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Effects of temperature and strain rate on the mechanical properties of hexagonal boron nitride

nanosheets

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2014 J. Phys. D: Appl. Phys. 47 025303

(http://iopscience.iop.org/0022-3727/47/2/025303)

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Journal of Physics D: Applied Physics

J. Phys. D: Appl. Phys. 47 (2014) 025303 (8pp) doi:10.1088/0022-3727/47/2/025303

Effects of temperature and strain rate onthe mechanical properties of hexagonalboron nitride nanosheetsTongwei Han, Ying Luo and Chengyuan WangSchool of Civil Engineering and Mechanics, Jiangsu University, Jiangsu Zhenjiang 212013,Peoples Republic of China

E-mail: chengyuan.wang@gmail.com (C Wang)

Received 28 August 2013, revised 4 November 2013Accepted for publication 7 November 2013Published 11 December 2013

AbstractThe effect of temperature and strain rate on mechanical properties remains an open topic inresearch of hexagonal boron nitride (h-BN) nanosheets. To examine these fundamental issueswe have performed molecular dynamics simulations to record the stressstrain curves intensile tests and measure Youngs modulus, fracture strength and fracture strain in armchairand zigzag directions. Comparing the results obtained at different temperatures and strain rateswe have quantified the effects of the two factors on the tensile properties of the h-BNnanosheets. The influence of crystal orientation is also examined in the present study. It isfound that the h-BN nanosheets are basically an anisotropic material whose tensile propertiesvary substantially with temperature and strain rate. In particular, a yielding platform isobserved for the h-BN nanomaterial at relatively low temperature.

Keywords: hexagonal boron nitride, temperature, strain rate, mechanical properties,molecular dynamics

(Some figures may appear in colour only in the online journal)

1. Introduction

Similar to graphene [1], other single-atom nanosheets, e.g.,h-BN, WS2, MoS2 and NbSe2 [24], have received consider-able attention due to their unique mechanical, electrical andchemical properties, and potential applications in nanotech-nology [58]. Among them, h-BN nanosheets are one of themost intriguing two-dimensional (2D) nanostructures, whereB and N atoms are organized in hexagonal rings. The boronnitride nanotubes (BNNTs) have also been synthesized, whichcan be imaged as a result of rolling up the h-BN nanosheets.

The most distinctive advantages of BN nanomaterialsover their carbon counterparts are that the BN systemsare electrically insulating [911] and more stable at hightemperature and various chemical environments [12]. In themeantime, the two systems are comparable in terms of thermalconductivity and mechanical robustness [1317]. Theseunique features of BN nanomaterials promise great potentialfor constructing nanodevices [18], functional nanocomposites[19, 20], hydrogen accumulators, etc [21, 22]. As reviewed in[23], a great deal of effort has already been made to quantify themechanical properties of BNNTs. The study of the mechanics

of 2D h-BN nanosheets has also started very recently. Bosaket al [24] measured the elastic moduli (811 GPa) of h-BNbased on inelastic x-ray scattering measurements. Usingatomic force microscopy, Golbergs group [14] found thatthe bending modulus of the h-BN sheets increases withdecreasing thickness and approaches an asymptotic value ofmonolayer BN sheets when the thickness is below 50 nm. Inaddition, notably improved thermal and mechanical propertieshave been observed for the polymer composites reinforcedby BN nanosheets [19]. In addition to the experimentalwork, theoretical studies have been conducted to simulate thebehaviour of h-BN nanosheets. Ohba et al [25] reported theelastic constants and bulk modulus based on first-principlescalculations. The ab initio studies were also carried out byseveral groups [2629], where Youngs modulus achieved forh-BN nanosheets fell in the range of [809.1 GPa, 846.1 GPa].More recently, Bohayra Mortazavi et al [30] investigated thetensile response of single layer BN sheets using moleculardynamics simulation (MDS). The obtained elastic moduli areclose to those of BN nanotubes, which vary between 0.8 and0.85 TPa depending on the chirality. A Youngs modulus of716.3 GPa was also obtained for h-BN nanosheets in Zhao

0022-3727/14/025303+08$33.00 1 2014 IOP Publishing Ltd Printed in the UK

J. Phys. D: Appl. Phys. 47 (2014) 025303 T Han et al

et als MDS [31]. So far, to the best of our knowledge,the effects of charility, temperature and strain rate on themechanical properties of h-BN nanosheets have not yet beenstudied, which, however, are shown to considerably alterYoungs modulus, fracture strength and strain of their carboncounterparts [3234]. It is thus of great interest to examinefurther these fundamental issues for the h-BN nanosheets.

In the present paper, the tensile properties were measuredfor monolayer h-BN nanosheets based on MDS at differenttemperatures and strain rates. The stressstrain relation wasstudied and the dependences of Youngs modulus, fracturestrength and strain on temperature and strain rate wereobtained for armchair and zigzag h-BN nanosheets. Theresults are expected to provide important guidelines for thepractical applications of h-BN nanosheets in nanodevices andnanoelectronics.

2. MDS on h-BN sheets

Many empirical model potentials have been developed forsemiconductors, among which Tersoff [3537] and TersoffBrenner (Tersoff-like) bond order potentials [38, 39] aremost successful in describing the interaction between boronand nitrogen atoms in boron nitride nanosystems. TheTersoffBrenner potential takes the same form as that ofthe Tersoff potential, except for repulsive and attractive pairpotentials. In the Tersoff potential, the energy E, between twoneighbouring atoms i and j , has the form [35]

E =

i

Ei = 12i =j

Vij

withVij = fC(rij )[fR(rij ) + bijfA(rij )],

wherefR(r) = Ae1r

fA(r) = Be2r

fC(r) =

1, r < R D12 12 sin (rR)2D , R D < r < R + D0, r > R + D.

Here fR(r) and fA(r) are the repulsive and attractive pairpotentials, respectively. The cutoff function fC(r) is defined tolimit the range of the potential and thus save the computationalresources required in the MDS. Normally the cutoff distance Ris chosen to include only the first-neighbour shell. In addition,bij is the bond order function that determines the strength ofthe attractive term. It takes the form below.

bij = (1 + n nij )1

2n

ij =k =i,j

fC(rij )g(ijk)em3 (rijrik)m

g() = 1 + c2

d2 c

2

(d2 + (h cos )2) .

In the literature, several sets of Tersoff and Tersoff-likepotential parameters have been developed for the interaction

Table 1. Tersoff-like interatomic potential parameters forBN [44, 45].

BN-interaction NN-interaction BB-interaction

m 3 3 3 1 1 13 1.9925 0 0c 1092.9287 17.7959 0.526 29d 12.38 5.9484 0.001 587h 0.5413 0 0.5n 0.364 153 367 0.618 4432 3.992 9061 0.000 011 134 0.019 251 0.000 00162 2.784 247 207 2.627 272 104 2.077 498 242B 3613.431 337 2563.560 342 1173.196 962R 2 2 2D 0.1 0.1 0.11 2.998 355 817 2.829 309 329 2.237 257 857A 4460.833 973 2978.952 79 1404.475 204

between boron and nitrogen atoms [4049]. For instance,Sekkal et al [40] and Verma et al [41] slightly changedthe parameters corresponding to carbon systems [36, 37] inorder to fit c-BN and BNNTs, respectively. Here the boronnitride was treated as a one-component system, where theBN interactions were neglected. Matsunaga et al [42, 43]considered c-BN as a real two-component system with BNinteractions. The Tersoff potential parameters of B were thenachieved and used to simulate cubic boron carbonitrides. Albeet al [44, 45] developed the Tersoff-like potential for BN,which is able to describe sp2 structures of BN polymorphs,BN clusters and pure B and N bonding. These potentialparameters have been successfully employed for describing thebonding interactions and investigating the structural, thermaland mechanical properties of BNNTs [5054], h-BN nanosheet[55] and BN nanobamboos [56]. Recently, based on theforce-matching method etc, the adjusted Tersoff-like potentialparameters were obtained for boron nitride [4649] by fittingthe obtained bond length and cohesive energy to experimentaldata. In the present study, the Tersoff-like potential withthe parameters proposed by Albe et al [44, 45] was chosento describe the interactions between B and N atoms. Theseparameters are shown in table 1, which were efficientlyused in studying BN nanostructures of various configurationspreviously. Here different coefficients are identified in table 1due to the distinct definitions of these coefficients given byAlbe et al [44, 45] and Tersoff [35].

To study the mechanical properties of h-BN nanosheetsunder various temperatures and loading conditions, MDSwere implemented by using LAMMPS (large-scale atomic/molecular massively parallel simulator) open-source package[57], developed by Sandia National Laboratories. Theschematics of a rectangular h-BN nanosheet investigated in thisstudy is shown in figure 1. The ochre and blue atoms representboron and nitrogen atoms, respectively. The model consistsof 3720 atoms and its dimensions are around 100 100 .The armchair and zigzag directions are oriented along the Xand Y axis, respectively. The tested h-BN nanosheet was firstoptimized by using the conjugate gradient method to fullyrelax and reach its equilibrium state. Subsequently, a uniaxialtension was applied to stretch the optimized nanosheets along

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J. Phys. D: Appl. Phys. 47 (2014) 025303 T Han et al

Figure 1. The simulation model of the h-BN nanosheets tested inthis study. The model size is 100 100 . Here boron andnitrogen atoms are represented by ochre and blue balls, respectively.

armchair or zigzag directions. A periodic boundary condition(PBC) is applied along the X and Y directions, which showsthat the simulations are representative of BN sheets withinfinite geometric size. The equations of motion were solvedusing the velocity-Verlet algorithm [58] with a time step of1 fs. In individual simulations, the temperature was keptat the specified value by using the NoseHoover method[59, 60]. The temperature effect was examined at the constantengineering strain rate 1 109 s1, while the study of thestrain rate effects was conducted at room temperature. Toobtain the stressstrain curves, the viral stress in the loadingdirection was calculated at each strain level. Youngs moduluswas represented by the slope of the linear part of the curves,and the fracture strength and strain were taken as the maximalstress and strain before the onset of fracture. It should bepointed out that the equivalent Youngs modulus of 2D h-BNnanosheets scale with their effective thickness. In other words,the specific value of Youngs modulus is associated with theeffective thickness selected. In the present study, the effectivethickness of h-BN nanosheets was taken as 0.333 nm, whichwas used previously [41].

3. Results and discussion

Based on the MDS technique and the chosen interatomicpotentials, the tensile tests have been performed for zigzag andarmchair h-BN sheets at different temperatures and strain rates.The fundamental mechanical properties, such as Youngsmodulus, fracture strength and strain, have been quantifiedfor the tested sample sheets and shown graphically againsttemperature or strain rates. In particular, the MDSs used hereare compared with previously used methods to demonstrateits efficiency and accuracy in studying the nanomechanics ofh-BN nanosheets.

3.1. Validation of the present MDS

To validate the present MDS we have calculated Youngsmodulus and the fracture strength of h-BN nanosheets based on

the chosen interatomic potential. The results are summarizedin table 2 in comparison with all available theoretical andexperimental data. As will be shown later, the h-BNnanosheets exhibit different Youngs modulus and fracturestrength in armchair and zigzag directions. In spite of this,some authors reported the values without giving the specificdirection [2529, 46, 62]. Thus, to compare with these data,the Youngs modulus, fracture strength and strain obtained forarmchair and zigzag directions in the present study and [30, 31]were averaged in table 2. First it is noted in the table that theYoungs modulus of 881.1 GPa given by the present MDS atvery low strain rate and room temperature falls right in themiddle of the range of 716 to 950 GPa achieved in an inelasticx-ray scattering measurement [24]. This value is also foundvery close to that of boron nitride nanotubes measured using theelectric-field-induced resonance method inside a transmissionelectron microscope [63]. Secondly, a fracture strength of133.3 GPa is obtained in this work, which is comparable tothe 165 and 120.4 GPa calculated previously based on MDS[30, 31]. Moreover, it is also noted in table 2 that the fracturestrain given by our MDS at room temperature reaches 0.332(averaged 0.260 for armchair and 0.405 for zigzag) very closeto 0.302 [30] (the average of 0.282 and 0.321) and 0.280 [31]calculated in previous MDS. From these comparison results,it is followed that the present MDS is reliable and efficientin calculating the tensile properties of the h-BN nanosheetsup to a large strain of more than 0.3. Here we would like topoint out that, in measuring the fracture strength and strain, adirect comparison cannot be made between the present studyand experiments (or quantum mechanics simulations) due tolack of data in the literature.

3.2. Thermal effect

In this section we studied the thermal effect on the tensileproperties of the h-BN nanosheets by performing tensile testsfor zigzag and armchair h-BN nanosheets. In doing this, thetemperature increased from 0 to 2000 K while the strain ratewas kept constant at 1 109 s1.

3.2.1. Tensile behaviour. In the tensile tests, the stressstraincurves were recorded and shown in figures 2(a) and (b) forarmchair and zigzag h-BN nanosheets, respectively. One ofthe interesting results is the yielding platform or material flowobserved at low temperature, e.g., T 400 K . In this case,figure 2 shows that the stress first increases with rising strain ata relatively low rate; when it reaches a critical value (yield), thestress remains constant while the strain increases substantially.In other words, the material flows without raising the externalloading further. This phenomenon indicates yielding the h-BNnanosheets. Subsequently, when the strain exceeds a certainvalue the regular stressstrain relation resumes, where thestress rises with growing strain at a rate even greater than that ofthe first stage. In figures 2, the yielding strength yield does notsignificantly change with temperature but varies considerablywith the chirality of the BN nanosheets. For example, yield isaround 75.5 GPa for the armchair sheets but increases to around93.5 GPa for zigzag BN sheets. Here the length of the yielding

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J. Phys. D: Appl. Phys. 47 (2014) 025303 T Han et alTable 2. Comparison of the calculated Youngs modulus and strength of h-BN nanosheets with previous experiments and calculations.Effective thickness of 0.333 nm of h-BN nanosheets is adopted when dealing with the published data.

Youngs modulusReference Year Method (GPa) Strength (GPa) StrainPresent study 2013 Molecular dynamics 881.1 133.2 0.332Mortazavi et al [30] 2012 Molecular dynamics 825 165 0.302Zhao et al [31] 2013 Molecular dynamics 716.3 120.4 0.280Bosak et al [24] 2006 Inelastic x-ray scattering 811Green et al [61] 1976 Lennard-Jones and electrostatic potentials 802.5Ohba et al [25] 2001 First-principles calculations 951.5Kudin et al [26] 2001 ab initio 810Topsakal et al [27] 2010 ab initio 809.1Peng et al [28] 2012 ab initio 846.1Mirnezhad et al [29] 2013 ab initio 829Eun-Suok Oh [46] 2011 Continuum lattice approach 977.2Boldrin et al [62] 2011 Molecular mechanics(SH-UFF) 797.0

Figure 2. The stressstrain curves obtained for (a) armchair and(b) zigzag h-BN nanosheets in uniaxial tensile tests. The strain rateis 1 109 s1 and temperature rises from 0 K to 2000 K.

platform can be measured by the associated increment of thestrain during the material yielding. At T = 0, this lengthis found to increase from around 10% of the armchair sheet(figure 2(a)) to around 20% of the zigzag sheet (figure 2(b)).

Figure 3. A hexagonal (h) ring elongated along the armchairdirection. Solid lines represent the original h-ring and dashed linesrepresent the deformed configuration.

On the other hand, when higher temperature is involved,e.g., T > 400 K, the length of the yielding platform turns out tobe very small and the stress keeps increasing with rising strainuntil the onset of fracture. Nevertheless, the conversion of theshape of the stressstrain curves from convex to concave canalways be observed in figure 2, showing a softeninghardeningtransition of the h-BN nanosheets at the vicinity of the point(75 GPa, 0.16). As a matter of the fact, such a transitionzone is also observed for some macroscopic metallic materialsand explained by sliding and strengthening of dislocations.This mechanism however cannot be validated in the presentsimulations as the breakage or formation of chemical bonds(i.e., the nucleation of defects) has not been observed in theh-BN nanosheets before the onset of fracture. As illustratedin figure 3, the present MDS showed that the stretching of thenanosheets is implemented mainly via the elongations of thebond lengths AB and ED, and the rotation of the bond angles and . These bond lengths and angles can be considered asequivalent nonlinear (line or angle) springs, whose behaviouris entirely controlled by the interatomic potentials in h-BNnanosheets. Thus the above-mentioned convexconcaveconversion in figure 2 reflects the softeningstrengtheningprocess of the equivalent springs (e.g., the increase anddecrease of the variable spring constants), which can onlybe understood via calculation based on molecular mechanicaltheory instead of morphological or structural analyses. Indeedthe physical mechanisms of this unique feature deserve to bestudied further in the near future.

3.2.2. Tensile properties. Based on the stressstrain curvesshown in figure 2 we have calculated some key material

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Figure 4. Temperature dependence of Youngs modulus obtainedfor h-BN nanosheets. The strain rate is kept constant at 1 109 s1.

Figure 5. Temperature dependence of the fracture strength obtainedfor h-BN nanosheets. The strain rate is kept constant at 1 109 s1.

properties for the sample sheets at a temperature rising from 0to 2000 K. The temperature dependence of Youngs modulus,fracture strength and strain is plotted in figures 4, 5 and 6,respectively, for armchair and zigzag h-BN nanosheets. Toconfirm the reliability of the present MDS, the compressiontests in the elastic region were also performed on the h-BNnanosheets at 0 K. The obtained Youngs modulus is shown inthe inset of figure 2, which has a magnitude nearly identical tothat obtained in tensile tests at the same temperature.

In figure 4 it is noted that Youngs modulus of the h-BNnanosheets generally decreases with increasing temperature.The average rate of change is about 121 MPa K1almostindependent of the nanosheet chirality. In the meantime,Youngs modulus of zigzag sheets is found to be greater thanthat of armchair sheets. The difference is around 30 GPa atall temperatures considered, showing the strong anisotropyof the h-BN nanosheets. Indeed, the hexagonal structuregenerally leads to anisotropic (overall) material propertieswith the largest discrepancy found between the armchair andzigzag directions. Such a discrepancy is usually neglected for

Figure 6. Temperature dependence of the fracture strain obtainedfor h-BN nanosheets. The strain rate is kept constant at 1 109 s1.

carbon nanotubes and graphene sheets consisting of hexagonalcarbon rings but has to be taken into consideration for h-BNsheets where different atoms (i.e., boron and nitride atoms) arefound.

The decrease of fracture strength with rising temperature isalso observed in figure 5. The reduction of the fracture strengthis around 100 GPa as the temperature rises from 0 to 2000 K.This is true regardless of the chirality of the nanosheets. Inthe meantime, as seen from figure 5, the armchair sheetsgenerally exhibit a fracture strength greater than that of thezigzag sheets. This chirality effect on the fracture strengthis found to be substantial at T < 1500 K, and leads to themaximum difference of 37 GPa in fracture strength betweenthe armchair and zigzag sheets. At higher temperature, i.e.,T > 1500 K, the fracture strengths obtained for the two typesof nanosheets are close to each other. The result shows thatthe fracture strength becomes less sensitive to the chirality athigh temperature.

A similar trend of fracture strain is shown in figure 6but its behaviour is more complicated than those of Youngsmodulus (figure 4) and fracture strength (figure 5). As shownin figure 6, the fracture strain of zigzag sheets is greater thanthat of armchair sheets at low temperature. At the sametime, the greater rate of decrease with temperature is alsoachieved for the fracture strain in the zigzag directions. Thesefinally lead to the distinct behaviour of the fracture strain,i.e., at low temperature T < 750 K, the zigzag sheets exhibithigher fracture strain whereas, at relatively high temperatureT > 750 K, the fracture strain of the armchair sheets becomeseven greater than that of the zigzag sheets. Consideringthe uncertainty in the MDS, we believe that the sensitivityof the ultimate strain to temperature does not significantlychange throughout the range of temperatures considered forboth armchair and zigzag h-BN sheets. But similar toYoungs modulus (figure 4) and ultimate strength (figure 5),the rate of change in the ultimate strain with temperature altersconsiderably with the crystal directions, i.e., the armchair andzigzag directions. This finally leads to the intersection of thetwo curves at around 750 K in figure 6.

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Figure 7. Youngs modulus of h-BN nanosheets as a function ofstrain rate. The results are obtained at room temperature.

Figure 8. Fracture strength of h-BN nanosheets as a function ofstrain rate. The results are obtained at room temperature.

3.3. Strain rate effect

It is well known that in a tensile test the strain rate cansubstantially affect the values of the material propertiesmeasured. It is thus expected that such an effect of strain ratewould also be significant for the h-BN nanosheets. To examinethis issue, the tensile tests were performed for the armchairand zigzag nanosheets at room temperature and strain rateincreasing from 107 to 1011 s1. The strain rate dependenceof Youngs modulus, fracture strength and fracture strain isshown in figures 7, 8 and 9, respectively.

As shown in figure 7, at low strain rate i.e., < 108 s1,Youngs modulus of the h-BN nanosheets is nearly a constant(around 880 GPa) independent of strain rate as well as chirality.It then declines slightly when rises from 108 to 109 s1.At a higher strain rate > 109 s1, Youngs modulus of theh-BN nanosheets is found to decrease rapidly with rising strainrate. In the process when the strain rate rises from 109 to1011 s1, Youngs modulus of the zigzag sheets declines by13.2% while that of the armchair sheets decreases by 16.8%.

Figure 9. Fracture strain of h-BN nanosheets as a function of strainrate. The results are obtained at room temperature.

Specifically, in the range of high strain rate ( > 109 s1),Youngs modulus of the zigzag sheets becomes greater than itsarmchair counterpart.

Subsequently we examined the strain rate effect on thefracture strength in figure 8. It is seen from the figure that,in general, the fracture strength tends to grow with increasingstrain rate . Also consistent with figure 5, figure 8 shows thatthe fracture strength of the armchair sheets is greater than thatof the zigzag sheets. The difference in the fracture strengthhowever decreases monotonically with increasing strain rateand almost vanishes when the strain rate approaches 1011 s1.To give some idea, at = 5 107 s1, the fracture strength ofthe armchair sheets is around 17 GPa greater than the strengthof the zigzag sheets. But the difference reduces to less than7 GPa when rises to 6 109 s1.

Finally, we investigated the effect of strain rate on thefracture strain in figure 9. The results indicate that thefracture strain of the armchair and zigzag nanosheets increasessignificantly with increasing strain rate. The fracture strainof the zigzag sheets is larger than its armchair counterpartand the difference due to the chirality effect remains nearlyunchanged throughout the length of the strain rate considered.To reveal the possible coupling effect of temperature and strainrate on the mechanical properties of h-BN nanosheets, asshown in figure 10, Youngs modulus and fracture strengthwere calculated as functions of strain rate at temperaturesT = 300 K, 900 K and 1500 K, respectively. The resultssuggest that temperature change does not significantly alterthe tendency of the material properties to change with strainrate. In the meantime, the figure also shows that the thermaleffect on the material properties remains qualitatively similarat different strain rates. It is thus concluded that the couplingeffect between temperature and strain rate is trivial for thetensile properties of h-BN nanosheets.

4. Conclusions

The tensile tests have been performed based on MDS forarmchair and zigzag h-BN nanosheets at different temperatures

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Figure 10. (a) Youngs modulus and (b) the fracture strength of theh-BN nanosheets as a function of strain rate at temperaturesT = 300, 900 and 1500 K.

and strain rates. The tensile response has been studied and theeffects of temperature and strain rate have been examined forthe tensile properties of h-BN nanosheets. The new findingsobtained in the present simulations are as follows.

(1) The single-atom layer h-BN nanosheets are basicallyanisotropic materials with Youngs modulus, fracture(yielding) strength and fracture strain varying substan-tially with crystal orientations. In the armchair direction,the h-BN nanosheets exhibit lower Youngs modulus buthigher fracture strength than those in the zigzag direction.Lower fracture strain is achieved in the armchair directionat low temperature but it turns out to be even greater thanthat along the zigzag direction at high temperature.

(2) Raising temperature generally exerts a softening effecton the h-BN nanosheets. As the temperature rises from0 to 2000 K, Youngs modulus, fracture strength andfracture strain decrease by around 26.5%, 62.1% and68.2%, respectively. The chirality effect on the rate of

decrease is negligible for Youngs modulus, small for thefracture strength but more pronounced for the fracturestrain. In addition, a yielding platform is observed forh-BN nanosheets at low temperature (e.g., T < 400 K)but vanishes at relatively high temperature (T 400 K).

(3) The higher strain rate generally leads to lower Youngsmodulus but higher fracture strength and strain of the h-BNnanosheets. This effect on Youngs modulus is negligibleat small strain rate (e.g., 108 s1) but becomes substantialat relatively high strain rate. The effect on the fracturestrength and strain is always significant throughout thelength of the strain rate considered. In addition, the strainrate effect varies significantly with crystal orientations forYoungs modulus and fracture strength but remains nearlyunchanged for the fracture strain.

Acknowledgments

This work is financially supported by the Natural ScienceFoundation of the Jiangsu Higher Education Institutions ofChina (12KJB130001), Natural Science Foundation of JiangsuProvince (BK2011490) and NSFC (21204031).

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8

1. Introduction2. MDS on h-BN sheets3. Results and discussion3.1. Validation of the present MDS3.2. Thermal effect3.3. Strain rate effect

4. ConclusionsAcknowledgmentsReferences