Criteria for Crack Deflection-Penetration in EBC Coated Ceramics: A Parametric Study

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. Nomenclature K = stress intensity factor [MPa.mm 1/2 ] E = modulus [MPa] U = strain energy [N/mm 2 ] G or dU/dA= strain energy release rate during a small crack extension dA = small crack extension where A = a • b; a and b are the crack length and the crack width, respectively [mm] G d = energy release rate, deflection G p = energy release rate, penetration u = displacement vector y = distance along the direction normal to the plane of the crack [mm] s = arc length along the contour [mm] t = coating thickness T = traction vector t s = incremental thickness of the substrate t c = incremental thickness of the coating T c = total thickness of the coating T s = total thickness of the substrate w = strain J = J-integral = G s = path taken to compute the integral M = bending moment [N.m] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/umcm. P = load applied [Pa] L and b = beam length and width, respectively [mm] E = Young modulus [MPa] ␯ = Poisson's ratio h = thickness of the beam [mm] ␴ ij = 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 …