A theoretical study has been made to predict overall thermal expansion characteristics of a two-phase material consisting of a matrix and aligned ellipsoidal inclusions. The calculation is based on Eshelby's theory on the transformation problem; an approximate method is Introduced to account for the effect of finite concentrations of the inclusions. The following two cases are treated: elastic matrix-elastic inclusions and elastoplastic matrix- elastic inclusions. The results are explicitly obtained when shapes of the inclusions are spherical, disc-shaped, and fiber-shaped. The calculated over all thermal expansion coefficient for the case of elastic matrix-elastic spheres agrees with Kerner's prediction.
For two-phase materials composed of ductile matrices reinforced with plastically nondeformable inclusions, the yield condition that has the same form as Tsai and Wu's phenomenological criterion has been deduced through a micromechanics analysis. Basic assumptions made are that the matrix material obeys the Levy-von Mises flow rule, and that matrix plastic strains are uniform. In general, the shape of the yield surface can be proved to be hyperellipsoidal. A further analysis is devoted to the case where the inclusions can be treated as identical ellipsoids with corresponding axes aligned. Based on the results, numerical computation of yield strength parameters is carried out for unidirectional boron fiber-aluminum composites subjected to uniform temperature changes prior to external loading. It is shown that yielding cannot take place under certain combined triaxial (not hydrostatic) stresses. Some discussion related to the effect of prior temperature changes is also given.
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