Nucleation and grains density in grey cast iron—A theoretical model and experimental verification

Abstract

A model for heterogeneous nucleation on substrates (places of the nucleation) which size distribution is of the Weibull type is proposed. The nuclei density λn is following function of the maximum undercooling ΔTm: λn=λexpl[(-b/ΔTm)—Γ(1+1/n)]n; where: n is a positive integer, λ—is the substrate density in melt and b is the nucleation coefficient (b > 0) (Γ- denotes the gamma function). In the case when nucleation occurs on all possible substrates, the grain density Nv after solidification is equal to λn. Consequently, from Nv measurements it is possible to conclude about the nucleation process. The experimental verification of the proposed model is performed for the solidification of cast iron. The grain density Nv was estimated from the density NA of grain sections by a stereological method. The experiment shows that nucleation follows the model for n = 1, ie.: λn=λexp[-b/ΔTm]. For inoculated cast iron, the empirical λ and b values are time dependent functions. The performed model analysis also indicates that the substrates size distribution is of the exponential type.