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Microscopic strain localisation in Ti-6Al-4V during uniaxial tensile loading
D. Lunt1, J. Quinta da Fonseca1, D. Rugg2, M. Preuss1
1Material Science Centre, University of Manchester, Manchester, M13 9PL, UK
2Rolls-Royce PLC, Elton Road, PO Box 31, Derby, DE24 8BJ, UK
KeywordsTitanium alloys, Macrozones, Tensile, EBSD, DIC, Plasticity
AbstractThe titanium alloy Ti-6Al-4V is investigated in terms of the effect of macrozones
within the microstructure through cross correlation of local strain measurements and
microstructure, using digital image correlation (DIC) and electron backscatter
diffraction (EBSD) techniques. Three different product forms of Ti-6Al-4V
including strong-, intermediate- and a no-macrozone condition with a weak texture
have been investigated focusing on the impact of the primary macrozone orientation,
macrozone dimensions and loading direction. Strain localisation was characterised at
the microscale using optical microscopy during in-situ uniaxial tensile loading and
analysing the recorded images using digital image correlation. The no-macrozone
material and the strong-macrozone condition loaded parallel to the macrozones
exhibited homogeneous strain behaviour in both the elastic and plastic strain regions.
The strong (soft-orientated) macrozone condition loaded at 45 and 90 both
exhibited heterogeneous strain behaviour in grains with their c-axis oriented
perpendicular to the loading direction, while the intermediate (hard-oriented)
macrozone material exhibited heterogeneous strain behaviour when the majority of
grains had their c-axis parallel to the loading direction. The strong-macrozone
1
material showed a direct correlation between macrozones with their grains
favourably oriented for prismatic slip and high strain regions when loaded at 45 to
the elongation direction. Correlating a region of high strain localisation with Schmid
factor maps for basal and prismatic slip, suggests a likelihood of basal slip when
loading at 90.
1. IntroductionTitanium alloys are widely used in the aerospace industry due to their high specific
strength, corrosion resistance, suitability for moderate temperature applications and
good fatigue performance [1]. The workhorse alloy for aerospace applications is Ti-
6Al-4V, which is a two-phase, α+β Ti alloy. The initial ingot has a coarse lamellar
microstructure, which is broken up by thermomechanical processing, typically below
β-transus temperature, producing an equiaxed or bimodal microstructure that
provides the best balance between fatigue strength and creep resistance in the alloy
[2]. However, in some cases, this process produces large macrozones which have
been linked with the retention of large prior β grains during processing [3] and
variant selection during cooling [4,5]. These macrozones have been shown to cause
scatter in the fatigue life [6].
It has been proposed that failure in α+β Titanium alloys is related to the high plastic
anisotropy of titanium, which gives rise to undesirable hard/soft grain interactions
[7–9], the effect of which could be magnified by the presence of macrozones. Soft
oriented grains are those, which are favourably oriented for easy slip whereas hard
grains are not. In Ti alloys slip occurs along the ⟨11 20 ⟩ and the ⟨11 23 ⟩ directions, in
the basal{0001}, prismatic {10 1 0 } and pyramidal planes. The planes associated with
c⃗+a⃗ slip are {10 11 } 1st order pyramidal planes and the {112 2 } 2nd order pyramidal
2
planes [10,11]. However, slip in the a⃗ type ⟨11 20 ⟩ direction on the basal or prismatic
is much easier than in the c⃗+a⃗ direction [12–14]. Slip in the c⃗+a⃗ direction is thought
to be about ~3 times more difficult in Ti-6Al-4V [10].
A macrozone is a set of neighbouring individual grains with a similar
crystallographic orientation that can potentially act as structural unit regions, that is,
they could act as one large grain despite being much larger than the mean grain size
[15–18]. Grain size is a key determinant of the mechanical properties and fatigue
resistance of titanium alloys, but microstructures exhibiting macrozones would be
expected to behave similar to alloys that have a grain size distribution with several
grains at the high end of the distribution. This is because similarly oriented grains are
more likely to deform in a compatible manner. The common orientation also means
that soft or hard oriented macrozones will contain many neighbouring grains where
slip occurs more easily or is more difficult, respectively. During plastic deformation
a soft oriented region might undergo a greater level of strain than a hard orientated
region, which in return will carry a higher level of elastic strain [19]. If such regions
are very small, i.e. in a material with a small grain size, the significant constraint
imposed by the hard grain on the soft grain will reduce the level of plastic
deformation in the soft grain. However a macrozone can deform as one single large
unit with less constraint, which could lead to damage nucleation during fatigue
loading. Le Biavant et al [16] observed a high density of crack initiation sites within
a single macrozone region in titanium alloys with large macrozones up to 1 mm in
diameter, that were subjected to fatigue loading. The concern is that materials
containing fine-grained macrozones could display fatigue behaviour close to a
coarsely grained material, causing scatter in the fatigue life.
3
In this paper, the digital image correlation (DIC) of optical micrographs is used to
study the deformation of different Ti-6Al-4V product forms, with different
microtextures. The use of DIC on microstructural images recorded during
mechanical loading to study the local strain behaviour is becoming increasingly
popular. The DIC technique enables full-field displacement and strain mapping
across an imaged region [19–28]. The principle behind DIC is the tracking of
features on 2 images of the same region before and after deformation. The images are
divided into sub-regions and subsequently the relative displacement of the features
within a single sub region is cross-correlated with respect to an image of the same
region at a different loading condition. Finally, the displacement field for the entire
image are differentiated to give the strain components [20].
The aim of this work was to quantify the differences in strain localisation and link
them to the underlying microstructure, in an effort to understand how the presence of
macrozones affects local deformation, and discuss the potential implications on the
fatigue behaviour of these important structural materials.
2. Experimental procedures
2.1 Starting materials
The materials studied were three different product forms of Ti-6Al-4V, all provided
by Rolls-Royce plc. The product forms are defined as strong-macrozone,
intermediate-macrozone and no-macrozone materials as they all exhibit different
degrees of macrozone formation. The strong-macrozone material originated from a
150 mm long round (70 mm diameter) extruded bar material intended for blade
applications, while the material with intermediate-macrozones was uni-directionally
rolled plate material with 20 mm thickness. The no-macrozone material was forged
4
and annealed but not rolled and had a rectangular shape with approximate
dimensions of 200 x 70 x 80 mm3. Specimens for tensile testing and microstructural
characterization were machined by electric discharge machining. The recast layer
was removed through grinding. The tensile specimens had a flat dog bone geometry
with a 26 mm gauge length; 3 mm gauge width and were 1 mm thick.
The tensile test specimens were hand polished on an OPS cloth with colloidal silica
for 3 h after initial polishing to #4000 grit paper. The etching pattern was applied to
the sample by using Kroll’s reagent for approximately 60 seconds. This
preferentially attacks the grain boundaries, providing the necessary features for
successful DIC. The microstructures were studied optically using a Zeiss microscope
with a cross-polarised differential interference contrast filter and a polarised prism to
estimate the dimensions of the macrozone regions, and to observe whether the
pattern applied to the specimen was suitable for DIC. A micro hardness indent grid
was applied to each specimen to allow the DIC region to be identified before and
after testing. The region of interested was also characterized using electron back
scattered diffraction (EBSD). EBSD analysis was performed in a FEI Quanta 650
field emission gun scanning electron microscope (FEG-SEM) equipped with an
AZtec EBSD system and a Nordlys II detector. EBSD scans were performed at an
operating voltage of 20 kV. An area of 4 x 4 mm2 with a step size of 10 μm was used
for macrotexture analysis. For microtexture scans a step size of 0.5 μm and an area of
0.5 x 0.5 µm2 were chosen. The data (confidence index > 0.1) were analysed using
HKL Channel 5TM software. The phase was not considered during orientation
mapping due to the very small size of the β ligaments.
5
2.2 Local strain measurements
In-situ loading experiments were conducted using a Kammrath-Zeiss 5 kN
microtester installed under an optical microscope with a fixed stage. The microtester
was controlled using proprietary software and the load data was converted to stress
and compared to the strain data at each load step to produce stress-strain curves. The
samples were loaded in displacement control and held at each displacement
increment for 30 seconds then images were captured for DIC.
The resolution of the DIC is affected by a number of factors, which are mainly: the
resolution of the microscope, image capture settings, speckle pattern size and nature
and sub-grid sizes for data processing [19,20,24,26]. Optical microscopy is typically
used for micro/macroscopic scales while electron microscopy imaging allows strain
mapping at the nanometre scale [24]. A potential issue of high spatial resolution
strain mapping is the limited number of grains that are studied in such cases. This
problem becomes particularly apparent when studying macrozones in Ti alloys that
typically extend across several hundreds of microns. The benefit of using optical
rather than electron microscopy is that the set up allows fast image capture avoiding
potential artefacts that might result from slow scanning techniques in an electron
microscope. Hence, optical microscopy in combination with mechanical loading is a
suitable tool for in-situ mapping strain localisation at a scale that is particularly
suitable for enhancing understanding of the effect of macrozones on mechanical
performance.
The images for DIC were acquired with a DaVis Axiocam connected to a computer
equipped with DaVis 7.2 software to handle and process the images. The images
taken were 2032 x 2032 pixels2 and were acquired at a rate of 2 per second. At each
load increment 15 images were taken and averaged to minimize the error from the
6
CCD camera caused by change in intensity at each pixel over time [20]. The stage of
the microtester is height adjustable to allow for real-time focus adjustment and real-
time image capture during interrupted tensile loading. The images captured were
reduced to 1000 x 1000 pixels2 in order to have the desired range of between 4 and
16 pixels2 for individual features that can be followed by DIC [20]. A sub region grid
size of 32 x 32 pixels2 with a 50% overlap was used during the analysis. The sub
region grid size was 36 x 36 µm2, equating to a grid containing 9-16 grains. The
macrozones in the material are typically 25-40 grains wide for the strong-macrozone
condition and 10-20 grains wide for the intermediate-macrozone material, meaning
that the chosen spatial resolution is sufficient to detect any heterogeneous strain
behaviour related to macrozones. The overlap maintains the spatial resolution, while
allowing a bigger sub-region to be used [29], although it also reduces the peak strains
measured. The images are divided into sub-regions and the relative displacement of
features is computed across the whole image. Once the displacements have been
computed they can be differentiated to obtain strain values. In order to study the
elastic and plastic strain relationship between crystallographic orientations of
macrozones in respect to the loading direction, the DIC strain maps were compared
with the corresponding orientation maps recorded by EBSD. As a result of the
elongated grains in the strong-macrozone material, the spatial resolution of the strain
maps is worse along the length of the grains, which are usually aligned with the
macrozone.
After deformation, the samples were OPS polished for 10 minutes to remove the
etching pattern used for image correlation purposes. The removal of the pattern
reveals the deformed sample surfaces and images were then taken with a Nikon
Digital SLR camera with a 100 mm macro lens to show the macro-scale deformation.
7
3. ResultsBackscatter electron images were compared for the 3 conditions as shown in Figure 1
and the maps were used to deduce the primary volume fractions and grain sizes
using the open source software ImageJ and the ASTM standard analysis techniques.
The values are listed in Table 1 together with estimated accuracies. The quantitative
analysis of each condition is based on ~ 250 grains. The microstructure for the no-
macrozone condition, shown in Figure 1a, has equiaxed grains with the phase
concentrated at the grain boundaries and triple points between grains. A similar
morphology is observed for the intermediate-macrozone condition in Figure 1b with
the only difference being that the phase appears more aligned in terms of the grain
boundaries. The strong-macrozone condition shown in Figure 1c has elongated
grains particularly within and along the direction of the macrozones. The grain size
for the strong-macrozone condition was determined by taking an average of the grain
size parallel and perpendicular to the direction of the macrozones. Table 1 shows that
primary volume fractions and average grain sizes for the 3 conditions are all
comparatively similar (88%, 93%, 91% and 7 μm, 10 μm and 8 μm, respectively).
Therefore, it can be assumed that any differences in heterogeneous strain behaviour
for the three conditions can be related to the presence or absence of macrozones and
their orientation (texture) rather than differences in grain size and primary volume
fraction.
3.1 Microstructure and Texture
Figure 2 shows macro orientation maps recorded by EBSD with a step size of 10 μm
and the corresponding (0002 ) and {10 1 0 } pole figures of the three product forms of
Ti-6Al-4V. The no-macrozone material displays a relatively weak texture with a
maximum intensity of 2.5 times random on the (0002 ) pole figure, Figure 2a. Figure
8
2b shows that the intermediate-macrozone material exhibits dispersed macrozones in
the ND-TD plane that stretch for approximately 500 μm in length along the
transverse direction and are 50 µm in width in the normal direction. The respective
pole figures show that the primary texture component has the c-axis aligned parallel
to TD and the {0002} pole figure intensity is around 4 times random. Further
analysis showed that the sporadic macrozones do dominate the observed texture.
Hence, when the material is subsequently loaded along the transverse direction, the
macrozones have their c-axis preferentially parallel to the loading direction and the
macrozones should appear as hard regions. Figure 2c shows that the strong
macrozone material exhibits specific regions that have a very distinct texture. There
are very pronounced macrozones stretching along the extrusion direction (ED) for
millimetres and approximately 200 µm in width along the normal direction. The
(0002 ) pole figure is strongly dominated by the macrozones with the c-axis aligned
parallel to TD and the intensity approximately 16 times random. In addition, the
{10 10 } pole figure shows that there is a strongly preferred crystallographic
orientation of the prismatic planes giving a distinct crystallographic orientation.
However, this macrozone region does not give an accurate representation of the bulk
texture of the material. Figure 2d combines the crystallographic orientation data for
several regions that were analysed for the strong-macrozone condition. The
subsequent pole figures highlight the more random nature of the texture (note the
different scale bar), with a clear reduction in the overall intensity. The 0002 pole
figure indicates a significant weakening in the overall texture, with a separate
intensity scale bar used to highlight this, and there is a shift of the c-axis alignment
away from the transverse direction. Also, the 10 1 0 pole figure shows a very weak
fibre distribution. Considering this heterogeneous texture distribution of the
9
macrozones, it is clear that depending on the loading direction a macrozone could
either behave like a soft or a hard region.
3.2 Strain Mapping
Tensile tests were performed along the forging direction (FD) in the case of the no-
macrozone material. For the intermediate-macrozone condition the material was
loaded along TD as this allows the impact of hard oriented macrozones to be studied.
The strong-macrozone condition was loaded in the ED-ND plane and at 0, 45 and
90 to ED, respectively, to allow the impact of soft orientations for different slip
systems to be investigated in more detail.
Optical micrographs were recorded at progressive strains in the elastic and plastic
region, to maximum strains of between 5-10%. Stress-strain curves were constructed
from each loading experiment by combining load cell data from the micro tester with
averaged strain data from the DIC analysis, Figure 3. The maximum tensile
strengths and yield strengths for each material are shown in Table 1. Figure 3a and
Table 1 demonstrate the excellent agreement of the elastic response for the three
conditions providing great confidence in the accuracy of the DIC strain calculations.
Figure 3b highlights the plastic behaviour and the respective yield points of the
different conditions. It should be noted that a single macrozone with a hard or soft
orientation, respectively, will exhibit a higher or lower elastic response when
analysed individually. All conditions appear to show similar work hardening
behaviour but all conditions have different yield points. The no-macrozone condition
and the strong-macrozone condition loaded at 0 are the two softest materials
followed by the intermediate-macrozone condition. The strongest response is
displayed by the strong-macrozone condition loaded at 45 and 90.
10
Macrographs of the tensile samples with the strong-macrozone after deforming 0,
45 and 90 to the loading direction are shown in Figure 4. The deformation bands
on the surface of the samples appear to be always parallel to the macrozones and are
comparable in width to the width of the macrozone regions. In all three cases, the
deformation bands clearly pass throughout the gauge volume suggesting that each
macrozone is deforming as a single structural unit.
The DIC results are presented as maps of maximum in-plane shear strain as this takes
into account all the components of the in-plane strain. The maximum shear strain
(εmax) was calculated using equation 1, where εxx is the strain in the loading direction,
εyy is the strain normal to the loading direction and εxy is the in-plane shear strain.
εmax=√( ε xx−ε yy2 )2
−εxy2 Equation 1
Presenting the results as maximum shear strain helps to reduce some of the
uncertainty provided by the lack of out-of-plane deformation data that is not taken
into account by 2D DIC. The maximum shear strain maps are related to the
microstructure through correlation with prismatic, basal and pyramidal c⃗+a⃗ Schmid
factor maps computed from EBSD data in Figure 5, at ~ 2.5% applied strain.
Although, from the Schmid factor maps it can be observed that the majority of grains
in each condition were favourably oriented for pyramidal c⃗+a⃗, it should be taken
into account that the CRSS associated with this type of slip is ~ 3 times higher than
prismatic and basal slip [10]. Therefore, this type of slip is only likely in grains that
are unfavourably oriented for prismatic and basal slip. Twinning was not considered
because it is very uncommon during RT tension testing at low strain rates in Ti-6Al-
4V. For the no-macrozone condition, shown in Figure 5a (i), the strain behaviour is
homogeneous at the microscale across the entire region. The prismatic, basal and
11
pyramidal c⃗+a⃗ Schmid factor maps in Figure 5a(ii), (iii) and (iv) also exhibit
homogeneous distributions, which is in agreement with the observed strain pattern.
The intermediate-macrozone condition shows some strain hot spots on the strain map
in Figure 5b (i), which are not correlated with the prismatic and basal slip Schmid
factor maps in Figure 5b (ii) and (iii). However, in the Schmid factor map for
pyramidal c⃗+a⃗ slip, Figure 5b (iv), there is a significantly higher number of grains
that are favourably oriented for this slip system. Although, there is still no direct
correlation between regions of high strain hot spots and a single slip system. The
strong-macrozone condition loaded with the macrozones parallel to the loading
direction (0) exhibits a similar homogeneous strain pattern as the no-macrozone
condition, Figure 5c (i). This region coincides with the presence of two large
macrozones that are both well orientated for prismatic slip, as can be seen in the
Schmid factor map in Figure 5c (ii). In contrast, when the macrozones are loaded at
45, the strong-macrozone material exhibits clear heterogeneous strain behaviour,
Figure 5d (i). By correlating the strain map with the Schmid factor maps for
prismatic and basal slip in Figure 5d (ii) and (iii), respectively, it can be observed
that the well developed strain bands coincide with regions that are well orientated for
prismatic but not basal slip, particularly in the case of the strongly developed strain
band that stretches across the centre of the strain map. It should also be noted that the
bands that show less strain also appear to have a low density of grains that are
favourably oriented for prismatic slip. The strong-macrozone material loaded with
the macrozones orientated 90 to the loading direction also exhibits heterogeneous
strain behaviour and strain localisation within a macrozone region as can be observed
from the strain map in Figure 5e (i). There is a single high strain region (band)
stretching along ED with a neighbouring region of very low strain. Here, the
12
prismatic and basal Schmid factor in Figure 5e (ii) and (iii) show that the high strain
band corresponds to a macrozone favourably oriented for basal slip (Schmid factor
0.5) and a lower Schmid factor for prismatic slip. However, this high strain band also
overlaps with a narrow macrozone region that has a favourable orientation for
prismatic slip. This suggests that both macrozone regions have contributed to the
high strain localisation.
The strain accumulation at progressive loading steps is displayed in Figure 6 in terms
of frequency plots for each loading step and the colours of the individual loading
steps correspond to approximately the same average strain. Initially, during elastic
loading, all material conditions and loading directions display similar homogeneous
strain behaviour resulting in sharp peaks in Figure 6a-e. Once plastic deformation
starts, the shear strain distribution widens noticeably but now also significant
differences can be seen between microstructures and loading conditions. The no-
macrozone condition, Figure 6a, shows gradual broadening of the shear strain
distributions with increasing overall shear strain. The intermediate-macrozone
condition shows a relatively similar behaviour, Figure 6b, although the shear strain
distributions seem somewhat wider in the plastic regime than for the no-macrozone
region. The strong-macrozone material loaded parallel to the macrozone direction
displays again a similar picture but with the sharpest shear strain distributions in the
plastic regime, Figure 6c. In the case of the strong-macrozone material loaded at 45
and 90 to the macrozones, Figure 6d and e display very early broadening of the
shear strain distribution that develop a very large range in shear strain for each load
step as the material is further strained. For instance, the 45 condition displays a shear
strain range of approximately 2% at 3.1% average shear strain. The 90 sample
develops bimodal shear strain distributions from an average shear strain of 1.5%. The
13
two distinct parts of the distribution both have a similar range of strain and appear to
represent the low and high strain bands, respectively.
By comparing the overall strain distribution for all conditions and loading directions,
it can be seen that the no-macrozone and strong-macrozone condition loaded parallel
to the macrozones show similar peak shapes and heights indicating the homogeneous
nature of the strain distributions. The other 3 conditions exhibit wider frequency
curves and this highlights the heterogeneous strain behaviour. The most extreme case
here is the strong-macrozone condition loaded at 90, which displays a bimodal strain
distribution.
4. DiscussionBoth the no-macrozone material and the strong-macrozone condition loaded at 0
exhibited homogeneous strain behaviour at the microscale. The intermediate-
macrozone condition exhibited some degree of heterogeneous strain behaviour while
the strong-macrozone condition loaded at 45 and 90 both displayed pronounced
heterogeneous strain behaviour with regions favourably oriented for a⃗ slip
correlating to high strain regions. By comparing these observations with the stress-
strain curves presented in Figure 3, it becomes apparent that the materials with the
highest yield stress exhibit the most heterogeneous strain behaviour whilst
homogenous strain behaviour corresponds to the lowest yield stress. However, it may
have been expected that the intermediate-macrozone condition would display the
highest yield strength, due to the pronounced basal texture, which hardens this
condition when loaded along TD. Where as the basal texture in the strong-macrozone
condition softens the material when loaded at 0 (along ED). In contrast, when the
strong-macrozone condition is loaded at 45 or 90, the majority of the grains are in
14
either a soft or hard orientation relative to the individual macrozone regions, as
shown in the Schmid factor maps in in Figure 5d and e. Therefore, the increase in
yield stress in these two loading conditions in comparison to the intermediate-
macrozone condition could be due to the relative size of the hard oriented macrozone
regions, which are larger in the strong-macrozone condition.
Further, the intermediate-macrozone condition displayed a modest level of strain
heterogeneity at the microscale, which cannot be correlated to the macrozones visible
at the surface of the sample. In contrast to the strong-macrozone conditions, the
intermediate-macrozone condition displays comparatively small and individual
macrozones, which do not extend through the thickness of the sample. The
orientations of these small macrozones would make them harder than the
surrounding grains. Singles areas of low and high strain are clearly evident from the
strain map, but cannot be directly linked to individual hard or soft grains,
respectively. Hence, while the macrozones cannot be directly correlated to the strain
localization in the strain maps, their presence nevertheless increases the
heterogeneity of the strain response. There also appears to be an increased likelihood
of pyramidal c⃗+a⃗ slip having a more prominent role in the deformation in this
material condition, as there is a higher number of grains that are favourably oriented
for this slip system and unfavourably oriented for basal and/or prismatic slip. This
could help explain the lack of a direct correlation with strain hot spots and a single
slip system, as the clustered regions are likely to be several neighbouring grains that
have deformed by different slip systems to give increased strain localisation.
For the strong-macrozone condition all three loading directions appear to show
distinctive strain behaviour relative to the underlying microstructure. Figure 7 depicts
the strain accumulation across the material for 0, 45 and 90 loading conditions to
15
give a representation of the onset and evolution of strain heterogeneity. The
normalised position is the position along the corresponding strain image depicted
under the figures. The shear strain lines in Figure 7 were drawn perpendicular to ED.
Therefore, in the case of the 0 loading condition, the normalised position represents
a direction transverse to the loading direction while for the 90 loading condition the
direction the line was drawn is parallel to the loading direction. Accordingly, Figure
7a shows almost no shear strain variation during the early stage of plasticity and only
some at high average strain levels of 8%. Note that such large overall plastic strain is
not observed during typical fatigue loading conditions, which is one of the drivers to
understand better strain heterogeneity. For the 45 and 90 loading condition, shown
in Figure 7b and c, respectively, a key observation from the high strain macrozone
regions are that the trend for strain localisation develops early in the loading regime,
i.e. after only very small amounts of plastic strain. Similar observations were made
by Littlewood and Wilkinson [19] during strain mapping of Ti-6Al-4V. Therefore,
these conditions and their resulting strain localisation are more likely to have a
detrimental impact on some fatigue loading conditions. Slight variations in strain for
the 45 and 90 condition begin at approximately 1.4% and 1.2% average strain,
respectively, and the trend then continues to progress and becomes more pronounced
with increasing load/average strain. The red arrows show when the variations in
strain become apparent. When fully loaded into the plastic regime, at 2.0% strain, the
strain behaviour continues to show pronounced heterogeneity. In the case of the 45
loading condition, there is a clear correlation between high strain bands and
macrozones with their c-axis oriented perpendicular to the loading direction. This
was also observed by Le Biavant et al [16] where macrozones well orientated for a⃗
slip accommodated significantly plastic strain than the regions in-between. They also
16
found that the strain heterogeneity between the two regions increases with continued
loading.
In order to relate the crystallographic orientation of the strong-macrozone condition
to the strain mapping conditions, the prismatic and basal Schmid factors have been
compared across two neighbouring regions that contain differently oriented
macrozones for each of the 3 loading conditions, Figure 8. In principle, the strong-
macrozone condition shows a strain response similar to a fibre reinforced composite
material. When the loading direction is parallel to the macrozones the two distinct
regions have to deform together, and consequently, no microscale strain
heterogeneity is observed. In addition, by analysing the Schmid factor distributions
of the macrozone and non-macrozone regions, it also becomes apparent that all
regions are well aligned for prismatic or for basal slip, Figure 8a. Therefore, the
macrozone and non-macrozone regions can both be considered soft under this
loading condition, which further explains the low strain heterogeneity and low yield
stress. However, this is only for the specific case when their c-axis is orientated
perpendicular to the loading direction and in this study only the strain behaviour in
the x-y plane was observed.
In the 45 loading condition the strong-macrozone material exhibits pronounced
heterogeneous strain bands that can be related to the macrozone and non-macrozone
regions. In Figure 8b, the macrozone region shows a high frequency of grains well
aligned for prismatic slip and it is this region that displays the high strain. In contrast,
the non-macrozone region exhibits an even distribution of the Schmid factor for
prismatic slip while there is a clear trend for grains being well aligned for basal slip. .
Similar observations have been reported previously by Padilla et al for strongly
textured Zirconium that was compression tested [22]. Here compressive strain
17
concentrations were observed in the neighbouring grains favourably oriented for
prismatic slip. Although, the macrozone region also displays a slightly increased
number of grains with a high Schmid factor for basal slip but one would assume that
prismatic slip is likely to be the more dominant of the slip systems due to its slightly
lower CRSS value. However, it is worth noting that since the ratio of basal to
prismatic slip resistance is estimated to be about 1.2 [10,30] , a grain with a basal
Schmid factor of 0.5 would yield at a lower stress than a grain with a prismatic
Schmid factor of 0.4. The difference in strain localisation between the macrozone
favourably oriented for prismatic slip and the non-macrozone favourably oriented for
basal slip is attributed to the higher volume fraction of grains with a favourable
orientation for prismatic slip in the macrozone region, indicated by a higher peak,
yielding preferential slip localisation within this region and therefore increased
strain.
Loading the strong-macrozone condition at 90 results again in pronounced
heterogeneous strain behaviour strongly correlated to macrozone and non-macrozone
regions. However, as a result of the texture of the strong-macrozone material relative
to the loading direction the macrozone and non-macrozones regions are in fact two
macrozone regions that are favourably oriented for either prismatic or basal slip. In
this case, the macrozone is the region favourably oriented for basal slip and the non-
macrozone is the region favourably oriented for prismatic slip. From Figure 8c, it can
be observed that the high strain band corresponds to the region that is well oriented
for basal slip. In contrast, the neighbouring low strain region is favourably oriented
for prismatic slip. Closer investigation of the region favourably oriented for basal slip
reveals a strong texture with the basal pole tilted by about 45 away from TD, as
illustrated by the {0001} pole figure in Figure 8d. Moreover, the normalised
18
frequency plot for the 90 loading condition shows that the macrozone oriented for
basal slip has a very high Schmid factor peak at 0.5 with increasing intensity from
0.4. Where as the Schmid factor in the non-macrozone region aligned for prismatic
slip shows a peak at 0.4 but with a significantly reduced frequency of grains than the
macrozone region favourably oriented for basal slip. Therefore the macrozone
oriented for basal slip should indeed be softer, as observed.
The link between the stress strain behaviour and the nature of strain distribution has
been highlighted previously. Table 2 summarises the average Schmid factor for
prismatic and basal slip across the analysed strain region covering at least 3000
grains. The three conditions that exhibit heterogeneous strain and overall high yield
stress show a lower Schmid factor for prismatic than basal slip and in addition the
average Schmid factor for both slip modes also tends to be lower compared to the no-
macrozone and strong-macrozone at 0 conditions, which display relatively low yield
stresses.
Both the 45 and 90 loading directions show significant strain localisation at the
microscale relative to macrozone regions favourably oriented for prismatic or basal
slip and the high strain regions stretch along the entire length of those regions. At a
microscale, the strain localisation in the favourably oriented macrozone appears as a
single band of high strain covering the entire macrozone region with little difference
in strain across the band. It is beyond the remit of the present paper to investigate
strain heterogeneity on the nanoscale, which is at a scale that allows the actual slip
traces to be resolved. Using the present approach, it has been observed that,
depending on the type of microstructural heterogeneity and loading direction, there
can be large differences in strain localisation at overall strain levels that are typically
observed during, for instance, low cycle fatigue loading. These strain heterogeneities
19
are likely to create compatibility issues between the two regions that will impact on
the fatigue performance of such material. As in the case for the strong-macrozone 45
and 90 loading conditions, the boundaries between macrozones and non-macrozones
would be subjected to significant stress concentrations and are therefore potential
sites for early crack initiation and high crack densities. Wilkinson and Littlewood
[19] observed crack formation in a single region where a grain well oriented for slip
deformed intensely to allow neighbouring unfavourably oriented grains to remain
non-deformed. It is therefore plausible that large favourably oriented macrozones
neighbouring poorly oriented regions can similarly create a high density of closely
located potential crack initiation sites. On the other hand, a strong macrozone-region
might be benign if loaded in a direction that does not create heterogeneous strain
between the two different regions. However, such arrangement might still show more
detrimental slip localisation at the nanoscale.
5. Summary and conclusionsStrain mapping at the microscale using digital image correlation of optical
micrographs was used to study the strain localisation behaviour in the strong,
intermediate and no macrozone materials, respectively. This has been correlated with
electron backscattered diffraction orientation maps to relate the strain behaviour to
the primary orientation of the macrozones within the material in regard to the loading
direction. The main conclusions are as follows:
In the three materials studied, increase in yield strength also meant more
heterogeneous strain localisation. The macroscopic yield stress is determined
by the overall texture of the material but it is clear that the microtexture
controls the onset of yield at the microstructural level. Thus the amount of
20
strain localisation, which can drive damage nucleation, can be higher in
materials with a higher yield strength.
Local deformation heterogeneity is established early in the plastic regime and
highly strained regions continued to deform more than the low strain regions
as deformation progresses.
Deformation was relatively homogeneous in the no-macrozone condition and
the strong-macrozone condition loaded parallel to ED, where most grains are
equally well aligned for either basal or prismatic slip. The hard-oriented
intermediate-macrozone condition showed moderate strain heterogeneity.
The strain distribution in the strong macrozone condition loaded at 45 and
90 to ED was highly heterogeneous. Strain localization was correlated with
macrozones preferentially oriented for prismatic and basal slip, respectively.
AcknowledgementsThe authors would like to thank the EPSRC for partially funding the project though
the CDT in Advanced Metallic Systems and Rolls-Royce for providing matching
funding and the provision of materials. The authors are also supported by EPSRC
funding through EP/K034332/1 and EP/I005420/1.
21
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23
Tables, Figures and Captions
Table 1-Mechanical and microstructural properties of Ti-6Al-4V in different product forms
Table 2- Summary of average Schmid factor for prismatic and basal slip for all conditions in DIC region
24
Material E(GPa)
σy
(MPa)σmax
(MPa)Volume fraction of α phase (%)
Average α grain size (μm)
Aspect ratio of α grains
No-macrozone (strained along LD)
89 876 938 881 70.5 1
Intermediate-macrozones (strained along LD)
90 882 974 931 100.5 1
Strong-macrozone (0) 90 885 957 911 80.5 2.5
Strong-macrozone (45) 94 931 1000 911 80.5 2.5
Strong-macrozone (90) 93 928 1000 911 80.5 2.5
Material Average Schmid Factor ~ no. of grains
Prismatic Basal
No-macrozone 0.35 0.35 5400
Intermediate-macrozones
0.28 0.36 3000
Strong-macrozone (0)
0.40 0.28 4000
Strong-macrozone (45)
0.32 0.37 4100
Strong-macrozone (90)
0.31 0.38 4050
Figure 1- Backscattered electron images of (a) No-macrozone, (b) Intermediate-macrozone and (c) Strong-macrozone
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Figure 2- IPF maps of Ti-6Al-4V alloy in different product forms (a) No-macrozone, (b) Intermediate-macrozone, (c) Strong-macrozone from a strongly textured region and (d) an average pole figure from several regions for the strong-macrozone condition for all loading directions. EBSD generated {0001} and {10 10 } pole figures are shown on the right side of each figure. For interpretation of the references to the colour in this figure legend the reader is referred to the web version of this article
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Figure 3- (a) Stress-strain curves obtained from the DaVis strain map data and (b) magnified view around the yield point
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Figure 4-Macro images of plastic deformation after in-situ tensile loading for the Strong-macrozone loaded at (a) 0, (b) 45 and (c) 90
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Figure 5- Correlation of strain to Basal and Prismatic Schmid factor, at ~ 2.5% applied strain, for (a) No-macrozone, (b) Intermediate-macrozone, and Strong-macrozone loaded at (c) 0, (d) 45 and (e) 90. (i) Shear strain maps corresponding to (ii) Prismatic, (iii) Basal and (iv) Pyramidal c⃗+a⃗ Schmid factor, processed from raw EBSD data with a 0.5 µm step size.
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Figure 6-Cumulative frequency plot of the strain progression during in-situ tensile loading for (a) No-macrozone, (b) Intermediate-macrozone and the Strong-macrozone loaded at (c) 0, (d) 45 and (e) 90.
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Figure 7 -Strain accumulations across a macrozone with increasing load for the Strong-macrozone loaded at (a) 0, (b) 45 and (c) 90.
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Figure 8-Comparison of prismatic and basal Schmid factor in two neighbouring macrozone and non-macrozone regions when loaded at (a) 0, (b) 45 and (c) 90, with the inset strain maps and EBSD orientation maps. (d)EBSD generated {0001} and {10 1 0 } pole figures for the non-macrozone region only in the 90 condition. For interpretation of the references to the colour in this figure legend the reader is referred to the web version of this article
32