Hybrid Discontinuous Galerkin Process Zone Models for Thermal Induced Fractures and Fracture Reduced Heat Transfer

We propose a coupled thermo-chemo-mechanics numerical framework suitable for the description of material response to extreme aerospace environments. The approach is based on a unified discontinuous Galerkin formulation of the equations describing the solid mechanics, the heat transfer, and the chemical reaction problem. The method effectively extends the well-established discontinuous Galerkin/cohesive zone model (DG/CZM) formulation for describing fracture in brittle solids to the coupled multiphysics problem. In addition, we advance post-failure models for fracture surface thermal response that complement the Dugdale-Barenblatt cohesive zone model for crack propagation. The resulting computational framework naturally describes crack-path dependent resistance to heat transfer as is required to model the failure of brittle structures under combined thermo-mechanical loading. For definiteness, a thermally-activated oxygen diffusion model is used to describe chemical oxidation in the material bulk, which is of interest in ceramic thermal protection systems. The chemistry model is tightly coupled with the heat transfer problem, which also naturally results in oxygen diffusion resistance across crack surfaces. We demonstrate the framework with parallel simulations of the growth of the oxidation layer and thermal stresses leading to fracture of a ceramic thermal protection system subject to high temperatures.