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Several critical issues in the mechanics of the interface between the fibers and matrix in ceramic matrix composites (CMCs) are studied. The first issue is the competition between crack deflection and penetration at the fiber/matrix interface. When a matrix crack, the first fracture mode in a CMC, reaches the interface, two different crack modes are possible; crack deflection along the interface and crack penetration into the fibers. A criterion based on strain energy release rates is developed to determine the crack propagation at the interface. The Axisymmetric Damage Model (ADM), a newly-developed numerical technique, is used to obtain the strain energy in the cracked composite. The results are compared with a commonly-used analytic solution provided by He and Hutchinson (HH), and also with experimental data on a limited basis. The second issue is the stress distribution near the debond/sliding interface. If the interface is weak enough for the main matrix crack to deflect and form a debond/sliding zone, then the stress distribution around the sliding interface is of interest because it provides insight into further cracking modes, i.e. multiple matrix cracking or possibly fiber failure. The stress distributions are obtained by the ADM and compared to a simple shear-lag model in which a constant sliding resistance is assumed. The results show that the matrix axial stress, which is responsible for further matrix cracking, is accurately predicted by the shear-lag model. Finally, the third issue is multiple matrix cracking. We present a theory to predict the stress/strain relations and unload/reload hysteresis behavior during the evolution of multiple matrix cracking. The random spacings between the matrix cracks as well as the crack interactions are taken into account in the model. The procedure to obtain the interfacial sliding resistance, thermal residual stress, and matrix flaw distribution from the experimental stress/strain data is discussed. The results are compared to a commonly-used approach in which uniform crack spacings are assumed. Overall, we have considered various crack modes in the fiber-reinforced CMCs; from a single matrix crack to multiple matrix cracking, and have suggested models to predict the microscopic crack behavior and to evaluate the macroscopic stress/strain relations. The damage tolerance or toughening due to the inelastic strains caused by matrix cracking phenomenon is the key issue of this study, and the interfacial mechanics in conjunction with the crack behavior is the main issue discussed here. The models can be used to interpret experimental data such as micrographs of crack surface or extent of crack damage, and stress/strain curves, and in general the models can be used as guidelines to design tougher composites. / Ph. D.

Many material properties depend on specific details of microstructure and both optimal material performance and material reliability often correlate directly to microstructure. In nano- and micro-systems, the material's microstructure has a characteristic length scale that approaches that of the device in which it is used. Fundamental understanding and prediction of material behavior in nano- and micro-systems depend critically on methods for computing the effect of microstructure. Methods for including the physics and spatial attributes of microstructures are presented for a number of materials applications in devices. The research in our group includes applications of computation of macroscopic response of material microstructures, the development of methods for calculating microstructural evolution, and the morphological stability of structures. In this review, research highlights are presented for particular methods for computing the response in: 1) rechargeable lithium ion battery microstructures, 2) photonic composites with anisotropic particulate morphologies, 3) crack deflection in partially devitrified metallic glasses. / Singapore-MIT Alliance (SMA)