13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- volume fraction and nanovoid size remain constant, the distinct softening behavior can be happened and then significantly promotes capability of dislocation emission from nanovoid surface in the nanoporous materials with improving the uniform distribution density of the neighboring nanovoids. In other words, increasing nanovoid spacing can impede the nanovoid growth and increase ductility. These conclusions are further confirmed by the earlier experiment from Dubensky and Koss [18], and the finite element analysis from Gao et al. [19]. 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 the density of nanovoid concentration and the surface residual stress have a significant effect on determining the deformation behavior of ductile materials. 20 40 60 80 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 c=2.5,δ=0.05 c=2.5,δ=-0.05 c=2.5,δ=-0.1 σcr0 θ c=2.5,δ=0 c=2,δ=0 c=1.5,δ=0 c=1.5,δ=0.05 c=1.5,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 fraction in the nanoporous materials makes the dislocation emission take place more easily, relative most probable critical emission angle more pronouncedly depart from the direction45o. Under the condition of constant void volume fraction, the larger the neighboring number of voids is, the higher the critical stress becomes. For given void volume fraction and nanovoid size, the distinct softening behavior can be happened and then significantly promotes capability of dislocation emission from nanovoid surface in the nanoporous materials with improving the uniform distribution density of the neighboring nanovoids. 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). References [1] V.A. Lubarda, Emission of dislocations from nanovoids under combined loading. Int J Plast, 27
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