13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Fig.3 shows normalized critical stress for dislocation emission to take place as a function of emission angle with different nanovoid sizes and surface residual stresses. When the nanovoid volume fraction is given, if the nanovoid size decreases, there must be larger number of same-size neighboring nanovoids. The figure shows the critical stress and relative most probable critical angle for dislocation emission decrease as the nanovoid size increases. That is, when the nanovoid volume fraction is fixed, the larger nanovoid size in the nanoporous materials makes the dislocation emission take place more easily, relative most probable critical emission angle less pronouncedly depart from the direction45o. In other words, the dependence of critical stress on the neighboring number of nanovoids under the same void volume fraction can evidently be observed. Under the condition of constant void volume fraction, the larger the neighboring number of nanovoids is, the higher the critical stress becomes. It indicates that the load-carrying capacity and the stress resistivity of materials can be enhanced by redistributing a large void into multiple small ones at nanoscale. These results are reasonable agreement with that of molecular dynamics simulations by Mi et al. [17]. As well-evident from the Fig. 3, we know that the negative surface residual stress would increase the critical stress, while the positive one reduces it. It means that the nanovoid surface characterized by the positive surface residual stress clearly promotes dislocation emission and improves the ductility of the nanoporous materials. The larger the positive surface residual stress is, the more easily the dislocation emitted from nanovoid surface is. The larger neighboring number of nanovoids under the same void volume fraction has a greater role in the critical stress required for dislocation emission. 20 40 60 80 0.05 0.06 0.07 0.08 0.09 σcr0 θ b=4,δ=0 b=8,δ=0 b=8,δ=0.01 b=8,δ=0.03 b=8,δ=-0.03 b=12,δ=0 b=12,δ=0.03 b=12,δ=-0.03 Fig. 3 Dependences of normalized critical stress 0 crσ on emission angle θwith different nanovoid sizes and surface residual stresses for 0 zb ρ = , 0 ε= , 1 1 j = , 2 3 0 j j = = , 0.9 a = , 1.5 c = , 0 α β = = . In this case in Fig. 4, namely 0.9 a = , it means that the void volume fraction keeps the same, and c characterizes the distance of neighboring nanovoids or the uniform distribution density of the neighboring nanovoids. The larger physical quantityc, it demonstrates the larger neighboring
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