Notch Ductile-to-Brittle Transition Due to Localized Inelastic Band

Holes are often drilled in a panel for cooling or fastening. For a panel made of a monolithic ceramic, such a hole concentrates stress, reducing load-carrying capacity of the panel by a factor of 3. By contrast, for a ductile alloy panel, plastic flow relieves stress concentration so that the small hole does not reduce load-carrying capacity. A panel made of ceramic-matrix composite behaves in the middle: matrix cracks permit unbroken fibers to slide against friction, leading to inelastic deformation which partially relieves stress concentration. Load-carrying capacity is studied in this paper as an outcome of the competition between stress concentration due to the notch, and stress relaxation due to inelastic deformation. The inelastic deformation is assumed to be localized as a planar band normal to the applied load, extending like a bridged crack. The basic model is large-scale bridging. A material length, δ₀E/σ₀, scales the size of the inelastic band, where σ₀ is the unnotched strength, δ₀ the inelastic stretch at the onset of rupture, and E Young’s modulus. Load-carrying capacity is shown to depend on notch size a, measured in units of δ₀E/σ₀. Calculations presented here define the regime of notch ductile-to-brittle transition, where ceramic-matrix composites with typical notch sizes would lie. Both sharp notches and circular holes are considered. The shape of the bridging law, as well as matrix toughness, is shown to be unimportant to load-carrying capacity.