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Recent experiment showed that nano-fibers composite ceramics, fabricated through SHS process, could acquire high toughening and strengthening. Composite ceramics are mainly composed of fiber eutectic with random orientation, in which nanometer sized zirconia fibers are dispersed within the alumina matrix. First, it can be visualized that tensile force is transmitted from the matrix to the nano-fiber by means of shear stress that develop along the fiber- matrix interface. Then the shear stress on the surface of the fiber eutectic is obtained. It related to the volume fraction and slenderness ratio of the nano-fibers, and external strain of the fiber eutectic. The maximum shear stress is at the ends of the fiber eutectic perpendicular to applied tensile stress. As maximum shear stress on the surface of the fiber eutectic is equal to the critical shear stress, the composite ceramics would crack. So the applied tensile stress on composite ceramics arousing the surface crack of the fiber eutectic is gotten.

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Rod-shaped oxide eutectic ceramics fabricated through SHS process can acquire outstanding mechanical properties. First, Eshebly-Mori-Tanaka method was used to study Thermal Stress Field of rod-shaped oxide eutectic ceramics, and then average strain of rod-shaped oxide eutectic ceramics aroused thermal inconsistency is obtained. The effective thermal expansion longitudinal strain and transverse strain of rod-shaped oxide eutectic ceramics are determined by the average strain. Rod-shaped oxide eutectic ceramics is transverse isotropy and has two independent thermal expansion coefficients. The results show that the thermal expansion coefficients of rod shaped oxide eutectic ceramics are dependent on the diameter of nano-fiber. The thermal expansion coefficients will decrease when the diameter of nano-fiber decrease. When the diameter of nano-fiber is bigger than 300nm, the thermal expansion coefficients of rod shaped oxide eutectic ceramics is constants.

According to the interaction between lamellar inclusion and interphase, forth-phase model is suggested to determine the micro-stress-field distribution of three-phase cell in eutectic composite ceramic. On the basis of the volumetric average strain, the effective compliance tensor increment of eutectic composite ceramic is obtained. The remote stress boundary condition of the eutectic composite ceramic is accounted for getting the micro-stress-field of lamellar inclusion in eutectic composite ceramic. Analysis shows that the micro-stress-field of the lamellar inclusion in eutectic composite ceramic is associated with the stiffness and the volume fractions of each component in eutectic composite ceramic, the shape of interphase and lamellar inclusion. The-micro-stress field has apparent size effect: three direction stresses increase with the thickness of lamellar inclusion.