複相材料の平均的ヤング率に及ぼす構成相の形状とポアソン比の影響

抄録

The average Young moduli are calculated analytically for composites containing aligned spheroidal second-phase particles whose axis of rotation is parallel to an external uniaxial stress. The Mori-Tanaka concept of “average stress” together with the equivalent inclusion idea of Eshelby is used for the calculations to include interactions between second-phase particles. The variation of the average Young moduli with the transitions of second-phase shapes from plate-like to fiber-like through spherical shapes are shown for isotropic elastic moduli of a matrix and second phase. When the volume fraction of the second phase and the Young moduli of the matrix and second phase are fixed, the Poisson ratios significantly change the variation of the average Young moduli of the composites with the transitions of the second-phase shape. Maps to show the Poisson-ratio effect are derived. Results obtained are compared with results given by the Reuss and Voight approximations where equi-stress and equi-strain conditions in the matrix and second phase are assumed respectively. For certain combinations of the Young moduli and the Poisson ratios of the matrix and second phase, the average Young moduli of the composites with various second-phase shapes are always larger than the value given by the Voight approximation, the rule of mixture of the Young moduli. We have shown that it is possible that the average Young moduli of the composites can be larger than those of the matrix and second phase.