Computer model for the characterisation of the size distribution of spheroidal graphite in ductile cast iron

Abstract

A computer model was developed to establish the relationship between the two-dimensional (2D) and the three-dimensional (3D) parameters, specifically the number of particles and particle size distribution. The computer experiments were performed for both monodispersed and lognormally polydispersed systems. The model was based on a random distribution of a number of spherical grains in a cubic unit, with no intersection between the grains. The cubic unit was cut by a random plane and the number of particles which appeared in the section and the area fraction were measured. This procedure was repeated until the average number of particles and the average area fraction became constant. Finally, the 2D size distribution of the particles over all sections was obtained.It was concluded that the volume fraction is equal to the area fraction, irrespective of the particle size distribution, providing that the total number of measured 2D particles is large enough. As for the number of particles, an equation was found to calculate the number of 3D particles in a monodispersed system from the number of 2D particles and the volume fraction. However, in lognormally polydispersed systems the number of 3D particles could be calculated using the 3D mean and standard deviation, estimated from the 2D mean and standard deviation by a method specifically developed for the purpose.Finally, the method was applied to two ductile cast iron specimens and the applicability of the present model was verified.