1Department of Mechanical Engineering, Imperial College London,
London SW7 2AZ, UK
2Department of Materials, Royal School of Mines, Imperial College
London, London SW7 2AZ, UK
3Department of Mechanical Engineering, Incheon National University,
Incheon 22012, South Korea
*Corresponding author. Email address:
[email protected]
Abstract
Titanium alloys are widely used in light weight applications such
as jet engine fans, where their mechanical performance under a
range of loading regimes is important. Titanium alloys are
mechanically anisotropic with respect to crystallographic
orientation, and remarkably titanium creeps at room temperature.
This means that the strain rate sensitivity (SRS) and stress
relaxation performance are critical in predicting component life.
In this work, we focus on systematically exploring the macroscopic
SRS of Grade 1 commercially pure titanium (CP Ti) with varying
grain sizes and texture using uniaxial compression. Briefly, we
find that Ti samples had positive SRS and samples compressed along
the sheet rolling direction (RD) (i.e. soft grains dominant) were
less rate sensitive than bars compressed along the sheet normal
direction (ND) (i.e. hard grains dominant). We attribute this rate
sensitivity to the relative activity of slip and twinning. Within
the grain size range of , we observe an increase in the rate
sensitivity, where volume fraction of T1 tensile twins was low, and
the twin width at different strain rates were similar. These
observations imply that the macroscopic rate sensitivity is
controlled by the ensemble behaviour of local deformation
processes: the amount of slips accumulated at grain boundaries
affects the SRS, which is grain size and texture dependent. We hope
that this experimental study motivates mechanistic modelling
studies using crystal plasticity, including strain rate sensitivity
and twinning, to predict the performance of titanium alloys.
Keywords: Strain rate sensitivity, pure titanium, macroscopic
uniaxial compression, twin, dislocation
Introduction
Jet engines are a critical engineering structure in the modern life
and in these structure titanium alloys are selected for use in the
fan and lower temperature sections due to their excellent specific
strength (strength to weight) and fatigue resistance [1,2]. In
these applications, the role of strain rate sensitivity is likely
important, especially in cold dwell fatigue where time sensitive
deformation modes are thought to control fatigue crack nucleation
and this has motivated some recent studies that focus on extracting
the strain rate sensitive slip strengths [2–4] and their role in
controlling the dwell susceptibility in Ti alloys [5,6].
The role of grain size in deformation has been widely studied,
often with a focus on simple empirical observations such as the
Hall-Petch effect [7–9] which promotes the idea that there is a
simple scaling law that links grain size to slip strength. However,
this correlative ‘law’ has recently been called into question, and
microstructure blind Bayesian analysis approaches suggest that
deformation could be vary from system to system and be controlled
using weakest link theory [10]. In practice, the role of strain
rate sensitivity, the activation of multiple different deformation
modes (e.g. slip [11,12], twinning [13,14]), and how the grain
boundaries impart strength due to pile-up [15–18] or forest
hardening mechanisms [19] likely complicates matters and therefore
we are motivated to study the correlation of microstructure and
mechanical performance across grain sizes and textures in these
alloys. Recently there has been a flurry of activity to extract the
mechanical response of individual slip systems using from single
grain tests with micro-cantilevers [20] or micropillars [2,4]. We
note that micro-cantilever bend tests are not well suited to strain
rate sensitivity testing, as the bending geometry naturally imparts
a significant strain gradient during testing and therefore are
likely to have a relative strain rate insensitivity compared to the
micro-pillar geometry. However, we note that recent work by Gong et
al. [20] in commercially pure zirconium has indicated a good
correlation between use of the micro-cantilever derived size
independent slip strengths and quasi-static macroscopic compression
tests of macroscopic ~70 µm grain size compression tests, where
slip is dominant and grain size strengthening is limited.
Scaling of direct slip strength from micro-scale tests up to
macroscopic polycrystalline samples has proved difficult, and as
such Cuddihy et al. [20] utilised calibration of their strain rate
sensitive crystal plasticity model using published work by Zhang et
al. [6]. We anticipate that this could be related to role of
complex hardening mechanisms near grain boundaries and in the
multi-axial deformation modes of polycrystalline deformation.
The stress-strain behaviour of many materials is significantly
strain rate, , sensitive [21]. This can be characterised through
analysis of the strain rate sensitivity (SRS) [22], where the
stress-strain curves are obtained using the uniaxial tension,
compression or indentation tests [23–28].
In these tests, often a very simple constitutive relationship is
used for the loading behaviour, the strain rate sensitivity
exponent (described as an m value) or the stress component
(described as n value, ) can be determined using either the
constant strain rate method (CSRM) [22], the stress relaxation
method (SRM) [29–33] or strain rate jump test (SRJ) [3,34]. In the
same alloy systems, there is significant variation in SRS values
can be different observed with respect to the experimental methods
[3,26,33] and in-part this is likely due to the different rate
sensitive deformation mechanisms, as well as the fact that the ‘m
factor’ varies systematically with crystal orientation due to
simple geometry [6].
This can be characterised through analysis of the strain rate
sensitivity (SRS) [22], where stress-strain curves are obtained
using the uniaxial tension, compression or indentation tests
[23–28] performed at different strain rates.
For constant strain rate method (CSRM) analysis, samples are
deformed uniaxially at a range of strain rates. The flow stress at
a particular strain is extracted from each curve and plotted
against strain rate and the gradient of these data is used to
extract using equation (2). If the gradient is flat, then it is
presumed that these tests probe the same deformation mechanisms and
therefore describes an empirical strain rate sensitivitiy of these
mechanisms[22].
Stress relaxation (SRM) tests [29–33] are carried out when samples
are deformed under displacement control, at a variable strain
rates. The displacement is ceased at a fixed value, and decay in
the recorded load is observed as a function of time [29]. The
strain rate sensitivity, , can be calculated from the relations of
applied stress ( and a stress relaxation rate (: . The recorded
stress-time relationship is dependent on the plastic properties of
specimen and the elastic properties of the testing machine and
specimen [29,30].
Recently there has been interest in strain rate jump (SRJ) tests,
as these offer the potential to probe strain rate sensitivity of
the same sample in one test [3,34]. In a SRJ test, deformation is
performed and the strain rate is abruptly changed during loading
The value from SRJ test is based on the logarithmic ratios of
stresses () and strain rates () before and after a stain rate jump
as following the equation described by Pilling and Ridley
[35]:
where is the jumped stress on the jumped strain rate curve, the
corresponding stress, , is determined from the specific
stress-strain curve, is the jumped strain rate, and is the original
strain rate.
Compared with constant strain rate method (CSRM), the advantage of
strain rate jump (SRJ) test is that the strain rate sensitivity is
determined from a nearly constant microstructure and the variation
of with strain (thus microstructure) can be found [22]. However,
Kim et al. [22] demonstrated that errors in strain rate can result
in considerable errors in calculated SRS values, since test errors
in strain rate could be of the same order as the strain rate jump (
per cent). The SRJ test, therefore, needs accurate imposition of
strain rate for the accurate determination of SRS. By contrast, the
CSRM considers a large range of strain rates covering several
orders of magnitude, so errors of strain rate of the order of 10
per cent do not influence too much for the result of SRS from CSRM.
In this situation, CSRM is likely to be provide more reliable
values of SRS.
In this work, we employ a constant strain rate method (CSRM) and
the SRS can be obtained from an empirical equation described by
Backofen et al. [36] from a flow stress and a strain rate at
constant strain and temperature:
(2)
where is a material constant, is the true flow stress and is the
true strain rate. From the stress-strain curves under constant
strain rate compression, the m value can be determined by the
following equation with a plot of stress () versus strain rate ()
in log-log form [21,22]:
(3)
As titanium alloys are typically anisotropic, the SRS is likely to
be varied with grain orientations and the associated slip systems
[37]. A previous study on micropillar test from Jun et al. [4] in
Ti 624x alloys demonstrated that prism slips are more rate
sensitive than basal slips in single phase within a dual-phase Ti
alloys. In Jun et al.’s work, this difference was attributed due to
the likely impact of wavy basal dislocations and cross slip in the
basal pillar, as compared to planar ‘deck of cards’ crystal slip in
pillars well oriented for prism slip [4].
While direct measurements of SRS using micro-tests can provide
insight into the nature of slip activity, we still have yet to
establish that slip system dependent SRS observed at micro-scale
[28,38] can be linked to the macroscopic SRS [25,39–42] in dual
phase or other Ti metals/alloys. As a first step in this story, we
investigate the macroscopic SRS with single (α) phase commercially
pure titanium (CP Ti). To explore the role of polycrystalline
deformation on SRS, we compare samples with different grain sizes
and textures at a range of strain rates within the same alloy
system, ultimately with the view to develop a correlation between
smaller scale tests and polycrystalline samples tested at different
strain rates.
In the present work, we generate a series of samples with varying
grain sizes and textures from rolled sheet of commercially pure
grade 1 titanium. Samples with varying grain sizes were generated
using 24 hr anneals at varying temperatures and two texture
components were deformed mechanically using compression.
Macroscopic stress-strain behaviour at varying displacement (i.e.
strain) rates, where stress was captured using the load cell and
strain was evaluated using in-situ macroscale digital image
correlation (DIC) [43–46]. Strain rate sensitivity was
characterised using m-factor analysis. Post deformation,
characterisation of deformation activity was evaluated using
optical microscopy and conventional electron backscatter
diffraction (EBSD).
Experimental methods
2.1. Material preparation
A rolled sheet of grade 1 CP Ti was kindly supplied by Timet UK Ltd
(Birmingham). To study the grain size effect on strain rate
sensitivity, as received CP Ti samples were heat treated at 700 ,
730 , 800 , 830 for 24 hours and furnace cooled with a rate of 1
°C/min so as to produce a microstructure with different grain size
(shown as Figure 1). The transus temperature for grade 1 CP Ti is
890 15 [47].
Figure 1. a) Heat treatment (HT) processing route for as received
CP Ti; b) optical microscope images and c) grain size measurement
of heat treated samples with Texture 1 (T1) and Texture 2
(T2).
Prior to mechanical testing, samples were ground to 10 after
cutting and polished with 50 OP-S (Oxide Polishing Suspensions)
diluted with by a ratio 1:5 of OP-S: for EBSD imaging. For
microstructural characterisation, polished samples were etched
using Kroll’s Reagent for 30 s (2% HF, 10% HN and 88% ).
2.2. Microstructural characterisation maps
Optical microscopy and electron backscatter diffraction (EBSD) were
used for the microstructural characterisation. Optical microscopy
was conducted using polarised light microscopy to reveal grain size
and morphology changes. Images (see Figure 1 and 4) were captured
and then interrogated using ImageJ software. The grain size of the
heat treated samples was measured from the optical microscope
images using a circular intercept method following ASTM E112 Abrams
Three-Circle procedure [48,49]. The number of intercepts in the
counting field was around 40 due to the large grain size of
annealed samples compared to the sample size. The variation in
grain size of was found by shifting the circles for intercept
analysis.
EBSD maps were captured on a FEI Quanta 650 with Bruker eFlashHR
EBSD system equipped with eFlashHR camera and Esprit v2.0 software.
A high current mode was used with an accelerating voltage of 25 kV.
An initial texture (see Figure 2) and EBSD maps (see Figure 3) of
with a step size of 20 were captured on a face perpendicular to the
ZZ axis and Schmid factor analysis (see Figure 5, using a simple
assessment of the remote loading configuration) were used to
evaluate likely active slip systems [37] to identify “soft” and
“hard” grains (with respect to loading axis).
Figure 2. {0001} Pole figures generated from EBSD Euler maps for
pure Ti after 24 hour heat treatment at (a) 700 C and (b) 830 C,
where the horizontal axis is the rolling direction (RD) and the
vertical is the transverse direction (TD) for Texture 1 (T1)
samples; the horizontal is the normal direction (ND) and vertical
is the rolling direction (RD) for Texture 2 (T2) samples: the
loading direction for T1 samples is the TD, for T2 samples is the
ND. The size of specimen is Geometry plots of performing the
microstructure characterisation on T1 and T2 pure Ti are shown in
(d).
Figure 3. EBSD maps (IPFZ colouring) showing grain structures and
textures in (a) 700 C and (b) 830 C annealed pure Ti samples.
2.3. Constant strain rate compression tests and DIC
The macroscopic compression tests were carried by Shimadzu AGX10
screw thread mechanical testing frame, under variable displacement
rates of the crosshead to obtain different target strain rates,
i.e. 0.1, 0.01 and 0.001 respectively. The heat treated CP Ti
samples were compressed along two directions, rolling direction and
normal direction (i.e. Texture 1 and Texture 2 samples), to get
stress-strain curves for the strain rate sensitivity (SRS)
calculation. The sample for each condition was tested once. The
error of stress component was found to be based on testing three
times on the sample with one condition.
Time-series images were taken for the compressed surface by a
microscope equipped with QCapture Pro 6.0 software. Those
time-series images of surface displacement, tracked using copier
toner particles, were then cross correlated and quantified by
Digital Image Correlation (DIC) technique to obtain the strain
response of large grain CP Ti under engineering compression.
DIC was performed using Davis 8.3 developed by LaVision Imaging
Company, Gettingen, Germany [50]. The “differential” (i.e. frame n
to frame n-1) correlation method in this software was chosen for
tracing the movement of 3 µm photocopier particles. After
correlating time-series images, the frame averaged strain and
achieved strain rate were calculated and temporally matched against
the load data reported from the load-cell.
The volume fraction of twins on deformed pure Ti was calculated by
measuring the area of twins on the characterisation face (see
Figure 4).
Figure 4. Polarised optical microscope images of heat treated pure
Ti after the deformation. Row a) to e) are pure Ti heat treated at
different temperature. Column 1) to 3) are pure Ti deformed at
different target strain rate (from 0.1 to 0.001 ).
In this study, the twin volume fraction of all types of twins was
artificially estimated from the twin area fraction [50] through a
combined manual and computer based imaging process for the
polarised optical microscope images. Twins were traced by hand on
tracing paper and coloured in. These images were scanned and
thresholded in ImageJ software [51] for area fraction calculations
[52] (see Figure 5). EBSD technique could also be used to estimate
the twin area fraction of different twin variants by measuring the
area bordered by the twin boundaries. The error comes from the
measured twin boundary length and scan step size [53]. However,
using optical microscope images makes the estimation on a bigger
map feasible [52].
Figure 5. An example of how to measure the area fraction of twins
from an optical microscope image: a) polarised optical image of
deformed 830 C heat treated pure Ti under 0.001 strain rate; b) the
traced twins by hand on a tracing paper; c) twins are filled with
black colour for area calculation.
2.4. Contribution of twinning and slips to the plastic strain
The total plastic strain is carried by twinning and slips in the
deformed sample, and the contribution from twinning can be
estimated using n: where is the volume fraction of twinning and s
is the twinning shear [54]. The area fraction of twinning was
measured from the optical microscope images under polarised light
(see Figure 4), and assumed to correlate with the volume fraction.
The twinning shear of T1 tensile twins in titanium alloy was 0.17
[37,55]. We assume that the remaining strain is supported by
plastic slip, and can calculate a ratio of strain accommodation for
slip vs twinning (see Figure 11).
Results
3.1. Initial grain size characterisation
The grain size of heat treated CP Ti samples with equiaxed grain
structure was measured from optical micrographs using the Abrams 3
circle procedure [56] and plotted in Figure 1(c).
3.2. Activation of <a> prism slips and pyramidal twin
The Schmid factors for <a> prismatic {10}slip systems along
the loading axes (XX direction shown in Figure 6). The white colour
(high value of 0.5) indicates a soft orientation well aligned for
slips in CP Ti, and the dark colour (low value of 0) indicates a
hard orientation poorly aligned for slips. Most grains in pure Ti
with T1 are favourably oriented for <a> prismatic slips while
most grains in T2 are hard to activate <a> prism slip.
Figure 6. Schmid factor maps with respect to <a> prismatic
slip system for (a) 700 C T1 CP Ti and (b) 830 C T1 & T2 CP Ti.
Grains with Light colour are favourably oriented for slip (i.e.
soft grains); grains with dark colour are unfavourably oriented
(i.e. hard grains). The line figures represent the proportion of
grains that have a high Schmid factor.
Among the four twinning systems in pure titanium [57], the most
commonly observed twinning system at room temperature and these
strain rates is T1 tensile twins [58]. Hence, the Schmid factors of
T1 pyramidal twins along the compression axis in CP Ti were checked
with the aid of MTEX [59] (see Figure 7). The grains with yellow
colour (0.5) indicates that T1 tensile twins can be easily
activated in these grains. The grains with green (0) and blue (−
0.5) colour indicates that twins are hardly activated in these
grains, as twinning only occurs for certain deformation
orientation, thus, pyramidal twinning cannot occur even when the
grains have a high absolute value of Schmid factor (e.g.
0.5).
Figure 7. Schmid factor maps with respect to T1 pyramidal twinning
system in (a) 700 C and (b) 830 C T1 & T2 pure Ti. Grains with
yellow colour are favourably oriented for pyramidal twinning and
grains with green and blue colour are unfavourably oriented.
Histograms show the distribution of Schmid factor for activating
the T1 pyramidal twins.
Compression along XX (see Figure 7) may result in activation of T1
extension twins (extension twins are activated due to local
compatibility strains during a compression test). The histograms in
Figure 7 indicate that T1 extension twins can be easily activated
for most grains in Texture 1 CP Ti and few grains in Texture 2 CP
Ti. This could be the reason for the higher volume fraction of
twins in T1 CP Ti. The more easily generated nucleation sites are
assumed to result in the higher value of twin volume
fraction.
3.3. SRS calculation
The stress values used for strain rate sensitivity calculation are
taken at three different plastic strains from DIC (i.e. 6%, 7% and
8%) and are plotted with the achieved strain rate in log-log form.
The plastic strain was calculated by using DIC corrected strain
minus strain at 0.2% proof stress. The SRS exponent, m, is measured
as the gradient of fitted line (see Figure 8), in accordance with
the Equation (3). The average value of the gradients is chosen as
the m value, while the standard deviation of three gradients is
calculated as the arm of error bar (see Figure 9).
Figure 8. Left column: engineering stress-strain curves for heat
treated pure titanium. Right column: flow stress vs. strain rate
(log-log form) for heat treated pure Ti: the gradient of fitted
line was calculated as the strain rate sensitivity component, , of
the material.
3.4. Grain size effect on SRS
In Figure 9 a), the plot shows the relationship between SRS and
grain size of T1 CP Ti: the SRS increases with the grain size of CP
Ti from to , but drops to a low value for grain size . The
macroscopic SRS values for heat treated CP Ti are in the range of ~
0 to ~ 0.08.
In Figure 9 b), volume faction of twins is compared for different
grain size T1 CP Ti under different strain rates. For samples with
the same grain size, T1 CP Ti tends to have higher volume fraction
of twins at higher strain rates (also shown in Figure 10 b)).
Hence, the nucleation of twins in CP Ti is likely to be strain rate
sensitive, i.e. more nucleation sites can be activated at high
strain rate. For samples with different grain size, but at the same
strain rates, the twin fraction drops down from to with the
increase of grain size from to , but increases to by increasing the
grain size to . This observation shows that the grain size of CP Ti
influences the number of nucleation sites of twining relating to
SRS. The twin fraction variation regarding to grain size shows an
opposite trend with the strain rate sensitivity (see Figure 9 a)
and b)).
The twin widths in deformed T1 CP Ti were measured to study the
growth of twin (shown in Figure 9 c)). For samples with the same
grain size, T1 CP Ti normally has thinner twins at higher strain
rates (also shown in Figure 10 c)). Hence, the growth of twins is
also rate sensitive. However, the rate sensitivity of twin growth
is not the same for T1 CP Ti with different grain sizes. For
samples with size and , the twin width growth is sensitive to the
higher strain rate between and ; for samples with size , the twin
width growth is more sensitive to the lower strain rate between and
. As a comparison with Figure 9 a), the flow stresses of samples
with size are more rate sensitive. Therefore, the high growth rate
of twin width at high strain rates (e.g.) could be an underlying
reason for the high rate sensitivity of flow stress.
Figure 9. The change of a) strain rate sensitivity (SRS), b) volume
fraction of twins and c) twin width with the variation of T1 CP Ti
grain size at different achieved strain rates, i.e. , and .
3.5. Texture effect on SRS
The T1 and T2 samples have the same grain size, but different
texture (see Figure 2). The SRS values of T1 & T2 830 ºC heat
treated CP (see Figure 10 a)) show that T2 is more rate sensitive
while the SRS values for both T1 and T2 are relatively low (less
than 0.04) compared with CP Ti with other grain size (above
0.07).
The twin fraction variation regarding to texture shows an opposite
trend with the strain rate sensitivity (see Figure 10 a) and b)).
For the twin width shown in Figure 10, the twin growth of T1 is
more sensitive to the lower strain rate between and , while T1 has
lower SRS. These two observations keep constant with the discussion
for Figure 9.
Figure 10. The comparison of a) strain rate sensitivity (SRS), b)
volume fraction of twins and c) twin width for 830 C heat treated
CP Ti with T1 and T2. The achieved strain rates for T1 are, and for
T2 are, and .
3.6. Contribution of twinning and slips to the plastic strain
In Figure 11 for 830 C annealed T1 CP Ti, the stacked bar shows the
contribution of twinning () and slips () to the plastic strain (),
the scattered points indicate the ratio of to at the strain rate of
0.001. The is high and the ratio of is also high for T1 CP Ti with
grain size . The relative high amount of slips could be crucial for
its high SRS (see Figure 9).
Figure 11. For 830 C heat treated CP Ti with T1, the stacked bars
represent the contribution of slips (, blue) and the contribution
of twinning (red) to plastic strain () at strain rate. The
scattered points represent the ratio of over .
Discussion
In this work, macroscopic compression tests were exploited to study
the macroscopic performance of orientation dependent rate response
of CP Ti. The DIC technique for the strain correction made the
determination of SRS (i.e. m values) from stress-strain curves more
reliable.
There are two crucial issues on macroscopic compression, i.e. the
shape of sample and the correlation between stress and strain for
the compression curve. Some of the samples were not the exact
cuboid (due to machining tolerances), thus, there could be a
contact misalignment between the top surface of sample and the flat
punch. This resulted in slight realignment of the sample during the
‘elastic portion’ of the stress-strain response, and once the
sample starts yielding artefacts due to machining tolerance were
not significant. Furthermore, strain was measuring using DIC to
reduce the impact of the initial compliance and realignment during
this stage.
For the stress-strain curves used for SRS study, stress values were
recorded by the Shimadzu machine as a function of time; strain
values were calculated from the time-series images of speckled
sample surface taken by a microscope equipped with QCapture Pro 6.0
software. Problem is that stress values cannot exactly be matched
with the strain values, especially for the deformation at high
strain rate. For the high target strain rate (e.g. 0.1 ), it took
several seconds, e.g. 8 in this study, to activate the software for
taking images. We have used a time offset correction to match the
DIC data to our experimental stress-strain data, due to a lag
between frame capture and mechanical testing, using the recording
time of both data sets.
4.1. Grain size effect
The morphology of CP Ti samples which were heat treated below the
transus temperature (i.e. 890 for grade 1 CP Ti) keeps the same,
but the grain size increases with the heat treatment temperature
(Figure 1). Therefore, the activation of slip systems and twinning
mechanisms are similar for those CP Ti treated in the range of 700
to 830 (see Figure 2, 6 and 7).
For these heat treated CP Ti samples, more grains are oriented as
‘soft’ grains in T1 CP Ti and more grains are oriented as ‘hard’
grains in T2 CP Ti. In T1 samples, <a> prism slips have a
high value of Schmid factor. Hence, <a> prism slips are
easier to activate during the deformation in T1 CP Ti. The twinning
system for T1 CP Ti is the T1 pyramidal tensile twins.
Therefore, the grain size should affect the macroscopic SRS values
by influencing the nucleation of twins, the growth of twins and/or
dislocation motion, instead of slip systems or twinning
types.
4.1.1. Effect of twinning nucleation on SRS
The small amount of twin volume fraction relating to a large amount
of slips probably results in the high SRS of CP Ti with grain size
, e.g. 730 C and 800 C heat treated T1 CP Ti.
For the T1 CP Ti that has high volume fraction of twins, plastic
strain would be mainly carried by twins, instead of by creating
slips. As a result, few dislocations can pile up at the grain
boundaries of ‘soft’ grain, reducing the possibility of facet
formation. Therefore, the CP Ti samples which are prone to
generating a high twin volume fraction have a lower rate
sensitivity (compare Figure 9 & 11).
Normally, the larger titanium grains should tend to give higher
twin volume fraction [60]. However, in this experiment, more twins
are likely to be generated in the CP Ti with smaller grain size,
resulting in a low value of SRS (see Figure 9). A possible
explanation is that even the smallest grain size (i.e. the 700 heat
treated CP Ti with grain size ) in this experiment is large enough
to provide enough twin nucleation sites. The relation of twin
volume fraction and grain size, therefore, becomes different with
those samples whose grain size is less than .
Another striking point is that there are inflections for the
evolution of SRS and twin volume fraction with grain size at 830
heat treated CP Ti (Figure 9). The exceptional trend for the twin
width is also observed for the 830 heat treated CP Ti in the
deformed sample. The 830 °C heat treatment is close to the
β-transus temperature for CP-Ti. This changes the microstructure
and influences the interrelationship between slip based mechanisms
and twinning. This highlights that engineering SRS measurements, as
performed here, need to be used with care when there is an
interplay of plastic slip and twinning.
4.1.2. Effect of twin growth on SRS
For CP Ti with grain size and , twin grows much faster at the
lowest strain rate , while the twin growth is similar and slow at
strain rate and . Hence, the twin width is much wider for the CP Ti
with low SRS at the lowest strain rate (see Figure 9). The twin
width for the CP Ti with high SRS (i.e. grain size ) is thinner at
the lowest strain rate.
If 830 C T1 CP Ti is excluded in the discussion of the grain size
effect on SRS, the twin width at the lowest strain rate should
decrease with the increase of grain size: the smaller grains have
wider twins. The slip length is longer in the bigger grains, more
dislocations can pile up at the grain boundary making the
nucleation of new twins easier and the growth slower. Hence, twins
in large grain are thinner. By contrast, in smaller grain size, new
twins are harder to nucleate and are easier to grow once nucleated.
Hence, twins in small grain are wider at the lowest strain rate.
However, 830 C T1 CP Ti with the largest grain size does not obey
this law, probably due to its abnormal high nucleation sites.
In summary, the wider twins at the lowest strain rate could
interrupt the continuous slip across the whole grain which changes
the effect of work hardening. Hence, less number of dislocations
pile-up on the grain boundary and a slight flow stress reduction is
observed leading to a low SRS eventually (see Figure 9). The
thinner twins at the lowest strain rate could not interrupt the
dislocation motion, leading to a high value of SRS.
4.2. Texture effect
Based on the Schmid factor calculation with respect to slip systems
and twinning systems for 700 830 CP Ti, <a> prism slips are
preferentially activated in T1 samples; T1 tensile twins are easily
activated in T1 CP Ti, but hardly activated in T2 CP Ti (see Figure
6 & 7). Hence, the dislocation motion in T1 CP Ti is likely to
be <a> prism slip and the twining is likely to be T1
pyramidal twins. The prism slips and twinning are unlikely to occur
in T2 CP Ti.
Based on the measurement of volume fraction of twins and width of
twins for 830 CP Ti (Figure 10), higher volume fraction of twins
and higher rate of twin growth have been found in T1 deformed CP
Ti. Hence, in T1 CP Ti, twinning can carry more plastic strain
(i.e. ratio of is higher for T1 CP Ti, see Figure 11) and thicker
twins could interrupt more dislocation motions, while the
nucleation of twins and growth of twins are harder in T2 CP
Ti.
From SRS values for T1 and T2 830 CP Ti shown in Figure 10, T2 CP
Ti is more rate sensitive. Therefore, it can be concluded that the
less volume fraction of twins, and thinner twins at the lowest
strain rate in T2 CP Ti are likely to result in the high value of
SRS. Because more slips are generated to carry the plastic strain
and thinner twins could not interrupt the continuous slip across
the grain in T2 CP Ti. This conclusion keeps consistent with the
observation on SRS regarding to the grain size, i.e. fewer twins
and thinner twins are found in the Ti alloys with high SRS.
For the effect of slip type on SRS, although Jun et al.
demonstrated that prism slip is more rate sensitive in phase of
Ti6242 compared with basal slip [4], it cannot conclude that the
prism slips attribute to the macroscopic SRS of CP Ti, since the
twinning effect is not considered and the chemical content of CP Ti
is different with Ti6242. Hence, the effect of basal slips and
prism slips on SRS of CP Ti is unknown.
4.3. Effect of strain rate on twinning
In this work, the strain rate is found to have effect on twinning
mechanism. In Figure 9 and Figure 10, the strain rate affects the
twin fraction and twin width: reducing the strain rate can decrease
the volume fraction of twins and increase the twin width.
As shown in Figure 8, CP Ti is stronger at high strain rate (e.g.
). This means that the SRS, m component, should be positive for the
large grain CP Ti. There are several possible reasons for its
stronger behaviour at high strain rate: the more easily nucleated
twins at high strain rate could contribute to this (i.e. positive
rate sensitivity of twin fraction); the limited number of
dislocation motion at high strain rate could also have an effect,
as the strain carried by twins increases with the strain rate while
the total plastic strain is fixed; the thin twin width at high
strain rate could be another reason for the higher stress at higher
strain rate.
In summary, high strain rate can introduce more nucleation sites
for twins (i.e. higher volume fraction of twins), but reduce the
twin width (i.e. not enough time for twin width growth), ultimately
resulting in the positive rate sensitivity of CP Ti.
Conclusions
The volume fraction of twins and twin width have a significant
effect on the macroscopic SRS of CP Ti with respect to grain size
and texture. Regarding to the grain size effect on SRS, low volume
fraction of twins and thin twins at the lowest strain rate have
been found in CP Ti with grains , leading to a high value of SRS (~
0.070). Regarding to the texture effect on SRS, 830 C T1 samples
(i.e. soft grains dominant) has a less rate sensitivity (~ 0.006)
than T2 CP Ti (i.e. hard grains dominant, ~ 0.011), where prism
slips and T1 tensile twins are more easily activated in T1
samples.
The mechanism of nucleation and growth of twining is important for
understanding the rate sensitivity of CP Ti. The CP Ti samples
which have easy mode for twin nucleation and wide twin at low
strain rate are more likely to have relatively low SRS, such as T1
CP Ti with grain size . Due to the higher volume fraction of twins
and wider twins in those CP Ti, less dislocations are generated to
carry the plastic strain, and thicker twins could interrupt the
continuous slip, thus, less dislocations can pile up at the grain
boundaries of ‘soft’ grain, resulting in a less possibility of
facet formation, thus, a lower rate sensitivity.
Data Statement
The data from this paper can be found as a Zenodo repository at
< 10.5281/zenodo.1038216>.
Author Contributions
QL conducted DIC, mechanical testing, characterisation and analysis
of the data. TSJ and QL conducted the EBSD characterisation. TBB
and TSJ jointly devised the experiments and supervised the work.
All authors contributed to drafting the final manuscript.
Acknowledgement
This work was conducted within the HexMat programme grant
(www.imperial.ac.uk/hexmat) funded by EPSRC (EP/ K034332/1). TBB is
also funded through his fellowship from the Royal Academy of
Engineering. We would like to thank Professor Fionn Dunne for many
helpful and enlightening discussions on strain rate sensitivity,
mechanical testing, crystal plasticity and the role of grain size.
EBSD Microscopy as carried out within the Harvey Flower Electron
Microscopy Suite at Imperial College and in particular, we would
like to thank Drs Mahmoud Ardakani and Vivian Tong for training and
support of instrument usage. Mechanical testing was performed using
equipment funded within the Shell AIMS UTC. We thank Matthew Thomas
of TIMET UK for kindly supplying the commercially pure titanium
sheet. We thank Dr Chris Gourlay for provision of the DaVis
software and helpful training and advice from Te-Cheng Su on its
use.
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