Ceramic matrix composites (CMC) have been widely studied to tailor desired properties at high temperatures. However, research applications involving design tool development for multi-phase material design are at an early stage of development. While numerical CMC modeling provides significant insight on the material performance, the computational cost of the numerical simulations and the type of variables involved in these models are a hindrance for the effective application of design methods. This technical challenge heightens with the need of considering the uncertainty of material processing and service. For this reason, few design researchers have addressed the design paradox that accompanies the rapid design space expansion in CMC material design.

The objective of this research is to establish a tractable approach for CMC design considering uncertainty. Traditionally, surrogate models of statistical data are incorporated in the design strategy. An alternative to surrogate modeling is the use of lower fidelity models, which captures some of the physics of the problem and avoids the generation of uncertainty quantification. A variable fidelity optimization (VFO) management framework is incorporated in this research. In the proposed VFO method, a high-fidelity, cohesive, finely meshed finite-element model guides the coarsely meshed, low-fidelity model towards the optimal material design. Uncertainty in CMC material processing (multiphase nucleation and growth) is quantified using a stochastic material microstructural lattice model. The lattice model is verified with laboratory processed microstructures.

Dimension reduction for reduction of the number of random variables under consideration. Linear data transformation and principal component analysis (PCA) is traditionally used in dimension reduction. However, nonlinear dimension reduction techniques are better handle complex nonlinear data. This work incorporates Maximum Variance Unfolding (MVU) that preserves global properties of the original data in the low-dimensional representation.

The proposed methodology is applied to the optimal distribution of the matrix and the disperse phases in the composite structure. Results are demonstrated in the design of silicon carbide (SiC) fibers in a silicon-nitride (Si3N4) matrix for maximum fracture energy. The results provide a reference for SiC-Si3N4 nanocomposite.

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