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Twin related domain formation is examined as a strain relaxation mechanism for a heteroepitaxial tetragonal film on a cubic substrate. Elastic relaxations are calculated for a single twin band in which the c axis of the tetragonal domains is either related by a 90" rotation about an axis in the plane of the film or by a 90" rotation about the surface normal, In all cases, the strain energy change is evaluated for both the film and the substrate. A domain pattern map is developed that predicts single domain and multiple domain fields depending on the relative misfit strains and domain wall energy. The concept of a critical thickness, h,, for domain formation is developed. For cases in which the c axis is rotated 90" about an axis in the plane of the film, the critical thickness depends only on the relative coherency strain between the substrate and ftlm and the ratio of the domain wall energy to the stored elastic energy. For the case of a pattern consisting of energetically equivalent domains with the c axis in plane, the equilibrium distance of multiple domains is derived. For such multiple domains, a minimum wall separation distance exists that depends nonlinearly on the film thickness.

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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.

The present article examines the in‐plane tensile properties of a two‐dimensional (2D) all‐oxide ceramic composite. The distinguishing characteristics of the material include fine‐scale porosity within the matrix and the absence of a fiber coating. The anisotropy in the elastic‐plastic properties has been studied through tension tests in the axial (fiber) direction and at 45° to the fiber axes, both in the presence and the absence of holes or notches. The notch sensitivity in the axial direction is comparable to that of conventional dense‐matrix, weak‐interface composites, demonstrating the effectiveness of the porous matrix in enabling crack deflection and damage tolerance. Furthermore, the notch sensitivity is rationalized using models that account for the effects of inelastic straining on the local stress distributions around notches and holes, coupled with a scale‐dependent failure criterion. In the off‐axis orientation, the tensile strength is dictated by a plastic instability, analogous to necking in metals. Following instability, deformation continues within a diffuse localized band, with a length comparable to the specimen width. Similar deformation and fracture characteristics are obtained both with and without holes. The off‐axis properties are discussed in terms of the comminution and rearrangement of matrix particles during straining.