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

摘要

A model for heterogeneous nucleation on substrates (places of the nucleation) which size distribution is of the Weibull type is proposed. The nuclei density λ{sub}n is following function of the maximum undercooling △T{sub}m :λ{sub}n=λ{sub}(exp)[(-b/△T{sub}m)Γ(1+1)]{sup}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 N{sub}v after solidification is equal to λ{sub}n. Consequently, from N{sub}v 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 N{sub}v was estimated from the density N{sub}A of grain sections by a stereological method. The experiment shows that nucleation follows the model for n = 1, ie.: λ{sub}n =λ{sub}(exp)[-b/△T{sub}m]. 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.