Mechanics of toughening, strengthening and splitting of ceramic composites

This thesis is concerned with three fundamental topics in the field of mechanical behavior of ceramic composites. The first topic deals with the fracture toughness and the matrix cracking stress of ceramics reinforced by both fibers and transforming particles. The Mode-I plane-strain fracture toughness and the matrix cracking strength of the ceramic composites are determined in terms of parameters associated with individual toughening mechanisms, and coupling parameters that characterize their interaction. A rigorous asymptotic analysis for the possible synergistic interaction is presented. An energy balance relation governing the steady state matrix cracking is derived.; The second topic deals with tensile strength of fibrous ceramic composites weakened by through-the-fiber cutouts such as cracks or holes. The tensile strength of a fiber reinforced ceramic is determined on the basis of a full analysis of crack growth in the matrix and the failure of crack bridging fibers. The strength of a composite containing a sharp crack normal to the direction of fibers is presented first. Some preliminary results on the strength of a composite containing an elliptical hole are then presented.; The third topic deals with splitting. The splitting is modeled as cracks with both Mode I opening and Mode II sliding. The sliding resistance on the closed portion of splitting crack is assumed to obey a Coulomb friction law. The stress intensity factors and the critical external load for splitting propagation are calculated as functions of splitting length. The results of stress redistribution due to splitting are also presented.; In closing, we give some basic two-dimensional anisotropic elastic solutions for an infinite matrix containing an elliptical inclusion. Along with their applications in modeling matrix cracking initiated in the vicinity of a hole and splitting tangent to a hole, these solutions have other potential applications as well.