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This is to certify that the

thesis entitled

Texture Evolution During High Rate Superplastic
Elongation In Mechanically Alloyed Aluminum‘

presented by
J 1' n , Zhe

has been accepted towards fulfillment
of the requirements for

MS. degree in MaanUZLLlS Science

 

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TEXTURE EVOLUTION DURING HIGH RATE SUPERPLASTIC

ELONGATION IN MECHANICALLY ALLOYED ALUMINUM

BY

Zhe Jin

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Metallurgy, Mechanics and Materials Science

1991

U '~./

’u. U“ ./’

ABSTRACT

TEXTURE EVOLUTION DURING HIGH RATE SUPERPLASTIC
ELONGATION IN MECHANICALLY ALLOYED ALUMINUM

BY

Zhe Jin

Texture analysis as a structure parameter is a very
powerful analytical tool for studying deformation behavior
due to its capability of isolating the individual
contributions from the various mechanisms, such as
dislocation slip, twinning, grain boundary sliding,
grain rotation, and recrystallization. The texture evolution
in the superplastically deformed specimens of IN90211 is
investigated as a function of strain using the three
dimensional crystal orientation distribution functions
(CODFs). At the lower strain rates (1/sec and 77/sec),
the textures are mainly concentrated along two fibres, a-fibre
(<101> parallel to ND) and {102}<uvw> (<102> parallel to ND).
At the higher strain rate (330/sec), the textures are mainly
composed of two fibres, {203}<uvw> and a skeleton line (<001>
orientation is tilted from ND towards TD by about 30°). The
results indicate that at small strains the specimen deforms
by grain boundary sliding and single slip, at large strain
the deformation is dominated by grain boundray sliding,
multiple slip and recrystallization. However, at the highest

strain rate, there is no evidence of recrystallization.

Copyright by

Zhe Jin

1991

ACKNOWLEDGEMENTS

The author would like to express his sincere
appreciation to his advisor, Professor Tom Bieler for his
continuous guidance and support during this work. The author

enjoyed the time closely working with him.

The author very grateful for the financial support from

Michigan State University through an All-University Research

Initiation Grant.

iv

TABLE OF CONTENTS

Page

ABSTRACT ................................................ ii
LIST OF FIGURES ......................................... viii
LIST OF TABLES ..... . .................................... xiii

CHAPTER 1. TEXTURE AND SUPERPLASTICITY .................. l

1.1. Deformation Texture ................................ 1

1.1.1. Slip. ....................................... 2

1.1.2. Stacking Fault Energy ....................... 10

1.1.3. Mechanical Twinning ......................... 10

1.1.4. Micro-Banding.. ............................. 16

1.1.5. Shear-Banding ............................... 17

1.2. Recrystallization Texture .......................... 19

1.2.1. Oriented Growth ............................. 20

1.2.2. Oriented Nucleation ......................... 23

1.2.3. Nucleation Sites ............................ 25

a. Nucleation in Grain Interiors ............. 25

b. Nucleation at Grain Boundaries ............ 27

c. Transition Bands... ....................... 28

d. Influences of Particles ................... 29

1.2.4. {100}<001> Cube Tuxture ................. .... 31

1.3. Grain Growth ............ .... ....................... 32

1.4. Superplasticity .................................... 34

1.4.1. Concept of Superplasticity... ............... 34
1.4.2. Mechanical Behavior of Superplasticity ...... 37
1.4.3. Microstructural Behavior of Superplasticity. 41
1.4.4. Mechanisms of Superplastic Deformation ...... 51
a. GBS with Diffusion Accommodation .......... 51
b. GBS with Dislocation Motion Accommodation. 55

c. Dislocation Slip .......................... 59

1.5. Relationship Between Texture and Superplastic

Deformation ............................... 59
1.5.1. Texture Effects on Superplasticity. ......... 59

1.5.2. Superplastic Deformation Effects on

Texture ............................... 65

1.6. Representation of An Orientation ................... 67
1.6.1. Introduction to Rotation System ............. 68

a. Euler Angles........... ............... .... 68

b. Rotation Axis and Angle ................... 70

1.6.2. Representation of the Orientation ........... 70

a. Representation of the Orientation in the Pole
Figure ................................ 70

b. Representation of the Orientation in the

Inverse Pole Figure ................... 71
c. Representation by Miller Indcies .......... 73
d. Matrix Representation ..................... 73

e. Orientation Distribution Function......... 74
f. Relationship Between Euler Angles and Miller

Indices ............................... 76

vi

Page

CHAPTER 2. EXPERIMENTAL PROCEDURES ...................... 81
CHAPTER 3. RESULTS ...................................... 83
3.1. Specimen Deformed at é=1/sec and T=425°C ........... 83
3.2. Specimen Deformed at é=77/sec and T=475°C .......... 93
3.3. Specimen Deformed at é=330/sec and T=475°C ......... 100
CHAPTER 4. ANALYSIS AND DISCUSSION ...................... 107
4.1. Deformation at Relative Low Strain Rate ............ 107
4.1.1. Grain Boundary Sliding ...................... 107
4.1.2. Slip.. ...................................... 110
4.1.3. Recrystallization ........................... 112
4.2. Deformation at High Strain Rate .................... 113
CHAPTER 5. CONCLUSIONS ................................. 115

APPENDIX A POLE FIGURES OF IN90211..................... 116

APPENDIX B INVERSE POLE FIGURES OF IN90211. ............ 133

LIST OF REFERENCES ...................................... 149

vii

LIST OF FIGURES

Figure Number Page

Fig.1.1

Fig.1.2

Fig.1.3

Fig.1.4

Fig.1.5

Fig.1.6

Fig.1.7

Fig.1.8

Stereographic projections showing deviation

of an effective stress axis Te from the

actual stress axis Ta. (a) Shear stress

contours. (b) Lines of maximum descent from

the point of maximum resolved shear stress

F... ..... . ...... . ............................. 2

Lattice rotations for {111}<110> slip. (a)

The smallest allowed shear (within the
confines of minimum work) is maximized. (b)
The largest allgwed shear is maximized.

(After Bishop ) ............................ 6
Texture rotations predicted by Bishop for

(a) copper and (b) 70/30 brass ................ 7

Computer-plotted lattice rotations obtained

for {111)<110> slip in which the activities

of colinear pairs have been maximized

within the confines of minimum work.
(Axisymmetric tension 5% strain) .............. 9

Hard-sphere model of [011] slip via [121]
(leading) and [112] (trailing) partials.

(a) The partials are unextended. (b) The

partials are extended...... ................... 9

Computer-plotted lattice rotations for

(111)<112> intrinsic foulting, according to
minimum work criterion. (Axisymmetric

tension 5% strain) ............................ 11

Orientation factors for (111}<110> slip

(full lines) and {111}<112> twinning

(dashed lines) under rolling (assuming a

plane stress state) and relative twin

orientation factor p (dashed dotted line).

(a) Along the a fibre, <110> parallel ND.

(b) Along the 8 fibre, <110> tilted 60°

from NT towards RD. (c) Along the f fibre,

<110> parallel TD ............................. 13

Orientation paths due to mechanical

twinning of {112}<111> and subsequent

deformation presented in the ¢2=45° section

of the Euler space ............................ 15

viii

Figure Number Page

Fig.1.9

Fig.1.10

Fig.1.11

Fig.1.12

Fig.1.13

Fig.1.14

Fig.1.15

Fig.1.16

Fig.1.17

Fig.1.18

Schematic representation of nucleation
sequence of recrystallized grains during
annealing of cold rolled steel ............... 26

Variation of some important texture
components during typical box-annealing
cycle ........................................ 27

The strain rate dependence of (a) the flow
stress and the strain rate sensitivity for

the Mg-Al alloy, grain size 10.6 pm

deformed at 350°C ............................ 37

Strain rate sensitivity versus strain rate
for Sn-5%Bi samples of varying Sn grain
size... ...................................... 39

The dependence of the strain-rate

sensitivity index on strain rate at

different temperatures for aluminium-copper
eutectic specimens ........................... 39

Microstructure of Sn-5%Bi alloy strained

1000% at room temperiture. (a) Cross

section. (b) Longitudinal section, tensile axis
vertical......................... ........ .... 42

Changes in surface appearance of same area

in specimen with increasing strain at

é=6.7x10 min in vacuum 2x10 mmHg.

Deformed (a) 9%, (b) 35%, (c) 64%, (d) 96%... 44

The value of the vertical component of the

grain boundary sliding versus boundary _4

angl with the tensile axis. (a3 é=1;6x10

sec (region I), (b) é=8;3x10 _1sec

(region II), (c) é=4.1x10 sec

(region III) ......... . ..... . ................. 45

Appearence of internal marker line

translatipns inlspecimens deformed at

é=6.7x10 min . Deformed (a) 30%,

(b) 60%, (c) 100%, (d) 200% .................. 47

Relative frequency of rotation of internal
marker lines to stress axis in spefimens
deformed 60%._5a) _ é =2x10 min , _1 _
(b) éB=6.7x10 min , 1c) at éC=1.1x10 min
............................................ 48

ix

Figure Number

Fig.1.19

Fig.1.20

Fig.1.21

Fig.1.22

Fig.1.23

Fig.1.24

Fig.1.25

Fig.1.26

Fig.1.27

Fig.1.28

Fig.1.29

Fig.1.30

Fig.1.31

Page

Relative frequency of rotation of internal
marker lines to stre§§ axi§1in specimens
deformed at é=6.7x10 min . (a) Deformed
30%, (b) deformed 60%, (c) deformed 100%,
(d) deformed 200%...................... ..... . 48
Densities of dislocations in twin

boundaries as a function of strain for

regions I-III ................................ 50

The unit step of the deformation
process..... ................................. 52

The accommodation strains required when
grains move from the initial to the
intermediate states ..... ... .................. 53

The trajectories of grain centers in
the emulsion, where a switching event
has occured .................................. 55

GBS and its accommodation to give
deformation in region II of
superplasticity .............................. 56

Slip accommodation of grain boundary
sliding.... ...... ...... ...................... 57

Slip accommodation from grain boundary
ledges.................... ......... . ......... 58

Variation of m with strain rate and
with direction of straining .................. 6O

Elongation at fracture as a function of

angle of the tensile axis to the

rolling direction at three strain rates

for aluminum-bronze sheet tested at 800°C.... 61

Elongation as a function of strain rate ...... 63

True stress / true strainzcuryfs on
extention with é =2.8x10 sec at 250°C
for different states of the alloy ............ 63

Strain rate sensitivity as a function of

strain rate (a) at 250°C, (b) at 150°C.

1. Quenching, rolling at 250°C, annealing at
350°C for 5h, water quenching. 2. Quenching,
96.6% rolling at 20°C, annealing at 350°C for

5h, quenching. 3. Quenching, 96.6% rolling at
20%. 4. Quenching, rolling to 96.6% at 1

250°C ........................................ 64

X

Figure Number

Fig.1.32

Fig.1.33

Fig.1.34

Fig.1.35

Fig.1.36

Fig.1.3?

Fig.1.38

Fig.3.1

Fig.3.2

Fig.3.3
Fig.3.4

Fig.3.5

Fig.3.6

Fig.3.7

Fig.3.8
Fig.4.1
Fig.4.2

Fig.A.l

Fig.A.2

The sample fixed coordinate system K
and the crystal fixed coordinate sys em

K in the sheet........ .....................

B

Definition of the Euler angles ¢l¢¢2 ........

On the definition of the Euler

angleswoo ...................................

Representation of a rotation by the
rotation axis d and the appropriate

rotation angle w ............................

The orientation of some crystal

directions in pole figures ..................

The orientation of the specimen

directions in inverse pole figure ...........

Relationships between the angles

<p1,¢,<,02 and ¢,9,¢ ............................

Some ideal components in ¢=O° section ........

Complete CODF of é=1 sch1 and T=425°C

(a)-(f).................. ....... .. ...........
The ¢=0° section of CODF vs. strain ..........

Orientation density vs. 0 and strain .........

Complete CODF of é=77 sec'1 and T=475°C

(a)-(b) ......................................

Orientation density vs. w and strain .........

Complete CODF of é=330 sch1 and T=475°C

(a)-(b) ..... . ................................

Orientation density vs. w and strain .........

Texture components vs. true strain ...........

Schematic diagram showing sliding of
platelet-shaped grains during superplastic

elongation ...................................

(111),(200),(220) pole figures of specimen

deformed at é=1/sec and T=425°C ..............

(111),(200),(220) pole figures of specimen

deformed at é=77/sec and T=475°C .............

xi

Page

69

69

71

72

72

80

83

85
91

93

94

101

102

106

108

108

117

123

LIST OF TABLES
Table Number Page
Table 1.1 Contribution of grain boundary sliding to
the total axial strain (6 b/et) in
regions I, II and III....q ................... 46

Table 2.2 Composition (wt%) of IN90211 ................. 81

xiii

CHAPTER 1

TEXTURE AND SUPERPLASTICITY

Texture is defined simply as a condition in which the
distribution of crystals is nonrandom , that is , the
orientations of all the grains in a polycrystalline
aggregate tend to cluster, to a greater or lesser degree ,
about some particular orientations , or an aggregate has a
preferred orientation. Like crystal structure and lattice
defects, texture is also a fundamental parameter
characterizing polycrystalline materials. It links the
anisotropic properties of single crystals and those of the

polycrystalline materials.

The formation of texture can be classified into four
parts: deformation texture, recrystallization texture, cast
texture and transformation texture. In the following
sections, we will discuss the deformation texture and

recrystallization texture only.

1.1. Deformation Texture

Deformation texture is produced by forming processes,
such as wire drawing, sheet rolling and torsion. It is due

to the tendency of the grains in a polycrystalline

aggregate to rotate during plastic deformation. Each grain
undergoes slip and rotation in a complex way that is
determined by the imposed stress and by the slip and
rotation of adjoining grains. The result is a preferred,

nonrandom orientation.

1.1.1. Slip

It is well known that the deformation textures are
developed as a result of lattice rotation brought on by
crystallographic shear during plastic deformation. When an
unconstrained crystal is loaded with an applied stress Ta,
the effective stress axis Te on the crystal will move
away from the initial applied stress Ta by crystal slip. In
the unit triangle of a stereographic projection of crystal,
Te moves towards the boundary of the unit triangle under

the single slip system, see Fig.1.l : when duplex slip

 

 

 

 

Fig.1.1 Stereographic projections showing deviation of an
effective stress axis Te from the actual stress axis
Ta. (a) Shear stress contours. (b) Lines of.maximum
descent from the point of maximum resolved shear
stress F.

system is operative, Te lies on a boundary of the unit
triangle; when four, six and eight slip systems operate, Te
lies at <110>,<111> and <100> directions respectively,
because the Schmid factor is equal among all equivalent

systems.

In polycrystalline materials, most of the grains will
be unable to deform by single slip or change their shape
freely because of constraints from each other. If applied
stress Ta is at P in Fig.1 , a slip should occur when
Ta=Tc/cosxcosz, where To is critical resolved shear stress,
cosxcosx is Schmid factor. But the build up of constraints
causes Te to move from Ta by moving down the line of
maximum rate of change of cosxcosx towards Q. Upon reaching
Q, Te is equal on two slip systems, but two systems are
insufficient to allow deformation in a polycrystalline
aggregate and Te axis will continue to rotate along the
symmetry boundary to <111>. At the point <111>, the value
of resolved shear stress is a minimum and any increase in
Ta will cause the grain to yield by slipping on six equally
favoured slip systems. For other initial orientation of Ta,
Te will rotate to <110> if Ta is within the region II or to

<100> if Ta is in III .

In the orientations <100>,<110> and <111>, there
is a multiplicity of slip systems available and since all

slip systems are symmetrically disposed, no rotation of the

grain relative to Ta occurs and consequently there would be
no development of preferred orientation. So the texture
arises from single or duplex slip rotations of grains. In
tension, Slip rotation cause grain to rotate so that the
movement of Te axis is towards the operative slip direction
and a texture with <112>,<111> and <100> directions is
parallel to tensile axis. In compression, Ta axis moves
towards the slip plane normal and a <110>,<100> texture
occurs. In rolling, the texture is constituted with the
orientations which satisfy mutually the requirements of a
tensile stress parallel to the rolling direction and a
compressive stress parallel to the sheet normal, that
is,the orientations with the spread from (110}<112> to

{311}<112> as well as {110}<111> and {110}<001>[2].

5], the slip in a

According to the theory of Taylor[
grain embedded in a polycrystalline aggregate requires at
least five independent slip systems in order to accommodate
five independent strains. Taylor assumed that among all
combinations of (five) slip systems which are capable of
satisfying the imposed strain, the active combination is
the one for which the sum of the glide shears is a minimum.
Bihop and Hill[4] strengthened Taylor’s theory by showing
that the shear stress reaches the critical level for slip
on the active slip systems chosen by Taylor without

exceeding it on the inactive slip systems. This theory

provides strain continuity across grain boundaries by

assuming that each grain deforms in the same way as the
aggregate, that is, although deformation is known to be
macroscopically and microscopically inhomogeous, it is
sufficient for a statistical problem such as texture
development to assume homogeneous deformation. From Bishop
and Hill’s principle of maximum work[4] , the stress system
required to impose the arbitrary strain can be found and
hence the slip systems can be determined. There are only
five stress systems which give rise to polyslip in single
crystals and these crystals give either six or eight
available slip systems, so that either one or three are
redundant in each grain. The choice of the five systems
from six or from eight depends on whether or not the
material exhibits "overshoot". According to Bishop’s
theory, metals which exhibit an alloy texture have
overshoot and those having the pure metal texture don’t
show overshoot. The overshoot is due to the hardening of
the latent slip system being greater than that of the
active system. When there is latent hardening, the most
extensively operated system will harden least and hence the
situation is represented by maximizing the largest shear.
But if the hardening of the latent slip system (latent
hardening) equals the hardening of the active slip system
(active hardening), then the combination is chosen such
that the smallest glide shear is as large as

[12.13].

possible Fig.1.2 shows these two cases under a

,3" g
./ J l
/ / / J
0 “Lip: x / f 1
2° ~. \ t l 1 l
flz’m .0 ‘b x, \e \b \ 1|
< 73403”- --.- ’“’ '“’ ““' --°- --°- -~o—<.7.;.'0>
<m>
if

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Fig.1.2 Lattice rotaions for {111}<110> slip. (a) The
smallest allowed shear (within the confines of
minimum work) is maximized. (b) Thflgargest allowed
shear is maximized. (After Bishop )

tension applied stress. In Fig.2a, both <111> and <100> are
stable for a metal where latent and active hardenings are
equal; but in Fig. 2b, the <100> texture is unstable and
rotates towards <111> orientation if latent hardening is
larger than active hardening. The rotations for compression
are the reverse of those for tension. In the case that
latent and active hardenings are equal, a <110> texture
will spread towards <113> (Fig.1.3a); If latent hardening

is larger than active hardenings, the

’ ,o'[m]

‘\:

(a) / / . (b)

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l

  

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Twog' f /; ); é é T ”\‘/’/; é

mo" .. °. \ i i X I \\\ix X\A
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Fig.1.3 Texture rotations predicted by Bishop for (a) copper
and (b) 70/30 brass.

rotation is more directly towards <110> (Fig.1.3b)[12]. The

[14] and Kocks[15] have shown

experiments done by Ramaswami
that prior slip on one system hardens all other systems
more than itself except a coplanar system where the

hardening is about equal. So there is a tendency for

hardening on non-coplanar systems to increase with
decreasing stacking fault energy of metals. Comparing Fig.2
with Fig.1 shows latent hardening (coplanar slip) mechanism

also favors an increase of the <111> texture.

But latent hardening mechanism can not explain the
phenomenon that silver (pure metal) has a alloy type
texture even though Smallman[7] suggested that trace of
dissolved oxygen was responsible for the alloy

behaviour. Calnan and Smallman later rejected this theory.

Cross-slip usually occurs in high stacking fault
energy materials and at high deformation

[9'10'11]. This mechanism implies that for the

temperature
multiple slip situation in constrained deformation, all
{111} <110> slip system pairs that share a common slip
direction (colinear slip) are favored. At large applied
stress, it is also possible that the materials undergo
cross-slip, but a low stacking fault energy material still
chooses other slip combinations wherever they are
available. Fig.1.4 shows the predicted rotations based on
cross-slip mechanism. As compared with Fig.1, it may be
seen that those crystals within the previous region II are
biased toward the <111>, thus partially accounting for the

drop in the <100> component for high stacking fault energy

metals.

/
/
COLIKM/// \
// / \
.//. I i I "

Fig.1.4 Computer-plotted lattice rotations obtained for
{111)<110> slip in which the activities of colinear
pairs have been maximized within the confines of
minimum work. (Axisymmetric tension 5% strain)

///fi2fl

 

bfi]
\\\\[H§]

 

 

 

”a”! Uzfl

 

 

SLIPPED

 

 

UNSLIPPED SLIPPED 1 UNSLIPPED

PARTIAL SLIP
(STACKING FAULT)

b

Fig.1.5 Hard-sphere model of [011] slip via [121] (leading)
and [112] (trailing) partials. (a) The partials are
unextended. (b) The partials are extended.

10
1.1.2. Stacking Fault Energy

For materials of low stacking fault energy, a
{111}<110> dislocation is normally split into two shockly
partial dislocations of the {111}<112> type connected by a
ribbon of stacking fault. Usually, the separated partial
dislocations move in zigzags. Two steps of slip of
separated partial dislocations are equal to one step of
normal dislocation, i.e., [1211+[11§]=[01i], see Fig.1.5.
However, if the partial dislocations are widely separated,
the effective slip direction of partial dislocation is.
shifted from <110> to <112>, that is, the leading partial
dislocation, [121], in Fig.1.5, moves ahead creating a
strip of intrinsic faulting, while the trailing partial
dislocation, [115], is pinned behind. The slip movement
would then be equivalent to (111)[121] in which case the
lattice rotation and hence the texture development would be
altered from the usual {111}<110> slip pattern. The
rotation by this mechanism is shown in Fig.1.6 for tension
stress. <100> component is no longer stable and intrinsic
faulting favors a strong <111> wire texture for very low

stacking fault energy materials.

1.1.3. Mechanical Twinning

Since the orientation of a twin differs drastically

from that of the matrix, the mechanical twinning is

11

 

%% 1H ---<

Fig.1.6 Computer-plotted lattice rotations for {111}<112>

intrinsic foulting, according to minimum work
criterion. (Axisymmetric tension 5% strain)

 

expected to play an important role in the development of
deformation texture. The {111}<112> will be formed if the

motion of the partial dislocation generates a stacking

fault on successive {111} layers.

According to the analysis of Chin, Hosford and

Mendorf[16], the incremental work done by a stress a

causing a strain c x is equal to

W = UXUXX = 151281 + ctIZti (1.1)
where rs is critical resolved shear stress of slip, rt is
critical resolved shear stress of twinning, S1 and ti are

the corresponding shear. The orientation factor M then

12

becomes

 

 

M= = (25. +a2t.)
l l

r c
S XX

where a = rt/rs . The operative combination of slip and
twin systems is formed if M is minimum. For {111)<110>

slip and {111}<112> twinning, mixed slip and twinning can
only occur for 1/J3 < a < 2/f3 ; if a > 2/J3 , only slip is

possible: if a < 1//§ , only twinning happens.

For the plane stress state, mechanical twinning happens
if relative twin orientation factor p = pt / ”s’ (where pt
is the Schmid factor for {111}<112> twinning and us is
the Schmid factor for {111}<110> slip), is larger than

[20]. In the case of p z 1, the {112}<111> copper

one
orientation undergoes mechanical twinning during rolling to
form the {255}<511> twinning copper orientation. Fig.1.7
shows the values of pt , “s and p for the relevant twin and
slip systems along the a , fl and r fibers of cold rolled
copper. It can be seen that the tendency for twinning
decreases steadily along the fi fiber from copper component
to brass component and p < 1 along the a-fiber. This means
that the part of fi-fiber near copper orientation should
twin more easily but for the a—fiber orientations no
twinning should occur. It also can be seen in Fig.1.7a that

two kinds of slip systems, i.e., colinear slip system

(111)[110]-(111)[110] and coplanar slip system (111)[101]-

13

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(111)[011] occur along a—fiber. Coplanar slip rotates the
orientation towards larger 0 angle while colinear slip
causes a rotation towards smaller 0. So at the position of
copper component (112)[111], the two rotations cancel each

other and the cooper orientation is stable.

Twinning explains not only the decrease in copper
component but also the increase of G and B components. The
orientation path of twinning is the one which the texture
transition from the copper-type rolling texture with
dominant C and S orientation to the brass-type rolling

texture where B and G predominate, as shown in Fig.1.8b.

Fig.1.8 schemeticslly shows orientation paths due to
mechanical twinning of {112}<111> and subsequent
deformation presented in the o2 = 45° section of the Euler
space.(a) is principle orientation occurring in the ¢2=45°
section (extended to p > 90°). (b) is mechanical twinning (1)
and subsequent normal slip (2,3). (c) is mechanical
twinning (1),subsequent abnormal slip (2), shear band
formation (3) and normal slip (4). (The corresponding
orientation changes of the S orientation {123)<412> (1* to
4*) are projected into the o2 = 45° section.) (d) is
mechanical twinning (1) with subsequent abnormal slip (2),
overshooting the matrix orientation C by preferred coplanar
slip (3) and normal slip (4). Mechanical twinning increases

with increasing strain and decreasing stacking fault energy.

15

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16
1.1.4. Micro-Banding

Deformation of polycrystalline materials is usually
inhomogeneous, occurring by deformation banding as a common
phenomena. There are two kinds of deformation banding. Type
one results from the operation of a different allowable
combination of slip systems in each of several portions of
a grain. Most of deformation bands are formed in this way.
Type two is formed if the work done by slip within the
bands is less than that for homogeneous deformation and if
the bands can‘be arranged such that the net strain

practically matches that for the overall deformation[19].

The mechanism of formation of deformation band is that
edge dislocations in the primary slip system of opposite
signs accumulate in two parallel subgrain walls, so
rotating the inner part in the opposite direction with
respect to the matrix[22]. These kinds of bands are
geometrically necessary to compensate for incompatible
strain effects. Therefore, the parts of a grain finally
rotate into a different stable orientation to compensate
the incompatible strain in polycrystalline deformation. The
mechanism of deformation banding is the same as that of

kink band in tensile strain of single crystal.

The formation of microbands is also related to

dislocation glide on (111} slip plane. The locally

17

concentrated dislocation gliding and the dislocation
channeling on one active slip system cause the microbands,

[23]. After

orientations of which coincide with {111} planes
their formation, they are still affected by the normal slip
processes and are finally rotated parallel to the sheet
plane without producing further misorientations. The
microbands can be seen at low and medium strain. Because
the orientation difference between microbands and matrix is

)[23,24]

very small ( 2° , they would not notably change the

orientation distribution.

1.1.5. Shear—Banding

At low to moderate levels of strain (generally a < 1.0 )
and at normal strain rates, the materials deform by slip or
twinning which is related to the crystallography of the
component grains. At somewhat higher strain levels,
instabilities develop and shear bands form. Shear bands
cross grain boundaries without deviation and the planes in
the shear bands are related to the specimen geometry and
the deformation process rather than to the crystallography
of the deforming materialEzs]. Shear bands develop with a
non-crystallographic geometry when normal crystallogaphic
slip is strongly inhibited. The bundles of microbands in
medium SFE materials and packages of twin/matrix lamellae,

for example, can inhibit the normal crystallographic slip.

18

Depending on the size of the bands, shear bands are
classified into two kinds: grain-scale shear band
(microscopic-shear band) which extends through one or a few
grains and sample-scale shear band (macroscopic shear band)
which extends through the entire specimen[26]. The grain-
scale shear bands can develop only if there is a certain
freedom for the local strain to be heterogeneous. They are
inclined at angles of 23° and 37° to the rolling direction
preferentially. When grain-scale shear bands at these
angles encompass larger and larger regions, they are
organized into sample-scale shear bands and the inclined

[271.

angle of 45° The sample-scale shear bands play an

important role in the texture softening which offers new

slip orientations for further deformation[28].

Clifton and co-workers[29] proposed a thermoplastic
instability mechanism of shear band formation. They
suggested that non-uniform heating caused by non-uniform
straining and different heat generation caused by different
strain rate make deformation become more non-uniform, thus

the shear band may develop.

According to the microstructures of shear bands, two
kinds of shear bands, copper-type shear band and brass-type

[21]. There are small orientation

shear band, are defined
differences ( < 10°) between orientations inside the copper

type shear band and the surrounding matrix[30]. For

19

example, In the C and B grains, the reported shear band
angles of 20°, 35° and 30°( 5°) correspond almost exactly
to shear deformation of {111}<112>, {001}<110> and

[30]. So copper-type shear bands have little

{112}<110>
influence on rolling texture development. Also, the volume
fraction of the bands is too small to give rise to a
separate texture component. But copper-type shear bands can
explain the presence and reappearance of G orientation at
high deformation since the bands often contain G

[21]. During rotation of the twin/matrix

orientation
lamellae by preferred slip on the coplanar slip systems I
and I’ in Fig.7c, the Schmid factor p for the hindered
slip systems II and III and the force exerted by the
piled-up dislocations continue to increase. This results in
a highly unstable structure with strong geometrical
softening effects so that the brass-type shear bands with
extremely large shear strains ( a up to 10) become

[25]. The orientation changes due to the shear

possible
0 ‘ e . *
banding are indicated in Fig.1.8c as stages 3 and 4 or 3

*
and 4 .

1.2. Recrystallization Texture

There are two main mechanisms to explain the
development of primary recrystallization texture: the
oriented growth mechanism and the oriented nucleation

mechanism. The oriented growth mechanism assumes that the

20

nuclei are considered as parts of the deformed matrix but
nuclei of many orientations are available. Their growth
rate into the matrix depends on their orientation with
respect to the matrix and the texture is finally determined

[31.32]. The

by the grains with largest growth rates
oriented nucleation mechanism assumes that the
recrystallization textures are only determined by the
orientation of nuclei and the oriented growth does not play

any role at all[33U35].

1.2.1. Oriented Growth

The oriented growth theory is based on the strong
dependence of growth rate of recrystallization nucleus on
the orientation relationship between the deformed matrix
and the growing grain. So it is assumed in this theory that
the recrystallization texture is determined by nuclei
oriented in such a way that they grow particularly fast. In
this case, the ratio of a fast growth rate of specially
oriented grains to the growth rate of randomly oriented
grains should be larger than one. That is, this is a grain
boundary property not a grain property[36]. For fcc metals,
low interface energies occur at 0° and 60° rotations around
<111>; high energies occur at intermediate rotations[43’44].
Thus the maximum growth rate orientation is determined as

[37-41]

about 40° <111> rotation But this relationship is

not exactly obeyed for all materials of fcc. For example,

21

copper and silver show 30° <111> rotations and aluminum-
manganese alloys containing 0.5%Mn show 84° <112> rotations
due to the occurrence of annealing twins in these

[42]. For polycrystalline fcc materials,

metals
recrystallization occurs at an approximate 40° <111>
relationships between the components of recrystallization

texture and one or several components of rolling

texture[2].

Beck[3l’45’46] explained that the development of cube
orientation followed the oriented growth mechanism. The
formation of the cube texture in a rolled sheet is
available if the recrystallized grains at an early stage of
the annealing process reach a size at which they come into
effective contact with several (or all four) principal
orientations of the deformation texture (e.g.{124}<211>).
Since these grains of the cube texture orientation are
related to each of these four deformation texture
components by a <111> rotation suited to high boundary
mobility, they can grow faster than any grains with other
orientations, and can grow into all four of these
components. Some other orientations also have this
relationship: the R-orientation has such a relationship to
3 components of the rolling texture, G-orientation to all 4
components and the rotated cube orietation ({001}<110>) to

all 4 components[47].

22

At the higher annealing temperatures, grain growth,
because of its importance, will often dominate the texture
change. It is possible that different texture components
recrystallize at different temperatures, thus, an annealing
texture may be a mixture of several components, because
individual crystals may have wide differences of
recrystallization tendency after a given amount of

deformation[48U51].

Microbands or transition bands are also important in
this mechanism when the boundary of one of these microbands
migrates or when adjacent microbands coalesce in a way that
develops high angle and highly mobile boundaries. Crystals
that have a sharp, single orientation deformation texture
tend to recover rather than recrystallize, and therefore
retain their deformation texture at least until they are
consumed by differently oriented grains. A low annealing
temperature favors retention of the cold—rolled

texture[52].

The driving forces for grain boundary movement usually
come from the reduction of strain energy in the region
swept over by a boundary and a reduction of boundary energy
from a reduction in boundary area and from a reduction in

energy per unit area.

Grain growth theory has its shortcomings. It can only

partially explain the details of recrystallization

23

texture development. It can’t explain that grains in
orientations deviating from the maximum of the grain
boundary energy by about 150 still grow at relativaly high

rates[32], and that there are certain variants of the

growth relationships[53], and also that the scatter
orientations in slightly deformed single crystals are not

related to the matrix orientation in any simple manner[32].

1.2.2. Oriented Nucleation

In this theory, the nucleation process is the important
factor in determining the range of available nuclei which
can contribute to the recrystallization texture. There are

three mechanisms of formation of recrystallion nuclei.

The first one is that nuclei are considered as a part
of the deformed matrix and subgrain growth[53U56].
there are three sub-mechanisms which are proposed by
Dillamore and Katoh: (i) Nuclei are formed by subgrain
growth in the regions of uniform orientation, i.e., it
occurs when a subgrain grows until one side meets a pre-
existing grain boundary. Recrystallization will then occur
if the free length of grain boundary is long enough to bow
out under the driving force provided by the energy stored
on the other side of the boundary. This is formed within

the stable deformation components. (ii) Nuclei are formed

in the region of sharp lattice curvature, i.e., in

24

orientations where a strong divergence of orientation
occurs upon further deformation and which lie near the
edges of the deformation texture. The example of this
mechanism is transition band nucleation, which requires low
thermal activation but needs increasing thermal energy as
the boundary angle increases. (iii) Nuclei are formed at
grain boundaries by migration of existing high angle
interfaces. t can also occur at grain edges and grain
corners. Grain boundary nuclei usually have orientations
either in the main stable texture components or in the

principal range of spread about these components.

The second is that nuclei are considered as
recrystallization twins formed at the early stages of
recrystallization or even during deformation. It is
possible for low stacking fault energy fcc materials.

[57.58]

Investigation of Peters on Cu—Sn shows that texture

(326)[634] is‘oriented to the deformed matrix (Oll)[2l1] by

a 40°<111> rotation in this mechanism.

The third mechanism is that nuclei are formed by an
inverse Rowland-transformation of the deformed matrix[54]

or by this transformation followed by further twinning.

The <111> fiber texture in recrystallized rolled steel

sheet is predicted by oriented nucleation theory. Deformed

25

grains with <111> normal to the rolling plane are found to
have higher stored energy than other oriented grains. Thus
new grains with <111> orientations nucleate first during
annealing and grow into other <111> region by rotations

about the fiber axis.

1.2.3. Nucleation Sites

There are several sites available for nucleations, such
as grain interiors,grain boundaries, transition bands,
interfaces between second phase and matrix and twins. In
the following, the nucleations at these sites will be

discussed.

(a) Nucleation in Grain Interiors. It is commonly
observed at moderate and high deformations, since at low
strains the lattice curvature is seldom sufficient to allow
a high angle boundary to be created. The distribution of
stored energy depends on orientation in the deformed
materials. Within the major texture components of bcc
metals, the stored energy increases in the order

[59,60]. The

{011}<011>,{100)<011>,{211}<Oll>,{lll}<uvw>
sequence of increasing stored energy corresponds to that of
increasing Taylor M value or corressponds to the total

amount of dislocation motion that has taken place. The ease

of nucleation within grains would be correspondingly

orientation sensitive. Fig.1.9 schematically shows this

26

 

I [ml
E
< 112
‘1‘ l I [100]
Z
2
2
E
g [110] [hm]
z ~~~~~~
I U“-

 

 

~
~—
—_

 

ANNEALING TIME -——>

Fig.1.9 Schematic representation of nucleation sequence of
recrystallized grains during annealing of cold
rooled steel.

relationship based on the stored energy consideration[6l].

so the final texture should be dominated by nuclei which
form soonest and which are most numerous. During the
annealing, the {011} and {111} texture components should
nucleate first and therefore have the longest available
time for growth before impingement occurs. The least
favoured orientation (100} is predicted to disappear on
annealing due to its consumption by the growth of other
grains, like (110} and {111} grains, which is shown in
Fig.1.10. The {111} oriented grains have the best
orientation with matrix to grow and therefore increase the
{111) texture component[62]. A fine initial grain size
increases the orientation sensitivity and therefore the
{111) texture component by increasing the homogeneity of

strain during rolling and so maximizing the stored energy

27

 

   
  
   
   

 

 

 

 

 

 

 

 

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10 ~ ~—»————. -
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fimn :
game;
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LLJ
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As-roUed 500 600 700 10hrs 20in:

TEMPERAlURE,°C TIME ,h
HEATING CYCLE

Fig.1.10 Variation of some important texture components
during typical box-annealing cycle.

differences between orientations.

(b) Nucleation at Grain Boundaries. This occurs in two
ways: One is by the existing boundary bowing out into the
grain which has the higher stored energy at the boundary.

The other is by growth of a subgrain close to that grain

28

boundary. In both cases, the orientation of nucleation is
close to the orientation of matrix near the boundaries in
which they form. Orientations near the grain boundaries
often rotate away from the grain center, so the nucleation
at grain boundaries introduces recrystallization texture
components that have orientations close to, but not at, the

[63]. The proportion of

deformation texture components
nucleations at grain boundaries is much higher than that

for intra-granular nucleations.

(c) Nucleation at Transition Bands (Microbands).
Transition bands are composed of closely spaced sub-
boundaries which manifest cumulative misorientations.
Nucleation at transition bands is possible because of their
high stored energy and rapid change of orientation which
allows a high angle boundary to be easily formed[64'65].
Because the orientations of the new grains may differ
widely from those of deformation texture, notable changes
in orientation may occur during annealing. But it is
important in development of recrystallization textures only
when the subsequent growth rates of new grains are
relatively high, since the number of transition band sites
which are much favoured is quite small compared to intra-
granular or grain boundary sites. Thus a small number of
nuclei must grow into a very large volume. The most
favoured orientations for nucleations at transition bands

for bcc metals are in order of {110}<001>, {100}<011> and

29

{11,11,8)<4,4,11>(near {111}<112>). But different
transition bands will be most favoured for nucleation after
different strains and they may cease to be viable after

[65]

heavy deformation The cube orientation{100)<001> of

fcc metals is also predicted to arise by this

[35]. The operation of different combinations of

mechanism
slip systems in different regions within one grain may give
rise to different crystal rotations. In general, at low or
moderate strains, almost any orientations of transition
bands may occur, but at high strains, the separate blocks
or deformation bands converge on a common final
orientation. So nucleations at transition bands may
contribute to the weak or nearly random recrystallization

6]

textures after low defrmation[6 .

(d) Influence of Particles. Influences of particles on
recrystallization depend on the size and distribution of
the particles. In general, widely spaced coarse particles
enhance nucleation and the rate of recrystallization if

[67], while finely

particles are present before deformation
dispersed particles normally reduce recrystallization
kinetics, having a greater retarding influence on
nucleation than on growth[68]. The change in texture is
usually accompanied by an increase of the as-recrystallized

[68]. The texture changes in the metal which has

grain size
finely dispersed particles can be rationalized on the basis

of the oriented nucleation mechanism. If nucleation of all

30

orientation components is retarded in equal proportions,
then the time available for growth of the first formed
grains is increased. The recrystallization texture will
therefore show increased selectivity and will become even
more strongly biased towards the most favoured orientation
nuclei. In the case of steel, the precipitates of AlN, NbC
and Cu lead to considerable strengthening of the {111}
texture components at the expense of those components near
{100}[69’70].Finely dispersed particles may also interact
with certain types of nucleation sites. In steel, AlN may
be effective in strengthening (111} textures and act to
suppress the {110) sheet-plane textures, particularly the
Goss component {110)<001>. This indicates that nucleation
within transition bands may be especially susceptible to
interference by finely dispersed particles. Precipitation
of A13Fe in pre-existing grain boundaries inhibits growth
of the early formed cube nuclei thereby forcing nucleation
in the abundant rolling texture components. Hornbogen et
al[7lU73] reported for aluminium-copper alloys and copper-
based and nickel based alloys that discontinuous
(conventional) recrystallization gives rise to normal
recrystallization textures, such as the cube textures,
while continuous (or in situ) recrystallization causes

retention of the rolling texture.

In addition to the oriented nucleation and oriented

growth, the formation of annealing twins play an essential

31

role for recrystallization texture formation because only
this mechanism creates all new orientations relative to the
deformed structure. In general, twins occur in materials
with low stacking fault energy. In this paper, we will not

discuss it further.

1.2.4. {100}<001> Cube Texture

As an example of recrystallization texture, cube
texture {100}<001> is often found in recrystallized fcc
metals and alloys. cube textures are more often formed
under the condition of heavy deformation and a fine
starting grain size, and may also be considerably
strenthened during grain growth after the completion of

primary recrystallization.

The cube texture arises because it has favoured
orientation relationship to the deformed structure for the
rapid growth of recrystallized grains. The orientations of
the most mobile grain boundaries are the misorientations of

[74’75]. On the basis

30°-40° around a common <111> pole
that rolling texture, which gives rise to the cube
component, is near {123}<412>, it is possible to explain
the origin of this component in terms of oriented growth
theory, since only {100}<001> bears the necessary

orientation relationship with all four equivalent

(123}<412> components. In the aluminum alloys and copper

32

with an initial coarse grain size, the cube texture co-
exists with a retained rolling texture, which is near
{123}<412>. This orientation is possibly consumed by

[76]. When enlarged subgrains or small

growing cube grains
recrystallized grains are present in the unannealed

deformed structure of 95% deformed copper, these are almost
invariantly of the cube orientation. These cube grains are
found to grow rapidly at low annealing temperatures before

any other recrystallized grains appear[77].

1.3. Grain Growth

It is very important to mention that grain growth plays
an important role in texture development after completion
of primary recrystallization. Upon completion of primary
recrystallization, there is usually a rather diffuse spread
of orientations together with the recrystallization texture
components, which are often not very strong. During grain
growth, these components are strengthened at the expense of
the diffuse spread of orientations, and sometimes there is
a redistribution of density between different components.
This type of texture sharpening is known for the cube
texture in aluminum, copper and nickel[78], while the Goss
component and the {111} sheet plane orientations are
enhanced in steel. During grain growth, large grains grow

[79,80]

at the expense of small ones If the grain size

distribution for grains of a particular texture component

33

is biased to larger size than the average distribution,
then these grains will prosper during the grain growth and
their texture will be correspondingly strengthened. If
there are sufficient number of second phase particles, they
may provide a constant reaction to the migration of grain
boundaries, and may cause transition from normal to
abnormal grain growth, and amplify the texture changes
occuring during grain growth[801. A limiting case is
secondary recrystallization, where a very small fraction of

grains grow intensively and thus very sharp textures may be

created.

34
1.4. Superplasticity

1.4.1. Concept of Superplasticity

Superplasticity is defined as the ability of a material
to undergo unusually extensive plastic deformation at high
temperature. There are two necessary prerequisites for
superplasticity: one is a deformation temperature greater
than half the absolute melting temperature, so that
diffusional processes occur rapidly, and the other is a
small stable equiaxed grain size, usually less than 10 pm.
The characteristic microstructure feature of superplastic
deformation is the retention of equiaxed grain structure

throughout deformation.

In broad outline, superplasticity may be divided into
two parts, i.e., structural superplasticity and
environmental superplasticity. For structural
superplasticity, a characteristic structural condition,
e.g., a stable ultra-fine grain size, is required and the
strain rate sensitivity m (= aloga / alogé ) is the order
of 0.3 to 0.8. In environmental superplasticity, the
special testing conditions are necessary, e.g., temperature
cycling under a small applied stress and the value of m is
equal to about one. In both parts of superplasticity, the
applied stress for superplastic deformation is markedly

dependent on the strain rate. this dependence is generally

35

evaluated in terms of the strain rate sensitivity index m

in the relationship[82]

a = Ké (1.3)

where a is the applied stress, E is the strain rate and K
is a constant for given testing conditions, m and K are
both dependent on test parameters such as temperature and
grain size. For Newtonian-viscous materials, m is equal to
one and the elongation in tension is uniform and
independent of irregularities in cross section. For
superplastic materials, m is usually in the range of 0.3 to
0.85 because resistance to necking can be predicted from

continuum mechanics for m greater than about 0.3.

\
At the temperature below 0.4 Tm (Tm is melting point of
material), the material being deformed obeys a true stress-

true strain law of the type[83]

a = Cc (1.4)

where C is the strength coefficient and n is the strain
hardening exponent. The true strain at which plastic

instability (necking) occurs can be shown aS‘

‘neckingU n (1'5)

and n usually lies within the range of 0.1 to 0.3.

36

At high temperature, the rate of strain hardening
decreases and extensive plastic deformation occurs without
necking which is due to an enhanced strain rate

[84.85]

sensitivity . So when both strain-hardening and

strain-rate effects need to be considered, the following

flow stress law is assumed to be obeyed[86U88],

n.m (1.6)

where K’ is a constant embracing C and K. If the condition
of n/(e+m) > 1 is satisfied, the deformation is stable.
This criterion is in agreement with those for strain
hardening materials and for viscous materials which are

resistant to necking for m=1[89].

Environmental superplasticity usually occurs under well

defined environmental conditions[90U93]

, such as (a) during
temperature cycling through a phase change, (b) during
temperature cycling of a thermally anisotropic material,
and (c) during neutron irradiation. Thus this phenomenon is
generally observed when a small stress is applied in
conjunction with the above conditions. Because the
environmental superplastic behavior is observed only in

very small number of materials, it is not discussed further

here.

37
1.4.2. Mechanical Behavior of Structural Superplasticity

Most superplastic materials exhibit a sigmoidal

relationship between the logarithms of stress and strain

[94]

rate (see Fig.1.11) . The region of maximum strain rate

 

'0’" U U M -<

 

I II in
'0 "' -(
i
\ (a)
z I
2
in
m 0.8 ~ 4
w
a: . i
p.
(n U 4
0.5 r d
r- a
l-
0.2 ~
r-

“) / \\'_L_ U

L 1 A 1
I0'5 IO“ :03 10'2 IO" |O° lo‘
STRAIN RATE min"

 

 

 

 

 

Fig.1.11 The strain rate dependence of (a) the flow stress
and the strain rate sensitivity for the Mg-Al alloy,
grain size 10.6 pm deformed at 350 C

sensitivity (region II) with slope m>0.3 delineates the

strain rate range over which the superplasticity occurs.

Both the low and high regions of strain rate (region I and

III) exhibit values of m<0.3 and correspond to

conventional plasticity. However, it must be emphasized

that the sigmoidal shape is by no means universal. Some

authers reported that they could find no evidence of

38

sigmoidal shape in the lower strain rate range(region I) of

[95-98]

the logo vs. logé curve . The sigmoidal

shape in superplastic deformation is often thought to

[99-104].

result from a threshold stress But several

authors reported that they could not find evidence for a
threshold stress in superplastic deformation[95’105’106].
The possible mechanism of formation of threshold stress

will be discussed in a later section.

In general, the resistance to neck formation during
superplastic deformation is ascribed to a high value of
m[86’107]. For large values of m , the strain rate of
materials near a neck and that in the rest of the specimen
are nearly equal. This minimizes the tendency for localized
necking and premature failure and therefore leads to large
overall total elongation. In this case, theoretically
stable flow is possible provided m>1/2 for constant
velocity testing and m>1/3 for constant strain rate
testing. So for creep deformation, the stress dependence of

e e n o 0
strain rate in £=A ,where n is inverse of m , should

not exceed 2 or 3 for stable flow to occur.

The strain rate sensitivity m increases with a decrease
in grain size in regions II and I, and the transition
between regions II and III is shifted to higher strain

2 [108]. The strain rate

rates. This is shown in Fig.1.1
corresponding to a given flow stress and temperature has

been shown to vary with grain size L as

39

 

 

 

 

1: 1 T i T I l i fl
L‘5.5 [523p _
L'IGF L‘LZp

>_ .6 r _
’—
S
E
U)

5.4 - ~
U)
Lu
2
O:

.2 5 1

l

1 1

O 1 1 1 l 1 . ‘- - - I 1 1 11

10'5 m4 10'3 m4 04

STRAIN RATE (Mw')

Fig.1.12 Strain rate sensitivity versus strain rate for
Sn-5%Bi samples of varying Sn grain size

 

 

 

 

 

0'7 Fllllilfl U IIIIUII T TTTHIII 1 ITIHH] l I IIIIII
SZO‘C

06»- ..

OS» 1
480%:

1141— ._

nu

«I40‘C

031- _.

02,_ 360°C _‘

Oi r- __

0 ' 1 1 111111 1 1 1 11111i 1, 1 1 11111i 1, 1 1.11111i 11111 5' 1111

‘7" 1°“ 10" 10‘2 10" I

é,sec"

Fig.1.13 The dependence of strain rate sensitivity index on
strain rate at different temperatures for aluminium-
copper eutectic specimens

40

E a ——— (1.7)

where the exponent a generally lies within 2 and 3[108U

113]. The dependence of flow stress on grain size at
constant strain rate and temperature follows the relation

of

a a L (1.8)

where b lies in the range 0.7 to 1.2[110’112’114U116].

The temperature effects on superplastic deformation are
shown in Fig.1.13[112], which shows that m increases with
increasing temperature. Increasing deformation temperature
reduces the overall level of the flow stress and displaces
the transitions between regions I and II and between
regions II and III to higher strain rates (see Fig.1.14).
There are two categories for activation energies of

deformation in region II: one is activation energies

[106,117]

similar to those for grain boundary diffusion and

the other is activation energies comparable to those for

[118]

lattice diffusion . The activation energies for region

III usually correspond to those for dislocation

[96,105,117,119,120]

creep . There are also two categories in

region I: activation energy in this region is equal to that

[105’117] and activation energy equals

196].

for volume diffusion

that for grain boundary diffusion The relationship

41

between strain rate ( é ) and activation energy (Q) is

expressed as

UaL a eXp(-Q/kT) (1.9)

where k is Boltzmanns constant. It is therefore apparent
that diffusional processes are of considerable importance
in superplastic deformation. And this point of View is
further reinforced by Morrison’s observation that alloying
elements which increased atomic mobility also enhanced
superplastic behavior[121]. The effects discussed above on
strain rate may, therefore, be combined into one relation
equation as

I1
0'

 

5 = A exp(-Q/kT) (1.10)

La
where A=constant, n=1/m.

1.4.3 Microstructural Behavior of Superplasticity

It has been shown that the grain structure remains
essentially equiaxed with little growth during deformation
under optimal conditions. Fig.1.14 shows that the Sn—5% Bi
alloy has an equiaxed shape even after 1000%

[122]. Fig.1.14a is cross section and Fig.1.14b

elongation
a longitudinal section. Grain deformation usually occurs

near the grain boundaries and grain boundaries become

42

L c ’3‘ U vi .%~
. _ I 14;) 'f'yi-i;

 

Fig.1.14 Microstructures of Sn-5%Bi alloy strained 1000% at
room temperature. (a) Cross section.
(b) Longitudinal section, tensile axis vertical.

43

curved after deformation. But grain shape still remains
equiaxed and grains do not elongate in the direction of

tensile axis during superplastic deformation.

Grain boundary sliding (GBS) is commonly observed
during superplastic deformation. Two initially adjacent
grains may end up many grain diameters apart. (see
Fig.1.15). The relative motion of two initially adjacent
grains depends on the resolved shear stress across the
grain boundary and grains with transverse or longitudinal
boundaries generally moving apart less rapidly than other

oriented grains during superplastic flow. Fig.1.16 shows a

GBS dependence of the angle between the axis of the applied

stress and the orientation of sliding boundary. The sliding

mainly occurs at the transverse boundaries in region I but

in regions II and III the main sliding is at the boundary

which lies at 45° to the applied stress axis. GBS occurs at

the onset of plastic flow. Small apparent gaps develop
between surface grains at low strains due to sliding. After
some amount of strain, new grains begin to emerge to the
surface from the interior to fill the gaps. This process
continues throughout the strain range. Most surface grains
present at large strains are initially located in the
specimen interior. The contribution of GBS is a maximum in
region II and decreases at higher (region III) and lower

(region I) strain rates, which can be seen in Table 1.1.

44

.wom :3 :13 E .wmm 3: Jam 23 oosnfioo
.omee mloaxm Eoooo> :fl :flE oaxn.wn w an :flmuum mcflmomuocfi
cues :wEflommm cfl wmumHMEmm mm mucouoommm womwusm :fl neoconu mH.H.mflm

...—canto; min :23:

 

45

 

 

 

30

25

20

15

x 10‘2 (pm)

10

Vettical Component of the Grain Boundary Sliding

 

 

 

 

 

 

 

 

 

 

 

<= €=6% :%
.L._5’=_.. -
33110-3

0 = p—T ‘

W‘-—- —." __ . :
1.5m“ *-- T-

41110’

t;
7‘ -

 

 

 

 

 

0° 45° 90°

0° 45° 90°

0° 45° 90°

Fig.1.16 The value of the vertical component of the grain
boundary sliding versus boupdary angle with the

tensile axis__.3 (a)_ '=l.6x10
é=8.3x10

(10)

SEC

(region III).

SEC

(region II),

(region I),_
é=4.1x10

(C)

SEC

Individual grain rotations are often observed during

superplastic flow. In Fig.1.17, it is apparent that the

internal marker lines are tilted with superplastic strain.

The amount of grain rotation during superplastic

deformation as a function of strain rate and strain are

shown in Fig.1.18 and Fig.1.19 respectively[

rotations higher than 35° are only at the lowest strain

123]

The

rate ( éA) and the intermediate degree of rotation of 5 to

25° are greatest at the intermediate strain rate ( EB)

-1

46

 

 

 

om om 0m pwouomusm H<ICN
mm we we H<wa.oucm
om om Hm capomuom :mnnm
Mm om Hanna
om meuav mm owm.ouczwm.aumz
mm v0 NH owuomusm aswmmlmz
om ms: om m<z
om ow: om onHucNWHHuH<
mm no we onanNwmua<
on: ofluompzm sowmmuaa

oe on: om woaam ooze

HHH scammm HH coflomm H coflmmm

Awe vinoU Hmflumumz

 

:wmuum Hawxm Hmuou mnu

HHH can HH .H msovaH ca Auu\nmwv

o» msfioflam humcsson Swahm mo cowufinfiuusoo H.H manna

47

 

Tension axis horizontal

Fig.1.17 Appearence of internal marker _13ine tfanslations in
specimens deformed at é=6.7x10 min . Deformed
(a) 30%, (b) 60%, (c) 100%, (d) 200%.

Fig.1.18 Relative frequency of rotation of internal marker
lines to stressBaxislin specimens deformfd

Fig.1.19

48

 

 

 

80 T 1 fiw fit I I T I T 1 i i I
(a) (b) "' (c)
$ W
>3 60- -<
U
2
‘5‘
o W
U.)
E 40" L—-——. ’1
DJ
2
’—
3
LU2o— a
m
1 J i

 

 

 

 

 

 

 

O 515253545515253545515253545

ROTATION ANGLE TO STRESS AXIS, dogmas

(a) At é =2x10 min 41(b) at éB=6.7x10 min

(c) at éc=l.1x10 min

 

 

 

 

 

 

 

1 i I I i 1 i 1 1
(a) (b)
4
>360...
U
z 1
m
=» 1
8
40 ~—
0: ”—1
L
w
>
z
320—
LU
cr
1 1 1 l

 

 

 

L

 

 

 

O 515253545515253545515253545515253545

ROTATION ANGLE TO STRESS AXIS, degrees

Relative frequency of rotation of internal marker
lines to stresslaxis in specimens deformed at

é =6.7x10' min” . Deformed (a) 30%,

(E) 100%, (d) 200%.

 

 

(b) 60%,

49

compared to the other two strain rates. As the strain
increases from 30 to 200, more grains rotate to

larger degrees since the greater degrees of grain rotations
are required to accommodate the increased amount of grain
boundary sliding during superplastic deformation. Whereas
the amount of rotation varies from grain to grain and the
rotation of a grain usually changes sign during
superplastic flow. Therefore the sense of rotation for any
one grain depends on its instentaneous

surroundings[104’125].

It is also found that grain boundaries become thicker
after larger strain when the grain size is noticeably
larger (see Fig.1.17) because of the grain rotation and

deformation in the grain mantle[123].

Whether or not the dislocation activity occurs during
superplastic deformation still is open to debate. Several

[107’127_129] reported that no dislocation activity

authors
accompanied the superplastic deformation in their
investigations. But evidence of dislocation

activity during superplastic deformation has been found
recently. Fig.1.20 shows dislocation density changes with
superplastic deformation in regions I to III. A large
number of dislocations in grain interior are active during
deformation in region III, and dislocation density

increases with increasing strain. In region II dislocation

has the same trend as that in region III but the

50

 

 

 

 

, O
A ram“
0 region NH 0
I region II
0 region III
'E 15 *-
3
3, II
'2
‘O I
S
'5 10*-
0
.§
23 o
51- I
///l v I
V-b A
O l l 1 l l l

 

 

 

0 10 20 30 340 so 60
Strain (°/o)

Fig.1.20 Densities of dislocations in twin boundaries as a
function of strain for regions I-III.

dislocation density decreases notably.In region III, a high

dislocation density was produced by deformation but there

were no regular cell structures. Only low angle boundaries

and dislocation tangles were observed. In region II,

dislocations were found in the grains

51

containing precipitates, but many grain free from
precipitates were without dislocations. Dislocation
activity was also found in region I. The Burger’s vector
distribution was similar at all but the lowest strain rate.
This might indicate that at low strain rate the
dislocations only accommodate the GBS, but at higher strain
rate the dislocations contribute to both GBS and A

intragranular slip.

1.4.4. Mechanisms of Superplastic Deformation

It is a common agreement that GBS plays a major role in
superplastic deformation. In order to maintain a
compatibility across grain boundaries, extensive
accommodations such as diffusion, grain rotation and

dislocation motion are required.

(a) GBS with Diffusion Accommodation

Ashby and Verralltgg]

proposed a mechanism in which
grains switch their neighbours and do not elongate
significantly as illustrated in Fig.1.21. The four

grains in the initial position, Fig.1.21a, move by

GBS along the inclined boundaries to an intermediate saddle
position, Fig.1.21b, and further grains move to the final
position, Fig.1.21c, by GBS and diffusion accommodation as

well as grain boundary migration. In Fig.1.21b, the shapes

of grains are changed by diffusion in the region in order

52

oniAmV mmmooum cofiumfiuoumo on» no Qmpm Has: one Hm.a.mwm

Sim :2: A:

Efiw :SBzmfiE 2:

WES .323 on

» a a S a a M
szg mo
222.5723
w>2<dm \

 
        

  

3
\Lizwujmma/
lei uz__o_._m 0i

53

to avoid formation of voids. The total true strain in this
process is 0.55 (73%). The grain switching event gives rise
to a threshold stress because significant energy is
required to change grain boundary area during the process
in Fig.1.21b. In detail, four irreversible processes are
involved in this mechanism: (i) Diffusional process, which

is schematically shown in Fig.1.22: The diffusional process

GRAIN 1

 

 

     
 

+ jg.»
DIFFUSIVE FLUX ”("21" BOUNDARY
. / DIFFUSIVE FLUX

.TENSILE i AXIS

Fig.1.22 The accommodation strains required when grains move
from the initial to the intermediate states.

may occur by bulk diffusion through the grains or by

diffusion via the grain boundaries. The diffusional path in

Fig.1.22 is short compared with those involved in normal

diffusion creep and it is for this reason that the strain

rate derived by this theory is faster than that for

54

diffusion creep. (ii) Grain boundary reaction: Grain
boundaries may be imperfect sinks or sources for point
defects, and therefore grain boundaries may be barriers for
vacancies to be removed from or added to the grain
boundaries. (iii) Grain boundary sliding: The shear
displacements occur in the grain boundary plane and these
displacements allow the grains to shift their position
relative to each other. (iv) Fluctuations of grain boundary
area: Grain boundary area increases as the grains move from
their initial state to their intermediate state, which
increases the free energy in the system. As the grains move
from the intermediate state to the final state, the grain
boundary area decreases again, which releases free energy
from the system. This process requires that the external
stress does enough work to cover the energy increment to
permit the superplastic flow to take place, the result of
which is a small threshold stress below which the

superplastic flow is impossible.

In summary, GBS with diffusion accommodation usually
accounts for almost all the strain rate in region I and
some part of strain rate in region II. According to this
mechanism, grains do not elongate much; the translations
and rotations of the grains should destroy any texture;
since dislocation motion is not involved, dislocation cells
or tangles do not exist; and the deformation occurs in the

way of non-uniform flow (see Fig.1.23).

55

 

 

3 SC I X/ i \ \
/ \7\ I/ / _
///. (I, \ N’/‘\\* \ K I
\1\ I) // // :\ \\ \
I I I\ ( j
\ ‘ // fr \ / \
\«H’ \ (// \
2 " l / h { ‘—I 1 (J 4
///’:\\\ f \\
J f: d K 1/ ‘ '\ \\\
\f ‘ / f \
L\ f ‘\ \ ,/ \ \
\ ‘K 'f‘ A
/ f /r -\
////O\/ [J // ~ \‘k
a Iv\ I
\ \1< Y I! / r (\\( Q KK’
* %\L\ I/ ,' \\’/
q \-""/ (., r ‘r
I 1' Y’ " r/ A

 

 

TENSILE I AXIS

Fig.1.23 The trajectories of grain centers in the emulsion,
where a switching event has occured.

(b) GBS with Dislocation Motion Accommodation

(i) Accommodation by grain boudary dislocation
movement. In this mechanism, grain boundary sliding occurs
either by grain boundary dislocation glide if the

dislocations dissociate so that some of the partial

56

dislocations have Burger’s vectors lying parallel to the
grain boundary surface or alternatively by dislocation
climb and glide movements if the dislocations retain their
original Burger’s vectors and remain undissociated. The
components of their Burger’s vectors parallel to the grain
boundary will then contribute to shear parallel to the
boundary. Thus grain boundary dislocation movement results
in GBS and dislocation pile up at the triple point,(see

Fig.1.24).

 

F—l

 

   
 

iCrystal
Dislocation

 

 

 

Fig.1.24 GBS and its accommodation to give deformation in
region II of superplasticity.

57

Accommodation at the triple edge is allowed by creating new
dislocation under the stress concentration followed by
their gliding and climb in the mantle among the adjacent
grain boundaries and eventually annihilating or recombining
to form new grain boundary dislocations. This mechanism can
explain the absence of grain elongation and dislocation

cell structure after superpladtic deformation.

(ii) Accommodation by intragranular dislocation
movement. When the sliding of groups of grains is blocked
by an unfavorably oriented grain, the resultant stress
concentration is released by dislocation motion in the

blocking grain (see Fig.1.25). The moving dislocation

 
 
    

PLANE or
swim.‘
BOUNDAR\\
SLIDING ‘~

\

   
  
  

PILE UP

BLOCKING
GRAN!

\

PH.E UP

Fig.1.25 Slip accommodation of grain boundary sliding.

58

glides across the grain and pile up at the opposite grain
boundary. The back stress from this dislocation pile up
will stop the dislocation source and therefore the GBS. The
continuation of GBS requires that the leading dislocation

[111]. In the

climbs into or along the grain boundary
individual grain sliding, the dislocations are generated by
ledges and protrusions at the grain boundaries (Fig.1.26).

The dislocations traverse the grain and

 

 

SLIDING
——"’ DIRECTION
fl
.,
.,
I,
.,
” LEDGE
J7

 

   

PH.E UP

 

Fig.1.26 Slip accommodation from grain boundary ledges.

59

pile up at grain boundaries. Therefore, the rate of GBS is
controlled by the climb rate of the leading dislocation
towards annihilation sites which are located at grain

boundaries.

The dislocation motion mechanisms can also account for
the higher part of strain rate in region I and the lower
part of strain rate in region II. The texture may destroyed

by this mechanism.
(c) Dislocation Slip.

This is a mechanism in common with deformation, which
is discussed above, and is appliable to the high strain
rate region. According to this mechanism, grains elongate
and do not change neighbors; dislocations move through the
grains and accumulate as cells or tangles; the texture may

be created by the deformation.

1.5. Relationship Between Texture and Superplastic

Deformation
1.5.1. Texture Effects on Superplasticity

Anisotropic behaviour in superplastic deformation
has been reported in many materials[136’l44-146]. This
indicates that preferred crystallographic orientations

affect the superplastic deformation behaviours. Fig.1.27

shows this anisotropic behaviour of Zn-O.4%Al alloy in

60

Q
00

SENSITIVITY (m)

STRAIN“ RATE

 

 

O- l 1 ‘ ‘
I0‘3 0* D“ D
STRAIN-RATE ImInr'I IéI

 

Fig.1.27 Variation of m with strain rate and with direction
of straining.
sheet form at angles of O°,45° and 90° to the rolling
direction. The strain rate sensitivity (m) increases with
increasing the angle to the rolling direction for Zn-O.4%Al
alloy. Fig.1.28 shows elongations at fracture as a function
of angle of the tensile axis to the rolling direction for
aluminum-bronze sheet tested at 800°C. It also indicates

that elongation increases with the angle of tensile axis to

the rolling direction.

61

 

 

 

 

 

600 _ 7.8“0-2 min-l . _
500 —- -2 - _
‘ :13XK) minI
2:
Q
'2: 400— ....
S
C)
_I
In
0 300 — a
F. . I I.6rrIin’l ’-
200 — __
IOO — S
O I I I
0 45° 90°

ANGLE OF TENSILE AXIS TO ROLLING DIRECTION

Fig.1.28 Elongation at fracture as a function of angle of the
tensile axis to the rolling direction at three
strain rates for alumimun-bronze sheet tested at
800°C

62

It was reported that the formation of a strong
crystallographic texture in Zn-22%Al alloy on prior rolling
enhenced elongation several times compared to the
textureless as-quenched alloy with the similar grain
size[134]. The influence of this initial texture on the
elongation increases with increasing strain rate. In
Fig.1.29 for as-quenched staes 1 and 2, the
difference in elongation increases from 150% at

4 l to 450% at é=2.8x10-lS-l, and for the as-

é=2.5x10’ 5’
rolled states 3 and 4, the difference in elongation
increases with strain rate even more, that is, at high
strain rate, this difference in elongation reaches 800%.
The pre-existing texture causes a decrease in the flow
stress of superplastic deformation, and this initial
defference in flow stress between the texture and
textureless material is retained up to a very high degree
of strain (see Fig.1.30). The initial texture also shifts

the optimum strain rate region to higher strain rate (see

Fig.1.31).

The texture effects on superplasticity increase
with a decrease in temperature. In the as-quenched alloy at
250° and .J:=2.8x10-48-1 in state 2, the elongation is 1.3
times higher and flow stress 1.25 times lower than those in
state 1, but at 150°C this difference is 2.1 and 1.5 times

respectively. Texture effects on an optimum strain rate are

much greater at 150°C than those at 250°C. The difference

63

2000 _

 

I500 *— ~

IOOO *— ' ._
/O
I

0/0
.

 

 

 

Fig.1.29 Elongation as a function of strain rate

 

 

l5 — I

2

5% 4
I0 ~—

6

3

5J—
I I I
o 50 I00 ISO

6, 0/0

Fig.1.30 True stresffitfue strain curves on extention with
é =2.8x10 s at 250 C for different states of the

afloy.

64

 

 

 

 

 

 

 

(b)
05’—
m
OAr— “
03 ~ ‘
l
.111" I l 1____S
10“ IO"3 IO’2 IO"
6, 5'I
(a)
ITI
OZL—

 

 

Ifiig.1.31 Strain rate sensitivity as a function of strain
rate. (a) At 250°C, (b) at 150°C.
1. quenching, rolling at 250°C, annealing at 350°C
for 5h, water quenching. 2. Quenching,96.6% rolling
at 20°C, annealing at 350°C for 5h, quenching.

3. Quenching, 96.6% rolling at 20°. 4. Quenching,
rolling to 96.6% at 250°

65

in optimum strain rates between states 1 and 2 at 250°C
makes 2-3 times whereas at 150°C it is 15 times. Texture
can extend the temperature range of superplastic

deformation into the lower temperture region.

It was proposed[134] that the effects of texture on the
superplastic flow could be connected mainly with the
dependence of grain boundary structure on the texture.

On the condition that the grain shape and size are the same,
the texture causes a change in grain misorientation and
different grain boundary structure and therefore the

defferent superplastic behaviors.

1.5.2. Superplastic Deformation Effects on Texture

Superplastic deformation has two principal effects on
the texture. First, there is a reduction in the overall
texture due to GBS and grain rotation. Second, in addition
to the overall texture reduction, some texture components
are stabilized and new ones are created, indicating
intergranular slip and dynamic recrystallization

OCCUI’I‘EDCE .

(1) Grain boundary sliding: GBS would,as discussed
loefbre, be expected to rotate the grains randomly,
tflnerefore, GBS results in the overall reduction in texture

druring superplastic deformation[138-l4o’l47].

66

[124,136,139,148-151]: Superplastic

(ii) Slip
deformation is one of the few polycrystalline deformation
modes in which diffusive flow may relax the need for five
independent slip systems to be operative and single slip
can be expected. The occurrence of single slip during
superplastic deformation manifests itself in the
stabilisation or build-up of material in <121> orientation
(for fcc crystal). During superplastic deformation, the
diffusional accommodation allows a grain to act as a
isolated single crystal in uniaxial tension and to rotate
until the second slip system activated stabilises the crystal
at <121>. Such orientations are stable in the sense that
any rotation away from them occasioned by GBS leads to a
counteracting slip rotation back towards <121>. Furthermore,
<121> orientations have a relatively high Schmid
factor(0.4l), so single slip is to be expected in grains at
or near these orientations. But it should be noticed that
the single slip which builds up <121> orientations is in
response to the imposed stress system and contributes some
part of the overall strain. If single slip, which results
from the internal stress concentrations caused by GBS,
coccurs as an accommodation mechanism, this slip will not be
:in directions related to the tensile axis and so will not

contribute to this texture component.

At higher strain rates (region III), multiple slip on

{1J113<110> systems in the fcc crystal occurs by forming a

67

strong <111> fiber texture. This is predicted to be the
stable end orientation under conditions of multiple slip on
(111)<110> systems in polycrystals, as five of the six
possible systems are required to provide the shape change
and thus the operation of the sixth allows only a rotation

about the tensile axis.

Therefore, it is concluded that (l) the number of
operating slip systems increases with increasing strain
rate, (2) the relative contributions of individual systems
change with strain rate, and (3) even when no shift in the
positions of the texture peaks is seen, it is due to slip
in two systems which rotate the grain by equal but opposite

amounts.

(iii) Dynamic recrystallization: Dynamic
recrystallization is of the type produced by short time
static annealing, which was discussed in previous section.

Here we are net going to discuss it further.

1.6. Representation of An Orientation

The crystallite orientation is defined as the
rotation (g) which transforms the sample coordinate system
KA(XYZ)into that of the crystallite KB(X’Y’Z'), (see
Fig.1.32). The orientation g may be characterized in many

different ways. In the following sections, we are going to

68

 

 

 

 

Fig.1.32 The sample fixed coordinate system K and the

crystal fixed coordinate system KB in the sheet.

discuss some of these representations.

1.6.1. Introduction to Rotation System
(a) Euler Angles.

Two kinds of variants, Bunge’s and Roe’s variants, are
usually used to represent the orientation g in Euler angle
space. In the Bunge’s rotation, the definition of Euler
angles is shown in Fig.1.33. At the begining of the
rotation, the axes of the crystal coordinate system
coincide with those of the sample coordinate system. The
crystal coordinate system is then first rotated about the
Z’-axis through the angle ¢1(gz’), then about the X’-axis
(in its new orientation) through ¢(gx'), and finally, once
again about the Z’-axis (in its new orientation) through
the angle ¢2(gzl). Thus the rotation g is represented in

the Bunge’s rotation system by

69

 

 

/
I

 

 

 

 

 

 

X

 

 

Fig.1.34 Definition of the Euler angles 06¢.

70

g = {cplulncpzi = 92' g)" gz' (1.11)
In the Roe’s Variants, the second rotation is not carried
out about the X'-axis, but about the Y’-axis. The first and
third rotations remain, as Bunge’s, about the Z’-axis,
which is shown in Fig.1.34. The Euler angles are defined by
000 in this case. Thus the rotation g can be represented by

2' Y’ 2'
{WP} =9 9 9 (1-12)

9

(b) Rotation Axis and Angle.

The rotation can be obtained by specifying the rotation

axis d and rotation angle w about the.direction d (see
Fig.1.35). So the rotation g is

g = {diw} = {Mm} (1.13)

1.6.2. Representation of the Orientation

(a) Representation of the Orientation in the Pole Figure.

The pole figure shows a specific crystal direction
[hkl] which is fixed in the crystal coordinate system KB
with respect to the sample coordinate system KA in
stereographic projection. Therefore, the orientation of the

pole can be described by the polar coordinates ¢hkl and

71

 

 

z' L‘ d=r0I0II0rI
CIXIS

 

 

 

 

 

Fig.1.35 Representation of a rotation by the rotation axis d
and the appropriate rotation angle w.

rhkl‘ As an example, Fig.1.36 shows the representations of
<100>,<110> and <111> poles in pole figures. This
representation of the orientation is redundant because the

orientation is specified by only two angles.

(b) Representation of the Orientation in the Inverse Pole

Figure.

The inverse pole figure shows the orientation of the

72

(1004.) (110) (III)

 

 

 

 

 

 

 

Fig.1.36 The orientations of some crystal directions in pole
figures.

 

 

Fig.1.37 The orientations of the specimen directions in
inverse pole figure.

73

specimen directions (for example, rolling
direction,transverse direction and normal direction)
relative to the crystal coordinate axes in stereographic
projection, which is shown in Fig.1.37. This representation

is also redundant as the pole figure is.

(c) Representation by Miller Indices.

A method rather frequently used for describing an
orientation is to indicate rolling plane and rolling
direction by the Miller indices (hkl)[uvw], where (hkl) is
the crystal plane which is parallel to the sheet plane and
[uvw] is the crystal direction which is parallel to the
sheet rolling direction. Therefore, the rotation by Miller

indices is writen as
g = (hkl)[uvw] (1.14)

This representation is redundant too because this
representation is related to the representation of the
inverse pole figure if we express the orientation of
directions Z=ND and X=RD by the corresponding miller

indices.

(d) Matrix Representation.

The coordinates x’y’z’ of an arbitary point in the

crystal coordinate system KB={x’y’z’) can be expressed in

74

terms of the coordinates xyz in the sample coordinate

system KA={xyz},

x’ = a11x+a12y+al3z (1.15)
y’ = a21x+a22y+a23z (1.16)
z’ = a31x+a32y+a33z (1.17)
or
x’i = aijxj i,j=1,2,3. (1.18)

From the inversion of equation (1.18), we can express the
coordinates xyz of an arbitary point in the sample
coordinate system KA={XYZ} by means of the coordinates

x'y’z’ in the crystal coordinate system KB=(X’Y’Z’},
x. = a.. x'. = a..x’. i,j=1,2,3. (1.19)

In equation (1.18), it is easily found that the columns

of aij are the direction cosines of the sample directions
X= RD, Y= TD, Z=ND in the crystal coordinate system, that
is, the direction cosines of the directions in the inverse
pole figure. Similarly, from the equation (1.19), the rows
of aij are the direction cosines of the directions
X’=[100], Y’=[010], Z’=[001] in the pole figure.

(e) Orientation Distribution Function.

For a complete description of the crystal orientation

75

of a polycrystalline material, one must specify the
relevant orientation g for each point with coordinates

x,y,z within the sample
9 = g(xl:{lz) (1.20)
If it is writen in Euler angles, then

9 = 9(‘P1I¢I'PZ) = g[‘pl(XIYIz)I¢(XIYIz)I‘P2(XIYIZ)] (1°21)

Such a representation of crystal orientation is very
complicated. If we consider only the orientation but not
the position coordinates x,y,z of a volume element in the
sample, we will get a much simpler representation.
Therefore, by‘assuming that V is the total sample volume,
dv is the volume element of the sample which possess the
orientation 9 within the element of orientation dg, we can

define an orientation distribution function f(g) (in this

case the orientation distribution function of the volume)

by

dV
= f(g)dg (1.22)
V
The orientation distribution function f(g) can be obtained
by a method of series expansion of spherical harmonics and

usually expressed in Euler angle coordinates, i.e.,

f(¢11¢1902) or f(III,0,<I>)

76

(f) Relationship between Euler Angles and Miller

Indices.

From the matrix representation, we can obtain the

matrix discription for the three Euler rotation

 

 

coswl sincpl 0
Z’ .
g = -51ncpl coswl 0 I (1.23)
_ 0 o lJI
”1 0 0 1
x' .
g = O cos¢ Sin¢ (1.24)
O —sin¢ cos¢
P cosm2 sinIp2 0 ~
I
g2 = --sinqo2 cosw2 0 (1.25)
_ O 0 1J

 

 

Therefore, the rotation g can be expressed as

Z’ X’ Z’

p-
I

I
1 O O I 0 o |
=:-cos Sln -51n cos cos -51n 51 +cos cos cos os Sln-

I 9P1 <22 <Pl $2 45 cpl 11902 901 «02 ¢ C 902 <25.

. . . . . . 3
cosolcosoz-51n¢151n¢2cos¢ Sln¢1COS¢2+COS¢1Sln¢2COS¢ Sin¢251n¢
I

L sinwlsinw -coswlsin¢ cos¢

(1.26)

77

In the miller index representation, we have

 

 

 

 

 

 

 

 

 

h k 1
z = ND = x'+ y'+ z’ (1.27)
m m m
u v w
x = RD = x’+ y’+ z’ (1.28)
n n n
where m = /h2+k2+l2 , n = ,/u2+v2+w2 . Thus,
according to Y = Z x X,
kw-lv lu-hw hv-ku
y = TD = x’+ y’+ z’ (l.29)
mn mn mn

so, the matrix of rotation defined by the Miller indices

(hkl)[uvw] is expressed by

 

 

 

 

u kw-lv h
n mn m
v _ lu-hw k
9((hk1)IUVW]) = -- -- (1-30)
n mn m
w hv-ku l
n mn m
— 3

 

Comparing the matrix elements of equation (1.26) with the
corresponding ones of equations (1.30), we obtain the
relation between the Euler angle representation and Miller

index representation‘

78
h = m sinqbsingo2 (1.31)
k = m sin¢cosw2 (1.32)
l = m cos¢ (1.33)
u = n(cosolcoswz-sinwlsinw2cos¢ ) (1.34)
v = n(-COS¢131n¢2-51n¢1cosmzcos¢ ) (1.35)
w = n sinolsin¢ (1.36)

By inversion of these relations, we obtain the Euler angles

which are expressed in terms of the miller indices

 

 

 

 

 

 

 

(hkl) [11W] I
1
¢ = arccos (1.37)
fh2+k7+12
k h
62 = arccos——————— = arcsin———§——§ (1.38)
h +k h +k
[ "I
E- w /h2+k2+12
w = arcsinf ' I (1.39)
1 :Jru2+v2+w2 J h2+k2 I

For the rotation in the Roe’s coordinate system, we have

cosw sinw 0

 

g = -sinw cosw 0 (1.40)
L 0 0 1 J
F cosa 0 -sin67

g =‘ 0 1 0 i (1.41)
sina O cosag

 

79
I cos¢ sino 07
I I
g = I-sino cos¢ 0 5 (1.42)
10 0 15
L. —4
_thus,
Z’ Y’ Z’

91999) = g g 9

T'cos¢cosacosW-sin¢sinw cosocosacosu+sin¢cosw -cos¢sin6:
= -sin¢cosacosv-cos¢sinw -sin¢cos€sinw+cos¢cosw sinésinfi

sinecosw sinesinw cosfi

L_.__._._______ _

(1.43)

Therefore, by comparing the equation (1.43) with equation
(1.30), the relation between the Euler angles and miller

indices in Roe coordinate system can be expressed as

h = —m cosésina (1.44)
k = m sin¢sin9 ' (1.45)
l = m coso (1.46)
u = n( cosocosocosw - sinésinw ) (1.47)
v = n(-sin¢cosocosw - costinv ) (1.48)
w = n sinocosw (1.49)

and by inverting these equations, we have

1

9 = arccos —.—————— (1.50)
:Ih2+k2+12

 

 

80

 

 

 

k h 1
0 = arcsin—F§==f= = arccos — ——————-, (1.51)
jh +k h +k I
r w h2+k2+12-]
W = arccos ° (1.52)
[Ju2+v2+w2 h2+k2 J

By comparing equations (1.37)-(1.39) with equations
(1.50)-1.52), we can easily find the relationship between

two Euler angle systems,

$1 = W + n/Z (1.53)
¢ = 6 (1.54)
$2 = Q - n/Z (1.55)

which is shown in Fig.1.38.

¢=const.
‘PI

 

{‘11

I
..--.f ________ {11
“a '

 

 

I
I
I
I
I
I

III

 

II)

e=const.

Fig.1.38 Relationships between the angles wl,¢,¢2 and w,9,¢.

CHAPTER 2

EXPERIMENTAL PROCEDURES

The material used in this study was IN90211, which has

a composition similar to 2124 aluminium alloy (Table 2.1).

In addition to solution hardening provided by magnesium

atoms and

Table 2.1 Composition(wt%) of IN90211

 

 

 

Mg Cu C O AlZCu A14C3 A1203 A1
2.0* 4.4* 1.1 0 8 * * * 91.7*
2.0 0.9 6 4 * 4.3 * 1.7 * 84.7
4.1vol% 4 lvol% l.2vol% 90.6vol
* Assuming 80% Cu in Al Cu, O and C in Al4C3,and Mg in

Solution. 2

precipitation hardening provided by copper in the form of

A12Cu phase,the mechanical alloying process introduce
about 5 vol% fine oxide and carbide dispersions that

stabilize the grain size.

S

The specimens were machined from a processed sheet of

IN90211. The sheet was made from an extruded 25mm rod

provided by Novamet Aluminum (lot 85V032). The rod wa

forge flattened and rolled at elevated temperature to a

S

thickness of 2.5mm. The sheet was annealed at 492°C for 1

hour and water quenched. The specimen was nominally

81

82
2.5x2.5mm2 in cross section, and the gage length was 6.4mm
long, with the tensile axis parallel to the rolling
direction. The specimens were quickly heated in about 10
minutes with a radiant furnace, and deformed at constant
true strain rate in a hydraulic testing machine. The
temperature gradient along the specimen was within 3°C, and

the specimen was air colled following fracture.

The specimens used in this study were superplastically
deformed at (l) i=1/sec, T=425°C; (2) é=77/sec, T=475° and

(3) é=330/sec, T=475°.

Texture measurements were made on a computer controlled
four axis goniometer system in a Scintag Diffractometer
with a graphite monochrometer. Specimens were mounted and
ground to the approximate center of the specimen.
Incomplete (111),(200), and (220) pole figures were made
along the superplastically deformed specimen shown in
Figure 2.1. The reflection method was used, with 5°
azimuthal and 5° tilt increments up to a maximum tilt of
70°. A 1mm diameter mask was used to limit the diffracted
signal to the desired part of the specimen. The CODF
(crystal orientation distribution function) was calculated
using the coefficients of the spherical harmonic expansion
of the orientation distribution with expansion to lmax=22°

The software was popLA (the preferred orientation package

from Los Alamos, Los Alamos National Laboratory).

CHAPTER 3

RESULTS

The CODF has the advantage of being a unique result
compared to the pole figure and inverse pole figure.
Therefore, we are investigated the texture evolution with
CODF. The experimental pole figure and inverse pole figure
are presented in the appendix. For convenience, an indexed

¢=0° section of CODF is ploted in Fig.3.l. Most of the

0‘ f
551x105) 3) (101) 02) (501) (103)

 

 

 

[1001501] I IIIOIII 3] [I05] [001)
I002) 201
3o°- [211] . 5112])
I 101
I I 11]
w ¢dT
(191)
60°-I -[121]
1001) (109403) (101) COLOOI) (100)

 

 

90.(0101 (0101(0101 [010) [010) [0101 [010)
W
0' 30 e (0' 9V

Fig.3.1 Some ideal components in ¢=O° section

important texture changes can be observed in this section.

Some aditional components will also be described.

3.1 Specimen Deformed at é=1/sec and T=425°C

83

84

The complete CODFs obtained from the specimen deformed
at the strain rate é=1/sec and the temperature T=425°C are
shown at sections of constant 0 in Fig.3.2. For brevity,
Changes in texture arising from superplastic deformation
are investigated in terms of the ¢=0° section of the CODF

for this specimen, which are shown in Fig.3.3.

(a) Undeformed Shoulder. The texture consists of three
fiber textures: (101)[uvw] (a-fiber texture), (102)[uvw]
and (201)[uvw]. Since the latter two textures are symmetric
about 0=45° in the ¢=O° section, only the components of
(102)[uvw] texture will be considered below. In a—fiber
texture the maximum density is at (101)[101] orientation,
but some other components also appear in the ¢=0° section.
No (001)[100] cube components exist in this initial

texture, (Fig.3.3.a).

(b) Texture at c=l.l. A notable decrease in the
a-fiber texture is observed. The components (101)[131],
(101)[121] and (101)[232] disappear. Slight changes occur
in the (102)[uvw] fiber texture, though the density of most

components is essentially unchanged, (Fig.3.3.b).

(c) Texture at 5:1.6. At this strain, the a-fiber
becomes very smooth, that is, almost every component has
the same density of about 1.5. The components between
(101)[323] and (101)[101] continue to weaken from their
initial intensities, but the rest of the components

increase in intensity. In the (102)[uvw] fiber, the maximum

 

 

 

 

6.-
©1111

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘1‘ Phi= 10.0 Ph1= 15.0
e “W
" I
Q 0 00‘}
53 1D» 9-4 0 (C) 5 ‘°
. I {A _ ,
Pnic 30.0 Phi= 35.0

 

 

 

 

 

 

 

 

 

 

Phi- 40. 0 Ph1= 45. 0 ' Phia 50. 0 ' Phi- 55. 0 '

 

 

 

 

 

 

 

 

‘1ng gd’j (7 6g
0

 

 

 

 

 

 

 

 

 

 

 

‘ Pm- 80.0 Phi- 5570 “P900

(a) Texture at e=0, contours at 1 2 3 4

Fig.3.2 Complete CODF of é=1 sec-1 and T=425°C (a)—(f).

 

 

 

 

$116
OBI

 

 

 

i P::E:§i:2f
‘ . J, _
In 10.0 Ph

 

 

 

 

 

I00

 

 

 

 

 

 

06

 

 

 

 

 

 

 

 

A5054 .

 

 

 

 

 

III

 

Phifl 709

 

 

 

 

 

 

 

 

 

 

 

III

 

 

 

 

PRDJ' ‘ '
ontours at 1 2 3 4 5

 

 

 

e<-

87

 

 

 

 

 

Iii

 

 

 

01
9.80

 

7V

(101) OK

 

 

Phi= 5.0

 

Phifl 10. 0

‘Phiu 15.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5’" I 01/ I,” (01
I 1 1 e!
I
‘0 J “W 11R m1
Ph‘1= 20. 0 Phi- 25.0 Phin 30.0 Prue 35.0
V \I U
0
I ”o I) 0
Phi- 40. 0 Phi- 45.0 Ph1- 50.0 Phi- 55.0
, \ _ , w ,
%> Q \I I 11 1 L”)
O \
.o 0 , R
Pm- 50. 0 thu 55.0 Ph1- 70. 0 Phi-:75.0
Q U
l U L? '
(:4AA JP1[\. 11(\1
Ph1= 50.0 Ph1= 35.0 PFIOd

 

 

 

 

 

 

 

(0) Texture at e=1.6, contours at 1 2 3

 

 

 

 

 

7

:55

 

 

II
I W

 

 

? AM

 

A

 

 

 

 

(L3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pn1= 0.0 Pn1= 5.0 Phi= 10.0 Pn1a 15. 0 '
‘ o 219' 111x:
DI " 550
m 1 MM
Pn1= 20.0 , Ph1= 25. 0 Phi= 30.0 Pn1= 35.0
(\KJQ: Jifl:}0 <3 C? [1:‘;;
RM e PM? )5:
Ph1- 40. 0 Pn1- 45. 0 Ph1- 50. 0 Pn1- 55. 0
_ 4 8KW 1A 0 C)J 9? 1 9
Ph1- 50.0 Pn1= 55. 0 Ph1= 70. 0 Ph1= 75.0
8; Jflfl
Pn1= 50.0 Ph1= 55. 0 PROJ

 

 

 

 

 

 

(d) Texture

 

 

 

 

 

9

 

 

 

0

w
A

 

 

M

 

 

315:7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 .
Phi- 50.0 Phi? 55.0 Ph1- 10.0 Ph1= 15.0
CS UU VLJ
[ . § m:
(1 Ag 0 m , f
Ph1= 20.0 Ph1= 25.0 Phia 30.0 Phi-P 35.0
V
K?% 0‘
O
{ft—hvéffl fl:@ (7 [P
Ph1- 40. 0 Ph1- 45. 0 Phi- 50.0 Phi- 55. 0
U
A I
Phi- 60.0 Phi!“I 65.0 Ph1= 70.0 Ph1- 75.0
W a R
I 0
Ph1= 80.0 PhiPI 85.0 PHOJf/L]

 

 

 

 

 

 

(e) Texture at

e=2.6, contours at 1 2 3 4

 

 

 

 

"“ 7'9
£023   I
lg <3:

I
1 ._ w
IM%-¢51 - ,
Phiu 0. 0 Phi= 5. 0 Ph1= 10. 0 Phi= 15.0

E55! 5; "‘y‘j “2:“.
5057.05

Ph1= 20. 0 Phi= 25. 0fl Phi- 30.0 Ph1= 35.0

5 5 55

Phi“ 40.0 Ph1= 45.0 Phi‘ 50p
.5...) Q
I
r\

‘Pma 50. 0 Ph1= 55.0 PM: 70.0 Ph1- 75.0
'" UK.

 

 

 

I
"I5

 

 

 

 

 

 

 

 

 

 

E

 

 

 

 

uj
JII

 

 

 

 

 

 

 

 

 

 

 

 

0‘

Phi- 55. 0

:33
@C’oO

 

 

 

%
5 A
6%
f

 

 

 

 

 

 

 

52..
55"
5

’.\

 

 

 

 

211

 

 

 

5’
-—
<

 

 

 

15
g
5

 

 

Phiu 80.0 Ph1= 85.0 'PROJ
(f) Texture at e=3.0, contours at l 2 3 4

 

 

91

 

 

 

 

 

 

 

 

 

 

 

b
b
b
D
I
p

w :
AWN E

 

 

I

 

 

 

 

 

 

 

 

 

 

(d) c=2.3 (e) 6=2.6 (f) e=3.0

Fig.3.3 The ¢=O° section of CODF vs strain.

92

intensity shifts slightly to (102)[251] orientation. The
peak (103)[010] is weakened slightly. There is no evidence

for development of a cube component,(Fig.3.3.c).

(d) Texture at 5:2.3. The components between
(101)[252] and (101)[101] in the a-fiber sharpen, instead
of reducing, compared to those at 2:1.6, but (101)[131] and
(101)[151] are reduced further. The overall intensity of
(102)[uvw] fiber declines and the highest intensity

continues to shift to a lower w angle,(Fig.3.3.d).

(e) Texture at c=2.6. The a-fiber continues to
sharpen, and the intensities of components at the lower W
angle also increase. For the (102)[uvw] fiber, the highest
intensity continues to shift to lower W angle so that only
(102)[501] component is sharpening drastically while other
components weaken slightly or remain unchanged. A
considerable sharpening is noted at the (203)[§02] peak,
but there is still no evidence for cube texture

development,(Fig.3.3.e).

(f) Texture at 5:3.0. Near the fracture tip, a new
fiber (h01)[0l0] has developed considerably, while the
other components among the previous fibers are weakened. A

strong cube texture emerges at this point, (Fig.3.3.f).

To summarize, some of the changes in texture described
above are plotted as a function of w and strain in

Figure 3.4.

93

(101) (391) (391) (191) (392) (102)
[101]J [111]! [12111 [010] [211] 1 [0T0]

6.0 “OW/Nb —D— 0 6.0- *Ci— 0 <10
. . “-0- 1.1 MIND

 

 

 

 

 

Orientation Density f(g)

 

 

 

 

Fig.3.4 Orientation density vs. w and strain

3.2. Specimen Deformed at é=77/sec and T=475°C

For the specimem deformed at a strain rate é=77/sec and
a temperature T=475°C, we are mainly considering the fiber
type texture in ¢=0° section of the CODF and some specific
peak type components in the sections from the whole range

of Q. The complete experimental CODFs of this specimen are
shown in Fig 3.5.

(a) Undeformed Shoulder. In ¢=0° section, it mainly

consists of three fiber textures: (101)[uvw], (102)[uvw]

and (201)[uvw], which is similar to those of undeformed

specimen in previous section 3.1. Here again, we are going

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A” A .i

. ll 1 ,. i . ,. A
‘i' 1511- 0.0 Ph1- 5. 0 9111- 10.0 1511- 15.0

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Pn1- 40.0 9111- 45.0 Pn1- 50. 0

.h' (9)

PM- 60.0 9111- 65.0 Pn1- 70. 0 ' 9111- 75. 0 ‘

ii.

I o

l .

 

 

 

 

 

 

 

 

 

 

   

Pn1- 35.0 '

 

 

 

 

 

 

 

 

 

 

 

 

<¢::

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

' P'n1- 50.0 " mm 55. 0 ”950.1

(a) Texture at e=0, contours at 1 2 3 4 5

Fig.3.5 Complete CODF of é=77 sec.1 and T=475°C (a)-(e).

 

 

 

 

L/

36

 

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A

Q

 

 

 

 

 

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m 0 0
Bu 6.
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h
P m

 

 

 

 

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Pn1- i0 0 ’

 

W

 

 

\

I
Pn1- 50.0

 

 

 

 

 

 

 

 

 

 

 

E! 25! 5 ram
Phi- 80.0 Phi- 85.0 PHOJ
(b) Texture at e=1.6, contours at 1 2 3 4

 

 

96
8
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99

to consider only the components of (102)[uvw] since the
components of(102)[uvw] and (201)[uvw] are symmetric about
o=45° in 0=0° section. In a-fiber texture, intensity
declines gradually with a maximum intensity at (101)[101]
and the intensities from (101)[E52] to (101)[010] are zero.
There are very high intensities at (203)[§02] and

(311)[0i1]. But there is no cube texture, (Fig. 3.5.a).

(b) Texture at £=l.6. The components of the fiber
texture and peak type texture at this point remain unchange
compared to the initial texture from the undeformed
shoulder, but the overall intensity is weakened,

(Fig.3.5.b).

(c) Texture at c=2.13. At this point, the intensities
of texture (102)[uvw] and peak (203)[302] continue
decreasing, but in the texture (101)[uvw], the components
from (101)[010] to (101)[552] which were zero in intensity
at lower strain are sharpened considerably and the previous
high intensity components from (101)[111} to (101)[101] are
weakened drastically. So the highest intensities shift to
the [0101,[151] and [ill] directions in this fiber. Several
new peaks are noted, developing at (312)[112],(321)[1 Z 11],
(231)[4§1],(123)[123] and (132)[1§4]. Meanwhile, a cube

texture is also developed, (see Fig.3.5.c).

(d) Texture at £=2.36. The intensities of texture

(102)[uvw] are sharpened but the intensities of (101)[uvw]

 

100

are noted to be weakened except for peak (101)[111]. The
cube texture disappears again. The formerly developed
(321)[1 Z 11] is shifted to (321)[§ 3 12] and a new peak
(321)[1§1] is developing, while the formerly present peaks
(312)[112], (231)[4§1], (123)[123] and (132)[1§4] are
weakened. It is also noted that a new fiber texture
(113)[uvw] is developed with a maximum intensity at peak

(113)[0§1], (see Fig.3.5.d).

(e) Texture at £=2.86. The intensities of (102)[uvw]
continue increasing with a maximum intensity at (102)[010],
and overall intensity of (101)[uvw] continues decreasing. A
new orientation <0§3>//RD, such as (11 2 3)[O§2],

(12 3 2)[0§3], (823)[o§2], (3 2 11)[2§0] and (3 2 12)[2§0],
is strongly developed even though the peak (203)[302]
reachs minimum intensity compared to that at lower strain.
New strong peaks (511)[i E 12] and (116)[6 15 1] are also
created. The overall intensity of texture at this point
increased markedly to reach the initial intensity,

(Fig.3.5.e).

In order to compare the results with the former
specimen, the texture changes in a-fiber texture and

(102)[uvw] texture are plotted in Fig.3.6.

3.3 Specimen Deformed at é=330/sec and T=475°C

The complete experimental CODFs of this specimen are

101

(101) (101) (101) (191) (392) (102)

 

 

 

 

 

 

[101’]J [1'11]. [111]. [010] 7 [211]! [0T0]
<10? NDc_D_ 0 ' —C]'- 0 <102> ND
»~ 6 $fi)€#45 5m ——£r—
£9 —0- 1.6 1-5 ¢=o° 9:27“
1—0— 2.13
€- 5- —o— 2.36
G
S:
E
.2
3
E
5

 

 

 

Fig.3.6 Orientation density vs. 0 and strain

shown in Fig.3.7. In this specimen, two fiber texture,
which are different from those in other two specimens, are
found: one is (203)[uvw] and the other is a skeleton line
in which the [001] orientation is tilted from ND by about
30° towards TD. The results are ploted in Fig.3.8. The
overall intensity of skeleton line keeps constant until the
c=1.38, where the some parts of the skeleton line are
sharpened slightly. But the overall intensity of the fiber

(203)[uvw] decreases with strain increasing.

 

 

 

  
 

 

 

 

 

 

 

 

 

 

 

 

 

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Ph1- 500 " 1511- 55.0 9500'

(a) Texture at e=0, contours at 1 2 4 6 8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

Fig.3.7 Complete CODF of é=330 sec"1 and T=475°C (a)-(d).

 

 

 

 

 

 

 

 

 

 

P lllllll

 

 

 

 

 

 

£0 0
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Ph1= 30.0 Phifl 35.0

 

 

 

 

 

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@300

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(c) Texture at

     

I ,1 1 -
Ph 1- 85 . 0 PROJ

 

 

 

 

 

 

 

 

 

 

e=0.73, contours at 1 2 4 6 8

105

 

 

 

 

 

 

 

 

 

 

 

 

 

  
   

 

  
   

 

 

 

 

 

h

. I1 , 1
Phi- 30.0 Phi- 35.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

U

0
PM- 80.0 Phi- 85.0 P800
(d) Texture at e=1.38, contours at l 2 4 6 8 10

 

 

 

 

 

 

      

Orientation Density f(g)

 

106

(102) (113M012) (011)
[0T0] [110L010] [111]

 

 

 

 

 

 

 

 

14 " ""D— 0 Skeleton
2 ‘ "A" .45 Line So
1 . "'"O .723 Z;
10- "-0"- 1.38 '3'
1 fl
0
8" D
‘ H
6 i . :9.
i 3
4 C% : ‘. . E
no (5 5

 

 

 

 

 

Fig.3.8 Orientation density vs. 0 and strain

CHAPTER 4

ANALYSIS AND DISCUSSION

4.1. Deformation at Relatively Lower Superplastic

Strain Rate

The specimens deformed at strain rate o=l/sec and
é=77/sec are mainly composed of two fiber textures, with
<101> and <102> directions parallel to the rolling plane
normal, and some individual peaks. During the superplastic
deformation, two fiber textures dominate the texture
components, even though the intensities of individual
components in these fibers change with strain. The texture
changes produced by superplastic deformation can be
described in terms of grain boundary sliding, slip and

dynamic recrystallization.

4.1.1. Grain Boundary sliding.

In Fig.4.1 some ideal components are plotted vs. strain.
It is noted that the overall texture intensity with strain
up to v=2.6 in the first specimen and strain up to a=2.13
in the second specimen decrease. The texture decline in
superplastic deformation can not be explained in terms of
:iLip or recrystallization, because annealing is found to

lead to only a slight or no reduction in intensity and

107

 

  

—Ci— (102)[0‘10]
‘13- (103)10i0]
"'"O (102)[51'1]
(101)[U1]

 
 

 

  

 

40
30
20
L0
0.0 I ' I v I
0 1 2
True Strain
( 6!)

 

7. —D— (102)[010]

“"A- (103)[0101
‘ "“<:>'" (102x511)
5 "-0-" (101)[111]
""i'" (203)[302]

 

 
      

Orientation Density f(g)
45

 

 

3
2 """
l
0 l I l
0 1 2 3
True Strain
(b) *

Fig.4.1 Texture components vs. true strain

Rolling Plane
Perpendicular
to Page

 

A -.>
Increas1ng Strain

1?? g

Plane
Parallel
to Page

V Rolling Direction

 

‘ Tensile Axis and

Fig.4.2 Schematic diagram showing sliding of platelet-shaped
grains during superplastic elongation.

109

recrystallization leads to the development of new and
distinct texture components. However, this overall
reduction can be easily accounted for in terms of grain
boundary sliding and grain rotation. The mechanism of GBS

154]. Because the grain

is schematically shown in Fig.4.2[
aspect ratio is about 1 to 8, the sliding in the direction
perpendicular to the plane of the grain is difficult. The
GBS and grain rotation take place in the plane parallel to
the rolling plane, and the grains remain in the same plane
as they started. It is proposed that grain boundary sliding
and grain rotation have a randomizing effect on any
existing texture components[138'l39’155’156’1. However, the
randomizing effect of GBS and rotation in these specimens
is restricted in the direction perpendicular to the rolling
plane due to the plate shape grains. Therefore, the sliding
stresses on the different types of boundaries are
accommodated by either grain rotation in the rolling plane
or dislocation slip in grain interiors, as show in
Fig.4.2.b. The relatively slow reduction of overall texture
implies that the grain rotation rate is limited. SEM and
TEM studies show that GBS and rotation are limited to an
axis normal to the rolling plane[154]. But it is difficult
to make a quantitative assessment of its contribution to an
individual orientation, since there are varying concurrent

sharpening and weakening of existing texture components due

to the occurrence of slip and recrystallization.

110
4.1.2. Slip.

Investigation of the [211] orientation in Fig.4.1 shows
the occurrence of single slip during superplastic
deformation. In Fig.4.1.a, high indensity of [211]
orientation is in the range of lower strain, and
intensities drop considerably close to the fracture
surface. However, in Fig.4.1.b, the intensity of [211]
orientation continues to increase after an initial drop of
overall intensity due to GBS and rotation. It is possible
to treat a grain as a isotated single crystal in uniaxial
tension in the case of diffusion accommodated superplastic
deformation, so that the single slip allows the grain to
rotate to <121> direction where the second slip system
operates and keeps the grain at <121>. Furthermore, <121>
orientations have a relatively high Schmid factor (0.41)
and thus slip is possible in grains at or near these

orientation[123]

. The sharpening of the [211] orientation
indicates that a large amount of single slip has occurred.
The reduction of the [211] orientation with further strain
may be attributed to an increase of the number of multiple
slips and an occurrence of dynamic recrystallization. The
increment of [211] orientation with strain in Fig.4.1.b
indicates more single slip occurring at high strain. Such
.an orientation is stable in the sense that any rotation

annay from it occasioned by grain boundary sliding leads to

a czounteracting slip rotation back towards <121>.

111

The gradual increase of a [111] orientation suggests
that multiple slip occurs in this specimen because the
<1ll> texture is commonly associated with multiple slip
under uniaxial tension in polycrystalline materials[149].
The <111> texture is stable during multiple slip, because
only five of the six active slip system in this orientation
are required to maintain grain compatibility and the
remaining one degree of freedom allows a rotation of the

grains about the tensile axis only[148].

There are strong <100> components in the starting
materials, compared to the other texture components, but
<100> texture gradually declines up to 2:2.6 at lower
strain rate (see Fig.4.1.a) and £=2.13 at é=77/sec (see
Fig.4.1.b). This is because the <100> orientation has eight
active slip system so that after providing five slip
systems for grain compatibility, the grain slill has three

[148]. Close

degrees of freedom and any rotation is possible
to the fracture surface in the specimen deformed at

é=l/sec, where neck formation and a rising local temperature
take place, and the higher strain in the specimen deformed
at é=77/sec, the slip system shifts from <111> to <100>
directions. It may be possible since the <100> orientation
is more likely to operate with strain increasing in this
Imaterial and the grain compatibility can be more strongly

assisted by diffusional processes due to the adiabatic

thermal effect. In this case the deformation

112

in each grain is more like that of an isolated single

[150]. Further, the Schmid

crystal in uniaxial tension
factors for the <100> and <111> orientations are 0.408 and
0.272, respectively. This leads to increasing intensity in

<100> orientation.

4.1.3. Recrystallization.

The appearance of cube texture at the highest strain in
the specimen deformed at 1/sec and at the median strain in
the specimen deformed at 77/sec suggests that
recrystallization occurs. The small amount of cube texture
is possibly due to the effects of the finely dispersed
particles and fine substructures. Local lattice rotations
are found at the large particles and the regions near the
particles rotate in the opposite sense to the matrix about
the same axis. The deformation zone at the particles is a
preferred nucleation site for recrystallization. Therefore,
the contribution of the particles to the overall texture is
expected to be a smearing out of the deformation texture
by an amount which depends on the volume fraction of
particles present[157-161]. But for small particles
(<0.10m), some studies have shown that the texture is
strengthened whereas in other cases a neutral or a

d[162-164]. In this study,

weakening effect has been observe
Because the particle size is very small ( 13.7nm) and the

Spacing between the particles is 40nm, the particles have

113

such a strong pinning effect on both substructures and
grain boundaries that subgrains are very difficut to grow
to a recrystallizing nucleus. So it requires large enough

strain to overcome this barrier for recrystallization.

The overall initial texture is retained after
superplastic deformation and dynamic recrystallization,
although the amounts of the different texture components
may be altered. This is in agreement with Humphreys and

[165]. This results may be also

Jensen's investigation
related to an effect of particles on the formation of
dynamic recrystallization nuelei which may take place at
the original high angle boundaries[166]. The nucleation
process is retarded by presence of small particles reducing
the rate of subgrain growth.This retarding effect may

be least pronounced at the original grain boundaries where
nucleation may require less subgrain growth than nucleation
in the grain interiors. The preference for nucleation at
the original grain boundaries may lead to an increased

retention of the initial texture[64'167].

4.2. Deformation at High Strain Rate

The specimen deformed at strain rate é=330/sec mainly
consists of one skeleton fiber texture which runs from
(102)[010] to (011)[111]. Contrary to the overall reduction
of intensity in the superplastically deformed specimen, the

overall intensity in this specimen keeps constant.

114

Therefore, it indicates that there should be a some kind of
balance between sharpening and weakening effects due to
slip, recrystallization, GBS and rotation. In this
specimen, components of (102)[010] and (001)[111} decrease
in intensity with strain while the intensities of
(113)[110] and (112)[110] components increase as strain
increases. This result is contrary to the traditional
deformation mechanism which predicts an increment of <001>
and <1ll> orientations by tensile deformation. It indicates
that a different deformation mechanism is occurring in this

case .

CHAPTER 5

CONCLUSIONS

1. Texture is a very powerful structure parameter to
study the deformation behaviors. It can isolate the
individual contributions from the various mechanisms, such as
dislocation slip, twinning, grain boundary sliding, grain

rotation and recrystallization.

2. The superplastic deformation mechanism of IN90211
consists of grain boundary sliding, dislocation slip (sigle
slip and multiple slip), grain ratation and
recrystallization. But at the highest strain rate, there is

no evidence of recrystallization.

3. At the lower strain rates (1/sec and 77/sec), the
textures are mainly two fibres, a-fibre (<101> parallel to
ND) and {102}<uvw> (<102> parallel to ND). At the highest
strain rate (330/sec), the textures are mainly composed of
two fibres, {203}<uvw> (<203> parallel to ND) and a skeleton

line (<001> orientation is tilted from ND towards TD by about

30°).

115

APPENDICES

APPENDIX A POLE FIGURES OF IN90211

Fig. A.1 (111), (200), (220) pole figures of

specimen deformed at é=1/sec and T=425°C.

Fig. A.2 (111), (200), (220) pole figures of specimen

deformed at é=77/sec and T=475°C.

Fig. A.3 (111), (200), (220) pole figures of specimen

deformed at é=330/sec and T=475°C.

116

117

‘ ¥

 

(200) pole figure

Contours at 1 2 3 4

(220) pole figure

Contours at .5 1 1.5 2 2.5

 

 

 

(a) e=0

Fj—<3.A.1 (111),(200),(220) pole figures of specimen deformed
at 1/sec and T=425°C. (a)-(f)

118

 

(111) pole figure

 

Contours at .5 l 1.5 2 2.5

 

 

 

(200) pole figure

 

 

 

 

 

 

 

Contours at .5 1 1.5 2 2.5

 

 

(220) pole figure

Contours at .5 l 1.5 2

 

(b) e=1.1

119

 

(111) pole figure

Contours at .5 1 1.5 2

 

 

 

(200) pole figure

Contours at .5 l 1.5 2

 

 

(220) pole figure

Contours at .5 1 1.5 2

 

(C) e=1.6

 

120

 

 

”455‘
0 7

(D

D

K) Conyours at .25 .5 .75 1
1.25 1.5

(111) pole figure

 

(200) pole figure

Contours at .5 1 1.5 2

 

(220) pole figure

Contours at .25 .5 .75 1
1.25 1.5 1.75

 

(d) e=2.3

121

(111) pole figure

Contours at .5 1 1.5 2 2.5

 

(200) pole figure

Contours at 1 2 3

 

 

(220) pole figure

Contours at .5 1 1.5 2

 

(e) e=2.6

122

(111) pole figure

 

Contours at .5 1 1.5 2

 

 

(200) pole figure

Contours at .5 1 1.5 2 2.5

 

(220) pole figure

 

 

 

Contours at .5 1 1.5 2

 

 

123

(111) pole figure

Contours at .5 1 1.5 2

 

(200) pole figure

Conyours at 1 2 3

 

 

 

(220) pole figure

Contours at .25 .5 .75 1
1.25 1.5 1.75

 

(a) e=0

Fig.A.2 (111),(200),(220) Pole figures of specimen deformed
at é=77/sec and T=475°C. (a)-(e)

124

:L (I; .
§§WIJ Contours at 1235.557315

O
O ...

 
 
 

 

(b) e=

 

 

(200) pole figure

' Contours at .25 .5 .75 1
1.25 1.5

 

(220) pole figure

Conyours at .25 .5 .75 1
1.25 1.5

1.6

125

(111) pole figure

Contours at .25 .5 .75 1
1.25 1.5 1.75 2

 

(200) pole figure

 

Contours at .25 .5 .75 1
' 1.25 1.5 1.75

 

 

 

(220) pole figure

Contours at .25 .5 .75 1
1.25 1.5 1.75

 

(C) e=2.13

126

 

(111) pole figure

Contours at 1 2 3

 

 

(200) pole figure

Contours at .5 1 1.5 2 2.5

 

 

(220) pole figure

.‘ Contours at .5 1 1.5 2

 

 

(d) e=2.36

128

(111) pole figure

Contours at 1 2 3

 

.:}:§,2¢fi .§g§§€.:2. (200) pole figure
. . . . .-.W. . .
Q3 fl Contours at 1 2 3 4

 

 

 

 

 

129

(111) pole figure

Contours at 1 2 3 4 5

 

 

o...
o 0 °
'0. o
.0

(Wm, (200) pole figure

‘ ”$3“ I :01'.‘ on ours a
!'?§¥S2Z¢F‘y ' C: t t 1 2 3 4

   

 

(220) pole figure

Contours at .5 1 1.5 2 2.5

 

(a) ¢=0

Fig.A.3 (111),(200),(220) pole figures of specimen deformed
at é=330/sec and T=475°C. (a)-(d)

130

 

‘ .. .. ‘ .

.’ “mm“ 1. (111) pole figure
gfl ‘ Contours at 1 2 3 4 5 6 7
‘ :2'..-°.' '

‘7
by

 

 

(200) pole figure

Contours at 1 2 3 4

 

 

(220) pole figure

Contours at 1 2 3

 

(b) c=0.45

130

(111) pole figure

Contours at 1 2 3 4 5 6 7

 

 

(200) pole figure

Contours at 1 2 3 4

 

 

(220) pole figure

Contours at 1 2 3

 

(b) e=0.45

131

 

 

 

 

‘ (if/r“ I ......... (200) pole figure
'J‘XXKJ/£\ .......... Contours at 12 3 4 5 6

 

(220) pole figure

Contours at 1 2 3 4

 

(C) 5:0.73

132

(111) pole figure

Contours at 1 2 3 4 5

 

 

, ' {1:1 (200) pole figure
wa'
. 5&9” - ”3.- Contours at 1 2 3 4 5 6

 

(220) pole figure

Contours at 1 2 3

 

(d) e=1.38

APPENDIX B INVERSE POLE FIGURES

Fig. 8.1 Inverse pole figures
é=1/sec and T=425°C. (a)-(f)

Fig. B.2 Inverse pole figures
é=77/sec and T=475°C. (a)-(e)

Fig. 3.3 Inverse pole figures

£=330/sec and T=475°C. (a)-(d)

133

OF

of

of

of

IN90211

specimen deformed at

specimen deformed at

specimen deformed at

134

Inverse PF of RD

Contours at .5 .75 1 1.25
1.5

 

 

Inverse PF of TD

Contours at .5 1 1.5 2

 

 

Inverse PF of ND

Contours at .5 1 1.5 2

 

 

 

(a) e=0

Fig. 8.1 Inverse pole figures of specimen deformed at
é=1/sec and T=425°C. (a)-(f)

 

 

 

 

 

 

 

136

'Contours at .8 .9 1 1.1 1.2

 

 

Inverse PF of TD

Contours at .25 .5 .75 1
1.25 1.5

 

 

Inverse PF of ND

Contours at .5 1 1.5 2

 

 

 

137

Inverse PF of RD

€EZ;?\ ' Contours at .6 .8 1 1.2 1.4

 

Inverse PF of TD

Contours at .25 .5 .75 1
1.25 1.5 1.75

 

 

 

 

 

...-

Inverse PF of ND

Contours at .25 .5 .75 1
1.25 1.5 1.75

 

 

 

(d) e=2.3

138

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(e) e=2.6

Inverse PF of RD

Contours at .25 .5 .75 1
1.25 1.5 1.75

Inverse PF of TD

Contours at .25 .5 .75 1
1.25 1.5 1.75

Inverse PF of ND

Contours at .5 1 1.5 2

 

139

 

 

 

 

 

 

(f)

e=3.

O

Inverse PF of RD

Contours at 1 2 3 4

Inverse PF of TD

Contours at 1 2 3

Inverse PF of ND

Contours at .25 .5
1.25 1.

.75

5

140

Inverse PF of RD

Contours at .6 .8 1 1.2 1.4

 

 

 

Inverse PF of TD

Contours at .5 1 1.5 2

 

Inverse PF of ND

 

Contours at 1 2 3

 

 

(a) e=O

Figure 8.2 Inverse pole figures of specimen deformed at
é=77/sec and T=475°C. (a)-(e)

 

141

 

 

 

 

 

 

(b) e=1.6

Inverse PF of RD

Contours at .6 .8 1 1.2 1.4
1.6

Inverse PF of TD

Contours at .25 .5 75 1 1.25
1.5 1.75

Inverse PF of ND

Contours at .5 1 1.5 2

142

Inverse PF of RD

Contours at .6 .8 1 1.2 1.4

 

 

Inverse PF of TD

 

Contours at .5 .75 1 1.25

 

ill

D
N
f
O
F
P
e
S
r
..v.
n
I

 

Contours at .5 1 1.5 2

 

e=2.13

(C)

143

Inverse PF of RD

'Contours at .4 .6 .8 1 1.2
1.4

 

 

 

Inverse PF of TD

Contours at .4 .6 .8 1 1.2
1.4 1.6

 

 

Inverse PF of ND

Contours at .25 .5 .75 1
1.25 1.5 1.75

 

 

 

(d) e=2.36

144

Inverse PF of RD

 

 

Contours at .75 1 1.25 1.5
1.75 2

 

 

Inverse PF of TD

 

 

 

 

Contours of .25 .5 .75 1
1.25 1.5

 

 

Inverse PF of ND

 

Contours at .5 1 1.5 2

 

\A

(e) e=2.86

145

Inverse PF of RD

Contours at .5 .75 1 1.25
1.5

 

 

  
   

Inverse PF of TD

') Contours at 1 2 3

 

 

'2: - //:. . Inverse PF of ND
3 .\\\_ //'12 Z 2 : Contours at 1 2 3
“:{m ffLI

(a) €=O

Fig.B.3 Inverse pole figures of specimen deformed at
é=330/sec and T=475°C. (a)-(d)

146

Inverse PF of RD

Contours at .4 .6 .8 1 1.2
1.4

 

 

Inverse PF of TD

 

Contours at 1 2 3

 

 

 

Inverse PF of ND

Contours at 1 2 3

 

 

(b) e=0.45

147

Inverse PF of RD

 

Contours at .5 1 1.5 2 2.5

 

 

Inverse PF of TD

Contours at 1 2 3

 

Inverse PF of ND

Contours at .5 1 1.5 2 2.5

 

 

(C) £=0.73

148

 

<3 Inverse PF of RD
, V , Contours at .25 .5 .75 1
ix /\ 1.25 1.5 1.75

 

 

Inverse PF of TD

Contours at 1 2 3 4 5

 

 

 

Inverse PF of ND

Contours at .5 1 1.5 2 2.5

 

 

(d) e=1.38

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