13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- material properties including both the mechanical and thermal properties are obtained as follows. According to the mean field model by MAXWELL [16], the conductivity of the equivalent meat KሺT, t,Xሻ can be described as: KሺT, t,Xሻൌሺଶାି ଶ൫ା൯ሻ ଶାାሺି ሻ , (1) Where ܭ and ܭ separately represent the conductivity of the matrix and the inclusion phase of fuel particles. This analysis adopts Mori-Tanaka Method [17] to calculate the equivalent Young’s modulus and Poisson’s ratio. That’s: EሺT, t,Xሻൌ ܧ ሺ1 ሺಶ ಶ ି ଵሻ ଵାሺଵି ሺா/ாି ଵሻ; υൌ߭ ሺ1 ሺഔ ഔ ି ଵሻ ଵାሺଵି ሺజ/జି ଵሻ, (2) where E is equivalent Young’s modulus (MPa) and υ is the equivalent Poisson’s ratio, they are related to the Young’s Modula and Poisson’s ratios of fuel particles and matrix. Only the fuel particles in the dispersion fuel meat can generate heat, and the heat generation rate of the particles corresponds to their fission rate. The heat generation rate of the fuel particles ݍ ሶ can be expressed as ݍ ሶ ሺܺ ሻൌܿ ∙݂ ሶ , (3) with the unit is W/݉݉ ଷ. Where cൌ3.204ൈ 10ି ଵଵJ/fission is the generated heat energy every fission event and ݂ ሶ is the fission rate of fuel particles, while in this analysis the value of ݂ ሶ is linearly distributed along the length direction like the fast neutrons, which has the largest one 0.6408 W/݉݉ ଷ in the middle location as twice as the lowest one at the margin of the fuel meat. The corresponding heat generation rate of the equivalent meat can be obtained as: ݍ ሺܺ ሶ ሻൌܸ ∙ ݍ ሶ (4) The swelling rate of the equivalent meat is obtained similarly as SWሺT, t, Xሻ ൌ∆ బ ൌܸ ∙ SW, (5) where ݍ ሶ and SW separately denote the heat generation rate and swelling rate of fuel particles, they are both location-dependent and SW increases with burnup [3]. The thermal expansion of the equivalent meat ߙ can be expressed as ߙ ሺܶ ሻൌ5.84ൈ10ି 1.9ൈ10ି ൈି. ହ .ଵ 2ൈ10ି ൈ்ି ସହ ଷ ହ, (6) where T is temperature in Kelvin with the application range from 350K to 730K. In the above equations, the subscript p represents the material parameters of the fuel particles and subscript m represents the ones of matrix, and ܸ denotes the volume fraction of fuel particles in the fuel meat. In this study, the considered volume fraction is 10%. Under heterogeneous irradiation conditions, the above obtained equivalent parameters vary with location, temperature and time. 2.1.2. Constitutive relationship of the equivalent meat The large-deformation elastic constitutive relationship for the equivalent meat in a co-rotational coordinate system can be expressed as the following relation between Cauchy stress and elastic logarithmic strain: ߪ ൌ ߣ ሺܶ , ܺ,ݐ ሻ ߜ ߝ 2 ߤ ሺܶ , ܺ,ݐ ሻ ߝ , (7) where ߣ ሺܶ , ܺ,ݐ ሻ and ߤ ሺܶ , ܺ,ݐ ሻ is the Lame constants, they are related to the Young’s Modulus and Poisson’s ratio in Eq. (2).
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