Theoretical modelling of fracture of functionally graded thermal barrier coatings at elevated temperatures, including oxidation effects

Abstract

The theoretical modeling of fracture of functionally graded materials, including oxidation effects, has focused on providing a suitable model for mechanical and fracture mechanics parameters for being able to address the material and oxide layer effects. Based on volumetric considerations, like, for example, the rule of mixtures model, the relevant parameters were modeled by profile functions implemented as adaptive interpolation rules. This adaptivity was achieved by using interpolation weights based on symmetric bounded distribution functions in combination with a symmetry-breaking median-adjustment parameter. Within this theoretical framework, novel distribution functions based on polynomials were developed, integrated into the semi-analytical fracture analysis model and checked for suitability. Profile functions for this model were validated against experimental data with no oxide layer, showing good accuracy after fitting. The model was applied to functionally graded materials with an oxide layer located on the free surface, and the response of the model was analyzed regarding crack interactions. Unfortunately, no experimental data was available for the determination of profiles in the presence of the oxide, but the current model is adaptive enough and thus expected to cover these cases equally well. A semi-analytical method based on singular integral equations was used to perform fracture mechanics analyses on a semi-infinite structure with cracks under thermo-mechanical stresses. Here, the material and oxide properties were implemented by interpolation with weights based on distribution functions. The main goal of the project regarding the modeling of oxidation and thermal effects was thus achieved for quasi-static case considerations. One additional benefit from modeling the weight functions with probability distributions was the development of novel bounded distributions and, finally, of a parameterized distribution, where an integer parameter controls the smoothness (differentiability class) of the related distribution function. These distributions are general tools with a wide range of applications, as demonstrated in this project on Monte Carlo simulations performing failure assessment with the R6 method.