Metallurgical and Materials Transactions A

, Volume 39, Issue 4, pp 934–944

Deformation Twinning and the Hall–Petch Relation in Commercial Purity Ti

Authors

    • Centre for Material and Fibre InnovationDeakin University
  • U. Carlson
    • Centre for Material and Fibre InnovationDeakin University
  • M.R. Barnett
    • Centre for Material and Fibre InnovationDeakin University
Article

DOI: 10.1007/s11661-007-9442-9

Cite this article as:
Stanford, N., Carlson, U. & Barnett, M. Metall and Mat Trans A (2008) 39: 934. doi:10.1007/s11661-007-9442-9

Abstract

The effect of grain size and deformation temperature on the behavior of wire-drawn α-Ti during compression has been examined. At strains of 0.3, the flow stress exhibited a negative Hall–Petch slope. This is proposed to result from the prevalence of twinning during the compressive deformation. Electron backscattered diffraction revealed that \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) was the most prolific twin type across all the deformation temperatures and grain sizes examined. Of the twinning modes observed, \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twinning was the most sensitive to the grain size and deformation temperature. The range of morphologies exhibited by deformation twins is also described.

1 Introduction

The Hall–Petch relationship[1,2] describes the increase in strength of a material with decreasing grain size. Mathematically,
$$ \sigma = \sigma _{{\text{o}}} + kd^{{ - 1/2}} $$
(1)

This relationship holds for not only the yield stress, but also the flow stress of many materials (e.g., Reference 3). This equation was derived originally by Hall,[1] based on the principle of dislocation “pileups” at the grain boundary during deformation. It has been found to be true for many material systems (e.g., References 1 through 4) and over a wide range of grain sizes. It also holds in cases where dislocation pileups are not observed. However, because this relationship is mostly associated with materials that deform by dislocation motion, materials that deform by twinning may well not follow the same law. Indeed, in Mg alloys, it has recently been shown that a negative Hall–Petch slope can be obtained; i.e., the strength of the material decreases with decreasing grain size.[5] In that instance, the texture was such that during the compression testing, many grains were well oriented for \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twinning. Twinning is known to be relatively temperature insensitive,[6] while slip is known to be much easier as the temperature is increased.[7] As a result of these two factors, a transitional region between slip-dominated and twinning-dominated deformation was observed at an intermediate temperature. It was in this transitional region that a negative Hall–Petch slope was observed.[5] Beyond this transitional region, the material returns to the commonly observed behavior of a positive Hall–Petch slope, that is, increasing strength with decreasing grain size.

Titanium is known to deform readily by prismatic slip on the \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}0\} \) planes in the \( {\left\langle {1\ifmmode\expandafter\bar\else\expandafter\=\fi{2}10} \right\rangle } \) directions.[8] This imparts Ti with only three independent “easy” slip systems, and to accommodate plastic strain, it exhibits twinning on the \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \), \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \), \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \), and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) planes.[810] In Ti, the \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) and \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twins result in extension of the c-axis, while \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) and \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \) twinning result in c-axis contraction. Consequently, the type of twins that form are a balance between the texture of the material and the direction of applied strain. There is some suggestion in the three grain sizes examined by Garde and Reed-Hill[11] of a negative Hall–Petch slope in material tested at 77 K. Extensive twinning was observed to occur in that case, and the phenomenon is possibly similar to that described previously for magnesium.

The aim of this work is to investigate the possibility of anomalous Hall–Petch behavior in α-titanium in the vicinity of twinning transitions. In order to promote twinning, the texture is manipulated to ensure prolific activation of the “easy” \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twinning mode. In the following, we report our results on the effect of grain size and temperature on the deformation mechanisms and stress-strain response.

2 Experimental Method

The material used in this study was commercial purity grade 2 Ti supplied by Timet UK Ltd. (Swansea, West Glamorgan, UK). In order to generate samples with different grain sizes, the as-received bars were cold drawn to reduction ratios of up to 2.5, and then annealed. This sample preparation was chosen so that the starting material would have a fiber texture typical of extruded hcp metals, that is, c-axes aligned perpendicular to the extrusion direction. Annealing was carried out at various times and at temperatures between 600 °C and 750 °C to recrystallize the microstructure. All annealing was carried out in a tube furnace under flowing argon atmosphere. This procedure generated a range of grain sizes between 13 and 85 μm, measured using the linear intercept method.

After drawing and annealing, samples with an approximate height of 8 mm were machined from the rods. These samples were then deformed in compression at a rate of 0.01 s−1 at temperatures between room temperature and 400 °C to a true strain of 0.3. Each deformation condition was repeated up to 3 times over the full range of grain sizes examined. The flow curves of the repeated experiments showed a consistent behavior, with the variation between stress-strain response of repeated tests being better than ±5 pct. The compression samples were oriented such that the compression direction was parallel to the prior drawing direction. In addition to these tests, selected samples were deformed to a strain of 0.2 to investigate the microstructural development.

For texture and microstructural analysis, samples were examined using electron backscattered diffraction (EBSD, Centre for Material and Fibre Innovation, Deakin University, Geelong, Australia). The EBSD was carried out on a LEO Gemini field emission gun scanning electron microscope (SEM, Centre for Material and Fibre Innovation, Deakin University, Geelong, Australia) fitted with HKL Channel 5 software. For electron microscopy, samples were polished down to 9-μm diamond paste followed by 12 hours of colloidal silica (Struers OPS, Struers@Intellection, Brisbane, Australia) on a Vibromet vibrating polishing pad. For optical microscopy, samples were polished with colloidal silica and examined using polarized light.

3 Results

3.1 Mechanical Behavior

The stress-strain curves obtained after compression of samples with a starting grain size of 59 μm are shown in Figure 1(a) and are typical of the stress-strain curves obtained in this study. At room temperature, the samples exhibited yielding at approximately 450 MPa. Yielding was followed by a steady increase in the stress with further strain, and at a strain of 0.2, the stress had reached in excess of 800 MPa. Other works report room-temperature σ0.2 on the order of 400 MPa in both tension[12] and compression,[13] which is approximately half of the values measured here. This difference is likely to result from interstitial content: grade 2 Ti has a maximum oxygen content of 0.25 wt pct, while the work described in References 12 and 13 has interstitial contents more than two orders of magnitude smaller.
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Fig. 1

(a) True-stress–true-strain curves for the deformation of α-Ti with a starting grain size of 58 μm. The deformation temperature for each test is as indicated in the figure. (b) True-stress–true-strain curves for samples with starting grain sizes as shown

In each temperature range, but particularly in the case of the sample deformed at 200 °C, a characteristic S shape is evident in the stress-strain curve. This has previously been observed in Ti,[13] as well as in other hexagonal metals such as Mg[5] and Zr.[14]

The compression test results after deformation at 25 °C, 200 °C, and 400 °C for selected grain sizes are shown in Figure 1(b). It can be seen that at the higher two temperatures (200 °C and 400 °C), the samples with the larger grain sizes actually exhibit higher flow stress values compared to the smaller grained samples, at a strain of 0.3.

The stresses corresponding to strains of 0.002 and 0.3 are plotted against the inverse square root of grain size, as described by the Hall–Petch equation (Figure 2). In all instances, the σ0.002 flow stress values exhibited a positive slope, that is, a positive k value. This is typical behavior exhibited by many metallic materials.[3] At the higher strain of 0.3, deformation at room temperature is also consistent with this behavior, and a positive value of k is obtained (Figure 2(a)). However, at higher deformation temperatures, it can be seen that a negative value of k is obtained at a strain of 0.3, shown by a negative slope on the graphs in Figure 2(b). After deformation at 100 °C, a transition in behavior at a grain size of ∼50 μm can be observed, below which a negative slope is obtained. At all deformation temperatures above 100 °C, the б0.3 values produce a negative k value across the full range of grain sizes tested. This negative slope indicates that the material will increase in strength with an increase in grain size.
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Fig. 2

Measured flow stress at true strains of 0.002 and 0.3 for samples with a range of starting grain sizes, measured at different deformation temperatures

The k values are shown in Figure 3 for each of the deformation conditions. The error bars derived from the data used to determine each point are considerable. However, it is clear that above room temperature, deformation of α-Ti to a strain of 0.3 results in negative Hall–Petch behavior. The value of k drops below zero at the transition temperature of 100 °C and remains constant with increasing deformation temperature. For the stresses close to yield, the Hall–Petch slope fell between 0.01 and 0.37 MPa mm−1/2. These values are surprisingly low compared to reports in the literature,[12] and a possible reason for this will be presented in the discussion.
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Fig. 3

The k values determined from the slope of the Hall–Petch plot, shown as a function of deformation temperature

In an attempt to further elucidate the deformation mechanisms, the stress-strain curves were examined for a change in their slope. This technique has been used by Salem et al.,[15,16] who identified three distinct deformation stages. Stage A is typified by a decreasing work-hardening rate, and stage B is defined as the portion of the curve that exhibits an increasing work-hardening rate and is purported to result from the activation of deformation by twinning. Finally, in stage C, the material returns to a decreasing work-hardening rate with further deformation. The analysis of three typical curves, obtained from deformation of samples with initial grain sizes of 17, 59, and 85 μm and deformed at 300 °C, is shown in Figure 4(a). These curves are consistent with those found by Salem et al.[15,16] and show that the onset of stage B occurs at a strain of about 0.06.
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Fig. 4

(a) Derivative of the stress-strain curve (/) for samples with starting grain sizes of 17, 58, and 85 μm deformed at a temperature of 300 °C. (b) Strain corresponding to the onset of stages B and C deformation behavior for samples with starting grain sizes of 17, 58, and 85 μm at the deformation temperatures shown

The flow curves obtained from specimens with starting grain sizes of 17, 59, and 85 μm that were deformed between room temperature and 400 °C were analyzed in the same way as those shown in Figure 4(a). The onset of stage B and stage C deformation was determined for each of these flow curves (Figure 4(b)). Figure 4(b) indicates that there is a slight decrease in the strain to the onset of stages B and C with increasing deformation temperature, but within the scatter of results, this is not likely to be significant.

This graph suggests that the strain at which twinning begins to dominate the plastic deformation is relatively insensitive to deformation temperature, grain size, or strain. This is clearly at odds with the microstructural observations that show the twinning to be more prevalent at larger grain sizes and lower deformation temperatures (this will be further discussed in Section III–B). Although it appears to be true that a rise in the work-hardening rate is a typical behavior displayed by materials that deform by twinning, the results presented here suggest that further information pertaining to the mechanisms of deformation at a given strain cannot be directly inferred from the work-hardening rate. This is most likely due to the complicating influence of concurrent deformation by dislocation glide and any associated dynamic recovery.

3.2 Microstructure and Twinning

The post-deformation microstructure was examined optically, and typical microstructures for selected deformation conditions and starting grain sizes are shown in Figure 5. It can be seen in Figure 5, in which the microstructures shown correspond to a strain of 0.2, that twinning is evident at both high and low deformation temperatures and in the coarse- and fine-grained samples.
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Fig. 5

(a) through (d) Polarized light optical micrographs, shown after a strain of 0.2, for the deformation conditions shown. Note the higher magnification in (c) and (d)

The microstructure and texture of selected samples was examined further by EBSD in order to distinguish between the different twin types and to investigate the texture development. Figure 6(a) shows that the starting texture was a fiber texture in which the basal poles are aligned perpendicular to the drawing direction. Grain size had a minimal effect on the strength or shape of the starting texture (Figure 6(b)). The deformation textures of four selected samples after a strain of 0.2 are shown in Figures 6(c) through (f). The examples shown are for grain sizes of 17 and 85 μm after deformation at room temperature and 400 °C. The fine-grained samples deformed at low and high temperatures both exhibit similar textures. The texture component at \( {\left\langle {1\ifmmode\expandafter\bar\else\expandafter\=\fi{2}10} \right\rangle } \) is a deformation texture and remains from the starting texture of the samples before deformation. The texture component at \( {\left\langle {0001} \right\rangle } \) results from \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twinning. Investigation of the EBSD orientation maps (Figure 7) showed that although the number of individual twins was lower in the fine-grained sample deformed at higher temperatures, these twins grew much larger during high-temperature deformation, compared to room-temperature deformation. The inverse pole figures indicate that, nominally, half of the microstructure twinned in the fine-grained cases.
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Fig. 6

Starting texture and final texture measured using EBSD. The texture strength for each inverse pole figure is given in times random intensity. Inverse pole figures refer to the drawing and compression directions, these directions being identical with respect to the sample geometry

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Fig. 7

EBSD orientation maps of samples after deformation to a strain of 0.2 at the temperatures shown. The EBSD maps are displayed with \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twin boundaries shown in red, \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twin boundaries shown in pink, and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) boundaries shown in blue. \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \) boundaries were not observed

The texture resulting from high-temperature deformation of the coarse-grained sample shows a strong peak at \( {\left\langle {0001} \right\rangle } \), indicating that a large portion of the microstructure has deformed by \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twinning, and this was confirmed by the orientation mapping (Figure 7). The coarse-grained sample, deformed at room temperature, showed a weaker \( {\left\langle {0001} \right\rangle } \) peak. The EBSD orientation maps showed that in addition to the \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twins that form a strong \( {\left\langle {0001} \right\rangle } \) texture, \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \), and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) twins were also formed during room-temperature deformation of the coarse-grained sample. These additional twinning modes weaken the \( {\left\langle {0001} \right\rangle } \) texture and promote a \( {\left\langle {1\ifmmode\expandafter\bar\else\expandafter\=\fi{2}10} \right\rangle } \) texture component.

The EBSD orientation maps show that there was some \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twinning in all samples over all deformation temperatures (shown in red in Figure 7). The coarse-grained sample deformed at room temperature exhibited the most prolific twinning, and the number of twins decreased with decreasing grain size and increasing deformation temperature. These observations are consistent with those previously made on hexagonal metals (e.g., Reference 17). Of the four samples examined using EBSD, only the coarse-grained sample deformed at room temperature exhibited \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) twins (shown in pink and blue, respectively, in Figure 7).

4 Discussion

4.1 Hall–Petch Relation

It is clear from Figure 2 that at temperatures above 100 °C, Ti exhibits a negative Hall–Petch slope at a strain of 0.3. Negative k values are an anomaly, but have been observed before in Mg.[5] In that case, and likely in the case here, the negative values of k result from the extensive twinning exhibited by Ti. According to this view, the region in which a negative slope is obtained is the transitional region between slip-dominated and twin-dominated flow.[5] This is shown schematically in Figure 8. The flow stress resulting from deformation of a material that deforms by slip will increase with decreasing grain size. This too is the case for twinning-dominated flow. However, the flow stress resulting from deformation by twinning is typically higher than that obtained for slip alone. This is due to the increased difficulty of slip in the presence of twins. When the texture and deformation conditions are such that the material moves through the transition from twinning-dominated flow to slip-dominated flow, a negative Hall–Petch slope can be obtained. This negative Hall–Petch slope does not result from the addition of two different hardening mechanisms; rather, it results from a transition from one dominant hardening mechanism to another.
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Fig. 8

Schematic representation of the flow stress resulting from slip-dominated and twin-dominated flow. The transitional region between these two flow behaviors is also shown and indicates the region in which a negative Hall–Petch slope may be obtained

The increased occurrence of twinning in the coarser grained samples confirms that the present experiments fall within the slip-twinning transition. Under these conditions, the contributions made by each mode are shared in proportions determined by the starting grain size and deformation temperature. The present effect does indeed seem to be quite similar to that observed previously in magnesium and described earlier. There is, however, at least one striking difference in behavior of the two metals. In the previous work on Mg-3Al-1Zn, the twinning-slip transition was readily observed in its entirety,[5] but in the current case, the full suppression of twinning was not attained. In the Mg study, the grain size range was 4 to 30 μm and the temperature range T/Tm ∼ 0.3 to 0.5. In the current case, the grain size range is 10 to 80 μm and the temperature range T/Tm = 0.15 to 0.35. The lower temperatures and coarser grain sizes employed here are clearly part of the reason for the persistence of twinning over the range of conditions employed. However, it is also true that there are more twinning modes that are readily activated in titanium, and this will tend to widen the grain size and temperature range over which the slip-twinning transition occurs.

The fact that the anomalous negative k values are seen only at higher strains is due to the heightened contribution of twinning to the flow stress required for slip. At lower strains, the interaction between the two modes is expected to be less. Nevertheless, the particularly low values for k0.002 seen here might be an indication of an early onset of the effect. Unfortunately, more extensive comparison with the literature is not possible because of the somewhat unique combination of compression with a wire drawing texture.

4.2 Deformation Twinning

There have been a number of different twinning modes proposed to occur in Ti: \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \), \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \), \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \), and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \). These planes are shown schematically in Figure 9. Of these twin types, all but the \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \) twins are commonly observed at room temperature.[10] Each twin type exhibits a distinct axis/angle misorientation across the twin boundary. This results from the unique lattice rotation corresponding to each twin type. Previously,[10] the crystallography of twins has been examined with TEM. However, the advent of EBSD has allowed investigation of much larger numbers of grain boundaries within samples. The TEM allows only a small number to be analyzed. The statistics involved in these measurements is particularly relevant in the study of deformation twins that are subject to further plastic deformation before being examined. Such twins are likely to display small deviations from the actual twin misorientation that existed when the twin was first formed. With these issues in mind, the EBSD data were used to examine more closely the twinning behavior of selected samples after a compression strain of 0.2. In particular, the aim was to determine which twins were operative during deformation at different temperatures and to quantify the effect of the starting grain size.
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Fig. 9

Schematic representation of the four planes that exhibit twinning in Ti. Also shown is an example of c-axis extension for the \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twin and c-axis contraction for the \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twin[7]

First, the axis and angle of misorientation arising from the different twinning modes were calculated for Ti assuming a c/a ratio of 1.587 (Table I). Also given in Table I are data regarding whether the twin causes c-axis extension or c-axis contraction. Those twin types that cause c-axis extension are operative when a tensile stress is applied to the c-axis or when compressive stress is applied perpendicular to it. In the same way, c-axis contraction twins are operative when a compressive strain is applied to the c-axis. Schematic illustrations of how twinning causes c-axis extension and contraction are given in Figure 9.
Table I

Angle and Axis of Misorientation for the Twinning Types Listed; the + and − Symbols Represent c-Axis Extension or Contraction, Respectively

Twin Type

Misorientation Angle

Misorientation Axis

\( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) +

85.0

\( {\left\langle {1\ifmmode\expandafter\bar\else\expandafter\=\fi{2}10} \right\rangle } \)

\( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \)

57.2

\( {\left\langle {1\ifmmode\expandafter\bar\else\expandafter\=\fi{2}10} \right\rangle } \)

\( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \)

64.4

\( {\left\langle {10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}0} \right\rangle } \)

\( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) +

35.0

\( {\left\langle {10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}0} \right\rangle } \)

Due to crystal symmetry, twins exhibit different crystallographically equivalent variants. For example, the \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twins can form on any of the six \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) planes. Each twin will exhibit the same axis/angle misorientations to the parent grain. However, if more than one twin variant operates within the same parent grain, the boundary where these variants impinge will have a characteristic misorientation. These have been calculated for c-axis extension twins in Ti and are shown in Figure 10. For completeness sake, the misorientations arising from the intersection of \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \) and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twin variants, which are both c-axis contraction twins, are also shown in Figure 10.
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Fig. 10

Axis and angle of misorientation between variants of the same twin type. \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) are c-axis extension twins, and \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \) and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) are c-axis contraction twins. The axis of misorientation is shown for each case on an inverse pole figure and is also given as low-order Miller indices. The angle in brackets represents the deviation between the actual misorientation axis and the low-order Miller indices given

The boundary misorientation data obtained from EBSD maps are shown in Figure 11. Let us begin by examining the data for the coarse-grained sample deformed at room temperature. This sample is best suited to exhibit extensive twinning, because it has the largest grain size and is deformed at the lowest temperature of the samples examined here, room temperature. The prolific twinning that occurred in this sample was also clearly evident through the EBSD orientation maps (Figure 7).
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Fig. 11

Misorientation distribution function for samples deformed at the temperatures indicated. Data are shown for samples with starting grain sizes of 17 and 85 μm. The axes of misorientation shown are for the coarse-grained sample only

In Figure 11, there is a peak in the grain boundary misorientation histogram at around 85 deg, and the corresponding misorientation axis data indicate that these boundaries have a misorientation axis of \( {\left\langle {1\ifmmode\expandafter\bar\else\expandafter\=\fi{2}10} \right\rangle } \). This corresponds to the \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twin boundary. This is the most prolific twinning type in this sample. There is another peak in the misorientations histogram at ∼65 deg, and this peak corresponds to an axis of rotation about \( {\left\langle {10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}0} \right\rangle } \), indicating that these boundaries have formed by the activation of \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twins. There is also a small rise in the misorientations at 35 deg in this sample. The inverse pole figure indicates that these have a misorientation axis of \( {\left\langle {10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}0} \right\rangle } \), indicating that \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) twins are also active in this specimen. The misorientation pole figure for misorientations of 57 deg (±5 deg) shows there is a cluster in misorientation axes, but these are not around \( {\left\langle {1\ifmmode\expandafter\bar\else\expandafter\=\fi{2}10} \right\rangle } \), and are therefore not from the operation of \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \) twins. These are likely to result from the intersection of different \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twin variants (Figure 10).

Comparing now the misorientation data for the coarse- and fine-grained samples deformed at room temperature, it can be seen that both samples exhibit extensive \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twinning. However, the fine-grained sample does not exhibit any evidence of \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) or \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) twinning.

At higher deformation temperatures, the amount of \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twinning evident in the misorientation data has decreased. This is consistent with the microstructural observations reported in the results section, which showed the amount of twinning to decrease with increasing deformation temperature. The misorientations arising from \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) twinning are not evident in either sample after high-temperature deformation. However, the coarse-grained sample exhibits a new peak at ∼58 deg after high-temperature deformation, which is not evident in the other EBSD maps. The axis for these misorientations is clustered around \( {\left\langle {1\ifmmode\expandafter\bar\else\expandafter\=\fi{2}10} \right\rangle } \). It is unlikely that these result from the operation of \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \) twins and are more likely to result from the intersection of \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) variants. This is consistent with the observation that the sample deformed at 400 °C showed larger twins than the sample deformed at room temperature. Larger twins are more likely to impinge one another and form boundaries with orientations shown in Figure 10.

The shear associated with twinning on each of the different twin systems has been calculated by Yoo.[9] By convention, a positive twinning shear refers to extension along the c-axis. In the samples examined here, the starting texture was such that the compression was applied perpendicular to the c-axis (Figure 6). It is therefore likely that the twinning modes that give c-axis extension would be the most prolific. For Ti, \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) and \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}1\} \) have negative shear, while \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) have positive shear. It is consistent with these calculated twinning shears that the most prolific twinning mode observed after all deformation conditions is \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \), a twinning mode that allows extension in the c-axis.

The analysis shown in Figure 11 was derived from a large data set. To examine more fully the twinning behavior, selected grains were examined individually. The grain shown in Figure 12 is from the sample with a starting grain size of 17 μm and was deformed to a strain of 0.2 at room temperature. This selected grain is oriented such that the c-axis is aligned almost exactly with the compression direction. As a result, it has twinned on four variants of the \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twin, which is a c-axis contraction twin. The twin type is confirmed by the misorientation inverse pole figure that shows the axis of misorientation to be 65 deg about \( {\left\langle {10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}0} \right\rangle } \). Figure 13 shows double twinning, or internal twinning.[18] This mechanism has been seen before in fcc metals and also in Mg.[19] Double twinning refers to the formation of a twin inside a region that has already twinned once. In the example shown in Figure 13, the parent orientation has first formed a \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twin, which is shown by the white boundary. As a result of further deformation, the c-axis inside the twin is closely aligned with the compression direction. Subsequently, this region formed a \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twin. There were also examples of parent grains being almost completely twinned (Figure 14). In this figure, it could be assumed that the twinned volumes are the smaller lath-shaped volumes protruding from the grain boundary toward the grain center. This is likely how the microstructure would be interpreted through optical microscopy. However, orientation analysis shows that these smaller lath-shaped volumes have very similar orientations and are, in fact, the parent orientation. The remainder of the grain has two distinct orientations, and these are separated by a boundary of ∼55 deg about \( {\left\langle {10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}0} \right\rangle } \), which results from the intersection of two \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twin variants.
https://static-content.springer.com/image/art%3A10.1007%2Fs11661-007-9442-9/MediaObjects/11661_2007_9442_Fig12_HTML.gif
Fig. 12

EBSD orientation map showing development of four \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twin variants within the one parent orientation. CD = compression direction

https://static-content.springer.com/image/art%3A10.1007%2Fs11661-007-9442-9/MediaObjects/11661_2007_9442_Fig13_HTML.gif
Fig. 13

EBSD orientation map of double twinning of a small \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twin inside a larger \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twin. CD = compression direction

https://static-content.springer.com/image/art%3A10.1007%2Fs11661-007-9442-9/MediaObjects/11661_2007_9442_Fig14_HTML.gif
Fig. 14

EBSD orientation map of a parent orientation (P) that has formed two different \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twin variants (T1 and T2). The boundaries between the parent orientation and the \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twins are shown in white. The intersection of the two different twin variants forms a boundary, shown in black, of around 55 deg about an axis of \( {\left\langle {10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}0} \right\rangle } \), as shown in Fig. 10

5 Conclusions

The effect of grain size and temperature on the deformation behaviour of α-Ti has been examined. The major conclusions are as follows:
  1. 1.

    The stress-strain curves exhibited a portion of increasing work-hardening rate between strains of approximately 0.05 and 0.2. This rise in work hardening has been attributed to the dominance of twinning as a deformation mode within this strain regime.

     
  2. 2.

    It has been shown that in α-Ti, a negative Hall–Petch slope can be obtained. This anomalous behavior, indicating that the strength of the material decreases with decreasing grain size, is ascribed to the prolific twinning that occurred during deformation.

     
  3. 3.

    The EBSD has been used to evaluate the twinning behavior, and it has been shown that in α-Ti, the most extensive twinning mode that operates during compressive deformation of wire drawn material is \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twinning. This twin type was observed after all deformation conditions and in samples of all starting grain sizes, from 17 to 85 μm.

     
  4. 4.

    Despite the starting texture being ideally suited to \( \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\} \) twinning, \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) and \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}1\} \) twinning were also observed after room-temperature deformation of coarse-grained samples.

     
  5. 5.

    The \( \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\} \) twinning has been shown to be very sensitive to grain size, being clearly observed after room-temperature deformation of the 85-μm grain-sized sample and completely inhibited in the 17-μm grain-sized sample.

     
  6. 6.

    The EBSD has been used to show that during deformation, twinning can occur on multiple variants within the one parent grain. Double twinning or secondary twinning of a volume that has already twinned once has been shown to occur during deformation.

     
  7. 7.

    It was observed that large twins that almost completely engulf the entire parent orientation can form during deformation. The axis and angle of misorientation resulting from the intersection of different twin variants of the same type have been calculated and correspond well with experimentally measured values.

     

Acknowledgments

The work described in this article was funded by the Australian Research Council through the Centre of Excellence in Light Metals. The assistance of Ms. Zohreh Keshavarz, Ms. Katrina Morgans, and Dr. Andrew Sullivan with the experimental work is also gratefully acknowledged.

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2008