## 5 Result and Discussion
### Model Validation  
In this study, the physical property parameters of the porous carbon substrate were experimentally determined, while the material properties of the transition zone and surface coating were estimated, as detailed in Section 5.1. The adopted values can be found in the Supplementary Materials. To bridge the experimental observations with theoretical simulations and validate the macroscopic model's accuracy, a comprehensive thermo-mechanical model was developed. Figure 7 provides both macroscopic and microscopic analyses of the sample surfaces and cross-sections before and after thermal shock treatment. Figure 7a shows the initial sample, while Figure 7b illustrates the sample post-thermal shock. Macroscopically, the structure of the sample remains intact, with no visible cracks on the surface, suggesting that the material effectively withstood the thermal shock. SEM images of Figure 7c,d reveal the presence of microcracks in the SiC coating after thermal shock. However, as seen in the cross-sectional images in Figure 7e,f, these microcracks are confined to the surface layer of the coating, not extending into the internal layers. The substrate remains undamaged, highlighting the protective function of the coating. This indicates that the SiC coating effectively shields the substrate from thermal shock damage, maintaining its structural integrity.  
Figure 6: (**a**) Effective Young’s modulus versus porosity [31, 33, 34, 36, 41], (**b**) effective Poisson’s ratio versus porosity [36, 37, 38, 42], (**c**) effective thermal conductivity versus porosity [39, 43, 44, 45, 46, 47, 48, 49, 50, 51], and (**d**) normalized tensile/flexural/compressive strength with porosity [52, 53, 54, 55, 56, 40].  
The model was employed to analyze the residual stresses induced during surface coating preparation and subsequent thermal shocks. These results were then compared to the experimental data, as presented in Table 2. The experimentally measured average residual stresses due to coating preparation and thermal shock were 784 MPa and 242 MPa, respectively, with each value being the mean of multiple tests conducted on individual samples. When the surface coating composition was 20% porosity, 64% SiC, and 16% carbon, the simulation results exhibited a high degree of concordance with experimental values. Specifically, the simulated average residual stresses during preparation and following the first thermal shock were 973 MPa and 204 MPa, respectively. Figure 8 depicts the residual stress distribution during the preparation phase and after the initial thermal shock. After thermal shock, a noticeable reduction in the coating's load-bearing capacity was observed. This reduction is likely due to material damage during the thermal shock process, where microcrack formation and propagation could release stress, thereby decreasing the overall residual stress in the coating. Furthermore, repeated thermal cycles can lead to a more uniform stress distribution, potentially eliminating some of the residual stresses from the initial thermal shock [57]. This alignment between the experimental and simulation data underscores the robustness of the developed thermo-mechanical model in accurately capturing the stress evolution mechanisms in porous materials subjected to thermal shocks. The findings provide a reliable foundation for further exploration and optimization of material properties in high-stress thermal environments.  
Figure 7: Macroscopic morphology of the sample: (**a**) before the thermal shock test (**b**) after the first thermal shock test; (**c**,**d**) SEM images on the surface and (**e**,**f**) SEM images on the cross-sectional surface.