PhD Thesis Luca Patriarca Final Version - Politecnico di Milano · 2013-05-03 · DOC EX MICR...

DOC

EX

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SupervisorProf. StefaProf. Huse

Tutor: Prof. Tulli

The Chair oProf. Bian

CTORAL PROG

XPERIME

ROSTRU

s: ano Beretta eyin Sehitog

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of the Doctonca Maria C

POLITE

MECHAN

GRAMME IN

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(Politecnicoglu (Universi

ral Program:olosimo

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13 – Cicle X

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XXV

ANICAL SYST

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Doctoral DissLuca

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TEMS

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sertation of: a Patriarca

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i

AbstractThis work presents an experimental approach to investigate the material behavior at

the micro-scale of two important alloys (FeCr and γ-TiAl) for structural applications.

Local strain fields at multiple length scales are measured using an advanced optical

technique. Local strain heterogeneities arises as a consequence of the local

microstructure and deformation mechanisms. This work aims to gain further insights

into the relation between the mechanical behavior of metals at the micro-scale with

the observed mechanical behavior on the meso and macro scales. The main findings

presented here provide valuable information into the deformation mechanisms

activated in bcc metals (slip and twinning), which can be utilized by researchers as

the basis of analytical models to be developed in the next future.

The work is divided into three main parts. In the first part, tension and compression

experiments were conducted on multiple single crystal orientations of body-centered

cubic Fe-47.8Cr single crystals. The critical resolved shear stress magnitudes for slip,

twin nucleation and twin migration were established. The results show that the

nucleation of slip always precedes twinning which nucleates with an associated load

drop at an higher critical resolved shear stress. Following twin nucleation, twin

migration proceeds at a critical resolved shear stress that is lower than the initiation

stress. The experimental results of the nucleation stresses indicate that the Schmid

law holds to a first approximation for the slip and twin nucleation cases, but to a

lesser extent for twin migration particularly when considerable slip strains preceded

twinning. The critical resolved shear stresses were determined experimentally using

digital image correlation in conjunction with electron back scattering diffraction. The

digital image correlation enabled pinpointing the precise stress on the stress-strain

curves where twins or slip were activated. The crystal orientations were obtained

using electron back scattering diffraction and used to determine the activated twin

and slip systems through trace analysis. The results presented in Chapter 2 provide a

considerable contribution in understanding the micro-mechanical behavior of bcc

alloys.

ii

In the second part of the present work slip transmission through grain boundaries is

investigated. The full slip dislocation blockage, or the partial slip dislocation

transmission processes at grain interfaces provide a significant contribution at the

material strengthening. The study focuses on the link from the deformation

mechanisms at the micro-scale to the global mechanical behavior (macro-scale).

Strain fields across grain boundaries were measured using advanced digital image

correlation techniques. In conjunction with strain measurements, grain orientations

from electron back-scattered diffraction were used to establish the dislocation

reactions at each boundary, providing the corresponding residual Burgers vectors due

to slip transmission across the interfaces. A close correlation was found between the

magnitude of the residual Burgers vector and the local strain change across the

boundary. When the residual Burgers vector magnitude (with respect to the lattice

spacing) exceeds 1.0, the high strains on one side of the boundary are paired with

low strains across the boundary. When the residual Burgers vector approaches zero,

the strain fields vary smoothly across the boundary. The FeCr bcc alloy exhibits

single slip per grain making the measurements and dislocation reactions rather

straightforward. The work points to the need to incorporate details of slip dislocation-

grain boundary interaction (slip transmission) in modeling research.

In the last part of the work, a γ-TiAl alloy manufactured with electron beam melting

technology is examined. The electron beam melting technology enables to avoid

typical manufacturing defects. It follows that experiments carried out on this material

provide several insights into the microstructural damage mechanisms leading to crack

initiation. Classical experimental methodologies for the fatigue characterization were

conducted adopting plain fatigue specimens, fatigue specimens with an initial artificial

defect, and crack propagation specimens. Preliminary considerations from these

experiments indicate that the interfaces between lamellar-lamellar grains, and

lamellar-equiaxed grains act as potential crack initiation sites. Taking into account the

typical lamellar grain size, the fatigue resistance of the duplex γ-TiAl alloy can be

predicted. Further investigations on the influence of the microstructure were obtained

using residual strain fields via high resolution digital image correlation in combination

with high resolution images of the local microstructure after etching.

iii

To all those who live their passions

And

To all those who let be led by those of others

v

AcknowledgementsFirst of all I would like to thank my parents, Paola and Oreste, for letting me follow my

dreams, even if this implied to give something up in their life. I’m also thankful for my

friends Mauro Madia and Paolo Berbenni (in Italy), and Wael Abuzaid (in US) who,

during my PhD program, never missed their support (especially in my difficult

periods), they became friends other than just colleagues. I’m also thankful for all the

other friends who came in my life in these three years, in which I crossed for five

times the ocean between Italy and US. In US I’d like to thank Piyas, Garrett, Mallory,

Tawhid, Jay, Avinesh, Jifeng, Alpay, Emre with whom I enjoyed the time in the office

and the lab. Simone, Claudia, Hannah, Beatriz, Riccardo, Giovanni, Francesco,

Chiara, Francesca, Lynn, Federico, Dave, Aya, Arnulfo for being my housemates,

friends, and “snack mates”. In Russia, my ex-colleague, and very close friend

Khaydar. In Italy I’d like to thank Daniele, Michele, Stefano and all the other

colleagues in Polimi, also Marta, Isabella, Paolo, Ottavio, Francesco, Andrea, Massi,

Sara, Enrico, Romina, Nonna for being a necessary support.

Special thanks go to my two advisors and mentors Prof. Huseyin Sehitoglu, and Prof.

Stefano Beretta. Prof. Huseyin Sehitoglu for helping me in my scientific and personal

growth with his weekly meetings, his daily suggestions, his strong encouragements in

improving the quality of the work, his persistence in helping me with my writings (for

sure not one of my best skills, at least in English), and his kindness in supporting and

being interested not only in our work in the office, but also in our life outside the office.

Prof. Stefano Beretta for letting me develop my research topic with no time-limits in

US, for his encouragements even from Italy, his visits in Champaign, his continuous

ideas and enthusiasm in the research work, and his patience in waiting for me for

setting up the lab in Polimi with the experimental tools I’ve been using in US.

Finally I’d like to thank everybody who shared my feelings, my ideas, my passions in

these three years. Without deep relations among people, the pure work would not

mean a thing.

1

TableofContents

INTRODUCTION ........................................................................................................................................... 5

I.1. EXPERIMENTAL APPROACH ........................................................................................................................... 6

I.2. TWIN NUCLEATION AND MIGRATION, SLIP ONSET IN FECR SINGLE CRYSTALS ............................................................ 7

I.3. SLIP TRANSMISSION THROUGH GRAIN BOUNDARIES IN FECR ............................................................................. 11

I.4. STRAIN LOCALIZATIONS IN A Γ‐TIAL ALLOY ..................................................................................................... 14

CHAPTER 1

EXPERIMENTAL METHODOLOGY ............................................................................................................... 17

1.1. DIGITAL IMAGE CORRELATION ..................................................................................................................... 17

1.1.1. In situ DIC ..................................................................................................................................... 19

1.1.2. Ex situ DIC .................................................................................................................................... 21

1.1.3. In situ versus ex situ DIC .............................................................................................................. 23

1.2. DIC APPLICATION FOR MEASURING TWIN NUCLEATION AND MIGRATION STRESSES IN FECR SINGLE CRYSTALS ............. 25

1.2.1. Incremental Digital Image Correlation ........................................................................................ 25

1.3. SLIP ONSET IN FECR SINGLE CRYSTALS ........................................................................................................... 27

1.4. STRAIN FIELDS FROM GRAIN‐BOUNDARY ‐ SLIP INTERACTION ............................................................................ 29

1.4.1. Strain accumulation on FeCr grain boundaries ............................................................................ 29

1.4.2. Strain accumulation on TiAl ......................................................................................................... 31

1.5. SLIP AND TWIN INDEXING ........................................................................................................................... 32

CHAPTER 2

TWIN NUCLEATION AND MIGRATION IN FECR SINGLE CRYSTALS ................................................................ 35

2.1. EXPERIMENTAL SETUP ................................................................................................................................ 36

2.1.1. Sample geometries ...................................................................................................................... 36

2.1.2. Digital Image Correlation setup ................................................................................................... 37

2.2. STRESS‐STRAIN CURVES .............................................................................................................................. 38

2.3. ACTIVATED TWIN AND SLIP SYSTEMS ............................................................................................................. 40

2.4. CRYSTAL ORIENTATION [010] ................................................................................................................... 42

2.4.1. Tension experiments .................................................................................................................... 43

2.4.2. Compression experiments ............................................................................................................ 46

2



2.6. CRYSTAL ORIENTATION [ 10 1] ................................................................................................................... 49

2.6.1. Tension experiments .................................................................................................................... 49




2.8. FURTHER ANALYSIS OF THE RESULTS .............................................................................................................. 56

2.8.1. Twin Migration Stress .................................................................................................................. 57

2.8.2. Strain Hardening .......................................................................................................................... 57

2.8.3. Twin Nucleation Stress ................................................................................................................. 58

2.8.4. Slip Nucleation Stress ................................................................................................................... 58

CHAPTER 3

SLIP TRANSMISSION THROUGH GRAIN BOUNDARIES IN FECR POLYCRYSTAL .............................................. 59

3.1. SCHEMATIC OF SLIP DISLOCATION–GRAIN BOUNDARY INTERACTION .................................................................. 59

3.2. MATERIAL AND METHODS .......................................................................................................................... 61

3.2.1. Microstructure characterization .................................................................................................. 61

3.2.2. Experimental set‐up and strain measurements ........................................................................... 62

3.3. RESULTS ................................................................................................................................................. 63

3.3.1. Stress‐strain curve and DIC strain measurements ....................................................................... 63

3.3.2. High resolution DIC strain measurements ................................................................................... 67

3.3.3. Strain measurements across grain boundaries ............................................................................ 70

3.4. DISCUSSION ............................................................................................................................................. 73

CHAPTER 4

DAMAGE ACCUMULATION ON Γ‐TIAL ......................................................................................................... 75

4.1 MANUFACTURING PROCESS ........................................................................................................................ 75

4.2 MATERIAL ............................................................................................................................................... 77

4.2.1 Microstructure ............................................................................................................................. 77

4.3 FATIGUE EXPERIMENTS WITH PLAIN SPECIMENS .............................................................................................. 80

4.3.1 Experimental set‐up ..................................................................................................................... 80

4.3.2 Results .......................................................................................................................................... 80

4.4 FATIGUE EXPERIMENTS WITH ARTIFICIAL DEFECTS ............................................................................................ 82

3


4.4.2 Results.......................................................................................................................................... 82

4.5 FATIGUE CRACK GROWTH EXPERIMENTS ........................................................................................................ 84


4.5.2 Results.......................................................................................................................................... 86

4.6 UNIAXIAL STATIC EXPERIMENTS USING DIC .................................................................................................... 90


4.6.2 Results.......................................................................................................................................... 92

4.6.3 Compression experiment ............................................................................................................. 92

4.6.4 Tension experiment ..................................................................................................................... 93

4.7 FINAL CONSIDERATIONS ............................................................................................................................. 95

CHAPTER 5

CONCLUDING REMARKS AND FUTURE DEVELOPMENTS ............................................................................. 97

5.5 CONCLUDING REMARKS ............................................................................................................................. 97

5.1.1. Results of Chapter 2 ..................................................................................................................... 97



5.2. FUTURE DEVELOPMENTS ............................................................................................................................ 99

5.2.1. High Temperature experiments on FeCr ...................................................................................... 99

5.2.2. Ex Situ Digital Image Correlation using SEM ............................................................................. 102

REFERENCES ............................................................................................................................................ 105

5

Introduction

The characterization of the material behavior under the effect of static or repeated loads is one of the

largest and most studied research field for mechanical and material science engineers. Nevertheless

the abilities to predict mechanical behaviors of materials increased in the last decades, new and

more reliable models are necessary in order to improve the quality and the safety of the component

design. The increased ability to predict material behavior resides in the ability of the scientists to

decrease the length-scales of the observations of the deformation mechanisms (micro and nano

scales), and use this knowledge for predicting the global mechanical behavior (macroscopic scale).

From the experimental point of view the investigation at the micro and nano scales involve different

difficulties which are not encountered using the classical approaches on the continuous medium

scale. First of all the active deformation mechanisms (slip and twin) depend on the atomistic structure

of the analyzed material. In addition, the active deformation mechanisms are typically strongly

dependent on the testing and environmental conditions: temperature, strain rate, etc., so the

analyses need to be implemented at specific and defined conditions. Another important aspect to

consider for these approaches is the limited area which can be studied. Since the phenomena

involving dislocation motions are observed at nano-scales, the target area is small, and a general

picture of the phenomena at meso-scale is difficult to draw. The main idea pursued in this work is to

link the phenomena which occur at micro-level (slip and twin) with the resolved strains on the meso-

scale. Experimentally, Digital Image Correlation (DIC) was used to investigate the local strain

heterogeneities on the sample surface and correlate them with the microscopically activated

deformation mechanisms.

In the following sections the main research areas covered in this work are introduced, along with an

introduction to the materials under investigation. Section I.1 gives an overview of the experimental

methodology adopted. Section I.2 introduces the study on FeCr single crystals, focusing on the

experimental determination of the critical resolved shear stresses for slip onset, twin nucleation and

migration. Section I.3 presents the fundamentals of the work on the FeCr polycrystal samples, DIC is

used to measure strain changes across the grain boundaries in order to correlate the microstructural

grain boundary behavior with the strains measured on the macro-scale. Finally, Section I.4

introduces the study on one γ-TiAl alloy in order to work out the effect of the microstructure on the

fatigue behavior for these alloys.

I.1. Ex

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7

Generally speaking, deformation mechanisms (slip and twinning) produce local strain heterogeneities

on the sample surface. Adopting an in-situ DIC set-up is possible to capture the onset of slip and

twinning measuring the localized strains on the sample area detected with the camera. This

experimental set-up is particularly suited for the experiments on the FeCr single crystal samples,

since the analyzed sample areas are characterized by the same crystal orientation, thus displaying

an homogeneous mechanical behavior in terms of active twin and slip systems. Moving the attention

to the polycrystal cases (FeCr and γ-TiAl alloy), the adoption of the DIC in-situ set-up is not adapted

for capturing local strain heterogeneities and correlate them with the local microstructure. In fact, for

these cases, the microstructure is small compared with the strain resolution typically used for in-situ

applications. Higher image resolutions are required, and they can be obtained only using ex-situ DIC.

The characteristics of the implementation of in-situ and ex-situ DIC are described in Chapter 1. In

particular, the chapter explains the different DIC applications for the specific cases addressed along

the work.

I.2. Twinnucleationandmigration,sliponsetinFeCrsinglecrystals

Chapter 1 presents the experimental results obtained from experiments on iron-chromium (FeCr)

single crystal samples loaded along selected crystal orientations. Understanding the deformation

response of iron based body-centered cubic (bcc) alloys has significant merit, as these alloys form

the basis of materials that are widely utilized in structures. In particular, the Fe-Cr alloys are widely

used in chemical and nuclear applications. For common structural applications, the percentage of

chromium content doesn’t exceed 30 at. pct. since higher chromium contents favor cleavage

fractures, as a consequence of the high stresses present at twin-twin intersections [14-16]. However,

adopting heat treatments that remove interstitial impurities drastically improve the brittleness of these

alloys, and good mechanical properties (in particular ductility) are obtained. It is of great importance

to provide a complete material characterization for these alloys, which can be also useful in order to

gain further insides into the mechanical behavior of bcc materials. The majority of the previous

investigations on FeCr alloys were carried out on polycrystals [17-22], whereas in the first part of this

study single crystals have been employed to activate specific twin and slip systems.

Macroscopically, deformation by slip is accommodated by the sliding of planes of atoms one over the

other as schematically reported in Figure I.2a. From the atomistic point of view, slip is originated by

dislocation motion. Depending on the crystal structure (fcc, bcc, hcp) different crystallographic planes

and different shear directions can be activated. For bcc materials, the typical slip planes are

contained on the well-known 011{ } , 112{ } , 123{ } families of planes, while the directions are

contained on the 111 family.

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9

Another important aspect of this approach is that the use of specimens manufactured as single

crystals with a specific crystal orientation in the load direction enables to study separately crystal

orientations which display predominantly slip and crystal orientations that display also twinning. The

complexity of using a polycrystal material relates to the difficulties of neglecting the effects of the

grain boundaries, and more important, the random choice of the grain orientation. The idea pursued

here is to load statically (in compression and tension) and study each selected crystal orientation

using a defined experimental approach (crystal orientation from EBSD and strain measurements

from DIC), and provide for each orientation the evolution of the local strain fields associated with slip

and twinning. Since by using DIC methodology it is also possible to capture the real-time evolution of

the strains during loading, the first point of the analysis is the measure of the exact point of twin and

slip nucleation along the stress-strain curve. Different works dealt already the existence of a critical

resolved shear stress for both slip and twinning. In particular, it is well established that the resolved

shear stress for twinning is constant when different factors are fixed: alloy composition, temperature,

strain rate, etc. For an exhaustive review on this topic and references see [23]. Many studies have

been carried out on the dependence of these factors on the occurrence of twinning, but less interest

has been devoted in understanding what is the effect of twinning on the local strain field, and more

important what is the effect on the crystal behavior based on the point of twin nucleation on the

stress-strain curve. In this sense, the use of EBSD and DIC can shed light into the study of twin

nucleation and subsequent twin growth, in particular in terms of associated strain fields. Moreover,

this work can provide a solid basis of experimental results which can be useful for understanding the

subsequent slip and twin evolution (for example twin migration) and the interactions (slip/twin,

slip/slip and twin/twin). In fact, since all the observed slip and twin systems have been indexed, the

results can also be useful for testing plasticity framework based on active slip and twin systems.

These concepts can be better understood analyzing the schematic proposed in Figure I.3 (obtained

from the experiments proposed in Chapter 2) which represents a conceptual summary of the different

stress-strain curves based on the load direction and the crystal orientation for bcc alloys. The stress-

strain curves reported in Figure I.3 schematize the different possible mechanical behaviors of the

FeCr single crystals depending on the active deformation mechanism (slip and/or twinning). It is

evident that, based on the active slip/twin systems, a different level of crystal hardening is observed,

along with a completely different mechanical behavior. Case (a) a load drop occurring in the

nominally elastic part of the stress-strain curve characterizes the deformation behavior for the

analyzed crystal orientation. The open questions are: what is the mechanism which leads to the

observed load drop (slip or twinning)? The deformation mechanisms preceding and following the load

drop are the same? What is the influence of the deformation mechanism activated during the load

drop on the subsequent crystal deformation? Case (b) describes a slightly different crystal behavior,

in fact along the stress-strain curve the load drop is preceded by a flat region which is characterized

by an active deformation mechanism which doesn’t provide hardening till the load drop. Also in this

case it is

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can represe

on occurring

of the alloy

ercome an e

these

other

s have

tion of

on the

dulus.

s work

Cr on ad ip

effect

ctions,

ent an

at the

y. For

energy

11

barrier in order to react with the twin boundary [31], thus leading to an increment of the material

strength. Twin-twin and twin-slip interactions can be beneficial for the strengthening of the material,

but on the other side, the intersection regions can promote high strain and stress localizations. For

example, twin-twin interactions are well-known for generating high localized stresses in the region of

interaction, in particular when one twin is blocked in front of another twin [32-34]. Moreover, when

loaded in tension, the reaction between some of the possible active twin systems for a particular

crystal orientation can lead to the formation of the Cottrell dislocation which leads to cleavage

fractures [32]. In general, in order to study the effect of the twin-twin interaction observed, it is useful

to study the possible outcome in terms of dislocation reaction. For bcc materials different authors

provided experimental studies showing the possible twin-twin and twin-slip reactions and the

consequences on the mechanical behavior, see for example [35-38]. It is not the objective of the

present work to focus on each twin-twin and twin-slip interaction observed and study the possible

dislocation reactions. On the other side, giving the local strain measurements in correspondence of

the twin-twin and twin-slip interactions can help in understanding the role of the interactions on the

observed crystal hardening.

I.3. SliptransmissionthroughGrainBoundariesinFeCr

Considerable research efforts have been devoted to incorporate dislocation slip at the crystal level to

predict the overall response of metals. Substantial progress has been gained in predicting crystal

orientation effects, strain hardening [39], slip-twin interactions [40], and change in crystallographic

texture [41, 42]. Grain boundaries have been treated as a contributor to geometric hardening and the

obstacle length has been incorporated in the models [40]. These models typically allow for predicting

the overall macroscopic stress-strain response upon use of various homogenization schemes.

Further advances in these models should encompass developments on grain boundary specifics. In

fact, one of the strengthening mechanism at grain level is provided by the presence of grain

boundaries which influence the slip dislocation transmission process. Grain boundaries act as a

barrier to dislocation motion, thus inducing a contribution to the hardening of the alloy. The level of

strengthening of the grain boundaries depends on the incoming and outgoing slip because of the

different residual Burgers vectors that remain at the boundary. The level of strengthening associated

with the grain boundaries can be quantified measuring the energetics of the slip transfer process.

Using molecular dynamics simulations, Abuzaid at all established the energy barrier levels for

different grain boundaries [43]. In particular, they analyzed different grain boundary specifics,

showing that high energy barriers result in case of high residual Burgers vector magnitudes. The

influence of the grain boundary specifics on the slip dislocation-GB interactions can also be

experimentally studied on the meso-scales, since the slip transmission process influences the local

deformation behavior at the grain boundaries. Over the years, studies examining dislocation-grain

boundary interactions have been undertaken [44-47]. Historically, experiments on slip transmission

were cond

techniques

Grain Bou

vector of

preceding

experimen

boundaries

through g

boundaries

systems th

in order to

formation,

introduced

one main s

In this sc

dislocation

Figuretransmdislocadisloca

ducted with o

s different a

ndary (see f

the residual

paragraphs

nts [49-53], e

s. The idea

grain bounda

s, and corre

hrough the g

o remove oth

strain aging

d by dislocati

slip system,

enario, the

n-grain bound

e I.4a. Sl imission, i.eation on thations are in

optical micro

uthors estab

for example [

l dislocation

s, experime

etc., provide

pursued in C

aries on th

elate these s

rain interface

er hardening

g in steels

ion-grain bou

even the pos

selected Fe

dary interact

p dislocati. cross sl ipe grain bouncorporated

oscopes or,

blished a ser

[48]). The ma

left at the

ental techniq

an exhaustiv

Chapter 3 is

he meso-sca

strain fields w

es. The use

g factors (for

[54]), allowe

undary intera

ssible harden

eCr polycrys

ions.

on-GB intep; b) directundary; c) inside the g

12

more recen

ries of poss

ain outcome

grain bound

ques such

ve, but locali

to study and

ale measuri

with the inte

of the FeCr

r example fin

ed to focus

actions. Sinc

ning introduc

stal represen

eractions int transmissindirect tragrain bound

tly, using TE

ible dislocat

e of these stu

dary. As alre

as TEM, m

ized analysis

d analyze th

ng the loca

eraction of th

polycrystal s

ne dispersion

the study o

ce every gra

ced by slip-s

nts the perfe

n polycrystsion with gnsmission;

dary.

EM (Figure I

ion reactions

udies is the r

eady briefly

micro and

s of the proc

he slip transm

al strain fie

he incoming

samples, pro

ns of hard pa

only on the

in analyzed

lip interaction

ect material

al materialeneration od) no trans

I.4b). Using

s occurring

role of the Bu

discussed

nano inden

cesses at the

mission proc

elds across

and outgoin

operly heat-tr

articles, mart

crystal hard

also display

ns is avoided

for studyin

ls: a) direof a residusmission, th

these

at the

urgers

in the

ntation

e grain

cesses

grain

ng slip

reated

ensite

dening

s only

d [55].

g slip

ct al

he

FDrebdb

Clark

outco

carrie

boun

obtain

grain

in two

the g

outgo

furthe

calcu

with t

depe

the a

From

react

the e

It is o

react

The i

speci

igure I.4b. Direct transfeesidual dislooundary froislocations oundary.

k et al. [56]

omes of the d

ed out here.

dary interac

ned via TEM

boundaries

o adjacent g

grain bounda

oing dislocat

er insight int

ulations of the

the grain int

nd on the m

doption of si

m the experim

ions propose

entire grain b

of high intere

ion occurring

idea pursued

ific slip-GB i

Examples er of dislocaocation left om an area

and the g

and Lee at

dislocation re

. The schem

ction mecha

M reported in

analyzed in

rains. The g

ary as a cons

tions from th

to energetic

e energy ba

terface. In pa

agnitude of t

mulation too

mental point

ed adopting

boundary, an

st to analyze

g at the inte

d here is to

nteraction, a

of sl ip tranation througat the grain

a different tgrain bound

t al. [48] uti

eactions occ

matic propos

nisms. The

Figure I.4b (

the present

eneral react

sequence of

he grain bou

s of these r

rriers which

articular, Eza

the residual

ols allow to fu

t of view, st

these simula

d thus on th

e the entire g

rface with th

use local s

as a tool to e

13

nsmission stgh the grain n boundary;than the podary; (d) s

lized in situ

curring at a G

sed in Figure

schematic

(from [48]). I

t work, only o

tion provides

f the interact

undary. Rece

reactions [3

need to be o

az and co-w

Burgers vec

ully characte

tudies adopt

ations. On th

he general po

grain bounda

he behavior

strain measu

experimenta

tudies usingboundary; (

; (c) Dislocaoint of interl ip dislocat

TEM image

GB. Such stu

e I.4a illustr

is paired w

n the cases

one slip syst

s an estimatio

tion between

ently, advan

1, 57, 58]. S

overcome by

workers [31]

ctor left at the

rize one sing

ting TEM (se

he other side

olycrystal be

ary, and try to

of the grain

rements, e.

lly quantify t

g in situ TE(b) Dislocatation emissiraction betwions absor

es and char

udies form th

ates the pos

with the expe

presented in

tem in each

on of the res

n the incomin

ced simulati

Such studie

y a slip dislo

showed that

e grain boun

gular local ev

ee Figure I.4

e, the effects

havior, has r

o link the out

interface se

g. the strain

the role of th

EM, from [4ion transferion from theween the inbed at the

racterized th

he basis of th

ssible disloc

erimental ob

n Figure I.4b

grain is typi

sidual disloca

ng dislocatio

ion tools als

es provide fu

ocation in ord

t these ener

ndary. In resp

vent on the n

4b) allow to

s of these re

received les

tcome of the

een on the m

n gradients

he grain bou

48]: (a) with a e grain ncident e grain

he possible

he analysis

cation-grain

bservations

, and in the

cally active

ation left at

ons and the

so provided

undamental

der to react

rgy barriers

pect to this,

nano-scale.

o verify the

eactions on

s attention.

dislocation

meso-scale.

following a

undaries on

14

the meso-scale. To this aim, Chapter 3 analyzes and correlates the potential outcome of the

dislocation reactions (local parameter) with the measured strain changes across grain boundaries

(meso-scale behavior). The open question is: is there any possible parameter which is able to

describe an average grain boundary behavior? Chapter 3 aims to answer this question, and shed

further light into the localization of plastic strains due to dislocation-GB interactions.

I.4. Strainlocalizationsinaγ‐TiAlalloy

Gamma titanium aluminide based alloys (γ-TiAl) have become an important alternative for high

temperature structural applications in the aircraft industry to supplant current nickel-based

superalloys as the material of choice for low-pressure turbine blades [59, 60]. The advantages

achieved by the use of γ-TiAl intermetallics are principally their low density (3.9-4.2 g/cm3 as a

function of their composition [61]), high specific yield strength, high specific stiffness, substantial

resistance to oxidation and good creep properties up to high temperatures. Although the application

of such materials appears very encouraging for the turbine engine industry, optimizing the

performance improvements requires more advanced approaches to accurately predict fatigue

strength and to demonstrate the damage tolerance of TiAl materials with respect to intrinsic or

service-generated defects. Therefore, there is a need to understand and address the specific fatigue

properties of these materials to assure adequate reliability of these alloys in structural applications

[62]. The peculiarity of the alloy analyzed here is that components (and thus the samples) are

manufactured using Electron Beam melting (EBM) technology. EBM is a technology based on a

manufacturing process “layer by layer”, which allows a drastic reduction of the presence of defects

such as inclusions, pores etc. In this scenario the influence of the material microstructure on the

fatigue resistance becomes more important since the possible crack initiation sites are found in

correspondence of defined microstructural features.

Figure I.5 shows the typical microstructures generally present on γ-TiAl alloys (this alloy is also

indicated as a duplex microstructure alloy): the equiaxed grains and the lamellar colonies. The

regions marked in red represent the critical regions for these alloys in terms of potential crack

nucleation sites. Strains can accumulate at the grain boundaries as other polycrystalline materials

(line marked (a) in Figure I.5a), or localized strains are detected in grain boundary regions where

twins are blocked [63], or in triple points where strain incompatibilities are large [64]. The presence of

the lamellar colonies create other potential sites where cracks can nucleate, for example as a

consequence of the interfacial delamination and decohesion of the lamellar colonies [65].

Finlas

Anoth

and

incom

(c) in

with

phase

48Al-

quant

exper

smoo

gene

initiat

ex-sit

discu

igure I.5. Pnterface betamellar colol ip blockage

her importan

α2-Ti3Al) in

mpatibility ins

n Figure I.5c)

the presenc

es. Chapter

-2Cr-2Nb allo

tify the mai

rimental resu

oth samples,

ral characte

tion sites are

tu DIC strai

ussed in the f

Potential cratween two eony; c) decoe at lamellae

nt factor whic

the same

side the lam

). It is eviden

ce of the tw

4 investigate

oy with the

in detriment

ults are pres

, fatigue of

rization of th

e discovered

n measurem

first part of th

ck init iationequiaxed graohesion bete interfaces

ch influences

microstructu

mellar packag

nt that each

wo microstru

es the mecha

aim to prop

al damage

sented. In the

samples wit

he alloy. Fro

. In the seco

ments which

he chapter.

15

n sites due tains; b) intetween lamel.

s the fatigue

ure (i.e. the

ge, thus favo

of these po

uctures, their

anical behav

pose an expe

mechanism

e first part c

th artificial d

om these ex

ond part more

confirm the

to the microerface betwlla phases o

behavior is

e lamellar c

oring the dec

tential dama

r geometries

vior of the ga

erimental me

s at micros

lassical expe

defects, crac

xperiments p

e information

e main crac

structure foeen an equor micro-cra

the presence

colony) whic

cohesion ph

age mechani

s, and the v

amma titanium

ethodology a

tructural lev

erimental me

ck propagati

preliminary in

n are obtaine

k nucleation

r a γ-TiAl aiaxed grain

acking indu

e of two pha

ch creates

henomena (li

isms are stri

volume frac

m aluminide

able to inves

vel. Two ma

ethodologies

ion) are ado

nformation a

ed using high

n sites disco

lloy: a) and a ced by

ases (γ-TiAl

an elastic

ine marked

ctly related

tion of the

(γ-TiAl) Ti-

stigate and

ain sets of

s (fatigue of

opted for a

about crack

h resolution

overed and

17

Chapter1

Experimentalmethodology

The present work is characterized by an extensive usage of experimental strain measurements

obtained via digital image correlation (DIC) methodology. An exhaustive reference on this technique

is contained in [2]. In this chapter are briefly introduced the basic concepts and the details of the

experimental techniques adopted along the work. Strain measurements from DIC and crystal

orientations from electron back scattered diffraction methodologies (EBSD) were mainly used for

studying the local strain fields associated with the different deformation mechanisms (slip, twinning,

slip transmission across grain boundaries, twin-twin and twin-slip interactions). Each application

requires a specific experimental set-up which will be analyzed in this chapter.

Section 1.1 contains general details on the DIC methodology. The first application of DIC is

introduced in Section 1.2 with the measurements of the twin nucleation and migration stresses. The

measurement of the stress required to initiate slip is analyzed separately in Section 1.3. High

resolution strain measurements were also used to capture the strain changes across grain

boundaries (GBs) on FeCr polycrystal (Section 1.4), the same section also provides the details of the

strain averaging process. Finally, section 1.5 describes the slip and twin indexing calculations using

grain orientations from EBSD and slip/twin traces on the sample surface.

1.1. DigitalImageCorrelation

DIC is a non-contact methodology for measuring local displacements on a flat area of the sample

surface. The extension of the analyzed area depends on the research purposes that indicate the

image resolution required (macro-scale, meso-scale, micro-scale, nano-scale), on the type of strain

measurements (real time or out of the load frame), on the available experimental set-up (lens,

camera), and on the preparation of the surface. The technique is based on reproducing on the target

surface a random speckle pattern which results in a groups of pixels on the grey scale (from 0 to

255) in the images captured with a monochrome digital camera. This speckle pattern can be

produced using different methodologies, in particular its preparation depends on the resolution

adopted for the images. For example, it is possible to obtain the speckle pattern painting the sample

using a commercial airbrush and a black paint. In other cases for which higher image resolutions are

required (i.e. for measuring the strain localization produced by slip) a different procedure for

generating

application

Figurepixel o

Figure 1.1

sample at

the applica

deformatio

square gr

(deformed

more than

visual prog

subsets in

of the sub

deposition

pixels. Th

defined ma

the resolut

mean size

has been

period grid

subset spa

subset). U

g the speckle

n in terms of

e 1.1. DIC on the defor

shows an e

zero load, w

ation of a lo

on of the sam

oupings of

) image is n

n one possib

gram used in

the deforme

bset (correla

, are typicall

e length of

arker that ca

tion of the im

e of the spec

successfully

d pattern us

acing which

Usually the ty

e patterns is

image resolu

technique ismed image,

xample of a

while the defo

oad. In this c

mple surface.

pixels called

ot unique. F

bility exists f

n this work (V

ed image, th

ation point).

ly used subs

the edge n

an be localize

mages strictly

ckle features

y used by d

sed in grid m

represents t

ypical subset

used. The a

ution is the c

s based on it is not po

speckle patt

ormed image

case the pix

. The ability o

d subsets, s

or example,

for the pixel

VIC 2D) cont

us allowing t

In this wor

set sizes from

eeds to con

ed in the def

y depends on

s. In the pres

ifferent auth

methods. An

the number o

t spacing ran

18

ability to gen

critical point o

the recognossible to tra

tern. The firs

e represents

xels on the s

of the DIC al

since the po

as shown in

with value

tains adapted

the definition

rk, with the

m 31 to 51 p

ntain a suffic

formed imag

n the quality

sent work is

ors (see i.e.

nother impor

of pixels bet

nges from 5 t

nerate the co

of the DIC m

nit ion of theack one sing

st reference i

the same ar

second imag

lgorithms res

osition of th

n Figure 1.1,

50 in the se

d algorithms

n of the vect

adopted m

ixels for eac

cient group

ge. It follows

of the speck

s adopted a

. [66]), and

rtant parame

ween each c

to 10 pixels

orrect speckl

ethodology.

e posit ion ofgle pixel.

mage is capt

rea of the spe

ges moved f

sides in track

e single pix

for the first

econd (defor

for defining

or displacem

methodologies

h edge of th

of pixels wh

that the cap

kle pattern, in

random spe

it is conside

eter for the

correlation p

(in the prese

le for the req

f a subset

tured on the

eckle pattern

following the

king the posit

xel in the se

(reference)

rmed) image

the position

ment for the c

s for the sp

he square gro

hich represe

pability to inc

n particular o

eckle patter,

ered better t

correlation

point (center

ent work is a

quired

of

virgin

n after

e local

tion of

econd

image

e. The

of the

center

peckle

oup of

ents a

crease

on the

which

han a

is the

of the

always

19

used 5 pixels). Repeating the process for different points inside the reference image determines the

displacement field of the deformed image.

Along this work DIC is used in two different modalities:

In situ DIC; the deformed images are captured during the experiment, the strain fields

obtained represent a real-time strain measurement.

Ex situ DIC; both the reference and deformed images are captured out of the load frame (at

zero load), the strain fields obtained represent the residual strains that remain on the sample

surface.

Digital image correlation is used to measure the evolution of local strains, in situ, on a full field basis

[11, 12, 67, 68]. In addition to in situ DIC (sample under stress in the load frame), was also used

higher resolution DIC strain measurements obtained ex situ (out of the load frame) for analyzing the

local effect of slip and twinning. In the following sections are described the methodologies along with

examples of the adopted speckles for both in situ and ex situ DIC.

1.1.1. InsituDIC

The typical experimental set-up for the implementation of in situ DIC is shown in Figure 1.2, in the

schematic is described a tension experiment. The nominal strain is measured using an

extensometer, and the strain signal is used to control the load during the experiment. An IMI model

IMB-202 FT CCD camera (1600 x 1200 pixels) with a Navitar optical lens (the resolved resolution is

about 3.0 μm/px) was used to capture the reference and deformed images. Using a dedicated

software was possible to capture the images during the loading and un-loading steps at an arbitrary

time interval. This DIC set-up is adapted for measuring increments of deformation, in situ DIC is also

referred to be a real time strain acquisition technique. The speckle pattern for DIC was obtained

using black paint and an Iwata Micron B airbrush. An example of the speckle pattern used for in situ

DIC is shown in Figure 1.3, in this case is shown a compression sample. This speckle pattern allows

to use a subset size of 51 px (4 μm/px).

Figurethe cacapturrefere

Figurecamerusing

magni

Typically, t

mm x 5 m

for examp

deformatio

allows to

e 1.2. Expeamera are cring imagesnce image i

e 1.3. Imagea (1600 x 1black paint

f ication ado

the speckle

m region (se

ple crack cl

on mechanis

capture a s

rimental secontrolled b during thes captured

e of the sam200 pixels) and an Iwa

opted is 51 p

pattern gene

ee Figure 1.3

losure meas

ms (slip/twin

significant po

t-up for they a central experimenbefore the e

mple surfacewith a Navi

ata Micron B

px (200 μm)

erated with th

3). Using this

surements d

n) for fcc mat

ortion of the

20

e in situ DICcomputer.

t providing experiment a

e captured uitar optical lB airbrush. T

.

he airbrush i

s DIC set-up

during fatigu

terials [70]. I

e surface in

C methodoloA monochra real t ime

at zero-load

using an IMIens. The spThe approxi

s adapted fo

several app

ue [69], or

n the presen

nvolved in th

ogy. The loaome camera

e image acq.

model IMBpeckle pattemate subse

or strain mea

plications can

similar stud

nt case, the s

he deformati

ad frame ana is used fquisit ion. Th

B-202 FT CCer is produceet size for th

asurements o

n be impleme

dies on act

selected DIC

ion, and wit

nd or he

CD ed he

on a 4

ented,

ivated

C area

th the

adopt

exam

Fin

Finall

nucle

1.1.2

For e

micro

image

meas

chara

twin-s

The a

when

intera

resolu

exper

increa

targe

the a

not fo

and r

sectio

cover

40 x 4

ted resolutio

mple Figure 1

igure 1.4 . ntroduced by

ly, as deform

eation and tw

2. Exsi

ex situ DIC, a

oscope allow

es (2x vers

surement res

acterization o

slip and slip-

adoption of e

n a local eva

action mecha

ution images

rimental poi

ased resolut

et area can m

pplied load.

ound on the

relates to the

on of the ten

ring all the s

4 = 160 imag

on strain hete

.4).

Strain hetey twinning a

mation meas

win migration

ituDIC

an optical mic

ws the images

sus 20x for

solution (3.0

of the local s

-slip interactio

ex situ high

aluation of t

anism (slip/s

s (from a min

nt of view.

tion the cove

move out of t

In this case

sequent def

e number of

nsion sample

urface of the

ges are need

erogeneities

rogeneit ies are much hig

surements v

can be eval

croscope wa

s to be captu

ex situ). T

0 μm/pixel v

train magnitu

on regions.

resolution D

he strain fie

slip, twin/slip

nimum resolu

First of all

ered region

he area cove

the correlat

formed imag

images to be

e, using the 5

e sample. Inc

ded in this ca

21

derived from

introducedgher than th

via in situ D

uated using

as used to ca

ured at a mu

The increas

versus 0.44

udes that are

DIC provides

eld is needed

p, slip/slip, s

ution of abou

real time a

becomes sm

ered by the c

ion cannot b

ges. A secon

e acquired. A

5x set up (re

creasing the

ase. If a furth

m slip or twin

by sl ip anhat of sl ip.

IC are made

the full field

apture the re

uch higher m

sed imaging

μm/pixel for

e associated

s the necess

d in order to

slip/GB). On

ut 1 µm/px) i

cquisition is

maller. It follo

camera beca

be implemen

nd issue is s

Adopting ex

esolution 0.87

image resolu

her incremen

nning can be

d twinning.

e real time,

strain contou

ference and

agnification

magnificati

r ex situ) [6

with slip-gra

ary strain fie

o study the

the other s

ntroduces m

partially ex

ows that dur

ause of the s

ted since the

chematically

situ DIC, for

7 µm/px) 40

ution (10x, re

nt of the imag

e recognized

The local

the onset o

ur plots obta

deformed im

compared to

on improve

66] and ena

ain boundary

eld resolution

particular ef

ide, the usa

more difficultie

xcluded sinc

ring the expe

specimen mo

e reference

y reported in

r covering the

images are

esolution 0.4

ge resolution

(see as an

strains

of slip, twin

ined.

mages. The

o the in situ

s the DIC

bles better

y, twin-twin,

ns required

ffect of the

age of high

es from the

ce with the

eriment the

oves due to

images are

Figure 1.5

e entire net

needed for

437 µm/px),

n is needed

(20x, reso

resolution

Moreover,

deformatio

introduce a

Figureallow sampleorder imageresolu

An examp

The rando

µm/px. In t

implement

contained

olution 0.22 µ

is required

further incr

ons the out-o

a problem on

e 1.5. Imagto use diff

es can be to improve s (10x), wtion (20x).

ple of the spe

om speckle

the inset ima

ted with the

inside the su

µm/px), a tot

, the numbe

rements of t

of-plane disp

n maintaining

ge acquisit ioferent opticcovered st ithe strain f i

while 640 im

eckle patter a

pattern is pa

age of Figure

adopted spe

ubset, this is

tal of 160 x

er of image

the resolutio

placements (

g a uniform fo

on for ex scal microsctching 40 ield resolutimages are

adopted for t

articularly ad

e 1.6 is also r

eckle. It is p

a first indica

22

4 = 640 ima

es quickly in

on limit the

(and potenti

focus of the i

itu DIC. Thope magnifmages withon is possib

needed w

the ex situ D

dapted for im

reported the

possible to n

ation of the g

ages are req

ncreases wit

applicable lo

ally also the

mage.

he adopted f ications. Th a nominalble to cover

with a furth

DIC along thi

mages captu

typical subs

notice that th

oodness of t

quired. So, w

h the adopt

oads since w

e non-planari

speckle forhe area of magnif icat

r the same aer improve

s work is sho

ured with a

et selected f

he features o

the correlatio

when a high

ted magnific

with high le

ity of the su

r ex situ Df the tensiot ion of 5x. area with 16ement of th

own in Figur

resolution o

for the correl

of the speck

on.

strain

cation.

evel of

urface)

IC on In

60 he

re 1.6.

f 0.44

ations

kle are

FTe

is

1.1.3

A sim

in Fig

the lo

the ce

(2.37

left,

meas

the s

using

the a

provid

strain

possi

evolu

igure 1.6. he sample x situ high

s 45 px (20

3. Insi

mple compari

gure 1.7. Th

oading axis o

entral part of

7 µm/px) cap

is possible

surements on

ame main sl

g the in situ s

analysis of t

ded much m

n fields is pos

ible activate

ution of the st

Image of thsurface is uresolution D

μm).

tuversus

ison between

e strain field

oriented 10[

f the sample

tured at zero

to notice th

n the same r

lip system, in

set-up was no

the strain fie

more informat

ssible to defi

d slip system

train associa

he sample sused for theDIC. The ap

exsituDI

n the strain r

ds reported r

1] . The stra

. It is obtaine

o load. From

he strain lo

region using

n addition tra

ot possible to

elds obtaine

tion than the

ine the strain

ms. In situ,

ated with thes

23

surface capte correlation

proximate s

IC

resolutions a

refer to a sta

ain field in th

ed correlating

m this strain f

ocalization d

g ex situ DIC

aces on a se

o clearly reco

ed combining

e adoption of

n introduced

supported b

se slip syste

tured using n providing asubset size

associated w

atic tension e

he bottom rep

g and stitchin

field, and fro

due to slip

at the a res

econdary slip

ognize the se

g the results

f only one se

by different

by the ex si

ms during th

an optical a speckle pfor the mag

with is-situ an

experiment o

presents the

ng 5 images

m the assoc

on one ma

solution of 0.

p system are

econdary slip

s using diffe

et up. In parti

slip systems

tu data, can

he deformatio

microscopeattern adap

gnif ication a

nd ex-situ DI

on a single c

e residual str

s using the in

ciated region

ain slip syst

.87 µm/px (5

e detected. In

p system. It f

erent strain

icular using

s, and so loca

n be used to

on.

(10x). ted for dopted

C is shown

crystal with

ain field for

n situ set up

in the top-

tem. Strain

5x) displays

n this case,

follows that

resolutions

ex situ DIC

alize all the

o track the

Figureobtainresoluactive

e 1.7. Comped with in-stion obtainedeformation

parison betwsitu DIC anded using exn mechanism

ween strain d ex situ DICx situ DIC m (slip or tw

24

f ields displaC methodoloallows to c

win).

aying strainogies for a scorrelate th

localizationsingle crystae strain f ie

ns due to slal. The stra

eld with eac

ip in

ch

25

1.2. DIC application formeasuringTwinNucleation andMigration

stressesinFeCrsinglecrystals

As introduced in Chapter I, adopting in situ DIC in conjunction with EBSD, the mechanical behavior in

terms of active slip and twin systems for different FeCr single crystal orientations was studied (see

Chapter 2). Real time strain fields enable to capture the strain heterogeneities associated with slip, or

twinning, during loading. In particular the application of this methodology for the selected single

crystals allow to establish the points on the stress-strain curve where slip and twin nucleate, and

follow the associated local strain evolution. The main advantage of using DIC relates to the possibility

to quantify the local strain values associated with the deformation mechanisms. Typically, for bcc

materials twin nucleation can also be identified on the stress-strain curve when a load drop occurs. In

some cases the load drop can occur even in the 'elastic' region of the stress-strain curve [23, 71]. It is

always better to verify the presence of twinned regions on the sample using for example EBSD, since

for some bcc materials, under particular conditions, also slip nucleation can produce noticeable load

drops [23]. In the following, all the crystal orientations displaying twinning have been successively

analyzed using EBSD and, in some cases, also Transmission Electron Microscope (TEM). Moreover,

as already described in the previous section, the local strains associated with slip and twinning are

different. It follows that twinning can also be detected when a high local strain increment is measured

following the load drop.

In general, depending on the alloy composition and in particular grain orientations, twinning can

occur in conjunction with slip resulting in complex mechanical behavior which is difficult to detect and

track with classical experimental approaches. For example, following twin nucleation at a critical

resolved shear stress level (CRSS) τT, usually twin migration proceeds at a stress level τM which is

lower [23]. Twin migration is also the result of twin-twin and twin-slip dislocation reactions occurring

at twin boundaries. Experimental evidence of twin migration, supported by local strain

measurements, can provide further insight for developments of bcc plasticity models, in particular on

the hardening effect related to twin growth induced by twin/slip interactions. From the experimental

point of view, measuring τT and τM requires local strain measurements and knowledge of the

activated twin systems. The idea is to establish the twin nucleation and migration stresses using real

time in situ strain measurements. In the following section are described the experimental details

adopting incremental in situ DIC for correctly detect the τT and τM stresses.

1.2.1. IncrementalDigitalImageCorrelation

The complexity of the strain fields when both slip and twin activate and provide strain localizations

can be overcome using in situ incremental DIC. The idea is described schematically in Figure 1.8. In

the schematic is represented a general stress-strain curve for a crystal orientation that displays both

slip and tw

marked. E

point on th

between th

initiation o

Figureand twenabledetails

Following

between th

system. Tw

the Refere

provided b

contributio

the stress-

for examp

contributio

developed

winning defor

Each point re

he stress-str

he reference

n the meso-s

e 1.8. Schemwin migratioes the charas).

the stress-s

he Referenc

win nucleatio

ence Image w

by the strain

ons due to sl

-strain curve

ple, the cor

on of twin n

d till Image 2

rmation for a

efers to a pa

ain curve ma

e Image and

scale.

matic of theon stressesacterization

strain curve,

ce Image with

on occurs be

with Image 3

fields of bo

ip and twinn

e using as th

rrelation betw

nucleation o

2. An examp

particular lo

articular ima

arked as Ima

the Image 1

process for using in sof the stra

only one m

h Image 2 q

etween Image

3 provides th

th slip and t

ing. Increme

e reference

ween Image

on the strain

ple of strain

26

oad direction

age captured

age 1 refers

1 enables to

r the identifsitu DIC. Uin associate

main slip syst

uantifies the

e 2 and Ima

he strain field

twinning. In

ental DIC is i

image the p

e 2 and Im

n field, thus

fields obtai

. Along the s

d during the

s to the point

o capture the

ication of slsage of difed by each

tem is active

e strain accum

ge 3. The su

d in which the

this cases is

implemented

point of slip o

mage 3 ena

s neglecting

ned using in

stress-strain

experiment.

t of slip onse

e strain local

ip onset, twferent refermechanism

e till Image 2

mulation due

ubsequent co

e local strain

s useful to s

d correlating

or twin nucle

ables to em

the contrib

ncremental D

curve 5 poin

. For examp

et. The corre

lization due t

win nucleatiorences imag (see text f

2. The corre

e to the activ

orrelation be

n contribution

separate the

two images

eation. In this

mphasize onl

bution of th

DIC is repor

nts are

ple the

elation

to slip

on ge or

elation

ve slip

tween

ns are

strain

along

s case

ly the

e slip

rted in

Figur

Figur

displa

mark

stress

Incre

indica

the lo

meas

nucle

F

o

to

(i

im

1.3.

Other

chara

re 1.9 in wh

re 1.9 refers

ays both slip

ed A display

s-strain curv

mental DIC

ates that bet

ocalized stra

sured correla

eated twins a

igure 1.9.

r ientation in

o twin nucle

nset image

mplemented

Slipon

r important r

acterization o

ich incremen

to an experi

p and twinnin

ys the strain

ve, the reso

is used in t

tween point

ains detecte

ating point B

at τT.

Stress-stra

n compressi

ation occur

marked B

using the im

nsetinFe

results using

of the slip on

ntal DIC disp

ment on a co

ng (for more

n field due to

olved shear

this case to

B and point

ed on the in

B and point

ain curve a

ion. The ins

red at τT (tw

- Bi) is use

mage B as t

eCrsingle

both the in s

nset. Differe

27

plays twin m

ompression

details on th

o the activa

stress τT in

o detect twin

Bi there is a

nset strain fi

Bi indicates

and in situ

set image m

win systems

ed to show

the referenc

ecrystals

situ and ex s

ent DIC imag

migration. Th

sample 10[

his crystal or

tion of one

ndicates nuc

n migration.

a strain accu

ield A. It fo

s increment

u DIC stra

marked A sh

1 11 121[ ]( ) an

twin migra

ce.

s

situ DIC on t

ge resolution

e stress-stra

1] oriented.

rientation see

slip system.

cleation of tw

The inset st

umulation in

llows that th

of local stra

in measure

ows the loc

nd 111 121[ ]( ) )

t ion τM , the

he single cry

s can be us

ain curve int

This crystal

e Chapter 2)

. Proceeding

twins on two

train field m

a region dif

he strain ac

rains on the

ements for

calized strai

). Increment

e correlat ion

ystal sample

sed for estab

troduced in

orientation

). The inset

g along the

o systems.

marked B-Bi

fferent than

ccumulation

previously

10 1[ ]

ns due

tal DIC

ns was

s cover the

blishing the

critical res

resolution

formed on

acquisition

the estima

available w

Figurethree f ield aimage

The solutio

the elastic

interval of

[010] crys

and a fine

resolution

solved shear

images are

n the sampl

n since the im

ation of the

with the in sit

e 1.10. Highdifferent loa

after each los are acquir

on adopted i

c region of t

stresses be

stal orientatio

e speckle has

of 0.87 µm/p

r stress for s

required to c

le surface.

mage acquis

point of sli

tu set-up.

h resolution ad stages. Hoad stage ared out of th

n the followi

the stress-st

etween which

on in compre

s been depo

px (nominal

slip onset τS.

capture the s

As previous

sition proces

p onset req

DIC strain High resolutl lowing to e

he load fram

ng is to use

train curve (

h slip initiate

ession. One

osed on the

5x magnifica

28

Along this w

strain localiza

sly described

s is obtained

quires higher

fields (5x) ot ion images estimate theme using an

ex situ DIC

(Figure 1.10)

es. The exam

side of the s

target surfac

ation) has be

work, ex situ

ations develo

d, ex situ D

d out of the

r image res

obtained aftal low to ca

e stress requoptical micr

implementin

). In this wa

mple reporte

sample has b

ce. 40 image

een captured

u DIC was ad

oping from th

DIC is not a

load frame. A

olution than

er loading tapture the reuired to initroscope.

g different sm

ay is possibl

ed in Figure

been prepare

es of the targ

d before the

dopted since

he initial slip t

a real-time

At the same

n the typical

the sample esidual straiate sl ip. Th

mall load ste

le to estima

1.10 refers

ed for ex situ

get surface w

experiment

e high

traces

strain

e time,

ones

at in

he

eps on

te the

to the

u DIC,

with a

(virgin

samp

curve

differ

been

displa

slip o

1.4.

1.4.1

In thi

trans

situ D

which

chara

is rep

using

obtain

are p

F

An E

schem

More

mark

inset

surfa

ple). Succes

e at three m

ent steps, a

acquired. In

aying traces

onset betwee

Strain

1. Strai

s work, the s

mission proc

DIC. High re

h allow to re

acterizing the

ported in [66

g SiC paper (

ned using a

placed at the

igure 1.11 .

BSD scan o

matic in Fig

eover, from th

ers provide

schematic i

ce and the e

sively the sa

aximum app

nd after eac

n the Figure

of strain loca

en the values

fieldsfro

inaccumu

strain measu

cess. All the

esolution stra

each higher

e strain fields

], and schem

(from P800 u

vibro-polish

corners of th

Experiment

f the selecte

gure 1.11),

he EBSD ma

the referenc

n Figure 1.1

experiment is

ample was

plied stresses

ch load stage

e 1.10 is rep

alization due

s of 180 and

omGrain

ulationon

urements ac

results pres

ain fields ha

deformation

s from DIC w

matically dep

up to P4000)

hing with coll

he selected a

tal techniqu

ed area enab

so the loca

ap is possibl

ce position fo

1). Success

s carried out.

29

loaded in th

s (180, 220

e all the 40

ported the re

e to the activa

220 MPa.

n‐Bounda

nFeCrgra

cross the gra

sented in Ch

ave been ob

ns than the

with the micr

picted in Figu

), and a fina

loidal silica

area (first ins

e for the ex

bles the char

al grain orie

e to recogniz

or the overla

ively a fine s

. Since from

he nominally

and 260 MP

(deformed)

esulted resid

ation of slip.

ary‐Slip

ainbound

ain boundarie

hapter 3 refe

btained for p

tensile case

rostructure d

ure 1.11. The

l polishing su

(0.05 μm). S

set schematic

periments o

racterization

entation and

ze the positi

ap of the EB

speckle patte

the images

elastic regi

Pa). The loa

images of th

ual strain fie

We consider

interact

daries

es are used

r to strain fie

olycrystal sa

e. The expe

data (grain or

e surface of

uitable for EB

Successively

c in Figure 1

on the FeCr

of the micro

the grain

on of the ind

BSD map wit

er has been

of the speck

ion of the s

ad was appli

he target su

eld of the sa

r the stress r

tion

to character

elds obtained

amples in co

erimental pro

rientations) f

the sample

BSD data ac

y 4 indentatio

.11).

polycrystal.

ostructure (se

boundary m

dentation ma

th the strain

applied on

kle pattern is

tress-strain

ed in three

urface have

ame region

required for

rize the slip

d using ex-

ompression

ocedure for

from EBSD

is polished

cquisition is

on markers

.

econd inset

morphology.

arks. These

data (third

the sample

possible to

detect the

obtained.

orientation

the trace a

grain boun

grain bou

polycrysta

Figure 1.1

boundary.

was possi

are availa

through a

with the re

residual B

of the grain

Figurerefer tfrom twith th

Special co

Figure 1.1

same show

were deter

was overla

the surface

position of t

This experim

n prior loadin

analysis for

ndary map w

ndaries whi

l hardening.

2 shows an

While with t

ble to chara

able with the

measure of

esult of the

urgers vecto

n boundary t

e 1.12. Strao the grain he EBSD dahe measured

odes for the c

3 shows an

wn in Figure

rmined using

apped at the

e. In order to

he indentatio

mental appr

ng and the d

slip and twi

with the resid

ch represen

n example o

the approach

cterize the r

ese techniqu

f the strain g

dislocation

or to predict t

to the materi

ain f ield in boundary re

ata acquiredd strain f ield

calculation o

n example of

e 1.12. The

g EBSD. Suc

EBSD map

o establish t

on markers, t

roach has tw

irection of th

n indexing (

dual strain fie

nts a critica

f the local s

hes adopted

reaction occu

ues. The ide

gradient acro

reaction. Th

the strain gra

al strengthen

proximity oeported in thd allow the id.

of the strains

f such calcu

crystal orien

ccessively the

. The strain

the strain fie

30

the final ove

wo main ad

he slip traces

(see Section

eld enables

l aspect on

strains assoc

in the literat

urring at the

ea pursued

oss the grain

e idea is to

adient at the

ning.

f a Grain Bhe EBSD maindexing of

across the g

ulation. The

ntation of the

e strain field

localizations

eld across th

rlap of the gr

dvantages. F

s on the sam

n 1.5). Secon

to character

n the grain

ciated with t

ture (as show

grain bound

here is to

n boundary,

show the p

e grain bound

Boundary. Tap. The graithe sl ip sys

grain bounda

strain field r

e grains, and

obtained us

s along band

e grain boun

rain map with

First of all k

mple surface

ndly, the ove

rize the strai

boundary c

the slip trace

wn for examp

dary, no stra

characterize

and relate th

possibility of

daries, and s

he strain min orientatiotems and th

aries are ado

reported in F

d the grain

sing high reso

s indicate th

ndary, and m

h the strain f

knowing the

is possible t

erlap betwee

in field acros

characterizat

es across a

ple in Figure

ain measure

e the slip pr

his strain gr

the usage

so the contri

measuremenon determinehe correlat io

opted in this

Figure 1.13

boundary po

olution ex sit

e traces of s

measure the

field is

grain

to use

en the

ss the

ion in

grain

e 1.4b)

ments

rocess

adient

of the

bution

ts ed on

work.

is the

osition

tu DIC

slip on

strain

gradi

Succ

recta

meas

selec

for th

Fmfothadb

The f

this c

is det

Burge

allow

trans

1.4.2

Strain

in Se

same

ent across

essively wa

ngular selec

surements a

ction side (pe

e Grain 1 so

igure 1.13magnitude aor the case he DIC straveraged, anetermined boundary det

final plot obta

case the stra

tected. In Ch

ers vector m

wing to derive

mission proc

2. Strai

n accumulati

ection 1.4.1 (

e experimen

it, a rectang

s determine

ction and the

and the grai

erpendicular

ome points be

3. Strain mssociated wreported in

ain f ields. And the f inalbetween thetermined pro

ained averag

in values ap

hapter 3 are

magnitudes. T

e important

cess.

inaccumu

ion on TiAl s

Figure 1.11)

ntal approac

gular selecti

ed the distan

e grain boun

n boundary

to the grain

elonging to G

measuremenwith the inco

Figure 1.1All the exp value is pl

e center of tojecting the

ging the stra

proaching th

also derived

These inform

consideratio

ulationon

samples is s

) for FeCr po

h for the T

31

ion of strain

nce betwee

ndary. The m

is represen

boundary),

Grain 2.

t methodoloming slip s2. The blac

perimental slotted versuthe rectang center of th

ains across th

he grain boun

d the disloca

mation help

ons on the r

nTiAl

studied follow

olycrystal sam

iAl experime

n measurem

n the coord

minimum dist

nted by half

avoiding to i

ogy for thsystem app

ck box represtrain valueus the distaular selectiohe selection

he grain bou

ndary are sim

ation reaction

in understan

role of the r

wing the sam

mples. Figur

ents. Due to

ments are ca

inates of th

tance betwee

f of the len

include in the

e calculat iroaching th

esents the ss containednce from th

on and the on the grai

ndary is rep

milar, a full s

ns for the es

nding the str

esidual Burg

me experime

e 1.14 show

o the fine m

aptured and

he central p

en the avera

gth of the

e strain mea

on of the e Grain Bo

selected regd in this bhe grain bopoint on thein boundary

ported in Figu

strain transm

stimation of t

rain plot obta

gers vector

ntal approac

ws the applica

microstructur

averaged.

oint of the

aged strain

rectangular

asurements

strain undary

gion on ox are undary e grain .

ure 1.13. In

ission case

he residual

ained, thus

on the slip

ch depicted

ation of the

re and the

complexity

complicate

FigureplacedSuccecaptur

The micro

visualize w

the equiax

enables to

resolution

1.5. Sl

Along this

measured

orientation

rotations b

Bunge con

c

[ ]g

The load d

sample su

y induced b

ed.

e 1.14. Sad at the cssively the

red in order

ostructural c

with an optica

xed grains. F

o easily char

DIC.

lipandtw

s work, index

through EB

n from EBSD

between the

nvention is ca

1 2

1 2

cos( )cos( )

cos( )sin( )

sin

direction is d

rface) ( )cr

ND

y the prese

mple prepaorner of asurface is eto characte

haracterizati

al microscop

For details on

racterize larg

winindex

xing of slip

BSD and th

D is given w

crystal fram

alculated the

1

1

1

sin( )sin(

) sin( )cos(

n( )sin( )

defined as (R

rystal : [001]S, a

ence of two

aration for selected etched and rize the ma

on is so im

pe the two m

n the solution

ge samples a

xing

and twin sys

e slope of

with Bunge c

me and the s

e rotation ma

2

2

)cos( )

)cos( )

)crystal

RD

: [10

and the tang

32

intermetallic

TiAl experiarea of tha set of imaterial micros

mplemented

main microstr

n compositio

areas which

stems is obt

the slip/twin

convention (

sample fram

atrix g [73]:

1 2

1 2

sin( )cos( )

sin( )sin( )

co

00]S, the norm

gential directi

c phases, th

iments. 4 ie sample ages using structure of

etching the

ructures pres

n for the etch

can be succ

tained using

n traces on

angles φ1, ϕ

me. From rot

1

1

1

cos( )sin(

) cos( )cos(

os( )sin( )

mal to the re

on ( )crystal

TD

:

he usage of

ndentation surface aftan optical mthe selecte

polished su

sent: the lam

hing see [72]

cessively an

g the crystal/

the sample

ϕ, φ2) and p

tation angles

2

2

)cos( ) s

)cos( ) c

eference sam

: [010]S (Figu

of EBSD is

markers ater polishinmicroscope

ed area.

urface in ord

mellar colonie

]. This proce

nalyzed using

/grain orient

e surface. C

provides the

s defined wi

2

2

sin( )sin( )

cos( )sin( )

c

os( )

mple surface

ure 1.15).

rather

re g. is

der to

es and

edures

g high

ations

Crystal

three

th the

(1.1)

e (DIC

Fs

Using

are d

In bc

{123}

direct

exper

twinn

in wh

tensil

on S

(whic

igure 1.15ample frame

g the rotation

etermined as

c materials,

} type, while

tions are fro

riment, the s

ning. mT/S are

hich is th

le axis and t

chmid facto

ch are define

. Schematice with the o

n matrix g, th

s:

the most co

twinning is r

om the <111

slip/twin syste

e defined as

e angle betw

he slip-plane

r analysis, t

d in the crys

c of the rorientation of

e crystal orie

( )crystal

RD g

( )crystal

ND

( )crystal

TD g

ommonly obs

restricted to t

> family. In

ems with the

/ coS Tm

ween the sli

e normal. On

the next ste

tal frame) in

{ }( )

abc samplen

33

otation matrf the crystal

entations on

( )sample

g RD

( )sample

g ND

( )sample

g TD

served slip p

the {112} fam

order to ind

e largest Sch

os( )cos( )

p direction a

nce establish

p is to repr

the sample

1

{ }(

e abcg n

r ix which rel frame.

the sample f

planes in bcc

mily [54, 74].

dex the slip/

hmid factors

and the tens

hed the pote

esent the se

frame:

)crystal

elates the o

frame ( )cry

RD

c materials a

In both twin

/twin system

are selected

ile axis,

ntial active s

elected slip/

orientation

rystal , ( )crysta

ND

are the {112}

nning and slip

ms activated

d: mS for slip

the angle be

slip/twin syst

/twin planes

of the

al , ( )crystal

TD

(1.2a)

(1.2b)

(1.2c)

, {011} and

p the shear

during the

and mT for

(1.3)

etween the

ems based

{ }( )

abc crystaln

(1.4)

Successiv

sample fra

From equ

compared

Figureslip pl

ely is determ

ame { }( )

abc samn

ation 1.5 is

with the slip

e 1.16. Slip anes (see te

mined the p

mple with the p

(tra

obtained a

p/twin traces

traces on text for deta

projection of

lane defining

) (sample

ace n

a vector whi

experimenta

the sample i ls).

34

f the interse

g the analyze

{ }) (

abc samplen N

ch lies on t

ally observed

surface whi

ction betwee

ed sample su

)sample

ND

the ( )sampl

ND

d on the sam

ich are com

en the slip/t

urface ( )sa

ND

le plane. Th

ple surface (

pared with

twin plane o

ample

his vector ca

(Figure 1.16)

the projecte

on the

(1.5)

an be

).

ed

35

Chapter2

TwinnucleationandmigrationinFeCr

SingleCrystalsPart of this work is published in [55].

In this Chapter are presented the results of the experiments on the FeCr single crystals implemented

for understanding the mechanical behavior of bcc materials, focusing on the evolution of the

deformation mechanisms (slip/twinning) during loading. The usage of single crystals allows to focus

on specific grain orientations, and it avoids the complexity introduced by grain boundaries in

polycrystals. In particular, the careful selection of the crystal orientations allowed to activate specific

twin and slip systems. Different crystal orientations and loading directions have been tested, leading

to a precise characterization of the strain fields due to the activation and interaction of twin and slip.

Based on the type and number of active systems, different stress-strain curves are then expected

(see schematic in Figure I.3).

In earlier works on Fe-47.8Cr alloy, Marcinkowski conducted indentation experiments and observed

the presence of twinning and slip predominantly on <111>{112} systems [22]. Since it is not easy to

identify the slip and twin systems coinciding with {112} planes by simple optical observations, DIC

and Electron Back Scattering Diffraction are then used, as the combination of these tools facilitates

this distinction. Indexing the twin systems with EBSD and measuring local strain fields allow to

monitor the nucleation and evolution of both slip and twinning during deformation. In the following,

particular emphasis is placed on the analysis of the deformation mechanism at the early stages of

plasticity (either corresponding to first yielding or twin migration subsequent to the load drop). DIC

was utilized at higher resolutions compared to conventional studies and provides micro scale

resolution measurements and allows pinpointing strain localizations due to slip and twin activation.

The characterization of the strain fields related to the active deformation mechanisms provides

further insight onto the evolution of the deformation for bcc materials.

In this chapter are addressed the following main issues: (i) Depending on the crystal orientation, the

precise determination of the critical resolved shear stresses (CRSSs) for twin (τT) and slip nucleation

(τS), by pinpointing local strain disturbances using DIC. Therefore, are discussed the implications of

these experimentally determined stresses with respect to the Schmid Law. (ii) Making a distinction

between tw

particular

cases of s

confirmed

2.1. Ex

2.1.1.

Single crys

technique

and a 10 m

0 10[ ] and

Figureusing cross-contro

Compress

loading ax

side of the

and throug

(EBSD). P

quench.

win nucleati

their influenc

slip-twin inte

with DIC res

xperime

Sampleg

stals of FeC

in a He atmo

mm gage len

d 10 1[ ] crys

e 2.1. SampElectron-Disection and

ol.

sion samples

xis was norm

e sample. Th

gh the thickn

Prior to loadi

on τT and tw

ce on the fo

eraction, whi

sults.

ntalsetu

geometri

Cr with a com

osphere. Ten

ngth were el

stallographic

ple geometrischarged M

d a 10 mm g

s were also s

mal to the 1[

e crystallogr

ness of each

ng, all samp

win migration

ormation of la

ich leads to

up

es

mposition of 4

nsile dog-bo

ectro-discha

directions (F

y adopted fMachining (gage. The e

sectioned into

0 1] , 11 1[ ]

raphic orienta

h sample, w

ples were so

36

n τM critical

arge local st

impedance

47.8 wt. % C

ne shaped s

arged machin

Figure 2.1).

for tension EDM). The

experiments

o 4 mm x 4 m

, 0 10[ ] , an

ations in the

were determi

olution annea

stresses. (ii)

trains and in

of slip and

Cr were man

specimens w

ned (EDM) w

experimentssamples hwere gener

mm x 10 mm

nd 314[ ] plan

other two di

ned using e

aled at 900

) The interac

ncrease in ha

ensuing str

nufactured us

ith a 1.5 x 3

with the load

s. The sampave a 1.5

ral ly conduc

m using EDM

nes and para

irections, i.e.

electron back

ºC for 1h fol

ctions of twi

ardening. (iv

rain hardeni

sing the Brid

mm cross-s

ing axis alon

ples were cmm x 3 m

cted on stra

M (Figure 2.2

allel to the 1

., across the

kscatter diffr

llowed by a

ins, in

v) The

ng as

dgman

ection

ng the

ut m in

). The

0 mm

width

action

water

Fcc

The e

Tens

while

2.1.2

The w

Chap

crysta

in situ

for a

samp

lower

for co

case

igure 2.2. Sut using Eleross-section

experiments

ion experime

e compressio

2. Digit

work present

pter 1). The s

al orientation

u DIC metho

tension sam

ples before th

r resolution (

ompression e

of compress

Sample geoectron-Discn. The expe

were condu

ents were c

on experimen

talImage

ted in this ch

stresses nece

ns using real

odology was

mple (Figure

he experime

(tension: 2.40

experiments

sive loads.

metry adoptharged Macriments wer

ucted at room

onducted on

nts were run

Correlati

hapter is mai

essary to nu

time strain m

2.5 µm/px. I

2.3a) and c

nt in the un-

0 µm/px vers

is higher, an

37

ted for comchining (EDre generally

m temperatu

n strain cont

in displacem

ionsetup

inly based on

cleate slip a

measuremen

n Figure 2.3

compression

-tested condi

sus compres

nd since duri

pression exM). The saconducted

ure by mean

trol, using a

ment control,

p

n experimen

nd twinning w

nts. The reso

3 are reported

sample (Fig

itions. For th

ssion: 3.94 µm

ing the test t

periments. Tmples haveon displace

ns of a servo

5 mm gage

both at a stra

ts conducted

were determ

olution of the

d two examp

gure 2.3b). T

he compressi

m/px) since t

he width of t

The samplee a 4 mm xment contro

o hydraulic l

e length exte

rain rate of 5X

d using in sit

mined for diffe

images cap

ples of spack

The images r

ion sample w

the width of

the sample in

s were 4 mm

ol.

oad frame.

ensometer,

X10-5 s.1.

tu DIC (see

erent single

tured using

kle patterns

refer to the

was used a

the sample

ncreases in

Figureusing

2.2. St

Table 2.1

samples t

successive

in function

Table

n

Figure 2.4

asymmetry

consequen

be activate

twin system

(tension) o

crystal orie

e 2.3. Referblack paint

tress‐str

provides a s

ested for ea

ely presented

of the activa

2.1. Crystal

Axis

n° experime

4 summariz

y between te

nce of the un

ed only with

ms nucleate

only slip is a

entation and

rence imageadapted for

aincurve

summary of t

ach combina

d the in situ

ated twin/slip

orientations

10[

ents

es the stre

ension and c

nidirectionali

a compress

in compress

activated. M

on the load

es for the sar in situ DIC

es

the single cry

ation of crys

DIC strain f

p systems.

and number

Tensile

0 1] 01[

3 11

ss-strain cu

compression

ty of twinning

sive or a tens

sion in corre

ore details o

direction is p

38

ample surfa: a) tension

ystal experim

stal orientati

field which e

r of repeated

0] 10 1[

1 3

urves obtain

n behavior fo

g [23]. Each

sile load. Fo

espondence t

on the poss

provided in th

aces with sp sample, b)

ments condu

on and load

nables to ch

experiments

Com

] 010[ ]

5

ned from th

or the same

twin system

or example, f

to the load d

ible twin sys

he next secti

peckle pattecompressio

cted along w

d direction.

haracterize th

s.

mpressive

11 1[ ]

7

e selected

crystal princ

m in the <111

for the [10 1

drops, while r

stems activa

on.

erns produceon sample.

with the num

For each ca

he strain evo

314[ ]

4

crystals. A

cipally arises

1>{112} fami

1] orientatio

reversing the

ated based o

ed

ber of

ase is

olution

clear

s as a

ly can

on two

e load

on the

Fp

Base

single

repre

strain

behav

activi

syste

clear

sectio

fields

igure 2.4. resented in

ed on the res

e crystal de

esents the m

n curve. Twin

vior is gove

ty. Case III

ems). Finally,

evidence o

ons along wi

s.

Summary this work.

sults of the

eformation b

main deforma

n-twin interac

rned by twin

represents o

, Case IV rep

of hardening

ith the critica

of the stre

experiments

behaviors ar

ation mechan

ctions govern

n-slip interac

orientations w

presents the

. Examples

al stress mag

39

ess-strain c

s (stress-stra

re broadly c

nism and it

n hardening

ctions and tw

with a limited

e occurrence

of each on

gnitudes, the

curves for

ain curves in

classified (F

initiates with

behavior for

win nucleatio

d number of

of multiple-s

e of the fou

e activated tw

different cr

n Figure 2.4)

Figure 2.5).

hin the elasti

r this case. In

on is preced

f activated sl

slip systems

ur cases wil

win/slip syste

rystal orien

) four gener

For Case

ic region of

n Case II the

ded by prono

lip systems

(> 2 slip sys

l be given i

ems, and the

tations

ral types of

I, twinning

the stress-

e hardening

ounced slip

(1 or 2 slip

stems) with

in the next

e DIC strain

Figureslip nmult ipactive

by twitwin-scharacsystem

2.3. A

The most

twinning is

<111> fam

the loading

the activat

using Schm

e 2.5. Scheucleation (τlying the aslip (mS) an

n-twin interl ip interacticterized by ms develop

Activated

commonly

s restricted t

mily. The acti

g direction (t

ted slip/twin

mid Factors

ematic of thτS), twin nuxial stress

nd/or twin (m

ractions. In ons dominaa l imited nleading to c

twinand

observed sli

o the {112}

ivation of cer

tension vers

systems is t

[75]: mS for s

/S

e possible ucleation (τT

in the loadmT) systems

Case II laate the hardumber of arystal harde

dslipsys

ip planes in

family. In bo

rtain twin/slip

us compress

the calculatio

slip and mT fo

/ /T Sm

40

crystal defoT) and twinding directios. Case I rep

rge sl ip acdening. Casctivated sl ip

ening.

stems

bcc materia

oth twinning

p systems de

sion). One o

on of the re

or twinning. m

/ cos(T

ormation be migration

on with thepresents cry

tivity precee III represp systems.

als are the

and slip the

epends on b

of the widely

solved shea

mS/T are defin

( )cos( )

haviors. Th(τM) are de Schmid fa

ystal harden

des twin nuents crystaIn Case IV

{112}, {011}

shear direct

both the cryst

used approa

r stress on t

ed as

he CRSSs fetermined b

actors for thning governe

ucleation anl orientation mult iple sl

} and {123},

ctions are fro

tal orientatio

aches to est

the slip/twin

or by he ed

nd ns ip

while

om the

on and

tablish

plane

(2.1)

in wh

tensil

slip [7

the S

deter

glidin

derive

Schm

FRdte

Base

slip/tw

neces

stress

stere

twinn

magn

syste

used

Table

and t

samp

Syste

activa

hich is th

le axis and th

75, 76] and

Schmid law is

rmined on th

ng on a defi

ed from stra

mid law for sl

igure 2.6. SRegions con

ependence ested in the

ed on Schmid

win systems

ssary since b

s direction (

ographic tria

ning in additio

nitudes of th

ems having m

as a criteria

e 2.2 lists all

twin systems

ple, hencefor

ems) display

ated twin an

e angle betw

he slip-plane

twinning [40

s well known

he atomistic

ned slip pla

ain measure

ip on the me

Stereographtaining twinfor bcc twipresent stu

d factor mag

s for a bcc c

bcc twinning

(twinning dir

angles separa

on to slip fro

e mS/T for the

mT larger tha

to define the

l the crystal

s. The Axis c

rth referred

ying the high

d slip system

ween the sli

e normal. His

0] in face-cen

[74, 77, 78].

scale, and t

ane. The me

ements, thus

eso and macr

hic tr ianglesn favored onning. The

udy.

gnitudes the

crystal struct

, unlike slip,

rection) that

ates the regi

m regions w

e possible tw

an 0.35 or, a

e regions (re

orientations

column refers

to as orienta

hest magnitu

ms for the cr

41

p direction a

storically the

ntered cubic

. In these stu

the meaning

easurements

s this study

ro scales.

s displayingorientations

grey-f i l led

stereograph

ture. The di

is uni-directi

leads to tw

ons in which

where only sli

win and slip

lternatively,

ed line) where

used in this

s to the orien

ation. We re

udes of mS/T

rystal orienta

and the tens

Schmid law

(fcc) crysta

udies, the cri

g of τS is the

s of τS propo

provides a

sl ip and tware plottedpoints repre

hic triangles

stinction bet

ional, i.e. the

winning [24,

h the crystal o

p is predicte

systems. In

much higher

e twinning is

s work along

ntation of the

eport the theT. Using this

ations classif

ile axis,

(equation 2.

ls, while for

tical resolved

stress requ

osed in the

set of resul

win systems considerin

esent the c

in Figure 2.6

tween tensio

ere exists a u

79]. The re

orientations

d. This line i

our analysi

r than the mS

expected.

g with the the

e crystal in t

eoretical slip/

table it is p

fied in the ex

the angle be

.1) has been

bcc slip dev

d shear stres

uired for the

following se

lts useful to

s with largesng the stresrystal orien

6 report the

on and com

unique sign o

ed line in e

are expected

is defined ba

s, the <111>

S for <111>{

eoretically po

the load direc

/twin system

possible to

xperimentally

etween the

utilized for

viation from

sses where

dislocation

ections are

check the

st mS/T. ss sign tat ions

theoretical

pression is

of the shear

ach of the

d to display

ased on the

>{112} twin

112} slip is

ossible slip

ction of the

ms (column:

predict the

y observed

42

Cases (schematic in Figure 2.5). For Cases I and II deformation via twinning is expected given the

high mT of the twin systems listed in Table 2.2. Crystal orientations belonging Case III display a

limited number of slip systems with high mS ( 10 1[ ] orientation in tension and 314[ ] orientation in

compression). Finally, we classify the 010[ ] orientation in compression in Case IV as there are

multiple slip systems with high mS.

Table 2.2. Theoretical slip and twin systems for the crystal orientations analyzed in this work. For each crystal orientation are reported the slip/twin systems displaying the largest mS/T.

1 2 3 4 5 6 7 8 9 10 11 12

111112[ ]

( ) 1 1112 1[ ]

( ) 1 1121 1[ ]

( ) 111112[ ]

( ) 111121[ ]

( )

1112 1 1[ ]

( )

111112[ ]

( )

111121[ ]

( )

111211[ ]

( )111112[ ]( )

111121[ ]

( ) 1 1121 1[ ]

( )

Axis Case Slip Twin

System mS System mT

Tensile 10 1[ ] III 2, 8 0.47 1, 3, 7, 9 0.24

010[ ] I 2, 5, 8, 11 0.47 2, 5, 8, 11 0.47

Compressive

10 1[ ] II 2, 8 0.47 0.47

2, 8 0.47

010[ ] IV 2, 5, 8, 11 0.47 1, 3, 4, 6,

7, 9, 10, 12 0.24

11 1[ ] II 4, 8, 12 0.31 4, 8, 12 0.31

314[ ] III 2

1 11 132[ ]( ) 0.49

0.50 2 0.49

2.4. Crystalorientation[010]

The crystal orientation 0 10[ ] represents the classical cleavage orientation for the bcc lattice when

the load is applied In tension [32]. The reason for this mechanical behavior along this crystal

orientation is that there are four possible twin systems activated with a tensile load (see Table 2.2).

Twin-twin interactions are geometrically studied based on the direction of the line which results from

the interaction between the two twin planes. Along all the possible interactions between the four twin

systems that can be activated for the 0 10[ ] orientation, there are couples of interacting twins which

have the direction of the intersecting line in the <011> family. The dislocation reaction between the

twin partials for these family of interactions leads to the formation of a Cottrel dislocation [35, 80],

which is the atomistic configuration leading to cleavage fractures.

2.4.1

Figur

repor

load d

high

inset

orient

more

match

locali

onset

onset

F

tesτT

fo

th(b

1. Tens

re 2.7 show

rted strains o

direction) in

resolution D

image mark

tation, we pr

e details see

hes the trac

zed strains

t of slip and

t of slip is τS=

igure 2.7.

ension (Caslip. ProceedT. The inset

our twin sys

he local strabands) form

sionexpe

s the stress

on the x-axis

the region co

DIC measure

ked A in Fig

roject all of t

Section 1.5)

ce of the 1[

appear mar

d the activate

=85 MPa (equ

Stress-strai

se I). The inding along tht image mar

stems in the

ain incremened at τT.

eriments

s-strain curv

s correspond

overed by D

ments indica

gure 2.7 (no

he possible s

). For the ins

11 1 121]( ) sl

ks the onse

ed slip syste

uation 2.1).

n curve and

nset image he stress-strked B disp

e 111 112{ nts visualize

43

ve for the 0[

d to the DIC

IC. In the no

ate localized

otice the hig

slip planes (

set marked A

lip system w

t of slip σS=

em (from tra

d DIC strain

marked A train curve tlays localiz

2} family. T

ed in the in

010] crystal

field averag

ominally elas

d slip initiatio

gh localized

(and twin pla

A, the strains

with mS=0.47

181 MPa. W

ace analysis)

n measurem

shows locathe load droation of str

Twin migrati

set image m

orientation

ges, i.e. aver

tic region of

on. This can

strains). Us

nes) onto th

s localize in b

7. The stress

With knowledg

), the resolv

ments for 0[

l ized strainp indicates ains due to

on starts at

marked C in

tested in te

rage axial st

the stress-s

be clearly s

sing the orig

he sample’s s

bands with a

s level at w

ge of the st

ved shear st

0 10] orienta

s due to ontwin nuclea the nuclea

t τM and pro

the same r

nsion. The

train (in the

train curve,

seen in the

inal crystal

surface (for

a slope that

which these

ress at the

ress at the

ation in

nset of ation at ation of

oduces

regions

With contin

observed

measurem

trace analy

mT=0.47, a

Following

shown by

plastic res

The strain

to twin nuc

bands. Th

Conseque

which plas

Twin migra

2.8 shows

were captu

situ DIC st

images ca

during the

Figure

situ Dblack to the

nued loading

(σT=373 M

ments show

ysis the activ

and the crit

the load dro

the second

ponse is obs

accumulatio

cleation (inse

ese observa

ently, the ons

stic strains st

ation is also

s five strain f

ured using th

train fields si

aptured mov

experiment.

e 2.8. Local

IC. In the scolor the ststrain meas

g, a stress le

MPa). This lo

high strain l

vated twin sy

ical resolved

p associated

linear region

served at a s

on beyond th

et market C,

ations indicat

set of twin m

tart to accum

observed fo

fields repres

he camera in

nce the sam

ving manually

strain f ield

stress-straintrain measusured using

vel is reache

oad drop is

ocalizations

ystems are id

d shear stre

d with twin nu

n of the stre

stress that is

his point take

Figure 2.7).

te that the p

migration τM=

mulate in the s

or the same

senting the r

n situ, so the

mple was at z

y the micros

on the 0 10[

curves on red using thDIC (averag

44

ed where a p

s associated

in four ban

dentified. All

ess for twin

ucleation, the

ess-strain cu

lower than t

es place in t

. The strain

plastic respo

114 MPa (Fi

same bands

010[ ] orienta

residual axia

sample was

zero load, an

scope used

0] tension s

the bottom he extensomge strain on

pronounced a

d with twin

nds (inset m

the activated

n nucleation

e material ap

rve in Figure

the stress re

the same reg

level increas

nse may be

gure 2.7) is

s that formed

ation using e

al strain after

in the load f

d each strain

for monitori

sample after

of the strameter, whilen the DIC re

and instantan

nucleation.

arked B in F

d twin system

is obtained

ppears to de

e 2.7. With a

ached prior t

gions (bands

ses as well a

dominated

marked as t

following tw

ex situ DIC st

r each load

frame. They

n field was ob

ng the surfa

r each load

in f ields is e blue coloregion).

neous load d

. Full field

Figure 2.7),

ms have the

d as τT=177

eform elastica

additional loa

to twin nucle

s) that were

as the width

by twin migr

the stress le

win nucleation

train fields. F

step. The im

are consider

btained stitc

ace of the s

step using e

reported wied l ine refe

drop is

strain

using

same

MPa.

ally as

ading,

eation.

linked

of the

ration.

evel at

n.

Figure

mages

red ex

hing 5

ample

ex

th rs

The t

the s

differ

The d

throu

the lo

field

green

misor

the o

F

re

in

re

m

In ad

SEM

obtain

B in F

block

twins nuclea

strains along

ent sample l

determinatio

gh EBSD m

ocal crystal o

represents t

n points ind

rientation wit

bserved twin

igure 2.9.

epresent a

ndicate the

espectively,

misorientatio

dition the tra

as shown i

ned from the

Figure 2.7. In

kage of the in

ted after the

the same b

location durin

n of the act

measurement

orientation fo

he orientatio

dicate region

th the matrix

ns matches w

EBSD data

400 μm x

crystal o

111 121[ ]( )

on (with resp

ace of the ac

n Figure 2.1

e ex situ stra

n particular b

ncoming twin

e load 1 (first

bands forme

ng load 4 (to

ivated twin a

s and SEM

or a 400 μm

on of the ma

ns displayin

x is about 60

with the trace

a for 0 10[ ]

200 μm re

rientation o

and 111[ ](

pect to the m

ctivated twin

0. Both of t

in field and t

both the twin-

n.

45

t strain field

ed after the

op area of th

and slip syst

images. Fig

x 200 μm re

trix (very clo

ng a differe

0°, this indica

es of 11 1 1[ ](

orientation

egion on th

of the mat

121( ) twin s

matrix crysta

and slip for

these observ

trace analysi

-twin interse

in Figure 2.8

load drop. O

e sample su

tems using

gure 2.9 repo

egion on the

ose to the or

nt crystal o

ates that the

121) and 11[

n in tensio

e sample’s

tr ix. Green

systems as

al orientatio

the 010[ ] or

vations are i

is previously

ctions shown

8) display pr

Other twinne

rface, see w

high resoluti

orts post-exp

sample’s su

riginal crysta

orientation. F

regions are

11 12 1]( ) twin

n (Case I).

surface. R

and blue

these two

n) of about

ientation can

n good agre

reported in

n in Figure 2

rogressive in

ed regions fo

white box in F

ion DIC was

periment EB

urface. The r

al orientation

For both re

twinned. Th

n systems.

. The EBSD

Red-colored

e points in

o regions s

60°.

n be detecte

eement with

the inset ima

2.10a-d displa

ncrement of

ormed in a

Figure 2.8).

s confirmed

SD data of

red-colored

). Blue and

egions, the

he slope on

D data

points

dicate,

show a

d using the

the results

ages A and

ay cases of

Figure

interse

2.4.2.

We classif

there are

stress-stra

image ma

111 121[ ]( )

stain band

(inset imag

slip system

oriented d

systems in

the slip sys

e 2.10. SEM

ections disp

Compres

fy the 0 10[ ]

four possibl

ain curve for

arked A repr

) slip system

ds of the sec

ge marked C

ms involved

differently fro

nvolved, but

stems involv

M image of t

play blockag

ssionexp

orientation

e slip syste

this crystal

resents the

m at a CRR

cond slip sys

C, Figure 2.1

in the crys

om the two

not clearly

ved lead to cr

twins in 0 1[

e of the inc

periments

in compress

ms in the <

orientation d

first evidenc

S of τS=85 M

stem 11 1 2[ ](

1) shows a d

tal deformat

main syste

visualized w

rystal harden

46

10] orientati

oming twin.

s

sion as a mul

<111>{112} f

displays a co

ce of strain

MPa. Succes

231) with mS

direct eviden

tion. Moreov

ems indicatin

with the avail

ning.

ion in tensio

lti-slip case (

family with h

onstant hard

localizations

ssively (inse

S=0.46 appea

ce of the inte

ver, the stra

ng the prese

able DIC re

on. Each of

schematic in

high mS=0.47

ening (Figure

s due to the

et image ma

ar. The in sit

eraction betw

in field disp

ence of othe

solution. In t

the twin-tw

n Figure 2.5)

7 (Table 2.2)

re 2.11). The

e activation

arked B), loc

tu axial strai

ween the two

plays strain

er secondar

this specific

win

since

). The

e inset

of the

calized

in plot

o main

bands

ry slip

case,

F

o

re

m

2.5.

2.5.1

Figur

(Case

syste

accum

obser

seen

obser

stress

displa

1 1 1[

igure 2.11

r ientation i

espectively,

marked C dis

Crysta

1. Com

re 2.12 disp

e II). High re

em with mS=0

mulates up

rved. With t

by the low

rve twinning

s σT=646 MP

ays the stra

1 12]( ) and [

. Stress-St

in compres

sl ip onset

splays evolu

alorienta

mpression

lays the stre

esolution DIC

0.31 at σS=2

to εB=1.07%

he activation

w slope of th

g nucleating

Pa leading to

ain field afte

1 11 2 11[ ]( ) .

rain curve

ssion (Case

t on the 1[

ution of the s

ation[11

experime

ess-strain cu

C measurem

84 MPa, lea

% (inset ima

n of only on

he stress-str

with a stres

a CRRS for

er twin nuc

47

and DIC s

e IV). The

111 121]( ) an

strain f ield a

1]

ents

urve for a [

ments (inset

ading to a C

age marked

ne single slip

rain curve (h

ss drop. Thr

r twin nuclea

cleation of t

strain f ield

inset ima

d 111 231[ ]( )

and slip-sl ip

11 1] orient

image marke

RRS of τS=8

B). No trac

p system, no

h=dσ/dε=0.00

ree twins sy

ation of τT=20

the three ob

measurem

ages marke

) systems.

p interaction

ed sample l

ed A) reveal

88 MPa. Slip

ces of slip

o significant

03E). Procee

ystems were

03 MPa. The

bserved twin

ment for the

ed A-B i l lu

The inset

ns.

loaded in co

l slip on the

p on the sa

on other sy

hardening r

eding with lo

e activated a

e inset image

n systems

e 010[ ]

ustrate,

image

ompression

111 121[ ]( )

me system

ystems are

resulted as

oading, we

at a critical

e marked C

111 121[ ]( ) ,

Figure

orienta

slip on

nuclealocalizfamily

In addition

provided. I

on various

e 2.12. St

ation in com

n the 111 2[ ](

ation (inset zations intro. All the stra

n to DIC stra

In Figure 2.1

s systems; an

ress-Strain

mpression (

211) system

image maoduced by tain plots are

ain fields, T

3 are report

nd (b) an hig

curve and

Case II). In

. Slip develo

rked B). Thhe nucleati

e obtained u

EM analyse

ed two TEM

h resolution

48

d DIC stra

set image m

ops on the s

he inset imon of three

using ex situ

es for the 1[

micrographs

image displa

ain f ield m

marked A s

same system

mage marke twin syste

u high resolu

11 1] orienta

s showing: (a

aying a twin.

easurement

hows traces

ms unti l the

d C displayms from theution DIC.

ation in com

a) different d

ts for 11[

s of localize

onset of tw

ys the strae <111>{11

mpression are

dislocations g

1] ed

win

in 2}

e also

gliding

F

d

2.6.

2.6.1

Case

Figur

mark

syste

fields

strain

111[ ]

igure 2.13

islocations

Crysta

1. Tens

e III represen

re 2.14 show

ed A, the st

em ( 0 4.Sm

s through the

ns developin

121( ) system

. TEM imag

from various

alorienta

sionexpe

nts cases ch

ws the stres

trains localiz

47 ), leading

e in situ DIC

g still on ba

m are also de

ges of a tw

s systems; b

ation[101

eriments

haracterized

ss-strain curv

ze in bands

to a CRSS

measuremen

nds correspo

etected (inset

49

win for the

b) High reso

1]

by limited

ve of a 10[

with a slope

of τS=87 MP

nts (inset ima

onding to th

t images ma

e 11 1[ ] or

olution imag

number of a

0 1] oriented

e that match

Pa. By follow

ages marked

e 111 121[ ]( )

rked B, C an

ientation in

e displaying

activated slip

d sample in

hes the trace

ing the evolu

d A, B, C and

slip system

nd D).

n compressi

g a twin.

p systems (

tension. Fo

e of the 11[

ution of the

d D) we obse

m. Traces of

ion: a)

Table 2.2).

or the inset

1 121]( ) slip

axial strain

erve higher

slip on the

Figure

orienta

111 1[ ](

image

are als

The in situ

elucidate t

reveals ag

(ε=1.8%). T

bands corr

crystal orie

conclusion

or two slip

e 2.14. Str

ation in tens

121) system

s marked B

so detected

u DIC also s

the differenc

gain how the

This can be

responding t

entation 10[

n that for rela

systems are

ess-Strain

sion (Case

. Sl ip on the

B-C-D. From

.

hows that th

ce, we utilize

slip system

clearly seen

to the 111 1[ ](

1] in tensio

atively low a

e active (Cas

curve and

III). The ins

e same syst

m the latter

e activated s

e high resol

111 121[ ]( ) p

n from the in

121) slip syst

on is an exam

pplied strain

se III, double

50

DIC strain

set image m

tem proceed

strain plots

slip systems

ution ex situ

provides high

set image m

tem display a

mple of the d

s (up to 3%)

e slip).

f ield meas

marked A sh

ds with load

traces of s

s accommoda

u axial strain

her strains a

marked A whe

axial strains

double slip c

) no hardeni

surement fo

ows onset o

ing as show

slip on 111[

ate deformat

n measurem

t this stage o

ere localized

up to 3%. Th

case (Table 2

ng is observ

or the 10 1[

of slip on th

wn in the ins

1 121]( ) syste

tion different

ments. Figure

of the deform

d strains alon

he specific ca

2.2). We dra

ved since on

1]

he

et

em

tly. To

e 2.15

mation

ng the

ase of

aw the

ly one

F

ofi

st

sy

F

fr

In Fi

disloc

strain

igure 2.15

r ientation ineld on the

train localiz

ystems (hig

igure 2.16.

rom mostly t

gure 2.16 T

cations glidin

n measureme

. Local str

n tension (Centire sam

zations alo

h resolution

. TEM imag

two sl ip sys

TEM microg

ng on two s

ents (Figure

rain measu

Case II I). Thple (low re

ng two tra

n DIC).

e for the [

tems.

graphs (obta

slip systems

2.15).

51

rements us

he inset imsolution DI

ces corres

10 1] orien

ained from t

confirming

sing high-re

age markedC). The ins

ponding to

tation in te

two differen

what observ

esolution D

d A shows tset image m

111 121[ ]( ) a

nsion displa

t samples)

ved on the m

IC for the

the residualmarked B d

and 111 12[ ](

aying disloc

providing e

macro-scale

101[ ]

strain isplays

21) sl ip

cations

evidence of

using DIC

2.6.2.

The results

both twin

migration f

orientation

as the 11[

strain curv

analyzed.

occurring a

Figure

orienta

localiz

nucleain the

Proceedin

indicates t

systems (

Compres

s presented

and slip. It

for that sam

n leading to t

1 1] orientati

ve for the 1[

The inset im

at σS=185 MP

e 2.17. St

ation in com

zed slip on

ation (inset inset image

g along the

twin nucleat

τT=194 MPa)

ssionexp

in Figure 2.1

t follows tha

ple is not po

twin-slip inter

on (both 11[

0 1] orienta

mage marked

Pa leading to

ress-Strain

mpression (

the 111 12[ ](

image marke marked C-

stress-strain

tion. Trace

). Increment

periments

12 for the 1[

at accurate

ossible. To ad

raction on a

1 1] and 10[

ation is show

d A indicates

a CRRS of

curve and

Case I I). T

21) system.

ked B). IncreCi (see text

n curve, at p

analysis ind

tal DIC is us

52

s

1 1] orientat

assessment

ddress this i

10 1[ ] sam

0 1] orientati

wn in Figure

s activation o

τS=87 MPa.

d DIC stra

The inset im

Slip on the

emental DIC for detai ls)

point B (σT=4

dicates twin

sed to analy

tion show ev

of strain a

ssue, we an

ple, having t

ions are clas

2.17. Three

of the 111[ ](

ain f ield m

mage marke

e same sys

C is used to.

413 MPa) the

nucleation

yze the evo

vidence of hig

accumulation

nalyze a simi

he same me

ssified as Ca

critical in sit

121) slip sys

easurement

d A shows

tem procee

o i l lustrate tw

e occurrence

on 111 121[ ](

lution of the

gh local stra

n induced by

ilar case of c

echanical be

ase II). The s

tu strain field

stem with mS

ts for 10[

the onset

eds unti l tw

win migratio

e of the load

1) and 111[

e axial strain

ins for

y twin

crystal

havior

stress-

ds are

S=0.47

1] of

win

on

d drop

121]( )

n field

betwe

point

accum

Twins

B). (ii

were

domin

band

point

F

o

Ex-sit

residu

surfa

obtain

visua

een point C

C as the r

mulation betw

s nucleated

i) The strain

linked to t

nated by twi

s that forme

Ci, another l

igure 2.18 .

r ientation in

tu high reso

ual strain fie

ce enable to

ned for a sm

alized the inc

(following tw

eference. Th

ween C and

in a region d

accumulatio

twin nucleat

n migration.

ed following t

load drop is

. Case of l

n compressi

olution DIC w

elds associat

o locate a re

mall sample a

coming twin

win nucleation

he strains d

C’ only. Ref

different from

on between p

ion. These

The stress le

twin nucleati

observed, th

ocal strain

on.

was also use

ted with larg

egion contain

area. In the

s which are

53

n) and Ci, the

isplayed in

ferring to this

m the preced

point C and C

observation

evel at which

ion marks th

his indicates

fields in ca

ed for analyz

ge twinned re

ned in the D

EBSD map

e stopped in

e correlation

the inset im

s inset image

ding region d

Ci takes plac

s indicate t

h plastic stra

he onset of tw

the nucleatio

ase of Twin

zing 101[ ]

egions. The

DIC region, a

reported in

n front of an

is implemen

mage marked

e two observ

displaying sli

ce in the sam

hat the plas

ains start to a

win migratio

on of addition

n-Twin inter

orientation.

markers intr

and overlap

the bottom-r

n obstacle tw

nted using th

d C-Ci repre

vations are p

ip (inset ima

me regions (b

stic respons

accumulate i

n τM=149 MP

nal twins.

ractions for

Figure 2.18

roduced on t

it with the E

right of Figu

win. In this

he image at

esent strain

provided. (i)

age marked

bands) that

se may be

n the same

Pa. Beyond

r 10 1[ ]

shows the

the sample

EBSD data

re 2.18 are

cases, the

resolved s

incoming t

regions ar

reported in

measured

Figure

Figure

two sy

Further ex

of twin-slip

are blocke

strain measu

twin reaches

re stopped i

n Figure 2.19

strain on the

e 2.19 . Stra

e 2.20. TEM

ystems; b) tw

xperiments u

p interaction

ed on the twin

red along th

s the obstac

n front of a

9), the assoc

e other side o

in measurem

M image for

win.

sing TEM co

(Figure 2.20

n boundary).

e incoming t

le twin interf

n obstacle t

ciated avera

of the obstac

ments acros

10 1[ ] orien

onfirm the pr

0b) which sho

54

twin is high o

face. It is ea

twin (Figure

ge strain fiel

cle twin (stra

ss the grain

ntation in co

resence of tw

ows a case o

on the side o

asily observe

2.18 and s

ld of the inco

in plot on the

boundary o

ompression:

wo slip syste

of slip blocka

of the obstac

ed that when

uccessively

oming twins

e right side o

f an obstacl

a) Planar d

ms (Figure 2

age (incomin

cle twin whe

n different tw

in the strain

is higher tha

of Figure 2.19

le twin.

dislocation o

2.20a) and a

ng slip disloc

ere the

winned

n field

an the

9).

on

a case

ations

2.7.

Cryst

obser

is me

2.7.1

The s

a res

F

o

Proce

orient

since

than

mech

meas

Crysta

tal orientation

rved in the f

easured (Figu

1. Com

stress-strain

olved shear

igure 2.21

r ientation in

eeding along

tation, as fo

e the presenc

the strain v

hanisms. In f

sured is arou

alorienta

n 314[ ] belo

irst part of th

ure 2.21).

mpression

curve for the

stress of τS=

. Stress-S

n compressi

g the stress-s

r the 10 1[ ]

ce of only on

values meas

fact, as show

und 6.4%, w

ation[314

ongs to Case

he stress-stra

experime

e 314[ ] orien

91 MPa (inse

train curve

on (Case III

strain curve,

orientation

e main slip s

ured for the

wn in the stra

while the ave

55

4]

e III. For this

ain curve, an

ents

ntation is rep

et marked A

e and DIC

I). The 1 11[ ]

only the 1 1[

tension (sec

system. The

e crystal orie

ain field repo

rage strain o

crystal orien

nd at micros

ported in Fig

in Figure 2.2

strain f ie

132( ) sl ip sy

11 1 32]( ) sli

ction 2.6.1), n

local strain m

entations wh

orted in the in

on the samp

ntation only o

copically lev

ure 2.19. Sli

21).

ld measure

ystem is obs

ip systems is

no crystal ha

magnitudes f

hich display

nset marked

ple surface is

one main slip

vel no crysta

ip onset is m

ements for

served.

s active. For

ardening wa

for this case

twin-twin an

D, the maxi

s about 4.15

p system is

l hardening

measured at

314[ ]

this crystal

s observed

s are lower

nd twin-slip

mum strain

5%. For the

56

twin-twin and twin-slip cases presented before much higher differences between local strains and

average strains were measured.

2.8. Furtheranalysisoftheresults

The usage of local deformation measurements from DIC allow for the precise determination of the

critical stresses associated with the activation of slip τS, twin τT, and twin migration τM which are

otherwise not accessible utilizing nominal sample response measurements. For example, slip can

occur locally despite the overall elastic response in a number of cases. Twin nucleation is associated

with a sudden load drop and can be measured by various experimental techniques, but the

subsequent migration can occur immediately after the load drop or after further deformation. In situ

local strain measurements via DIC permitted measurement of corresponding stress level at which

twin migration initiates. The results from all the crystal orientations tested are summarized in Table

2.3.

The crystal orientations analyzed are classified in four different cases (see schematic in Figure 2.5).

These four cases represent the possible crystal deformation behaviors based on the type of

deformation mechanism involved (slip/twin). Each case displays a crystal hardening that is function

of the main mechanism involved (twin-twin, twin/slip or slip/slip interactions). The real-time acquisition

of the strain fields using DIC in conjunction with crystal orientations from EBSD determined the

systems (planes and directions) and the CRSSs for slip onset τS, twin nucleation τT and migration τM

for each crystal orientation analyzed (Table 2.3). While for slip and twin nucleation the CRSSs are

constant, the twin migration stresses display deviations which are discussed in the following section.

Table 2.3. CRRSs for onset of slip τS, twin nucleation τT, twin migration τM as a function of the crystal orientation and load direction. The sequences S-T, S-S refer to slip-twin and slip-slip cases.

Mechanism Twinning (T) Slip (S)

Axis Case Sequence τT

(MPa) τM

(MPa) τS

(MPa)

Compressive

10 1[ ] II S-T 194±8 149±19 87±16

0 10[ ] IV S-S Not observed 85

11 1[ ] II S-T 203±3 157±3 88

314[ ] III S-S Not observed 91

Tensile 10 1[ ] III S-S Not observed 93±1

0 10[ ] I S-T 173±13 114±3 85

57

2.8.1. TwinMigrationStress

In the experimental results reported in this chapter, the twin migration stress σM (τM) represents the

point of macroscopic yielding on the stress-strain curves subsequent to twin nucleation. In fact, as

evident from DIC strain measurements (Figure 2.7, 2.8 and 2.17), strains localize starting from τM in

the same region formed after the load drop. In Table 2.3, the reported values for the CRSS for twin

migration show variation depending on crystal orientation. The CRSS magnitudes for the 0 10[ ]

orientation in tension was 114 MPa while for 11 1[ ] and 10 1[ ] orientations in compression 153

MPa was measured. The first case is classified as Case I, and the second one as Case II. Two

possible explanations are introduced to explain the difference in the CRSS values for twin migration

for Case I and Case II. First of all, for the 11 1[ ] and 10 1[ ] crystal orientations in compression

(Case II) twin nucleation is preceded by appreciable deformation (1.5% slip strain) developing in one

primary slip system (Figure 2.12 and 2.17). It is conceivable to argue that this large slip activity

preceding twin nucleation influences the subsequent twin growth process. A growing twin can

encounter slip bands [23] thus having difficulties in penetrating them. Secondly, twin growth is

influenced by the dominant intersection mechanism involved, i. e. twin-twin (Case I) or twin-slip

(Case II), hence the product of the dislocation reactions occurring in the intersection region. The high

stresses in the intersecting regions can promote the dislocation reactions that facilitate twin growth.

Therefore for Case I, where twin activity is not preceded by prior large slip activity, and twin-twin

interaction (high local stress) is the primary intersection mechanism, we measured lower τM.

2.8.2. StrainHardening

It is also well-known that twin-twin, twin-slip and slip-slip intersections have an important effect on the

crystal hardening. As shown in an analogous work on fcc steel by Efstathiou at al. [81], the visualized

accumulation of plastic deformation in the twin-twin and twin-slip intersection regions can be

correlated with the observed crystal hardening. In our experiments, at the point where twin migration

is observed (at twin migration stress σM (τM)) on the stress-strain curves, all the crystal orientations

displaying twinning (leading to twin-twin and twin-slip interactions) show high values of the hardening

parameter h=dσ/dεpl=0.2E, and high localized strains (up to 10% for the 0 10[ ] orientation in tension,

and up to 8% for the 11 1[ ] orientation in compression). For the same level of deformation, the

double-slip case doesn’t show hardening ( 1 0 1[ ] in tension, Case III, Figure 9), while the multi-slip

case analyzed ( 0 10[ ] in compression, Case IV, Figure 11) displays a constant hardening

parameter from the onset of macroscopic plasticity (h=dσ/dεpl=0.01E) that is lower compared to the

twin-twin and twin-slip cases. For both the cases displaying slip, the localized strains (up to 3%) are

much lower than the localized strains measured for Case I and II indicating that the level of strain

58

accumulation in the region of twin/twin, twin/slip and slip/slip intersection can be correlated with the

observed level of hardening.

2.8.3. TwinNucleationStress

For each of the crystal orientations displaying twinning ( 0 10[ ] in tension, 11 1[ ] and 10 1[ ] in

compression, Table 2.2), a CRSS of 191 MPa was measured for twin nucleation (see Table 2.3).

Moreover, all the twin systems having the highest magnitudes of the Schmid factors mT activate

simultaneously. These observations support the prediction of the activated twin systems using

Schmid factor analysis along with the knowledge of the twinning direction for each crystal orientation

and load direction (see Section 3). The existence of a constant CRSS is noteworthy because if the

measurement techniques is not precise, it is possible to report a deviation contrary to the current

findings. For the crystal orientations 0 10[ ] and 314[ ] in compression, and 10 1[ ] in tension only

slip is observed since the resolved shear stress for twinning is rather low mT=0.24 (Table 2.2). The

choice of single crystals in this study is rather unique to isolate specific mechanisms.

2.8.4. SlipNucleationStress

For all the crystal orientations tested in our study (Table 2.2), slip develops on planes and directions

having the highest SFs, <111>{112} in most cases and <111>{123} in others. Using high resolution

images (3.0 - 0.44 μm/pixel) we pinpoint strain localization due to the slip onset appearing for each

crystal orientation and load direction at a constant CRSS of 88 MPa. This type of resolution during

deformation is rather unique. The results conform to the Schmid law for slip (Table 2.3) and slip

precedes twin nucleation. Precise measurements are needed because slip nucleation in the elastic

region of the stress-strain curve (see inset image marked A in Figure 2.7, image resolution used for

DIC is 0.9 μm/pixel) was detected which cannot be gleaned clearly from macroscopic observations.

Overall, the experimental results point to the utility of DIC to analyze the response of metals

undergoing complex slip-twin evolution. The progression of these mechanisms are not readily

explainable by macroscopic stress-strain measurements alone, and localized strain measurements

shed light to the activation of slip and twinning during deformation and their interactions. Hence, the

present approach provides insight for bridging the scales ranging from macroscopic response to

localized behavior at micro-scales.

59

Chapter3

SlipTransmissionthroughGrain

BoundariesinFeCrpolycrystal

Understanding the interaction between slip dislocations and grain boundaries (GBs) has a paramount

importance on the mechanical response of metals [82, 83]. In fact, extensive research has been

reported during the last decades on the strengthening effect introduced by partial or full blockage of

slip dislocations at GBs. In particular, much interest has been devoted on the results of the slip

dislocation-GB reactions which provide deep insight into the slip transmission process across the

GB. In this regard, early research focused on the details of these reactions at GBs utilized

transmission electron microscopy (TEM) [48, 56]. Several insights into the transmission of the

incoming dislocation, and incorporation into the GB with extrinsic (residual) dislocations have been

gained as a result of these studies. Further experimental efforts are required to overcome the

difficulties in correlating the results of these dislocation reactions with the associated strain fields

across the GBs (on the meso-scale). A measure of the strengthening associated with a GB is

decided based on whether dislocation strain fields undergo a continuous variation (full dislocation

transmission), or whether large strains accumulate on one side of the GB (dislocation blockage).

Therefore, a focused study on the experimental determination of the localized strains across GBs is

important and will provide considerable insight into dislocation transmission and GB contribution to

hardening. In this chapter are studied local strain fields at the meso-length scales covering multiple

grains in Fe-Cr alloy. The strain measurements are used to establish the possible outcome of slip-GB

interaction and provide further insight into the importance of the residual dislocation due to slip

transmission.

3.1. SchematicofSlipDislocation–GrainBoundaryinteraction

A schematic of a GB is shown in Figure 3.1. Grain 1 contains the incoming slip system, while Grain 2

contains the outgoing slip system. In this schematic, the dislocations leave the GB in the second

crystal (outgoing slip plane) as a result of the dislocation-GB interaction. Of particular importance is

the residual Burgers vector of the dislocation left at the GB [84-86].

Figurethe incand n2

betweeBurge

1 2b b

Based on

occur [83]

0 whe

dislocation

parallel, a

not paralle

cross the

from zero

residual Bu

where 1b

the GB res

with the st

as a funct

in case o

e 3.1. Schemcoming and

2) and the B

en the l inesrs vector of

rb

.

the geometr

: a) transmis

ere is the

n is left on th

partial resid

el, a partial r

GB and rem

for the case

urgers vecto

(incoming) a

sistance to s

trains induce

ion of the re

of low residu

matic of the outgoing s

Burgers vec

s of intersethe residua

ry of the inco

ssion by cros

e intersecting

e grain boun

ual dislocatio

esidual dislo

main in the G

e (a) to highe

or magnitude

1b

and 2b

are d

slip transmiss

ed by disloca

esidual Burge

ual Burgers

e dislocationslip planes actors of the

ction betweal dislocation

oming and o

ss-slip: the s

g angle), 1b

ndary; b) dire

on is left on t

ocation is left

GB. For these

er values in

, | |rb

, can b

2 |r

b b b

determined o

sion, with the

ation slip on

ers vector m

vector mag

60

n-grain bounare indicatedislocation

en the two n left at the

outgoing slip

slip planes in

and 2b

are p

ect transmiss

the GB; c) in

t on the GB;

e cases the

case (b) an

be evaluated

1 2| | |rb b b

on the same

e aim to link

the meso-sc

magnitude, th

gnitudes, wh

ndary interaed the norms (b1 and b

slip planesGB is deter

p systems, di

ntersect the

parallel to th

sion: 0 ,

ndirect transm

d) no trans

residual Bu

d (c) [48], a

d from

|

coordinate b

the reaction

cale. For the

e strains are

hile they acc

ction geomemal to the sl

2). ϑ indicat

and the Grmined from

ifferent poss

GB plane on

e intersectio

in this case

mission:

mission, the

rgers vector

nd to a max

basis. | |rb

i

n occurring a

GBs analyz

e transmitted

cumulate on

etry. For bolip planes (tes the ang

B plane. Thm the equatio

sible reaction

n a common

on line, no re

1b

and 2b

a

0 , 1b

and b

dislocations

magnitude

ximum for (d

s used to qu

at the atomic

zed is shown

d almost una

n one side o

th n1

le

he on

ns can

line (

esidual

are not

2b

are

s don’t

varies

). The

(3.1)

uantify

scale

n how,

altered

of the

interf

accum

confid

choos

makin

assoc

gene

magn

trans

3.2.

3.2.1

A Fe

comp

900 º

(from

a vibr

Fmsd

A sel

(the p

the se

the a

Bung

face in the h

mulation acr

ded to small

sing the FeC

ng the Burg

ciated with m

rated at the

nitude of the

mission at a

Materi

1. Micros

Cr alloy with

pression sam

ºC for 1 h fo

m P800 up to

ro-polishing w

igure 3.2. Gmm region o

hown in thisplaying th

ected 2 mm

procedure is

elected regio

rea analyzed

ge convention

igh residual

ross GBs is

deformation

Cr alloy is tha

ers vector c

multiple slip

e GBs. The

residual Bur

GB.

ialandM

tructure

h a composi

mple by elect

ollowed by a

P4000), and

with colloida

Grain orienton the same stereograe largest SF

x 2 mm reg

discussed i

on of the spe

d in the pres

n (φ1, Φ, φ2)

Burgers vec

achieved a

ns in compre

at we could

conservation

systems. Su

correlation

rgers vector

Methods

character

tion of 47.8

ro-discharge

a water quen

d a final polis

l silica (0.05

tations in thple surfaceaphic tr iangFs.

ion of the sa

n [66], also u

ecimen surfa

sent paper is

for each gra

61

ctor magnitu

as a result o

ession with e

observe pre

analysis rat

uccessively,

between th

provides an

rization

at. pct. % C

ed machining

nch. For EB

shing suitable

μm).

he load dire. Grain orie

gle along w

ample surfac

used in [43,

ce were obta

shown in Fi

ain are report

de cases. A

of this expe

external strai

dominantly o

ther simple,

the analysis

he strain gr

excellent too

Cr was secti

g (EDM). The

SD the surfa

e for EBSD d

ction obtainentations in

with the sl ip

ce was mark

87]). The cr

ained using E

gure 3.2 and

ted in Table

clear charac

rimental stu

ns less than

one single sl

and avoidin

s is focused

radients acro

ol to quantify

oned into 4

e material wa

ace was pol

data acquisit

ned via EBSn the load dp systems

ed using Vic

ystallograph

EBSD. The g

d the corresp

3.1.

cterization o

udy. The exp

2%. The ad

lip system in

ng complex i

on the strain

oss the GB

y the capabil

mm x 4 mm

as solution a

lished using

tion was obta

SD for a 2 mdirection arfor bcc ma

ckers indenta

ic grain orie

grain orienta

ponding Eule

of the strain

periment is

dvantage of

n the grains

nteractions

n gradients

Bs with the

ity of strain

m x 10 mm

annealed at

SiC paper

ained using

mm x 2 re also aterials

ation marks

ntations for

tion map of

er angles in

62

A total of nine grains are visualized in the selected area, with an approximately mean grain size of

about 1 mm. In Figure 3.2, the stereographic triangle along with the crystal orientations of each grain

in the load direction is also reported. The stereographic triangle is subdivided into five regions ([88])

that indicate the slip systems with the largest Schmidt Factors (SFs) for bcc materials. SF analysis

was used in combination with slip trace analysis (from strain fields) for indexing the observed slip

systems (see Section 1.5).

Table 3.1. Euler angles obtained from EBSD for each grain in the selected area of the sample surface.

Grain 1 2 3 4 5 6 7 8 9

φ1 [°] 205.8 314.95 260.11 286.41 300.41 220.23 236.51 242.12 231.9

Φ [°] 41.56 49.86 19.92 32.46 34.42 46.03 45.97 43.49 37.21

φ2 [°] 46.47 52.21 359.49 2.24 52.63 34.38 28.82 19.69 19.42

3.2.2. Experimentalset‐upandstrainmeasurements

The experiments were conducted at room temperature using a servo hydraulic load frame. The

sample was deformed in displacement control at a mean strain rate of 5x10-5 s-1. In situ DIC [2, 11,

12, 89] was used for measuring the real-time evolution of the strain fields during loading (see also

Chapter 1). The images were captured using an IMI model IMB-202 FT CCD camera (1600 x 1200

pixels) with a Navitar optical lens, providing for a resolution of 3.0 μm/pixel. The speckle pattern for

DIC was obtained using black paint and an Iwata Micron B airbrush. A reference image of the sample

surface was captured at zero load, and the deformed images of the same area every 2 seconds

during the loading. The strain data obtained from in situ DIC were used to construct the stress-strain

curve using the average axial strain for the selected in situ DIC region.

The main results were obtained using ex situ high resolution DIC. Adopting special fine speckles, the

strain resolution obtained reveals the local strain intensities at grain level, in particular strain

heterogeneities across grain boundaries were clearly established. As already explained in Chapter 1,

the usage of ex situ DIC requires that the reference and deformed images are acquired out of the

load frame using an optical microscope which enables capturing higher magnification images. The

strain fields obtained refer to the un-loaded condition (residual strains). A speckle pattern suitable for

high resolution DIC was applied on the surface sample after the initial EBSD scan (Figure 3.2). A set

of 140 images covering the analyzed region was captured before the experiment (reference

condition) and after loading the sample (deformed condition). The correlation was implemented for

each pair of images (reference and deformed) and the results were successively stitched together.

The grain map was overlaid with the strain fields using the Vickers indentation marks which are

visible in the EBSD grain orientation map and the optical microscope images. The observed slip

syste

trace

3.3.

In the

exper

stress

are a

which

rb

) fo

strain

Fw

3.3.1

Figur

polyc

a me

the p

(twin-

the p

show

an im

obtain

ems were ind

s on the stra

Result

e following s

riments. All t

s-strain curv

analyzed. Hig

h allow the s

or each GB.

n changes in

igure 3.3. with the poly

1. Stress‐

re 3.3 shows

crystal case a

chanical beh

polycrystal ca

-slip case) an

polycrystal sa

wn by the po

mportant asp

ned across

dexed using

ain fields obta

ts

sections are

the strain fie

ve along with

gher ex-situ s

slip systems

In section 3

proximity of

Comparisoncrystal case

straincur

s a comparis

and the sing

havior which

ase displays

nd the 010[

ample analyz

lycrystal cas

pect of the a

the grain b

grain orienta

ained from h

reported the

elds report th

h two ex-situ

strain measu

indexing, an

3.3.3 local str

the GBs.

n between e.

rveandD

son between

le crystal sam

is located b

an hardenin

0] orientation

zed displays

se is induced

analysis pres

boundaries re

63

ations from E

igh resolutio

e DIC strain

he axial strai

u DIC strain f

urements are

nd successiv

rain measure

single cryst

DICstrain

n the stress-

mples analyz

between the

ng modulus

n (multi-slip c

s one main s

d by the pres

sented in th

refer to loca

EBSD, and c

n DIC strain

measureme

n yy in the

fields obtain

e provided in

vely the evalu

ements acros

tal experim

measure

-strain curve

zed in Chapt

single crysta

which is co

case, see Ch

slip system a

sence of the

his chapter,

al strain hete

combining S

fields.

nts obtained

load directio

ed after two

Section 3.3

uation of the

ss GBs are u

ents presen

ments

es obtained

ter 2. The po

al stress-stra

mparable to

hapter 2). Mo

active. It follo

e grain bound

since all the

erogeneities

F analysis w

d from the co

on. In sectio

o successive

.2 for the firs

e dislocation

used for calc

nted in Cha

in compress

olycrystal ca

ain curves. In

o the 101[ ]

oreover, all th

ows that the

daries. This

e strain mea

that follows

with the slip

ompression

on 3.3.1 the

load steps

st load step

reactions (

culating the

apter 2

sion for the

se displays

n particular,

orientation

he grains in

e hardening

represents

asurements

s to partial

64

transmission of slip dislocations and that induce hardening due to the presence of the grain

boundaries.

In Figure 3.4a, the strain fields shown in the inset images marked Ai and Bi represent the residual

axial strain fields for the 2 mm x 2 mm region obtained via ex-situ DIC. Each strain field is a

composition of 9 images (resolution 0.87 μm/pixel) captured outside the load frame and after

unloading from points A and B on the stress-strain curve. Strain heterogeneities develop as a

consequence of the local material microstructure (see also the EBSD map in Figure 3.2).

Two regions are selected from the global strain fields: 1A and 2A after load step Ai, and 1B and 2B

after load step Bi (Figure 3.4a). In Figure 3.4b the same regions are paired with the schematic of the

slip plane geometries. The GB plane is drawn using the GB trace from the EBSD map assuming that

the normal lies on the plane of the sample surface. For the region marked 1, the observed incoming

slip system is 11 1 231[ ]( ) , while the outgoing slip system is 11 1 321[ ]( ) . In that case, the residual

Burgers vector magnitude is low:

2 4111 111 0 382 2[ ] [ ] | | .

Grain Grain r r

a ab b a

(3.2)

The strain fields 1A and 1B clearly show an accumulation of strains for both sides of the GB. In

particular, this condition of strain transmission is held for both the loading steps. For the second case

shown, a GB for which the reaction occurring between the incoming and the outgoing slip systems

leads to a high residual Burgers vector magnitude was selected:

2 7111 111 1 282 2[ ] [ ] | | .

Grain Grain r r

a ab b a

(3.3)

The incoming slip system is 11 1 231[ ]( ) , while the outgoing slip system is 11 1 2 11[ ]( ) .

Fsstreb

For th

same

slip s

proje

indica

igure 3.4a.ample. Theteps, Ai anegions 1A-B

lockage on

he Grain 7 a

e | |rb

value

system was

ction of the

ating the diffi

. Stress-str strain f ieldd Bi. The t and 2A-B one side of

also the 11[

e (the two alt

selected com

two slip plan

iculty for the

ain curve ads are obtatwo rectangwhich showthe GB, res

1 321]( ) slip

ternative slip

mparing the

nes. In this c

incoming dis

65

and DIC strined using

gles drawn w strain traspectively.

system has

p systems ha

direction of

case the stra

slocations to

rain measurex-situ DICin the insansmission

s high 0SF

ave the sam

the slip trac

ains clearly a

o be transmitt

rements forC measuremet images (through th

0 49. , and th

e Burgers ve

ces on the sa

accumulate o

ted through t

r the comprments for tw

(Ai and Bi he GB and

e reaction le

ector). The [

ample surfac

on one side

the GB.

ression wo load

) mark strain

eads to the

11 1 2 11[ ]( )

ce with the

of the GB,

Figurefrom

disloca

across

side o

The accum

loading ste

are given

shear plan

higher for

17 6.

e 3.4b. GeoFigure 3a.

ation left at

s the GB. F

f the GB an

mulation of s

eps. More de

in Figure 3.4

ne which has

the case of

and 0| |rb

ometric analOn the to

t the GB ha

For the seco

d the assoc

strains on th

etails on the

4c. All the ac

s SF=0.5. Th

f slip blocka

0 38. ).

ysis of the op a sl ip t

s a low | rb

ond case sh

iated | |rb

i

he GB side

slip-GB inter

ctive slip sys

he angle

age ( 1| | .rb

66

sl ip systemtransmission

|r and the s

hown strain

is high.

of the incom

raction for th

stems have S

and the res

28 , 48.

ms for the sen case is

strains are

ns accumula

ming slip sys

e cases ana

SF values cl

sidual Burge

5 ) than for

elected graidescribed,

continuousl

ate preferen

stem is obse

lyzed in equ

ose to the m

rs vector ma

r the slip tra

in boundariethe residu

y transmitte

ntially on on

erved for bo

uations 3.2 an

maximum res

agnitude | rb

ansmission c

es al

ed

ne

th the

nd 3.3

solved

|r are

case (

F

a

c

s

v

b

3.3.2

Figur

of 14

3.4a)

plane

famili

Facto

surfa

In Ta

and 8

igure 3.4c.

ngle for

ases the SF

hear stress

ector magn

lockage cas

2. Highre

re 3.5 display

0 images we

). Slip system

es for bcc ma

ies were pro

ors are succ

ce.

able 3.2 the s

8 only one s

. SFs for th

the sl ip-GB

F values of

plane ( SF

i tude | |rb

se ( 1 28| | .rb

esolution

ys the strain

ere captured

ms were inde

aterials on th

ojected on th

essively sele

slip systems

lip system is

he incoming

B interaction

the activat

0 5. ). In c

0 38. and th

8, 48 5.

DICstrai

field obtaine

d before the

exed using g

he well-know

he plane of t

ected compa

for each gra

s observed, w

67

g and outgo

n cases sho

ted sl ip pla

case of sl ip

he angle

).

nmeasur

ed using ima

experiment a

grain orientat

wn 111 1{

the sample

aring the pro

ain along wit

while for gra

oing sl ip sy

own in Figu

nes are clo

transmissio

17 6. are

rements

ages at highe

and after loa

tions from EB

110} , 111

surface. The

ojected lines

th the SFs a

ains 1 and 6

stems, | |r

b

re 3a. For

ose to the m

on both the

e low compa

er resolution

ading the sam

BSD. In part

112{ } , 1

e slip system

with the slip

re reported.

traces of a s

| magnitude

both the an

maximum re

e residual B

ared to the

(0.18 μm/pix

mple (point A

ticular, the p

111 123{ } s

ms with large

p traces on t

For grains 2

secondary s

es and

nalyzed

esolved

Burgers

to the

xel). A total

Ai in Figure

ossible slip

slip system

est Schmid

the sample

2, 3, 4, 5, 7

lip systems

68

are visualized. In the schematic on the bottom of Figure 3.5 the | |rb

values for each GB are also

reported. GBs on the DIC strain field with T indicate case of strain transmission visualized as a strain

continuity along the slip traces, while B indicates the GBs for which no strain continuity is observed.

For GBs 1-2, 2-4, 2-6, 7-8, 7-6 it is evident how the strains induced by slip continued almost

unaltered through the interfaces, while for GBs 2-3, 3-4, 4-5, 5-6, 2-7, 2-8, 6-4 the strains accumulate

on one side of the GB. Strain accumulation is particularly evident for GBs 4-5 and 2-7. Each GB can

be also characterized by the estimation of the | |rb

magnitude (see schematic in Figure 3.5). In

Table 3.3 a summary of the observed slip mechanism (T: slip transmission, B: slip blockage) and the

correlation with the | |rb

magnitudes is given. It is clear that slip transmission corresponds to low

| |rb

, while for high | |rb

magnitudes the slip mechanism observed is blockage.

Table 3.2. Activated slip systems and SFs.

Grain 1 2 3 4 5 6 7 8

Slip

System

(SF)

111011[ ]

( )

0.46

111123[ ]

( )

0.45

111231[ ]

( )

0.48

111110[ ]

( )

0.49

111321[ ]

( )

0.47

111121[ ]

( )

0.45

111211[ ]

( )

0.42

111123[ ]

( )

0.37

111211[ ]

( )

0.49

111211[ ]

( )

0.49

F

resoSobd

|

lo

igure 3.5. H

eference imitu), correlarientations

SFs. Dependn the activelocked at ti f ferent disl

|rb

, while t

ocal strains

High resolut

ages and 14ated and sufrom EBSD

ding on the e sl ip systethe GB. Difocation-gra

they are blo

can be obse

tion DIC stra

40 deformeduccessively selecting tmagnitude

em in one gfferent strain boundary

cked at the

erved on on

69

ain f ield me

d images wstitched. S

the systemsof the resid

grain can bein f ields in

y interaction

GB in case

ne side of th

easurements

ere captureSlip systemss with sl ipdual Burgere transmitte

n the proximns. Strains a

e of high |b

e GB (see f

s ( yy ). A to

d outside ths were indetraces disp

rs vector, ded through tmity of the are transmit

|rb

. In case

or example

otal number

he load framexed using playing the islocations the GB or c GBs resul

tted in case

of blockag

GB 2-7).

of 140

me (ex-crystal largest gl iding can be lt from of low

e, high

70

3.3.3. Strainmeasurementsacrossgrainboundaries

In order to quantify the magnitude of the strain change across the GB sides, we provide two sets of

strain measurements for low and high | |rb

magnitudes. The inset image marked A in Figure 3.6

shows the strain field across grains 1 and 2 (see also Figure 3.5). In this case a clear strain continuity

associated with the incoming slip system 111 123[ ]( ) and outgoing slip system 11 1 231[ ]( ) is

observed through the GB, and the residual Burgers vector magnitude is low:

1 2111 111 0 162 2[ ] [ ] | | .

Grain Grain r r

a ab b a

(3.4)

Each point on the strain plots reported (Figures 3.6 and 3.7) refers to the average axial strain of a

rectangular selection of strain values oriented along the GB side with an approximate size of 40 μm x

400 μm. For the case A (GB 1-2, Figure 3.6) the difference of the strain magnitudes approaching the

GB is equal to 1 2 0 09| | . %GB .

Table 3.3. Comparison between the observations on the DIC strain field on the slip

mechanism (T: strain transmission, B: strain blockage) with the residual Burgers vector | |rb

.

GB 1-2 2-3 3-4 2-4 4-5 5-6 2-6 2-7 2-8 7-8 7-6 6-4

Slip mechanism

T B B T B B T B B T T B

| |rb

0.16 1.07 1.14 0.38 1.14 0.64 0.28 1.28 1.31 0.07 0.18 0.94

The second case (inset marked B, Figure 3.6) represents the strain measurements through grains 2

and 6 (see also Figure 3.5). Strain bands associated with the incoming slip system 11 1 231[ ]( ) and

the outgoing slip system 111 123[ ]( ) are still observed to propagate continuously across the GB. The

DIC strain field displays also intermediate values of strain bands (green color) between the incoming

slip bands on the left side of the GB. These additional strain bands developing in proximity of the GB

can be associated with the partial dislocations left in the GB having a residual Burgers vector

magnitude equal to:

2 6111 111 0 282 2[ ] [ ] | | .

Grain Grain r r

a ab b a

(3.5)

In the

slight

magn

F

in

|

inst

c

In Fig

case

e associated

tly increasing

nitudes appro

igure 3.6.

nset marked

0 16| .rb a

.

nset markedtrain accum

alculated is

gure 6 two c

refers to the

d strain plot

g value appr

oaching the G

Strain mea

d A display

. For this c

d B, a stepmulation on

higher than

cases of slip

e strain mea

(inset marke

roaching the

GB is higher

surements

ys the lowe

ase strain

on the strthe left side

n in the prev

blockage co

asurements a

71

ed B, Figure

left side of t

r than the pre

across a gr

est residua

transmit alm

ain f ield is e of the GB

vious case w

orresponding

across grain

e 3.6) the lo

the GB. In th

evious case a

rain bounda

l burgers v

most unalte

observed wB, the residu

with 0| |rb

g to high | rb

s 4 and 5 (s

cal strain m

his case the

and equal to

ary in case

vector magn

red through

which repreual burgers

28. a .

| magnitude

see also Fig

easurements

difference in

o 2 6 0| |GB

of low | rb

nitude calc

h the GB. F

esents prefevector mag

es are show

ure 3.5). Th

s display a

n the strain

0 22. % .

|. The

ulated,

For the

erential gnitude

wn. The first

e incoming

dislocation

11 1 321[ ](

vector mag

Figure

cases

discon

From the D

high | |rb

,

ns glide on

1) slip system

gnitude equ

e 3.7. Strain

1| |rb

a

ntinuity on th

DIC strain pl

, strains are

the 1 1 1[ ](

m. The dislo

al to

1112[ ]

Grain

a

n measurem

nd the sl ip

he strain f ie

lot (inset ima

not transmit

121) slip sy

ocation react

4 1112[ ]

G

a

ents across

p blockage

ld.

age marked

tted and acc

72

ystem, while

tion on the in

5 |Grain r

b

s a grain bo

on one s

A, Figure 3.

umulate on t

e the outgo

nterface resu

1 14| .rb a

undary in ca

side of the

7) it is clear

the right side

ing dislocati

ults in a high

ase of high

GB gener

that as a co

e of the GB

ions glide o

h residual Bu

| |rb

. In bo

rates a hig

onsequence

leading to an

on the

urgers

(3.6)

th

gh

of the

n high

73

strain gradient equal to 4 5 0 47| | . %GB . The last case analyzed (inset image marked B, Figure 3.7)

has been already introduced in Figure 3.4b (strain field 2A) using lower image resolution (0.87 versus

0.18 μm/pixel). For the dislocation reaction between the incoming 11 1 231[ ]( ) and the outgoing

11 1 2 11[ ]( ) slip systems see Eq. (3.2). From the strain measurements obtained, the strain change

across the GB is particularly high 2 7 1 29| | . %GB .

3.4. Discussion

The concept of residual Burgers vector has been established in earlier works and its importance is

well known in the materials science community [83, 90]. What has been lacking is a quantitative

illustration of the link between the residual Burgers vector and the local strain fields. This became

possible with the development of digital image correlation techniques, and special codes in this

study, written for the purpose of analyzing the strains as the slip approaches the boundary, and

emanates or gets blocked at the boundary. Using this methodology, in Section 3.3 are provided

different types of strain fields across selected GBs which display different residual Burgers vector

magnitudes. The strain fields are directly correlated with the mechanism of interaction:

Low 0| |rb

, the dislocations are transmitted through the grain boundary and the strains

are continuous across the interface (Figure 5, inset marked A, 0 16| | .rb a

).

Intermediate 0 2 1| | ( . )rb a to

, a residual dislocation is left on the grain boundary, this

represents the most common case, the strains accumulate on one side of the grain boundary

depending on the | |rb

magnitude (Figure 5, inset marked B, 0 28| | .rb a

).

High 1| |rb

, dislocations are blocked at the grain boundary, high strain accumulation is

measured on one side of the grain boundary (Figure 6, insets marked A and B, 1 14| | .rb a

and 1 28| | .rb a

).

These results can be utilized to illustrate the significant role that grain boundaries play in the slip

transfer process, in particular they can be useful in further modeling efforts, which include the

strengthening associated with slip dislocation-GB interactions. The accumulation of residual

dislocations at the grain boundary induces a strain discontinuity across the interface that is

proportional to the | |rb

magnitude. It follows that | |rb

can be used as a parameter to quantify (i) the

strain accumulation at the grain boundaries, and (ii) the strengthening effect due to the single grain

boundary. We note the judicial choice of FeCr polycrystals with relatively large grain sizes, and most

74

importantly the activation of a single slip system in each grain. In the presence of two or more

activated slip systems and also twinning, the interpretation of DIC strain fields become more complex

and additional strengthening effects are introduced. Our experiments on single crystals of the same

material and conditions (sample geometry, heat treatment and strain rate) indicate that no hardening

is observed (for low deformations 3% ) when only one or two slip systems are activated [91]. It

follows that the contribution to the hardening observed in the present case ( 0 014.h E ) is provided

by partial or full blockage of the dislocations at the grain boundaries. Therefore, the isolated single

slip system results for the present polycrystal sample shed light into the mechanism very clearly,

hence present unique findings in this work. In summary, in this chapter are illustrated the

considerable promise of the digital image correlation method when utilized in conjunction with EBSD

in gaining insight on the strain fields at the grain boundaries. Other techniques such as TEM can be

used in conjunction with these results presented here as well. These results can be utilized to check

the confidence of crystal plasticity calculations as well as the simulations conducted with molecular

dynamics methods which provide a better description of grain boundaries.

Ch

DaPart o

In thi

2Nb a

analy

The

techn

class

micro

4.1

It is d

and m

meltin

condi

F

EBM

comp

hapte

amagof this work i

s chapter ar

alloy. Local s

yze the influe

analyzed T

nology. EMD

sical manufac

ostructure of

Manufa

difficult to ob

microstructu

ng (EBM) te

itions, thereb

igure 4.1. S

technology

peting techno

er4

geaccis published

re presented

strain measu

ence of the m

Ti-48Al-2Cr-2

D allows to

cturing proce

γ-TiAl alloys

acturingp

btain a comp

re desired a

echnology (F

by reducing t

Schematic o

for “layer b

ologies and

cumuin [91].

d the results

urements via

microstructur

2Nb alloy w

manufactur

esses. Such

s in the dama

process

ponent produ

adopting the

igure 4.1), t

the risk of ox

of the EBM m

by layer” pro

it is possible

75

ulation

obtained fro

a high resolu

re on the da

was manufa

re compone

‘defect-free

age accumula

uced with γ-T

classical m

the process

xidation in the

machine (fro

oductions off

e to operate

non

om the fatigu

ution digital im

amage accum

ctured using

ents without

’ alloy enabl

ation proces

TiAl interme

manufacturing

of material p

e material of

om [92]).

fers several

at temperat

γ‐TiA

ue experimen

mage correla

mulation for t

g Electron

the typical

es to focus

s.

tallics with e

g processes.

production o

the final com

advantages

ures closer t

Al

nts on the T

ation enable

this duplex γ

Beam Melt

defects de

on the influe

exactly the c

. Using Elec

operates und

mponents.

s with respe

to the meltin

Ti-48Al-2Cr-

d to further

γ-TiAl alloy.

ting (EBM)

erived from

ence of the

composition

ctron Beam

der vacuum

ect to other

ng points of

the interm

the powde

titanium an

componen

defects su

has to be

between e

necessitat

concept is

correspond

shows how

initiation s

strains loc

formation o

In the fol

approache

material se

samples w

C(T) spec

cracks).

Figuretempe

The classi

neglecting

order to o

attempt to

etallic alloys

ers of the in

nd aluminum

nts are produ

uch as inclus

accounted

equiaxed and

es to focus

s shown in F

dence of a

w the EBM p

sites derive f

calize before

of a crack.

lowing para

es based on

ensibility to d

with an artific

cimens allow

e 4.2. Typicrature fai led

cal experime

all the effec

overcome th

o rationalize

s [93]. In the

nitial materia

m with the sa

uced. The m

ions, pores e

since the p

d lamellar gra

on the effec

Figure 4.2. T

flat area res

process dras

from the loca

crack initiat

agraphs the

fatigue exp

defects in hig

cial defect ar

wed to analy

al fai lure inid after 3.2 1

ental method

cts correlated

he limitations

e the effec

e EBM proce

al and the p

ame chemica

main advanta

etc. In this sc

possible crac

ains. In this s

ct of the mat

The crack in

sulted from t

stically reduc

al microstruc

ion occurs, a

Ti-48Al-2Cr

periments. A

gh cycle fatig

e firstly pres

yze the crac

it iat ion site 06 cycles (R

dologies allow

d with the loc

s of the cla

ct of the m

76

ess, compon

owders are

al compositio

age of the E

cenario more

ck initiation

scenario the

terial micros

nitiation site

the decohes

ces the pres

ctural feature

and determin

r-2Nb alloy

series of ex

gue (HCF) re

sented. Furth

ck growth fo

found in fatR=0; σmax=3

w to charact

cal material c

ssical exper

material mic

ents are pro

made of an

on as the fin

EBM process

e relevance

sites can be

e application

structure. An

after a fatig

sion of a lam

ence of man

es. It is so im

ne the critica

is character

xperiments f

egime using

her crack gro

or different c

tigue tests. 340 MPa), fr

terize the ma

composition

rimental met

rostructure

oduced witho

n intermetall

nal intermeta

s consists on

on the mate

e found at g

of the defec

example w

gue experim

mellar packa

nufacturing d

mportant to u

al conditions

rized using

for the chara

classical sm

owth experim

crack lengths

Specimen teom [91].

aterial on the

on the micro

thodologies,

using high

out vaporizat

ic alloy bas

allic with whic

n the reduct

erial microstru

general inte

ct tolerance d

which support

ment was fou

age. This exa

defects, and

understand w

which lead

the experim

acterization

mooth sample

ments by mea

s (short and

ested at roo

e meso-scale

o-scale lengt

we made

resolution

tion of

ed on

ch the

tion of

ucture

rfaces

design

ts this

und in

ample

crack

where

to the

mental

of the

es and

ans of

d long

om

e, thus

ths. In

a first

strain

meas

of str

alloy

4.2

The g

by m

paten

condi

press

to ob

Figur

altern

no ev

Mate

geom

remo

4.2.1

Interm

those

F

The p

is ma

surements vi

rains and co

(lamellar or

Materia

gamma titani

eans of the

nted process

itions (Figure

sure of 1700

btain the dup

re 4.5, the d

nated with la

vidence of m

rial has bee

metry was ma

oving the mac

1 Micros

metallics are

e of the cons

igure 4.3. B

present alloy

ainly compo

ia digital ima

orrelate thes

equiaxed gra

al

ium aluminid

EBM A2 ma

s [94] which

e 4.1). The E

bar for 4 h.

plex microst

uplex micros

amellar grain

material defe

en produced

anufactured b

chining allow

tructure

e defined as

stituent metal

Binary Ti-Al

y examined i

osed by the

age correlatio

se localizatio

ains).

de (γ-TiAl) Ti-

achine produc

h allows foc

EBM materia

An heat trea

ructure (2h

structure is

ns with rando

ects like inc

in the form

by conventio

wance.

the compou

ls, and thus i

phase diag

n this chapte

e intermetall

77

on (DIC) tec

ons with the

-48Al-2Cr-2N

ced and dist

used electro

al was hot is

atment (TT),

at 1320 °C)

composed o

omly distribu

clusions, por

m of near-ne

onal machinin

unds of met

intermetallic

ram, [96].

er, the gamm

ic phase γ-

hnique. The

local micros

Nb alloy stud

tributed by A

on beam me

ostatically p

to be perfor

. As it may

of aggregate

uted orientati

res or dendr

et-shape spe

ng with caref

tals whose c

phases and

ma titanium a

-TiAl. From

idea is to m

structural fea

died in this w

Arcam AB (Sw

elting to be

ressed (HIPe

rmed after H

be observed

es (or cluste

ons. From t

rites was fou

ecimens and

fully selected

crystal struct

ordered allo

aluminide (γ

the phase

measure the

atures of the

work has bee

weden), acc

performed

ed) at 1260

HIP, was set

d in the mic

ers) of equia

the observat

und in the s

d final the fin

d cutting para

tures are dif

oys are includ

γ-TiAl) Ti-48A

diagram pr

localization

e analyzed

n produced

cording to a

in vacuum

°C under a

up in order

crograph of

axed grains

ions made,

specimens.

nal sample

ameters for

fferent from

ded [95].

Al-2Cr-2Nb,

oposed by

McCulloug

TiAl. Since

TiAl), sma

grain boun

deformatio

different c

has a L10

temperatu

Figure 4.4

limited num

the small v

Figure

schem

110 d

The phas

microstruc

For the pre

equiaxed g

for both th

propagatio

Crack initi

modes are

of relativel

crack initia

grain boun

for crack

available,

mechanism

grains due

gh, [96], follo

e the heat tr

all fractions o

ndaries [97].

on behaviors

rystal structu

crystal struc

re are provid

4 [63, 65]. T

mber of poss

volume fracti

e 4.4. (a) L

matic indicat

direction an

es can soli

cture has a d

esent alloy, t

grain micros

he microstruc

on character

iation is favo

e interfacial d

ly large initia

ation mechan

ndaries [63],

initiation are

since also

ms. On the

e to the difficu

owing the hea

reatment falls

of the second

. In general

s of the pres

ures. The de

ture (Figure

ded by ordina

The deforma

sible slip pla

on.

10 crystal s

tes one of t

d twinning d

idify in two

ifferent mech

the term dup

structures. In

ctures, given

ristics two di

ored by the

delamination

al cracks whe

nisms can be

or in triple po

e different, a

many chem

other side, c

ulties encoun

at treatment

s in the inte

dary α2-Ti3A

the deforma

sent phases,

eformation is

4.4). For this

ary dislocatio

tion provide

anes of the h

tructure for

the 111 p

develops alo

different m

hanical beha

plex microstr

Table 4.1 a

n for two diff

fferent beha

presence o

and decohe

en one of the

e activated d

oints where s

and a gener

mical, manufa

crack propag

ntered by a c

78

adopted (13

rmediate reg

Al intermetalli

ation behavi

, γ-TiAl and

s predominan

s structure, t

ons and twin

ed by the se

hcp crystal s

the main in

lanes along

ong 1 6 11 2/

microstructure

avior, in parti

ructure indica

are summari

ferent sizes

aviors are ob

of lamellar c

esion of the l

ese mechan

due to localiz

strain incom

ral statemen

acturing and

gation in lam

crack to prop

320 °C for 2h

gion between

c phase can

or of the all

α2-Ti3Al, wh

ntly determin

the main defo

nning on the

econdary pha

structure, an

ntermetall ic

g with sl ip d

111 .

es: equiaxed

cular for the

ates the pres

zed the typic

(fine or coar

bserved dep

colonies, sinc

amellar colo

nism activate

zed strains in

patibilities ar

t on the mo

d other facto

mellar colonie

pagate throug

h) the main p

n the γ-TiAl

n also be pre

oy is determ

hich are cha

ned by the γ-

ormation me

planes and d

ase α2-Ti3Al

d in the pres

phase γ-Ti

dislocation g

d and lame

fatigue prop

sence of both

cal mechanic

rse). From c

ending on th

ce the most

nies which fa

s [65]. More

nduced by blo

re large [64].

ost detriment

ors influence

es is slower

gh the lamell

phase presen

and (α2-Ti3A

esent along

mined by bo

aracterized b

-TiAl phase

echanisms at

directions giv

is limited fo

sent case al

Al. In (b) th

glides on th

ellar grains.

perties of the

h the lamella

cal characte

crack initiatio

he microstru

t important f

favor the form

eover, other m

ocked twinni

. The mecha

tal one is n

es each of

r than in equ

lar interfaces

nt is γ-

Al + γ-

the γ-

th the

by two

which

t room

ven in

or the

so for

he

he

Each

alloy.

ar and

eristics

on and

ucture.

failure

mation

micro-

ing on

nisms

ot yet

these

uiaxed

s.

Tfr

In F

micro

a me

avera

Fm[9

Seve

micro

the F

resolu

local

the

micro

exper

obser

Table 4.1. Mrom [65].

igure 4.5 i

ostructures a

ean colony s

age grain siz

igure 4.5. material is c98]) is repor

ral difficultie

omechanical

FeCr alloy. F

ution. It follow

strains introd

microstructu

omechanical

rimental set-

rve differenc

Mechanical c

s shown a

are clearly ob

size of 100 μ

e of 15 μm [9

Optical micomposed byrted the typi

es arise fo

deformation

First of all th

ws that with

duced by slip

re have tw

deformation

-up. The sca

ces in the loc

haracteristic

a micrograp

bserved. Lam

μm, while th

92].

croscope imy uniaxial gcal compos

or adopting

n mechanism

he average g

the adopted

p and twinnin

wo different

n behaviors

ale adopted

cal microstru

79

cs of the lam

h obtained

mellar colonie

he equiaxed

mage followgrains and lit ion of the

an experim

ms (slip and t

grain size is

d DIC experim

ng separately

crystal lat

. These asp

in the proce

ucture, with a

mellar and e

after etchi

es have a m

grained mic

wing etchingamellar cololamellae.

mental proc

twinning) as

s too small c

mental set-up

y. On the oth

ttices, leadi

pects canno

eeding will b

a clear chara

equiaxed gra

ng a samp

ean fraction

crostructure

g. The micronies. In the

edure which

shown in the

compared w

p, it is not po

her hand, the

ng to com

ot be overta

e the length

acterization o

ain microstru

ple, the tw

in volume o

is character

rostructure e schematic

h considers

e previous c

with the avai

ossible to rec

e phases ins

mpletely diffe

aken with th

h scale whic

of the lamell

uctures,

o different

of 40%, and

rized by an

of the c (from

s also the

chapters for

lable strain

cognize the

ide each of

erent local

he adopted

h allows to

ar colonies

and the eq

the differen

4.3 Fat

4.3.1 Ex

A set of 60

diameter

Testronic t

the numbe

out with t

R=σmin/σma

been pre-o

4.3.2 Re

The fatigu

Figure 4.6

FigureHCF te

This mean

in the num

condensed

ratios in te

quiaxed grai

nt intermetal

tigueexp

xperimen

0 unnotched

D=6.35 mm

test system.

er of cycles o

hree differe

ax=-1 (pure a

oxidized, by f

esults

e experimen

a. In all the e

e 4.6 . Resuest results a

ns that a sma

mber of cyc

d in a single

erms of maxim

ns, neglectin

llic phases.

periment

ntalset‐up

specimens s

m) for room

Fatigue tes

of censored t

nt loading r

alternating s

furnace treat

nts results o

experiments

ults from HCat R=0.6; b)

all variation

cles to failur

e (Haigh) dia

mum stress,

ng the micro

tswithpl

p

suitable for h

temperature

sts have bee

test (runout)

atio: i) R=σ

stress). Prior

tment in air f

f the set car

the Wöhler c

CF experim Haigh diag

in the applie

e. The HCF

agram, Figur

reported in t

80

o-scale effec

lainspec

high cycle fat

e (RT) fatig

en conducted

has been fix

σmin/σmax=0 (z

r to fatigue t

for 20 hr at a

rried out with

curves are e

ents: a) Wöram for the

ed stress am

F test result

re 4.6b. By

the diagram

ts derived by

cimens

tigue testing

ue testing a

d by applying

xed at 107 cy

zero to tens

testing, the s

a temperature

h plain spec

xtremely ind

öhler diagraHCF tests w

mplitude can

s obtained

comparing t

of Figure 4.6

y the local c

have been p

and carried

g the stairca

ycles. Tests

sion); ii) R=σ

surface of th

e of 650°C.

cimens at R=

ependently o

am of roomwith plain sp

lead to subs

in the test c

he results a

6a in parenth

crystal struct

produced (no

out on a R

ase techniqu

have been c

σmin/σmax =0

he specimen

=0.6 are sho

of the R ratio

m temperatupecimens.

stantial differ

campaign ca

at different lo

heses ( ), it c

ure of

ominal

Rumul

e and

carried

.6; iii)

ns has

own in

o.

re

rences

an be

oading

can be

obser

In the

dashe

and a

earlie

with p

near

stress

Fs

The f

lamel

initial

lamel

phase

trans

[99].

relativ

avera

µm. T

poten

rved that the

e diagram o

ed curve, rep

alternating st

er experimen

plain specim

or above the

s equal or be

igure 4.7. Tmooth samp

fracture surf

llas that, due

fracture. O

llar package

es. Another

mission indu

These flat re

vely darker

age defect a

The adoption

ntial influence

e fatigue limit

of Figure 4.6

presenting th

tress, respec

nts. This spe

mens, with ne

e ultimate te

elow 320 MP

Typical nuclples.

faces analyz

e to their unf

ne of the m

es, due to th

potential cra

uced by the i

egions obser

area with re

rea of about

n of fatigue s

e of the micr

t, in terms of

6b, the expe

he equation

ctively, while

ecific behavio

early all spec

nsile strengt

Pa, irrespectiv

eation sites

zed by SEM

favorable dire

echanisms t

he elastic in

ack nucleatio

nterface betw

rved in the S

espect to the

t 22000 µm2

samples with

rostructure in

81

f maximum s

erimentally o

max m

UTS is the (

or has been

cimen failing

th, with no sp

vely of the lo

s observed o

(Figure 4.7

ection with r

that can lea

compatibility

on mechanis

ween two dif

SEM pictures

e surroundin

, correspond

h initial artific

n the crack n

tress, is nea

obtained fatig

aUTS , whe

(minimum) u

n observed t

in the case

pecimen faili

oading ratio R

on the f inal f

7a-b) reveal

respect to tha

d to this typ

y between th

sms can also

fferent phase

s of the fract

g microstruc

ding to an eq

cial defects c

ucleation pro

rly independ

gue limit va

ere m

and

ultimate tensi

hrough all th

the applied

ng (within 10

R.

fracture surf

that fatigue

at of loading

pe of fracture

he γ-TiAl an

o be provide

es which can

ture surface

cture which a

quivalent cra

can provide f

ocess.

dent of the lo

lues lie just

a represen

ile strength,

he fatigue e

(maximum)

07 cycles) fo

face of the

failures orig

g, determine

e is decohe

nd α2-Ti3Al in

ed by the ba

n lead to mic

(Figure 4.7a

allowed to e

ack size of √

further insig

ading ratio.

below the

nt the mean

obtained in

experiments

stress was

r maximum

fatigue

ginate from

a cleavage

sion of the

ntermetallic

arrier to slip

ro-cracking

a-b) have a

estimate an

√area = 150

hts into the

4.4 Fat

4.4.1 Ex

A set of 40

defects in

the specim

a)

Figurefat igue√area=

The artifici

x 100 µm

notches, a

consisting

procedure

minimum

pre-oxidize

unnotched

staircase

respective

4.4.2 Re

By employ

defects) as

R ratio can

(Figure 4.9

√area. In t

non-propa

4.10a. A f

indicate th

tigueexp

xperimen

0 specimens

the form of t

mens by EDM

e 4.8. Geome experimen=644 µm; b)

ial defects in

(√area=220

all specimen

of fatigue lo

ensures tha

compressive

ed by furna

d and FCG s

procedure a

ely.

esults

ying the Mura

s ∆K=0.65∆σ

n be evaluat

9b) enduranc

he case of ru

agating crack

fracture surf

e lamellar co

periment

ntalset‐up

s with a gaug

tiny rectangu

M, as shown

metry of thents (8 mm g) SEM pictur

ntroduced ha

0 µm), Figur

ns with artif

oading in cy

at fatigue cr

e residual st

ce treatmen

specimens. F

at R=0 and

akami mode

σ (π√area)1/2

ted. In the pl

ce strength s

un-out specim

ks has been

face of a sa

olonies wher

tswithar

p

ge diameter o

ular micro-slo

in Figure 4.8

specimensauge diamere of art if icia

ave dimensio

e 4.8. In ord

icial defects

ycling compr

racks are ge

resses at cr

nt in air for

Finally, fatigu

R=0.6, with

l for the asse2, the thresh

ots of Figure

stress range

mens tested

observed in

ample failed

re crack prop

82

rtificiald

of 8 mm hav

ots have bee

8.

s for assesseter) and a) al defects p

ons of 1500 µ

der to gener

s have been

ression for a

enerated at t

rack tip. Afte

20h at a te

ue experimen

h defects wit

essment of t

old correspo

e 4.9, for loa

es are given

at stress am

corresponde

at R=0.6 is

pagated throu

defects

ve been prod

en carefully p

b)

sing defect snominal shroduced by

µm x 300 µm

rate small c

n submitted

a number of

the root of t

er pre-cracki

emperature

nts have bee

th √area eq

he range of

onding to the

ading ratio of

as a function

mplitudes cor

ence of the i

s shown in

ugh two lame

uced, and tw

produced in

sensit ivity iape of arti f iEDM.

m (√area=644

racks at the

to a pre-cr

cycles up to

he EDM not

ng, all spec

of 650°C, a

en performed

ual to 220

stress intens

e endurance

f R=0 (Figure

n of the equi

rresponding t

nitial (artificia

Figure 4.10b

ellar colonies

wo type of ar

the mid-sect

n short cracicial defect

4 µm) and 50

e root of the

racking proc

o 107 cycles

tch by keep

cimens have

as in the ca

d according

µm and 644

sity factor (su

strength for

e 4.9a) and

ivalent defec

to the fatigue

al) defects, F

b, the red a

s.

rtificial

tion of

ck of

00 µm

EDM

cedure

s. This

ping to

been

ase of

to the

4 µm,

urface

r each

R=0.6

ct size

e limit,

Figure

arrows

Fatig

with a

been

th

where

speci

ratio

proba

lower

Theo

increa

the c

micro

dimen

F

ue failures in

a typical size

applied in th

ie

are

e ∆σie repre

imens and a

R=0 and R=

ability of act

r, i.e. the in

oretically, as

ased fatigue

case of bend

ostructural fe

nsions [101]

igure 4.9. K

n plain speci

e of √areai=1

he form:

0

0

area

a area

esents the

an inherent d

=0.6. If a sma

tivating an i

nitial active

the Kitagaw

e strength of

ding loading

eatures of

.

Kitagawa dia

mens were f

150 µm, the

iarea

w

fatigue endu

defect √area

aller volume

nherent “mic

defect size

wa diagrams

the materia

of thin sectio

150 µm mad

agrams for:

83

found in corr

modification

with area

urance stren

ai of 150 µm

of material w

crostructural

e may be s

s in Figure 4

l when a no

ons. Additio

de in the p

a) loading r

espondence

of the El-Ha

01

0.65

FthK

a

ngth obtaine

has been ta

would be stre

” feature wi

smaller for s

4.9 reveal, th

n-uniformly d

nally, it may

present stud

radio R=0; b

of peculiar m

addad mode

2

FCGh

ie

are

ed in the fa

aken into ac

essed up to

th size √are

smaller stres

here is a po

distributed lo

y be noted th

dy is in the

b) loading ra

microstructu

l by Tanaka

0 iea area

atigue tests

ccount both

the threshol

eai is likely

ssed materi

ossibility to o

oading is ap

hat the size

e range of

at io R=0.6.

ral features

[100] have

(4.1)

with plain

for loading

d level, the

to become

al volume.

observe an

plied, as in

of inherent

the colony

Figure(∆σ=1

Figurefai led region

4.5 Fat

4.5.1 Ex

A smaller

EDM for p

cracked in

order to ge

generated

local posit

crack whic

e 4.10a . N25 MPa, R=

e 4.10b. Seafter 90297

ns where the

tiguecra

xperimen

set of 6 spec

producing th

n cyclic com

enerate a sm

in case of p

ive (tensile)

ch propagat

Near thresh=0.6; 107 cyc

ection of a f7 cycles wite crack prop

ackgrowt

ntalset‐up

cimens suita

he notch (Fi

pression [10

mall crack in

re-cracking p

stresses whe

es and succ

old fatigue cles without

fat igue samth ∆σ=300 M

pagates thro

thexperi

p

ble for crack

gure 4.11).

02]. Compres

front of the

procedures u

en the extern

cessively sto

84

cracks art specimen f

ple with anMPa at R=0

ough the lam

iments

k propagation

The fractur

ssion pre-cr

notch and t

using tensile

nal load appr

ops once re

re observedfailure).

init ial art i f0.05. The a

mellar packa

n testing hav

e mechanics

acking (CP)

thus limit the

loads. The s

roaches zero

ached the i

d in run-ou

icial defectrrows indicages.

ve been prod

s specimens

procedure i

e residual pla

small yielded

o. These stre

nitial plastic

ut specimen

. The sampated the ‘f la

duced using

s have been

is implemen

astic deform

d region gene

esses nuclea

(in compre

ns

le at ’

a wire

n pre-

ted in

ations

erates

ate the

ssion)

mono

of th

ampli

F

For s

blade

Fnn

Fatig

mach

deter

behav

(R=0

value

otonic region

e crack gro

itude the fina

igure 4.11 .

starting a cra

e polishing te

igure 4.12.otch which ucleation of

ue crack gro

hine (Figure

rmine the thr

vior, fatigue

.05 and R=0

e for a long c

n. Using the p

owth test ar

al pre-crack l

Sample geo

ack in cyclic

echnique (Fig

SENVB medisplay hig

f non-propag

owth tests h

4.13a) and

reshold stres

crack growt

0.6) by increa

rack is reach

pre-cracking

re cancelled

ength can be

ometry for c

c compressio

gure 4.12).

ethod appliegh localizedgating small

ave been ca

the crack le

ss intensity f

th tests at ro

asing the ap

hed.

85

procedure, t

d. Moreover,

e controlled.

crack growth

on the wire

ed to the ord strains al cracks in f

arried out by

ength monito

factor for lon

oom tempera

pplied ∆K (lo

the effects o

, selecting t

h experimen

EDM starter

riginal notchnd stressesront of the o

y means of

ored by COD

ng cracks ∆K

ature have b

ad amplitude

f the crack c

the appropr

ts.

r notch was

h in order tos. This metoriginal notc

a servo-hydr

D gage (Figu

Kth and the l

een carried

e) in small st

closure at the

riate compre

sharpened

o obtain a sthodology ech.

raulic MTS 8

ure 4.13b).

long crack p

out at const

steps until the

e beginning

essive load

by a razor

shallow nables

810 testing

In order to

propagation

tant R ratio

e threshold

Figuregrip se

4.5.2 Re

In the fatig

at R=0.05

about 4 M

crack grow

cases wa

advancem

Cr

3.2

ob

∆K

Ho

ap

to

to

e 4.13. Expeet-up; b) pa

esults

gue crack gr

no crack gro

MPa√m. Two

wth curve dis

s observed

ments were m

rack growth

25x106 cycl

bserved. Foll

K=6.13 MPa

olding the lo

ppreciable cr

∆K=6.70 MP

the final failu

erimental serticular of th

rowth experim

owth was ob

crack growt

splays a simi

a stable c

measured wh

curve 1 (Fi

es (with a

lowing an in

a√m) an ins

oad at ∆K=6

rack propaga

Pa√m) starte

ure.

et-up for crahe COD gag

ments a coh

served for ∆

th curves for

lar crack pro

crack propag

en the load w

igure 4.14a)

final ∆K=5.

ncrement of t

stantaneous

6.13 MPa√m

ation. A furth

ed the fast c

86

ack propagage for the me

herent behav

∆K below 6 M

r each load

opagation be

gation beha

was increase

), R=0.05. In

.77 MPa√m)

the applied

crack adva

m for about

her small inc

crack propag

ation experimeasure of th

vior was obse

MPa√m, while

ratio R are

havior. In pa

avior, while

ed.

nitially, the s

) and a sm

load amplitu

ancement o

additional

rement of th

ation which

ments, a) loe crack leng

erved: for th

e for the tests

reported in F

rticular, in an

several ins

sample was

mall crack a

ude (from ∆K

of ∆a=0.6mm

1.5x106 cycl

e load (from

quickly cond

ad frame angth.

e tests cond

ts at R=0.6, ∆

Figure 4.14.

ny of the ana

stantaneous

s cycled for

advancemen

K=5.77 MPa

m was obse

les didn’t le

m ∆K=6.13 M

ducted the s

nd

ducted

∆Kth is

Each

alyzed

crack

about

t was

√m to

erved.

ead to

Pa√m

ample

F2c

igure 4.14a refers to eonducted at

Crack gro

MPa√m f

incremen

produced

MPa√m t

Crack gro

also for t

amplitude

doesn’t d

curves, 1

(as cases

enabled t

Crack gr

technique

to a final

a . Crack groexperiments t load ratio R

owth curve 2

for more tha

nt was succ

d a small cra

o ∆K=6.24 M

owth curve 3

he experime

e equivalent

display any s

and 2, the f

s 3 and 4). In

to measure s

rowth curve

e in order to

value of a=7

owth curvesconducted

R=0.6.

(Figure 4.14

an 9x106 cyc

essively app

ck advancem

MPa√m) gene

3 (Figure 4.1

ents carried o

to ∆K=3.8 M

stable crack

final propaga

n the previou

several point

4 (Figure 4

measure the

7.5mm for 5x

87

from differat load rati

4a), R=0.05.

cles without

plied (from

ment of ∆a=0

erated the fa

14a), R=0.6.

out at a load

MPa√m was r

k propagation

ation stage w

us cases, thi

ts for the fatig

4.14a). In th

e threshold s

x106 cycles, a

ent samplesio R=0.05, w

The initial lo

appreciable

∆K=5.75 MP

0.5mm. A fur

ast crack prop

Similar crac

d ration R=0.

required to s

n region. In

was “almost-

s characteris

gue crack gr

his case was

tress intensit

at this point (

s. Crack growhile 3 and

oad was hold

crack adva

Pa√m to ∆K

rther load inc

pagation.

ck growth be

6. For crack

tart the prop

fact, in the

-unstable”, b

stic of the fin

owth rate cu

s implement

ty range ∆Kth

(∆K=4.1 MPa

owth curvesd 4 to exper

d at a consta

ncement. A

K=6.04 MPa

crement (fro

ehaviors were

k growth curv

pagation whic

first two cra

but not “totall

nal crack gro

urves (Figure

ted the load

h. The crack

a√m) the loa

s 1 and riments

nt ∆K=5.75

small load

a√m) which

m ∆K=6.04

e observed

ve 3 a load

ch basically

ack growth

ly-unstable”

owth curves

4.16).

d reduction

was grown

d reduction

pr

re

dis

im

(w

the

The crack

crack grow

paths due

stages of

propagatio

particular,

barrier to t

applied ΔK

crack pro

advancem

Figurecrack from e

The increm

progressiv

explained

sliding of

microstruc

ocedure wa

ducing the a

splayed on

mplies that th

where we firs

e load of the

k growth cur

wth curves d

to local micr

small crac

on. The loc

the crack en

the crack adv

K) is necessa

pagation sin

ments (Figure

e 4.14b. Varlength. Dat

experiment a

ment of ∆Kt

ve developm

that the obs

the crack

ctural effects

as implemen

applied ∆K w

the crack gr

he value of

st observed a

e unstable pro

rves present

isplay a non

rostructural e

k propagatio

al microstru

ncountered l

vancement.

ary to advanc

nce it incre

e 4.14b).

r iat ion of tha extrapolatat R=0.05.

th with crack

ment of crack

served closu

flanks indu

s. This effec

nted. The l

while the cra

rowth curve

the thresho

a crack adva

opagation).

ed here allo

-linear crack

effects [103,

on for whic

ucture strong

lamellar colo

In this scena

ce the crack.

eases the ra

e stress inteted from the

k advanceme

k closure eff

ure effects (e

uced by the

ct becomes

88

oad reducti

ack is propag

4, the crac

old is contai

ancement) to

owed to prov

k growth beh

104]. Figure

ch is eviden

gly influence

onies which

ario, a load in

. This effect

ange of str

ensity threse crack grow

ent for sma

fects. In the

especially w

e non-linear

important

on procedu

gating till the

ck didn’t stop

ned in the

o ∆K=4.06 M

vide two ma

avior which

e 4.15 shows

nt the non-li

es the sma

are not well

ncrement (an

is beneficial

ress intensit

hold range wth curves

ll crack leng

eir work, Gar

when the cra

r nature of

especially fo

re consists

e crack front

p during this

interval from

MPa√m (whic

ain considera

characterize

s two images

inear charac

ll crack gro

oriented and

nd so also an

in terms of r

ty threshold

with the increported in

gths can be

rcia and Seh

ck is small)

the growin

or materials

of progres

t stops. As c

s procedure

m ∆K=3.8 M

ch correspon

ations. First

es non-linear

s obtained at

cter of the

owth behavi

d provided a

n increment

resistance of

∆Kth with

rement of thFigure 4.14

correlated t

hitoglu [103

derive from

ng crack d

s that exhib

ssively

clearly

. This

Pa√m

nds to

of all

r crack

t early

crack

or. In

a local

of the

f small

crack

he 4a

to the

, 104]

m local

ue to

it low

plasti

the d

Fm

Two

range

The

indep

accor

be ob

differ

with o

route

obser

growt

proce

icity-induced

ifference in t

igure 4.15microstructur

different abs

e ∆K, while in

critical Kmax

pendently of

rdance with t

bserved that

ence betwee

other data p

e, resulting in

rved that the

th threshold

ess [62, 105]

closure (as

the crack gro

. Non-l inearal effects.

scissa were

n Figure 4.16

x value, corr

f the applie

those reporte

the available

en ∆Kth and

published in

n different m

e γ-TiAl prod

characterist

, where a ∆K

in γ-TiAl allo

owth rate cur

ar crack pa

used, in par

6b was used

responding

ed R=Kmin/Km

ed in literatu

e ∆K range f

Kmax, resulti

the literature

microstructure

uced with th

tics with res

Kth of about 5

89

oys). This co

rves reported

aths at ear

rticular in Fig

d the maximu

to specimen

max ratio. Th

re for the du

for crack grow

ing in high v

e are difficu

es for the sa

he EBM proc

spect to thos

5 MPa√m for

onsideration

d in Figure 4.

ly stages o

gure 4.16a w

um stress int

n failure, is

he threshold

uplex microst

wth is rather

value of the

lt, due to dif

ame (nomina

cess employe

se of TiAl al

r R=0.1 was

is also impor

16a-b.

of propagat

was used the

tensity factor

in the ran

d values de

tructure of γ-

r limited, due

slope. Even

fferent heat

al) chemical

ed here offer

loys obtaine

reported.

rtant in orde

tion due to

e stress inte

r of the cyclic

nge 10.5-11.

etermined h

-TiAl alloys [

e to the relati

n if a direct c

treatment an

composition

r superior fa

ed by conve

r to explain

o local

nsity factor

c load Kmax.

5 MPa√m,

ere are in

105]. It can

vely limited

comparison

nd process

, it may be

tigue crack

ntional PM

Figureintens

The obser

the non-lin

4.6 Un

4.6.1 Ex

Local dam

measurem

geometries

Figureimage

e 4.16. Fatity factor (S

rved differen

near crack gr

niaxialsta

xperimen

mage effects

ments throug

s for uniaxia

e 4.17. Geo correlation

igue crack SIF); b) max

ce on the cr

rowth induce

aticexpe

ntalset‐up

induced by t

gh digital i

l tension/com

ometry of thin a) tensio

growth rateimum SIF in

rack growth

d closure wh

eriments

p

the material

mage corre

mpression ex

he specimenon and b) co

90

e curves inn the loading

rates for dif

hich is typica

usingDI

microstructu

elation (DIC

xperiments w

ns for uniaxompression.

n terms of: g cycle Kmax

fferent load r

al of materials

C

ure are studie

C) methodol

were adopted

xial stat ic e

a) ∆K, ran

x.

ratios is con

s with lamella

ed using hig

ogy. Specia

d, Figure 4.17

experiments

nge of stres

nsidered rela

ar microstruc

h resolution

al plane sa

7.

using digit

ss

ated to

cture.

strain

ample

tal

In pa

gage

disch

were

DIC w

mate

IMB-2

was 3

F(f

Fcw

For e

increa

rticular, tens

length and

harged mach

conducted

was used to

rial [66]. For

202 FT CCD

3.0 μm per p

igure 4.18.from P800 u

igure 4.19 .orner of a 1

with the optic

ex situ DIC, a

ased imagin

sile dog-bone

compressio

hining (EDM)

in displacem

o measure t

r in situ DIC

D camera (1

pixel.

Preparationup to P4000)

The sampl1 x 1 mm2 scal microsco

an optical mic

ng magnifica

e shaped spe

on samples

) with the re

ment control

he residual

C, reference

600 x 1200

n of the TiA), and succe

e has beensquare regioope at differ

croscope wa

tion improve

91

ecimens with

sectioned in

equired toler

at a strain r

strain field

and deform

pixels) with

Al samples. Tessively etc

n marked wion. This regrent magnif i

as used to ca

es the DIC

h a 1.5 mm x

nto 4 mm x

rances. Tens

rate of about

and correlat

ed images w

a Navitar o

The samplehed.

th four Vickion has beecations.

apture the re

measuremen

x 3 mm cros

4 mm were

sion and com

t 5x10-5 s.1.

te it with the

were capture

optical lens, t

s are polish

kers indentaen analyzed

ference and

nt resolution

ss-section an

e produced

mpression e

High resolut

e microstruc

ed using an

the resolved

hed with SiC

ation marke capturing i

deformed im

n (3.0 μm/ p

nd a 10 mm

by electro-

xperiments

tion ex situ

cture of the

IMI model

d resolution

C paper

rs at a images

mages. The

pixel versus

0.44 μm/p

lamellar an

paper grit

4.18. The

optical mi

changes.

4.6.2 Re

In situ DIC

tension/co

were deriv

surface, F

possible to

Figurefracturto 3%.

The comp

possible to

obtain the

4.6.3 Co

Figure 4.2

2.5%. In c

is possible

an examp

highlighted

pixel for ex s

nd equiaxed

sizes (from 1

1 mm x 1 m

croscope m

esults

C was used

ompression s

ved averagin

igure 4.20. A

o reach highe

e 4.20 . Sumred at less t.

pression exp

o monitor an

stress-strain

ompressi

21 shows the

ompression.

e to reach hi

le of these r

d box is show

situ) and ena

grains, resp

1200 to 2500

mm region co

magnifications

d to measur

specimens. T

ng the DIC a

As expected,

er deformatio

mmary of thethan 1% of

periments w

n area of the

n curve repor

onexperi

e strain field

As already

gher strains

regions is sh

wn the effect

ables better

pectively. Prio

0), and a fine

overed with

s the numbe

re the evolu

The stress-st

axial strain m

in tension th

ons.

experimentnominal stra

ere conduct

e sample and

rted in Figure

iment

for a compr

shown in us

. In this case

own in the z

t of the differ

92

characteriza

or to etching

e polishing w

ex situ DIC

er of image

ution of loca

rain curves f

measuremen

he alloy disp

ts conducteain, while c

ted in displa

d average th

e 4.20.

ression samp

ing the stres

e clear local

zoomed regio

rent orientati

ation of the l

g, the sample

with diamond

is depicted

es required

al strains du

for tension/co

nts in the mo

lays low duc

d on TiAl saompression

acement con

he strains in

ple with a re

ss-strain curv

strain accu

on of the str

on of two pa

local strain m

es were polis

paste (6, 3

in Figure 4.1

for covering

ring the loa

ompression s

onitored reg

tility, while in

amples. Ten samples we

ntrol. Adopti

the load dir

sidual avera

ves, with a co

mulations ar

rain field in F

ackages of la

magnitudes

shed with dif

and 1 µm), F

19, using dif

g the target

ading for bot

static experi

ion of the sa

n compressio

nsion sampleere tested u

ing in-situ D

rection in or

age deformat

ompressive

re easily dete

Figure 4.21.

amellar grain

in the

fferent

Figure

fferent

t area

th the

ments

ample

on it is

es up

DIC is

rder to

tion of

load it

ected,

In the

ns. For

the p

plane

orient

high r

Fmlod7dde

4.6.4

Unde

comp

curve

stress

interm

succe

not re

than

micro

introd

present level

e which resp

ted lamellar

residual stra

igure 4.21microstructuroad directioisplay differ% are obseformation. ecohesion xperiments.

4 Tensio

er tensile lo

parison betw

e of the tensi

s of about σ

mediate load

essively unlo

eported in th

the compres

ostructure on

ducing cyclin

of the anal

pect to the lo

colony (on

ins, while for

. Example re map obtan. In the serent strain fserved, whi

The localimechanism

nexperim

oads, the a

ween compre

on experime

σ=400 MPa

ding step. The

oaded till a fi

he stress-str

ssion case. T

n the local

g loadings.

lysis is not p

oad direction

the left insid

r the other la

of ex situ ained after elected regioields. On thle on the ized strains between

ment

nalyzed ma

ession-tensio

ent analyzed

at a deform

e sample wa

nal residual

rain curve). I

This analysis

strain fields

93

possible to d

n. Neverthel

de the analyz

amellar colon

high resoluetching. Th

on is possibe lamellar ccolony on

s observed lamellar co

aterial shows

on stress-str

is reported i

mation of up

as statically l

deformation

In this case,

s is only a fir

in tension,

determine th

ess this limi

zed strain fie

ny no residua

ution DIC ohe strain f i leble to obsercolony on th the right

in the lamolonies alre

s the typica

rain curves

in Figure 4.2

to 0.7%. Ex

oaded till a m

n of 0.24% (t

, it is expect

rst attempt to

and newel

he third com

itation, it is c

eld selection

al strains wer

overlapped ed refers torve two lamee left strainis almost

mellar packeady obser

al brittleness

in Figure 4

2. The samp

x-situ DIC w

maximum str

he unloading

ted much low

o understand

experiments

mponent of th

clear how a

n, Figure 4.2

re observed.

with the mo the strain el lar colonie

n localizatiofree of re

kage confirmrved in the

ss of TiAl a

4.20). The s

ple failed at a

was impleme

ress of σ=35

g part of the

wer strain lo

d the effect

ts will be im

he lamellar

a favorable-

1) displays

material in the

es that n up to esidual ms the e HCF

alloys (see

tress-strain

a maximum

ented at an

50 MPa and

diagram is

ocalizations

of the local

mplemented

Figurerefere

(ex-sit

Figure 4.2

about 340

capturing t

localized r

Figureof 0.2microson the

From the

region of

intersects

e 4.22. Strnce images

tu) with an a

3 reports the

0 µm x 640

the images

residual strai

e 4.23. Stra24%. Locastructure; ine interface re

local residua

high localize

also the inte

ress-Strain and deform

average res

e residual str

µm, success

before the e

ns was succ

in plot for al ization of

n particular egions betw

al strain field

ed strains pr

erface with th

curve for med images

idual strain

rain field for

sively overla

experiment. A

essively sele

region of thstrains a

on the regioween two lam

d and the sc

ropagates al

e upper grai

94

the tensions has been

of ε=0.24%

a selected re

apped with th

A smaller re

ected and an

he sample wre measuron analyzedmellar colon

chematic of t

long the inte

n.

n experimeimplemente

.

ectangular re

he images o

gion of 225

nalyzed.

with an avered in diffe

d the high loies.

the local mic

erface betwe

nt. Correlated out of th

egion of the

of the micros

µm x 225 µ

age residuaerent locatocalized stra

crostructure i

een the lame

tion betweehe load fram

sample surfa

structure obt

µm displaying

al deformatiotions of thains nuclea

is evident th

ellar colonie

en me

ace of

tained

g high

on he te

at the

es and

95

4.7 Finalconsiderations

A potential disadvantage of cast and PM γ-TiAl alloys, in terms of component design, is their limited

fatigue crack growth resistance and damage tolerance. Additionally, in the case of cast and

conventional PM TiAl alloys, due to the unfavourable combination of fatigue crack growth threshold,

propagation behaviour and bigger inherent defects-porosity, non-metallic inclusions and metallurgical

defects, like dendrites, the usable fatigue endurance strength may be quite limited. In general, there

is a small difference between the fatigue threshold stress-intensity-range of long cracks and the

apparent fracture toughness, leading to shortened lifetimes for small changes in applied stress. For

the analysed Ti-48Al-2Cr-2Nb alloy, the manufacturing process adopted (EBM) allows to avoid the

typical defects of cast or PM materials, providing higher fatigue threshold and fatigue strength.

In this chapter were firstly depicted the results adopting the classical fatigue experiments. Fatigue

experiments were implemented on fatigue specimens with an artificial defect, in this case the fatigue

threshold were estimated for two different initial defect depths. The experimental results can be

accurately described by a modified El-Haddad model, see equation (4.1). In Figure 4.9 is reported

the equation representing the adopted model, along with the experimental fatigue limits for the

samples with the artificial defects. In addition, the results obtained for plain samples are also reported

in the same diagrams (see Figure 4.9). HCF limits for plain specimens are required to be translated

at an initial defect size of √areai of 150 µm for both for loading ratio R=0 and R=0.6 in order to match

the prevision made with equation (4.1). This fundamental consideration points to the fact that

nevertheless the material is free from initial manufacturing defects, the fatigue limits for smooth

samples display values which can be explained only assuming the presence of initial defects with an

average size of √areai=150 µm. Analyses of the fracture surfaces show the presence of flat areas

corresponding to the lamellar colonies which are considered to be potential crack initiation sites

(Figure 4.7). In particular these regions display an average area √areaLamellarColonies=150 µm which

corresponds to the observed initial crack length defect √areai. Not only fatigue limits are affected by

the microstructure, but also the small crack propagation, and thus stress intensity threshold ranges

(section 4.4). The lamellar colonies are observed to provide an initial tortuous crack path which

provides barriers to crack advancement when the crack front encounters unfavourable lamellar

packages (see micrographs in Figure 4.15). Moreover, roughness induced crack closure also

develops as a consequence of the non-linear crack path (Section 4.5.2). This observation suggests

that the reduction of the grain size is potentially detrimental for the capability to develop roughness-

induced crack closure, thus reducing the crack propagation resistance of the alloy.

Along the classical experimental approaches just discussed, in this chapter is also introduced the

implementation of high resolution DIC for determining the local effect of the material microstructure

on the strain fields. The results presented using DIC strain fields clearly confirm the critical role on

96

crack initiation played by the lamellar grains previously argued. The high local strains reported in

Figure 4.21 and 4.23 are discovered to originate along the lamellar colonies, and along the interfaces

between the lamellar colonies and the equiaxed grains. Similar results were introduced to explain the

fracture surfaces discovered after the experiments on the smooth samples (Figure 4.17). Of course,

from this analysis is not possible to detect the exact point where, successively, cracks originate.

More analyses are required, in particular adopting post-analyses via SEM. A combination between

crack locations using SEM images and the present strain maps (Figures 4.21 and 4.23) can be

useful for assessing a potential correlation between the regions displaying the highest strain

localizations with the regions which, successively, favor crack initiation. Again, the present results

suggest that the advantage of using DIC strain maps provides simultaneous analysis of several

microstructural locations on significant sample’s areas (damage-map of the potential and more

detrimental microstructural features). In this way, the choice of the best compromise for the

microstructure composition (volume fraction of equiaxed/lamellar grains and average grain size)

based on the design requirements can be operated.

97

Chapter5

ConcludingRemarksandFuture

Developments

5.5 ConcludingRemarks

In order to continuously improve the knowledge of the material behavior and provide more reliable

models able to correctly predict the stresses and deformations inside components, newel

experimental approaches are required to follow the natural evolution of the research. This work

presented the usage of a promising experimental approach which is able to link the material behavior

on the microscopic scales with the material behavior on the meso and macro scales through local

strain measurements. High resolution strain fields have been obtained from Digital Image Correlation

(DIC), and the combination of these results with the microstructural information of the alloy provided

important conclusions on bcc crystal plasticity, and on damage accumulation on γ-TiAl alloys. The

main results obtained are summarized in the following paragraphs.

5.1.1. ResultsofChapter2

In Chapter 2, the results provide the basis for discussion of pertinent issues regarding deformation in

bcc materials when both slip and twinning occurs, and support the following conclusions: (i) the

observed stress-strain behaviors are classified in four different Cases (schematic in Figure 2.5)

based on the activated mechanisms (twin/slip) that lead to a different crystal hardening (twin-twin and

twin-slip interactions display higher hardening than slip-slip interactions). (ii) For Case I (twinning

dominated) is observed a lower critical resolved shear stress for twin migration (124 MPa) compared

to the Case II (153 MPa) where twin nucleation is preceded by significant slip activity. (iii) Twin

nucleation occurs at an average critical resolved shear stress of 190 MPa. For the cases analyzed in

this study this observation suggests that a critical shear stress for twin nucleation holds to a first

approximation. (iv) The nucleation of slip occurs at an average critical resolved shear stress of 90

MPa and always precedes twin nucleation. (v) Local strain measurements are provided on twin-twin

and twin-slip intersection regions for two specific crystal orientations. Twin-twin intersections lead to

higher strain localizations (up to 10%) compared to the twin-slip case (up to 6%).

98

These conclusions provide deep insight into deformation behavior of bcc alloys, in particular on the

active deformation mechanisms based on the crystal orientation. Moreover, strain fields can be used

as a check of crystal plasticity calculations.


In Chapter 3 were investigated dislocation-grain boundary interactions for a FeCr alloy using strain

fields determined by digital image correlation. Strain fields across GBs provide a direct quantification

of the GB capability to transmit or block slip dislocations. The study elucidates the role of the residual

Burgers vector magnitude in predicting full/partial slip transmission, or slip blockage. Along the

Chapter are provided the strain fields across four GBs displaying different residual Burgers vector

magnitudes. In particular, for low 0| |r

b

no residual dislocation is left on the grain boundary. In this

case slip is observed to transmit unaltered across the interface and the resulting strain field is

continuous. For intermediate 0 2 1| | ( . )rb a to

, depending on the | |r

b

magnitude a step on the strain

field is observed on the interface that represents the strain accumulation on the GB side of the

incoming slip system. Finally, for high 1| |r

b a

, dislocations are blocked at the grain boundary, and

high strain accumulation is measured on one side of the grain. The results clearly show a direct

correlation of the strain change across the interfaces with the | |r

b

magnitude thus indicating the

possibility to use the | |r

b

as a parameter for predicting the slip transmission capability of the grain

boundaries in a polycrystal material.


In the case of the Ti-48Al-2Cr-2Nb alloy examined in Chapter 4, the advantage of the γ-TiAl

produced by the EBM process is that typical defects of cast or PM materials can be avoided and

higher fatigue threshold and fatigue strength with respect to competing technologies can be obtained.

Thus, the experiments carried out on this duplex γ-TiAl alloy allow to focus on the influence of the

microstructure (lamellar and equiaxed grains) on the fatigue properties. From the observation of the

experimental results the following conclusions may be drawn. (i) The fatigue experiments with

artificial defects show that ∆Kth for defects larger than 100-150 µm can be described very accurately

by a modified El-Haddad relationship, taking into account the inherent microstructural features of the

material; the values of the threshold stress intensity factor range depend on the loading ratio R, so

that the mechanism does not seem to be governed by Kmax. only, as it might be assumed from the

fatigue experiments with un-notched specimens at different R ratios. This apparently simple material

model, illustrated in the diagrams of Figure 4.17 gives to the designers useful indications about the

influence of defects size on the fatigue endurance strength that may employed for the safe design of

gas turbine components. (ii) High resolution DIC strain fields were also measured in conjunction with

99

microstructural maps for determining the local effect of the material microstructure and locate

potential micro-crack sites. From the static uniaxial tension/compression experiments were observed

high localized strains accumulated along lamellar colonies and in the interfaces regions between

lamellar and equiaxed grains. (iii) Further experiments adopting high resolution DIC will be carried

out under cyclic loads in order to obtain more detailed damage maps of the microstructure. As shown

in this work, these tools provide valuable information on the microstructure design (volume fraction

and average size of the lamellar and equiaxed grains) in order to reach the required mechanical

properties.

5.2. Futuredevelopments

Following the experiments depicted in the preceding chapters, some possible developments on the

DIC technique, and some different applications are here presented. Some of these results refer to

experiments obtained by the author and aim to provide further insight for future research works. The

aim of this chapter is to show potential advanced applications of the experimental methodology

adopted. In section 5.1 is presented an application of the in situ DIC methodology at high

temperature (400°C) for a FeCr single crystal with 10 1[ ] crystal orientation. A comparison between

the strain fields obtained at room temperature (chapter 2) and at high temperature is shown. In

section 5.2 a promising application of ex situ DIC via SEM is investigated for studying twin-twin

interactions. The strain field in correspondence of a twin-twin intersection is analyzed and the

improvements obtained using these high resolution images are compared with the previous strain

field resolutions available.

5.2.1. HighTemperatureexperimentsonFeCr

One of the main issues in the usage of DIC at high temperature arises with the choice of the correct

speckle. In fact, the increment of the temperature introduces difficulties in generating a speckle patter

that doesn’t change during the experiment. Paint burning and oxidation are the main sources of

modification of the speckle pattern during the experiment. If the experiment is particularly long (e. g.

fatigue, creep, etc.) these problems can void the strain measurements. Different solutions for

producing the speckle are available depending on the type of the experiment. The experiments

carried out in this study are all static experiments, in this case the duration of the experiment is

limited. Moreover also the temperature is limited (400°C). This allows to use the same type of

speckle patter (black pain applied with an Iwata airbrush) providing that the speckle is pre-heated

before the experiment.

Figure(a) roopreced

The pre-he

Figure 5.1

Figure 5.1

Figurehorizohomogon thethe sa

This proce

occur to th

heated ag

a final cor

e 5.1. Compom temperading the exp

eating phase

. Figure 5.1

b shows the

e 5.2. The ntal directio

geneous dise induction hmple-grips

edure enable

he speckle p

ain at the tes

rrelation betw

parison betwature, and (bperiment is n

e induces a

a shows the

same samp

sample heons. The mestribution ofheating. Mosystem.

es to stabiliz

pattern durin

st temperatu

ween the sur

ween the speb) after heanecessary fo

modification

e speckle pa

le heated up

eating produeasure of th the displacreover it is

ze the speck

g the experi

ure (400°C).

rface at room

100

eckle patterating the saor the stabil

on the origi

attern used

p to 400 °C u

uces elonghe displacecement, andpossible to

kle pattern, it

ment. Follow

During this p

m temperatu

produced wmple at 400lization of th

inal speckle

for room te

using load co

ations in thment using d verify eve verify also

t is so expec

wing the pre-

procedure so

ure and the s

with the Iwat0 C. The sahe black pai

patter, whic

mperature e

ntrol with no

he (a) vertDIC allows

entual dis-hthe correct

cted that lim

-heating pha

ome images

surface at hi

ta airbrush ample heatinnt at 400 C

ch can be se

experiments,

ominal stress

ical, and ( to verify thomogeneit ie

t al ignment

mited modific

ase, the sam

are acquired

igh temperat

at ng .

een on

while

σ=0.

b) he es in

ations

mple is

d, and

ture is

availa

samp

set-u

from

In fig

(400

obtain

temp

temp

Fhdn

Digita

mark

mark

displa

C) th

able. The dis

ple induced

p. The expe

the averaged

ure 5.3 is pr

°C) experim

ned two mai

erature (R

erature is sm

igure 5.3. Cigh temperaecreases thucleation of

al Image Cor

ed A in Fig

ed B and C

ay two activa

he strain fie

splacement

by the temp

eriment is co

d strains obt

roposed a co

ents for the

in observatio

420T MPa

mooth, while

Comparisonature (400°he yield strf the slip ba

rrelation ena

ure 5.3 disp

C show the

ated slip syst

elds (inset

filed (Figure

perature grad

onducted in d

ained from th

omparison be

10 1[ ] crysta

ons are evide

and HT

for the high t

between roC) experimess. At hignds leads to

ables also to

plays the str

strain fields

tems as desc

marked A,

101

e 5.2) can be

dient, and so

displacemen

he DIC strain

etween the r

al orientation

ent. First of

330MPa ).

temperature

oom temperment (A). As

h temperato small load

compare th

rain field for

for the room

cribed in Cha

B and C)

e used to ve

o is an indire

t control, an

n fields.

oom temper

n.in tension.

all the nomi

Secondly,

experiment

ature (23°Cs expected,ure two sl ip

d drops in th

e strain field

the high te

m temperatu

apter 2. At th

display diffe

erify the corr

ect verificatio

nd the nomin

ature (23 °C

Comparing t

nal yield stre

the stress-s

are observe

) experimen increasing

p systems ae stress-str

s at the sam

emperature e

ure experime

he same nom

erences bet

rect deforma

on of the gr

nal strain is d

C) and high te

the stress-st

ess decreas

strain curve

ed small load

nts (B and Cg the tempeare activaterain curve.

me nominal s

experiment,

ents. Both s

minal strain (

tween room

ation of the

rips-sample

determined

emperature

train curves

es with the

e for room

drops.

C), and erature ed, the

strain. Inset

while inset

strain fields

points A-B-

m and high

temperatu

the slip lin

Moreover,

systems cl

5.2.2.

Further im

Scanning

used as a

shows one

strain field

cannot be

from the re

Figure(a) Spaxial interac

For the ca

field surro

re experime

es appear in

strains are

learly appea

ExSituD

mprovements

Electron Mic

speckle pat

e of the firs

d surrounding

correlated.

egions which

e 5.4. Twin-peckle pattedirection, hction, in par

ase of twin-tw

unding the r

nts. In partic

nstantaneous

more local

r on the surf

DigitalIm

in the strain

croscope (S

ttern, this all

st correlation

g the twins. D

Nevertheles

h were correl

-twin interacern adopted high strain rt icular on th

win interacti

region of int

cular for high

sly (similar to

ized than th

ace.

ageCorre

n resolution c

EM). In the

lowed to rea

ns implemen

Due to the p

ss these limi

ated.

ction studieand subset

localizationhe obstacle

on reported

teraction, tha

102

h temperatur

o twinning at

he room tem

elationus

can be achie

experiment

ach very high

nted. Twin-tw

particular spe

itations, othe

d using higt size 5x5 µ are obsertwin side w

in Figure 5.

at is the reg

e strain field

t room tempe

mperature st

singSEM

eved using hi

presented h

h image mag

win interactio

eckle pattern

er important

h resolutionµm2; (b) Reved in the here the inc

.4 is possibl

gion where th

s, localizatio

erature) with

train fields, a

gh resolution

here the sam

gnifications (

on is studied

adopted, th

information

n DIC from sidual strairegion of

coming twin

e to notice t

he 111 12[ ](

on of strains

h small load d

and both th

n images fro

mple surface

(900x). Figu

d focusing o

he twinned re

can be extr

SEM imagen field in ththe twin-twis blocked.

the residual

1) twin syst

along

drops.

he slip

om the

e was

re 5.4

on the

egions

racted

s. he

win

strain

tem is

103

blocked in front of the obstacle 11 1 121[ ]( ) twin system. In particular on the twin boundary where the

incoming 111 121[ ]( ) is blocked high strains are measured in the surrounding matrix. This is true for

the intersection region (zoomed region on Figure 5.4b), and also along the blocked twin, on the side

of the incoming twin. These results can be analyzed and interpreted with Molecular Dynamics. The

dislocation mechanisms can be derived and used to interpret the measured strain fields shown.

105

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