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Temperature and strain rate effect of the deformation-induced phase transformation in pure titanium nanopillars oriented along [0 0 0 1]
Computational Materials Science 126 (2017) 66–73
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Temperature and strain rate effect of the deformation-induced phase transformation in pure titanium nanopillars oriented along [0 0 0 1] Junqiang Ren a,b,c, Qiaoyan Sun c, Lin Xiao c,⇑, Jun Sun c a
State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metals, Lanzhou University of Technology, Lanzhou 730050, China Key Laboratory of Nonferrous Metal Alloys and Processing, Ministry of Education, Lanzhou University of Technology, Lanzhou 730050, China c State Key Laboratory for Mechanical Behaviour of Materials, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China b
a r t i c l e
i n f o
Article history: Received 23 May 2016 Received in revised form 12 September 2016 Accepted 13 September 2016
Keywords: Molecular dynamics simulation Titanium Phase transformations Twinning Dislocations
a b s t r a c t The tensile deformation behavior is studied in pure titanium (Ti) nanopillars subjected to loading along the [0 0 0 1] orientation based on molecular dynamics (MD) simulations. The double yielding phenomenon is displayed in stress-strain curves when the deformation temperature is less than 380 K. One new type of deformation-induced phase transformation from the hexagonal close-packed (hcp) to face-centered cubic (fcc) phase has been predicted. The effects of temperature and strain rate on this type 2gh1 0 1 1i twinning of phase transformation are systematically investigated. It is revealed that f1 0 1 plays an essential role in inducing the phase transformation, which is produced through dislocation glide 2gh1 0 1 1i twin. A group of high-density stackof multiple Shockley partial dislocations inside the f1 0 1 ing faults is accumulated though the continuous glide of multiple Shockley partial dislocations inside the twinning region, eventually leading to the allotropic phase transformation from the hcp to fcc phase. After twinning, two thermally activated dislocation slip processes compete with one another: Shockley partial dislocations and full dislocation slip. The deformation mechanism changes from phase transformation to dislocation slip when the temperature is higher than 380 K or the strain rate is lower than 1g pyramidal plane is clearly observed under tensile loading 108 s1. The dislocation slip on the f1 0 1 at higher temperatures. Furthermore, our simulations indicate that the nucleation rate has a strong effect on the deformation mechanism on the nanoscale. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction It is well known that allotropic transformation occurs at 882 °C in pure titanium (Ti) from hexagonal close-packed (hcp) a-Ti to body-centered cubic (bcc), b-Ti [1]. At lower temperature, hcp aTi is stable, whereas b-Ti is stable at higher temperature. However, some studies demonstrate that severe deformation processes can facilitate phase transformations in pure Ti at ambient temperature [2–5]. Hydrostatic pressure, shock loading or high-pressure torsion processing can induce the hcp a to hexagonal x phase transformation in a-Ti [2–4]. The dependence of the microstructure evolution on the crystallographic shock direction was recently investigated using molecular dynamics (MD) simulations [5]. A transformation from the x phase to the orthorhombic c phase was observed in Ti under an external pressure of 116 GPa [6]. The first-principles calculations by Sliwko et al. [7] demonstrated the possible occurrence of a face-centered cubic (fcc) phase in pure Ti because this struc⇑ Corresponding author. E-mail address: [email protected] (L. Xiao). http://dx.doi.org/10.1016/j.commatsci.2016.09.013 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.
ture along the Bain path has a minimum total energy for fcc. Similar calculation results were also reported by Aguayo et al. [8]. Some experimental results have demonstrated that the hcp to fcc allotropic phase transformation could occur and the metastable fcc-Ti became stable in the Ti-Al multilayer films when the thickness of the individual layer was less than 10.5 nm [9,10] and in the milled Ti when the grain size was less than 5.3 nm [11]. The structural instability is attributed to the negative hydrostatic pressure due to the nanocrystallization process resulting from mechanical attrition, lattice expansion, and high plastic strain/strain rate. An epitaxial growth of fcc-Ti was experimentally observed in the thin films with metallic and semiconductor substrates [12–17]. A metastable fcc-Ti phase was produced in bulk Ti powders during mechanical milling [11,18], Ti/Ni and Ti/Al epitaxial multilayer films [19,20] and heat-treated Ti alloys [21–23]. Recent work shows that the fcc phase was formed during microstructural refinement by cryogenic plane-strain compression [24]. Some researchers suggest that the hcp to fcc allotropic transformation is induced by significant contamination of the milled powder by fcc-phase-forming elements such as nitrogen and carbon [25].
J. Ren et al. / Computational Materials Science 126 (2017) 66–73
The fcc-Ti observed in Ti/Al multilayers is merely an artifact of TEM specimen preparation [26]. The hcp to fcc polymorphic transformation in Ti is dominated by the high density of dislocations and twins but not stacking faults introduced by ball milling [18]. The stress-induced hcp to fcc phase transformation was related to the gliding of Shockley partial dislocations [24]. In the heat-treated Ti alloys [21,22], the fcc-Ti was obtained in the Ti–6Al–4V alloy by adding Zr, which can decrease the basal stacking fault energy of the a phase and promote the formation of the fcc structure in the modified alloy [21]. Even though many experimental and simulation works have demonstrated the phase transformation in pure Ti at ambient temperature under extreme pressure, temperature and size restriction conditions, the fundamental mechanism of this phase transformation is not clear thus far. In our previous work [27], the phase 2gh1 0 1 1i twinning region has transformation inside the f1 0 1 also been predicted in a-Ti single-crystal nanopillars orientated along [0 0 0 1] during tension according to MD simulations. These results indicate that hcp to fcc phase transformation is induced by dislocation glide of multiple Shockley partial dislocations under the condition of size restriction. However, the occurrence of this phase transformation is conditional. In this study, the phase transformation dependence on temperature and strain rate has been systematically studied. In addition, the phase transformation also has an influence on the mechanical properties. Thus, it is worthy to investigate the effect of deformation temperature and strain rare on the phase transformation. In order to clarify the phase transformation mechanism, and the relationships among mechanical behavior, twinning and phase transformation are established.
2. Simulation method MD simulations were conducted with the software LAMMPS [28] using a Finnis–Sinclair many-body potential for pure Ti [29]. We first created the hcp h0 0 0 1i-oriented single-crystalline Ti nanopillar with a width of 11 nm. The height-to-width ratio of the nanopillar is 2:1. To obtain an equilibrium state before loading, the structure was initially relaxed using the conjugate gradient algorithm. Then, an additional annealing under zero load was performed for 300 picoseconds (ps) at the deformation temperature. All directions were maintained under free-surface boundary conditions. The selected temperature range varied from 77 K to 600 K. A canonical ensemble – i.e., a constant atom number, volume and temperature (NVT) – was applied to maintain the system at a constant temperature. A time step of 1.0 fs (fs) and a strain rate of 1 108 s1 were selected. To investigate the strain rate effect, the configuration was deformed under uniaxial tension at different
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strain rates in the range of 107–1010 s1. The system was controlled at 300 K with the NVT ensemble. The average stresses in the atomistic systems were calculated by the Virial theorem [30]. Visualization was performed using the open visualization tool Atomeye [31]. 3. Results 3.1. Temperature effect of stress-strain response in a-Ti nanopillars Fig. 1 presents the typical stress-strain response of a-Ti singlecrystal nanopillars subjected to tensile deformation along the [0 0 0 1] direction at a strain rate ðe_ Þ of 1 108 s1 and different temperatures that vary from 77 K to 600 K. The Ti nanopillars exhibit two distinct types of plastic deformation behavior. For the first type, when the temperature is lower than 380 K, the stress-strain curve can be divided into three stages with two obvious yield stress points. The elastic strain reaches as high as approximately 5% during tensile loading. The first yield stress of the Ti nanopillar decreases with increasing temperature, as observed in Fig. 1(a). The second yield point, which is lower than the first one, is displayed at a strain of approximately 12%. After second yielding, further loading causes an extensive plateau with a constant stress of approximately 1.0 GPa (Fig. 1(a)). For the second type, only one yield point is displayed at the strain of 6% when the temperature is larger than 380 K, as observed in Fig. 1(b). As plastic deformation progresses, no obvious second yield point could be observed in the stress-strain curve. 3.2. Deformed microstructure of a-Ti nanopillars at different temperatures Fig. 2(a–d) presents the representative microstructures of the nanopillar subjected to 5% deformation at 77 K and a strain rate 2gh1 0 1 1i twin embryo nucleates from of 1 108 s1. The f1 0 1 0g and f1 21 0g surthe corner of the nanopillar between f1 0 1 faces, as indicated by a white arrow in Fig. 2(a). After nucleation, the twin rapidly grows toward the ends of the pillar at the strain of 5%, where the first yield occurs. Therefore, it is reasonable to believe that the initial tensile yielding is caused by the nucleation 2g twin. Fig. 2(d) demonstrates that the and growth of the f1 0 1 middle part of the pillar has been twinned and two twin/matrix interfaces are formed. Further examination reveals that the coher 0 by approximately ent twin part is nominally rotated along ½1 1 2 1 0 0Þ prismatic plane inside the twin 90°; consequently, the ð1 becomes parallel to the basal plane in the matrix, as observed in Fig. 2(d). The atoms are colored according to common neighbor
Fig. 1. Tensile stress–strain curves of Ti nanopillars at a strain rate of 1 108 s1 under uniaxial tensile loading along [0 0 0 1] at various temperatures (a) below 400 K and (b) above 400 K.
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Fig. 2. Snapshots of twin nucleation and growth during incipient yielding under tensile loading at 77 K. (a) The nucleation of a twin embryo from the corner of single-crystal nanopillars. (b–d) Observation of twin growth toward the ends of the nanopillars.
Fig. 3. Snapshots of partial dislocation nucleation and propagation during the second yielding under tensile loading at 77 K. (a) Nucleation of Shockley partial dislocations 2g twin. from the corner of a single-crystal nanopillar. (b–d) A transformation from the hexagonal close-packed (hcp) to the face-centered cubic (fcc) phase inside the f1 0 1
analysis (CNA) [32]. Hcp atoms are blue, fcc atoms are dark blue, and defect and surface atoms are red. The front surface is removed so as to show the inner defects. As the plastic deformation progresses, the twin boundary gradually moves to two ends of the nanopillar under the shear strain produced during external tensile loading. Fig. 3 presents snapshots that demonstrate the hcp to fcc phase transformation at the second tensile yielding at 77 K. The phase transformation is formed through the nucleation and propagation of Shockley partial dislo 0i [27]. The partial cations with Burgers vector b = ½ a/3 h1 1 2 dislocation initiates from the corner of the pillar and slips along 0g plane, as indicated by the white arrow in Fig. 3(a). the f1 0 1 The partial dislocation leaves a stacking fault behind in the twinning region. A group of high-density stacking faults is accumulated through continuous gliding of multiple Shockley partial dislocations inside the twinning region, eventually leading to the allotropic phase transformation from hcp to fcc [33]. This hcp to fcc transformation follows the Burgers orientation 0i kh0 1 1i relation [24], h0 0 0 1ihcp||h0 0 1ifcc, h0 1 1 and hcp fcc
1 0i kh0 1 1i . A similar hcp to fcc transition mechanism h2 1 hcp fcc was also observed in other tensile pillars at a temperature lower than 380 K. The dependence of the volume fraction of each phase on the strain level at 77 K is observed in Fig. 4(a). For comparison, the stress response curves are also included. The fcc phase rapidly increases at the cost of the hcp phase and reaches a maximum volume fraction of 22% at a strain of 17.5%. The fcc phase is less than 3% when the strain is less than 14% and mainly exists in the form of stacking faults in the hcp lattice in the vicinity of the twin boundary (Fig. 2(d)). The fraction of unidentified atom amounts is approximately 10%. These unidentified atoms are located on the surface, twin boundary, and ragged boundaries between the hcp and fcc phases in the pillar. Fig. 4(b) shows that the fraction of unidentified atom amounts is close to 20% at 450 K, which indicates that there are more disordered atoms and dislocations and that more ragged boundaries are produced by the twin variant in the pillar (Fig. 5). In contrast to the behavior at lower temperature, the deformation is more complicated at 450 K. Numerous disordered atoms
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Fig. 4. Evolution of the volume fraction of phase transformation with strain at a rate of 1 108 s1, as detected by CNA, at (a) 77 K and (b) 450 K.
Fig. 5. Snapshots of twin nucleation and growth during incipient yielding under tensile loading at 450 K. (a) Disordered atoms inside the nanopillar with red color before yielding. (b) The twin variant I nucleated from the corner of the nanopillar. (c) The twin variant II nucleated in the inner region of the nanopillar. (d–h) The growth of the twin variants. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
exist inside the pillar before yielding, as observed in Fig. 5(a). As the strain increases further, disordered atoms gradually reduce 2g twin variant I is formed at the first tensile yield point, and f1 0 1
as observed in Fig. 5(b). The nucleation site for twin variant I is located at the lateral edge of the pillar. The other representative nucleation site for twin variant II is in the middle of the side sur-
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face, which is atomically flat [34]. The two twin variants grow steadily and finally merge. No second tensile yield point is displayed on the stress-strain curve, and no hcp to fcc phase transformation can be observed at 450 K, as shown in Fig. 4(b). We also simulated the tensile loading at 600 K. The simulation results reveal that the deformation process is very similar to that at 450 K. No Shockley partial dislocation was activated. However, it is noted that the dis 1g pyramidal plane is clearly observed location glide on the f1 0 1 under tensile loading at the higher temperature. After twinning, full dislocation slip is activated. The plastic deformation is controlled by the full dislocation slip inside the twinning region at the higher temperatures.
3.3. Strain rate effect of stress-strain response in a-Ti nanopillar A series of MD simulations were performed at various strain rates from 107 s1 to 1010 s1 at 300 K. Fig. 6 presents a representative simulation results at various strain rates. It is revealed that the strain rate has a significant effect on the stress–strain behavior: at a low strain rate of 5 107 s1, the stress decreases abruptly after the first yield point at a strain of 3.8%, followed by wavy stress between 12% and 16%, as observed in Fig. 6(a). Two obvious stress yield points are displayed in the stress-strain curve at strain rates of 108 s1 and strains of approximately 5% and 12%, respectively, as observed in Fig. 6(b). However, there is no obvious stress yield
Fig. 6. Stress-strain curves at 300 K under uniaxial loading along [0 0 0 1] at different strain rates: (a) 107 s1, (b) 108 s1 and (c) 109–1010 s1. Evolution of the volume fraction of phase transformation with strain at 300 K, as detected by CNA, at strain rates of (a) 5 107 s1, (b) 5 108 s1 and (c) 5 109 s1.
Fig. 7. Snapshots of full dislocation nucleation and propagation during the second yielding under tensile loading at 300 K and a strain rate of 5 107 s1. Atomic-level snapshots of the microstructure viewed from the top and prism sides of the pillar.
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after the first yield when the strain rate is larger than 109 s1 (Fig. 6 (c)). When the strain rate is lower than 109 s1, the first yield stress of the Ti nanopillar increases with the strain rate. However, the trend disappeared at the higher strain rate of 109 s1 and 1010 s1, as observed in Fig. 6(c). The difference between the three types of stress-strain curves indicates that the deformation mechanism has changed with the applied strain rate.
3.4. Dynamic evolution of microstructure at different strain rates At the strain of 12%, the twin boundary migrates through almost the entire pillar, leading to a conversion to the twinned ori 1 0 0 entation, and the applied stress direction is rotated to the ½1 direction under tension at the strain rate of 5 107 s1. The dislocation clearly nucleates and grows at the top of the pillar along the 0 1 0Þ and ð0 1 1 0Þ double prismatic slip planes, which form a ð1 60° angle, as the tension deformation progresses, as observed in Fig. 7. The Burgers vectors were determined to be 1 0 and b2 = a/3½2 1 1 0, which indicate that the prisb1 = a/3½1 2 0Þ ½2 1 1 0 were matic double slips ð1 0 1 0Þ ½1 2 1 0 and ð0 1 1 activated under tension at the strain rate of 5 107 s1. No hcp to fcc phase transformation was observed after twinning deformation at the low strain rate. The fraction of each phase as a function of the strain is plotted in Fig. 6. The volume fraction of fcc atoms is close to zero (Fig. 6(a)). Only a few fcc atoms were formed in the form of stacking faults in the hcp phase. The phenomenon was also observed at the higher strain rates of 109 s1 and 1010 s1 (Fig. 6 (c)). The difference is that the pillar would fail through grain boundary sliding under continuous tension loading at the high strain rate. Upon close examination, remarkable serrated-like deformation behavior is displayed in Fig. 7(a). It is caused by the repeated glide and escape events of dislocations on the surface at 300 K and the strain rate of 5 107 s1. A similar result was reported in a-Ti nanopillars orientated for double prismatic slips 0 [35]. under compression along ½1 1 2 Fig. 8 shows atomistic configurations in a Ti single crystal at a strain rate of 1 109 s1 at 300 K. In these images, the perfect lattice of the Ti single crystal is segmented into different parts by the twinning boundaries. The boundary between two twins is similar to the grain boundary. Compared with the lower (e_ = 107 s1) and higher strain rates (e_ P 109 s1), the deformation at a strain rate of 108 s1 is the similar to that mentioned in Section 3.2 at lower temperature. The initial sharp increase of the fcc phase corresponds to the decrease of the hcp phase (Fig. 6(b)). This result is
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attributed to the multiplication of Shockley partial dislocations (Fig. 3). At the strain of 12%, the volume fraction of the fcc phase is approximately 24% and that of the hcp phase is approximately 60% in the system. 4. Discussion 4.1. Temperature and strain-rate dependence of the nucleation rate at the onset of plasticity Dislocation nucleation from the surface potentially plays a critical role in controlling plastic deformation when the sample size is tens of nanometers. The strength of a-Ti nanopillars is controlled by twin nucleation from free surfaces in this study. MD results reveal that the temperature and strain rate have considerable effects on the plastic deformation mechanism, particularly on the twin nucleation, which is a thermally activated process and is sensitive to both temperature and strain rate. For thermally activated deformation processes in metals, at a given temperature T and stress r, the nucleation rate v(T) can be expressed by [36]
mðTÞ ¼ Nm0 exp
Q ðr; TÞ ; kB T
ð1Þ
where N is the number of equivalent surface nucleation sites, v0 is the attempt frequency, Q is the active free energy [37], and kB is Boltzmann’s constant. Eq. (1) gives the nucleation rate when the system is under constant stress. However, in this study, Eq. (1) is used to describe the relationship between the nucleation rate and temperature. Combined with the Eq. (5), the activation energy barrier Q decrease with the temperature increasing. Meanwhile, two twin nucleation sites were observed at 450 K in Fig. 5. This means that the number of equivalent surface nucleation sites N increases with the temperature. The nucleation rate is proportional to the temperature, which indicates that the twin nucleation rate is dependent on the temperature. The corresponding tensile yield stress decreases with increasing temperature. To gain further insight into the strain rate sensitivity of the twin nucleation in the a-Ti single-crystal nanopillar, an implicit expression is derived for the nucleation stress when the nanopillar is deformed at a constant temperature and a strain rate [37–39],
Qðr; TÞ kB TN m0 ¼ ln ; kB T Ee_ Xðr; TÞ
ð2Þ
where E denotes the apparent Young’s modulus and Xðr; TÞ is the activation volume. Eq. (2) can be rewritten as:
1 0g plane under tension along the c-axis at a strain rate of 1 109 s1. (a–d) Two twin variants of Fig. 8. Atomistic configurations of the Ti single crystal in the f1 2 nucleation and growth. (e) Grain boundary sliding (GB sliding) under continuous tension loading.
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Q ðr; TÞ ¼ kB T ln
kB TN m0 : Ee_ Xðr; TÞ
ð3Þ
Inserting Q ðr; TÞ from Eq. (3) into Eq. (1), v(e_ ) can be expressed in the form
mðe_ Þ ¼
Ee_ Xðr; TÞ : kB T
ð4Þ
Atomistic simulations have predicted that the surface dislocation source has an activation volume of approximately 1–10b3, which results in a significant thermal contribution to the source’s strength [37]. b is the magnitude of the Burger’s vector. We hypothesized that the activation volume is a constant at a given temperature in Eq. (4). The nucleation rate v(e_ ) is proportional to the strain rate e_ , which indicates that the twin nucleation rate is dependent on the strain rate. The number of nucleation sites obviously increases when the strain rate is larger than 1 109 s1. Twin nucleation and growth play an important role in inducing plastic deformation in a-Ti single-crystal nanopillars at different temperatures and strain rates. Eqs. (1) and (4) reveal that the temperature and strain rate directly affect the twin nucleation rate. The number of equivalent surface nucleation sites N increases with the temperature and strain rate. 4.2. Temperature and strain-rate dependence of plastic deformation in the twinning region It has been demonstrated that the nucleation rate of twins is significantly dependent on the strain rate at 300 K, particularly 2g deformawhen the strain rate is larger than 109 s1. The f1 0 1 tion twin is a primary deformation mode in hcp metals. The orien 2g deformation twin is akin to that tation relationship of the f1 0 1 of conventional f1 0 1 2g twinning but without a crystallographic mirror plane [40]. Simulations and experiments have revealed that the boundary between parent and twin lattices is predominantly composed of semi-coherent basal-prismatic interfaces. The boundary migration is dominated by the movement of these interfaces via the local rearrangements of atoms. This deformation mode 2g twinning results in a disordered atom band between two f1 0 1 variants. The twin boundary between two variants is similar to that of a grain boundary in nanocrystalline [41,42]. The amount of disordered atoms in the twin boundary implies that the grain boundary sliding can be easily activated at a high strain rate. The decrease of the energy barrier for grain boundary sliding is faster than that of dislocation nucleation. Therefore, grain boundary sliding becomes the dominant deformation mechanism. The peak stress at the strain of approximately 12% at the high strain rate is reduced compared with that at the low strain rate. The plastic deformation behavior of crystalline materials is usually controlled by the motion of dislocations. Dislocation nucleation is a thermally activated process that is sensitive to both temperature and strain rate. It is believed that the thermally activated nucleation will become dominant at lower strain rates and higher temperatures [43]. After twin deformation, the plastic deformation mode changes from phase transformation to full dislocation gliding when the strain rate is less than 108 s1 or the temperature exceeds 380 K. The competition between the Shockley partial dislocation and full dislocation emission is controlled by thermal activation. The thermally activated process is often described by the activation energy barrier Q [44]. The effect of temperature on Q is [37,45]
Q ¼ ð1 T=T m ÞQ 0 ðrÞ;
ð5Þ
where Tm is the surface disordering temperature, and Q0 is the activation energy on the zero-T potential energy surface. The activation
barrier for dislocation nucleation in fcc metals is temperaturedependent and has been demonstrated using multi-scale simulation and analytical models [45]. Eq. (5) shows that the activation energy Q decreases with increasing temperature. Our simulation results reveal that full dislocation emission from the surface of the twin becomes favored over partial dislocations at elevated temperatures and low strain rates due to the increase of the thermal active process at lower activation energy. So the plastic deformation mode changes from phase transformation to full dislocation gliding when the temperature exceeds 380 K. In short, the temperature and strain rate have significant effects on the flow stress and deformation mechanism. It has been demonstrated that a small activation volume led to a sensitive temperature and strain rate dependence of the nucleation stress [37,46]. Recent simulation work demonstrated that the same dislocationobstacle interaction unit could lead to entirely different mechanisms at different strain rates [47]. Thus, the temperature and strain rate dependences of deformation mechanisms should be carefully considered when attempting to compare experimental data against MD simulations. 5. Conclusions (1) The double yielding phenomenon is displayed in the stressstrain curves of Ti single-crystal nanopillars subjected to uniaxial tension along the [0 0 0 1] direction when the deformation temperature is less than 380 K. The first peak is induced by twin nucleation, and the second peak is attributed to the nucleation of phase transformation. 2gh1 0 1 1i twinning is the primary deformation mode (2) f1 0 1 in Ti single-crystal nanopillars subjected to uniaxial tension along the [0 0 0 1] direction at the first yield. After twinning, a rare metastable fcc-Ti phase is formed inside the twinning region of the hcp-Ti phase at the second yield point when the temperature is less than 380 K or the strain rate is larger than 108 s1. A group of high-density stacking faults is accumulated though the continuous glide of multiple Shockley partial dislocations inside the twinning region, eventually leading to the allotropic phase transformation from hcp to fcc. (3) The phase transformation is strongly effected by temperature and strain rate. After twin deformation, the plastic deformation is dominated by the full dislocation gliding rather than Shockley partial dislocations when the temperature is higher than 380 K or the strain rate is less than 1g pyramidal 108 s1. The dislocation glide on the f1 0 1 plane is clearly observed, and the plastic deformation is controlled by the full dislocation slip inside the twinning region under tensile loading above 380 K. Prismatic double slips 0 1 0Þ ½1 2 1 0 and ð0 1 10Þ ½2 1 1 0 were activated under ð1 tension at strain rate less than 108 s1. The competition of two deformation mechanisms between phase transformation and full dislocation slip is controlled by the thermal activation. (4) The twin nucleation rate increases with the deformation temperature and the strain rate at the initial stage of plasticity deformation. At the higher strain rate (e_ P 109 s1), the deformation mechanism changes from dislocationmediated plasticity to grain boundary sliding.
Acknowledgements This project was financially supported by the National Natural Science Foundation of China (51471129 and 51321003), the 973
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Program of China (2014CB644003), and the 111 Project of China (B06025).
[22] [23] [24] [25]
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Temperature and strain rate effect of the deformation-induced phase transformation in pure titanium nanopillars oriented along [0 0 0 1] Junqiang Ren a,b,c, Qiaoyan Sun c, Lin Xiao c,⇑, Jun Sun c a
State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metals, Lanzhou University of Technology, Lanzhou 730050, China Key Laboratory of Nonferrous Metal Alloys and Processing, Ministry of Education, Lanzhou University of Technology, Lanzhou 730050, China c State Key Laboratory for Mechanical Behaviour of Materials, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China b
a r t i c l e
i n f o
Article history: Received 23 May 2016 Received in revised form 12 September 2016 Accepted 13 September 2016
Keywords: Molecular dynamics simulation Titanium Phase transformations Twinning Dislocations
a b s t r a c t The tensile deformation behavior is studied in pure titanium (Ti) nanopillars subjected to loading along the [0 0 0 1] orientation based on molecular dynamics (MD) simulations. The double yielding phenomenon is displayed in stress-strain curves when the deformation temperature is less than 380 K. One new type of deformation-induced phase transformation from the hexagonal close-packed (hcp) to face-centered cubic (fcc) phase has been predicted. The effects of temperature and strain rate on this type 2gh1 0 1 1i twinning of phase transformation are systematically investigated. It is revealed that f1 0 1 plays an essential role in inducing the phase transformation, which is produced through dislocation glide 2gh1 0 1 1i twin. A group of high-density stackof multiple Shockley partial dislocations inside the f1 0 1 ing faults is accumulated though the continuous glide of multiple Shockley partial dislocations inside the twinning region, eventually leading to the allotropic phase transformation from the hcp to fcc phase. After twinning, two thermally activated dislocation slip processes compete with one another: Shockley partial dislocations and full dislocation slip. The deformation mechanism changes from phase transformation to dislocation slip when the temperature is higher than 380 K or the strain rate is lower than 1g pyramidal plane is clearly observed under tensile loading 108 s1. The dislocation slip on the f1 0 1 at higher temperatures. Furthermore, our simulations indicate that the nucleation rate has a strong effect on the deformation mechanism on the nanoscale. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction It is well known that allotropic transformation occurs at 882 °C in pure titanium (Ti) from hexagonal close-packed (hcp) a-Ti to body-centered cubic (bcc), b-Ti [1]. At lower temperature, hcp aTi is stable, whereas b-Ti is stable at higher temperature. However, some studies demonstrate that severe deformation processes can facilitate phase transformations in pure Ti at ambient temperature [2–5]. Hydrostatic pressure, shock loading or high-pressure torsion processing can induce the hcp a to hexagonal x phase transformation in a-Ti [2–4]. The dependence of the microstructure evolution on the crystallographic shock direction was recently investigated using molecular dynamics (MD) simulations [5]. A transformation from the x phase to the orthorhombic c phase was observed in Ti under an external pressure of 116 GPa [6]. The first-principles calculations by Sliwko et al. [7] demonstrated the possible occurrence of a face-centered cubic (fcc) phase in pure Ti because this struc⇑ Corresponding author. E-mail address: [email protected] (L. Xiao). http://dx.doi.org/10.1016/j.commatsci.2016.09.013 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.
ture along the Bain path has a minimum total energy for fcc. Similar calculation results were also reported by Aguayo et al. [8]. Some experimental results have demonstrated that the hcp to fcc allotropic phase transformation could occur and the metastable fcc-Ti became stable in the Ti-Al multilayer films when the thickness of the individual layer was less than 10.5 nm [9,10] and in the milled Ti when the grain size was less than 5.3 nm [11]. The structural instability is attributed to the negative hydrostatic pressure due to the nanocrystallization process resulting from mechanical attrition, lattice expansion, and high plastic strain/strain rate. An epitaxial growth of fcc-Ti was experimentally observed in the thin films with metallic and semiconductor substrates [12–17]. A metastable fcc-Ti phase was produced in bulk Ti powders during mechanical milling [11,18], Ti/Ni and Ti/Al epitaxial multilayer films [19,20] and heat-treated Ti alloys [21–23]. Recent work shows that the fcc phase was formed during microstructural refinement by cryogenic plane-strain compression [24]. Some researchers suggest that the hcp to fcc allotropic transformation is induced by significant contamination of the milled powder by fcc-phase-forming elements such as nitrogen and carbon [25].
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The fcc-Ti observed in Ti/Al multilayers is merely an artifact of TEM specimen preparation [26]. The hcp to fcc polymorphic transformation in Ti is dominated by the high density of dislocations and twins but not stacking faults introduced by ball milling [18]. The stress-induced hcp to fcc phase transformation was related to the gliding of Shockley partial dislocations [24]. In the heat-treated Ti alloys [21,22], the fcc-Ti was obtained in the Ti–6Al–4V alloy by adding Zr, which can decrease the basal stacking fault energy of the a phase and promote the formation of the fcc structure in the modified alloy [21]. Even though many experimental and simulation works have demonstrated the phase transformation in pure Ti at ambient temperature under extreme pressure, temperature and size restriction conditions, the fundamental mechanism of this phase transformation is not clear thus far. In our previous work [27], the phase 2gh1 0 1 1i twinning region has transformation inside the f1 0 1 also been predicted in a-Ti single-crystal nanopillars orientated along [0 0 0 1] during tension according to MD simulations. These results indicate that hcp to fcc phase transformation is induced by dislocation glide of multiple Shockley partial dislocations under the condition of size restriction. However, the occurrence of this phase transformation is conditional. In this study, the phase transformation dependence on temperature and strain rate has been systematically studied. In addition, the phase transformation also has an influence on the mechanical properties. Thus, it is worthy to investigate the effect of deformation temperature and strain rare on the phase transformation. In order to clarify the phase transformation mechanism, and the relationships among mechanical behavior, twinning and phase transformation are established.
2. Simulation method MD simulations were conducted with the software LAMMPS [28] using a Finnis–Sinclair many-body potential for pure Ti [29]. We first created the hcp h0 0 0 1i-oriented single-crystalline Ti nanopillar with a width of 11 nm. The height-to-width ratio of the nanopillar is 2:1. To obtain an equilibrium state before loading, the structure was initially relaxed using the conjugate gradient algorithm. Then, an additional annealing under zero load was performed for 300 picoseconds (ps) at the deformation temperature. All directions were maintained under free-surface boundary conditions. The selected temperature range varied from 77 K to 600 K. A canonical ensemble – i.e., a constant atom number, volume and temperature (NVT) – was applied to maintain the system at a constant temperature. A time step of 1.0 fs (fs) and a strain rate of 1 108 s1 were selected. To investigate the strain rate effect, the configuration was deformed under uniaxial tension at different
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strain rates in the range of 107–1010 s1. The system was controlled at 300 K with the NVT ensemble. The average stresses in the atomistic systems were calculated by the Virial theorem [30]. Visualization was performed using the open visualization tool Atomeye [31]. 3. Results 3.1. Temperature effect of stress-strain response in a-Ti nanopillars Fig. 1 presents the typical stress-strain response of a-Ti singlecrystal nanopillars subjected to tensile deformation along the [0 0 0 1] direction at a strain rate ðe_ Þ of 1 108 s1 and different temperatures that vary from 77 K to 600 K. The Ti nanopillars exhibit two distinct types of plastic deformation behavior. For the first type, when the temperature is lower than 380 K, the stress-strain curve can be divided into three stages with two obvious yield stress points. The elastic strain reaches as high as approximately 5% during tensile loading. The first yield stress of the Ti nanopillar decreases with increasing temperature, as observed in Fig. 1(a). The second yield point, which is lower than the first one, is displayed at a strain of approximately 12%. After second yielding, further loading causes an extensive plateau with a constant stress of approximately 1.0 GPa (Fig. 1(a)). For the second type, only one yield point is displayed at the strain of 6% when the temperature is larger than 380 K, as observed in Fig. 1(b). As plastic deformation progresses, no obvious second yield point could be observed in the stress-strain curve. 3.2. Deformed microstructure of a-Ti nanopillars at different temperatures Fig. 2(a–d) presents the representative microstructures of the nanopillar subjected to 5% deformation at 77 K and a strain rate 2gh1 0 1 1i twin embryo nucleates from of 1 108 s1. The f1 0 1 0g and f1 21 0g surthe corner of the nanopillar between f1 0 1 faces, as indicated by a white arrow in Fig. 2(a). After nucleation, the twin rapidly grows toward the ends of the pillar at the strain of 5%, where the first yield occurs. Therefore, it is reasonable to believe that the initial tensile yielding is caused by the nucleation 2g twin. Fig. 2(d) demonstrates that the and growth of the f1 0 1 middle part of the pillar has been twinned and two twin/matrix interfaces are formed. Further examination reveals that the coher 0 by approximately ent twin part is nominally rotated along ½1 1 2 1 0 0Þ prismatic plane inside the twin 90°; consequently, the ð1 becomes parallel to the basal plane in the matrix, as observed in Fig. 2(d). The atoms are colored according to common neighbor
Fig. 1. Tensile stress–strain curves of Ti nanopillars at a strain rate of 1 108 s1 under uniaxial tensile loading along [0 0 0 1] at various temperatures (a) below 400 K and (b) above 400 K.
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Fig. 2. Snapshots of twin nucleation and growth during incipient yielding under tensile loading at 77 K. (a) The nucleation of a twin embryo from the corner of single-crystal nanopillars. (b–d) Observation of twin growth toward the ends of the nanopillars.
Fig. 3. Snapshots of partial dislocation nucleation and propagation during the second yielding under tensile loading at 77 K. (a) Nucleation of Shockley partial dislocations 2g twin. from the corner of a single-crystal nanopillar. (b–d) A transformation from the hexagonal close-packed (hcp) to the face-centered cubic (fcc) phase inside the f1 0 1
analysis (CNA) [32]. Hcp atoms are blue, fcc atoms are dark blue, and defect and surface atoms are red. The front surface is removed so as to show the inner defects. As the plastic deformation progresses, the twin boundary gradually moves to two ends of the nanopillar under the shear strain produced during external tensile loading. Fig. 3 presents snapshots that demonstrate the hcp to fcc phase transformation at the second tensile yielding at 77 K. The phase transformation is formed through the nucleation and propagation of Shockley partial dislo 0i [27]. The partial cations with Burgers vector b = ½ a/3 h1 1 2 dislocation initiates from the corner of the pillar and slips along 0g plane, as indicated by the white arrow in Fig. 3(a). the f1 0 1 The partial dislocation leaves a stacking fault behind in the twinning region. A group of high-density stacking faults is accumulated through continuous gliding of multiple Shockley partial dislocations inside the twinning region, eventually leading to the allotropic phase transformation from hcp to fcc [33]. This hcp to fcc transformation follows the Burgers orientation 0i kh0 1 1i relation [24], h0 0 0 1ihcp||h0 0 1ifcc, h0 1 1 and hcp fcc
1 0i kh0 1 1i . A similar hcp to fcc transition mechanism h2 1 hcp fcc was also observed in other tensile pillars at a temperature lower than 380 K. The dependence of the volume fraction of each phase on the strain level at 77 K is observed in Fig. 4(a). For comparison, the stress response curves are also included. The fcc phase rapidly increases at the cost of the hcp phase and reaches a maximum volume fraction of 22% at a strain of 17.5%. The fcc phase is less than 3% when the strain is less than 14% and mainly exists in the form of stacking faults in the hcp lattice in the vicinity of the twin boundary (Fig. 2(d)). The fraction of unidentified atom amounts is approximately 10%. These unidentified atoms are located on the surface, twin boundary, and ragged boundaries between the hcp and fcc phases in the pillar. Fig. 4(b) shows that the fraction of unidentified atom amounts is close to 20% at 450 K, which indicates that there are more disordered atoms and dislocations and that more ragged boundaries are produced by the twin variant in the pillar (Fig. 5). In contrast to the behavior at lower temperature, the deformation is more complicated at 450 K. Numerous disordered atoms
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Fig. 4. Evolution of the volume fraction of phase transformation with strain at a rate of 1 108 s1, as detected by CNA, at (a) 77 K and (b) 450 K.
Fig. 5. Snapshots of twin nucleation and growth during incipient yielding under tensile loading at 450 K. (a) Disordered atoms inside the nanopillar with red color before yielding. (b) The twin variant I nucleated from the corner of the nanopillar. (c) The twin variant II nucleated in the inner region of the nanopillar. (d–h) The growth of the twin variants. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
exist inside the pillar before yielding, as observed in Fig. 5(a). As the strain increases further, disordered atoms gradually reduce 2g twin variant I is formed at the first tensile yield point, and f1 0 1
as observed in Fig. 5(b). The nucleation site for twin variant I is located at the lateral edge of the pillar. The other representative nucleation site for twin variant II is in the middle of the side sur-
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face, which is atomically flat [34]. The two twin variants grow steadily and finally merge. No second tensile yield point is displayed on the stress-strain curve, and no hcp to fcc phase transformation can be observed at 450 K, as shown in Fig. 4(b). We also simulated the tensile loading at 600 K. The simulation results reveal that the deformation process is very similar to that at 450 K. No Shockley partial dislocation was activated. However, it is noted that the dis 1g pyramidal plane is clearly observed location glide on the f1 0 1 under tensile loading at the higher temperature. After twinning, full dislocation slip is activated. The plastic deformation is controlled by the full dislocation slip inside the twinning region at the higher temperatures.
3.3. Strain rate effect of stress-strain response in a-Ti nanopillar A series of MD simulations were performed at various strain rates from 107 s1 to 1010 s1 at 300 K. Fig. 6 presents a representative simulation results at various strain rates. It is revealed that the strain rate has a significant effect on the stress–strain behavior: at a low strain rate of 5 107 s1, the stress decreases abruptly after the first yield point at a strain of 3.8%, followed by wavy stress between 12% and 16%, as observed in Fig. 6(a). Two obvious stress yield points are displayed in the stress-strain curve at strain rates of 108 s1 and strains of approximately 5% and 12%, respectively, as observed in Fig. 6(b). However, there is no obvious stress yield
Fig. 6. Stress-strain curves at 300 K under uniaxial loading along [0 0 0 1] at different strain rates: (a) 107 s1, (b) 108 s1 and (c) 109–1010 s1. Evolution of the volume fraction of phase transformation with strain at 300 K, as detected by CNA, at strain rates of (a) 5 107 s1, (b) 5 108 s1 and (c) 5 109 s1.
Fig. 7. Snapshots of full dislocation nucleation and propagation during the second yielding under tensile loading at 300 K and a strain rate of 5 107 s1. Atomic-level snapshots of the microstructure viewed from the top and prism sides of the pillar.
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after the first yield when the strain rate is larger than 109 s1 (Fig. 6 (c)). When the strain rate is lower than 109 s1, the first yield stress of the Ti nanopillar increases with the strain rate. However, the trend disappeared at the higher strain rate of 109 s1 and 1010 s1, as observed in Fig. 6(c). The difference between the three types of stress-strain curves indicates that the deformation mechanism has changed with the applied strain rate.
3.4. Dynamic evolution of microstructure at different strain rates At the strain of 12%, the twin boundary migrates through almost the entire pillar, leading to a conversion to the twinned ori 1 0 0 entation, and the applied stress direction is rotated to the ½1 direction under tension at the strain rate of 5 107 s1. The dislocation clearly nucleates and grows at the top of the pillar along the 0 1 0Þ and ð0 1 1 0Þ double prismatic slip planes, which form a ð1 60° angle, as the tension deformation progresses, as observed in Fig. 7. The Burgers vectors were determined to be 1 0 and b2 = a/3½2 1 1 0, which indicate that the prisb1 = a/3½1 2 0Þ ½2 1 1 0 were matic double slips ð1 0 1 0Þ ½1 2 1 0 and ð0 1 1 activated under tension at the strain rate of 5 107 s1. No hcp to fcc phase transformation was observed after twinning deformation at the low strain rate. The fraction of each phase as a function of the strain is plotted in Fig. 6. The volume fraction of fcc atoms is close to zero (Fig. 6(a)). Only a few fcc atoms were formed in the form of stacking faults in the hcp phase. The phenomenon was also observed at the higher strain rates of 109 s1 and 1010 s1 (Fig. 6 (c)). The difference is that the pillar would fail through grain boundary sliding under continuous tension loading at the high strain rate. Upon close examination, remarkable serrated-like deformation behavior is displayed in Fig. 7(a). It is caused by the repeated glide and escape events of dislocations on the surface at 300 K and the strain rate of 5 107 s1. A similar result was reported in a-Ti nanopillars orientated for double prismatic slips 0 [35]. under compression along ½1 1 2 Fig. 8 shows atomistic configurations in a Ti single crystal at a strain rate of 1 109 s1 at 300 K. In these images, the perfect lattice of the Ti single crystal is segmented into different parts by the twinning boundaries. The boundary between two twins is similar to the grain boundary. Compared with the lower (e_ = 107 s1) and higher strain rates (e_ P 109 s1), the deformation at a strain rate of 108 s1 is the similar to that mentioned in Section 3.2 at lower temperature. The initial sharp increase of the fcc phase corresponds to the decrease of the hcp phase (Fig. 6(b)). This result is
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attributed to the multiplication of Shockley partial dislocations (Fig. 3). At the strain of 12%, the volume fraction of the fcc phase is approximately 24% and that of the hcp phase is approximately 60% in the system. 4. Discussion 4.1. Temperature and strain-rate dependence of the nucleation rate at the onset of plasticity Dislocation nucleation from the surface potentially plays a critical role in controlling plastic deformation when the sample size is tens of nanometers. The strength of a-Ti nanopillars is controlled by twin nucleation from free surfaces in this study. MD results reveal that the temperature and strain rate have considerable effects on the plastic deformation mechanism, particularly on the twin nucleation, which is a thermally activated process and is sensitive to both temperature and strain rate. For thermally activated deformation processes in metals, at a given temperature T and stress r, the nucleation rate v(T) can be expressed by [36]
mðTÞ ¼ Nm0 exp
Q ðr; TÞ ; kB T
ð1Þ
where N is the number of equivalent surface nucleation sites, v0 is the attempt frequency, Q is the active free energy [37], and kB is Boltzmann’s constant. Eq. (1) gives the nucleation rate when the system is under constant stress. However, in this study, Eq. (1) is used to describe the relationship between the nucleation rate and temperature. Combined with the Eq. (5), the activation energy barrier Q decrease with the temperature increasing. Meanwhile, two twin nucleation sites were observed at 450 K in Fig. 5. This means that the number of equivalent surface nucleation sites N increases with the temperature. The nucleation rate is proportional to the temperature, which indicates that the twin nucleation rate is dependent on the temperature. The corresponding tensile yield stress decreases with increasing temperature. To gain further insight into the strain rate sensitivity of the twin nucleation in the a-Ti single-crystal nanopillar, an implicit expression is derived for the nucleation stress when the nanopillar is deformed at a constant temperature and a strain rate [37–39],
Qðr; TÞ kB TN m0 ¼ ln ; kB T Ee_ Xðr; TÞ
ð2Þ
where E denotes the apparent Young’s modulus and Xðr; TÞ is the activation volume. Eq. (2) can be rewritten as:
1 0g plane under tension along the c-axis at a strain rate of 1 109 s1. (a–d) Two twin variants of Fig. 8. Atomistic configurations of the Ti single crystal in the f1 2 nucleation and growth. (e) Grain boundary sliding (GB sliding) under continuous tension loading.
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Q ðr; TÞ ¼ kB T ln
kB TN m0 : Ee_ Xðr; TÞ
ð3Þ
Inserting Q ðr; TÞ from Eq. (3) into Eq. (1), v(e_ ) can be expressed in the form
mðe_ Þ ¼
Ee_ Xðr; TÞ : kB T
ð4Þ
Atomistic simulations have predicted that the surface dislocation source has an activation volume of approximately 1–10b3, which results in a significant thermal contribution to the source’s strength [37]. b is the magnitude of the Burger’s vector. We hypothesized that the activation volume is a constant at a given temperature in Eq. (4). The nucleation rate v(e_ ) is proportional to the strain rate e_ , which indicates that the twin nucleation rate is dependent on the strain rate. The number of nucleation sites obviously increases when the strain rate is larger than 1 109 s1. Twin nucleation and growth play an important role in inducing plastic deformation in a-Ti single-crystal nanopillars at different temperatures and strain rates. Eqs. (1) and (4) reveal that the temperature and strain rate directly affect the twin nucleation rate. The number of equivalent surface nucleation sites N increases with the temperature and strain rate. 4.2. Temperature and strain-rate dependence of plastic deformation in the twinning region It has been demonstrated that the nucleation rate of twins is significantly dependent on the strain rate at 300 K, particularly 2g deformawhen the strain rate is larger than 109 s1. The f1 0 1 tion twin is a primary deformation mode in hcp metals. The orien 2g deformation twin is akin to that tation relationship of the f1 0 1 of conventional f1 0 1 2g twinning but without a crystallographic mirror plane [40]. Simulations and experiments have revealed that the boundary between parent and twin lattices is predominantly composed of semi-coherent basal-prismatic interfaces. The boundary migration is dominated by the movement of these interfaces via the local rearrangements of atoms. This deformation mode 2g twinning results in a disordered atom band between two f1 0 1 variants. The twin boundary between two variants is similar to that of a grain boundary in nanocrystalline [41,42]. The amount of disordered atoms in the twin boundary implies that the grain boundary sliding can be easily activated at a high strain rate. The decrease of the energy barrier for grain boundary sliding is faster than that of dislocation nucleation. Therefore, grain boundary sliding becomes the dominant deformation mechanism. The peak stress at the strain of approximately 12% at the high strain rate is reduced compared with that at the low strain rate. The plastic deformation behavior of crystalline materials is usually controlled by the motion of dislocations. Dislocation nucleation is a thermally activated process that is sensitive to both temperature and strain rate. It is believed that the thermally activated nucleation will become dominant at lower strain rates and higher temperatures [43]. After twin deformation, the plastic deformation mode changes from phase transformation to full dislocation gliding when the strain rate is less than 108 s1 or the temperature exceeds 380 K. The competition between the Shockley partial dislocation and full dislocation emission is controlled by thermal activation. The thermally activated process is often described by the activation energy barrier Q [44]. The effect of temperature on Q is [37,45]
Q ¼ ð1 T=T m ÞQ 0 ðrÞ;
ð5Þ
where Tm is the surface disordering temperature, and Q0 is the activation energy on the zero-T potential energy surface. The activation
barrier for dislocation nucleation in fcc metals is temperaturedependent and has been demonstrated using multi-scale simulation and analytical models [45]. Eq. (5) shows that the activation energy Q decreases with increasing temperature. Our simulation results reveal that full dislocation emission from the surface of the twin becomes favored over partial dislocations at elevated temperatures and low strain rates due to the increase of the thermal active process at lower activation energy. So the plastic deformation mode changes from phase transformation to full dislocation gliding when the temperature exceeds 380 K. In short, the temperature and strain rate have significant effects on the flow stress and deformation mechanism. It has been demonstrated that a small activation volume led to a sensitive temperature and strain rate dependence of the nucleation stress [37,46]. Recent simulation work demonstrated that the same dislocationobstacle interaction unit could lead to entirely different mechanisms at different strain rates [47]. Thus, the temperature and strain rate dependences of deformation mechanisms should be carefully considered when attempting to compare experimental data against MD simulations. 5. Conclusions (1) The double yielding phenomenon is displayed in the stressstrain curves of Ti single-crystal nanopillars subjected to uniaxial tension along the [0 0 0 1] direction when the deformation temperature is less than 380 K. The first peak is induced by twin nucleation, and the second peak is attributed to the nucleation of phase transformation. 2gh1 0 1 1i twinning is the primary deformation mode (2) f1 0 1 in Ti single-crystal nanopillars subjected to uniaxial tension along the [0 0 0 1] direction at the first yield. After twinning, a rare metastable fcc-Ti phase is formed inside the twinning region of the hcp-Ti phase at the second yield point when the temperature is less than 380 K or the strain rate is larger than 108 s1. A group of high-density stacking faults is accumulated though the continuous glide of multiple Shockley partial dislocations inside the twinning region, eventually leading to the allotropic phase transformation from hcp to fcc. (3) The phase transformation is strongly effected by temperature and strain rate. After twin deformation, the plastic deformation is dominated by the full dislocation gliding rather than Shockley partial dislocations when the temperature is higher than 380 K or the strain rate is less than 1g pyramidal 108 s1. The dislocation glide on the f1 0 1 plane is clearly observed, and the plastic deformation is controlled by the full dislocation slip inside the twinning region under tensile loading above 380 K. Prismatic double slips 0 1 0Þ ½1 2 1 0 and ð0 1 10Þ ½2 1 1 0 were activated under ð1 tension at strain rate less than 108 s1. The competition of two deformation mechanisms between phase transformation and full dislocation slip is controlled by the thermal activation. (4) The twin nucleation rate increases with the deformation temperature and the strain rate at the initial stage of plasticity deformation. At the higher strain rate (e_ P 109 s1), the deformation mechanism changes from dislocationmediated plasticity to grain boundary sliding.
Acknowledgements This project was financially supported by the National Natural Science Foundation of China (51471129 and 51321003), the 973
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Program of China (2014CB644003), and the 111 Project of China (B06025).
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