13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- relation, which is determined by experiment; and t is the reaction time. Fig.2 shows the recession location of the ablation surface during the ablation process. Figure 2. Recession location of the ablation surface The ablation reaction of C/C composites with high-temperature oxidation resistant coating follows the parabolic-rate law, and the reaction rate is inversely proportional to the square root of time, which is determined by the diffusion rate of oxygen in the inner material, as shown in Equation 2. 2 p m k t A ⎛Δ ⎞ = ⎜ ⎟ ⎝ ⎠ (2) where pk is the parabolic rate constant or diffusion constant, which is derived from Arrhenius law as shown in Equation 3. 0 p Q k k exp RT ⎛ ⎞ = ⎜ − ⎟ ⎝ ⎠ (3) where 0k is the constant obtained by experiment; Q is the activation energy of oxidation; and R presents gas constant; T is the reaction temperature. Logarithmic rate reaction is suitable for C/C composites with silicon elements. Early in the reaction process of ablation, the oxidation of silicon elements is rapidly, and silicon oxide produced from the oxidation between silicon and oxygen can generate a compact oxide layer covering the surface of C/C composites. The generated SiO2 layer will prevent further diffusion of the oxygen and then increase the ablation resistance of the C/C. With the exacerbated of oxidation, the ablation of C/C composites will become severe and accompany with mass loss. Hence, the logarithmic-rate reaction mechanism is only appropriate for representing the early reaction of the C/C composites with silicon in lower high temperature. 3. Analytical model C/C composite is a homogeneous multi-scale material. In microstructure, the “skeleton” of the composite consists of unidirectional bundles made of several thousands of fibers which are linked together by a pitch-based matrix. The formation of the typical roughness patterns of C/C composites in ablation process depends on the unidirectional fibers perpendicular to material surface. Due to the different ablation rates between carbon matrix and carbon fibers, the unidirectional fibers perpendicular to material surface will separate from the carbon base, expose to the external
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