13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- [18–21]. ( ) 0 exp G kT τ γ γ ∗ ⎡ ⎤ ⎢ ⎥ = − ⎢ ⎥ ⎣ ⎦ & & (2) where 0γ& is a pre-exponential factor, ( ) G τ ∗ the stress-dependent activation energy for the thermally activated dislocation motion, k the Boltzmann constant. The present contribution mainly tackles the influence of thermally activated effect on the critical stress intensity factors when dislocation is assumed to be emitted under mode I and mode II loads. 2. Modeling According to the work of Lubarda [22], the stress fields of an edge dislocation emitted from the surface of the void correspond to the imposed displacement discontinuity along the cut from the surface of the void to the center of the dislocation. As shown in Fig.1, an infinite elastic medium with the elastic properties ν and μ contains a blunted crack (an elliptically hole) of a the radius of curvature 2b a ρ= , where μ is the shear modulus and ν is the Poisson’s ratio. The blunted crack is straight and infinitely extended in a direction perpendicular to the xy -plane. Edge dislocation 1 with Burgers vector 1b was emitted from the surface of the blunted crack to the point 0 0 2 i z a r e θ ρ = − + , which represent polar coordinates based on an origin behind the crack root, and edge dislocation 2 with Burgers vector 2b is located at the surface of crack 2 i d d z a r e θ ρ = − + . They are both assumed to be straight and infinite along the direction perpendicular to the xy-plane, and 1 2 i x y r b b b ib b e θ =− = + = . Figure 1 Dislocation emission from an elliptically blunted crack tip. we first consider only a short range thermal barrier and the associated effective stress component τ∗ . The activation energy ( ) G τ∗ in Eq. (2) is frequently expressed as[20] 0 ( ) 1 , 0 1, 1 2 p q m G G p q τ τ τ ∗ ∗ ⎡ ⎤ ⎛ ⎞ ⎢ ⎥ = − ≤ ≤ ≤ ≤ ⎜ ⎟ ⎢ ⎥ ⎣ ⎝ ⎠ ⎦ , (3) where p and q are phenomenological parameters reflecting the shape of a resistance profile, y x 1 b 2b 2a 2ρ dr θ b 0r
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