13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- 0 10 20 30 40 50 -3 -2 -1 0 1 2 K0 IC d (nm) ϕ= 90° ϕ=120° ϕ=150° Fig. 7 Dependences of the critical normalized SIFs 0 IC K on the grain size d with different angles ϕ ( π 6 ω= , 0 π 6 θ = , 100nm L= , p d= , 0.3 x d = , 0.1 y d = ) 0.0 0.5 1.0 1.5 2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 K0 IC p/d ϕ= 90° ϕ=120° ϕ=150° Fig. 8 Dependences of the critical normalized SIFs 0 IC K on the ratio p d with different angles ϕ ( π 6 ω= , 0 π 6 θ = , 100nm L= , 15nm d = , 0.3 x d = , 0.1 y d = ) Fig. 8 plots the variations of the critical normalized SIFs with respect to the ratio p d with different angles ϕ between grain boundaries. We found that the critical normalized SIFs first increase then decrease to constants with the increment of the ratio p d for 90 ϕ= ° and 120° , but just increase to a constant for 150 ϕ= °. And in this situation, if the angle ϕ between the grain boundaries is large enough, the critical normalized SIF is always negative, which means the dislocation emission from the crack tip is very easy. 0 200 400 600 800 1000 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 K0 IC L (nm) ω= 0° ω=30° ω=45° ω=60° Fig. 9 Dependences of the critical normalized SIFs 0 IC K on the crack length L with different strengths ω ( 0 π 6 θ = , 2π 3 ϕ= , 15nm d = , 0 p = , 0.3 x d = , 0.1 y d = ) The dependences of the critical normalized SIFs on the crack length with different disclination strengths are shown in Fig. 9. The critical normalized SIFs 0 IC K increase with the increment of the crack length, and tend to constants when the crack length is large enough. So the dislocation emission from the short crack tip is much easier, and growth of the long crack is easier. We can also see that, when the cooperative grain boundary sliding and migration does not exist, the crack length just slightly affects the critical normalized SIFs. In comparison, the cooperative grain boundary sliding and migration contributes a lot to the dislocation emission and the crack blunting. 0 20 40 60 80 100 0.0 0.1 0.2 0.3 0.4 0.5 K0 IC p′ (nm) ω=30° ω=45° ω=60°
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