An explicit elastic solution for a brittle film with periodic cracks

Abstract

A two-dimensional explicit elastic solution is derived for a brittle film bonded to a ductile substrate through either a frictional interface or a fully bonded interface, in which periodically distributed discontinuities are formed within the film due to the applied tensile stress in the substrate and consideration of a "weak form stress boundary condition" at the crack surface. This solution is applied to calculate the energy release rate of three-dimensional channeling cracks. Fracture toughness and nominal tensile strength of the film are obtained through the relation between crack spacing and tensile strain in the substrate. Comparisons of this solution with finite element simulations show that the proposed model provides an accurate solution for the film/substrate system with a frictional interface; whereas for a fully bonded interface it produces a good prediction only when the substrate is not overly compliant or when the crack spacing is large compared with the thickness of the film. If the section is idealized as infinitely long, this solution in terms of the energy release rate recovers Beuth's exact solution for a fully cracked film bonded to a semi-infinite substrate. Interfacial shear stress and the edge effect on the energy release rate of an asymmetric crack are analyzed. Fracture toughness and crack spacing are calculated and are in good agreement with available experiments.

Evolving fracture patterns: columnar joints, mud cracks and polygonal terrain

“…Tension is released when a crack opens in the brittle layer, as the normal stresses in the film must vanish on the new crack surfaces. The substrate will resist deformation, however, and exert a restoring force on the film-substrate interface, approximately proportional to the local in-plane strain [12,13]. For a long straight crack in a thin film, as shown in figure 2b, these conditions give rise to an exponential dependence of the height-averaged film stress on the distance x away from the crack,…”

Opening-mode fractures of a brittle coating bonded to an elasto-plastic substrate

“…In this context, Yin and his colleagues have proposed a 2-D elastic model (Yin et al, 2008;Yin and Prieto-Munoz, 2013), which was successfully applied to interpret fracture initiation, infilling, and saturation caused by tension or temperature loads in layered materials. This simplified 2-D theoretical analysis using the first term of a series solution exhibits a high accuracy for the substrate made with comparable thickness of the coatings (Yin and PrietoMunoz, 2013).…”

“…However, when the coating thickness is much smaller than the substrate thickness, the simplified solution exhibits considerable errors. Therefore, a one-body analysis has been conducted based on a frictional interface between the two surfaces while disregarding the substrate thickness (Yin et al, 2008;. Moreover, this 2-D analysis was only applicable to the cases where both the coating and the substrate are subjected to elastic deformation.…”

Epitaxial growth and cracking of highly tough 7YSZ splats by thermal spray technology

“…Because the substrate was much thicker than the splat, the stress in the splat was considered to be uniformly distributed along thickness direction, and this was ignored in the substrate [37,62]. In the present study, three failure modes mainly occurred, i.e., channeling [63,64], penetration [56,65,66], and spallation [54,57,61], as shown in Figs.…”