Size-dependent deformation mechanism transition in titanium nanowires under high strain rate tension

Accepted Manuscript Size-dependent deformation mechanism transition in titanium nanowires under high strain rate tension

Le Chang, Chang-Yu Zhou, Xiang-Ming Pan, Xiao-Hua He PII: DOI: Reference:

S0264-1275(17)30816-X doi: 10.1016/j.matdes.2017.08.058 JMADE 3317

To appear in:

Materials & Design

Received date: Revised date: Accepted date:

28 April 2017 11 July 2017 28 August 2017

Please cite this article as: Le Chang, Chang-Yu Zhou, Xiang-Ming Pan, Xiao-Hua He , Size-dependent deformation mechanism transition in titanium nanowires under high strain rate tension, Materials & Design (2017), doi: 10.1016/j.matdes.2017.08.058

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ACCEPTED MANUSCRIPT Size-dependent deformation mechanism transition in titanium nanowires under high strain rate tension Le Chang, Chang-Yu Zhou*, Xiang-Ming Pan, Xiao-Hua He School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing 211816, China * Corresponding author. Prof., Ph.D.; Tel.: +86-25-58139951; Fax: +86-25-58139951. E-mail address: [email protected] (C.Y. Zhou).

Abstract

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Tensile deformation of single crystal titanium nanowires (NWs) with size ranging from 3nm to 20nm along [0001] orientation is investigated by molecular dynamics (MD) simulations. For all NWs, the initial yielding at different strain rates is induced by the nucleation of {101̅2} twinning. Following the saturation of twin volume fraction, the size dependent transition of deformation mechanisms in twinned regions is observed. At the strain rate from 108s-1 to 109s-1, following the deformation twinning, the phase transformation from HCP to FCC dominates the plastic deformation of Ti NWs. By increasing sample size to 20nm, phase transformation can be replaced by prismatic dislocation slip. At the strain rate from 109s-1 to 1010s-1, the critical size for the transition from phase transformation to full dislocation slip decreases with the applied strain rate. With further increasing sample size, after the saturation of {101̅2} twins, the initial single crystal NW transforms to nanocrystalline NW. Subsequent plastic deformation mechanism in the nanocrystalline Ti NW with large size is transferred from grain boundary dominate deformation to the cooperation of grain boundary deformation and dislocation activity. Furthermore, deformation mechanism map is proposed to provide a deep understanding of the plastic deformation of Ti NWs.

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Key words: molecular dynamics simulation; titanium nanowire; size effect; tensile deformation 1. Introduction

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One-dimensional metal NWs have garnered much attention in recent years due to their unique properties, structures and the potential as the fundamental building blocks of the nanotechnological applications [1-2]. The mechanical behavior and properties of NWs are not well established due to the complex mechanical testing at the nanoscale level. Thus, molecular dynamics (MD) simulations have been performed extensively to obtain material properties at the nanoscale. The atoms on NWs surfaces have fewer neighbors than atoms in the interior. The surface effects have a great effect on the properties of NWs, as the high surface to volume ratio. With the increase of the structure dimensions of NWs, the surface effects become negligible. The surface stress induced phase transformation and pseudo-elastic and shape memory effect have been studied extensively [3-6]. For example, MD simulations have shown that the phase transformation from FCC structure to a BCT structure can be driven by surface stress in FCC NWs [3-4]. MD simulations on BCC NWs show that the strain induced solid-solid phase transitions in iron NWs and the transition temperature was dependent on the wire diameter [7]. Also, plastic deformation mechanism is strongly dependent on the size of NWs [8-13]. MD simulations in [8] demonstrate the size-dependent transition, from super-plastic deformation mediated by twin propagation to the rupture by localized slips in deformed region as the Au nanowire diameter decreases. Iron NWs up to 11.42nm size can undergo twinning mediated

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reorientation and then deform by slip mode at high strains resulting in high ductility and failure by necking [9]. Titanium is an attractive material with a confluence of properties not found in many other metals, such as high strength, low density, excellent corrosion resistance, and biocompatibility. Ti NWs will enable nanoelectronics and biomedical technologies [14–17]. Therefore, it is critically important to gain fundamental insight in to their deformation mechanisms at the nanometer scale before applications. Deformation twinning is known to play an important role in the deformation of HCP titanium due to the limited number of dislocation slip systems. Besides, twinning in HCP titanium is more complicated than FCC metals owing to various twin systems that may not obey Schmid's law [18]. The sample size has significant influence on the deformation mechanism of titanium and its alloys. For the conventional coarse-grain materials, the activation of twinning during plastic deformation is sensitive to grain size [19]. In recent years, experiments about the plastic deformation behavior of single crystal HCP metal at the microscale and nanoscale have revealed the dependence of deformation mechanism on sample size. Yu et al. [20] reported that deformation mechanism in the submicrometre-sized titanium alloy transformed from twinning to dislocation slip when the sample size decreased to below 1μm. Sun et al. [21] found that double prismatic slip was activated in titanium micropillars compressed along [112̅0] orientation from 350 nm to 3μm. Further, through ex situ and in situ compression and tension tests, they found that the emergence of a large number of basal stacking faults (SFs) led to both high strength and enhanced plasticity in single crystal Ti samples of 150nm [22]. Aitken et al. [23] conducted uniaxial compression of single crystalline Mg alloy with diameters between 300 and 5000 nm. They found the “smaller is stronger” size effect in single crystals and observed strain bursts caused by dislocation slip. Micropillar and macropillar compression responses of magnesium single crystals oriented for single slip or extension twinning were investigated by Prasad et al. [24]. It was reported that twin nucleation stress exhibited strong size dependence, with micropillars requiring substantially higher stress than the bulk samples. At the nanoscale, MD simulations can be an important tool to study the deformation behavior of metallic crystals. MD simulations in [18,25-27] have found the presence of deformation twinning in the single crystal titanium with [0001] orientation during tensile process at the nanoscale. Also, in single crystal Mg at the nanoscale, extension twinning is the dominate deformation mechanism for the plastic deformation along c-axial tension [28-30]. Under compression loading condition, the pyramidal 〈c + a〉 slip is the main deformation mechanism in [0001] orientated titanium nanopillars with size ranging from 5nm to 19nm [31]. MD simulations in HCP magnesium NW show the size-dependent effects on the formation of secondary twin [32]. However, the effects of sample size on deformation behavior of titanium NWs with [0001] orientation is unclear. Therefore, the purpose of this work is to investigate the effects of sample size on deformation mechanisms in [0001] orientated titanium NWs subjected to uniaxial loading at different strain rates.

2. Methods MD simulations were carried out by employing the LAMMPS code [33]. To model the atomic interactions, the Finnis–Sinclair many body potential developed by Ackland [34] for pure Ti was adopted, as the simulation results of previous MD simulations [26-27,31] using this potential show good agreement with the experimental results. The Finnis–Sinclair many body

ACCEPTED MANUSCRIPT potential is suitable for describing the defect evolution in Ti single crystal during tension loading. Single crystal Ti NWs were constructed with the X, Y, Z axis parallel to the [112̅0], [1̅100] and [0001] orientation respectively. The cross section sizes range from 10a ([112̅0] orientation, approximately 3nm) × 6√3a ([1̅100] orientation, approximately 3nm) to 68a (approximately

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20nm) ×40√3a (approximately 20nm), where a is lattice constant. Fixed length to cross section ratio of all the NWs was 2:1 in the simulations [9]. Periodic boundary conditions were chosen along the NWs length direction (Z axis) and the other dimensions were kept free. After the construction of the NW, energy minimization was performed by the conjugate gradient algorithm to obtain a stable structure. Then, the system was thermally equilibrated to 300 K by running 100ps. During the relaxation process, the temperature kept constant at 300 K and the initial system stress along the loading direction was adjusted to zero using constant NPT integration. After relaxation, these NWs were subjected to a uniaxial loading process with NVT integration. Nosé-Hoover thermostat with characteristic time fitted to the experimental Ti heat conductivity to remove temperature from the system at an appropriate rate was adopted to maintain the system temperature at 300K [35-36]. The NWs underwent homogeneous tensile deformation by rescaling of the z-coordinates of all atoms [8]. Due to the inherent timescale limitations from MD simulations, the applied strain rate in MD simulations is usually in the range of 107s-1-1010s-1 [8,9,18,27,29] which is significantly higher than that in typical experiment. Though MD simulations provide less quantitative information regarding plasticity in normal laboratory experiments because of the extreme strain rate applied, they can be used to get insight into the atomic-scale details of dislocation nucleation processes [37]. Therefore, in our simulation, different strain rates ranging from 108s-1-1010s-1 were applied. The average stresses in the systems were calculated by the Virial theorem [38]. The visualization of the simulation results were performed by OVITO [39]. Common neighbor analysis (CNA) [40] was used to distinguish defects from HCP environments. Dislocation analysis was carried out by dislocation extraction algorithm (DXA) [41] to identify all the dislocations during the deformation process.

3. Results

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3.1. Stress-strain behavior

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Tensile stress-strain curves for [0001] orientated single crystal Ti NWs with different cross section sizes varying from 3nm to 20nm at different strain rates ranging from 108s-1 to 1010 s-1 are shown in Fig. 1(a)-(f). It can be seen that the characteristics of stress-strain curves are affected by both strain rate and sample size. In Fig. 1(a)-(e) three distinct stages of stress-strain curves are displayed, however in Fig. (f) stress-strain curves only the two samples with 3nm and 6nm width show three stage variations, as in Fig. 1(a)-(e) an obvious second yielding occurs and in Fig. (f) it disappears except that for samples with 3nm and 6nm width . Besides, in Fig. 1(a) when the size of NW is smaller than 20nm, as the second peak stress reaches, the flow stress then almost keeps constant fluctuating in the range from 1 to 2GPa. For NW with the largest size, following the second yielding, stress-strain curve shows wavelike characteristic, as the repeated sharp decrease and increases of the stress can be observed. When NW is deformed at 5×108s-1, the size dependent characteristic of stress-strain curves in Fig. 1(b) is similar to that in Fig. 1(a). Therefore, the critical size for stress-strain curves transferring from fluctuating around an almost constant stress to sharp decrease and increase is 20nm at the strain rate of 108s-1 and 5×108s-1. As the strain rate increases to 109s-1, this critical size is 10nm, below which the stress in the third stage of

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Fig. 1. Size and strain rate dependent stress-strain curves 3.2 Variation of yield stress According to stress-strain curves, the yield strengths of all the NWs are shown in Fig. 2.

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From Fig. 2(a), it can be seen that at low strain rates (108s-1 to 109s-1), with the increase of the cross section size, the yield stress decreases. The relationship between the yield stress and the sample size follows a Hall-Petch-type law. This dependence of yield stress on size is related to the surface effect in small-scale systems [42-43]. As the sample size increases, the ratio of the number of surface atoms to total atoms decreases, leading to the smaller surface effect. Therefore, when the cross section size of NW is above 10nm, the yield stress of the NW tends to constant at different strain rates. At the strain rates above 109s-1, the yield stress of 3nm width NW is close to that of 6nm width. As the size reaches 8nm, with the increase of the size, the yield stress shows a remarkable increase. To explain this phenomenon, the dependence of yield stress on the applied strain rate is shown in Fig. 2(b). In our previous study [18], the yield stress for Ti NW with size less than 6nm shows strong dependence on strain rate beyond 1010s-1 and weak dependence below 1010s-1. It is interesting that this critical dynamic strain rate is dependent on the size of NW as shown in Fig. 2(b). For NW with size ranging from 8nm to 10nm, the critical dynamic strain rate is about 5×109s-1. Below this, the yield stress of NW is less sensitive to the applied strain rate. The critical dynamic strain rate for NW with size ranging from 15nm to 20nm is about 109s-1. This critical dynamic strain rate decreases with the increase of the size of NW. Therefore, at the strain rates above 109s-1, the strengthen effect of strain rate on the yield stress leads to the increase of the yield stress with the size of NW. At the strain rates below 109s-1, strain rate dependence can be neglected and surface effect dominates the variation of the yield stress with the cross section size.

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3.3.Microstructure evolution analysis First, tensile deformation processes of Ti NWs with different cross section sizes at the strain rate of 108s-1 were analyzed. Typical microstructure evolution of small (10nm) size is shown in Fig. 3. The initial yielding event is characterised as {101̅2} tension twinning embryo nucleates from some location along one edge of the specimen, as shown in Fig. 3(a). With the applied strain, multiple twin variants are simultaneously activated from different corners of the NW. Fig. 3(b) displays four twin variants. To view along with [2̅110], the angel between basal plane of the twinned regions marked by number "1" and "4" and that of the matrix is about 90°. The specific twin system is identified as (011̅2). Similarly, twin variants of number "2" and "3" are identified as (1̅012) twin variants by viewing from [1̅21̅0]. With the growth of different twin variants, the intersection of twin boundaries (TBs) is observed and consequently the merging of different twin variants occurs, as shown in Fig. 3(c). Therefore, at the strain of 0.052, only the initial nucleated

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(011̅2) twin variant exists in NW. The misorientation between the matrix and the twinned region is about 90°, as shown in Fig. 3(d). With the migration of TBs at the two ends of NW towards the centre of NW, at the strain of about 0.082, the entire NW converts to twins. Then, with the applied strain, no dislocation or twins can be found as NW undergoes second elastic deformation. At the strain of 0.140, second yielding is observed as partial dislocations nucleate from the corner of NW. With the propagation of partial dislocations, the transformation from HCP to FCC-Ti appears, as shown in Fig. (e)-(g). According to DXA analysis, a high-density 〈c + a〉 and 1/3〈1̅100〉 partial dislocations distribute on the interface between twins and FCC-Ti. The HCP to FCC phase transformation in single crystal titanium was also observed by Ren et al. [29]. They suggested that the continuous gliding of multiple Shockley partial dislocations inside the twinning region, eventually leading to the phase transformation from HCP to FCC. Fig. 4 shows the volume fraction evolutions of different atoms and the corresponding deformation feature during the deformation process. The first stage in stress-strain curve is the elastic deformation stage. At the strain ranging from 0.048 to 0.082, plastic deformation is carried out by deformation twinning. As the NW is completely twined, twin volume fraction is saturated. Then, the twined NW undergoes elastic deformation again. At the strain of 0.140, second yielding caused by partial dislocation slip occurs. The propagation of the partial dislocations leads to the transformation from HCP to FCC atom. The volume fraction of FCC phase increases rapidly and reaches about 21% at the strain of 0.30.

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Fig. 3 Microstructure evolution of NW with 10nm width at 108s-1. Snapshot in (a) shows the nucleation of one twin variant, (b) the simultaneous nucleation of multiple twin variants, (c) the merging of different variants and (d) the growth of twins towards the centre of NW. Snapshots in (e)-(g) show the transformation from HCP to FCC atoms in twined region. Snapshots in (h) shows the distribution of 〈c + a〉 and 1/3〈1̅100〉 partial dislocations on the interface between FCC-Ti and twins. Atoms in Fig. (a)-(g) are rendered by CNA, where red, white and green represents HCP, other and FCC atoms, respectively. For the visualization of interior microstructure surface atoms are removed.

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Fig. 4 The variations of other, FCC and HCP atoms with the applied strain in the 10nm NW at 108s-1 . As the sample size increases to 20nm, the third stage of stress-strain curve converts from slight fluctuation to wavelike shape, indicating the transition of deformation mechanism in the third stage. Fig. 5 displays the detailed deformation process of NW with 20nm width at the strain rate of 108s-1. The initial yielding is still attributed to the nucleation of one twin variant from the corner of the NW, as shown in Fig. 5(a). With the imposed strain, more and more twin variants are activated from different corners of the NW. Fig. 5(b) displays the simultaneous growth of six twin variants. Compared with Fig. 3(b), it is obvious that with the increase of sample size, the number of twin variants activated during tension process increases. Besides, it is worth noting that multiple parallel stacking faults reside on basal planes in the twinned region. These stacking faults always nucleate from the TBs, which may be probably significant for the TB migration and twin growth. Though multiple twin variants can be activated, with the merging of different twin variants, finally only the initial twin variant nucleated at the yielding exists in the NW. Fig. 5(d) shows that when the twin volume fraction is saturated, the entire NW is occupied by the initial nucleated twin variant. Following this event, deformation mechanism for plastic deformation of the NW is mainly prismatic dislocation slip indicated by blue arrow in Fig. 5(d). Besides, stacking faults caused by the propagation of Shockley partial dislocations are observed indicated by green arrow in Fig. 5(d). Fig. 5(e)-(h) illustrates the movement of prismatic dislocations inside the NW. The prismatic dislocation with Burger vectors b1=1/3[112̅0] nucleates from the bottom right corner of the NW. Before the prismatic dislocation b1 run through the NW, another prismatic dislocation with Burger vectors b2=1/3[1̅21̅0] nucleates from the opposite corner of the NW. Finally, theses dislocations are absorbed by the free surface and consequently slip steps on the surface are generated. With the emission and annihilation of prismatic dislocations, the repeated

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decrease-increase in the third stage of stress-strain curves for the NW with 20nm width are observed, as shown in Fig. 1(a). Fig. 5(i) show the atomic shear strain distribution. The light blue and green atoms have high atomic shear strains, while the dark blue atoms have low atomic shear strains. The series prismatic dislocation slip traces can be found as they traverse a path which runs at approximately 60° to the direction of tension. Besides, few traces of stacking faults are observed, as they are parallel to the tension direction. Therefore, as the sample size increases to 20nm at 108s-1, the deformation mechanism in the third stage of stress-strain curve transforms into the full dislocation slip.

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Fig. 5 Deformation process for the NW with 20nm width 108s-1. (a)-(d) show the evolution of twin variants. (e)-(h) show the movement of prismatic dislocations inside the NW. (i) shows the atomic shear strain distribution. Fig. 5(a)-(d) are rendered by CNA. To clearly show the movement of dislocations inside the NW, only other atoms in dislocations rendered by grey are displayed in Fig. 5(e)-(h). At the strain rate of 5×108s-1, the dependence of the cross section size on strain-strain curve is as same as that at 108s-1. According to microstructure evolution analysis, for small size NW (≤15nm), deformation mechanism in the third stage is phase transformation. For large size NW, prismatic dislocation slip is the prominent deformation mechanism in the third stage. With increasing strain rate to 109s-1, plastic deformation mechanism is significantly dependent on the cross section size of NW. The critical size for deformation mechanism transition from phase transformation to dislocation slip decreases to 10nm. However, as the size of NW increases to 20nm, stress-strain curve in the third stage shows slow decrease, indicating that deformation mechanism is different from full dislocation slip.

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Microstructure evolution of 20nm NW is displayed in Fig. 6. More twin variants are observed during the second stage deformation, compared with the condition at 108s-1 and 5×108s-1. Besides, three twin variants exist in the post-twinned NW, as shown in Fig. 6(c). Therefore, the initial single crystal NW transforms to nanocrystalline NW and the NW are segmented into three individual grains. The previous TBs act like grain boundaries (GBs). Consequently, multiple deformation mode are activated. It is worth noting that a lenticular shaped nano-grain is formed at the GBs and grows with the applied strain. The development of this new grain (NG) are marked by "A". Besides, prismatic dislocation marked by "B" emitted from GB glides through the grain until it is absorbed into the opposite GB. However, full dislocation slip is not the major accommodation mechanism. Also, the propagation of Shockley partial dislocations nucleated from GBs can be observed, leading to the appearance of stacking faults marked by "C". GB sliding is marked by "D", which also contributes to the plastic deformation. With the applied strain, another NG is formed at GBs, as shown in Fig. 6(d). Fig. 6(e) provides an illustration of the misorientations between different grains and the initial matrix. The basal planes of the three twin variants ( two (1̅012) and one (011̅2)) are all perpendicular to that of the initial matrix by viewing from [1̅21̅0] and [2̅110], respectively. By viewing from [112̅0] orientation, the misorientation of the basal plane between the NGs and the initial matrix is about 74°. The TBs acting like GBs provide the source for dislocation nucleation. Fig. 6(f) shows that considerable numbers of dislocations pile up at GBs. Further, the distribution of atomic shear strain is displayed in Fig. 6(g). Atomic strain tensor analysis shows the traces of multiple deformation modes. Local high shear strain can be observed in the region of NGs and stacking faults marked by "A" and "C", respectively. Also, the traces of full dislocations glide through the (011̅2) grain marked by "B" can be observed. The red atoms in GBs marked by "D" reveal that GB associated deformation also accommodates the imposed plastic strain.

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Fig. 6 Microstructure evolution of the 20nm NW at 109s-1. (a)-(d) are rendered by CNA, where red, green and white represents HCP, FCC and other atoms, respectively. Fig. 6(a) shows the simultaneous nucleation of multiple twin variants from different corners of NW. Fig. 6(b) shows the merging of different variants. Fig. 6(c) shows multiple deformation modes in NW, i.e., the appearance of new grains marked as "A", full dislocation slip emitted from GB marked as "B", stacking faults marked as "C" and GB deformation marked as "D". The misorientation between the two NGs and the initial matrix is illustrated in Fig. 6(e). Fig. 6(f) shows the distribution of multiple dislocations on the GBs. Fig. 6(g) are colored according to atomic shear strain. At the strain rate of 5×109s-1, deformation mechanisms in the third stage of plastic deformation for 3nm and 6nm NW are phase transformation and full dislocation slip, respectively. With the increases of the size of NW, due to the lack of dislocation source, GB deformation becomes the main deformation mechanism for the NW with size ranging from 8nm to 12nm. These GBs are formed by deformation twinning. Fig. 7 displays GB deformation of the post-twinned NW with 8nm width in the third stage. Fig. 7(a) shows the displacement vector map derived from the initial to the deformed configurations at the strain of 0.20. The black arrows point to the directions of atomic motions. Typical GB deformation, i.e., GB sliding, GB rotation, etc. is observed during the deformation process, as marked out in regions A, B and C in Fig. 7(a).

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The activation of full dislocation is rarely observed. Besides, Fig. 7(b)-(c) show that the GBs become thicker with the applied strain, as considerable numbers of disordered atoms accumulate at GBs due to the increase of strain rate. According to CNA results, an obvious increase of other atoms volume fraction in the third stage deformation is displayed in Fig. 8. These disordered atoms are non-dislocations and rearranged at GBs. Therefore, GB deformation caused by the motion of disordered atoms at GBs is the primary deformation mechanism for these NWs in the third stage of tensile deformation.

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Fig. 7 GB deformation of the NW with 8nm width at 5×109s-1. Snapshot in (a) provides displacement vector map. White atoms represent the regions of GBs and black arrows represent the atomic motion direction. (b)-(c) show the accumulation of disordered atoms at GBs.

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many adjacent stacking faults caused by the propagation of partial dislocations nucleated from GBs, as indicated by white arrows in Fig. 9(b) and (e). The Shockley partial dislocations emitted from GBs completely across the grain and become absorbed into the opposite GBs prior to the emission of the trailing partial dislocation, leaving behind stacking faults that traverse the entire grain. Also, full dislocation slip indicated by black arrows is observed, though it is not the major accommodation mechanism. Compared with the initial TBs, due to the motion of disordered atoms around GBs, GBs become thick, which is more remarkable at the strain rate of 1010s-1, as indicated by blue arrows. Compared with Fig. 7, microstructure configuration of 20 nm NW shows a much larger fractions of stacking faults. Due to the lack of partial and full dislocation slip, GB deformation such as GB sliding and migration must be activated to accommodate the imposed tensile strain, as shown in Fig.7. Therefore, the increase of the sample size leads to the transition in deformation accommodation from GB deformation to the cooperation of GB deformation and dislocation activity.

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Fig. 9 Microstructure configurations of 20nm NW at the strain rates of 5×109s-1 and 1010s-1. Snapshots in (a)-(b) and (d)-(e) are colored by CNA. Snapshots in (a) and (d) show that multiple twin variants are distributed along the edges of the NW. Snapshots in (b) and (e) show that following the deformation twinning, typical deformation defection are observed including GB deformation, full dislocation and stacking faults indicated by blue, dark and white arrows, respectively. Snapshots in (c) and (d) show the spatial distribution of dislocations inside the NW. To quantificationally compare dislocation activity during the deformation process in the nanocrystalline Ti NW, the evolution of dislocation density are plotted in Fig. 10 and 11. From Fig. 10(a) and 11(a), it can be seen that total dislocation density shows a significant increase when the sample size increases to 15nm. In other words, dislocation activity in small sample size is little. The main dislocation found in the microstructure are 〈c + a〉 partial dislocation, 1/3〈1̅100〉 partial dislocation and 1/3〈112̅0〉 full dislocation. Prismatic dislocation slip inside the NW is rare, as its density is much lower than other dislocations. The majority of 〈c + a〉 partial dislocations formed during the growth of different twin variants are piled up in the GBs. Therefore, partial dislocation slip is the dominated slip mode. The propagation of these partial dislocations lead to the accumulation of stacking faults inside the NW. Besides, the density of 1/3〈1̅100〉 partial dislocation at the strain rate of 1010s-1 is higher than that at 5×10-9s-1. Therefore, the fractions of stacking faults in Fig. 9e is more than that in Fig. 9b.

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4. Discussion 4.1. Effect of size on yield stress For the defect-free metallic NWs, dislocation nucleation from the free surface is the predominant mechanism underlying plastic yielding due to dislocation starvation in the bulk. In

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this paper, the incipient plasticity was triggered by the nucleation of deformation twinning at free surfaces. At the lowest strain rate, the saturated yield stress (≈4.5GPa) for large size NWs is close to the reported theoretical strength of single crystal Ti [44]. Also, this saturation value is close to the maximum flow stress of single crystal Ti observed in micro-compression and in situ nano-compression experiments [20]. The inverse dependence of cross section size on strength was obtained, as shown in Fig. 2(a). This Hall-Petch type relationship (σ = σ0 + kd−α ) describes the inverse dependence of grain size on strength regardless of deformation mechanism, which is consistent with the results of previous MD simulations [45-47] and experiments in [20-21]. However, the size effect on the yield strength of Ti NW is small, as the power law exponent (≈ 0.35) is smaller than that typically ranges from 0.5-1, which is frequently discussed for larger pillars with micron sizes [20-21]. Such transition of scaling behavior of yield stress on the sample size in an approximate range of tens of nanometers is caused by the size effect arising from surface dislocation nucleation, compared to that in micropillars arising from collective dislocation dynamics [37]. By using transition state theory, Li et al. [37] proposed an atomistic modeling framework to predict the nucleation stress needed to activate surface defect nucleation at a given temperature T and strain rate 𝜀̇, which can be expressed by: 𝑉

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Where 𝑄 ∗ is the nucleation barrier, V the activation volume, k the Boltzmann's constant, N the number of equivalent nucleation sites, 𝜈0 the nucleation rate and E the Young's modulus. This equation explicitly shows the functional dependence of nucleation stress on temperature and strain rate. Ren et al. [27] explained the effects of the temperature and strain rate on the initial plastic deformation of single crystal Ti according to the above equation. According to this equation, nucleation stress is most sensitive to deformation temperature. However, as N is in the logarithmic function of Eq. (3), the size effect arising from surface nucleation is expected to be weak, compared to that in micropillars. In this paper, the weak size effect on the yield strength at the nanoscale is consistent with previous MD simulations [29,47] and experiments [48-49]. For instance, MD simulations [47] on the plastic deformation of Al nanopillars within tens of nanometers revealed that the power law exponent was in the range of 0.06–0.21. MD simulations in single crystal HCP Mg subjected to tension along [0001] orientation at nanoscale by Luque [29] also found that at the strain rate ranging from 108s-1 to 109s-1, the size effect on yield stress was weak as the nucleation stress for large samples (10nm) and small samples (5nm) was so close (see Figure 4 in [29]). The experimental results of in situ nano-tension tests performed on single crystal Pd NWs indicated weak size effects in defect-free metallic nanostructures [48]. Therefore, at the strain rate ranging from 108s-1 to 109s-1, size effect on yield stress is weak and consequently power law exponent α in Fig. 2(a) is rather small, due to surface dislocation nucleation-mediated plastic deformation in NWs. It is interesting that for all the simulated NWs, the yield stress show a much weaker dependence on strain rate ranging from 108s-1 to 109s-1, compared to that at relatively high strain rate. Similar results was observed by Luque [29]. He found that nucleation stress of {101̅2} twinning rises rapidly at the strain rate of 1010s-1 and more twin variants nucleate at the initial yielding, which is consistent with our results. Besides, the strain rate sensitivity is affected by the size of NW, as larger samples exhibits a stronger rate dependence and smaller samples exhibits a much weaker rate dependence, which can be seen in Fig. 2(b). MD simulations in [50] also show different dependences of the size on yield stress for large and small samples. Through in situ

ACCEPTED MANUSCRIPT scanning electron microscope microcompression tests, Huang et al. [51] confirmed the decreasing trend of strain-rate sensitivity with decreasing sample size. The critical dynamic strain rate decreases with the increase of the size of NW, above which the yield stress increases sharply. Similar findings was reported by Xu et al. [52] in Cu NWs. 4.2 Effect of size on deformation mechanism transition

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As the loading direction is along c-axial , so that the resolved shear stress for basal slip activation is zero and the only possible deformation mechanisms are pyramidal slip with ˂c+a˃ Burgers vector has a non-zero Schmid factor and deformation twinning ({101̅2} and {101̅1}). Under tension loading along c-axial, {101̅2} twinning mode has the maximum Schmid factors, therefore, it is easier than other deformation modes to activate [28,53]. Thus, the initial plastic deformation was controlled by {101̅2} tension twinning. This is consistent with the results of other MD simulations [27-30]. By increasing strain rate and the cross section size, the number of twin variants increases, as more sites on the free surface are available for defect nucleation. At the strain rate from 108s-1 to 109s-1, after the initial matrix completely converts to twins, phase transform dominates the plastic deformation of NW ranging from 3nm to 15nm. It has been confirmed by experiment results that the HCP-Ti to FCC-Ti phase transformation can occur at nanoscale [54-55]. When grain size reduces to about 5 nm through the high-energy ball milling, a HCP to FCC transition at room temperature occurs [54]. Chakraborty et al. [55] suggested that FCC Ti was stable in ultrathin Ti films much thinner than 144nm. Recent MD simulations [26-27,56] also found this phase transformation in Ti at the nanoscale. However, as the cross section size increases to 20nm, following the saturation of tension twinning, deformation mechanism transfers from phase transformation to full dislocation slip, which indicates that the HCP to FCC phase transformation in Ti NW has a strong dependence on sample size. In MD simulation [26], the HCP to FCC phase transformation in a Ti nanocrystal with constant cross section size (10nm) was only observed at the strain rate from 108s-1 to 5×108s-1. According to the MD simulation results in this paper, at constant temperature this transformation is not only dependent on strain rate, but also dependent on sample size. Fig. 12 provides the size dependent phase transformation at different strain rates. At the strain rate of 109s-1, the critical size for phase transformation is about 9nm, above which phase transformation is absent. As the strain rate increases to 5×109s-1, phase transformation only occurs in the NW with 3nm width. At the strain rate of 5×109s-1 to 1010s-1, the appearance of few FCC atoms is in the form of stacking faults. The size dependent phase transformation in Ti NWs can be interpreted by the variation of Gibbs free energy (GFE) with sample size. GFE is regarded as a criterion for phase transformation. At a given thermodynamic condition, the metastable phase will transform into the stable one with minimal GFE [57-58]. Besides, with the decrease of samples size, GFE difference between HCP and FCC structure increases [57]. Therefore, phase transformation is more remarkable in small size range. At a constant temperature and strain rate, as the cross section size of NW increases to a critical value, phase transformation will not occur. Besides, phase transformation is also dependent on deformation temperature [57-58].

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Fig. 12 The dependence of phase transformation on the sample size. According to the microstructure evolution analysis, the size and strain rate dependent deformation mechanism map can be obtained, as shown in Fig. 13. At 109s-1, the critical size for phase transformation in Ti NW is about 9nm, above which HCP to FCC transformation is absent. For NWs with cross section size in the range of 10nm-15nm, following the nucleation and growth of {101̅2} twinning, dislocation slip occurs, leading to the appearance of serrated stress-strain curves, as shown in Fig. 2. Prismatic dislocation slip is activated more easily due to a change of crystallographic orientation from lower Schmid factor (0) to higher Schmid factor (0.433). Besides, dislocation density is low during deformation process, due to lack of dislocation source. For nanostructured materials, dislocation multiplication is severely confined by the nanometre-scale geometries so that continued plasticity can be expected to be source-controlled [59]. When sample size is above 15nm, after the saturation of the volume fraction of twins, NW is occupied by multiple twin variants and the single crystal NW transfers to polycrystalline NW. It is interesting that the development of new grain in GBs accommodates the plastic deformation. The formation of new grains around GBs was also observed by Amitava et al. [60] and Song et al. [61-62] in nanocrystalline HCP Mg, which may be caused by strain-induced local stress concentration and atomic rearrangement in GBs. Besides, full dislocation slip, partial dislocation slip and GB sliding are also observed. At the strain rates of 5×109s-1 to 1010s-1, for the post-twinned samples in small size (≤12nm) GB sliding dominates the third stage plastic deformation, as dislocation activity is very little. It is well known that in nanocrystalline with size below ten nanometers, the main deformation mechanism is GB-mediated process [63]. With increasing grain size, there is a transition from GB-mediated process to dislocation-mediated deformation. Therefore, for the post-twinned samples with large size (15-20nm), intragranular dislocation slip was observed. These previous TBs acting as GBs in nanocrystalline metals provide considerable amounts of sites for dislocation nucleation. The increased dislocation plasticity leads to the improvement of resistance to plastic deformation and correspondingly stress-strain curve of 20nm NW is higher than that of smaller NWs. It is worth noting that for NW with large size, the maximum fraction of FCC atoms increases with sample size, as shown in Fig.12. These FCC atoms is in the form of SFs. The more quantities of SFs were caused by the partial dislocations slip frequently emitted from GBs, which may primarily accommodate the plastic deformation of the nanocyrstalline NW. Our simulation results reveal that basal slip mode is the dominate slip mode in

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nanocrystalline Ti with grain size within about ten nanometers, as the basal slip mode is easier to generate than the prismatic or pyramidal modes [64]. The basal slip mode appears as partial dislocations, as basal ˂a˃ dislocation with b= 1/3〈1̅21̅0〉 can be dissociated into partial dislocations with Burgers vector b=1/3〈1̅100〉. Kim et al. [64] also found that basal slip mode was the dominate slip mode in nanocrystalline Ti with grain size below the critical size. Similarly, plastic deformation was primarily controlled by partial dislocation slip dissociated from basal ˂a˃ dislocation in HCP cobalt with grain size below 10nm [65]. Similar conclusions can be found in nanocrystalline HCP Mg with very small size at the nanoscale [60-61]. With the increase of grain size, the contribution from other dislocation slip modes (i.e. prismatic slip and pyramidal slip) and deformation twinning to the plastic deformation increases [60-61,64]. Though our results agree well with these studies, to study the grain size dependent deformation behavior in nanocrystalline Ti, further study is needed, as 3D structures with randomly oriented grains based on Voronoi construction are more proper to be applied to reproduce the mechanical properties of nanocrystalline metals in experiments.

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In this paper, MD simulations were performed to probe the effects of sample size on tensile behaviors of single crystal Ti NW at different strain rates. The stress-strain behaviors, yield stress and deformation mechanism of Ti NWs with size ranging from 3nm to 20nm were evaluated based on the simulation results. The main conclusions are as follows: (1) Stress-strain curves present three distinct stages at the strain rates from 108s-1 to 5×109s-1, as the double yielding phenomenon is displayed in stress-strain curves. Following the second yielding, the third stage presents three typical characteristics at different deformation conditions, i.e., fluctuation within a narrow range, wavelike shape and gradual decrease. (2) At the strain rate from 108s-1 to 109s-1, an inverse dependence of sample size on the yield stress is acquired due to the surface effect. Above the strain rate of 109s-1, the yield stress almost increases with the cross section size of the NW, as the yield stress shows strong strain rate dependence on the strain rate in this range and the surface effect could be neglected. Besides, the critical dynamic strain rate decreases with the increase of sample size.

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(3) According to microstructure evolution analysis, for all NWs, the first yielding is induced by the nucleation of {101̅2} twinning, regardless of the variation of sample size and the applied strain rate. Following the saturation of twin volume fraction, different deformation mechanisms dependent on sample size and the applied strain rate in the third stage can be activated. The almost constant flow stress fluctuating from 1 to 2GPa is led by the continuous phase transformation from HCP to FCC in twinned regions. The wavelike shape in the third stage of stress-strain curves is induced by the prismatic dislocation slip, due to the change of crystallographic orientation. Deformation mechanisms attributed for the slow decreasing stress-strain curves in the third stage are complex. With the increase of the applied strain rate and sample size, the transition in deformation mechanism from GB dominate deformation to the cooperation of GB deformation and dislocation activity is observed. Furthermore, based on the study of the present work, deformation mechanism map is established to predict the condition about the transition among the four different deformation mechanisms.

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The authors gratefully acknowledge the financial supports of the National Natural Science Foundation of China (51475223, 51675260) and the Graduate Student Scientific Innovative Project of Jiangsu Province (KYLX16_0595).

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Highlights Sample size-dependent strain rate sensitivity was found. The incipient plasticity is induced by {101̅2} extension twinning. The tendency of hexagonal close-packed Ti to face-centered cubic Ti phase transformation decreases with sample size and strain rate. Dislocation activity increases with sample size in the post-twinned nanocstalline samples.

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