Graphite Nodule and Eutectic Cell Count in Cast Iron: Theoretical Model Based on Weibull Statistics and Experimental Verification

Abstract

In this work, a model is proposed for heterogeneous nucleation on substrates whose size distribution can be described by the Weibull statistics. It is found that the nuclei density, N nuc can be given in terms of the maximum undercooling, ΔT m , by N nuc = N s exp (–b/ΔT m ), where N s is the density of nucleation sites in the melt and b is the nucleation coefficient (b > 0). When nucleation occurs on all possible substrates, the graphite nodule density, N V,n , or eutectic cell density, N V , after solidification equals N s . In this work, measurements of N V,n and N V values were carried out on experimental nodular and flake graphite iron castings processed under various inoculation conditions. The volumetric nodule N V,n or graphite eutectic cell N V count was estimated from the area nodule count, N A,n , or eutectic cell count, N A , on polished cast iron surface sections by stereological means. In addition, maximum undercoolings, ΔT m , were measured using thermal analysis. The experimental outcome indicates that the N V,n or N V count can be properly described by the proposed expression N V,n = N V = N s exp (–b/ΔT m ). Moreover, the N s and b values were experimentally determined. In particular, the proposed model suggests that the size distribution of nucleation sites is exponential in nature.