13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- oxidation environment, and take the shape of “needle clusters”. This paper focuses on the unit cell model of C/C composites in micromechanical structure, analyzing the change laws of C/C composites in high temperature thermal radiation and predicting the ablation morphology change. There are two basic kinds of unit cell model of C/C composites. The first model, as shown in figure 3, is a hexahedron representative volume element (RVE), in which matrix and fibers are assumed homogeneous and isotropic, and the internal pores are negligible. The second model is a cylinder RVE, in which the fiber bundles are fit together into a 3D C/C structure. This meso-structure forms a network of meso-scale pores, as shown in figure 4. Figure 3. Hexahedron RVE of C/C Figure 4. Cylinder RVE of C/C In the finite element software of Abaqus, the thermal radiation analysis can be conducted according to the following steps: (ⅰ)modeling, (ⅱ) defining the materials property, (ⅲ) assembly model, (ⅳ) creating heat conduction steps and interaction, (ⅴ) applying boundary condition and load, (ⅵ) meshing and selecting element type, (ⅶ) creating analysis job, (ⅷ) results visualization. The physical properties of C/C composite in the two models are listed in table 1. In the thermal radiation analysis, the physical constants of absolute zero temperature and Stefan-Boltzmann constants are -273.15 ℃ and 5.67E-8 W/(m2·k4). Table 1. Physical properties of C/C composites in the simulation models Characteristic Density Elastic modulus Poission’s ratio Thermal conductivity Specific heat Unit kg/m3 GPa -- W/(m·℃) J/(Kg·℃) Fiber 2000 230 0.22 1.15 5000 Matrix 1600 4.07 0.25 10.38 1000 Both of the two models use standard linear heat transfer element type DCC3D8 to analyze the thermal radiation. We assume the heat transfer is a transient state. It is subjected to surface radiation with ambient temperature of 2000℃ on top of the RVE and predefined temperature field of 300℃. We ignore the mass diffusion during the ablation process. The governing equation is [ ]{ } [ ]{ } { } { } q r C T K T F F + = + & , where [C] is the element capacitance matrix, [K] is the sum conductivity matrix of heat conduction and thermal radiation. {Fq } and { Fr} are the load vectors due to applied heat flux and radiation respectively. We can obtain the temperature distribution in the C/C composite, and then calculate the heat flux by the following rule: 4 0 4 Z Z q A((T T) (T T)) = − − − where A is the radiation constant , which was set to be one emissivity times the Stefan-Boltzmann constant; TZ is the value of absolute zero on the temperature scale being used.
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