# Surface Erosion Analysis for Thermal Insulation Materials of Graphite and Carbon-Carbon Composite
## 3 Experimental Results and Discussion  
Figure 6 shows the erosion surface of five specimens, Graphite R4340, Graphite G6520, Graphite EX60, Graphite EX70, and 3D C-C composite, after the flame was injected for 120 s. The upper right picture in each figure is the one before the flame was applied to the specimen. In the case of graphite material, erosion occurred most in the center of the flame, and the white dot in the figure shows the surface groove due to erosion. The roughness of the specimen was increased due to the surface groove toward the center of the specimen. In the C-C composite material, the surface groove was larger than that of graphite as the matrix was burned and absent, and the fiber-reinforced composite material under the laminate was exposed due to erosion, appearing as a circular pattern. It was confirmed that five fibers were exposed by each 90\({}^{\circ}\) downward directions, but they were resistant to surface erosion while the matrix was removed. Figure 5: Erosion test results for the 3D C–C composite specimen after 5 s (**upper left**), 40 s (**upper right**), 100 s (**lower left**), and 120 s (**lower right**). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Graphite**} & \multicolumn{3}{c}{**C–C**} \\ \cline{2-6}  & **G6520** & **R4340** & **EX60** & **EX70** & **3D** \\ \hline Density & 1750 & 1770 & 1800 & 1850 & 1700 \\ (kg/m\({}^{3}\)) & 17 & 15 & 14 & 10 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Density and porosity of the graphite and C–C composite. particle changes are erosion phenomena and the released particles are in the form of grooves on the surface. The surface temperatures of the graphite and C-C composite specimens were measured to investigate the characteristics of the above described particle surface change. As shown in Figure 8, the 3D C-C composite (thermal conductivity of 18 W/m K) reached a high temperature faster than Graphite G6520 (thermal conductivity of 160 W/m K). The amount of erosion and erosion rate for each material for the erosion test conducted for 120 s are shown in Table 3, and the erosion cross section for each material is shown in Figure 9. To compare the measured erosion rates with the theoretical values, the thermochemical erosion rate (\(\dot{\mathrm{r}}_{\mathrm{ch}}\)) described in Table 4 was calculated using the chemical-controlled recession rate (\(\dot{\mathrm{r}}_{\mathrm{c,ch}}\)) in Equation (3). Figure 8: Comparison of surface temperature of Graphite G6520 and the 3D C–C composite. Figure 7: Surface particle changes of 3D C–C composite. The diffusion-controlled recession rate (\(\dot{\mathrm{r}}_{\mathrm{c,d}}\)) in Equation (7) is based on values from Table 1. Density, one of main factors influencing the erosion, was obtained from material data sheet and inspection report provided by the manufacturer, the mass fraction of the combustion gas was obtained by NASA CEA [21], and the pressures were measured at 3.6 bar and 5.0 bar. As shown in Table 3, a rather large difference between the measured and predicted erosion rates was observed, and it was found that accurate erosion rate can be predicted only by mechanical erosion considering porosity and shear stress, which is a measure of structural resistance. Porosity is an important factor affecting the erosion resistance of heat-resistant materials and should be considered for erosion prediction. The mechanical erosion rate (\(\dot{\mathrm{r}}_{\mathrm{m}}\)) was calculated by Equation (10) where the characteristic exhaust velocity of 1008.83 m/s was applied according to the conditions of this experiment, and the porosity was 15% for R4340, 17% for G6520, 14% for EX60, 10% for EX70, and 12% for the 3D C-C composite. Experimental constant (a) was \(8.8491\times 10^{-9}\) derived by curve fitting the experimental data. The mechanical erosion rate was thus calculated by Equation (12), and the rates were computed as 0.01235 mm/s of R4340, 0.01352 mm/s of G6520, 0.01173 mm/s of EX60, 0.00893 mm/s of EX70, and 0.0104 mm/s of the 3D C-C composite.