UC Santa Barbara

The use of ceramic materials in propulsion and power generation turbines allows for significant improvements in efficiency by allowing for higher operating temperatures. A central challenge in the development of ceramic systems is the propensity for cracking driven by thermal expansion mismatch and oxidation driven by harsh environmental conditions. Many strategies to improve durability involve geometric or material features that have not been previously considered in simulations of failure, such as non-planar interfaces associated with woven ceramic matrix composites and sprayed coatings, and the impact of oxide formation underneath coatings and near cracks. This work focuses on advances in computational frameworks tailored to address such phenomena, with sufficient speed to conduct parametric studies to quantify important material and geometric interactions.

The use of distributed cohesive zone models holds distinct advantages for simulations of crack evolution in brittle systems, notably the ability to predict crack path evolution (as opposed to the onset of initial advance). However, a significant drawback is that the method is slow compared to conventional finite element models, and numerical stability can be sensitive to the details of implementation. To address these concerns, a systematic study of computational methods has identified methods to improve simulation speeds and stability. Specifically, the use of sub-domains near crack tips provides a basis to limit model size with locally refined meshes, and mitigate the cost of simulating loading that is below the cracking threshold. The numerical accuracy and performance of these sub-domains has been fully quantified, and used as the basis for novel adaptive remeshing strategies, which are capable of tracking crack tip propagation across significant length-scales.

To illustrate the utility of these advances, a detailed examination of cracking along wavy interfaces was conducted to quantify the potential benefits of crack deflections driven by local geometric features. The cohesive simulation framework is ideal for such studies, since a single simulation can determine whether an interface crack will advance along the interface or through the adjacent bulk material, without a priori assumptions or a broad parameter study involving an enormous range of crack configurations. The simulations on wavy interfaces demonstrate that for specific combinations of interface toughness, bulk toughness and interface waveforms, the far-field loading required to drive cracking along any path can be three times higher than that associated with a flat interface. Regime maps are presented to illustrate crack paths as a function of system properties, which provide useful guidance regarding the potential impact of non-planar interfaces in ceramic systems.

Even if the initial system consists of relatively planar coatings, local oxidation can lead to non-planar features that drive cracking; for example, cracks in environmental barrier coatings provide fast diffusion pathways to exposure the interior of ceramic-based components to reactants that subsequently form local oxide ``bubbles''. These local domains drive cracking in the system due to the large volume change associated with the conversion of the monolithic ceramic to oxide: examples include Si being converted to SiO2 and and SiC being converted to SiO2. Unlike interface cracking problems where the geometry is presumably constant, oxidation phenomena involves several highly coupled phenomena: transport of reactants (i.e. diffusion), domain evolution (i.e. growth of the oxide), and creep in oxides at high temperature. To address this problem, a multiphysics simulation framework was developed with features that make it amenable to future integration with cohesive cracking simulations. The framework integrates transport, boundary evolution and time-dependent constitutive descriptions within a single discretization scheme, such that behaviors can be evolved concurrently, with remeshing to account for large changes in system geometry.

The multiphysics framework was then applied to several case studies to gain insight regarding coupling between these phenomena. Oxidation of a bare circular fiber was used to explore the development of tensile stresses on the outer surface of the evolving oxide layer, which likely plays a role in fiber degradation. This study is compared with previous analytical models and shown to be highly accurate. Also, local oxidation at the tip of a crack in an environmental barrier coating was simulated to quantify the effects of crack density and layer diffusivities. A key finding is that local tensile stresses in the underlying substrate (which experiences oxidation) are significant and reach a peak at a critical time. That is, the local oxide domain must be large enough to induce significant stress concentrations, requiring a finite time based on oxide growth kinetics. At longer times, however, creep relaxation intervenes such that local stresses decay. The simulations have important implications for experimental studies of oxidation in ceramic-based components, since cracking may or may not occur based on system parameters and experimental design. Peak stress concentrations have been tabulated as a function of system properties to guide future efforts in this area.