Effect of Poisson's ratio on the variation of the average Young's moduli of composites with transitions of second-phase shape

Abstract

Abstract The average Young's moduli are calculated under a plane strain condition for composites containing second phases aligned perpendicular or parallel to an applied uniaxial stress. The Mori—Tanaka concept of ‘average stress’ together with the equivalent inclusion idea of Eshelby are used. The variation of the average Young's moduli with the transitions of second-phase shape is discussed. When both the Poisson's ratios of the matrix and second phase are zero, the average Young's modulus of the composites monotonically increases with increasing aspect ratio of the second phase. However, when the Poisson's ratios of the matrix and second phase are different from each other, the second-phase shape dependence of the average Young's modulus is not always simple. Maps are derived to show the Poisson's ratio effect. For certain combinations of the Young's moduli and Poisson's ratios of the matrix and second phase, the mixture rule gives the lower bound of the average Young's modulus among those of composites containing a second phase with various shapes. It is also possible that the average Young's moduli of the composites become larger than those of the matrix and second phase.