell, M. Tornberg, F. Lindberg and
M. Thuvander: Acta Mater., 59(2011), 5845
[30] T. Gladman: Mat. Sci. Tech., 15(1999), 30
[31] LA. Nordstrom: Scand. J. Metall., 5(1976), 159
[32] E. Hornbogen, EA. Starke Jr. : Acta Metall., 45(1993), 1.[33] Y. Han, J. Shi, L. Xu,
WQ. Cao and H. Dong: Mater. Sci. Eng. A., A530(2011), 643
[34] G. Thomas, J. Washburn: Electron Microscopy and Strength of Crystals, Interscience
Publ, New York, USA, 1963
[35] S. Morito, J. Nishikawa and T. Maki: ISIJ Int., 43(2003), 1475
[36] S. Takebayashi, T. Kunieda, N. Yoshinaga, K. Ushioda and S. Ogata: ISIJ Int.,
50(2010), 875
[37] CK. Ande and MHF. Sluiter: Acta Mater., 58(2010), 6276
[38] P. Klugkist and C. Herzig: Phys. Status. Solidi. (a)., 148(1995), 413
[39] SH. Moll and RE. Ogilvie: Trans MS AIME., 215(1959), 613
[40] A. Borgenstam, A. Engstrom, L. Hoglund and J. Agren: J. Phase Equilibria.,
21(2000), 269
[41] SGE. Te Velthuis, NH. Van Dijk, MTH. Rekveldt, J. Sietsma and S. Van der Zwaag:
Mater. Sci. Eng. A., 277(2000), 218
[42] SE. Offerman, NH. Van Dijk, J. Sietsma, EM. Lauridsen, L. Margulies, S. Grigull, HF.
Poulsen and S. Van der Zwaag: Acta mater., 52(2004), 4757
[43] M. Perez M: Scr. Mater., 52(2005), 709
[44] JH. Jang, CH. Lee, YU. Heo and DW. Suh: , Acta Mater., 60(2012), 208
[45] DHR. Fors and G. Wahnstrom: Phys. Rev., 82(2010), 195410-1
[46] ZM. Wang and GJ. Shiflet: Metall. Mater. Trans., 29A(1998), 2073
[47] DA. Porter and KE. Easterling: Phase transformations in metals and alloys, Van
Norstrand Reinhold, New York, USA (1981)
[48] Y. Shima, Y. Ishikawa, H. Nitta, Y. Yamazaki, K. Mimura, M. Isshiki and Y. Iijima:
Mater. Trans. 43(2002), 173
[49] FF. Buffington, K. Hirano and M. Cohen: Acta Metall., 9(1961), 434
5 Modelling the evolution of multiple hardening
mechanisms during tempering of Fe-C-Mn-Ti
martensite
C. Emmy I. C. Ohlund, Dennis den Ouden, Jonathan Weidow, Mattias Thuvander and S.
Erik Offerman
ISIJ International, Vol. 55 (2015), No. 4, pp. 883-892
Abstract
We model the hardness evolution of martensite during tempering as a linear
addition of multiple hardening mechanisms that is combined with a microstructural
Kampmann-Wagner-Numerical (KWN) model to simulate the nucleation and
growth of TiC-precipitates during tempering. The combined model is fitted to the
measured hardness evolution during tempering at 300°C and 550°C of the
martensitic steels with and without the addition of titanium. The model predicts
TiC-precipitate sizes in agreement with experimental observations and generates
fitting parameters in good agreement with literature. The microstructural
components that give the highest contribution to the overall hardness are Fe3C
precipitates (88 HV) and dislocations (54 HV). Both Fe 3C- and dislocationstrengthening decreases rapidly during the initial stage and stabilise after 10
minutes of tempering. The model shows that the decrease in dislocation density
due to recovery is slowed down due to the presence of TiC-precipitates. Titanium
atoms in solid solution give a stable hardness contribution (25 HV) throughout the
tempering process. TiC-precipitate strengthening generates a minor contribution
(3.5 HV). The model shows that less than 1% of the equilibrium volume fraction of
TiC-precipitates forms during isothermal tempering at 550 °C due to the large misfit
strain (1.34 GJ/m3) and a limited density of potential nucleation sites in the
martensite. The model shows that the hardness of tempered martensitic steels
could potentially be increased by increasing the TiC-precipitate density by reducing
the misfit strain.
127
5.1 Introduction
Tempered martensitic steel is the most commonly used material for high-strength
fasteners in mass-produced car engines today [1]. These steels fulfil the typical
requirements for the service conditions of fasteners used in current passenger cars:
ultimate tensile strengths up to 1200 MPa and a recommended service
temperature of max 300 °C. However, the ongoing trend of engine down-sizing in
order to reduce weight and CO2-emmissions results in higher mechanical and
thermal loading of the engines. Stronger and yet tough steels are now required for
engine fasteners. An important boundary condition for fastener steels is a low
concentration of alloying elements that are abundantly available in order to assure
cost efficiency and suitability of the steel for cold forging.
The strength of martensite originates from multiple strengthening
mechanisms: 1) elements in solid solution, 2) grain boundaries, 3) dislocations, and
4) precipitates [2]. The strength of martensite is therefore a complicated function
of the martensite microstructure as this evolves during tempering of the martensite.
The microstructure of martensite consists of the parent austenite grain structure
which is sub-divided into packets. Each packet is divided into blocks and each block
consists of parallel laths which are divided by walls of dislocations (lath boundaries)
[3]. Moreover, the microstructure of martensite consists of free dislocations,
carbides, carbon atoms and other alloy atoms in solution. The carbon atoms are
present in solid solution, as atoms segregated into lattice defects such as
dislocations and/or as part of the different carbides. Substitutional alloying
elements such as Ti are present in solid solution or in carbides.
The traditional fastener steels with strength levels up to 1200 MPa, such as 33B2
and 34Cr4, are essentially based on the first three strengthening mechanisms
mentioned above. New steels for stronger fasteners have now been developed with
additional strengthening from precipitates according to similar principles as used in
HSLA steels [4]. Precipitates of V- and Ti-carbides are used to increase the strength
to levels higher than 1200 MPa [5].The tempering temperature which is required
for the nucleation and growth of secondary V or Ti-containing precipitates is above
500 °C, which fits with the requirements of the fastener standard ISO 898-1 [1] and
the low alloy additions enable the steel to be suitable for cold forming. More
importantly, TiC-precipitates have the potential to act as hydrogen traps and
improve the resistance to hydrogen-induced damage [6] during processing and
service of the fastener. In addition to enhancing strength, thermally stable
precipitates are also known to improve the temperature resistance of steels, by
acting as pinning points for movement of dislocations [7]. The high thermal stability
of TiC precipitates [8] therefore makes medium-carbon steel with a small addition
of Ti an interesting candidate for high-strength engine fasteners intended for
service temperatures which exceed the current limit of 300 °C. The mechanical
properties of such fasteners will be directly related to the martensite
microstructure with precipitates. Fundamental understanding of the evolution of
the microstructure and the resulting hardness during tempering of martensite with
small additions of Ti is required to optimise the heat treatment process and the
mechanical properties of the fastener.
The aim of this study is to model the evolution of the multiple hardening
mechanisms during tempering of Fe-C-Mn-Ti martensite. We simulate the hardness
evolution of martensite via linear addition of the hardening mechanisms. This
hardness model is combined with a microstructural multi-component and multiphase Kampmann-Wagner-Numerical (KWN) model as developed by Den Ouden et
al. [9], for the simulation of TiC-precipitate nucleation and growth during tempering.
The KWN-model takes into account the distribution of carbon atoms between
phase fractions of TiC- and Fe3C-precipitates. Moreover, the model simulates the
evolution of recovery in order to estimate the effective diffusivity of Ti-atoms and
in order to estimate the number of available nucleation sites for TiC-precipitates.
The combined models are fitted to the experimental work of Ö hlund et al.
presented in ref [10].
5.2 Modelling the evolution of multiple hardness components
during tempering
We assume that the separate hardening mechanisms of grain size (gb), solid solution (ss),
precipitates (P) and dislocations (d) can be added linearly, in agreement with [2]:
𝜎𝑡𝑜𝑡 = ∆𝜎𝑔𝑏 + ∆𝜎𝑠𝑠 + ∆𝜎𝑃 + ∆𝜎𝑑 ,
Equation 5.1
where ∆𝜎𝑔𝑏 is the hardness contribution from grain boundaries, ∆𝜎𝑠𝑠 is the hardness
contribution form elements in solid solution, ∆𝜎𝑝 is the hardness contribution from
precipitates and ∆𝜎𝑑 is the hardness contribution from dislocations.
The increase of strength due to grain size is simulated by the Hall-Petch relationship is
[11]:
∆𝜎𝑔𝑏 = 𝜎𝑙 + 𝑘𝐷 𝑑𝑑 −1⁄2 ,
Equation 5.2
129
where 𝜎𝑙 is the lattice friction, 𝑘𝐷 the Hall-Petch factor and 𝑑𝑔 the average diameter of
the martensite grains. 𝑑𝑔 is a function of time if grain coarsening takes place.
The effective grain size of martensite is reported to be the block size [12]. A Hall-Petch
term has also been suggested for the lath sub-structure within the block, but we choose
to include this effect in the term for dislocation density contribution [13], because a lath
boundary can be described by a stack of dislocations.
The increase in yield strength due to elements in solid solution, i.e. C, Ti and Mn, is
simulated by the general form [14]:
𝑛𝑠,𝑖
∆𝜎𝑠𝑠,𝑖 = 𝐾𝑖 𝐶𝑖
Equation 5.3
,
where 𝐾𝑖 is a constant for alloy element i, 𝐶𝑖 is the concentration of element i and 𝑛𝑠,𝑖 is
a constant that can vary from 0.5 to 2 depending on the alloying element [14]. The
concentrations of C, Ti and Mn in the matrix are functions of time, due to redistribution
into TiC and/or Fe3C.
We set 𝑛𝑠,𝑀𝑛 = 1 in agreement with [13] and we assume that 𝑛𝑠,𝑇𝑖 = 1 due to that both
Mn and Ti are substitutional atoms.
We do not include the effect of carbon atoms in solid solution in Eq. 5.3. Literature reports
that that the well-known square root effect of carbon concentration on martensite yield
strength is associated with the dislocation density of the martensite, rather than the solid
solution effect of carbon atoms [13, 15]. An increased carbon content of the steel
generates a linear increase of the dislocation density of the quenched martensite. Carbon
atoms diffuse to the Cottrell atmospheres of dislocation during quenching of the
martensite and thereby maintain a higher dislocation density of the martensite, as
recovery is hindered via pinning of dislocations by segregated carbon atoms. The
dislocation density of martensite also generates a square root contribution to the
martensite yield strength (see Eq. 5.5) and the effect of increased carbon concentration
on martensite therefore follows the well-established square-root dependency.
The increase in strength due to precipitates is calculated according to the Orowan-Ashby equation
[16]:
1⁄2
∆𝜎𝑃,𝑗 = (
0.538𝐺𝑏𝑓𝑗
2𝑟𝑝,𝑗
) ∙ ln (
𝑟𝑝,𝑗
𝑏
),
Equation 5.4
where G is the shear modulus of the matrix (calculated to be 80.4 GPa by a linear
interpolation between the systems of Fe and Fe-1C at as concentration of 0.4 wt.%C [17]),
b is the length of the Burgers vector (0.248 nm [18]), fj is the volume fraction of precipitate
phase j and rp,j is the average precipitate radius of phase j (TiC and Fe3C). fj and rp,j are
functions of time due to the nucleation and growth of Fe3C- and TiC-precipitates.
The increase in yield strength by dislocations is calculated according to [19]:
∆𝜎𝑑 = 𝑀𝛼𝐺𝑏𝜌1⁄2 ,
Equation 5.5
where M = 2.733 (the Taylor factor) [20] and 𝛼 (an empirical parameter) are constants.
The dislocation density, 𝜌, is a function of time due to recovery. Recovery is in turn
affected by the number of precipitates present in the material, as precipitates pin
dislocations. The effect of precipitates on the recovery kinetics can be described
according to [19] by
𝑑(∆𝜎𝑑 )
𝑑𝑡
2
= [−
64(∆𝜎𝜌 ) 𝜈𝑑
9𝑀 3 𝛼2 𝐸
𝑑(∆𝜎𝑑 )
𝑑𝑡
𝑈
∆𝜎𝜌𝑉𝑎
𝐵
𝑘𝐵 𝑇
exp (− 𝑘 𝑎𝑇 ) sinh (
= 0 for N≥Nc,
𝑁(𝑡)
)] (1 − 𝑁
𝑐 (𝑡)
) for N<Nc and
Equation 5.6
where 𝜈𝑑 and 𝐸 are the Debye frequency and Youngs modulus respectively and 𝛼 has the
same meaning as in Eq. 5.5, 𝑈𝑎 and 𝑉𝑎 are the activation energy and activation volume
for recovery respectively, kB is the Boltzmanns constant, N(t) is the number density of TiC
precipitates and Nc(t) is the total number density of dislocation nodes and T is the
temperature. We use the same approximation as [19] for the number of dislocation nodes:
0.5𝜌(𝑡)1.5 . Similar to [19], we also approximate 𝜈𝑑 and 𝑈𝑎 using the self-diffusivity of iron
in martensite [21] and the lattice parameter of martensite [22]. 𝑉𝑎 is assumed to be
temperature independent. The parameters 𝛼 and 𝑉𝑎 are assumed unknown and will be
fitted to the experimental data.
We use Eq. 5.6 to model the evolution of ∆𝜎𝑑 as a function of time, and we thereafter
calculate 𝜌(𝑡) via Eq. 5.5. We assume that microstructure in the as-quenched state
corresponds to 0 % recovery and the dislocation density 𝜌𝐴𝑠𝑄 in the as-quenched state is
14.2×1014 m-2, as found in the literature [23].
The total yield strength of each strengthening mechanism can thereafter be converted to
hardness according to [24]:
𝐻𝑉 = 𝜎𝑡𝑜𝑡 /3.
Equation 5.7
The unknown parameters in the hardness model are 𝜎0 , 𝐾𝑀𝑛 , 𝐾𝑇𝑖 , 𝛼 and 𝑉𝑎 . The values for
𝑓𝐹𝑒3 𝐶 and 𝑟𝑝,𝐹𝑒3 𝐶 are obtained from the experimental measurements presented in later
sections. The values for 𝑓𝑇𝑖𝐶 and 𝑟𝑝,𝑇𝑖𝐶 are obtained from simulations with the
multicomponent KWN model which is discussed in the next section. The concentrations
of C, Ti and Mn in solid solution can be obtained from the measured and simulated data.
131
5.3 Modelling the nucleation and growth of TiC-precipitates during
tempering
Literature reports that TiC precipitates in steel nucleate near dislocations [25] and that
the nucleation rate of TiC is high, followed by slower growth and coarsening [26]. Studies
have furthermore shown that both TiC nucleation and growth is enhanced by the
presence of dislocations [10]. Literature furthermore reports that the presence of TiC
precipitates in martensite affects the evolution of the dislocation density in steel during
the heat treatment [10, 18]. The modelling of TiC nucleation and growth in martensite
must therefore be linked to dislocation density and recovery in martensite during
tempering.
5.3.1
Nucleation of TiC
We assume that the nucleation barrier for TiC nucleation in martensite is lowered via
interactions between the strain field surrounding the dislocation and the nuclei, without
annihilation of the dislocation core, in agreement with [27-28]. We furthermore assume
that at the moment of nucleation the TiC precipitates are coherent with the matrix in
three dimensions, which implies a cubic nucleus shape.
The classical nucleation theory describes the change in Gibbs free energy associated with
a nucleation event of one such cubic nucleus as:
Δ𝐺 = 𝑙 3 (Δ𝑔𝑣 + Δ𝑔𝑠 ) + 6𝑙 2 𝛾𝑒𝑓𝑓 ,
Equation 5.8
where 𝑙 is the edge of the cubic nuclei, Δ𝑔𝑣 is the chemical free energy change per unit
of volume due to the formation of the precipitate phase (also called the driving force for
nucleation) which has a negative sign in case of an oversaturated matrix, Δ𝑔𝑠 is the misfit
strain energy due to the formation of the precipitate in the host lattice and 𝛾𝑒𝑓𝑓 is the
effective interface energy of a precipitate which interacts with a nearby dislocation strain
field. The effective surface energy is calculated according to [29]:
3
𝜋 𝐺𝑏(1+𝜈)
𝛾𝑒𝑓𝑓 = 𝛾 − √ 6 3𝜋(1−𝜈) 𝑒 𝑇 ,
Equation 5.9
where 𝛾 is the interface energy between TiC and ferrite (0.339 Jm -2) [30], G is the shear
modulus of the matrix, 𝜈 the Poisson’s ratio of the matrix (calculated to be 0.286 by same
approach as for the value of G [17]) and 𝑒 𝑇 is the relative lattice misfit (6% according to
[30]).
The driving force for TiC-nucleation, Δ𝑔𝑣 , is calculated by assuming a dilute solution
approximation according to [9]:
𝑅𝑇
Δ𝑔𝑣 = − 𝑉 𝑚𝑜𝑙𝑒 ∑𝑖 𝓍 𝑇𝑖𝐶,𝑖 ln (
𝑇𝑖𝐶
𝓍𝑚,𝑖
𝑇𝑖𝐶/𝑚
𝓍𝑚,𝑖
),
Equation 5.10
𝑚𝑜𝑙𝑒
where 𝑉𝑇𝑖𝐶
is the molar volume of TiC, 𝓍 𝑇𝑖𝐶,𝑖 is the mole fraction of element i in the TiC
𝑇𝑖𝐶/𝑚
precipitate, 𝓍𝑚,𝑖 the mole fraction of element i in the matrix, 𝓍𝑚,𝑖
the equilibrium mole
fraction of element i in the matrix at the TiC/Matrix interface and R is the gas constant.
The smallest possible nucleus of TiC is assumed to consist of one unit cell of TiC. This
correspond to 14 titanium atoms, when all titanium atoms on the surface are counted as
whole atoms. The length of the cube-shaped nucleus is therefore:
3
𝑙𝑚𝑖𝑛 ≥ √3.5𝑎 𝑇𝑖𝐶 ,
Equation 5.11
where 𝑎 𝑇𝑖𝐶 = 4.33Å [31] is the lattice parameter of TiC. The critical nucleus size 𝑙 ∗ is
thereafter expressed by differentiation of Eq. 5.8 with respect to 𝑙, equating to zero and
solving for 𝑙:
−4𝛾𝑒𝑓𝑓
𝑙 ∗ = ∆𝑔
𝑣 +∆𝑔𝑠
Equation 5.12
.
The time dependent nucleation rate of TiC precipitates, ITiC, is expressed as [32]:
𝐼𝑇𝑖𝐶 = 𝑁𝑣,𝑇𝑖𝐶 𝑍𝛽 ∗ exp [−
∗
∆𝐺𝑇𝑖𝐶
𝑘𝐵 𝑇
𝜏
] exp [− ],
𝑡
Equation 5.13
where, Nv,TiC is the number density of potential nuclei sites for TiC, Z is the Zeldovich
factor, 𝛽 ∗ is the frequency of atomic attachment to the growing precipitate and 𝜏 is the
incubation time.
The number density of possible nucleation sites is as assumed to be all substitutional
atomic sites within the capture radius of the dislocation:
𝑁𝑣,𝑇𝑖𝐶 = 𝜋𝑟𝑐2 𝜌(𝑡)𝑁𝑣,0 .
Equation 5.14
We use the same 𝜌(𝑡) as modelled according to Eq. 5.5-5.6. 𝑁𝑣,0 is the number density of
substitutional atomic sites and rc is the capture radius of each dislocation. The capture
radius of the dislocations is calculated according to [33]:
133
𝐴
𝑟𝑐 = 𝑒 0.577 4𝑘𝑇
with
𝜇𝑏 (1+𝜐)
𝐴 = 3𝜋 (1−𝜐) Δ𝕧,
Equation 5.15
where ∆𝕧 is the volume difference between matrix and solute atoms [33]. We calculate
the volume difference between matrix and solute atoms by comparing the volume of one
single Fe atom in a BCC unit cell of iron with the volume of one single Ti atom in a BCC
unit cell of Ti using the lattice parameters as reported by [34]. The capture radius as
calculated from Eq. 5.15 is 8.7 Å at 550 °C.
The Zeldovich factor is described according to [9]:
𝑍=
𝑎𝑡𝑜𝑚
√2 𝑉𝑇𝑖𝐶 √𝛾𝑒𝑓𝑓
√𝑘𝐵 𝑇
√3
1 2
(𝑙∗ ) ,
Equation 5.16
𝑎𝑡𝑜𝑚
where 𝑉𝑇𝑖𝐶
is the atomic volume of TiC. The frequency of atomic attachment to the
growing sub-critical nucleus is expressed as [9]:
𝛽∗ =
6(𝑙∗ )2 𝑚
𝜆 𝑇𝑖𝐶 ,
2
𝑎𝑇𝑖𝐶
Equation 5.17
where 𝜆𝑚
𝑇𝑖𝐶 is the effective attachment frequency of a TiC molecule, modelled as in [9].
The incubation time 𝜏𝑝 is given by
1
𝜏𝑝 = 2𝑍 2 𝛽∗ .
5.3.2
Equipment 5.18
Growth of TiC
The shape of the critical nucleus is converted from a cubical to a spherical nucleus, while
keeping the precipitate volume and the total Gibbs free energy constant. This leads to a
critical nucleus radius 𝑟 ∗ and an effective spherical interface energy 𝛾𝑟 with equations:
3
3
𝑟 ∗ = √4𝜋 𝑙 ∗
and
3
𝛾𝑟 = √6⁄𝜋 𝛾𝑒𝑓𝑓 .
Equation 5.19
The growth of all precipitates is thereafter modelled using a Zener approach for spherical
precipitates, where the growth rate, 𝜐𝑇𝑖𝐶 , of each precipitate with radius r is expressed
as [35]:
𝑇𝑖𝐶⁄𝑚,𝑟
𝜐𝑇𝑖𝐶 =
𝐷𝑖 𝑐𝑚,𝑖 −𝑐𝑚,𝑖
𝑟 𝑐𝑇𝑖𝐶,𝑖 −𝑐 𝑇𝑖𝐶⁄𝑚,𝑟
𝑚,𝑖
,
Equation 5.20
where 𝐷𝑖 is the effective diffusivity if element 𝑖 in martensite, 𝑐𝑚,𝑖 is the concentration of
element 𝑖 in the matrix, 𝑐𝑇𝑖𝐶,𝑖 is the concentration of element 𝑖 in the precipitate and
𝑇𝑖𝐶 ⁄𝑚,𝑟
𝑐𝑚,𝑖
is the concentration of element 𝑖 in the matrix at the precipitate/matrix interface.
All concentrations are in the units moles per m3. The above equation must be true for
each of the elements C, Ti and Mn, which leads to three equations with the four unknowns
⁄𝑚,𝑟
𝑇𝑖𝐶
𝜐𝑇𝑖𝐶 , 𝑐𝑚,𝐶
⁄
⁄
𝑇𝑖𝐶 𝑚,𝑟
𝑇𝑖𝐶 𝑚,𝑟
, 𝑐𝑚,𝑇𝑖
and 𝑐𝑚,𝑀𝑛
. The concentrations for iron are obtained by a mole
balance.
The fourth equation needed to solve for the four unknowns is given by an adjusted form
of the Gibbs-Thomson effect, which includes the effects of misfit strain energy:
∑𝑖∈{𝐹𝑒,𝐶,𝑇𝑖,𝑀𝑛} 𝑥 𝑇𝑖𝐶,𝑖 ln (
𝑇𝑖𝐶/𝑚,𝑟
𝑥𝑚,𝑖
𝑇𝑖𝐶/𝑚,∞
𝑥𝑚,𝑖
)=
𝑎𝑡𝑜𝑚
𝑉𝑇𝑖𝐶
𝛾𝑟 2
𝑘𝐵 𝑇
𝑟
+
𝑎𝑡𝑜𝑚
𝑉𝑇𝑖𝐶
𝑘𝐵 𝑇
∆𝑔𝑠 . Equation 5.21
This equation can be derived similar to the procedure given in [36]. We adjust the GibbsThomson effect to account for the misfit strain energy to obtain consistency between the
nucleation part of the model and the growth part of the model: if the Gibbs-Thomson
effect is not adjusted for the effect of the misfit strain energy, a precipitate with zero
growth rate, i.e. 𝑣 𝑇𝑖𝐶 = 0, will have a radius unequal to 𝑟 ∗, which is physically incorrect.
Earlier studies have shown that the high dislocation density of martensite
increases the diffusion rate in martensite [10]. The effective diffusivities of C, Ti and Mn
in martensite, 〈𝐷𝐶 〉, 〈𝐷𝑇𝑖 〉, 〈𝐷𝑀𝑛 〉, are therefore taken as a balance between the lattice
diffusivities, 𝐷𝐿 𝐶/𝑀 , 𝐷𝐿 𝑇𝑖/𝑀 , 𝐷𝐿 𝑀𝑛/𝑀 , and the pipe diffusivities, 𝐷𝑝 𝐶/𝑀 , 𝐷𝑝 𝑇𝑖/𝑀 , 𝐷𝑝 𝑀𝑛/𝑀 ,
on the format given by [37] where we remove the cross section area for pipe diffusivity
from the area of lattice diffusivity:
〈𝐷𝑒 〉 = (1 − 𝑔(𝑡))𝐷𝐿 𝑒⁄𝑀 + 𝑔𝑠 (𝑡)𝐷𝑝 𝑒⁄𝑀
for 𝑒 = 𝐶, 𝑇𝑖, 𝑀𝑛.
Equation 5.22
Here 𝑔𝑠 (𝑡) is the cross sectional area of dislocation pipe per unit area of matrix. The pipe
diffusivities for Ti and Mn are unknown, but under the assumption that the presence of a
dislocation lowers the energy barrier for diffusion, it is reasonable to assume that the
ratio between the bulk diffusivities and the pipe diffusivities of the elements C, Ti and Mn
is equal to the ratio between the bulk diffusivity and pipe diffusivity of Fe:
𝐷𝑝 𝑒/𝑀
𝐷𝐿
𝑒/𝑀
=
𝐷𝑝 𝐹𝑒/𝑀
𝐷𝐿 𝐹𝑒/𝑀
for 𝑒 = 𝐶, 𝑇𝑖, 𝑀,
𝐹𝑒/𝑀
where the ratio
𝐷𝑝
𝐹𝑒/𝑀
𝐷𝐿
is found in [21].
135
Equation 5.23
The effective pipe radius of a dislocation is set equal to the Burgers vector, b, and the
cross sectional area of dislocation per unit area of matrix is expressed as:
𝑔𝑠 (𝑡) = 𝜌(𝑡)𝜋𝑏2 .
Equation 5.24
The number balance of precipitates in the model is described according to [9]
𝜕𝜙
𝜕𝑡
=−
𝜕[𝑣𝑇𝑖𝐶𝜙]
𝜕𝑟
+ 𝛿(𝑟 − 𝑟𝑘∗𝐵𝑇 )𝐼𝑇𝑖𝐶 ,
Equation 5.25
in which 𝜙 ≡ 𝜙(𝑟, 𝑡) in m-4 is the number density distribution of precipitates of radius r
at time t and 𝑣 𝑇𝑖𝐶 in ms-1 represents the growth rate of precipitates of radius r at time t.
The radius 𝑟𝑘∗𝐵𝑇 is the radius for which the energy of nucleation is 𝑘𝐵 𝑇 less than the
energy for 𝑟 ∗ (𝑟𝑘∗𝐵𝑇 > 𝑟 ∗ ).
The key features of the model for TiC precipitation [9] are the inclusion of multicomponent and multi-phase effects within the model. In [9] it has been shown that the
model is capable of dealing with the multiple secondary phases which compete for the
same solid solution elements. We choose a different numerical method than that from
[9]. We use a combination of Strang splitting, first-order upwinding [38], Implicit and
Explicit Euler time-integration and adaptive mesh techniques. The initial mesh contains
500 bins on a logarithmic scale, similar to [9]. The simulation is following the same
temperature profile as applied directly after quenching during the experiments of Ö hlund
et al. [10].
5.4 Experimental
We have published the experimental methods and results elsewhere before [10]. The
experimental results are now being used as input parameters and validation for the
proposed model. Two high-purity Fe-C-Mn steels are investigated: one without Ti and one
with the addition of 0.042 wt.% Ti. The compositions of the steels are given in table 5.1.
Table 5.1 Chemical composition of the examined steels (wt.%)
Steel
C
Mn
Si
P
S
Al
Ti
Cu
Cr
O
V
Ti-free
Ti-containing
0,39
0,39
0,8700
0,8700
0,0035
0,0040
0,0010
0,0011
0,0007
0,0007
0,0050
0,0047
0,0420
0,0012
0,0012
0,0018
0,0022
0,0080
0,0046
0,0023
0,0022
The Ti-free steel is austenitized at 940 ˚C for 40 min and the Ti-containing steel is
homogenised and austenitized at 1350 ˚C for 30 min. The austenization temperature of
1350°C is chosen to assure that all Ti atoms are in solid solution. The different
austenization times are chosen to obtain similar austenite grain sizes. Both steels are
quenched to room temperature from their respective austenization temperature, using
He-gas followed by tempering treatments performed at 300 ˚C and 550 °C for 5, 10, 30
and 60 min. The heating time up to the full tempering temperature is 138 seconds. The
tempering temperature of 300 °C is chosen to assure that all Ti atoms remain in solid
solution, as nucleation of TiC does not take place during tempering at 300°C 6). The
tempering level of 550 °C is chosen to assure that TiC nucleation and growth takes place
during tempering, as literature report that TiC nucleation take place when tempering
temperatures are in the range of 550°C [6].
Micro-Vickers hardness (HV0.5) is used to study the evolution of macroscopic hardness.
Scanning electron microscopy (SEM, JEOL JSM-6500F with field emission gun) is used to
study the evolution of Fe3C-particle size volume fraction. Electron back-scatter diffraction
(EBSD with a Nordlys detector) is used to study the coarsening of martensite blocks and
to estimate the evolution of recovery in the martensite. We estimate the evolution of
recovery from the crystallographic indexing results. Block boundaries, high surface
roughness, high elastic strain and high strain levels due to e.g. dislocations reduces the
band contrast of the Kikuchi patterns of the EBSD signal. If the degradation is high enough,
the measurement point cannot be indexed. As no block coarsening takes place during
annealing and the surface roughness and elastic strain is comparable for all specimens,
we consider the improvement of the band contrast during annealing to be a result of
recovery. However, since only regions close to block boundaries contain dislocation
densities which are high enough to prevent indexing in the as quenched state, the results
are only representative for regions adjacent to block boundaries. The indexing results for
the as-quenched specimen is considered to be representative for martensite with no
recovery and the indexing results for the specimens tempered for 60 min is considered to
be representative for the fully recovered state. The dislocation density in the as quenched
state is set to the value measured by Morito et al. [23] and the dislocation density in the
fully recovered state after annealing is given by Takebayashi et al [39]. The indexing result
is thereafter used to estimate the recovery evolution and the dislocation density during
annealing.
Atom probe tomography (APT, Imago LEAP 3000X HR with laser pulsing) is used to
measure the concentration of carbon and titanium atoms in solid solution and the TiCprecipitates in the Ti-containing martensite after 60 min of tempering at 550 °C.
137
5.5 Model fitting
5.5.1
Input parameters
The EBSD measurements in ref. [10] show that no grain coarsening takes place during
tempering. Therefore, we take ∆𝜎𝑔𝑏 in Eq. 5.2 as a constant. The measured volume
fraction of Fe3C-particles as a function of annealing time and temperature is used as an
input to the model. The SEM-measurements in ref. [10] are used to determine the Fe3Cparticle width, w, and length, l, which are used to calculate the volume fraction of Fe3C
precipitates. We calculate the volume of each Fe 3C-particle that is measured within a
square area of SEM images using:
𝑤 2
𝑙
2
2
𝑉 = 4𝜋 ( ) ( ).
Equation 5.26
The total volume of all particles is summarized within each sample. The volume fraction
of Fe3C-precipitates as a function of annealing time and temperature is determined,
assuming a cubic measurement volume. We observe that the equilibrium volume fraction
of Fe3C-precipitates is 0.087 for the Ti-containing steel after 60 min of isothermal
tempering at 550 °C. However, ThermoCalc simulations (TCFE6) for the Ti-containing steel
show that the equilibrium volume fraction of Fe3C is equal to 0.058 at 550 °C. The higher
volume fraction we measure from SEM can be due to a slight overestimation of particle
dimensions from SEM pictures and due to the assumption of oval particle shape (Eq. (26)).
We now use the APT measurements to estimate the volume fraction of Fe 3C in the Ticontaining steel after 60 min of tempering at 550 °C. The APT measurement show that
the concentration of carbon atoms in solid solution is 35 ∙ 10−3 at% C. This is higher than
the simulated equilibrium concentration of C atoms in solid solution in ferrite at 550 °C
(1.8 ∙ 10−3 at% according to ThermoCalc). From the APT results we can also estimate the
fraction of carbon atoms that is used for the formation of TiC-precipitates. We assume
that carbon is distributed between TiC, Fe 3C and C in solid solution and derive that the
volume fraction of Fe3C is 0.057 (98% of the equilibrium volume fraction) after 60 min of
isothermal tempering at 550 °C.
We therefore create a scale factor from the relationship we find between the SEM and
APT volume fractions for the Ti-containing steel after 60 minutes of tempering at 550°C.
The volume fraction of Fe3C, as determined by SEM, is thereafter scaled for each
examined specimen. The effective radius of the Fe 3C-particles is also used as an input
parameter to the model. The effective radius of the Fe 3C-particles in each specimen is
calculated from the scaled SEM volume fraction of Fe3C by assuming spherical particles.
30
0.060
0.054
20
0.048
15
0.042
Ti-free
Ti
10
550°C
300 °C
0.036
550°C
300°C
5
Volume fraction Fe3C
Effective Fe3C radius (nm)
Volume fraction
25
0.030
0
600
1200
1800
2400
3000
3600
Tempering time (Seconds)
Figure 5.1 Effective Fe3C radius [nm] of Ti-free and Ti-containing martensite during annealing at
300°C and 550°C as a function of annealing time and the volume fraction of Fe3C in the Ticontaining steel after annealing at 550°C. Error bars represent 95% confidence interval.
Fig. 5.1 shows the effective Fe3C radius and volume fraction of Fe3C, as a function of
tempering time, that are used as input parameters in the model. The four curves for
volume fraction of Fe3C are overlapping, and we therefore show only the Ti-containing
steel at 550 °C. Both the effective precipitate size and the volume fraction of Fe 3C grow
rapidly during the first 5 min of isothermal tempering. After 5 min of isothermal
tempering the growth continues at a lower rate, and after 10 min the values stabilises.
We note that the spread in cementite particle size increases with tempering time, during
tempering at 550 °C, which is reflected by the increase in the size of error bar for the
average cementite particle size.
The small carbides which are observed in the as-quenched state could correspond to 𝜀carbides, based on their size and that they are present directly after quenching. In the
present model, all the iron-carbides are modelled as Fe3C-particles. The volume fraction
of Fe3C is used to calculate the input parameter of carbon concentration in solid solution
to the model, as only one data point for the carbon concentration in solid-solution was
measured by APT (at 60 min of isothermal tempering at 550 °C for the Ti-containing steel).
5.5.2
Fitting approach
The parameters 𝜎𝑔𝑏 , 𝐾𝑀𝑛 , 𝐾𝑇𝑖 , 𝛼 and 𝑉𝑎 of the hardness model are currently unknown.
Two of these parameters, 𝛼 and 𝑉𝑎 , are also used within the KWN TiC precipitation model,
139
together with the misfit strain energy Δ𝑔𝑠 for the TiC precipitates. We will use the
following approach to obtain estimates of these parameters:
1. 𝜎𝑔𝑏 , 𝐾𝐶 , 𝐾𝑀𝑛 , 𝐾𝑇𝑖 , 𝛼 and 𝑉𝑎 are fitted using least-squares techniques by minimising
the residual between the simulated hardness given by Eqs. 5.1 and 5.7 of the model
and the measured hardness from experiments. We simultaneously fit the model to
the experimental data from the Ti containing steel at 300 °C and the Ti free steel
at 300 °C and 550 °C at 0, 5, 10, 30 and 60 min of tempering. The Ti-containing steel
heat-treated at 550 °C is excluded from the fitting of the above parameters in order
to avoid the influence of TiC precipitates.
2. Δ𝑔𝑠 is obtained by using a least-squares techniques by minimising again the
residual between the predicted hardness and the measured hardness, where the
values for the parameters 𝜎𝑔𝑏 , 𝐾𝑀𝑛 , 𝐾𝑇𝑖 , 𝛼 and 𝑉𝑎 from the previous step are used
within the hardness model and the TiC precipitation model. Only the data for the
Ti-containing steel during tempering at 550 °C after 0, 5, 10, 30 and 60 min is used
to obtain the value of ∆𝑔𝑠 .
5.6 Results and discussion
5.6.1
Fitting parameters
Fig. 5.2 shows the measured hardness (symbols) and the fitted (lines) hardness as a
function of annealing time of (a) the Ti-free steel at 300°C and 550°C and the Ti-containing
steel at 300°C and (b) the Ti-containing steel at 550°C.
600
b)
a)
550
Hardness (HV)
500
Ti-free
450
550°C
300°C
400
Ti
550°C
300°C
350
300
250
Fitted model Ti-free
Fitted model Ti
200
0
500
1000
1500
2000
2500
Time (Seconds)
3000
3500
4000 0
500
1000
1500
2000
2500
3000
3500
4000
Time (Seconds)
Figure 5.2 The measured hardness (symbols) and the fitted model (lines) of a) the Ti-free steel at
300°C and 550°C and the Ti-containing steel at 300°C as a function of annealing time and b) the
Ti containing steel at 550°C. 95% confidence intervals are covered by the symbols. The error bars
(representing 95% confidence intervals) are smaller than the symbols size.
The comparison between the experiment and the model in Fig. 5.2(a) is used obtain
values for the fitting parameters 𝜎𝑔𝑏 , 𝐾𝑀𝑛 , 𝐾𝑇𝑖 , 𝛼 and 𝑉𝑎 . The comparison between the
experiment and the model in Fig. 2(b) is used to fit a value for the strain energy. From Fig.
5.2(a) & (b). it can be seen that the fitted model correctly describes the evolution of the
hardness during tempering. The fitted parameters 𝜎𝑔𝑏 , 𝐾𝑀𝑛 , 𝐾𝑇𝑖 , 𝛼, 𝑉𝑎 , and ∆𝑔𝑠 are given
in Table 5.2.
Parameter
𝝈𝒈𝒃 (MPa)
𝑲𝑪 (MPa(wt%)-1/2)
𝑲𝑴𝒏 (MPa(wt%)-1)
𝑲𝑻𝒊 (MPa(wt%)-1)
𝜶
𝑽𝒂 (m3)
∆𝒈𝒔 (GJ/m3)
Value
340
0
0
1679
0.401
16.99𝑏3
1.34
Table 5.2 Results from
least-squares fitting
of Eqs. 5.7-5.8 to the
measured hardness.
In the following section we compare the values of the fitted parameters to the values
reported in literature. The 𝜎𝑔𝑏 of our model is the combination of lattice friction and the
hardness contribution of the martensite block structure (grain size hardening). The model
predicts ∆𝜎𝑔𝑏 = 340 𝑀𝑃𝑎 (113 𝐻𝑉) . This calculated value is lower than the value of
413 MPa which is given in literature [2]. This difference can be due to the difference in
grain size that we use and the grain size that is used in literature. The literature value of
413 MPa is based on the grain size the average lath width of 0.25 µm. This is smaller than
the effective grain size (determined by the block boundaries) that we used in our model.
The value that we find for 𝛼 = 0.401 is in good agreement with the literature reports
ranging from 0.24 to 1 [18, 40]. We note that the experimental work of [10] shows that
the concentration of carbon atoms in true solid solution (between laths) and the
concentration of carbon atoms segregated to lath boundaries (high dislocation density)
are 0.005 wt% and 0.045 wt% respectively, after 60 min of tempering at 550°C. This
indicates that the majority of carbon atoms in the martensite have segregated to
dislocations and that Eq. 5.3 therefore cover the major influence of carbon atoms in solid
solution on the martensite strength. The activation volume of the recovery process in
martensite, 𝑉𝑎 , is compared to the literature value for the activation volume of the
recovery process in BCC iron. Our model predicts a value of 17b 3 or 0.26 nm3, which is in
good agreement with the reported value of 0.1 to 0.6 nm [3, 41]. The fitted values of the
𝐾𝑀𝑛 -parameter is zero, whereas literature reports a value of 𝐾𝑀𝑛 = 35 MPa(wt%)-1 [13].
141
The difference between our fitted value of KMn=0 and the literature value of KMn=35
MPa(wt%)-1, falls within the uncertainties of our experiments and the uncertainties of the
experiments reported in literature. We estimate that Mn in solid solution contributes with
maximum 10 HV to the total hardness in our system. Here we assume that the Mn-atoms
do not have time to redistribute during the formation of cementite so that the overall
manganese concentration in the matrix corresponds to the overall concentration of 0.87
wt% Mn in the steel. The strengthening effect of Mn in solid solution in the as-quenched
martensite is therefore approx. 30 MPa (or 10 HV), in case we use the literature value for
KMn =35 MPa(wt%)-1 and Eq. 9.3. In case the Mn-atoms would redistribute into cementite,
the Mn-concentration in the matrix would be even lower and subsequently the added
strength. The error in our hardness measurements is approx. ±5 HV. The steels used by
[13] contain sulphur, which may form MnS precipitates. The formation of MnS can
influence the hardness by precipitate strengthening and the literature value of 35
MPa(wt%)-1 for KMn may therefore be biased.
There are not many reports in the literature about the strain energy if TiCprecipitates in martensite. Jang et al [30] have used first principles calculations to
estimate a value of 4.10kJ/mol or 1.16 GJ/m3. This value corresponds well to our fitted
value of 1.34 GJ/m3 or 4.74 kJ/mol.
5.6.2
TiC-precipitates and recovery
Density distribution (1029 m-4)
Fig. 5.3 shows the calculated TiC precipitate size distribution together with the TiC
precipitate sizes measured by Ö hlund et al.[10]. The precipitate size as measured by APT
is based on the APT atom count for each precipitate2.
Measured by APT
4
Figure 5.3 The simulated TiC precipitate size
distribution (line) and the experimental
precipitate sizes (symbols) as measured by
APT in the Ti-containing martensite after 60
minutes of tempering at 550°C.
3
2
1
0
0.4
2
0.6
0.8
1.0 1.2 1.4 1.6
Radius (nm)
1.8
2.0
2.2
We convert the atom count to a radius, assuming spherical precipitates, by the volume estimated from
the lattice parameter of TiC. We add the distance of one Ti atom radius to the calculated radius as the
volume estimated by the lattice parameters only measure to the centre of the outer atoms.
The KWN model predicts that 0.27 % of the equilibrium volume fraction of TiC forms and
that the average TiC precipitate radius is 1.38 nm after 60 min of isothermal tempering at
550 °C. Furthermore, the model predicts that nucleation of TiC precipitates starts during
the heating stage, 10 seconds before reaching the isothermal temperature of 550 °C and
that the peak in number density of TiC-precipitates is reached after 385 seconds of
heating and tempering (after 4 min and 7 seconds of isothermal tempering). The
predicted average radius and size distribution from the KWN model are slightly higher
than the values measured by APT. However, the measured precipitates sizes fall within
the nonzero part of the predicted distribution and is therefore in agreement with the
model. The predicted volume fraction of formed TiC-precipitates is lower than what is
measured by APT. This could be due to the small sample size inherent to APT.
Dislocation density (1014 m-2)
16
Ti-free
14
Ti
2
1.6
1.2
550°C
550°C
12
300°C
300°C
10
Simulated value Ti-free
Simulated value Ti
Zoom in on simulated value Ti
for low dislocation densities
0.8
0.4
0
8
1000 2000 3000 4000
6
4
0
550°C
300°C
2
0
500
1000 1500 2000 2500 3000 3500 4000 0
Time (seconds)
500
1000 1500 2000 2500 3000 3500 4000
Time (seconds)
Figure 5.4 The measured (symbols) and the simulated (lines) dislocation density in Ti-free and Ticontaining steel as a function of annealing time during annealing at 300°C and 550°C. The
simulated value of Ti-containing and Ti-free steel overlap at 300°C.
Fig. 5.4 shows the dislocation density as a function of tempering time for Ti-free
(precipitate free) and Ti-containing steel at different temperatures, as simulated via Eqs.
5.5-5.6 and as measured by EBSD experiments [10].
We use the simulated dislocation density as input to our model. The simulation of the
evolution of the dislocation density does not take into consideration the pinning of
dislocations by small iron carbides and cementite particles. We observe that these type
of particles are present in the steels after quenching and at all annealing times. The
pinning of dislocations by iron carbides is therefore expected to be approximately
constant throughout the annealing of the steels and our simulation might overestimate
the amount of recovery which has occurred at times between 5 to 60 minutes of
isothermal tempering.
143
Fig. 5.4(a) shows the dislocation density of Ti-free and Ti-containing martensite during
tempering at 300 °C (where no TiC precipitates are present). We observe that the
evolution of the recovery is slightly faster in the simulated values than in the experimental
values and that the simulation results in a higher degree of recovery. Figure 4b shows the
dislocation density of Ti-free and Ti-containing martensite during tempering at 550 °C. We
observe that the simulated and the experimental values do not correlate. The simulation
of recovery in the Ti-containing steel shows faster recovery and a much higher degree of
recovery than the experimental values. However, we observe a recovery delay in the
simulated values, with a maximum delay effect between 200 and 550 seconds of
tempering. We note that the recovery delay of the simulated dislocation density and the
recovery delay observed by experiments show a similar evolution in time (see the zoomed
in panel). The recovery delay of the simulations of the Ti-containing steel at 550°C results
in a slightly higher dislocation density in the Ti-containing steel than in the Ti-free steel
during isothermal annealing at 550 °C.
The recovery delay of the simulated dislocation density is a result of the high
number of TiC-precipitates which are present at that time. The KWN model predicts that
the highest number of TiC precipitates, which can act as pinning points for dislocations,
appears after 385 seconds of tempering. The large disagreement between simulated and
experimentally estimated values at 550°C is a result of that the experimentally established
recovery is representative for regions close to block boundaries. Nucleation of TiC is faster
in the regions close to block boundaries, which reduces the rate of recovery in these
regions [10]. The experimentally estimated dislocation density therefore becomes too
high.
5.6.3
Evolution of multiple hardening components during tempering
Fig 5.5 shows the evolution of the hardness contribution from different microstructural
components of the martensite as a function of time during tempering at 550 °C.
Figure 5.5 The evolution
of the contribution of
multiple hardness
components to the
overall hardness of
martensite as a function
of time during tempering
at 550°C.
The microstructural components which give the largest direct contributions to the overall
hardness of martensite during tempering are 1) Fe3C precipitates and 2) dislocations.
The strengthening effect of Fe3C precipitates is decreasing by 50 HV during heating
to 550°C and the first 8 min of isothermal tempering at 550°C. This rapid decrease takes
place due to the fast coarsening of Fe3C particles during the same time period, as
presented in Fig 5.1. After 8 min of isothermal tempering the strengthening effect
stabilises and our hardness model predicts that the hardness contribution of Fe3C is
approx. 88 HV, which remains stable from 8 to 60 min of isothermal annealing at 550 °C.
The high hardness contribution of Fe3C by precipitation strengthening is supported by the
literature: 𝜀 -carbides that form during low temperature annealing or during autotempering, have been measured to significantly increase the hardness of lath martensite
[42]. Small iron-carbides can therefore be a very effective way of increasing the strength
and hardness of martensite. However, the strengthening effect of iron carbides could be
sensitive to long time service at elevated temperatures due to rapid diffusion of carbon
atoms, which could enable cementite coarsening via Ostwald ripening. As coarsening
proceeds, the spread in particle size will increase (but the average size might remain
constant). At a certain critical point, all small precipitates are consumed and the average
precipitate size increases, while the number density decreases. This change in precipitate
size and number of precipitates will lead to a reduction in the precipitation strengthening
effect of Fe3C. The experimental results show that the spread in cementite particle size
145
increases with annealing time (see Fig. 5.1). The strengthening effect of dislocations
decreases very rapidly by approx. 200 HV during the 138 seconds of heating to the
isothermal annealing temperature. This rapid decrease is a result of the rapid recovery
which is shown in Fig 5.4(b). The strengthening effect of dislocations stabilises during
tempering. Our hardness model predicts that the hardness contribution of dislocations is
approximately stable at 54 HV from 10 to 60 minutes of isothermal tempering at 550 °C.
The microstructural components which give minor direct contributions to the
overall hardness of martensite are 1) Ti atoms in solid solution and 2) TiC, as shown in Fig.
5.5. The strengthening due to Ti in solid solution increases slightly during heating up and
the first minutes of isothermal tempering at 550°C and is thereafter stable. The hardness
increases slightly due to a slight increase in the concentration of Ti atoms in the matrix as
a result of formation of Fe3C which redistributes a high number of Fe and C atoms from
the matrix to Fe3C. ThermoCalc simulations show that Ti does not dissolve in Fe3C and is
therefore remaining in the matrix. Our hardness model predict that the hardness
contribution due to Ti in solid solution is approx. 25 HV after 60 min of isothermal
tempering at 550 °C. The strengthening effect of TiC precipitates is zero during the
majority of the heating up of the steel, and is thereafter increasing rapidly during the first
7 min of isothermal tempering at 550 °C. After 8 min of isothermal tempering the
hardness increases slowly. The hardness model predicts that the strengthening effect due
to precipitation strengthening of TiC is approximately 3.5 HV after 60 min of isothermal
tempering at 550 °C. We note that the theoretical maximum precipitation strengthening
effect of TiC is 42 HV. The direct strengthening effect of Mn atoms in solid solution is zero
during the entire process of tempering, as shown in Fig. 5.5.
The microstructural components which give combined contributions to the overall
hardness of martensite are TiC precipitates combined with dislocations.
Our model predicts that the recovery process in the Ti containing steel is delayed
during isothermal tempering at 550 °C as a result of TiC precipitates which pin dislocations
(see Fig. 5.4(b)). The resulting dislocation density of the Ti containing steel is therefore
higher than the dislocation density of the Ti-free steel. This higher dislocation density
contributes to a 20 HV higher hardness contribution in the Ti-containing steel after 60 min
of isothermal tempering at 550 °C, as compared to the Ti-free steel. The total strength
contribution due to formation of TiC in martensite is therefore the sum of the TiC
precipitation strengthening effect, and the extra dislocation strengthening effect due to
less recovery. Our hardness model predicts that this combined strengthening effect is
23.5 HV after 60 min of isothermal tempering at 550 °C. The low strengthening effect of
TiC-precipitates is a result of the low volume fraction of TiC-precipitates that is predicted
by our model. We note that when the model is run for longer holding times at 550 °C,
there is only a slight increase in the volume fraction of formed TiC-precipitates. The
resulting hardness increase is small: 5.9 HV after three hours of isothermal annealing at
550 °C. An extended heat-treatment time will therefore not improve the properties of the
martensite by much. The low volume fraction of TiC-precipitates is related to the large
misfit strain (1.34 GJ/m3) that we find during fitting and the low density of potential
nucleation sites (Eq. (14)) that we use as input parameter to the model. Both factors
reduce the nucleation rate. The low density of potential nucleation sites is a result of the
rapid recovery of the simulated dislocation density which is used as an input to our model,
and the calculated capture radius.
We investigate the influence of a higher number of available nucleation sites by
repeating the fitting of our model to the measured hardness at 550°C, using 1) an
increased capture radius of 2 ∙ 𝑟𝑐 , as calculated by Eq. 5.15 and 2) a higher dislocation
density of the martensite. To increase the dislocation density we use the experimental
dislocation density as input to the model, instead of simulating the dislocation density
according to Eqs. 5.5-5.6 within the model.
We investigate the effect of lower mis-fit strain by setting a fixed value of the mis-fit strain
(75% of the value predicted by our fit to the measured hardness) as input parameter to
the model. We investigate the effect of a lower mis-fit strain energy combined with a
higher number of available nucleation sites, by setting the mis-fit strain energy to 1.3359
GJ/m3 and using the experimental dislocation density as input parameters to the KWN
model. The results from the repeated fit of our model and the accuracy of the simulated
values to the measured hardness (given as the sum of squared errors) are given in table
5.3, together with the values from our original fitting.
Table 5.3 Results from least-squares fitting of model after 60 minutes of tempering at 550°C,
using modified input parameters
𝒇𝑻𝒊𝑪
∆𝒈𝒔
Modified input parameter
Accuracy of
model
Original model (no modification)
0.27%
793
1.3359 GJ/m3
Capture radius 𝟐 ∙ 𝒓𝒄
0.28%
788
1.3347 GJ/m3
Higher Dislocation density (experimental)
0%
41638
2.3189 GJ/m3
3
∆𝒈𝒔 =1.0019 GJ/m
17%
973
3
Higher dislocation density & ∆𝒈𝒔 =1.3359 GJ/m
44.9%
1.336x109
An increased capture radius does not generate a higher volume fraction of TiCprecipitates, but it slightly improves the accuracy of the fitting of the model. Increasing
the dislocation density alone results in a considerably higher value for the misfit strain
energy after fitting, which does not correspond anymore to first-principles calculations30.
Moreover, in this case the model predicts that no nucleation of TiC-precipitates takes
place. A reduction of the misfit strain energy results in a higher volume fraction of formed
147
TiC, and a slight reduction of the accuracy of the fit. A reduction of the mis-fit strain energy
and a higher dislocation density results in a significantly increased volume fraction of TiCprecipitates and a smaller precipitate size. The latter results are more in agreement with
the APT measurement. However, the model is no longer capable of fitting to the
measured hardness.
5.7 Conclusions
We quantify the evolution of the multiple hardness contributions to the overall hardness
of martensite containing TiC-precipitates during isothermal annealing. We simulate the
hardness of martensite as a linear addition of multiple hardening mechanisms. This
hardness model is combined with a microstructural model based on the KampmannWagner-Numerical (KWN) approach for a multi-component and multi-phase system to
simulate the nucleation and growth of TiC-precipitates.
The two microstructural components which contribute most to the overall
hardness of the investigated Fe-C-Mn-Ti steel are Fe3C precipitates (88 HV) and
dislocations (54 HV). Both contributions decrease rapidly during initial stages of annealing
and stabilise after 10 minutes of annealing. The addition of titanium to the steel gives a
minor hardness contribution via Ti-atoms in solid solution and TiC precipitates. Ti atoms
in solid solution give a hardness contribution which increases slightly during the first
minutes of annealing and thereafter remains stable (at 25 HV). The direct contribution of
TiC precipitates to the overall hardness is limited (3.5 HV). However, TiC-precipitates also
contribute to the overall hardness by pinning of dislocations during the recovery that
takes place during the tempering. The model predicts that only a small volume fraction of
TiC-precipitates forms during isothermal annealing at 550 °C due to the large misfit strain
(1.34 GJ/m3 ) and the low density of potential nucleation sites.
5.8 References
[1] ISO898-1, Mechanical properties of fasteners made of carbon steel and alloy steelPart 1. Fifth edition, Switzerland, 2013
[2] G. Krauss: Mater Sci Eng A., 273-275(1999), 40
[3] S. Morito, X. Huang, T. Furuhara, T. Maki and N. Hansen: Acta. Mater., 54(2006),
5323
[4] T. N. Baker: Mater Sci. Technol: 25(2009), 1083
[5] Y. Namimura, N. Ibaraki, W. Urushihara and T. Nakayama: Wire J. Int., 36(2003), 62
[6] F.G. Wei, T. Hara, T. Tsuchida and K. Tsuzaki: ISIJ Int., 43(2003), 539
[7] F. Abe, M. Taneike and K. Sawada: Int. J. Press. Vessel Pip., 87(2007), 3
[8] M. Taneike, M. Fujitsuna and F. Abe: Mater. Sci. Technol., 20(2004), 1455
[9] D. den Ouden, L. Zhao, C. Vuik, J. Sietsma and F. J. Vermolen: Comp. Mater. Sci.,
79(2013), 933
[10] C. E. I. C. Ohlund, J. Weidow, M. Thuvander and S. E. Offerman, ISIJ Int., 54(2014),
2890-2899
[11] L. H. Friedman and D. C. Chrzan: Phys. Rev. Lett., 81(1998), 2715.
[12] T. Ohmura, K. Tsuzaki and S. Matsuoka: Scripta Mater., 45(2001), 889.
[13] L. A. Nordstrom: Scand. J. Metall., 5(1976), 159.
[14] Martensite, ed. By G. B. Olsen and W. S. Owen, ASM International Materials Park,
Ohio, (1992)
[15] M. Kehoe and P. M. Kelley: Scripta Metall, 4(1970), 473
[16] T. Gladman: The physical metallurgy of microalloyed steels, The University press,
London, UK, (1997)
[17] G. R. Speich, A. J. Schwoeble and W. C. Leslie: Metall. Trans., 3(1972), 2031
[18] Y. Han, J. Shi, L. Xu, W. Q. Cao and H. Dong: Mater. Sci. Eng. A., A530(2011), 643
[19] H. S. Zurob, C. R. Hutchinson, Y. Brechet and G. Purdy: Acta Mater., 50(2002), 3075
[20] J. M. Rosenberg and H. R. Piehler: Metall. Trans., 2(1971), 257
[21] Y. Shima, Y. Ishikawa, H. Nitta, Y. Yamazaki, K. Mimura, M. Isshiki and Y. Iijima:
Mater. Trans., 43(2002), 173
[22] L. Cheng, C. M. Brakman, B. M. Korevaar and E.J. Mittemeijer: Metall. Trans. A.,
19(1988), 2415
[23] S. Morito, J. Nishikawa and T. Maki: ISIJ Int., 43(2003), 1475
[24] B. Huthcinson, J. Hagstrom, O. Karlsson, D. Lindell, M. Tornberg, F. Lindberg and M.
Thuvander: Acta Mater., 59(2011), 5845
[25] Z. Wang, X. Mao, Z. Yang, X. Sun, Q. Yong, Z. Li and Y. Weng: Mater. Sci. Eng. A.,
A529(2011), 459
[26] M. Sawahata, M. Enomoto, K. Okuda and T. Yamashita: Tetsu-to-Hagane.,
94(2008), 21
[27] S. Q. Xiao and P. Haasen: Scripta Metall., 23(1989), 365
[28] S. Y. Hu and L. Q. Chen: Acta Mater., 49(2001), 463
[29] H.I. Aaronsons, M. Enomoto and JK. Lee: Mechanisms of diffusion phase
transformations in metals and alloys, CRC Press, Boca Raton, (2010)
149
[30] J. H. Jang, C. H. Lee, Y. U. Heo and D. W. Suh: Acta Mater., 60(2012), 208
[31] A. Teresiak and H. Kubsch: NanoStructured Mater., 6(1995), 671
[32] J. W. Cahn: Acta Metall., 4(1956), 449
[33] Z. M. Wang and G. J. Shiflet: Metall. Mater. Trans. A., 29A(1998), 2073
[34] D. S. Rickerby: Metall Science., 16(1982), 495
[35] C. Zener: J. Applied Phys., 20(1949), 950
[36] M. Perez: Scripta Mater., 52(2005), 709
[37] D. A. Porter and K. E. Easterling: Phase transformations in metals and alloys, Van
Norstrand Reinhold, New York, USA, (1981)
[38] R. LeVeque: Finite Volume Methods for Hyperbolic Problems, Camebridge
Univeristy Press, New York, (2002)
[39] S. Takebayashi, T. Kunieda, N. Yoshinaga, K. Ushioda and S. Ogata: ISIJ Int.,
50(2010), 875
[40] R. Lagneborg and B. Bergman: Metal. Sci., January(1976), 20
[41] A. Smith, H. Luo, D. Hanlon, J. Sietsma and S. Van der Zwaag: ISIJ Int., 44(2004),
1188
[42] R. N. Caron and G. Krauss: Metall. Trans., 3(1972), 2381.
6 A comparison between ultra-high-strength and
conventional high-strength fastener steels:
mechanical properties at elevated temperature and
microstructural mechanisms
C.Emmy I.C. Ohlund, Mladena Lucovic, Jonathan Weidow, Mattias
Thuvander and S.Erik Offerman
To be Submitted
Abstract
The ongoing trend of engine down-sizing has resulted in the need for stronger automotive
fasteners at more elevated temperatures. A comparison is made between the mechanical
properties of the ultrahigh-strength steel KNDS4 of fastener grade 14.9 and of
conventional, high-strength steels 34Cr4 of fastener grade 12.9 and 33B2 of grade 10.9.
The results show that the ratio of the yield strength at elevated temperatures to the yield
strength at room temperatures is much higher for the ultra-high-strength steel than for
both conventional high-strength steels, especially at 500°C. Moreover, the results show a
trend in which the nano-indentation creep rate is lower as the strength of the steels is
higher. The better mechanical properties of the KNDS4 steel are related to the smaller
size of the alloy carbides in the KNDS4 steel. In order to further improve the properties
of the steel, we investigated the effect of an alternative (industrial) heat-treatment on
the evolution of the microstructure and hardness of the KNDS4 steel. Changing the
industrial heat treatment can increase the hardness of KNDS4 by 8%, since more alloy
carbides can nucleate and grow. However, the standard industrial heat treatment results
in a smaller martensite block size, which might be more beneficial for the toughness of
the steel. Independent of the heat treatment, we find that the mechanical performance
of KNDS4 fasteners at elevated temperature and the low nano-indentation creep rates
are two strong indicators that fasteners made from KNDS4 steel might be used at higher
service temperatures than traditional high strength fasteners.
151
6.1 Introduction
The trend of engine down-sizing has led to smaller engines with higher mechanical and
thermal loading of the components inside the engine. High strength engine fasteners
must therefore be able to maintain a high yield strength at elevated temperatures and to
withstand creep at elevated temperatures. Martensitic low and medium carbon steels,
alloyed with mainly Mn and B or Mn and Cr, are the work-horse materials for current high
strength engine fasteners [1]. These fasteners have a tensile strength up to maximum
tensile strength of 1200 MPa and yield strength of 0.9 times the tensile strength (grade
12.9), according to international fastener standards [2]. Higher strength fasteners are not
yet listed in the fastener standards, because the susceptibility to hydrogen embrittlement
increases in traditional fastener steels in case the strength exceeds 1200 MPa [3]. The
fastener standards furthermore list a recommended service temperature of maximum
150°C [2]. The reason behind the latter restriction is related to the fact that the traditional
fastener steels can lose strength and/or experience creep at elevated temperatures.
New fastener steels have already been developed, based on the need for higher
strength and improved resistance to hydrogen embrittlement [4]. The improvement in
strength at room temperature of these fastener steels is achieved by a tempered
martensite matrix and the addition of carbide-forming elements such as titanium (Ti),
vanadium (V) and molybdenum (Mo) [5-11]. The potential improvements of the
mechanical properties of fastener steel at elevated temperatures due to the formation of
alloy carbides was not taken into account during the development of novel ultra-highstrength steels for fasteners. However, literature shows that the creep properties of
martensitic steel are improved by the presence of alloy carbides [12-14]. Moreover, a
report demonstrates the combined improvement of the room temperature and high
temperature tensile strengths of martensite due to a fine dispersion of alloy carbides [15].
Creep measurements are very time consuming. In this study we aim to obtain more
insight into the mechanical properties of ultra-high-strength steels for fasteners at
elevated temperatures without performing time-consuming creep measurements by
applying a nano-indentation technique.
The aim of the present study is 1) to compare the mechanical properties of the ultrahighstrength steel KNDS4 of fastener grade 14.9 and of conventional high-strength steels
34Cr4 of fastener grade 12.9 and 33B2 of grade 10.9 at room temperature and at elevated
temperatures, 2) to characterize the alloy carbides in the steels in order to investigate the
underlying microstructural mechanisms that give rise to the different properties of the
three fastener steels and 3) to optimize the thermal processing of the ultra-high-strength
KNDS4 steel for fasteners. KNDS4 contains the strong carbide-forming elements V, Ti and
Mo. These elements form complex alloy carbides during heat treatment and we therefore
expect that KNDS4 can have better mechanical properties at elevated temperatures than
conventional high-strength steels for fasteners.
6.2 Experimental
The following three experiments are carried out: 1) mechanical testing of fasteners made
of KNDS4, 34Cr4 and 33B2 steel to compare room temperature and elevated temperature
mechanical properties, 2) characterization of the alloy carbides to investigate the
underlying microstructural mechanisms that give rise to the different properties of the
three fastener steels and 3) optimizing the thermal processing of KNDS4 in order to
further improve the mechanical properties of the steel. The chemical composition of the
investigated steels are shown in table 6.1. The Fe-C-Mn-Ti steel was examined in an earlier
investigation [16-17] and is now used as a reference during the microstructure study of
KNDS4 steel for the optimization of the thermal processing of KNDS4 steel.
Table 6.1, Main elements of the examined steels [wt%]
Steel
C
Mn
Si
P
S
Al
Cr
Mo
Ni
Ti
V
B
KNDS4
0.39
0.45
0.05
0.004
0.006
0.033
1.07
1.09
0.60
0.042
0.085
-
34Cr4
0.36
0.85
0.10
0.006
0.007
0.036
1.09
0.050
0.05
0.001
0.003
-
33B2
0.32
0.72
0.09
0.010
0.010
0.031
0.23
0.008
0.04
0.051
0.004
0.002
Fe-C-Mn-Ti
0.39
0.87
0.004
0.001
0.001
0.005
0.00
-
-
0.042
0.002
-
6.2.1
Mechanical testing of KNDS4, 34Cr4 and 33B2 fasteners
We compare the performance of the different fastener steels at elevated temperature by
measuring the yield strength as a function of temperature and by the nano-indentation
creep rate of the three steels. Due to the time consuming measurement of creep
parameters during traditional creep testing we choose to estimate the relative creep
behaviour of the three steels by comparing the tendency of the steels to deform in
constant-load nano-indentation experiments. We perform these experiments at room
temperature, based on literature reports that a large number of metallic materials exhibit
indentation creep at temperatures down to room temperature [18].
We prepare the test specimens from traditionally cold-formed M14 fasteners
made from KNDS4, 33B2 and 34Cr4 steel. The fasteners are industrially heat treated in
continuous belt furnaces with oil quenching. The heat treatment parameters of the three
steels are given in Table 6.2.
153
Table 6.2, Heat treatment parameters of industrial steels
Steel
Austenitization
Tempering
33B2
890°C, 45 minutes
460°C, 50-55 minutes
34Cr4
890°C, 45 minutes
460°C, 50-55 minutes
KNDS4
930°C, 60 minutes
560°C, 90 minutes
The temperature accuracy of the furnace is ±5°C. The total time that the steel is in the
furnace includes heating of the steel. The heating time is between 20-30 minutes for both
austenitization and tempering. The longer heat treatment times for industrial heat
treatment of KNDS4 are a recommendation from the steel producer. A separate batch of
specimens received an additional heat treatment for 100 hours at 200°C, 300°C, 400°C or
500°C. These are the same temperatures as the temperatures at which the mechanical
properties are tested.
We perform tensile tests on bar-shaped specimens with diameter 12 mm and length 135
mm that are machined from heat treated fasteners. The specimens have a reduced
diameter 4.00±0.02 mm over a length of 22±2 mm in the middle of the specimen. The
radius of curvature of the transition region from the reduced to the full diameter is 30
mm. Tensile testing is performed at room temperature and at elevated temperatures,
using a table top MTS 858 system (25 kN) equipped with model 793.00 system software
in combination with Multiple Purpose Testware operated in displacement mode. Heating
is performed using an induction coil surrounding the test specimen and an ultra-high
frequency induction generator TruHeat HF 3005 of capacity 6 kW. The temperature of
the specimens is measured using three K-type thermocouples. The ends of the
thermocouples are welded together to a junction. This junction is thereafter flattened to
create a ribbon type thermocouple [19]. The three thermocouple loops are separated by
approx. 3 mm and stretched to make contact with the specimen, using small springs. The
middle thermocouple is used for temperature control. The heating rate is 10°C/s,
followed by 5 seconds soaking time at the test temperature, prior to axial loading. Axial
loading is performed using a constant strain rate of 0.136 s -1 (cross head speed of 3
mm/minute) until fracture. Tensile tests are performed at room temperature, 200°C,
300°C, 400°C and at 500°C. Three specimens are examined for all tests.
The nano-indentation creep measurements are performed on electro-polished steel
specimens (see section 6.2.3) using an Agilent G200 nano-indenter equipped with a
Berkovich-indenter. The tip is calibrated using a reference specimen of fused silica. We
perform 20 indentation experiments on each specimen, according to constant load
principles [20]. The maximum load, Fmax, is 16 mN for all specimens. The load is selected
to assure an indentation depth of minimum 150 nm, in order to measure macroscopic
behaviour of the material [21]. The indenter is loaded up to Fmax during 20 seconds. The
maximum load is thereafter maintained for 600 seconds, while measuring the indentation
depth. After the constant load section is finalized the load is decreased to 0.2Fmax and
maintained for 20 seconds to investigate thermal drift. The experiments are evaluated
according to the method proposed by Goodall et al. [20].
Goodall et al. propose the parameter P, the tendency of a material to deform
under constant load indentation for comparing creep behaviour of different materials at
a given temperature. The parameter P is defined by:
𝑑ℎ
𝑃(𝑡 ∗ , 𝜎) = ∆ℎ ( 𝑑𝑡 ) ,
Equation 6.1
𝑡
where ∆ℎ is the distance the indenter have penetrated into the material between the
start of the constant load section and the evaluation time 𝑡 ∗ , (𝑑ℎ⁄𝑑𝑡)𝑡 is the gradient of
the depth-time curve at the evaluation time 𝑡 ∗ and 𝜎 is the applied stress.
During indentation experiments the stresses in the metal, under the indenter,
range from high in the vicinity of the indenter tip, to low values far from the indenter tip.
Studies have shown that dislocation glide plasticity is the main mechanism for indentation
creep due to the high stresses near the indenter tip. However, materials with small grain
size may be dominated by Coble creep as well [18]. Since our investigated materials
contain grains that are smaller 0.4 µm, we expect that diffusional creep may be involved.
Goodall et al. [20] suggest that different materials should be compared at the
same time, 𝑡 ∗ , and load, Fmax, during indentation experiments. We therefore evaluate the
parameter P for the three steels at 𝑡 ∗ = 570 𝑠. However, since the three investigated
steels have different hardness, the evaluation at 𝑡 ∗ = 570 𝑠 will result in different indent
depths. This will result in different contact pressures between the indenter and the steels,
since all experiments are done at similar load. High contact pressures are expected to
generate a higher degree of dislocation glide plasticity. We therefore also evaluate the
parameter P for the three steels at the same depth; i.e. at the same 𝜎 but different 𝑡 ∗ .
Evaluation at similar depth allow us to compare the nano-indentation creep of the three
steels at the same contact pressure, at similar sizes of the elastic/plastic hemisphere
under the indenter and at the same distance from the indenter centre-line to the surface
(diffusion paths are comparable and a similar free surface area is available for dislocation
escape at the steel surface [22]). The evaluation at a similar depth is done at ∆ℎ = 300 ∓
20 𝑛𝑚, since this indent depth is reached during the constant hold period, at a point
where the depth-time curve has stabilized to a linear trend for all three steels.
155
6.2.2
Characterization of alloy carbides in KNDS4 and 34Cr4
The underlying microstructural mechanisms for the difference in mechanical properties
of the three steels (see section 3.1) are examined by thermodynamic calculations and by
measuring the size and composition of the alloy carbides in the microstructure of the
steels after heat treatment using Atom Probe Tomography (APT).
Database TCFE06 is used for the thermodynamic calculations with the ThermoCalc
software. We simulate the volume fractions of the stable phases in the three steels in the
temperature range from room temperature up to 1350°C. The compositions of the stable
phases are furthermore examined at the temperatures that are used during industrial
heat treatment by APT observations after quenching of the specimens.
The specimens used for APT investigations are produced with an in-situ lift-out method
[23] using the FEI Strata 235 DualBeal workstation. A wedge shaped strip (width 1 µm,
maximum thickness 1 µm) is cut loose from the material surface and welded to a presharpened silicon micro-tip using a Pt-rich gas. The specimen is sharpened by Ga+
sputtering using a pattern shaped as an annulus circle. APT is performed in an Imago LEAP
3000X HR atom probe tomography instrument. The analyses are performed using laser
pulsing. The pulse frequency is set to 200 kHz, the laser energy to 0.25 nJ, the specimen
temperature to 50 K and the evaporation rate to 0.5 %. The reconstruction and data
evaluation is performed using the IVAS 3.6.1 software. The quantitative analysis is based
on isotope distributions of different ions of relevant atom types [24]. The APT
measurements are only performed for the KNDS4 and 34Cr4 steels, because the two
conventional steels did not show a significant difference in mechanical behavior at
elevated temperature (see section 6.3.1 and Fig. 6.1).
6.2.3
Optimization of the thermal processing of KNDS4
The investigation of different thermal processing of KNDS4 is performed on steel
specimens that are machined to a cylindrical shape with a diameter of 4 mm and a
length of 10 mm. The samples are heat treated in a Bähr 805 A/D dilatometer (BährThermoanayse GmbH, Hüllhorst Germany). We perform heat treatments at two
different austenitization temperatures; 1) at 940°C to simulate industrial heat
treatment equipment, which is limited to max. 940°C, and 2) at 1350°C to explore if it
is possible to further improve the mechanical properties via optimal dissolution of
alloying elements in order to maximize the volume fraction of alloy carbides during
subsequent tempering. The soaking time of 30 minutes at 1350°C is chosen to compare
the results to our earlier studies [16-17], in section 3.3. We note that ThermoCalc
simulations show that a small volume fraction of Ti4C2S2 phase can form in the
temperature range of 1070°C to 1456°C. It may therefore not be possible to assure that
all Ti-atoms are in solid solution. The KNDS4 steel that is quenched from 1350°C is from
here on called KNDS4_1350 and the KNDS4 steel that is quenched from 940°C is called
KNDS4_940. The austenitization treatment is followed by quenching to room
temperature using He-gas, at a cooling rate of approx. 175-180°C/s from the start of
quench to the martensite start (Ms) temperature and a cooling rate of approx. 45˚C/s
below the Ms temperature. All specimens are subsequently isothermally tempered at
550°C for 5, 10, 30 or 60 minutes. The heating time to the isothermal tempering
temperature is 138 s. The tempering temperature of 550°C is chosen because it
correlates with industrial heat treatment of KNDS4 steel and in order to stay in line with
our earlier investigations [16-17]. All heat-treated specimens are prepared by grinding
and polishing to 1 µm diamond dispersion. Optical microscopy and Scanning electron
microscopy SEM (JEOL JSM-6500F with a field emission gun) is performed on nitaletched (5%) surfaces. Electron back-scatter diffraction EBSD (using the SEM with a
Nordlys detector) is performed on electro-polished surfaces, conducted in a solution of
8% perchloric, 10% butylcellosolve, 60% ethanol and 22% water. The EBSD data is
acquired and post-processed with Channel 5 software. The beam diameter during EBSD
mapping is approx. 16 nm, resulting in a spot dimension of 16 nm x35 nm. This spot
dimension is combined with a step size of 100 nm. Conventional micro-Vickers hardness
is measured at 20 locations using a load of 500 g.
6.3 Results and Discussion
6.3.1
Mechanical testing
Yield strength
The room temperature tensile strength and yield strength of industrially heat treated
fasteners are shown in table 6.3.
Table 6. 3 Tensile strength and yield strength of high strength fasteners at room temperature
Rm (MPa)
Yield point (MPa)
33B2
1094 ±12
989±4
34Cr4
1339±10
1081±6
157
KNDS4
1504±16
1267±17
Figure 6.1 shows the ratio of the yield strength at elevated temperature to the yield
strength at room temperature of industrially heat treated 33B2, 34Cr4 and KNDS4
fastener steels as a function of test temperature after 5 seconds of soaking time and after
100 hours of soaking time. The yield strength reduces with increasing temperatures, for
each of the three steels. However, the yield strength ratio at 500 °C is /0  0.65±0.06
for the KNDS4 steel, which is much higher than the yield strength ratio at 500 °C of /0
 0.40±0.04 for the 34Cr4 and 33B2 steels.
1.1
KNDS4
34Cr4
33B2
1.0

0.9
0.8
0.7
0.6
0.5
0.4 Solid soymbols: 5 seconds soaking
Open symbols: 100 hours soaking
0.3
50
100 150 200 250 300 350 400 450 500 550
Temperature (°C)
Figure 6.1 Yield point strength ratio of industrially heat treated 33B2, 34Cr4 and KNDS4 steel as
a function of test temperature after 5 seconds and 100 hours soaking time.
Furthermore, the yield strength ratio of KNDS4 at 500°C is the same after 100 hours of
soaking time as after 5 minutes of soaking time. The yield strength ratio of 34Cr4 and
33B2 is similar. The improved properties of the KNDS4 steel is believed to be a result of
secondary alloy carbides, which form during the tempering of KNDS4. This is discussed in
later sections.
Nano-indentation creep rate
Tendency of metal to deform P(nm2s-1)
Figure 6.2 shows the tendency of the metals to deform under constant load nanoindentation, P (Eq. 6.1), for fastener steels KNDS4, 34Cr4 and 33B2, as evaluated both at
𝑡 ∗ = 570 𝑠 and at indent depth 300 ± 20 nm during nano-indentation creep testing.
0.4
Solid symbols: Evaluated at time 520s to 620s
Open symbols: Evalauted at depth 300±20nm
0.3
0.2
0.1
0.0
KNDS4
34Cr4
33B2
Figure 6.2, Tendency of metal to deform under constant load nano-indentation for the three
commercial steels KNDS4, 34Cr4 and 33B2, evaluated at the end of the constant load period
(solid symbols) and at indent depth 300±20nm (open symbols).
Figure 6.2 shows that at 𝑡 ∗ = 570 𝑠 KNDS4 displays the smallest tendency to deform and
34Cr4 and 33B2 demonstrate similar values of P. Studies have suggested that harder
materials creeps faster, since the indentation stress is higher [18]. The better
performance of KNDS4 steel suggests that the microstructure of KNDS4 contains features
which hinder dislocation glide plasticity.
Figure 6.2 furthermore shows that at similar depth, ∆ℎ=300 ± 20 nm the tendency
to deform decreases with increasing tensile strength of the three steels; KNDS4 steel
shows the smallest tendency to deform and steel 33B2 shows the highest tendency to
deform. At similar indentation depth the contact stress is similar, and the driving force for
dislocation glide plasticity in the three steels should be similar. We therefore expect that
the resistance of the microstructure to dislocation glide plasticity in the three steels follow
an inverse trend compared to parameter P; the microstructure of KNDS4 generates the
highest resistance to dislocation glide plasticity and 33B2 the lowest. The better
performance of the KNDS4 steel is believed to be a result of a higher density of small and
stable alloy carbides in the KNDS4 steel as compared to the 34Cr4 and 33B2 steels. We
159
emphasize that the parameter P does not represent fundamental creep characteristics,
but is only used to compare the behavior of the three fastener materials to each other.
Traditional axial creep testing is required in a subsequent study to fully establish the creep
performance of KNDS4 in a subsequent study.
6.3.2
Characterization of the alloy carbides
ThermoCalc study
Figure 6.3 shows the stable alloy carbide phases in the KNDS4, 34Cr4 and 33B2 steels,
as a function of temperature, in the temperature ranges of the tempering treatment.
Phases with a mole of fraction less than 0.0005 are excluded from the pictures.
The fractions of stable alloy carbide phases are significantly higher in the KNDS4 and
34Cr4 steel than in the 33B3 steel (note the scale) at the tempering temperature during
the industrial heat treatment. The main equilibrium alloy carbides of KNDS4 steel are
of M7C3-, TiC- and MC-type. The main equilibrium alloy carbide in steel 34Cr4 is of M7C3
type. The main alloy carbide type of 33B2 steel is of FCC-type consisting mainly of C, Ti
and Cr.
0.05
0.05
0.05
34Cr4
KNDS4
33B2
0.03
0.02
0.01
0.03
0.02
0.01
0.00
0.04
FCC (TiC)
M23C6
M7C3
MC (M=Mo & V)
MC (M=Mo)
0.00
530 540 550 560 570
Temperature ( °C)
°
0.03
°
0.02
°
0.01
0.00
440 450 460 470 480
Temperature ( °C)
Mole fraction
0.04
Mole fraction
Mole fraction
0.04
440 450 460 470 480
Temperature ( °C)
°
Figure 6.3, Stable alloy carbide phases in KNDS4, 34Cr4 and 33B2 steel as a function of
temperature, in the temperature range surrounding the tempering temperature.
The higher mole fractions of alloy carbides in KNDS4 and 34Cr4 can lead to increased
precipitation strengthening. Small precipitates can pin dislocations and thereby prevent
dislocation movement at both room temperature and elevated temperature. This can
increase the yield strength ratio at elevated temperatures and reduce creep rates of
KNDS4 and 34Cr4 steels. The ThermoCalc simulations furthermore show that the majority
of Ti does not dissolve in the austenite of KNDS4 steel at 940°C, and we therefore expect
that the formation of the TiC carbide in industrially heat treated KNDS4 is limited.
Undissolved Ti is expected to be present as coarse primary TiC-carbides [25].
APT study of KNDS4 and 34Cr4
We exclude steel 33B2 from the APT study since ThermoCalc calculations show that the
fraction of alloy carbide precipitates is very low in steel 33B2 and since the tensile-to-yield
strength ratios of 34Cr4 and 33B2 are similar. Figure 6.4 shows APT images of industrially
heat treated KNDS4 (a) and 34Cr4 (b) steel where carbon atoms are shown as red dots,
cementite is shown as blue iso-concentration-surfaces and alloy carbides are shown as
green iso-concentration-surfaces.
(a)
(b)
Figure 6.4 APT images of as-quenched steels where carbon atoms are shown as red dots,
cementite is shown as blue iso-surfaces and alloy carbides are shown as green iso-surfaces: (a)
KNDS4, length 176 nm and (b) 34Cr4, length 469 nm.
The cementite and alloy carbides are identified by the carbon concentration. The
cementite and alloy carbides are thereafter separated by the Cr and Mn concentration.
The atomic concentrations as measured by APT cannot be directly compared to the
compositions as calculated by ThermoCalc since the overall detection rate of APT is 37%
and since especially carbon atoms might not be detected due to surface migration of
carbon atoms [26]. For small carbides the APT measurement will furthermore include
161
some matrix atoms in the voxels that encapsulate the surface of the carbide. This is
especially the case for small particles.
The measured concentration of carbon atoms in the matrix of KNDS4 and 34Cr4 is
approx. 0.3 at% and the measured carbon concentration in cementite and alloy carbides
exceeds 15 at%. The concentration of Cr and Mn in the cementite is measured to 1.7 at%
and 1.3 at% in KNDS4 and 1.5 at% and 0.9 at% in 34Cr4.
The concentration of Cr and Mn in the alloy carbides is approx. 3 at% and 0.7-3.3
at% in KNS4 and 5% and 3% in 34Cr4. In 34Cr4 there are two large carbides which show a
composition with 1.5 at% Mn and 2.2 at% Cr. These two carbides are believed to be alloy
carbides based on that their carbon concentration is similar to the values measured in the
smaller alloy carbides. None of the alloy carbides have a composition that correlates to a
MC type of carbide. The alloy carbides in KNDS4 steel are therefore of M 7C3, M23C6 or a
mix of M7C3 and M23C6. According to ThermoCalc the concentration of Mn in M7C3 and
M23C6 is 6.0 at% and 0.8 at% respectively. The range of measured Mn concentration in
the alloy carbides of KNDS4 therefore indicates that the carbides are of M7C3 type and a
mix of M7C3 and M23C6. The alloy carbides in 34Cr4 are identified to be of type M 7C3.
The average number of atoms measured in the alloy carbides are 2000 atoms in
KNDS4 and 39000 atoms in 34Cr4. We calculate the average sizes of the alloy carbides by
assuming spherical shape and alloy carbides of M7C3 type. M7C3 carbides have an
orthorhombic crystal structure with lattice parameters 𝑎 =0.4526 nm, 𝑐 =0.7010 nm and
𝑑 =1.2142 nm and 40 atoms per unit cell [27]). We calculate that the average alloy carbide
diameter is 3.3 nm in KNDS4 steel and 8.9 nm in 34Cr4.
The strengthening effect of the alloy carbides, ∆𝜎𝑃 is thereafter calculated according to
the Orowan-Ashby equation:
∆𝜎𝑃 = (
0.538𝐺𝑏𝑓1⁄2
𝑑
𝑑
) ∙ ln (2𝑏 ),
Equation 6.1
where d is the average precipitate diameter, G is the shear modulus of the matrix
(calculated to be 80.4 GPa by a linear interpolation between the systems of Fe and Fe-1C
at as concentration of 0.4 wt.%C17), b is the length of the Burgers vector (0.248 nm [11])
and f is the volume fraction of precipitates. We use the ThermoCalc simulation values of
mole fractions at the respective tempering temperature of KNDS4 and 34Cr4 as input for
f. We thereafter convert the strength to hardness HV using 𝐻𝑉 = 𝜎𝑃 /3 [28].
The strengthening effect of the alloy carbides in KNDS4 contributes to 395 HV
hardness and the alloy carbides in 34Cr4 contribute 238 HV hardness. We note that this
calculation represent the strengthening effect of the equilibrium volume fraction of alloy
carbides in the two steels, and therefore is an over-estimation. The calculation indicates
that pinning of dislocations by alloy carbides is more efficient in KNDS4 steel, due to the
size of the carbides. The better yield strength ratio of KNDS4 at elevated temperatures is
therefore considered to be a result of the smaller alloy carbide precipitate size in KNDS4,
as compared to 34Cr4. The small alloy carbide precipitates of KNDS4 will act to pin
dislocations and prevent dislocation movement, which furthermore reduces the nanoindentation creep rate of KNDS4.
Table 6.4 shows the APT measurements of the concentration of alloy elements in the
matrix (excluding cementite and alloy carbides) of KNDS4 and 34Cr4 steel, after heat
treatment.
Table 6.4, Alloy elements in the matrix (excluding cementite and alloy carbides) after heat
treatment [wt%] determined by APT
Steel
Mn
Cr
Mo
Ni
V
KNDS4
0.52
0.97
0.55
0.77
0.068
34Cr4
0.79
1.07
0.09
0.16
0.001
The APT measurements show that the concentration of alloy elements in the matrix of
KNDS4 and 34Cr4 steel is similar to the overall composition of the steel, as given in table
6.1, after heat treatment. We therefore conclude that the redistribution of alloy atoms
into both cementite and alloy carbides does not significantly affect the average
composition of the matrix during tempering up to 60 minutes. After 60 minutes of
tempering the martensite matrix is still supersaturated with alloying elements. Further
growth, and possible nucleation, of alloy carbides is therefore likely to take place during
prolonged tempering of both steels. No Ti-atoms were detected by APT in the KNDS4
specimen. ThermoCalc simulations show that at 940°C the mole fraction of stable TiC is
0.002 and that only 9 ∙ 10−6 wt% Ti is in solid solution. The lack of detected Ti atoms can
be a result of the distribution of the stable, primary TiC carbides, and a concentration of
Ti atoms in solid solution that is below the resolution of the APT detection level (37%).
6.3.3
Optimizing the thermal processing of KNDS4
We compare the microstructure and hardness evolution during tempering of KNDS4 after
different austenization temperatures with the results of earlier investigations that we
performed on a model alloy of Fe-C-Mn-Ti steel, which has similar concentrations of
carbon and titanium [16-17]. This helps to unravel the microstructural mechanisms that
lead to the hardness evolution during tempering of the KNDS4 steel.
Microscopy
163
The former austenite grain size is estimated from the length and orientation of the
martensite structures, as revealed by nital etching on as-quenched specimens. The visible
martensite arrays are measured using the line intercept method. The former austenite
grain size of KNDS4_1350 is 750 ± 179 µm whereas the former austenite grain size of
KNDS4_940 is 8 ± 1.5 µm (95% confidence interval). The smaller grain size KNDS4_940 is
a result of stable TiC and MnS -phases which pin austenite grain boundaries during
austenitization treatment at 940°C (calculated by ThermoCalc study). These phases are
not present at 1350°C, which allow the austenite grains to grow rapidly in KNDS4_1350.
Figure 6.5 shows SEM images of a) KNDS4_1350, b) KNDS4_940 and c) Fe-C-Mn-Ti steel
at low magnification in the as-quenched state and d) the average radius of the cementite
particles of the three steels as a function of tempering time. The auto-tempered regions
in the SEM images (Fig 10.5(a)-(c) appear as white regions due to the small iron carbides.
We note from the SEM images that the degree of auto-tempering is higher in the KNDS4
steels than in Fe-C-Mn-Ti steel. The area fraction of auto-tempered regions is estimated
to 80-90% in KNDS4 and 40-50% in Fe-C-Mn-Ti steel. The study of individual cementite
particle sizes was performed at higher magnification SEM images presented in Figure 6.6
The average cementite radius, R, is calculated according to:
𝑤
𝑙
𝑅 = √( 2 ) (2),
Equation 6.2
where w and l are the average width and length of cementite particles in the SEM images.
The cementite particles grow rapidly during the first 5-10 minutes of annealing, and are
thereafter stabilizing.
Figure 6.5 SEM images of the asquenched microstructure in a)
KNDS4_1350, b) KNDS4_940 and
c) Fe-C-Mn-Ti steel [16] and d) the
average radius of the cementite
particles of the three steels as a
function of tempering time at
550°C.
Figure 6.6 SEM images of the cementite particles in KNDS4_1350 in a) the as-quenched state and
b) after 5 minutes, c) after 10 minutes, d) after 30 minutes and e) after 60 minutes of tempering
at 550°C.
6.3.3.1 EBSD
We define the martensite block boundaries as boundaries between two neighboring
pixels with a misorientation that exceeds 10˚ [29]. The average block size is measured
from Inverse Pole Figure maps of the martensite. The average martensite block size after
quenching is 4.1 µm2 in KNDS4_1350 and 2.4 µm2 in KNDS4_940. The spread in grain size
is large in both KNDS4 steels. The largest and the smallest grain we measure in
KNDS_1350 are 30.0 µm2 and 0.1 µm2 respectively and the largest and smallest grain we
measure in KNDS4_940 and 19.6 µm2 and 0.1 µm2 respectively. We observe that no block
coarsening takes place during tempering at 550°C by comparing the measured block size
165
Average width of block boundaries (um)
after 60 minutes of annealing, which is 4.4 µm 2 and 2.2 µm2 for KNDS4_1350 and
KNDS4_940, respectively.
If identification of the Kikuchi pattern during EBSD measurement is not possible,
the measurement point cannot be indexed. Kikuchi patterns are typically degraded by
surface roughness, grain boundaries, dislocations or precipitates which induce strain in
the measured lattice [30]. In our earlier studies we showed that the regions adjacent to
block boundaries in martensite cannot be indexed because these regions contain high
dislocation densities. The EBSD results in the present study show that no block coarsening
takes place in KNDS4_1350 and KNDS4_940 during tempering at 550°C. We therefore
conclude that the relative changes in the number of non-indexed points during tempering
are a result of changes in the strain level of the steel, e.g. via recovery of dislocations and
nucleation of precipitates. Recovery leads to a reduction of non-indexed points whereas
nucleation of precipitates leads to an increase of non-indexed points since precipitates
are too small to be indexed (the beam spot size will cover both matrix and precipitate)
and induce strains in the surrounding lattice. Small carbides will furthermore prevent
recovery (by pinning of dislocations). We use the width of the non-indexed regions of the
martensite block boundaries to study the evolution of strain in the martensite during
tempering.
0.60
KNDS4_1350
KNDS4_940
Fe-C-Mn-Ti
0.55
0.50
0.45
0.40
0.35
0.30
0
10
20
30
40
50
60
Time (minutes)
Figure 6.7 Width of non-indexed martensite block boundaries in KNDS4_1350, KNDS4_940 and
Fe-C-Mn-Ti steel [16] as a function of tempering time at 550°C.
Figure 6.7 shows the average width of the non-indexed martensite block boundaries in
the KNDS4_1350, KNDS4_940 and Fe-C-Mn-Ti steels, as a function of tempering time at
550°C. The width of the non-indexed block boundaries in the two KNDS4 steels is similar,
and a little lower than the width of the non-indexed block boundaries in the Fe-C-Mn-Ti
steel, in the as-quenched state.
During the first 5 minutes of tempering the width of the non-indexed regions
decreases at a high rate in KNDS4_940 and Fe-C-Mn-Ti steel and with a slightly lower rate
in KNDS4_1350. The rapid decrease of the non-indexed boundary width in Fe-C-Mn-Ti
steel during the first 5 minutes of tempering was shown to be a result of recovery in the
martensite in [16-17].
During tempering from 5 to 10 minutes the width of the non-indexed boundary
regions continue to decrease in Fe-C-Mn-Ti, whereas KNDS4_1350 shows a significant
increase of the non-indexed boundary width. The increase of non-indexed boundary
width of KNDS4_1350 is a result of rapid nucleation and growth of precipitates. The earlier
studies of Fe-C-Mn-Ti steel indicate that TiC-precipitate nucleation and growth takes
place between 5 and 10 minutes. The increase of non-indexed points at the block
boundaries of KNDS4_1350 steel therefore indicates that a higher density of precipitates
nucleate and grow in KNDS4_1350, as compared to Fe-C-Mn-Ti steel. The data points for
10 minutes and 30 minutes are missing for KNDS4_940.
During tempering from 10 minutes to 30 minutes, the width of the non-indexed
boundaries decreases slightly in KNDS4_1350 and Fe-C-Mn-Ti. The slight decrease
indicates that recovery takes place parallel to nucleation and growth of alloy carbides.
During tempering from 30 minutes to 60 minutes the width of the non-indexed
boundaries in KNDS4_1350 continues to increase again whereas the width of the nonindexed block boundaries continues to decrease in Fe-C-Mn-Ti. The increase observed for
KNDS4_1350 indicates that ally carbide precipitates in KNDS4_1350 have grown into a
size which induces strain in the lattice and distorts the Kikuchi pattern enough to prevent
indexing. Since no increase of the width of the non-indexed block boundaries is observed
in Fe-C-Mn-Ti we conclude that the alloy carbides in Fe-C-Mn-Ti are of smaller size and
possibly have a lower number density.
Both Fe-C-Mn-Ti and KNDS4_940 show a decreasing width of non-indexed boundaries
from 5 minutes of tempering to 60 minutes of tempering. The overall decrease of nonindexed block boundary width in KNDS4_940, from 5 minutes to 60 minutes, indicates
that the density of alloy carbides that nucleate and grow during tempering is lower in
KNDS4_940 than in KNDS4_1350.
167
Conventional MicroVickers
Figure 6.8 shows the hardness of KNDS4_1350, KNDS4_940 and Fe-C-Mn-Ti steel as a
function of time during tempering at 550°C.
Hardness (HV)
700
KNDS_940
KNDS4_1350
Fe-C-Mn-Ti
600
500
400
300
200
0
10
20
30
40
50
60
Time (minutes)
Figure 6.8, MicroVickers hardness of KNDS4_1450, KNDS4_940 and Fe-C-Mn-Ti [16] steel, as a
function of time during tempering at 550°C.
KNDS4_1350 is harder than KNDS4_940, after all tempering times. The hardness
difference is 29 HV in the as-quenched state and during the first 10 minutes of tempering.
After 30 minutes of tempering the hardness difference increases to 35 HV and after
increases to 37 HV after 60 minutes of tempering. This hardness difference can be caused
by (i) different dislocation density, (ii) different concentrations of elements in solid
solution, (iii) differences in grain boundary strengthening and/or (iv) different densities of
small precipitates. We investigate the root cause to the hardness difference between
KNDS4_1350 and KNDS4_940 in the as quenched state via a review of (i) to (iv).
The EBSD studies showed that the width of the non-indexed block boundary regions of
the two KNDS4 steels is similar in the as-quenched state (Fig. 6.7). We therefore expect
that the dislocation density is similar in the two steels.
We calculate the difference in the strengthening effect of elements in solid solution of
KNDS4_1350 and KNDS4_940 in the as-quenched state using according to [31]:
∆𝜎𝑠𝑠 = ∑𝑖 𝐾𝑖 𝑐𝑖 ,
Equation 6.3
where 𝐾𝑖 is a constant for alloy element i, and 𝑐𝑖 is the concentration of element i in
weight percent. We assume that all elements which are in solid solution during
austenitization treatment remain in solid solution in the as quenched state. The
calculations can therefore lead to differences only for the elements that are present in
stable phases at the respective austenitization temperature since both KNDS4 steels have
the same overall composition. ThermoCalc simulations show that TiC-phase and MnSphase are stable at 940°C and that Ti4C2S2 is stable at 1350°C. The concentration of Ti
atoms in solid solution of the austenite is 9 ∙ 10−6 wt% at 940°C and 0.03wt% at 1350°C
and the concentration of Mn atoms in solid solution of the austenite at 940°C is 0.0044
wt%. ThermoCalc furthermore shows that the concentration of S-atoms is similar at 940°C
and at 1350°C where S redistributes to MnS at 940°C and to Ti4C2S2 at 1350°C. The
calculation is therefore performed only for elements Ti and Mn. The concentration of Ti
atoms in solid solution of the austenite is 9 ∙ 10−6 wt% at 940°C and 0.03wt% at 1350°C
and the concentration of Mn atoms in solid solution of the austenite at 940°C is 0.0044
wt%. We use KMn=35 MPa%-1 [32] and KTi=1680 MPa2%-1 [17]. The calculated hardness
difference of KNDS4_1350 and KNDS4_940, due to Mn and Ti is 22 HV, with KNDS4_1350
the harder microstructure.
We calculate the different strength contribution due to different block size of the
martensite, 𝜎𝑔𝑏 , in KNDS4_1350 and KNDS4_940 using the Hall-Petch equation [33]:
𝜎𝑔𝑏 = 𝑘𝑔𝑏 𝐷−1⁄2 ,
Equation 6.4
where 𝑘𝑔𝑏 is the Hall-Petch factor and D the average diameter of the martensite blocks.
We assume round block and use the average block diameter as measured by EBSD.
We use 𝑘𝑔𝑏 = 17.4 𝑀𝑃𝑎 𝑚𝑚1⁄2 according to [11]. The strengthening effect of the
martensite block is 138.7 HV in KNDS4_940 and 121.3 HV in KNDS4_1350. The hardness
difference between KNDS4_1350 and KNDS4_940 is 17.4 HV, with KNDS4_940 the harder
microstructure.
Taking (i), (ii) and (iii) into account, we expect that precipitates generate a hardness
increase of 24.4 HV in KNDS4_1350, in order for our calculations to correlate with the
measured hardness difference of 29 HV between KNDS4_1350 and KNDS4_940 in the as
quenched state. There are several precipitate types which can generate precipitation
strengthening in KNDS4_1350: M7C3- alloy carbides which form during quenching, Ti4C2S2
169
which can form during the austenitization and possibly small iron carbides from autotempering.
According to Eq. 6.1, the smallest precipitate size (diameter) that can generate
precipitation strengthening is 0.5 nm. The lattice parameters for M7C3 alloy carbides (see
section 3.2) show that approx. 7 atoms are needed to form a M7C3 precipitate of diameter
0.5 nm. Nucleation of alloy carbides of the type M 7C3 can therefore rapidly generate
precipitation strengthening to the steel. In order to generate 24.4 HV, these small
precipitates do however require a volume fraction close to 0.18 and we therefore
consider precipitates which form during quenching an unlikely root cause to the
measured hardness difference. ThermoCalc shows that Ti4C2S2 is stable in austenite at
temperatures higher than 1070 °C. It is therefore possible that Ti4C2S2 nucleates as small
precipitates during austenitization of KNDS4_1350. The equilibrium volume fraction of
Ti4C2S2 in KNDS4_1350 is 3.77 ∙ 10−4 at 1350°C. This volume fraction of precipitates in
size 0.62 nm can generate a hardness increase of 25 HV. The hardness that difference
different degrees of auto-tempering can generate in KNDS4_940 and KNDS4_1350, within
the tolerance of the measured degree of auto-tempering with the area fraction of autotempering of 80% in KNDS4_1350 and 90% in KNDS4_1350 is 12.5 HV, for the average
iron carbide precipitate size of 12.5 nm. We conclude that the hardness difference of
24.4 HV can be generated by a combination of different precipitate types in KNDS4_1350.
The increase of the hardness difference between KNDS4_1350 and KNDS4_940, from 29
HV in the as-quenched state, to 35 HV after 30 minutes of tempering confirm the EBSD
result that a higher number density of precipitates nucleate and grow in KNDS4_1350
than in KNDS4_940, since no other hardening mechanism leads to increased
strengthening in these two steels during tempering (no grain refinement is observed by
EBSD, the number of dislocations does not increase and the APT study of section 3.2
confirmed that the concentration of alloy elements in the matrix of the martensite of
KNDS4 is not increased during tempering.
Figure 6.8 furthermore shows that the hardness evolution of the two KNDS4 steels is
similar during tempering at 550°C. The hardness decreases by 190 HV during the first 5
minutes of tempering and is thereafter showing an increasing trend. Earlier studies have
shown that the hardness decrease of the Fe-C-Mn-Ti steel during the first 5 minutes of
tempering at 550°C mainly originate from recovery (approx. 210 HV) and coarsening of
Fe3C (approx. 60 HV) [17].
We use Eq. 6.1 to calculate the strengthening effect of the cementite precipitates of
KNDS4 steel, similar to [17]. The hardness contribution due to small cementite particles
in the two KNDS4 steels is 191 HV in the as-quenched state. The hardness decrease due
to coarsening of cementite during the first 5 minutes of tempering is thereafter calculated
to 98 HV for both KNDS4 steels, since there is no significant difference in the cementite
particles of the two KNDS4 steels (Fig. 5). The root cause for the high hardness decrease
of KNDS4 steel is that KNDS4 contains a higher volume fraction of small iron carbides in
the as-quenched state due to auto-tempering (the auto-tempered regions cover 40-50%
of the area in Fe-C-Mn-Ti steel and 80-90% of the area in KNDS4 steel). The coarsening of
the iron carbides during early stages of tempering therefore generates a large hardness
loss in KNDS4.
The remaining 92.6 HV hardness decrease of KNDS4 steel during the first 5
minutes of tempering (from the total 190 HV measured hardness decrease) is generated
by a reduction of the strengthening effect from a combination of solid solution,
precipitates and dislocations (recovery). The combined effect of solid solution,
precipitates and dislocations is complex. When new precipitates nucleate and grow, they
can pin dislocations and reduce recovery. Formation of precipitates will furthermore
redistribute alloy atoms from solid solution to the precipitates, which will result in a
reduction of solid solution strengthening.
Dislocation strengthening in martensite can contribute to very high levels of
hardness in the as quenched state (up to 274 HV) [17], whereas precipitation
strengthening gives lower hardness contribution since the precipitates need to grow in
size before they generate a hardness contribution. As precipitates nucleate and grow,
alloying elements will be redistributed from solid solution to the precipitates. Our APT
measurements of the matrix composition of the industrially heat treated KNDS4 steel
(table 6.4) do however show that the concentration of the alloying elements appear to
remain stable in the matrix during tempering. The unaccounted hardness loss of 92.6 HV
is therefore expected to be a result of recovery only. Recovery reduces the number of
non-indexed points in EBSD whereas carbide nucleation and growth can increase the
number of non-indexed points. It is therefore possible that we do not observe any
changes in number of non-indexed points during early stages of tempering of KNDS4.
We conclude that the strength and hardness of KNDS4 can be improved by applying a
higher austentization temperature than the current industrial heat treatment. However,
the higher temperature generates an austenite grain size which is more than 10 times
higher than the one resulting from the industrial heat treatment, which can reduce the
toughness of the KNDS4 steel [34] and is therefore not suitable for engine fasteners. We
furthermore conclude that nucleation of complex alloy carbides in martensitic steel that
contains several carbide forming elements is more rapid than nucleation of alloy carbides
in a steel that contains only one carbide forming element. This observation is supported
171
by literature studies which have shown that nucleation of vanadium and titan carbides in
steel is promoted by Mo addition to the steel [35-37].
6.4 Conclusions
We compare the properties of the ultra-high tensile strength fastener steel KNDS4 and
the conventional high strength fasteners steels 34Cr4 and 33B2 at room temperature and
at elevated temperatures. We thereafter explain the difference in properties based on a
study of the underlying microstructural mechanisms. Finally we perform a heat treatment
study of KNDS4 steel to investigate if the microstructure and properties can be further
improved.
KNDS4 steel has a higher yield strength ratio than both conventional high strength steels
at 500°C, which have similar yield strength ratios at 500°C. Increased soaking time at
elevated temperatures does not influence the yield strength ratio. The nano-indentation
creep rate shows a weak trend in which the nano-indentation creep rate is lower as the
strength of the different steel grades is higher; KNDS4 shows the lowest nano-indentation
creep rate, followed by 34Cr4 and 33B2. The better mechanical properties of the KNDS4
steel are related to alloy carbides in the microstructure. The alloy carbides in KNDS4 are
smaller than the alloy carbides in 34Cr4 steel, and the properties are therefore better.
The heat treatment study of the KNDS4 steel shows that changing the standard industrial
heat treatment to an austenitization temperature of 1350°C can increase the hardness of
KNDS4 by 8%. The increase stems from a more effective dissolution of alloying elements
during the austenitization treatment, which increases the volume fraction of alloy
carbides that form during subsequent tempering and thereby pin dislocations and
generate precipitation strengthening. However, the standard industrial heat-treatment
results in smaller martensite block sizes, which might be more beneficial for the
toughness of the steel. Independent of the heat treatment, we find that the mechanical
performance of KNDS4 fasteners at elevated temperature and the low nano-indentation
creep rates are two strong indicators that fasteners made from KNDS4 steel might be
used at higher service temperatures than traditional high strength fasteners.
6.5 References
[1] Current production materials used within Nedschroef
[2] ISO898-1, Mechanical properties of fasteners made of carbon steel and alloy steelPart 1. Fifth edition, Switzerland, 2013
[3] T. Seguchi, C. Hanai, O. Nakano and Y. Namimura: JSAE paper 20037061, 255-260
[4] Y. Namimura, N. Ibaraki, W. Urushihara and T. Nakayama: Wire J. Int., January(2003),
62-67
[5] S. Freeman and RWK Honeycombe: Metal Science., Feb (1977), 59-64
[6] T. Gladman: Mater. Sci. Tech., 15(1999), 30-36
[7] M. Charleux, WJ. Poole, M. Militzer and A. Deschamps: Metall. Mater. Trans. A.,
32A(2001), 1635-1647
[8] CY. Chen, HW. Yen, FH. Kao, WC. Li, CY. Huang, JR. Yang and SH. Wang: Mater. Sci.
Eng., 499(2009), 162-166
[9] S. Shanmugam, M. Tanniru, RDK. Misra, D. Panda and S. Jansto: Mater. Sci. Tech.,
21(2005), 883-892
[10] L. Xu, J. Shi, WQ. Cao, MQ. Want, WJ. Hui and H. Dong: J. Mater. Sci., 46(2011),
3653-3658
[11] Y. Han, J. Shi, L. Xu, W.Q. Cao and H. Dong: Mater. Sci. Eng., A530(2011), 643-651
[12] RL. Klueh, N. Hashimoto and PJ. Maziasz: J. Nuclear Mater., 367-370(2007), 48-53
[13] K. Maruyama, K. Sawada and JI. Koike: ISIJ Int. 41(2001), 641-653
[14] M. Taneike, N. Fujitsuna and F. Abe: Mater. Sci. Tech., 20(2004), 1455-1461
[15] P. Michaud, D. Delagnes, P. Lamesle, MH. Masthon and C. Levaillant: Acta Mater.,
55(2007), 4877-4889
[16] CEIC. Ohlund, J. Weidow, M. Thuvander and SE. Offerman: ISIJ Int., 54(2014), 28902899
[17] CEIC. Ohlund, D. den Ouden, J. Weidow, M. Thuvander and SE. Offerman: ISIJ Int.,
55(2015), 883-892
[18] WB. Li, JL. Henshall, RM. Hopper and KE. Easterling: Acta Metall. Mater., 39(1991),
3099-3110
[19] S. Ghodrat: Thermo-Mechanical Fatigue of compacted graphite iron in diesel engine
components, TU Delft, Delft, 2013
[20] R. Goodall and TW Clyne: Acta Mater., 54(2006), 5489-5499
[21] CEIC. Ohlund, SE. Offerman and E. Schlangen: Mater. Sci. Eng. A., 560(2013), 351357
[22] L. Zhang, N. Sekido and T. Ohmura: Mater. Sci. Eng. A., 611(2014), 188-193
[23] DJ. Larson, DT. Foord, AK. Petford-Long, TC. Anthony, IM. Rozdilsky, A. Cerezo and
GWD. Smith: Ultramicrosc., 75(1998), 147-159
[24] M. Thuvander, J. Weidow, J. Angseryd, LK. Falk, M. Sonestedt, K. Stiller and HO.
Andre’n: Ultramicrosc., 111(2011), 604-608
[25] F-G. Wei, T. Hara, T. Tsuchida and K. Tsuzaki: ISIJ Int., 43(2003), 539-547
173
[26] B. Gault, F. Danoix, K. Hoummada, D. Mangelinck and H. Leitner: Ultramicroscopy.,
113(2012), 182-191
[27] B. Xiao, JD. Xing, J. Feng, CT. Zhou, YF. Li, XJ. Xie and YH. Cheng: J. App.Phys.,
42(2009), 5415
[28] B. Huthcinson, J. Hagstrom, O. Karlsson, D. Lindell, M. Tornberg, F. Lindberg and
M. Thuvander: Acta Mater., 59(2011), 5845-5858.
[29] T. Ohmura, K. Tsuzaki and S. Matsuoka: Philos. Mag., A 82(2002), 1903–1910
[30] SI. Wright, MM. Nowell and DP. Field: Microsc. Microanal., 17(2011), 316–329
[31] T. Gladman: The physical metallurgy of microalloyed steels, The University press,
London, 1997.
[32] LA. Nordstrom: Scand. J. Metall., 5(1976), 159-165
[33] LH. Friedman and DC. Chrzan: Phys. Rev. Lett., 81 (1998), 2715-2718
[34] C. Want, M. Wang, J. Shi, W. Hui and H. Dong: Scripta Mater., 58(2008), 492-495
[35] A. Vyrostakove, A. Kroupa, J. Janovec and M. Svoboda: Acta Mater., 46(1998), 3138
[36] A. Vyrostakove, A. Kroupa, J. Janovec and M. Svoboda: Acta Mater., 46(1998), 39-41
[37] JH. Jang, YU. Heo, CH. Lee, HKDH. Bhadeshia and DW. Suh: Mater. Sci. Tech,
29(2013) 309-313
7 Conclusions
The trend of engine down-sizing of passenger cars has led to higher mechanical and
thermal loading of the components inside the engine. This has driven a need for stronger
and yet tough steels for engine fasteners, that can be used at higher temperatures.
New, ultra-high strength, fastener steels have already been developed, based on
the need for higher strength and improved resistance to hydrogen embrittlement. The
improvement in strength at room temperature of these fastener steels is achieved by
creating a steel with a microstructure that consists of a tempered martensite matrix that
is strengthened by the addition of small amounts of carbide-forming elements such as
titanium (Ti), vanadium (V) and molybdenum (Mo). These elements react with carbon
atoms to form nanometer-sized carbides, e.g. titanium carbide (TiC), vanadium carbide
(VC), and molybdenum carbide (Mo2C). Titanium is a particularly interesting microalloying element, because TiC-precipitates are also known to improve the resistance to
hydrogen embrittlement of the steel. However, the novel, ultra-high strength steels for
fasteners have not been designed for use at elevated temperatures.
From the literature, it is known that thermally stable carbides/precipitates are also known
to improve the temperature or fire-resistance resistance of other steels that are used
high-rise buildings and in power plants, by acting as pinning points for movement of
dislocations. In theory, the ultra-high strength steels for fasteners could potentially also
be processed in such a way that they could be used at higher temperatures than the
current limit of 150C.
In order to find out the optimal processing parameters, a deeper understanding
of the effects of micro-alloying elements on the evolution of the microstructure and
mechanical properties is needed during the tempering of martensitic steel. Tempering of
martensite is a process in which the martensitic steel is heated to a temperature between
150 and 700C for some time to make the initially hard and brittle steel tougher.
In this thesis high-purity, model alloys are investigated with and without the carbideforming element Ti, to study the effect of Ti on the mechanisms underlying the
microstructure and hardness evolution of martensitic steel during tempering.
Thereafter, industrial fastener steels are studied, where the results from the model
alloys are used to better understand the origins of the mechanical properties of the
industrial steels at room and elevated temperatures.
175
The results from the research of the high purity model alloys led to the conclusions that
the hardness of martensite block boundaries is significantly higher than the hardness
inside the block matrix, due to a higher dislocation density in the regions adjacent to
the block boundaries.
The softening kinetics during tempering of martensite that does not contain
alloy carbides can be described by three stages, which are related to the evolution of
the microstructure: Stage I (0-5 min) is characterized by fast macroscopic softening
kinetics that is strongly related to: (a) fast and simultaneous softening and reduction in
area fraction of boundaries regions that contain a high dislocation density and (b) fast
reduction in area fraction of non-tempered matrix regions. Stage II (5-10 min) is
characterized by slow macroscopic softening kinetics that is related to slow softening
and reduction in area fraction of the boundaries regions that contain a high dislocation
density. Stage III (10-60 min) is characterized by very slow softening kinetics that is
related to very slow softening and reduction in area fraction of boundary regions.
An addition of 0.042 wt.% Ti to the model steel results in a slight hardness increase.
The microstructure and hardness evolution during tempering at 300 °C remain similar
as before the Ti-addition, but when tempering is done at 550°C the hardness starts to
increase after 30 minutes of tempering. The hardness increase is related to the
formation of TiC-precipitates at 550°C. Nucleation of TiC-precipitates starts in the
regions close to the martensite block boundaries (between 5-10 minutes) and
subsequently nucleates in the block matrix (between 10-30 minutes) due to the higher
dislocation density in the regions close to the block boundaries. The formation of TiCprecipitates slows down the recovery in the regions close to the martensite block
boundaries, especially between 5 and 10 minutes of annealing. Pipe diffusion of
titanium atoms in the martensite contributes to the growth of the TiC-precipitates.
Simulations of the hardness evolution and the nucleation and growth of TiC
precipitates in the model alloy show that the two microstructural components which
contribute most to the overall hardness are Fe3C precipitates (88 HV) and dislocations (54
HV). Both contributions decrease rapidly during the initial stages of annealing and
stabilise after 10 minutes of annealing. The addition of titanium to the steel gives a minor
hardness contribution via Ti-atoms in solid solution and TiC precipitates. Ti atoms in solid
solution give a hardness contribution which increases slightly during the first few minutes
of annealing and then remains stable (at 25 HV). The direct contribution of TiC
precipitates to the overall hardness is limited (3.5 HV). However, TiC-precipitates also
contribute to the overall hardness of martensite by pinning of dislocations during the
recovery that takes place during the tempering. The model predicts that only a small
volume fraction of TiC-precipitates forms during isothermal annealing at 550 °C due to
the large misfit strain (1.34 GJ/m3) and the low density of potential nucleation sites.
The alloy carbides which form in the ultra-high strength KNDS4 steel are smaller than the
alloy carbides that form in the conventional high-strength 34Cr4 steel during industrial
heat treatment. This could be due to the higher concentration of molybdenum, which is
known to reduce the coarsening of TiC- and VC-precipitates, in the KNDS4 steel. KNDS4
steel has a higher ratio of the yield strength at elevated to the yield strength at room
temperature than conventional fastener steels 33B2 and 34Cr4 at 500°C. Increasing the
soaking time from 5 seconds up to 100 hours at elevated temperatures does not have an
impact on the yield strength ratio, which suggest that the microstructure is at least stable
100h at elevated temperature (500°C). The nano-indentation creep rate shows a weak
trend in which the tendency for deformation during constant load nano-indentation is
lower in KNDS4 than in the 34Cr4 and 33B2 steels. This is measured both at similar indent
depths and at the same indent time. The improved mechanical properties of the KNDS4
steel compared to the conventional high-strength steels are related alloy carbides in the
microstructure that hinder dislocation movement. Changing the standard industrial heattreatment of KNDS4 from an austenitization temperature of 940 to 1350°C can increase
the hardness of KNDS4 by 8%. The increase stems from more effective dissolution of
mainly Ti-atoms during the austenitization treatment. Titanium in solid solution enables
the nucleation and growth of precipitates, which generates precipitation strengthening
during subsequent tempering. However, the standard industrial heat-treatment results in
a smaller martensite block sizes, which might be more beneficial for the toughness of the
steel. Independent of the heat-treatment, we find that the mechanical performance of
KNDS4 fasteners at elevated temperature and the low nano-indentation creep rates are
two strong indicators that fasteners made from KNDS4 steel might be used at higher
service temperatures than traditional high strength fasteners due to the presence of small
alloy carbides in the microstructure of KNDS4. More research, in particular conventional
creep measurements that are very time consuming, are needed to provide evidence that
the ultra-high strength KNDS4 steel can be used at higher temperature in real engine
conditions.
Higher strength of a fastener steel enables for development of smaller, but stronger
fasteners. These fasteners can be used in critical applications inside the engine, to downsize e.g. connecting rods, which will make it possible to significantly reduce the size and
weight of modern combustion engines. Furthermore, the improved temperature
resistance of new martensitic fastener steels will allow using the fastener at elevated
service temperatures. These fasteners can therefore be used in applications where the
177
temperature exceeds the recommended service temperature of 150 °C (with the
maximum upper boundary of 300°C) as stated in ISO898-1. This make is possible to reduce
the use of highly alloyed high temperature fasteners (which are designed for service
temperatures of 500°C or more) that are used in engines today due to the lack of cost
efficient, resource-efficient, micro-alloyed fastener steels suitable for service at 300500°C.
Acknowledgements
It’s easy to do anything in victory. It’s in defeat that a man reveals himself
-Floyd Patterson
The most important thing that I learned during the time of my study at TU Delft was to
fail. And that failures leads to extraordinary good results, if you let them.
To realize this has changed me as an engineer, as an athlete and as a person. I am forever
grateful to the persons who taught me this lesson.
First of all I want to thank my daily supervisor Erik Offerman and my promotor Jilt Sietsma
for their supervision, support and encouragement. Your efforts have transformed me
from an industrial engineer to a scientist! Thank you for allowing me the freedom to split
my time between Helmond and Delft, and for letting me design the study. Thank you for
always expecting a lot, and for setting high standards. I would like to especially thank Erik
Offerman for his fantastic patience! You let me to do things “my way”, even though (in
many cases) it meant that things were going to fail. I am too stubborn to learn things in
any other way!
I also want to thank company Nedschroef, for trusting me with this study, and for
investing in me!
I am forever grateful to all the persons who gave me fantastic support during my
experimental work. Some of you really stood out in your efforts to help me! Thank you
Kees Kwakernaak, for spending so many hours helping me with the SEM and EBSD studies.
Without the flexibility you allowed me for scheduling the equipment I would never have
been able to finish in time. I want to thank Nico Geerlofs, who supported and worked with
me on the dilatometer! Without your support I would never have been able to prepare
all my samples. And I want to thank Ton Riemslag, who took the time to teach me how to
perform the hot tensile testing, despite a full agenda and a fully occupied laboratory.
I would also like to thank the team of persons who were performing experiments for my
research. Thank you Erik Schlangen, for introducing me to the field of nano-indentation,
for your great enthusiasm and for keeping up with my tight schedule. I also want to thank
Mladena Lukovic, in the team of Erik Schlangen, for performing so many of the
indentation experiments.
179
I want to thank the team at Chalmers University of Technology in Sweden, Mattias
Thuvander and Jonathan Weidow, for their APT measurements. Thank you for your
patience in explaining the reconstruction analyze for me in detail, despite my limited
knowledge within this field.
At Nedschroef I want to thank Ferrie Kersten, who believed in me and fought to get the
budget to realize this study. IT would not have happened otherwise. I also want to thank
all my colleagues at the Techno Centre in Helmond; Rene, Lianne, Rob, Frank, Erik and
Max. Thank you for your support and for covering for me during the days I spent in Delft.
I also want to acknowledge the persons who gave me the energy to keep up with my
schedule and provided the places where I could recover my (exhausted) brain and let my
unconscious work on all failed experiments and rejected papers. I know for sure that,
without the heavy physical training I did during these years, I would not have been able
to finalize neither my work, nor my studies.
Charles and Niels Verschuren, with family; I am forever grateful for your training
and support. The cross-fit box in Gemert have always felt like a second home to me. You
have coached and trained me in a way that made me reach overall targets and set
personal records that I never ever imagined I was able to.
Frans Bosman; the work you do and the commitment you have, to keep the gym
of the basement in Delft open at all times is truly fantastic! Thank you!
Finally I want to thank my husband, Bosko Pavlovic. Your support is the most important
support I have! Thank you for enduring life with someone who spends most of the time
at the office (or school), the free time at the gym, and most time in-between in her own
head. I am finished with my studies now. Whatever my next challenge will be, I promise
to do it together with you!!!
About the author
Carin Emmy Ingrid Christersdotter Ö hlund was born on the 7th of February 1980 in
Sundsvall (Alnö), Sweden.
She acquired her master’s degree in Chemical Engineering with Engineering Physics at
Chalmers University of Technology in Sweden on the 13th of January 2004. Her master’s
thesis was done at Volvo Materials Technology department, on the topic of aluminum
fasteners in Magnesium components. She currently work for Koninklijke Nedschroef
Holding B.V, at their production plant in Kunshan, China, in the position as Nedschroef
Group R&D director.
2015-Present
Group R&D Director (temporary located in Kunshan)
Koninklijke Nedschroef Holding B.V, Helmond, The Netherlands
2010-2015:
PhD Researcher at Materials Science and Engineering Dept.
Delft University of Technology, Delft, The Netherland
2014-2015:
Manager Techno Centre Kunshan
Nedschroef Techno Centre, Kunshan, China
2009-2014:
Manager Materials Development
Nedschroef Techno Centre, Helmond, The Netherlands
2007-2009:
Technical Support and Project Manager
Nedschroef Fasteners AB, Billdal, Sweden
2004-2007:
Development Engineer for Engine Fasteners
Volvo Powertrain, Gothenburg, Sweden
181
List of publications

The kinetics of softening and microstructure evolution of martensite in Fe-C-Mn
steel during tempering at 300°C.
C.E.I.C. Ö hlund, E. Schlangen and S.E. Offerman
Mater. Sci Eng A. Vol. 560, pp, 351-357, 2013

Effect of Ti on evolution of microstructure and hardness of martensitic Fe-C-Mn
steel during tempering
C.E.I.C. Ö hlund, J. Weidow, M. Thuvander and S.E. Offerman
ISIJ Int., Vol. 54, pp 2890-2899, 2014

Modelling the evolution of multiple hardening mechanisms during tempering of
Fe-C-Mn-Ti martensite
C.E.I.C. Ö hlund, D. den Ouden, J. Weidow, M. Thuvander and S.E. Offerman
ISIJ Int., Vol. 55, pp 883-892, 2015

A comparison between ultra-high-strength and conventional high-strength
fastener steels: mechanical properties at elevated temperature and
microstructural mechanisms
C.E.I.C. Ö hlund, M. Lucovic, J. Weidow, M. Thuvander and S.E. Offerman
(To be submitted)

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project