(6.4)--LENGTH-SCALE EFFECTS IN THE NUCL机械工程材料机械工程材料.pdf

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1、Acta mater.49(2001) EFFECTS IN THE NUCLEATION OFEXTENDED DISLOCATIONS IN NANOCRYSTALLINE Al BYMOLECULAR-DYNAMICS SIMULATIONV.YAMAKOV1,2,D.WOLF1,M.SALAZAR1,2,3,S.R.PHILLPOT1and H.GLEITER21Materials Science Division,Argonne National Laboratory,Argonne,IL 60439,USA,2ForschungszentrumKarlsruhe,76021 Kar

2、lsruhe,Germany and3Universite de Bourgogne,Fac.Des Sciences Mirande,LRRSUMR-CNRS 5613 B.P.47870-21078 Dijon,Cedex,France(Received 5 February 2001;accepted 19 April 2001)AbstractThe nucleation of extended dislocations from the grain boundaries in nanocrystalline aluminumis studied by molecular-dynami

3、cs simulation.The length of the stacking fault connecting the two Shockleypartials that form the extended dislocation,i.e.,the dislocation splitting distance,rsplit,depends not only onthe stacking-fault energy but also on the resolved nucleation stress.Our simulations for columnar grainmicrostructur

4、es with a grain diameter,d,of up to 70 nm reveal that the magnitude of rsplitrelative to drepresents a critical length scale controlling the low-temperature mechanical behavior of nanocrystallinematerials.For rsplitd,the first partials nucleated from the boundaries glide across the grains and become

5、incorporated into the boundaries on the opposite side,leaving behind a grain transected by a stacking fault.By contrast,for rsplit?d two Shockley partials connected by a stacking fault are emitted consecutively fromthe boundary,leading to a deformation microstructure similar to that of coarse-graine

6、d aluminum.The mech-anical properties of nanocrystalline materials,such as the yield stress,therefore depend critically on the grainsize.2001 Acta Materialia Inc.Published by Elsevier Science Ltd.All rights reserved.Keywords:Computer simulation;Nanocrystal;Aluminium;Dislocations;Grain boundaries1.IN

7、TRODUCTIONThe mechanism by which nanocrystalline metals plas-tically deform at relatively low temperature has beenthe subject of considerable debate ever since the firstpolycrystalline metals with a grain size of typicallyless than 0.1 m were first synthesized in bulk formapproximately 20 years ago(

8、for a recent review see1).From the study of coarse-grained fcc metals itis known that the common low-temperature mech-anism of plastic deformation involves the continuousnucleation of dislocations from FrankRead sourcesand their glide motion through the crystal 24.In apolycrystalline material the si

9、ze of the source cannotexceed the grain size;since the stress needed for aFrankRead source to operate is inversely pro-portional to the size of the source,this dislocationnucleation mechanism can only operate down to aminimum grain size of typically about 1 m.Dislocations can also be nucleated from

10、grainboundaries(GBs)4,5.In the past,the interaction(nucleation and annihilation)of dislocations with GBs To whom all correspondence should be addressed.E-mail address:wolfanl.gov(D.Wolf)1359-6454/01/$20.00 2001 Acta Materialia Inc.Published by Elsevier Science Ltd.All rights reserved.PII:S1359-6454(

11、01)00167-7has been studied theoretically and experimentally.ThetheoreticalworkofLirevealedthatthenucleation of a dislocation involves GB ledges 68.Experimental studies of the plastic deformation ofpolycrystals at low temperatures suggest that GBsbecome the dominant dislocation sources for smallgrain

12、 sizes.Assuming that the process of dislocationnucleation is not significantly affected by alreadyexisting forest dislocations or dislocation pile-ups,thenucleation process may be expected to be inde-pendent of grain size 79.The GBs should thereforeprovide the necessary dislocation sources for the l

13、ow-temperature deformation of nanocrystalline materials.Hence,at the relatively high stresses required for thenucleation process,the dislocationglide mechanismshould,in principle,take place even in nanocrystal-line materials.Here we demonstrate by molecular-dynamics(MD)simulation that this is,indeed

14、,true.The most common dislocations responsible for theslip deformation of fcc metals are 1/2110 edge dis-locations.However,the cores of these dislocations areusually split into two partial dislocations(calledShockley partials),with a Burgers vector of 1/6112and connected by a stacking fault.Such a s

15、tructureis known as an extended dislocation 2;its splitting2714YAMAKOV et al.:DISLOCATIONS IN NANOCRYSTALLINE ALUMINUMdistance,rsplit,depends on the stacking-fault energy?and the applied stress s as 10rsplit=Kb2?bms,(1)where b=a0/6 is the length of the Burgers vectorof the partials,a0the lattice par

16、ameter,K a factor thatdepends on the elastic constants of the material andm the Schmid factor.In the absence of external stress(s=0),the equilibrium splitting distance is given byr0=Kb2?.(2)For a typical fcc metal,r0is of the order of a fewlattice parameters and hence usually considered negli-gible

17、compared to the grain size.Under the high stresses required to nucleateextended dislocations from GBs,the magnitude ofrsplitcan be significant and,in a nanocrystalline fccmetal,becomes comparable to or even larger than thegrain size,d.The splitting distance thus introduces anew length scale into the

18、 problem,in addition to d,because a complete extended dislocation cannot benucleated unless drsplit(s).This represents a neces-sary condition for the dislocationglide mechanism tobe operational in a nanocrystalline fcc metal.Here wedemonstrate the interplay between these two lengthscales and their p

19、rofound influence on the mechanicalproperties of nanocrystalline materials.Recent simulations have already demonstrated that,indeed,dislocations may play a role in the defor-mation of nanocrystalline fcc metals 1113.How-ever,for the rather small grain diameters(of up to 12nm)considered in these simu

20、lations,only incompletedislocations were observed to be nucleated from theGBs,i.e.,single partials which produce stackingfaults as they glide through the grain and becomeincorporated into the GBs on the opposite side.Thesestacking faults remain in the grains as planar defectswhich are not recovered.

21、After the grain interior hasbeen transected by a number of such stacking faults,further dislocation propagation cannot take place.This process can therefore operate only during theinitial stages of deformation and thus differs signifi-cantly from the usual slip mechanism in coarse-grained materials.

22、It is further worth noting that evenfor the largest grain sizes considered in these simula-tions(of the order of d=12 nm)13,the dislocationscould account for only about 30%of the total defor-mation,and practically no dislocations were observedin grains smaller than 8 nm.The dominant defor-mation mec

23、hanism observed in practically all pre-viousMDsimulationsthereforeinvolvedGB-mediated processes,such as GB sliding 1113 orGB diffusion 14,15.In order to investigate more fully the role of dislo-cation processes in their low-temperature plastic-deformation behavior,nanocrystalline materials witha con

24、siderably larger grain size have to be explored.This will enable us to not only observe the nucleationof complete extended dislocations from the GBs butalso establish at what grain size the entire plasticstrain can be attributed to the conventional slip-defor-mation mechanism.2.SIMULATION APPROACHA

25、textured or columnar microstructure is ideal forthis study because,while providing a fully three-dimensional(3d)treatment of the underlying physics,the GB and dislocation events taking place during thedeformation are readily visualized;also,it enables usto simulate relatively large grains,because on

26、ly a fewlattice planes need to be considered in the periodicallyrepeated texture direction.The simulation cell sketched in Fig.1 contains fourcolumnar,uniform hexagonal fcc grains that arerotated with respect to each other about the 110 tex-ture(or tilt)axis which defines the z direction.Forsimplici

27、ty,the misorientation angles,y,chosen forthis study are 30,60 and 90.The 24 high-angleGBs in the system therefore consist of three groupsof identical asymmetric 110 tilt GBs:whereas the30 and 90 boundaries are high-energy GBs,with ahighly disordered atomic structure 1619,the 60tilt GBs have a disloc

28、ation structure because theirmisorientation is vicinal to the?=3,y=70.53orientation.The minimum thickness of the simulation cell inthe z direction is determined by the cutoff radius ofthe interatomic potential used for the simulations(seebelow).Specifically,our cell contains only 10(110)planes;their

29、 interplanar spacing of 2/4a0results inan initial z thickness of?3.5a0(or?1.42 nm fora0=4.03 A;see below).The simulation-cell size inthe xy plane is determined solely by the grain size.Fig.1.Schematic view of our 3d-periodic simulation cell con-taining four cylindrical grains in the shape of regular

30、 hexagons.The tensile stress is applied along the x direction.In the texture(z)direction,the cell contains only 10(110)planes,resultingin a total z thickness of?3.5a0(or?1.42 nm)for the Al EAMpotential 18.The lateral dimensions range from 3632 nm(for d=20 nm,giving a total of 97,000 atoms)up to11710

31、1 nm(for d=70 nm,and a total of 1,021,000 atoms).2715YAMAKOV et al.:DISLOCATIONS IN NANOCRYSTALLINE ALUMINUMSpecifically we will present results for grain sizes ofd=20,30,45 and 70 nm;our simulated systems thuscontained from 97,000 to 1,021,000 atoms.Particular thought went into our choice of the 11

32、0texture direction(see Fig.1).Most importantly,the110 direction is the common axis of the(111)and(111)glide planes,ensuring that the dislocationsemitted from the GBs lie in favorable glide planes.In a general 3d grain microstructure,dislocation emis-sion could involve any of the 12 slip systems(illu

33、strated by the Thompson tetrahedron 20,21)and the appearance of four distinct types of split dis-location structures.However,the high degree ofperiodicity in the 110 texture direction(Fig.1)imposes a constraint on the types of extended dislo-cations that one can expect to be nucleated,allowingfor on

34、ly four slip systems to be present and only onetype of extended dislocation to be nucleated.In particular,because of the very small thicknessof the simulation cell in the z direction,only straight(i.e.,kink-free)dislocations with dislocation linesparallel to 110 direction whose Burgers vectors pro-j

35、ected onto the 110 direction are commensurate withthe periodicity of the fcc lattice in this direction canbe nucleated.This leaves only one type of extendeddislocation that can be emitted from the GBs,namelya 60(with respect to the dislocation line along110 direction)extended dislocation dissociated

36、 intoa 30 partial and a pure-edge(i.e.,90)partial.The fact that there are only four slip systems fol-lows from the two possible signs of the 30 partial(30)which gives two possible signs of the extendeddislocation(60).This defines two possible glidedirections on each of the(111)and(111)glide planes,r

37、esulting in a total of four slip systems in our simul-ation setup.For example,the two possible extendeddislocations on the(111)glide plane are the 601/2011 dislocation(which dissociates into a 30 1/6121 partial and a pure-edge 1/6112 partial)and the?60 1/2101 dislocation(which dissociates into a?30

38、1/6211 partial and a pure-edge 1/6112partial);the two glide directions on the(111)planeare therefore 011 and 101.Another analogous setof two glide directions,011 and 101,can exist inthe(111)plane,and eventually a number of cross-slip formations between the(111)and(111)glideplanes may be possible.As

39、far as the dislocation dynamics is concerned,our columnar system therefore incorporates the neces-sary ingredients of a fully 3d microstructure,althoughthe particular nucleation mechanism is restricted tothe nucleation of only one type of dislocation,namely60 extended dislocations.However,this type

40、of dis-location is commonly present in the deformation offcc metals.It therefore appears that the insights intothe deformation behavior of our carefully selectedcolumnar microstructure gained from this simulationstudy are more widely applicable.An EAM potential parameterized for Al 22 isused through

41、out this study.This particular choice wasmotivated by the high stacking-fault energy of Al(with experimental values ranging between 120 and142 mJ/m223)which results in a relatively smallsplitting distance of the extended dislocations andfavors their observation for a relatively smaller grainsize tha

42、n in an fcc metal with a low stacking-faultenergy.Previous zero-temperature dislocation simula-tions for this potential yielded a stacking-fault energyof?=104 mJ/m2and a zero-stress splitting distancesee equation(1)of 10.1 A24.In all our simula-tions,the potential and its derivatives are shiftedsmoo

43、thly to zero at the cutoff radius of Rc=1.35 a0.However,by contrast with the original potential 22,this“shifted-force”procedure 25 is applied not onlyto the short-range repulsive part of the EAM potentialbut also to the electron density,thus ensuring aslightly higher degree of smoothness at the cuto

44、ffradius.This cutoff procedure increases the stackingfault energy to 122 mJ/m2,i.e.,closer to the experi-mental value,while rendering the lattice parameter(a0=4.03A)andthemeltingtemperature(Tm=940 K)practically unchanged.This value of thestacking-fault energy yields a zero-stress splitting dis-tance

45、 see equation(1)of 8.6 A.MD simulations with full 3d-periodic border con-ditions of the ParrinelloRahman type 26 were car-ried out at a temperature of T=300 K and a constanttensile load between 2.0 and 3.0 GPa applied alongthe X direction in Fig.1.(Details of the simulationprocedure are given in our

46、 recent work on graingrowth in nanocrystalline metals with columnarmicrostructure 27).The MD time step for our poten-tial is?t?0.5 fs;because of the lower atomic weightof Al,this time step is about five times shorter thanthat for the Pd EAM potential used in our grain-growth27andgrain-boundarydiffus

47、ioncreepsimulations 14,15.Similar to the earlier simulations1113,stacking faults are visualized by a common-neighbor analysis 28,29 which permits the distinc-tion between atoms in a local hcp environment andthose in an fcc environment.A single line of hcpatoms thus represents a twin boundary;two adj

48、acenthcp lines indicate an intrinsic stacking fault and twohcp lines with an fcc line between them represents anextrinsicstackingfault.Anewalgorithmwasdeveloped to identify atoms belonging to the samegrain;this procedure enables us to characterize thestructure and behavior of each grain,such as the

49、aver-age stress,grain orientation,etc.during the defor-mation.3.SIMULATION RESULTS3.1.Length-scale effects in dislocation nucleationTo investigate the effect of the grain size on thenucleation of extended dislocations,we first considerthe system with d=20 nm.At this grain size,beforeany deformation

50、has taken place,about 86%of theatoms are in a perfect fcc environment;the remainder2716YAMAKOV et al.:DISLOCATIONS IN NANOCRYSTALLINE ALUMINUMare miscoordinated atoms belonging to the GBs.While gradually increasing the tensile stress s,wemonitor the strain of the system with time(see Fig.2).Even at