SIMULATION OF SCALE DEPENDENCY ON TENSILE MECHANICAL PROPERTIES OF SINGLE CRYSTAL COPPER NANO ROD

6 È 1 Vol.6 No.1 1 ¾ 1 Ä 1173 118 ACTA METALLURGICA SINICA Oct. 1 pp.1173 118 Ø Ô ± Cu ÌÅ ÀÓ Ð Õ ÐÉÎ ß Ð Đ ( Á, 151) Ý Ý Ý Û Cu µ Ñ ÝÎ ß µå ÚÅ ¼. ¾ÎÙÙ ºÆ ¼ Ý Ñ µæ Ý Ë µ ÑÚŵ Û, Cu µ ÑÚŵ ÛÀ. ¼ Ì : Î̹Ô, µ È Ý Ñ Ù² Å ½Ù² Û» Þ ÖÍ, Õ Ý; Ý µ Ñ ÝÛà ²Ò, µ ÑÚŵ Û ²; ÛË, ÞÜ Ý Ûµ Å Î̹, ̹¼Ú Ò Ò ËÛ ; Ý Ý µ, Ý Ý µ Û̹¼ÚÛ Û«²Ò, Ò Û Û«²; Ô Ë 5 nm Ô, ÞÜ Ý µ ÛÒ Ç Á, µ Ñ 8 GPa. ± Æ Ô, Ë µ Û ÑÚŵ Æ. µå ÚÅ, Ñ, µ, Ý, Úŵ Ý º¾ TG113.5, TB33 à A Ù 1 1961(1)1 1173 8 SIMULATION OF SCALE DEPENDENCY ON TENSILE MECHANICAL PROPERTIES OF SINGLE CRYSTAL COPPER NANO ROD BAI Qingshun, TONG Zhen, LIANG Yingchun, CHEN Jiaxuan, WANG Zhiguo School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 151 Correspondent: TONG Zhen, Tel: (51)86138, E-mail: hit tz@163.com Supported by National Funds for Distinguished Young Scholars (No.59551) and National Natural Science Foundation of China (No.5753) and Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (No.HIT.NSRIF.91) and Natural Science Foundation of Heilongjiang Province in China (No.E93) Manuscript received 1 6 3, in revised form 1 8 ABSTRACT The tension process of single crystal Cu nano rods with different cross section shapes were simulated by molecular dynamics at atomic scale. Based on centrosymmetry parameter method and combined with the dislocation nucleation theory, the effect of cross section shape, cross sectional area and slenderness ratio on the tensile mechanical properties of the nano rods were analyzed, and the scale dependency of tensile mechanical properties of the single crystal Cu nano rods has been studied. The results show that after first yield, the nano rods produce plastic deformation under the dislocation nucleation extended dislocation and sliding lattice atom cross slip mechanism of the alternating cycle. The geometry of cross-section has negligible effects on the tensile initial plasticity of the nano rods, while it shows apparent effects on the tensile mechanical properties. With the increase of cross sectional area, two types of nano rods have the phenomenon of early yield point, yield strength decreases and Young s modulus increases. Compared with that of the square cross sectional nano rod, the variable rate of yield stress of the circular cross-sectional nano rod is smaller and the variable rate of Young s modulus is larger. As the cross sectional area increases to 5 nm, the Young s modulus of the two types of nano rods become stable, and is close to the theoretical value of 8 GPa. Moreover, the slenderness ratio of the nano rods has a slight effect on the tensile mechanical properties when the * ʻŠŠ± 59551, Ê Å ± 5753, Å Ê ± HIT.NSRIF.91 Ø Å ± E93 à : 1 6 3, ¾ : 1 8 : Ä,, 197 Õ,»±, ± DOI: 1.37/SP.J.137.1.66

117 6 È simulation size increased. KEY WORDS molecular dynamics, tension, nano rod, dislocation nucleation, mechanical property ÖÉ (MEMS) Ü Î ÖÉ (NEMS) ÜÆ [1], À ÆÓ Đ¾ Á Î ÜÛ«Û«Đ. Ü, Û«Đ ÌÐ Ä Þ ¹. Á Ü Ó, Ú Ü É ß,, Ü Þ Ò Û«Đ Æ º ² ÔÓ Ü Đ. Michalske Þ [] É Û Û Ú, º Àͺ½Û ± Æ Ü Ó ( 5 nm Ø 5 nm) Ì. Greer Þ [3] É É Ð (. 8 µm) ÜÐ Au Ð Û Ú, Ð Au Üͺ½Û ØĐ GPa Ð, Áͺ½Û Ì º Ü Ó. Ñ Å ÃÛ ½ Ü, ² Û ÜÁ Ü ³ Å., «Ü ½ Šн Û«ĐÜ Ú, É º Û«Ü «Û«½ ÏÙĐ ¹Ü Í. Komanduri Þ [] Á ÎÜ fcc «(Al, Cu Ni) bcc «(Fe, Cr W) ÜÒ Þ Đ³ Ð. Ý Þ [5,6] Þ [7] Ô «Û«½Đ K ÎÒ Cu ÜÒ ÞÏ, ĐĐ Ü Õ Þ Ï Ò, Å Ü½Û ½ ÃÉ ½ Ô½ Ô½Á Ô½. Doyama Þ [8] Nozaki Þ [9] ¹ «½Đ «Ü Ð Cu Ü Ò Ë Ï, ½Û ÚÉ, Ö Þ ÜÀ. Ð Þ [1] ĐÐ Ni É K ÎÜ Ò ÝÏ, ½Í Ni Ü Đ, Ni É Ï Æ Ü Đ. Ý ÌÞ [11] Ô «Û«½Đ Õ ÜÒÏ, Ï Ç ÙĐ Ò ÜÒÛ«Đ. Tschopp McDowell [1] ½ĐÐ Cu ÜÐ Ò Þ, Đ ½Û Ð Cu Þ. Þ [13] Đ K Î Cu ÉÐ ÒÇ ÎÓĐ Đ¹Ü½ Ô½Á Ô½. Û ½½Í, º Ü Đ Ä ÜÁ ± Đ., ² Ü, Ú Ï Þ¹ Þ ÓÁ Ü, Þ¹ Þ Á Ü ³. ĐÓ Ð Cu ÜÒÛ«Đ, À ØĐ ÝÇ ÎÜ Þ Þ¹ Þ Ü Ü, Ï Ç Ù Đ ÜÛ«Đ, ÇĐ¹ Þ ¹ Ì Û«Đ¹Ü, ĐĐ ÄÁ ÎÐ Cu Ò ÞÜÁ ± Đ. 1 ÈÍ»¹ 1.1 ÊÏÊ µ Þ Þ¹ ÜÄÐ ÜÅÆ Ö, 1 Đ. x, y z Ð ½ fcc Ü [1], [1] [1] ; ¹ yz, x Ð Ò, «ÕÅÒ. Ù Û Ü² ½Í, Ü ØÚ Ê¹ ½, Ú, É Ò ÜÊ Â Ü Ï, ÕÜ Þ 1d 1e Đ. ß ÉÒÏ ÚÈ, Ò½ ÊÏ.61 1 8 s 1. 1 Cu µ Û Fig.1 Initial configuration of copper nano rod (a) schematic of reference frame (b) copper nano rod with circular cross section (c) copper nano rod with square cross section (d) copper nano rod with circular cross section after relaxtion (e) copper nano rod with square cross section after relaxtion

~ 1 ; 1. K y : j= Cu ( alu (}vg\#e} / 1w ^Zx Cu E g x as 7-7*V { ~! x EAM EdE [1] : X 1X φij (rij ) U= Fi (ρi ) + i (1) j6=i ρi = X ρj (rij ) () j6=i ~v, U AQ5xÆ-}, ρi O i <E *;x!;?"e x a; Q i <E P6 r x M g, rij i <E? j <E g xml. Fi (ρi ) Ed-; φij (rij ) g, ρj (rij ) A x * (. Q Q5E x Virial 1w αβ [15] -A Y αβ = 1 X 1 XX α β (3) mi viα viβ + Fij rij Ω i i j6=i ~v, Ω AQ5. ; mi vi AE i x t } ; Fijα AE i?e j g x 7 w; α, β A Cartesian * } l ; rijβ AE M i } ~rij (= ri rj ) β x 65. Q 3W* Virial 1w ue i xe 1w αβ i Y αβ i σiαβ = 1 X ωi σiαβ Ω i 1 X α β 1 = mi viα viβ + Fij rij ωi () (5) j6=i ~v, σiαβ AE i xe 1w, ωi = Ω, ωi AE i x ;p.. k * - 7 Verlet [16], 3W Nose Hoover $ [17,18] G. o 93 K, OW C v - 7 {Q5 D l x G 93 K. nw CvE,*Z\-7vv </ (Centrosymmetry Parameter)[19] d y. E i x vv </ A P 6 9 L=6a, Gz - Æ E R=11a, $z - 9 A=a (a =.3615 nm, A Cu l? x? ; 7 ). * 6 < nwcx1w 1 S_ :!,?K* 6 zx&z$, < nwc*a 3 <+ : o z+ (OA ) V+ (AC ) + (CD ). L;&- z x* 61w 1 S_ x. xp "p. Q o z +, * 6 x1w 1?_ KQ, Y*NuGz $z- z * 6xo!}* A 71.6 8.1 GPa. \ Q1 &^I V, $z- * 6V z-w Gz- * 6G, \?ml I V* 6 x w * ;! &. Q A (ε=.9), { y - z x * 6 x 1 w v at dk, Y? -A* 6xL}U.1w. 9:Y*U N, $z- z x* 6xL}U.1w Xd=Gz - z x * 6. 1 xd O, { y* 6 x 1w 1 S_?NF $ V ". : 3 * AGz $z - z x * 6Q nwcvxz\e x:. 9: 3a : a Y*UN, L ;&- z x* 6Q E C= >q, 9 xe 9= Y w x 7, z6 ln? ;Fq, :v! * 6 x nh = he. Q o z +, * 6E x? ; r _ n 9, za o z; * 6,*LF`6r, 8;j}xE A ati *x - } 7 j ', X 6 rj }[ F. Q o zq=, E uu ;.ÆY[x J 1 Table 1 The default value of atomic defects structure in centrosymmetry parameter Lattice structure ~i + R ~ i+6 R P <3 Yellow 3< P <5 Cyan Stacking fault 5< P <9 Blue Surface atom 9< P < Orange Whole dislocation P > Red 8 Elastic Plastic extension Fracture stage A (6) i=1 ~v, R~ i R~ i+6 A fcc? ;a < E x 6 i }. HvE Z\1Gy xk 1!.?. 1 G x L x C - 7 E i* ( (radial distribution function, RDF) d b. a=njz'slb[7!v A G- z * 6 nw * x5e, k { y - z * 6 x9? - a,?v, * Represent color Ideal fcc structure Stress, GPa ρi = Pi Partial dislocation 6 6 X 1175 C B D....6.8 1. Fy #y, y k> Cu ) 5bmv R^ Strain Fig. Tension stress strain curves of single crystal copper nano rod with circular and square cross section shapes

1176 5 Fy, y ) 5bm ywd ~ 6 P F w9 3 Fig.3 Evolution of defects in circular cross section nano rod during tensile process (a) ε= (b) ε=.89 (c) ε=.9 (d) ε=.9 (e) ε=.16 (f) ε=.857 (g) ε=.87 Z\N O, v, * 6, * RE } ~ T, j}[ J " z>[ FY IE B'M_ XT, : 3b b v! xhh he. 9: 3c c Y * U N, Q ε=.9 v, { y* 6!xx 9 R;F`T }za, * 6:d WU. +. 1 xd T, F ` Q 9 P za # {111}v'Qv'. * 6 n j x - } QF ` N v ', * 61 w V ". \ 9=Q* I V, F`v'x[ ;, h^ <v' T}'. Q1 w 1 S_i x ZA: qat +k1 w *q, 1 w r8 ", qq"< ' o x 1 w 7 < ` r ( :! AB ). i Zk, F ` za rq gd, Q* I V, 7 l?, xl }U. 9F`zaQ x. \yzk ew S,;aK [ l? Cu w * x G1U [11,]. WU.*q, F`{~ `Vz> <= x `, #Q* 6 r>f`n x#+, : 3e!. q1wj t" kq, d}txf`qv' i i, # Qv' x $3 P R > F ` g, ` a s $ ` m F `x : " ) ` V, { u 1 w ;!~s. q 1 w is t *V F ` N v, F ` T } n, * *? ;E v' : $v'. UWC ZA1w 1 S_? N F $ V " ( :! BC ). * 6Q F`za F` n?v'?;e $v' x$ Æ{ 7 sv, 6r V. 1 xd O, * 6 9 ~ n 9, h E ~ o, * 6, *? ;Z \ v x* F T } 6 r k ml x A Zk, : 3f f!. : 5 A D= (ε=.85), {y- z * 6x E i* ( :. 9: Y * U N, Q D=, * 6 x ; X " {, 8? Æ C ; X " {, v 9C ; ZA~)L $. 1f nwcx E x: (: 3f f) Ei*( Y*UN, * 6Q +, A Qx**?;E?Z(?$, 1 e

~ 1 ; K y : j= Cu ( alu (}vg\#e} / #y, y ) 5bm ywd 1177 F w9 Fig. Evolution of defects in square section copper nano rod during tensile process (a) ε= (b) ε=.89 (c) ε=.9 (d) ε=.9 (e) ε=.11 (f) ε=.917 (g) ε=.91 O, un 3! x 1 K. v, Gz $z- z x* 69 RA L=6a. 3 v, A f $z - 9, R f Gz - Æ E. L } o!}a.< ε <.1! x o x_ 1fk, q= o! } A.3< ε < εσs! x o x_ 1fk (?v, εσs AU. 1x1 ). 8 Radial distribution function 6 1 Radius, 5 a 3 ) 5 C<Dh)'\Æ9 (ε=.85) Fig.5 Radial distribution function of nano rod with cross section at ε=.85 xd O, A Qv **xe M d, d} E, * 6h E O T, wwz* 6 x (: 3g 3 >OO:,Y3X*)sh X 3 Yf, - xtd, {y- z x * 6 R N ZU.1,D, U.G " {x Zk. \yak x&^1uq?"* 7x!1? 3.1 [7,1] *I xw v ;! Z, \ I^p1? * I V fcc 7?., x:. Hirth z [1] U G WF ` za n # > N F `{z>x 9- G x a~ [,3] G = πrw πr bτ + πr γ (7) v Gb r ln (1 v) π r (8) g). =NN9+SLB[Gn_k'rg Aod G- * 6 n w * x 5e W = ~v, W F ` {_-, r F ` { Æ E, τ 7QF

1178 6 È Ý Ý µ ÛÀ ¼Ì Table Size parameters and simulation results of circular cross section nano rod Group 1 3 5 6 R/a 11 17 3 8 3 Real size, nm 5 118 17 3 7 656 Surface atoms, % 5.9. 3.3.9.5.3 Yield strength, 5.9 6. 6. 6.7 5.63 5.77 GPa Yield point.9.9.87.8.77.76 Initial Young s 5.3 6.9 6.7 66.99 71.3 76. Finial Young s 71.61 76.5 78.53 79.8 8.7 8.1 3 Ý Ý µ ÛÀ ¼Ì Table 3 Size parameters and simulation results of square section nano rod Group 1 3 5 6 A/a 3 5 6 7 Real size, nm 5 118 9 37 7 6 Surface atoms, %.3 1.8 1.6 1.5 1. 1.3 Yield strength, 6.7 5.9 5.1.7.6 3.9 GPa Yield point.89.8.7.65.6.55 Initial Young s 61.9 6.81 65.6 68. 7. 76.18 Finial Young s 8.9 8.1 81.3 8.7 8.91 8.1 ß Ü À½Û, b Burgers ÞÐ, γ ¼ ¹, G À Ð, v Poisson, r Æ. Þ Ü½ É ß Ü À½Û Ü Þ Þ ß Ü¹Ð. (8) (7), G=, ÙØ À½Û τ c τ c = 1 v Gb ( ln r ) + γ r 1 v π r b (9) (9), Đ, ÍÞ Ü ß³, ³ Ò Ù ³ÓÜ À½ÛÀ ß Ì. ÒÏ Ú «½ Ü, É Á Î, ² ¹ Þ ÜÄÐ ĐÊ ÏÉ Þ, «Ð ÜÄÐÍ ºĐ Þ Ã.»Í, ÄÐͺ½ÛÜÁ Ô½ Û À É Þ Ï Ú ÄÆ Á Ü. É ÓĐ ÞÜÕ, ÐÞ, ³ ܹ Ü Đ Þ ³ ß Ü Đ, ¹É³Óͺ½ÛÎÞ, Ïͺ. Í, Michalske Þ [] Í ÏÛ Ç, ÜÌ, Þ ß, Þ Ó ß Ù. É Ü½Û½ ½ Î, ³ ¹ Ü Þ Ü Ð.»Í, Ì ¹ Õ, ͺ½Û ß, ͺ½ Ó. 6 «Ö ¹ Ü, ÍÆ, ¹ ÜÌ, «Ö Ó, Õ¹ Ì Ø 5 nm Õ, ßÝ Ü «ÖÊ ÓÁ ܳÓ. 7 ßݹ Þ Üͺ½Û ¹ Ü. ¹ ÜÌ, Þ¹ Þ ÜÍ º½ÛÄ ÏÌÕ ÜÏ, Þ¹ Þ Ü Íº½Û ¾, ¹ Ü µì, ͺ Ü Ü ³Ó, ͺ Þ¹ Þ. à ÇÙØ, ÄÐͺ½ÛÜÁ Ô½Û À É Þ Ï Ú ÄÆ Á Ü. ßÝ Ü ¹ Ê, Ñ ß Ü ÄÆ ² (Ö, É ¹ Î, ßÝ Ü «Ö², 6 Đ), ß ßÝ Üͺ ÖĐ º. 3. ÇÇ ²ÑÊÁµ 8 ÍÆ, ¹ ÜÌ, ßݹ Þ Ü ÓĐ ÐÊÌ, Û [] Ä ØÜ Ag ÜÓĐ Ð Ó ÜÜÈ Ô. Ú, ¹ Î, Þ¹ Þ ÜÄÐÓĐ ÐÕ ÓĐ ÐÊ Þ¹ Þ, Ñ ÓĐ Ð ¹ Ü Ü Ó Þ¹ Þ. Õ¹ Ì Ø 5 nm Õ (A 6a, R 3a ), ßݹ Þ Ü ÓĐ Ð Þ Ò 8 GPa. ½ 6, ÉÓÇ Á Î, Ô½ Û«Đ, ßÝ «ÖÜ º¹À ÓĐ Ð Ö³ Ü ; Õ¹ Á Ì Ø Õ, ² ¹ Þ Ü «Ö É º, Ñ Í² Á Î, «Ö Ó, Ö Proportion of surface atom, % 7 6 5 3 1 1 3 5 6 7 Cross section size, nm 6 Å Õ ÛÊ Fig.6 The proportion of surface atoms as a function of cross sectional area

1 Ã Ý : Cu ÐÙ ÐÚ Ð» 1179 Yield strength, GPa 7. 6.5 6. 5.5 5..5. 1 3 5 6 7 Cross section size, nm 7 ̹ ÛÊ Fig.7 Yield strength as a function of cross sectional area Iinial Young's Finial Young's 8 75 7 65 6 55 (a) 5 1 3 5 6 7 Cross section size, nm 87 8 81 78 75 7 (b) 69 1 3 5 6 7 Cross section size, nm 8 Ò ÛÊ Fig.8 Young s modulus as a function of cross sectional area (a) Initial Young s modulus modulus (b)finial Young s ², ÁßÝ ÜÓĐ Ð È Â. ËÄ Ò ³Ö µ Dz Ç Á Î Ì ÓĐ Ðͺ Ü, À Đ² Ç, Đ 5 Đ 1 Ã. 9 ÍÆ, ² Ç Õ, Ì ÜÌ, Ä ² ¹ Þ Ü Üͺ½ÛÓĐ ÐÊ Ó, ÓĐ ÐÆ Ü Ü. ½² ½Í Ý Ý µ ± ºÆ ¼Ì Table Size parameters and simulation results of circular cross section nano rod Group 1 3 5 Length of nano staff/a 6 8 1 1 R/a 11 11 11 11 11 Slenderness ratio :1 3:1 :1 5:1 6:1 Yield strength, GPa 6.1 5.99 5.91 5.89 5.9 Yield point.91.91.9.91.9 Initial Young s 56.7 53.51 53.7 5.7 5.9 Finial Young s 71.77 7.99 7. 7.17 69.89 5 Ý Ý µ ± ºÆ ¼Ì Table 5 Size parameters and simulation results of square section nano rod Group 1 3 5 Length of nano staff/a 6 8 1 1 A/a Slenderness ratio :1 3:1 :1 5:1 6:1 Yield strength, GPa 6.83 6.78 6.65 6.5 6.39 Yield strength, GPa Finial Young's Yield point.9.91.89.87.88 Initial Young s 63.9 61.56 61.5 6.11 58.79 Finial Young s 81.8 8.6 8. 79.68 77.73 7.5 7. 6.5 6. 5.5 (a) 5. 1 3 5 6 7 Slenderness ratio 8 (b) 81 78 75 7 69 1 3 5 6 7 Slenderness ratio 9 ̹ Ò Ë ÛÊ Fig.9 Yield strength and Young s modulus as a function of slenderness ratio (a) Yield strength (b) Finial Young s modulus

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