A novel distribution function for modeling oxygen diffusion in functionally graded materials with cracks

Oxygen diffusion in a functionally graded material (FGM) is modeled by an elastic modulus profile that covers the FGM and the thermally grown oxide (TGO) areas. The profile is based on a novel Gaussian-like distribution that becomes an adaptive weight function by scaling, shifting and using a (symmetry breaking) median adjustment parameter. The properties of this new type of distribution are analyzed and the pure FGM (no oxygen) is compared with the FGM+TGO scenario for a semi-infinite structure with three edge cracks. The fracture analysis is based on critical loads, determined for different crack distances and inclination angles. • Novel double bounded Gaussian-like distribution based on a polynomial. • Distribution bounds from required (statistical) mean and variance. • Median adjustment parameter for non-symmetric transition/interpolation. • Functionally graded material with cracks and oxygen diffusion. • Recursive (double interpolation) rule for elastic modulus profile.