13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- distance or the rougher distribution of the neighboring nanovoids under the same void volume fraction. From Fig. 4, it is found that the critical stress decreases clearly, while the relative most probable critical angle for dislocation emission increases as the physical quantitycincreases. That is, with the initial void volume fraction and nanovoid size keep the same, the distinct hardening behavior can be happened and then significantly suppresses capability of dislocation emission from nanovoid surface in the nanoporous materials with improving the uniform distribution density of the neighboring nanovoids. It is also visibly indicates that the larger the negative surface residual stress is, the harder the dislocation emitted from nanovoid surface becomes. These observations demonstrate that at nanoscale void distribution plays a role in determining the deformation behavior of ductile metals. 20 40 60 80 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 c=1.5,δ=0.05 c=1.5,δ=-0.05 c=1.5,δ=-0.1 σcr0 θ c=1.5,δ=0 c=2,δ=0 c=2.5,δ=0 c=2.5,δ=0.05 c=2.5,δ=-0.05 Fig. 4 Dependences of normalized critical stress 0 crσ on emission angle θ with different uniform distribution densities of the neighboring nanovoids and surface residual stresses for 0 zb ρ = , 0 ε= , 1 1 j = , 2 3 0 j j = = , 0.9 a = , 8 b= , 0 α β = = . 5. Conclusions In conclusion, when nanovoid size is fixed, the larger nanovoid volume fractions in the nanoporous materials make the dislocation emission take place more easily. Under the condition of constant void volume fraction, the larger the neighboring number of voids is, the higher the critical stress becomes. With the initial void volume fraction and nanovoid size keep the same, the distinct hardening behavior can be happened and then significantly suppresses capability of dislocation emission from nanovoid surface in the nanoporous materials with improving the uniform distribution density of the neighboring nanovoids. Softening or hardening of nanovoid surface due to surface effect has a pronounced effect on the critical condition for dislocation emission. Acknowledgements The authors would like to deeply appreciate the support from the NNSFC (11172094 and 11172095) and the NCET-11-0122. This work was also supported by Hunan Provincial Natural Science Foundation for Creative Research Groups of China (Grant No.12JJ7001).
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