Abstract

Keywords : 3D4d braided composites, Effective thermal conductivities, Unit cell, Uncertainty quantification
 

1. Introduction

Carbon fiber fabric-reinforced composites exhibit complex microstructures and unconventional heat transfer behavior, leading to >10% errors in traditional thermal property predictions. Experimental characterization under extreme conditions suffers from low accuracy and prohibitive costs, severely limiting fidelity in aircraft thermal analysis.
To address these limitations, this study develops a minimal unit cell (UC) modeling framework. By leveraging material symmetry and rigorously derived periodic boundary conditions, the method reduces computational costs while maintaining <0.2% prediction error, enabling efficient thermal property prediction for aerospace thermal protection systems.
 

1. Methodology

This study established a complete uncertainty analysis process for 3D4d braided composites, which achieved accurate prediction of thermal properties parameters of composite materials through three key steps: uncertainty description, cross scale propagation, and quantitative analysis. Specifically:In terms of uncertainty modeling, a normal distribution is used to characterize the geometric and compositional uncertainties at three scales: fibers, fiber bundles, and composite materials. Through the Nataf transformation method, considering parameter correlation, accurate propagation of component property uncertainties from the fiber/matrix scale to higher scales is achieved. In terms of computational efficiency optimization, based on systematic analysis of material symmetry, minimal unit cell models of 1/4 and 1/8 size have been successfully constructed,as shown in Fig.1, significantly reducing computational costs while maintaining the accuracy of single simulations. Compared with traditional full-size unit cell methods, this approach significantly improves computational efficiency while ensuring prediction accuracy, providing a practical solution for multiscale thermophysical property analysis of composite materials.

 Fig.1 Three models of 3D4d braided composites
 

1. Results

In order to evaluate the calculation accuracy and efficiency of the three types of unit cells in 3D4d braided composites, normality tests were conducted on the output parameters of these three models. The results showed that the isotropic equivalent thermal conductivity calculated by the three models were very close and approximately followed a normal distribution. From the temperature cloud maps in the x and z directions in Figure 2, it can be seen that the three types of cells have the same distribution on the same temperature scale, which proves the correctness of the boundary conditions. As the cell and grid sizes decrease, the computation time also decreases. The UC3 model achieves the highest computational efficiency while maintaining computational accuracy, making it suitable for multi-scale analysis.
For the uncertainty analysis of 3D4d braided composites, UC3 is used to analyze their correlation coefficients, as shown in Figure 3. From the correlation coefficient graph, it can be seen that the size input parameters of 3D4d braided composites are independent of each other; There is a strong correlation between the input thermal conductivity and the output parameters of the fiber bundle, which verifies the accuracy of the Nataf transform. After the calculation, uncertainty propagates to the calculation results, resulting in a clear correlation between the output parameters. Parameter sensitivity analysis indicates that the matrix performance plays a dominant role in the overall thermal conductivity behavior.

 Fig.2 Output result diagram of 3D4d braided composites           Fig.3 UC3 correlation coefficient chart
 

1. Conclusion

This study establishes a high-fidelity UQ framework for 3D4dBC thermal properties, featuring:

1. 90.8% computational cost reduction via symmetry-exploited minimal UCs

1. Multi-scale uncertainty propagation using Nataf transformation
2. Matrix-dominated thermal behavior with quantified sensitivity (89% variance contribution)

The framework enables reliable thermal database generation (<2% error) for hypersonic thermal protection system design.
 

3D4d braided composites, Effective thermal conductivities, Unit cell, Uncertainty quantification