Estimation Procedure for Volume Fraction of Minor and Rod Phase Aligned Unidirectionally in a Matrix

Abstract

Knowing the volume fraction of a minor phase in a composite material is important for characterizing its mechanical properties. Assuming that a rod-like phase with a constant diameter is aligned but dispersed randomly in a matrix, a mathematical model for estimating the volume fraction of a rod-like phase has been developed. This model predicts how many rods are required for an accurate estimation of volume fraction. One of the effective features of this model is that the real dimensions do not need to be considered due to the similarity of their shape. According to this model, it is sufficient to measure the area that includes at least 20 rods to estimate an accurate value for volume fraction. This prediction was confirmed by measuring a unidirectionally solidified Sn-Cu eutectic alloy system.

Relation between the Solidification Condition and Volume Fraction of Rod-Like Eutectic Cu₆Sn₅ Phase in the Eutectic Structure in Sn-Cu Alloys

“…In this figure, the volume fraction was estimated from the equilibrium phase diagram (2.05%), which is indicated by a dotted line. 8) Almost all results were larger than the equilibrium value, and the f ECu 6 Sn 5 appeared nearly constant with respect to the copper content. This value purely depended upon the growth velocity.…”

“…The cross sections of the eutectic Cu 6 Sn 5 were carefully traced by hand, with their area analyzed using an image analyzer. Following a predetermined method, 8) a measurement area that included at least 20 rods of the eutectic Cu 6 Sn 5 was analyzed. Five measurements were taken under the same experimental conditions with the average values used in this study.…”