Local deformation mechanisms of two-phase Ti alloy

This paper describes a study of local deformation mechanisms in two-phase Ti alloy, Ti–6Al–2Sn–4Zr– 2Mo, by performing in-situ micropillar compression tests. A colony microstructure was examined and select grains identified for examination were chosen with EBSD measurements. These grains were chosen to isolate individual slip systems within each test. Micropillars of tri-crystal (α–β–α) structure were fabricated from four determined regions, and compression tests were performed using a displacement-controlled nanoindenter set inside a SEM, with a constant displacement rate. The results show that the α/β morphology significantly affects the local deformation behaviour. For these colony structures, Schmid's law in general enables anticipation of local slip activity, but the presence and morphology of the β phase can significantly alter the apparent yielding point and work hardening response. The role of interfaces within these tri-crystal pillars is discussed. & 2015 Published by Elsevier B.V.


Introduction
High strength-to-weight ratio, corrosion resistance and excellent mechanical properties have made titanium alloys attractive to many industrial applications, particularly in gas turbine and aerostructures. However, their highly anisotropic and localised deformation behaviour, when significant fractions of the α (Hexagonal Close Packed, HCP) phase are present, lead to difficulties in understanding fatigue crack nucleation and hence in predicting lifetime and failure of components in service [1]. In the last few decades, extensive researches have been devoted to understanding deformation mechanisms in α phase titanium (e.g., CP-Ti or Ti-Al single crystals) [2][3][4][5][6][7]. These investigations have clearly shown slip/ twinning behaviours and the corresponding dislocation evaluation as a function of Al content, temperature and crystallographic orientation. On the other hand, relatively little is known about the precise micromechanical deformation mechanisms in two-phase Ti alloys. Complexities on studying α/β Ti alloys arise due to the microstructure-dependent-mechanical properties, room temperature creep behaviour, microtexture and interaction between the α and β (Body Centred Cubic, BCC) phases [8][9][10][11][12].
Early work by Chan et al. [8] showed the deformation behaviour of a colony-structured α/β Ti alloy, Ti-8Al-1Mo-1V. Compression experiments of individual colony samples revealed that significant yield stress variations were found with respect to the angle between the slip direction and the normal to the α/β interface, and failure of Schmid's law was observed in α colony orientations where angles between the slip plane normal and the loading direction vary from 15°to 63°, except the case when slip occurred parallel to the β phase. Slip system activity strongly influences stress-strain behaviour and interestingly the authors insisted based on experimental observation that the β phase is stronger than the α phase, although this has not yet been confirmed.
Savage et al. [11] and Suri et al. [12] investigated the effects of α/β interfaces in Ti-6Al-2Sn-4Zr-2Mo-0.1Si and Ti-5Al-2.5Sn-0.5Fe, respectively, with respect to slip transmission mechanisms between the α and β phases governed by Burgers orientation relationship (BOR). Experimental observation revealed that significant anisotropy in deformation behaviour occurs in three distinctive (a 1 , a 2 and a 3 ) basal and prismatic slip systems in the α phase which was caused by the relative misalignment with a slip system in the β phase. The morphological effect of the β phase in deformation was studied by Sandala [10] using lamellar structured Ti-6Al-2Sn-4Zr-6Mo with different widths of β. It revealed that the β width significantly affects plastic deformation behaviour, whilst no pronounced effect was found in the elastic regime. Some effects of β volume fraction can be found in recent work done by Qiu et al. [9]. With a higher β volume fraction obtained by increasing Mo content in Ti-6Al-2Sn-4Zr-xMo (x¼ 2-6), a smaller slip band spacing was produced and significantly reduced accumulated strains were observed during dwell fatigue tests. Previous studies have shown some aspects of deformation mechanisms in macroscopic polycrystalline two-phase Ti alloy samples, but it is thought that small-scale experiments on a localised, confined area are required to improve understanding of the fundamental mechanisms on the level of the individual microstructural constituents. In recent years, Uchic et al. [13] have developed an innovative methodology for studying micromechanical behaviour of materials by adopting experiments on small-scale architectures fabricated by focused ion beam, with a nanoindenter as a means of applying force. Extensive research contributions have been devoted to investigate the length scale and size effects in plasticity of metallic materials [13][14][15][16][17], yet this has mainly focused on FCC materials such as Cu and Ni. Some work on Ti single crystals has been carried out to study the size effect on slip [18] and deformation twinning [19]. Recently, Ding, Gong and colleagues [20] have worked on two-phase Ti-6Al-4V using micro-cantilevers, investigating slip activities through the α/β interface. They found a cross-slip away from the 1011 { ̅ } pyramidal plane only for compression case (not for tension) and this could elucidate asymmetric CRSS behaviour, which was similarly observed by Jones and Hutchinson [21].
In this work, we investigate local deformation mechanisms in two-phase Ti alloys using micropillar compression focusing on how two phase structures change local slip behaviour. We investigate the significance of α/β structural morphology on deformation and its effect on Schmid's law, which is used for anticipating local slip activity. This work provides the basis for further investigation on fundamental micromechanics of two-phase Ti alloys and potentially other materials.

Material preparation
A titanium alloy 6242 (hereinafter referred to as Ti6242), with the chemical composition (in wt%): 6.12Al-2.00Sn-3.95Zr-2.00Mo-0.012C-0.031Fe-0.021Si-0.0002H-0.072O-0.0069N and Ti balance was supplied by IMR (Institute of Metal Research, China) as a forged bar of 20 mm diameter. The bar had been produced by a triple VAR melt, followed by β forging at the temperature of T β (β transus)þ150°C with 30% deformation (resulting in the ingot diameter from 205-210 mm to 170 mm) and α/β forging at the temperature of 30% α p (primary α phase) with 70% deformation giving a finishing diameter of 90 mm.
The sample was sectioned perpendicular to the bar axis and prepared metallographically with SiC papers (up to 4000 grit) and then polished with ∼50 nm OP-S (Oxide Polishing Suspensions) diluted with H 2 O by a ratio 1:5 of OP-S:H 2 O. The sample was lightly etched with Kroll's reagent for ∼15 s (2% HF, 10% HNO 3 and 88% H 2 O). The final etch and polish procedure was repeated 2-3 times until the grain structure was clearly visible with polarised light microscopy.
Initial studies of the as-received Ti bars revealed complex lamellar structures, where isolation of individual microstructure features would be difficult and the effect of prior strain would make interpretation of the results difficult (see Fig 1). Therefore the sample was heat treated to produce a colony microstructure with large α-lamella separated by thin β-ligaments, in clear priorβ grain structures to make micropillars of a tri-crystal (α-β-α) structure (see Fig. 2(i)). For this heat treatment, the as-received sample was held at the temperature of β transusþ50°C (i.e., 1040°C) for 8 h and cooled down with a rate of 1°C/min. This provided a microstructure with α phase lamella, with average widths of ∼3.7 mm, and β phase ligaments of width ∼0.8 mm. Note that the widths of the as-received condition were ∼2 mm for α lamella and ∼0.5 mm for β ligament.

EBSD maps
Electron backscatter diffraction (EBSD) maps were generated in a Carl Zeiss Auriga CrossBeam FIB-SEM with Bruker EBSD system consisting of an eFlashHR camera and Esprit v1.9 software, in order to characterise the microstructure (an example is shown in Fig. 1). High current mode was used with a probe current of 10.5 nA and an aperture size of 120 mm. The accelerating voltage of 20 kV was selected for EBSD. A larger area map (∼1.6 Â 1.2 mm 2 and step size with 1.2 mm) was first mapped, yet due to the large step size the β orientation was not regularly revealed within this map. Therefore higher magnification maps (∼151 Â 113 mm 2 ) with finer step sizes of 0.05-0.5 mm were captured for areas with desired crystal orientations for the micropillar tests. Crystal orientations were selected to maximise the resolved shear stress on individual slip systems and trigger single slip.

Micropillar fabrication
Micropillars of square cross-section were machined using a FEI Helios Nanolab 600. An automated routine was used for fabrication in AutoScript TM . A Ga þ ion beam of 30 kV was used with a series of currents decreasing from 9.3 nA (rough milling) to 2.8 nA (medium milling) and finally to 0.92 nA (final milling). The fabrication time for each pillar was about 17 min.
Micropillars were fabricated in grains of specific crystallographic orientations to control slip activity. Furthermore, pillars were fabricated with the β phase running near vertical in the pillar. Due to different crystallographic orientations of the α and β phases, anisotropic milling led to roughening between the phases [22].
Each pillar was carefully measured after fabrication (see Fig. 2 (ii)). The pillar widths (w t and w b ) and the side length (l s ) were measured, where the taper angle (θ t ) and a height (h) are then defined by the following equations: As the pillars are flat faced, slip trace analysis can be easily performed and the slip angle (θ s ) can be expressed as follows: where θ′ is an angle on any pillar faces after tilting and ϕ a tilting angle. Note that a tilting angle of 52°was predominantly used in this study. Among several micropillars fabricated, a total of nine pillars were selected for this study with a top width of 2 mm, an aspect ratio of 1.9:1-2.6:1, and a taper angle of 4.4-6.0°. The details of each pillar are summarised in Table 1.

Micropillar compression test
In-situ SEM based micropillar compression tests were performed using an Alemnis nanoindentation platform. This platform is actuated with a piezoelectric transducer and therefore operates in displacement control with up to maximum displacement of 35 mm and load of 500 mN. The samples were mounted on top of a calibrated load cell. The whole system was aligned to indent the pillars with a 30°tilt between sample and the horizontal plane. Insitu imaging was performed at a low working distance using the secondary electron (SE) detector with an accelerating voltage of 5 kV. The pillars were aligned such that tri-crystal phase was visible during the mechanical test. The indenter was loaded with a flat punch (10 mm diameter, set on top of a 60°cone).
The micropillars were near uniaxially compressed by the diamond flat punch tip at displacement rates of 2 and 5 nm s À 1 , to a peak tip displacement of 1 mm. This is approximately strain rate of ∼5 Â 10 À 4 s À 1 and ∼1 Â 10 À 3 s À 1 respectively, assuming a uniform cross section. The punch was withdrawn, and held with 1/10th of the maximum displacement to measure thermal drift. This was used to correct the load-displacement results, although this correction was very small once the indenter was left to stabilise in the vacuum chamber (∼2 h).
During each test, the SEM was used to generate an in-situ video of the surface, using a reduced window and an effective frame capture time of ∼600 ms. These videos were synchronised with the loaddisplacement data in a post-processing script written within Matlab.
After each test, the samples were loaded in the SEM using a more standard holder for high resolution surface imaging, with micrographs of the faces of the pillar taken with a tilt angle of 52°. Engineering stresses and strains were calculated by dividing the applied load by the cross-section area at the mid-height of each pillar and the displacement by the height, respectively (see Fig. 2 (ii)). Note that the uncertainties associated with the cross-sectional area and the height of the pillars were ∼2% and ∼1% respectively and the magnification of the microscope was verified using a standard sample.

Initial microstructural characterisation
The crystal orientation maps are shown in Fig. 3(i) and (ii), with inserts showing the crystal orientations of α and β phases. The orientations of each region, as described in Table 1, indicate that the c-axis of α phase with respect to loading direction varies from 14°(harder grain in region 'A') to 68°(softer grain in region 'D'). Note that the uncertainties associated with absolute crystal (i) Schematic diagram of tri-crystal(α-β-α) structured micropillar and (ii) SEM image of a square-shape micropillar fabricated using focused ion beam with a script created by AutoScript TM : α (darker) and β (brighter) phases are seen clearly on the pillar, and their orientation difference causes a surface stepping within a trench. Four faces shown in black rectangle are used for slip trace analysis. In sub-window, pillar height (h) and area (w m 2 ) were used to calculate engineering strain and stress, respectively.  orientation for each each region were within a range of 2° [23].
Furthermore, the related orientations of the α and β phases show that the BOR (Eq. 3) is obeyed within this colony (see overlapping poles in pole figures of each region in Fig. 3(iii)). The morphology of the β ligaments changes subtly in each of the different orientations, with long straight ligaments for the hard-grain orientation, and more wavy and divergent ligaments in the soft grain. and 0001 // 110 1120 // 111

Effect of α/β morphology
This section outlines mechanical tests of pillars fabricated within the same colony. The pillars were fabricated with an aim of producing tri-crystals with similar internal morphologies, idealised as a vertical 'sandwich' of the thin β ligament between two α crystals, as shown in Fig. 2(i). However, despite best efforts to obtain idealised microstructures, the resultant pillars often have differing internal morphologies.
In Fig. 4 micrographs of nine micropillars before deformation are shown with views taken from the front face (at a tilt angle of 52°in Helios) and back face (at a tilt angle of 30°when mounted on the Alemnis in Auriga). Pillars were fabricated using the same script and have similar dimensions (see Table 1). There are three distinct internal morphologies: sandwichpillars 2, 4, 7 and 8; minimal βpillars 1,3 and 9; and mixed α/βpillars 5 and 6. Steps in the β phase were observed, but typically these were less strong and therefore harder to observe. Slip progressed through the pillars, and in P2 the surface slip step was significantly different in the second α crystal, associated with the α/β interface. This is very different to the observation in P4, where slip continued on a similar slip plane in both α crystals.
When the morphology of the β phase is significantly changed, as shown in P5-7 (Fig. 6), the response of the micropillar tricrystal can be quite significantly different. In each of these cases, evidence of slip can be seen with surface trace analysis. The slip seems to start in the α crystals but progresses through the pillar quite differently to the response seen in pillars 2-4. P5 and P7 show slip starting towards the top of the pillar, whereas P6 shows slip starting towards the middle of the pillar. Deformation then progressed through the β phase. Deformation of the second α crystal was typically governed by the morphology of the β crystal.
The different surface traces as observed support the significant variations in the load-displacement responses. In particular, pillars 5 and 7 show similar (though subtly different) load-displacement responses whereas pillar 6 shows significantly less hardening and a lower final stress.

The structurally-affected resolved shear stress
The governing factors to activate slip are the Schmid factor (M), the critical resolved shear stress (CRSS), crystallographic orientation and the loading direction [24]. Orientations from EBSD were used to calculate Schmid factors (with the methodology shown in the Appendix) for a slip on the basal, prismatic, pyramidal planes and c a + slip on the pyramidal planes. For a slip on the basal and prismatic plane these are reported with respect to the Burgers orientation relationship (see Fig. 3 Table 2.

(iii)). A table of the Schmid factors for each pillar is shown in
Note that among pillars fabricated in region 'B', pillar 7 was chosen to represent this region and furthermore compare its deformation behaviour with pillars in other regions, by minimising the strain rate effect (see Table 1). The anticipated primary slip system and the corresponding maximum Schmid factor (M max ) were determined based on previous works that a slip on the basal and c a + slip on the 1st order pyramidal plane of α-Ti are typically at room temperature around 20% and 2.3-2.6 times harder to be activated than a slip on the prismatic slip [6,25]. These are shown in Table 3 and enable us to anticipate the slip activity such that a slip on the basal plane would be primarily activated in pillars 1, 7 and 8 and a slip on the prismatic plane in pillar 9. Due to the tri-crystal pillar structure, the Schmid factor was then used to determine the structurally-affected resolved shear stress (τ structure ) of each pillar using:

Pillar2
where the yield strength (s y ) was determined by 0.2% proof stress (R p0.2 ). The offset yield points of each pillar were carefully obtained using stress-strain curves (see Fig. 7) and Table 3 shows the R p0.2 and τ structure values of micropillars 1 and 7-9. It should be noted that interpreting the results is rather difficult due to the non-uniform stress distribution that occurred through the tapered pillar. However, the observed trend is nevertheless informative.
Pillars 1 and 9 are close to single α crystals (see Fig. 4), showing a ⟨ ⟩slip on basal plane has about 23% higher τ structure (here, close to CRSS) than a slip on the prismatic plane. This trend is similar to those typically found in the literature [6,25]. Pillars 7 and 8 have lower τ structure than pillar 1, although their slip activities were similarly anticipated. This is likely experienced by the effect of structural morphology within the pillars. More details are discussed in the next section.

Discussion
The significant anisotropic behaviour of the α phase at the single grain crystallite level is well-known and directly related to elastic properties (i.e., stiffness) and plastic deformation (i.e., slip resistance on different crystallographic planes). This indicates that not only are mechanical properties within grains highly dependent on their crystallographic orientation, but the deformation mechanism is strongly localised even at the macroscopic level. Micropillar compression testing with the aid of SEM/EBSD, FIB and nanoindenter (Alemnis) has been demonstrated to offer huge potential as an effective technique in investigating micromechanics of two-phase Ti alloys and other materials. Micropillars with square cross-section were machined to simplify slip trace analysis. This geometry has its drawback, as square shape pillars may have a higher strain hardening and earlier strain bursts compared to cylindrical geometry [26]. However, the aim of the present study is not to obtain precise mechanical properties but to find the morphological effects of α/β phases and phenomenological observation of local deformation with differently activated slip systems.  An important aspect regarding the morphological effect is shown in Figs. 5 and 6. Strain rates were similar for pillars 2-4 (4.5-5.1 Â 10 À 4 s À 1 ) and 5-7 (1.1-1.2 Â 10 À 3 s À 1 ) and hence the rate effects were minimised. Note, however, that we only considered here the α/β morphology and it is thought that the volume fraction of each phase may also have some effects on local deformation. Interestingly, in pillars 2-7 all slip steps formed first within the α phase, mostly toward the top of the pillar except pillar 6 showing slip starting towards the middle. The mechanistic basis for this phenomenon remains elusive, because the slip steps only indicate the out of pillar slip events and do not necessarily reflect the in-pillar deformation. It may be conjectured that this is either due to different dislocation evolution mechanism of each phase and the associated slip system or difference of phase properties. The figures also show that yield points vary through pillar morphologies and hardening behaviours are quite different, particularly in pillar 5 and 6 (mixed α/β), resulting in quite different stress-strain response in plastic regime. The results suggest that it might be argued that similar β morphologies lead to similar stress-strain response in the elastic and early plastic regimes.
Local slip activities with respect to crystal orientations were studied with pillars 1 and 7-9. The pillars have sandwich or minimal β structures, which may be less affected by structural morphologies. In the previous section, the primary slip system of each pillar was anticipated. Possible slip on HCP crystals at room temperature is described as a slip on the basal plane 1120 0001 ⟨¯⟩{ }, the prismatic plane 1120 1010  Fig. 8 shows the SE micrographs of deformed pillars 1 and 7-9, and the associated unit cell structures. Loading directions for unit Table 3 0.2% proof stress (R p0.2 ) and the structurally-affected resolved shear stress (τ structure ) determined in micropillars 1 and 7-9.

P1
P7 P8 P9  Fig. 7. Engineering stress-strain curves of micropillars 1 and 7-9, all fabricated in different regions (harder grain toward pillar 1 and softer toward pillar 9): Open circles marked on the curves indicate the 'yield' points observed for each pillar, and the corresponding primary slip system activated also noted. cell and pillars are out of plane and vertical, respectively. The a 1 -, a 2 -and a 3 -directions of HCP crystals were determined based on the BOR analysis shown in Fig. 3(iii). The yellow-double arrow on the unit cell indicates the primary slip direction anticipated from the Schmid factor calculation. It is seen in the micrographs of front and side2 views that all pillars deformed following the anticipated primary slip plane and direction. The slip angles caused by the primary slip (see the black dashed line on pillars) are approximately 13.1°(pillar 1), 19.5°(pillar 7), 25°(pillar 8) and 123°(pillar 9). Not surprisingly the angles are similar to the angle γ, between the c-axis of a crystal and loading direction, 14°for pillar 1 and 20°f or pillar 7, except for pillar 8 (38°) due to significant angle changes during deformation. The secondary slip can be seen in the micrographs and the angles were indicated with yellow-dot line. In pillars 1 and 7, it might be thought that c a + slip on the pyramidal plane was activated, although at this stage it is difficult to confirm the corresponding slip system and further investigation is required. a slip on the basal plane was found in pillar 9, with the slip angle of approximately 66°which is well matched with the angle γ of 68°.
Schmid's law enables the reasonable prediction of the primary and further secondary slip activities through various crystal orientations within localised areas. However, it should be noted that Schmid's law can be ineffective when the β structure varies significantly. Fig. 9 reveals τ structure variations determined for all the micropillars studied. τ structure values vary through pillars 2-7, all of which were fabricated in region 'B'. Particular difference is found in both P3 and P6; the former shows an earlier α/β phase interaction than other (see Fig. 5), and the latter shows a quite different β morphology to others (see Fig. 6). This suggests that structural morphology is a sensitive trigger of material yielding within localised areas.

Conclusions
In the present paper, micromechanical testing using a micropillar compression technique was carried out in order to investigate the local deformation mechanisms of two-phase Ti alloy.
The elastic and plastic anisotropy inherent to α crystal leads to significant inhomogeneity in stress and strain at the microstructural level. In addition, interaction between α and β crystal gives rise to a complex interplay of morphological and orientation relationship. It is therefore insightful to demonstrate local deformation mechanisms by testing local mechanical responses within isolated morphologies.
A total of nine micropillars were fabricated in four determined regions, each of which has distinct α crystal orientations. Euler angles of each phase were effectively obtained with EBSD measurements and subsequently used to calculate the Schmid factor. The main findings are summarised as:   Fig. 9. Distribution of the structurally-affected resolved shear stress (τ structure ) determined for micropillars 1-9.
1. It is shown that a combination of SEM/EBSD, FIB and in-situ deformation with a nanoindenter (Alemnis) are effective tools to investigate micromechanical deformation of two-phase Ti alloys and potentially other materials. 2. The structurally-affected resolved shear stress (τ structure ) was determined based on experimental observations. In pillars with near α crystal structure, a slip on basal planes gives about 23% higher τ structure (here, close to CRSS) than a slip on prismatic planes, which is typically found in the literature. 3. We found that local slip activities were in general anticipated by Schmid's law, though it became ineffective when β structure significantly changed. This indicates that structural morphology highly affects material yielding within a localised area. 4. Morphology of the α/β phases has significant effect on local deformation behaviour: (1) similar β morphology and similar α slip systems lead to similar stress-strain response, yet the effect of β volume fraction is not clear; (2) the β structure (or shape) within a pillar significantly affect the stress-strain response and the maximum stress level. The findings suggest the need for further investigations by testing pillars of similar morphology to confine morphological effects. 5. The advantage of micropillar compression is to obtain information of (unconstrained) mechanical properties at small volumes. This provides a basis from which to investigate grainto-grain (e.g., slip transfer) and phase-to-phase (e.g., dislocation density evolution at phase interface) interactions, which are not yet understood.