13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- was obtained. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) n i j k n i j k n i j k n i j k n i j k n i j k n i j k n i j k n i j k n i j k n i j k n i j k n i j k n i j k I x y z C G x y z C H x y z C F x y z C Bxyz C ExyzC A x y z C I x y z C G x y z C H x y z C F x y z C Bxyz C ExyzC A x y z C , , 1 , , 1 , 1, , 1, 1, , , , 1, , 1 , , 1 1 , , 1 1 , 1, 1 , 1, 1 1, , 1 , , 1 1, , , , , , , , , , , , , , 1 , , , , , , , , , , , , , , 1 , , − + + + − + + + − + + + + + − + + + + + − + + + + + − + + + + + + − − − − − + − =− + + + + + − + (5) where, ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ∑ ∑ ∑ − = + + − = + + − = + + + + + + + + − + − + + + − + + + + − + + + + + + + + − + − + + + − + + + + − + + + + + + + + − + − + + + + + + + + + − + − + + + + − + − + + + + − + − + + + + + − + + − + + − + + + + − + + + + − + + = Δ = Δ = Δ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ Δ Δ ∂ + Δ Δ +Δ Δ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ Δ Δ ∂ − Δ Δ +Δ Δ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ Δ Δ ∂ + Δ Δ +Δ Δ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ Δ Δ ∂ − Δ Δ +Δ Δ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ Δ Δ ∂ + Δ Δ +Δ Δ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ + ∂ ∂ + ∂ Δ Δ ∂ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ Δ Δ Δ −Δ + ∂ ∂ Δ Δ Δ −Δ + ∂ ∂ Δ Δ Δ Δ Δ −Δ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Δ Δ + Δ Δ + Δ Δ =− Δ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ Δ Δ ∂ − Δ Δ +Δ Δ = 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 1 2 1 1 2 1 1 1 2 2 2 2 2 2 3 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 , , 2 , , 2 , , 2 , , 2 , , 2 , , 2 2 1 1 1 , , 2 , , k n n j m m i l l p k k k k p k k k k p j j j j p j j j j p i i i i p p p p k k k k p j j j j p i i i i k k j j i i p i i i i z y z x y x z RT D V z D z z z t I x y z z RT D V z D z z z t H x y z y RT D V y D y y y t G x y z y RT D V y D y y y t F x y z x RT D V x D x x x t E x y z z y x RT D V t z z z z z y y y y y x x x x x RT D V t z z y y x x B x y z D t x RT D V x D x x x t A x y z σ α α σ α α σ α α σ α α σ α α σ σ σ α σ σ σ α α σ α α (6) The obtained simultaneous equations were solved by the successive over relaxation (SOR) method. The material properties of P92 steel used in the FDA were shown in Table 4. It is known that vacancies were generated with the progress of the plastic deformation [18]. Therefore, distribution of initial vacancy concentration C0 was set based on the distribution of equivalent plastic strain obtained by 3D-FEA as follows. p b C ε = + 1.0 0 (7)
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