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thesis entitled

TEXTURE ANALYSIS OF GAMMA-BASED TITANIUM
ALUMINIDE IN COMPRESSION
AT ROOM TEMPERATURE AND ELEVATED TEMPERATURES

presented by

Soonwuk Cheong

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has been accepted towards fulfillment
of the requirements for

Master's Materials Science

degree in

 

 

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MSU IoAn Afflmotivo Action/Emu! Opportunity Imtttwon
WW1

TEXTURE ANALYSIS OF GAMMA-BASED TITANIUM
ALUMINIDE IN COMPRESSION
AT ROOM TEMPERATURE AND ELEVATED TEMPERATURES

By

800an Cheong

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of
MASTER ‘OF SCIENCE

Department of Materials Science and Mechanics

_ 1995

ABSTRACT

TEXTURE ANANLYSIS OF GAMNIA-BASED TITIANIUM
ALUMINIDE IN COMPRESSION
AT ROOM TEMPERATURE AND ELEVATED TEMPERATURES

By

Soonwuk Cheong

Deformation of TiAl based materials is affected by the way strain is distributed between
three distinct deformation systems, l/2<110] normal dislocation slip on the basal plane,
<011] super-dislocation slip out of the basal plane, and mechanical twinning resulting from
1/6<11§] dislocation motion. Prior work has shown that the relative contributions of these
three deformation systems affects the amount of strain that occurs before fracture. Since
mechanical twinning results in a dramatic change in crystal orientation, changes in texture
after 5-10% strain were investigated on the surface of compression specimens deformed at
22, 650 and 850°C. With these small strains, changes in crystal orientation due to disloca-
tion slip are small, on the order of a few degrees. Large changes in orientation observed
in texture measurements were shown to be consistent with crystal rotations resulting from
twinning. Estimations of the volume fraction of twinned crystals were obtained, and the
maximum contribution of mechanical twinning to deformation occurred at 650°C, where

mechanical twinning accounted for as much as 50% of the total strain.

TABLE OF CONTENTS

LIST OF FIGURES ................................................... v
LIST OF TABELS ................................................... ix
1. INTRODUCTION ................................................. 1
2. LITERATURE SURVEY ........................................... 3
2.1 THE MICROSTRUCTURE ................................... 3

2.1.1 Crystal Structure ..................................... 3

2.1.2 Phase Diagram ....................................... 3

2.1.3 Microstructure ....................................... 7

2.2 MECHANICAL BEHAVIOR ................................. 12

2.2.1 Effects of lamellar grains .............................. 12

2.2.2 Temperature Effect ................................... 13

2.2.3 Strain Rate ......................................... l7

2.2.4.Yield Stress Behavior on DB'I'I‘ ........................ 17

2.3 TWINNING AND SLIP IN TIAL .............................. 19
2.3.1Deformation Twinning ................................ 19

2.3.2 Twinning in TiAl .................................... 20

2.3.3 Plasticity of TiAl .................................... 24

2.4 DESCRIPTION OF TEXTURE ............................... 26

2.4.1 Definition of Texture ................................. 26

2.4.2 Eulerian Angles ..................................... 26

2.4.3 Eulerian Angles and Miller Indices ...................... 32

2.4.4 Pole Figures and Inverse Pole Figures ................... 33

iii

2.5 PLASTIC DEFORMATION OF POLYCRYSTAL ................. 34

2.5.1 Plastic Deformation in Polycrystal ........ . ............. 34

2.5.2 Formation of Deformation Texture ...................... 36

2.5.3 The effect of Stacking Fault Energy on Deformation Texture. . 40

3. EXPERIMENTAL PROCEDURE ................................... 43
3.1 SPECIMEN PREPARATION ................................. 43

3.2 EXPERIMENTAL PROCEDURES FOR COMPRESSION TESTS . . . 44

3.2.1 Compression test system .............................. 44

3.2.2 Compression test procedures .......................... 45

3.3 TEXTURE MEASUREMENT ................................ 48

3.3.1 Texture measurement ................................ 48

3.3.2 Procedures in using popLA ............................ 49

4. RESULTS ........................................................ 58
4.1 STRESS-ST RAIN BEHAVIOR ............................... 58

4.2 TEXTURE AFTER COMPRESSION ........................... 59

4.2.1 Texture at room temperature ........................... 59

4.2.2 Texture at 650°C and 850°C ........................... 60

5. ANALYSIS AND DISCUSSION ..................................... 68
5.1 TEXTURE FORMATION .................................... 68

5.2 THE PREDICTION OF TWINNING ........................... 75

5.2.1 Schmid Law ....................................... 75

5.2.2 Detection of Mechanical Twinning ...................... 78

5.2.3 Volume Fraction of Twinning .......................... 94

iv

5.3 MAIN COMPONENT OF TEXTURE ........................... 96

5.4 MECHANISM OF TEXTURE FORMATION .................... 96

5.4.1 Grain Rotation ...................................... 96

5.4.2 Slip .............................................. 97

5.4.3 Mechanical Twinning ................................ 98

5.4.4 Dynamic Recrystallization ............................ 98

5.4.5 Crack formation and deformation of TiAl ................ 99

6. CONCLUSION ................................................. 101
7. REFERENCES .................................................. 102

FIGURES

2.1 (a) Lattice structure of Llo
(b) Lattice structure of D019 ........................................ 5

2.2 (a) A comparison of the Margolin and Murray Ti-Al phase diagram
(b) The central portion of the recently refined TiAl phase diagram ........... 6

2.3 The three types of larnellar structures ................................. 8

2.4 <110> directions and the atomic arrangement on a (111) plane in L10 and
<1120> directions and the atomic arrangement on the basal plane in D019 . . . 10

2.5 The stereographic projection of (111)y and (0001)ov2 showing the six
possible orientation variants of <110>y with respect to <1120> (12 matrix. . . 11

2.6 The compositional effect on the room-temperature tensile properties of
y-base alloys at HIPed condition .................................... 15

2.7 Tensile test data if single phase TiAl (60 pct Ti-40 pct Al) from 25 to 1000°C
with yield strength and fracture strength ............................. 16

2.8 The spatial relationships are given K1, K2, n1, 112 and the plane of shear ..... 21
2.9 The atomic arrangement on the (111) plane ............................ 22

2.10 The atomic arrangement
(a) true twinning

(b) pseudo twinning ............................................. 23
2.11 The sample fixed coordinate system Ks and the crystal coordinate system Kc

in the sheet ................................................... 28
2.12 The definition of the Euler angles .................................. 29
2.13 Orientation Distribution .......................................... 30
2.14 The Euler space ................................................ 31
2.15 Yield Locus and Latent Hardening ................................. 35

2.16 Lines of maximum descent from the point of maximum resolved shear stress
F and directions of rotation ....................................... 37

vi

2.17 (a) General trends of rotation in copper under tension
(b) General trends of rotation in a-brass under tension ................. 38

2.18 (a) General trends of rotation in copper under compression
(b) General trends of rotation in a-brass under compression ............. 39

2.19 (a) Formation of Copper rolling orientation

(b) Orientation paths due to mechanical twinning ..................... 42

3.1 The schematic view of compression test system ........................ 52
3.2 (a) Shape of specimen

(b) Specimen orientation in the specimen holder ....................... 53

3.3 Comparison between compliance and compression curves at room temperature54

3.4 Comparison between compliance and compression curves at 650°C ........ 55
3.5 Comparison between compliance and compression curves at 8500C ........ 56
3.6 Stress-Strain Curves at three temperatures ............................ 57
4.1 (111) Pole Figures before and after compression at room temperature ....... 62
4.2 (200) Pole Figures before and after compression at room temperature ...... 63
4.3 (220) Pole Figures before and after compression at room temperature ...... 64

4.4 (a) (111) Pole Figures before and after compression at 650°C
(b) (111) Pole F1 gures before and after compression at 850°C ............. 65

4.5 (a) (200) Pole Figures before and after compression at 650°C
(b) (200) Pole Figures before and after compression at 850°C ............ 66

4.6 (a) (220) Pole F1 gures before and after compression at 650°C
(b) (220) Pole Figures before and after compression at 8500C ............ 67

5.1 Complete SODF after compression at room temperature in inside specimen . . 69

5.2 Complete SODF after compression at room temperature in outside specimen . 70

5.3 Complete SODF after compression at 650°C .......................... 71

vii

5.4 Complete SODF after compression at 850°C .......................... 72

5.5 (a) Inverse pole figures before and after compression in inside specimen
(b) Inverse pole figures before and after compression in inside specimen . . . 73

5.6 (a) Inverse pole figures before and after compression at 650°C
(b) Inverse pole figures before and after compression at 850°C ........... 74

5.7 (a) Tension (b) Compression deformation geometry ..................... 76

5.8 Schmid factor contours with respect to the true twinning system of (l 1 DH 12]

for tension and compression ...................................... 77
5.9 (111) Pole Figures before and after twinning .......................... 79
5.10 Several stress axis orientations in 001 101 111 unit triangle .............. 82

5.11 (110) component density diagram before and after compression
at room temperature ............................................. 84

5.12 (110) component density diagram before and after compression
at 650°C and 850°C ............................................ 85

5.13 (a) Substraction of textured region from initial orientation distribution
(b) Substraction of initial orientation distribution from textured state
for normal direction in inverse pole figure at room temperature ........... 86

5.14 (a) Substraction of textured region from initial orientation distribution
(b) Substraction of initial orientation distribution from textured state

for normal direction in inverse pole figure at 650°C ................... 87

5.15 (a) Substraction of textured region from initial orientation distribution
(b) Substraction of initial orientation distribution from textured state

for normal direction in inverse pole figure at 850°C ................... 88

5.16 SOD sections which include twinning component after deformation
at room temperature ............................................. 91

5.17 SOD sections which include twinning component after deformation

at 650°C ..................................................... 92
5.18 SOD sectiOns which include twinning component after deformation

at 850°C ..................................................... 93

viii

TABLES

3.1 Chemical composition of specimen ...................................... 43
3.2 The order of experiments and conditions of each test ........................ 48
5.1 Schmid factors of several deformation systems according to stress axis orientations 83
5.2 Euler angles for twinned components ..................................... 90

5.3 Data of strain due to mechanical twinning ................................ 94

ix

1. INTRODUCTION

There is at present a great deal of interest in the intermetallic compound TiAl.
This material has attractive properties, such as a high melting temperature, a low density, a
high modulus, and good oxidation resistance. But low room-temperature ductility and
poor formability of this material prevent many industrial applications. The deformation

behavior of TiAl is related to its L10 crystal structure, which is based on an ordered face

centered tetragonal cell in which the Ti and Al atoms occupy alternating (002) planes. The
slip phenomena which include the normal slip of l/2<110] dislocations and the superdislo—
cation slip of <011] type dislocations in {111} slip planes has only recently been
explained. Twinning on {111} planes is also an important mode of deformation. These

deformation modes lead to strongly anisotropic deformation behavior.

Many important materials, such as metals, ceramics and some plastics, are poly-
crystalline structures. When the properties of their constituent crystals are strongly direc-
tionally dependent, the crystallographic orientations of the crystallites within the
polycrystalline aggregate play an important role in the properties of the material. Texture
is a fundamental material parameter that describes the overall characteristics of polycrys-

tal materials in a macroscopic view.

The present work is concerned with studies of the deformation mechanisms of
gamma-based TiAl alloys at room temperature and elevated temperatures. A major

emphasis was to characterize the deformation behavior of polycrystalline TiAl through

texture analysis. In addition, the possibility to detect and quantify the formation of
mechanical twins after compression was investigated. Since the L10 crystal structure is

similar to FCC metals, comparison of texture development on TiAl and FCC metals is

useful to determine the important differences that are caused by the L10 structure.

2. LITERATURE SURVEY

2.1 THE MICROSTRUCTURE

2.1.1 Crystal Structure

The 7 phase of TiAl has the L10 crystal structure, which is based on an ordered

face centered tetragonal cell in which the Ti and Al atoms occupy alternating (002) planes.
This phase has a wide range of solubility (49-66 at% aluminum) that varies with tempera—
ture. The tetragonality ranges from c/a ratios between 1.02 and 1.03 (Figure 2.1.(a)). The
012 (D019) structure is based on the composition A38 and it is one of the most typical
superlattice structures derived from h.c.p. lattice. The sequence ...ababab. .. in Figure 2.1.

(b) represents the D019 structure [1].

2.1.2 Phase Diagram

The microstructure of gamma titanium aluminide is fundamentally dependent on
the composition. The binary phase diagram of Ti-Al has been under dispute especially in
the high temperature region near the Ti rich boundary of y-TiAl. There are two versions of
the binary phase diagram. The first one is the Hansen-Murray version [2]. According to
this version, cr-Ti is unstable at high temperature above 1250 °C and B-phase is in equilib-
rium with y-phase (L10). Then the B-phase undergoes a solid-state transformation to form
the (02+y). The other version is the Jaffe-Margolin version [3,4]. In this version, the high

temperature region is a-Ti, i.e. the disordered solid solution based on the hexagonal close

packed structure of Ti. Figure 2.2.(a) shows the comparison of the two phase-diagrams

[5]-

The common factor between these two phase diagrams is the (12(D019) + y eutec-
toid structure in the range between 40 and 50 at %A1 at room temperature. However, they
support different high temperature history and phases which can influence the microstruc-
tural evolution. To decode this ambiguity, there have been efforts by several workers
[6,7]. Even though the precise location of the phase boundary still remains under investi-

gation, the recent experimental data have shown that the phase in equilibrium with y -TiAl

which is the near y-region above 1250°C is the hexagonal close packed solid solution
based on the a-Ti, rather than the body centered form of fi-Ti [7]. The most recent phase
diagram is shown in Figure 2.2.(b) [8]. It shows the peritectoid reaction (L+or(a—Ti) —v y)

and the eutectoid reaction (a -t a2+y), which are different transformation history from the

Hansen-Murray version.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[2T10]

(b)
FIGURE 2.1. (a) Lattice structure of Llo (b) Lattice structure of D019 [1]

 

 

 

 

 

 

 

 

 

 

 

 

 

1550
1500
5
3g 1450
g
4 1400
re. 1350
1""
1'"
1300
l 1 I l 1
12004244464i850§2 54
Al CONCENTRATION (at.%)
g
*2
a
94
5.
. +7,
F 012-113“ a2
800 _
l l l l L
30 35 4o 45 50 55
Al CONCENTRATION (at. %)

(b)

FIGURE 2.2. (a) A comparison of the Jaffe-Margolin (Solid lines) and Hansen-
Murray (dashed lines) Ti-AI phase diagram. The Hansen-Murray diagram shows
that or-Ti does not exist above ~1285°C [5]. (b) The central portion of the recently
refined TiAI phase diagram and dashed lines indicate the microstructure changes
according to heat treatment conditions (L: lamellar, NL: near lamellar, Duplex

and NG: near gamma structures) [8].

2.1.3 Microstructure.

The microstructure of TiAl varies largely according to the aluminum content.
Generally, as-cast stoichiometric TiAl shows a microstructure consisting of grains of

TiAl(y)-Ti3Al(a2) lamellar structure together with equiaxed y grains. Aluminium rich sin-
gle phase alloys are not of engineering importance because of their poor ductility and frac-
ture toughness. The two phase microstructure, TiAl-Ti3Al, has more ductility than the
single phase alloy, but the room temperature ductility is still limited to 2~3% [8,9]. The
microstructure of TiAl is also sensitive to cooling rate, so it can vary from a duplex

microstructure containing the az/y lamellar structure together with y grains to a very fine

lamellar structure with VVrdmannstatten—type morphology [10,11,12].

Since the existence of the two phase lamellar structure in the duplex structure has a
considerable effect on mechanical properties, the following two factors are important in

controlling the mechanical properties. The first one is the size of TiAl-Ti3Al two phase

lamellar grains and TiAl single phase equiaxed grains. The second one is the volume f rac-
tion and distribution of lamellar grains. Therefore, understanding of the phase transforma-
tion is quite important because the final microstructure depends on the phase
transformation history. The microstructure of gamma alloys may be classified into four
groups: near-gamma, duplex, nearly lamellar and fully lamellar [13]. This classification is
based upon heat treatment as illustrated in Figure 2.2(b). The NG (near -gamma) micro-
structures are obtained by a heat treatment just above the eutectoid temperature. The
duplex microstructure is obtained after heat treatment at temperatures where equal

amounts of a and y exist. The NL (nearly lamellar) microstructure is obtained at tempera-

tures where the predominant phase is alpha in the (1+7 region. The FL (fully lamellar)

structure is obtained in the single phase a field.

Three types of lamellar structures, called Types 1, II and III, have been identified
through several microstructural development studies [13,14,15]. The orientation relation
between (12 plates and gamma plates has been investigated through electron diffraction
analysis and it shows that the phase transformation occurs during h.c.p. —> f .c.c. That is,

the disordered h.c.p. phase that forms from the melt starts to order to the D019 structure at
the h.c.p. -> f .c.c. transformation temperature (eutectoid temperature). Then, the D019 —§

L10 phase transformation begins as the D019 phase cools down [16,17].

TYPElzor —>a+Yp——p Met/y) ——> Mag/y)
TYPEII: or. —>a2 —> a2+ypt —p a2+yp —>L(012/y)
TYPElllzym+012p meym+ap —»

v... + up» Mir/a) EL» We.) (1)

heatin
Ym—L’ Ym + apt —’

vm+ a, —> L<yIa>J°ihl£g—> 117/02) (2)

FIGURE 2.3. The three types of lamellar structures [13]

The analysis indicates that the orientation relationship between a2 and y is
{0001}a2 // {lll}v and <1120> <12 // <110>y, which involves six possible orientation
variants of <110>y with respect to <1120>a2 [18]. Figure 2.4 shows the orientation rela-

tionship between (111) plane which is the close-packed plane in TiAl and (0001) plane

which is the basal plane in Ti3Al [1]. Figure 2.5 illustrates this relationships with the aid

of the stereographic projection [19].

10

(111) (0001)

 

 

c B Y B
[0T1] ~ [161] [1170] [5110]

 

 

 

 

 

(111) (0001)

FIGURE 2. 4. <110> directions and the atomic arrangement on a (111) plane in
Llo and <1120> directions and the atomic arrangement on the basal plane in

13019 [1]

_ VariantA
[110]y/<11 t .

[10T]yl<l 120x12
Variant D

[OlIh/<1120>a2

Variant E

 

Variant F

011]y/<1120>cv2

101 /<11§0>o:2
run/(000m; [“317th

[I10]y/<1120>a2

Variant B

FIGURE 2.5. The stereographic projection of (lll)y and (0001)a2 show the six
possible orientation variants of <110>v with respect to <ll2tba2 matrix [19].

12

2.2 MECHANICAL BEHAVIOR.

2.2.1 Effects of lamellar graim

The ductility of gamma alloys is controlled by alloy chemistry and microstructure.
Room temperature elongation of TiAl varies with aluminum content, exhibiting a maxi-
mum centered around the two—phase composition of Ti-48Al at HIPed (hot isostatic press-
ing) condition [20]. Figure 2.6 show the compositional effect on the room-temperature
tensile properties of y-base alloys [21]. Therefore, the strength of TiAl is thought to be

related to the existence of y—az lamellar grains [22,23]. The factors which can control the

ductility in terms of microstructure distribution are:

(i) the thickness of TiAl lamellae

(ii) the size of ordered domains in TiAl lamellae

(iii) the volume fraction, distribution, and thickness of Ti3Al lamellae

(iv) the size of lamellar grains.

13
2.2.2 Temperature Effect

In 1975, Lipsitt and colleagues presented the tensile test data for y - single phase
alloy [24]. In their work, it was shown that the yield stress decreased with increasing de-
formation temperature, and that the yield stress dropped abruptly at the DBTT (Ductile-
Brittle Transition Temperature) in the range 600°C to 900 °C. Recently, more intensive
analysis of the yield behavior showed the relationship between the yield phenomena and
the microstructure which is very sensitive to the Al content of TiAl [25,26,27]. Huang and
Hall [25] and Rao and Tangri [26] noted the positive temperature dependence of the yield
stress in high A] content alloy. Their results indicated that the yield stress dependence on
temperature depends strongly on microstructure. Actually, they identified three different
types of the yield behavior of TiAl, one for the single-phase 012 alloy, one for the single A
phase 7 alloy and a third type for the two-phase alloy. For low Al content materials such
as 012 single phase, the yield stress decreased with increasing temperature. But for high Al
content materials such as single phase 7 alloy, the yield stress was irregular with increasing
temperature, which indicates the influence of the positive temperature dependence of yield
stress up to the DBTT. The two-phase alloys were insensitive to temperature. These dif—
ferences in yield behavior can be explained by the different roles of the deformation mech-
anism in each phase. The content of Al of this alloy affects the final microstructure during

heat treatment.

14

In the 7 phase, there are 3 kinds of deformation possible, slip of normal 1/2 <110]
dislocation, <101] superdislocation and twinning 1/6<112]. The mixed general and specif-
ic brackets are normally used in TiAl, to recognize the anisotropic qualities of the L10 crys-
tal structure (see F1 gure 2.1 (a)). The activity of each deformation system depends on the
final microstructure. As temperature increases, the activity of each deformation mecha-
nism changes due to thermal energy and this can affects their contribution to deformation
[28]. Thus, the complexity of microstructure, deformation mechanism and thermal activa-
tion results in the different yield behaviors. But, this phenomena is most apparent below
the DBTT. Above this range, decreasing yield stress with increasing temperature is a gen-

eral situation for all three cases.

15

duplex structure —> 4— single phase

 

     

 

 

 

structure

205 '- I I I I I I I I I I I I I I I I I I I l I I I .
’8 I 1
e 2.0 ;- i
a: " '1
E : I
m 1.5 '_' j
g . .
LE ' : q
.9. I I
Z 0-5 :' ':
a: : 1

0.0'I1111111...I1.11.1.1.
44 46 48 50 52 S4 56

Al CONCENTRATION (at %)

FIGURE 2.6. The compositional effect on the room-temperature tensile
properties of y-base alloys at HIPed condition [21].

l6

STRENGTH OF TIAL AS A FUNCTION OF TEMPERATURE

 

500 F—VfF'UUIYTTlIIIIVYr'VII

 

 

 

 

 

450 :- -:
1.: 400 E- -2
z E 1
2 350 .- J.
m“ E 5
g] 300 .- 1
m = ‘. 2
i7: 250 E“ : 1.

200 é—zFRACTURESTRESS : _ _-

E ---:0.2%YIELDSTRESS ‘\ 2
15° :' “3 ‘:
100:4..1...|...1...1..\'.ra..‘

0 200 400 600 800 1000 I 200

TEMPERATURE,°C

FIGURE 2.7. Tensile test data of single phase TiAI (60 pct Ti-40 pct Al) from 25 to
1000°C with yield strength and fracture strength [24].

17
2.2.3 Strain Rate

Another factor which can influence the yield stress and elongation values is the
strain rate [29]. While the mechanical behavior of titanium aluminides appears to be very
sensitive to strain rate, limited work has been done. Shih and Schwartz recently found that
a higher strain rate increases the DBTT [30]. Seetharman et al. showed a quantitative rela-
tionship between strain rate and DBTT enhancement [31]. But, the understanding of ef-

fects of strain rate on yield phenomena is still far from being complete.

2.2.4 Yield Stress Behavior on DBTT (Ductile-Brittle 'II'ansition Temperature)

Recent experiments indicate that mechanical properties of this alloy also depend on
both the area of grain boundaries and grain boundary structure which practically influences
the interaction between lattice dislocations and grain boundaries [32,33,34]. The role of
grain boundaries on mechanical behavior especially in the range of the DBTT was very im-
portant in the recent research by Imayev et al [33,34]. The brittleness of TiAl at room tem-
perature results from the restrictions of normal slip caused by high Peierls stress and
superdislocation slip by the anisotropic tetragonality of TiAl, which indicates that there is
a low density of active sources of dislocations [25]. In addition, the shear transfer through
the grain boundaries is difficult because of the blocking effect of grain boundaries at low
temperature. These unfavorable conditions for plastic behavior of TiAl at low temperature
localize the stress condition and initiate fracture instead of plastic deformation. However,
as the testing temperature rises, deformation becomes delocalized. First, as temperature in-

creases, the activation of each slip system increases, which results in increasing active

18

sources for plastic deformation. Secondly, the role of grain boundaries in deformation
changes from an effective barrier for dislocation motion to a source or sink for dislocations.
An increasing density of dislocations piled up at grain boundaries makes it easy to transfer
the shear from one grain to another by building up low angle grain boundaries. Thus, The
absorption of lattice dislocations in grain boundaries and the shear transfer from grain to

grain increases the plasticity of TiAl in the ductile-brittle transition range.

19

2.3 TWINNING AND SLIP IN TIAL.

2.3.1 Deformation Twinning

The standard mode of twinning shown in Figure 2.8 is completely defined by the

elements K1 and 1'2, but it is common to use the four elements K1, K2, in and n2. K1 is
the twinning plane or the first undistorted plane in the twinning process; 711 is the direction
of shear in the K1 plane. K2 is the second undistorted plane and n2 is the plane of shear
[35]. The plane that lies perpendicular to K1 and contains the shear direction is called as

the plane of shear. There are four twinning modes which fulfill the condition that the lat-

tice is to be reproduced [36].

(1) reflection in K1,

(2) rotation of at about 111,

(3) reflection in the plane normal to m,

(4) rotation of at about the normal to K1.

In the first two modes, K1 and 112 are rational and in the last two modes, K2 and 711

are rational. When modes 1 and 2 occur simultaneously, the twinning is described as com-

pound twinning, and this mode is observed in FCC crystals.

In FCC metals, the symmetry rule connecting the differently oriented parts is that
one part is the mirror image of the other in a (111) plane. It can be observed that nearest

neighbor relations are preserved at the boundary, but that an error in the stacking

20

sequences of the (111) planes occurs, such that the stacking sequence abcabc is turned into

abcbac. For a shear of 0.707 the twinning elements are

K1=(111). m=i11§L K2=(11T>. n2=[112]

2.3.2 Twinning in TIA].

In TiAl, there is a type of twin {111}<112> variant of the normal FCC twinning
mode that causes an anti-phase boundary at the interface so that the twin plane is no longer
a true reflecting plane. While the structure requirement for symmetry is met, the composi-
tional symmetry is not, as illustrated in Figures 2.9 and 2.10. These are called pseudo-
twins, and 2 of the 3 possible twinning directions have this asymmetric nature where the

L1o structure is no longer preserved [37,38]. Figure 2.9 shows the stacking of (111)

atomic planes in the sequence abcabc...[1,39,40]. When it is homogeneously sheared by

operating one of the {lll}[112> FCC true twinning systems, the symmetry of the L1o

structure is preserved after twinning deformation. Since there is only one true twinning
system in each {111} plane, and since twinning can only occur in one direction. There are
only four true twinning systems, (111)[112], (lIl)[l'i2], (I11)[I12] and (fil)[II2]. The
number of operative twinning systems depends on the local grain orientation and principle
stress state [41.42.43]. With a particular principle stress condition, only two true twinning
systems which have components in the principle stress direction can possibly operate at

one time.

21

 

 

 

 

 

 

The summary of the basic nomenclature

K1 : the twinning plane, or the first undistorted plane

K2 : the second undistorted plane

in : the shear direction

112 : the direction defined by the intersection of the plane of shear with K2
S

: the plane of shear

FIGURE 2.8. The spatial relatiomhips are given K1, K2, 1“, 712 and the plane of
shear [35].

22

 

 

 

[011] [1le [101]
A Ti
[121] /['511]
O O
O 0...... °
b

 

 

FIGURE 2.9. The atomic arrangement on the (111) plane, the layers labelled a, b
and c define the abcabc... sequence along [111] (bt: true twinning direction,

bp: puudo twinning direction) [1].

 

(111)

 

 

 

 

 

 

0))

FIGURE 2.10. The atomic arrangement of true twinning (a) and pseudo twinning
(b)

2.3.3 Plasticity of mu.

Slip in TiAl occurs on {111} planes, as in f.c.c. structures. The possible slip direc-
tions are <110],<011] and <112]. The first systematic research on flow stress and ductility
has been done by Schechtman et al. [44]. They reported that two major types of disloca-
tions occur in TiAl: b=1/2[110] unit, perfect dislocations and b=[101], superdislocations.
The first one is called the easy slip type dislocation and the latter one is called the hard slip

type dislocation. This differentiation comes from the anisotropic L10 ordered crystal

structure of TiAl which has tetragonality of 1.02 c/a ratio. Mechanical twinning also plays
important role in the overall deformation. Lipsitt and Schechtman also reported that the
deformation modes play different roles at elevated temperatures [24]. Following their
results, the dominant slip mode at room temperature is the 1/2<1 10] easy slip type but as
temperature increases, the <011] hard slip type, designated by superdislocation starts to
contribute to the deformation considerably. So, they summarized that the mobility of the

l/6[ll2] partial dislocation which is a constituent of the [011] superdislocation and is

immobilized below 700°C, controls the plasticity of TiAl. However, the easy slip mode 1/
2[110] dislocation has been called into question by Greenberg and co-workers [45,46].
They suggested that in the {110} planes filled with Ti atoms, the bonds, which are directed
along both <ll_0> and <001>, are covalent. The results of Court support this theory
[47,48]. Thus, the Peierls stress caused by these covalent bonding blocks movement of 1/
2[110] dislocations [49,50]. They concluded that the lack of ductility shown at room tem-
perature of this alloy results from a lack of mobility of dislocations with b=1/2<110]
caused by covalency, and the immobilization of dislocation with b=<011]. But, at higher

temperatures, the increasing contribution of partial dislocation 1/6[ll2] and glissile

25

1/2[110] dislocation by thermal activation energy increase the ductility of TiAl. Kawabata

and Vasudevan suggested that the purity and the existence of second phase Ti3Al could
increase the ductility of TiAl [51,52,53]. That is, the phase Ti3Al absorbs the interstitial

elements which increase the covalent bonds nature of Ti in TiAl, since the solubility of

these elements in Ti3Al is much larger than in TiAl. So, the removal of interstitials from

TiAl decreases the degree of directionality of bonding between the Ti atoms, and reduces
the anisotropy in Peierls stress [54]. A duplex structure, which contains both single phase
y-TiAl and two-phase lamellar grains, is more ductile than a single phase or a fully lamel-
lar structure. The deformation of this duplex structure occurs by primary twins and a/
2[110] easy slip dislocations. Finally, the deformation modes may be controlled by aniso-
tropic tetragonality, bonding, interstitial elements, grain size and grain boundary chemis-
try. So, the presence of second phases and the alloy composition are crucial factors that

affect the ductility of TiAl [55].

26

2.4 DESCRIPTION OF TEXTURE

2.4.1 Definition of Texture

When non-random distributions of grain orientations occur by any kind of manu-
facturing process in materials, the orientation state of the grains is called texture. Signifi-
cantly different texture can result from solidification, deformation, recrystallization and

phase transformation.

2.4.2 Eulerian Angles

Texture is described by two coordinate systems, the sample coordinate system and
the crystal coordinate system. The sample coordinate system defines the three principal
directions of the sample geometries and the crystal coordinate system defines the principal
axes of the crystal orientation. The relationship is shown in Figure 2.11. The sample
coordinate system and the crystal coordinate system can define a textured state by rota-
tional angle vector g represented by three Eulerian angles. The Eulerian angles are com-
monly defined using two variations, Bunge’s system and Roe’s system. The schematic
view of each system is shown in Figure 2.12. The sequence of rotations for Bunge’s sys-
tem starts with the two orientation coordinate systems lying parallel to each other. Then,

the crystal coordinate system (xyz) is rotated about the z-axis through the angle qr] and the

second rotation is done about the -x—axis through the angle <I>. Finally, by rotation of the

crystal coordinate system about -z- axis through the angle (1)2, the rotational angle vector g

is defined by the three Eulerian angles cpl, <I>, (pz.

27

g. = {$1. ‘1’. $2} = {al. 8". g’z} (EQ 2.1)

In the case of Roe’s system, the second rotation is not carried out about the x-axis,

but about the y-axis. The Eulerian angles are represented by ‘1’, 9 and Q

gc = {‘I‘. 9. <I>} = {gz. g”, '2} (EQ 2.2)

\

Considering the fact that both kinds of Euler angles represent a same physical con-
dition of material with different notations, they have a close relationship to each other. EQ.

2.3 shows the relationship between them [56].

q)1=‘P+:rt/2;<I)=G;q)2=<I>-Jt/2 (EQ2.3)

The third version of the Euler angle definition is the Kocks’ system, which is
employed in the present study. The Kooks convention is ‘1’, 8, d). It is the same as Roe’s
except that the rotation axis is +z rather than -z for the third rotation. The sample coordi-
nate system rotation from the crystal’s perspective is obtained by the reverse order of rota-

tions gs = 4), 9, ‘I‘ about the opposite axes. Figure 2.13 shows the comparison of each

orientation system.

In the representation of the Euler space, generally, two types of the Euler spaces
are used. First one is the unit cell orientation space and the next one is the cylindrical ori-
entation space. The Bunge’s orientation system is well described by the unit cell orienta-
tion space, so called g-space and the Kocks’ system operates the spherical orientation

space. Figure 2.14 shows each Euler space.

 

 

 

 

 

 

FIGURE 2.11. The sample fixed coordinate system Ks and the crystal fixed
coordinate system Kc in the sheet [56].

29

 

 

 

 

(b) (C)

FIGURE 2.12. The definition of the Euler angles: (a) the crystal coordinate
system K¢(xyz) lies parallel to the sample coordinate system Ks(XYZ); (b) on the

definition of the Euler angles (p1 Q (p2; (c) on the definition of the Euler angles ‘1‘ 8
Q [56].

30

 

 

 

 

 

 

(l) (2)
COD (Crystal Orientation Distribution) SOD (Sample Orientation Distribution)

FIGURE 2.13. Euler angle rotations according to a) Bunge’s system b) Roe’s
system c) Kock’s system [57].

31

 

 

/—>q)1 (Pr
([5 W2 | f

 

 

 

 

 

 

 

 

   

(a) o ‘
I; 30°
60° Projection

 

 

(b)

 

 

FIGURE 2.14. (a) Unit cell in Euler space (b) Spherical orientation space in Euler
space, where Y can be viewed as the label for a shell having a particular rotation
magnitude about the radial axis [58].

32
2.4.3 Eulerian Angles and Miller Indices

Miller indices are commonly used to describe the crystal orientation with respect

to sample orientation description. For example, in rolled sheet,

g = (hkl)[uvw]. (EQ 2.4)

(hkl) indicates the crystal plane which is parallel to the plane of the sheet and
[uvw] indicates the crystal direction parallel to the rolling direction. It is also possible to
obtain the relationship between the miller indices and the Euler angles by using a matrice
conversion process [56]. The relation between the Euler angle representation and the rep-

resentation of an orientation by Miller indices in terms of Bunge’ system is:

 

ch = acos l (EQ 2.5)

Jh2+ k2+l2

 

 

(EQ 26)

k .
tpz=acos =asrn

h
M + k2 M + k2

w 2 k2+l2
(pl = asin 2 2 2- —2 2 (EQ2.7)
Ju +v +w 1‘ +k

The relation in terms of Roe’s system is:

 

 

= acos l (EQ 2.8)

Jh2+ k2+ I2

 

33

 

 

Q=asin k =acos[- h ] (EQ2.9)

 

(EQ 2.10)

 

2.4.4 Pole Figures and Inverse Pole Figures

A two-dimensional representation of crystal orientation space is carried out using
two approaches. The pole figure is the distribution of the specified crystal plane normals
{hkl} with respect to the sample coordinate system in the stereographic projection. The
inverse pole figure shows the distribution of crystal directions in a specified sample direc-
tion, such as the normal direction in terms of a crystal coordinate system, and it is
expressed in a stereographic projection. For visualization purposes, the projection is often
presented using an equal area net rather than the wulff net, so that the visual image does

not contain any distortions.

34

2.5 PLASTIC DEFORMATION OF POLYCRYSTAL

2.5.1 Plastic Deformation in Polycrystal

The Schmid law requires that only resolved shear stress on slip plane and slip
direction makes a crystal yield in a particular slip system. The fundamental idea of the
plastic deformation of a polycrystal is such that simultaneous glide of dislocations in
many slip systems in each grain are responsible for the deformation. In polycrystalline
materials, it is not possible for each grain to deform by single slip or strain independently
without being affected by the constraint of neighbor grains [59,60,61]. Taylor assumed
that a slip in a grain in polycrystal requires five independent slip system and that each
grain undergoes the same strain as the aggregate [62,63]. A macroscopic yielding behav-
ior can be interpreted by an yield locus which can be represented by a polyhedron in 3-D
stress space surrounding the origin [59]. A 2-D section through the origin of stress spaces
reveals a polygon, as shown in Figure 2.15. In the yield locus, each facet indicates the cri-
teria for yielding on each slip system. When a resolved shear stress reaches a yield surface
of a specific slip system, the minimum condition for yielding is satisfied. But, as men-
tioned above, in polycrystal deformation, at least five slip systems are required. There-
fore, only a single yield criteria is insufficient for polycrystal slip. At a corner orientation
on the yield locus, several slip systems can be activated simultaneously. This indicates
that for polycrystal yielding, each grain orientation should rotates to meet such a yield cor-

ner that can produce poly slip conditions [64,65,66,67].

 

/
s
\W/
/ \
\<Q/>

 

 

 

 

 

 

 

36

2.5.2 Formation of Deformation Texture

The formation of deformation texture starts with such considerations. Figure 2.16
shows that an orientation rotates due to a given stress state indicated by a c it b in p q [68].
The arrows I and 11 indicate the rotations resulting from single and duplex slip respec-
tively. In the stress axis rotation which follows a minimum resolved shear stress, single
crystal slip occurs when the path of the stress axis lies within a unit triangle and duplex
crystal slip occurs when the path is along the unit triangle boundary. The final rotation is

determined by the competition between these two slip systems.

Figures 2.17-18 show the general trends of rotation in copper and (ii-brass under
tension.For tension in FCC structures, the final texture components are [111], [100] and
[112] and for compression, the final components are [110] with a spread toward [311] and
[100] for copper and toward [311] and [111] for brass. The characteristics of deformation
texture in FCC mostly result from the comparison between copper type texture and or-
brass type texture. The difference comes from the operation of latent hardening in each
case, which is illustrated in Figure 2.15. There are two assumptions in the description of
latent hardening [59,69,70]. First, the latent slip systems do not harden at all or they
harden at the same rate as the primary slip system. In second case, the latent slip systems
harden faster than the primary slip system. For the or -brass case, when the latent harden-
ing exceeds the active hardening, the [100] component disappears. Figure 2.18 shows the

general trends of rotation in copper and in or- brass under compression.

37

 

 

A
f 111

211

 

 

 

 

100

 

FIGURE 2.16. Lines of maximum descent from the point of maximum resolved
shear stress F and directions of rotation due to single crystal slip (-’I) and duplex
slip (-’II) in copper under tension [68].

38

 

 

 

110

 

 

 

110

(b)

FIGURE 2.17. (a) General trends of rotation in copper under tension (b) General
trends of rotation in (ii-brass under tension [68]

39

 

 

 

 

 

 

110

0?)

FIGURE 2.18. (a) General trends of rotation in copper under compression (b)
General trends of rotation in ci-brass under compression [68].

40

As descriptions of deformation textures, drawing texture and rolling texture are
used frequently [68,71,72,73]. The process of wire—drawing is such that a tensile stress is
applied in the direction of drawing together with compressive stresses in all radial direc-
tions perpendicular to the tensile direction. Thus, texture forms on the basis of the tension
rotation which leads to [111], [112] and [100] in the drawing direction, simultaneously
with compression rotation with respect to radial direction. In a (ii-brass, the [100] compo-
nent disappears due to latent hardening. In the case of the sheet rolling texture, the pro-
cess is described by compression parallel to the rolling plane normal and tension in the
rolling direction perpendicular to the rolling plane normal. Thus, the polycrystal aggre-
gate is interpreted by compression axes all over the triangle [100][110][111] and tension
axes all over the area 90 degrees from this triangle. The final rolling textures are {4 4

11}<11 118> for copper and {110} <112> for brass.

2.5.3 The Effect of Stacking Fault Energy on Deformation Texture

In FCC materials, the composition can affect the overall plastic deformation
behavior, which is affected by materials of different stacking fault energy. For high SFE
(Stacking Fault Energy) materials such as gold and copper, cross-slip is possible. This
mechanism indicates that dislocation segments which are all {lll}<110> slip system
pairs in f .c.c. materials can move from its slip plane on to an intersecting slip plane shar-
ing a common slip direction (colinear slip). In aluminum the dislocations cross-slip easily,
even at relatively low stress levels [74]. But, this homogeneous slip theory does not take
into account deformation inhomogeneities which usually occur in medium and low SFE

materials such as Cu-Zn alloy. The deformation inhomogeneities are caused by deforma-

41

tion bands, shear bands (consequence of latent hardening) and also, mechanical twinning

[75]-

In the case of twinning, since mechanical twinning causes a drastic orientation
change from that of the matrix, it is expected that mechanical twinning plays an important
role in the development of deformation texture. For the plane stress state, occurrence of

mechanical twinning is determined by the Schmid factors p. for {lll}<112> twin defor-
mation and by us for {lll}<110> slip. If it = 111/ us is larger than one, mechanical twin-

ning occurs assuming that CRSS is the same. In the case of Cu-Zn system, the orientation
described by the {112}<111> which is called C- orientation develops during the initial
rolling. With further rolling, the material undergoes mechanical twinning, so the final
component is the {552}<115> TC (twinning copper orientation). The procedure to find
the twinned orientation with respect to the initial orientation will be explained in section 6.
Hirsch and Lucke showed that increasing Zn in Cu-Zn system and increasing deformation
decrease the C-orientation, but increases the G-component {111}<001> which is near the
TC orientation [76]. The generation of the G-component is caused by a subsequent slip of
the TC orientation after twinning. For high Zn Cu-Zn system, mechanical twinning
occurs after a much smaller strain, compared to the low Zn case. These results indicate
that the transition from the high SFE condition of pure copper to the low SFE condition of
Cu-Zn by adding Zn not only increases the generation of mechanical twinning but also
decreases the critical strain which is necessary for mechanical twinning to occur. Figure
2.19 shows the orientation paths due to mechanical twinning of {112}<111> and subse-

quent deformation.

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42

  

 

 

 

 

 

 

 

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5:83 I ”swim—:83 AV mu 85 I
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3. EXPERIMENTAL PROCEDURE

3.1 SPECINIEN PREPARATION.

The purpose of this experiment is to investigate the deformation mechanisms of
gamma-based TiAl alloys at room temperature and elevated temperatures. The material
used in the present work was investment-cast near-gamma Ti-46Al-2Cr-2Nb (at%). The
chemical composition is shown in Table 3.1. The material was supplied in the form of a
rod ~18 mm in diameter and about 100 mm long by Howmet Corp., Whitehall, MI. The
material had been hot isostatically pressed (HIP’ed) and heat treated to form a duplex
microstructure. The duplex microstructure consists of approximately equal fractions of

equiaxed gamma, and (y + a?) lamellar grains, which were transformed from alpha single

phase during heat-treatment process.

Table 3.1 Chemical composition of specimen

 

Ti |Al(at%) Nb(at%) Cr(at%) O(ppm) N(ppm) H(ppm)
| 46.3 1.9 1.6 510 49 20

 

 

 

 

 

 

 

 

 

TiAl shows higher strength compared with most steels commercially used in
machining tools. Thus, the preparation of specimens required use of a diamond saw and
EDM (Electron Discharge Machining). First, the cast circular rod was cut into a quarter
section having a 7.6 mm radius. A diamond saw was used to section this quarter section

specimen into several pieces with 10 mm height. All cuts were perpendicular to the sides

43

44

to reduce the possibility of shear strains during the uniaxial compression. Due to experi-

mental difficulties which will be described in the next section, the cross sectioned area of

the quarter-specimen was cut into three pieces having 15 mm2 area in each piece shown in
Figure 3.2, and the height was also reduced to 5 min, half of the size of the original height.
This was done by EDM because of the lack of ability to maintain accuracy with a diamond

saw.

3.2 EXPERIMENTAL PROCEDURES FOR COMPRESSION TESTS

3.2.1 Compression test system

The equipment used for compression tests was an ATS series 2710 creep testing
machine and the compression data were recorded by a data acquisition system developed
by Wu [‘77]. The machine has a lever aim ratio of 20:1 to provide high load capacity and
loading rate. The frame controller made by ATS (Applied Test systems INC.) and EIR
(Electric Instrument Research Corp.) provides signal processing and feedback control for
various kinds of experiments. The compression tests were conducted by imposing a con-
stant velocity on the lever arm with the jack shown in Figure 3.1. The compression speci-
men was put on Inconnel loading platens inside a compression cage. The displacement of
the specimen was measured by LVCT (Linear Variable Capacitance Transducers) that
monitored the change in distance between the upper and lower surfaces of the compres-
sion cage. The function of LVCT is to convert the physical displacement to an electrical
voltage change. The load was measured with a load cell in the lower end of the load train.

The LCVT and load cell signals were conditioned to provide output voltages that were

45

monitored by the data acquisition board of a computer which consists of IBM PS/2 286
computer and AT-MIO-l6L-25 multifuction data acquisition board. The LCVT exhibited
a range of -10 to 10 volts for a displacement of 5.08 mm (0.2 in.). The experiment started

in a negative voltage of about -7 V and the voltage increased as the specimen was com-

pressed. The resolution limit in the data acquisition system was about SmV (1 pm, 5 x 10'

5 in, or 250 us). The testing temperature was controlled by an ATS furnace control unit.

The furnace has three heating zones. Thus, the furnace control unit allows the user adjust
the temperature profile in the range of the specimen. The temperature was monitored at

the top and bottom of the loading platens and adjustments in the heating zones were made

to keep the specimen within :1: 2 °C fluctuation range.

3.2.2 Compression test procedures

The geometrical complexity of the specimen and the testing machine required
measurement of the compliance for each experiment condition. Figures 3.3-3.5 show the
comparison between the compliance curve and the compression curve for the specimen at
each temperature. After each compression test, the stress-strain curve was obtained by
substracting the compliance curve from the data. The first experiment was done at room
temperature, and it is illustrated in Figure 3.3

In using the creep tester for the compression experiment, one problem arose during

the first room temperature experiment, which occurred using a specimen with a full quar-

ter section of the cross sectioned area of 45 mmz. The thread failed in one of couplings in

the load train made from a mild steel due to the high yield stress of TiAl. This failure led

46

to reducing the loaded area of the specimen to one third of the original specimen size. The
area reduction of the stress area in the specimen was determined by the thread design anal-
ysis and the yield stress analysis of each material used in the testing machine and speci-
men. The thread design analysis follows the Dimension of Unified and American National
Screw Threads (DNAT) [78]. In the stress distribution on the threads, the major portion of
the load is transferred at the first pair of contacting thread and a large stress concentration
is present here. Stress concentration factors for threads with static loads are usually deter-
mined by photoelastic analysis and it is reported that a stress concentration factor is 3.85

at the root of the first engaged thread.

AL
MS — CFxS—A EQ.3.1

In EQ. 3.1, the Maximum Stress (MS) on the first thread is calculated by the stress
concentration factor (CF), applied load (AL) and stress area (SA). And the stress area
(SA) is obtained by the thread size and the number of threads per inch. Therefore, by
comparison between the maximum applied load of the testing machine, the yield strength
of the thread material, in the coupling, and the yield strength of TiAl, the criteria for load-
ing condition can be determined. In this experiment, the yield strength of TiAl at the room
temperature was estimated to be 500 MPa and with that stress, the applied load had to be
about 50001b.. in the loaded area of specimen which was a quarter section of the circular

area with 7.6 mm radius. The thread size used in the coupling was 3/8”-24-2A. So the

stress area in the thread was 0.0878 in2 which is indicated in the DANT. Thus, the maxi-
mum stress on the first thread was about 400 MPa by EQ. 3.1 and this value was about two

times of the yield strength of mild steel. Therefore, it was necessary to reduce the loading

47

area in the specimen, and the area was reduced to 1/3 of the original size shown in Figure
3.2. The specimen was fit into the specimen holder in the compression cage in order to get
uniaxial compression state. The specimen was sprayed with boron nitride to prevent fric-
tional damage and diffusion effects between the specimen surface and compression cage
during high temperature compression.

The experiment was conducted under as shown in Figure 3.1 constant displace-

ment rate condition. The strain rate was nominally 4.4 x 10‘5 3’1.

The experiment was
conducted in two environments. Room temperature tests were done in laboratory air. At
higher temperatures, the testing condition was in a flowing Ar atmosphere in order to
reduce oxidation of the TiAl. In the high temperature experiments, each specimen was
kept at the test temperature for 20 minutes to homogenize the temperature before the com-
pression test. The testing temperature was held constant. The final strain after each test
was obtained from the thickness and cross sectional area change before and after compres-
sion. Practically, a pre-loading condition was applied in each test to maintain continuity in
the load train. It also influenced each stress-strain curve by shifting the origin of the strain
axis to the left. The direct comparison between the stress-strain curve and the measured
specimen dimensions indicated a lower strain than recorded in the stress-strain data, by
about 0.02 e. The difference may be due to lubrication and deformation in the platens.
The first room temperature test caused an indentation in the Inconnel loading platens. The
loading of the platens in the subsequent compliance test caused a reversed strain in the
platens as illustrated in Figure 3.3. Consequently the stress-strain curve at room tempera-

ture is not completely accurate. All these effects are illustrated in Table 3.2 and Figure 3.6

where the load displacement data are converted to engineering stress-strain curves.

48

Table 3.2 The order of experiments and conditions of each test.

 

 

 

 

 

 

 

 

 

 

 

 

 

Temperature Shape ed, em Comments

room temp. D 0, 0 thread failure in couplings

room temp. B 5.5%, 8.3% dents were formed in platens

room temp. compliance test: dents partially removed
850°C 0 2.9%, 4.8%

850°C compliance test

room temp. a 3.3%, 5.6% lost 2 pole figures before compression
room temp. compliance test

6500C 0 5.9%, 8.2%

650°C compliance test

room temp. 0 NA, 9.7% lost load-displacement data

 

 

 

 

 

* ed: strain obtained from data, em: strain measured from specimen

3.3 TEXTURE MEASUREMENT

3.3.1 Texture measurement

The texture measurements were carried out with a Scintag diff ractometer, SDS-
2000, which has a computer controlled four axis rotation system with no slits and a 1 mm
collimator. For a precise measurement before and after deformation, the specimen center
was mounted and aligned as accurately as possible in the specimen holder as shown in
Figure 3.2 (b). For the determination of textures in the v- phase, the following incomplete
pole figures were measured using Cu K01 -radiation: {111}, {200}+{002}, and

{220}+(022}. The Llo structure of TiAl is a tetragonal, fcc-related, ordered structure with

49

a c/a ratio close to unity (c/a = 1.02). Thus, X-Ray reflections originated from the lattice
planes in the same group with slightly different d-spacings. The separation of two close
peaks is possible using appropriate slits and a monochromator. In this experiment, no
attempt was made to separate the reflections. The superlattice reflections (001), (110)

were not utilized in this experiment because of their low intensity.
The intensity for a given pole figure was obtained at 5° increments in azimuthal

rotation, 0, up to 360°, and with 5° tilt increments of x up to a maximum tilt angle of 80°.
The scanning time at each increment of azimuthal angle was set at 4 sec. which provided a
sufficient intensity.

The grain size distribution of the specimen was obtained by J.Sadowitz [79]. Fol-
lowing his analysis, the majority of equiaxed grains were in the 1000 square microns to
the 4000 square microns size range and the spatial distribution of grains was quite random.

Some grain sizes were 8000 square microns. The lamellar grains were much lager than

equiaxed grains in grain size. The exposed area by X-iay beam was about 3.8 mm2. This
implied that at about 600 equiaxed and 150 lamellar grains contributed to the texture mea-

surement.

3.3.2 Procedures in using popLA

Texture data reduction in this experiment was carried out with Scintag XDS, a
software, a pole figure measuring code entitled SCINSA and the software popLA (Pre-

f erred Orientation Package from Los Alarnos, Los Alarnos National Laboratory) [80]. The

steps used in measuring texture are;

50

1. Measure 2-theta angle with a command C:\POLEFIG SCINSA J. Here, the
user can do omega(theta) or chi scan. The purpose of the 2-theta scan was to determine
the peak and the width of the peak so as to identify 26 positions to measure background
intensity. The number of 2-theta measurements depends on how many poles are required
in the experiment.

2. Start measuring pole figures. In this step, the user decides the number of poles,
scanning time and the maximum tilt angle (x). Considering the geometrical limitations of
defocusing of the X ray beam on an highly tilted surface, the maximum tilt angle is limited
to 80°.

3. After measuring pole figures, data are stored in a file named <FILE-
NAME>.RAW.

4. Run popLA with a command c:\x popla J.

5. Make DFB file. The .DFB (defocusing and background) file contains informa-
tion necessary for popLA to estimate a correction for geometric defocusing and back-
ground X-Ray intensity. The program requires a slit size to compute the correction file
and the value supplied was 1 mm. A 1mm collimator is used in the pole figure measure-
ment instead of normal slit. The collimator size is determined by the diameter of the cir-
cular shape of the tip of the collimator. The DFB file corrections are only approximate,
and not calibrated for the machine, but they do give a systematic correction that permits
meaningful comparison.

6. Make EPF file. With the .DFB file, the raw data file is normalized and the out-
put file is narned <FILENAME>.EPF (Experimental Pole Figure). With the EPF file, the

user can visualize the pole figure on the screen and print it out.

51

7. Complete pole figures using spherical harmonics. The outer rim of the experi-
mental pole figure is estimated. This permits a more accurate normalization of the pole
figure.

8. Compute the sample orientation distribution (SOD). The WIMV algorithm is
used and file named <FILENAME>.SOD is created. As discussed in the section 2, the
description of SOD or COD (crystal orientation distribution) is determined by the relation-
ship between sample coordinate system and crystal coordinate system. Thus, it is neces-
sary to specify the symmetry of sample coordinate system (orthogonal) and the crystal
coordinate system (cubic).

9. Calculate Inverse Pole Figures from .SOD. The file extension is WIP.

10. The files with extensions like EPF, SOD and WIPcan be visualized and printed
out in the form of two dimensional graphic image using the program POD.

11. Save a image using a conventional image capturing program (HiJE‘T Pro).

52

 

 

 

 

 

 

 

 

 

 

 

 

 

‘- Upper Pull Rod ,9
Furnace Controller
Vacuuni [Chamber
. i I]. Furnace

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P‘ v
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Egg LoadCell

 

 

 

 

 

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Data Acquisition System Draw Head

VJ ’ Lower Pull Rod

 

FIGURE 3.1 Schematic view of the compression system

 

Draw Jack

53

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

ti
E
15 mm2 8
a m e
E __________________ E
q o
l‘ H
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15 mm2
Ii 7
V 7.6 mm 7.6 mm
Y (a)
if A
specimen
K hOIder T
. x
; x ::::':: " ,.,
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FIGURE 3.2 (a) Shape of specimen (b) specimen orientation in the specimen

holder for the pole figure analysis

 

   
   
 
  

 

 

 

3500 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I d

3000 .— yielding _'

I in platens . :

rs 2500 E \‘ 1 g

2 r V . .

“o 2000 :— .3
to _ .

_°_, :

1500 :— ‘ A :compliance "

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. o _:

I Goo. O : 8% compression:

500 I. l l l ‘ l 1 ‘ ‘ ' I l l l l I r r 1 1 I r r L 1 I r r r r 'l

-4500 -4000 -3500 -3000 -2500 -2000 -1500
Displacement (mV)

FIGURE 3.3 Comparison between compliance and compression curve at

room temperature

55

 

3W) rIrIIIIIIlIIIIIIIIIllIIIIIIIIlIIII?
.e’

 

e :compression data I

O IllllJLlllllllILLJllllllllllllllllllllJJ‘

2500 E- / -:

.I-I. 2000 E J
2 . I
13 1500 — _‘
to . I
O ; I
—' 1000 :- 2.
500 L o :compliance data -:

 

 

 

-7000 -5000 -3000 -1000 0 1000

Displacement (mV)

FIGURE 3.4 Comparison between compliance and compression curves at

650°C

850

 

 

1400I-IIII'IIII'IIIIIIIUT'IIIIII
1200}

1000 3- __ .3

800 :-
600 _-

400 j—
200 '_ g : compliance data:
. e : compression data 1
0 l l l l I l I l l l J J I I l J l l l I I l l l l L4 1 l

-5500 -5000 -4500 -4000 -3500 -3000 -2500
Displacement (mV)

Load (lb)

   

 

 

 

FIGURE 3.5 Comparison between compliance and compression curves at

850°C

57

 

   

 

 

1 000 I I I l j I I I I I I l r If I I I I I u

: 650°C :

800 - M -

A ' o .-

g : MW‘W 0°00 ‘ “a :

E 600 :' ‘ g A ‘ roomtemp :
A

U) - ‘ ‘ a -

.. ‘A ..

E 400 - -

CK : '0 o ‘

(.0 C 9'0 o 0 850°C :

200 -

 

L l l l l l l l l l l l l l l I l l l

0
0 0.02 0.04 0.06 0.08 0.1
STRAIN

FIGURE 3.6 Stress-Strain curves at each testing temperature after deforma-

tion

4. RESULTS

4.1 STRESS-STRAIN BEHAVIOR

Figure 3.6 shows the engineering stress-strain curves measured at three tempera-

tures at the strain rate of 4.4 x 10‘5 s'l. At 850°C, the curve starts to show the work soft-
ening effect just after peak stress about at e = 0.3. But, for the two lower temperature

experiments, the work softening effect is not detected. The gaps in the strain record at

850°C resulted from the slowness of the computer when it was storing data to disk. The
lower temperature samples exhibited work hardening throughout the strain range. In these
experiments, the final strain was after strain of 5~8%. The curve at the room temperature
shows a lower slope in the elastic region. The optical microscopic observation indicated

many cracks in the room temperature experiment. The strain obtained at room tempera-

ture in inside specimen was 8.3%. The curves at 650°C and 850°C show a consistency in

the elastic region, and the final strains were 8.2% and 4.8% respectively.

59

4.2 TEXTURE AFTER COMPRESSION

4.2.1. Texture at room temperature

Figure 4.1 shows (111) pole figures which include the undeformed state and the
deformed case. In the undeformed case, the distribution of high intensities of (111) poles

appears randomly distributed. However, the strongest and largest group of (111) poles are

observed in the vicinity of 8 = 30~40°. After compression, the poles which existed indi-

vidually in the undeformed state, appear to be clustered, which indicates a more strongly
textured state. The strong clusters are observed around 6 = 35°. Even though the strong

(111) poles were already situated around 8 = 30~40° before compression, the pattern of
their existence was spike-like single peaks. But the characteristics of poles after compres-
sion indicate that they were more grouped after deformation, following the compressed
state. Figure 4.3 shows (220) pole figures before and after compression. The clustering
phenomena are also observed after compression in the same manner as the (111) pole fig-
ures. The strong component is located around 9 = 0° after compression. The (200) pole
figures are shown in Figure 4.2 and they exhibit similar characteristics. After compres-
sion, peaks were smoothed and grouped. If the angular relationship of the strongest peaks
among three pole figures is considered before and after compression, it appears that a pre-

existing <110> fiber texture in the normal direction is strengthened by deformation. The
(111) poles observed in the range of 8 = 30~40° and the (200) poles in the range of 9 =

40~50° are consistent with <110> fiber texture, and the same grains contribute to the

higher intensities in all 3 pole figures. After compression, most of the grains contributing

60

to the <110> texture were not moved from their original orientation. Instead of rotation,
these zones accumulated more grains in these orientations, so apparently the neighbor
grains rotated to the preferred directions pre-existing before deformation. Qualitatively,
similar texture changes occurred on both the inside and outside specimens. However, the
changes in maximum intensity were opposite in the two specimens. The outside specimen
had a much stronger initial intensity that resulted from a larger grain size [80]. These
increases in intensity in orientations contribute to the <110> fiber texture but in the {220}

pole figure, these orientations are near but not at the {220} pole.

4.2.2. Texture at 650°C and 850°C

Figure 4.4 (a) shows the (111) pole figures before and after compression at 650°C.
The initial texture also exhibits an apparently random distribution of high intensity poles
but the deformed one indicates that several clusters are formed around at 8 = 30~40°.
The (200) pole and (220) pole figures are shown in Fig. 4.5 (a) and 4.6 (a). The (220)
strong texture component exists not at the center but near the center. In every pole figure,

the maximum intensity has decreased, so deformation caused a spreading of crystal orien-

tations.

Figure 4.4 (b) shows the (111) pole figures after compression at 850°C. The tex-

ture observed is similar to the other undeformed outside specimens, but the deformed one
shows the textured state. The clustering effect is also detected at 850°C as in the other
I

specimens. The maximum intensity in each cluster is located around 8 = 35°, even

61

though the range of each cluster spreads out around the poles with the maximum intensi-

ties. Figure 4.5 (b) shows the (200) pole figure. The majority of the textured component

appears to be situated around 8 = 40 ~ 50° in the deformed case. Figure 4.6 (b) shows the
(220) pole figure. Unlike the other specimens, it is difficult to observe the formation of

any strong textured component just by looking at the pole figures, even though the slight
increase in texture component about 8 = 0° is barely observed. As with the 650°C speci-

men the maximum intensity tends to decrease, and this indicates a general spreading of

crystal orientations.

Although all pole figures exhibit similar features, the undeformed specimen in the
center of the cast rod in Figure 4.1 (a) has a weaker texture, that correlates with a smaller

grain size [80].

62

111 lex.=11.01 111 lax.=12.?1

      

mm ZB.U

9.16 9.46

1.17 1.47

2.11 2.11

1.8 L”

.17 .1?

.2 .2

.11 ~11

-2 log. scale - scale
BEFORE AFTER

(a) B eA = 8.3%

 

-2 log. scale

 

FIGURE 4. l (111) Pole Figures before and after compression at room tem-
perature in inside specimen (a) a = 8.3% and (b) outside specimen a = 9.7 %.

   

lux.=1.3.33 9.23
a.m ass

9.16 9.16

1.17 1.17

2.11 2.11

1 1.“ LE!
.17 .17

_a .22

.11 .11

log. scale log. scale

   

4.17
2.11
LN

.17

.11

 

-2 log. scale -2 log. scale

FIGURE 4. 2 (200) pole Figure before and after compression at room temper-
ature in inside specimen (a) e = 8.3% and (b) outside specimen a = 9.7%

 

 

lax.=17.11

23.88
9.16
1.17

2.11

 

log. scale

FIGURE 4. 3 (220) Pole Figures before and after compression at room tem-

perature in inside specimen (a) e = 8.3% and (b) outside specimen a = 9.7 %.

65

 

 

log. scale

 

y (b) L] 1T =sso°c

\I’
x

FIGURE 4. 4 (a) (111) pole figures before and after compression at 650°C,
9 = 8.2% (b) (111) pole figures before and after compression at 850°, 8 = 4.8%

log. scale

 

y (b) 0 T =sso°c

‘11
1:

FIGURE 4. 5 (a) (200) pole figures before and after compression at 650°C,
8 = 8.2% and (b) at 850°C, 2 = 4.8%

67

log. scale

 

(a) a 1‘ = 650°C

 

FIGURE 4. 6 (a) (220) pole figures before and after compression at 650°C,
8 = 8.2% and (b) at 850°C, 8 = 4.8%

5. ANALYSIS AND DISCUSSION

5.1. TEXTURE FORMATION

Figures 5.1- 5.4 show the SOD’s (Sample Orientation Distribution) after compres-
sion at room temperature, 650°C and 850°C. In homogeneous axisymmetric uniaxial de-
formation of a specimen with truly random grain orientations, SOD sections (‘1’ = constant)
should be all the same and identical to the projection, which represents the inverse pole fig-
ure in the axial direction. The SOD sections of the TiAl specimen indicate dependence
upon ‘1‘ which arises from the initially non random texture. The inverse pole figures after
compression in Figure 5.5 show that the dominant final component is the <110> type fiber
component in the normal direction in every specimen. With strain, the maximum intensity
of the inverse pole figures increase dramatically, but the maximum intensities in the elevat-

ed temperature deformation decrease slightly.

69

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FIGURE 5. 5 Inverse pole figures at normal direction before and after compression
at room temperature in inside specimen (a) and outside specimen (b).

74

 

log . scale

 

log. scale

  

(b) a T = 850°C

FIGURE 5. 6 Inverse pole figures before and after compression (at) at 650°C, 2 = 8.2%
and (b) at 850°C, 8 = 4.8%

75

5.2.THE PREDICTION OF TWINNING

5.2.1. Schmid Law

One of purposes in this research is to examine the possibility of detecting mechan-
ical twinning by analysis of texture changes. For this purpose, the Schmid factor for twin-
ning in TiAl was calculated and represented on a stereographic projection. For tension and
compression, different stress geometries are required. In Figure 5.7, assuming the bottom
of the specimen is fixed, the twinning critical resolved shear stress must have a component
parallel to the principle stress direction. Since twinning only occurs in one direction, the
same twinning system must be rotated 90° from tension geometry to compression geome-
try. Frgure 5.8 shows the comparison of the Schmid factor contours between tension and
compression. For the case of tension, the maximum Schmid factor is positioned in the vi-
cinity of [441] crystal direction for the (111)[11§] true twinning system [39]. The maxi-
mum Schmid factor for compression is located in the vicinity of [118] for the (111)[11§]
true twinning system. The stress axis which produces the highest Schmid factor for twin-
ning in compression is close to a [001] cube orientation, while in tension, the stress axis is

near the [110] orientation.

76

 

 

 

 

 

 

 

W W

(a) (b)

FIGURE 5. 7 (a) Tension (b) Compression, Slip plane normal Kl, slip direction in,
stress axis a, and loading direction F.

 

 

 

   

12 —
13 ‘15
COMPRESSION
0117
112
,x 0.17
/.
110 -" 111
t“ . 251
221
331
551
101:
TENSION
111
112

FIGURE 5. 8 Estimated Schmid factor contours with respect to the true twinning sys-
tem of (lll)[1 12] which indicates that the highest Schmid factor is in the vicinity of
[441'] tensile principal stress axis [39] but in the vicinity of [l 18] for compression.

78

5.2.2. Detection of Mechanical Twinning
For detecting a change of texture due to the mechanical twinning, two theoretical
approaches are used. The first can be called a pre-deformation approach and the second
one can be called a post-deformation approach. The first case is related to the crystallo-
graphic approach for twinning. Basically, it assumes that the initial distribution of grains
before deformation is random. With this initial condition, as the stress is imposed in the
compressive direction, the randomly oriented grains start to rotate, according to the orien-
tation of each crystal with respect to the local stress state during deformation. For mechan-
ical twinning, the stress condition is estimated with the Schmid law. Generally,
crystallographic twinning is described by one of two possible rotation axes. The true twin-
ning system in TiAl is described by the normal direction of the (111) plane and the [115]
slip direction which are identified as the K1 plane normal and the 111 slip direction, respec-
tively, in the crystallographic description of twinning. These directions are shown in Fig-
ure 5.7. If a grain is rotated about 180° around either of these two rotation axes for
twinning, it will arrive at the final twinning orientation after deformation. The (111) pole
figure will give an appropriate way to illustrate the detection of the orientation change of
each grain. In Figure 5.9, a grain is oriented in a way so that the normal direction coin-
cides with the principal stress axis that provides the highest Schmid factor for true twin-
ning in the initial condition (Figure 5.9 (a)). The twinning deformation resulting from
loading in the normal direction will rotate the grain around the (111) rotation axis and the

grain will reach the twinned orientation in Figure 5.9 (b).

79

 

 

[118] (b)

 

FIGURE 5. 9 (111) Pole figures before (a) and after true twinning (b) illustrate how
texture changes.

80

However, this approach has theoretical and experimental inaccuracy. In polycrystal
deformation, grains do not rotate just following the Schmid law but deformation must sat-
isfy much more complicated polycrystalline plasticity theories. Therefore, the initial as-
sumption that only used the Schmid law is oversimplified in the theoretical view. Also, the
clustering effect in the pole figures in Figures 4. 1~6 is the dominant phenomena after de-

formation, which makes it difficult to identify a specific grain orientation.

Compared with this first approach, the post-deformation approach presents a more
practical approach. The fundamental idea of the post def orrnation approach is to compare
a component of texture in the initial condition before compression with the texture change
after compression. For this, an inverse pole figure is employed as a tool for detecting the
texture evolution, because it shows the general texture change at a glance. Figures 5.5~6
show inverse pole figures in four testing conditions which are recalculated from the ODF.
The texture change before and after deformation, can be viewed by the difference between
the pole figures. Figures 5.10~13 illustrate the orientations that were weakened, and the
orientations that were strengthened. From initial orientations, the region near the <110>
component is always stronger after deformation. Figures 5.11~12 show a comparison of
orientations along the bottom of the inverse pole figures in Figures 5.5~6. There also exist
several weakened portions in each inverse pole figure as illustrated in Figures 5.13~15.
Then a deterministic relationship is considered between the weakened and the strengthened
components shown in each inverse pole figure. In order to evaluate potential relationships,
the Schmid factors for each possible deformation system are calculated. Table 5.1 shows

the Schmid factors of slip systems, primary (111)[ll§] true twinning system and other

81

possible true twinning systems for several stress axis orientations in the 001- 110- 010 unit
triangle (Figure 5.10). It should be noted that twinning shear is unidirectional, unlike slip.
The region shaded in gray represents the stress axis orientations which have high Schmid

factors for primary twinning and superdislocation slip.

From experimental observations, there is strengthening of the <110> fiber compo-
nent, but also two weakened regions are observed at orientations of [212] and [328] direc-
tions respectively in Figure 5.13. For example, the [212] orientation has a Schmid factor
for (111)<110> dislocation slip that is higher than the primary (111)[112] true twinning
system. But for the [328] orientation, the Schmid factor for the primary true twinning sys-
tem and superdislocation slip have a high values of Schmid factors. If superdislocation slip
accounted for the deformation, then one would expect rotation of less than 4° for a strain
of ~10%. So, it is likely that the grains oriented to [328] were mechanically twinned after
the deformation at room temperature, if the critical resolved shear stress for twinning is
similar or smaller than superdislocation. Similar considerations permit a comparison for

superdislocation and normal slip that is also illustrated on Figure 5.10.

82

110

 

 

 

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FIGURE 5. 11 (110) component density diagram according to change of 9 at (p = 0
before compression and after compression at room temperature in specimen (A) e =
0% and e = 8.3%, and (B) c = 0% and e = 9.7%.

8S

 

 

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FIGURE 5. 12 (110) component density diagram according to change of 6 at ‘1‘ = 0
before compression and after compression at 650°C in s = 0 and e = 8.2%, and at
850°Cin c=0ande=4.8%

max.= 5.27

IIII:ZB.BB

9.46
4.17
2.11
1.88
.4?
.22

.11

 

log. scale
max.=18.13

   

log. scale

FIGURE 5. 13 (a) SubWaction of textured region from initial orientation distribution
(b) Substraction of initial orientation distribution from textured state at room tem-
perature experiment for normal direction in inverse pole figure in inside specimen

B eA=8.3%

    

3 (a)

L] T = 650°C

 

 

..... ” “ log. scale

 

(b)

4.47
2.11
1.88
.‘I?
.22
.11

   

log. scale

FIGURE 5. 14 (a) Substraction of textured region from initial orientation distribution

(b) Substraction of initial orientation distribution from textured state at 650°C exper-
iment for normal direction in inverse pole figure

max.= 5.83
28.88
9.46
4.4?
2.11
1.88

.4?

.22

.11

 

log. scale

max.= 5.21
ll. 28.88
9.46
4.4?

2.11
I. 1 .88
,p_, .4?

.22

.11

 

log. scale

FIGURE 5. 15 (a) Substraction of textured region from initial orientation distribution

(b) Substraction of initial orientation distribution from textured state at 850°C exper-
iment for normal direction in inverse pole figure

89

At this point, the pre-deformation approach is employed as a verification tool for
this result. Once the origin of the twinned area is identified as [328], it is assumed that
(328)[211] is the original texture component ([211] is chosen arbitrarily in rolling direc-
tion). This component is rotated about 1800 around the (111) pole or the [112] direction.
The resultant component after this rotation is (891)[11T] where the [TIT] is in the resulting
in -plane direction. The Euler angles of this component are shown in Table 5.2. Figure
5.16 shows the SOD sections after deformation which correspond to each Euler angle at
room temperature. As shown in Figure 5.16, it appears that the twinning component is de-
tected in each SOD section. Similar exercises with different choices of the in-plane direc-
tion resulted in similar values of 8 and oi), but ‘I’ varies with the choice of the in-plane
direction. However, since the inverse pole figure is the summation of the ‘1' sections of the
SOD, it can be shown that any in-plane direction will lead to a twinned orientation near to

110 or 101.

Figures 5.6 (a) and 5.14 show the inverse pole figure and the difference pole f i g-
ures for the compression at 650°C. Here, the most weakened area is detected near in the
[115] direction. The Schmid factor for this direction has larger value for the true twinning
system than those for other deformation systems. If the initial component for the twinning
is (115)[1T0], the twinning component becomes (W121)[ITO]. The Euler angles for the
twinning component are also shown in the table 2. Figure 5.17 shows the SOD section for
these Euler angles. The twinning component is shown in the SOD. Figures 5.6 (b) and 5.15
show the inverse pole figure and the difference pole figures for the deformation at 850°C.

It appears that [328] is also a twinned position similar to the room temperature experiment.

90

But, the amount of weakening is less than the case at room temperature. The Euler angles

and SOD sections are shown in Figure 5.18.

 

‘1’: 69 ¢ ‘1’, 9’ ¢ 11” 6’ ¢
(891)[TIT] 30, 42, 82 39, 48, 6 54, 85, 41
(_121'21)[Tlo] 3, 45, 4 90, 86, 45

 

 

 

 

 

 

 

 

Table 5. 2 Euler angles for twinned components

These particular examples suggest that the orientation change in the range of 0 < 8
QS° occurred by twinning. As shown in the literature survey, deformation due to slip caus-
es gradual changes in texture such that after 40% rolling, the strength of the texture is only
about 6 x random, but in TiAl, 5-9% compression can causes much greater increases in the
texture strength. In conventional metals, twinning occurs after much slip hardening has oc-
cuned, but in TiAl it appears that twinning occurs with very early strains. A similar trend

was also shown in the outside specimen at room temperature.

91

nex.=14.56
28.88
9.46
4.4?
2.11
1.88
.4?
.22

.11

   

log. scale
nax.=16.85

28.88
9.46
4.47
2.11
1.88

.17
.22

.11

   

log. scale
max.=13.81

28.88
9.16
4.4?
2.11
1.88

.4?
.22
.11

   

ml 1m log . scale

FIGURE 5. 16 SOD sections which include twinning component after deformation at
room temperature in inside specimen (A) (T = Twin component).

 

931 1E8 109 . scale

FIGURE 5. l7 SOD sections which include twinning component after deformation at
650°C (T = Twin component)

max.=14.56
28.88
9.46
4.47
2.11
1.88
.47
.22
.11

 

log. scale
nax.=15.82

28.88
9.16
4.17
2.11
1.88

.17
.22
.11

 

log. scale
nax.=2?.23

28.88
9.46
4.4?
2.11
1.88

.4?
.22
.11

   

log. scale

FIGURE 5. 18 SOD sections which include twinning component after deformation at
850°C ('1‘ = Twin component)

5.2.3. Volume Fraction of Twinning

Up to this point, the analysis of the mechanical twinning has been the major focus,

which can be demonstrated in a qualitative matter. Next, a quantitative approach is used to

determine the volume fraction Vf of twinning. The volume fraction of twinning is calculat-

ed in the following procedure

:MEA .MWB _2AminMWA

 

 

 

 

 

 

 

EQ. 5.1
—2AtoralMWT 2AtoraIMWT

Vf = Volume Fraction of Twinning

Ami" = Twinned Area

Atotal = Total Area

MWB = Mean Weight of T wrnned Area Before Compression

MWA = Mean Wei ht of Twinned Area After Compression

MWT = Mean Weig t of Total Area

Table 5.3 Data of strain due to mechanical twinning.
Temperature Shape atom] Vf of twinning atom] due fraction of
(%) (%), range of 9 to twin- 10131 8 (11.13
ning (%) to twmnmg
(%)

room tCmp. B 8.3 2.05, 10~200 , 1.45 17.5
room temp. g 9.7 2. 17’ 0~200 1.53 15.7
650°C 0 8-2 5.90, ro~20° 4.17 50.8
850°C 0 4-8 2.39, 10~20° 1-69 35-2

 

 

 

 

 

 

 

 

95

The IPF data is stored as an array of data at 5° increments of 6 and 0. Since these
data represent an orientation density at a position on the surface of a sphere, the area asso-
ciated with each data point must be computed. The popLA was used that determines the
area bounded by 5° data points on the surface of a sphere, and averages the density values

D (8,0) on the corners of the area linearly.

In EQ. 5.1, the twinned area indicates the region with a weakened intensity where
has higher Schmid factors for the primary twinning than those for other deformation sys-
tems (Figure 5.10). By applying this equation to the inverse pole figures of the inside spec-
imen at room temperature, 650°C and 850°C in Figure 5.56, the volume fraction transfer
by twinning at each temperature were about 20% at 22°C, 50% at 650°C and 35% at 850°C.
The interesting point is that at 850°C, the volume fraction dropped by a large amount. This
result is consistent with Loiseau’s and Jin’s studies [39, 81]. Their suggestion is that there
may be a transition temperature which determines the activity of the mechanical twinning.
Actually, at the highest temperature, dislocations become more mobile due to the thermal
activation, and some cube <100> dislocations become mobile, and mechanical twinning is
relatively less favorable than dislocation motion. This lower amount may be a result of the
initially strong [110] component. Further if it is assumed that the majority of the def orma-
tion occurred on the primary lip or twinning system, then the amount of strain caused by
mechanical twinning can be estimated by multiplying the volume fraction by the FCC twin-
ning shear strain of 0.707. These computations indicate that at 650°C, most of the defor-
mation occurred by twinning, and less fractions twinned at room temperature and at 850°C

in Table 5.3. This result suggests that the texture analysis can detect mechanical twinning

96

quantitatively. More theoretical approach using texture simulation should be used in future
work, to determine if the starting texture in these experiments will generate the deformed
textures experimentally measured, if mechanical twinning has a low critical resolved shear

stress.

5.3.MAIN COMPONENT OF TEXTURE.

As shown in section 5.2.2, pole densities are high at about <110> direction in the
three inverse pole figures. The main component of texture in uniaxial compression has
been identified as <110> fiber component in previous works [82,83] and the present result
is consistent with the literature. In the present work, {220} pole figures taken at RT and
650° show a slight deviation of the main texture component from 6 = 0° even though the
inverse pole figures show {110} fiber. The above analysis can explain that twinning ac-
count for this. The initial assumption in the ODF calculation was Cubic symmetry of TiAl,
even though the actual symmetry is tetragonal. Thus, it seems that the ODF calculation

could be improved by using the correct tetragonal symmetry conditions.

5.4.MECHANISM OF TEXTURE FORMATION.

5.4.1. Grain Rotation

Figures 4.1, 4.4 (a) and 4.4 (b) show (111) pole figures before and after compression
at each testing temperature. For the three cases, the initial orientation shows a slightly tex-
tured state. The inverse pole figures of the three initial states indicates a weak {110] fiber

component. Thus, it is assumed that these initial textures were formed during the casting

97

and heat treatment history of the specimen. Formation of a sharp deformation texture from
a nearly random orientation after a small deformation implies that dramatic orientation
changes occur by polycrystal plasticity that includes twinning. The sharpness of texture in
the deformed specimen is related to the amount of grain rotation that occurred. If there is
any specific orientation of existing grains before deformation and it is a stable orientation
after deformation, the orientation is reinforced by the grains which continuously rotate to-
ward the stable orientation, as the deformation proceeds. In present works, the stable ori-
entation is <110> in both cases before and after compression. This is consistent with the
classical FCC compression case. The effect of twinning is that orientations far from 110
are discontinuously rotated to orientations near 110 which can then rotate with subsequent

strain toward the <110> terminal orientation.

5.4.2. Slip

The difference between TiAl and classical FCC deformation textures depends upon
the anisotropic characteristic of TiAl which results in the constraints on each deformation
mechanism. The first trial in this experiment to analyze the quantitative differentiation of
the 022 reflection from the 220 reflection was not successful due to the limited resolution
of the X-ray system. Theoretical simulation considering polycrystal plasticity has been
done by Harti g et al. [84]. The results indicate that the final texture component depends on
the value of the CRSS (Critical Reserved Shear Stress) of each deformation mechanism. If
the CRSS value of slip on {1 l 1}<110> is larger than slip on {1 l 1}<101>, the final texture

component is shifted to <110> fiber type and if the CRSS value is reversed, the resultant

texture component is close to <101>. This indicates that the prevailing deformation mode

98

determines how the final texture component develops. In the present work, this distinction

cannot be made.

5.4.3. Mechanical Twinning

Since the {1 l 1}<112> type mechanical twinning is a crucial deformation mecha-
nism in the plasticity of TiAl, its role in the texture formation is expected to be important.
The activation of sessile 1/6<112> partial dislocation which becomes mobile in the elevat-
ed temperature is believed to help the generation of the twinning. As discussed in section
5.2.2, mechanical twinning was detected at room temperature as well as at the elevated
temperature and even more, the twinning component appears to contribute to the <110> fi-
ber component. Thus, the mechanical twinning is cleariy to be a significant deformation
mechanism regardless of the testing temperature. Furthermore, the fact that the region near
<110> becomes very strong with rather low strains due to mechanical twinning indicates

that the CRSS for twinning is probably lower that for superdislocation slip.

5.4.4. Dynamic Recrystallization

Recent research has shown that dynamic recrystallization occurs during high tem-
perature deformation [85,86]. The reason why high temperature deformation involves re-
crystallization originates from the accumulation of deformation energy and the release
through nucleation and growth of the recrystallized grains. With increasing temperature,
There is a greater driving force for dynamic recrystallization. It is reported that in the tex-
ture formation of TiAl during high temperature compression, the dynamic recrystallization

effect causes shifting of the pure <011> fiber deformation texture component to <032>

99

which is located between <011> and <010>. Thus, the transition from deformation texture
to recrystallization texture occurs in the process of the competition between these two sta-
ble components during high temperature deformation. In the present work, the high tem-
perature compression was performed at 850°C. The results of pole figures and ODF
calculation indicate no detectable formation of this recrystallization component. For this re-
sult, two explanation can exist. First, Lee and his coworkers found that the BD'I'I‘ (Brittle-
Ductile Transition Temperature), about 800°C, is the initiation temperature of recrystalli-
zation in tension and compression and no evidence has been shown for dynamic recrystal-
lization at lower temperatures [85]. Second, the strain is probably too low for dynamic
recrystallization in this present work. At the BD'I'I‘, only the necking region, which is a
hi ghiy stress concentrated region during deformation has shown dynamic recrystallization
in tension. In this regard, dynamic recrystallization seems to occur in higher temperature
and higher strain than this present work. Even if recrystallization occurred at the transition
interval at low strain, the recrystallization region would be limited only to stress concentra-
tion region such as grain triple junctions or grain boundaries and the recrystallized grains
would be so small compared with most of original grains which contribute to texture for-

mation that they would be hard to be detected in the final texture.

5.4.5. Crack formation and deformation of TiAl

The stress-strain curve at room temperature showed a deviation from those at higher
temperatures especially in the elastic region. The final microstructure showed many cracks
in the present specimen ['79]. At low temperature deformation of TiAl, the poor mobility

of slip systems causes the localization of stress, which is directly related to the initiation of

100

a crack Thus, even if the applied stress reached the CRSS (Critical Reserved Shear Stress)
for the 5 preferred slip and twinning systems, the localized stress condition would nucleate
a crack ahead of starting plastic deformation. However, the curve at 650°C showed a con-
sistency with one at 850°C in elastic region, so, it suggests that increasing temperature
might release the localized stress condition by thermal activation. However, the question
is which temperature would be the turning point from fracture dominant circumstance to a
deformation dominant one. At this moment, this question remains for further investigation.
As a result, it is assumed that the kinetics of the fracture nucleation mechanism and the de-
formation mechanism control the deforrnability of TiAl. Thus, the overall structure failure
and plastic deformation occurs by a process of competition between crack nucleation and

plastic deformation by slip and mechanical twinning.

6. CONCLUSION

1. The results of the texture analysis of TiAl in compression showed that the
<110> fiber component is the dominant component through all testing temperatures in

compression. The result is quite consistent with conventional FCC compression.

2. Specimens taken from different parts of a cast and heat treated cylindrical rod
have highly variable textures. They are stronger near the outside and weaker toward the

center.

3. The present work indicated that the analysis of mechanical twinning in com-
pression is possible through texture analysis. The present experiments indicate that
mechanical twinning occurs at very low strains, and that it accounts for nearly all of the
total strain at 650°C. At 850°C, where thermal activation makes all dislocation motion
easier, the contribution of mechanical twinning is smaller. At room temperature, cracking
complicates the interpretation, but mechanical twinning is clearly a significant contributor

to the deformation.

101

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