The authors show using atomistic simulations that stress-driven grain growth can be obtained in the athermal limit during nanocrystalline aluminum indentation. They find that the grain growth results from rotation of nanograins and propagation of shear bands. Together, these mechanisms are shown to lead to the unstable migration of grain boundaries via process of coupled motion. An analytical model is used to explain this behavior based on the atomic-level shear stress acting on the interfaces during the shear band propagation. This study sheds light on the atomic mechanism at play during the abnormal grain coarsening observed at low temperature in nanocrystalline metal

Dupont, V.

Sansoz, F.

English

The authors show using atomistic simulations that stress-driven grain growth can be obtained in the athermal limit during nanocrystalline aluminum indentation. They find that the grain growth results from rotation of nanograins and propagation of shear bands. Together, these mechanisms are shown to lead to the unstable migration of grain boundaries via process of coupled motion. An analytical model is used to explain this behavior based on the atomic-level shear stress acting on the interfaces during the shear band propagation. This study sheds light on the atomic mechanism at play during the abnormal grain coarsening observed at low temperature in nanocrystalline metals

Rollin, Virginie

Sansoz, Frederic

Embry-Riddle Aeronautical University

Grain growth behavior at absolute zero during nanocrystalline metal indentation

Aerospace Engineering - Daytona Beach College of Engineering 9-2006 Grain Growth Behavior at Absolute Zero during Nanocrystalline Metal Indentation F. Sansoz The University of Vermont V. Dupont Embry Riddle Aeronautical University, dupontv@erau.edu Follow this and additional works at: https://commons.erau.edu/db-aerospace-engineering  Part of the Aerospace Engineering Commons Scholarly Commons Citation Sansoz, F., & Dupont, V. (2006). Grain Growth Behavior at Absolute Zero during Nanocrystalline Metal Indentation. Applied Physics Letters, 89(11). Retrieved from https://commons.erau.edu/db-aerospace-engineering/2 This Article is brought to you for free and open access by the College of Engineering at Scholarly Commons. It has been accepted for inclusion in Aerospace Engineering - Daytona Beach by an authorized administrator of Scholarly Commons. For more information, please contact commons@erau.edu. Grain growth behavior at absolute zero during nanocrystalline metalindentationF. Sansoz and V. Dupont  Citation: Appl. Phys. Lett. 89, 111901 (2006); doi: 10.1063/1.2352725 View online: http://dx.doi.org/10.1063/1.2352725 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v89/i11 Published by the American Institute of Physics.  Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors Downloaded 27 Oct 2011 to 192.12.184.7. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsGrain growth behavior at absolute zero during nanocrystalline metalindentationF. Sansoza and V. DupontSchool of Engineering, The University of Vermont, Burlington, Vermont 05405Received 5 June 2006; accepted 21 July 2006; published online 12 September 2006The authors show using atomistic simulations that stress-driven grain growth can be obtained in theathermal limit during nanocrystalline aluminum indentation. They find that the grain growth resultsfrom rotation of nanograins and propagation of shear bands. Together, these mechanisms are shownto lead to the unstable migration of grain boundaries via process of coupled motion. An analyticalmodel is used to explain this behavior based on the atomic-level shear stress acting on the interfacesduring the shear band propagation. This study sheds light on the atomic mechanism at play duringthe abnormal grain coarsening observed at low temperature in nanocrystalline metals. © 2006American Institute of Physics. DOI: 10.1063/1.2352725Intense grain refinement can promote drastic changes ofplasticity mechanism in bulk materials and thin films.1–8 Inmetals containing nanosized grains 100 nm, several inde-pendent experiments have recently revealed abnormal graincoarsening phenomena at room temperature under large ap-plied stress.9–16 Surprisingly, during microindentation, thiscoarsening effect was found to occur faster at cryogenictemperatures.11 This finding is opposite to the thermodynam-ics of grain growth commonly observed in coarse-grainedmaterials.17 The underlying mechanisms governing the ab-normal coarsening of nanograins during indentation, how-ever, remained an open question.In order to investigate the atomic mechanism ofindentation-induced grain growth at very low temperature,we perform a numerical experiment: With the aid of concur-rent multiscale simulations, we investigate the indentationprocess with the total exclusion of thermally assisted mecha-nism. We perform molecular static simulations of indentationat absolute zero 0 K using the quasicontinuum method;18details on this numerical procedure are provided elsewhere.19In this letter, we simulate the indentation of 200-nm-thickfilms subjected to a perfectly rigid 15 nm radius cylindricalindenter using an embedded-atom-method potential for Al.20Thin films with either single crystal or columnar grain struc-tures are investigated. In the latter case, all simulated grainboundaries are tilt boundaries and the grains have a randomin-plane crystal orientation. The nanocrystalline models in-vestigated have average grain sizes of 5 and 7 nm.The indentation response at zero temperature is found todiffer markedly between single crystal and nanocrystallineAl Fig. 1. In the single crystal film, the onset of plasticity ischaracterized by a single dislocation pop-in event,21 whilethe plasticity of the nanocrystalline metals is governed byflow serrations. Our simulations confirm that the serratedyielding observed in the nanocrystalline metals is directlycaused by the formation of thin shear bands under the con-tact interface, which is largely in agreement with the modelsproposed in the literature.7,22 The shear bands are formed bysliding of several aligned grain boundaries and concurrentlyextend by intragranular slip into the grains that are in theprolongation of the band. The intragranular slip is found tobe dominated by the emission and propagation of partial dis-locations, each leaving an extended stacking fault along itspath.3 The formed stacking faults are also found to initiatethe growth of deformation twins.4 The propagation of theshear bands is clearly indicative that a significant shear flowis operative over distances much larger than the averagegrain size under consideration.We also explore the atomic mechanisms of deformationat larger depths of indentation. It is manifested from thestudy of the two grain sizes investigated that motion of grainboundaries and disappearance of nanosized grains occur si-multaneously during shear band propagation. For brevity, inthe following, we only focus our analysis of the deformationprocesses on a representative cluster of grains in the 7 nmgrain size model dashed area in Fig. 2a. Figures 2b–2hshow the evolution of the structure of this grain cluster dur-ing indentation. In these figures, the force value in the lower-aElectronic mail: frederic.sansoz@uvm.eduFIG. 1. Loading and unloading indentation responses of Al films at absolutezero simulated by quasicontinuum method. a Single crystal film. Filmplasticity occurring by typical dislocation pop-in events. Dashed circle cor-responds to the emission of the first dislocation. b 5 nm grain size film. c7 nm grain size film. Nanocrystalline metal response characterized by flowserration is indicative of the propagation of shear bands. Curves b and chave been shifted to the right for clarity.APPLIED PHYSICS LETTERS 89, 111901 20060003-6951/2006/8911/111901/3/$23.00 © 2006 American Institute of Physics89, 111901-1Downloaded 27 Oct 2011 to 192.12.184.7. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsleft corner of the images represents the contact force appliedby the indenter to the film. Early in the indentation process,significant rotation of grain 1 central grain takes place dueto grain boundary sliding between grains 1 and 5 left grain,as shown in Fig. 2c. It is also important to note that thestructure of the grain boundaries changes significantly duringgrain rotation. More specifically, grains 1 and 2 lower grainare separated by a high-angle grain boundary misorientationangle between grains of 22° before initial indentationFig. 2b; but the same boundary is transformed into a low-angle grain boundary misorientation angle of 13.5° aftergrain 1 rotation. In addition, grain 1 is in the prolongation ofa shear band, which is noticeable by the presence of stackingfaults in grain 3 right grain that are represented by blueatom lines inside this grain Fig. 2c. As the contact forceexerted by the indenter increases, there is clear evidence ofmotion of the boundary separating grains 1 and 2. Thisboundary begins to migrate in the direction normal to itsplane until it is absorbed by the interface made with grain 4upper grain. The atomic mechanism of migration is accom-plished by local lattice rotations forming vortexlike patternssimilar to those found in fluid shear flows Fig. 3a. There-fore, the lattice atoms of grain 1 are collectively shuffledacross the interface to become atoms arranged in the latticeof grain 2. In this process, grain 2 grows while grain 1 tendsto disappear. The grain boundary motion necessitates severalloading increments in order to be completed. Furthermore,upon unloading, only one grain remains. A possible interpre-tation of this result is that the grain boundary motion be-comes rapidly unstable as shown below.One can calculate the shear stress causing migration of atilt boundary as a function of tilt misorientation betweengrains using the theory developed by Gutkin and Ovid’ko.23This theory predicts the minimum external shear stress caus-ing stable interface motion and an estimate of the largershear stress leading to unstable grain boundary motion. Thelatter is given byc2 0.8G21 − , 1where G denotes the shear modulus,  Poisson’s ratio, and the tilt misorientation between grains. For the migrationproblem described above, using G=32 GPa, =0.31, and =13.5°, we find that the critical shear stress c2 is equal to696 MPa. This value is compared to the atomic-level shearstress obtained in our simulation with respect to the orienta-tion of the boundary plane between grains 1 and 2 Fig.3b. Each stress map represented in Fig. 3b correspondsto a different loading level taken from the rotation of grain 1top left to the complete disappearance of this grain bottomright. From this figure, it is evident that the local shear stressgradient causing the migration of the interface between thetwo grains becomes significantly larger than the unstablecritical shear stress c2 calculated above. This result is alsosupported by the fact that the contact force becomes almostconstant or even decreases when the interface is displacedbeyond the center of the grain Figs. 2f–2h. Conse-quently, it is found that the interface migration processcauses a strong stress relief in the grain boundary networksimilar to that found in the superplasticity studies of micro-scale Al alloys.24 Furthermore, a direct effect of the stressrelief is the tangential translation of grain 1 relative to grain2, which is indicated by horizontal arrows on the left bound-ary of grain 1 in Fig. 3b. This effect clearly suggests thatthe mechanism of stress-assisted grain growth found in thepresent study corresponds to the normal motion of grainboundaries resulting from a shear stress applied tangential tothem and causing tangential motion, a mechanism referred toas coupled motion of grain boundaries.25–27Earlier theoretical works have been conducted using mo-lecular dynamics simulation to understand the mechanismsof indentation in fully three-dimensional nanocrystallinemetal films at zero and finite temperatures.28,29 No atomisticstudies, however, have shown the occurrence of grain growthunder indentation at very low temperature. Here, we haveused a multiscale simulation method which helps investigat-ing large depths of indentation in thin films. As a result, ithas been possible to simulate the propagation of shear bandswhich are found to play a key role on the coupled motion ofFIG. 2. Color online Deformation of a representative grain cluster in theprolongation of a shear band in the 7 nm grain size Al film. a Contact zonebefore indentation. Dimensions and location of the fully refined atomisticregion are indicated with respect to the atomistically informed finite elementdomain not to scale. Dashed area showing the location of the grain cluster.b–d Rotation of grain 1. e–h Motion of the boundary separatinggrains 1 and 2. The applied contact force is indicated in the lower-left cornerof the images. The color scheme used for each atom corresponds to thecentrosymmetry parameter Ref. 21.111901-2 F. Sansoz and V. Dupont Appl. Phys. Lett. 89, 111901 2006Downloaded 27 Oct 2011 to 192.12.184.7. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissionsthe grain boundaries. This mechanism is certainly differentfrom that of curvature-driven grain growth and rotation-induced grain coalescence, which have been suggested in thepast for the grain growth observed in nanocrystallinemetals.12,30 More specifically, the latter mechanism wouldhave required more significant grain rotation in order to beaccomplished.30 Coupled motion of grain boundaries hasbeen investigated both theoretically25 and by atomisticsimulation26,27 in infinitely long bicrystals made of puremetal. Here, it is shown that coupled grain boundary motionis also an important mode of deformation in nanocrystallinematerials under stress, which can account for grain coarsen-ing phenomena in the absence of thermally activated pro-cesses. Understanding the fundamental mechanism leadingto stress-assisted grain growth in nanocrystalline materialswill show considerable promise toward achieving superplas-ticity in thin film materials.This work was conducted under the auspices of the Ver-mont Experimental Program to Stimulate Competitive Re-search VT EPSCoR under Grant No. NSF EPS 0236976.The authors would like to thank Yves Dubief for helpfulcomments during the preparation of the manuscript.1J. Schiotz, F. D. Di Tolla, and K. W. Jacobsen, Nature London 391, 5611998.2L. Lu, M. L. Sui, and K. Lu, Science 287, 1463 2000.3V. Yamakov, D. Wolf, S. R. Phillpot, A. K. Mukherjee, and H. Gleiter,Nat. Mater. 1, 45 2002.4M. W. Chen, E. Ma, K. J. Hemker, Y. M. Wang, and X. Cheng, Science300, 1275 2003.5J. Schiotz and K. W. Jacobsen, Science 301, 1357 2003.6K. S. Kumar, S. Suresh, M. F. Chisholm, J. A. Horton, and P. Wang, ActaMater. 51, 387 2003.7A. Hasnaoui, H. Van Swygenhoven, and P. M. Derlet, Science 300, 15502003.8X. Huang, N. Hansen, and N. Tsuji, Science 312, 249 2006.9M. Jin, A. M. Minor, E. A. Stach, and J. W. Morris, Jr., Acta Mater. 52,5381 2004.10K. Zhang, J. R. Weertman, and J. A. Eastman, Appl. Phys. Lett. 85, 51972004.11K. Zhang, J. R. Weertman, and J. A. Eastman, Appl. Phys. Lett. 87,061921 2005.12Q. Wei, D. Jia, K. T. Ramesh, and E. Ma, Appl. Phys. Lett. 81, 12402002.13Z. Shan, E. A. Stach, J. M. K. Wiezorek, J. A. Knapp, D. M. Follstaedt,and S. X. Mao, Science 305, 654 2004.14X. Z. Liao, A. R. Kilmametov, R. Z. Valiev, H. S. Gao, X. D. Li, A. K.Mukherjee, J. F. Bingert, and Y. T. Zhu, Appl. Phys. Lett. 88, 0219092006.15D. S. Gianola, S. Van Petegem, M. Legros, S. Brandstetter, H. Van Swy-genhoven, and K. J. Hemker, Acta Mater. 54, 2253 2006.16G. J. Fan, Y. D. Wang, L. F. Fu, H. Choo, P. K. Liaw, Y. Ren, and N. D.Browning, Appl. Phys. Lett. 88, 171914 2006.17G. Gottstein and L. S. Shvindlerman, Grain boundary Migration in Met-als: Thermodynamics, Kinetics, Applications CRC, Boca Raton, FL,1998.18R. Miller and E. B. Tadmor, J. Comput.-Aided Mater. Des. 9, 203 2002.19V. Dupont and F. Sansoz, Mater. Res. Soc. Symp. Proc. 903E, 0903-Z06-05.1 2005.20A. F. Voter and S. P. Chen, Mater. Res. Soc. Symp. Proc. 82, 175 1987.21C. L. Kelchner, S. J. Plimpton, and J. C. Hamilton, Phys. Rev. B 58,11085 1998.22A. C. Lund and C. A. Schuh, Mater. Res. Soc. Symp. Proc. 806, MM7.4.12004.23M. Y. Gutkin and I. A. Ovid’ko, Appl. Phys. Lett. 87, 251916 2005.24L. M. Dougherty, I. M. Roberston, and J. S. Vetrano, Acta Mater. 51,4367 2003.25J. W. Cahn and J. E. Taylor, Acta Mater. 52, 4887 2004.26A. Suzuki and Y. Mishin, Mater. Sci. Forum 502, 157 2005.27F. Sansoz and J. F. Molinari, Acta Mater. 53, 1931 2005.28D. Feichtinger, P. M. Derlet, and H. Van Swygenhoven, Phys. Rev. B 67,024113 2003.29X. L. Ma and W. Yang, Nanotechnology 14, 1208 2003.30A. J. Haslam, D. Moldovan, V. Yamakov, D. Wolf, S. R. Phillpot, and H.Gleiter, Acta Mater. 51, 2097 2003.FIG. 3. Color online a Magnitude and orientation ofthe atomic trajectories between two loading incrementsduring the motion of the boundary separating grains 1and 2. Coupled boundary motion via local lattice rota-tions forming vortexlike patterns. b Atomic-levelshear stress with respect to the orientation of the inter-face between grains 1 and 2 at different stages of theboundary motion in units of GPa. The boundaries ofgrains 1 and 2 have been highlighted for clarity. c2 isthe critical stress value leading to unstable boundarymotion. Grain boundary motion produces stress relief inthe grain cluster. Note in the bottom-right image thatthe tangential motion of grain 1 represented by light-colored arrows parallel to its moving interface also in-dicates that the grain boundary motion is coupled. Scalebars are 3 nm.111901-3 F. Sansoz and V. Dupont Appl. Phys. Lett. 89, 111901 2006Downloaded 27 Oct 2011 to 192.12.184.7. 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Grain Growth Behavior at Absolute Zero during Nanocrystalline Metal Indentation

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Grain Growth Behavior at Absolute Zero during Nanocrystalline Metal Indentation

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