Effect of twinning on microstructure and texture evolutions of pure Ti during dynamic plastic deformation

Materials Science & Engineering A 564 (2013) 22–33

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Effect of twinning on microstructure and texture evolutions of pure Ti during dynamic plastic deformation Feng Xu a, Xiyan Zhang a,n, Haitao Ni b, Youming Cheng a, Yutao Zhu c, Qing Liu a a

School of Materials Science and Engineering, Chongqing University, Chongqing 400044, China School of Materials and Chemical Engineering, Chongqing University of Arts and Sciences, Chongqing 402160, China c Guangxi Alnan Alumium Fabrication Co. Ltd, Nanning 530031, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 11 July 2012 Received in revised form 11 October 2012 Accepted 26 November 2012 Available online 1 December 2012

The microstructure and texture evolution of pure Ti during dynamic plastic deformation were systematically investigated. The dynamic plastic deformation (e_ ¼ 4–6  102 s  1) on cylindrical Ti specimens realized by high-speed impact. The microstructure and texture were examined by electron backscattering diffraction (EBSD) and x-ray diffraction (XRD). Four types of deformation twins were observed at all strains, and twins played an important role in the grain fragmentation and texture evolution. At low strain levels (e o 0.2), the deformation was accommodated by the dominant twinning and the subsidiary dislocation slip. Then deformation twins eventually evolved into a saturation level when strain increased to 0.2. From medium to high levels of deformation (e ¼ 0.3–0.8), slip became predominant and shear bands developed. The initial texture with a bimodal distribution (undeformed) was weakened and transformed into a ring-like distribution by twinning when the strain approached to 0.2, and then further evolved into a basal texture by slip when the strain exceeded 0.4. & 2012 Elsevier B.V. All rights reserved.

Keywords: Twinning Microstructure Texture Titanium Dynamic plastic deformation

1. Introduction The evolution of microstructure and texture in cubic metals has been well investigated in past decades [1–3]. However, the microstructure and texture evolutions in hexagonal-close-packed (h.c.p) metals have not been well understood [4–8]. The deformation mechanisms of h.c.p metals, which usually have a few number of independent slip systems, usually require twinning deformation during plastic deformation. For titanium (Ti), the deformation mechanism is even more complex due to its less-than-ideal c/a ratio of 1.587 and the twin-slip coordinated deformation. The commonly observed deformation mechanisms for Ti at room temperature include {1010}/1210Sprismatic slip, {0 0 0 2}/1 1 2 0S basal slip, {1 0 1 1}/1 2 1 0Sand {1 0 1 2}/1 2 1 0S pyramidal slip; {1 0 1 2}/1 0 1 1S tensile twinning, {1 1 2 1}/1 1 2 6Stensile twinning, {1 1 2 2} /1 1 2 3S compressive twinning [9–12](Table 1). The activation of deformation twinning results in further grain fragmentation induced by the intersection of twins and the possible formation of secondary and tertiary twins. In turn, this leads to a gradual decrease in the twinning ability of Ti. Thus, dislocation slip becomes dominate at high strain levels [13–16].

n

Corresponding authors: Tel./fax: þ 86 23 6511 2154. E-mail address: [email protected] (X. Zhang).

0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.11.097

The microstructure and texture evolutions for Ti and Ti alloys have been extensively investigated during low strain rate deformation, such as cold/hot rolling and uniaxial compression [17–23]. The rolling microstructure and texture of Ti were first studied by Williams et al. [21] and continued by other authors [22]. Chun et al. [23] have found that the primal bimodal distribution of basal pole transforms to a basal texture at low to medium levels of deformation during cold rolling (e_ is estimated to be 0.8 s  1), afterwards, the typical rolling texture forms in the final 90% cold rolled condition. Recently, dynamic plastic deformation (DPD) of cubic and h.c.p metals raises research attention. DPD is initially developed to realize high-strain-rate deformation of bulk Cu or Cu–Zn materials at liquid nitrogen temperature [24,25]. The strain rate of DPD (102–103 s  1) is higher than quasi static deformation (o10  1 s  1) or rolling (0.8 s  1) but lower than explosive cladding (5  105–106 s  1) or compression Hopkinson bar (9  102– 7.6  106 s  1) [26,27]. Previous experimental results show that DPD could enhance the occurrence of deformation twinning and the refinement of grains, particularly for h.c.p metals. In previous research of author [28], the rare {1 1 2 4}/2 2 4 3S compressive twinning has been found to be associated with the {1 1 2 2} twinning during DPD at room temperature. Wulf et al. [29] studied high strain-rate behavior of pure titanium at room temperature using Hopkinson bar. Nenat-Nasser et al. [30] investigated the mechanical properties of commercially pure titanium in a wide range of strain rates and temperature.

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Table 1 Slip and twinning systems in Ti. Shear strain Slip systems

Basal Prismatic Pyramidal cþ a

Twin systems

Tensile

Compressive

{0 0 0 1}/1210S {1010}/1210S {1011}/1123S {1122}/1123S {1012}/1011S {1121}/1126S {1123}/3362S {1122}/1123S {1124}/1121S {1011}/1012S

0.167 0.638 0.533 0.225 0.254 0.105

However, to our knowledge, little has been done on studying the microstructure and texture evolutions of pure Ti during DPD. In this work, the microstructure and texture evolutions in pure Ti during room-temperature DPD were investigated by optical microscopy (OM), x-ray diffraction (XRD) and electron back scatter diffraction (EBSD) techniques. We sought to gain a better understanding deformation twinning systems and their effects on the microstructure and texture evolution during DPD.

2. Experimental procedures The material used in this study was a high purity a-Ti (99.99%) received as 100 mm  100 mm  10 mm rolled plate. As shown in Fig. 1(a), the material was fully recrystallized producing an equiaxed grain structure with an average grain size of 10 mm. There was only a-phase obtained in it, which would be attributed to the disappearance of few b-stabilizer effecting. The (0 0 0 2) pole figures as shown in Fig. 1(b) indicate that the c-axes of many grains located 7351 from the loading direction (LD) to the Y. The samples were prepared with dimensions of 8 mm in diameter and 10 mm in height, and then deformed at room temperature by DPD. In deformation experiments, the compression direction of DPD was designed to be perpendicular to the X–Y plane. The deformation strain was calculated by the reduction of height, as e ¼(L0  Ld)/L0, where L0 and Ld were the initial and final height of the deformed sample, respectively. According to the deformation mechanism and texture evolution, the whole deformation process was divided into three stages: low levels (0.05r e r0.2), medium levels (0.2o e r0.4) and high levels (0.4 o e r0.8) of deformation. The detailed experimental method was presented in [31,32]. High-strain-rate uniaxial compression experiments were performed using Instron Dynatup 8120 system by means of DPD. The strain rate was estimated to be 4–6  102 s  1. Solid lubricant was used to reduce frictional effects in the experimentations. The microstructure and misorientation of samples were obtained by EBSD. For EBSD analysis, the samples were cut in the longitudinal direction, then mechanically polished and electro-polished in a solution consisting of 6 ml perchloric acid and 90 ml glacial acetic acid at 30 V and 288 K. EBSD scans were obtained using FEI Nova 400 field emission gun scanning electron microscope operating at 20 kV. The data were acquired and processed with the HKL Channel 5 software to get some useful maps, such as Kikuchi band contrast (KBC). The KBC is very sensitive to the crystalline defects, which could clearly indicate the grain boundaries and twin interfaces [33]. The texture and orientation distribution function (ODF) measurements were obtained by XRD technique on a Rigaku D/max 2500PC (18 kW). The samples had a minimum of 0.5 cm2 surface area. The (1 0 1 0), (0 0 0 2), (1 0 1 1), (1 0 1 2) and (1 1 2 0) pole figures were measured separately on the head face using the Schulz

Fig. 1. Microstructure and texture of the initial sample: (a) optical microstructure and (b) pole figures obtained by XRD.

reflection method. The data were analyzed using LaboTex 3.0 texture analysis software, to achieve corrected and recalculated pole figures and orientation distribution. Then using the five pole figures, the ODF was calculated based on the arbitrarily defined cell (ADC) method. Concerning the texture representation, only j2 ¼301 ODF section, containing the major texture components, is given here. The {j1, f, j2} Euler angles were represented with reference to a crystal coordinate system consisting of X¼[1 0 1 0], Y ¼[1 2 1 0], Z¼ [0 0 0 1].

3. Results 3.1. Microstructure evolution during low-to-medium levels of deformation The development of non-uniform microstructure at lowto-medium levels (e ¼0.05–0.4) of deformation is due to the fragmentation of some grains deformed by twinning and the

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elongation of other grains deformed by slip alone. As shown in Fig. 2, the different kinds of twinning boundaries are clearly distinguished. It is found that the amount of deformation twins gradually increase with the increasing deformation levels. For example, the microstructure of e ¼ 0.1 sample in Fig. 2(a) is similar to that of the starting material, except for some twins occur in a few grains. However, more twinning is activated in more grains with the increasing deformation levels. At yet the higher levels of deformation, a striking refinement of the microstructure is shown in more grains (Fig. 2(b)–(d)). Moreover, the initial grains are elongated and their length-width ratios gradually increase. Due to the self-intersection of deformation twins, a twinned lamellar structure develops with the strain. Comparing with the starting grain size of 10 mm, there is a significant refinement of the twinned lamellar structure with a thickness of 0.5–2 mm. On the other hand, those grains are deformed by slip rather than twinning, remain coarse, albeit elongated along the horizontal plane perpendicular to LD. It is worth noting that, when the strain exceeds 0.2, more fine grains (about 0.4–0.7 mm) form at the grain boundary and new twins are hard to occur (Fig. 2(c)–(d)). It seems that the twins achieve saturation when the strain increases to 0.2. In order to distinguish the types of deformation twinning activated during low-to-medium levels of DPD, the misorientation angle and rotation axis of each twinning relation to the matrix orientation are established from EBSD system. The same four types of twins are observed at all strains. This result is

different from normal deformation, only three types of twins are observed at room temperature in previous research. Because of the high strain rate (4–6  102 s  1), {1 1 2 4} twinning has been activated during DPD [28]. Furthermore, the twin boundaries with a specific misorientation induced by variants of double twinning are quite rare and not found in DPD Ti. In Fig. 2, all kinds of twin boundaries are clearly indicated by four different colour lines. Their rotation axis and different misorientation angles are shown in Fig. 3. The boundary length frequencies of LABs at low-medium deformation levels are shown in Table 2. It is distinctly shown that the amount of LABs in initial material (without annealing twins or deformation twins) is only 5.06% and gradually increases to 49.90% at e ¼0.4. It also shows that the {1 0 1 2}/1 0 1 1S tensile twinning and the {1 1 2 2}/ 1 1 2 3Scompressive twinning are dominant during plastic deformation, however, the {1 1 2 1}/1 1 2 6S tensile twinning and the {1 1 2 4}/1 1 2 1Scompressive twinning are quite rare (almost less than 0.5%) with a little influence on texture evolution. The (0 0 0 2), (1 0 1 0) and (1 1 2 0) pole figures indicate that the special grain orientation relationships corresponding to four types of deformation twins and the matrix. According to analysis result for the selected grains with four types of twins (Fig. 3), the activation of different twinning models is dependent on the local crystallographic orientation of parent grains. Where, Mi and Ti (i¼1–4) represent the matrix and twins, respectively. For a few coarse grains without twins in Fig. 2, it is

Fig. 2. KBC maps from EBSD show the development of microstructure at low-to-medium levels of deformation: (a) e ¼ 0.1, (b) e ¼ 0.2, (c) e ¼ 0.3 and (d) e ¼0.4. The red, green, blue and yellow lines are used to indicate {1 0 1 2}, {1 1 2 1}, {1 1 2 2} and {1 1 2 4} twinning boundaries, respectively. The black lines indicate the other normal grain boundaries. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

F. Xu et al. / Materials Science & Engineering A 564 (2013) 22–33

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Fig. 3. The microstructure of e ¼ 0.1 DPD sample is shown in (a). The red, green, blue and yellow lines are used to indicate {1 0 1 2}, {1 1 2 1}, {1 1 2 2} and {1 1 2 4} twin boundaries, respectively. Their rotation axis and different misorientation angles are listed in (b). Crystallographic orientation relations of each type of twins are shown in (c).

Table 2 The boundary length frequencies of LABs and four types of twins.

Fraction of boundary length (%)

Strain

0

LABs {1 0 1 2} twins

5.06 –

{1 1 2 1} twins

–

1.08

0.21

0.14

0.05

0.06

0.09

{1 1 2 2} twins

–

16.50

9.26

8.13

4.80

4.17

2.01

{1 1 2 4} twins Total twins

–

0.57

0.37

0.48

0.56

0.37

0.29

–

22.05

14.70

16.04

12.17

10.26

5.57

Number of grains

265

42

0.10

0.15

0.20

0.30

0.40

10.65 3.90

24.89 4.86

30.54 7.29

34.45 6.76

41.31 5.66

49.90 3.18

3.2. Microstructure evolution during high levels of deformation

Table 3 The statistic analysis of grains with various twins in e ¼0.1 sample. Total grains without twins

0.05

With twins {1 0 1 2}

{1 1 2 1}

{1 1 2 2}

{1 1 2 4}

97

8

139

11

observed that they are deformed mainly by slip. As a local orientation measurement, the orientation relationship of each twinning model is precisely established by EBSD results (see Fig. 3). For the statistic analysis of orientation distribution, Table 3 shows that 265 selected grains with various twins have been measured in e ¼0.1 DPD sample. The result indicates that 223 grains have formed twins but 42 grains not. Among the 223 grains with twins, 97 grains containing {1 0 1 2} twinning, 139 grains containing {1 1 2 2} twinning, 8 grains containing {1 1 2 1} twinning and 11 grains containing {1 1 2 4} twinning, respectively. It is obviously that some grains contain more than one type of twinning.

At higher levels of deformation (e ¼0.5–0.8), the microstructures become more heterogeneous, but more refined as well. One time impacts are applied to obtain a pancake-like pure Ti sample during DPD, the maximum strain could increase to 0.8 without cracks. This also exhibits their excellent character of continuous plastic deformation, which could attribute to the slip only at high levels of deformation. At e ¼0.5, elongated coarse grains are interspersed with fine grains formed by intersecting of deformation twins at lower strain (Fig. 4). The thickness of the elongated coarse grains is reduced to 1 mm. Since the initial material is equiaxed with an average grain size of 10 mm, the aspect ratio of the elongated coarse grains reflects the amount of deformation imposed by DPD. Furthermore, a small amount of adiabatic shear bands is noted when the strain exceeds 0.6. At e ¼0.8, the microstructure becomes much more refined and the macroscopic shear bands are more evident (see Fig. 5). At high levels of deformation, due to the lattice is so severely deformed that it could not analyze about 60–80% of the data by EBSD. The previous studies have indicated that adiabatic shear bands are composed of

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Fig. 4. Microstructure of pure Ti deformed at strain of (a) 0.5 and (b) 0.8 (via scanning electron microscope).

Fig. 5. Microstructure of e ¼ 0.8 DPD sample shows that shear banding is formed in fine and elongated grains.

a lamellar microstructure with fine and elongated grains, and a similar observation is reported by Yang et al. [34]. 3.3. Texture evolution Pole figures determined from XRD measurement suggest that the initial bimodal distribution has transformed to a ring-like distribution when the strain equal to or below 0.2, and then it forms a similar basal texture as the strain increases to 0.4 (Fig. 6). The original texture is a typical recrystallization texture of the rolled Ti, which is characterized by a main orientation identified as {1 0 1 3}/1 2 1 0S or characterized by (j1 ¼01, f ¼351, j2 ¼301) angles in the Euler space. It is generally attributed to the combination of {1 0 1 0}/1 2 1 0S prismatic slip and {0 0 0 2}/1 1 2 0S basal slip in pure Ti [4,22,35]. When the strain increase to 0.2, the primal basal poles of the split distribution along the Y (/2 1 1 0S direction) begin to disperse toward a homogeneous intensity ring located 20–401 around the pole point, which is just like the fiber texture lying about 20–351 to the LD direction [36]. This ring-like c-axis fiber texture component is similar to the result reported by Wu et al. [37]. When the strain exceeds 0.2, the original basal poles of ring-like distribution are centralized progressively to pole point. As a result, the maximum basal pole intensities of e ¼0.3 and 0.4 samples are observed close to the direction parallel to the LD. Unlike the distribution of the basal poles, the maximum intensities for the prism poles, although not very strong, increases around the rim of (0 0 0 2)

pole figures when the strain increases. Compared with the basal poles, the intensities of the prism poles are lower and do not fluctuate much more, which is quite similar to the simulate results of reference [4]. Fig. 7 also shows that the split-basal texture is further translated to basal texture at high levels of deformation. This is different from the rolling texture which exhibits a typical bimodal distribution [22]. The basal pole has an intensity of 3.1 times random at e ¼0.5. With higher levels of deformation, the basal texture has been gradually strengthened to the intensities of 3.8 and 7.0 times random at e ¼0.6 and 0.8, respectively. During the process of deformation, the maximum intensities are all observed in the (0 0 0 2) pole figures. The distributions of the prism poles are located at a ring-range titled about 60–801 from the pole point. Although the maximum intensities of prism poles in (1 0 1 0) pole figures are not very strong and have a little fluctuation, they are found not affected noticeably by the level of deformation. In Fig. 8(a)–(g), the development of orientation distribution during DPD is also interpreted in terms of the j2 ¼301 section of ODF maps. The exact value of f has been measured at every strain (Fig. 8(h)).The development of the distribution function of the j2 ¼ 301 section shows that a banding distribution at the location (f ¼ 30–351, j2 ¼301) gradually forms with the strain increasing from 0 (undeformed) to 0.2. Furthermore, the location of the maximum function intensity f(g)max, do not change until the strain exceeds 0.2. Then the banding distribution at the location (f ¼ 30–351, j2 ¼301) disappears, meanwhile, another banding distribution reappears at the location (f ¼0–151, j2 ¼301) as the strain increases to 0.3–0.4. Associated with the change of banding distribution, the locations of the f(g)max move to f ¼241 (e ¼0.3) and f ¼ 141 (e ¼0.4), as shown in Fig. 8(d) and (e), respectively. They shift toward the location (f ¼01, j2 ¼301) with the increasing strain. Furthermore, the locations of the f(g)max eventually translate to f ¼01, j2 ¼301 when strain exceeds 0.5 and stay there unmoved at higher strain. It is also proved that a (0 0 0 2) basal texture component forms progressively just as shown in Fig. 7.

4. Discussion 4.1. Grain boundary According to the researchers reported by Hansen and Liu et al. [38–40], the microstructure could be subdivided into cell-blocks containing ordinary dislocation cells. The cell-block boundaries are geometrically necessary boundaries (GNBs) and the cell boundaries are incidental dislocation boundaries (IDBs). The two types of boundaries are formed by different mechanisms and

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Fig. 6. (0 0 0 2) pole figures measurements for pure Ti deformed at low-to-medium levels by DPD.

Fig. 7. (0 0 0 2) pole figures measurements for pure Ti deformed at high levels by DPD.

evolve differently as a function of strain and temperature [41]. It also has been shown that the formation of cell blocks during plastic deformation attribute to the IDBs, and they tend to saturate quickly with the increased strain. Furthermore, the large angle cell-block boundaries are evolved by the GNBs [40,42]. In general the IDBs are formed by mutual trapping of glide dislocations, while, the GNBs are formed from the dislocation boundaries which are deduced by applying Frank’s formula in a low-energy structures [42]. It suggests that the formation of the IDBs and the GNBs is attributed to the activity of dislocation multiplication as a function of slip systems. Even though the IDBs and the GNBs are formed by different mechanisms, their misorientation angles are all lower than 151. In EBSD, the IDBs and the GNBs are included in the low angle boundaries (LABs, r151), which could indicate the contribution of slip systems to the deformation.

The EBSD results show that even though the deformation twins in DPD Ti saturate at e ¼0.2, the amount of LABs increases quickly and exhibits saturation at e ¼ 0.4. However, the high angle boundaries (HABs) do not exhibit saturation (in Fig. 9). As shown in Fig. 10, the length frequencies of LABs at all levels of deformation exhibit an obvious increase. With the formation of deformation twins, the amount of HABs increases (see Fig. 2). In general, the percentage composition of HABs increased and the percentage composition of LABs would decrease accordingly. However, the percentage composition of LABs does not correspondingly decrease but increase obviously. This tend suggests that although the deformation twinning systems are dominant at low levels of deformation (e ¼0.05– 0.2), the active slip systems almost always provide a significant action to accommodate the deformation. At medium levels of formation (e ¼0.3–0.4), the deformation twins evolve into saturation

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Fig. 8. ODF maps for the j2 ¼301 section: (a) initial material and DPD samples (b) e ¼0.1, (c) e ¼0.2, (d) e ¼ 0.3, (e) e ¼0.4, (f) e ¼0.5, (g) e ¼ 0.8. In (h), variation of the maximum intensity of f(g) in pure Ti during DPD indicating the effects of twinning and slip in texture evolution. The values of f shows the process of the location of the maximum intensity f(g) progressed from (j1 ¼ 01, f ¼ 351, j2 ¼301) in the initial (undeformed) condition toward (j1 ¼ 01, f ¼ 01, j2 ¼ 301).

and the percentage composition of HABs decreases, whereas the LABs exhibit a stabilized increase due to the slip systems are further activated (see Fig. 10). These results exhibit that the slip systems are activated to accommodate the deformation at the whole. The misorientation distribution analysis reveal that 641 /1 0 1 0S and 851/1 1 2 0S boundaries (corresponding to {1 0 1 2}/1 0 1 1S and {1 1 2 2}/1 1 2 3S, respectively) are most frequently observed. The quantity of other types of twin boundaries ({1 1 2 1} and {1 1 2 4} twins) is quite rare (Table 2). From a statistically analysis, the activation of these four twinning modes are confirmed from misorientation angle distributions, as shown in Fig. 10. In previous work of Bozzolo et al. [33], a misorientation peak at 411/5 1 4 3S was induced by variants of double twinning. However, there is not a salient peak around 411 in this work. The misorientation angle distributions show high peaks near the misorientation angles of 641 and 851 and slightly prominent peaks near the 351 and 771. It can be also seen from Fig. 10 that the boundaries with a misorientation angle near 641 are dominant at low levels of deformation (e ¼0.05–0.1). However, boundaries with a misorientation angle

near 851 become comparable to those with the 641 misorientation with the increasing strain. Although the peaks of misorientation angle distribution near 351 and 771 are smoothed and close to the average value of other high angle boundaries at higher strain, the two ones near 641 and 851 are still higher than the others. The sharp peaks near 641 and 851 (e ¼0.05) become spread with increased strain. The peak height ratio of misorientation angle near 641 and 851 decreases clearly from 4.4 to about 1. This trend confirms that the degree of difficulty of the {1 1 2 2} and {1 0 1 2} twinning models is different [8]. Meanwhile, in order to accommodate the consecutive deformation, the ideal twin-matrix orientation relationship breaks down due to the deformation by slip in both twins and matrix [43]. Due to the change of twin-matrix orientation relationship at higher strain plastic deformation, the misorientation peaks of twins become further smooth. But it is shown that the growth of LABs is faster than that of HABs. To some extent, twins evolve into saturation and the HABs induced by slip increase less than LABs. Both of the two reasons result in the relative frequency of HABs decreasing.

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Fig. 9. The LAB and HAB figure shows the LABs increase quickly with the gradually increased strain of (a) 0.1, (b) 0.2, (c) 0.3 and (d) 0.4. The HABs are indicated by black lines, and the LABs are indicated by red ones.

4.2. Twinning and slip The formation of a twin leads to a deflected rotation of the c-axis in the twinned volume, and the rotation axis/angle depend on the twinning models [30,44]. Due to the deflected rotation of c-axis, twinning has a nonnegligible influence on the microstructure, texture evolution and mechanical behaviour of the material after deformation, like Ti, Mg and Zr [45–47]. For DPD pure Ti, the experimental results show that there are four types of twins observed at all strains. In the two dominant types of twins (see Table 2), the shear of {1 0 1 2} twinning is 0.167 which is lower than {1 1 2 2} twinning (0.225) [8,10], {1 0 1 2} twins are much easier to form. It has been proved by the development of the peak height ratio of 641/1 0 1 0S and 851/1 1 2 0S. In this work, the initial martial has a weak bimodal texture, the c-axes orientations of most grains are close to LD. On the other hand, {1 1 2 2} compressive twins form easily in initial martial. With the increased strain, more grains will deviate from their starting orientation by twinning. Then more {1 0 1 2} twins are activated in those grains with suitable orientation and increases exponentially until the twins get saturated. As shown in Fig. 11, the frequency of {1 0 1 2} twins have a striking increase at e ¼0.05– 0.15, while the other types of twins decrease or remain unchanged. But the more activated dislocation slips result in the decrease of the frequency of all twins. Furthermore, the competition mechanism of {1 0 1 2} and {1 1 2 2} twinning during

DPD would be researched by comparison of the relative length frequencies. Table 4 show that the increasing trend of {1 0 1 2} twins is stopped abruptly at e ¼0.2 (see Fig. 12). It is suggested that the twins evolve into saturation which is also consistent with the observed result. From the microstructure of DPD Ti at low levels of deformation (Fig. 2), twinning plays an important role at e ¼0.05–0.2 and gradually saturates at e ¼ 0.2. After the initial grains are fragmentized to fine grains with a critical value, the slip resistances of the various slip systems in the parent and offspring grains are considered to be the same as which in the grain prior to fragmentation. But the resistance of any twinning system in the parent and offspring grains is considered too high to form more twins. When the twinning is restricted, the deformation mechanism eventually changes and the slip become dominant completely when the strain exceeds 0.2. This result is different from the research of Chun et al. [23], the twins saturating at lower deformation level (about 40% thickness reduction in cold rolling) may be attributed to the effect of higher Zener–Hollomon parameter (lnZ) induced by high strain rate in DPD Ti [28,48]. It is generally accepted that high strain rate could suppress the dislocation activities and promote the twinning formation. It has been found that slip occurs along the /aS direction on the {0 0 0 2} basal, {1 0 1 0} prismatic, or {1 0 1 1} pyramidal planes, and along the /c þa’’S direction on the {1 0 1 1} or {1 1 2 2} planes in Ti [49]. To some extent, the activation of the slip systems is related to the grain orientation, which can be indicated by the Schmid factor, although some evidence has been

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F. Xu et al. / Materials Science & Engineering A 564 (2013) 22–33

Fig. 10. Grain-boundary misorientation angle distribution for DPD Ti samples deformed at (a) e ¼ 0.05, (b) e ¼ 0.1, (c) e ¼0.15, (d) e ¼ 0.2, (e) e ¼0.3 and (f) e ¼ 0.4. The peaks at 351, 641, 771 and 851 correspond to {1 1 2 1}, {1 1 2 2}, {1 1 2 4} and {1 0 1 2} deformation twinning, respectively. LAB: low angle boundaries of less than 151 misorientation.

shown a break-down of the Schmid law for prismatic slip [50]. In the current study, incorporation of slip inside twins with suitable grain orientation is considered as a significant contributor to accommodating the overall imposed plastic deformation. According to the analysis results of misorientation angle distribution in the previous section, the fraction of LABs increases quasilinearly with the increased strain (see Fig. 12). The slip systems play a ‘‘supplementary role’’ in accommodating deformation at low levels of deformation, and an ‘‘exclusive role’’ at medium-high levels.

In addition, a small amount of macroscopic shear bands are found when the strain exceeds 0.6. With the increased strain, the microstructure becomes much more refined and the macroscopic shear banding is more evident. This is different from the results of the cold rolling and uni-axial compression at room temperature [23,51]. In cold rolling, the shear bands occur when the strain exceeds 0.4, however, which are not found in uni-axial compression at room temperature at all. The shear bands seem to initiate from the sample surface, which may be due to stress condition at the edges of DPD samples is tensile stress component which often

F. Xu et al. / Materials Science & Engineering A 564 (2013) 22–33

Fig. 11. The frequencies of various types of deformation twins and total twins.

Table 4 The relative length frequencies of {1 0 1 2} and {1 1 2 2} twins. Strain

0.05 (%)

0.10 (%)

0.15 (%)

0.20 (%)

0.30 (%)

0.40 (%)

{1 0 1 2} twins

17.7

33.1

45.5

55.5

55.2

57.1

{1 1 2 2} twins The other twins

74.8

63.0

50.6

39.4

40.6

36.1

7.5

3.9

3.9

5.1

4.2

6.8

Fig. 12. The frequency of LABs increases with the strain. However, the comparison of the relative frequencies of {1 0 1 2} and {1 1 2 2} twins shows that the increase tend of {1 0 1 2} twins is stopped abruptly at e ¼ 0.2. Thus, it exhibits that the deformation twins evolve into saturation.

leads to edge cracking. Different criteria may be operative in the strain compression region [34]. The difference in the shear band formation may be related to a complex result of the slip system activation and stain rate under different deformation conditions [52]. To some extent, the high strain rate of DPD aggravates the heterogeneous deformation and promotes the formation of adiabatic shear bands. 4.3. Texture evolution In prior research, deformation twins have a nonnegligible influence on texture evolution, which is attributed to the deflected rotation of c-axis [17]. Specifically, the orientation transformation by twinning has an effect on the development of

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texture [51–54]. The activation of various twins is dependent on local crystallographic orientation of the matrix grains. According to the statistic analysis results (Table 3), the (0 0 0 2) pole figures of twin-matrix orientation distribution in the grains with various twins at e ¼0.1 are shown in Fig. 13. It shows that the c axes of most matrixes in the grains with {1 0 1 2} and {1 1 2 1} tension twins are oriented perpendicular to the LD. From Fig. 13(c) and (d), the c axes of all matrixes in the grains with {1 1 2 2} and {1 1 2 4} compression twins are oriented parallel to LD and their corresponding twins are deflected to perpendicular to LD. And the orientation distributions of these twins are located randomly at the periphery of (0 0 0 2) pole figures, indicating that the initial bimodal distribution is weakened. Furthermore, the c axes of all matrixes in the grains with {1 0 1 2} and {1 1 2 1} twins are oriented perpendicular to LD and their corresponding twins are deflected to the orientation near LD (Fig. 13(a and b)). Because of the rarity of {1 1 2 1} and {1 1 2 4} twins, they have little influence on texture development. Therefore, the {1 0 1 2} twins form a ring-like distribution around the (0 0 0 2) pole point and {1 1 2 2} twins are randomly distributed at the edge of (0 0 0 2) pole figures. At low levels of deformation, twinning mode takes precedence over slip during the consecutive plastic deformation. The weakening of initial bimodal distribution and strengthening of ring-like distribution result in the texture development until twins saturating at e ¼0.2 in Fig. 6. This texture is just similar to the deformation texture during uniaxial compression [17,36]. As shown in Fig. 8, the evolution of the f(g)max and the value of f which delegates the location of f(g)max (j1 ¼01, j2 ¼301) are, which provide further information of the general trend of the texture evolution during DPD. The intensity variation trend of the f(g)max can be divided into four stages by strain:I. Decline stage (0–0.05), II. Raise stage (0.05–0.15), IIIs. Second decline stage (0.15–0.4) and IV. Last raise stage (0.4–0.8). The evolution of the f(g)max is related to texture and microstructure evolutions. The formation of a small quantity of twins weakens the initial bimodal texture (Stage I), and then more deformation twins strengthen the ring-like distribution (Stage II). In the Stage III and IV, twinning systems have been suppressed but slip becomes the effective deformation mode. On the other hand, the values of f are located at 351 when the strain equal to or below 0.2 and exhibit a linear downtrend to f ¼ 01 at the strain from 0.2 to 0.8. In the evolution of texture, three principal types of textures are found: a bimodal distribution (undeformed), a ring-like distribution (e ¼0.2) and a basal texture (e ¼0.8). According to these typical textures as dividing lines, the development could be divided into three stages by strain: I. Bimodal texture evolves into a ring-like distribution (0–0.2), II. Ring-like distribution evolves into basal texture (0.2–0.4), III. Basal texture (0.4–0.8). This variation trend is an exact match for the deformation mechanism which exhibits that deformation twins get saturated at e ¼0.2. The initial recrystallization texture has been investigated in the past decades [35], but how and why it could transform to a ring-like distribution and eventually evolve into basal texture have not been reported. Using a Taylor-type crystalplasticity model, Thornburg and Piehler [55] have suggested that the basal texture originates from a combination of prism /aSand the pyramidal /c þaS slip. However, the probability of slip systems seems not very active at low deformation levels (e r0.2) because twinning can accommodate the strain along the /cSaxis as well as the fact that the critical resolved shear stress for slip systems is relatively high. This change in deformation mechanism also results in the development of microstructure, as shown in Fig. 2, various twinning boundaries become saturated at e ¼0.2 and slip plays a dominant role in further fragmentation of most grains at higher strains.

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F. Xu et al. / Materials Science & Engineering A 564 (2013) 22–33

Fig. 13. The (0 0 0 2) pole figures of twin-matrix orientation distribution in the grains with various twins at e ¼ 0.1. (a) 73 grains containing {1 0 1 2} twins; (b) 131 grains containing {1 1 2 2} twins; (c) 8 grains containing {1 1 2 1} twins; (d) 11 grains containing {1 1 2 4} twins.

5. Conclusions The dynamic plastic deformation of pure Ti is achieved by both twinning and slip at low strain levels (e ¼0.05–0.2), while slip becomes dominant at medium to high strain levels (e 40.2). The deformation twinning results in grain refinement and evolve into a saturation level at e ¼0.2. When the size of initial grains is refined to a critical value, the resistances of twinning prevents further twinning deformation. The shear bands development becomes obvious at high strains (e Z0.6),. There are four types of deformation twins during DPD including {1 0 1 2}, {1 1 2 1}, {1 1 2 2} and {1 1 2 4} twinning. However, the frequencies of {1 1 2 1} and {1 1 2 4} twins are quite low ( o0.5%). The {1 0 1 2} twins form a ring-like distribution around the (0 0 0 2) pole point. The {1 1 2 2} twins are randomly distributed at the edge in (0 0 0 2) pole figures. The weakening of initial bimodal distribution and strengthening of ring-like distribution result in the formation of specific texture at the strain level of e ¼0.2. The texture evolution can be divided to three stages: I. Bimodal distribution transforms to ring-like distribution (e ¼0.05–0.2); II. Ring-like distribution transforms to basal texture (e ¼0.2–0.4); and III. Basal texture (e ¼ 0.4–0.8). The formation of ring-like distribution is attributed to the predominant role of twinning. The orientation distribution function (ODF) indicates that the f(g)max maintains at the initial location (j1 ¼01, f ¼351, j2 ¼301) during low strain deformation but it shifts toward the basal pole (f ¼01) when the strain exceeds 0.2. The basal texture is due to the slip activation at the medium-high levels of deformation.

Acknowledgement This work was supported by National Natural Science Foundation of China (Nos. 51071183, 51271208) and the Major State Basic Research Development Program of China (973 Program) No. 2010CB631004.

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