13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- theory [19] as ∆ ߝ ൌଷௌ ೕ శ∆ ଶఙഥశ∆ ∆ ̅ߝ ; (20) ߪ ௧ ା∆௧ ൌ ߪ ௧ ∆ ߪ (21) Where ܵ ௧ ା∆௧ are the components of the deviatoric tensor of the Cauchy stress at ݐ ∆ ݐ; ߪ ത௧ା∆௧ is the Mises stress at ݐ ∆ ݐ , which is dependent on the equivalent plastic strain increment ∆ ߝ ഥ. After some manipulations, a closed form expression for ∆ ̅ߝ can be obtained: ߪ ത௧ା∆௧ 3 ܩ ∆ ߝ ഥ െ ߪ തሺ௧ା∆௧ሻ ൌ0, (22) Where the Mises stress and equivalent plastic strain at ݐ ∆ ݐ should obey the irradiated strain-hardening curve in Section 2.2.1; ߪ തሺ௧ା∆௧ሻ is the trial Mises stress with the assumption of no plastic strain increments in Eq. (19). Eq. (22) is a nonlinear equation of ∆ ߝ ഥ. Newton Iteration is applied to solve this nonlinear equation. When the converged equivalent plastic strain increment is obtained, the stress and strain can be updated. Based on the developed constitutive relations and stress update methods for the fuel meat and cladding, the subroutines UMAT are written to simulate the non-homogeneous irradiation-induced mechanical behaviors. 3. Finite element model 3.1. Finite element geometric model A dispersion nuclear fuel plate is taken as the research object, whose length and width is much larger than its thickness. The bonding between the fuel meat and the cladding is assumed perfect. As mentioned above, the thermo-mechanical behaviors evolution for un-uniform irradiation conditions is to be simulated. According to the symmetry in geometry and loading, a 1/8 part of the whole fuel plate is set as the finite element geometric model including the corresponding parts of fuel meat and cladding, as illustrated in Fig.1. Using the reduced Integration element C3D8RT, the FE model in Fig.1 is meshed with 49950 elements and 56848 nodes. Figure.1 FEM Model 3.2 .boundary conditions The boundary conditions to determine the temperature field are given as (1) The surface to contact with the coolant water satisfies the convection boundary condition െKడ డ் ൌ݄ ሺܶ െܶ ሻ, where the temperature of periphery fluid ܶ is 573K. And the used heat transfer coefficient is 2ൈ10ି ଶ ܹ/݉݉ ଶ ܭ. Fixed boundary Free boundary
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