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Scripta Materialia 59 (2008) 792–795

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Dislocation-assisted grain growth in nanocrystallinecopper under large deformation

Xin Ling Maa,* and Wei Yangb

aSchool of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, ChinabSchool of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310058, China

Received 25 March 2008; revised 10 June 2008; accepted 12 June 2008Available online 24 June 2008

Dislocation plasticity conventionally induces textures in polycrystalline metals after a large deformation. We used parallel molec-ular dynamics to simulate the plastic deformation of nanocrystalline copper to an isochoric stretch up to 100% logarithmic strain.We found that the movements of partial dislocations that dominate the deformation process do not lead to texture formation. Thegrain size distribution becomes extremely inhomogeneous. By observing the structural evolution, we demonstrate that grain growthassisted by partial dislocations suppresses the texture formation.Crown Copyright � 2008 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved.

Keywords: Dislocation; Grain growth; Molecular dynamics; Nanocrystalline; Large deformation

Plastic deformation in polycrystalline metals atroom temperature is generally caused by the movementsof dislocations. Limited by the number of available slipsystems, grains will change their shape and rotate to-wards a limited number of stable configurations, thuscreating a texture after a large deformation [1]. Nano-crystalline metals may behave differently from theircoarse-grained counterparts. It is thus natural to askwhether the same deformation-induced textures will de-velop in nanocrystalline metals. Cold-rolling experi-ments on nanocrystalline copper [2] and palladium [3]showed no trace of texture formation and the grainshape remained equiaxed. Dislocation activities wereevidenced during the rolling processes by the increaseof the microstrain or the stacking fault density. How-ever, the rather low strain rate suggested that the defor-mation mechanism was dominated by the grainboundary sliding and that grain rotation was assistedby grain boundary diffusion [2,3]. The formation of tex-tures was greatly suppressed by the grain boundaryactivities, similar to what had been observed in fine-grained superplastic alloys and ceramics deformed athigh temperatures. The important role of partial disloca-tions was recognized by molecular dynamics (MD) sim-ulations [4] in rapidly deforming the nanocrystallinemetals. Komanduri et al. [5] simulated uniaxial tension

1359-6462/$ - see front matter Crown Copyright � 2008 Published by Elsevdoi:10.1016/j.scriptamat.2008.06.022

* Corresponding author. E-mail: xlma@ecust.edu.cn

at the nanoscopic level at a constant loading rate in bothface-centered cubic (fcc) and body-centered cubic (bcc)single-crystal metals to investigate the nature of defor-mation and fracture. Froseth et al. [6] found that thepresence of grown-in twins in nanocrystalline-Al en-hanced plastic deformation via twin-migration in whichpartial dislocations emitted at the intersection of thetwin boundary and the grain boundary travel throughthe entire grain. Farkas et al. [7] noted that stress-drivengrain boundary migration in nanocrystalline materialscould be part of a basic deformation mechanism. Gian-ola et al. [8] simulated stress-assisted discontinuousgrain growth and its effect on the deformation behaviorof nanocrystalline aluminum thin films. Yuan et al. [9]simulated tensile deformation of nano-single-crystal alu-minum. These simulations are typically performed un-der high strain rates and low temperatures. Therefore,the grain boundary diffusion was greatly reduced andthe deformation process was mainly controlled by themovements of partial dislocations. The logarithmicstrains achieved in the early MD simulations were nomore than 10%, which is not sufficient to predict textureformation. This paper will examine, by MD simulations,this process for nanocrystalline copper for the regime oflarge deformations, which naturally minimizes the effectof grain boundary diffusion.

The simulation was carried out by standard MDtechniques, with the atomic interactions for copper[10] described by an embedded atom method potential.

ier Ltd. on behalf of Acta Materialia Inc. All rights reserved.

X. L. Ma, W. Yang / Scripta Materialia 59 (2008) 792–795 793

A three-dimensional Voronoi construction [11] was usedto generate the nanocrystalline model for computation.The sample configuration involves 1,048,645 atomsand 64 randomly oriented grains with an average grainsize of �7 nm. Periodic side boundaries were maintainedthroughout the simulation. The isochoric stretching of ananocrystalline copper box was conducted by parallelMD simulations under the Linked-Cell-List algorithm[12]. The initial MD simulation involved 3000 annealingrelaxation steps at 300 K, using the Verlet leapfrog algo-rithm [13] with a MD time step of 2 fs. The loading wasimposed in a quasi-homogeneous manner. A homoge-neous affine deformation of 0.1% stretching and 0.05%lateral contraction was enforced. Then 500 relaxingsteps were executed at 300 K by maintaining a NVTensemble. The stretching rate was 109 s�1 and the totalsimulation time was 1.006 ns. Figure 1a and b showthe atom configurations for 6% and 91% logarithmicstrains, respectively. The atoms in grain boundaries, instacking faults or inside grains were identified by localcrystalline order [14]. Comparing the two configurationsin Figure 1, one finds the grain boundaries were widenedand the disordered atoms increased after a large defor-mation. In order to maintain the plastic deformation,more and more partial dislocations emitted from grainboundaries or triple junctions and passed throughgrains. Partial dislocations are left behind the stackingfaults. At the stage of both small (Fig. 1a) and largedeformation (Fig. 1b), only a few slip systems, generallyless than three in each grain, were activated. The straincompatibility could not be met along the grain bound-aries if the plasticity was only mediated by movementsof partial dislocations. The atoms near grain boundariesadjusted their locations locally under the high flow

Figure 1. Local crystalline order of nanocrystalline copper underuniform stretching of (a) 6% and (b) 91% logarithmic strains. Theatoms in the fcc stacking sequence are referred to as the perfect latticeand are colored green; the atoms in the hexagonal close-packed (hcp)stacking sequence are regarded as the stacking fault and are coloredred, while the atoms with other crystalline orders are thought of as thegrain boundary and are painted blue. (For interpretation of thereferences to color in this figure legend, the reader is referred to theweb version of this article.)

stress, in the form of a large number of small slidingevents. These small slippages facilitated the grain rota-tion process. It was found in the simulation that thegrains tended to rotate to the tensile direction, with agrain rotation rate less than 4� per 1% logarithmicstrain. As the deformation continued, the grain bound-aries widened and triple junctions enlarged to accommo-date the accumulated misfit strain among grains.

The flow stress, shown in Figure 2a, was kept about2.25 GPa after about 10% logarithmic strain. However,a stable flow stress does not necessarily imply a steadystate. The atom configuration kept evolving as thedeformation proceeded. Figure 2b showed the percent-age variations of perfect fcc, stacking fault and grainboundary atoms. The regular fcc atoms steadily declinefrom the initial percentage of about 70% to only 30% at30% logarithmic strain. At the same strain level, the per-centage of atoms in stacking faults shoots up to nearly30%. The percentage of atoms in grain boundaries variesfrom the initial percentage of 30 to 40%. After 30% log-arithmic strain, these percentages remained steadily withdeformation up to 100% logarithmic strain. The in-creases on the percentages of the stacking fault andgrain boundary atoms indicated that the disorder ofthe nanocrystalline sample was enhanced at large defor-mation. Hidden behind the steady percentages of perfectfcc, stacking fault and grain boundary atoms, thechanges in the grain configuration were still enormousin the large stretch regime. To reveal this change, onemay classify atoms of the sample into three categories:‘‘grain boundary atoms” unrecognized by the local crys-talline order method; ‘‘pseudo-boundary atoms” locatedwithin a three-layer thickness between the perfect fccatoms and the grain boundary atoms; and the remaining‘‘pure grain atoms”. This classification yields clean iso-lated grains and eliminates the scattering clusters of afew atoms which observe the fcc crystalline order. Thenumber of grains that are larger than the average de-creases sharply at the initial 20% logarithmic strain.Then the trend became slow with stretching strain, as

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794 X. L. Ma, W. Yang / Scripta Materialia 59 (2008) 792–795

plotted in Figure 2c. At the end of the deformation,most of the grains merged into a few super grains andothers were cut into small colonies, containing only sev-eral thousands of atoms.

The grain size distribution became inhomogeneous inthe regime of large deformation, as shown in Figure 3.The grain size distribution became bimodal after 10%of deformation (Fig. 3b). A few grains obviously grew.When the deformation reached 50% logarithmic strain,the first peak moved toward a smaller size and thesecond peak became flat (Fig. 3c). Two grains grew torather large sizes. After 91% logarithmic strain, the sizedistribution of the grains in the sample became verydispersive (Fig. 3d). The largest grain contained about3.8 � 105 atoms and an approximate size of 18 nm.The upper right inset showed that the number of thesmaller grains also decreased. The reason might lie inthe merging process among grains. The process of grainrefinement is unlikely since grain boundary sliding,rather than the movements of partial dislocations,would dominate the deformation mechanisms for asmall grain size of 4 or 5 nm.

Along with the longitudinal stretching, the lateral sizeof the box shrinks. The limiting case occurs when thereis only one grain across the lateral direction. Underhomogeneous affine deformation, a unit box would bestretched to (1.001)1000 = 2.717 in the longitudinal direc-tion, and be contracted to (0.9995)1000 = 0.606 in the lat-eral direction at 100% logarithmic strain. By assumingequiaxed grain shape, one has the limiting case of onegrain in the lateral direction, and about four grains inthe elongated direction at 100% logarithmic strain. Ifthe periodic boundary conditions are still enforced insuch a situation, the effect of the boundary will severelyperturb the simulation results. Single grains across theperiodic boundary will merge together in the lateraldirection. Accordingly, the simulation is no longer reli-able when the number of grains is below four. Figure2c indicates that the number of grains was about fourat 55% logarithmic strain, and then this number fluctu-

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Figure 3. Size distribution of grains at (a) 0%, (b) 10%, (c) 50% and (d)91% logarithmic strains. Only grains containing more than 1000 atomsare considered.

ates with the stretching strain, corresponding to theunrealistic influence from the periodic boundary condi-tions. Therefore, the periodic boundary conditions arenot suitable after 55% logarithmic strain.

Two modes of grain combination processes were re-vealed: penetration of the stacking faults through low-angle grain boundaries at small deformation (Fig. 4a)and the formation of twin-like structures at large defor-mation (Fig. 4b). The two mechanisms were differentfrom the observations of MD simulation by Haslam etal. [15]. In Ref. [15] a sample of the nanocrystalline pal-ladium was deformed at 0.46 Tm, with Tm being themelting temperature. At this relatively high temperature,grain boundary diffusion was more mobile, therebyreplacing the role of partial dislocations. In Ref. [15],low-angle grain boundaries were found to disassociateinto partial dislocations, propagate into grains and leadto grain coalescence, and grain boundary migration as-sisted by diffusion accounted for most of the graingrowth.

The simulation presented in this paper was under-taken at rather low temperature, i.e. 0.22 Tm. Twomodes modes of grain growth are involved in the kine-matics of stacking fault propagation and grain rotation.In the small deformation regime, grain merging givespriority to those neighboring grains whose misorienta-tions are <10�. The stacking faults burst verticallythrough the boundary between the neighboring grains:see Figure 4a, from left to right. The misorientation oftwo neighboring grains is eliminated gradually, asshown by the partial merging (the middle graph inFig. 4a) and final consolidation (the right graph ofFig. 4a) processes. The larger grain formed in this waywas stable during subsequent evolution. Another modedominated the merging in the large strain regime forneighboring grains with large misorientations. Themerging process featured parallel (instead of vertical as

Figure 4. Stacking faults vertically pass through small-angle grainboundaries (from left to right). Three stages of the stacking faultpenetration are shown: onset of stacking fault passing (left); partialmerging of neighboring grains (middle) and complete merging (right).(b) Configuration of a large pure grain under 40% stretching strain.The connection area has a twin-like structure manifested by stackingfaults parallel to the previous grain boundary. The cross-sectional viewgives the orthomorphic projection of the area circled on the left.

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in the small strain regime) passing of stacking faultsthrough the grain boundary. Figure 4b shows the config-uration of a large grain under 40% logarithmic strain.The grain evolved by combining two small ones situatedat the top and bottom of the figure. The central connec-tion neck is composed of stacking faults that are parallelto the previous grain boundary. A cross-sectional viewof the orthomorphic projection of the area circled onthe left was delineated in the right of Figure 4b. Thered neck-like hcp configuration area can be viewed asthe twin-type grain boundary layer for the adjacentgrains (in green), as evidenced by the twin-type orienta-tions marked by the arrows. The zigzag path indicates alinking route through the closest atoms to depict thetwin-like structure. As suggested by Derlet et al. [16]and Kumar et al. [17], this twin-like structure wasformed at large deformations and was caused by emis-sion of a second partial dislocation on an adjacent slipplane. The merged grain was comparatively unstableand might separate again.

Careful observations on the structure evolutionshowed no textures were formed in our simulation. Ini-tial deformation was dominated by partial dislocations.As the deformation continued, the disordered atoms andthe formation of twin-like structures hindered the activ-ities of partial dislocations. The twin-like structures,formed at large deformations, are effective barriers tothe movements of dislocations and thus disturb and hin-der the texture evolution among large grains. The grainmerging process gives rise to inhomogeneous grain sizedistribution in the sample. The extremely small grainswould facilitate the grain boundary activities that alsoserved for the reduction of textures. This nature ofnanocrystalline metals provides a mechanism to explainhow these materials keep their physical properties iso-tropic even after large deformations.

Computation of this work was supported by theInstitute of Applied Physics and Computational Mathe-matics, as carried out in its Milky-Way super parallelcomputer.

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