The composite ceramics is composed of fiber-eutectics, transformation particles and matrix particles. First, the recessive expression between the effective stress in fiber-eutectic and the flexibility increment tensor is obtained according to the four-phase model. Second, the analytical formula which contains elastic constant of the fiber-eutectic is obtained applying Taylor’s formula. The eutectic is transverse isotropy, so there are five elastic constants. Third, the effective elastic constants of composite ceramics are predicted. The result shows that the elastic modulus of composite ceramic is reduced with the increase of fibers fraction and fibers diameter.

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Rod-shaped oxide eutectic ceramics fabricated through SHS process can acquire outstanding mechanical properties. First, Four-phase model method was used to study effective disturbance strain of rod-shaped oxide eutectic ceramics produced by nano fibers with inter-phases, 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.