This article discusses results obtained from a parametric study to analytically evaluate the impingement of a crack at the interface of an environmental barrier coating (EBC) and a monolithic Silicon nitride (Si 3 N 4 ) layered ceramics substrate. The study establishes a correlation that leads to determine if the crack is arrested or advanced by either penetrating or deflecting along the EBC/substrate interface. A finite-element-based fracture mechanics methodology is utilized to perform these calculations. Critical parameters determining penetration-deflection conditions in relation to EBC's physical characteristics, such as porosity level, voids, and mini cracks, are determined for a single layer and multi-layered coating system coordinating the interactions between the EBCs (Mullite, Mullite mixture, Silicon nitride, etc.) and the substrate structure. Results showing thermo-mechanical stresses and stress/strain energy release relations with respect to crack penetration-deflection are presented and discussed as the crack is advanced. = stress at the interface r and = radial distance and the polar angle f ij ( ) = angular distribution of the singular stress field = defines the strength of stress singularity ␣ and  = Dundurs bi-material parameters E' j = E j is for plane stress E' j = E j /(1 -j ) for plane strain (1 and 2 denote the material) = shear modulus [MPa] G d = (material 1) is the strain energy release rate associated with the "deflected" crack or adhesive failure G p = (material 2) is the strain energy release rate associated with the "penetrated" crack (or cohesive failure of adjacent material) G pc = cohesive or penetrated fracture energy G dc = adhesive or deflected fracture energy, respectively K 1 and K 2 = stress intensity factors for the interface crack ε = a function of material constants
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