MULTISCALE SIMULATION OF NANOINDENTATION ON Al THIN FILM

45 2 Vol.45 No.2 09 2 129 136 ACTA METALLURGICA SINICA Feb. 09 pp.129 136 Al ÌÅ ÙÔ ¾ ¼ º ( ÉÂÉ µ É, 0433) ½» (Faculty of Built Environment and Engineering, Queensland University of Technology, Brisbane QLD4001, Australia) ± ¹Ý Ð ÅÄ ½Æ Ô ² ³Ð ²Ç, Al Ý ÎÄ, «¹Ö µ Ö Đ «µ. Ê ² Ý ÎÄ «Í Peierls ÖÃ Ñ«Í Ø¹. Ñ, ±Ý ÎÄ Ê Ç«Í ¾, ² Ø 1 Ø 3 «Í ع, Å Ø 2 «Í ³ÐÑ ÉÝ, ÐÏÆ ¾; ß ²Ô ÌÐ, ¹ ÛÖ Đ «ÍÆÝ Peierls Öà Ü; ÏÆ, Ø 2 «ÍÁ Ü, ÏÆ Ë, «Í Á. Ô Ý ÚÐ Peierls Öà Á. Òß Al, Ý ÎÄ, Ð, ÅÄ ½Æ, ² ¹ ÑĐÕ TB383 Ï A ÍÕ 0412 1961(09)02 0129 08 MULTISCALE SIMULATION OF NANOINDENTATION ON Al THIN FILM LI Junwan, NI Yushan, LIN Yihan, LUO Cheng Department of Mechanics and Engineering Science, Fudan University, Shanghai 0433 JIANG Wugui Faculty of Built Environment and Engineering, Queensland University of Technology, Brisbane QLD4001, Australia Correspondent: NI Yushan, associate professor, Tel: (021)65642745, E-mail: niyushan@fudan.edu.cn Supported by National Natural Science Foundation of China (No.10576010) Manuscript received 08 07, in revised form 08 10 16 ABSTRACT In order to study the early stages of plastic deformation with initial defect under the action of an indenter, the nanoindentation processes of the single crystal aluminum thin film were simulated using the quasicontinuum method. The load vs displacement response curves and strain energy vs displacement curves of the single crystal aluminum thin film with initial defect and defect free were presented, respectively. The nanoindentation processes under influences of the initial defect were investigated about dislocation nucleation, dislocation emission, Peierls stress and load necessary for dislocation emission. The results demonstrate that the load vs displacement response curves experience many times abrupt drops with the emission of dislocations beneath the indenter. The initial defect is found to be insignificant on nucleation and emission of the 1 st and 3 rd dislocation dipoles, but has a distinct effect on the 2 nd dislocation dipole. The nucleation and emission of the 2 nd dislocation dipole is postponed obviously because of the effect of initial defect, and then crack propagation is accompanied. The strain energy of single crystal aluminum thin film and Peierls stress of dislocation dipole beneath the indenter increase with deformation processes due to the severe lattice distortion in the thin film. Before the cleavage occurs, the load necessary for the 2 nd dislocation dipole nucleation and emission increases in nanoindentation with initial defect, on the contrary, it decreases after the cleavage occurred. The nanohardness and Peierls stress in this simulation show a good agreement with relevant theoretical and experimental results. KEY WORDS Al film, nanoindentation, multiscale, quasicontinuum method, initial defect * ÛÁ³ Ê»Ú 10576010 Ç : 08 07, Ç À : 08 10 16 É ß : º, ß, 1980, Â

130 Ì È 45 Þ ÏÅ [1] Ä Ö ½ÅØ ÍÄË Ð, Õ Ë Ê Ð Ò. Ù Þ ÏÅ ÅØ ÍлÉ, ¹ ÕÉ Þ Û µ À Ä Ó [2 6], «¼ ÁÅØ Í Ð ¼. Û Ö Ï ½ÅØ ÍÄË Ð ÖÏ, ÛÀ Û ÜÀÅ ¾ ÍÓ Ë Ð Þ. Þ ÏÅ ËÆ Ó ÐÙº, Á¹ Å [7 9] [10,11] Ë ½ [12,13] Ó, Ó Ä ÚÐ À ØĐ Þ ÏÅ Ð «, ÓÆÅÀÕ ÖÏ Þ ÏÅ Ð Ð. ÀÞÄË (molecular dynamics, MD) ÄÛ ÞÐ ÅÀÕ ÖÏ, Ä ËØ Ø ÄÐÙºÆ, ÉÐÅÀÕ Ä, «ÆÅ ¾ÄË Þ ÅÀ Ð ¼, ÓÆ Ã Þ ÌÐÅÀÕ. ÆÅ ¾ (quasicontinuum method, QC) Ä ÅÀÕ ³, «Õ ÐÚ, ¼ Õ Ø ÕÀ, Þ Î [14 16] Þ Ï Å [17 22] Ò [23,24] ÐÕ. Û, ÐÞ ÏÅ µõ ßÐ Í ±³Ð Ð, «Ù Þ ÍË ±³. ÍлÉÀÄË»ÐÉ, Í ¼ À Þ Ð±³ À ¾Ó», ÓÆ ±³ Þ ÏÅ ÐÙº. [25 29] Æ fcc Þ ÏÅ ±³Ð, Ä ±³ ÍÞ ÏÅ ÐÙº ¼ Ò ±³ ÍÞ ÏÅ Ð Â ³. ºÞ ÆÅ ¾ Õ Ë ±³À ±³È Ð Al ÅØÞ ÏÅ, É º Ò Î ¼Ó, Ë ±³ Þ ÏÅ ÐÙº. 1 «Ø Ý Ü 1.1 Þ QC Ä Tadmor [30] 1996 É ÕÀÐ µ, Ð Ä: ÀÞÄË Â, Ó Ð ºÞ ÅÀ (representative atoms) Ê Ø Ú; Ó Ð ºÞ ÅÀ Æ., ÖÕ ÅÀ ÜÐ Þ, «Ü ²ÅÀ Ø, ÜÐÂ, Õ Ø Ð ÕÀ, Ø ºÞËÂÅ, ²«ÅÀ Ð «Ð 1 ³Ð ² Al Ý ÎÄ Æ ÀÑ Fig.1 Schematic of local and non local representative atoms and tessellation during nanoindentation on ( 1 12) plane of Al film with initial defect [31 33]. Al ÅØ Í, ºÞ EAM Ã Õ Ð. fcc Al ÅØ, ºÞ Ercolessi À Adams Ð EAM à [34], ÍÐ a 0.4032 nm, Burgers É b 0.285 nm, Ð ÕÉ µ 33.14 GPa, Poisson ν 0.319, (111) Ð γ 111 0.869 J/m 2. Ð 1 ±³ Al ÅØÞ ÏÅ Ð ÅÀÇ ÁÒ Ð, Ð ÀË µ µ ÅÀ, Ú Á µ ÅÀ, Ú Á µ ÅÀ. ºÞ Ó Å, ±³ ºÞ ÅÀÐ, «ºÞ ʼÐ, Ó Ð «ÂÅ Ü, É«ËÕ Â Ã ÐÅÀ Û, Ì 100 nm 0 nm Ð Al ÕÅÀ Ü,  à ÐÅÀ Û Ô ², ¾ ÀºÞ QC ÅÀÕ ¼ «Ø ÐÚ Õ Ø, ²Õ ÆÙÐ PC. 1.2 Ú Ë ±³ Þ ÏÅ ÐÙº, ±³À ±³È ÐÞ ÏÅ Ë µõ. ÏÞºÞ ÏÞ, ÏÞ«110 {111} [ 110] ½Ïº Al ÅØ, Ç ² ½ÏºÅØÄÓ ½ À ¾ ÎÐ À. Ë Õ, Õ Î Ù Õ À Ó Þ ÏÅ ÐÙº, Ú ±³ Þ ÏÅ ÐÙº. Þ ÏÅÕ ÁÒйР2 Á, ÅØÐ L 0 nm, H 100 nm, ÏÞÐ d 0.932 nm, ±³ Ð l 0.7 nm, h 2 nm, ±³ ÏÞ

2 ¹ Ñ : Al ÖÜ ÍÃ Ó 131 2 Ý ÎÄÔ ÀÑ Fig.2 Schematic representation of the nanoindentation model (a) defect free (b) with initial defect е s 2.15 nm, Õ Ä Ð z ½, ² Ü 2D Ð Ã. Ï Þ Al Ø ºÞ Ù Ð ØĐ, ¼ Ð Ý, ³ É 0.02 nm, ¹Ý 60 ³, Ç ÐÏÞϺ 1.2 nm. Al ÅØ ÈĐÈĐ«Â, Õµ Õ, ÏÞÐ ÄÅØ Ð 1/0, ÏÞÐÇ Ïº ÅØÊ Ð 1/100, Ö Á ÐÙº. 2 Ó Ð 2.1 Ö ² ³ È ÐÞ ÏÅ µ Õ, Ë Ð º. Ð 3 ÁËÈ Ð º (, P ÏÞÄ ËÐÄ Á, N/m; Ï º η y Ó ÏÞÐ, nm). ÉÐ ¾ À, È ÏÞ ÅØ ÍÐ ÚÐ, Ó È Ð º à º Ú, ²Ý ß Ë È Ò Ð. Ý, ÈØ ß Ë ², Ä Ý ÏÞ Ð Al ÅØ ÍÉ. ÆÈ Ï ÐÇ 14.70 N/m (A Ú, ±³ ) À 13.82 N/m (A Ú, ±³ ), ±³ Ï ÐÇ ±³, Ä ±³ ÏÅ ÐÙº, Ä Ùº. Ç ÚÌ, ÈØ ß À ²ß Ð, ÚÚ B ( B Ú), ÆÏÞÐ 0.5 nm, 7.69 N/m, ß ÐÅÓÄÏÞ ÐÅØ Í¼, Ò, ÏÞ 0.48 nm ÄÏÞ ÅØ ÍÉ ½ Ð Ï Ú, Æ ÐÞ Û µ 15.8 GPa ( ±³ ) À 14.8 GPa ( ±³ ), ± [35] ÐÛ µ (14.7 GPa) Â. Ù 1 È Ð P, N/m Defect-free With initial defect 16 C' A C A' E' E 12 D' 8 F' F B' B D 4 Elasticity Plasticity 0 0 2 4 6 8 10 12, y 10-1 nm 3 Al Ý ÎÄ «¹Ö µ Fig.3 Load P vs displacement η y response curves for nanoindentation of single crystal Al thin film ß ³Ì, ÈØ ¼, ÏÇ C Ú ( ±³, ÏÞ 0.76 nm, 15.73 N/m) À C Ú ( ±³, ÏÞ 0.82 nm, 17.13 N/m). Ì D Ú ( ±³, ÏÞ 0.78 nm, 8.43 N/m) À D Ú ( ±³, ÏÞ 0.92 nm, 12.79 N/m). È Ðß, ÆÈ Ð Ú, : ±³ Ð Ë Þ, Ä Ð ß, ¹ Ð 3 C D Á. ÉÐ ¾À, ±³ È Ð ÐÙº, Ë ±³, º Ð Ç µ ±³ Ð 9%, ÏÞÐϺ 17.95%, ÒÅ Ë ±³ ÝË Ù 2 È Â ÐÏ, ±³ Ù 2 È Ð Đ ÊÞ. Ù 2 È Ì, È E Ú ( ±³, ÏÞ 1.04 nm, 16.05 N/m) À E Ú ( ±³, ÏÞ 1.02 nm, 15.50 N/m), Ì F Ú ( ±³, ÏÞ 1.1 nm, 10.03 N/m) À F Ú ( ±³, ÏÞ 1.12 nm,

132 Ì È 45 10.40 N/m), ±³ Ù 3 È Ùº, Ä ±³ Ð Ë Þ, ¹Ð 3 E F Á,, È Ð ±³ ÐÔ, Ä ÏÞÝ ÐÝ, ±³ ºÅØ Í Ð. 2.2 ³ÎÆ ²ÎÛ ÎÄ Ð ±³, Ë ±³ Õ ÐÅÀ Î, Ð, ² ÂË. E ȵ Æ : µ  ΠРE c, µ  ΠРE e [36]. ÅØ Í Ë ±³, Õ Ü Ð, É«º Ü Ð. Ù Üà ÉÐ, Þ ÏÅ Ð. Ð 4 Al ÅØÞ ÏÅ Ð (, E Ð ev, ÏÞϺ η y Ð nm)., ²Ý È Þ, ÄÃÐ ÃÄ Ð, ÄÓ ²Ý ÅØ Í ÖÝ, º Ö Ý. ÉÐ 4 ¾À, ±³ Ü Ð Ùº, Ý Ð È Ò ß, Ü Ë Þ. ÅØ ÍÉ ½ Ï Ã, ÓÏÞϺ 0.48 nm, È Ð 24.68 ev ( ±³ ) À 37.26 ev ( ±³ ), ±³ Ð ±³ Ð, ± ³ º Ü ÝË 50.97%. ÌÐ ÈÈ ß Ð Ü 30.46 À 38.90 ev ( ±³ ) 49.51 À 53.70 ev ( ±³ ), ÝË 62.54% À 38.05%, ²Þ ÏÅ ±³ Ð ±³. ± Î [36] ², ÍÐ Ð E, ev 70 60 50 40 30 Elasticity Plasticity Defect-free With initial defect 53.70 ev 49.51 ev 37.26 ev 38.90 ev 24.68 ev 30.46 ev 10 0 2 4 6 8 10 12, y 10-1 nm 4 Al Ý ÎÄ Ö Đ «µ Fig.4 Strain energy E vs displacement η y curves for nanoindentation of single crystal Al thin film, Í µ Ð. ²Þ ÏÅ ÏÞ Ïº, ÅØ Í µ, º Ü Ý. ± ³, ±³ ºÅØ Í µ, ÓÆ Ùº, Õ º. ¹Ð 4 Á, ±³ Ð ±³ Ð 3. 3.1 µ Ë ³ ±³ Þ ÏÅ ÐÙº ¼, ¾ÅØ ÍÞ ÏÅ ÐÅÀ»Ð, º Ð È ß ß ÎÐ [21]. ²ÏÅ È À Ë È Ðß, Ó ²Ý À Ë È Î. ÉÐ 3 º ¾À, ±³ Ù 1 ÀÙ 3 ÎÐ Ùº, Ä Ù 2 È ÎÐ Ùº, Ȳ : (1) Î ÐϺ, ±³ÐϺ ± ³ 17.95%; (2) Î Ð, ±³Ð ±³ 9%. Ð 5 Ý Ù 60 ³ ÏÞ Î»À ÅÀ»Ð. ÉÐ Ö¾À, ²Ý ¹ Ë¼È Î (dislocation dipole, DD). ±³, Ϻ Ð Ý, ÏÞÐÈĐ ÈĐ Æ Ð ÄÐ. ÏÞÈĐÈĐ ¼ Þ ½Î (stacking fault, SF)  РÉ, ÏÞÈĐ¼Þ½Î, ½Î Î, Æ ÏÞÝ Ð, ÉÐ 5a ¾À, ÏÞ ÈĐÈĐРΫÐ. ±³, Ϻ Ð Ý, ÁËÏÞ ÈĐÈĐ, ±³ÈĐÕ Ð ÄÐ, ÏÞÈĐÈĐ Ð ±³ÈĐ Ð, º ÏÞÈĐÈĐ ¼Þ ½Î, Ù 1 Î. Ì ±³ÈĐ ÄÐ Ð, º Ð Ý, ¼Þ ½ÎÂ Ð É ¼Þ нÎ, ½Î Ù 2 Î, ÆÏ Þ Î Ð. ¾Ð 5b Рλ, ¼Þ ½ÎÐÚ ¼ Ð, Ó Ù 2 Î ÐÚ ±³ÈĐ ² Ð ÄÐ, ºË ÍÐ, Ë ¼. Ð 6 Ù 2 Î ±³Õ ÌÓ ±Ð. ÉÐ Ò Ö ¾ ÌÐ. Ð Æ Ë É, º±³ÈĐ, ÆÐ

s2 B- m : Al rxfuk<;j B o 133 x et &? F#CVy g Æ G G. 5 60 Fig.5 Contour plots of the out of plane displacement (left) and dislocated and atomic structures (right) beneath the rigid knife like indenter at 60 steps (DD dislocation dipole, SF stacking fault, ηz the out of plane displacement) (a) defect free (b) with initial defect V 7Jbl Q, #LkDF 7>l V, W z D* # y*, u 3 VvM Wz DF 7, on, u 3 VlDF 7>==b SWzlu., SFF%'u.#Z, } 3 4l D h.s!* \ ; $BS ev. #&zhwm> = 4, F F%' u 1 H u 3 VlDF 7u.#Z, `L u 2 P VlDF 7>=(~n"l ARz, -} 3 fi, FF%'d.Su 2 VDFH 7 / ;S h, QWz hf%'p, V 7 T d~x > $3, -} 6 fi. q X >, F F% ' PZQs,U(~") Rz; `LbX

134 Ì È 45 6 Ø 2 «Í ²Ô ÏÆ Ò Ö Fig.6 Von Mises strain ε distribution of crack propagation at the 2 nd dislocation dipole nucleation and emission during nanoindentation with initial defect, before (a) and after (b) cleavage occurred Ì, ±³Æ ÈÐ É,, Í. 3.2 Peierls ³ Ë ±³ Î ÞÐÙº, ³Ò Î Þ ËÐ Ú ÅÄ Peierls Ä. ÁË Ù Ä³, ÅØ Í Ð Î Ë È ²ÄÐÊÞ, ²Ä ÏÞ Ä Õ Ð Þ Î½ Í µ Ð Peach Koehler Ä F PK, ²Ä ν Í ÐÜ¼Ä F I, Î Í µ ËÐÄ ÄÐÃÀ [17]. Î Í µã «Ç F PK + F I = bσ p (1), b Burgers ÉÐÕ, σ p Peierls Ä. ÏÞ h ÃÐ Peach Koehler Ä F PK (h) = bσ xy (h) (2), σ xy ÏÞ ÐÐ Ä. 2a Ð Ù ÏÞ, σ xy Á [17] σ xy = Pr2 sin θ [ π(r 1 r 2 ) sin θ 3 ] 3/2 2 (θ 1 + θ 2 ) (3), P ÏÞ ; (r, θ) ÏÞ h à ΠРË, Á r = a 2 + h 2, θ = arctan(h/a), ÏÞÈĐÈĐ Î, Á (r 1, θ 1 ) À (r 2, θ 2 ),, r 1 = h, θ 1 = π/2, r 2 = 4a 2 + h 2, θ 2 = arctan(h/(2a)). ÊÞ Î ÐÜ¼Ä [ F I = µb2 1 π(1 ν) 4h 4h3 (4h 2 3d 2 ) ] (4h 2 + d 2 ) 3 (4), d Î Ð. Î «ÇÐ h Ø À Î ËÐ Peierls Ä, Ù Õ Ð È Î «ÇÐ : H 1 =8.5 nm, H 2 =14.5 nm, H 3 = nm ( ±³ ) À h 1 =8.5 nm, h 2 =16.3 nm, h 3 =22.3 nm ( ±³ ), Ø Ð Peierls ÄÒ ±³ Peierls ÄÐÙº¹ Ð 7 Á, Õ ± [37] Ð Peierls Ä 0.9 35 MPa Â. Ð ², ±³»Ë Í, Ë¼Þ ½Î РÉ, Ð, ºÙ 1 Î, Ú ÅÄ Ô, ÎË Ð Peierls Ä. ÌÐ Î, ±³ ÎË Ð Peierls Ä ±³. ±³ Ù 2 ÎÐ Peierls ÄÙºÇ, ºÙ 2 Î Peierls Ä ÝË 25.73%; «Ù 3 ÎÐ Peierls ÄÙ ºÆ, 4.28%. Ä ±³ÈĐ

2 ¹ Ñ : Al ÖÜ ÍÃ Ó 135 P, MPa 40 30 10 0 Defect-free With initial defect 22.82% 5.22 4.25 10.65 13.39 25.73% Influence quantity 34.74 36.23 4.28% 1 2 3 Dislocation dipole 7 ÎÝ «Í Peierls Öà 35 30 25 15 10 5 0 Influence quantity, % Fig.7 Peierls stress beneath the indenter σ p vs dislocation dipole P cr, N/m 18 16 14 12 18 (a) (b) QC method Dislocation theory 1 2 3 Dislocation dipole ¼, ¼Þ ½ÎÂ È É, ÝË Î ÞÅÄ; «½Î¼Þ̱³ È ÉÐ ÄÌ, º Î ÞÅÄ. 3.3 Ð Ö ±³ Î ÐÙº, Î Â Ð, Î «Î «. ³± Tadmor Ó [17] ºÞРΠɽ ², Î ³ ÜÐÃ É U be = 1 2 P crη cr = 1 2 kη 2 cr (5), P cr Î Ð, η cr Î Ï ÞϺÐ, k Å Ð. Î Ì, ÏÞϺР(η cr b), Æ ÜÐ Ã É U af = 1 2 k(η cr b) 2 + U (6), U ΠÝÐ É. Ü Ã ÉÊÈ ², (5) Ó (6), P cr = U b + 1 kb (7) 2 Î Î ÀÏÞ Ä ³ÞÐÊÞ, U ¼µ ÉÆ : (1) ܼ Ð µb 2 [ U I = ln 2h 4π(1 ν) b + d) ] + ln2(h b (2) à «Ç»Ð Î ÏÊÞ Ud min µb 2 2a = 2π(1 ν) ln2 b (3) ÝÐ (8) (9) U γ = 2γ 111 b (10) (8) (10) º (7) Î Ð P cr, N/m 16 14 1 2 3 Dislocation dipole 8 «Í Á Fig.8 Load necessary for dislocation emission P cr vs dislocation dipole (QC quasicontinuum method) (a) defect free Ø Ï P cr = (b) with initial defect µb + 2a)a2 ln32h(h 4π(1 ν) b 4 +2γ 111 + 1 kb (11) 2 ÏÞ ÀÈ Î ÐÏ º, Ø À Î Ð. Î Ø Õ Ð, ¹Ð 8 Á. ÉÐ ¾ À, Õ Ø Î Ø Â. Ð 8a Ò, ±³, Ä Î Ø ÄÕ ß Ò, Í ÐÝ, µ Î Â Ð, Î ¼Þ, ÄÓ Ð ÝÏÞ Ð Î Ý, º Í Ð ; Ð 8b Ò, ±³, ± ³ Ù 2 Î Â Ð Ùº, Ì, ÄÓ ±³ Õ Â È É É Í Ë µ ÊÞ, Ì Í º. 4 (1) º Ð È ß ß ÎÐ, ²Ý È À Ë È Î. ±³ Ù 1 Î ÔÍ Ùº, È ÎÐ ÌÏ

136 Ì È 45 Þ ÅØ Í¼ É ½, Ï 0.48 nm, Æ ÐÛ 15.8 GPa ( ± ³ ) À 14.8 GPa ( ±³ ), Â. ±³ Ù 2 Î Ùº, ÎÐ Ò ÐĐ ÊÞ, Î À»ÉÏÞĐĐ ±³ÈĐ,. ±³ Ù 3 Î Ùº, Æ Í. (2) ²Ý ÅØ Í Ý, Ý. ±³ ºÅØ Í µ, ÓÆ ±³ Ùº, Õ º, ¼È Î º ÝË 50.97%, 62.54% À 38.05%. (3) ±³ ¼Þ ½Î Â È É, ÝË Î ÞÅÄ, ÓÆ ±³ Ù 2 ÎÐ Peierls ÄÙº, «½Î¼Þ̱³ È ÉÐ ÄÌ, Î ÞÅÄ ; Ù 3 Î Ð Peierls ÄÙº. Õ Ð Peierls Ä Â. (4) Õ Ð Î Î Ø Â. ±³, Í ÐÝ µ Î, Î Â Ð, Î ¼Þ, Í ÊÞ; ± ³, ±³ Õ Â È É É Í µ ÊÞ, Ä Ì, Æ ÈÐ É,, Í. Dr. Ellad B. Tadmor (Aerospace Engineering and Mechanics, University of Minnesota) Ô Õα. [1] Oliver W C, Pharr G M. J Mater Res, 1992; 7: 1564 [2] Li X D, Bhushan B. Mater Charact, 02; 48: 11 [3] Bamber M J, Cooke K E, Mann A B, Derby B. Thin Solid Films, 01; 399: 299 [4] Bhushan B, Koinkar V N. Appl Phys Lett, 1994; 64: 1653 [5] Chen J, Bull S J. Thin Solid Films, 06; 494: 1 [6] Sangwal K, Gorostiza P, Sanz F. Surf Sci, 00; 446: 314 [7] Zimmerman J A, Kelchner C L, Klein P A, Hamilton J C, Foiles S M. Phys Rev Lett, 01; 87: 165507 [8] Shankar R M. Appl Phys Lett, 07; 90: 171924 [9] Kiely J D, Hwang R Q, Houston J E. Phys Rev Lett, 1998; 81: 4424 [10] Yang B, Vehoff H. Acta Mater, 07; 55: 849 [11] Soifer Y M, Verdyan A, Kazakevich M, Rabkin E. Scr Mater, 02; 47: 799 [12] Liu Y, Varghese S, Ma J, Yoshino M, Lu H, Komanduri R. Int J Plast, 08; 24: 1990 [13] Kiely J D, Houston J E. Phys Rev, 1998; 19B: 12588 [14] Phillips R, Rodney D, Shenoy V, Tadmor E, Ortiz M. Modell Simul Mater Sci Eng, 1999; 7: 769 [15] Shenoy V B, Phillips R, Tadmor E B. J Mech Phys Solids, 00; 48: 649 [16] Ni Y S, Wang H T. Chin Q Mech, 05; 26: 366 ( ½, Ñ ÃÊ ½, 05; 26: 366) [17] Tadmor E B, Miller R, Phillips R. J Mater Res, 1999; 14: 2233 [18] Shan D, Yuan L, Guo B. Mater Sci Eng, 05; A412: 264 [19] Iglesias R A, Leiva E P. Acta Mater, 06; 54: 2655 [] Li J W, Jiang W G. Acta Metall Sin, 07; 43: 851 ( º, ÍÊ, 07; 43: 851) [21] Jiang W G, Li J W, Su J J, Tang J L. Acta Mech Solida Sin, 07; 28: 375 (, º,», Ð ¾ÖÃÊÊ, 07; 28: 375) [22] Ni Y S, Wang H T. Chin J Mech Eng, 07; 43: 101 ( ½, Ñ Ê, 07; 43: 101) [23] Tadmor E B, Hai S. J Mech Phys Solids, 03; 51: 765 [24] Miller R, Ortiz M, Phillips R, Shenoy V, Tadmor E B. Eng Fract Mech, 1998; 61: 427 [25] Gannepalli A, Mallapragada S K. Phys Rev, 02; 66B: 104103 [26] Jarausch K F, Kiely J D, Houston J E, Russell P E. J Mater Res, 00; 15: 1693 [27] Smith R, Christopher D, Kenny S D, Richter A, Wolf B. Phys Rev, 03; 67B: 245405 [28] Van Vliet K J, Li J, Zhu T, Choi Y J, Yip S, Suresh S. Solid Mech Its Appl, 04; 115: 3 [29] Kelchner C L, Plimpton S J, Hamilton J C. Phys Rev, 1998; 58B: 11085 [30] Tadmor E B. PhD Thesis, Brown University, Providence, Rhode Island, 1996 [31] Tadmor E B, Ortiz M, Phillips R. Philos Mag, 1996; 73A: 1529 [32] Tadmor E B, Phillips R, Ortiz M. Langmuir, 1996; 12: 4529 [33] Shenoy V B, Miller R, Tadmor E B, Rodney D, Phillips R, Ortiz M. J Mech Phys Solids, 1999; 47: 611 [34] Ercolessi F, Adams J B. Europhys Lett, 1994; 28: 538 [35] Minor A M, Lilleodden E T, Stach E A, Morris J W. J Mater Res, 04; 19: 176 [36] Hirth J P, Lothe J. Theory of Dislocations. New York: John Wiley and Sons, 1982: 757 [37] Kosugi T, Kino T. Mater Sci Eng, 1993; A164: 368