13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- ( ) ( ) ( ) ( ) 2 2 2 2 dt d x t t x t t x t x t +Δ + −Δ = + Δ (8) Using Eq. (8), xi,n+1 is given by Eq. (9). ( ) ∗ − + = − + Δ i n i n i n i n t I x x x , 2 , 1 , , 1 2 (9) In this paper, these two methods were adopted to conduct this numerical analysis and results obtained by these methods were compared from the view point of accuracy, the number of atoms which can be calculated and calculation time of numerical analysis. The converged conditions on the equilibrium positions of atoms were given by Eqs. (10) and (11). 9 , , , 1 10− + < − i n i n i n x x x (10) 4 1 * , 10− = < ∑ N I N i i n (11) The center position of atomic distance and atomic density and the changing rate of atomic density to the initial atomic density were given by Eqs. (12)-(14). 2 1 i i i x x X + = − (12) 1 1 − − = i i i x x d (13) ,0 ,0 i i i i d d d D − = (14) The center position of atomic density was shown in Fig. 3. The positive value of D means that the distance between neighboring atoms expands due to local stress field. The region with negative value of D was defined as the disordered region of atomic array and it is related to the process region which dominates brittle fracture [7, 8]. Conditions of analyses were shown in Table 1. Figure 3. The definition of the center position of atomic distance Table 1. Conditions of analyses Condition1 Condition2 Condition3 KII (MPam1/2) 20 40 20 nA*(MPa) 0.049 0.049 0.1 N 10~1000 (Direct method) 10~3000 (Verlet method) xi xi-1 The center position of atomic distance
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