Materials 2015, 8, 5250-5264; doi:10.3390/ma8085250

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materials ISSN 1996-1944 www.mdpi.com/journal/materials Article

Dislocation-Governed Plastic Deformation and Fracture Toughness of Nanotwinned Magnesium Lei Zhou and Ya-Fang Guo * Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, China; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel./Fax: +86-10-5168-2094. Academic Editor: Daolun Chen Received: 15 May 2015 / Accepted: 4 August 2015 / Published: 13 August 2015

Abstract: In this work, the plastic deformation mechanisms responsible for mechanical ( properties and fracture toughness in 1012 ă 1011 ąnanotwinned (NT). magnesium is studied by molecular dynamics (MD) simulation. The influence of twin boundary (TBs) spacing and crack position on deformation behaviors are investigated. The microstructure evolution at the crack tip are not exactly the same for the left edge crack (LEC) and the right edge crack (REC) models according to calculations of the energy release rate for dislocation nucleation at the crack tip. The LEC growth initiates in a ductile pattern and then turns into a brittle cleavage. In the REC model, the atomic decohesion occurs at the crack tip to create a new free surface which directly induces a brittle cleavage. A ductile to brittle transition is observed which mainly depends on the competition between dislocation motion and crack growth. This competition mechanism is found to be correlated with the TB spacing. The critical values are 10 nm and 13.5 nm for this transition in LEC and REC models, respectively. Essentially, the dislocation densities affected by the TB spacing play a crucial role in the ductile to brittle transition. Keywords: nanotwinned magnesium; molecular dynamics; twin boundaries; plastic deformation; fracture toughness

1. Introduction Strength and ductility are two important mechanical properties pursued by industry applications. Currently, nanocrystalline (NC) metals and alloys are widely studied for their superb mechanical

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properties with grain refinement into the nano-scale, which is mostly less than 100 nm. Because of the introduction of interface defects such as grain boundaries (GBs), coherent twin boundaries (CTBs) and incoherent twin boundaries (ICTBs) into macrostructure, strength is significantly enhanced since these defects serve as dislocation sources which provide sufficient dislocation nucleation sites along the interfaces [? ? ? ? ]. However, dislocation mobility is also impeded by GBs. As a result, the localized stress can concentrate on the GBs and then make it favor the crack propagation [? ]. In contrast to the GBs, CTB has a lower interface energy and is more vulnerable for the nucleation and motion of dislocations. For the purpose of improving the combination of strength and ductility, nanotwinned (NT) materials consisting of a lamella structure, namely grains with twin boundaries (TBs) parallel to each other underlying the microstructure, are synthesized. To date, NT Cu has been widely synthesized [? ? ]. However, magnesium, a newly used metal for its unique properties such as low density and relatively high strength, is rarely mentioned for use in NT materials. Existing experiments showed that NT structure in magnesium alloys could be obtained by applying a tensile loading or using surface mechanical attrition treatment (SMAT) [? ? ]. Recently, Pozuelo et al. [? ] proposed a comprehensive approach to form NT structure in NC Mg-based alloys. In NT Cu, it has been reported that there are different TB densities, as TB spacing results in a transition in the yielding mechanism from the interaction between TBs and dislocations to multiple dislocation activities [? ]. With the refinement of grains, the interaction between TBs and dislocations gradually dominates the strain hardening. Thus, the capacity of dislocation storage is highly enhanced by the strength of NT Cu reaching its maximum at a critical value of TB spacing, about 15 nm. In NT magnesium, mechanical properties of magnesium alloy can be improved via pre-twinning [? ]. Recently, using the molecular dynamics (MD) method, Song et al. [? ] investigated the temperature and TB spacing effects on strength of NT magnesium. It has been reported that the basal dislocation emissions dominate the plastic deformation. Moreover, dislocation storage ability was also pronounced a key role to the yield strength shift through changing TB spacing as well as the repulsive force between TBs and dislocations. In addition to promoting yielding strength, more and more attention is currently focused on the fracture toughness of NT materials. It is well known that avoiding the crack initiation or providing high resistance to the crack propagation will improve the fracture toughness. Experiment results [? ] showed that parallel TBs protect dimples from coalescing which serve as crack initiation sites in bulk nanostructure Cu. Also, because of the dislocation emission from interface defects, crack is likely to be blunted or deflected if they propagate towards TBs. Therefore, the NT structure improves the local plasticity in bulk Cu. However, the existent research on fracture toughness of NT materials mainly focused on FCC Cu. Because of the limited numbers of slip systems in hexagonal close-packed (HCP) materials, the deformation mechanism in NT Mg seems not similar to those in FCC metals. According to previous experiments [? ? ], dislocation slip played a significant role in plastic deformation of pre-twinning magnesium alloy. moreover, basal dislocation motions can also occur at the crack tip, thereby affecting the crack growth [? ] and they also potentially being arrested by the TBs [? ]. it is thus necessary to reveal the effects of dislocation motions on the crack propagation in nanotwinned magnesium.

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In the the present present work, work, we we create create models models with with the the pre-existing pre-existing crack crack to to investigate investigate mechanical mechanical properties properties In and plastic plastic deformation deformation mechanisms mechanisms of of NT NT magnesium. magnesium. Crack Crack positions positions and and TB TB spacing spacing variations variations are are and addressed. We We aim aim to to get get aa better better insight insight of of the the fracture fracture toughness toughness by by studying studying the the factors factors affecting affecting the the addressed. crack propagation. propagation. crack 2. Simulation Simulation Models Models and and Method Method 2. As shown shownin inFigure Figure??, 1, two perform MD MD simulations simulations at at the the nano-scale. nano-scale. As two types types of of models models are are adopted adopted to to perform In type type A, A, five five TBs TBs are are contained type B, In contained in in the the model, model,while whileTB TBspacing spacing(λ) (λ)varies variesininthe thesimulation. simulation.In In type TBTB spacing (λ)(λ) keeps are contained. contained. B, spacing keepsa aconstant constant(7.5 (7.5nm), nm),while whiledifferent different numbers numbers of of grains grains (1–4) (1–4) are Moreover,the thesizes sizesof of the the top top and and bottom bottom grains grains on on the the models models are are larger larger than than that that of of the the interior interior grainin grainin Moreover, ( TB in simulations, which is thewhich most order to useuse the the {10121012 }  101ă1  1011 ą our > TB in our simulations, order to reduce reduce the thesurface surfaceeffect. effect.WeWe common TBcommon in magnesium [19,20]. An [19,20]. elementary of NT magnesium set up by is rotating is the most TB in magnesium An unit elementary unit of NT is magnesium set up two by ( single magnesium crystal grains according the {1012to} the  101012 11  twinning relationship. ă 1011 ąorientational > twinning orientational rotating two single magnesium crystal grainsto according Then, we duplicated elementary unit severalunit times to get an to NTgetmodel several relationship. Then, wethe duplicated the elementary several times an NTwhich modelcontained which contained ( within it. The x-, it.y- The andx-,z- y-direction lies along 1011] r1011s , [1012]>,and [121and 0] , {1012}  1012 1011  ăTBs 1011 ą > TBs within and z- direction lies [along r1012s several , respectively, as in shown in 1. Figure Free boundary conditions areto applied x- and y-direction; r1210s respectively, as shown Figure Free ??. boundary conditions are applied x- andtoy-direction; periodic periodic is assigned to the z-direction for simulating mode I crack. boundaryboundary conditioncondition is assigned to the z-direction for simulating the modethe I crack.

Figure 1. A schematic diagram of two types of MD models: (a) type A; (b) type B. Figure 1. A schematic diagram of two types of MD models: (a) type A; (b) type B. Table presents parameters parameters of of type type A A models. According to to the the experimental experimental results Table ?? 1 presents models. According results reported reported by by Yu et al. [? ], we introduce six different dimensions of the interior grains in y-direction ranging from Yu et al. [9], we introduce six different dimensions of the interior grains in y-direction ranging from 5 5toto15.5 15.5nm nmtotoinvestigate investigatethe the TB TB spacing spacing effect effect on on the the plastic plastic deformation deformation mechanisms mechanisms in in type type A. A. Considering Considering the the effect effect of of crack crack position position in in samples, samples, two two types types of of crack crack were were employed employed in in type type A—the A—the left left edge edge crack crack (LEC) (LEC) and and right right edge edge crack crack (REC)—by (REC)—by removing removing several severalatom atomlayers layersalong alongthe theTBs. TBs. The The intergranular crack length is all about 4 nm. In type B models, the number of interior grains is changed intergranular crack length is all about 4 nm. In type B models, the number of interior grains is changed from from 11 to to 4, 4, while while TB TB spacing spacing isis aa constant constant 7.5 7.5 nm. nm. Only Only LEC LEC isis studied studied in in type type B. B.

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D (nm)

W (nm)

t (nm)

Number of Atoms

5

16

40

2.4

159,368

7.5

16

40

2.4

191,368

10

16

40

2.4

235,520

12

16

40

2.4

268,088

13.5

16

40

2.4

299,720

15.5

16

40

2.4

320,256

These two models were simulated in constant NPT ensemble with a velocity-Verlet integrator. The temperature was kept at 5 k and the pressure in z-direction was controlled at 0 bar by the Nosé–Hoover thermostat. We employed the embedded atom method (EAM) developed for magnesium by Liu et al. [? ] to describe the atomic interactions. This potential has been proved useful in investigating the dislocation nucleation and twinning behavior by many studies [? ? ? ]. The molecular dynamics program LAMMPS [? ] was employed in simulations. The common neighbor analysis (CNA) method [? ] and Atomeye software [? ] were used for visualizing the evolution of the atomistic structures. After introducing an intergranular crack in the model, we first relaxed the initial simulation system (both type A and type B) 10,000 steps to achieve the equilibrium state. Then, uniaxial tensile loadings were applied by imposing tensile displacements to atoms in the fixed layers at the top and the bottom of models along the y-direction. The systems were relaxed for 5000 steps after every 0.3% stretch strain applied. A constant strain rate 1 ˆ 108 s´1 was applied to simulations with each time step in 6 femtosecond. We recorded the atomic configuration, and stress conditions were recorded at each tensile loading for further analysis. 3. Results and Analysis In this section, we present atomistic configurations, stress fields and stress-strain curves of LEC and REC models for clarifying the microstructure evolution and the effect of the TB spacing and crack position on crack propagation. The relationship between dislocation density and fracture toughness is also investigated. 3.1. Left Edge Crack (LEC) Model vs. Right Edge Crack (REC) Model Figure ?? shows the atomistic configurations of LEC and REC models with TB spacing of 15.5 nm under various tensile strains. In the LEC model (Figure ??a), the first (0001) r1010s partial dislocation is observed to emit at the junction of crack tip and TB interface under 3.5% tensile strain. Subsequently, partial dislocation emissions are observed from the neighboring TB interfaces. With the strain increasing, dislocation emissions both at the crack tip and the TBs are observed accompanying the LEC propagations. Voids induced by the dislocation motions are captured ahead of the crack tip under 4.2% tensile strain. In the REC model (Figure ??b), it is found that the crack tip is sharper than that in the LEC model after crack propagation. Moreover, we can only observe dislocation emission at the TB interface, but no dislocation emission at the crack tip. With the strain increasing, most of the dislocations ahead

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of the crack are originated from the neighboring TBs during the propagation process. Besides, a few the crack are originated from the neighboring TBs during the propagation process. Besides, a few dislocations generated at the crack coherencyloss lossofof TBs. dislocations generated at the cracktip tipinduce induce slight slight coherency TBs.

Figure 2. The atomistic configurations of (a) LEC model and (b) REC model at 5 K with Figure 2. The the TB spacing ofatomistic 15.5 nm.configurations of (a) LEC model and (b) REC model at 5 K with the TB spacing of 15.5 nm.

In order to to investigate differentcrack crack propagation and dislocation mechanisms In order investigate the the different propagation and dislocation emissionemission mechanisms for LEC for LECand andREC RECmodels, models,thetheenergy energy release dislocation nucleation the crack is calculated. release raterate forfor dislocation nucleation at theat crack tip istip calculated. Considering basal dislocationisisthe theonly only dislocation dislocation activated thethe beginning of the Considering thatthat basal dislocation activatedat at beginning of deformation, the deformation, we calculate the energy release rate for the basal dislocation nucleation based on the Rice model [28]. [? ]. we calculate the energy release rate for the basal dislocation nucleation based on the Rice model The formula is given as follow: The formula is given as follow: Gdisl  8 usf [1  (1  ) tan 2 ] / [(1  cos )sin 2 ] 2

2

Gdisl “ 8γusf r1 ` p1 ´ νq tan ϕs{rp1 ` cos θq sin θs

(1)

(1)

where γusf is the unstable stacking fault energy; ν is Poisson’s ratio of magnesium; φ is the angle between Burgers and a line in the fault slip plane perpendicular to the crack θ is the ϕ angle between where γusf is vector the unstable stacking energy; ν is Poisson’s ratio of front; magnesium; is the angle the between slip plane and the crack surface. It is worth noting the aforementioned formula is based on the perfect Burgers vector and a line in the slip plane perpendicular to the crack front; θ is the angle between the sharp crack model. Though the LEC and REC employed in our simulations are not atomically sharp at slip plane and the crack surface. It is worth noting the aforementioned formula is based on the perfect the beginning of the simulation, they both possess a sharp crack tip after propagation. Thus it is suitable sharptocrack model. Though the LEC and REC in our sharp at roughly compare dislocation motions at the employed LEC tip with thosesimulations at the RECare tip not usingatomically this formula. the beginning ofthe theenergy simulation, both possess a sharp tip after propagation. Thus it is suitable Table 2 lists cost forthey dislocation generation alongcrack the basal plane.

to roughly compare dislocation motions at the LEC tip with those at the REC tip using this formula. Table ?? lists the energy cost for dislocation generation along the basal plane.

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Table 2. Energy cost for dislocation generation along the basal plane. The value of parameters γusf is taken from the work of Muzyk et al. [? ]. The Poisson’s ratio is captured from typical experimental values, and the rest of the parameters are calculated based on the Materials 2015, 8 5254 same interatomic potential used in present work. 2) Table 2. Energy costνfor dislocation basal2 plane. of Crack φ generation θ alongγ the GdislThe (J/mvalue usf (J/m ) parameters γusf is taken from the work of Muzyk et al. [29]. The Poisson’s ratio is captured LECexperimental 0.31 values, and 0 the rest of43 0.092 0.914 from typical the parameters are calculated based on the REC 0.31 0 137 0.092 5.888 same interatomic potential used in present work.

Crack Comparing the LEC energy obvious that theREC partial

ν ɸ θ γusf (J/m2) Gdisl (J/m2) release dislocation 0.092 nucleation in the LEC and REC models, it 0.31 rate 0for basal 43 0.914 0.31 0are favorable 137 to emit0.092 dislocations from the crack 5.888 tip in the LEC model. This

is result is consistent with the phenomena observed in our simulation that LEC propagates accompanying Comparing the energy release rate for basal dislocation nucleation in the LEC and REC models, it is the dislocation the crack tip ??a). LECfrom propagation caninbethedescribed in four obvious thatemission the partialatdislocations are(Figure favorable to emit the crack tip LEC model. Thissteps: (i) the basal dislocation at the crack tip; in(ii) are generated ahead of accompanying the crack tip due result is consistent withemits the phenomena observed ourvoids simulation that LEC propagates to the (iii) the crack whichcan results in the crack thedislocation dislocation motion; emission at thevoids crack coalescet tip (Figurewith 2a). LEC propagation be described in fourpropagation steps: (i) the (iv) basalatomic dislocation emits at the crackwhich tip; (ii)sharpens voids arethe generated aheadThis of the crack tip due to the initiation; decohesion occurs crack tip. process indicates that the dislocation motion; (iii) voids coalescet with the crack which results in the crack propagation initiation; crack propagation in the LEC model experiences a ductile to brittle transition from dislocation emission atomic decohesion occurs which sharpens the crack tip. This process indicates that the crack at the(iv) crack tip to crack surface cleavage due to atomic decohesion. propagation in the LEC model experiences a ductile to brittle transition from dislocation emission at the The situation in the REC model is not exactly same. During the crack growth process, dislocation crack tip to crack surface cleavage due to atomic decohesion. emissions from the crack tip are seldom observed (Figure ??b). The crack propagation can be only The situation in the REC model is not exactly same. During the crack growth process, dislocation attributed to the atomic decohesion. The crack tip is(Figure directly the beginning of only the crack emissions from the crack tip are seldom observed 2b).sharpened The crackatpropagation can be growth. Further evidence accessed The by plotting stress distribution theofcrack tip in the attributed to the atomic is decohesion. crack tiptensile is directly sharpened at the around beginning the crack LECgrowth. and REC models respectively at thebyonset of the crack growth in Figure ??. The concentration Further evidence is accessed plotting tensile stress distribution around the stress crack tip in the LEC and REC models respectively at the onset Figure 3. The stress concentration is located at about 3 nm away from the crack tipofinthe thecrack LECgrowth modelin(Figure ??a). Moreover, the direction is located at about 3 is nmalong awaythe from the crack tip in the LEC (Figure the direction of stress concentration basal slip plane. It can bemodel expected that3a). theMoreover, basal dislocation emission of stress concentration is along the basal slip plane. It can be expected that the basal dislocation emission is preferred over the crack cleavage in the LEC model. In the REC model, the stress concentration is is preferred over the crack cleavage in the LEC model. In the REC model, the stress concentration is very close to the crack tip along the incoherent TB (Figure ??b). Thus the high tensile stress can directly very close to the crack tip along the incoherent TB (Figure 3b). Thus the high tensile stress can directly induce a new free surface nucleation at the crack tip along the TB interface, which induces the brittle induce a new free surface nucleation at the crack tip along the TB interface, which induces the brittle crackcrack propagation (Figure Therefore,thethe mechanisms of crack growth LEC and RECare models propagation (Figure??b). 2b). Therefore, mechanisms of crack growth in LECinand REC models are not the same samedue duetotothethe different microstructure evolutions the tip. crack tip. notexactly exactly the different microstructure evolutions at the at crack

Figure 3. Tensile stress δyyδyydistribution cracktips tipsinin LEC model under 4% strain Figure 3. Tensile stress distribution around around crack (a)(a) LEC model under 4% strain and and (b) (b) REC model under onsetofof crack propagation. REC model under6.2% 6.2%strain strain respectively respectively atatonset crack propagation.

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3.2. Effect Effect of of TB TB Spacing Spacing on on Crack Crack Propagation 3.2. Propagation 3.2.1. Stress-Strain Stress-Strain Curves Curves 3.2.1. Figure ??a showsthe thetypical typicalstress-strain stress-straincurves curves of of LEC LEC models models with with different different TB TB spacings spacings ranging Figure 4a shows ranging from 5 to 15.5 nm. The The variation variation of of the the stress-strain stress-strain relationship induced by different TB spacings is remarkable. When the TB spacing is below 10 nm, the flow stress is clearly higher than that of samples TBspacing spacingabove above1010nm. nm. Moreover, when the spacing TB spacing beyond 10significant nm, significant with aa TB Moreover, when the TB rises rises beyond 10 nm, stress stress droppings are observed LEC models. theofcurve of thelength crack vs. length vs.forstrain for droppings are observed in LECinmodels. We plotWe theplot curve the crack strain five TB five TB spacing Figure ??b. Crack propagation is effectively nm nm and spacing 7.5 nm spacing samples samples in Figurein4b. Crack propagation is effectively impeded impeded in 5 nm in and5 7.5 spacing samples. Remarkable crack propagation be observed the spacing is over when samples. Remarkable crack propagation can becan observed until until the spacing is over 10 10 nm,nm, when it it corresponds a stress dropping onstress-strain the stress-strain curves. The similar situation in REC corresponds to atostress dropping on the curves. The similar situation happenshappens in REC models. models. sharp stress droppings can be onlyinobserved 15.5 nm spacing models The sharpThe stress droppings can be only observed 13.5 nm in and13.5 15.5nm nmand spacing models (Figure 4c). (Figurepropagations ??c). Crackalso propagations alsoonset happen at thedropping onset ofinstress in (Figure these two Crack happen at the of stress these dropping two models 4d).models When (Figure ??d). When the TB is in smaller than 13.5 in REC flow stress presents the TB spacing is smaller thanspacing 13.5 nm REC models, thenm flow stress models, presentsthe a relatively stable state a relatively stable state and no obvious crack growthallis the observed. the models, samplesbrittle in LEC and no obvious crack growth is observed. Reviewing samplesReviewing in LEC andall REC to and REC models,isbrittle to ductile transition observed decreasing the TB We propose ductile transition observed by decreasing theisTB spacing.byWe propose there is aspacing. critical value for this transition, which is 10 nm LEC models which and 13.5 nmnm in REC models, respectively. When TB models, spacing there is a critical value for in this transition, is 10 in LEC models and 13.5 nm in REC is below the critical value, samples represent ductile value, properties where the crack growth is impeded by respectively. When TB spacing is below the critical samples represent ductile properties where dislocation emissions. the crack growth is impeded by dislocation emissions.

Figure 4. The stress-strain curves with different TB spacings and the variation of crack Figure 4. The stress-strain curves with different TB spacings and the variation of crack length with increasing strain. (a,b): LEC models; (c,d): REC models. length with increasing strain. (a,b): LEC models; (c,d): REC models.

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3.2.2. Atomistic Atomistic Configurations ??a–cshows showsatomistic atomisticconfiguration configurationof ofcrack cracktips tips under under 6% 6% strains strains with with different different TB spacing Figure 5a–c (5 nm, nm, 10 10nm nmand and15.5 15.5 nm) in LEC models. all three samples, stacking faults[1along r1010s (5 nm) in LEC models. In allInthree samples, stacking faults along 010] and [101and 0] r1010s directions are observed, accompanying dislocation emission from the TBs and crack tip. Due directions are observed, accompanying dislocation emission from the TBs and crack tip. Due to the to the coalescence of plane basal stacking plane stacking transformations from original HCP structure to coalescence of basal faults,faults, phase phase transformations from original HCP structure to FCC FCC structure are found. Stacking phase transformation themain main plastic plastic deformation structure are found. Stacking faultsfaults and and phase transformation arearethe mechanisms in all six LEC samples.

Figure 5. The atomistic configurations of LEC model under 6% tensile strain at 5 K with Figure 5. The atomistic configurations of LEC model under 6% tensile strain at 5 K with TB spacing (a) 5 nm; (b) 10 nm and (c) 15.5 nm. TB spacing (a) 5 nm; (b) 10 nm and (c) 15.5 nm. Moreover, the Moreover, the region region of of stacking stackingfaults faultsand andphase phasetransformation transformationininFigure Figure??a,b 5a,b is is significantly significantly larger larger than that in Figure ??c. When the TB spacing is below 10 nm (including 10 nm sample), more stacking than that in Figure 5c. When the TB spacing is below 10 nm (including 10 nm sample), more stacking faults faults and transformations phase transformations are formed due todislocation drastic dislocation motionsthearound the Instead crack tip. and phase are formed due to drastic motions around crack tip. of Instead of generating voids ahead of dislocations the crack, dislocations up at tip theand crack tip and emissions from generating voids ahead of the crack, piling up atpiling the crack emissions from the crack the crack ledge significantly blunttip, the which crack tip, which results in theofenlarging the crack rather ledge significantly blunt the crack results in the enlarging the crackofwidth ratherwidth than length than length ??). As a result, crack propagations are This impeded. This phenomenon is consistent (Figure 6). (Figure As a result, crack propagations are impeded. phenomenon is consistent with the with the description of the stress-strain in Figure ??a no considerable stress description of the stress-strain curves in curves Figure 4a whereby nowhereby considerable stress dropping in 5dropping nm and in 5 nm nm samples and 7.5 nm samples isMeanwhile, observed. Meanwhile, TB migrations with the interaction 7.5 is observed. TB migrations associated associated with the interaction between between dislocations TBs are more Thus intense. Thusfaults, stacking faults, phase transformation and TB dislocations and TBs and are more intense. stacking phase transformation and TB migration migration the dominate plastic deformation TB spacing is below nm. According to Zhu et al. [? dominate plasticthe deformation when TBwhen spacing is below 10 nm.10According to Zhu et al. [30], ], the coherency lossofofthe theTBs TBsalso alsoattributes attributestotoenhanced enhancedductility, ductility,itit isis assumed assumed that that NT magnesium the coherency loss samples present ductile properties with a TB spacing below 10 nm. When the the TB TBspacing spacingis is over cleavage is observed (Figure ??c). This means When over 10 10 nm,nm, crackcrack cleavage is observed (Figure 5c). This means there is a competition between crack propagation and plastic deformation the crack tipatwith variation of the there is a competition between crack propagation and plastic at deformation the the crack tip with the TB spacing. When TB spacing nm, crack variation of the TB the spacing. When is theover TB 10 spacing is overcleavage 10 nm, takes crack priority cleavageover takesstacking priorityfaults over emission phase transformation. a result, fractureAstoughness weakened by the crack propagations. stacking and faults emission and phaseAs transformation. a result, isfracture toughness is weakened by the In Figure 5, TB motion and migration are also clearly observed due to the formation of stacking faults crack propagations. andInphase transformation. In and Figure 7a, the are detail of clearly a basalobserved partial dislocation byofa stacking Figure ??, TB motion migration also due to thefollowed formation stacking fault from TB is presented. the dislocation stacking fault are arrested faultsemitting and phase transformation. In Moreover, Figure ??a,thethepartial detaildislocation of a basal and partial followed by a by the TB,fault leaving a stepfrom and twinning dislocations (TDs) atthe thepartial TB interface, which is the alsostacking in agreement stacking emitting TB is presented. Moreover, dislocation and fault

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Materials 2015, 8 5257 are arrested by the TB, leaving a step and twinning dislocations (TDs) at the TB interface, which is also in agreement with the by Serra et al. 7b,c, [? ].the In detail Figureof??b,c, the detail of TB migration with the description by description Serra et al. [31]. In Figure TB migration is presented, which is presented, due tothe TDs along the TB interface. due to TDswhich glidingis along TBgliding interface.

Figure 6. 6. Details Details of of the the atomistic atomistic configuration configuration around around the the crack crack tip tip under under 8% Figure 8% tensile tensile strain strain with 5 nm TB spacing in the LEC model, showing that the crack tip is significantly blunted with 5 nm TB spacing in the LEC model, showing that the crack tip is significantly blunted because of of the the dislocation dislocation emission because emission and and motion. motion.

Figure 7. (a) A basal partial dislocation emits from TB followed by stacking faults, and Figure 7. (a) A basal partial dislocation emits from TB followed by stacking faults, and the the basal dislocation and stacking fault are arrested by TB; (b) TDs gliding along the TB basal dislocation and stacking fault are arrested by TB; (b) TDs gliding along the TB interface; and (c) TB migration. interface; and (c) TB migration. To reveal and plastic deformation at crack tip, tip, we reveal the therelationship relationshipbetween betweenlocal localstress stressconcentration concentration and plastic deformation at crack plotplot the the distribution of von Mises stress δmises andand tensile stress δyyδyy ininFigure we distribution of von Mises stress δmises tensile stress Figure??a–d 8a–d for for 55 nm nm and 15.5 nm samples under 6.2% strain in LEC model, respectively. The von Mises stress is for isotropic materials, roughestimate estimateforfor location of plastic deformation our present is still reasonable. but aa rough thethe location of plastic deformation in ourinpresent work iswork still reasonable. The von Mises stress δmises has three peak value points along the TB interfaces in the 5 nm sample (Figure 8a).

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Materials 2015, 8 5258 The von Mises stress δmises has three peak value points along the TB interfaces in the 5 nm sample (Figure ??a). One of the stresssites concentration sitesnmis ahead located ahead of thethecrack the One of the stress concentration is located 1.5 of 1.5 the nm crack tip along TBs tip andalong the other TBs andonthe two lie on neighboring to the pilinginup of dislocations in TBs. two lie theother neighboring TBthe interface, due toTB theinterface, piling up due of dislocations TBs. Figure 8b shows the Figure ??b shows the tensile stress δ distribution around the crack tip in the 5 nm spacing sample. yy crack tip in the 5 nm spacing sample. The peak value is about tensile stress δyy distribution around the The peak is about Gpa the andcrack 4.5 nm from the However, the stressregion concentration 9 Gpa andvalue 4.5 nm away9from tip.away However, thecrack stresstip. concentration in this is not as in this region is not as intense since themotions sufficient canThus effectively release is it. hardly Thus intense since the sufficient dislocation candislocation effectivelymotions release it. a new surface acreated new surface hardly created by the weak stress of crack the crack tip. Instead, crack by theisweak stress concentration ahead of concentration the crack tip. ahead Instead, blunting occurs by the blunting occurs by the dislocation emission. In contrast to the 5 nm spacing sample, the situation in the dislocation emission. In contrast to the 5 nm spacing sample, the situation in the 15.5 nm spacing sample 15.5 nm spacing sample is different. peaklocated value of is mainly located the TB junction of 8c). the is different. The peak value of δmises isThe mainly at δthe junction of the crackatand (Figure mises crack and TB (Figure ??c). Less spacing dislocation motions in in large resultstress in theconcentration difficulty of Less dislocation motions in large samples result the spacing difficultysamples of releasing releasing tip. Figuretensile ??d shows tensile δyy around thestress crackconcentration tip. Figure 8daround showsthe thecrack corresponding stressthe δyy corresponding distribution which hasstress the peak distribution hasGpa the and peak3 value as high 10.8 Gpatip. andThe 3 nm away from the crack tip.ofThe value as highwhich as 10.8 nm away fromasthe crack stress concentration ahead the stress crack concentration ahead of thewhich crack tip is muchchances more intense, which provides for voids generating at tip is much more intense, provides for voids generating atchances this location. Therefore, crack this location.occurs Therefore, crack propagation occurs by the the crack. coalescence of voids withasthe crack. TBs favor propagation by the coalescence of voids with TBs favor serving a cleavage plane in serving a cleavage in the largeisTB spacing samples, which is consistent with other studies [? ? the largeasTB spacing plane samples, which consistent with other studies [32,33]. Thus, the large spacing ]. Thus,exhibits the largebrittle spacing sample exhibits brittlepropagation. properties for the crack propagation. sample properties for the crack

Figure Stress fields fields of Figure 8. 8. Stress of 55 nm nm and and 15.5 15.5 nm nm samples samples around around crack crack tips tips under under 6% 6% strain strain in in LEC model respectively. (a) Von Mises stress δ distribution; and (b) tensile stress δ mises LEC model respectively. (a) Von Mises stress δmises distribution; and (b) tensile stress δyyyy distribution distribution; and (d) tensile stress δyy distribution in in 55 nm nm sample; sample; (c) (c) Von VonMises Misesstress stressδδmises mises distribution; and (d) tensile stress δyy distribution distribution in in 15.5 15.5 nm nm sample. sample.

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Figure 9a–c ??a–c shows atomistic configurations of crack tip under strains with different TB Figure shows atomistic configurations of crack tip under variousvarious strains with different TB spacings spacings 12 nm 15.5 models. nm) in When REC models. Whenisthe TB13.5 spacing is below 13.5crack nm (5 nm, 12 (5 nmnm, and 15.5 nm)and in REC the TB spacing below nm (Figure 9a,b), (Figureis??a,b), crack is transformation impeded due toatphase transformation the crack tip which is induced growth impeded duegrowth to phase the crack tip which is at induced by dislocation emissions by dislocation emissions the neighboring TBs. ahead Moreover, TBwhich interface ahead serves of the as crack from the neighboring TBs.from Moreover, the TB interface of thethe crack originally the which originally serves as the crack plane is almost annihilated due to the dislocation motions and phase crack plane is almost annihilated due to the dislocation motions and phase transformations, and the crack transformations, andthe theTB crack tip is isblunted. When TB spacing is dislocations above 13.5 nm ??c), tip is blunted. When spacing above 13.5 nmthe (Figure 9c), less are (Figure observed, andless no dislocations are observed, and no remarkable phase transformation ahead of the crack tip are found. Thus remarkable phase transformation ahead of the crack tip are found. Thus brittle cleavage is captured which brittle deteriorates cleavage is captured which badly deteriorates the fracture toughness However, badly the fracture toughness of these samples. However, with of thethese strainsamples. increasing, weak with the strain increasing, weak phase transformation can still be observed accompanying crack growth, phase transformation can still be observed accompanying crack growth, which prevents the excessively whichpropagation prevents theofexcessively propagation of models, the crack. LEC for models, thetocritical quick the crack. quick Compared with LEC theCompared critical TBwith spacing ductile brittle TB spacing for ductile to brittle transition is larger in REC models. transition is larger in REC models.

Figure 9. The atomistic configurations of REC models under 6.5% tensile strain at 5 K, the Figure 9. The atomistic configurations of REC models under 6.5% tensile strain at 5 K, TB spacing (a) 5 nm; (b) 12 nm; (c) 15.5 nm. the TB spacing (a) 5 nm; (b) 12 nm; (c) 15.5 nm. 3.3. Dislocation Dislocation Density Density vs. vs. Fracture Fracture Toughness Toughness 3.3. In LEC and REC models, the dislocation motion originating from TBs plays a crucial role in crack In LEC and REC models, the dislocation motion originating from TBs plays a crucial role in crack propagation behaviors. As a matter of fact, different TB spacings stands for different dislocation densities propagation behaviors. As a matter of fact, different TB spacings stands for different dislocation since TBssince serveTBs as the main generationgeneration source. Bysource. calculating the numberthe of the dislocation densities serve asdislocation the main dislocation By calculating number of the cores per square meter, we plot the trend of dislocation density with strain increasing by choosing three dislocation cores per square meter, we plot the trend of dislocation density with strain increasing by typical TB spacings (5 nm, 10 nm and 13.5 nm) in the LEC model. In Figure ??a, the dislocation density choosing three typical TB spacings (5 nm, 10 nm and 13.5 nm) in the LEC model. In Figure 10a, the in the 5 nmdensity sampleinranges 0.8 ˆ ranges 1017 tofrom 1.1 ˆ0.810×1710 m17´2to . It1.1is ×much those in 10than nm dislocation the 5 from nm sample 1017 higher m−2. It than is much higher 17 ´2 17 ´2 and 13.5 nmnm samples which approximately ˆ 10 m 0.40 and× 0.25 , respectively. those in 10 and 13.5 nm are samples which are 0.40 approximately 1017 ˆ m−210andm0.25 × 1017 m−2, Dislocation density vs. strain diagram illustrates a smaller spacing higher respectively. Dislocation densityscatter vs. strain scatter diagram that illustrates that aTB smaller TBinduces spacingainduces density. Comparing with the trend of crack lengthofvs.crack strainlength in Figure weinconclude adislocation higher dislocation density. Comparing with the trend vs. ??b, strain Figure that 5b, a low dislocation density condition may favor the crack propagation of NT magnesium. we conclude that a low dislocation density condition may favor the crack propagation of NT magnesium. To further further verify verify the the conclusion conclusion above, above, we we built built type type B B models models with with different different numbers numbers of of interior interior To grains but but aa constant constant TB TB spacing spacing of The crack crack employed employed in in this this model model is is LEC. LEC. According According to to grains of 7.5 7.5 nm. nm. The simulation results results in observed onon thethe stress-strain curve of an simulation in Section Section ??, 3.1,no noremarkable remarkablestress stressdropping droppingis is observed stress-strain curve of LEC sample in type A with nm7.5 TBnm spacing below a tensile of 20%, means pre-existing an LEC sample in type A 7.5 with TB spacing below strain a tensile strainwhich of 20%, which means

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crack propagation is impeded. isWhen we reduce numberthe of number interior of grains, thegrains, situation to pre-existing crack propagation impeded. When the we reduce interior the seems situation be changed. We onlyWe plot theplot stress-strain curvescurves for 1–4 graingrain samples to demonstrate the seems to be changed. only the stress-strain forinterior 1–4 interior samples to demonstrate competition between dislocation motion and crack In Figure average stressflow decreases the competition between dislocation motion and growth. crack growth. In ??b, Figure 10b, flow average stress with the reduction of the grain numbers. There is a remarkable stress dropping under 10% strain in decreases with the reduction of the grain numbers. There is a remarkable stress dropping under 10% the one-grain sample, which the crackthepropagation is obtained. The reason for thisfor stress strain in the one-grain sample,indicates which indicates crack propagation is obtained. The reason this dropping on a 7.5 spacing sample sample is mainly due to the of dislocation nucleation and motion. stress dropping onnm a 7.5 nm spacing is mainly duelack to the lack of dislocation nucleation and The stressThe concentration at the crackattip not effectively by stacking emission, thus motion. stress concentration theis crack tip is notreleased effectively releaseddislocation by stacking dislocation the crack initiates with propagation the strain increasing the one-grain sample. higher emission, thus thepropagation crack initiates with theinstrain increasing in theTherefore, one-grain asample. dislocation moredensity, TBs and smaller TB TBs spacing, enhance the fracture of Therefore, adensity, higher namely dislocation namely more and can smaller TB spacing, cantoughness enhance the NT magnesium. fracture toughness of NT magnesium.

Figure 10. (a) The trend of dislocation density with strain increasing by choosing three Figure 10. (a) The trend of dislocation density with strain increasing by choosing three typical TB spacings in the LEC model; (b) The stress-strain curves of LEC models with typical TB spacings in the LEC model; (b) The stress-strain curves of LEC models with different interior grains with a constant TB spacing. different interior grains with a constant TB spacing. 4. Conclusions 4. Conclusions In MD simulations simulations to to investigate investigate the In the the present present work, work, we we performed performed aa series series of of MD the mechanical mechanical behaviors behaviors ( and plastic deformation mechanisms of crack in 1012 ă 1011 ą NT magnesium. TB spacing and plastic deformation mechanisms of crack in {1012}  1011  NT magnesium. TB spacing variations variations are considered revealing their the fracture toughness. Main conclusions are are considered as revealingas their effects on theeffects fractureontoughness. Main conclusions are listed as follows: listed follows: (1)as Basal dislocation nucleates and emits from TBs and crack tip in {1012}  1011(  NT magnesium. (1) Basal dislocation nucleates and emits from TBs and crack tip in 1012 ă 1011 ą NT Stacking faults and phase transformation are main deformation mechanisms. Moreover, TBs effectively magnesium. Stacking faults and phase transformation are main deformation mechanisms. Moreover, hinder the dislocation motion and reserve dislocations to accommodate plastic strain. Because of the TBs effectively hinder the dislocation motion and reserve dislocations to accommodate plastic strain. TDs gliding along the TB interface, TB migration is obtained. Because of the TDs gliding along the TB interface, TB migration is obtained. (2) Different crack propagation behaviors are observed for samples with different crack positions (2) Different crack propagation behaviors are observed for samples with different crack positions (LEC and REC). By calculating the energy release rate for dislocation nucleation at the crack tip, (LEC and REC). By calculating the energy release rate for dislocation nucleation at the crack tip, it is it is indicated that dislocation motions more favorably occur in the LEC tip. Thus in the LEC model, the indicated dislocation morethefavorably occur in the LEC in tip theinitiates LEC model, the formationthat of voids which motions result from dislocation emission aheadtip. of aThus crack a ductile formation of LEC voidsgrowth which experiences result from athe dislocation of apattern, crack tip initiates ductile fracture. The transition fromemission a ductileahead to brittle whereas for athe REC fracture. The LEC growth experiences a transition from a ductile to brittle pattern, whereas for the REC model, a brittle cleavage is observed due to the suppression of dislocation emission at the crack tip. model, a brittle cleavage is observed due to the suppression of dislocation emission at the crack tip.

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(3) The ductile to brittle transition is found to mainly depend on the competition between dislocation motion and crack growth. TB spacing plays an important role in this competition mechanism. In LEC models when the spacing is below 10 nm, dislocation emission, stacking faults and phase transformation dominate the plastic deformation, thus the crack tip is blunted due to the dislocation motions. When the spacing is above 10 nm, crack cleavage is more likely. In REC models, the critical TB spacing is about 13.5 nm, which is larger than that in LEC models. (4) It is revealed that the dislocation density changed by the TB spacing variation accounts for the ductile to brittle transition. Decreasing TB spacing leads to the rise of dislocation densities, which provides more dislocation motions to accommodate the plastic deformation and suppress the crack ( growth. Thus a better fracture toughness of 1012 ă 1011 ą NT magnesium can be realized by enhancing the dislocation densities. Acknowledgments This work was supported by Chinese Nature Science Foundation (11372032) and The Open Project of Key Laboratory of Computational Physics in China. Author Contributions Lei Zhou contributed to the whole process of the preparation of molecular dynamics simulations, analysis of the results and preparation of the manuscript. Ya-Fang Guo supervised the whole procedure and also contributed to the data interpretation and preparation of the manuscript. Conflicts of Interest The authors declare no conflict of interest. References 1. Dalla Torre, F.; Lapovok, R.; Sandlin, J.; Thomson, P.F.; Davies, C.H.J.; Pereloma, E.V. Microstructures and properties of copper processed by equal channel angular extrusion for 1–16 passes. Acta Mater. 2004, 52, 4819–4832. [CrossRef] 2. Iwasaki, H.; Higashi, K.; Nieh, T.G. Tensile deformation and microstructure of a nanocrystalline Ni-W alloy produced by electrodeposition. Scr. Mater. 2004, 50, 395–399. [CrossRef] 3. Meyers, M.A.; Mishra, A.; Benson, D.J. Mechanical properties of nanocrystalline materials. Prog. Mater. Sci. 2006, 51, 427–556. [CrossRef] 4. Wang, Y.M.; Sansoz, F.; LaGrange, T.; Ott, R.T.; Marian, J.; Barbee, T.W., Jr.; Hamza, A.V. Defective twin boundaries in nanotwinned metals. Nat. Mater. 2013, 12, 697–702. [CrossRef] [PubMed] 5. Mirshams, R.A.; Xiao, C.H.; Whang, S.H.; Yin, W.M. R-curve characterization of the fracture toughness of nanocrystalline nickel thin sheets. Mater. Sci. Eng. A 2001, 315, 21–27. [CrossRef] 6. Li, Y.S.; Tao, N.R.; Lu, K. Microstructural evolution and nanostructure formation in copper during dynamic plastic deformation at cryogenic temperatures. Acta Mater. 2008, 56, 230–241. [CrossRef]

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