## 4 Results and Discussions
### Results with Different ATCs  
The results discussed above were based on the 2.5-D braided CMC sample, as shown in Figure 1. In the engineering application, the material's ATCs were different if the internal components and the structure were changed. To make the present results and conclusions more applicable, the influence of the thickness and the critical thickness that were suitable for the RVE model were further investigated under different operating conditions of the ATCs.  
Figure 12 shows the thermal conductivities k\({}_{Z}\) based on the RVE model and the full-size model with an increasing thickness L\({}_{Z}\), when the absolute value ratio n and the level of anisotropy \(r\) of the thermal conductivities of the fiber bundles were changed.  
The results in Figure 11(a) show that when the values of \(k_{\zeta},k_{\eta}\), and \(k_{\
u}\) were different, the influence of the thickness was also changed. In Case 1 and Case 2, the value of k\({}_{Z}\) decreased with the increase of L\({}_{Z}\), while in Cases 3-5, k\({}_{Z}\) increased with the increase of L\({}_{Z}\). Figure 11(b) gives the influence law of the level of anisotropy r. It can be seen that when r increased, the k\({}_{Z}\)'s variation curves always monotonically decreased, but the range became smaller. The reason for this was that the main difference between the RVE model and the full-size models was the existence of the boundary parts and that its influence was affected by the relative variations between the thermal conductivities of the fiber bundles and the matrix, which changed with the absolute value ratio \(n\) and the level of anisotropy \(r\).  
Additionally, the results in Figure 12 show that when the absolute value ratio and the level of anisotropy changed, the lines based on the full-size models always tended to converge on the corresponding dash lines of the RVE models. This phenomenon was explained in Section 4.2. In this paper, the convergence criteria was set to that standard, and the relative variation between the results  
Figure 12: The variations of the thermal conductivities k\({}_{Z}\) with different ATCs.  
based on the RVE model and the full-size model was smaller than 5%. Figure 13 shows the variation of the \"critical thickness\" L\({}_{Z}\) under different ATCs. The results show that when the absolute value ratio n increased, the \"critical thickness\" L\({}_{Z}\) first decreased and then increased. When the absolute value ratios were 1, 2, 4, 6, and 10, the corresponding critical thicknesses were 11.2 mm, 2.8 mm, 4.0 mm, 7.6 mm, and 11.2 mm, respectively. When the level of anisotropy r increased, the \"critical thickness\" L\({}_{Z}\) decreased almost monotonously. When the levels of anisotropy r were 6.53, 10, 13, 16, and 20, the corresponding critical thicknesses were 11.2 mm, 7.6 mm, 7.6 mm, 4.0 mm, and 2.8 mm, respectively.  
In general, the structure of the boundary part of the braided CMC, which was different for a periodic internal structure, was the main reason for the difference between the results of the full-size model and the RVE model. This influence depended on the value and the level of anisotropy of the ATC, i.e., the relative difference between the thermal conductivities of the matrix and the fibers.