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

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.