Strain rate sensitivity in commercial pure titanium:the competition between slip and deformation twinning

Qinmeng Luan1,2, T. Benjamin Britton2, Tea-Sung Jun2,3,*

1Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK

2Department of Materials, Royal School of Mines, Imperial College London, London SW7 2AZ, UK

3Department of Mechanical Engineering, Incheon National University, Incheon 22012, South Korea

*Corresponding author. Email address: t.jun@inu.ac.kr

Abstract

Titanium alloys are widely used in light weight applications such as jet engine fans, where their mechanical performance under a range of loading regimes is important. Titanium alloys are mechanically anisotropic with respect to crystallographic orientation, and remarkably titanium creeps at room temperature. This means that the strain rate sensitivity (SRS) and stress relaxation performance are critical in predicting component life. In this work, we focus on systematically exploring the macroscopic SRS of Grade 1 commercially pure titanium (CP Ti) with varying grain sizes and texture using uniaxial compression. Briefly, we find that Ti samples had positive SRS and samples compressed along the sheet rolling direction (RD) (i.e. soft grains dominant) were less rate sensitive than bars compressed along the sheet normal direction (ND) (i.e. hard grains dominant). We attribute this rate sensitivity to the relative activity of slip and twinning. Within the grain size range of , we observe an increase in the rate sensitivity, where volume fraction of T1 tensile twins was low, and the twin width at different strain rates were similar. These observations imply that the macroscopic rate sensitivity is controlled by the ensemble behaviour of local deformation processes: the amount of slips accumulated at grain boundaries affects the SRS, which is grain size and texture dependent. We hope that this experimental study motivates mechanistic modelling studies using crystal plasticity, including strain rate sensitivity and twinning, to predict the performance of titanium alloys.

Keywords: Strain rate sensitivity, pure titanium, macroscopic uniaxial compression, twin, dislocation

Introduction

Jet engines are a critical engineering structure in the modern life and in these structure titanium alloys are selected for use in the fan and lower temperature sections due to their excellent specific strength (strength to weight) and fatigue resistance [1,2]. In these applications, the role of strain rate sensitivity is likely important, especially in cold dwell fatigue where time sensitive deformation modes are thought to control fatigue crack nucleation and this has motivated some recent studies that focus on extracting the strain rate sensitive slip strengths [2–4] and their role in controlling the dwell susceptibility in Ti alloys [5,6].

The role of grain size in deformation has been widely studied, often with a focus on simple empirical observations such as the Hall-Petch effect [7–9] which promotes the idea that there is a simple scaling law that links grain size to slip strength. However, this correlative ‘law’ has recently been called into question, and microstructure blind Bayesian analysis approaches suggest that deformation could be vary from system to system and be controlled using weakest link theory [10]. In practice, the role of strain rate sensitivity, the activation of multiple different deformation modes (e.g. slip [11,12], twinning [13,14]), and how the grain boundaries impart strength due to pile-up [15–18] or forest hardening mechanisms [19] likely complicates matters and therefore we are motivated to study the correlation of microstructure and mechanical performance across grain sizes and textures in these alloys. Recently there has been a flurry of activity to extract the mechanical response of individual slip systems using from single grain tests with micro-cantilevers [20] or micropillars [2,4]. We note that micro-cantilever bend tests are not well suited to strain rate sensitivity testing, as the bending geometry naturally imparts a significant strain gradient during testing and therefore are likely to have a relative strain rate insensitivity compared to the micro-pillar geometry. However, we note that recent work by Gong et al. [20] in commercially pure zirconium has indicated a good correlation between use of the micro-cantilever derived size independent slip strengths and quasi-static macroscopic compression tests of macroscopic ~70 µm grain size compression tests, where slip is dominant and grain size strengthening is limited.

Scaling of direct slip strength from micro-scale tests up to macroscopic polycrystalline samples has proved difficult, and as such Cuddihy et al. [20] utilised calibration of their strain rate sensitive crystal plasticity model using published work by Zhang et al. [6]. We anticipate that this could be related to role of complex hardening mechanisms near grain boundaries and in the multi-axial deformation modes of polycrystalline deformation.

The stress-strain behaviour of many materials is significantly strain rate, , sensitive [21]. This can be characterised through analysis of the strain rate sensitivity (SRS) [22], where the stress-strain curves are obtained using the uniaxial tension, compression or indentation tests [23–28].

In these tests, often a very simple constitutive relationship is used for the loading behaviour, the strain rate sensitivity exponent (described as an m value) or the stress component (described as n value, ) can be determined using either the constant strain rate method (CSRM) [22], the stress relaxation method (SRM) [29–33] or strain rate jump test (SRJ) [3,34]. In the same alloy systems, there is significant variation in SRS values can be different observed with respect to the experimental methods [3,26,33] and in-part this is likely due to the different rate sensitive deformation mechanisms, as well as the fact that the ‘m factor’ varies systematically with crystal orientation due to simple geometry [6].

This can be characterised through analysis of the strain rate sensitivity (SRS) [22], where stress-strain curves are obtained using the uniaxial tension, compression or indentation tests [23–28] performed at different strain rates.

For constant strain rate method (CSRM) analysis, samples are deformed uniaxially at a range of strain rates. The flow stress at a particular strain is extracted from each curve and plotted against strain rate and the gradient of these data is used to extract using equation (2). If the gradient is flat, then it is presumed that these tests probe the same deformation mechanisms and therefore describes an empirical strain rate sensitivitiy of these mechanisms[22].

Stress relaxation (SRM) tests [29–33] are carried out when samples are deformed under displacement control, at a variable strain rates. The displacement is ceased at a fixed value, and decay in the recorded load is observed as a function of time [29]. The strain rate sensitivity, , can be calculated from the relations of applied stress ( and a stress relaxation rate (: . The recorded stress-time relationship is dependent on the plastic properties of specimen and the elastic properties of the testing machine and specimen [29,30].

Recently there has been interest in strain rate jump (SRJ) tests, as these offer the potential to probe strain rate sensitivity of the same sample in one test [3,34]. In a SRJ test, deformation is performed and the strain rate is abruptly changed during loading The value from SRJ test is based on the logarithmic ratios of stresses () and strain rates () before and after a stain rate jump as following the equation described by Pilling and Ridley [35]:

where is the jumped stress on the jumped strain rate curve, the corresponding stress, , is determined from the specific stress-strain curve, is the jumped strain rate, and is the original strain rate.

Compared with constant strain rate method (CSRM), the advantage of strain rate jump (SRJ) test is that the strain rate sensitivity is determined from a nearly constant microstructure and the variation of with strain (thus microstructure) can be found [22]. However, Kim et al. [22] demonstrated that errors in strain rate can result in considerable errors in calculated SRS values, since test errors in strain rate could be of the same order as the strain rate jump ( per cent). The SRJ test, therefore, needs accurate imposition of strain rate for the accurate determination of SRS. By contrast, the CSRM considers a large range of strain rates covering several orders of magnitude, so errors of strain rate of the order of 10 per cent do not influence too much for the result of SRS from CSRM. In this situation, CSRM is likely to be provide more reliable values of SRS.

In this work, we employ a constant strain rate method (CSRM) and the SRS can be obtained from an empirical equation described by Backofen et al. [36] from a flow stress and a strain rate at constant strain and temperature:

(2)

where is a material constant, is the true flow stress and is the true strain rate. From the stress-strain curves under constant strain rate compression, the m value can be determined by the following equation with a plot of stress () versus strain rate () in log-log form [21,22]:

(3)

As titanium alloys are typically anisotropic, the SRS is likely to be varied with grain orientations and the associated slip systems [37]. A previous study on micropillar test from Jun et al. [4] in Ti 624x alloys demonstrated that prism slips are more rate sensitive than basal slips in single phase within a dual-phase Ti alloys. In Jun et al.’s work, this difference was attributed due to the likely impact of wavy basal dislocations and cross slip in the basal pillar, as compared to planar ‘deck of cards’ crystal slip in pillars well oriented for prism slip [4].

While direct measurements of SRS using micro-tests can provide insight into the nature of slip activity, we still have yet to establish that slip system dependent SRS observed at micro-scale [28,38] can be linked to the macroscopic SRS [25,39–42] in dual phase or other Ti metals/alloys. As a first step in this story, we investigate the macroscopic SRS with single (α) phase commercially pure titanium (CP Ti). To explore the role of polycrystalline deformation on SRS, we compare samples with different grain sizes and textures at a range of strain rates within the same alloy system, ultimately with the view to develop a correlation between smaller scale tests and polycrystalline samples tested at different strain rates.

In the present work, we generate a series of samples with varying grain sizes and textures from rolled sheet of commercially pure grade 1 titanium. Samples with varying grain sizes were generated using 24 hr anneals at varying temperatures and two texture components were deformed mechanically using compression. Macroscopic stress-strain behaviour at varying displacement (i.e. strain) rates, where stress was captured using the load cell and strain was evaluated using in-situ macroscale digital image correlation (DIC) [43–46]. Strain rate sensitivity was characterised using m-factor analysis. Post deformation, characterisation of deformation activity was evaluated using optical microscopy and conventional electron backscatter diffraction (EBSD).

Experimental methods2.1. Material preparation

A rolled sheet of grade 1 CP Ti was kindly supplied by Timet UK Ltd (Birmingham). To study the grain size effect on strain rate sensitivity, as received CP Ti samples were heat treated at 700 , 730 , 800 , 830 for 24 hours and furnace cooled with a rate of 1 °C/min so as to produce a microstructure with different grain size (shown as Figure 1). The transus temperature for grade 1 CP Ti is 890 15 [47].

Figure 1. a) Heat treatment (HT) processing route for as received CP Ti; b) optical microscope images and c) grain size measurement of heat treated samples with Texture 1 (T1) and Texture 2 (T2).

Prior to mechanical testing, samples were ground to 10 after cutting and polished with 50 OP-S (Oxide Polishing Suspensions) diluted with by a ratio 1:5 of OP-S: for EBSD imaging. For microstructural characterisation, polished samples were etched using Kroll’s Reagent for 30 s (2% HF, 10% HN and 88% ).

2.2. Microstructural characterisation maps

Optical microscopy and electron backscatter diffraction (EBSD) were used for the microstructural characterisation. Optical microscopy was conducted using polarised light microscopy to reveal grain size and morphology changes. Images (see Figure 1 and 4) were captured and then interrogated using ImageJ software. The grain size of the heat treated samples was measured from the optical microscope images using a circular intercept method following ASTM E112 Abrams Three-Circle procedure [48,49]. The number of intercepts in the counting field was around 40 due to the large grain size of annealed samples compared to the sample size. The variation in grain size of was found by shifting the circles for intercept analysis.

EBSD maps were captured on a FEI Quanta 650 with Bruker eFlashHR EBSD system equipped with eFlashHR camera and Esprit v2.0 software. A high current mode was used with an accelerating voltage of 25 kV. An initial texture (see Figure 2) and EBSD maps (see Figure 3) of with a step size of 20 were captured on a face perpendicular to the ZZ axis and Schmid factor analysis (see Figure 5, using a simple assessment of the remote loading configuration) were used to evaluate likely active slip systems [37] to identify “soft” and “hard” grains (with respect to loading axis).

Figure 2. {0001} Pole figures generated from EBSD Euler maps for pure Ti after 24 hour heat treatment at (a) 700 ˚C and (b) 830 ˚C, where the horizontal axis is the rolling direction (RD) and the vertical is the transverse direction (TD) for Texture 1 (T1) samples; the horizontal is the normal direction (ND) and vertical is the rolling direction (RD) for Texture 2 (T2) samples: the loading direction for T1 samples is the TD, for T2 samples is the ND. The size of specimen is Geometry plots of performing the microstructure characterisation on T1 and T2 pure Ti are shown in (d).

Figure 3. EBSD maps (IPFZ colouring) showing grain structures and textures in (a) 700 ˚C and (b) 830 ˚C annealed pure Ti samples.

2.3. Constant strain rate compression tests and DIC

The macroscopic compression tests were carried by Shimadzu AGX10 screw thread mechanical testing frame, under variable displacement rates of the crosshead to obtain different target strain rates, i.e. 0.1, 0.01 and 0.001 respectively. The heat treated CP Ti samples were compressed along two directions, rolling direction and normal direction (i.e. Texture 1 and Texture 2 samples), to get stress-strain curves for the strain rate sensitivity (SRS) calculation. The sample for each condition was tested once. The error of stress component was found to be based on testing three times on the sample with one condition.

Time-series images were taken for the compressed surface by a microscope equipped with QCapture Pro 6.0 software. Those time-series images of surface displacement, tracked using copier toner particles, were then cross correlated and quantified by Digital Image Correlation (DIC) technique to obtain the strain response of large grain CP Ti under engineering compression.

DIC was performed using Davis 8.3 developed by LaVision Imaging Company, Gettingen, Germany [50]. The “differential” (i.e. frame n to frame n-1) correlation method in this software was chosen for tracing the movement of 3 µm photocopier particles. After correlating time-series images, the frame averaged strain and achieved strain rate were calculated and temporally matched against the load data reported from the load-cell.

The volume fraction of twins on deformed pure Ti was calculated by measuring the area of twins on the characterisation face (see Figure 4).

Figure 4. Polarised optical microscope images of heat treated pure Ti after the deformation. Row a) to e) are pure Ti heat treated at different temperature. Column 1) to 3) are pure Ti deformed at different target strain rate (from 0.1 to 0.001 ).

In this study, the twin volume fraction of all types of twins was artificially estimated from the twin area fraction [50] through a combined manual and computer based imaging process for the polarised optical microscope images. Twins were traced by hand on tracing paper and coloured in. These images were scanned and thresholded in ImageJ software [51] for area fraction calculations [52] (see Figure 5). EBSD technique could also be used to estimate the twin area fraction of different twin variants by measuring the area bordered by the twin boundaries. The error comes from the measured twin boundary length and scan step size [53]. However, using optical microscope images makes the estimation on a bigger map feasible [52].

Figure 5. An example of how to measure the area fraction of twins from an optical microscope image: a) polarised optical image of deformed 830 ˚C heat treated pure Ti under 0.001 strain rate; b) the traced twins by hand on a tracing paper; c) twins are filled with black colour for area calculation.

2.4. Contribution of twinning and slips to the plastic strain

The total plastic strain is carried by twinning and slips in the deformed sample, and the contribution from twinning can be estimated using n: where is the volume fraction of twinning and s is the twinning shear [54]. The area fraction of twinning was measured from the optical microscope images under polarised light (see Figure 4), and assumed to correlate with the volume fraction. The twinning shear of T1 tensile twins in titanium alloy was 0.17 [37,55]. We assume that the remaining strain is supported by plastic slip, and can calculate a ratio of strain accommodation for slip vs twinning (see Figure 11).

Results3.1. Initial grain size characterisation

The grain size of heat treated CP Ti samples with equiaxed grain structure was measured from optical micrographs using the Abrams 3 circle procedure [56] and plotted in Figure 1(c).

3.2. Activation of prism slips and pyramidal twin

The Schmid factors for prismatic {10}slip systems along the loading axes (XX direction shown in Figure 6). The white colour (high value of 0.5) indicates a soft orientation well aligned for slips in CP Ti, and the dark colour (low value of 0) indicates a hard orientation poorly aligned for slips. Most grains in pure Ti with T1 are favourably oriented for prismatic slips while most grains in T2 are hard to activate prism slip.

Figure 6. Schmid factor maps with respect to prismatic slip system for (a) 700 ˚C T1 CP Ti and (b) 830 ˚C T1 & T2 CP Ti. Grains with Light colour are favourably oriented for slip (i.e. soft grains); grains with dark colour are unfavourably oriented (i.e. hard grains). The line figures represent the proportion of grains that have a high Schmid factor.

Among the four twinning systems in pure titanium [57], the most commonly observed twinning system at room temperature and these strain rates is T1 tensile twins [58]. Hence, the Schmid factors of T1 pyramidal twins along the compression axis in CP Ti were checked with the aid of MTEX [59] (see Figure 7). The grains with yellow colour (0.5) indicates that T1 tensile twins can be easily activated in these grains. The grains with green (0) and blue (− 0.5) colour indicates that twins are hardly activated in these grains, as twinning only occurs for certain deformation orientation, thus, pyramidal twinning cannot occur even when the grains have a high absolute value of Schmid factor (e.g. 0.5).

Figure 7. Schmid factor maps with respect to T1 pyramidal twinning system in (a) 700 ˚C and (b) 830 ˚C T1 & T2 pure Ti. Grains with yellow colour are favourably oriented for pyramidal twinning and grains with green and blue colour are unfavourably oriented. Histograms show the distribution of Schmid factor for activating the T1 pyramidal twins.

Compression along XX (see Figure 7) may result in activation of T1 extension twins (extension twins are activated due to local compatibility strains during a compression test). The histograms in Figure 7 indicate that T1 extension twins can be easily activated for most grains in Texture 1 CP Ti and few grains in Texture 2 CP Ti. This could be the reason for the higher volume fraction of twins in T1 CP Ti. The more easily generated nucleation sites are assumed to result in the higher value of twin volume fraction.

3.3. SRS calculation

The stress values used for strain rate sensitivity calculation are taken at three different plastic strains from DIC (i.e. 6%, 7% and 8%) and are plotted with the achieved strain rate in log-log form. The plastic strain was calculated by using DIC corrected strain minus strain at 0.2% proof stress. The SRS exponent, m, is measured as the gradient of fitted line (see Figure 8), in accordance with the Equation (3). The average value of the gradients is chosen as the m value, while the standard deviation of three gradients is calculated as the arm of error bar (see Figure 9).

Figure 8. Left column: engineering stress-strain curves for heat treated pure titanium. Right column: flow stress vs. strain rate (log-log form) for heat treated pure Ti: the gradient of fitted line was calculated as the strain rate sensitivity component, , of the material.

3.4. Grain size effect on SRS

In Figure 9 a), the plot shows the relationship between SRS and grain size of T1 CP Ti: the SRS increases with the grain size of CP Ti from to , but drops to a low value for grain size . The macroscopic SRS values for heat treated CP Ti are in the range of ~ 0 to ~ 0.08.

In Figure 9 b), volume faction of twins is compared for different grain size T1 CP Ti under different strain rates. For samples with the same grain size, T1 CP Ti tends to have higher volume fraction of twins at higher strain rates (also shown in Figure 10 b)). Hence, the nucleation of twins in CP Ti is likely to be strain rate sensitive, i.e. more nucleation sites can be activated at high strain rate. For samples with different grain size, but at the same strain rates, the twin fraction drops down from to with the increase of grain size from to , but increases to by increasing the grain size to . This observation shows that the grain size of CP Ti influences the number of nucleation sites of twining relating to SRS. The twin fraction variation regarding to grain size shows an opposite trend with the strain rate sensitivity (see Figure 9 a) and b)).

The twin widths in deformed T1 CP Ti were measured to study the growth of twin (shown in Figure 9 c)). For samples with the same grain size, T1 CP Ti normally has thinner twins at higher strain rates (also shown in Figure 10 c)). Hence, the growth of twins is also rate sensitive. However, the rate sensitivity of twin growth is not the same for T1 CP Ti with different grain sizes. For samples with size and , the twin width growth is sensitive to the higher strain rate between and ; for samples with size , the twin width growth is more sensitive to the lower strain rate between and . As a comparison with Figure 9 a), the flow stresses of samples with size are more rate sensitive. Therefore, the high growth rate of twin width at high strain rates (e.g.) could be an underlying reason for the high rate sensitivity of flow stress.

Figure 9. The change of a) strain rate sensitivity (SRS), b) volume fraction of twins and c) twin width with the variation of T1 CP Ti grain size at different achieved strain rates, i.e. , and .

3.5. Texture effect on SRS

The T1 and T2 samples have the same grain size, but different texture (see Figure 2). The SRS values of T1 & T2 830 ºC heat treated CP (see Figure 10 a)) show that T2 is more rate sensitive while the SRS values for both T1 and T2 are relatively low (less than 0.04) compared with CP Ti with other grain size (above 0.07).

The twin fraction variation regarding to texture shows an opposite trend with the strain rate sensitivity (see Figure 10 a) and b)). For the twin width shown in Figure 10, the twin growth of T1 is more sensitive to the lower strain rate between and , while T1 has lower SRS. These two observations keep constant with the discussion for Figure 9.

Figure 10. The comparison of a) strain rate sensitivity (SRS), b) volume fraction of twins and c) twin width for 830 ˚C heat treated CP Ti with T1 and T2. The achieved strain rates for T1 are, and for T2 are, and .

3.6. Contribution of twinning and slips to the plastic strain

In Figure 11 for 830 ˚C annealed T1 CP Ti, the stacked bar shows the contribution of twinning () and slips () to the plastic strain (), the scattered points indicate the ratio of to at the strain rate of 0.001. The is high and the ratio of is also high for T1 CP Ti with grain size . The relative high amount of slips could be crucial for its high SRS (see Figure 9).

Figure 11. For 830 ˚C heat treated CP Ti with T1, the stacked bars represent the contribution of slips (, blue) and the contribution of twinning (red) to plastic strain () at strain rate. The scattered points represent the ratio of over .

Discussion

In this work, macroscopic compression tests were exploited to study the macroscopic performance of orientation dependent rate response of CP Ti. The DIC technique for the strain correction made the determination of SRS (i.e. m values) from stress-strain curves more reliable.

There are two crucial issues on macroscopic compression, i.e. the shape of sample and the correlation between stress and strain for the compression curve. Some of the samples were not the exact cuboid (due to machining tolerances), thus, there could be a contact misalignment between the top surface of sample and the flat punch. This resulted in slight realignment of the sample during the ‘elastic portion’ of the stress-strain response, and once the sample starts yielding artefacts due to machining tolerance were not significant. Furthermore, strain was measuring using DIC to reduce the impact of the initial compliance and realignment during this stage.

For the stress-strain curves used for SRS study, stress values were recorded by the Shimadzu machine as a function of time; strain values were calculated from the time-series images of speckled sample surface taken by a microscope equipped with QCapture Pro 6.0 software. Problem is that stress values cannot exactly be matched with the strain values, especially for the deformation at high strain rate. For the high target strain rate (e.g. 0.1 ), it took several seconds, e.g. 8 in this study, to activate the software for taking images. We have used a time offset correction to match the DIC data to our experimental stress-strain data, due to a lag between frame capture and mechanical testing, using the recording time of both data sets.

4.1. Grain size effect

The morphology of CP Ti samples which were heat treated below the transus temperature (i.e. 890 for grade 1 CP Ti) keeps the same, but the grain size increases with the heat treatment temperature (Figure 1). Therefore, the activation of slip systems and twinning mechanisms are similar for those CP Ti treated in the range of 700 to 830 (see Figure 2, 6 and 7).

For these heat treated CP Ti samples, more grains are oriented as ‘soft’ grains in T1 CP Ti and more grains are oriented as ‘hard’ grains in T2 CP Ti. In T1 samples, prism slips have a high value of Schmid factor. Hence, prism slips are easier to activate during the deformation in T1 CP Ti. The twinning system for T1 CP Ti is the T1 pyramidal tensile twins.

Therefore, the grain size should affect the macroscopic SRS values by influencing the nucleation of twins, the growth of twins and/or dislocation motion, instead of slip systems or twinning types.

4.1.1. Effect of twinning nucleation on SRS

The small amount of twin volume fraction relating to a large amount of slips probably results in the high SRS of CP Ti with grain size , e.g. 730 ˚C and 800 ˚C heat treated T1 CP Ti.

For the T1 CP Ti that has high volume fraction of twins, plastic strain would be mainly carried by twins, instead of by creating slips. As a result, few dislocations can pile up at the grain boundaries of ‘soft’ grain, reducing the possibility of facet formation. Therefore, the CP Ti samples which are prone to generating a high twin volume fraction have a lower rate sensitivity (compare Figure 9 & 11).

Normally, the larger titanium grains should tend to give higher twin volume fraction [60]. However, in this experiment, more twins are likely to be generated in the CP Ti with smaller grain size, resulting in a low value of SRS (see Figure 9). A possible explanation is that even the smallest grain size (i.e. the 700 heat treated CP Ti with grain size ) in this experiment is large enough to provide enough twin nucleation sites. The relation of twin volume fraction and grain size, therefore, becomes different with those samples whose grain size is less than .

Another striking point is that there are inflections for the evolution of SRS and twin volume fraction with grain size at 830 heat treated CP Ti (Figure 9). The exceptional trend for the twin width is also observed for the 830 heat treated CP Ti in the deformed sample. The 830 °C heat treatment is close to the β-transus temperature for CP-Ti. This changes the microstructure and influences the interrelationship between slip based mechanisms and twinning. This highlights that engineering SRS measurements, as performed here, need to be used with care when there is an interplay of plastic slip and twinning.

4.1.2. Effect of twin growth on SRS

For CP Ti with grain size and , twin grows much faster at the lowest strain rate , while the twin growth is similar and slow at strain rate and . Hence, the twin width is much wider for the CP Ti with low SRS at the lowest strain rate (see Figure 9). The twin width for the CP Ti with high SRS (i.e. grain size ) is thinner at the lowest strain rate.

If 830 ˚C T1 CP Ti is excluded in the discussion of the grain size effect on SRS, the twin width at the lowest strain rate should decrease with the increase of grain size: the smaller grains have wider twins. The slip length is longer in the bigger grains, more dislocations can pile up at the grain boundary making the nucleation of new twins easier and the growth slower. Hence, twins in large grain are thinner. By contrast, in smaller grain size, new twins are harder to nucleate and are easier to grow once nucleated. Hence, twins in small grain are wider at the lowest strain rate. However, 830 ˚C T1 CP Ti with the largest grain size does not obey this law, probably due to its abnormal high nucleation sites.

In summary, the wider twins at the lowest strain rate could interrupt the continuous slip across the whole grain which changes the effect of work hardening. Hence, less number of dislocations pile-up on the grain boundary and a slight flow stress reduction is observed leading to a low SRS eventually (see Figure 9). The thinner twins at the lowest strain rate could not interrupt the dislocation motion, leading to a high value of SRS.

4.2. Texture effect

Based on the Schmid factor calculation with respect to slip systems and twinning systems for 700 830 CP Ti, prism slips are preferentially activated in T1 samples; T1 tensile twins are easily activated in T1 CP Ti, but hardly activated in T2 CP Ti (see Figure 6 & 7). Hence, the dislocation motion in T1 CP Ti is likely to be prism slip and the twining is likely to be T1 pyramidal twins. The prism slips and twinning are unlikely to occur in T2 CP Ti.

Based on the measurement of volume fraction of twins and width of twins for 830 CP Ti (Figure 10), higher volume fraction of twins and higher rate of twin growth have been found in T1 deformed CP Ti. Hence, in T1 CP Ti, twinning can carry more plastic strain (i.e. ratio of is higher for T1 CP Ti, see Figure 11) and thicker twins could interrupt more dislocation motions, while the nucleation of twins and growth of twins are harder in T2 CP Ti.

From SRS values for T1 and T2 830 CP Ti shown in Figure 10, T2 CP Ti is more rate sensitive. Therefore, it can be concluded that the less volume fraction of twins, and thinner twins at the lowest strain rate in T2 CP Ti are likely to result in the high value of SRS. Because more slips are generated to carry the plastic strain and thinner twins could not interrupt the continuous slip across the grain in T2 CP Ti. This conclusion keeps consistent with the observation on SRS regarding to the grain size, i.e. fewer twins and thinner twins are found in the Ti alloys with high SRS.

For the effect of slip type on SRS, although Jun et al. demonstrated that prism slip is more rate sensitive in phase of Ti6242 compared with basal slip [4], it cannot conclude that the prism slips attribute to the macroscopic SRS of CP Ti, since the twinning effect is not considered and the chemical content of CP Ti is different with Ti6242. Hence, the effect of basal slips and prism slips on SRS of CP Ti is unknown.

4.3. Effect of strain rate on twinning

In this work, the strain rate is found to have effect on twinning mechanism. In Figure 9 and Figure 10, the strain rate affects the twin fraction and twin width: reducing the strain rate can decrease the volume fraction of twins and increase the twin width.

As shown in Figure 8, CP Ti is stronger at high strain rate (e.g. ). This means that the SRS, m component, should be positive for the large grain CP Ti. There are several possible reasons for its stronger behaviour at high strain rate: the more easily nucleated twins at high strain rate could contribute to this (i.e. positive rate sensitivity of twin fraction); the limited number of dislocation motion at high strain rate could also have an effect, as the strain carried by twins increases with the strain rate while the total plastic strain is fixed; the thin twin width at high strain rate could be another reason for the higher stress at higher strain rate.

In summary, high strain rate can introduce more nucleation sites for twins (i.e. higher volume fraction of twins), but reduce the twin width (i.e. not enough time for twin width growth), ultimately resulting in the positive rate sensitivity of CP Ti.

Conclusions

The volume fraction of twins and twin width have a significant effect on the macroscopic SRS of CP Ti with respect to grain size and texture. Regarding to the grain size effect on SRS, low volume fraction of twins and thin twins at the lowest strain rate have been found in CP Ti with grains , leading to a high value of SRS (~ 0.070). Regarding to the texture effect on SRS, 830 ˚C T1 samples (i.e. soft grains dominant) has a less rate sensitivity (~ 0.006) than T2 CP Ti (i.e. hard grains dominant, ~ 0.011), where prism slips and T1 tensile twins are more easily activated in T1 samples.

The mechanism of nucleation and growth of twining is important for understanding the rate sensitivity of CP Ti. The CP Ti samples which have easy mode for twin nucleation and wide twin at low strain rate are more likely to have relatively low SRS, such as T1 CP Ti with grain size . Due to the higher volume fraction of twins and wider twins in those CP Ti, less dislocations are generated to carry the plastic strain, and thicker twins could interrupt the continuous slip, thus, less dislocations can pile up at the grain boundaries of ‘soft’ grain, resulting in a less possibility of facet formation, thus, a lower rate sensitivity.

Data Statement

The data from this paper can be found as a Zenodo repository at < 10.5281/zenodo.1038216>.

Author Contributions

QL conducted DIC, mechanical testing, characterisation and analysis of the data. TSJ and QL conducted the EBSD characterisation. TBB and TSJ jointly devised the experiments and supervised the work. All authors contributed to drafting the final manuscript.

Acknowledgement

This work was conducted within the HexMat programme grant (www.imperial.ac.uk/hexmat) funded by EPSRC (EP/ K034332/1). TBB is also funded through his fellowship from the Royal Academy of Engineering. We would like to thank Professor Fionn Dunne for many helpful and enlightening discussions on strain rate sensitivity, mechanical testing, crystal plasticity and the role of grain size. EBSD Microscopy as carried out within the Harvey Flower Electron Microscopy Suite at Imperial College and in particular, we would like to thank Drs Mahmoud Ardakani and Vivian Tong for training and support of instrument usage. Mechanical testing was performed using equipment funded within the Shell AIMS UTC. We thank Matthew Thomas of TIMET UK for kindly supplying the commercially pure titanium sheet. We thank Dr Chris Gourlay for provision of the DaVis software and helpful training and advice from Te-Cheng Su on its use.

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