PhD_Thesis_Ron_van_Tol.

PhD_Thesis_Ron_van_Tol.
Microstructural evolution in deformed
austenitic TWinning Induced Plasticity steels
Ronald Theodoor VAN TOL
Microstructural evolution in deformed
austenitic TWinning Induced Plasticity steels
Proefschrift
ter verkrijging van de graad 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 donderdag 17 april 2014 om 12:30 uur
door
Ronald Theodoor VAN TOL
werktuigbouwkundig ingenieur,
geboren te ’s-Gravenzande.
Dit proefschrift is goedgekeurd door de promotor:
Prof.dr.ir. J. Sietsma
Samenstelling promotiecommissie:
Rector Magnificus
Voorzitter
Prof.dr.ir. J. Sietsma
Technische Universiteit Delft, promotor
Prof.dr. R. Boom
Technische Universiteit Delft
Prof.dr.ir. L.A.I. Kestens
Universiteit Gent, Belgium
Prof.dr.ir. B.C. De Cooman
Pohang University of Science and Technology, South-Korea
Prof.dr. K. Tsuzaki
Kyushu University, Japan
Dr. L. Zhao
VDL Weweler, Apeldoorn
Dr.ir. M. van der Winden
TATA Steel Europe, IJmuiden
Prof.dr. I.M. Richardson
Technische Universiteit Delft, reservelid
Dr. L. Zhao heeft als begeleider in belangrijke mate aan de totstandkoming van het
proefschrift bijgedragen.
This research was carried out under the project number MC10.07292 in the framework of the
Research Program of the Materials innovation institute (M2i, www.m2i.nl). The support of
Tata Steel Europe is gratefully acknowledged.
Copyright  2014 by R.T. van Tol
All rights reserved. No part of this book may be reproduced, stored in a retrieval system or
transmitted, in any form or by any means, without the prior permission from the copyright
owner.
ISBN: 978-94-6108-650-1
Printed by: Gildeprint Drukkerijen, Enschede, The Netherlands
Cover and chapter headings by A-creation (www.a-creation.nl) and Mak van Tol
To our twins
Dankwoord
Dit boekje markeert het einde van een prachtige tijd in Delft en IJmuiden, maar nu is het
mooi geweest. Dank
aan mijn begeleiders voor dit ‘geschenk’. Jilt, we zijn begonnen met Callister en geëindigd
met een paper in Acta. Bedankt voor al je aandacht en vooral je geduld. Lie, we hebben
elkaar goed leren kennen en waarderen. Bedankt voor je kritische houding en oog voor
detail. Henk, een goed begin is het halve werk: jouw vakmanschap en bovenal schrijfkunsten
hebben mij goed op weg geholpen.
aan de Hoogovenaren voor deze kans, de (financiële) steun en toeverlaat; ik ben mij ervan
bewust dat ik de afgelopen jaren in een bevoorrechte positie heb verkeerd. Een aantal
mensen wil ik hiervoor in het bijzonder bedanken. Mark (Maier), Pieter en Richard voor het
steunen en aanmoedigen van dit initiatief. Rob, Leo, Jan (Bottema), René, Lene en Arjan
voor de totstandkoming van dit project. Marc (Cornelissen), ik heb veel van je geleerd, vooral
van je scherpe blik. Freek, bedankt voor het realisme. Basjan, Pascal, Patricia, Menno,
Maxim en Jan (Heijne) voor jullie inbreng en nog belangrijker luisterend oor. Jan (Brussel),
Floor, Edward, Lieven en Guido voor de mooie tijd, we hebben veel gelachen. Peter, ‘samen’
een promotietraject in, een uitstekende gelegenheid om eens te bomen en dat hebben we
geweten! Verder natuurlijk al mijn andere collega’s in de kennisgroepen en IJmuiden. Helaas
zijn we geen directe collega’s meer.
aan de Delftenaren voor het bij tijd en wijle onderbreken van de eenzaamheid, in het
bijzonder aan Andrea voor de ‘Duitse onderonsjes’ en Monica voor de spontaniteit.
vii
aan de ‘Koreanen’ voor de gastvrijheid, met name Bruno (Prof. De Cooman) en Jin-Kyung.
aan de technici voor het doen wat ikzelf liever laat doen: Leon, Aad en Bert van DEMO, Niek,
Rob, Ruud en Kees van 3mE en Mohammed van SKF, bedankt!
aan de studenten voor jullie interesse en enthousiasme, in het bijzonder Tjerk.
aan mijn (schoon)familie en vrienden voor alles wat niets met dit proefschrift van doen heeft.
aan Annemieke, Mak, Cas† en Lem voor waar het eigenlijk om te doen is.
Ron van Tol
’s-Gravenzande, maart 2014
viii
Summary
This thesis studies the effect of plastic deformation on the stability of the austenitic
microstructure against martensitic transformation and diffusional decomposition and its role
in the phenomenon of delayed fracture in austenitic manganese (Mn)-based TWinning
Induced Plasticity (TWIP) steels. The transformation to α’-martensite upon mechanical
loading and diffusional decomposition into pearlite upon annealing at intermediate
temperatures shows the austenite to be metastable. An increase in the austenite stability is
expected to improve the resistance against delayed fracture.
In the automotive industry, the requirements for fuel economy and safety are continuously
increasing. Improvements in fuel economy require a lower weight of the vehicle whereas
improvements in safety often result in additional weight. To resolve this contradiction, the
requirements for strength and formability of steel increase continuously. To this purpose, the
steel industry develops (Advanced) High Strength Steels and Press Hardening Steels. One
of the latest developments is fully austenitic Mn-based TWIP steels that combine a high
strength with a very high uniform elongation. These superior mechanical properties result
from the high work-hardening of these austenitic Mn-based TWIP steels. The main reasons
for this high work-hardening are deformation mechanisms combining slip of dislocations with
strain induced microtwinning and martensite transformation. The deformation mechanisms
relate to the austenite stability and form shear bands like slip bands, twins and/or εmartensite laths, which are obstacles for further dislocation glide increasing work-hardening.
In addition to usual application issues like formability and weldability, a problem
encountered with austenitic Mn-based TWIP steels is delayed fracture. This is the
phenomenon that even after successful forming, fracture may still occur. The time until
fracture can range from seconds to weeks. Increased understanding of the phenomenon of
ix
delayed fracture would accelerate the introduction of austenitic Mn-based TWIP steels to the
automotive industry, enabling further weight reduction and improved safety and fuel
economy.
The susceptibility to delayed fracture is a combination of (1) the austenite stability
against microstructural defect formation, (2) the internal residual stress and (3) the presence
of mobile hydrogen. Most research on delayed fracture concentrates on the role of hydrogen,
leaving the austenite stability against defect formation and internal residual stress
underexposed. Increasing the austenite stability against microstructural defect formation like
strain-induced transformation improves the resistance against delayed fracture. This work
discusses the effect of plastic deformation on the stability of the austenitic microstructure
against martensitic transformation and diffusional decomposition and its role in the
phenomenon of delayed fracture.
The effect of deep drawing on the generation of structural defects in austenitic Mn-based
TWIP steels is investigated experimentally using X-ray diffraction, positron annihilation
Doppler broadening spectroscopy and magnetic measurements. To this purpose, the
characteristics of defects were studied along the wall of deep-drawn cups, representing a
gradually changing deformation state. Positron annihilation detects that two different defect
types result from plastic deformation during deep drawing. The two defect types can be
expected to be dislocations and partial dislocations. Magnetic field measurements reveal the
formation of α’-martensite which correlates with the density of the defects identified as partial
dislocations.
The effect of strain on the defect and microstructure evolution in austenitic Mn-based
TWIP steels is experimentally investigated using magnetic measurements, X-ray diffraction,
positron beam Doppler Spectroscopy and Transmission Electron Microscopy techniques.
The strain evolution during deep drawing is simulated by means of Finite Element Method
simulations. The formation of α’-martensite is attributed to the accumulated equivalent strain
and crystallographic texture. The presence of α’-martensite is observed at shear band and
twin intersections and questions the sequential γ → ε → α’ martensitic transformation. The
results indicate that the formation of α’-martensite in a high Stacking Fault Energy (SFE)
Face Centred Cubic alloy does not necessarily require the intermediate formation of εmartensite laths. A model for α’-martensite volume fraction evolution upon straining is
proposed and the estimated fraction of intersected shear bands - the preferred nucleation
sites for α’-martensite formation - as a function of accumulated equivalent strain is in good
agreement with the experimentally determined α’-martensite fraction.
x
The role of α’-martensite in the phenomenon of delayed fracture is studied in austenitic Mnbased TWIP steels after deep drawing, observed by in-situ video recording. The formation of
α’-martensite indicates the formation of crack initiation sites, which is discussed as a possible
cause of delayed fracture. Delayed fracture occurs where the α’-martensite fraction is the
highest. An intermittent crack propagation concept and model is proposed based on the
coalescence of initial cracks into a macrocrack. A higher α’-martensite fraction indicates a
higher density of shear-band intersections, resulting in more potential crack-initiation sites
and easier coalescence. The SFE in the tested range of 22 to 52 mJ/m2 does not affect the
formation of α’-martensite and does not relate to the delayed fracture susceptibility.
The transformation of austenite by martensitic mechanisms upon plastic deformation
shows the metastability of the austenite and indicates diffusional decomposition of austenite
into pearlite in case the material is annealed at temperatures below the A1-temperature. This
transformation and the effect of prior plastic deformation on the austenite decomposition into
pearlite at intermediate temperatures is investigated. The transformation kinetics are
governed by Mn-partitioning between ferrite and cementite within the pearlite. Mn-diffusion is
too slow to allow partitioning between pearlite and austenite, and a mixed equilibrium
condition is established of ortho-equilibrium between ferrite and pearlite and para-equilibrium
between pearlite and austenite. Nucleation of pearlite takes place only in the initial stages of
the transformation. Prior plastic deformation enhances the formation rate of pearlite from
austenite and increases the number density of pearlite colonies, primarily through increased
nucleation efficiency. Prior plastic deformation does not significantly affect the nucleation rate
or growth rate in the observed timescale.
xi
Samenvatting
Dit proefschrift bestudeert het effect van plastische vervorming op de stabiliteit van de
austenitische microstructuur tegen transformatie naar martensiet en perliet en haar rol in het
fenomeen van vertraagde scheurvorming bij austenitische mangaan (Mn)-gelegeerde
staalsoorten met tweeling-geïnduceerde plasticiteit (TWIP). De transformaties naar α’martensiet door mechanische belasting en naar perliet op basis van diffusie door
warmtebehandelingen laten zien dat het austeniet metastabiel is. Een toename van de
austenietstabiliteit leidt naar verwachting tot een verbeterde weerstand tegen vertraagde
scheurvorming.
De eisen voor brandstofverbruik en veiligheid in de automobielindustrie nemen gestaag toe.
Een lager brandstofverbruik vereist een lager gewicht van het voertuig, terwijl een hogere
veiligheid vaak in meer gewicht resulteert. Om deze tegenstelling het hoofd te bieden,
moeten de sterkte en vervormbaarheid van staal omhoog. Hiervoor ontwikkelt de
staalindustrie geavanceerde hoge sterkte en warmvervormbare staalsoorten. Een van de
laatste ontwikkelingen is volledig austenitische Mn-gelegeerde TWIP-staalsoorten met hoge
sterkte en zeer hoge uniforme rek. Deze superieure mechanische eigenschappen zijn het
resultaat van de hoge werkversteviging van deze austenitische Mn-gelegeerde TWIPstaalsoorten. De hoofdredenen voor deze hoge werkversteviging zijn vervormingsmechanismen
die
slip
van
dislocaties
combineren
met
vervormingsgeïnduceerde
tweelingvorming en martensiet transformatie. De vervormingsmechanismen hangen samen
met de austenietstabiliteit en vormen slipbanden, tweelingen en/of ε-martensietnaalden,
welke obstakels zijn voor verdere dislocatiebeweging en daarmee de werkversteviging
verhogen.
xiii
Naast gebruikelijke toepassingsproblemen zoals vervorm- en lasbaarheid, doet zich bij
austenitische
Mn-gelegeerde
TWIP-staalsoorten
het
probleem
van
vertraagde
scheurvorming voor. Dit is het fenomeen dat zelfs na succesvol vervormen, scheurvorming
op kan treden. De tijd tot scheuren kan variëren van secondes tot weken. Een beter begrip
van het fenomeen van vertraagde scheurvorming zal de introductie van austenitische Mngelegeerde TWIP-staalsoorten versnellen, met verdere gewichtsreductie en verbeterde
veiligheid en brandstofverbruik tot gevolg.
De gevoeligheid voor vertraagde scheurvorming wordt bepaald door een combinatie
van (1) de austenietstabiliteit tegen de vorming van microstructurele defecten, (2) de interne
residuele spanning en (3) de aanwezigheid van mobiel waterstof. Het merendeel van het
onderzoek naar vertraagde scheurvorming concentreert zich op de rol van waterstof,
waardoor de austenietstabiliteit tegen de vorming van microstructurele defecten en de
interne residuele spanning onderbelicht blijven. Een verhoogde austenietstabiliteit tegen de
vorming van microstructurele defecten, zoals vervormingsgeïnduceerde transformatie,
verbetert de weerstand tegen vertraagde scheurvorming. Dit proefschrift behandelt het effect
van plastische vervorming op de stabiliteit van de austenitische microstructuur tegen
transformatie naar martensiet en perliet en haar rol in het fenomeen van vertraagde
scheurvorming.
Het effect van dieptrekken op de vorming van structurele defecten in austenitische Mngelegeerde
TWIP-staalsoorten
is
experimenteel
onderzocht
door
middel
van
rӧntgendiffractie, positronannihilatie Doppler verbredingspectroscopie en magnetische
metingen. Hiervoor zijn de defect karakteristieken langs de wand van diepgetrokken bekers
bestudeerd,
die
een
geleidelijk
veranderende
vervormingstoestand
representeren.
Positronannihilatie heeft als gevolg van de plastische vervorming tijdens het dieptrekken
twee verschillende soorten defecten waargenomen. De twee soorten defecten zijn naar
verwachting dislocaties en partiële dislocaties. Magnetische metingen geven de vorming van
α’-martensiet aan, welke samenhangt met de dichtheid van de defectsoort geïdentificeerd als
partiële dislocaties.
Het effect van rek op de defect- en microstructuurevolutie bij austenitische Mngelegeerde TWIP-staalsoorten is experimenteel onderzocht door middel van magnetische
metingen,
rӧntgendiffractie,
positronannihilatie
Doppler
verbredingspectroscopie
en
transmissie-electronenmicroscopie. De evolutie van de rek tijdens het dieptrekken is
gesimuleerd met behulp van eindige-elementen-methode simulaties. De vorming van α’martensiet
wordt
toegeschreven
aan
de
geaccumuleerde
equivalente
rek
en
kristallografische textuur. De aanwezigheid van α’-martensiet is geobserveerd bij
xiv
vervormingsbanden en tweelingen en zet vraagtekens bij de sequentiële γ → ε → α’
martensitische transformatie. De resultaten geven aan dat de vorming van α’-martensiet in
een kubisch vlakken gecentreerde legering met een hoge StapelFoutEnergie (SFE) niet
noodzakelijkerwijs de tussentijdse vorming van ε-martensietnaalden nodig heeft. Een model
voor de evolutie van de α’-martensiet volumefractie afhankelijk van de rek wordt voorgesteld
en de geschatte fractie van gekruiste vervormingsbanden - de voorkeurslocatie voor de
nucleatie en vorming van α’-martensiet - als functie van de geaccumuleerde equivalente rek
komt goed overeen met de experimenteel vastgestelde α’-martensietvolumefractie.
De rol van α’-martensiet in het fenomeen van vertraagde scheurvorming is
onderzocht
bij
austenitische Mn-gelegeerde TWIP-staalsoorten na dieptrekken en
waargenomen met behulp van in-situ video-opnames. De vorming van α’-martensiet wijst op
de vorming van scheurinitiatiepunten, welke besproken worden als mogelijke oorzaak van
vertraagde scheurvorming. Vertraagde scheurvorming treedt op daar waar de α’martensietfractie het hoogst is. Een concept en een model voor schoksgewijze scheurgroei
worden voorgesteld op basis van het samengroeien van initiële scheurtjes tot een scheur.
Een
hogere
α’-martensietfractie
duidt
op
een
hogere
dichtheid
van
gekruisde
vervormingsbanden met als gevolg meer potentiële scheurinitiatiepunten en een
eenvoudigere samengroei. De SFE in het geteste bereik van 22 tot 52 mJ/m2 heeft geen
invloed op de vorming van α’-martensiet en hangt niet samen met de gevoeligheid voor
vertraagde scheurvorming.
De transformatie van austeniet door martensitische mechanismen als gevolg van
plastische vervorming geeft de metastabiliteit van het austeniet aan en daarmee de
transformatie van austeniet naar perliet in het geval van verhitting bij temperaturen onder de
A1-temperatuur. Deze transformatie van austeniet naar perliet en het effect van plastische
vervorming hierop is onderzocht. De transformatiekinetiek wordt bepaald door de Mnafscheiding tussen ferriet en cementiet binnenin het perliet. De Mn-diffusie is te langzaam
voor Mn-afscheiding tussen perliet en austeniet. Een gemengde evenwichtstoestand vormt
zich, bestaande uit een ortho-evenwicht tussen ferriet en perliet en een para-evenwicht
tussen perliet en austeniet. De nucleatie van perliet vindt alleen plaats in de beginfase van
de transformatie. Voorafgaande plastische vervorming versnelt de vorming van perliet en
verhoogt de dichtheid van het aantal perlietkolonies, hoofdzakelijk door de toegenomen
efficiëntie van de nucleatie. Voorafgaande plastische vervorming heeft binnen de
onderzochte tijdspanne geen significant effect op de nucleatie- en groeisnelheid.
xv
List of publications
R.T. van Tol, L. Zhao and J. Sietsma, Effect of strain on the deformation mechanism in
austenitic Mn-based TWIP steels, The 1st International Conference on High Mn TWIP Steels
HMnS2011, Seoul, South Korea, 2011.
R.T. van Tol, L. Zhao, H. Schut and J. Sietsma, Experimental investigation of structural
defects in deep-drawn austenitic Mn-based TWIP steel, Material Science and Technology,
vol. 28, no. 3, pp. 348-353, 2012 (Chapter 3).
R.T. van Tol, L. Zhao, H. Schut and J. Sietsma, Investigation of deformation mechanisms in
deep-drawn and tensile-strained austenitic Mn-based TWIP steel, Metallurgical and Materials
Transactions A, vol. 43, no. 9, pp. 3070-3077, 2012 (Chapter 4).
R.T. van Tol, J.K. Kim, L. Zhao, J. Sietsma and B.C. De Cooman, α’-Martensite Formation in
deep-drawn Mn-based TWIP Steel, Journal of Materials Science, vol. 47, pp. 4845-4850,
2012 (Chapter 4).
R.T. van Tol, L. Zhao, L. Bracke, P. Kömmelt and J. Sietsma, Investigation of the delayed
fracture phenomenon in deep-drawn austenitic manganese-based Twinning Induced
Plasticity steels, Metallurgical and Materials Transactions A, vol. 44, no. 10, pp. 4654-4660,
2013 (Chapter 5).
R.T. van Tol, L. Zhao and J. Sietsma, Kinetics of austenite decomposition in manganesebased steel, Acta Materialia, vol. 64, pp. 33-40, 2014 (Chapter 6).
xvii
About the author
Ronald (Ron) Theodoor van Tol was born on July, 9th 1979 in ‘s-Gravenzande, The
Netherlands. After his ‘Athenaeum’ (Dutch A-levels) at the Zandevelt College in ‘sGravenzande, he embarked on his studies in Mechanical Engineering at the Technische
Universiteit Delft in 1997. In 2003 he obtained his ‘ir’ (M.Sc.) degree on the subject of Paint
Bake Response of the Aluminium Body Front-end of the BMW 5-series, in close cooperation
with the BMW Group in Munich (Germany).
After a year at Mitsubishi Heavy Industries, he joined Corus to work on the development of
steel grades for the automotive industry in the Knowledge Group Strip Metallurgy for
Automotive and Packaging in 2005. After three years, he was given the opportunity to start a
PhD research at the Materials innovation institute (M2i) under the supervision of Prof.dr.ir. J.
Sietsma and Dr. L. Zhao from the group of Microstructure Control in Metals (MCM) of the
Department of Materials Science and Engineering (MSE) of the Faculty of Mechanical,
Maritime and Materials Engineering (3mE) at the Technische Universiteit Delft.
Ron is currently Research Engineer Materials & Corrosion at Shell Projects & Technology,
Innovation, Research & Development in Amsterdam.
xix
Outline
Dankwoord..........................................................................................................................vii
Summary ..............................................................................................................................ix
Samenvatting.....................................................................................................................xiii
List of publications ..........................................................................................................xvii
About the author ...............................................................................................................xix
1
Introduction .................................................................................................................. 1
1.1
Phenomenon of delayed fracture ................................................................................ 3
1.2
Origin and development of austenitic manganese-based steels.................................. 4
1.3
Austenite stability and deformation mechanisms......................................................... 5
1.3.1
Mechanical twinning ................................................................................................................ 9
1.3.2
Mechanisms and kinetics of martensitic transformation ........................................................ 10
1.4
Role of hydrogen .......................................................................................................12
1.5
Scope of thesis ..........................................................................................................14
1.6
Outline of thesis .........................................................................................................15
xxi
2
Materials and experimental ........................................................................................17
2.1
Composition and properties .......................................................................................18
2.2
Delayed fracture testing .............................................................................................18
2.2.1
Deep drawing......................................................................................................................... 18
2.2.2
Finite Element Method simulations ....................................................................................... 19
2.3
Magnetometry ............................................................................................................21
2.4
Positron beam Doppler broadening spectroscopy ......................................................24
2.5
Microscopy ................................................................................................................27
2.5.1
Optical Microscopy ................................................................................................................ 27
2.5.2
Scanning Electron Microscopy .............................................................................................. 27
2.5.3
Transmission Electron Microscopy ........................................................................................ 28
2.6
3
X-ray diffraction..........................................................................................................28
Effect of deep drawing on the generation of structural defects ..............................29
3.1
Introduction ................................................................................................................30
3.2
Characterization of defects ........................................................................................30
3.2.1
Line broadening ..................................................................................................................... 30
3.2.2
Line-shape parameters .......................................................................................................... 31
3.2.3
Trapping fractions .................................................................................................................. 33
3.2.4
Ferromagnetic phase ............................................................................................................. 35
3.3
Discussion of defect characteristics ...........................................................................36
3.3.1
Perfect dislocations ............................................................................................................... 36
3.3.2
Partial dislocations ................................................................................................................. 37
3.4
4
Conclusions ...............................................................................................................38
Effect of strain on the formation of α’-martensite .....................................................39
4.1
Introduction ................................................................................................................40
4.2
Microstructural evolution upon plastic deformation.....................................................40
4.2.1
Formation of α’-martensite .................................................................................................... 41
4.2.2
Dislocation multiplication and twinning .................................................................................. 42
xxii
4.2.3
Dislocation glide and dissociation into partial dislocations .................................................... 43
4.2.4
Observation of α’-martensite ................................................................................................. 45
4.3
Martensitic transformation ..........................................................................................47
4.3.1
Strain-induced nucleation of α’-martensite ............................................................................ 47
4.3.2
Relation to the development of crystallographic texture during deep drawing ...................... 48
4.4
Evolution of α’-martensite volume fraction upon straining ..........................................49
4.4.1
The Olson and Cohen model................................................................................................. 49
4.4.2
The sequential behavior upon straining ................................................................................ 50
4.5
5
Conclusions ...............................................................................................................52
Role of α’-martensite in the phenomenon of delayed fracture.................................53
5.1
Introduction ................................................................................................................54
5.2
Susceptibility to delayed fracture and the presence of α’-martensite ..........................54
5.2.1
Visual observations of delayed fracture ................................................................................ 54
5.2.2
Stacking Fault Energy and the formation of α’-martensite .................................................... 58
5.3
Proposed mechanism for delayed fracture .................................................................59
5.3.1
Role of α’-martensite ............................................................................................................. 59
5.3.2
Intermittent crack propagation concept ................................................................................. 60
5.3.3
Evolution of crack initiation sites upon straining .................................................................... 60
5.4
6
Conclusions ...............................................................................................................64
Effect of prior plastic deformation on the kinetics of austenite decomposition .....65
6.1
Introduction ................................................................................................................66
6.2
Isothermal transformation ..........................................................................................67
6.2.1
Formation of ferromagnetic phases ....................................................................................... 67
6.2.2
Formation of pearlite .............................................................................................................. 68
6.2.3
Nucleation and growth of pearlite colonies ............................................................................ 69
6.3
Transformation kinetics ..............................................................................................74
6.3.1
Manganese partitioning ......................................................................................................... 74
6.3.2
Effect of prior plastic deformation .......................................................................................... 77
6.4
Conclusions ...............................................................................................................78
xxiii
7
Conclusions.................................................................................................................79
Bibliography .......................................................................................................................81
xxiv
1
Introduction
Steel is the most commonly used material in our daily life. Through time, steel technology
has developed empirically into one of the most important drivers for human prosperity. It
owes most of its success to the abundance of iron ore and coal and the good combination of
price and properties, like manufacturing, mechanical, chemical, electrical, magnetic or
thermal properties. This is a result of the ability of steel to allow for a variety of
microstructural phases through alloying and thermomechanical treatment. The main
disadvantage of steel however is weight. The automotive industry is one of the industries
where steel is primarily used and the reduction of weight is of increasing importance. In the
last decade the use of High Strength Steels (HSS), Advanced High Strength Steels (AHSS)
and Press Hardening Steels (PHS) in the automotive industry has increased significantly in
order to reduce weight and improve safety and fuel economy. The Automotive Group of the
World Steel Association has developed the Future Steel Vehicle (Figure 1.1a)) to
demonstrate the potential of (A)HSS and PHS. Figure 1.1b) shows the steel usage in the
body structure of the Future Steel Vehicle [1] enabling a weight reduction of 35% compared
to an equivalent design with Mild Steel.
Figure 1.2 shows the uniform elongation against ultimate tensile strength for the
following categories of steel grades, shown in Figure 1.1b):
•
Mild Steels: Interstitial Free (IF), Bake Hardening (BH);
•
HSS: High Strength Low Alloy (HSLA);
•
AHSS: Dual Phase (DP), TRansformation Induced Plasticity (TRIP), Multi Phase (MP),
Martensitic Steels (MS);
•
Press Hardening Steels.
1
a)
TWIP IF
2% 3%
b)
MS
1%
PHS
11%
MP
9%
BH, HSLA
31%
TRIP
9%
DP
34%
Figure 1.1
a) Picture of the Future Steel Vehicle [1] and b) Pie-chart of the used steel grades.
The increased strength level is a result of precipitation hardening (IF, HSLA), Bake
Hardening (BH) through C-diffusion, hardening by multi phase microstructures (DP, TRIP,
MP, MS) or press hardening (PHS).
60
50
Elongation (ε f )[%]
TWIP
40
IF
BH
30
HSLA
20
TRIP
DP
10
MP
CP
MS
PHS
0
0
Figure 1.2
2
200
400
600
800
1000
1200
1400
Ultimate Tensile Strength (σ UTS )[MPa]
1600
1800
Elongation against Ultimate Tensile Strength for Mild Steels, HSS, AHSS and PHS [1].
One of the latest developments in steel grades in the automotive industry is austenitic
manganese (Mn)-based TWinning Induced Plasticity (TWIP) steels that combine a high
strength with a very high uniform elongation [1, 2] as shown in Figure 1.2. These superior
mechanical properties are a result of deformation mechanisms combining slip of dislocations,
twinning (TWIP effect) and strain induced martensite transformation (TRIP effect) [3]. The
formation of twins and/or strain induced martensite leads to a strongly increased and
sustained work-hardening, resulting in very high uniform elongation and high strength [4].
In addition to usual application issues like formability and weldability, a problem
encountered with austenitic Mn-based TWIP steels is delayed fracture. This is the
phenomenon that even after successful forming, fracture may still occur. The time until
fracture can range from seconds to weeks. Figure 1.3 shows an example of delayed fracture
after deep drawing. Increased understanding of the phenomenon of delayed fracture would
accelerate the introduction of austenitic Mn-based TWIP steels to the automotive industry,
enabling further weight reduction and improved safety and fuel economy.
1.1
Phenomenon of delayed fracture
The assessment of delayed fracture in thin sheet material is currently not defined in a
universal testing standard. Testing usually comprises deep drawing into a cup with a specific
deep drawing ratio (see Figure 1.3a)), and monitoring the appearance of cracks in a
specified time frame. Guo et al. [5] observed the delay time to range from seconds to weeks
in a stainless steel. Deep drawing is a process where round blanks are formed into cups
using press. This is also the main deformation method to be applied in the present research.
To accelerate the phenomenon of delayed fracture, more severe and controlled testing
conditions can be applied using an active corrosive environment, typically by submerging a
deep-drawn sample in water or by H-charging in an electrolytic cell [5]. Figure 1.3 shows an
example of delayed fracture after deep drawing. After initiation at the cup edge, the crack
advances along the vertical direction and finally proceeds to a length of 19 mm. The top-view
image reveals that there are two cracks on opposite sides of the cup. Delayed fracture
predominantly occurs close to the transverse direction (TD), i.e. perpendicular to the rolling
direction of the original cold rolled sheet. In the course of the delayed fracture process, the
shape of the cup edge changes from circular to oval. The two cracks are situated farthermost
from one another, drawing up the larger axis of symmetry of the oval.
3
a)
b)
5 mm
RD
5 mm
Figure 1.3
a) Side- and b) top-view images of a deep-drawn cup showing delayed fracture. The
white-dashed circles indicate the original cup diameter. The white arrows indicate the
rolling direction (RD). The white full circles indicate the crack positions.
Most research in the field of delayed fracture has been performed on austenitic stainless
steels, like AISI 301 and 304 series [5, 6]. The phenomenon observed in austenitic steels is
mainly related to three potential causes: (1) the limited stability of austenite, (2) the residual
stress/strain state and (3) the environmental conditions (related to the presence of
hydrogen). The first cause - the austenite stability - is associated with the stacking fault
energy (SFE). The two other potential causes relate delayed fracture to stress corrosion
cracking and hydrogen embrittlement [7]. The combination of hydrogen embrittlement and
residual stress strongly influences the behaviour of high strength steels in the presence of
water or water vapour.
1.2
Origin and development of austenitic manganese-based steels
Bouaziz [8] and De Cooman [9] gave a comprehensive overview on austenitic Mn-based
steels, ranging from the development over the last century to the current knowledge of
microstructural effects on the mechanical properties. In 1888, Sir Robert Hadfield invented
the first type of Mn-based steels showing very high uniform elongation and high strength [10].
Since then different classes of Mn-based steels have found application as shape memory,
damping, seismic-resistant, cryogenic, TRansformation Induced Plasticity and TWinning
Induced Plasticity steels [11]. The addition of manganese and carbon is essential to stabilize
the austenitic microstructure [12]. Mechanical loading was found to lead to the formation of
hard phases which are responsible for the impressive mechanical properties and which were
identified as two different kinds of martensite: ε- and α’-martensite [13-14]. The discovery of
high work-hardening rate without the transformation to martensite (halfway the 20th century)
introduced the mechanism of mechanical twinning [15-17], as confirmed by Transmission
Electron Microscopy in the sixties [18-20]. Meanwhile the difficulty of cross slip of
dislocations also materialized as the concept responsible for the high strain-hardening [21].
4
Over time, the composition of Hadfield steels evolved towards higher Mn-contents and lower
C-contents. The idea arose that twins function as barriers for dislocation movement based on
observed dislocation pile-ups at twin boundaries [22]. Severe twinning at low temperature
resulted in excellent mechanical properties, allowing the first cryogenic applications in the
‘80s [23]. A change in composition moves the temperature region for twinning to room
temperature, suitable for application in the automotive industry.
In the automotive industry, the requirements for fuel economy and safety are
continuously increasing. Improvements in fuel economy require a lower weight of the vehicle
whereas higher standard requirements and improvements in safety often result in additional
weight. To resolve this contradiction, the requirements for strength and formability of steel
increase continuously. To this purpose, the steel industry develops (A)HSS and PHS. One of
the latest developments is fully austenitic Mn-based TWIP steels that combine a high
strength with a very high uniform elongation [3]. These superior mechanical properties result
from the high work-hardening of these austenitic Mn-based TWIP steels. The main reasons
for this high work-hardening are deformation mechanisms combining slip of dislocations with
strain induced microtwinning
and martensite transformation [3]. The deformation
mechanisms relate to the austenite stability and form shear bands like slip bands, twins
and/or ε-martensite laths [3], which are obstacles for further dislocation glide, increasing
work-hardening. These shear bands divide grains into smaller areas decreasing the
dislocation mean free path: the dynamic Hall-Petch effect [9].
1.3
Austenite stability and deformation mechanisms
Figure 1.4 presents the equilibrium Fe-Mn binary phase diagram. A large region of the
equilibrium Fe-Mn binary phase diagram has an austenitic phase [24]. At room temperature,
the stable microstructure consists of ferrite below 4 wt% Mn, ferrite and austenite from 4 to
28 wt% Mn and austenite between 28 and 53 wt% Mn. Crystal structures like α-, β- and δ-Mn
existing at Mn-contents above 53 wt% fall outside the scope of this thesis.
An equilibrium phase diagram does not account for the transformation kinetics, which
can result in the presence of metastable phases in the microstructure. Figure 1.5 shows the
microstructural phases present in Fe-Mn-C ternary alloys in undeformed condition and after
plastic deformation [25]. The martensitic phases are metastable at room temperature after
quenching from annealing at 950°C and their presence depends on the Mn- and C-content. A
higher Mn- and C-content stabilizes the austenite. At Mn-contents above 10 wt% the
metastable martensitic regions increase with plastic deformation due to strain-induced
transformation.
5
0
10
20
30
40
Mn [wt.%]
50
60
70
80
90
100
1600
δ-Fe
L
Temperature [°C]
1400
δ-Mn
1200
1000
γ-Fe, Mn
β-Mn
800
600
αFe
α-Mn
400
0
Figure 1.4
35
10
20
30
40
50
60
Mn [at.%]
70
80
90
100
Equilibrium binary Fe-Mn phase diagram [24].
γ
30
Mn [wt%]
25
γ+ ε
20
15
γ + ε + α'
10
5
γ + α'
0
0.0
Figure 1.5
0.2
0.4
0.6
C [wt%]
0.8
1.0
1.2
Microstructural phases present at room temperature after quenching from annealing at
950°C as a function of Mn- and C-content in undeformed condition and after plastic
deformation [25]. The dashed lines indicate the effect of plastic deformation.
6
a)
1.0
Austenite
Mass fraction of phases
0.8
Ferrite
0.6
0.4
0.2
Cementite
0.0
200
b)
Mass fraction of Mn in each phase
1.0
300
400
500
600
700
Temperature [°C]
800
900
1000
400
500
600
700
Temperature [°C]
800
900
1000
Cementite
0.8
0.6
Austenite
0.4
0.2
Ferrite
0.0
200
Figure 1.6
300
a) Equilibrium phase fractions and b) equilibrium Mn-concentration phase compositions in
each of the three phases as a function of temperature as calculated by ThermoCalc for
one of the Fe-Mn-C-Si-Al grades used in this work, containing 14.55 wt% Mn, 0.71 wt%
C, 0.07 wt% Si and 2.93 wt% Al.
7
Thermodynamic calculations using ThermoCalc software (TCW version 4, TCS Steels/FeAlloys database version 6) give the equilibrium phase fractions as a function of temperature
for one of the Fe-Mn-C-Si-Al grades used in this work, containing 14.55 wt% Mn, 0.71 wt%
C, 0.07 wt% Si and 2.93 wt% Al.
Figure 1.6a) shows the mass fraction of phases in equilibrium as calculated by
Thermo-Calc. Above 700°C, the equilibrium microstructure fully consists of austenite. At
lower temperatures, ferrite and cementite are present in equilibrium with austenite. Below
400°C, the equilibrium fraction of austenite appears to stabilise at approximately 5%.
Figure 1.6b) shows the Mn-concentration as a function of temperature in the phases
ferrite, austenite and cementite, as calculated by Thermo-Calc. The equilibrium Mnconcentration in ferrite does not exceed 5% in the temperature range below 600°C, whereas
carbides are strongly enriched in manganese. A strong tendency for Mn-partitioning between
ferrite and carbides is therefore expected to occur during the formation of ferrite and carbides
from austenite, requiring Mn-diffusion. The diffusion rate of manganese will be of significant
importance for the transformation process. Thermocalc calculations also show that the
almost 3 wt% Al in the alloy will be subject to partitioning, although to a much lesser extent
than manganese (not more than 4% concentration difference between the phases, whereas
Figure 1.6b) shows more than 80% difference for manganese). Although the diffusivity of
aluminium is slightly lower than that of manganese, due to its much higher content and its
much stronger partitioning, manganese is expected to be the dominant alloying element for
the phase-transformation kinetics.
The movement of dislocations enables a material to deform plastically. A partial
dislocation is a dislocation with a Burgers vector b unequal to the interatomic distance. The
glide of a partial dislocation leaves behind an imperfect crystal containing a stacking fault. A
stacking fault in Face Centred Cubic (FCC) material is a planar defect on the close packed
{111}γ planes [26].
SFE
perfect dislocations ⊥
stacking faults ⊥….⊥
mechanical twinning γtw
ε-martensite
α’-martensite
Figure 1.7
Effect of the SFE through composition and temperature on deformation mechanisms,
after [27]. The grey scale indicates the presence of the deformation mechanism.
8
The austenite stability against deformation is related to the Stacking Fault Energy (SFE). The
SFE helps to indicate the dominant deformation mechanism during plastic deformation:
perfect/partial dislocation glide, twinning, ε-/α’-martensite formation. The SFE depends on
the composition and deformation temperature. Manganese, carbon and aluminium increase
the SFE, whereas silicon decreases the SFE [24]. Figure 1.7 illustrates the effect of the SFE
on the deformation mechanisms. A high SFE leads to the formation of perfect dislocations (or
narrow stacking faults). High SFE materials can cross-slip and climb easily, resulting in a
rather low strain-hardening. A lower SFE leads to the dissociation of a perfect dislocation into
partial dislocations with a stacking fault. Low SFE materials have much more difficulty with
cross-slip and climb, increasing work-hardening. The array of stacking faults determines the
deformation mechanism at hand: stacking faults, mechanical twinning or ε-martensite. α’Martensite can form at the intersections of shear bands like slip bands, twins and/or εmartensite laths [27].
1.3.1
Mechanical twinning
Mechanical twinning is a homogeneous shape deformation of a region of the crystal resulting
in a structure identical to the parent structure, but with a different orientation. A twin consists
of a crystal with a mirror plane reflection about {111}γ or twin boundary. Plastic deformation
can induce mechanical twinning in a FCC crystal structure as a consequence of partial
dislocation slip on every close packed plane [27] (Figure 1.8).
C
B
A
⊥
⊥
⊥
⊥
C
A
B
C
A
C
B
A
Figure 1.8
Partial dislocation slip on every close packed plane in a FCC crystal structure resulting in
the formation of a twinned crystal structure [27].
9
Figure 1.8 illustrates partial dislocation slip on every close packed plane in a FCC crystal
structure, resulting in the formation of a twin. Partial dislocation slip on a close packed plane
changes the stacking sequence of the close packed plane from ABC ABC ABC to ABC AC
ABC. The slip of four partial dislocations on every close packed plane inverses the initial
stacking sequence from ABC ABC ABC to ABC A CBA C ABC, forming a structure identical
to the parent structure, but with a different orientation: a twin.
1.3.2
Mechanisms and kinetics of martensitic transformation
Figure 1.9 illustrates partial dislocation slip on every second close packed plane in a FCC
crystal structure, resulting in the formation of a HCP crystal structure or ε-martensite. Partial
dislocation slip on a close packed plane changes the stacking sequence of the close packed
plane from ABC ABC ABC to ABC AB ABC. The slip of several partial dislocations on every
second close packed plane changes the initial stacking sequence from ABC ABC to AB AB
AB, forming a HCP crystal structure or ε-martensite.
B
⊥
A
B
⊥
A
B
A
C
B
A
Figure 1.9
Partial dislocation slip on every second close packed plane in a FCC crystal structure
resulting in the formation of a HCP crystal structure [27].
α’-Martensite does not form by such a relatively simple slip mechanism, but can form at the
intersections of shear bands like slip bands, twins and/or ε-martensite laths [28], due to the
high stress concentrations occurring at these intersections [29]. According to Olson and
Cohen [28], a low SFE promotes strain-induced nucleation of α’-martensite, without prior
formation of ε-martensite. With plastic deformation, the intersected volume can act as very
effective nucleation site, allowing the passage of dislocations blocked by bands or laths,
inducing the formation of α’-martensite [28] and releasing stress concentrations [29]. It is
10
worth to note that α’-martensite has a larger volume per atom than austenite, resulting in
coherency strains in the austenite.
Figure 1.10 illustrates the possibility for nucleation of α’-martensite at the intersection
of two shear bands according to the model developed by Olson and Cohen [28]. This model
gives a suitable description of the formation of α’-martensite, but does not give a full
explanation of the mechanism of α’-martensite formation. One array consists of one-half FCC
twinning shears with a/6[21-1] partial dislocations every second {111}γ plane (denoted as
T/2), whereas the other consists of one-third FCC twinning shears with a/6[211] partial
dislocations every third {111}γ plane (denoted as T/3). Note that T/2 corresponds to the
formation of a Hexagonal Close Packed structure, like ε-martensite shown in Figure 1.9. The
intersection results in a perfect Body Centred Cubic microstructure.
[001]
(1 1 1)
a
[211]
6
T/2
a
[21 1 ]
6
T/3
(1 11)
Figure 1.10 Schematic illustration of a shear band intersection for α’-martensite nucleation [28].
11
Olson and Owen made the following overview of models for deformation induced martensitic
transformation as a function of strain [30]. Several approaches are predominantly empirical,
resulting in equations like [31, 32]
fα ' = A ⋅ ε B ⋅ f γ
(1.1)
where fα’ is the martensite volume fraction, A and B are constants, ε is the strain and fγ is the
austenite volume fraction. For stainless steel B is approximately 3. Gerberich [33] suggested
f α ' = A'⋅ε 1 2
(1.2)
Guimaraes [34] observed that the nature of α’-martensite formation as a function of strain
changes from initially parabolic to linear. To obtain the sigmoidal behaviour of α’-martensite
formation as a function of strain, he proposed
(
f α ' = 1 − exp − kε z
)
(1.3)
where k and z are constants. For Fe-Ni-C alloys, k and z are 28 and 3.7 respectively. Olson
and Cohen [35] introduced a theoretical approach for the transformation kinetics, based on
the mechanism for strain-induced nucleation. Their model treats the nucleation kinetics of α’martensite through the intersection of shear bands as a function of strain and results in
{
f α ' = 1 − exp − β [1 − exp(− α ⋅ ε )]
n
}
(1.4)
where α, β and n are constants. α represents the formation of shear bands as a function of
strain and is dependent upon temperature through the SFE. β indicates the probability for α’martensite nucleation at a shear band intersection, which is sensitive to temperature due to
the chemical driving force.
1.4
Role of hydrogen
Over the last two decades, the scientific and industrial community dedicated an increasing
research effort into austenitic Mn-based steels. The recent interest concentrates on the
deformation mechanisms and the relation with crystallographic orientation, work-hardening,
and mechanical properties from a conceptual as well as modelling point of view. According to
Bouaziz [8], future research efforts should focus on (1) twin volume fraction determination,
12
(2) the Bauschinger effect, (3) the fundamentals behind twin formation, (4) work-hardening in
relation to the C-content, (5) fracture resulting from hydrogen, like stress corrosion cracking,
hydrogen embrittlement and delayed fracture and (6) joining to more conventional steels.
This thesis concentrates on the stability of the austenitic microstructure against martensitic
transformation and diffusional decomposition and its role in the phenomenon of delayed
fracture.
The phenomenon of delayed fracture in austenitic Mn-based steels recently received
a lot of attention, in particular from Koyama [36-39]. He investigated the effect of different
strain rates on delayed fracture and found that a higher strain rate reduces the susceptibility
to delayed fracture due to the lower dynamic strain-hardening. The diffusion of carbon
influences the hardening mechanism of dynamic strain-hardening and therefore delayed
fracture [36]. Besides hydrogen, the diffusion of carbon is also of relevance for delayed
fracture.
Another study investigated the introduction of hydrogen into the microstructure [37,
38]. Hydrogen enters the material through diffusion and dislocation activity. The presence of
hydrogen affects dislocation slip, reduces the cohesive energy of grain boundaries and
promotes mechanical twinning and transformation to martensite, inducing intergranular
fracture. Lath-like microstructural features like deformation twins and martensite cause stress
concentrations at grain boundaries. Hydrogen-induced mechanical twinning and martensite
transformation could result in intergranular fracture [37]. An increasing concentration of
mobile hydrogen decreases the fracture stress at which intergranular fracture occurs. The
mobile H-content does not affect the work-hardening behaviour. Embrittlement is therefore
independent of the H-induced microstructural behavioural change in deformation
mechanisms like mechanical twinning and martensite transformation [38].
Other research concentrated on hydrogen cracking at grain and twin boundaries. The
observations indicated primarily intergranular fracture and partially transgranular fracture
parallel to twin boundaries. Intergranular fracture results from the presence of hydrogen,
decreasing grain boundary cohesion. The high stress concentrations occurring at the
intersections of primary and secondary twin systems provide crack initiation sites for
transgranular fracture. Further crack propagation relates to crystallographic texture. The
relation between crack initiation and mechanical twinning is an essential finding, since the
superior mechanical properties rely on the deformation mechanisms [11]. Further work on
crack initiation showed that cracks initiated at the interception of annealing twin boundaries
by strain-induced ε-martensite [39].
Chun [40] also investigated the effect of ε-martensite on the interaction between
hydrogen and mechanical properties. Microstructural defects influence the hydrogen
embrittlement properties through their interaction with hydrogen as trapping site. Two types
13
of trapping sites exist, depending on the activation energy for detrapping: (1) mobile trapping
sites and (2) non-mobile trapping sites. Mobile traps have a low activation energy for
detrapping and comprise grain boundaries, dislocations and coherent carbide interfaces.
These traps are responsible for hydrogen embrittlement. Non-mobile traps have a high
activation energy for detrapping and consist of inclusions, voids and incoherent carbide
interfaces. The introduction of a significant density of non-mobile traps improves the
resistance to hydrogen embrittlement. Chun showed that deformation twin boundaries with
relatively low coherency function as non-mobile traps, whereas coherent ε-martensite
boundaries have a low activation energy for detrapping. Therefore, the presence of εmartensite increases the susceptibility to hydrogen embrittlement [40].
The stabilization of austenite against martensitic transformations improves the
delayed fracture resistance. The BCC microstructure of α’-martensite has a higher Hdiffusivity compared to FCC microstructure of austenite. The resistance to delayed fracture
further benefits from twinning induced plasticity, providing non-mobile traps in the form of
twin boundaries [41].
Other work from Chun investigated the effect of aluminium on the delayed fracture
resistance. The microstructural defect morphology resulting from plastic deformation is of
critical importance for hydrogen embrittlement, since it provides trapping sites for hydrogen.
The addition of aluminium decreases the dislocation density at equal deformation, reducing
the number of mobile trapping sites. A higher dislocation density also increases the diffusion
rate of hydrogen, further reducing the resistance against delayed fracture [42].
Chin [43] evaluated the deformation mechanisms upon deep drawing in relation to the
Al-content. Deep drawing results in an increased twin fraction due to higher strain rates
compared to tensile straining. A deep-drawn cup shows highly localized stresses at the inner
side of the cup edge. The addition of aluminium increases the SFE, distributing twins more
homogenously and lowering stress concentrations [43].
Ronevich [44] focussed on the effects of H-charging on the austenitic microstructure.
Due the low diffusivity of hydrogen in austenite a very high H-concentration develops near
the surface. This is not observed in a ferritic microstructure due to the higher H-diffusivity.
This high hydrogen build-up in FCC can lead to surface cracking [44].
1.5
Scope of thesis
The susceptibility to delayed fracture is a combination of (1) the austenite stability against
microstructural defect formation, (2) the internal residual stress and (3) the presence of
mobile hydrogen [40]. Most research on delayed fracture concentrates on the role of
hydrogen, leaving the austenite stability against defect formation and internal residual stress
underexposed. Increasing the austenite stability against microstructural defect formation like
14
strain-induced transformation improves the resistance against delayed fracture [42]. This
work discusses the effect of plastic deformation on the stability of the austenitic
microstructure against martensitic transformation and diffusional decomposition and its role
in the phenomenon of delayed fracture.
The effect of strain on the microstructural defect morphology has been most
intensively investigated for tensile straining [45-48]. The assessment of delayed fracture
usually comprises deep drawing. Therefore this work investigates the effect of deep drawing
on the generation of structural defects and the austenite stability against strain-induced
transformation to α’-martensite. Deep drawing can result in a larger strain path compared to
tensile straining, leading to a larger accumulated equivalent strain (εeqac). The formation of α’martensite indicates the formation of crack initiation sites, which is discussed as a possible
cause of delayed fracture. The martensitic transformation of metastable austenite upon
mechanical loading indicates the instability of the austenite which leads to diffusional
decomposition of the austenite at intermediate temperatures. The kinetics of austenite
decomposition upon reheating and the effect of prior plastic deformation on the kinetics finish
this work.
1.6
Outline of thesis
In this thesis, chapter 2 will describe the materials and experimental techniques used
throughout this thesis.
Chapter 3 presents an experimental study on the effect of deep drawing on the
generation of structural defects in austenitic Mn-based TWIP steels using X-ray diffraction,
positron beam Doppler broadening spectroscopy and magnetic measurements. To this
purpose, the characteristics of defects were studied along the wall of deep-drawn cups in the
transverse direction, representing a gradually changing deformation state.
In chapter 4 the effect of strain on the defect and microstructure evolution in
austenitic Mn-based TWIP steels was experimentally investigated using magnetic
measurements, X-ray diffraction and positron beam Doppler broadening spectroscopy. The
direct formation of α’-martensite from austenite in a deep-drawn austenitic Mn-based TWIP
steel with high Stacking Fault Energy was investigated using Transmission Electron
Microscopy techniques. The strain evolution during deep drawing was simulated by means of
Finite Element Method simulations and a model for α’-martensite volume fraction evolution
upon straining is proposed.
Chapter 5 will present the role of α’-martensite in the phenomenon of delayed fracture
on austenitic Mn-based TWIP steels after deep drawing, observed by in-situ video recording.
The formation of α’-martensite indicates the formation of crack initiation sites, which is
15
discussed as a possible cause of delayed fracture. The transformation of metastable
austenite by martensitic mechanisms upon plastic deformation indicates diffusional
decomposition of austenite into pearlite in case the material is annealed at temperatures
below the A1-temperature.
Chapter 6 will study this austenite decomposition into pearlite at intermediate
temperatures and the effect of prior plastic deformation. The isothermal transformation to
pearlite and the role of manganese on the transformation kinetics, in particular Mnpartitioning between pearlitic cementite and ferrite, will be discussed.
Finally, Chapter 7 will finish this thesis with the main conclusions.
16
2
Materials and experimental
This chapter gives a description of the experimental and simulation techniques extensively
used throughout this work. We will present an overview of the materials and deformation
modes (deep drawing and tensile straining) studied in this thesis. We will indicate how to
determine the examined strain states through Finite Element Method simulations, to
calculate the mass fraction of the phases using ThermoCalc and to perform delayed fracture
testing. We will explain how direct (Optical, Scanning and Transmission Electron Microscopy)
and indirect measurement techniques (magnetic measurements, positron beam Doppler
spectroscopy and X-ray diffraction) enable the examination of the microstructure and
identification of the defect structure respectively.
17
2.1
Composition and properties
This work examined three 1.7 mm thick austenitic Fe-Mn-C-Si-Al grades, denoted as A, B
and C. The compositions, Stacking Fault Energies (SFEs) and mechanical properties are
listed in Table 2.1. The mechanical properties are averaged over three directions, 0°, 45° and
90° to the rolling direction (RD). The SFE was calculated according to the thermodynamical
approach proposed by Bleck et al. [49], with empirical correction factors for the Si- (−7 mJ/m2
per wt% Si) as reported by Gallagher [50] and Al- (+10 mJ/m2 per wt% Al) content by Oh et
al. [51]. Note that the calculated values are expected to be accurate within 10 mJ/m2 and
thus the grades represent a decrease of SFE in the sequence A-B-C.
Table 2.1
Grade
Compositions, stacking fault energies (SFEs) and mechanical properties.
C
Si
Mn
Al
SFE
σ0.2
σUTS
εUTS
εf
[wt%]
[wt%]
[wt%]
[wt%]
[mJ/m ]
[MPa]
[MPa]
[%]
[%]
A
0.71
0.07
14.55
2.93
52
508
875
42.1
45.9
B
0.69
0.06
14.44
1.41
42
447
959
56.0
61.0
C
0.69
2.69
15.80
2.35
22
645
1028
41.9
45.5
2
The three grades were produced via a semi-industrial process route, starting from ingots.
The investigated materials were in a recrystallised condition after cold rolling. Further
information on the processing of the grades is confidential. Tensile straining was performed
at room temperature according to the Euro-norm, using standard A80 tensile samples and a
Zwick tensile tester. 10% Tensile deformation is small enough to avoid recrystallisation of the
austenite in the applied heat treatments at 500°C, 550°C and 600°C.
2.2
Delayed fracture testing
The assessment of delayed fracture in thin sheet material is currently not defined in a
universal testing standard. Testing usually comprises deep drawing with a specific deep
drawing ratio and monitoring the appearance of cracks in a specified time frame. The insert
in Table 2.2 shows a deep-drawn cup.
2.2.1
Deep drawing
The materials were cut into round blanks with a diameter of 102.5 mm (Db) using water jet
cutting technology. The blanks were formed into cups on an Erichsen press, using a punch
with a diameter Dp of 50 mm. This resulted in a deep drawing ratio (Rdd = Db/Dp) of 2.05.
Other relevant deep drawing parameters are shown in Table 2.2.
18
Table 2.2
Deep drawing parameters.
Blank holder force [kN]
20-30
Die diameter [mm]
54.8
Speed [mm/s]
1.5
Die edge radius [mm]
6.0
Punch diameter [mm]
50
Lubrication
Teflon foil
Punch edge radius [mm]
7.5
Temperature [°C]
20
Figure 2.1 shows an example of a deep-drawn cup. The deep-drawn cups were examined as
a function of the position from the cup bottom primarily in the transverse direction (TD) that
was originally perpendicular to the sheet RD, the RD and along the circumference of the cup
at 35 mm from the cup bottom.
a)
b)
35 mm from
the cup bottom
Position from
the cup bottom
5 mm
5 mm
Figure 2.1
Example a deep-drawn cup indicating the position a) from the cup bottom and b) along
the circumference of the cup at 35 mm from the cup bottom.
2.2.2
Finite Element Method simulations
Finite Element Method (FEM) simulations were performed to calculate the true local major
and minor strain resulting from deep drawing and tensile straining, using the Bergström-Van
Liempt hardening rule and Vegter yield locus [52] optimised for conventional steel grades.
Pam-Stamp 2G calculations were carried out with the deep drawing parameters given in
Table 2.2 and the material input parameters given in Table 2.1. Figure 2.2 shows the strain
paths in terms of ε1, the major true strain in axial direction, and ε2, the minor true strain in
tangential direction, for different degrees of tensile straining and deep drawing at the outside,
centre and inside of the cup at 10 mm and at 35 mm from the cup bottom. ε3 along the cup
thickness in radial direction is related to ε1 and ε2 according to the constraint
ε1 + ε 2 + ε 3 = 0
(2.1)
19
With the use of Equation (2.1) the accumulated equivalent strain (εeqac), which will be used in
this thesis as the characteristic strain parameter, is given by [52]
ε
dε
ε eq ac = 4 3 ⋅ ∫ 1 + ρ + ρ 2 dε 1 , ρ = 2
dε 1
0
0.6
(2.2)
Deep-drawn
Tensile-strained
Major true strain (ε 1)
0.5
outside
0.4
35
middle
inside
40%
0.3
30%
middle inside
20%
outside
0.2
10
0.1
10%
ε1
ε3
0.0
ε2
5 mm
-0.1
-0.8
Figure 2.2
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
Minor true strain (ε 2)
-0.1
0.0
0.1
Strain paths for tensile straining and deep drawing at 10 and 35 mm from the cup bottom
at the inside, middle and outside of the cup. The tensile strain (in %) and the position
from the deep-drawn cup bottom (in mm) are indicated. The inset shows an example of a
deep-drawn cup and the directions of ε1 (axial direction), ε2 (tangential direction) and ε3
(radial direction).
In addition, values for the cup wall thickness as a function of the position along the wall
height are obtained. Figure 2.3 shows the effect of deep drawing on the cup wall thickness,
both experimentally and according to the FEM simulation. The thickness, normalized with
respect to the original blank thickness (1.7 mm), is plotted as a function of the position from
the cup bottom. At the lower part of the cup the material is slightly thinner than the original
blank. From approximately 25 mm from the cup bottom, the wall of the cup becomes
increasingly thicker due to the compression effect of deep drawing.
20
1.5
Experimental
Simulation
Normalized thickness
1.4
Position from
the cup bottom
1.3
5 mm
1.2
1.1
1.0
0.9
0.8
0
Figure 2.3
5
10
15
20
25
30
Position from the cup bottom [mm]
35
40
45
The effect of deep drawing on the cup wall thickness, experimentally and according to the
FEM simulation. The normalized thickness is plotted as a function of the position from the
cup bottom. The inset shows an example of a deep-drawn cup.
The delayed-fracture experiments were performed at room temperature in air for 1680 hours
(70 days) and in stagnant tap water for 504 hours (21 days) after deep drawing. Crack
initiation was awaited and the crack length and number of cracks was monitored at different
time intervals by visual inspection and determined by the average of three simultaneously
assessed cups of identical condition. The specimens submersed in stagnant tap water were
temporarily taken out of the water for visual inspection. The in-situ development of delayed
fracture of a cup of grade B was recorded on video.
2.3
Magnetometry
For the magnetization experiments approximately cubic samples with a size of approximately
2 mm × 2 mm × t, where t is the local thickness, were machined from the sheet material,
deep-drawn cups and tensile-strained specimens using an electro-discharging machine. The
deep-drawn cups were examined as a function of the position from the cup bottom, starting
at 10 mm from the cup bottom up to 40 mm with 5 mm intervals. The samples were taken
along the cup wall primarily in the transverse direction (TD) that was originally perpendicular
to the sheet rolling direction (RD), the RD and along the circumference of the cup at 35 mm
from the cup bottom with 30° intervals to the angle with the RD. At 35 mm from the cup
21
bottom in the TD, a sample was cut into two pieces using an electro-discharging machine:
one sample was taken from the inner side of the cup, another sample was taken from the
outer side of the cup. The magnetic measurements were performed with a Lake Shore 7307
Vibrating Sample Magnetometer, which includes a furnace for experiments at elevated
temperature (See Figure 2.4).
Figure 2.4
Lake Shore 7307 Vibrating Sample Magnetometer.
Before the experiments the Vibrating Sample Magnetometer was calibrated with a standard
NIST nickel specimen. Two types of experiments were performed: in-situ thermo-magnetic
experiments at 500°C, 550°C and 600°C in a magnetic field of 1.0 Tesla, which is high
enough to reach the saturation magnetisation [53]. Secondly, ex-situ measurements of
magnetic hysteresis curves were performed at room temperature, varying the magnetic field
from −1.5 Tesla to +1.5 Tesla. Figure 2.5 shows an example of a magnetic hysteresis curve.
22
2.0
Magnetization [Am2/kg]
1.5
1.0
Ms
0.5
0.0
-0.5
Ms
-1.0
-1.5
-2.0
-2.0
Figure 2.5
-1.5
-1.0
-0.5
0.0
0.5
Magnetic field (T)
1.0
1.5
2.0
Example of a magnetic hysteresis curve measurement varying the magnetic field from
−1.5 Tesla to +1.5 Tesla.
The fraction of ferromagnetic phases in the microstructure is derived from the saturation
magnetisation by [54]
f (α ') =
Ms
,
x Fe M s , Fe
(2.3)
where Ms is the sample magnetization, calculated from the measured magnetization of the
sample minus the contribution of the paramagnetic austenite. The quantity Ms,Fe is the
saturation magnetization of pure iron at room temperature, which was determined in a
separate measurement being 215 Am2/kg and xFe represents the atomic fraction of iron in the
material. In case of low fractions, the difference between weight and volume fractions can be
considered negligible due to the small difference in density between austenite, α’-martensite
and pearlite.
The magnetic flux density of the deep-drawn cup at the appropriate positions from the
cup bottom was examined with a Gauss meter (RFL Model 912 Gaussmeter, Dowty RFL
Industries Inc.) in the radial, axial and tangential plane.
23
2.4
Positron beam Doppler broadening spectroscopy
The deep-drawn and the tensile-strained samples of grade A were subjected to positron
beam Doppler broadening spectroscopy, performed with the Delft Variable Energy Positron
(VEP) beam [55]. Four cup conditions were investigated: (i) deep-drawn; (ii) deep-drawn and
subsequently annealed in a hot-air furnace for 15 minutes at 400°C; (iii) deep-drawn and
subsequently electrolytically hydrogen charged at a current density of 33 A/m2 for 300
seconds; (iv) deep-drawn, subsequently annealed similar to condition (ii) and electrolytically
hydrogen charged similar to condition (iii). Annealing was performed at 400°C for 15 minutes
to relieve the residual stresses.
Figure 2.6 gives a schematic illustration of positron beam Doppler broadening
spectroscopy. Positrons emitted from a
22
Na source are - after moderation to thermal energy
and subsequent controlled acceleration - injected in the samples with a kinetic energy of 25
keV. In steels with a density of 7800 kg/m3, the implantation energy of 25 keV corresponds to
an implantation depth of approximately 1 µm. The beam intensity is 104 positrons per second
and the beam diameter at target is about 8 mm. Note that the deep-drawn samples refer to a
complete cup and the tensile-strained samples to the section at the centre of the tensile bar.
After having slowed down to thermal energy, each positron eventually annihilates with an
electron in the material. The electron involved can either be a relatively free valence electron
or a relatively strongly bound core electron. Because of conservation of energy and
momentum, the annihilation results in the emission of two annihilation γ-quanta with an
energy of about 511 keV each, emitted in (nearly) opposite directions. The positive or
negative momentum component of the electron in the direction of the γ-emission (p//) Doppler
shifts the measured γ-energy by
∆E =
1
2
cp //
(2.4)
with c the speed of light. Here we have neglected the contribution of the positron to the
momentum of the annihilating pair. In an annihilation γ-spectrum these shifts lead to a
broadening of the 511 keV photo peak. This broadening is quantified by the specific lineshape parameters S and W. The S (sharpness)-parameter is calculated as the ratio of the
counts registered in a fixed central momentum window (|p//| < 3.5 × 10-3 m0c, with m0 the mass
of the electron) to the total number of counts in the photo peak, see Figure 2.7. This choice
of the momentum window makes the S-parameter sensitive to annihilation with lowmomentum valence electrons. Similarly, the W (wing)-parameter is obtained from the highmomentum regions (1.0 × 10-2 m0c < |p//| < 2.6 × 10-2 m0c) and accounts for annihilation with
high-momentum core electrons.
24
a) Detector 1
v≈ 0
Detector 2
e+
e+
ev >0
Detector 1
Detector 2
γ
γ
γ energy:
m 0 c2
γ energy:
m 0 c2
b) Detector 1
v≈ 0
Detector 2
e+
e+
ev >0
Detector 1
Detector 2
γ
γ energy:
m0c2 - ∆E
Figure 2.6
γ
γ energy:
m0c2 + ∆E
Positrons are injected in the samples. After having slowed down to thermal energy, each
positron eventually annihilates with an electron in the material. The electron involved can
either be a relatively a) free low-momentum valence electron or b) strongly bound highmomentum core electron. Because of conservation of energy and momentum, the
annihilation results in the emission of two annihilation γ-quanta with an energy of about
511 keV each, emitted in (nearly) opposite directions. In general, for a positron trapped in
a defect (such as a dislocation, a vacancy or vacancy cluster), the probability of
annihilation with strongly bound high-momentum core electrons is reduced compared to
that for free low-momentum valence electrons.
25
502
504
506
508
Gamma energy [keV]
510
512
514
516
518
520
Counts
S
Wleft
-35
Figure 2.7
-30
-25
-20
Wright
-15 -10 -5
0
5
10
15
Electron momentum p // [ x 10-3 m0c]
20
25
30
35
The annihilation γ spectrum around the 511 keV photo peak. The specific line-shape
parameters S and W are calculated as the ratio’s of the counts registered in a fixed central
-3
momentum window (S: | p//| < 3.5 × 10 m0c) or from the high-momentum regions (W: 10 ×
-3
-3
10 m0c < | p//| < 26 × 10 m0c) to the total number of counts in the photo peak, indicated
by the arced areas.
In general, for a positron trapped in a defect (such as a dislocation, a vacancy or vacancy
cluster), the probability of annihilation with core electrons is reduced compared to that for
valence electrons, resulting in a higher S-parameter and a lower W-parameter value. In case
several different types of defects are present the measured S-parameter is
k
k


S = 1 − ∑η i  ⋅ S b + ∑η i ⋅ S di
i =1
i =1


(2.5)
as proposed by [56], where ηi is the fraction of positrons trapped and subsequently
annihilated in defects of type i, k is the total number of defect types and Sb and Sdi are the
bulk and defect-specific S-parameters. Equation (2.5) can be defined in an analogous
manner for the W-parameter.
The examined positions corresponded to the centre of the positron beam. Three
Doppler broadening spectra were obtained for each position to check the reproducibility. This
accounted for a minimum of 3 × 106 registered positron annihilations per position.
26
2.5
Microscopy
2.5.1
Optical Microscopy
The samples for optical microscopy were mechanically polished and electro-polished,
followed by electro-etching. Optical bright-field images were taken on a Polyvar microscope.
A matrix of 4(x) × 5(y) fields was scanned with a motorized stage, resulting in a total scanned
area of 2.6 × 2.4 mm2. The area fractions were determined by Leica QWin Pro (version
V3.5.1) automatic quantitative image analysis software in combination with QUIPS
(Quantimet Interactive Programming System). The minimum feature area was 1 µm2, no
maximum feature area was set. An in-house routine was used to determine the area fraction.
2.5.2
Scanning Electron Microscopy
Scanning Electron Microscopy (SEM) was performed on a Zeiss Ultra 55 Field Emission Gun
Scanning Electron Microscope to characterize the microstructure. The microscope was
equipped with an in-lens electron optic system. Specimens were mounted in Polyfast resin,
which was electrically conductive with low emission in the vacuum chamber during
examination. All micrographs were obtained using a beam of 15 keV electrons. Figure 2.8
shows the microstructure in the undeformed condition and after deep drawing taken at 20
and 40 mm from the cup bottom. The undeformed microstructure is fully recrystallised, with
an equi-axial austenite grain size of about 5 µm. Upon straining, micro shear bands appear in
some of the grains. It is believed that the majority of these bands are microtwins, even
though a more detailed, diffraction-based study is required to prove this. At 20 mm from the
cup bottom the microstructure is dominated by primary shear bands (Figure 2.8b)). At very
high strains (Figure 2.8c)), clear distinction between individual shear bands is no longer
possible.
a)
c)
b)
TD
TD
RD
Figure 2.8
TD
5 µm
5 µm
RD
5 µm
RD
Scanning Electron Micrographs: a) prior to deep drawing, b) deep-drawn at 20 mm and c)
deep-drawn at 40 mm from the cup bottom. The white thin arrows indicate the TD and
RD. The white thick arrows indicate grains with typical shear bands. The black arrows
indicate grains essentially without shear bands.
27
2.5.3
Transmission Electron Microscopy
Transmission Electron Microscopy (TEM) was carried out on a JEOL JEM-2100F
transmission electron microscope operating at 200 kV to verify the presence of α’-martensite
in the microstructure by electron diffraction. Focus Ion Beam was performed on a FEI
Company Quanta 3D FEG to prepare the TEM sample at the position with the highest
accumulated equivalent strain, 35 mm from the cup bottom at the inner side of the deepdrawn cup in TD, indicated by the white circle (Figure 2.9). The accumulated equivalent
strain was determined by FEM simulations of the cup deep drawing process [57].
a)
b)
c)
Outer side cup
± 35 mm from
cup bottom
ND
ND
ND
4 µm
4 µm
TD
TD
Figure 2.9
TD
50 µm
Inner side cup
Focus Ion Beam: a) cutting and b) removal of the TEM sample from the cross-section c)
at the inner side of the deep-drawn cup at 35 mm from the cup bottom in TD, indicated by
the white circle.
2.6
X-ray diffraction
X-ray diffraction was performed using a Bruker-AXS D8 Discover diffractometer with Eulerian
cradle. CoKα-radiation was used for conventional θ-2θ scans. The diffraction patterns were
recorded using a step size of 0.02° in 2θ and the intensity was evaluated by DIFFRACplus
BASIC Evaluation Package 14. The XRD line broadening was determined by the integral
breadth of the {111}γ reflection.
28
3
Effect of deep drawing on the
generation of structural defects
X-ray diffraction (XRD), positron annihilation Doppler broadening spectroscopy and magnetic
measurements have been used to investigate the effect of deep drawing on the generation of
structural defects in austenitic manganese-based TWinning Induced Plasticity steels. The
effect of plastic deformation and hydrogen on structural defects in austenitic manganesebased TWinning Induced Plasticity steels has not extensively been investigated, leaving the
understanding of the effect of the deformation mechanisms involving twinning or plasticityinduced transformation on the structural defects incomplete. XRD measurements show an
initial increase in defect concentration with increasing equivalent strain. Positron annihilation
Doppler broadening revealed the existence of two defect types, with a different degree of
open volume. The interpretation in terms of dislocations, stacking faults and/or twins
corroborated with the line broadening results from XRD measurements. Magnetization
measurements revealed the formation of α’-martensite, which was related to the fraction of
positrons annihilating at the smaller structural defects. The presented findings attribute the
larger defect type to perfect dislocations, whereas the smaller defect type is attributed to
partial dislocations, and is consequently related to twinning or plasticity-induced
transformation.
29
3.1
Introduction
In this chapter, X-ray diffraction (XRD), positron annihilation Doppler broadening
spectroscopy and magnetic measurements were used for an experimental study on the
effect of plastic deformation on the generation of structural defects in austenitic manganese
(Mn)-based TWinning Induced Plasticity (TWIP) steels. To this purpose, the characteristics of
defects were studied along the wall of deep-drawn cups, representing a gradually changing
deformation state.
Plastic deformation increases the susceptibility to hydrogen embrittlement due to the
formation of structural defects, such as dislocations and vacancies [58, 59]. This interaction
has often been related to the phenomenon of delayed fracture [59]. Research on the joint
action of hydrogen and defects in metals has been carried out experimentally and
theoretically [60, 61]. Still, the direct observation of defects remains difficult, impelling the use
of indirect measurement techniques with XRD the most commonly used one. This technique
is based on the fact that stress fields around defects, in particular dislocations, distort the
lattice and produce line broadening [62]. Positron annihilation Doppler broadening
spectroscopy is a more sophisticated indirect technique capable of distinguishing between
different open volume defect types. Several positron annihilation studies [63, 64] investigated
the effects of plastic deformation, annealing and hydrogen on the structural defects in metals.
However, in austenitic Mn-based TWIP steels these effects have not been investigated
extensively, leaving the understanding of the effect of the deformation mechanisms involving
twinning or plasticity-induced transformation on the structural defects incomplete.
3.2
Characterization of defects
3.2.1
Line broadening
Figure 3.1 shows the integral breadth of the {111}γ reflection as a function of the position
from the cup bottom. For each examined position, the appropriate equivalent strain resulting
from the Finite Element Method (FEM) simulations is given along the horizontal axis. In the
XRD-data all observed reflections showed the same trend, so, for clarity only the data for the
{111}γ reflection is plotted. With increasing strain the deep-drawn sample shows an initial
increase in integral breadth, followed by a small decrease.
30
0.75
Deep-drawn
0.70
Integral breadth [°2θθ ]
0.65
0.60
0.55
0.50
0.45
Position from
the cup bottom
0.40
5 mm
0.35
εeq ac = 0.26 εeqac = 0.49 εeqac = 0.55 εeq ac = 0.61 εeq ac = 0.69 εeq ac = 0.73 εeq ac = 0.71
0.30
0
Figure 3.1
5
10
15
20
25
30
Position from the cup bottom [mm]
35
40
45
The integral breadth of the {111}γ reflection as a function of the position from the cup
bottom and the appropriate equivalent strain derived from the FEM simulation. The drawn
line is to guide the eye.
3.2.2
Line-shape parameters
Figure 3.2 shows the normalized S- and W-parameters as a function of the position from the
cup bottom. The normalization is with respect to the reference state of the material, which
was accomplished by annealing during 1 hour at 800°C to minimize the defect
concentrations. For each examined position, the appropriate equivalent strain resulting from
the FEM simulations is given along the horizontal axis. With increasing strain all results show
an initial increase in S-parameter, followed by a small decrease for non-annealed cups. The
W-parameter shows an initial decrease with increasing strain for all results and eventual
saturation for the non-annealed cups. The fraction of positrons trapped and annihilated at
defects increases as a result of deep drawing and to a lesser degree from H-charging.
Annealing decreases the concentration of defects, thereby lowering the fraction of trapped
positrons. As a result the material approaches the low defect concentrations of the reference
state at 10 mm from the cup bottom, whereas at higher equivalent strains the applied
annealing treatment is not sufficient to fully remove the deformation-induced structural
defects. Given the lower fraction of trapped positrons after annealing, the effect of hydrogen
is more pronounced.
31
1.06
S
1.04
Normalized S and W
1.02
1.00
Deep-drawn
Annealed
H-charged
Annealed and H-charged
W
0.98
0.96
0.94
0.92
0.90
0.88
0.86
εeq ac = 0.26 εeqac = 0.49 εeqac = 0.55 εeq ac = 0.61 εeq ac = 0.69 εeq ac = 0.73 εeq ac = 0.71
0.84
0
Figure 3.2
5
10
15
20
25
30
Position from the cup bottom [mm]
35
40
45
The S- and W-parameter as a function of the position from the cup bottom and the
appropriate equivalent strain derived from the FEM simulation. The error is approximately
the size of the symbols. The drawn lines are to guide the eye.
Figure 3.3 shows the effect of annealing and/or H-charging on the combined W-Scharacteristics as a function of the position from the cup bottom. Starting from reference
point R, all curves initially (that is, for low cup heights) are close to the line connecting the
points R and D1. In literature, gradients dW/dS similar to the slope of the line R-D1 are
attributed to the formation of dislocations or vacancy-type defects [65, 66]. With increasing
deformation along the cup wall, the W-S-characteristics start to deviate from the line R-D1.
The observed trends for the different cups converge in a second specific point D2 in the W-Smap. The observed change in slope indicates the development of a different (as seen by the
positrons) type of defect along the cup wall. Since the normalized S-values are much smaller
than those reported for vacancy type defects [65, 66], both defect types can be associated
with dislocations, with the defect type related to point D2 having the smaller volume as
follows from its lower S-value.
32
1.02
R
1.00
Deep-drawn
Annealed
H-charged
Annealed and H-charged
Normalized W
0.98
0.96
0.94
0.92
0.90
0.88
D1
0.86
D2
0.84
0.99
Figure 3.3
1.00
1.01
1.02
1.03
Normalized S
1.04
1.05
1.06
W-S map for austenitic Mn-based TWIP steel cups as a function of the position from the
cup-bottom.
3.2.3
Trapping fractions
Using Equation (2.5), the trapping fractions η1 and η2 have been calculated, assuming two
defect trapping states with characteristic S-W values S1 = 1.052, W1 = 0.870 for defect D1 and
S2 = 1.037, W2 = 0.860 for defect D2. The result is given in Figure 3.4 as a function of the
position from the cup bottom. It is observed that for deformation to relatively low strain levels
η1 initially increases as a function of the position from the cup bottom. For cup heights above
25 mm, positron trapping at the second defect type D2 starts to increase at the expense of
trapping at defect D1.
33
a)
1.0
Deep-drawn
Annealed
H-charged
Annealed and H-charged
0.8
η1
0.6
H-charged
0.4
Deep drawn
0.2
Annealed and
H-charged
Annealed
0.0
0
b)
1.0
5
10
15
20
25
30
Position from the cup bottom [mm]
35
40
45
35
40
45
Deep-drawn
Annealed
H-charged
Annealed and H-charged
0.8
η2
0.6
0.4
0.2
0.0
0
Figure 3.4
5
10
15
20
25
30
Position from the cup bottom [mm]
a) The fraction (η1) of positrons trapped at defect type D1 as a function of the position
from the cup bottom. b) The fraction (η2) of positrons trapped at defect type D2 as a
function of the position from the cup bottom.
34
On the basis of the observed XRD-line broadening alone (Figure 3.1), it is not possible to
distinguish between different defect types. Hence, in Figure 3.5 the total fraction of positrons
trapped at the defects η1 + η2 is plotted against the integral breadth. From this Figure it is
concluded that for the deep-drawn cup the integral breadth varies linearly with the total
positron trapping fraction η1 + η2.
1.2
Deep-drawn
40 30 35
1.0
20 25
η1 + η2
0.8
15
10
0.6
0.4
0.2
0.0
0.30
Figure 3.5
0.35
0.40
0.45
0.50
0.55
0.60
Integral breadth [°2θ ]
0.65
0.70
0.75
The total defect fraction η1 + η2 as a function of the integral breadth of the {111}γ
reflection for the deep-drawn cup. The position from the cup bottom (in mm) is indicated.
3.2.4
Ferromagnetic phase
Magnetic measurements were performed to verify changes in the fraction of ferromagnetic
phases, which can reveal the formation of α’-martensite. Figure 3.6 plots the magnitude of
the local magnetic flux density caused by local magnetization as a function of η2 for the deepdrawn cup (at 40 mm the magnetization could not be determined because this position is too
close to the cup edge). Clearly, the magnetic flux density increases approximately linearly
with increase in η2. No such relationship could be found when the data was plotted as
function of η1 or η1 + η2.
35
2.0
Deep-drawn
Magnetic flux density [10-4 T]
1.8
35
1.6
30
1.4
1.2
25
1.0
0.8
20
0.6
10
0.4
15
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
η2
Figure 3.6
Magnetic flux density as a function of positron trapping fraction η2 for the deep-drawn
cup. The position from the cup bottom (in mm) is indicated.
3.3
Discussion of defect characteristics
Three indirect measurement techniques were used to investigate the generation of structural
defects in austenitic Mn-based TWIP steels due to deep drawing. With increasing strain,
XRD measurements indicate an initial increase in defect concentration, followed by a small
decrease starting at 20 mm from the cup bottom. The positron annihilation results reveal that
at least two types of positron trapping defects emerge with concentrations depending on the
local strain conditions in the cup wall. Finally, magnetization measurements revealed an
increase in the fraction of ferromagnetic phases, most likely the α’-martensite content.
3.3.1
Perfect dislocations
The development of the positron annihilation characteristics show that at low strain values
the deformation in austenitic Mn-based TWIP steel is facilitated by dislocation slip. The W-S
map and the derived trapping fractions, together with the results in literature [65, 66],
suggests that η1 can be related to perfect dislocations. This assumption is further
corroborated by the fact that η1 is sensitive to annealing and H-charging. Indeed annealing
shows a similar effect on dislocations as stress relief. The introduction of hydrogen
decreases the repulsive force and interaction energy between dislocations, resulting in
36
increasing dislocation mobility [61, 67]. In combination with the residual stress this may
increase the dislocation density, reflected by the increase in the trapping fraction η1 observed
in Figure 3.4a).
3.3.2
Partial dislocations
At higher strain, deviating defect characteristics are observed. Since the S-parameter for
defect type D2 is structurally lower, but otherwise comparable to that of defect type D1 the
related defect can be expected to be also dislocation-like. A partial dislocation is a likely
candidate to account for this observation. Partial dislocations play a role in twinning and
plasticity-induced transformation and can therefore be expected to be generated in this
material. The dissociation of a perfect dislocation into two Shockley partial dislocations (and
consequently a stacking fault) is known to evolve differently for tension and compression
deformation. According to Christian [68], on average this dissociation is more favourable
under compression than under tension. The FEM simulations indicate that above 25 mm
from the cup bottom the material is in compression. Partial dislocations have a smaller
Burgers vector than perfect dislocations and consequently lead to a smaller normalized Svalue. This and the fact that above 25 mm the material is in compression further confirms the
suggestion that η2 is related to partial dislocations. These partial dislocations play a role in
twinning and plasticity-induced transformation and can be accompanied by stacking faults,
twins, ε- and α’-martensite [27, 69]. Because of their thermal stability [27, 68] and the fact
that η2 is hardly sensitive to annealing (see Figure 3.4b)) we have another reason to relate η2
to partial dislocations. In addition, the limited sensitivity of η2 to hydrogen may be due to the
smaller defect size, which results in the defect being a less attractive trapping site.
The observed relationship of the XRD-line broadening with the positron annihilation
results corroborates the interpretation of the observed effects in terms of dislocations. On the
other hand, the magnetization measurements show that α’-martensite formation takes place
in the upper half of the cup. The fraction of martensite formed increases with the trapping
fraction η2 (Figure 3.6). It is therefore likely that α’-martensite forms through plasticityinduced transformation. The presence of α’-martensite can be accompanied by ε-martensite
and twins [27]. The present findings attribute the defect type related to η1 to perfect
dislocations, whereas the defect type related to η2 is attributed to partial dislocations and
defects related to twinning or plasticity-induced transformation, which is shown to lead to the
formation of α’-martensite. It is interesting to emphasize that the trapping fraction η2 is found
to show increasing values above a cup height of 20–25 mm (see Figure 3.4b)). It is at this
cup height that the deformation state undergoes a transition from tensile to compressive. The
formation of α’-martensite, as observed in magnetization measurements (Figure 3.6), can
37
therefore be concluded to correlate to the mode of deformation, being stronger in
compression.
3.4
Conclusions
The presented investigation on the effect of deep drawing on defect generation in austenitic
Mn-based TWIP steels leads to the following conclusions:
1.
Positron annihilation detects that two different defect types result from plastic
deformation during deep drawing. The two defect types can be expected to be perfect
dislocations and partial dislocations.
2.
Magnetic field measurements reveal the formation of α’-martensite which correlates
with the density of the defects identified as partial dislocations. Martensite formation
only takes place in those regions of the deep-drawn cup that are subjected to
compressive deformation.
38
4
Effect of strain on the formation
of α’-martensite
The effect of strain on the deformation mechanisms in deep-drawn and tensile-strained
austenitic manganese-based TWinning Induced Plasticity steel is investigated using ex-situ
magnetic
measurements,
X-ray
diffraction,
positron
beam
Doppler
Spectroscopy,
Transmission Electron Microscopy (TEM) and Finite Element Method simulations. The
experimental observations reveal the formation of small fractions of α’-martensite at specific
degrees of deformation, despite the high Stacking Fault Energy of the material (52 mJ/m2).
To understand the formation of α’-martensite in high Stacking Fault Energy TWinning
Induced Plasticity steel deformed in the deep drawing mode, the existing phases were
investigated using TEM. TEM revealed the formation of α’-martensite at shear band and twin
intersections. The observed fraction α’-martensite is consistent with the estimated fraction of
intersected shear bands acting as preferred nucleation sites for α’-martensite formation as a
function of accumulated equivalent strain.
39
4.1
Introduction
In this chapter the effect of both deep drawing and tensile straining on the defect and
microstructure evolution in austenitic manganese (Mn)-based TWinning Induced Plasticity
(TWIP) steels was experimentally investigated using ex-situ magnetic measurements, X-ray
diffraction (XRD) and positron beam Doppler Spectroscopy. The direct formation of α’martensite from austenite in a deep-drawn austenitic Mn-based TWIP steel with high
Stacking Fault Energy (SFE) is investigated using Transmission Electron Microscopy (TEM)
techniques. The strain evolution during deep drawing was simulated by means of Finite
Element Method simulations.
The superior mechanical properties of austenitic Mn-based TWIP steels are a result
of deformation mechanisms involving twinning or plasticity-induced transformation [3, 45-48,
70] related to the austenite (γ) stability. The deformation mechanisms in these Mn-based
TWIP steels have been most intensively investigated for tensile straining [45-48], leaving the
role of large strain on the twinning or transformation-induced plastic deformation mechanism
less exposed [71].
Austenite with a relatively low stability can transform to α’-martensite by means of the
γ (Face Centred Cubic, FCC) → ε (Hexagonal Close Packed, HCP) → α’ (Body Centred
Cubic, BCC) sequence of martensitic transformations. Suppression of the strain-induced γ →
ε-martensite transformation is therefore considered to imply stability against α’-martensite
formation [8]. It has been argued on the basis of thermodynamic considerations [27, 51, 72]
that Mn-based TWIP steel with a SFE higher than approximately 18 mJ/m2 will not undergo
strain-induced ε-martensite formation. Olson [28, 35] and other authors [57, 73-76]
suggested the possibility of a direct α’-martensite formation from austenite without the
intermediate transformation to ε-martensite. The material examined in the present
contribution did not show any evidence of α’-martensite formation when tested in a
conventional uni-axial test [57]. Direct experimental evidence for the γ → α’-martensite
transformation has never been reported for Mn-based TWIP steel [77].
4.2
Microstructural evolution upon plastic deformation
It is important to note that positron beam Doppler spectroscopy and XRD only probe the
outer side of the cup (penetration depths 1 µm and 10 µm, respectively) at a specific position
from the cup bottom, whereas the magnetization measurements concern the full thickness of
the cup. For that reason, magnetization results are related to the average accumulated
equivalent strain εeqac over the cup thickness, whereas the XRD and positron annihilation
results are related to εeqac at the outer side of the cup.
40
4.2.1
Formation of α’-martensite
Figure 4.1 shows the α’-martensite fraction as a function of εeqac averaged over the sample
thickness measured by Vibrating Sample Magnetometry. There is an initial α’-martensite
fraction of approximately 0.2%. Tensile straining does not affect the α’-martensite fraction.
Deep drawing promotes the formation of α’-martensite. Straining at εeqac ≥ 0.6 results in the
formation of strain-induced α’-martensite. At 35 mm from the cup bottom in the TD, a sample
was taken and cut into two pieces by spark erosion: one sample was taken from the inner
side of the cup, another sample was taken from the outer side of the cup. For the sample at
the inner side of the cup the accumulated equivalent strain was approximately 0.85. The
maximum volume fraction of 1.2% α’-martensite was measured at this position, an amount
too small to be detected by XRD.
0.014
Deep-drawn
Tensile-strained
Olson-Cohen [14]
This work
0.012
35
inner
side
α '-Martensite fraction
0.010
Position from
the cup bottom
0.008
35
outer
side
5 mm
0.006
0.004
25
30
0.6
0.7
35
40
40%
10%
0.002
20%
20
30%
15
10
0.000
0.0
0.1
0.2
0.3
0.4
0.5
0.8
0.9
ε eqac
Figure 4.1
α’-Martensite fraction, determined by ex-situ magnetic measurements, for deep drawing
and tensile straining as a function of εeqac averaged over the cup thickness. The tensile
strain (in %) and the position from the deep-drawn cup bottom (in mm) are also indicated.
At 35 mm from the cup bottom in the TD, a sample was taken and cut into two pieces by
spark erosion: one sample was taken from the inner side of the cup, another sample was
taken from the outer side of the cup. The labels ‘inner side’ and ‘outer side’ refer to these
two samples.
41
0.008
Deep-drawn
35 mm from
the cup bottom
α '-Martensite fraction
0.007
5 mm
0.006
0.005
0.004
0.003
0
Figure 4.2
30
60
90
120
150 180 210
Angle to RD [°]
240
270
300
330
360
α’-Martensite fraction in a deep-drawn cup at a distance of 35 mm from the cup bottom as
a function of the angle to the RD.
Figure 4.2 shows the α’-martensite fraction as a function of the angle to the rolling direction
(RD). The measurements were made on the deep-drawn cup at 35 mm from the cup bottom
where the accumulated equivalent strain was about 0.73. The results indicate a systematic
trend as a function of the angle to the RD. The maximum α’-martensite fraction in the
material can be found located in the transverse direction (TD) from the original centre of the
blank, which most probably is related to the development of texture.
4.2.2
Dislocation multiplication and twinning
Figure 4.3 presents the integral breadth of the {111}γ XRD reflection, the most accurately
determined reflection, as a function of εeqac at the outer side of the cup. The increase of
tensile strain clearly increases the integral breadth. Increased straining during deep drawing
initially increases the integral breadth in a similar way, followed by saturation for εeqac ≥ 0.6.
This increase in integral breadth prior to the formation of α’-martensite (see Figure 4.1)
indicates dislocation multiplication and/or twinning. Straining at εeqac ≥ 0.5 induces the
formation of α’-martensite by allowing the passage of previously blocked dislocations [28,
35]. At εeqac ≥ 0.6 α’-martensite formation increases more significantly, which does not cause
further increase of the integral breadth. Later in this chapter positron beam Doppler data will
enable to distinguish the different deformation mechanisms already indicated in Figure 4.3.
42
0.80
Dislocation
multiplication
and twinning
0.75
Twinning and dislocation glide
Dislocation
multiplication and
twinning
α'-Martensite formation and
dissociation of perfect
into partial dislocations
20
Integral breadth [°2θ ]
0.70
25
15
30 35
40
0.65
0.60
40%
30%
0.55
0.50
α'-Martensite
formation,
dislocation
multiplication
and twinning
20%
10%
0.45
10
0.40
0.35
Deep-drawn
Tensile-strained
0.30
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
ε eqac
Figure 4.3
Integral breadth of the {111}γ reflection in XRD for deep drawing and tensile straining as a
function of εeqac at the outer side of the cup. The tensile strain (in %) and the position from
the deep-drawn cup bottom (in mm) are also indicated. Deformation mechanisms are
schematically indicated.
4.2.3
Dislocation glide and dissociation into partial dislocations
Figure 4.4 shows the W-S map for deep drawing and tensile straining in which the S- and Wparameters are normalized with respect to the annealed material, Sb and Wb. Chapter 3 on
positron beam Doppler spectroscopy on the present steel revealed the existence of two
defect types D1 and D2 [76]. With characteristic S-W values (SD1/Sb = 1.052, WD1/Wb = 0.870)
for defect D1 and (SD2/Sb = 1.037, WD2/Wb = 0.860) for defect D2 the fractions of positrons
trapped at these defects η1 and η2 have been calculated, assuming two defect trapping
states and using Equation (2.5). Equation (2.5) can be defined in an analogous manner for
the W-parameter. In chapter 3 the larger defect type D1 was attributed to perfect dislocations,
whereas the smaller defect type D2 was attributed to partial dislocations [76].
The positron annihilation results enable a further distinction of deformation
mechanisms prior to and during α’-martensite formation. Figure 4.5 shows η1 and η2 as a
function of εeqac at the outer side of the cup. At εeqac ≈ 0.1-0.4, positron annihilation reveals no
change in trapping fractions η1 and η2, excluding dislocation multiplication and indicating
twinning and dislocation glide as the dominant deformation mechanisms [27]. These twins
43
and their intersections act as barriers for further dislocation glide and eventually immobilize
dislocations. Further straining requires dislocation multiplication and results in high stress
concentrations at shear bands and their intersections, as evidenced by an increasing
trapping fraction η1 at εeqac up to 0.6. Once these high stress concentrations enable the
passage of previously blocked (immobilized) dislocations and induce α’-martensite formation
(see Figure 4.1), there is no need for further dislocation multiplication (as observed in Figure
4.3). At this stage, the positron annihilation results disclose that the formation of α’martensite leads to a decreasing η1. The simultaneous increase in η2 indicates the formation
of energetically more favourable partial dislocations enabling further relaxation of the internal
stresses caused by the α’-martensite formation due to the lower density of α’-martensite in
comparison to the original microstructure. These partial dislocations could originate from the
dissociation of perfect dislocations, since both the integral breadth and the total defect
fraction η1 + η2 remain constant with increasing α’-martensite fraction.
1.02
R
1.00
Deep-drawn
Tensile-strained
Normalized W
0.98
0.96
10%
20%
0.94
40%
30%
10
0.92
0.90
15
30
0.88
40
0.86
35 25
20
D1
D2
0.84
0.99
Figure 4.4
1.00
1.01
1.02
1.03
Normalized S
1.04
1.05
1.06
W-S map for austenitic Mn-based TWIP steel cups for deep drawing and tensile straining.
R is the reference point, D1 and D2 are defect types [55]. The tensile strain (in %) and the
position from the deep-drawn cup bottom (in mm) are also indicated.
44
1.0
Dislocation
multiplication
and twinning
Twinning and dislocation glide
Dislocation
multiplication and
twinning
15
20 α'-Martensite formation and
dissociation of perfect
into partial dislocations
25
0.8
40
30
35
0.6
η
α'-Martensite
formation,
dislocation
multiplication
and twinning
10%
0.4
20%
30%10 40%
η1
η2
0.2
η1
Deep-drawn h1
Tensile-strained η 1
η2
Deep-drawn h2
Tensile-strained η 2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
ε eqac
Figure 4.5
Fraction (η1 and η2) of positrons trapped at defect type D1 (perfect dislocation [76]) and D2
(partial dislocation [76]) resulting from positron beam Doppler spectroscopy as a function
of εeqac at the outer side of the cup for deep drawing and tensile straining. The tensile
strain (in %) and the position from the deep-drawn cup bottom (in mm) are also indicated.
4.2.4
Observation of α’-martensite
Figure 4.5 shows Bright Field (BF) images and related Selected Area Diffraction Patterns
(SADP) from the TEM sample taken at 35 mm from the cup bottom on the inner side of a
deep-drawn cup in TD. For the sampling the reader is referred to section 2.5.3 and Figure
2.9. The plasticity mechanisms were found to consist of a pronounced planar dislocation
glide and the formation of planar features and bands related to the overlapping of multiple
planar stacking faults, i.e. shear bands and narrow twins. The SADPs clearly indicate that not
all narrow planar features in the highly deformed TWIP steel are twins. In fact many bandtype features are found to be shear bands rather than twins. None of the diffraction patterns
indicates the presence of ε-martensite. Considering the SFE of the alloy, the absence of εmartensite and the presence of shear bands is expected.
45
a)
50 nm
b)
c)
020
110
d)
111
101
01 1
111
111
5 1/nm
111
1 10
020
BF image
e)
50 nm
SADP
SADP γ
f)
g)
SADP α’-martensite
020
111
h)1 1 0
020T
111
2 1/nm
011
101
101
111
020T
01 1
101
011
1 10
111 020
BF image
i)
100 nm
SADP
SADP twinned γ
j)
k)
1 1 1T
020T1 1 1
111
SADP α’-martensite
020
l)
111
1 1 1T 1 1 1 020T
020
m)
100 nm
01 1
011
2 1/nm
BF image
110
101
101
1 10
SADP
SADP twinned γ
SADP α’-martensite
n)
o)
p)
020
111
2 1/nm
111
111
110
101
01 1
101
111
011
1 10
020
BF image
Figure 4.6
SADP
SADP γ
SADP α’-martensite
α’-Martensite at intersection of a)-d) shear bands, e)-h) twin and shear band, i)-l) twins,
m)-p) shear bands. The TEM sample was taken 35 mm from the cup bottom on the inner
side of the deep-drawn cup. The Figures a), d), i) and m) indicate the BF images, the
Figures b), e), j) and n) indicate the SADPs, the Figures c), f), k) and o) indicate the
SADPs, BF images. The white circles indicate the positions where the SADPs were
taken. The dashed white lines in a) and i) indicate the position of shear bands with a low
contrast. The black diffraction spots in the schematic SADPs in the third column are for
the γ phase and include the relevant twin reflections. The black diffraction spots in the
schematic SADPs in the fourth column are for the α'-martensite. The grey spots in the
schematic SADPs indicate the diffraction spots of the other phase.
46
The orientation relationships between austenite and α’-martensite obey the KurdjumovSachs orientation relationship between α’-martensite and austenite:
{111}γ //{110}α '
(4.1)
110
γ
// 111 α '
The micrograph in Figure 4.6a) shows a highly dislocated microstructure containing one clear
band. The SADP reveals the band to be a shear band, rather than a twin, and shows the
presence of α’-martensite. A secondary shear band system is also present, indicated by
dashed white lines. The BF image (Figure 4.6e) and the corresponding SADP (Figure 4.6f)
are for the two shear band systems and their intersection. The microstructure is severely
deformed and contains a high dislocation density. The diffraction pattern reveals the
presence of α’-martensite at the intersection between twins and shear bands. The high
defect concentration at this type of intersections makes them very effective nucleation sites
for strain-induced transformation [28, 35, 51]. Figures 4.6i)-n) show additional BF images and
corresponding SADPs from the TEM sample. Due to the intense deformation, the
deformation bands have a low diffraction contrast and the dashed white lines indicate the
position of parallel shear bands, which are not clearly visible. The diffraction pattern however
clearly reveals the presence of α’-martensite. The BF image in Figure 4.6m) shows two
intersecting shear band systems, which are clearly visible despite the high dislocation
density. The SADPs clearly reveal the presence of α’-martensite at shear band-shear band
intersections.
4.3
Martensitic transformation
It has been reported that the deformation mechanisms responsible for the mechanical
properties of austenitic Mn-based TWIP steels are related to the austenite (γ) stability and
involve dislocation slip, twinning and plasticity-induced transformation to martensite [3, 4548, 70]. With increasing εeqac, deformation is facilitated initially by dislocation multiplication,
followed by twinning and/or martensitic transformations, providing barriers for further
dislocation slip [3, 45-48, 70, 71].
4.3.1
Strain-induced nucleation of α’-martensite
Austenite with a relatively low stability can transform by means of γ → ε → α’ martensitic
transformations, resulting in a high work-hardening rate. Stability against the γ → ε-
47
martensite transformation is usually considered to imply stability against the γ → α’martensite transformation [8], since ε-martensite laths form as an intermediate phase. The
present magnetic measurements indicate strain-induced α’-martensite formation by revealing
a small volume fraction of α’-martensite when the accumulated equivalent strain is 0.5 or
higher. TEM foil preparation does not induce such high accumulated equivalent strains and
will therefore not be the origin for α’-martensite formation. The formation of α’-martensite is a
three-dimensional phenomenon, being observed by TEM through thin sections. The widely
held view is that α’-martensite must have ε-martensite as a precursor in Mn-based steels
with Mn-contents above 10 wt% (see Figure 1.5) [8]. In Mn-based TWIP steels, α’-martensite
is known to form at the intersections of shear bands like slip bands, twins and/or ε-martensite
laths [28, 35]. The sequential nature of the γ → ε → α’ martensitic transformation at
intersected ε-martensite laths and the increasing volume fraction of α’-martensite upon
straining implies the simultaneous presence of ε- and α’-martensite. According to Olson and
Cohen [28, 35], the sequential γ → ε → α’ martensitic transformation requires the intersection
of at least one ε-martensite lath, which was not observed (Figure 4.6). ε-Martensite could
only have been a precursor of α’-martensite formation in case of complete ε → α’-martensite
transformation. Transformation from ε-martensite laths would have led to α’-martensite
formation outside the intersected regions and higher α’-martensite fractions, which was not
observed. The presence of ε-martensite as an intermediate phase at the intersected regions
is untraceable after complete transformation to α’-martensite. We can conclude that the
present observations question the γ → ε → α’ martensitic transformation as described by
Olson and Cohen [28, 35]. The results strongly indicate that strain-induced nucleation of α’martensite does not necessarily require the intermediate formation of ε-martensite laths.
In Mn-based TWIP steels with low SFE, α’-martensite is known to form at the
intersections of bands like shear bands, twins and/or ε-martensite laths [28, 35] as seen in
Figures 4.6e) and 4.6m). These intersected bands can be very effective as nucleation sites,
allowing the passage of previously blocked dislocations, inducing the formation of α’martensite [28, 35] and releasing stress concentrations [51]. Also in the Figures 4.6a) and
4.6i) secondary band systems have been observed, although less clearly as in the Figures
4.6e) and 4.6m).
4.3.2
Relation to the development of crystallographic texture during deep drawing
The results show that the formation of α’-martensite in the bulk material is related to both the
accumulated equivalent strain and the crystallographic texture. One can assume the
crystallographic texture components of the examined material to be a function of the angle to
48
the RD. The formation of α’-martensite in the material relates to the location of the material
with respect to the RD. This observation is indicative of a relation between the formation of
α’-martensite and the development of crystallographic texture during deep drawing. Similar
Mn-based TWIP steels do not show planar anisotropy [78], suggesting subtle texture effects
leading to anisotropy in strain-induced martensite formation. The TD has apparently a more
favourable crystallographic texture for α’-martensite formation than the RD. Lo et al. [79]
mentioned that twin-matrix lamellae, generated by heavy rolling deformation, are often
oriented along the RD. Slip along the {111}γ planes in the RD and twinning is gradually
suppressed as deformation proceeds, but slip along the {111}γ planes that are not parallel to
the lamellae is activated. Deep-drawn material shows a high accumulated strain. It is also
known that tensile deformation of medium SFE FCC metals or alloys favours the formation of
twins in grains oriented with a <111> direction parallel to the tensile axis. It is therefore
possible that straining in the TD can also activate the formation of strain induced martensitic
transformation along the TD.
4.4
Evolution of α’-martensite volume fraction upon straining
The α’-martensite formation can be attributed to the magnitude of εeqac, providing the required
density of shear band intersections and high stress concentrations. Liang et al. [47] also
indicated the importance of the strain path for the microstructural evolution. Oh et al. [51]
also observed the sequential formation of deformation twins and α’-martensite, which
corresponds to the occurrence of intersections and consequent α’-formation at larger εeqac (in
the present study due to deep drawing). The strain occurring in tensile straining (also in case
of ‘deep drawing’ at 10 mm from the cup bottom) is too small to induce α’-formation.
4.4.1
The Olson and Cohen model
As the intersections only account for a small fraction of the material, a relatively low α’martensite fraction is formed, as observed in Figure 4.1. Based on their theory of embryo
formation by strain, Olson and Cohen [35] proposed the following relation for the evolution of
α’-martensite volume fraction upon straining
fα '
OC
{ [
(
= 1 − exp − β OC 1 − exp − α OC ⋅ ε eq
ac
)] }+ f
n
0
(4.2)
where αOC and βOC are two physically-significant, temperature-dependent parameters, εeqac is
the accumulated equivalent strain, n is a fixed exponent, with a suggested value n = 2 and f0
is the initial α’-martensite fraction. We introduce f0 in order to consider the initial α’-martensite
49
fraction. The orientation of the shear bands will not be random, but will tend to be initially
parallel until secondary shear systems start to form. The formation of primary and secondary
shear systems is not arbitrary and shows a sequential nature upon straining increasing the
number of intersections exponentially. Olson and Cohen [35] claim that this behavior can be
approximated by applying a higher exponent than n = 2 and found that βOC = 1.18 and n = 4.5
gave the best overall result. Using their βOC and n, Figure 4.1 shows that for αOC = 0.48 the fit
is in good agreement with the experimental results. Note that the fit includes an initial α’martensite fraction of f0 = 2 × 10-3.
4.4.2
The sequential behavior upon straining
We propose a similar approach for α’-martensite volume fraction evolution upon straining, in
particular the sequential nature of the formation of primary and secondary shear systems
upon straining. The proposed model describes the same physical process, but with slightly
different approach, making the use of n > 2 as artificial approximation of the sequential
behaviour of primary and secondary shear systems upon straining redundant. Figure 4.7
gives a schematic illustration for the formation of intersections of deformation shear-bands.
The intersected area Aint is defined as
Aint =
d2
sin (θ )
(4.3)
with d the average width of a shear band (slip band, twin and/or ε-martensite lath) and θ the
angle between the primary and secondary shear systems (see Figure 4.7).
The volume fraction of intersected shear bands fintsb can be estimated by
f int
sb
(d , l ) = 
d 

d +l
2
(4.4)
where l is the average distance between two shear bands of an shear system and g is the
grain size, which is cancelled out in Equation (4.4). The volume fraction of intersected shear
bands is related to the ratio between d and l and is independent of their absolute values.
According to Elhami et al. [80], the deformation mode influences the number and size of
twins. In literature [8], the mean twin width is assumed to be 0.03 µm, leaving the average
distance between two shear bands of a shear system as remaining parameter. As Olson and
Cohen [35] pointed out, the formation of primary and secondary shear systems is not
arbitrary and shows a sequential nature upon straining. This sequential behavior requires the
50
introduction of Equation (4.5). Equation (4.4) can therefore be rewritten as α’-martensite
volume fraction evolution upon straining
 d   d 
sb
 ⋅ 

f α ' = f 0 + p
 d + l1   d + l 2 
(4.5)
where l1 is the average distance between two shear bands of the primary shear system, l2 is
the average distance between two shear bands of the secondary shear system and p is the
probability for nucleation of α’-martensite at the shear band intersection. Taking into account
the sigmoidal shape of α’-martensite formation upon straining, l1 and l2 can be defined as
(
l1 = g ⋅ exp − α sb ⋅ ε eq
ac
)
(4.6)
and
(
(
ac
))
ac
l2 = g ⋅ exp − α sb ⋅ ε eq − ε α ' , ε eq > ε α '
(4.7)
where αsb is a fitting parameter and ε2 the strain at which α’-martensite formation starts.
Fitting the experimental results of Figure 4.1 for d = 0.03 µm [8], g = 5 µm, αsb = 9 and εα’ =
0.2 leads to a probability p = 0.03.
θ
d
g
l2
l1
d
g
Figure 4.7
Schematic illustration for the formation of intersections of deformation shear-bands with
(1) deformation shear-bands and (2) grain boundaries. The dark grey shear-bands
indicate the primary shear-band system and the light grey shear-bands indicate the
secondary shear-band system.
51
The comparison between the proposed model and the Olson-Cohen model does not
proclaim a clear preference. However, the proposed model does not require the artificial
approximation of the sequential behaviour upon straining, but describes this behaviour
according to the geometrical model put forward by Olson and Cohen [28]. Fitting this model
reveals a very low probability for nucleation of α’-martensite at shear band intersections,
confirming the physical meaning of this approach.
The accumulated equivalent strain εeqac is suggested as a relevant measure of strain
enabling the comparison between tensile straining and deep drawing. With increasing εeqac,
deformation is facilitated by dislocation multiplication, dislocation glide and twinning,
providing the required intersections of shear bands for eventual α’-martensite formation at
high εeqac. It is therefore suggested that the appropriate deformation mechanisms, in particular
the formation of α’-martensite, can be related to εeqac.
4.5
Conclusions
The presented investigation of the relation between the strain and the deformation
mechanisms (in particular the formation of α’-martensite) in austenitic Mn-based TWIP steel
in tensile and deep drawing deformation leads to the following conclusions:
1.
Despite its high SFE (52 mJ/m2), deep drawing deformation results in the formation of
α’-martensite, which is attributed to the accumulated equivalent strain and
crystallographic texture.
2.
The presence of α’-martensite at shear band and twin intersections is observed and
questions the sequential γ → ε → α’ martensitic transformation. The results indicate
that the formation of α’-martensite in a high SFE FCC alloy does not necessarily
require the intermediate formation of ε-martensite laths.
3.
A model for α’-martensite volume fraction evolution upon straining is proposed and the
estimated fraction of intersected shear bands - the preferred nucleation sites for α’martensite formation - as a function of accumulated equivalent strain is in good
agreement with the experimentally determined α’-martensite fraction.
52
5
Role of α’-martensite in the
phenomenon of delayed fracture
The phenomenon of delayed fracture in three austenitic manganese-based TWinning
Induced Plasticity steels is investigated by means of video observation and ex-situ magnetic
measurements. Delayed fracture is observed in the direction perpendicular to the rolling
direction, in coincidence with the highest α’-martensite fraction in a deep-drawn cup. The
formation of a small fraction of α’-martensite, irrespective of the chemical composition
examined, is indicative for the formation of crack initiation sites. We propose an intermittent
crack propagation concept and model for the phenomenon of delayed fracture.
53
5.1
Introduction
This chapter investigates the role of α’-martensite in the phenomenon of delayed fracture on
austenitic manganese (Mn)-based TWinning Induced Plasticity (TWIP) steels after deep
drawing, observed by in-situ video recording. Ex-situ magnetic measurements have been
used to systematically measure the fraction of α’-martensite. The formation of α’-martensite
indicates the formation of crack initiation sites, which is discussed as a possible cause of
delayed fracture.
McCoy and Gerberich [81] showed that in case of TRansformation Induced Plasticity
(TRIP) steel it is the α’-martensite which is susceptible to hydrogen embrittlement. The slow
crack growth in TRansformation Induced Plasticity steel involves the diffusion of hydrogen
through the α’-martensite. Cathodic charging injects the hydrogen at the surface of the
material, embrittling the α’-martensite in the surface layer. The coalescence of cracks
initiated at the embrittled α’-martensite into a macrocrack results in slow crack growth from
the surface inward consisting of discontinuous jumps. According to McCoy and Gerberich
[81], the presence of α’-martensite in combination with a sufficient H-concentration results in
embrittlement.
The α’-martensite fraction strongly affects the delayed fracture susceptibility [6].
Chapter 4 [82] investigates the formation of α’-martensite after deep drawing a blank into a
cup. It shows that the maximum α’-martensite fraction occurs in transverse direction (TD)
close to the surface at the edge of the deep-drawn cup, enhancing the risk for embrittled α’martensite. Deformation along the rolling direction (RD) leads to a higher fraction of grains
orientated for deformation twinning than in the TD [8]. Material at the RD in the cup has a
higher twinning rate and volume fraction of twins than material at the TD, due to the higher
density of grains suitably orientated for deformation twinning [83]. This chapter investigates
the phenomenon of delayed fracture of three austenitic Mn-based TWIP steel grades and
measured the α’-martensite fraction.
5.2
Susceptibility to delayed fracture and the presence of α’-martensite
5.2.1
Visual observations of delayed fracture
To reveal the phenomenon of delayed fracture, Figure 5.1 shows some examples of sideview images from the video observation of delayed fracture in air of material B. After initiation
at the cup edge after 37 hours, the crack advances along the vertical direction and finally
proceeds to a length of approximately 19 mm after 60 hours. The top-view images reveal that
there are two cracks and the observed crack in the side-view images is the second crack to
54
occur. The crack growth of the first one was not monitored by the equipment. Delayed
fracture predominantly occurs close to the TD, i.e. perpendicular to the RD of the cold rolled
sheet. In the course of the delayed fracture process, the shape of the cup edge changes
from circular to oval. The two cracks are situated farthermost from one another, drawing up
the larger axis of symmetry of the oval.
37 h
≈ 42 mm
41 h
60 h
5 mm
5 mm
5 mm
41 h
37 h
5 mm
Figure 5.1
60 h
5 mm
5 mm
Side-(upper) and top-(lower) view images from the video observation of delayed fracture
in air after 37, 41 and 60 hours of testing for material B. The labels on the lower left
corner of the images denote the time after deep drawing. The white-dashed ellipsoids
indicate the original cup diameter. The white arrows indicate the RD. The white full circles
indicate the crack positions.
The observed crack growth is also shown in Figure 5.2, where the crack length is determined
by image analysis. The fracture consists of three stages [5]: an incubation period, an active
period and an inert period. After the incubation period, fracture is first observed at t0 and
proceeds intermittently to t1 (active period) and eventually stagnates at a final crack length Lf
(inert period). The final crack length observed for the crack in Figure 5.1 is 19 mm. The
incubation period refers to the delay time in fracture. All delayed fracture monitoring results
are elaborated in this manner to enable comparison. The macroscopic crack growth has an
intermittent character resembling the crack growth behaviour in [81].
All delayed fracture results are summarized in Figure 5.3 and Table 5.1. Figure 5.3a)
shows the crack length L as a function of time for grades A, B and C in air and in tap water.
The crack length here is the average of three simultaneously assessed cups of identical
conditions. The order of delayed fracture in terms of the final crack length Lf is B > A > C in
55
air and C > B > A in water. The order of delayed fracture in terms of delay time t0 and activeperiod length t1 - t0 is B > A > C in air and water. The difference between the grades is more
distinct in air than in water. For all three grades, submersion in tap water results in a shorter
average incubation period, a shorter average active period and a larger average crack
length. Grade C does not show fracture in the entire period of 1680 hours of testing in air, but
shows the largest crack length when submersed in tap water.
20
incubation period
active
period
inert period
Crack length L [mm]
15
10
5
0
30
Figure 5.2
35
t0
40 t1
45
Time [h]
50
55
60
Crack length as a function of time of material B in air.
Figure 5.3b) shows the number of cracks n as a function of time for grades A, B and C in air
and in tap water. The number of cracks is the average of three simultaneously assessed
cups of identical conditions. Grade C in air does not show delayed fracture. The order of
delayed fracture in terms of the final number of cracks nf is B > A > C in air and in water. For
all three grades, submersion in tap water results in a higher average number of cracks. The
number of cracks saturates after a certain time for all grades and conditions, except nBf in
water which continues to increase with time.
Table 5.1 summarizes the delayed fracture results of Figure 5.3. The time t0 indicates
the average time until first observation of fracture (incubation period, start of active period)
and the time t1 indicates the average time until stagnation of the crack (end of active period,
start of inert period). The given t0- and t1-values are based on the average of three
simultaneously assessed cups of identical conditions. The order of delayed fracture
56
susceptibility in terms of crack length L, delay time t0 and active-period duration t1 - t0 is B > A
> C, except for the order in terms of the crack length in water.
a)
30
A - air
A - water
B - air
B - water
C - air
C - water
Average crack length L [mm]
25
20
15
10
5
0
0.01
0.1
1
10
100
1000
10
100
1000
Time [h]
b)
12
A - air
A - water
B - air
B - water
C - air
C - water
Average number of cracks n
10
8
6
4
2
0
0.01
0.1
1
Time [h]
Figure 5.3
a) Average crack length as a function of time for grade A, B and C in air and water. b)
Number of cracks as a function of time for grade A, B and C in air and water.
57
Table 5.1
Summary of delayed fracture results.
Grade
Air
Water
f
f
t0
t1
t1 - t0
Lf
[h]
[h]
[h]
[mm]
0.5
0.5
1.0
0.5
22
3.0
2.3
0.1
0.5
0.4
26
11.0
0.0
6.0
24.0
18.0
27
2.0
t0
t1
t1 - t0
L
[h]
[h]
[h]
[m]
A
6.0
96.0
90.0
14
B
0.1
24.0
23.9
23
C
>1680
-
-
0
5.2.2
Stacking Fault Energy and the formation of α’-martensite
n
nf
The magnetic saturation, from which the small α’-martensite fraction is determined [53], was
measured along the cup wall at the TD for all grades and also at the RD for Grade A.
0.008
A - TD
B - TD
C - TD
A - RD
Position from
the cup bottom
α '-Martensite fraction
0.006
5 mm
0.004
0.002
0.000
0
Figure 5.4
10
20
30
Position from the cup bottom [mm]
40
50
α’-Martensite fraction after deep drawing as a function of the position from the cup bottom
for grade A, B and C at the TD and for grade A at the RD. The full and dashed lines are
to guide the eye.
Figure 5.4 shows that after deep drawing a very small α’-martensite fraction (fα’ < 0.007) is
present as a function of the position from the cup bottom for all three grades and it is worthy
to note that the fraction in all cases is less than 0.7%. The α’-martensite fraction starts to
increase at 15 mm from the cup bottom as a result from deep drawing. No significant
differences in the α’-martensite fraction are found for the different grades, despite their
58
difference in Stacking Fault Energy (SFE). Figure 5.4 shows that the α’-martensite fraction at
a higher position from the cup bottom is higher at the TD than at the RD.
5.3
Proposed mechanism for delayed fracture
This chapter investigated the phenomenon of delayed fracture of three austenitic Mn-based
TWIP steel grades and measured the α’-martensite fraction. For all three grades, submersion
in tap water results in a shorter average incubation period, a shorter average active period, a
larger average crack length and a higher average number of cracks. A small fraction of α’martensite is detected (less than 0.7%), which increases with the position from the cup
bottom and is higher in material at the TD than at the RD. Delayed fracture is observed in the
direction perpendicular to the RD, in coincidence with the highest α’-martensite fraction in a
deep-drawn cup.
5.3.1
Role of α’-martensite
One of the influencing factors for the phenomenon of delayed fracture in TWIP steels is
reported to be the austenite stability [6], often indicated by the SFE. It is well known that the
SFE predominantly determines the deformation mechanisms, but its role with respect to
austenite stability per se has to be put in perspective [2-4]. Rather than the SFE as such, the
formation of α’-martensite indicates the (meta-)stability of the austenite [82]. α’-Martensite is
shown to form at the intersections of slip bands, twins and/or ε-martensite laths [4, 28], due
to the high stress concentrations occurring at these intersections [51, 82, 84]. Chapter 4 [82],
using TEM techniques, confirmed the presence of α’-martensite after deep drawing in the
high SFE steel grade A. The magnetic experiments indeed reveal no significant difference in
α’-martensite fraction between the examined compositions, indicating that the formation of
α’-martensite is rather a geometrical mechanism of intersecting shear bands than governed
by the SFE in the range covered by the steels in this study. This is in agreement with
Chapter 4 [82, 84], stating that the formation of α’-martensite does not require the formation
of intermediate ε-martensite laths [82] and is a function of the estimated fraction of
intersected shear bands [84].
Intersected shear bands can be very effective as nucleation sites, allowing the
passage of previously blocked dislocations, inducing the formation of α’-martensite and
releasing stress concentrations [51], indicating the link between the presence of α’martensite and the residual stress. Berrahmoune [6] showed that the highest tangential
stresses were approximately halfway the cup height. These results apply to the deep drawing
of a cup in general, irrespective of the occurrence of delayed fracture. For that reason the
residual stress is not of more importance than the presence of α’-martensite.
59
Koyama [11] observed the formation of crack initiation sites at twin boundaries resulting from
high stress concentrations at intersections of grain and twin boundaries with deformation
twins in TWIP steel. Intersections of twin boundaries with deformation twins are potential
nucleation sites for α’-martensite [28]. The α’-martensite fraction is an indication for the
formation of crack initiation sites.
5.3.2
Intermittent crack propagation concept
To reveal the delayed fracture mechanism observed, Figure 5.5 gives a schematic view of
the intermittent crack propagation concept. Crack initiation sites form at potential nucleation
sites for α’-martensite [11] and coalesce into a macrocrack. A higher α’-martensite fraction
relates to a higher density of potential crack initiation sites and easier coalescence. Cracking
is most likely to occur first at locations with a relatively high α’-martensite fraction, advancing
until the density of crack initiation sites is too low for further crack propagation. Crack arrest
is likely to occur at shear band intersections.
Density of shearband intersections
crack
Position from
the cup bottom
shear-band
intersection
Figure 5.5
Schematic illustration of the proposed intermittent crack propagation concept. Crack
propagation occurs through the coalescence of microcracks from shear-band intersection
to shear-band intersection. The density of shear-band intersections increases with the
position from the cup bottom.
5.3.3
Evolution of crack initiation sites upon straining
Based on the geometrical model introduced in Chapter 4 [84], we adapt the model for crack
initiation site evolution upon straining through the accumulated interface length per unit grain
area of intersections of deformation shear-bands with (1) deformation shear-bands and (2)
60
grain boundaries. A schematic illustration for the formation of intersections of deformation
shear bands deformation with shear bands and grain boundaries is shown in Figure 4.6.
The density of crack initiation sites as a function of strain is related to the
accumulated interface density Itotalac, which can be written as
I total
ac
=
4d 
g
1
1 


+
+
g sin (θ )  (d + l1 )(d + l2 ) d + l1 d + l2 
(5.1)
with d the average width of shear bands, g the grain size, θ the angle between the primary
and secondary shear-band systems, l1 the average distance between shear bands of the
primary shear-band system (see Equation (4.6)) and l2 the average distance between shear
bands of the secondary shear-band system (see Equation (4.7)). The first term between the
parentheses of Equation (5.1) accounts for the accumulated interface density of shear-band
intersections Isb-sbac. The second and third term between the parentheses of Equation (5.1)
consider the accumulated interface density of intersections of grain boundaries with
deformation shear bands Igb-sbac.
0.12
Grain
Igb-sbacboundary - shear band
intersections
Shear
Isb-sbacas a function of
Total
Itotalac
0.10
Series4
Itotalac
Iac [*10-3 m-1]
0.08
0.06
35
40
30
0.04
0.02
25
20
15
10
0.00
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
ε eqac
Figure 5.6
Accumulated interface density of intersections of grain boundaries with deformation shear
bands (Igb-sbac), of shear band intersections (Isb-sbac) and total (Itotalac) as a function of strain.
The position from the deep-drawn cup bottom (in mm) are indicated.
61
Figure 5.6 shows Igb-sbac, Isb-sbac and Itotalac as a function of strain, using θ = 70°, d = 30 nm, g =
5 µm, αsb = 9 and ε2 = 0.2 obtained in [84]. Straining results in the formation of crack initiation
sites, leading to a significant increase of Itotalac for εeqac ≥ 0.4. The contribution of Igb-sbac to Itotalac
is very limited, Isb-sbac is mainly responsible for the increase in Itotalac, indicating that the density
of intersections of the secondary shear-band systems with the primary shear-band system
controls the evolution of crack initiation sites upon straining. Figure 5.6 indicates the position
from the deep-drawn cup bottom, based on the Finite Element Method simulations of the cup
deep drawing process performed in [84]. The highest Itotalac is achieved at 35 mm from the
deep-drawn cup bottom.
Figure 5.7 shows Itotalac for austenite grain sizes g = 50, 10, 5 and 1 µm. Chapter 2 and
4 [84] indicated that the initial grain size is approximately 5 µm. The calculations show that a
larger grain size can significantly reduce Itotalac. Crack propagation occurs parallel to primary
and secondary shear-band systems [11]. The length increase l’ for cracks to propagate from
one shear band to another can be written as
l' =
l
sin (θ )
(5.2)
0.16
g50
= 50 µm
g10
= 10 µm
g5= 5 µm
g1= 1 µm
0.14
1 µm
Itotalac [*10-3 m-1]
0.12
5 µm
0.10
10 µm
0.08
0.06
0.04
50 µm
0.02
0.00
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
ε eqac
Figure 5.7
Total accumulated interface length per unit area for g = 50, 10, 5 and 1 µm, using θ = 70°,
d = 30 nm, αsb = 9 and ε2 = 0.2 obtained in [84].
62
Figure 5.8 shows l’ for the primary and secondary shear-band system as a function of strain.
l’ decreases upon straining, easing crack coalescence. The strain ε2 at which the secondary
shear-band system starts to form is key for the formation of shear-band intersections. Crack
coalescence from crack initiation sites at intersections uses both shear-band systems,
crossing different lengths, resulting in discontinuous jumps and explaining the observed
intermittent crack growth behaviour.
The results of Figure 4.1b) and 5.4 show that α’-martensite formation in the material
relates to the direction at which the material is with respect to the RD in the blank, indicating
a relation of the shear-band intersections with respect to the RD. As reported, there is a
higher density of grains suitably orientated for deformation twinning resulting in a higher twin
production rate and twin volume fraction at the RD than at the TD [83]. In order to facilitate
deformation in material at the TD, the secondary shear-band system will be activated at
lower strain ε2, resulting in more shear band intersections. Figures 5.6 and 5.8 show the
importance of the secondary shear-band system for the formation of crack initiation sites with
increasing strain and therefore for delayed fracture. Delayed fracture predominantly occurs
close to the TD, where the highest α’-martensite fraction is detected, providing further proof
for this concept.
6
l'P1
l'S2
5
l' [*10-6 m]
4
3
2
1
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
ε eqac
Figure 5.8
Crack propagation length for the primary and secondary shear-band system, using θ =
70°, d = 30 nm, αsb = 9 and ε2 = 0.2 obtained in [84].
63
The order in SFE (grade A > B > C) does not correspond to the order in delayed fracture
susceptibility (grade B > A > C) and does not affect the formation of α’-martensite. The
formation of α’-martensite indicates the presence of crack-initiation sites, which are formed
during deep drawing. The coalescence of these microcracks might be responsible for the
delay time. A higher density of crack-initiation sites eases crack coalescence and could
influence the delay time. The α’-martensite fraction of the three steel grades covered in this
study are equal and represent an equal density of crack-initiation sites. This cannot explain
the difference in delayed fracture susceptibility between these three steel grades. The
difference is attributed to two other factors influencing crack coalescence: (1) the residual
stress and (2) the resistance against crack propagation.
5.4
Conclusions
The presented investigation of delayed fracture in three austenitic Mn-based TWIP steels
after deep drawing leads to the following conclusions:
1.
Delayed fracture occurs along the TD where the α’-martensite fraction is the highest.
An intermittent crack propagation concept and model is proposed based on the
coalescence of initial cracks into a macrocrack. A higher α’-martensite fraction
indicates a higher density of shear-band intersections, resulting in more potential crackinitiation sites and easier coalescence.
2.
The order of delayed fracture susceptibility in terms of crack length L, delay time t0 and
duration of the active period of crack growth t1 - t0 is B > A > C, except for the order in
terms of crack length L in water. This indicates no direct relation with the SFE.
3.
64
The SFE in the SFE range tested does not affect the formation of α’-martensite.
6
Effect of prior plastic deformation on
the kinetics of austenite decomposition
In this chapter, pearlite formation in undeformed and deformed austenitic manganese-based
TWinning Induced Plasticity steel is investigated by means of in- and ex-situ magnetisation
measurements and optical and scanning electron microscopy. The metastable austenitic
microstructure partially transforms to pearlite upon isothermal aging in the temperature range
500-600°C on a time scale of tens of hours. The observed transformation kinetics and
microstructure development are interpreted in terms of the nucleation and growth of pearlite
colonies. Preferential nucleation sites for pearlite formation are grain boundaries and prior
plastic deformation increases the density of nucleation sites. Mn-partitioning between the
ferrite and cementite lamellae in pearlite appears to control the growth rate, which is the
underlying reason for the slow transformation kinetics.
65
6.1
Introduction
The austenitic phase in TWinning Induced Plasticity (TWIP) steel with 14 wt% Mn is
metastable at room temperature, and is seen to transform to martensite by means of stressinduced γ (Face Centred Cubic, FCC) → ε (Hexagonal Close Packed, HCP) → α’ (Body
Centred Cubic, BCC) martensitic transformations [57, 76, 82, 84]. The mere occurrence of
this γ → α’-martensite transformation indicates the austenite not to be stable at room
temperature, but metastable [77]. Mn-contents below approximately 20 wt% form the basis
for this meta-stability at room temperature, allowing the study of a broad domain of
deformation and temperature conditions [85]. Whereas the metastable austenite transforms
by martensitic mechanisms upon mechanical loading, diffusional decomposition of austenite
into pearlite is expected when the material is annealed at temperatures below the A1temperature. This diffusional growth of pearlite has been subject of research for steels with
relatively low Mn-contents (less than 1.8 wt%) [86, 87], studying the role of manganese
during austenite to pearlite transformation in particular Mn-partitioning between pearlitic
cementite and ferrite. The present work investigates the austenite decomposition at
intermediate temperatures into pearlite in Mn-based steels with 14 wt% Mn.
Pearlite nucleates preferentially at prior austenite grain boundaries, compared to the
grain interior, due to the interfacial energy [88]. Plastic deformation increases the stored
energy within the austenite grains and of the austenite grain boundaries, enhancing the
density of effective nucleation sites [89]. According to Xiao et al. [89], isothermal
transformation of austenite results from the combined effect of short distance Fe-diffusion
across the interface and long distance C-diffusion, with plastic deformation predominantly
accelerating the latter.
Plastic deformation introduces microstructural defects like dislocations, twin
boundaries and deformation bands within the austenite grains which are preferential
nucleation sites for ferrite [85, 88-91] and pearlite [91, 92]. The number density of potential
nucleation sites therefore increases with prior plastic deformation. Beladi et al. suggest that
this process is static, providing more favourable nucleation conditions, but not affecting the
transformation process itself [85]. In this chapter, using in-situ thermo-magnetic techniques
and ex-situ magnetic techniques, optical microscopy and scanning electron microscopy, the
nucleation and growth of the pearlite colonies in undeformed and deformed condition are
systematically investigated. From observations on the pearlite fraction and the size
distribution and number density of pearlite colonies, the characteristics of the austenite-topearlite transformation are derived.
66
6.2
Isothermal transformation
6.2.1
Formation of ferromagnetic phases
40
500˚C Undeformed
550˚C Undeformed
550˚C 10% Tensile-strained
600˚C Undeformed
∆Magnetization [Am2/kg]
35
550°C 10% Tensile-strained
550°C
30
25
20
600°C
15
500°C
10
5
0
0
Figure 6.1
5
10
Time [h]
15
20
The change in magnetization during isothermal annealing at 500°C, 550°C and 600°C in
undeformed condition and at 550°C in tensile-strained condition.
Figure 6.1 shows the change in magnetization in a field of 1.0 Tesla during in-situ isothermal
annealing at 500°C, 550°C and 600°C in undeformed condition and at 550°C after 10%
tensile straining. Isothermal annealing experiments performed at 400°C show no
ferromagnetic phases to form within 20 hours. At the higher temperatures shown in Figure
6.1, initially the magnetization as a function of time remains low, but later increases more
rapidly, indicating the formation of ferromagnetic phases. Note that the time scale of the
transformation is on the order of 10 hours, which is orders of magnitude slower than for
conventional pearlite formation. Isothermal annealing at 550°C displays the fastest
transformation kinetics of the three studied temperatures, reaching the highest magnetization
in the first 20 hours. Figure 6.1 also compares the magnetization during isothermal annealing
at 550°C in undeformed condition and after tensile straining. Prior plastic deformation
enhances the overall transformation rate and increases the degree of transformation reached
within 20 hours. The curves in Figure 6.1 show the temperature dependence of the
transformation kinetics that is also reflected in the well-known C-shaped curves in
Temperature-Time-Transformation diagrams, with the transformation being slow at high
temperature because of limited driving force and at low temperature because of limited
67
atomic mobility. Prior plastic deformation, in this case not more than 10% tensile straining,
causes a significant shift to shorter times.
6.2.2
Formation of pearlite
SEM micrographs in Figure 6.2 show that pearlite is formed in isolated colonies with an
internal lamella thickness in the order of tens of nanometres and give examples in which
nucleation has taken place at grain boundaries.
a)
b)
200 nm
1 µm
d)
c)
1µm
Figure 6.2
1µm
Scanning Electron Micrographs of the a) and b) ferromagnetic pearlite phase and c) and
d) nucleation of a pearlite colony at (intersections of) grain boundaries in undeformed
condition after 6 hours of isothermal annealing at 550°C.
Figure 6.3 shows the pearlite fraction from magnetisation measurements at room
temperature after isothermal annealing at 550°C for different time intervals in undeformed
condition and after 10% tensile straining. These room-temperature measurements were
performed to obtain a more accurate quantification of the phase fractions. Also in these exsitu measurements, prior plastic deformation is shown to enhance the formation rate of
pearlite and to lead to a higher eventual fraction. Isothermal annealing during 70 hours at
550°C results in the formation of approximately 30% pearlite. The difference with the
equilibrium fraction of 67% given by ThermoCalc (Figure 1.6) can be related to incomplete
partitioning of manganese (see also the Transformation kinetics section of this chapter).
68
0.35
Undeformed
10% Tensile-strained
0.30
Pearlite fraction
0.25
0.20
0.15
0.10
0.05
0.00
0
10
20
30
40
50
60
70
Time [h]
Figure 6.3
Pearlite fraction at room temperature after isothermal annealing at 550°C as a function of
time in undeformed condition and after 10% tensile straining. The solid lines represent
the fits of the Johnson-Mehl-Avrami Equation (6.1) [93-95].
The pearlite fraction as a function of holding time can be described by the Johnson-MehlAvrami Equation [93-95], adapted for the final ferrite fraction, given by
(
(
f (α ) = f α 1 − exp − (kt )
f
n
))
,
(6.1)
where fαf is the final pearlite fraction at which saturation occurs, k is the rate parameter, n is
the Avrami coefficient and t is the isothermal annealing time at 550°C. The parameters k and
n reflect the nature of transformation. Figure 6.3 shows that the fit is in good agreement with
the experimental results for fαf = 0.28, k = 0.06 s-1 and n = 2 in undeformed condition and fαf =
0.30, k = 0.17 s-1 and n = 1 for transformation after tensile straining.
6.2.3
Nucleation and growth of pearlite colonies
Figure 6.4a)-d) show microstructures of the undeformed and tensile-strained samples after
isothermal annealing at 550°C. Isothermal annealing at 550°C results in the formation of
pearlite colonies in the otherwise austenitic microstructure. The number density and size of
pearlite colonies increase with isothermal annealing time. Prior plastic deformation is seen in
the microstructures to increase the number density of pearlite colonies compared to the
69
undeformed condition for equal pearlite fractions. This observation is in agreement with the
enhanced transformation kinetics, as expressed by the Avrami parameters resulting from
Figure 6.3, an effect that is also presumably due to more effective nucleation [89, 96]. The
decrease in the Avrami coefficient n due to prior deformation indicates nucleation to take
place predominantly in the initial stage of the transformation, since the dimensionality of
pearlite growth is not affected.
a)
0.03
b)
50 m
c)
0.04
50 m
d)
50 m
Figure 6.4
0.17
0.19
50 m
Optical micrographs of austenite (light grey) and pearlite (black) in undeformed condition
after a) 6.1 hours and b) 14.3 hours of isothermal annealing at 550°C and in tensilestrained condition after c) 2.0 hours and d) 5.9 hours of isothermal annealing. The
number in the top-right boxes indicates the pearlite fraction.
The optical micrographs were systematically analysed to quantify the number density of
pearlite colonies during the transformation. In this analysis only those microstructures were
considered in which all colonies could be distinguished separately. Figure 6.5 shows the
number density of pearlite colonies in 2D micrographs against pearlite fraction in undeformed
condition and after tensile straining.
70
Density of pearlite colonies in 2D [mm-2]
5000
Undeformed
10% Tensile-strained
4500
6h
4000
3500
2h
3000
2500
2000
1500
14 h
1000
500
6h
0
0.00
Figure 6.5
0.05
0.10
0.15
Pearlite fraction
0.20
0.25
Density of pearlite colonies in 2D micrographs versus pearlite phase fraction.
Nucleation takes place within the first 5% of the transformation, where prior plastic
deformation is shown to increase the density of pearlite colonies by approximately a factor
three. The nucleation rate decreases to zero at a pearlite phase fraction of 5% for both the
undeformed and the deformed microstructure. The nucleation rate can be expressed as [97,
98]


ψ
N& = ω ⋅ C1 ⋅ exp  −

 k T ( ∆G + E )2 
c
s
 B

(6.2)
in which ω is a factor including the atom vibration frequency and critical nucleus area, C1
reflects the density of potential nucleation sites, ψ is a constant related to the creation and
annihilation of interfaces during nucleation, kB the Boltzmann constant, T the temperature,
∆Gc the free-energy difference between austenite and pearlite and Es the deformation energy
stored in the austenite.
71
12
Undeformed
10% Tensile-strained
Figure 6.7b)
10
<d> [µm]
8
Figure 6.7a)
6
4
Figure 6.7b)
2
0
0
Figure 6.6
5
10
Time [h]
15
20
Experimental average equivalent diameter <d> of pearlite colonies as a function of time in
undeformed condition and after tensile straining. The solid line is a linear fit of all data
points. The samples taken for Figure 6.7a) and b) are indicated.
Figure 6.6 shows the experimental average equivalent diameter <d> of pearlite colonies as a
function of time in undeformed condition and after tensile straining. The results show a
constant average growth rate that is equal for both conditions. The initial average growth rate
is significantly higher than the constant average growth rate shown by the data in Figure 6.6,
since at t = 0 no pearlite colonies were present in the microstructure. An effect of prior plastic
deformation on the initial average growth rate of the nuclei cannot be distinguished from the
results of Figure 6.6.
The growth rate is represented by the interface velocity v [97], which can be
expressed as
 Q 
 ⋅ (∆G + Es )
v = M 0 ⋅ exp −
 k BT 
(6.3)
where M0 is the pre-exponential factor for the mobility and Q is the activation energy for
interface motion [99]. Considering the interface velocity in relation to the free-energy
difference (rather than in relation to undercooling) enables incorporation of the stored energy,
showing the effect of prior deformation.
72
a) 0.22
Undeformed - 6 h
10% Tensile-strained - 6 h
0.20
0.18
0.16
P [µm-1]
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
35
d [µm]
b) 0.22
Undeformed - 14 h
10% Tensile-strained - 2 h
0.20
0.18
0.16
P [µm-1]
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
35
d [µm]
Figure 6.7
a) Distribution P of the equivalent diameter of pearlite colonies in undeformed condition
and after tensile straining after 6 hours of isothermal annealing at 550°C. The
corresponding pearlite fractions are 0.03 and 0.19, respectively. The minimum detected
equivalent diameter for a pearlite colony is 1 µm. b) Distribution P of the equivalent
diameter of pearlite colonies in undeformed condition after 14 hours annealing and after
tensile straining and 2 hours annealing.
73
Whereas Figure 6.6 shows the average colony size, Figure 6.7 shows the size distribution P
of pearlite colonies in some of the microstructures. The size distribution can in all cases be
approximated by
P=
 d 
1

⋅ exp −
 d 
〈d 〉


(6.4)
where d is the equivalent diameter of the pearlite colony and <d> represents the average
equivalent diameter of the pearlite colonies. Equation (6.4) is in good agreement with the
experimental results of Figure 6.7. In Figure 6.7a) the size distribution is shown for the
microstructures after 6 hours of isothermal annealing at 550°C, both in undeformed condition
and after tensile straining. The phase fractions at this point are approximately 3% in
undeformed condition and 20% after tensile straining (see Figure 6.3). The Figure shows that
there is no significant difference between the size distributions for the undeformed and
tensile-strained condition after 6 hours of isothermal annealing at 550°C, confirming the
conclusion from Figure 6.6, namely that prior plastic deformation does not significantly affect
the growth kinetics. Note that the number density of pearlite colonies differs by almost a
factor 10 between these two conditions (see Figure 6.5). Figure 6.7b) shows that the
description of the size distributions of the pearlite colonies by Equation (6.4) consistently
applies also for the smallest (after 2 hours annealing in deformed condition) and largest size
(after 14 hours annealing in undeformed condition).
The results of Figures 6.5-6.7 show that the increase in pearlite fraction due to prior
plastic deformation is primarily a result of a higher density of potential nuclei and not a higher
nucleation rate and/or a higher growth rate.
6.3
Transformation kinetics
The aim of this chapter is to investigate the pearlite formation in undeformed and deformed
Mn-based TWIP steels, in particular the nucleation and growth of pearlite colonies, using
magnetic measurements at room temperature and elevated temperature and optical
microscopy. Isothermal annealing at 550°C results in a microstructure consisting of austenite
and pearlite, which is a three-phase assembly as predicted by ThermoCalc (Figure 1.6). The
presented observations show that a fully austenitic microstructure for this Mn-based TWIP
steel grade is in a metastable state at temperatures below 600°C.
6.3.1
Manganese partitioning
Figure 6.8a) shows a schematic illustration of the Gibbs free energy as a function of the Mnconcentration for the three phases ferrite, austenite and cementite. This representation is just
74
schematic, because the C-concentrations in the three phases are distinctly different: very low
in ferrite, initially equal to the overall concentration (0.71 wt%) in the austenite and 6.7 wt% in
the cementite. This is depicted in Figure 6.8b), in which the equilibrium concentrations from
ThermoCalc (Figure 1.6b)) are used. The open symbol in Figure 6.8b) indicates the overall
composition of the steel, equal to the austenite composition before the transformation. The
decomposition of austenite into ferrite and cementite according to equilibrium, indicated by
the arrows, involves partitioning of both carbon and manganese between the three phases.
Evidently at the time scale of this transformation complete partitioning of the carbon can be
assumed. To indicate the length scales involved in the phase transformation, the diffusion
distance of manganese in ferrite and austenite has been calculated for 10 hours of
isothermal annealing at a temperature of 550°C, with a diffusivity of 4 × 10−22 m2/s for
austenite and 2 × 10−19 m2/s for ferrite [90]. After 10 hours annealing the diffusion distances
are in the order of 5 nm in austenite and 100 nm in ferrite. These distances indicate that Mnpartitioning between the ferrite and cementite lamellae within the pearlite can be
accomplished (see the internal pearlite structure in Figure 6.2b), but significant partitioning
between pearlite and austenite would involve much larger distances, see for instance Figure
6.4, and therefore much longer times (for instance 4 × 105 hours for 1 µm diffusion distance
for manganese in austenite). Ortho-equilibrium conditions will therefore be reached between
ferrite and cementite, but diffusion of manganese in the austenite over length scales on the
order of 10 nm prevents accomplishing ortho-equilibrium between all three phases. The
equilibrium state that is reached at the present time scales is therefore a combined condition
of ortho-equilibrium between ferrite and cementite and para-equilibrium between pearlite and
austenite. Since pearlite consists of two phases, the latter condition is characterised by the
Mn-concentration in the austenite being equal to the average Mn-concentration of ferrite and
cementite. The composition of the austenite is estimated by the triangle in Figure 6.8b). The
corresponding austenite fraction is approximately 0.65, which is much higher than the
equilibrium fraction of 0.25 given by ThermoCalc for equilibrium (see Figure 1.6). Figure 6.3
indicates that the austenite fraction approaches saturation at a value that is still somewhat
larger than the fraction of 0.55 estimated from Figure 6.8b). This deviation is caused by the
ferrite and cementite also assuming different concentrations in this combined equilibrium
conditions, which cannot be accurately quantified from the present observations. The
plastically deformed austenite phase will have a slightly higher free energy than the
undeformed phase (see Figure 6.8a)), which causes its equilibrium fraction to be slightly
lower. This is experimentally observed, as is shown in Figure 6.3.
75
Gibbs free energy
a)
γ
Es Deformed
Undeformed
α
0.0
θ
0.1
0.2
0.3
0.4
0.5
Mn
0.6
0.7
0.8
0.9
1.0
b) 0.03
θ
C
0.02
0.01
γ
α
0.00
0.0
0.1
0.2
0.3
Mn
Figure 6.8
a) Schematic illustration of the Gibbs free energy for austenite, ferrite and cementite as a
function of the Mn-content at 550°C. Note that the C-concentration of the three phases is
different (see Figure 6.8b). b) The three phase region austenite-ferrite-cementite in the
ternary Fe-C-Mn phase diagram. The open square is the average composition.
76
6.3.2
Effect of prior plastic deformation
The main effect of prior plastic deformation is to enhance the transformation rate from
austenite to pearlite. According to Equations (6.2) and (6.3) prior plastic deformation will
affect both the nucleation rate and the growth rate through the stored energy Es. The stored
energy can be determined by [100]
Es = α
(σ − σ 0.2 )2
µ
(6.5)
where α is a constant, σ0.2 the yield stress, σ the flow stress after deformation, and µ the
shear modulus. After 10% tensile straining Es equals 5.35 J/mol, using α = 2.3 [89] and µ =
72 GPa [101]. This value is distinctly lower than the chemical driving force ∆G, which is on
the order of kJ/mol [102]. The stored energy Es is therefore negligible as a contribution to the
driving force for transformation and does not significantly affect the nucleation rate or growth
rate in the observed timescale, as evidenced by the experimental results (Figures 6.5-6.7).
The increase in transformation rate is primarily due to a higher density of nuclei
(Figure 6.5). During the transformation the nucleation rate is practically zero, so site
saturation (i.e. nucleation taking place only in the initial stage of the transformation) governs
the nucleation behaviour. As a consequence, the nucleation kinetics cannot be analysed
from the present data (Figure 6.5). However, 10% tensile straining does not result in a
heavily deformed microstructure [84], indicating that the density of potential nucleation sites
at the grain boundaries will not significantly increase. The increased nucleation is therefore
likely to result, on the one hand, from microstructural defects like dislocations, twin
boundaries and deformation bands within the austenite grains (increasing C1 in Equation
(6.2)), on the other hand from an increased nucleation potency at grain boundaries
(decreasing Ψ in Equation (6.2)). The presented results correspond to the static nucleation
process proposed by Beladi et al. [85] and the growth rate being independent of prior plastic
deformation as evidenced by Schmidt et al. [92].
In Mn-based TWIP steel, strain-induced α’-martensite is known to form at the
intersections of shear bands such as slip bands, twins and/or ε-martensite laths [28, 35]. This
indicates that these intersections are efficient nucleation sites for a body centred structure
due to their incoherency and locally high stored deformation energy. For the same reason,
(intersections of) grain boundaries and shear bands can be preferential nucleation sites for
the formation of pearlite colonies. The presence of α’-martensite potentially facilitates the
formation of ferrite within pearlite. Thus, prior plastic deformation results in the formation of
77
incoherent sites with locally high stored energy, which enhance the nucleation potential of
pearlite.
The consequences of the transformation behaviour of this steel for controlling its
microstructure and mechanical properties can be significant. The formation of pearlite
colonies in the microstructure can form an additional strenghtening factor, the effect of which
can be tailored through the number density of pearlite colonies by applying a small degree of
prior deformation. Secondly, partial transformation of austenite to pearlite will enhance the
stability of the austenite, reducing the susceptibility to α’-martensite formation, which is
believed to be at the basis of delayed cracking in this material [57]. Finally, the Cconcentration in the austenitic phase is significantly reduced during the phase
transformation.
6.4
Conclusions
The presented investigation on the austenite stability in a Mn-based TWIP steel, using
magnetic measurements at room and elevated temperature and optical microscopy leads to
the following conclusions:
1.
The austenitic microstructure of Mn-based TWIP steel is metastable and partly
transforms to pearlite during isothermal annealing at temperatures in the range of 500600°C.
2.
The transformation kinetics are governed by Mn-partitioning between ferrite and
cementite within the pearlite. Mn-diffusion is too slow to allow partitioning between
pearlite and austenite, and a mixed equilibrium condition is established of orthoequilibrium between ferrite and pearlite and para-equilibrium between pearlite and
austenite. Nucleation of pearlite takes place only in the initial stages of the
transformation.
3.
Prior plastic deformation enhances the formation rate of pearlite from austenite and
increases the number density of pearlite colonies, primarily through increased
nucleation efficiency. Prior plastic deformation does not significantly affect the
nucleation rate or growth rate in the observed timescale.
78
7
Conclusions
This thesis studies the effect of plastic deformation on the stability of the austenitic
microstructure against martensitic transformation and diffusional decomposition and its role
in the phenomenon of delayed fracture in austenitic manganese based TWinning Induced
Plasticity steels. The transformation to α’-martensite and diffusional decomposition into
pearlite shows the austenite to be metastable. An increase in the austenite stability is
expected to improve the resistance against delayed fracture, based on these conclusions:
1.
Positron annihilation detects that two different defect types result from plastic
deformation during deep drawing. The two defect types can be expected to be
dislocations and partial dislocations. Magnetic field measurements reveal the formation
of α’-martensite which correlates with the density of the defects identified as partial
dislocations.
2.
The formation of α’-martensite is attributed to the accumulated equivalent strain and
crystallographic texture. A model for α’-martensite volume fraction evolution upon
straining is proposed and the estimated fraction of intersected shear bands - the
preferred nucleation sites for α’-martensite formation - as a function of accumulated
equivalent strain is in good agreement with the experimentally determined α’martensite fraction.
3.
The presence of α’-martensite at shear band and twin intersections is observed and
questions the sequential γ → ε → α’ martensitic transformation. The Stacking Fault
Energy (SFE) in the SFE range tested does not affect the formation of α’-martensite.
4.
Delayed fracture occurs along the transverse direction where the α’-martensite fraction
is the highest. An intermittent crack propagation concept and model is proposed based
on the coalescence of initial cracks into a macrocrack. A higher α’-martensite fraction
indicates a higher density of shear-band intersections, resulting in more potential crack79
initiation sites and easier coalescence. The order of delayed fracture susceptibility in
terms of crack length L, delay time t0 and duration of the active period of crack growth t1
- t0 indicates no direct relation with the SFE.
5.
The austenite decomposition into pearlite upon annealing at intermediate temperatures
is governed by Mn-partitioning between ferrite and cementite within the pearlite.
Nucleation of pearlite takes place only in the initial stages of the transformation. Prior
plastic deformation enhances the formation rate of pearlite from austenite and
increases the number density of pearlite colonies, primarily through increased
nucleation efficiency. Prior plastic deformation does not significantly affect the
nucleation rate or growth rate in the observed timescale.
80
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