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

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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

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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.

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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

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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.

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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

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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.

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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

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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

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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.

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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

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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

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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

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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

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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

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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

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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

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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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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

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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

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