13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- distribution density of neighboring nanovoids 2 1 c R R = . Former studies have indicated that the surface properties can be either positive or negative, depending upon the material type and the surface crystallographic orientation. According to their results, the absolute values of intrinsic lengths α, βand δare nearly 1A o [15]. In addition, let 1 2 0.25 υ υ = = . The present study focuses exclusively on the effect of nanovoid content and uniform distribution density of neighboring nanovoids in the effective medium on the critical condition for splitting of dislocation from nanovoid surface, providing a remote equal biaxial loading. Fig. 2 shows the critical stress to induce dislocation emission from the nanovoid surface as a function of emission angle θ with different ratios of the shear modulus of the matrix and the effective medium 2 1 a μ μ = and surface elasticity. One should notice that, when nanovoid size b is fixed, the smaller the chosen ratio of the shear modulus a is, the larger nanovoid volume fraction the nanoporous materials contain. The figure presents the critical stress required to emit dislocation decreases, while relative most probable critical angle for dislocation emission increases as the ratio of the shear modulus decreases. That is to say, when nanovoid size is fixed, the larger nanovoid volume fraction in the nanoporous materials makes the dislocation emission take place more easily, and relative most probable critical emission angle more pronouncedly depart from the direction45o. They mean that the distinct softening behavior can be happened and the interaction among neighboring nanovoids becomes important as nanovoid volume fraction increases. Therefore, it can significantly enhance capability of dislocation emission from nanovoid surface, favor the nanovoid growth, and then result in decreased ductility of the nanoporous materials. So it is well shown that the ductility of the material depresses with increasing nanosize void volume fraction and the porosity would evidently affect the ductility of structural materials, in agreement with the analysis by Tvergaard and Hutchinson [16]. We have observed a strong influence of surface effect on critical condition for dislocation emission. The positive surface elasticity increases the critical stress and the relative most probable critical angle for dislocation emission, while the negative surface elasticity reduces them. And the larger positive value of surface elasticity makes the dislocation emission from nanovoid take place more difficultly. 20 40 60 80 0.02 0.04 0.06 0.08 0.10 a=0.95,α=β=0.05 a=0.95,α=β=0.1 a=0.95,α=β=-0.05 a=0.7,α=β=0.05 a=0.7,α=β=-0.05 a=1,α=β=0 a=0.95,α=β=0 a=0.85,α=β=0 a=0.7,α=β=0 σcr0 θ Fig. 2 Dependences of normalized critical stress 0 crσ on emission angle θ with different ratios of the shear modulus of the matrix and the effective medium 2 1 a μ μ = and surface elasticity for 0 zb ρ = , 0 ε= , 1 1 j = , 2 3 0 j j = = , 8 b = , 1.5 c = , 0 δ= .
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