13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- effective medium 2 1 a μ μ = , the radius of the nanovoid 1 z b R b = , the relative uniform 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 [16]. 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 with different ratios of the shear modulus of the matrix and the effective medium and surface elasticity. One should notice that, when nanovoid size is fixed, the smaller the chosen ratio of the shear modulus is, the larger nanovoid volume fractions 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 fractions in the nanoporous materials make the dislocation emission take place more easily, relative most probable critical emission angle more pronouncedly depart from the direction45o. They mean that the distinct softening behavior can be happened and then significantly enhances capability of dislocation emission from nanovoid surface in the nanoporous materials. 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. So it is well shown that the ductility of the material increases with increasing nanosize void volume fraction and the porosity would evidently affect the ductility of structural materials. 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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