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The evolution of microstructure and texture during room temperature compression of commercially pure Ti with four different initial
�4 �1
materials that are extensively used in mechanical and struc-
and zirconium [12–19], due to their technological impor-
tance. In particular, titanium and its alloys find extensive
use in aerospace and biomedical applications due to their
investigation from the fundamental as well as engineering
sively for different deformation modes [3–7]. A good num-
ber of studies have focussed on the strain hardening
characteristics of titanium during deformation [8–10].
Modelling texture evolution in hcp metals has been an
intriguing problem due to a propensity for twinning during
deformation. Tome´ and co-workers [12,13] employed the
⇑ Corresponding author. Tel.: +91 80 22933245; fax: +91 80 23600472.
E-mail address: satyamsuwas@materials.iisc.ernet.in (S. Suwas).
Available online at www.sciencedirect.com
Acta Materialia 59 (2011) 3431–34
tural applications. The deformation response of hexagonal
close-packed (hcp) metals and alloys is generally guided by
their axial (c/a) ratio [1]. The deformation behaviour of hcp
materials is, however, very complex, due to activation of
different type of slip as well as twinning systems under dif-
ferent conditions. The onset of twinning during the initial
stages of deformation leads to a unique hardening response
of these materials. Crystallographic texture also plays an
important role in deciding the mechanical behaviour of
hcp metals and alloys. Amongst the hcp metals, the major-
ity of investigations have been directed at titanium [2–11]
points of view.
Various characterization techniques, such as electron
backscatter diffraction (EBSD) [20] and X-ray [21] and
neutron diffraction [22], have been employed to fully
understand the evolution of microstructure and texture
during different deformation processes. Attempts have
been made to simulate the experimental stress–strain curves
and texture evolution using various crystal plasticity mod-
els ranging from the simple Taylor model to the advanced
crystal plasticity finite element (CPFEM) model. The
mechanical response of titanium has been studied exten-
orientations were studied under quasi-static and dynamic loading conditions. At a low strain rate _e = 3 � 10 s all the different initial
textures yielded the same end texture, despite different microstructural evolution in terms of twin boundaries. High strain rate deforma-
tion at _e = 1.5 � 103 s�1 was characterized by extensive twinning and evolution of a texture that was similar to that at low strain rate with
minor differences. However, there was a significant difference in the strength of the texture for different orientations that was absent for
low strain rate deformed samples at high strain rate. A viscoplastic self-consistent model with a secant approach was used to corroborate
the experimental results by simulation.
� 2011 Published by Elsevier Ltd. on behalf of Acta Materialia Inc.
Keywords: Titanium; Texture; Twinning; Electron backscatter diffraction
1. Introduction
Hexagonal materials form a class of low symmetry
excellent mechanical and physical properties, like high spe-
cific strength, good ductility and excellent corrosion resis-
tance [2]. Hence, it has been the subject of detailed
Deformation behaviour of comm
strain
N.P. Gurao a, Rajeev K
aDepartment of Materials Engineering, India
bMaterials Group, Bhabha Atomic R
Received 21 June 2010; received in revised for
Abstract
1359-6454/$36.00 � 2011 Published by Elsevier Ltd. on behalf of Acta Mater
doi:10.1016/j.actamat.2011.02.018
rcially pure titanium at extreme
ates
oor b, Satyam Suwas a,⇑
stitute of Science, Bangalore 560 012, India
rch Centre, Mumbai 400 085, India
0 December 2010; accepted 14 February 2011
www.elsevier.com/locate/actamat
46
ialia Inc.
ter
volume fraction transfer (VFT) scheme of Van Houtte [23]
and proposed the predominant twin reorientation (PTR)
scheme to model the deformation behaviour of zirconium.
Kalidindi and co-workers [10,11], on the other hand,
employed a Taylor-type rate sensitive crystal plasticity
model to simulate the deformation behaviour of Ti. The
effect of initial orientation has been investigated exten-
sively, with most studies being carried out on two different
orientations, namely the through thickness orientation with
strong basal texture and the in-plane orientation with pris-
matic texture [11,19]. It has been observed that the two
extremely different initial textures lead to different mechan-
ical responses. The basal orientation shows a higher yield
strength but a lower strain hardening rate, while the pris-
matic orientation shows lower yield strength and a higher
strain hardening rate. Crystal plasticity models have been
able to predict different mechanical responses with respect
to the initial orientation. The mechanical response of differ-
ent initial orientations can be indirectly influenced by the
value of stacking fault energy (SFE), which is different
for different planes in hcp metals like titanium (300 mJ m�2
in the basal plane and 150 mJ m�2 in the prismatic plane)
[24].
The deformation of titanium by virtue of its less than
ideal c/a ratio (1.588) is contributed by prismatic slip.
However, since the basal and the prismatic slip systems
provide only four independent slip systems, plastic defor-
mation in Ti has to be accommodated by hc + ai slip or
twinning. The major twinning systems that can operate in
compression of a single crystal Ti are {1 0 �1 2}h1 0 �1�1i,
{1 1 �2 2}h1 1 �2�3i and {1 1 �2 1}h�1�1 2 6i. The choice of the
twinning system depends on the initial orientation [5].
Twinning, being a polar transformation, is sensitive not
only to the magnitude of shear but also to the direction
of shear [25]. Depending on the loading direction, different
twin systems become active and alter the deformation
response, as well as the texture evolution, in Ti. A detailed
study of the strain hardening behaviour of polycrystalline
titanium under compression, plane strain compression
and torsion has been carried out by Salem et al. [8–10].
The authors [8] categorized three distinct stages in the
stress–strain curve, labelled A, B and C. The first regime,
stage A, was characterized by a decreasing strain hardening
rate, similar to the dynamic recovery regime observed in
high stacking fault energy (SFE) metals. This was followed
by stage B, a region with increasing strain hardening rate in
both plane strain and uniaxial compression. Stage C exhib-
ited a decreasing strain hardening rate. During stage A,
deformation was accommodated only by slip. The activa-
tion of cross slip between the basal and prism planes with
a common slip direction leads to easy dynamic recovery
and, hence, a lower strain hardening rate. The pyramidal
hc + ai slip system, being considerably harder than the
prism or basal slip systems, could be activated to make
up the five independent slip systems. In stage B, twinning
3432 N.P. Gurao et al. / Acta Ma
led to an increase in strain hardening rate as twin activity
increased with increasing strain. As the twin systems oper-
ative in hcp materials are non-coplanar with the slip sys-
tems, a considerable amount of hardening occurred
during stage B. The decreasing strain hardening rate in
stage C was explained due to increasing difficulty in pro-
ducing deformation twins with further straining. This the-
ory proposed by the authors [8] was further supported by
simulations obtained from a Taylor-type crystal plasticity
model by Wu et al. [11]. However, most of these studies
did not consider the effect of strain rate on the strain hard-
ening response and texture evolution. Such studies are of
paramount importance, as twinning and additional mecha-
nisms such as shear banding are expected to play a very
important role in the deformation behaviour of hexagonal
materials at high strain rates. The present work is an
attempt to complement the findings of Salem et al. [8] for
the quasi-static deformation of titanium and to explore
the validity of these concepts in a dynamic strain rate
regime.
2. Experimental
Cylindrical samples of 6 mm diameter and 9 mm height
were obtained from a rolled block of commercially pure
(CP) Ti plate with a strong basal texture. Samples were
machined in four different orientations (Fig. 1a), namely
I–IV, to ensure different starting textures. Samples I–III
were machined along the RD, ND and TD directions of
the rolled block while sample IV was machined at a 45�
angle to the RD–ND plane. Each of these samples was sub-
jected to compression testing at a strain rate of 3 � 10�4 s�1
in a servo-hydraulic DARTEC mechanical testing set-up to
a true strain of e = 0.36. The high strain rate tests at
1500 s�1 were carried out using a split Hopkinson pressure
bar (SHPB) with incident and transmission bars of 13 mm
diameter and 1300 mm length. Cylindrical specimens of
all four orientations with diameters and heights of 6 mm
were used for the test. A MoS2 lubricant was used between
the sample and the bar interfaces. For a general discussion
see the relevant ASM Handbook [26]. The samples were
then sectioned along the compression direction and sub-
jected to metallographic preparation with electropolishing
in a solution of 60 ml of perchloric acid in 600 ml of meth-
anol and 400 ml of butycellosolve. The samples were etched
with Krolls reagent for optical microscopy, while EBSD
studies were carried out by field emission gun scanning elec-
tron microscopy (FEG-SEM) (SIRION). A step size of
1 lm was used to capture large area scans for the starting
and deformed samples. High resolution EBSD measure-
ments were done using a step size of 50 nm for the samples
deformed at high strain rate. Data acquisition and analysis
were carried out using TSL software version 5.2.
3. Viscoplastic self-consistent simulations
In the present investigation viscoplastic self-consistent
ialia 59 (2011) 3431–3446
simulation code VPSC-6 was used to simulate the experi-
mental texture. The VPSC model is described in detail in
ater
RD (x)
TD (y)
ND (z)
I
III
0110
0110
01122000
N.P. Gurao et al. / Acta M
Tome´ et al. [27] and the PTR scheme in Lebensohn and
Tome´ [13]. The texture measured by EBSD was discretized
to obtain 2000 single orientations, that were used as input
to the model. The critical resolved shear stress (CRSS) and
hardening parameters for Voce type hardening were
obtained by fitting the stress–strain curve for sample II,
for which minimum twin activity is observed. Wu et al.
[11] obtained these values from shear tests on titanium,
wherein twinning is minimal, from the hardening curves,
as against stress–strain curves in the present case. In addi-
tion to extended Voce hardening (for statistical disloca-
tions), hardening due to the presence of twin barriers is
superimposed [13].
We have adopted the uncoupled approach as against the
coupled grain approach used by Proust et al. [18]. In this
approach the increase in twin activity and subsequent sat-
uration with the amount of deformation in Zr was mod-
elled by using negative hardening parameters for
twinning. However, they followed this strategy to model
up to a strain of 0.3. As a consequence, with the increase
in amount of strain there was an increase in twinning activ-
ity. This is not the case for titanium, where it has been
shown experimentally that twinning is replaced by pyrami-
dal slip at higher strains. In the present work the minimum
volume fraction of twins in a grain is assumed to be 0.1,
while a saturation value of 0.5 has been used in the simula-
01122000
Fig. 1. (a) Geometry of samples obtained from a Ti plate with initial strong ba
figures for samples with different orientations.
(a)
IIIII
I
IV
II
IV
0110
0110
01122000
ialia 59 (2011) 3431–3446 3433
tions. The activation of any particular slip system as well as
twin system is a strong function of initial orientation and,
hence, different samples with different orientations show
dissimilar stress–strain and strain hardening responses. In
the present investigation, microstructural evidence of twin
boundaries was used to fine tune the model. The fraction
of the twin boundaries obtained from orientation imaging
microscopy (OIM) by EBSD was used as an indication of
the activity of that particular twin system. A higher frac-
tion of a particular type of twin boundary indicates a
higher activity of that particular twin system.
4. Results
4.1. Initial texture
Inverse pole figures corresponding to the compression
direction (CD) representing the initial texture of the start-
ing samples as measured from large area EBSD scans are
shown in Fig. 1b. The differently oriented Ti samples
extracted from the rolled plate ensured that the initial tex-
ture was significantly different for each sample. Sample I,
cut along RD, showed a majority of orientations along
the h1 0 �1 0i and h2 �1�1 0i lines, with maximum intensity
at h3 �1�2 0i, while sample II, cut along ND, had a strong
near basal texture with a maxima for the h2 �1�1 4i compo-
(b)
01122000
sal texture and (b) corresponding compression direction (CD) inverse pole
nent. Sample III, cut along TD, was characterized by a
spread of orientations along the h1 0 �1 0i–h2 �1�1 0i line.
The texture was relatively weaker and showed higher inten-
sities for the h6 �3�3 2i and h1 0 �1 0i orientations. For sample
IV, cut at 45� to the ND–RD plane, most of the crystallites
were oriented towards the h2 �1�1 0i–h1 0 �1 0i region of the
inverse pole figure with a maximum intensity at h1 0 �1 0i.
4.2. Mechanical behaviour
The plastic region of the true stress–strains curve
obtained from the compression tests at low strain rate,
shown in Fig. 2a, indicates that the differently oriented
samples have distinctly different responses. The yield
strength of sample II was higher than that of the other
three samples and also showed a low strain hardening rate.
In the case of sample I the true stress increased steadily
with strain up to e = 0.15 and then increased steeply to
reach a maximum value amongst all the studied samples
at e = 0.36. The stress in the case of sample II increased
gently to reach a value slightly less than that for sample
I. Samples III and IV showed almost the same true stress
at e = 0.36, which was lower than that for sample II. The
stress–strain curve of sample IV coincided with the
stress–strain curve of sample I up to e = 0.15 and then devi-
ated to coincide with the sample III curve, giving the same
stress at e = 0.36. The samples tested at high strain rate
pared with the low strain rate deformed samples. The
increase in yield strength was lower for samples I and II,
while a substantial increase was observed for samples III
and IV. However, the nature of the stress–strain curve
remained similar for sample II at low and high strain rates,
showing minimum strain hardening compared with the
other three samples. In order to study the dependence of
orientation on the strain hardening behaviour of titanium
the strain hardening curves were calculated numerically.
The strain hardening rate and stress were normalized with
respect to the shear modulus of titanium (44 GPa) and the
normalized strain hardening rate dðr�r0Þ=deG
� �
versus normal-
ized stress ðr�r0ÞG
� �
for the low and high strain rate
deformed samples are plotted in Fig. 2b. As expected, the
hardening curves showed the three regimes of strain hard-
ening observed by Salem et al. [8]. Samples I, III and IV
deformed at low strain rate showed the three stages of
strain hardening quite distinctly, while sample II showed
dominant stages A and C. The onset of stages B and C
was different for these samples. Amongst these samples
sample III showed the onset of stage B at higher values
of strain, indicating late onset of twinning for this texture.
Sample II with a strong basal texture was markedly dis-
tinct, with stage A dominant to large strains, indicating
an absence of twinning. Also, the slope of the hardening
(a
(b
3434 N.P. Gurao et al. / Acta Materialia 59 (2011) 3431–3446
showed an increase in stress level at a given strain com-
0
200
400
600
800
1000
0 0.1 0.2 0.3 0.4
Strain
St
re
ss
(M
Pa
)
I
II
III
IV
RSL
0
0.01
0.02
0.03
0.04
0.05
0.06
0 0.005 0.01 0.015 0.02
Normalized Stress
N
or
m
al
iz
ed
S
tra
in
H
ar
de
ni
ng
R
at
e
I
II
III
IV
RSL
Fig. 2. (a) True stress–strain curves and (b) hardening curves for
curve showed the minimum strain hardening rate for
sample II. Another important observation is that the hard-
0
200
400
600
800
1000
Strain
St
re
ss
(M
Pa
)
I
II
III
IV
0 0.1 0.2 0.3 0.4
RSH
0
0.02
0.04
0.06
0.08
0.1
0.12
0 0.005 0.01 0.015 0.02 0.025
Normalized Stress
N
or
m
al
iz
ed
S
tr
ai
n
H
ar
de
ni
ng
R
at
e I
II
III
IV
RSH
)
)
samples I–IV tested at low and high strain rates, respectively.
ening curve for sample II was shifted to the right, as it had
got a higher yield point but a lower strain hardening rate
due to the absence of twinning.
The hardening curves for the samples tested at the high
strain rate were similar to those at the low strain rate, how-
ever, there were some important distinctions. A higher
hardening rate was observed at the high strain rate, in addi-
tion to a higher stress level. However, the difference between
various samples disappeared and the hardening curves of
samples I, III and IV almost coincided. The strain harden-
ing curves for all four orientations were similar, unlike at
the low strain rate, where stage B is absent in sample II.
4.3. Evolution of texture
Despite a marked difference in the initial texture of the
four samples, the overall texture evolution in all the cases
was near basal at low strain rate (Fig. 3a). In addition,
there was a clustering of orientations near h2 �1�1 4i for all
four samples. Some crystallites were oriented near the
h2 �1�1 0i corner of the inverse pole figure. A spread of ori-
entations from h2 �1�1 4i to h1 0 �1 4i was observed in sam-
ples I, II and IV, while sample III shows a spread of
orientations along the h0 0 0 1i–h2 �1�1 0i line. The reorien-
tation of crystallites towards the basal orientation was
dominant in samples I and IV, while there was little change
in texture of sample II, which had a strong basal texture.
Although the texture in sample II was different from the
remaining three samples, it is believed that with increasing
strain it will also form the near basal h2 �1�1 4i orientation,
which is a stable end orientation. At a high strain rate,
there was a slight weakening of texture and an additional,
however weak, h1 0�1 0i component appeared that was
absent from the samples deformed at a low strain rate
(Fig. 3b). All the samples showed a texture characterized
by the presence of orientations near the h2 �1�1 0i and
h2 �1�1 4i components. There was a spread of orientations
from these components towards the line joining the lines
h2 �1�1 0i–h1 0 �1 0i and h0 0 0 1i–h1 0 �1 0i. It can be
observed that the high strain rate deformed samples mani-
fest a higher strength of the h2 �1�1 0i component compared
with the h2 �1�1 4i component, which is dominant at the low
I II
IIIIV
01100110
0110 0110
0112
01120002 0002
4112
002
N.P. Gurao et al. / Acta Materialia 59 (2011) 3431–3446 3435
01120002 0002
I
III
0002 0002
00002
0112
0112
0110
0110
(a)
(b)
Fig. 3. Compression direction (CD) inverse pole figure showing final texture a
strain rate (HSR).
0112
II
IV
0112
0112
0110
0110
fter deformation of samples I–IV at (a) low strain rate (LSR) and (b) high
strain rate. Another important observation was the spread
of orientations towards h1 0 �1 0i from h2 �1�1 0i in the high
strain rate deformed samples. The texture was stronger
for samples I and II while a weaker texture evolves in sam-
ples III and IV.
4.4. Evolution of microstructure
Optical microscopy as well as scanning ele
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