13th International Conference on Fracture June 16–21, 2013, Beijing, China -11- Appendix The embedding function is defined as F !( ) = Fni ! !n !1 " #$ % &' i i=0 3 ( !< !n, !n =0.85 ! ( ) Fi ! !e !1 " #$ % &' i i=0 3 ( !< !e, !e =1.15 ! ( ) Fe 1!ln ! !e " #$ % &' n ) * + + , - . . ! !e " #$ % &' n / 0 1 1 1 1 2 1 1 1 1 (10) V r( ) = Aexp !! r re !1 " #$ % &' ( ) * + , - 1+ r re ! " " #$ % &' 20 + Bexp ! # r re !1 " #$ % &' ( ) * + , - 1+ r re ! $ " #$ % &' 20 (11) != g r( ) "!# ( ) " (12) g r( ) = ge exp ! ! r re !1 " #$ % &' ( ) * + , - 1+ r re ! " " #$ % &' 20 (13) The two-body cross potential VCu-Au(r) between Au and Cu is constructed as VCu!Au r( ) = 1 2 gCu r( ) gAu r( ) VAu!Au r( )+ gAu r( ) gCu r( ) VCu!Cu r( ) " # $ % & ' (14) where gA(r) and VA-A(r) are the functions of g(r) and V(r) for material A, respectively, g ε, rε, ρε, α, β, A, B, κ, λ, Fni, Fi, η, and Fε are potential parameters (4),(5). Table 1 Values of potential functions Au Cu Au Cu re 2.88503 2.556162 Fn0 -2.937772 -2.170269 ge 1.529021 1.554485 Fn1 -0.500288 -0.263788 ρe 19.991632 21.175871 Fn2 1.601954 1.088878 ρn 19.991509 21.175395 Fn3 -0.83553 -0.817603 ι 9.516052 8.12762 F0 -2.98 -2.19 χ 5.075228 4.334731 F1 0 0 B 0.229762 0.39662 F2 1.706587 0.56183 κ 0.356666 0.548085 F3 -1.134778 -2.100595 λ 0.35657 0.308782 η 1.021095 0.31049 λ n 0.748798 0.756515 Fe -2.978815 -2.186568
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