A class of inclusion problems for the strengthening of brittle and ductile composites

Using Eshelby's solution of an ellipsoidal inclusion as the point of departure, a class of inhomogeneity and transformation problems for the strengthening of brittle and ductile composites are investigated in this thesis.; First, the effective elastic moduli of a two-phase composite containing aligned, 2-D, and 3-D randomly oriented ellipsoidal inclusions are derived. The nine, five, and two independent elastic constants for these three different classes of composites are found as a function of inclusion shape and volume concentration. The moduli are found to always lie in or on the bounds of Willis and of Hashin and Shtrikman. These results are then developed into a form suitable for the elliptic cracks, and then, the influence of crack density parameters on the reduction of the effective moduli of cracked bodies is brought about.; The established results for the effective moduli with softer inclusions, and with elliptic cracks, are then applied to study the microcracks and inhomogeneity, as well as the transformation, toughening of brittle solids. It is found that the toughness of brittle materials (e.g. ceramics) can always be enhanced by addition of soft particles, and by the dilatational nature of the phase transformation from tetragonal to monoclinic crystal structure. In the case of microcrack toughening, the theory derived is shown to be very close to Hutchinson's modified lowest order formula.; The investigation finally is directed towards the thermal stress problems in dual-phase solids during a cooling process. For a dual-phase steel, it is found that dilational tensile stress develops in the ferrite matrix during martensitic transformation. The volume of the dual-phase steel is found to decrease first during cooling, but increase upon the occurrence of phase transformation. The thermal stress analysis is finally studied for the two-phase metal-matrix composites. An exact, local theory is derived to determine the extent of thermal stress in the inclusions and the ductile matrix for both particle and fiber-reinforced composites. For a two-phase composite containing aligned spheroidal inclusions, an energy approach is developed at the end. It is demonstrated that the thermal stress in the ductile matrix can be significantly relieved by its plastic flow.